[duncan c wyllie] foundations on rock second edit(bookza.org)

Foundations on Rock

Second edition

Foundations on Rock

Duncan C.WylliePrincipal, Golder Associates, Consulting Engineers Vancouver,

Canada

With a Foreword by Richard E.GoodmanProfessor of Geological Engineering, University of California,

Berkeley, USASecond edition

E & FN SPONAn imprint of RoutledgeLondon and New York

First edition published 1992 by E & FN Spon, an imprint of Chapman &Hall

Second edition published 1999 by E & FN Spon,11 New Fetter Lane, London EC4P 4EE

Simultaneously published in the USA and Canadaby Routledge

29 West 35th Street, New York, NY 10001

E & FN Spon is an imprint of the Taylor & Francis Group

This edition published in the Taylor & Francis e-Library, 2005.

“To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks pleasego to www.eBookstore.tandf.co.uk.”

© 1992, 1999 Duncan C.Wyllie

All rights reserved. No part of this book may be reprinted or reproduced orutilised in any form or by any electronic, mechanical, or other means, nowknown or hereafter invented, including photocopying and recording, or inany information storage or retrieval system, without permission in writing

from the publishers.

The publisher makes no representation, express or implied, with regard tothe accuracy of the information contained in this book and cannot accept anylegal responsibility or liability for any errors or omissions that may be made.

The right of Duncan C.Wyllie to be identified as the author of this publication has been asserted by him in accordance withthe Copyright, Designand Patents Act 1988.

British Library Cataloguing in Publication DataA catalogue record for this book is available from the British Library

Library of Congress Cataloging in Publication DataA catalogue record for this book has been requested

ISBN 0-203-47767-7 Master e-book ISBN

ISBN 0-203-78591-6 (Adobe eReader Format)ISBN 0-419-23210-9 (Print Edition)

Contents

Foreword to first edition xiv

Introduction xv

Introduction to first edition xvii

Notation xix

Note xxi

1 Characteristics of rock foundations 1

1.1 Types of rock foundation 1

1.1.1 Spread footings 2

1.1.2 Socketed piers 3

1.1.3 Tension foundations 3

1.2 Performance of foundations on rock 4

1.2.1 Settlement and bearing capacity failures 4

1.2.2 Creep 5

1.2.3 Block failure 5

1.2.4 Failure of socketed piers and tension anchors 6

1.2.5 Influence of geological structure 7

1.2.6 Excavation methods 7

1.2.7 Reinforcement 7

1.3 Structural loads 8

1.3.1 Buildings 9

1.3.2 Bridges 10

1.3.3 Dams 11


1.4 Allowable settlement 11

1.4.1 Buildings 11

1.4.2 Bridges 12

1.4.3 Dams 13

1.5 Influence of ground water on foundation performance 14

1.5.1 Foundation stability 14

1.5.2 Dams 14


1.6 Factor of safety and reliability analysis 16

1.6.1 Factor of safety analysis 16

1.6.2 Limit states design 17

1.6.3 Sensitivity analysis 18

1.6.4 Coefficient of reliability 18

1.7 References 25

2 Structural geology 27

2.1 Discontinuity characteristics 27

2.1.1 Types of discontinuity 27

2.1.2 Discontinuity orientation and dimensions 29

2.2 Orientation of discontinuities 30

2.3 Stereographic projection 31

2.3.1 Pole plots 34

2.3.2 Pole density 34

2.3.3 Great circles 36

2.3.4 Stochastic modeling of discontinuities 38

2.4 Types of foundation failure 39

2.5 Kinematic analysis 39

2.5.1 Planar failure 41

2.5.2 Wedge failure 41

2.5.3 Toppling failure 41

2.5.4 Friction cone 41

2.6 Probabilistic analysis of structural geology 43

v

2.6.1 Discontinuity orientation 43

2.6.2 Discontinuity length and spacing 45

2.7 References 48

3 Rock strength and deformability 50

3.1 Range of rock strength conditions 50

3.2 Deformation modulus 52

3.2.1 Intact rock modulus 53

3.2.2 Stress-strain behavior of fractured rock 55

3.2.3 Size effects on deformation modulus 58

3.2.4 Discontinuity spacing and modulus 60

3.2.5 Modulus of anisotropic rock 61

3.2.6 Modulus-rock mass quality relationships 62

3.3 Compressive strength 64

3.3.1 Compressive strength of intact rock 66

3.3.2 Compressive strength of fractured rock 66

3.4 Shear strength 71

3.4.1 Mohr-Coulomb materials 71

3.4.2 Shear strength of discontinuities 71

3.4.3 Shear strength testing 77

3.4.4 Shear strength of fractured rock 80

3.5 Tensile strength 82

3.6 Time-dependent properties 83

3.6.1 Weathering 84

3.6.2 Swelling 86

3.6.3 Creep 87

3.6.4 Fatigue 92

3.7 References 92

4 Investigation and in situ testing methods 97

4.1 Site selection 97

4.1.1 Aerial and terrestrial photography 98

vi

4.1.2 Geophysics 100

4.2 Geological mapping 103

4.2.1 Standard geology descriptions 103

4.2.2 Discontinuity mapping 108

4.3 Drilling 110

4.3.1 Diamond drilling 110

4.3.2 Percussion drilling 115

4.3.3 Calyx drilling 116

4.4 Ground water measurements 116

4.4.1 Water pressure measurements 118

4.4.2 Permeability measurements 121

4.5 In situ modulus and shear strength testing 124

4.5.1 Modulus testing 124

4.5.2 Direct shear tests 132

4.6 References 132

5 Bearing capacity, settlement and stress distribution 138

5.1 Introduction 138

5.2 Bearing capacity 140

5.2.1 Building codes 140

5.2.2 Bearing capacity of fractured rock 141

5.2.3 Recessed footings 145

5.2.4 Bearing capacity factors 146

5.2.5 Foundations on sloping ground 147

5.2.6 Bearing capacity of shallow dipping bedded formations 147

5.2.7 Bearing capacity of layered formations 152

5.3 Bearing capacity of karstic formations 153

5.3.1 Characteristics of solution features 154

5.3.2 Detection of solution features 155

5.3.3 Foundation types in karstic terrain 157

5.4 Settlement 163

vii

5.4.1 Settlement on elastic rock 164

5.4.2 Settlement on transversely isotropic rock 169

5.4.3 Settlement on inelastic rock 173

5.4.4 Settlement due to ground subsidence 174

5.5 Stress distributions in foundations 175

5.5.1 Stress distributions in isotropic rock 175

5.5.2 Stress distributions in layered formations 179

5.5.3 Stress distributions in transversely isotropic rock 180

5.5.4 Stress distributions in eccentrically loaded footings 182

5.6 References 185

6 Stability of foundations 189


6.2 Stability of sliding blocks 189

6.2.1 Deterministic stability analysis 191

6.2.2 Probabilistic stability analysis 195

6.3 Stability of wedge blocks 196

6.4 Three-dimensional stability analysis 201

6.5 Stability of toppling blocks 202

6.6 Stability of fractured rock masses 206

6.7 External effects on stability 209

6.7.1 Seismic design 209

6.7.2 Scour 210

6.8 References 213

7 Foundations of gravity and embankment dams 215


7.1.1 Dam performance statistics 216

7.1.2 Foundation design for gravity and embankment dams 217

7.1.3 Loads on dams 218

7.1.4 Loading combinations 219

7.2 Sliding stability 220

viii

7.2.1 Geological conditions causing sliding 220

7.2.2 Shear strength 221

7.2.3 Water pressure distributions 221

7.2.4 Stability analysis 223

7.2.5 Factor of safety 227

7.2.6 Examples of stabilization 227

7.3 Overturning and stress distributions in foundations 228

7.3.1 Overturning 230

7.3.2 Stress and strain in foundations 230

7.4 Earthquake response of dams 235

7.4.1 Introduction 235

7.4.2 Measured motions of foundation rock 236

7.4.3 Sliding stability and overturning under seismic loads 237

7.4.4 Finite element analysis 238

7.4.5 Earthquake displacement analysis 239

7.5 Preparation of rock surfaces 243

7.5.1 Shaping 244

7.5.2 Cleaning and sealing 245

7.5.3 Rebound 246

7.5.4 Solution cavities 246

7.6 Foundation rehabilitation 247

7.6.1 Monitoring 248

7.6.2 Grouting, sealing and drainage 248

7.6.3 Anchoring 249

7.6.4 Scour protection 249

7.7 Grouting and drainage 250

7.7.1 Grouting functions 252

7.7.2 Grout types 252

7.7.3 Mechanism of grouting 253

7.7.4 Drilling method 254

ix

7.7.5 Hole patterns 255

7.7.6 Grout mixes 256

7.7.7 Grout strength 257

7.7.8 Grout pressures 257

7.7.9 Grouting procedures 259

7.7.10 Permeability criteria for grouted rock 259

7.7.11 Monitoring grouting operations 261

7.7.12 Leaching 261

7.7.13 Drainage 263

7.8 References 263

8 Rock socketed piers 269


8.1.1 Types of deep foundations 269

8.1.2 Investigations for socketed piers 269

8.2 Load capacity of socketed piers in compression 271

8.2.1 Mechanism of load transfer 272

8.2.2 Shear behavior of rock sockets 272

8.2.3 Factors affecting the load capacity of socketed piers 274

8.2.4 Socketed piers in karstic formation 283

8.3 Design values: side-wall resistance and end bearing 283

8.3.1 Side-wall shear resistance 283

8.3.2 End-bearing capacity 285

8.4 Axial deformation 286

8.4.1 Settlement mechanism of socketed piers 286

8.4.2 Settlement of side-wall resistance sockets 287

8.4.3 Settlement of end loaded piers 288

8.4.4 Settlement of socketed, end bearing piers 289

8.4.5 Socketed piers with pre-load applied at base 294

8.5 Uplift 294

8.5.1 Uplift resistance in side-wall shear 295

x

8.5.2 Uplift resistance of belled piers 296

8.6 Laterally loaded socketed piers 297

8.6.1 Computing lateral deflection with p-y curves 297

8.6.2 p-y curves for rock 300

8.6.3 Socket stability under lateral load 303

8.7 References 304

9 Tension foundations 310


9.2 Anchor materials and anchorage methods 311

9.2.1 Allowable working loads and safety factors 311

9.2.2 Steel relaxation 314

9.2.3 Strength properties of steel bar and strand 315

9.2.4 Applications of rigid bar anchors 315

9.2.5 Applications of strand anchors 317

9.2.6 Cement grout anchorage 318

9.2.7 Resin grout anchorage 324

9.2.8 Mechanical anchorage 326

9.3 Design procedure for tensioned anchors 326

9.3.1 Mechanics of load transfer mechanism between anchor, grout and rock 326

9.3.2 Allowable bond stresses and anchor design 329

9.3.3 Prestressed and passive anchors 332

9.3.4 Uplift capacity on rock anchors 333

9.3.5 Group action 342

9.3.6 Cyclic loading of anchors 342

9.3.7 Time-dependent behavior and creep 342

9.3.8 Effect of blasting on anchorage 344

9.3.9 Anchors in permafrost 345

9.4 Corrosion protection 345

9.4.1 Mechanism of corrosion 346

9.4.2 Types of corrosion 347

xi

9.4.3 Corrosive conditions 349

9.4.4 Corrosion protection methods 350

9.4.5 Corrosion monitoring 352

9.5 Installation and testing 353

9.5.1 Water testing 353

9.5.2 Load testing 354

9.5.3 Acceptance criteria 356

9.6 References 357

10 Construction methods in rock 360


10.2 Drilling 360

10.2.1 Diamond drilling 362

10.2.2 Percussion drilling 363

10.2.3 Rotary drills 365

10.2.4 Overburden drilling 367

10.2.5 Large diameter drilling 368

10.2.6 Directional drilling 370

10.3 Blasting and non-explosive rock excavation 373

10.3.1 Rock fracture by explosives 374

10.3.2 Controlled blasting 376

10.3.3 Blasting horizontal surfaces 378

10.3.4 Ground vibration control 379

10.3.5 Vibrations in uncured concrete 383

10.3.6 Non-explosive excavation 384

10.4 Bearing surface improvement and rock reinforcement 386

10.4.1 Trim blasting 386

10.4.2 Surface preparation 386

10.4.3 Dental concrete 388

10.4.4 Shotcrete 388

10.4.5 Shear keys 390

xii

10.4.6 Rock bolts 391

10.4.7 Tensioned rock anchors 391

10.4.8 Concrete buttress 391

10.4.9 Drain holes 391

10.5 Contracts and specifications 392

10.5.1 Components of contract documents 392

10.5.2 Types of contract 393

10.5.3 Rock excavation and reinforcement specifications 394

10.6 References 398

Appendix I

Stereonets for handplotting of structural geology data 401

Appendix II

Quantitative description of discontinuities in rock masses 405

Appendix III

Conversion factors 422

Index 425

xiii

Foreword to first edition

Duncan Wyllie has given us a complete, useful textbook on rock foundations. It is complete in its coverageof all parts of this important subject and in providing reference material for follow-up study. It is eminentlyuseful in being well organized, clearly presented, and logical.

Rock would seem to be the ultimate excellent reaction for engineering loads, and often it is. But the term‘rock’ includes a variety of types and conditions of material, some of which are surely not ‘excellent’ andsome that are potentially dangerous. Examples of frequently hazardous rock masses are those that containdissolved limestones, undermined coal-bearing sediments, decomposed granites, swelling shales and highlyjointed or faulted schists or slates. Moreover, the experience record of construction in rocks includesnumerous examples of economic difficulties revolving around mistaken or apparently malevloent behaviorof rock foundations. Such cases have involved excavation overbreak, deterioration of prepared surfaces,flooding or icing by ground water seepage, accumulation of boulders from excavation, gullying or piping oferodible banks, and misclassification or misidentification of materials in the weathered zone. Another classof difficult problems involve the forensic side of siting in evaluating potentialities for rock slides, faultmovement, or long-term behavior.

Problems of investigating and characterizing rock foundations are intellectually challenging; and it mayrequire imagination to tailor the design of a foundation to the particular morphological, structural andmaterial properties of a given rock site. Thus the field of engineering activity encompassed in this book isinteresting and demanding. The subject is worthy of a book on this subject and of your time in studying it.

Richard E.GoodmanBerkeley, California

Introduction

The first edition of Foundations on Rock was written during the period 1988 to 1990. In the decade that haspassed since the initial material was collected on this subject, there has been steady development in the fieldof rock engineering applied to foundations, but no new techniques that have significantly changed designand construction practices. Consequently, the purpose of preparing this second edition, which has beenwritten between 1996 and 1998, has been to update the technical material, and add information on newprojects where valuable experience on rock foundations has been documented.

The following is a summary of the material that has been added:

• Chapter 1: expanded discussion on acceptable reliability levels for different types of structures in relationto the consequences of failure, as well as methods of risk analysis;

• Chapter 2: new material has been added on typical probability distributions for discontinuity lengths andspacing, and methods of collecting data on these features;

• Chapter 3: information is included on the deformation behavior of very weak rock that has beendetermined from in situ testing;

• Chapter 4: the procedures for mapping geological structure has been extensively revised to conform to theprocedures drawn up by the International Society of Rock Mechanics, and has now been consolidated inAppendix II. It is intended that this information will help in the production of standard mapping resultsthat are comparable from project to project;

• Chapter 5: a list of projects with substantial foundations bearing on rock has been included describing therock conditions and the actual bearing pressures that have been successfully used. Also, the section onthe detection of karstic features and the design of foundations in this geological environment has beengreatly expanded. With respect to prediction of foundation performance, an example of numeric analysisof the stability of jointed rock masses has been included;

• Chapter 6: an example has been prepared of probabilistic stability analysis to calculate the coefficient ofreliability of a foundation. Also, a technique for assessing scour potential of rock is presented in detail;

• Chapter 7: with the increasing need to rehabilitate existing dams either to meet new design standards, orto repair deterioration, a section on foundation improvement, scour potential and tie-down anchors hasbeen added;

• Chapter 8: for the design of laterally loaded rock socketed piers, new information is provided on p-ycurves for very weak rock;

• Chapter 9: the testing procedures and acceptance criteria for tensioned anchors has been updated toconform with 1990’s recommended practice;

• Chapter 10: new information has been added on contracting procedures, and in particular Partnering.

It is believed that this is still one of the few books devoted entirely to the subject of rock foundations. Aswith the first edition, it is still intended to be a book that can be used by practitioners in a wide range ofgeological conditions, while still providing a sound theoretical basis for design.

The preparation of this edition has drawn extensively on the knowledge of many of the author’s collegesin both the design and construction fields, all or which are gratefully acknowledged. In addition, GlendaGurtina has provided great assistance in the preparation of the manuscript and Sonia Skermer has preparedall the new artwork to her usual high standard. Finally, I would like to thank my family for supporting methrough yet another book project.

Duncan WyllieVancouver, 1998

xvi

Introduction to first edition

Foundations on Rock has been written to fill an apparent gap in the geotechnical engineering literature.Although there is wide experience and expertise in the design and construction of rock foundations, this hasnot, to date, been collected in one volume. A possible reason for the absence of a book on rock foundationsis that the design and construction of soil foundations is usually more challenging than that of rockfoundations. Consequentially, there is a vast collection of literature on soil foundations, and a tendency toassume that any structure founded on ‘bedrock’ will be totally safe against settlement and instability.Unfortunately, rock has a habit of containing nasty surprises in the form of geological features such assolution cavities, variable depths of weathering, and clay-filled faults. All of these features, and manyothers, can result in catastrophic failure of foundations located on what appear to be sound rock surfaces.

The main purpose of this book is to assist the reader in the identification of potentially unstable rockfoundations, to demonstrate design methods appropriate for a wide range of geological conditions andfoundation types, and to describe rock construction methods. The book is divided into three main section.Chapters 1–4 describe the investigation and measurement of the primary factors that influence theperformances of rock foundations. Namely, rock strength and modulus, fracture characteristics andorientation, and ground water conditions. Chapters 5–9 provide details of design procedures for spreadfootings, dam foundations, rock socketed piers, and tension foundations. These chapters contain workedexamples illustrating the practical application of the design methods. The third section, Chapter 10,describes a variety of excavation and stabilization methods that are applicable to the construction of rockfoundations.

The anticipated audience for this book, which has been written by a practising rock mechanics engineer,is the design professional in the field of geotechnical engineering. The practical examples illustrate thedesign methods, and descriptions are provided of investigation methods that are used widely in thegeotechnical engineering community. It is also intended that the book will be used by graduate geotechnicalengineers as a supplement to the books currently available on rock slope engineering, geologicalengineering and rock mechanics. Foundations on Rock describes techniques that are common to a wideselection of projects involving excavations in rock and these techniques have been adapted and modified,where appropriate, to rock foundation engineering.

Much of the material contained in this book has been acquired from the author’s experience on projects ina wide range of geological and construction environments. On all these projects there have, of course, beenmany other persons involved: colleagues, owners, contractors and, equally importantly, the constructionworkers. The author acknowledges the valuable advice and experience that have been acquired from themall.

There are many people who have made specific contributions to this book and their assistance is greatlyappreciated. Sections of the book were reviewed by Herb Hawson, Graham Rawlings, Hugh Armitage, Vic

Milligan, Dennis Moore, Larry Cornish, Norm Norrish and Upul Atukorala. In additon a number of peoplecontributed photographs and computer plots and they are acknowledged in the text. Important contributionswere also made by Ron Dick who produced all the drawings, and Glenys Sykes who diligently searched outinnumerable references. Finally, I appreciate the support of my family who tolerated, barely, the endlessearly-morning and late-night sessions that were involved in preparing this book.

D.C.Wyllie

xviii

Notation

The following symbols are used in this book.

A Cross-sectional area (m2, inch2)B Width of footing, diameter of pier,

burden (blasting) (m, ft)b Radius of footing (m, ft)Cd Dispersion coefficient (structural

geology); influence factor for foundationdisplacement

Cf Correction factor for foundation shapeCR Coefficient of reliabilityc Cohesion (MPa, p.s.i.)D Diameter, depth of embedment (m, ft)d Diameter (m, ft)

Mean value of displacing force (MN, lbf)Em Deformation modulus of rock mass

(MPa, p.s.i.)Er Deformation modulus of intact rock

(MPa, p.s.i.)Em(b) Deformation modulus of rock mass in

base of pier (MPa, p.s.i.)Em(s) Deformation modulus of rock mass in

shaft of pier (MPa, p.s.i.)e Eccentricity in foundation bearing

pressureFS Factor of safetyF Foundation factor (seismic design); shape

factor (falling head tests)fr Resisting force (MN, lbf)fd Displacing force (MN, lbf); factor in

limit states designGr, m Shear modulus: intact rock (r), rock mass

(m) (MPa, p.s.i.)G1, 2 Viscoelastic constants defining creep

characteristics of rock (MPa, p.s.i.)H Height (m, ft); horizontal component of

force(s) (MN, lbf)h Head measurement in falling head test (m)I Importance factor in seismic designIs Point load strength (MPa, p.s.i.)ih Pressure gradientK Bulk modulus (MPa, p.s.i.)Ks Factor for construction type in seismic

designk Permeability (m/s); blast vibration

attentuation factorkn, s Stiffness, normal and shear (GPa/m,

p.s.i./in)L, l Length of foundation, outcrop, socket

(m, ft)l, m, n Unit vectors of direction cosines

(structural geology)m Rock mass strength factor (Hoek-Brown

strength)N Normal force (MN, lbf); number (of

analyses) bearing capacity factorP Probability; rate of energy dissipation

(kW/m2)

p Pressure (MPa, p.s.i.)PF Probability of failureQ Foundation load (MN, lbf)Qs Seepage rate (l/s, ft3/s)q Flow rate (l/s, gal/s); foundation bearing

pressure (MPa, p.s.i.)qa Allowable foundation bearing pressure

(MPa, p.s.i.)R Force modification factor in seismic design

Resultant unit vectorRe Reynolds numberr Radius (m, ft)S Spacing (m, ft); shear force (MN, lbf);

seismic response factorS Siemen (unit of conductivity)SD Standard deviations Rock mass strength factor (Hoek-Brown

strength)T Basic time lag (s); rock bolt tension (MN,

lbf)U Water uplift force (MN, lbf)u Water uplift pressure (MPa, p.s.i.)V Water force in tension crack (MN, lbf);

vertical component of force(s) (MN, lbf);base shear

v Zonal velocity ratio in seismic designW Weight of sliding block; weight factor in

seismic designMean value

Z Factor for seismic intensitya Dip direction of plane, or trend of force

(degrees); adhesion factor of pier side-

wallsß Settlement angular distortion, dip

(degrees); blast vibration attenuation factor? Unit weight (kN/m3, lbf/ft3)?w Unit weight of water (kN/m3, lbf/ft3)d Settlement; displacement (mm, in)? Settlement relative deflection;

displacement (mm, in)e Strain (%)? Dynamic viscosity—rock creep (MPa

min., p.s.i. min., poise (cgs units))? Apex angle of rock cone (degrees)v Poisson’s ratios Normal stress (MPa, p.s.i.)su(m) Uniaxial compressive strength of rock

mass (MPa, p.s.i.)su(r) Uniaxial compressive strength of intact

rock (MPa, p.s.i.)t Shear stress (MPa, p.s.i.)ø Friction angle (degrees)? Dip of plane or force (degrees)? Settlement tilt (degrees)? Factor in rock anchor bond strength

calculationWater table

xx

Note

The recommendations and procedures contained herein are intended as a general guide and prior to their usein connection with any design, report or specification they should be reviewed with regard to the fullcircumstances of such use. Accordingly, although every care has taken in the preparation of this book, noliability for negligence or otherwise can be accepted by the author or the publisher.

1Characteristics of rock foundations

1.1Types of rock foundation

There are two distinguishing features of foundationson rock. First, the ability of the rock to withstandmuch higher loads than soil, and second, thepresence of defects in the rock which result in thestrength of the rock mass being considerably lessthan that of the intact rock. The compressivestrength of rock may range from less than 5 MPa(725 p.s.i.) to more than 200 MPa (30 000 p.s.i.),and where the rock is strong, substantial loads can besupported on small spread footings. However, asingle, low strength discontinuity oriented in aparticular direction may cause sliding failure of theentire foundation.The ability of rock to sustain significant shear andtensile loads means that there are many types ofstructures that can be constructed more readily onrock than they can be on soil. Examples of suchstructures are dams and arch bridges which produceinclined loads in the foundation, the anchorages forsuspension bridges and other tie-down anchorswhich develop uplift forces, and rock socketed pierswhich support substantial loads in both compressiveand uplift. Some of these loading conditions areillustrated in Fig. 1.1 which shows the abutment ofan arch bridge. The load on the footing for the archis inclined along the tangent to the arch, while theloads on the column and abutment are vertical; theload capacity of these footings depends primarily onthe strength and deformability of the rock mass. Thewall supporting the cut below the abutment isanchored with tensioned and grouted rock bolts; theload capacity of these bolts depends upon the shear

strength developed at rock-grout interface in theanchorage zone.If the material forming the foundations of the bridgeshown in Fig. 1.1 was all strong, massive,homogeneous rock with properties similar toconcrete, design and construction of the footingswould be a trivial matter because the loads appliedby a structure are generally much less than the rockstrength. However, rock almost always containsdiscontinuities that can range from joints with roughsurfaces and cohesive infillings that have significantshear strength, to massive faulted zones containingexpansive clays with relatively low strength.Figure 1.1 shows how the geological structure canaffect the stability of the foundations. First, there isthe possibility of overall failure of the abutmentalong a failure plane (a-a) passing along the fault,and through intact rock at the toe of the slope.Second, local failure (b) of the foundation of thevertical column could occur on joints dipping out ofthe slope face. Third, settlement of the archfoundation may occur as a result of compression ofweak materials in the fault zone (c), and fourth,poor quality rock in the bolt anchor zone couldresult in failure of the bolts (d) and loss of support ofthe abutment.Foundations on rock can be classified into threegroups—spread footings, socketed piers and tensionfoundations—depending on the magnitude anddirection of loading, and the geotechnicalconditions in the bearing area. Figure 1.2 showsexamples of the three types of foundations and thefollowing is a brief description of the principalfeatures of each. The basic geotechnical information

required for the design of all three types offoundation consists of the structural geology, rockstrength properties, and the ground water conditionsas described in Chapters 2–4. The application ofthis data to the design of each type of foundation isdescribed in Chapters 5–9.

1.1.1Spread footings

Spread footings are the most common type offoundation and are the least expensive to construct.They can be constructed on any surface which hasadequate bearing capacity and settlementcharacteristics, and is accessible for construction.The bearing surface may be inclined, in which casesteel dowels or tensioned anchors may be requiredto secure the footing to the rock. For footingslocated at the crest or on the face of steep slopes,

the stability of the overall slopes, taking intoaccount the loads imposed by the structure, must beconsidered (Fig. 1.2(a)).Dam foundations, which fall into the category ofspread footings, are treated as a special case in thisbook. Loads on dam foundations comprise theweight of the dam together with the horizontalwater force which exert a non-vertical resultant load(Fig. 1.2(b)). Furthermore, uplift forces aredeveloped by water pressures in the foundation.These loads can be much larger than the loadsimposed by structures such as bridges andbuild ings. In addition there is the need for a highlevel of safety because the consequences of failureare often catastrophic. Dams must also be designedto withstand flood conditions, and whereappropriate, earthquake loading. The design of damfoundations, excluding foundations for arch dams,is discussed in Chapter 7.

Figure 1.1 Stability of bridge abutment founded on rock: (a-a) overall failure of abutment on steeply dipping fault zone;(b) shear failure of foundation on daylighting joints; (c) movement of arch foundation due to compression of low-modulus rock; and (d) tied-back wall to support weak rock in abutment foundation.

2 CHARACTERISTICS OF ROCK FOUNDATIONS

1.1.2Socketed piers

Where the loads on individual footings are veryhigh and/or the accessible bearing surface hasinadequate bearing capacity, it may be necessary tosink or drill a shaft into the underlying rock andconstruct a socketed pier. For example, in Fig. 1.2(c)a spread footing could not be located on the edge ofthe excavation made for the existing building, and asocketed pier was constructed to bear in sound rockbelow the adjacent foundation level. The supportprovided by socketed piers comprises the shearstrength around the periphery of the drill hole, and

the end bearing on the bottom of the hole. Socketedpiers can be designed to withstand axial loads, bothcompressive and tensile, and lateral forces withminimal displacement. Design methods for socketedpiers are discussed in Chapter 8.

1.1.3Tension foundations

For structures that produce either permanent ortransient uplift loads, support can be provided bythe weight of the structure and, if necessary, tie-down anchors grouted into the underlying rock(Fig. 1.2(d)). The uplift capacity of an anchor is

Figure 1.2 Types of foundations on rock: (a) spread footing located at crest of steep slope; (b) dam foundation withresultant load on foundation acting in downstream direction; (c) socketed pier to transfer structural load to elevationbelow base of adjacent excavation; and (d) tie-down anchors, with staggered lengths, to prevent uplift of submergedstructure.

TYPES OF ROCK FOUNDATION 3

determined by the shear strength of the rock-groutbond and the characteristics of the rock cone that isdeveloped by the anchor. The dimensions of thiscone are defined by the developed anchor length,and the apex angle of the cone. The position of theapex is usually assumed to be at mid-point of theanchor length, and the apex angle can vary fromabout 60° to 120°. An apex angle of about 60°would be used where there are persistentdiscontinuities aligned parallel to the load direction,while an angle of about 120° would be used inmassive rock, or rock with persistent discontinuitiesat right angles to the load direction.In calculating uplift capacity, a very conservativeassumption can be made that the cone is ‘detached’from the surrounding rock and that only the weightof the cone resists uplift. However, unless the anchoris installed in a rock mass with a cone-shapeddiscontinuity pattern, significant uplift resistancewill be provided by the rock strength on the surfaceof the cone. The value of the rock strength dependson the strength of the intact rock, and on theorientation of the geological structure with respectto the cone surface. As shown in Fig. 1.2(d), thelengths of the anchors can be staggered so that thestresses in the rock around the bond zones are notconcentrated on a single plane.Design methods for tension anchors, includingtesting procedures and methods of corrosionprotection, are described in Chapter 9.

1.2Performance of foundations on rock

Despite the apparently favorable stability conditionsfor structures founded on strong rock, there are,unfortunately, instances of foundation failures.Failures may include excessive settlement due to thepresence of undetected weak seams or cavities,deterioration of the rock with time, or collapseresulting from scour and movement of blocks ofrock in the foundation. Factors that may influencestability are the structural geology of thefoundation, strength of the intact rock anddiscontinuities, ground water pressures, and the

methods used during construction to excavate andreinforce the rock.The most complete documentation of foundationfailures has been made for dams because theconsequences of failure are often catastrophic.Also, the loading conditions on dam foundations areusually more severe than those of other structures sostudy of these failures gives a good insight on thebehavior and failure modes of rock foundations.The importance of foundation design is illustratedby Gruner’s examination of dam failures in whichhe found that one third could be directly attributedto foundation failure (Gruner, 1964, 1967). Thefollowing is a review of the stability conditions ofrock foundations.

1.2.1Settlement and bearing capacity failures

Settlement and bearing capacity type failures inrock are rare but may occur where large structures,sensitive to settlement, are constructed on veryweak rock (Tatsuoka et al., 1995), and where bedsof low strength rock or cavities formed byweathering, scour or solution occur beneath thestructure (James and Kirkpatrick, 1980). The mostpotentially hazardous conditions are in karstic areaswhere solution cavities may form under, or close to,the structure so that the foundation consists of onlya thin shell of competent rock (Kaderabek andReynolds, 1981). Rock types susceptible to solutionare limestone, anhydrite, halite, calcium carbonateand gypsum. The failure mechanism of thefoundation under these conditions may be punchingand shear failure, or more rarely bending and tensilefailure. Lowering of the water table may acceleratethe solution process and cause failure long afterconstruction is complete. A related problem is thatof a thin bed of competent rock overlying a thickbed of much more compressible rock which mayresult in settlement as a result of compression of theunderlying material (mechanism (c) in Fig. 1.1).Loss of bearing capacity with time may also occurdue to weathering of the foundation rock. Rocktypes which are susceptible to weathering include


poorly cemented sandstones, and shales, especiallyif they contain swelling clays. Common causes ofweathering are freeze-thaw action, and in the caseof such rocks as shales, wetting and drying cycles.Foundations which undergo a significant change inenvironmental conditions as a result ofconstruction, such as dam sites where the previouslydry rock in the sides of the valley becomessaturated, should be carefully checked for anymaterials that may deteriorate with time in theirchanged environment.

1.2.2Creep

There are two circumstances under which rocksmay creep, that is, experience increasing strain withtime under the application of a constant stress. First,creep may occur in elastic rock if the applied stressis a significant fraction (greater than about 40%) ofthe uniaxial compressive strength (σu). However, atthe relatively low stress level of 40% of σu the rateof creep will decrease with time. At stress levelsgreater than about 60% of σu, the rate will increasewith time and eventually failure may take place. Atthe stress levels usually employed in foundations itis unlikely that creep will be significant.A second condition under which creep may occur isin ductile rocks such as halite and some sediments.A ductile material will behave elastically up to itsyield stress but is able to sustain no stress greaterthan this so that it will flow indefinitely at thisstress unless restricted by some out-side agency.This is known as elastic-plastic behavior andfoundations on such materials should be designed sothat the applied stress is well below the yield stress.Where this is not possible, the design andconstruction methods should accommodate time-dependent deformations.Time-dependent behavior of rock is discussed inmore detail in Section 3.6.

1.2.3Block failure

The most common cause of rock foundation failureis the movement and collapse of blocks of rockformed by intersecting discontinuities (mechanism(b) in Fig. 1.1). The orientation, spacing and lengthof the discontinuities determines the shape and sizeof the blocks, as well as the direction in which theycan slide. Stability of the blocks depends on theshear strength of the discontinuity surfaces, and theexternal forces which can comprise water,structural, earthquake and reinforcement loads.Analysis of stability conditions involves thedetermination of the factor of safety or coefficientof reliability, and is described in more detail inSection 1.6.4 and Chapter 6.An example of a block movement failure occurredin the Malpasset Dam in France where a wedgeformed by intersecting faults moved when subjectedto the water uplift forces as the dam was filled(Londe, 1987). The failure resulted in the loss of400 lives. Bridge foundations also experiencefailure or movement as a result of instability ofblocks of rock (Wyllie, 1979, 1995). One cause ofthese failures is the geometry of bridge foundations,with the frequent construction of abutments andpiers on steep rock faces from which blocks canslide. Other causes of failure are ground watereffects which include weathering, uplift pressureson blocks which have a potential to slide, riverscour and wave action which can undermine thefoundation, and traffic vibration which can slowlyloosen closely fractured rock. It is standard practiceon most highways and railways to carry out regularbridge inspections which will often identifydeteriorating foundations and allow remedial workto be carried out. It is the author’s experience thatrock will usually undergo observable movementsufficient to provide a warning of instability beforecollapse occurs.An example of the influence of structural geologyon stability is shown in Fig. 1.3 where a retainingwall is founded on very strong granite containingsheeting joints dipping at about 40° out of the face.Although the bearing capacity of the rock was


ample for this loading condition, movement alongthe joints and failure of a block in the foundationresulted in rotation of the wall. Fortunately, earlydetection of this condition allowed remedial work tobe carried out. Thisconsisted of concrete to fill thecavity formed by the failed rock and the installationof tensioned bolts to prevent further movement onthe joints.

1.2.4Failure of socketed piers and tension anchors

The failure of socketed piers is usually limited tounacceptable movement which may occur as aresult of loss of bond at the rock-concrete interfaceon the side walls, or compression of loose material

at the base of the pier. A frequent cause ofmovement is poor cleaning of the sides and base ofthe hole, or in the case of karstic terrain, collapse ofrock into an undetected solution cavity. In the caseof tensioned anchors, loss of bond at the rock-groutinterface on the walls of the hole may result inexcessive movement of the head, while corrosionfailure of the steel may result in sudden failure longafter installation. The long term reliability oftensioned anchors depends to a large degree on thedetails of fabrication and installation procedures asdiscussed in Chapter 9.

Figure 1.3 Retaining wall foundation stabilized with reinforced concrete buttress and rock bolts.


1.2.5Influence of geological structure

The illustrations of foundation conditions shown inFigs 1.1 and 1.3, and the analysis of foundationfailures, show that geologic structure is often asignificant feature influencing the design andconstruction of rock foundations. Detailedknowledge of discontinuity characteristics—orientation, spacing, length, surface features andinfilling properties—are all essential informationrequired for design. The examination of thestructural geology of a site usually requires a three-dimensional analysis which can be mostconveniently carried out using stereographicprojections as described in Chapter 2. Thistechnique can be used to identify the orientation andshape of blocks in the foundation that may fail bysliding or toppling.It is also necessary to determine the shear strength ofdiscontinuities along which failure could take place.This involves direct shear tests, which may becarried out in the laboratory on pieces of core, or insitu on undisturbed samples. Methods of rocktesting are described in Chapter 4.

1.2.6Excavation methods

Blasting is often required to excavate rockfoundations and it is essential that controlledblasting methods be used that minimize the damageto rock that will support the planned structure.Damage caused by excessively heavy blasting canrange from fracturing of the rock with a resultantloss of bearing capacity, to failure of the slopeseither above or below the foundation. There are somecircumstances, when, for example, existingstructures are in close proximity or when excavationlimits are precise, in which blasting is not possible.In these situations, non-explosive rock excavationmethods, which include hydraulic splitting,hydraulic hammers and expansive cement, may bejustified despite their relative expense and slow rateof excavation (see Section 10.3.6).A typical effect of geological conditions on

foundation excavations is shown in Fig. 1.4 wherethe design called for a notch to be cut in stronggranite to form a shear key to resist horizontalforces generated in the backfill. However, thebearing surface formed along pre-existing joints andit was impractical to cut the required notch; it wasnecessary to install dowels to anchor the wall. Onlyin very weak rock is it possible to ‘sculpt’ the rockto fit the structure, and even this may be bothexpensive and ineffective.Methods of rock excavation are discussed inChapter 10.

1.2.7Reinforcement

The reinforcement of rock to stabilize slopes aboveand below foundations, or to improve bearingcapacity and deformation modulus, has wideapplication in rock engineering. Where the intactrock is strong but contains discontinuities whichform potentially unstable blocks, the foundation canbe reinforced by installing tensioned cables or rigidbolts across the failure plane. The function of suchreinforcement is to apply a normal stress across thesliding surface which increases the frictionalresistance on the surface; the shear strength of thesteel bar provides little support in comparison withthe friction component of the rock strength. Anotherfunction of the reinforcement is to preventloosening of the rock mass, because reduction in theinterlock between blocks results in a significantreduction in rock mass strength.Where the rock is closely fractured, pumping ofcement grout into holes drilled into the foundationcan be used to increase the bearing capacity andmodulus. The effect of the grout is to limitinterblock movement and closure of discontinuitiesunder load, both of which increase the strength ofthe rock mass and reduce settlement. Where itis required to protect closely fractured or faultedrock faces from weathering and degradation thatmay undermine a foundation, shotcrete can often beused to support the face. However, shotcrete willhave no effect on the stability of the overall


foundation.Methods of construction and rock reinforcement arediscussed in Chapter 10.

1.3Structural loads

The following is a summary of typical loading

conditions produced by different types of structuresbased on United States’ building codes and designpractices (Merritt, 1976). The design informationrequired on loading conditions consists of themagnitude of both the dead and live loads, as wellas the direction and point of application of theseloads. This information is then used to calculate thebearing pressure, and any overturning moments

Figure 1.4 Construction of rock foundation: (a) attempted ‘sculpting’ of rock foundation to form shear key; and (b) ‘as-built’ condition with footing located on surface formed by joints.


acting on the foundation.An important aspect in foundation design iscommunication between the structural andfoundation engineers on the factors of safety thatare incorporated in each part of the design. If thestructural engineer calculates the dead and liveloads acting on the foundation and multiplies this bya factor of safety, it is important that the foundationengineers do not apply their own factors of safety.Such multiplication of factors of safety can result inoverdesigned and expensive foundations.Conversely, failure to incorporate adequate factorsof safety can result in unsafe foundations. Adescription of methods of calculating loads imposedby structures on their foundations is beyond thescope of this book; this is usually the responsibilityof structural engineers. The following four sectionsprovide a summary of the design methods, and theappropriate references should be consulted fordetailed procedures.

1.3.1Buildings

Loads on building foundations consist of the deadload of the structural components, and the live loadassociated with its usage, both of which are closelydefined in various building codes. For dead loads,the codes describe a wide range of constructionmaterials such as various types of walls, partitions,floors finishes and roofing materials and theminimum loads which they exert. An option thatmay be suitable for poor foundation conditions isthe use of lightweight aggregate in concrete whichreduces the dead load for concrete slabs from 24Paper millimeter of thickness (12.5 p.s.f. per inch)for standard concrete, to 17 Pa per millimeter ofthickness (9 p.s.f. per inch).A special case is the dead load on buried structuresin which a considerable load is exerted by thebackfill—granular fill has a density of about 19 kN/m3 (120 lb/ft3), and a 3 m thick backfill will exert adead load equal to about seven floors of an officebuilding. A very significant reduction in thefoundation loads can be achieved by using

lightweight fills such as styrofoam which has adensity of 0.3 kN/m3 (2 lb/ft3) and is used in roadfills on low strength soils. The disadvantage ofstyrofoam is that it is flammable and soluble in oil,so must be carefully protected.The live loads, which are determined by thebuilding usage, are defined in the codes and rangefrom 12 kN/m2 (250 lb/ft2) for warehouses andheavy manufacturing areas, 7.2 kN/m2 (150 lb/ft2)for kitchens and book storage areas, and 1.9 kN/ m2

(40 lb/ft2) for apartments and family housing. Liveloads are generally uniformly distributed, but areconcentrated for such usage as garages and elevatormachine rooms.Additional loads result from snow, wind andseismic events, which vary with the design of thestructure and the geographic location. Wind, snowand live loads are assumed to act simultaneously,but wind and snow are generally not combined withseismic forces.Ground motion in an earthquake is multidirectionaland can induce forces in the foundation of astructure that can include base shear, torsion, upliftand overturning moments. The magnitude of theforces depends, for a single-degree-of-freedomstructure, on the fundamental period and dampingcharacteristics of the structure, and on the frequencycontent and amplitude of the ground motion. Theresistance to the base shear, torsion forces andoverturning moments is provided by the weight ofthe structure, the friction on the base, and ifnecessary, the installation of tie-down anchors.The total base shear at the foundation, which can beused as measure of the response of the structure tothe ground motion, is the sum of the horizontalforces acting in the structure and is given by(Canadian Geotechnical Society, 1992; NationalBuilding Code of Canada, 1990):

(1.1)where Ve is the equivalent lateral seismic forcerepresenting elastic response, R is a forcemodification factor and Ue is a calibration factorwith a value of 0.6. The lateral seismic force Ve isdefined by:


(1.2)The following is a discussion on each of thesefactors.• R, force modification factor, is assigned todifferent types of structure reflecting design andconstruction experience, and the evaluation of theperformance of structures during earthquakes. Itendeavors to account for the energy-absorptioncapacity of the structural system by damping andinelastic action through several load reversals. Abuilding with a value of R equal to 1.0 correspondsto a structural system exhibiting little or no ductility,while construction types that have performed wellin earthquakes are assigned higher values of R.Types of structures assigned high values of R arethose capable of absorbing energy within acceptabledeformations and without failure, structures withalternate load paths or redundant structural systems,and structures capable of undergoing inelastic cyclicdeformations in a ductile manner.• v, zonal velocity ratio, which varies from 0.0 forseismic zone 0 located in areas with low risk ofseismic events, to 0.4 for seismic zone 6 wherethere is active seismic activity resulting from crustalmovement. For example, in North America, zone 0lies in the central part of the continent, while zone 6lies along the east and west coasts.• S, seismic response factor, which depends on thefundamental period of the structure, and the seismiczone for a particular geographic location.• I, importance factor, has a value of 1.5 forbuildings that should be operative after anearthquake. Such buildings include powergeneration and distribution systems, hospitals, fireand police stations, radio stations and towers,telephone ex changes, water and sewage pumpingstations, fuel supplies and civil defense buildings.Schools, which may be needed for shelter after anearthquake, are assigned an I value of 1.3, and mostother buildings are assigned a value of 1.0.• F, foundation factor, accounts for the geologicalconditions in the foundation. As earthquake motionspropagate from the bedrock to the ground surface,soil may amplify the motions in selected frequencyranges close to the natural frequencies of the

surficial layer. In addition, a structure founded onthe surficial layer and having some of its naturalfrequencies close to that of the layer, mayexperience increased shaking due to thedevelopment of a state of quasi-resonance betweenthe structure and the soil. For structures founded onrock, the foundation factor F is usually taken as 1.0.However, in steep topography there may beamplification of the ground motions related to thethree-dimensional geometry of the site. Forexample, at the Long Valley Dam in California, themeasured acceleration on the abutment at anelevation of 75 m (250 ft) above the base of the damwas a maximum of 0.35g compared with themaximum acceleration at the base of 0.18g (Lai andSeed, 1985). The amplification of ground motion incanyons has been studied extensively for damdesign and both three-dimensional and two-dimensional models have been developed to predictthese conditions (Gazetas and Dakoulas, 1991).• Q, weight factor, is the weight of the structure.

1.3.2Bridges

Loads that bridge foundations support consist of thedead load determined by the size and type ofstructure, and the live load as defined in the codesfor a variety of traffic conditions. For example, anHS20–44 highway load, representing a truck andtrailer with three loaded axles, is a uniform load of9.34 kN per lineal meter of load lane (0.64 kips perlineal foot) together with concentrated loads at thewheel locations for moment and shear. For railwaybridges, the live load is specified by the E number ofa ‘Cooper’s train’, consisting of two locomotivesand an indefinite number of freight cars. Cooper’strain numbers range from E10 to E80, with E80being for heavy diesel locomotives with bulkfreight cars.For both highway and railway bridges, impact loadsare calculated as a fraction of the live load, with themagnitude of the impact load diminishing as thespan length increases. Methods of calculatingimpact loads vary with the span length, method of


construction and the traffic type. Other forces thatmay affect the foundations are centrifugal forcesresulting from traffic motion, wind, seismic, streamflow, earth and ice forces, and elastic and thermaldeformations. The magnitude of these forces isevaluated for the particular conditions at each site.

1.3.3Dams

Loads on dam foundations are usually of muchgreater magnitude than those on bridge and buildingfoundations because of the size of the structuresthemselves, and the forces exerted by the waterimpounded behind the dam. The water forces areusually taken as the peak maximum flood (PMF),with an allowance for accumulations of silt behindthe dam, as appropriate. Any earthquake loadingcan be simulated most simply as a horizontalpseudostatic force proportional to the weight of thedam. The resultant of these forces acts in adownstream direction, and the dam must bedesigned to resist both sliding and overturningunder this loading condition. There may also beconcentrated compressive stresses at the toe of thedam and it is necessary to check that these stressesdo not cause excessive deformation.A significant difference between dams and mostother structures is the water uplift pressures that aregenerated within the foundations. In most casesthere are high pressure gradients beneath the heel ofthe dam where drain holes and grout curtains areinstalled to relieve water pressures and controlseepage. The combination of these load conditions,together with the high degree of safety required forany dam, requires that the in vestigation, design andconstruction of the foundation be both thorough andcomprehensive.


Typical tension loads on foundations consist ofbouyancy forces generated by submerged tanks,angle transmission line towers and the tension in

suspension bridge cables. Foundations may also bedesigned to resist uplift forces generated byoverturning moments acting on the structureresulting from horizontal loads such as wind, ice,traffic and earthquake forces.

1.4Allowable settlement

Undoubtedly the most famous case of foundationsettlement is that of the Leaning Tower of Pisawhich has successfully withstood a differentialsettlement of 2 m and is now leaning at an angle ofat least 5°11' (Mitchell et al., 1977). However, thissituation would not be tolerated in most structures,except as a tourist attraction! The following is areview of allowable settlement values for differenttypes of structures.

1.4.1Buildings

Settlement of building foundations that isinsufficient to cause structural damage may still beunacceptable if it causes significant cracking ofarchitectural elements. Some of the factors that canaffect settlement are the size and type of structure,the properties of the structural materials and thesubsurface soil and rock, and the rate anduniformity of settlement. Because of thesecomplexities, the settlement that will causesignificant cracking of structural members orarchitectural elements, or both, cannot readily becalculated. Instead, almost all criteria for tolerablesettlement have been established empirically on thebasis of observations of settlement and damage inexisting buildings (Wahls, 1981).Damage due to settlement is usually the result ofdifferential settlement, i.e. variations in verticaldisplacement at different locations in the building,rather than the absolute settlement. Means ofdefining both differential and absolute settlementare illustrated in Fig. 1.5, together with the termsdefining the various components of settlement.Study of cracking of walls, floors and structural


members shows that damage was most often theresult of distortional deformation, so ‘angulardistortion’ ß has been selected as the critical indexof settlement. These studies have resulted in thefollowing limiting values of angular distortion beingrecommended for frame buildings (Terzaghi andPeck, 1967; Skempton and McDonald, 1956;Polshin and Tokar, 1957):

– structural damage probable;– cracking of load bearing or

panel walls likely;– safe level of distortion at

which cracking will not occur.

In the case of load bearing walls, it is found that thedeflection ratio ?/L is a more reliable indicator ofdamage because it is related to the direct and

diagonal tension developed in the wall as a result ofbending (Burland and Wroth, 1974). The proposedlimiting values of ?/L for design purposes are in therange 0.0005–0.0015.

1.4.2Bridges

Extensive surveys of horizontal and verticalmovement of highway bridges have been carriedout to assess allowable settlement values(Walkinshaw, 1978; Grover, 1978; Bozozuk, 1978).It is concluded that settlement can be divided intothree categories depending on its effect on thestructure:

1. tolerable movements;2. intolerable movements resulting only in poor

riding characteristics; and 3. intolerable movements resulting in structural

damage.

It is not feasible to specify limiting settlementvalues for each of these three categories because ofthe wide variety of bridge designs and subsurface

Figure 1.5 Definition of settlement terminology for buildings (Wahls, 1981): (a) settlement without tilt; (b) settlementwith tilt. di is the vertical displacement at i; dmax is the maximum displacement; dij is the displacement between twopoints i and j with distance apart lij; ? is the relative deflection which is the maximum displacement from a straight lineconnecting two reference points; ? is the tilt, or rigid body rotation; is the angular distortion; and ?/Lis the deflection ratio, or the approximate curvature of the settlement curve.


conditions. For example, Walkinshaw reports oftolerable vertical movements that ranged from 13 to450 mm (0.5 to 17.7 in), although the average valuewas about 85 mm (3.3 in). Intolerable verticalmovements causing only poor riding qualityaveraged about 200 mm (7.9 in), while verticalmovements causing structural damage varied from13 to 600 mm (0.5 to 23.6 in) with an average valueof about 250 mm (10 in). As a comparison withthese results, Fig. 1.6 shows the results of thesurvey carried out by Bozozuk of bridge abutmentsand piers on spread footings with lines giving thelimits of tolerable, harmful but tolerable, andintolerable movements.The conclusions that can be drawn from thesestudies are that tolerable movements can be as greatas 50–100 mm (2–4 in), and that structural damagemay not occur until movements are in excess of 200

mm (8 in). Also, differential and horizontalmovements are more likely to cause damage thatvertical movements alone. One possible reason isthat vertical settlement of simply supported spanscan readily be corrected by lifting and shimming atthe bearing points (Grover, 1978). In comparison,horizontal movements are more difficult to correct,with one of the most important effects being thelocking of expansion joints.

1.4.3Dams

Allowable settlement of dams is directly related tothe type of dam: concrete dams are much lesstolerant of movement and deformation thanembankment dams. There are no general guidelineson allowable settlements for dams because the

Figure 1.6 Engineering performance of bridge abutments and piers on spread footings (Bozozuk, 1978).


foundation conditions for each structure should beexamined individually. However, in all cases,particular attention should be paid to the presenceof rock types with differing moduli, or seams ofweathered and faulted rock that are morecompressible than the adjacent rock. Either of theseconditions may result in differential settlement of thestructure.

1.5Influence of ground water on foundation

performance

The effect of ground water on the performance offoundations should be considered in design,particularly in the case of dams and bridges. Theseeffects include movement and instability resultingfrom uplift pressures, weathering, scour of seams ofweak rock, and solution (Fig. 1.7). In almost allcases, geological structure influences ground waterconditions because most intact rock is effectivelyimpermeable and water flow through rock masses isconcentrated in the discontinuities. Flow quantitiesand pressure distributions are related to theaperture, spacing and continuous length of thediscontinuities: tight, impersistent discontinuitieswill tend to produce low seepage quantities andhigh pressure gradients. Furthermore, the directionof flow will tend to be parallel to the orientation ofthe main discontinuity set.

1.5.1Foundation stability

Typical instability caused by water uplift forcesacting on potential sliding planes in the foundationis illustrated in Fig. 1.7(a). The uplift force U actingon the sliding plane reduces the effective normalforce on this surface, which produces acorresponding reduction the shear strength (seeChapter 3). For the condition shown in Fig. 1.7(a),the greatest potential for instability is when a rapiddraw down in the water level occurs andthere is insufficient time for the uplift force todissipate.

The flow of water through and around a foundationcan have a number of effects on stability apart fromreducing the shear strength. First, rapid flow canscour low strength seams and infillings, and developopenings that undermine the foundation (Fig. 1.7(a)). Second, percolation of water through solublerocks such as limestone can cause cavities todevelop. Third, rocks such as shale may weatherand deteriorate with time resulting in loss of bearingcapacity. Such weathering may occur either sorapidly that it is necessary to protect bearingsurfaces as soon as they are excavated, or it mayoccur a considerable time after construction causinglong term settlement of the structure. Fourth, flowof water into an excavation can make cleaning andinspection of bearing surfaces difficult (Fig. 1.7(b))and result in increased construction costs.

1.5.2Dams

In dam foundations it is necessary to control bothuplift due to water pressures to ensure stability, andseepage to limit water loss (Fig. 1.7(c)). Controlmeasures consist of grout curtains and drains tolimit seepage and reduce water pressure asdescribed in Chapter 7. The rock property thatdetermines seepage quantities and head loss ispermeability, which relates the quantity of water flow through the rock to the pressure gradientacross it. As discussed at the start of this section,water flow is usually concentrated in thediscontinuities, so seepage quantities will be closelyrelated to the geological structure. For example,seepage losses may be high where there arecontinuous, open discontinuities that form a seepagepath under the dam, while a clay filled fault mayform a barrier to seepage. The study of seepagepaths and quantities, and calculation of waterpressure distributions in the foundation is carried outby means of flow nets (Cedergren, 1989). A flownet comprises two sets of lines—equipotential lines(lines joining points along which the total head isthe same) and flow lines (paths followed by waterflowing through the saturated rock)— that are


drawn to form a series of curvilinear squares as

Figure 1.7 Typical effects of ground water flow on rock foundations: (a) uplift pressures developed along continuousfracture surface; (b) water flow into hole drilled for socketed pier; and (c) typical flow net depicting water flow anduplift pressure distribution in dam foundation (after Cedergren, 1989).


shown in Fig. 1.7(c). The distribution ofequipotential lines can also be used to determine theuplift pressure under a foundation which is alsoshown in Fig. 1.7(c).


Where tension foundations are secured with anchorslocated below the water table, it is necessary to usethe buoyant weight of the rock in calculating upliftresistance provided by the ‘cone’ of rock mobilizedby the anchor. Figure 1.2(d) shows an example ofsuch an installation where the rock in which the tie-down anchors is located below the water table andthe effective unit weight of the rock is about 16 kN/m3 (100 lb/ft3). Another important factor in designis provision for protection of the steel againstcorrosion, with corrosion occurring most rapidly inlow-pH and salt-water environments. Protectivemeasures for ‘permanent’ installations consist ofplastic sheaths grouted on to the anchors and fullgrout encapsulation which produces a crackresistant, high-pH environment around the steel (seeChapter 9).

1.6Factor of safety and reliability analysis

Structural design and geotechnical analysis areusually based on the following two main requirements. First, the structure and its componentsmust, during the intended service life, have anadequate margin of safety against collapse under themaximum loads and forces that might reasonablyoccur. Second, the structure and its componentsmust serve the designed functions without excessivedeformations and deterioration. These two servicelevels are the ultimate and serviceability limit statesrespectively and are defined as follows. Collapse ofthe structure and foundation failure includinginstability due to sliding, overturning, bearingfailure, uplift and excessive seepage, is termed theultimate limit state of the structure. The onset ofexcessive deformation and of deterioration

including unacceptable total and differentialmovements, cracking and vibration is termed theserviceability limit state (Meyerhof, 1984).The following is a discussion on a number ofdifferent design methods for geotechnicalstructures. Factor of safety analysis is by far themost widely used technique and factor of safetyvalues for a variety of structures are generallyaccepted in the engineering community. Thisprovides for each type of structure to be designed toapproximately equivalent levels of safety.Adaptations to the factor of safety analysis includethe limit states and sensitivity analysis methods,both of which examine the effect of variability indesign parameters on the calculated factor of safety.An additional design method, reliability analysis,expresses the design parameters as probabilitydensity functions representing the range and degreeof variability of the parameter. The theory ofreliability analysis is well developed and its majorstrength is that it quantifies the variability in all thedesign parameters and calculates the effect of thisvariability on the factor of safety (Harr, 1977).However, despite the analytical benefits ofreliability analysis, it is not widely used ingeotechnical engineering practice (as of 1998).

1.6.1Factor of safety analysis

Design of geotechnical structures involves a certainamount of uncertainty in the value of the inputparameters which include the structural ge ology,material strengths and ground water pressures.Additional uncertainties to be considered in designare extreme loading conditions such as floods andseismic events, reliability of the analysis procedure,and construction methods. Allowance for theseuncertainties is made by including a factor of safetyin design. The factor of safety is the ratio of thetotal resistance forces—the rock strength and anyinstalled reinforcement, to the total displacing forces—downslope components of the applied loads andthe foundation weight. That is,


(1.3)

The ranges of minimum total factors of safety asproposed by Terzaghi and Peck (1967) and theCanadian Foundation Engineering Manual (1992)are given in Table 1.1.The upper values of the total factors of safety applyto normal loads and service conditions, while thelower values apply to maximum loads and the worstexpected geological conditions. The lower valueshave been used in conjunction with performance

observations, large field tests, analysis of similarstructures at the end of the service life and fortemporary works.The factors of safety quoted in Table 1.1 areemployed in engineering practice, and can be usedas a reliable guideline in the determination ofappropriate values for particular structures andconditions. However, the design process stillrequires a considerable amount of judgment becauseof the variety of geological and construction factorsthat must be considered. Examples of conditionsthat would generally require the use of

Table 1.1 Values of minimum total safety factors

Failure type Category Safety factor

Shearing Earthworks 1.3–1.5Earth retaining structures, excavations 1.5–2.0Foundations 2–3

factors of safety at the high end of the ranges quotedin Table 1.1 include:

1. a limited drilling program that does notadequately sample conditions at the site, ordrill core in which there is extensive mechanicalbreakage or core loss;

2. absence of rock outcrops so that detailedmapping of geological structure is not possible;

3. inability to obtain undisturbed samples forstrength testing, or difficulty in extrapolatinglaboratory test results to in situ conditions;

4. absence of information on ground waterconditions, and significant seasonal fluctuationsin ground water levels;

5. uncertainty in failure mechanisms of thefoundation and the reliability of the analysismethod. For example, planar type failures canbe analyzed with considerable confidence,while the detailed mechanism of topplingfailures is less well understood;

6. uncertainty in load values, particularly in thecase of environmental factors such as wind,water, ice and earthquakes where existing datais limited;

7. concern regarding the quality of construction,including materials, inspection and weather

conditions. Equally important are contractualmatters such as the use of open bidding ratherthan pre-qualified contractors, and lump sumrather than unit price contracts;

8. lack of experience of local foundationperformance; and

9. usage of the structures; hospitals, policestations and fire halls and bridges on majortransportation routes are all designed to higherfactors of safety than, for example, residentialbuildings and warehouses.

1.6.2Limit states design

In order to produce a more uniform margin of safetyfor different types and components of earthstructures and foundations under different loadingconditions, the limit states design method has beenproposed (Meyerhof, 1984; OntarioHighway Bridge Design Code, 1983; NationalBuilding Code of Canada, 1985). The two Canadiancodes are based on unified limit states designprinciples with common safety and serviceabilitycriteria for all materials and types of construction.Limit states design uses partial factors of safetywhich are applied to both the loads, and the


resistance characteristics of the foundationmaterials. The procedure is to multiply the loads bya load factor fd and the resistances, friction andcohesion, by resistance factors , fc as shown inTable 1.2. The values given in parenthesis apply tobeneficial loading conditions such as dead loadsthat resist overturning or uplift.In limit states design the Mohr-Coulomb equationfor the shear resistance of a sliding surface isexpressed as

(1.4)The cohesion c, friction coefficient, tan , and waterpressure U are all multiplied by partial factors withvalues less than unity, while the normal stress a on

the sliding surface is calculated using a partial loadfactor greater than unity applied to the foundationload.

1.6.3Sensitivity analysis

Another means of assessing the effects of thevariability of design parameters on the factor ofsafety is to use sensitivity analysis. This procedureconsists of calculating the factor of safety for arange of values of parameters, such as the waterpressure, which cannot be precisely defined. Forexample, Hoek and Bray (1981) describe the sta

Table 1.2 Values of minimum partial factors (Meyerhof, 1984)

Category Item Load factor Resistance factor

Loads Dead loads (fDL) 1.25 (0.8)Live loads, wind, earthquake (fLL) 1.5Water pressure (U) (fu) 1.25 (0.8)

Shear strength Cohesion (c)—stability, earth pressure (fc) 0.65Cohesion (c)—foundations (fc) 0.5Friction angle f( ) 0.8

bility analysis of a quarry slope in which sensitivityanalyses were carried out for both the friction angle(range 15°–25°) and the water pressure—fullydrained to fully saturated (Fig. 1.8). This plot showsthat water pressures have more influence onstability than the friction angle. That is, a fullydrained, vertical slope is stable for a friction angleas low as 15°, while a fully saturated slope is unstableat an angle of 60°, even if the friction angle is 25°.

1.6.4Coefficient of reliability

The factor of safety and limit states analysesdescribed in this section involves selection of asingle value for each of the parameters that definethe loads and resistance of the foundation. Inreality, each parameter has a range of values. Amethod of examining the effect of this variability onthe factor of safety is to carry out sensitivityanalyses as described in Section 1.6.3 using upper

and lower bound values for what are considered tobe critical parameters. However, to carry outsensitivity analyses for more than three parametersis a cumbersome process and it is difficult toexamine the relationship between each of theparameters. Consequently, the usual designprocedure involves a combination of analysis andjudgment in assessing the influence on stability ofvariability in the design parameters, and thenselecting an appropriate factor of safety.An alternative design method is reliability analysis,which systematically examines the effect of thevariability of each parameter on the stability of thefoundation. This procedure calculates thecoefficient of reliability CR of the foundation whichis related to the more commonly used expressionprobability of failure PF by the following equation:

(1.5)The term coefficient of reliability is preferred forpsychological reasons: a coefficient of reliability of


99% is more acceptable to an owner than aprobability of failure of 1%.Reliability analysis was first developed in the1940’s and is used in the structural and aeronauticalengineering fields to examine the reliability ofcomplex systems. Among its early uses ingeotechnical engineering was in the design of openpit mine slopes where a certain risk of failure isacceptable and this type of analysis can be readilyincorporated into the economic planning of the mine(Canada DEMR, 1978; Pentz, 1981; Savely, 1987).Examples of its use in civil engineering are in theplanning of slope stabilization programmes fortransportation systems (Wyllie et al., 1979;McGuffey et al., 1980), landslide hazards (Crudenand Fell, 1997) and in design of storage facilitiesfor hazardous waste (Roberds, 1984, 1986).There is sometimes reluctance to use probabilisticdesign when there is a limited amount of designdata which may not be representative of thepopulation. In these circumstances it is possible to

use subjective assessment techniques that providereliable probability values from small samples(Roberds, 1990). The basis of these techniques isthe assessment and analysis of available data, by anexpert or group of experts in the field, in order toarrive at a consensus on the probability distributionsthat represent the opinions of these individuals. Thedegree of defensibility of the results tends toincrease with the time and cost that is expended inthe analysis. For example, the assessmenttechniques range from, most simply, informalexpert opinion, to more reliable and defensibletechniques such as Delphi panels (Rohrbaugh,1979). A Delphi panel comprises a group of expertswho are each provided with the same set of data andare required to produce a written assessment of thisdata. These documents are then providedanonymously to each of the other assessors who areencouraged to adjust their assessments in light oftheir peer’s assessments. After several iterations ofthis process, it should be possible to arrive at a

Figure 1.8 Sensitivity analysis showing the relationship between factor of safety and slope angle for range of waterpressures and friction angles (Hoek and Bray, 1981).


consensus that maintains anonymity andindependence of thought.The use of reliability analysis in design requires thatthere be generally accepted ranges of reliabilityvalues for different types of structure, as there arefor factors of safety. To assist in selectingappropriate reliability values, Athanasiou-Grivas(1979) provides charts relating factor of safety andprobability of failure. Also, Fig. 1.9 gives arelationship between required levels of annualprobability of failure for a variety of engineeringprojects, and the consequence of failure in terms oflives lost. For example, for structures such as low

rise buildings and bridges with low traffic densitywhere failure could result in less than about fivelives lost, the range of annual probability of failureshould not excced about 10-2–10-3

In comparison, for damswhere failure could result in the loss of severalhundred lives, annual probability of failure shouldnot exceed about 10-4–10-5

Despite the wide range ofvalues shown in Fig. 1.9, this approach provides auseful benchmark for the ongoing development ofreliability based design (Salmon and Hartford, 1995).(a) Distribution functions

Figure 1.9 Risks for selected engineering projects (Whitman, 1984).


In reliability analysis each parameter for whichthere is some uncertainty is assigned a range ofvalues which is defined by a probability densityfunction. Some types of distribution functions thatare appropriate for geotechnical data include thenormal, beta, negative exponential andtriangular distributions. The most common type offunction is the normal distribution in which themean value is the most frequently occurring value(Fig. 1.10(a)). The density of the normaldistribution is defined by:

(1.6)

where is the mean value given by

(1.7)

and SD is the standard deviation given by

(1.8)

and is the number of samples.As shown in Fig. 1.10(a), the scatter in the data, asrepresented by the width of the curve, is mea suredby the standard deviation. Important properties ofthis function are that the total area under the curveis equal to 1.0. That is, there is a probability of unitythat all values of the parameter fall within thebounds of the curve. Also, 68% of the values willlie within a range of one standard deviation eitherside of the mean and 95% will lie within twostandard deviations either side of the mean.Conversely it is possible to determine the value of aparameter defined by a normal distribution bystating the probability of its occurrence. This isshown graphically in Fig. 1.10(b) where F(z) is thedistribution function with mean 0 and standard

Figure 1.10 Properties of the normal distribution (Kreyszig, 1976): (a) density of the normal distribution with mean and various standard deviations (SD); and (b) distribution function F(z) of the normal distribution with mean 0 andstandard deviation 1.


deviation 1. For example, a value which has aprobability of being greater than 50% of all valuesis equal to the mean, and a value which has aprobability of being greater than 16% of all valuesis equal to the mean minus one standard deviation.The normal distribution extends to infinity in bothdirections which is often not a realistic expressionof geotechnical data in which the likely upper andlower bounds of a parameter can be defined. Forthese conditions, it is appropriate to use the betadistribution which has finite maximum andminimum points, and can be uniform, skewed to theleft or right, U-shaped or J-shaped (Harr, 1977). Forconditions in which there is little information on thedistribution of the data, a simple triangulardistribution can be used which is defined by threevalues: the most likely and the minimum andmaximum values. Examples of probabilitydistributions are shown in the worked example inSection 6.2.(b) Coefficient of reliability calculationThe coefficient of reliability is calculated in asimilar manner to that of the factor of safety in that

the relative magnitude of the displacing andresisting forces in the foundation are examined (seeSection 1.6.1). Two common methods of calculatingthe coefficient of reliability are the margin of safetymethod and the Monte Carlo method as discussedbelow.The margin of safety is the difference between theresisting and displacing forces, with the foundationbeing unstable if the margin of safety is negative.If the resisting and displacing forces aremathematically defined probability distributions—fD(r) and fD(d) respectively in Fig. 1.11(a)—then itis possible to calculate a third probabilitydistribution for the margin of safety. As shown inFig. 1.11, there is a probability of failure if the lowerlimit of the resisting force distribution fD(r) is lessthan the upper limit of the displacing forcedistribution fD(d). This is shown as the shaded areaon Fig. 1.11(a), with the probability of failure beingproportional to the area of the shaded zone. Themethod of calculating the area of the shaded zone isto calculate the probability density function of themargin of safety: the area of the negative portion of

Figure 1.11 Calculation of coefficient of reliability using normal distributions: (a) probability density functions of theresisting force fr and the displacing force fd in a foundation; and (b) probability density function of difference betweenresisting and displacing force distributions


this function is the probability of failure, and thearea of the positive portion is the coefficient ofreliability (Fig. 1.11(b)). If the resisting anddisplacing forces are defined by normaldistributions, the margin of safety is also a normaldistribution, the mean and standard deviation ofwhich are calculated as follows (Canada DEMR,1978):

(1.9)

(1.10)

where and are the mean values, and SDr andSDd are the standard deviations of the distributionsof the resisting and displacing forces respectively.Note that the definition of the conventional factor ofsafety is given by Having determined the mean and standard deviationof the margin of safety, the coefficient of reliabilitycan be calculated from the properties of the normaldistribution. For example, if the mean margin ofsafety is 2000 MN and the standard deviation is1200 MN, then the margin of safety is zero at 2000/1200, or 1.67 standard deviations. From Fig. 1.10(b), where the margin of safety distribution isrepresented by F(z), the probability of failure is 5%,

and the coefficient of reliability is 95%.Note that the margin of safety concept discussed inthis section can only be used where the resisting anddisplacing forces are independent variables. Thiscondition would apply where the displacing forcewas the structural load, and the resisting force wasthe installed reinforcement. However, where theresisting force is the shear strength of the rock, thenthis force and the displacing force are bothfunctions of the weight of the foundation, and arenot independent variables. Under thesecircumstances, it is necessary to use Monte Carloanalysis as described below.Monte Carlo analysis is an alternative method ofcalculating the coefficient of reliability which ismore versatile than the margin of safety methoddescribed above. Monte Carlo analysis avoids theintegration operations which can become quitecomplex, and in the case of the beta distributioncannot be solved explicitly. The particular strengthof Monte Carlo analysis is the ability to work withany mixture of distribution types, and any number ofvariables, which may or may not be independent ofeach other.The Monte Carlo technique is an iterative procedurecomprising the following four steps (Fig. 1.12).


Figure 1.12 Flow chart for Monte Carlo simulation to calculate coefficient of reliability of a structure (Athanasiou-Grivas,1980).

1. Estimate probability distributions for each ofthe variable input parameters.

2. Generate random values for each parameter;Fig. 1.10(b) illustrates the relationship for anormal distribution between a random numberbetween 0 and 1 and the corresponding value of

the parameter.3. Calculate values for the displacing and resisting

forces and determine if the resisting force isgreater than the displacing force.

4. Repeat the process at least 100 times and thendetermine the ratio:


(1.11)where M is the number of times the resisting forceexceeded the displacing force (i.e. the factor ofsafety is greater than 1.0) and N is the number ofanalyses.An example of the use of Monte Carlo analysis tocalculate the coefficient of reliability of a bridgefoundation against sliding is given in Section 6.2 inChapter 6—Stability of Foundations (Figs 6.4 and6.5). This example shows the relationship betweenthe deterministic and probabilistic analyses. Thefactor of safety is calculated from the mean or mostlikely values of the input variables, while theprobabilistic analysis calculates the distribution ofthe factor of safety when selected input variablesare expressed as probability density functions. Forthe unsupported foundation, the deterministic factorof safety has a value of 1.28, while the probabilisticanalysis shows that the factor of safety can rangefrom a minimum value of 0.38 to a maximum valueof 3.99. The proportion of this distribution with avalue greater than 1.0 is 0.78, which represents thecoefficient of reliability of the foundation. Thisexample illustrates that, for these particularconditions, the coefficient of reliability is wellbelow the target level for foundations shown inFig. 1.9. This low value for the coefficient ofreliability is a function of both the low factor ofsafety, and the wide ranges of uncertainty in theinput parameters.

1.7References

Athanasiou-Grivas, D. (1979) Probabilistic evaluation ofsafety of soil structures. ASCE, J. Geotech. Eng., 105(GT9), 1091–5.

Athanasiou-Grivas, D. (1980) A reliability approach tothe design of geotechnical systems. RensselaerPolytechnic Institute Research Paper, TransportationResearch Board Conference, Washington, DC.

Bozozuk, M. (1978) Bridge abutments move. ResearchRecord 678, Transportation Research Board,Washington, DC.

Burland, J.B. and Wroth, C.P. (1974) Allowable anddifferentiated settlement of structures, including

damage and soil-structure interaction. Proc. Conf. onSettlement of Structures, Cambridge, England,pp. 611–54.

Canada Department of Energy, Mines and Resources(1978) Pit Slope Manual., DEMR, Ottawa.

Canadian Geotechnical Society (1992) CanadianFoundation Engineering Manual. BiTech PublishersLtd, Vancouver, Canada.

Cedergren, H.R. (1989) Seepage, Drainage and FlowNets, 3rd edn, Wiley, New York.

Cruden, D.M. and Fell, R. (eds) (1997) Landslide riskassessment. Proc. International Workshop onLandslide Risk Assessment, Honolulu, HI, Balkema,Rotterdam.

Gazetas, G. and Dakoulas, P. (1991) Aspects of seismicanalysis and design of rockfill dams. Proc. 2nd Int.Conf. on Recent Advances in Geotechnical EarthquakeEngineering and Soil Dynamics, St. Louis, MO, PaperNo. SOA12, pp. 1851–88.

Grover, R.A. (1978) Movements of bridge abutments andsettlements of approach pavements in Ohio.Transportation Research Board, Research Record 678,Washington, DC.

Gruner, E. (1964) Dam disasters. Proc. Inst. of CivilEng., 24, Jan., 47–60. Discussion, 27, Jan., 344.

Gruner, E. (1967) The mechanism of dam failure. 9thICOLD Congress, Istanbul, 11, Q.34, R.12, 197–206.

Harr, M.E. (1977) Mechanics of Particulate Media—aProbabilistic Approach. McGraw-Hill, New York.

Hoek, E. and Bray, J. (1981) Rock Slope Engineering,2nd. edn, IMM, London.

James, A.N., Kirkpatrick, I.M. (1980) Design offoundations of dams containing soluble rocks and soils.Q. J. Eng. Geol., London, 13, 189–98.

Kaderabek, T.J. and Reynolds, R.T. (1981) Miamilimestone foundation design and construction. ASCEGeotech. Eng. Div., 7 (GT7), 859–72.

Kreyszig, E. (1976) Advanced Engineering Mathematics.Wiley, New York, 770–6.

Lai, S.S. and Seed, H.B. (1985) Dynamic response ofLong Valley Dam in the Mammoth Lake earthquakeseries on May 25–27, 1980. University of California,Berkeley, Report No. UCB/EERC-85/12, November.

Londe, P. (1987) Malpasset Dam. Proc. InternationalWorkshop on Dam Failures, Purdue Uni., EngineeringGeology (ed. Leonards), 24, Nos. 1–4, Elsevier,Amsterdam.

McGuffey, V., Athanasion-Grivas, D., Iori, J. and Kyfor,Z. (1980) Probabilistic Embankment Design—A Case


Study. Transportation Research Board, Washington,DC.

Merritt, F.S. (1976) Standard Handbook for CivilEngineers, McGraw-Hill, New York, Ch. 15.

Meyerhof, G.G. (1984) Safety factors and limit statesanalysis in geotechnical engineering. Can. Geotech. J.,21, 1–7.

Mitchell, J.K., Vivatrat, V. and Lambe, T.W. (1977)Foundation performance of the Tower of Pisa. Proc.ASCE, 103(GT3), 227–49.

National Building Code of Canada, (1990) AssociateCommittee on the National Building Code, NationalResearch Council of Canada, Ottawa.

Ontario Ministry of Transportation and Communication(1983) Highway Bridge Design Code. Toronto, Canada.

Peck, R.B. (1976) Rock foundations for structures. Proc.of Specialty Conference on Rock Engineering forFoundations and Slopes, ASCE, Boulder, Colorado, II,1–21.

Pentz, D.L. (1981) Slope stability analysis techniquesincorporating uncertainty in the critical parameters.Third Int. Conf. on Stability in Open Pit Mining,Vancouver, Canada.

Polshin, D.E., Tokar, R.A. (1957) Maximum allowablenonuniform settlement of structures. Proc. 4th Int.Conf. on Soil Mechanics and Foundation Engineering,London 1, 402–6.

Roberds, W.J. (1984) Risk-based decision making ingeotechnical engineering: overview of case studies.Engineering Foundation Conf. on Risk-based DecisionMaking in Water Resources. Santa Barbara, California.

Roberds, W.J. (1986) Applications of decision theory tohazardous waste disposal. ASCE Specialty Conf.GEOTECH IV, Boston, Massachusetts.

Roberds, W.J. (1990) Methods of developing defensiblesubjective probability assessments. TransportationResearch Board, Annual Meeting, Washington, DC.

Rohrbaugh, J. (1979) Improving the quality of groupjudgment: social judgment analysis and the Delphi

technique. Organizational Behaviour and HumanPerformance, 24, 73–92.

Salmon, G.M. and Hartford, N.D. (1995) Risk analysisfor dam safety. International Water Power and DamConstruction, 21, 38–9.

Savely, J.P. (1987) Probabilistic analysis of intenselyfractured rock masses. Sixth International Congress onRock Mechanics, Montreal, 509–14.

Skempton, A.W. and MacDonald, D.H. (1956) Allowablesettlement of buildings. Proc. Inst. Civil Eng., Part III,5, 727–68

Tatsuoka, F., Kohata, Y., Ochi, K. and Tsubouchi, T.(1995) Stiffness of soft rocks in Tokyo metropolitanarea—from laboratory to full-scale behaviour. Proc.8th Int. Congress on Rock Mechanics, Workshop onRock Foundation, Tokyo, Balkema, September, 3–17.

Terzaghi, K. and Peck R. (1967) Soil Mechanics inEngineering Practice. Wiley, New York.

Wahls, H.E. (1981). Tolerable settlement of buildings.ASCE, 107(GT11), 1489–504.

Walkinshaw, J.L. (1978) Survey of bridge movements inthe western United States. Research Record 678,Transportation Research Board, Washington, DC.

Whitman, R.V. (1984) Evaluating calculated risk ingeotechnical engineering. J. Geotechnical Eng., ASCE,110(2), 145–88.

Wyllie, D.C. (1979) Fractured bridge supports stabilizedunder traffic. Railway Track and Structures, July,29–32.

Wyllie, D.C., McCammon, N.R. and Brumund, W.F.(1979) Use of risk analysis in planning slopestabilization programmes on transportation routes.Research Record 749, Transportation Research Board,Washington, DC.

Wyllie, D.C. (1995) Stability of foundations on jointedrock—case studies. Proc. 8th Int. Congress on RockMechanics, Workshop on Rock Foundation, Tokyo,A.A.Balkema, Postbus 1675, NL–3000BR, September,253–8.


2Structural geology

2.1Discontinuity characteristics

The design of any structure located either in or onrock, must include a thorough examination of thestructural geology of the site. Even the strongestrock may contain potentially unstable blocks formedby sets of discontinuities, or possibly even a singlediscontinuity. These blocks may fail by sliding ortoppling. Where such blocks occur in a cut abovethe foundation, they may impact the structure,whereas unstable blocks in the foundation may movecausing settlement, or fail entirely, resulting incollapse of the structure.The photograph in Fig. 2.1 shows a wedge shapedblock of rock, formed by two intersectingdiscontinuities, that has failed forming a steep cliffface. Houses have been constructed along the crestof this cliff and any further excavation at the toe islikely to cause similar wedge failures which woulddestroy a number of the buildings. The stability ofthe foundation of these houses is entirely dependentupon the properties of the discontinuities, that is,their orientation, length and shear strength. Thestrength of the intact rock, which has amplecapacity to support the light loads imposed by thehouses, is not an issue. This is a typical example ofa situation where foundation design must focus onthe structural geology of the site, and not on therock strength.Analysis of the stability of blocks of rock infoundations requires reliable information on thefollowing two categories of discontinuitycharacteristics:

1. the orientation and dimensions of thediscontinuities, which define the shape and sizeof the blocks, and the direction in which theymay slide (this chapter describes methods ofanalyzing data on the orientation anddimensions of discontinuities);

2. the shear strength properties of thediscontinuities which determines the resistanceof the block to sliding (this is discussed inChapter 3).

2.1.1Types of discontinuity

Geological investigations usually categorizediscontinuities according to the manner in whichthey were formed. This is useful for geotechnicalengineering because discontinuities within eachcategory have similar properties as regards bothdimensions and shear strength properties which canbe used in the initial review of stability conditions ofa site. The following are standard definitions of themost commonly encountered types ofdiscontinuities.(a) FaultA discontinuity along which there has been anobservable amount of displacement. Faults arerarely single planar units; normally they occur asparallel or sub-parallel sets of discontinuities alongwhich movement has taken place to a greater or lessextent.(b) Bedding planeThis is a surface parallel to the surface of deposition,which may or may not have a physical expression.

Note that the original attitude of the bedding planeshould not be assumed to be horizontal. (c) FoliationFoliation is the parallel orientation of platy minerals,or mineral banding in metamorphic rocks.(d) JointA joint is a discontinuity in which there has been noobservable relative movement. In general, jointsintersect primary surfaces such as bedding, cleavageand schistosity. A series of parallel joints is called ajoint set; two or more intersecting sets produce ajoint system; two sets of joints approximately atright angles to one another are said to beorthogonal.(e) CleavageParallel discontinuities formed in incompetentlayers in a series of beds of varying degrees ofcompetency are known as cleavages. In general, theterm implies that the cleavage planes are not

controlled by mineral particles in parallelorientation.(f) SchistosityThis is the foliation in schist or other coarse grainedcrystalline rock due to the parallel arrangement ofmineral grains of the platy or prismatic type, such asmica.These descriptions of discontinuity categories arewell established in engineering practice and thelikely properties of each can be anticipated from theircategories. For example, faults are major structurescontaining weak infillings such as crushed rock andclay gouge, whereas joints have lengths which aremuch shorter than faults and joint infillings areoften thin and cohesive, or entirely absent.However, standard geological names alone rarelygive sufficient detailed information for designpurposes on the properties of a dis continuity,especially for foundations where particulars of such

Figure 2.1 Intersecting discontinuities in strong rock produced wedge failure in foundation of houses along crest ofslope (photograph by Turgut Çanli).

28 STRUCTURAL GEOLOGY

characteristics as the infilling thickness can have asignificant influence on settlement. For this reason,geological descriptions are useful in understandingthe general conditions at a site, but further specificgeotechnical studies are almost always requiredbefore proceeding to final design.

2.1.2Discontinuity orientation and dimensions

The four important properties of discontinuities thatdetermine the shape and size of blocks are:

1. Orientation;2. Position;3. Length;4. Spacing.

The two sketches in Fig. 2.2 illustrate how thesefour properties influence the stability of afoundation. In both cases there are two sets ofdiscontinuities: set A dips out of the face at an angleof about 40°, and set B dips into the face at a steep

angle. In Fig. 2.2(a) set A is discontinuous and morewidely spaced than set B. This foundation would bestable because the discontinuities daylighting in theface are not continuous and only one small, unstableblock has been formed on the face. In contrast, inFig. 2.2(b), the discontinuities dipping out of theface are continuous and movement of the entirefoundation on these discontinuities is possible, withset B forming tension cracks. A typical example ofsuch a condition would be a bedded sandstonecontaining a discontinuous conjugate joint set. If thebeds dip into the face the foundation would bestable, and if they dip out of the face at an angle of40°, which is usually greater than the friction angleof sandstone surfaces, it is likely that the foundationwould slide on the beds.The conditions shown in Fig. 2.2 also illustrate theinfluence of discontinuity spacing on settlement. Inthis example, the spacing of the discon tinuities issuch that the footing is predominantly on intactrock. Consequently, closure of the discontinuities isunlikely to be of concern and settlement will be afunction of the deformation modulus of the intactrock. However, in the case of highly fractured rock,

Figure 2.2 Influence of discontinuity length and orientation on the stability of a foundation: (a) continuous joints dipinto slope—stable foundation; and (b) continuous joints dip out of slope—unstable foundation.

DISCONTINUITY CHARACTERISTICS 29

settlement may occur as a result of discontinuityclosure, particularly if the joint infilling comprisescompressible materials such as clay. In this casesettlement would be a function of the rock massdeformation modulus. As regards the overallstability of the foundation, closely fractured rockmay be sufficiently interlocked to preventmovement of the entire foundation in a block typefailure as shown in Fig. 2.2(b). However, ravelingof small fragments may occur as a result of frostaction or river scour, and this may eventuallyundermine the footing (Fig. 2.2(a)).

2.2Orientation of discontinuities

The first step in the investigation of discontinuitiesin a foundation is to analyze their orientation andidentify sets of discontinuities, or singlediscontinuities, that could form potentially unstableblocks of rock. Information on discontinuityorientation may be obtained from such sources assurface and underground mapping, diamond drillcore and geophysics, and it is necessary to combinethis data into a system that is readily amenable toanalysis. This analysis is facilitated by the use of asimple and unambiguous method of expressing theorientation of a fracture. The recommendedterminology for orientation is the dip and dipdirection which are defined as follows and shownschematically in Fig. 2.3.

1. Dip is the maximum inclination of adiscontinuity to the horizontal (angle ?).

2. Dip direction or dip azimuth is the direction ofthe horizontal trace of the line of dip, measuredclockwise from north (angle a).

As will be demonstrated in Section 2.3, the dip/dipdirection system facilitates field mapping and theplotting of stereonets, and the analysis ofdiscontinuity orientation data.Strike, which is an alternative means of definingthe orientation of a plane, is the trace of theintersection of an inclined plane with a horizontal

reference plane.The strike is at right angles to the dip direction of theinclined plane. The relationship between the strikeand the dip direction is illustrated in Fig. 2.3(b)where the plane has a strike of N60E and a dip of30SE. In terms of dip and dip direction, theorientation of the plane is 30/150 which isconsidered to be a simpler nomenclature. By alwayswriting the dip as two digits and the dip direction asthree digits, e.g. 090 for 90°, there can be noconfusion as to which set of figures refers to whichmeasurement. Strike and dip measurements can bereadily converted into dip and dip directionmeasurements if this mapping system is preferred.In defining the orientation of a line, the termsplunge and trend are used. The plunge is the dip ofthe line, with a positive plunge being below thehorizontal and a negative plunge being above thehorizontal. The trend is the direction of thehorizontal projection of the line measured clockwisefrom north, and it corresponds to the dip directionof a plane.Discontinuity mapping is carried out with ageological compass, of which there are severaldifferent types. The Brunton compass is widelyavailable, but has a disadvantage in thatmeasurement of the dip and dip direction requireseparate operations. Also, it is designed to measurestrike rather than dip direction; this requires that aconversion be made which can be a possible sourceof error. There are a number of compassesspecifically designed for structural mapping whichallow dip and dip direction to be measuredsimultaneously; these compasses are manufacturedby the Breihthaupt Company and the FreibergCompany, both in Germany, and the Showa SokkiCompany in Japan. A particular feature of thesestructural compasses is their ability to map adiscontinuity accurately when only a small portionof a plane is exposed. In these circumstances it canbe difficult to determine the true dip, as opposed tothe apparent dip which is always a flatter angle. Thetrue dip can be visualized by rolling a ball down theplane: the ball will roll down the line of maximuminclination which corresponds to the true dip of the


plane. Figure 2.4 shows the operation of a structuralcompass; the lid is placed on the discontinuitysurface and the body of the compass is leveled usingthe spirit level before reading the dip direction onthe 360° compass scale, and the dip on a scale onthe hinge. The orientation of overhanging surfacescan also be measured by placing the partially closed

compass lid on the discontinuity surface and makingthe readings in the usual way.

2.3Stereographic projection

The analysis of structural geology orientation

Figure 2.3 Terminology defining discontinuity orientation (dip and dip direction): (a) isometric view; and (b) plan view.


measurements requires a convenient method ofhandling three-dimensional data. Fortunately thestereographic projection, which is used extensivelyin the fields of cartography, navigation andcrystallography, is ideally suited to geologicalapplications. The stereographic projection is aprocedure for mapping data located on the surface ofa sphere on to a horizontal plane, and can be usedfor the analysis of the orientation of planes, linesand forces (Donn and Shimmer, 1958; Phillips,1972; Goodman, 1976; Hoek and Bray; 1981).There are several different types of stereographicprojections, but the one most suitable for geologicalapplications is the equal area net, or Lambertprojection, which is also used by geographers torepresent the spherical shape of the Earth on a flatsurface. In structural geology, a point or line onthe sphere representing the dip and dip direction ofa discontinuity can be projected on to a horizontalsurface. In this way an analysis of three-dimensional data can be carried out in twodimensions. An important property of the equal areaprojection is that any solid angle on the surface ofthe reference sphere is projected as an equal area onto a horizontal surface. One of the applications of thisproperty is in the contouring of pole populations tofind the orientation of sets of discontinuities asdescribed in Section 2.3.2.

The principle of the projection method is illustratedin Fig. 2.5. The basic element of the pro-jection is areference sphere which is oriented in space, usuallywith respect to true north. When a plane(discontinuity) is centered in the reference sphere,the intersection between the plane and the surfaceof the sphere is a circle which is commonly knownas a great circle (Fig. 2.5(a)). The orientation of thegreat circle is a unique representation of theorientation of the plane. The upper and lower halvesof the sphere give identical information and inengineering applications the usual procedure is touse the lower half of the sphere only. The projectionis known, therefore, as a lower hemisphereprojection. Note that this projection techniqueonly examines the orientation of planes and there isno information on their position in space. That is, itis assumed that all the planes pass through the centerof the reference sphere. If the stereographicprojection identified a plane on which thefoundation could slide, its location on thegeological map would have to be examined todetermine if it intersected the foundation.An alternative means of representing the orientationof a plane is the pole of the plane. The pole is thepoint at which the surface of the sphere is piercedby a radial line in a direction normal to the plane.The merit of the pole projection is that the complete

Figure 2.4 Photograph of structural compass measuring dip and dip direction of discontinuity surface.


orientation of the plane is represented by a singlepoint which facilitates analysis of a large number ofplanes compared with the use of great circles.The most convenient means of examining theorientation data provided by the great circles andthe poles is to project the lines and points on to ahorizontal reference plane which is a two-dimensional representation of the surface of thesphere. The equal-area projection for any point onthe surface of the reference sphere is accomplishedby drawing an arc about the lower end of the verticalaxis of the sphere from the point to the horizontalbase plane (Fig. 3.5(b)). Figure 3.5(c) shows a plan

view of the horizontal reference plane, and thepositions of the pole and great circle of a plane witha dip of 30° and a dip direction of 150°. The greatcircle and the pole for the same plane lie onopposite sides of the stereonet, so the dip directionis measured from the top of the circle for the greatcircle, and from the bottom of the circle for thepole. Also, a plane with a shallow dip has a pole closeto the center of the reference circle, while the greatcircle for the same plane is located close to theperimeter of the circle.Stereographic projections of both planes and greatcircles can be prepared by hand by plotting the data

Figure 2.5 Stereographic representation of the orientation of a plane: (a) plane surface location in lower hemisphere ofthe reference spehere showing great circle and pole to plane; (b) vertical section through reference sphere showing lowerhemisphere, equal-area projections of great circle and pole; and (c) plan view of reference plane showing projections ofgreat circle and pole.


on standard sheets with lines representing dip anddip direction values (Appendix I). Alternatively,there are computer programs available that will notonly plot poles and great circles, but will also plotselected data. This selection feature will prepareplots, for example, of only faults, or of only jointswith lengths greater than a specified length.Selective plots have particular value where there isa great quantity of geological data and it is importantto identify features that have a particularsignificance to stability.The analysis of structural geological data bystereographic methods is usually a three stageprocess as follows.

1. Plot poles to show the orientation of all thediscontinuities.

2. Contour the data to find the prominentdiscontinuity sets.

3. Use great circles of the discontinuity sets orprominent discontinuities to show the shape ofblocks that they form, and the direction inwhich they may slide or topple.

Two different types of stereonet, the polar net andthe equatorial net, are used when plotting this databy hand. The polar plot is used to plot poles, whilethe equatorial net can be used to plot either poles orgreat circles (see Appendix I).These three stages of the analysis of structuralgeology data are described in this section.

2.3.1Pole plots

Pole plots, in which each plane is represented by asingle point, are the most convenient means ofexamining the orientation of a large number ofdiscontinuities. The plot provides an immediatevisual depiction of concentrations of polesrepresenting the orientations of sets ofdiscontinuities, and the analysis is facilitated by theuse of different symbols for different types ofdiscontinuities. A typical pole plot generated by astereo-graphic computer program is shown in

Fig. 2.6. This is a lower hemisphere, equal angleprojection of 1391 original poles at a site where therock type is a highly metamorphosed phyllite. Therock contains discontinuity sets comprising thefoliation and two sets of joints; where more thanone pole has the same orientation, a number orletter is plotted indicating the number of poles atthat point on the net, as shown by the legend. If thegeological mapping data has identified the type ofeach dis continuity, the data can also be plotted withthe symbol F representing the foliation and Jrepresenting the joints, for example.The dip direction scale (0°–360°) shown around theperiphery of the pole plot has zero degrees at thebottom of the plot because the poles lie at theopposite side of the circle to the great circles (seeFig. 2.5(c)). Therefore the foliation planes lying inthe NE quadrant and close to the periphery of thecircle, have a dip direction of between about 220°and 280°, and a steep dip between about 60° and80°.Pole plots can also be prepared by hand on a polarnet in which the dip and dip directions are directlylocated by the radial and circular lines respectively(Appendix I).

2.3.2Pole density

All natural discontinuities have a certain amount ofvariation in their orientations which results inscatter of the pole plots. If the plot contains polesfrom a number of discontinuity sets, it can bedifficult to distinguish between the poles from thedifferent sets, and to find the most likely orientationof each set. However, by contouring the plot, themost highly concentrated areas of poles can be morereadily identified. The usual method of generatingcontours is to use the contouring package containedwith most stereographic projection computerprograms. However, contouring can also be readilybe carried out by hand using the techniquesdescribed by Hoek and Bray (1981).Figure 2.7 shows a contour plot of a the polesplotted in Fig. 2.6. The pole plot in Fig. 2.6 shows


that the orientation of the foliation planes hasrelatively little scatter; the contour plot of thesepoles has a maximum concentration of 16% at a dipof 65° and a dip direction of 245°. In contrast, thejoint orientations show much more scatter, and onthe pole plot it is difficult to identify discontinuitysets. However, on the contoured plot, it is possibleto distinguish clearly two sets of orthogonal joints.Set A has a shallow dip of about 28°, and a dipdirection of about 080° which is in a direction at180° to the foliation. Set B has a near vertical dipand a dip direction approximately at right angles toset A. The poles for set B lie on opposite sides ofthe contour plot because some dip steeply to the NWand some steeply to the SE.In Fig. 2.7 the different pole concentrations areshown by symbols for each 4% contour interval.The percentage concentration refers to the number

of poles in each 1% area of the surface of the lowerhemisphere. Thus if the computer counts 28 polesout of a total of 1391 poles in a 1% area of thelower hemisphere, then the concentration level inthat area is 2%. By successively counting each area,a contour plot showing the pole concentrations ofall the data can be developed.A further use of the stereographic projectionprogram in analyzing structural data is to prepareplots of data selected from the total data collected.For example, joints with lengths which are only asmall fraction of the foundation dimensions areunlikely to have a significant influence on stabilityor settlement. Therefore it would facilitate design toprepare a stereographic plot showing only thosediscontinuities which have lengths greater than aspecified length. Figure 2.8 is a pole plot of thesame data shown in Fig. 2.6 in which only

Figure 2.6 Pole plot of foliation and joints; lower hemisphere, equal-area projection (plot by Mark Goldbach).


discontinuities with lengths greater than 4m (13 ft)have been plotted. This plot shows that only 163discontinuities, or 12% of the total number havelengths greater than 4 m, and that virtually all ofthese discontinuities are either the foliation or jointset A. Similar selections can be made, for example,of discontinuities that have a certain type ofinfilling, or are slickensided, or show evidence ofseepage, provided that the mapping identifies thislevel of detail of each surface. Appendix II containsfield mapping sheets for recording details ofdiscontinuity properties by the use of codes that areinput directly into the stereographic analysisprogram.The assignment of poles into discontinuity sets isusually achieved by a combination of contouring,visual examination of the stereonet, and a knowledge

of geological conditions at the site which willfrequently show the trends in orientation of the sets.It is also possible to identify discontinuity sets byrigorous and less subjective analysis of clusters inorientation data. A technique presented by Mahtaband Yegulalp (1982) identifies clusters from randomdistributions of orientations using the Poissondistribution.

2.3.3Great circles

Once the orientation of the discontinuity sets, aswell as important discontinuities such as faults,have been identified on the pole plots, the next stepin the analysis is to determine if thesediscontinuities form potentially unstable blocks in

Figure 2.7 Contour plot of the poles shown in Fig. 2.6.


the foundation. This analysis is carried out byplotting great circles of each of the discontinuity setorientations, as well as the orientation of the face ofthe cut on which the foundation is located. In thisway the orientation of all the surfaces that have aninfluence on stability are represented on a singlediagram. Figure 2.9 shows the great circles of thejoint sets identified on the contoured pole plot inFig. 2.7. It is usually only possible to have amaximum of about six great circles on a plot,because with a greater number, it is difficult toidentify all the intersection points of the circles. Theprocedure for plotting great circles using anequatorial net is shown in Appendix I.The primary purpose of plotting great circles ofdiscontinuity sets in a foundation is to determine the

shape of blocks formed by intersectingdiscontinuities, and the direction in which they mayslide. For example, in Fig. 2.1 the foundation failureonly occurred at the location where thediscontinuities intersected to form a wedge with aparticular shape and orientation with respect to theface. It is, of course, important to identifysuchpotential failures before movement and collapseactually occurs. This requires an ability to visualizethe three-dimensional shape of the wedge from thetraces of the discontinuities on the face of theoriginal slope. The stereographic projection is aconvenient means of carrying out the required three-dimensional analysis, keeping in mind that thisprocedure examines only the orientation of thediscontinuities and not their position. If the stereonet

Figure 2.8 Selective pole plot of data in Fig. 2.6 for all discontinuities with lengths greater than 4 m (plot by M.Wise).


shows the possible occurrence of a potentiallyunstable block, examination of the location of thediscontinuities on the geological map woulddetermine if they intersect the foundation.Two intersecting planes may form a wedge shapedblock as shown in Fig. 2.1. The direction in whichthis block may slide is determined by the trend ofthe line of intersection, with failure being possibleonly if the trend is out of the slope face. The plungeof the line of intersection gives an indication of thestability condition of the block: the block is unlikelyto slide if the plunge is at a shallow angle. Theorientation of the line of intersection between twoplanes is represented by the point where the twogreat circles intersect. For the data shown on thepole plot (Fig. 2.6), intersections occur betweenjoint sets A and B (I1), between set B and thefoliation (I2), and set A and the foliation (I3). Theorientation of intersection line I3 is shown inFig. 2.9, and the method of determining the trendand plunge of lines is described in Appendix I. Forthe conditions shown in Fig. 2.9, the wedge formedby intersection I3 will slide towards a direction of

158° and at a shallow dip angle of 8°.

2.3.4Stochastic modeling of discontinuities

The main limitation of the use of stereonets infoundation design is that they provide only theorientation, but no spatial information on thediscontinuities. In fact, discontinuities aredistributed in space and have variable attitudes,sizes and shapes which lend themselves to theirrepresentation as stochastic models (Dershowitz andEinstein, 1988; Kulatilake, 1988; Einstein, 1993).The development of a three-dimensional model ofthe rock mass incorporating the discontinuity setsand the intersections between discontinuitiesprovides a useful tool for the study of a number ofrock mechanics applications, including fluid flowthrough fractured rock masses which may proveuseful in consolidation grouting of foundations.With respect to the stability of rock f oundations,the model of the rock mass will indicate the shapeand size of potentially unstable blocks of rock, and

Figure 2.9 Plot of great circles representing the three discontinuity sets identified on the contour plot of Fig. 2.7.


the extent of intact rock that lies on the boundariesof the block. The existence of such intact ‘rockbridges’ has a significant influence on stabilitybecause the strength of the intact rock is very muchgreater than that of the discontinuity surfaces, andthe three-dimensional model of rock mass helps todefine the location and size of the bridges (Einstein,1993). In turn this information can be used to designrock bolting patterns to reinforce the rock. Thestochastic model will show the probability of failurerather than the factor of safety (see Section 1.6).

2.4Types of foundation failure

A great circle stereographic plot of discontinuitysets can be used to identify the shape of blocks in thefoundation, and make an assessment of theirstability conditions (Fig. 2.10). Four distinct types ofslope failure can be distinguished, thecharacteristics of which depend on the relativeorientation between the slope face and thediscontinuity (Hoek and Bray, 1981). For each ofthe failure types there is a distinct method ofstability analysis which takes into account the shapeand size of the block, the shear strength of thesliding surfaces, water pressures and the foundationloads. These analysis methods are described inChapter 6.The first three block types—plane, wedge andtoppling blocks—have distinct shapes as defined bythe geological structure. The differences betweenthese three shapes are that in the case of the planarand wedge blocks (Figs. 2.10(a) and (b)), thestructure dips out of the face, and on the stereonetthe poles are on the opposite side of the net from thegreat circle of the face. In the case of toppling blocks(Fig. 2.10(c)), the structure dips into the face and onthe stereonet the poles are on the same side of thenet as the great circle of the face.The fourth type of failure, circular failure, occurs insoil, rock fill or closely fractured rock containing nopersistent discontinuities dipping out of the slope(Fig. 2.10(d)). For cuts in fractured rock, the slidingsurface forms partially along discontinuities that are

oriented approximately parallel to this surface, andpartially through intact rock. Because of the relativehigh shear strength of rock compared with that ofdiscontinuities, this type of failure will only occur inclosely fractured rock where the major portion ofthe sliding surface comprises discontinuity surfaces.It is found that where a failure occurs under theseconditions, the sliding surface can be approximatedby a large-radius circular arc forming a shallowfailure surface. Stability analysis of this failuremode in rock can be carried out in an identicalmanner to that of a soil, with the use of appropriatestrength parameters.

2.5Kinematic analysis

Once the type of block failure has been identified onthe stereonet, the same diagram can also be used toexamine the direction in which a block will slideand give an indication of possible stabilityconditions. This procedure is known as kinematicanalysis. An application of kinematic analysis is therock face shown in Fig. 2.1 where two joint planesform a wedge which has slid out of the face andtowards the photographer. If the slope face had beenless steep than the line of intersection between thetwo planes, or had a strike at 90° to the actualstrike, then the wedge formed by the two planeswould not have been able to slide. This relationshipbetween the direction in which the block of rockwill slide and the orientation of the face is readilyapparent on the stereonet. However, while analysisof the stereonet gives a good indication of stabilityconditions, it does not account for external forcessuch as foundation loads, water pressures orreinforcement comprising tensioned rock bolts,which can have a significant effect on stability. Theusual design procedure is to use kinematic analysison the stereonet to identify potentially unstableblocks, followed by detailed stability analysis ofthese blocks using the procedures described inChapter 6.An example of kinematic analysis is shown inFig. 2.11 where a footing is located at the crest of a


Figure 2.10 Main types of block failures in foundations, and structural geology conditions likely to cause these failures(after Hoek and Bray, 1981): (a) plane failure in rock containing continuous joints dipping out of slope face, andstriking parallel to face; (b) wedge failure on two intersecting discontinuities; (c) toppling failure in strong rockcontaining discontinuities dipping steeply into face; and (d) circular failure in rock fill, soil, and closely fractured rockwith randomly oriented discontinuities.


discontinuities. The potential for thesediscontinuities to form unstable blocks in thefoundation depends on their dip and dip directionrelative to the face; stability conditions can bestudied on the stereonet as described below.

2.5.1Planar failure

A potentially unstable planar block is formed byplane AA, which dips at a flatter angle than the face

and is said to ‘daylight’ on the face(Fig. 2.11(a)). However, sliding is not possible onplane BB which dips steeper than the face and does not daylight. Similarly, discontinuity setCC dips into the face and sliding cannot occur onthese planes, although toppling is possible. Thepoles of the slope face and the discontinuity sets(symbol p) are plotted on the stereonet in Fig. 2.11(b), assuming that all the discontinuities strikeparallel to the face. The position of these poles inrelation to the slope face shows that the poles of allplanes that daylight, and are potentially unstable, lieinside the pole of the slope face (pf). This area istermed the daylight envelope and can be used toidentify potentially unstable blocks quickly.The dip direction of the discontinuity sets will alsoinfluence stability. Sliding is not possible if the dipdirection of the discontinuity differs from the dipdirection of the face by more than about 20°. Thatis, the block will be stable if ,because under these conditions there will be anincreasing thickness of intact rock at one end of theblock which will have sufficient strength to resistfailure. On the stereonet this restriction on the dipdirection of the planes is shown by two linesdefining dip directions of and . These two lines designate the lateral limits of thedaylight envelope on Fig. 2.11(b).

2.5.2Wedge failure

Kinematic analysis of wedge failures (Fig. 2.10(b))can be carried out in a similar manner to that of

plane failures. In this case the pole of the line ofintersection of the two discontinuities is plotted onthe stereonet and sliding is possible if the poledaylights on the face, i.e. The direction ofsliding of kinematically permissible wedges is lessrestrictive than that of plane failures because thereare two planes to form release surfaces. Adaylighting envelope for the line of intersection, asshown on Fig. 2.11(b), is wider than the envelopefor plane failures. The wedge daylight envelope isthe locus of all poles representing lines ofintersection whose dip directions lie in the plane ofthe slope face.

2.5.3Toppling failure

For a toppling failure to occur the dip direction ofthe discontinuities dipping into the face must bewithin about 20° of the dip direction of the face sothat a series of slabs are formed parallel to the face.Also, the dip of the planes must be steep enough forinterlayer slip to occur. If the faces of the layershave a friction angle , then slip will only occur ifthe direction of the applied com pressive stress is atangle greater than with the normal to the layers.The direction of the major principal stress in the cutis parallel to the face of the cut (dip angle ?f), sointerlayer slip and toppling failure will occur onplanes with dip ?p when the following conditionsare met (Goodman and Bray, 1976):

(2.1)These conditions on the dip and dip direction ofplanes that can develop toppling failures are definedon Fig. 2.11(b). The envelope defining theorientation of these planes lies at the opposite side ofthe stereonet from the sliding envelopes.

2.5.4Friction cone

Once one has determined from the daylightenvelopes whether a block in the foundation iskinematically permissible, it is possible to examinestability conditions on the same stereonet. This


steep slope which contains three sets of

analysis is carried out assuming that the shearstrength of the sliding surface comprises only thefriction component and the cohesion is zero.Consider a block at rest on an inclined plane with afriction angle of between the block and the plane(Fig. 2.12(a)). For an at-rest condition, the forcevector normal to the plane must lie within the

friction cone. When the only force acting on theblock is gravity, the pole to the plane is in the samedirection as the normal force, so the block will bestable when the pole lies within the friction circle.The envelopes on Fig. 2.12(b) show the possiblepositions of poles that may form unstable blocks.Envelopes have been drawn for slope face angles of

Figure 2.11 Kinematic analysis of blocks in foundations: (a) discontinuity sets in foundation; and (b) daylightenvelopes plotted on equal-area projection stereonet.


60° and 80° which show that the risk of instabilityincreases as the slope becomes steeper as indicatedby the larger envelopes for the steeper slope. Also,the envelopes become larger as the friction anglediminishes. The envelopes also indicate that, for thesimple gravity loading condition, instability willonly occur in a limited range of geometricconditions.

2.6Probabilistic analysis of structural geology

In carrying out probabilistic design of foundations itis necessary to express the orientation and length ofdiscontinuities in terms of probability distributionsrather than single values. This information will givethe most likely value of each parameter as well asthe probability of its occurrence within a range ofpossible values. The probability distribution ofdiscontinuity orientation can be calculated from thestereonet, while the distributions of length andspacing are calculated from field measurements asdescribed in the following sections. The calculatedvalues of the mean and standard deviation of thedesign parameters can be input into the Monte Carloanalysis to determine the coefficient of reliability asdescribed in Section 1.6.4.

2.6.1Discontinuity orientation

The natural variation in orientation ofdiscontinuities results in there being scatter of thepoles when they are plotted on the stereonet. It isuseful to incorporate this scatter into the stabilityanalysis of the foundation because, for example, awedge analysis using the mean values of pair ofdiscontinuity sets may show that the line ofintersection of the wedge does not daylight in theface and that the foundation is stable. However, ananalysis using orientations other than the meanvalues may show that some unstable wedges can beformed. The risk of occurrence of this conditionwould be quantified by calculating the mean andstandard deviation of the dip and dip direction as

described below.A measure of the dispersion, and from this thestandard deviation, of a discontinuity set can becalculated from the direction cosines as follows(Goodman, 1980). The direction cosines of anyplane with dip ? and dip direction a are the unitvectors l, m and n, where:

(2.2)

For a number of poles, i, in one set the directioncosines (lR, mR and nR) of the mean orientation ofthe discontinuity set is the sum of the individualdirection cosines, as follows:

(2.3)

where is the magnitude of the resultant vectorgiven by

(2.4)The dip ?R and dip direction aR of the meanorientation are:

(2.5)

A measure of the scatter of a set of discontinuitiescomprising N poles can be obtained from thedispersion coefficient Cd which is calculated asfollows:

(2.6)

If there is little scatter in the orientation of thediscontinuities, the value of Cd is large, and itsvalue diminishes as the scatter increases.From the dispersion coefficient it is possible tocalculate from equation 2.7 the probability P that apole will make an angle ?° or less than the meanorientation, where

(2.7)For example, the angle from the mean defined byone standard deviation occurs at a probability P of 0.


16 (refer to Fig. 1.10). If the dispersion is 20, one standard deviation lies at 7.6° from the mean.

Figure 2.12 Combined kinematic and simple stability analysis using friction cone concept: (a) friction cone in relationto block at rest on an inclined plane; and (b) stereographic projection of friction cone superimposed on daylightingenvelopes.


Equation 2.7 is applicable when the dispersion inthe scatter is approximately uniform about the meanorientation, which is the case in joint set A inFig. 2.6. However, in the case of the foliation inFig. 2.6, there is much less scatter in the dip than inthe dip direction. The standard deviations in the twodirections can be calculated approximately asfollows from the stereonet. First, two great circlesare drawn at right angles corresponding to thedirections of dip and dip direction respectively.Then the angles corresponding to the 7% and 93%levels, P7 and P93 respectively, are determined bycounting the number of poles in the set andremoving the poles outside these percentiles. Theequation for the standard deviation along either ofthe great circles is as follows (Morriss, 1984):

(2.8)More precise methods of determining the standarddeviation are described by McMahon (1982), butthe approximate method given by equation 2.8 maybe sufficiently accurate, considering the difficulty inobtaining a representative sample of thediscontinuities in the set. An important aspect ofaccurate geological investigations is to account forbias when mapping a single face or logging a singleborehole when few of the discontinuities alignedparallel to the line of mapping are measured. Thisbias in the data can be corrected by applying theTerzaghi correction as described in Section 4.2.

2.6.2Discontinuity length and spacing

The length and spacing of discontinuitiesdetermines the size of blocks that will be formed inthe foundation. Designs are usually concerned withpersistent discontinuities that could form blockswith dimensions great enough to influence overallstability of the foundation. However, discontinuitydimensions have a range of values and it is useful tohave an understanding of the distribution of thesevalues in order to predict how the extreme valuesmay be compared with values obtained from a smallsample. This section discusses probabilitydistributions for the length and spacing of

discontinuities, and discusses the limitations ofmaking accurate predictions over a wide range ofdimensions.(a) Probability distributionsDiscontinuities are usually mapped along ascanline, such as drill core, slope face or wall of atunnel, and individual measurements are made ofthe properties of each fracture, including its visiblelength and the spacing between discontinuities ineach set (Appendix II). The properties ofdiscontinuities typically vary over a wide range andit is possible to describe the distribution of theseproperties by means of probability distributions. Anormal distribution is applicable if a particularproperty has values in which the mean value is themost commonly occurring. This condition wouldindicate that the property of each discontinuity, suchas its orientation, is related to the property of theadjacent discontinuities reflecting that thediscontinuities were formed by stress relief. Forproperties that are normally distributed, the meanand standard deviation are given by equations 1.7and 1.8.A negative exponential distribution is applicable forproperties of discontinuities, such as their lengthand spacing, that are randomlydistributed indicating that the discontinuities aremutually independent. A negative exponentialdistribution would show that the most commonlyoccurring discontinuities are short and closelyspaced, while long, widely spaced discontinuitiesare less common. The general form of a probabilitydensity function f(x) of a negative exponentialdistribution is (Priest and Hudson, 1981):

(2.9)

and the associated cumulative probability F(x) that agiven spacing or length value will be less thandimension x will is given by:

(2.10)

where x is a measured length or spacing and is themean value of that parameter. A property of thenegative exponential distribution is that the standarddeviation is equal to the mean value.


From equation 2.10 for a set of discontinuities inwhich the mean spacing is 2 m, the probabilitiesthat the spacing will be less than 1 m and 5 mrespectively are:

Equation 2.10 could be used to estimate theprobability of occurrence of discontinuities with aspecified length. This result could be used, forexample, to determine the likelihood of a planebeing continuous through a foundation.Another distribution that can be used to describe thedimensions of discontinuities is the log-normaldistribution which is applicable where the variable

is normally distributed (Baecher et al.,1977). The log-normal distribution function for thevariable y is

(2.11)

where is the mean value and SDx is the standarddeviation of the variable x.Figure 2.13 shows the measured lengths of 122

joints in a Cambrian sandstone for lengths of lessthan 4 m; the mean length is 1.2 m (Priest andHudson, 1981). To this data have been fitted bothexponential and log-normal curves for whichthe correlation coefficients r are 0.69 and 0.89respectively. While the log-normal curve has ahigher correlation coefficient, the exponential curvehas a better fit at the longer discontinuity lengths.This demonstrates that for each set of data the mostappropriate distribution should be determined.(b) Discontinuity length (persistence)Discontinuities are often mapped on a rock face orwall of a tunnel where the lengths of some of thediscontinuities are greater than the dimension of themapped face. In this case it is not possible tomeasure the actual discontinuity lengths.Techniques have been developed whereby the meanlength of the discontinuities in the outcrop can beestimated from observations of the lengths of thediscontinuities relative to the dimension of themapped face, without making any measurements ofthe actual discontinuity lengths (Kulatilake and Wu,1984; Pahl, 1981; Priest and Hudson, 1981).Figure 2.14 illustrates a rock face containing a

Figure 2.13 Histogram of joint trace lengths, and best fit exponential and log-normal curves (Priest and Hudson, 1981).


number of discontinuities of a single set, the lengthsof which fall into one of the following threecategories:

1. contained discontinuities (Nc)—the length isless than the height of the face and both ends ofthe discontinuity are visible;

2. intersecting discontinuities—one end of thediscontinuity is visible in the face;

3. transecting discontinuities (Nt)—the length ofthe discontinuity is greater than the height ofthe face and neither end is visible.

Based on this categorization of the discontinuitylength, the mean length can be estimated from thefollowing equation which is independent of theassumed form of the statistical distribution of thediscontinuity lengths (Pahl, 1981):

(2.12)

where

(2.13)

and

(2.14)

and ? is the dip of the discontinuities, L is the lengthof the mapped face, H is the height of a horizontalscan line above the base of the outcrop and N' istotal number of discontinuities within the scanline.Figure 2.14 shows discontinuities for a single setfor which the average length and spacing have becalculated. For the joints illustrated in Fig. 2.14 theaverage length calculated using equations 2.12, 2.13and 2.14 is 4.3 m (14.1 ft) and this is drawn to scaleon the Figure.In reality, the face would contain several sets ofdiscontinuities and the mapping method woulddepend on the use to which the data would beapplied. For example, if the properties of the rockmass were being studied, then it would beappropriate to map every discontinuity within thescanline area to find the average length of alldiscontinuities. However, if the mapping were being

carried to investigate a specific set of discontinuitiesthat would form potential sliding planes in afoundation, then it would be appropriate todistinguish those discontinuities belonging to theset in question.While the calculated average length is an estimatebecause it is not possible to measure the full lengthof many of the discontinuities, this value isconsistent with the observation that about half thediscontinuities have lengths less than the height ofthe scan line. Furthermore, the lengths aredistributed such that there are only fourdiscontinuities with lengths more than about twicethe height of the scan line and it is likely that therange of lengths would fit either an exponential orlog-normal distribution (Fig. 2.13).(c) Discontinuity spacingThe spacing of discontinuities can be measuredalong a scan line on a slope face or wall of a tunnel(Priest and Hudson, 1976), or in a borehole.Discontinuities in a diamond drill hole can beexamined in the core if the recovery is acceptable,and it is possible to distinguish the naturaldiscontinuities from mechanical breaks. It is alsopossible to examine the spacing and orientation ofdiscontinuities in the wall of the hole using aborehole camera (see Section 4.3). As discussed in(b) above, the design application will determine ifall discontinuities are to be considered in measuringspacing, or only those belonging to a single set. Oneapproach that may be taken to study the spacings ofdifferent sets of discontinuities is to makemeasurements along scanlines with differentorientations, preferably with a scanline at rightangles to each set if this is physically possible(Hudson and Priest, 1979; 1983).The average spacing of discontinuities is found bycounting the number, N'', that intersect a scanline ofknown length L, with an adjustment being made ifthe discontinuities are not oriented at right angles tothe scanline. For the condition shown in Fig. 2.14where the scanline is horizontal and the dip of thediscontinuities is ?, the average spacing is givenby:


(2.15)

Figure 2.14 shows that there are a total of 13discontinuities with an average dip of 65° thatintersect the 27 m long scanline. From equation 2.15, the average spacing is 1.9 m (6.2 ft) which isdrawn to scale on the Figure. If the variation in thespacing can be described by an exponentialdistribution, then the probability that the spacingwill be less than a specified value is given byequation 2.10.

2.7References

Baecher, G.B., Lanney, N.A. and Einstein, H. (1977)Statistical description of rock properties and sampling.Proc. 18th U. S. Symp. Rock Mech. Johnson Publishing,Keystone, Colorado.

Cruden, D.M. (1977) Describing the size ofdiscontinuities. Int. J. Rock Mech. Min. Sci. &Geomech. Abstr., 14, 133–7.

Dershowitz, W.S. and Einstein, H.H. (1988)

Characterizing rock joint geometry with joint systemmodels. Rock Mech. Rock Eng., 20(1), 21–51.

Donn, W.L. and Shimer, J.A. (1958) Graphic Methods inStructural Geology. Appleton Century Crofts, NewYork.

Einstein, H.H. (1993) Modern developments indiscontinuity analysis. Comprehensive RockEngineering, Pergamon Press, pp. 193–213.

Einstein, H.H., Veneziano, D., Baecher, G.B. andO’Reilly, K.J. (1983) The effect of discontinuitypersistence on slope stability. Int. J. Rock Mech. Min.Sci. & Geomech. Abstr., 20, 227–36.

Goodman, R.E. (1976) Methods of GeologicalEngineering in Discontinuous Rocks, West, St. Paul,MN.

Goodman, R.E. (1980) Introduction to Rock Mechanics,Wiley, New York.

Goodman, R.E. and Bray, J. (1976) Toppling of rockslopes. Proc. Speciality Conf. On Rock Engineering forFoundations and Slopes, Boulder Colorado, ASCE, VolII.

Hoek, E. and Bray, J. (1981) Rock Slope Engineering, 3rdedn, IMM, London.

Hudson, J.A. and Priest, S.D. (1979) Discontinuities and

Figure 2.14 Rock outcrop showing discontinuity length, termination and spacing; terminations categorized as eithercontained (c) or transecting (t) discontinuities.


rock mass geometry. Int. J. Rock Mech. Min. Sci. &Geomech. Abstr., 16, 336–62.

Hudson, J.A. and Priest, S.D. (1983) Discontinuityfrequency in rock masses. Int. J. Rock Mech. Min. Sci.& Geomech. Abstr., 20, 73–89.

Kikuchi, K., Kuroda, H. and Mito, Y. (1987) Stochasticestimation and modelling of rock joint distributionbased on statistical sampling. Sixth Int. Conf. on RockMechanics, Montreal, pp. 425–8.

Kulatilake, P.H. S. (1988) State of the art in stochasticjoint geometry modeling. Proc. 29th U.S. Symp. RockMech. (eds. P.A.Cundall, R.I.Sterling andA.M.Starfield) Balkema, Rotterdam, pp. 215–29.

Kulatilake, P.H.S. and Wu, T.H. (1984) Estimation of themean length of discontinuities. Rock Mech. and RockEng., 17(4), 215–32.

Mahtab, M.A. and Yegulalp, T.M. (1982) A rejectioncriterion for definition of clusters in orientation data.Proc. 22nd. Symp. Rock Mechanics, Berkeley, CA, Soc.Min. Eng., American Inst. of Mining, Metallurgical,

Petroleum Eng., pp. 116–23.McMahon, B.K. (1982) Probabalistic Design in

Geotechnical Engineering, Australian MineralFoundation, AMF Course 187/82, Sydney.

Morriss, P. (1984) Notes on the Probabalistic Design ofRock Slopes, Australian Mineral Foundation, notes forcourse on Rock Slope Engineering, Adelaide, April.

Pahl, P.J. (1981) Estimating the mean length ofdiscontinuity traces. Int. J. Rock Mech. Min. Sci. &Geomech. Abstr., 18, 221–8.

Phillips, F.C. (1972) The Use of Stereographic Projectionin Structural Geology, 3rd edn, Arnold, London.

Priest, S.D. and Hudson, J.A. (1981) Estimation ofdiscontinuity spacing and trace length using scanlinesurveys. Int. J. Rock Mech. Min. Sci. & Geomech.Abstr., 18, 183–97.

Priest, S.D. and Hudson, J.A. (1976) Discontinuityspacings in rock. Int. J. Rock Mech. Min. Sci. &Geomech. Abstr., 13, 135–48.


3Rock strength and deformability

3.1Range of rock strength conditions

Determination of the appropriate strengthparameters to use in the design of foundationsdepends on the type of foundation, the loadconditions, and the characteristics of the rock in thebearing area. The importance of using theappropriate strength parameter is illustrated inFig. 3.1, which shows a number of differentfoundation loading conditions and the rock strengthparameters that apply to the design of each. Thefollowing is a list of basic rock strength parametersand their applications in foundation design:

1. deformation modulus—calculation ofsettlement (Fig. 3.1(a, b));

2. compressive strength; of rock mass—bearingcapacity of spread footings (Fig. 3.1(b));

3. compressive strength of intact rock—bondstress of socketed piers and tensioned anchorsis correlated with intact rock strength on thebasis of empirical tests (Figs 3.1(c, d);

4. shear strength—shear resistance at interfacebetween structure and foundation, and stabilityof sliding blocks (Fig. 3.1(b, e))

5. tensile strength—punching or flexural failureswhere a weak bed underlies a layer of stifferrock (Fig. 3.1(f));

6. time dependent properties—settlement mayoccur with time as a result of rock creep, ordegradation of the rock due to weathering.

In determining the rock strength for each of theseapplications, it is most important to account for the

presence of discontinuities, such as joints, faults orbedding planes. For most conditions this requiresthat the rock mass strength properties, rather thanthe intact rock properties be used in design. Therock mass is the in situ, fractured rock which willalmost always have significantly lower strengththan the intact rock because the discontinuitiesdivide the rock mass into blocks. The strength of therock mass will depend on such factors as the shearstrength of the surfaces of the blocks, their spacingand continuous length, and their alignment relativeto the load direction. For example, the wedge ofrock at the downstream toe of the dam foundationshown in Fig. 3.1(b) could fail in shear along asurface lying partially through intact rock andpartially along existing discontinuities.Furthermore, if the loads are great enough to extenddiscontinuities and break intact rock, or if the rockmass can dilate resulting in loss of interlockbetween the blocks, then the rock mass strengthmay be significantly diminished from that of the insitu rock. Foundations located in fractured rockwhich are designed using the strength values ofintact samples tested in the laboratory are likely tobe significantly under-designed.Other conditions that may be encountered arefoundations containing potentially unstable blocks,formed by single or intersecting discontinuities, thatmay slide from the foundation (Fig. 3.1(e)). In thesecircumstances, the shear strength parameters of thediscontinuities themselves must be used in designrather than the shear strength of the rock mass. Thisshows the importance of carrying out carefulgeological mapping to identify such critical

geological features and ensure that the strengthtesting program is appropriate for the likely modeof failure and rupture surface position.Chapter 4 describes methods of in situ modulus andstrength testing, and Chapters 5–9 describe theapplication of the test results to the design ofdifferent types of foundations.One of the first decisions to be made in drawing upa testing program is whether to rely solely onlaboratory tests, or to carry out more expensive insitu tests. Laboratory testing is appropriate wherethe test sample, which will usually have dimensionsno larger than 100 mm (4 in) diameter, isrepresentative of the rock properties. Tests that can

be carried out in the laboratory are uniaxialcompressive strength testing, and shear testing todetermine the friction angle of rock surfaces.However, it is rarely possible to carry out laboratorytests on a fractured rock mass because of thedifficulty in obtaining undisturbed samples whichare large enough, i.e. at least 1 m (3 ft) in diameter,to be representative of the in situ rock. If a largesample is available, then correspondingly largetesting equipment will be required to load thesample to stress levels that will be acting in thefoundation. One of the few laboratories capable oftesting fractured rock masses is the University ofCalifornia at Berkeley which has a 0.9 m (36 in)

Figure 3.1 Rock strength parameters related to the design of rock foundations: (a) settlement due to compression of softseams and intact rock; (b) shear and deformation of fractured rock mass; (c) side-wall bond strength and end bearing ofa socketed pier; (d) shear strength of rock-grout interface; (e) shear failure on a continuous fracture dipping out of theface; and (f) punching or flexural failure of a thin bed of rock overlying weaker material.

ROCK STRENGTH AND DEFORMABILITY 51

diameter triaxial cell to which an axial load of 17.6MN (4×106 lb) and a confining pressure of 5.1 MPa(750 p.s.i.) can be applied. The cell has been used totest rock fills. Laboratory tests on fractured rockhave been carried out by Brown (1970), andsimulations of fractured rock made up of blocks ofmaterials such as cement and plaster of paris (Reikand Zacas, 1978).In situ testing is sometimes carried out in the designof dams and major bridges. This testing can consistof borehole jacking tests, plate load tests, and radialjacking tests to determine rock mass modulus, anddirect shear tests to determine the shear strength ofdiscontinuities critical to stability. These tests arecarried out where there is access during theexploration program to a site that is representative ofthe foundation conditions.As a back up to laboratory or in situ tests, it is usefulto check the test results against values calculatedfrom the performance of actual foundations insimilar geological conditions. Observations ofsettlement under known loading conditions willprovide information on rock mass modulus values,while shear strength parameters can be backcalculated from slope failures. While theseobservations will provide modulus and shearstrength values of much larger samples than ispossible with in situ testing, the reliability of theresult will depend on the accuracy with which theloads, water pressures and movement mechanismsare known.

3.2Deformation modulus

For many structures founded on rock, loads are wellwithin the elastic limit of the rock mass.Consequently all deformation and settlement occursas soon as the load is applied, and there is no timedependent effect. Furthermore, settlement that doesoccur will be minimal and is not considered as aspecific item in design.However, circumstances where foundationsettlement must be considered are heavily loadedstructures, particularly where the rock conditions

vary across the site. Such structures include high-rise buildings, with individual footings on differentrock types, and long bridges where differentialsettlement between piers must be controlled. In thecase of settlement, concrete structures are, of course,much more susceptible to damage from differentialsettlement than embankment dams, and conditionsare most severe where the foundations comprisematerials with different moduli. For the conditionsshown in Fig. 3.2, differential settlement can inducestresses in the concrete sufficient to developcracking. The cracks will develop at the contactsbetween the foundation materials where theconcrete attempts to bridge across the lowermodulus rock (E2) and concentrates the load on thehigher modulus rock (E1). This effect will be ofmost concern for arch dams if the width of the lowmodulus rock is equal to or greater than the widthof the foundation, or where one abutment has amoduli different from the reminder of thefoundation. Also, the cyclic loading that oftenoccurs in dams due to changing reservoir levels canproduce permanent displacement as a result of non-recoverable strain in the foundation rock.The ratio of the deformation moduli of the concretein the dam Ec and the foundation rock Er willinfluence the magnitude of stresses in the concrete.However, even for arch dams if the ratio Ec/Er isconstantacross the foundation, its magnitude haslittle effect on the stress levels. Even if the ratio Ec/Er varies by a factor of five, the stress levelsdetermined by the Trial Load Method show that thestresses only vary by about 20%, so there is usuallyno need to determine precise values for the rockmodulus (ICOLD, 1993)In most structures, the area of the bearing surfacewill be greater than the discontinuity spacing sosettlement will be the result of both the deformationof the intact rock and the clo sure of discontinuities.That is, settlement will depend on the rock massmodulus and not the intact rock modulus. Thedifficulty and expense of obtaining large,undisturbed rock mass samples has meant thatmodulus measurements are made by in situ testing.The test methods include borehole pressuremeter,

52 RANGE OF ROCK STRENGTH CONDITIONS

plate load, flat jacks, pressure chamber andgeophysical testing as described in Chapter 4.Deformation measurements have also been made ofthe foundations of structures during and afterconstruction so as to compare the moduluscalculated from these displacements with thoseobtained from testing. Guidici (1979) describes themodulus testing programme at the Gordon Dam inTasmania where the plate jacking tests gavedeformation modulus: back analysis values ofbetween 12 and 40 GPa (1.74×106-5.8×106 p.s.i.)while the modulus calculated from deformationmeasurements ranged from about 12 to 24 GPa (1.74×106-3.48×106p.s.i.). The lower modulusexhibited by the larger, in situ sample could beaccounted for by the number of discontinuitiesincreasing with increasing sample size.The deformability of rock as discussed in theprevious paragraph is characterized by a modulusdescribing the relationship between the applied loadand the resulting deformation. The fact that jointedrock masses do not behave elastically has promptedthe usage of the term deformation modulus ratherthan the elastic modulus or Young’s modulus. Theirdefinitions are as follows (ISRM, 1975):

• deformation modulus—the ratio of stress tocorresponding strain during loading of a rockmass including elastic and inelastic behavior;

• elastic modulus—the ratio of stress tocorresponding strain below the proportional limitof a material.

The following sections describe the moduluscharacteristics of a variety of different rock masses,and the influence of the measurement method on thetest results.

3.2.1Intact rock modulus

The usual method of measuring the deformationmodulus of intact rock is to test pieces of diamonddrill core in uniaxial compression, with the testbeing a component of a compressive strength test.The most common core size used in geotechnicalstudies is NQ core with a diameter of 52 mm (2 in),and the test sample is cut so that the lengthto diameter ratio is 2.0. As there is some influence ofspecimen size on strength and modulus, it ispreferable to standardize sample dimensions if

Figure 3.2 Shear stresses developed in a concrete dam founded on rock with variable modulus (after Goodman, 1980).


possible. It is also necessary to grind the ends of thesample parallel and to use platens with the samediameter as the core; these procedures willminimize the development of stress concentrationsat the ends of the sample. The International Societyof Rock Mechanics Committee on Laboratory Tests(1972) gives the following tolerances for cylindricaltest specimens.

1. The ends of the specimen shall be flat to 0.02mm (0.0008 in).

2. The ends of the specimen shall beperpendicular to the axis of the specimen within0.001 radian.

3. The sides of the specimen shall be smooth andfree of abrupt irregularities and straight towithin 0.3 mm (0.012 in) over the full length ofthe specimen.

Strain measurements are usually made with straingauges glued to the surface of the sample; with acombination of axial and circumferential straingauges it is possible to measure both the modulusand Poisson’s ratio of the sample. The stress-strainbehavior of a rock can be plotted directly on an X–Yplotter during testing as shown in Fig. 3.3. Note thatit is preferable to use strain gauges glued to the rocksurface to measure strain in the rock directly, ratherthan such instruments as LVDTs (linear variabledifferential transformers) mounted on the platens.The reason for this is that slight imperfections at thecontact between the steel and the rock may lead tomovements of the platens that are not related tostrain in the rock.The plots in Fig. 3.3 show two cycles of acompression test on a sample of strong gneissicrock which exhibits approximately linear stress-strain behavior, no hysteresis and no permanent

Figure 3.3 Axial and diametral stress-strain curves for intact rock tested in uniaxial compression.


deformation. The rock is therefore showingnear perfect elastic behavior. A perfectly elasticmaterial is one that follows the same path duringboth the loading and unloading cycles, that is,hysteresis is zero and all the energy stored in therock during loading is released during unloading.An elastic material is one that returns to zero strainat the end of the unloading cycle, although theloading and unloading cycles may follow differentpaths indicating that some energy is dissipated inthe rock mass during the loading and unloading

cycles.The elastic constants calculated from the plots inFig. 3.3 over the linear portion of the stress-straincurve are as follows:

Table 3.1 Typical elastic constants for intact rock

Rock type Young’s modulus GPa (p.s.i.×106) Poisson’s ratio Reference

Andesite, Nevada 37.0(5.5) 0.23 Brandon (1974)Argillite, Alaska 68.0(9.9) 0.22 Brandon (1974)Basalt, Brazil 61.0(8.8) 0.19 Ruiz (1966)Chalk, USA 2.8(0.4) – Underwood (1961)Chert, Canada 95.2(13.8) 0.22 Herget (1973)Claystone, Canada 0.26(0.04) – Brandon (1974)Coal, USA 3.45(0.5) 0.42 Ko and Gerstle (1976)Diabase, Michigan 68.9(10) 0.25 Wuerker (1956)Dolomite, USA 51.7(7.5) 0.29 Haimson and Fairhurst (1970)Dolomite, Canada 64.0(9.3) 0.29 Lo and Hori (1979)Gneiss, Brazil 79.9(11.6) 0.24 Ruiz (1966)Granite, California 58.6(8.5) 0.26 Michalopoulos and Triandafilidis (1976)Limestone, USSR 53.9(8.5) 0.32 Belikov (1967)Salt, Ohio 28.5(4.1) 0.22 Sellers (1970)Sandstone, Germany 29.9(4.3) 0.31 van der Vlis (1970)Shale, Japan 21.9(3.2) 0.38 Kitahara et al. (1974)Siltstone, Michigan 53.0(7.7) 0.09 Parker and Scott (1964)Tuff, Nevada 3.45(0.5) 0.24 Cording (1967)Table 3.1 shows the results of uniaxial compressiontests carried out to determine the elastic constants ofa variety of rock types (Lama and Vutukuri, 1978a,b)).

3.2.2Stress-strain behavior of fractured rock

The typical load-deformation behavior of two rockmasses subjected to cyclic loading is shown inFig. 3.4. Figure 3.4(a) shows the results of a plate

load test carried out on massive gneiss with anaverage compressive strength of 110 MPa (16 000p.s.i.) from the Churchill Falls project in Quebec,Canada (Benson, 1970). Figure. 3.4(b) shows theresults of Goodman jack tests carried out insandstone with a compressive strength of about 4MPa (580 p.s.i.) on the Peace River in Alberta,Canada (Saint Simon et al., 1979).The stress-deformation curves in Fig. 3.4 showtypical inelastic behavior as characterized by themodulus of deformation. The pertinent features


of these tests are first, the increase in gradient of thecurve with each load increment, and second, thepermanent deformation that occurs on removal ofthe load. With each load cycle at a progressivelyhigher stress, the modulus increases as indicated bythe increase in gradient of the stress-strain curves;this is more noted in the case of the relatively largervolume of rock in the plate load test. This increasein modulus is the result of closure of discontinuitiesin the rock mass, and the progression of loading intodeeper lying, and less disturbed rock. Thesediscontinuities may be both natural surfaces andfractures opened by blasting in preparing the site.The test conditions and results should be carefullyevaluated and related to the likely foundationconditions of the structure where the rock may beeither more or less stress relieved depending onsuch factors as the method of preparation of thebearing surface, and whether geological conditionsat the test site are representative of the overallfoundation.Other features of the stress-strain curves in Fig. 3.4are the permanent deformation that occurs after theremoval of the load, and the envelopes indicatingthe relationship between stress and deformationwith increasing stress. The permanent deformationis the result of both closure of discontinuities, and

crushing of rock in areas of stress concentration. Inthe case of the gneiss, the permanent deformationhas stabilized after two cycles, whereas in theweaker sandstone, there is additional deformationafter each cycle, possibly as the result ofprogressive rock fracture.The changing modulus of the rock mass withincrementally increasing load is shown by thedeformability envelope as illustrated in Fig. 3.4. Ifthe envelope is concave downwards (Fig. 3.4(a)),this demonstrates an increasing modulus with loadas the discontinuities close (as discussed above)which would be favorable for foundation stability.However, a concave upwards envelope (Fig. 3.4(b)), may indicate the development of plasticprocesses in the rock and the possibility of creep inthe foundation.The deformation properties of rock masses isusually only of concern for weak rocks where thereis a possibility of creep or excessive deformation inthe foundation. In contrast, for foundations in strongrock the stresses are usually well below the plasticlimit so that settlement will be elastic with no timedependency and there is less need for extensive insitu testing. An example of deformation modulimeasurements of weak rocks are a series of plateload tests carried out in Poland as part of the

Figure 3.4 Typical results of in situ modulus testing: (a) plate load test in gneiss (Benson, 1970); and (b) Goodman jacktest in sandstone (Saint Simon et al., 1979).


foundation investigation and design work for twogravity dams (Thiel and Zabuski, 1993; Thiel,1974). One site is in the Carpathian Mountainswhere the predominant rock types are flyschs, andlimestones, marls and shales. The beds in theseunits are generally steeply dipping, but the rocks arehighly tectonically disturbed, faulted, and containirregularly spaced orthogonal jointing; the shaleusually occurs as a weak and degradable interbed.The other site is in the Brystrzyckie Mountainswhere the rock is a distinctly foliated andanisotropic mica schist containing biotite andmuscovite aligned parallel to the foliation.

The plate load tests were set up in tunnels andcomprised a set of four hydraulic jacks, applying avertical load, that were capable of applying amaximum pressure of 4 MPa (580 p.s.i.) to a samplewith an area of 2 m2 (21.5 ft2). Multistage testingwas carried out with the load increased in 0.08 to 0.2 MPa increments to a maximum pressure that was1.5–2 times the maximum design bearing pressurein the foundation. Creep measurements were alsocarried out by applying a constant load for up to 30hours, with the test being terminated when the creeprate was less

Table 3.2 Deformation moduli for very poor quality rock determined by plate load tests (Thiel and Zabuski, 1993)

Rock type Geological characteristics RMR ≈ 45 to 18 Deformation modulus MPa

Sandstone Sandstone containing shale interbeds comprising 5–10% of rock;layer thickness 500–1500 mm (20–60 in)

10

Shale/sandstone Interbedded sequence with approximately equal proportions of shaleand sandstone; layer thickness 300–600 mm (12–25 in.):

Slightly folded and fractured 3–5Highly folded and fractured 1.5–2.0

Shale Interbedded sequence of clay shale with 5–10% sandstone, veryhighly folded and fractured; layer thickness less than 300 mm (<12in)

0.3–0.8

Limestone Interbedded with clayey-shale infilling, infilling thickness 1–5 mm (0.04–0.2 in); layer thickness 60–200 mm (2–8 in)

2.1

Marl Layer thickness 15–150 mm (0.6–6 in) 1.6Clayey shale Layer thickness less than 1 mm (<0.04 in) 0.4Mica schist Biotite/muscovite 4.5

Muscovite/biotite 1.3than 0.01 mm (0.0004 in) per hour over four hours.Table 3.2 shows the deformation moduli measuredin the plate load tests for a variety of very weakrocks. The quality of these rocks has been expressedin terms of the rock mass rating (RMR) and hadvalues of between 18 and 45 which arecharacterized as poor quality rock. The RMR ratingsystem is described in more detail in Section 3.2.6and Fig. 3.10 shows the relationship between RMRvalues and the in situ deformation moduli for a widerange of rock quality.The possibility of permanent deformation offoundation rocks should be considered for damssubjected to significant cyclic loading as a result offluctuations in reservoir level. As shown in Fig. 3.5,

incremental inelastic deformation may occur witheach cycle, with the greatest deformation occurringin the center of the dam where the foundation is themost heavily loaded. Such differential settlementcan induce fractures in the structure. The plate loadtests, reported in Table 3.2, also measured thepermanent deformation resulting from cyclicloading and found, for these particular conditions,that significant permanent deformation occurred forrocks with deformation moduli less than about 2GPa (Fig. 3.6).


3.2.3Size effects on deformation modulus

Deformation moduli tests are performed on pieces ofrock core, on small volumes of in situ rock, andoccasionally by measuring the settlement ofstructures. Because the objective of these tests is todetermine the modulus of large rock masses infoundations, it is necessary to have a means ofrelating test results from a variety of methods to themodulus of foundation-scale rock volumes. Of

particular importance is the determination ofmodulus values under earthquake loading.The results of many test methods have beencompared to determine if relationships can beestablished between modulus and test volume. Ithas been concluded that the following approximaterelationship between moduli measured by differentmethods will generally apply (Raphael andGoodman 1979):

Figure 3.5 Permanent deformation of abutments and foundation due to cyclic reservoir levels (Goodman, 1980).

Figure 3.6 Relationship between irreversible displacement dirr and deformation modulus Em for rock masses listed inTable 3.2 (Thiel and Zabuski, 1993).


where Estatic is the modulus for rock loaded by platebearing, borehole jack or dilatometer/test;Eearthquake is the modulus for rock mass subject toshaking at 1–10 Hz; Eseismic is the modulus for rockmass subject shock waves with frequency of severalhundred hertz in seismic geophysical testing; andEintact rock is the modulus for intact rockspecimens.The basis of this relationship is that intact rocksamples containing no discontinuities will have thehighest modulus, while larger, fractured samplestested in situ will have lower modulus values as aresult of closure of the discontinuities. Rock massessubjected to shock waves (seismic or earthquake)will show intermediate modulus values where thestress levels are low and there is less closure of thediscontinuities than that induced by the higherstresses in plate load tests. Methods of modulustesting are described in Section 4.5.Values of Estatic have been compared with resultsdetermined by seismic testing, Eseismic, and tests inthe laboratory on pieces of intact rock core, Eintactrock. Theratio Eseismic/Estatic, which has beendetermined by Schneider (1967) from tests at 14different sites, was found to vary between 2 and 13(Fig. 3.7). This ratio, as well as the wavelength ofthe shear seismic wave, increases as the fracturing ofthe rock becomes more intense. The ratio Eseismic/

Estatic increases with closer fracturing because thevalue of Estatic diminishes significantly when therock mass is more readily deformed under localloading.Other modulus results have been examined tocompare a variety of in situ tests, Estatic, withlaboratory tests on pieces of rock core, Eintact, fromthe same site. These results of 78 such tests havebeen used to establish values for the ratio Eintact rock/Estatic as shown in Table 3.3 (Heuze, 1980).Information on the degree of fracturing at these sitesis not available.The conclusions that can be drawn from the modulusvalues determined by different methods of testingare, first, that the modulus of fractured rockdiminishes as the discontinuity intensity increases.Second, there is considerable scatter in the results,especially when the volume of rock being tested islarge and the properties variable. As a consequenceof this scatter, the relationship given in this sectionbetween modulus values determined by differentmethods is only approximate, and for final designpurposes, results from a number of test methods arepreferred.

Figure 3.7 Relation between seismic and static moduli as a function of shear wave length in hammer seismic profiles(Raphael and Goodman, 1979).


3.2.4Discontinuity spacing and modulus

With the very great influence of geological structure

on the rock mass modulus, it is useful

Table 3.3 Ratios Eintact rock/Estatic for various types of field deformability tests

Type of test Number of tests Mean ratio

Platebearing 27 3.1Full scale deformation 14 2.4Flat jacks 10 1.9Borehole jack or dilatometer 9 3.0Pressure chamber 8 2.2Petit seismique 5 2.9Others 5 2.4to have a method of relating the properties of thediscontinuities to the relationship betweenlaboratory and field modulus values. Goodman andDuncan (1971) describe such a procedure, andRaphael and Goodman (1979) describe theapplication of the method to the determination ofthe rock mass modulus of closely fractured rockforming the foundation of a dam in California.Consider an isotropic and linearly elastic rock withelastic constants for the intact rock of Er (Young’smodulus) and vr (Poisson’s ratio). The properties ofthe discontinuities that determine the relationshipbetween the modulus of the intact rock and that ofthe rock mass are the fracture spacing S andstiffness k of the discontinuities in each set. Thenormal stiffness kn of a discontinuity is defined asthe normal closure dn that occurs on the applicationof a normal load a and is given by (Fig. 3.8(a)):

(3.1)

Normal stiffness of a discontinuity tends to behighly non-linear, with the major portion of theclosure taking place at low stress levels.The deformation of discontinuities is defined bytheir normal and shear stiffnesses kn and ksrespectively, where kn is the slope of normal stress-normal displacement curve s/dn, and ks is the slopeof the shear stress-shear displacement curve t/ds.Both these parameters can be obtained from theresults of direct shear tests to determine the frictionangle of discontinuity surfaces. If the spacing of the

discontinuities is S and the modulus of the intactrock is Er, then on application of a normal stress a,the deformations will be as follows (Fig. 3.8(b)):

The total deformation of a rock mass uponapplication of a stress a is the sum of the rockdeformation S(s/Er) and the joint deformation s/kn.Therefore, the deformation modulus of the rockmass Em is related to the properties of the intactrock and the discontinuities by:

(3.2)

An application of this equation is as follows. Thevalue of Er is determined by laboratory testing andthe value of Em by in situ methods such as plateload tests. For a particular set of joints with spacing,S, the stiffness can be calculated. This result canthen be used to estimate the influence on rock massdeformation modulus of different discontinuityspacings.Similarly, an equation can be developed for the rockmass shear modulus Gm in the case of shear loadingof the model shown in Fig. 3.8:

(3.3)

where Gr is the shear modulus of the intact rock andks is the shear stiffness of the discontinuities.Equations 3.2 and 3.3 can be combined to estimate


the deformation modulus of a rock mass containingseveral sets of discontinuities inclined at differentorientations with respect to the applied load(Chappell and Maurice, 1980). These equations willprovide some indication of the influence of thegeological structure on the rock mass modulus, andmay be of value in interpreting the results of in situ

modulus measurements.

3.2.5Modulus of anisotropic rock

Many rock types exhibit anisotropic strength andmodulus, and it is important that the values used in

Figure 3.8 Model of rock mass relating discontinuity stiffness to rock mass modulus: (a) typical normal stress-normalclosure behavior of discontinuity in rock; and (b) model of fractured rock mass containing one set of uniformly spaceddiscontinuities.


design are appropriate for the direction of loading.Typical anisotropic rock types are the sedimentary-metamorphic sequence of shale-slate-phyllite-schistwhich will usually contain sets of paralleldiscontinuities and, in the case of schist and phyllite,have low strength mica aligned with thesediscontinuities. The mass modulus of these rocktypes is likely to be lower in the direction normal tothe orientation of the predominant geologicalstructure as a result of closure of thesediscontinuities (Fig. 3.9).Laboratory and in situ testing programs have beenconducted to determine elastic constants indirections parallel and perpendicular to theorientation of the predominant geological structurein anisotropic rock. The modulus ratio is known asthe degree of anisotropy, and is given the term E0/E90—modulus parallel/perpendicular to planes ofweakness (bedding or foliation) in the rock. Surveys

conducted by Lama and Vutukuri (1978a, b) of rockmodulus testing programs show that the modulus isusually higher in the direction parallel to thestructure and that the degree of anisotropy variesbetween 1 and 3.2 (Table 3.4).Seismic testing to determine the dynamic modulusshows values of the E0/E90 ratio of between 1.0 and1.2. These low ratios can be attributed to the lowstress levels of seismic testing that produces littleclosure of discontinuities.Note that the shear strength of anisotropic rocktypes is usually much lower in the direction parallelto the main structure because displacement will takeplace more readily along these planes (Section 3.4).Therefore it is important to examine both thedirection and type of loading with respect to theorientation of the geological structure in the designof any foundation in these rock types.

Table 3.4 Modulus ratios of anisotropic rock

Rock type E0/E90 Reference

Clay shale 1.36–2.86 Stepanov and Batugin (1967)Slate 1.7 Bamford (1969)Phyllite 1.28–1.33 Lekhnitskii (1966)Schist 1.3–3.2 Pinto (1970)3.2.6Modulus-rock mass quality relationships

With rock mass modulus being highly dependent on

both the geological structure and the size of the testsample, Bieniawski (1978) has proposed a methodof estimating in situ modulus from an index which

Figure 3.9 Variation in modulus of elasticity with direction of loading in anisotropic (schistose) rock (Pinto, 1970).


characterizes the overall properties of the rock massquality. This index is known as the rock mass rating(RMR) and is widely used in the assessment oftunnel support requirements (Bieniawski, 1976).The advantage of this approach is that the index isdetermined from readily measured parameters: thecompressive strength of the intact rock, thecharacteristics of the discontinuities determined bymapping and drilling, and ground water conditions.Table 3.5 shows the six parameters that describe therock mass and the rating points that are assigned toeach range of values of the parameters. The RMRrating is calculated by adding the points for each

parameter.The influence of discontinuity orientation onfoundation performance is taken into account in thesettlement and stability analyses, rather than byadjusting the RMR value. An unfavorable jointorientation with respect to settlement would be in adirection at right angles to the load directionresulting in closure of discontinuities andsettlement. This contrasts with an unfavorableorientation with respect to sliding, where thediscontinuities would be in a direction parallel tothe load direction (Chappell and Maurice, 1980).

Table 3.5 RMR classification of jointed rock masses (extract from Bieniawski, 1974)

Parameter Ranges of values

A. Classification parameters and their ratings1 Strength

of intactrockmaterial

Point loadstrengthindex

>8 MPa 4–8 MPa 2–4 MPa 1–2 MPa For this low range

>1.2 ksi 0.6–1.2ksi

0.3–0.6ksi

0.8–0.3ksi

uniaxial compressive test is preferred

Uniaxialcompressivestrength

>200 MPa 100–200MPa

50–100MPa

25–50MPa

10–25 3–10 1–3

MPa MPa MPaRating 15 12 7 4 2 1 0

2 Drill core quality RQD 90%–100%

75%–90% 50%–75% 25%–50% <25%

Rating 20 17 13 8 33 Spacing

of joints>3 m (>10ft)

1–3 m (3–10 ft)

0.3–1 m(1–3 ft)

50–300mm (2–12in)

<50 mm (<2 in)

Rating 30 25 20 10 54 Condition

of jointsVeryroughsurfaces

Slightlyroughsurfaces

Slightlyroughsurfaces

Slickensidedsurfaces or

Soft gouge >5 mm thick or

NotcontinuousNoseparation

Separation <1 mm

Separation <1 mm

Gouge <5mm thickor

Joints open >5 mm Continuousjoints

Hard jointwall rock

Hard jointwall rock

Soft jointwall rock

Jointsopen 1–5mmContinuou


Parameter Ranges of valuess joints

Rating 25 20 12 6 05 Ground

waterCompletely dry

Moistonly(interstitial water)

Waterundermoderatepressure

Severe water problem

Rating 10 7 4 0When calculating rock strength using Table 3.7, rating=10; ground water pressuresaccounted for in stability analysis.

B. Rating adjustment for joint orientationsOrientation of joints Very

favorableFavorable Fair Unfavorab

leVery unfavorable

Adjustment forfoundations

0 −2 −7 −15 −25

When calculating rock strength using Table 3.7, adjustment=0; joint orientationaccounted for in stability analysis.

The empirical relationship between the RMR ratingvalue and the in situ rock mass modulus is shown inFig. 3.10. For the seven different projects studied byBieniawski in developing this relationship, Em isgiven by the following equation:

(3.4)The obvious deficiency of this equation is that itdoes not give modulus values for RMR values lessthan 50. Additional studies carried out on rockmasses with qualities ranging from poor to verygood indicates that the modulus is related to therock mass rating over the range of about 20–85 bythe following equation (Serafim and Periera, 1983):

(3.5)

3.3Compressive strength

Compressive strength values of rock are used in thedetermination of rock mass strength parameters asdescribed below in Section 3.3.2, the bond strengthsat the rock-concrete interface in drilled piers andtensioned anchors, for the bearing capacity ofspread footings and the calculation of rock massstrengths. In the case of bond strength, empiricalrelationships have been developed between

compressive strength of intact rock and workingbond strengths that have been found to operatesatisfactorily in practice. In the case of spreadfootings where the bearing area is larger than thespacing between discontinuities, the bearingcapacity can be calculated from the compressivestrength of the rock mass. The following is adiscussion on methods of determining thecompressive strength of both intact rock, and therock mass.In many instances it is not necessary to makeaccurate measurements of compressive strength,particularly during the reconnaissance stage of aproject and where the compressive strength is notused directly in foundation design. In thesecircumstances it is satisfactory to make an estimateof the compressive strength based on observations ofthe in situ rock condition and simple field tests.Table 3.6 shows the relationship between thesedescriptions of the rock mass and ranges of uniaxialcompressive strength. For comparison purposes, thesoil descriptions and strengths are also


Table 3.6 Classification of rock material strengths (ISRM, 1981)

Grade Description Field identification Approximate range of compressive strength

MPa (p.s.i)

R6 Extremely strong rock Specimen can only be chipped withgeological hammer

>250 (>36 000)

R5 Very strong rock Specimen requires many blows ofgeological hammer to fracture it

100–250 (15 000–36 000)

R4 Strong rock Specimen requires more than one blowwith a geological hammer to fractureit.

50–100 (7 000–15 000)

R3 Medium weak rock Cannot be scraped or peeled with apocket knife; specimen can befractured with single firm blow ofgeological hammer

25–50 (3 500–7 000)

R2 Weak rock Can be peeled with a pocket knife;shallow indentations made by firmblow with point of geological hammer

5–25 (725–3 500)

R1 Very weak rock Crumbles under firm blows with pointof geological hammer; can be peeledby a pocket knife

1–5 (150–725)

R0 Extremely weak rock Indented by thumbnail 0.25–1 (35–150)S6 Hard clay Indented with difficulty by thumbnail >0.5 (>70)S5 Very stiff clay Readily indented by thumbnail 0.25–0.5 (35–70)S4 Stiff clay Readily indented by thumb but

penetrated only with great difficulty0.1–0.25 (15–35)

Figure 3.10 Relationship between in situ modulus and rock mass rating (Bieniawski, 1978; Serafim and Pereira, 1983).



MPa (p.s.i)

S3 Firm clay Can be penetrated several inches bythumb with moderate effort

0.05–0.1 (7–15)

S2 Soft clay Easily penetrated several inches bythumb

0.025–0.05 (4–7)

S1 Very soft clay Easily penetrated several inches by fist <0.025 (<4)shown in Table 3.6. The letter designations (R0etc.) can be used on drill logs and field mappingsheets to record the rock strength values(Appendix II).

3.3.1Compressive strength of intact rock

The compressive strength of intact rock can readilybe measured using either a compression machine ora point load tester (Fig. 3.11(a)). The compressionmachine gives the more precise results but it isnecessary to prepare the samples in the mannerdescribed in Section 3.2.1 on modulus testing.Estimation of compressive strength with the pointload testing equipment has the advantage that testscan be conducted on lengths of unprepared core inaxial and diametral directions, as well as on irregularlumps of rock (ISRM, 1985). The equipment isportable and can readily be used in the field. Theprinciple of operation is that a compressive load isapplied through two conical platens which causesthe rock to break in tension between these twopoints. If the distance between the platens is D andthe breaking load is P, then the point load index, Isis given by:

(3.6)where De, the equivalent core diameter is givenby:

or

and . A is the minimum cross-sectionalarea of a lump sample for a plane through the platencontact points, where W is the specimen width.The size-corrected point load strength index Is(50)

of a rock specimen or sample is defined as the valueof Is that would have been measured by a diametraltest with For tests conducted onsamples with dimensions different from 50 mm, theresults can be standardized to a size-corrected pointload strength index by applying a correction factorkPLT as follows:

(3.7a)The value of the size correction factor kPLT is shownin Fig. 3.11(b) and is given by:

(3.7b)It has been found on average that the uniaxialcompressive strength is about 20–25 times the pointload strength index. However, tests on manydifferent types of rock show that the ratio can varybetween 15 and 50, especially for anisotropic rocks.Consequentially, the most reliable results areobtained if a series of uniaxial compression tests arecarried out to calibrate the point load tests.Point load test results are not acceptable if thefailure plane lies partially along a pre-existingdiscontinuity in the rock, or is not coincident withthe line between the platens. For tests in weak rockwhere the platens indent the rock, the test resultsshould be adjusted by measuring the amount ofindentation and correcting the distance D.

3.3.2Compressive strength of fractured rock

Fractured rock will, of course, have a much lowercompressive strength than intact rock. Studies havebeen conducted on the load capacity of mine pillarswhich demonstrate the decrease in strength thatoccurs as the sample size is increased (Bieniawski,1968; Pratt, 1972). These tests show that once the


side length is greater than about 1 m (3 ft) there islittle decrease in strength with larger samples(Fig. 3.12). The minimum strength is about 20–30%of the maximum strength measured on core samples,provided that the sample contains no through-goingplane that would control the rock strength.

It is difficult to determine the compressive strengthof fractured rock in the laboratory. First, it isnecessary to obtain undisturbed samples of fracturedrock, and then second to test a sufficiently largesample that is representative of the discontinuityconditions. To avoid the expense of carrying out

Figure 3.11 Point load testing (ISRM, 1985): (a) point load test equipment; and (b) relationship between sampleequivalent core diameter De and size correction factor kPLT.


laboratory testing, it is usual to use empiricalrelationships between the rock mass strength andthe discontinuity characteristics as described in thissection.For most foundations, the rock is loaded in atriaxial stress field consisting of the foundation loadand the confinement produced by the surroundingrock. Therefore, in calculating the bearing capacityof the rock, it is necessary to have a strengthcriterion that is expressed in terms of the principalstresses acting on the rock, and takes into accountthe characteristics of the fractured rock mass. Sucha criterion will allow the state ofstress at any pointin the foundation to be compared with the rockmass strength at that point, which will identify areaswhere there is excessive compressive stress, ortensile stress, so that the design can be modifiedaccordingly. This approach is useful in the case ofdam foundations where the stress distribution isusually non-uniform across the bearing surface, andalso for foundations located on the crest of steepslopes.A strength criterion for fractured rock has beendeveloped by Hoek (1995, 1988) and Hoek andBrown (1988) which can be applied readily to thedesign of foundations. This is an empirical criterionthat has been developed by trial and error and is

based on the observed behavior of rock masses,model studies to simulate the failure mechanism ofjointed rock, and triaxial compression tests offractured rock. Hoek’s expression for the maximumprincipal effective stress at failure is:

(3.8)where is the minimum principal stress orconfining stress; su(r) is the uniaxial compressivestrength of the intact rock; and m and s aredimensionless constants.It is assumed that failure process is defined by themajor and minor principal stresses and that theintermediate principal stress has no particularinfluence on failure (Jaeger and Cook, 1976).The constants m and s depend on both the rock typeand the discontinuity characteristics. The values ofm and s given in Table 3.7 are those of disturbedrock because of the loosening that occurs in surfaceexcavations made for foundations. In usingTable 3.7 it is necessary to define the condition ofthe rock mass in terms of one of five categories ofrock type, one of six categories of rock quality, andthe intact rock strength. The rock quality categoriesvary from intact rock, to weathered, heavilyfractured rock, or rock fill, with each categorydefined either by a description of the rock mass or

Figure 3.12 Effect of specimen size on measured uniaxial strength (Heuze, 1980).


by the RMR quality rating (see Table 3.5). Wherepossible, the strength values determined fromequation 3.8 are compared with other sources of

rock strength such as those obtained from the backanalysis of failures of slopes

Table 3.7 Approximate relationship between rock mass quality and material constants (Hoek and Brown, 1988)


in similar geological conditions (see Fig. 3.21 and Table 3.8).

Figure 3.13 Strength of fractured rock (Hoek, 1983).


The typical shape of the strength envelope definedby equation 3.8 is shown in Fig. 3.13. The steepgradient of this curve clearly demonstrates thatincreasing confining pressure has a significanteffect on improving the strength and bearingcapacity of the rock. Foundations on steep slopeswhere there is little confining pressure andloosening of the rock mass can occur, will have alower bearing capacity than foundations on acontinuous horizontal surface where the bearingrock is confined. The curve in Fig. 3.13 also showsthat the uniaxial compressive strength of the rockmass su(m) is defined by the following equation:

(3.9)or

(3.10)

Equation 3.10 shows that the ratio su(m)/su(r)diminishes rapidly as the rock becomes morefractured, and that the rock mass has essentiallyzero compressive strength when the discontinuityspacing is less than about 0.3 m (parameter

. This relationship between thecompressive strengths of the rock mass and intactrock can be compared with the rapid decrease inrock mass strength with specimen size shown inFig. 3.12.

3.4Shear strength

Where a structure is located on a steep slope, orwhere lateral loads are substantial such as in a damfoundation, shear failure of the entire foundationcan take place even though the bearing stress is wellbelow the allowable bearing capacity of the rock.The shear failure surface may, in strong, jointedrock, lie on a single discontinuity oriented sub-parallel to the direction of the applied load (seeFig. 3.1(e)), or in weak, closely fractured rockfollow a path comprising both discontinuities andintact rock (see Fig. 3.1(b)). Shear type failures mayalso occur where a cavity or bed of very weakmaterial underlies the rock in the bearing area and a

disk of competent rock punches through into thecavity (see Fig. 3.1(f)).

3.4.1Mohr-Coulomb materials

For all shear type failures, the rock can be assumedto be a Mohr-Coulomb material in which the shearstrength of the sliding surface is expressed in termsof the cohesion c and the friction angle . Theshear strength t developed when an effective normalstress a’ is acting on a sliding surface is (Fig. 3.14(a)):

(3.11)Equation 3.11 is expressed as a straight line onFig. 3.14(b) which also shows the relationshipbetween the available shear strength t and the actualshear stress acting in the foundation tf. Thefoundation will be stable when the ratio t/tf, or thefactor of safety FS, is greater than 1.0. Figure 3.14(b) also illustrates how the factor of safety willdiminish if the normal stress is reduced by waterpressures acting on the shear plane, or the cohesionis lost as a result of heavy blasting duringconstruction.The following sections describe typical values forfriction angle and cohesion and methods ofmeasuring these rock properties.

3.4.2Shear strength of discontinuities

If structural mapping identifies discontinuities in afoundation on which shear type failures may takeplace, it will be necessary to determine the friction angle and cohesion of the discontinuity surface inorder to carry out stability analyses, and designremedial work if required. Data collected in themapping program will include the roughness of thediscontinuity surface, the strength of the rock on thesliding surface, and the thickness and characteristicsof any infilling material (Appendix II). All theseparameters modify the shear strength of thediscontinuity surfaces.(a) Friction angle


For a planar, clean discontinuity in rock, thecohesion will be zero and the shear strength will bedefined solely by the friction angle. The followingare typical ranges of basic friction angles for avariety of rock types (Barton, 1973; Stimpson,1975). Generally, fine grained rock and rock with ahigh mica content will tend to have a low frictionangle, while course grained, strong rock will have ahigh friction angle. The friction angles listed belowshould be used as a guideline only because actualvalues will vary widely with site conditions.

1. Low friction rocks—friction angle about 20–27°:

schist, high mica content;shale;marl;

2. Medium friction rocks—friction angle about27–34°:

sandstone;siltstone;chalk;gneiss;slate;

3. High friction rocks—friction angle about 34–40°:

basalt;granite;limestone;conglomerate.

(b) Surface roughnessAll natural rock surfaces are rough and irregular tovarying degrees. These surface irregularities, whichare given the general term asperities, produceinterlock between discontinuity surfaces which cancontribute significantly to their shear strength(Patton, 1966). Asperities can be considered in theirsimplest form as a series of saw teeth in which theinclination of the face of each tooth is at an angle i.When normal and shear forces are applied to ablock of rock containing a saw-tooth discontinuitywith no infilling, the shear strength of thediscontinuity is:

(3.12)This relationship shows that effective friction angleof a rough surface is equal to the sum of the basicfriction angle of the rock and the inclination of theasperities (Fig. 3.15). Methods of measuring theinclination angle i of natural discontinuities whichconsider both the direction of sliding and the scaleof irregularities are described in Section 4.2.Another factor to consider in determining thefriction angle of a rough surface is that theasperities may be sheared off as displacementoccurs with a consequent reduction in the frictionangle. With increasing stress levels, there is atransition from dilation to shearing, and the degreeto which the asperities are sheared off will dependon both the magnitude of the normal force inrelation to the compressive strength of the rock onthe discontinuity surface, and the displacement

Figure 3.14 Shear strength of a Mohr-Coulomb material: (a) normal (sf) and shear (tf) forces acting on sliding surface infoundation; and (b) Mohr diagram of linear strength envelope.


distance. A rough discontinuity that is initiallyundisturbed and interlocked will have a frictionangle of known as the peak shear strength.With increasing normal stress and displacement theasperities will be sheared off and the friction anglewill progressively diminish to a minimum value ofthe basic, or residual friction angle of the rock, (Fig. 3.15).Barton (1973) studied the shear strength behavior ofartificially produced rough, clean joints anddeveloped the following empirical equation:

(3.13)

where JRC is the joint roughness coefficient, JCS isthe compressive strength of the rock on thediscontinuity surface, and a’ is the applied normalstress on this surface. The value of the coefficientJRC can be estimated by comparing the conditionof the discontinuity surface with the description ofthe surface and standard profiles with JRC valuesranging from 20 to 5 as shown in Fig. 3.16. Thevariation in the degree of roughness shown on the

profiles is a function of both the wavelength andamplitude of the asperities. Rough surfaces havehigh amplitude, short wavelength asperitiescompared with smoother surfaces, and the degree ofroughness can be expressed approximately as theratio between the amplitude and the wavelength.The amplitude/wavelength ratio varies from a highvalue of about 30% for a JRC of 20 (surface (a)), toa low value of about 3% for a JRC of 5 (surface (c)).The term (JRC log10 JCS/s') is equivalent to theroughness angle i, and is equal to 0 at high stresslevels when , and the asperities aresheared off. At low stress levels the ratio JCS/s'tends to infinity and the roughness component ofthe strength becomes very large. For realistic designvalues of the roughness component, the term should not exceed about 50°, and the useful rangefor the ratio JCS/s' is between about 3 and 100. (c) CohesionThe preceding section discussed rough, cleandiscontinuity surfaces with rock to rock contactand no infilling, in which the cohesion is zero andthe shear strength is composed solely of the friction

Figure 3.16 Definition of joint roughness coefficient, JRC (Barton, 1973): (a) rough undulating—tension joints, roughsheeting, rough bedding,

; (b) smooth undulating—smooth sheeting, non-planar foliation, undulating bedding,

; and (c) smooth nearly planar—planar shear joints, planar foliation, planar bedding,

.angle of the rock material. However, cohesion isdeveloped on discontinuity surfaces in manyconditions and because even a small cohesivestrength can have a significant effect on the shearstrength of rock, it is important that this rock

strength parameter be properly accounted for indesign. In the worked example discussed in Section6.2 there is a cohesion of just 25 kPa (3.6 p.s.i.) on asliding surface with an area of 190 m2 (2045 ft2),and the shear strength due to cohesion is 4.8 MN (1.


07E6 lbf). The frictional component of the shearstrength due only to the weight of the block

is 13.3 MN (3E6 lbf) so thecohesive strength is about one quarter of the totalshear strength. This illustrates the importance ofboth measuring cohesion and using careful blastingduring construction that does not disturb the surfaceand diminish the cohesion.The following are some of the conditions in whichcohesion is developed on sliding surfaces. For intactrock and jointed, strong rock masses with nothrough-going discontinuities parallel to the slidingsurface, the cohesion will usually have values ofseveral hundred kilopascals and at these highstrengths there is very little risk of shear failure. Forrough rock surfaces, an apparent cohesion isdeveloped as the asperities are sheared off whenmovement occurs. The magnitude of the apparent

cohesion is the intercept on the shear stress axis of atangent to the curved shear strength envelope on aMohr diagram (Fig. 3.22); the apparent cohesionwill increase with increasing normal stress until theresidual strength of the surface is reached. Fordiscontinuities containing infillings, the cohesionwill depend on both the characteristics andthickness of the infilling as described in the nextsection.An indirect method of determining the cohesion ofintact rock is to measure the uniaxial compressivestrength in a compression machine or point loadtester, and tensile strength by means of the Braziliantest on disks of core. This data can be used togenerate a Mohr’s envelope, the intercept of whichwith the shear stress axis gives the cohesion. Anapplication of this method was in the design offootings located on weak limestone beds overlyingcompressible materials where punching failure of

Figure 3.15 Effect of surface roughness and normal stress on the friction angle of a discontinuty surface.


the limestone was likely (Kaderabek and Reynolds1981). To account for the reduced strength of the in-place, fractured rock, the design shear strength wastaken as 20% of the strength determined from thelaboratory results. This indirect method was usedbecause of the difficulty of performing direct sheartests on intact rock.(d) InfillingsIf the discontinuity contains an infilling then theshear strength properties of the discontinuity areoften modified, with both the cohesion and frictionangle of the surface being influenced by thethickness and properties of the infilling. Forexample, for a clay-filled fault zone in granite, itwould be assumed that the shear strength of thediscontinuity would be that of the clay and not thegranite. In the case of a healed, calcite-filleddiscontinuity, a high cohesion would only be usedin design if it were certain that the discontinuitywould still be healed after any disturbance causedby blasting in preparing the foundation. Thepresence of infillings in a foundation can have asignificant effect on performance and it is importantthat infillings be identified in the investigationprogram, and appropriate strength parameters usedin design. If the infilling thickness is more thanabout 25–50% of the amplitude of the asperities,then there will be little or no rock to rock contact,and the shear strength properties of the discontinuitywill be the properties of the infilling.Figure 3.17 shows the results of direct shear testscarried out to determine the peak friction angle andcohesion of filled discontinuities (Barton, 1974).Examination of these tests shows that the results canbe divided into two groups as follows:

1. Clays—montmorillonite and bentonitic clays,and clays associated with coal measures havefriction angles ranging from about 8° to 20° andcohesion ranging from 0 to about 200 kPa(4000 p.s.f.). Some cohesion were measured ashigh as 380 kPa (8000 p.s.f.).

2. Faults, shears and breccias—the materialformed in f ault zones and shears in rocks suchas granite, diorite, basalt, and limestone will

contain clay as well as granular fragments.These materials have friction angles rangingfrom about 25° to 45°, and cohesion rangingfrom 0 to about 100 kPa (2000 p.s.f.). Thecoarser grained rocks such as granites tend tohave higher friction angles than finer grainedlimestones.

Some of the tests also determined residual shearstrength values. It was found that the residualfriction angle was only about 2–4° less than thepeak friction angle, while the residual cohesion wasessentially zero.An additional factor to consider regarding shearstrength is the shear strength-displacement behaviorof the discontinuity infilling. In analyzing thestability of foundations, this behavior will indicatewhether there is likely to be a reduction in shearstrength with displacement, possibly resulting infailure following a small amount of movement.Filled discontinuities can be divided into twogeneral categories, depending on whether there hasbeen previous displacement (Nicholson, 1983;Barton, 1974). These categories are furthersubdivided into either normally-consolidated (N-C)or over-consolidated (O-C) materials(Transportation Research Board, 1996) as follows.

1. Recently displaced discontinuities—thesetypes include faults, shear zones, claymylonites, and bedding-surface shears. In faultsand shear zones, the infilling is formed by theshearing process, which may have occurredmany times and produced considerabledisplacement. The gouge formed in this processmay include both clay-size particles, andbreccia with the particle orientation andstriations of the breccia aligned parallel to thedirection of shearing. In contrast, mylonites andbedding-surface slips are discontinuities thatwere originally clay bearing and along whichslip occurred during folding or sliding(Fig. 3.18).

For these types of discontinuities their shearstrength will be at or close to the residual


strength and there will be little reduction instrength with further shearing (Fig. 3.18, graphI). Any cohesive bonds that existed in the claydue to previous over-consolidation will havebeen destroyed by shearing, and the infillingwill be equivalent to the normally consolidatedstate. However, with increased water content,strain softening may occur resulting in a furtherreduction in strength.

For infillings of displaced discontinuities,peak shear strengths may be used in design.

2. Undisplaced discontinuities—infilleddiscontinuities that have undergone no previousdisplacement include igneous and metamorphicrocks that have weathered along discontinuitysurfaces to form clay layers. For example,diabase weathers to amphibolite and eventu allyto clay. Other undisplaced discontinuities

include thin beds of clay and weak shales thatare sometimes found with sandstone ininterbedded sedimentary formations.Hydrothermal alteration is another process thatforms infillings that can include low-strengthmaterials such as montmorillonite, and high-strength materials such as quartz and calcite.

The infillings of undisplaced discontinuitiescan be divided into normally-consolidated (N-C) and over-consolidated (O-C) materials thathave significant differences in peak strengthvalues, but similar residual strengths (Fig. 3.18,graphs II and III). While the peak shear strengthof over-consolidated clay infillings may behigh, there can be a significant loss of strengthdue to softening, swelling and pore-pressurechanges on unloading. Unloading occurs whenrock is excavated for a foundation or slope, for

Figure 3.17 Peak shear strength of filled discontinuities (Barton, 1974). Note that pairs of numbers indicate ranges ofstrength.


example. Strength loss also occurs ondisplacement of brittle materials such ascalcite, but there is little strength loss with sandand gravel infillings.

For infillings of undisplaced discontinuities,residual shear strengths should be used indesign.

3.4.3Shear strength testing

The friction angle of a rock surface can bedetermined in the laboratory using the direct sheartest equipment shown in Fig. 3.19. This is portableequipment that can be used in the field if required,and is ideally suited to testing samples withdimensions up to about 75 mm (3 in), such as NQand HQ drill core. The most reliable values areobtained if a sample with a smooth, planar surface

Figure 3.18 Simplified division of filled discontinuities into displaced and undisplaced, and normally-consolidated(N-C) and over-consolidated (O-C) categories.


is used because it is found that with an irregularsurface, the test results can be difficult to interpret.The test procedure consists first of using plaster ofParis or sulphur to set the two halves of the samplein a pair of steel boxes. Particular care is taken thatthe two pieces of core are in their original, matchedposition and the discontinuity surface is exactlyparallel to the direction of the shear force. A normalload is then applied using the cantilevers and theshear load is gradually increased until a slidingfailure occurs. Dial gauges or LVDT’s (linearvariable differential transformers) are used tomeasure both the shear and horizontaldisplacements from which a pair of plots of sheardisplacement against shear stress, and sheardisplacement against normal displacement isproduced (Fig. 3.20(a)). Examination of the shearstress-shear displacement plot will usually show anapproximate peak shear stress. The normal stress atthis shear stress value is calculated from the appliednormal load and the contact area, with a correctionmade for the decrease in contact area that takesplace with shear displacement. The sample is then

reset to its original position, the normal loadincreased and another shear test conducted. Eachtest will produce a pair of peak shear stress-normalstress points which are plotted to determine thefriction angle of the surface (Fig. 3.20(b)).The plots of shear and normal displacement (ds anddn respectively) are used to estimate the surfaceroughness angle (i) of the sample as follows:

(3.14)This value of i is then subtracted from the frictionangle calculated from the plot of shear and normalstresses at failure to obtain the basic friction angleof the rock. In some cases, the shear test can beconducted on a sawn sample so that there is noroughness component of the friction angle.The first test on any sample will often give a higher(peak) shear strength (symbol than thesubsequent tests (residual shear strength, symbol because the interlock between the surface asperitieswill be progressively sheared off with each test atincreasing normal loads as shown by the curvedshear strength envelope shown in Fig. 3.20(b). The

Figure 3.19 Equipment for performing direct shear tests on rock fractures with diameters up to about 75 mm. Truevertical displacement= gauge reading×(a/b).


degree to which the asperities are sheared off will, ofcourse, depend on the ratio JCS/s' (refer to equation3.13), with the asperities being sheared off readilywhen the value of the ratio is low. Note that the

shear strength envelope for a clean discontinuitywith no cohesion passes through the origin of theMohr diagram.It is rarely possible to measure the cohesion of a

Figure 3.20 Typical results of a direct shear test to determine the friction angle of a fracture surface: (a) plots of sheardisplacement against shear stress and normal displacement; and (b) plot of normal stress against shear stress.


surface with the direct shear test because if thecohesion is very low, it is difficult to obtain anundisturbed sample, and with higher cohesion, theplaster of Paris holding the sample is likely to failbefore the sample shears.

3.4.4Shear strength of fractured rock

Structures founded on fractured rock containing nodistinct discontinuity surface on which sliding cantake place may still fail in shear if the shear strengthof the rock mass is exceeded. The rupture surfacewill be composed of both natural discontinuities andshearing through intact rock. Because of thedifficulty and expense of sampling and testing largesamples of fractured rock, two em-pirical methodsof determining the friction angle and cohesion ofrock masses are described in this section. In bothmethods it is necessary to categorize the rock massin terms of the intact rock strength and thecharacteristics of the discontinuities. This requiresconsiderable experience and it is advisable tocompare the strength values obtained by bothmethods to check that consistent values are used indesign.(a) Back analysis of failuresThe strength of a rock mass can be found bycarrying out a back analysis of a failed slope orfoundation. This involves performing a stabilityanalysis with the factor of safety set at 1.0 and using

available information on the position of the failuresurface, the ground water conditions at the time offailure, and the foundation load if applicable. Thereare, of course, two unknowns in this analysis: thefriction angle and the cohesion. By carrying out anumber of stability analyses with a range ofcohesion values it is possible to calculate acorresponding value for the friction angle (at and prepare a plot of cohesion against frictionangle. From this plot a pair of values can beselected for design purposes. Hoek and Bray (1981)describe the back analysis of three different slopefailures from which rock mass strengths weredetermined (Section 1.6.3).If it is not feasible to carry out a back analysis insimilar geological conditions to that in which thefoundation is to be constructed, it is possible to usepublished results of strength values as shown inFig. 3.21. Figure 3.21 shows the results of backanalyses of slope failures in a variety of geologicalconditions, and the shear strength parameters (c and

values) calculated at failure at the sites listed inTable 3.8. The properties of the rock mass arecategorized according to the strength of the intactrock, and the discontinuity characteristics—spacing, orientation and surface properties.By adding additional points to Fig. 3.21 for localgeological conditions, it is possible to draw up areadily applicable rock mass strength design chartfor shear type failures.

Table 3.8 Source of shear strength data plotted in Fig. 3.21

Point number Material Location Slope heightm (ft)

Reference

1 Disturbed slates andquartzites

Knob Lake, Canada – Coates et al. (1965)

2 Soil – Whitman and Bailey(1967)

3 Jointed porphyry Rio Tinto, Spain 50–110 (150–360) Hoek (1974)4 Ore body hanging wall in

granitic rocksGrangesberg, Sweden 60–240 (200–800) Hoek (1974)

5 Rock slopes with slopeangles of 50° to 60°

300 (1000) Ross-Brown (1973)

6 Bedding planes inlimestone

Somerset, England 60 (200) Roberts and Hoek (1972)


Point number Material Location Slope heightm (ft)

Reference

7 London clay England – Skempton andHutchinson (1969)

8 Gravelly alluvium Pima, Arizona – Hamel (1970)9 Faulted rhyolite Ruth, Nevada – Hamel (1971a)10 Sedimentary series Pittsburgh, Pennsylvania – Hamel (1971b)11 Koalinized granite Cornwall, England 75 (250) Ley (1972)12 Clay shale Fort Peck Dam, Montana – Middlebrooks (1942)13 Clay shale Gradiner Dam, Canada – Fleming et al. (1970)14 Chalk Chalk cliffs, England 15 (50) Hutchinson (1970)15 Bentonite/clay Oahe Dam, South Dakota – Fleming et al. (1970)16 Clay Garrison Dam, North

Dakota– Fleming et al. (1970)

17 Weathered granites Hong Kong 13–30 (40–100) Hoek and Richards(1974)

18 Weathered volcanics Hong Kong 30–100 (100–300) Hoek and Richards(1974)

19 Sandstone, siltstone Alberta, Canada 240 (800) Wyllie and Munn (1979)20 Argillite Yukon, Canada 100 (300) Wyllie (1977)

(b) Curved shear strength envelopes (Hoek-Brown strength criterion)In conditions where the characteristics of a fracturedrock mass can be defined in terms of an RMR rating(Table 3.5), the shear strength can be defined by acurved envelope given by the following equation(Hoek, 1998, 1983):

(3.15)

where t is the shear stress at failure, and is theinstantaneous friction angle at given values of t ands'. The value of is the inclination of the tangent tothe Mohr failure envelope at the point (s, t) asshown in Fig. 3.22 and is given by:

(3.16)

where

(3.17)

(3.18)

The dimensionless constants m and s depend on therock type and the degree of fracturing of the rockmass and are defined in Table 3.7 in Section 3.3.The instantaneous cohesion ci is the intercept of theline defining the instantaneous friction angle on theshear stress axis, and is given by:

(3.19)The features of the curved shear strength envelopeare that at low normal stress levels, the blocks ofrock are interlocked and the friction angle is high,whereas at higher normal stress levels, shearing ofthe rock is initiated with the result that the frictionangle diminishes. The cohesion progressivelyincreases with the normal stress as a result of thegreater confinement of the rock mass.The procedure for using the curved strengthenvelopes in stability analysis is to determine thenormal stress levels acting on a potential failuresurface in the foundation and calculate theinstantaneous cohesions and friction angles in thisstress range. The stability analysis is carried out inthe normal manner, except that a range of ci and values are used corresponding to the variation in


normal stress distribution along the sliding surface(see Chapter 6).

3.5Tensile strength

Tensile stresses are very rarely permitted in thedesign of structures in rock because the tensile

Figure 3.21 Relationship between friction angles and cohesive strength mobilized at failure for the analyzed slopeslisted in Table 3.8 (Hoek and Bray, 1981).


strength of a fractured rock mass is effectively zero.Some loading conditions that will result in thedevelopment of tensile stresses are tie-downanchors for structures subject to uplift loads such astowers and submerged tanks, and overturningmoments as a result of high wind/seismic/waterloading on tall structures. While tensile testing of rock is not commonlycarried out, the following is a summary of possiblemethods. Direct testing in pure tension gives themost reliable results, and can be performed bygluing steel platens to the ends of a core sample.The platens are attached to the testing machine withchains or cables so that there are no bendingmoments developed as the load is applied. Indirecttesting methods include bending tests on lengths ofcore, and the Brazilian test which involves applyinga diametral compressive stress to a disk of rock. Theindirect test methods are relatively simple toperform but the test results can be difficult tointerpret. In general, it is recommended that the testmethod simulate the actual loading condition in thefoundation as closely as possible.Lama and Vutukuri (1978a, b) have carried out asurvey of tensile strength tests carried out onlaboratory samples of intact rock. Comparison ofthese results with compressive strengths of intactrock shows that the ratio between the tensile andcompressive strengths st(r)/su(r) lies within a narrow

range. The majority of these rocks have tensilestrengths which are about 4–7% of the compressivestrength, while some sedimentary rocks show st(r)/su

(r) ratios of 14–16%. One test carried out on schistshowed st(r)/su(r) ratios of 6% and 1% in directionsperpendicular and parallel respectively to thefoliation.The non-linear Mohr strength envelope developedby Hoek (Hoek and Brown, 1988; Hoek, 1983) alsoapproximates the tensile strength of a fractured rockmass as:

(3.20)Evaluation of this equation shows that for a goodquality rock mass—slightly weathered rock,discontinuity spacing 1–0.3 m ,

—and a compressive strength of intactrock of 80 MPa, the tensile strength isapproximately 0.4 MPa . Thisresult illustrates that the tensile strength of thefractured rock mass is significantly less (1/200) thanthe compressive strength of the intact rock.

3.6Time-dependent properties

The design of a foundation must consider its longterm performance because, unfortunately, rockproperties change with time (Deere and Patton,

Figure 3.22 Non-linear Mohr envelope for shear strength of fractured rock mass (Hoek, 1983).


1971). These property changes include weatheringthat results in loss of bearing capacity, swellingresulting in uplift of the structure, creep resulting inlong term settlement and fatigue resulting infracture of the rock (Fig. 3.23). The following is adiscussion on the geological, environmental andmechanical conditions that can cause foundationconditions to change with time (see Section 5.3).

3.6.1Weathering

Weathering can be either a surface phenomenon inwhich case it may be visible and thereforecontrollable, or it may occur beneath the exposedsurface and can be difficult to detect (Fig. 3.23(a)).In either case, the depth and extent of weatheringcan be highly variable and in conditions where therock is susceptible to weathering, thoroughexploration programs are required to detect anyzones of weakness such as solution cavities, scourchannels, compressible seams or low strengthformations. Table 3.9 lists weathering grades anddescriptions based on visual examination of fieldsamples that can be used in investigation programs.The processes of weathering are divided into thosewhich cause disintegration and those which causedecomposition as described in this section (Krynine

and Judd, 1957).(a) Disintegration weatheringDisintegration of rock is the result of cyclicalchanges in environmental conditions such aswetting and drying, and freezing and thawing. Inaddition, weathering will be accelerated where thefoundation is exposed to wind or flowing waterresulting in fragments of weathered rock beingcontinuously removed to expose a new surface andstart another weathering cycle. Rock types whichare susceptible to disintegration weathering aresedimentary rocks such as weak sandstones andshales, particularly if they contain swelling clay,and metamorphic rocks with a high mica content.(b) Decomposition weatheringDecomposition refers to the changes in rockproduced by chemical agents such as oxidation,hydration, carbonation and the chemical effects ofvegetation. Oxidation is the process wherebyoxygen is added to the minerals composing the rockas seen, for example, as yellow discoloration inrocks containing iron. An example of hydration,which is the chemical addition of water to minerals,is the decomposition of the feldspar in granite toform clay of the kaolinite type. Carbonation is thesolution of the rock material by water containing aconsiderable amount of carbon dioxide, which is thecase in most surface waters.

Table 3.9 Weathering and alteration grades (ISRM, 1981)

Grade Term Description

I Fresh No visible sign of rock material weathering; perhaps slight discoloration on majordiscontinuity surfaces.

II Slightly weathered Discoloration indicates weathering of rock material and discontinuity surfaces. Allthe rock material may be discolored by weathering and may be somewhat weakerexternally than in its fresh condition.

III Moderately weathered Less than half of the rock material is decomposed and/or disintegrated to a soil.Fresh or discolored rock is present either as a discontinuous framework or ascorestones.

IV Highly weathered More than half of the rock material is decomposed and/or disintegrated to a soil.Fresh or discolored rock is present either as a discontinuous framework or ascorestones.

V Completely weathered All rock material is decomposed and/or disintegrated to soil. The original massstructure is still largely intact.

VI Residual soil All rock material is converted to soil. The mass structure and material fabric aredestroyed. There is a large change in volume, but the soil has not been significantlytransported.


Rock types which have a low solubility aredolomite, calcite and strong limestone, while somehigh-solubility rocks are halite, gypsum and sylvite.Vegetation also contributes to weathering becauseorganic acids formed when vegetation decays tendto increase the solution power of natural water.Another type of decomposition weathering is that ofrocks containing sulfides such as pyrrhotite which

release sulphuric acid that attacks concrete andsteel, and has harmful environmental effects if theacidic water reaches the ground water.Where weathering occurs at depth in thefoundation, it will preferentially be initiated alongdiscontinuities which are the flow paths for groundwater seepage. Where the rock is soluble, groundwater seepage may develop cavities in the

Figure 3.23 Time-dependent effects on rock foundations: (a) weathering: surface disintegration and solution; (b) upliftdue to swelling of clay seams; (c) settlement due to rock creep; and (d) fatigue failure due to cyclic loading.


foundation, while in other cases there may bereduction in shear strength as low strength materialsform on the discontinuity surfaces. Particularattention should be paid to weathering whereconstruction, such as filling of a reservoir, willchange the ground water conditions resulting insaturation and increased seepage that mayaccelerate weathering and rock degradation.Common methods of controlling weathering offoundation rock are protection of exposed bearingsurfaces with shotcrete, grouting to minimizeseepage, and burying the foundation below the frostlevel. Shotcrete is discussed in Section 10.4 inconstruction procedures, while grouting is discussedin Chapter 7, related to the construction of damfoundations.

3.6.2Swelling

The causes of swelling in rock can be divided intotwo broad categories related either to changes instress conditions, or to chemical reactions (Lindner,1976). The effect of swell on structures may beoverall or differential heave (Fig. 3.23(b)), as wellas the development of external pressures in rigid,buried structures. For example, measurement ofswelling pressures in Jurassic claystone haverecorded values as high as 1400 kPa (200 p.s.i.) aftera period of one day (Madsen, 1979) and heaves ofmore than 100 mm (4 in) have been measured. Theusual method of foundation construction onswelling rock is the use of piles that extend to belowthe depth of potential swelling. As described inSection 8.5, the piles must be capable ofwithstanding any tensile forces developed byswelling of the ground through which they pass.Also of importance in design is the attachment ofall ground supported appurtenances such asservices, tunnels and driveways that will undergorelative movement with respect to the pile supportedstructure.(a) Stress reliefThere are two common causes of stress relief inrock foundations. First, changes in ground water

conditions, as may be caused by filling a reservoirin the case of dams, or fluctuations in river levels inthe case of bridges, can result in internal non-equilibrium swell. Second, reduction in externalforces as a result of making a deep excavation, forexample, may cause viscoelastic heave.Swelling due to reduction of internal forces in intactrock can occur in rock types such as mudstones,shales and weakly-cemented sandstones. Theserocks may undergo large volumetric increases uponthe addition of water in a process which is unrelatedto chemical reaction; such swelling is also timedependent. The primary reasons for swelling arecation hydration of the particle structure, theattraction of water to the surface of particles, andthe interaction of particle force fields. All thesephenomenon are influenced by the presence orabsence of water. Another factor influencing swellis the cementation of the rock and its ability toresist the tendency for the particles to separate uponcontact with water.Heave may also occur as the result of swelling ofclay contained in faults or weathered seams. Typesof clay that exhibit swelling behavior aremontmorillonite, saponite and vermicullite, whilenon-swelling clays are kaolinite, illite and chlorite(Mitchell, 1976).The potential for swelling can be relatedapproximately to the Atterburg limits and the clayfraction of the sample. When the plasticity indexand the clay content are both greater than about 20–30%, the potential for swelling may be high (Holtzand Gibbs, 1956; van der Merwe, 1964).Identification of swelling clays can also be carriedout using X-ray diffraction analysis which will showthe proportions of the different types of clay presentin a sample.Rocks may also swell as a result of stress reliefwhich takes the form of viscoelastic deformation ofthe rock on removal of the confining stress. Forexample, in eastern Canada where the ratio of thehorizontal to vertical stress field can be as high asone order of magnitude (Lo, 1978; Sbar and Sykes,1973), excavation of a few meters of overburdencan induce the floor of excavations to buckle or


‘pop-up’, and the sides of excavations to movehorizontally. The heave can take the form of someinstantaneous movement, followed by creep. Creepcan be partially suppressed by applying an externalpressure with tensioned rock anchors, for example(Trow and Lo, 1988). Creep is discussed further inSection 3.6.3.(b) Swelling related to chemical reactionsSwelling can result from chemical reactions such ashydration, oxidation or carbonation which create by-products that occupy a larger volume than theoriginal materials. For example, the addition ofwater to some types of sulfides can cause very largedeformations and pressures (Dougherty andBarsotti, 1972). Hydration causes the conversion ofanhydrite (CaSO4) to gypsum (CaSO4.2H2O) whichoccurs with an expansion in volume which can takeplace violently (Brune, 1967). Einfalt et al. (1979)discuss tests to measure swelling pressure and theuse of sodium chloride solution as a drilling fluid toobtain undisturbed samples of these sensitivematerials. Another chemical reaction resulting inswelling is the decomposition of ultrabasic, mainlyolivine bearing rock, into serpentine (Widerhofer,1972).

3.6.3Creep

Creep is the term given to the slow and continuousdistortion of rock in response to shearing stresses.Under these conditions rock behaves partly as aviscous liquid in which the relationship between theshear stress t and the shear strain rate e is

(3.21)

where ? is the dynamic viscosity which has thedimensions force-time/length2. Most rocks exhibitboth instantaneous (elastic) deformation anddelayed deformation when loaded, and are knowntherefore as viscoelastic.The general form of a complete strain curve for rockhas up to four components (Fig. 3.23(c)). For stresslevel s1, there is first, the instantaneous strain due tothe elastic deformation of the rock, and this isfollowed by three time dependent straincomponents. During primary creep (I) the strain ratediminishes with time (transient creep), which isfollowed by secondary creep (II) during which thestrain rate is constant (steady state creep). If theapplied stress is near the peak strength, the rock canexhibit tertiary creep (III) in which the strain rateincreases with time (accelerating creep) andeventually rupture occurs. At lower stress levels (s2in Fig. 3.23(c)), deformation will comprise anelastic component, followed by short period ofprimary creep after which the strain is constant.Of great importance in the design of foundations isthe stress level that will initiate creep. It is normalpractice to design footings such that the bearingpressure is well below that which would develop theonset of creep. As a guideline on allowablepressures, Table 3.10 shows transition pressuresfrom brittle to ductile behavior at roomtemperature. Rock types that are susceptible tocreep under low pressures are weak clay shales andtar sands, while salt will creep at all stress levels. Aseries of creep tests were conducted by Hardy et al.(1970) on samples of intact limestone

Table 3.10 Brittle to ductile transition for rocks (Goodman, 1980)

Rock type Gauge pressure,MPa (p.s.i.)

Rock salt 0 (0)Chalk <10 (<1500)Compaction shale 0–20 (0–3000)Limestone 20–100 (3000–15 000)Sandstone >100 (>15 000)Granite


with a uniaxial compressive strength (su(r)) of 62–76 MPa (9000–11 000 p.s.i.). These tests showedthat no creep occurred at stress levels less than about40% of su(r) and that secondary creep was notinitiated at stress levels below about 60% of su(r).If creep were to occur in a foundation, it would bepreferable that it be primary or transient creep suchthat the creep rate rapidly diminished to zero. Therate of primary creep at time t is approximated bythe following equation:

(3.22)where and a are determined by curve fitting totransient laboratory or in situ creep data. Thisequation does not express any physical mechanismof creep, but assumes that the decay rate is a linearfunction of the currently remaining transient creepconcentration.(a) Creep mechanismsThe mechanism of creep, which is related to boththe mineralogy and crystal structure of rock, issomewhat different for different rock types(Dusseault and Fordham, 1993).• Strong rock In rock containing low porositysilicates the dominant creep mechanism ismicrocrack generation and propagation along grainboundaries, a cumulative and irreversible damagingprocess that either stabilizes with no further strain(e?0), or accelerates to exhibit tertiary creep andfailure (e?8). Under conditions usually found infoundations, these rock cannot display steady-statecreep. Dilation accompanies creep in low porosityrocks as polycrystal debonding and microcrackpropagation results in volume increases. Thepresence of water reduces surface energyrequirements for microcrack propagation, andapparently ‘dry’ in situ rocks have sufficientmoisture to aid hydration of covalent silica bonds

withconsequent cumulative and irreversible damage.• Carbonates Carbonates are highly soluble inmildly acidic waters and have excellent cleavagecompared with most silicates. Thus they canmore easily display dislocation behavior,microcracking, crushing, dissolution and fabricdeterioration. Under high stresses and with water

flow in joints, carbonates creep through dissolutionand plastic yield of reduced area contacts. Marls andargillaceous limestones of intermediate porositymay show rapid creep rates, depending on claycontent and whether it exists in discrete bandsrather than as a disseminated constituent.• Sandstones Strong, quartzose sandstones usuallybehave similarly to low porosity silicates andexhibit, at most, some transient creep beforestabilizing. However, high porosity, poorlycemented sandstones may undergo an increase ingrain packing density on loading which is only timedependent if accompanied by grain-scale creepprocesses such as solution, microcracking ordislocation glide, or transient pore pressures. Forhigh porosity (>30%) sandstones and chalk under anapplied constant stress, the creep rate may suddenlyincrease due to structural collapse and densification,followed by stabilization (e?0). The creep rate isalso related to the grain size, with finer grained rockcreeping more than course grained. Creep ratesdecrease in the following sequence: gypsum sands?chalk?calcarenites? lithic arenites?feldspathicarenites?quartz arenites.• Shales Highly overconsolidated and metamorphicshales and slates tend not to creep except alongdiscontinuities and fissility planes, particularly ifthey are filled with low friction materials such asgraphite, phyllosilicates or gypsum. However, highporosity or chemically susceptible shales willdisplay discontinuity creep as well as bulk creepdeformation due to consolidation and deteriorationupon exposure to different chemical conditions.Chemical changes can include pyrite alteration,gypsum dissolution or hydration, or stress reliefswelling triggered by pore pressure chemistrychanges, particularly if the shale contains swellingclays such as smectite.• Salt Saltrocks such as halite and sylvite creepwhen subject to any appreciable shear stress. Uponstress change they exhibit instantaneous strainfollowed by creep that is initially rapid but thendecelerates (primary creep) to steady state creep constant) if conditions remain constant. However, ifmicrocracking occurs will change and the fabric


will adjust to a new equilibrium structure. Ingeneral, creep in saltrocks is dependent on both thestress level and the moisture content.(b) Creep simulationThe creep behavior of rock can be simulated bymodels comprising springs and dashpots, with thespring representing elastic strain and the dashpotrepresenting viscous strain. The best simulation ofrock creep is provided by a combination of a springand a dashpot in series and another spring anddashpot in parallel known as a Burger substance(Fig. 3.24(a)). The axial strain with time, e1(t), in aBurger substance subjected to a constant axial stresss1 is (Goodman, 1980):

where is the bulk modulus(assumed to be independent of time), ?1 determinesthe rate of delayed viscosity, ?2 determines the rate

of viscous flow, G1 determines the amount ofdelayed elasticity, and G2 is the elastic shearmodulus.Values for the viscoelastic constants can beobtained by conducting creep tests either in thelaboratory, or in situ by means of radial jackingtests or plate jacking tests. The general procedure isto measure both the elastic strain, and the strain withtime from which the strain rate and the intercepts e0and eB (Fig. 3.24(b)) are determined. Theviscoelastic constants are calculated from thesemeasured results using equations 3.24 and 3.25(Goodman, 1980).

(3.24)

(3.25)

The constants G1 and ?1 are determined fromequation 3.26 where q is the positive distancebetween the creep curve and the line asymptotic to

Figure 3.24 Simulation of rock creep behavior: (a) spring and dashpot model (Burger substance) simulating creepbehavior for rock loaded in uniaxial compression; and (b) typical creep curve for Burger substance.


the secondary creep curve at any time t.

(3.26)

A semilog plot of log10 q versus t has intercept (s1/3G1) and slope (-G1/2.3?1).(c) In situ creep measurementEstimation of possible creep rates for foundationswill require information on the long termdeformation characteristics of the in situ rock mass,rather than laboratory testing of intact samples. Animportant requirement for in situ testing, that mayhave a duration of days or weeks, is thattemperature and humidity be as uniform as possibleand similar to conditions that are likely to exist inthe actual foundation. This is most easily achievedin a borehole or exploration adit, but is likely to bemore difficult at the ground surface. Two commonmethods of conducting in situ creep tests are thedilatometer test and the plate load test (Goodman,1980).• Dilatometer: the dilatometer applies a uniformradial stress a to the circumference of a drill hole(radius r) to produce an outward radialdisplacement ur(t) at the wall of the hole that ismeasured over time t. The procedure is to conduct aseries of tests at sustained pressure increments, foreach of which the radial displacement with time isgiven by:

(3.27)

For this loading condition there is no change in themean stress with time, compared with a cylindricalcore loaded in uniaxial compression, so there is noterm in K (bulk modulus) influencing the timehistory of radial displacement. The radialdisplacement with time follows a curve similarto that shown in Fig. 3.24(b) and the viscoelasticconstants are calculated as follows. At time the radial displacement is:

(3.27a)

The asymptote to the displacement-time curve hasintercept on the displacement axis:

(3.27b)

and slope (sr/?2). The constants G1 and ?1 are againdetermined from a semilog plot of log10 q versus t(see Fig. 3.24(b)) in which sr/2G1 is the intercept onthe time axis and -G1/2.3?1 is the slope.• Plate load test: the plate load test is carried out ona larger volume of rock than is possible with adilatometer in a drill hole, and will provideinformation on the creep behavior of the rock mass.Figures 4.17 and 4.18 show typical arrangementsfor plate load tests. For the test at the surface thereaction is provided by a steel beam secured to therock with rock anchors, while the test arrangementin the tunnel allows deformation measurements tobe made in any direction normal to the tunnel axis.The application of a constant pressure a that isapplied suddenly to a flexible bearing plate ofcircular shape with radius r produces an averagedisplacement at the rock surface. If it is assumedthat the rock is incompressible (bulk modulus, and the Poisson’s ratio v equals 0.5, the averagesettlement varies with time according to:

(3.28)

The initial displacement d0 is given by

(3.28a)

and after the delayed elasticity has occurred, theaverage settlement of the plate tends to the line

(3.28b)

(d) Viscoelastic constants for in situ rockCreep tests carried out in the laboratory on coresamples of intact rock provide information on theviscoelastic properties of the rock under carefullycontrolled conditions. However, if the possibility ofcreep in a foundation is of concern, it may benecessary to carry out in situ tests to determine theinfluence on the creep characteristics of the jointedrock mass, as well as the influence ofenvironmental conditions such as temperature andhumidity that will occur in the actual foundation.


The difference in creep characteristics of intact rockand the rock mass is illustrated by comparingviscoelastic constants obtained from laboratory andin situ tests. Hardy et al. (1970) conducted creeptests on samples of intact Indiana limestone with aunconfined compressive strength of 62–76 MPa(9000–11 000 p.s.i.), a mean grain size of 14 mmand a porosity of 17.2%. The test procedure was toload cylindrical samples with diameter 28.5 mm (1.12 in) in uniaxial compression by the use of deadweights, and to increase the load in increments. Itwas found that steady state creep was initiated at astress level of about 39.5 MPa (5723 p.s.i.), whichis about 60% of the uniaxial compressive strengthof the rock. The viscoelastic constants obtained inthis test are listed in Table 3.11.

In situ methods for creep testing include theapplication of radial compression in boreholes(dilatometer), and plate load tests in tunnels and atthe ground surface. For example, Pusch (1993)conducted a series of plate load tests at the surfaceon slightly weathered gneiss with subhorizontallayering to investigate creep behavior of foundationrock. Also, Chin and Rogers (1987) conducted insitu creep tests using a water-filled rubbermembrane in 137 mm (5.4 in) diameter, 230 mm (9in) deep drill holes lined with a segmental castconcrete lining that allowed radial expansion.Application of a water pressure produced a uniformradial pressure to the walls of the drill hole and theradial displacement was mea

Table 3.11 Viscoelastic constants for intact and in situ rock obtained from creep tests

Rock type, test method Applied pressure,MPa(p.s.i.)

Bulk modulus,GPa(106p.s.i)

G1GPa(106p.s.i)

G2GPa(106p.s.i)

η1GPa(106p.s.i)

η2GPa(106p.s.i)

Limestone, 40 26.2 159 17.2 495 14 617fresh1 (5723) (3.8) (23.0) (2.5) (71.8) (2.120)Limestone, 0.25 – 0.195 0.22 653 973 502weathered2 (35.6) (0.028) (0.032) (94.7) (141.1950)Carbonic 0.29 – 0.818 0.186 349 1535shale3 (42.7) (0.118) (0.027) (50.7) (223)Tuff, 0.15 – 0.339 0.049 355 1010Weathered4 (21.3) (0.049) (0.007) (51.4) (147)Notes: 1Indiana Limestone, strong, fresh rock—core samples loaded in uniaxial compression (Hardy et al., 1970).2Limestone, thin bedded, weathered—radial compression loading in borehole (Chin and Rogers, 1987).3Carbonic shale with clayey shale—radial compression loading in borehole (Chin and Rogers, 1987).4Tuff, weathered—radial compression loading in borehole (Chin and Rogers, 1987).sured in four directions with dial gauges mountedhorizontally at the mid-height of the cylinder. Testswere carried out in shale, on thin-bedded, weatheredlimestone and tuff; the calculated values of theviscoelastic constants are shown in Table 3.11.(e) Creep in shear loadingAn extensive series of tests to determine the creepcharacteristics of a bedded sandstone-siltstone-mudstone sequence under shear load has beencarried out for the foundation design of the GheZhou Ba gravity dam in China (refer toSection 7.2.6 and Fig. 7.8(b)). The bedding dipsdownstream at an angle of about 4°-6° and there are

extensive clay infillings in the bedding planes whichare potential sliding surfaces within the foundation.Tests were carried out in the laboratory and in situwith blocks as large as 1700 mm by 11 700 mmwith combinations of normal and shear stress ratios,and test durations as long as 70 000 minutes (Tan,1993). One result of this investigation was to showthe shear strength determined in the long term creeptest, which simulates the loading condition in thefoundation, is significantly less than that shown bythe conventional rapid test. The 29 000 minuteduration creep test gave cohesion and friction anglevalues of 4.9 kPa (0.7 p.s.i.) and 11.3° respectively,


while the rapid test gave cohesion and friction anglevalues of 29.4 kPa (4.3 p.s.i.) and 16.7°. The testsalso showed that creep occurred at shear stresslevels as low as 3.9 kPa (0.6 p.s.i.) at a normalstress level of 49 kPa (7.1 p.s.i.) but was linear on asemilogarithmic time plot indicating that secondarycreep was taking place. An incremental increase inthe shear stress to 11.8 kPa (1.7 p.s.i.) wassufficient to cause increasing strain and rupture ofthe sample. However, an increase in the normalstress resulted in a corresponding increase in theshear stress required to cause rupture.This testing showed the potential for sliding failuresin the foundation and it was decided to strengthenthe rock against buckling and dilatancy. Thesemeasures included the construction of a concreteapron downstream of the dam and installation of168 vertical piles, 20 m deep with diameters of 850mm and 210 mm; the piles were securely attachedto the apron and extended to the depth of a morecompetent sandstone layer. This arrangementprovided confinement of the rock between therelatively stiff apron and the sand stone beds.Furthermore, uplift pressures were reduced byconstructing an upstream apron and installing agrout curtain and system of drain holes.

3.6.4Fatigue

Foundations of vibrating or rotating machinery maybe subjected to stresses which vary with time andresult in fatigue failure of the bearing rock (Fig. 2.23(d)). Such failure could take the form of fracture ofintact rock and loosening of fractured rock due tocrushing of points of contact between blocks ofrock.The results of cyclic loading tests on pieces ofintact rock in the laboratory indicate that the fatiguelimit of rock may be in the range 10 000– 100 000cycles. The stress at failure under this loadingcondition is about 80% of the static strength forcompressive loading only, and about 60% of thestatic strength for tensile loading only. Incomparison, for compression-tension loading the

fatigue strength drops to about 30% of the staticstrength (Brighenti, 1979). The fatigue strength ofrock has been studied only to a limited extent andthe results obtained have been somewhatcontradictory because of the wide range of loadingand geological conditions that need to be studied.The loading conditions include vibration frequency,duration, magnitude and sign (compression only,tension only or compression-tension combined).Testing has generally been carried out in thelaboratory on samples of intact rock forcomminution studies, and the fatigue behavior offractured rock is less well known.These results are only indicative of the reduction instrength that may occur due to fatigue loading, anda prudent design procedure would be to use abearing pressure of perhaps 25–50% of the normalstatic bearing pressure to allow for the loss ofstrength with time. Another important designconsideration is the loss of bearing capacity incyclic loading due to the progressive loosening ofclosely fractured rock.

3.7References

Bamford, W.E. (1969) Anisotropy, and the naturalvariability of rock properties. Proc. Symp. Rock Mech.,Sydney, 1–10.

Barton, N.R. (1973) Review of a new shear strengthcriteria for rock joints. Engineering Geology, 7,189–236.

Barton, N.R. (1974) Review of the Shear Strength ofFilled Discontinuities. Norwegian GeotechnicalInstitute, Publication No. 105.

Barton, N.R., Lien, B. and Lunde, J. (1974) Engineeringclassification of rock masses for the design of tunnelsupport. Rock Mechanics, 6(4), 189–236.

Belikov, B.P. (1967) Plastic constants of rock formingminerals and their effect on the elasticity of rock. InPhysical and Mechanical Properties of Rock (ed.B.V.Zalesskii) Israel Programme for ScientificTranslations, Jerusalem, pp. 124–40.

Benson, R.P. (1970) Rock mechanics aspects in thedesign of the Churchill Falls underground power-house,Labrador. PhD Thesis Univ. of Illinois at Urbana-Champaign.


Bieniawski, Z.T. (1968) The effect of specimen size oncompressive strength of coal. J. Rock Mech. MiningSci., 5, 325–53.

Bieniawski, Z.T. (1974) Geomechanics classification ofrock masses and its application in tunnelling. Proc. 3rdInt. Cong. Rock Mech., Denver 2(2), 27–32.

Bieniawski, Z.T. (1976) Rock mass classifications in rockengineering. Proc. Symp. Exploration for RockEngineering (ed. Z.T.Bieniawski), Vol. 1, A.A.Balkema, Rotterdam, pp. 97–106.

Bieniawski, Z.T. (1978) Determining rock massdeformability: experience from case histories. Int. J.Rock Mech. Min. Sci. & Geomech. Abstr. 15, 237–47.

Brandon, T.R. (1974) Rock Mechanics Properties ofTypical Foundation Rocks. US Bureau of Reclamation,Denver, Rep. REC-ERC-74–10, pp. 61.

Brighenti, G. (1979) Reactions of rock to fatigue loading.Proc. 4th Int. Con. on Rock Mechanics, Montreux,Vol. 1, pp. 65–70.

Brown, E.T. (1970) Strength of models of rocks withintermittent joints. J. Soil Mech. Fdn. Eng., ASCE, 96,1935–9.

Brune, J.D. (1967) Anhydrite and gypsum problems inengineering geology. Eng. Geol. Bull. A. E. G., 52,191.

Chappell, B.A. and Maurice, R. (1980) Classification ofrock mass related to foundations. Int. Conf. onStructural Foundations on Rock, Sydney, pp. 29–35.

Coates, D.F., Gyenge, M. and Stubbins, J.B. (1965) Slopestability studies at Knob Lake. Proc. Rock Mech.Symp., Toronto, pp. 35–46.

Cording, E.J. (1967) The stability during construction ofthree large underground openings in rock. Ph. D.Thesis, Univ. 111., Urbana, 111.

D’Andrea, D.V., Fischer, R.L. and Fogelson, D.E. (1965)Prediction of Compressive Strength from Other RockProperties. US Bureau of Mines Report ofInvestigations, RI 6702, 23.

Deere, D.U. and Patton, F.D. (1971) Slope stability inresidual soils. Proc. 4th Pan American Conf. on SoilMechanics and Foundation Engineering, San Juan,p. 87.

Dougherty, M.T. and Barsotti, N.J. (1972) Structuraldamage and potentially expansive sulphide materials.Bull Eng. Geol., Vol. IX(2), 105–25.

Dusseault, M.B. and Fordham, C.J. (1993) Time-dependent behavior of rocks. Comprehensive RockEngineering, Pergamon Press, UK, Vol. 3, pp. 119–49.

Einfalt, H.-C., Fecker, E. and Gotz, H.-P. (1979) The

three-phase-system clay-anhydrite-gypsum and its time-dependent behavior on saturation with water-basesolutions. Proc. 4th Int. Con. on Rock Mechanics,Montreux, Vol. 1, pp. 123–9.

Fleming, R.W., Spencer, G.S. and Banks, D.C. (1970)Empirical study of the Behavior of Clay Shale Slopes.US Army Nuclear Cratering Group Technical Report,No. 15.

Gerrard, C.M., Davis, E.H. and Wardle, L.J. (1975).Estimation of the settlement of cross-anisotropicdeposits using isotropic theory. Univ. Sydney, SchoolCivil Eng., Res. Rep. No. R-191.

Goodman, R.E. (1980) Introduction to Rock Mechanics,Wiley, New York, pp. 193–204.

Goodman, R.E. and Duncan, J.M. (1971) The role ofstructure and solid mechanics in the design of surfaceand underground excavations in rock. Proc. Conf. onStructure, Solid Mechanics and Engineering Design,Part 2, Paper 105, Wiley, New York, p. 1379.

Guidici, S. (1979) Measurements of rock deformation inthe abutment of an arch dam. Int. Conf. on RockMechanics, Montreux, Vol. 2, pp. 167–73.

Gysel, M. (1987) Design methods for structures inswelling rock. Int. Conf. on Rock Mechanics, Montreal,pp. 377–81.

Haimson, B.C. and Fairhurst, C. (1970) Some bitpenetrations characteristics in pink Tennessee marble.Proc. 12th Symp. Rock Mech, Rolla, Missouri,pp. 547–559.

Hamel, J.V. (1970) The Pima Mine slide, Pima County,Arizona. Geol. Soc. of America, Abstracts withPrograms, 2(5), 335.

Hamel, J.V. (1971a) Kimberley Pit slope failure. Proc.4th Pan-American Conf. on Soil Mechanics andFoundation Engineering, Puerto Rico, Vol. 2,pp. 117–27.

Hamel, J.V. (1971b) The slide at Brilliant cut. Proc. 13thSymp. on Rock Mechanics, Urbana, Illinois,pp. 487–510.

Hardy, H.R., Jr., Kim, R.Y., Stefanko, R. and Wang. Y.J.(1970) Creep and microseismic activity in geologicmaterials. Proc. 11th Symp. on Rock Mechanics,AIME, pp. 377–414.

Herget, G. (1973) Variation in rock stresses with depth ata Canadian iron mine. Int. J. Rock Mech. Min. Sci., 10,37–51.

Heuze, F.E. (1980) Scale effects in the determination ofrock mass strength and deformability. Rock Mechanics12, 167–92.


Hoek, E. (1970) Estimating the stability of excavatedslopes in opencast mines. Trans. Inst. of Mining andMetall, 79, A109–32.

Hoek, E. (1974) Progressive caving caused by mining aninclined ore body. Trans. Inst. of Mining and Metall,83, A133–9.

Hoek, E. (1983) Strength of jointed rock masses.Geotechnique 33,3, 187–223.

Hoek, E. (1998) Practical estimates of rock massstrength. Int. J. Rock. Mech. Mining Sci. (inpublication)

Hoek, E. and Bray, J. (1981) Rock Slope Engineering, 3rdedn. IMM, London.

Hoek, E. and Brown, E.T. (1988) The Hoek-Brownfailure criterion—a 1988 update. 15th Canadian RockMechanics Symposium, Toronto, Canada.

Hoek, E. and Richards, L.R. (1974) Rock Slope DesignReview. Golder Associates Report to the PrincipalGovt Highway Engineer, Hong Kong.

Holtz, W.G. and Gibbs, H.T. (1956) Engineering problemsin expansive soils. ASCE Trans., 121, 641– 8.

Hutchinson, J.N. (1970) Field and laboratory studies of afall in upper chalk cliffs at Joss Bay, Isle of Thanet.Proc. Roscoe Memorial Symp., Cambridge.

ICOLD (1993) Rock Foundations for Dams. ICOLD,Bulletin 88, Paris.

International Society for Rock Mechanics (ISRM),Committee on Laboratory Testing (1979) Suggestedmethods for determining the uniaxial compressivestrength and deformability of rock materials. Int.J. ofRock Mech., 16(2), 137–40.

International Society for Rock Mechanics (1981)Suggested Methods for the Quantitative Description ofDiscontinuities in Rock Masses. Pergamon Press, UK.

International Society for Rock Mechanics (ISRM) (1985)Suggested method for determining point load strength.Int. J. of Rock Mech., 22(2), 53–60.

Jaeger, J.C. and Cook, N.G. W. (1976) Fundamentals ofRock Mechanics. Chapman &; Hall, London, p. 99.

Kaderabek, T.J. and Reynolds, R.T. (1981) Miamilimestone foundation design and construction. ASCE,107(GT7), pp. 859–72.

Kitahara, Y., Fujiwara, Y., Kawamura, M. (1974) Thestability of slope during excavation—the method ofobservation and analysis. Rock Mech. in Japan, II,187–9.

Ko, H.Y. and Gerstle, K.H. (1976) Elastic properties oftwo coals. Int. J. Rock Mech. and Min. Sci. & Geomech.Abstr., 13, 81–90.

Krynine, D.P. and Judd, W.R. (1957) Principles ofEngineering Geology and Geotechnics. McGraw-Hill,New York, p. 84.

Kutter, H.K. and Rautenberg, A. (1979) The residualshear strength of filled joints in rock. Int. Conf. onRock Mechanics, Montreux, Vol. 1, 221–7.

Lama, R.D. and Vutukuri, V.S. (1978a) Handbook on theMechanical Properties of Rocks. Vol. I, Trans TechPublications, Claustal, Germany, pp. 87–138.

Lama, R.D. and Vutukuri, V.S. (1978b) Handbook on theMechanical Properties of Rocks. Vol. II, Trans TechPublications, Claustal, Germany, pp 105–48.

Lee, C.F. and Lo, K.Y. (1976) Rock squeeze study of twodeep excavations at Niagara Falls. Proc. SpecialtyConf. on Rock Engineering for Foundations andSlopes, Vol. 1, ASCE Boulder, Co, Boulder CO,pp. 116–31.

Lekhnitskii, S.G. (1966) Stress distribution close to ahorizontal working of elliptical shape in a transverselyisotropic mass with inclined planes of isotropy. Mech.Solids, 1(2), 35–41.

Ley, G.M.M. (1972) The properties of hydrothermallyaltered granite and their application to slope stability inopen cast mining. MSc Thesis, London University.

Lindner, E. (1976) Swelling rock: a review. Proc.Specialty Conf. on Rock Engineering for Foundationsand Slopes, ASCE, Boulder, CO, pp. 141–81.

Lo, K.Y. (1978) Regional distribution of in situhorizontal stresses in rocks of southern Ontario. Can.Geotech. J., 15, 371–81.

Lo, K.Y. and Hori, M. (1979) Deformation and strengthproperties of some rocks in southern Ontario. Can.Geotech. J. 16, 108–20.

Madsen, F.T. (1979) Determination of the swellingpressure of claystones and marlstones usingmineralogical data. Int. Conf. on Rock Mechanics,Montreux, Vol. 1, pp. 237–41.

Michalopoulos, A.P. and Triandafilidis, G.E. (1976)Influence of water on the hardness, strength andcompressibility of rock. Bull. Assoc. Eng. Geol., XIII(1), 1–22.

Middlebrook, T.A. (1942) Fort Peck slide. Proc. ASCE,107 (Paper 2144), 723.

Mitchell, J.K. (1976) Fundamentals of Soil Behaviour.Wiley, New York, pp. 24–46.

Nicholson, G.A. (1983) Design of Gravity Dams on RockFoundations: Sliding Stability Assessment by LimitEquilibrium and Selection of Shear StrengthParameters. Technical Report GL-83–13,


Geotechnical Laboratory, US Army EngineerWaterways Experiment Station, Vicksburg, MS.

Nose, M. (1964) Rock tests in situ, conventional tests onrock properties and design of Kurobegwa No. 4 DamTrans. ICOLD, Edinburgh, Vol. 1, pp. 219–52.

Parker, J. and Scott, J.J. (1964) Instrumentation for roomand pillar workings in a copper mine of the CopperRange Company, White Pine, Michigan. Proc. 6thSymp. Rock Mech., Rolla, Missouri, pp. 669–720.

Patton, F.D. (1966) Multiple modes of shear failure inrock. Proc. 1st Int. Cong. on Rock Mechanics., Lisbon,Vol. 1, pp. 509–13.

Peterson, R. and Peters, N. (1963) Heave of spillwaystructures on clay shales. Can. Geotech. J., 1(1), 5–15.

Pinnaduwa, H.S.W. and Kulatilake, A.M. (1985)Estimating elastic constants and strength ofdiscontinuous rock. ASCE, J. Geotech. Eng., V.111(7),847–64.

Pinto, J.L. (1970) Deformability of schistose rock. Proc.2nd Cong. Int. Rock Mech., Belgrade, Vol. 1,pp. 491–6.

Pratt, H.R. (1972) The effect of specimen size on themechanical strength of unjointed diorite. Int. J. RockMech. & Min. Sci., 9, 513–29.

Pusch, R. (1993) Mechanisms and consequences of creepin crystalline rock. Comprehensive Rock Engineering,Pergamon Press, UK, Vol. 1, pp. 227–41

Raphael, J.M. and Goodman, R.E. (1979) Strength anddeformability of highly fractured rock. ASCE, 105(GT11), 1285–300.

Reik, G. and Zacas, M. (1978) Strength and deformationcharacteristics of jointed media in true triaxialcompression. Int. J. Rock Mech. Min. Sci. andGeomech. Abstr., 15, 295–303.

Roberts, D. and Hoek, E. (1972) A study of the stability ofa disused limestone quarry face in the Mendip Hills,England. 1st Int. Conf. on Stability in Open Pit Mining,Vancouver, AIME, New York, pp. 239–56.

Ross-Brown, D.R. (1973) Slope design in open castmines. Ph. D. Thesis, London University.

Rowe, R.K. (1982) The determination of rock massmodulus variation with depth for weathered or jointedrock. Can. Geotech. J., 19, 29–43.

Ruiz, M.O. (1966) Some technological characteristics of26 Brazilian rocks. Proc. 1st. Cong. Int. Soc. RockMech., Libon, Vol. 1, pp. 115–19.

Saint Simon, P.G. R., Solymar, Z.V. and Thompson, W.J.(1979). Dam site investigations in soft rocks of PeaceRiver Valley, Alberta. 4th Int. Conf. on Rock

Mechanics, Montreux, pp. 553–60.Sbar, M.L. and Sykes, L.R. (1973) Contemporary

compressive stress and seismicity in North America, anexample of intra-plate tectonics. Geological Survey ofAmerica, 84(6), 1861–82.

Schneider, B. (1967) Moyens Nouveaux deReconnaissance des Massifs Rocheux. Supplement toAnnales de L’Institut Technique de Batiment et desTravaux Publics, 20(235–6), 1055–93.

Sellers, J.B. (1970) The measurement of rock stresschanges using hydraulic borehole gauges. Int. J. RockMech. Min. Sci., 7, 423–35.

Serafim, J.L. and Pereira, J.P. (1983) Considerations ofthe geomechanics classification of Bieniawski. Proc.Intl. Symp. Eng. Geol. and UndergroundConstruction., Lisbon, pp. 1133–44.

Skempton, A.W. and Hutchinson, J.N. (1969) Stability ofnatural slopes and embankment foundations. State ofthe art report. Proc. 7th Intl. Conf. on Soil Mechanics,Mexico, Vol. 1, pp. 291–340.

Stepanov, V. and Batugin, S. (1967) Assessing the effectof the anisotropy of rocks on the accuracy of stressdeterminations by the relief method. Sov. Min. Sci., 3,312–5.

Stimpson, B. (1975) Personal communication.Tan, T.K. (1993) The importance of creep and time-

dependent dilatancy, as revealed from case records inChina. Comprehensive Rock Engineering, PergamonPress, UK, Vol. 3, pp. 709–44.

Thiel, K. (1974) Influence of the system of static load onthe deformability of rocks in field tests. Proc. ThirdCong. of Int. Society of Rock Mechanics, Denver, Vol.2, pp. 209–15.

Thiel, K. and Zabuski, L. (1993) Rock massinvestigations in hydroengineering. ComprehensiveRock Engineering, Pergamon Press, UK, Vol. 3,pp. 839–61.

Transportation Research Board, (1996) Landslides—Investigation and Mitigation. National ResearchCouncil, Special Report 247, Washington, DC.

Trow, W.A. and Lo, K.Y. (1988) Horizontaldisplacements induced by rock excavation: ScotiaPlaza, Toronto, Ontario. Can. Geotech. J., 26, 114–21.

Tschebotarioff, K. (1973) Foundations, Retaining andEarth Structures. McGraw-Hill, New Yorkpp. 173–83.

Underwood, L.B. (1961) Chalk foundations at four majordams in the Missouri River basin. Trans. 8th Cong. onLarge Dams, Vol. 1, 23–47.


van der Merwe, D.H. (1964) The prediction of heave fromplasticity index and percentage clay fraction of soils.The Civil Engineer in South Africa, 103–7.

van der Vlis, A.C. (1970) Rock classification by thesimple hardness test. Proc. 2nd Cong. Int. Soc. RockMech., Belgrade, Vol. 2, pp. 23–30.

Wuerker, R.G. (1956) Annotated tables of strength ofrock. Trans. AIME, Pet. Paper N-663-G.

Whitman, R.V. and Bailey, W.A. (1967) Use ofcomputers in slope stability analysis. ASCE, J. of SoilMech. and Foundation Division, 93, 475–98.

Widerhofer, R. (1972) Method of recent Japanese tunnel

construction through ground of expansive character.Int. Sym. for Underground Construction, Lucerne,pp. 146–57.

Working Group on Bridge Foundations, Committee onSoft Rock Mechanics, JSCE (1981) Proc. Int. Sym. onWeak Rock, Tokyo, pp. 1303–14.

Wyllie, D.C. (1977) Project files.Wyllie, D.C. and Munn, F.J. (1979) Use of movement

monitoring to minimize production losses due to pitslope failure. 1st Symp. on Stability in Coal Mining,Miller Freeman Publications, pp. 75–95.


4Investigation and in-situ testing methods

4.1Site selection

Investigations for foundations follow the usualprocedure for geotechnical projects comprising astaged program with the objective of progressivelyrefining the information required for final design.Typically, the four stages of a completeinvestigation are as follows:

1. Reconnaissance—examination of publishedgeological maps and reports, study of airphotographs, gathering of local experience onfoundation performance, field visits;

2. site selection—test pits, outcrop mapping,geophysics, index tests of rock properties,limited diamond drilling at alternative sites;

3. preliminary site investigation—diamonddrilling of selected site, detailed mapping ofout-crops and exploration adits, laboratorytesting;

4. detailed investigations—drilling of selectedgeological features critical to foundationperformance, in situ testing, laboratory testing.

A distinguishing feature of investigations for rockfoundations is that it is particularly important tofocus on the details of the structural geology. Forexample, the.orientation of one clay-filleddiscontinuity can make the difference betweenstability and instability, or a compressible seam maycause settlement of the structure. This conditionmeans that it is usually necessary to carry out adrilling program to investigate sub-surfaceconditions, and in some cases drive exploration

adits to examine in situ conditions. Figure 4.1shows a diamond drill on a platform on a steep cliffinvestigating the foundations for a bridge abutment.However, drilling may not be required incircumstances where the applied loads aresignificantly less than the bearing capacity of therock, where there is no possibility of a sliding typefailure, or where there are extensive outcrops andthe sub-surface conditions can be confidentlyestablished by interpretation.This chapter describes investigation methods forrock foundations, with emphasis on in situ testingmethods and detailed structural geology studies. Insitu testing is one of the particular features ofinvestigation programs for major structures foundedon rock because of the difficulty in sampling andtesting large samples representative of the rockmass. Samples that are representative of both theintact rock and the discontinuities may be as largeas 1 m (3 ft) in diameter. Samples this large are verydifficult to recover undisturbed, and the requiredtesting equipment would have to exert extremelyhigh forces even to deform the rock mass.At the early stages of most projects there may besome choice available in the site of the structure.Under these circumstances, one of the first tasks inthe geotechnical program is to evaluate alternativesites and to recommend which site is the mostfavorable. In this reconnaissance stage of theproject the objective of the investigation wouldbe to concentrate on large scale geological featuresthat would influence the overall stability of thestructure. These features include landslides,contacts between rock types with significantly

different engineering properties, fault zones andpersistent sets of discontinuities sets that dip out ofany face in which a steep cut is to be made.Geological information of this nature would formpart of the input for the overall site selection studythat would include alignment studies in the case ofbridges on transportation routes. In the case of damprojects, the site selection should take intoconsideration the foundations of the dam itself, thespillway and the powerhouse. Geological conditionsthat could justify moving a structure would be avery significant hazard such as a major landslide,movement of which could destroy the structure, orkarstic terrain which contains substantial cavities.For other geological features such as faults orcontinuous bedding planes that would only causelocal instability, remedial measures such as rockreinforcement could be carried out duringconstruction (see Chapter 10).The following is a discussion on some of the

reconnaissance techniques that may be used early ina project, mainly for the purpose of site selection. Itis very rare that the information gathered at thisstage of a project would be adequate for use in finaldesign, so these studies would have to be followedby more detailed investigations such as surfacemapping and drilling.

4.1.1Aerial and terrestrial photography

The study of stereo pairs of vertical aerialphotographs and oblique terrestrial photographsprovides much useful information on the largerscale geological conditions at a site (Peterson et al.,1982). Often these large features will be difficult toidentify in surface mapping because theyare obscured by vegetation, rock falls or moreclosely spaced discontinuities. Photographs mostcommonly used in geotechnical engineering are

Figure 4.1 Photograph of diamond drill investigating rock conditions for bridge abutment (photograph by Tony Rice).

98 INVESTIGATION AND IN-SITU TESTING METHODS

black and white, vertical photographs taken atheights of between 500 and 3000 m (1500 and 10000 ft) with scales ranging from 1:10 000 to 1:30000. On some projects it is necessary to have bothhigh and low level photographs, with the high levelphotographs being used to identify landslides, forexample, while the low level photographs providemore detailed information on geological structure.One of the most important uses in foundationengineering of aerial photographs is theidentification of landslides which have the potentialfor causing movement, or even destruction offacilities on which they are constructed. Landslidesfeatures that are often readily apparent on verticalaerial photographs are tension cracks and scarpsalong the crest of the slide, hummocky terrain in thebody of the slide and areas of fresh disturbance inthe toe, including sudden changes in riverdirections. Figure 4.2 shows a landslide area in theside of a steep glacial valley in the Coastal Range ofwestern Canada. Area a, which is a talus slope, is anancient slide, while in area b, which is a potentialslide of similar proportions, there are a number oftension cracks with widths up to 15 m (50 ft). Thecause of these slides are sets of orthogonal joints,one of which dips out of the valley wall at an angleof about 50°, and a second vertical set striking atright angles to the valley that forms side releasesurfaces. By comparing photographs taken over anumber of years it may be possible to determine therate of movement of a slide, and whether it isgrowing in size.Related to landslides are debris flows which occurin mountainous terrain with high precipitationlevels such as occurs on the north west coast ofNorth America, in Japan, the Alps and Himalayas.Potential sites of debris flows are evident on aerialphotographs as areas of erosion in steep banks inthe upper reaches of the creeks, as well as fans ofaccumulated debris at the toe of the slope.Debris flows are highly fluid mixtures of water,solid particles and organic matter. This mixture hasa consistency of wet concrete and consists of about70–80% water, and solid material ranging from clayand silt sizes up to boulders several meters in

diameter. The organic matter can include barkmulch as well as large trees and logs swept from thesides of the channel. Debris flows usually occurduring periods of intense rainfall or rapid snow meltand a possible triggering event can be the failure ofa temporary dam, formed by slope failure or a log-jam, that releases a surge of water and solidmaterial. Where such flows originate in streamswith gradients steeper than about 20°– 30°, theymove at velocities of approximately 3–5 m/s (10–16ft/s), with pulses as great as 30 m/s (100 ft/s). Atthis speed, material is scoured from the base andsides of the channel so the volume of the flowincreases as it descends. This combination of highdensity and high velocity can cause devastation toany structure built in their path. Bridges constructedover creeks which are susceptible to debris flowsmust be adequately sized to accommodate the likelyflow volume, and footings should not be located inthe creek bed unless they are designed to withstandthe considerable impact loads (Skermer, 1984;VanDine and Lister, 1983).Other features that may be evident on aerialphotographs are major geological structures such asfaults, bedding planes and continuous joint sets. Thephotographs will give some information on theposition, length and continuity of these features.However, to establish the orientation (dip and dipdirection) of a discontinuity, it is necessary to fixthe positions of a minimum of three, and preferablyfour, points on the same surface. This technique hasbeen used predominately with terrestrialphotographs where individual discontinuities withlarge exposures can be clearly identified; even onlow level aerial photographs it is rare to be able tosee exposures of a single discontinuity surface,except perhaps in the case of a fault scarp. Structuralmapping from aerial photographs is normally onlycarried out when there is no access to the face; directsurface mapping which allows the characteristics ofeach discontinuity to be examined in detail ispreferable.Other information that can be obtained from aerialphotographs is the location of gravel deposits, rockoutcrops and the study of river hydraulics for siting

SITE SELECTION 99

dams and bridges.

4.1.2Geophysics

Geophysical methods are often used in thepreliminary stages of a site investigation to providesuch information as the depth of weathering, thebedrock profile, contacts between rock types ofsignificantly different density, the location of major

faults and solution cavities, and the degree offracturing of the rock (Griffiths and King, 1988).The results obtained from geophysicalmeasurements are usually not sufficiently accurateto be used in final design and they should always becalibrated by putting down a number of test pits ordrill holes to spot check actual properties andcontact elevations. However, geophysical surveysprovide a continuous profile of subsurfacecondi tions and this information can be used as a

Figure 4.2 Vertical aerial photograph stereo pair showing typical features of a major rock slide in a glaciated valley: (a)slide scarp; (b) slide debris; (c) tension cracks; (d) valley floor; and (e) talus slope.


fill-in between drill holes. Most geophysicalinvestigations for engineering purposes consist ofseismic, resistivity or ground penetrating radarsurveys carried out on the ground surface asdescribed in this section. Downhole techniques arealso available to measure the properties of materialsin the walls of the drill hole, or alternativelybetween adjacent holes. Downhole geophysics maybe used in percussion drill holes, which are lessexpensive and faster to drill than diamond drillholes, as part of the preliminary investigation of asite.(a) Seismic surveysThe primary purposes of seismic surveys are todetermine the approximate location and density oflayers of soil and rock, a well defined water table,or the degree of fracturing, porosity and saturationof the rock. Seismic velocity can also be related tothe rippability of the rock mass (see Section 10.5.3).The seismic method is effective to depths in therange of tens of meters to a maximum of a fewhundred meters. Discontinuities within the rocksuch as joints and shears will not be detected byseismic methods unless there is shear displacementand a distinct elevation change of a layer with aparticular density as a result of fault movement.However, continuous overwater seismic profilingusing a repeating shock source called a ‘sparker’may recognize discontinuity zones.Seismic surveys measure the relative arrival times,and thus the velocity of propagation of elasticwaves traveling between a shallow energy sourceand a number of transducers set out in a straight linealong the required profile. The energy source maybe a hammer blow, an explosion of a propane-oxygen mixture in a heavy chamber (gasgun), or alight explosive charge. In elastically homogeneousground subject to a sudden stress near its surface,three elastic pulses travel outward at differentspeeds. Two are body waves that are propagated asspherical fronts affected to only a minor extent bythe free surface of the ground, and the third is asurface wave which is confined to the region nearthe surface, its amplitude falling off rapidly withdepth. The two body waves, namely the primary or

‘P’ wave and the secondary or ‘S’ wave, differ inboth their direction of motion and speed. The Pwave is a longitudinal compressive wave in thedirection of propagation, while the S wave inducesshear stresses in the medium. The velocities of theprimary (Vp) and secondary (Vs) waves are relatedto the elastic constants and density of the mediumby the equations

(4.1)

(4.2)

where K is the bulk modulus, G is the shearmodulus and ? is the density. The velocity of the Swave in most rocks is about one half that of thevelocity of the P wave. The S wave is notpropagated at all in fluids. The value of the ratio Vp/Vs depends only on the Poisson’s ratio of themedium. Figure 4.3 shows typical P wave velocitiesfor a range of different materials.The surface wave, which travels about 10% slowerthan the S waves, causes a surface disturbance inhomogeneous ground called the Raleigh wave. TheRaleigh wave has both vertical and horizontalcomponents, with the horizontal motion being ofrather smaller amplitude than the vertical, and 90°out of phase with it. The resultant path of an elementof the medium during passage of a Raleigh wavecycle follows an ellipse lying on the plane ofpropagation. The magnitude of the ground motionbecomes negligibly small within a distance belowthe free surface of the same order of magnitude asthe wavelength of the disturbance.The amplitude of the waves decreases with distancefrom their source as a result of spreading of the waveenergy over the increasing wave front area. Earthmaterials are imperfectly elastic leading to energyloss and attenuation of the seismic waves that isgreater than would be expected from geometricspreading alone. This reduction in amplitude ismore pronounced for less consolidated rocks. Also,the reduction in amplitude is greater for higherfrequencies resulting in selective loss of the higher

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frequencies as the pulse propagates.The sonic velocity of the elastic wave will begreater in higher density material, and in moremassive rock compared with closely fractured rock.Where a layer of denser material underlies a lessdense layer, such as soil overlying bedrock, then theelastic wave velocity will be greater in the bedrockand the contact between the layers will act as arefracting surface. In a specific range of distancesfrom the shot point, the times of first arrival atdifferent distances from the shot point willrepresent waves traveling along this surface. Thisinformation can be used to plot the profile of thecontact between the two layers.(b) Resistivity surveysAt locations where the rock types have similardensities and seismic surveys would be ineffective,

resistivity surveys can provide information onvariations in the geological structure and materialtype. Since most rocks are themselvesnonconductive, the electrical resistivity of a rockderives mainly from the salinity of the ground wateroccupying pores and discontinuities. Accordingly,rock formations will differ in resistivity because ofporosity and jointing differences, with the resistivitydecreasing with greater discontinuity frequency. Forexample, in faults and shears the water content maybe higher than the country rock and anomalouslylow resistivity will be measured. Conversely, inporous country rock, a discontinuity may act as adrain and appear as an anomaly of high resistivity(Stahl, 1973).Resistivity surveys may also be used to detect suchstructures as clay-filled sinkholes in limestone

Figure 4.3 Approximate ranges of P wave velocities Vp for some common geological materials (Griffiths and King,1988).


because the clay will tend to have a relatively lowresistivity compared with the surrounding rock andwill show up as an anomaly. The conductivity ofclay takes place by way of weakly bonded surfaceions whereas rocks are themselves nonconducting.In general, the resistivities of formations varywidely not only from formation to formation butalso within a particular deposit, this beingparticularly true for near surface unconsolidatedmaterials (Griffiths and King, 1988). Consequentlythere is no precise correlation of lithology withresistivity and it is preferable that the results ofresistivity surveys be calibrated with boreholes ortest pits.(c) Ground penetrating radarGround penetrating radar (GPR) is a technique formapping bedrock depth, changes in rock type,discontinuities in bedrock, soil strata and the watertable in course grained soils, as well as voids, pipesand solution cavities (Inkster et al., 1989). Thetechnique has been used to detect features withthickness of a few tens of millimeters at a range ofseveral meters, and to map geological structures atdepths of up to 50 m.GPR systems for geological investigations usuallycomprise a sled equipped with transmitting,receiving and recording equipment that is towedalong the survey line at a fixed distance above theground surface to produce a continuous subsurfaceprofile. The transmitter introduces a short pulse ofhigh frequency (10–1000 MHz) electromagneticenergy into the ground that is reflected by layerswith differing electrical properties and detected atthe receiver.The propagation characteristics of the GPR signaldepend largely on the electrical properties of thematerials being probed, with the two parameters ofconcern being the conductivity which controls theattenuation of the signal through the ground, and thedielectric constant which controls the signalvelocity. The most important factor is theconductivity: higher conductivity materialsattenuate the radar signal more quickly, giving riseto radar reflections. The electrical properties ofgeological materials are primarily controlled by the

water content with the conductivity of soils beingrelated to the volumetric water content. In rocks, theradar is sensitive to changes in rock type and water-filled or dry discontinuities. GPR is of limited usewhen the conductivity is greater than about 10–15mS/m. Clays, for example, are relatively conductiveand opaque so the depth of penetration in thesematerials may be limited to about 1 m (3 ft), whilein sands and gravels it is possible to achievepenetrations of as much as 10 m (30 ft). GPR is alsoused to map discontinuities in rock, with reflectionsbeing generated as a result of the dielectric constantof the infilling material being different from that ofthe host rock, or where the discontinuities are filledwith water. Discontinuities in granite have beendetected at depths up to 50 m (Davis and Annan,1989).

4.2Geological mapping

Geological mapping of surface outcrops orexploration adits usually furnishes the fundamentalinformation on site conditions, and is often the basisfor many subsequent engineering decisions such asrelocation of the structure, type of structure that willbe built, or the need for rock reinforcement. Whilemapping is a vital part of the investigation program,it is also an inexact process because a certainamount of judgment is usually required toextrapolate the small amount of informationavailable from surface outcrops and drill core to theoverall foundation. This section describes mappingtechniques that have been developed to assist inproducing both consistent results, and informationthat can be used directly in design.

4.2.1Standard geology descriptions

In order to produce geological maps and descriptionsof the engineering properties of the rock mass thatcan be used with confidence in design, is itimportant to have a well defined process thatproduces comparable results obtained by different

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personnel working at several sites. To meet theserequirements, standard mapping procedures havebeen drawn up which have the following objectives:

• They should provide a language enablingobservers to transmit their general impressionof a rock mass, particularly with regard to itsanticipated mechanical behavior. The language ofthe geological description must be unambiguous;different observers of a given rock mass shoulddescribe the rock mass in the same way.

• They should contain, as far as possible,quantitative data of interest to the solution ofdefinite practical problems.

• Whenever possible, they should use simplemeasurements rather than visual observationsalone.

• They should provide a complete specification ofthe rock mass for engineering purposes.

The process of drawing up the descriptions of therock material and the rock mass is a progressiveprocess that starts with general informationcollected during reconnaissance surveys, andprogressively provides more detailed informationrequired for design. The types of informationcollected and the detail to which they areinvestigated will depend on site conditions, therequirements of the project and the importance ofeach rock property to the long term performance ofthe structure. As all these factors will vary fromproject to project, it is important that investigationsprograms remain flexible and are drawn up to suitthe particular requirements of each site. Thefollowing is a summary of information that may becollected to provide a complete description of therock mass, and some brief comments on how theseproperties influence the performance of the rockmass. This information is based primarily on theprocedures developed by the International Society ofRock Mechanics (1981b), with some additionalinformation from the Geological SocietyEngineering Group Working Party (1977). Moredetails of the mapping data are provided inAppendix II which includes mapping field sheets,

and tables relating descriptions of rock massproperties to quantitative measurements.An important first step in any reconnaissance stageof a project is to define zones, in each of which thegeological properties are uniform with regards tothe requirements of the project (InternationalSociety of Rock Mechanics, 1981 a or b). Thezoning of the rock mass should provide informationon the location, orientation and type of boundarybetween each zone, as well as some information onthe engineering properties of the rock mass in eachzone. By defining the boundaries of each zone it ispossible to determine the extent to which thefoundation characteristics will vary across the site,as well as the possible need to move the structure toavoid materials with insufficient bearing capacity,or locations with a potential for instability.The following is a list, and a brief description of theparameters that define the characteristics of the rockmass. Sets of discontinuities usually occur inorthogonal sets (mutually at right angles) inresponse to the stress field that has deformed therock. This is shown in the photograph in Fig. 4.4(a),where the bedding dips into the face and the jointsform wedges. Orthogonal structure is also illustratedin the stereonet in Fig. 2.7. Figure 4.4(b) shows therock mass characteristics in diagrammatic form.This section describes each of these 12 parameters,and discusses their influence on foundationperformance. Many of the rock mass parameters arediscussed in more detail in Chapters 2 and 3 onstructural geology and rock strength respectivelyand the appropriate references are quoted. Completemapping and measurement procedures are describedin the ISRM publication Suggested Methods for theQuantitative Description of Discontinuities in RockMasses (ISRM, 1981b).I Rock material description(A) Rock type The rock type is defined by theorigin of the rock (i.e. sedimentary, metamorphic or igneous), the mineralogy, the colour and grainsize as shown in Tables II.1 and II.2 (Deere andMiller, 1966). The importance of defining the rocktype is that there is wide experience in theperformance of different rock types and this


Figure 4.4 Characteristics of discontinuities in rock masses: (a) photograph of rock mass containing three orthogonal

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behavior of the rock.(B) Wall strength The strength of the rock formingthe walls of discontinuities will influence the shearstrength of rough discontinuities because highstresses are generated at local contact points duringshearing. If the rock strength is low relative to themagnitude of these stresses the asperities will besheared off resulting in a loss of the roughnesscomponent of the friction angle. The rock strengthis quantified by the Joint Compressive Strength(JCS) term discussed in Section 3.4.2(b). It is oftenadequate to estimate the compressive strength fromthe simple field tests as shown in Table II.3, or if coreor lump samples are available, by carrying out pointload tests. The Schmidt hammer test is also amethod of estimating the compressive strength ofrock at discontinuity surfaces.(C) Weathering Loss of rock strength due toweathering will influence both bearing capacity ofstructures founded at shallow depth, and the shearstrength of discontinuities due to the reduction inthe roughness component during shearing.Weathering of rock takes the form of bothdisintegration and decomposition as discussed inmore detail in Section 3.6.1. Table II.4 lists termsused to describe weathering grades with respect tothe proportion of decomposed rock. Thesecategories can be used to estimate the rock strength(see (B) above).II Discontinuity description(D) Discontinuity type Discontinuity types rangefrom clean tension joints of limited length to faultscontaining several centimeters of clay gouge andlengths of several kilometers; obviously the shearstrength of such discontinuities will be verydifferent. Section 2.1.1 lists the most common typesof discontinuities.(E) Discontinuity orientation The orientation ofdiscontinuities is expressed as the dip and dipdirection (or strike) of the surface (Section 2.2). Thedefinition of the dip and dip direction, and theprocedures for analyzing orientation measurementsusing the stereonet are discussed in detail inChapter 2.(F) Roughness The roughness of a discontinuity

surface is often an important component of theshear strength, especially where the discontinuity isundisplaced and interlocked. Roughness becomesless important where the discontinuity is infilled ordisplaced and interlock is lost. Roughness should bemeasured in the field on exposed surfaces withlengths of at least 2 m if possible, and in theanticipated direction of sliding. A quantitativemeasure of roughness based on observations of thecombination of surface irregularities (at a scale ofseveral centimeters) and waviness (at a scale of aseveral meters) of discontinuity surfaces is shown inFig. II.3 and Table II.5. These observations ofroughness can be related to a roughness angle (i) bydirect measurement using the procedures describedin Section 4.2.2(c), or by the use of the jointroughness factor (JRC) as described inSection 3.4.2(b). Usual practice would be to use theroughness scale shown in Fig. II.3 when mappingthe discontinuity surfaces, and then to calibratethese observations with a limited number of detailedmeasurements of actual roughness angles of criticalfeatures using the technique shown in Fig. 4.6.(G) Aperture Aperture is the perpendiculardistance separating the adjacent rock walls of anopen discontinuity, in which the intervening spaceis air or water filled; Table II.6 lists termsdescribing aperture dimensions. Aperture is therebydistinguished from the width of a filleddiscontinuity. It is important in predicting the likelybehavior of the rock mass, such as deformationunder stress changes and permeability, tounderstand the reason that open discontinuitiesdevelop. Possible causes include washing out ofinfillings, solution of the rock forming the walls of adiscontinuity, shear displacement of roughdiscontinuities, tension features at the head oflandslides and relaxation of steep valley wallsfollowing glacial retreat or erosion. Aperture maybe measured in outcrops or tunnels provided thatcare is taken to discount blast induced openfractures, in drill core if recovery is excellent, and inboreholes using a borehole camera if the walls ofthe hole are clean.III Infilling


(H) Infilling type and width Infilling is the term formaterial separating the adjacent walls ofdiscontinuities, such as calcite or fault gouge; theperpendicular distance between the adjacent rockwalls is termed the width of the filled discontinuity.A complete description of filling material requiredto predict the behavior of the discontinuity includethe following: mineralogy, particle size, over-consolidation ratio, water content/permeability, wallroughness, width and fracturing/crushing of thewall rock. If the infilling is likely to influence theperformance of the foundation, samples of thematerial (undisturbed if possible) should becollected, or an in situ test may be carried out.Details of the influence of fillings on shear strengthare discussed in Section 3.4.2(d), and on settlementof footings in Section 5.3.1.IV Rock mass description(I) Spacing Discontinuity spacing can be mapped inrock faces and in drill core, with the true spacingbeing calculated from the apparent spacing fordiscontinuities inclined to the face as shown inFig. 4.5. Tables II.7 and II.9 provides terms that canbe used to express spacing and block sizerespectively. Measurement of discontinuity spacingof each set of discontinuities will define the size andshape of blocks and give an indication of stabilitymodes such as toppling failure. The spacing is alsorelated to the rock mass strength because in closelyfractured rock the individual discontinuities willmore readily join together to form a continuouszone of weakness. A qualitative relationship

between discontinuity spacing and the strength ofdiscontinuity rock masses is discussed in Sections3.3.2 and 3.4.4.(J) Persistence Persistence is a measure ofcontinuous length or area of the discontinuity.Table II. 8 provides terms that can be used toexpress persistence values. This parameter definesthe size of blocks and the length of potential slidingsurfaces, so the mapping should concentrate onmeasuring the persistence of the set ofdiscontinuities that will have the greatest influenceon stability. Persistence of discontinuities is one ofthe most important rock mass parameters, and alsoone of the most difficult to measure. This is becauseusually only a small part of the discontinuity isvisible in the face, and in the case of drill core noinformation on persistence is available. Proceduresfor estimating the probability distributions ofpersistence from field measurements in an outcropor tunnel, where the dimensions of the face are lessthan the persistence of some of the discontinuities,are discussed in Section 2.6.2.(K) Number of sets The number of sets ofdiscontinuities that intersect one another willinfluence the extent to which the rock mass candeform without failure of the intact rock. As thenumber of discontinuity sets increases and the blocksize diminishes, the greater the opportunity forblocks to rotate, translate and crush under appliedloads. The mapping should distinguish betweensystematic discontinuities that are members of a setand random discontinuities the orientation of which

Figure 4.5 Bias in the occurrence of discontinuities in rock faces and tunnel walls.

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are less predictable. Appendix II provides termsdescribing the number of discontinuity sets.(L) Block size/shape The block size and shape aredetermined by the discontinuity spacing andpersistence, and the number of sets. The block sizecan be estimated by selecting several typical blocksand measuring their average dimensions which arethen recorded using the terms in Table II.9. Blockshapes include massive, blocky, tabular, columnar,irregular and crushed.V Groundwater(M) Seepage Observations of the location ofseepage provides information on aperture andpersistence because ground water flow is confinedalmost entirely in the discontinuity (secondarypermeability). Table II.10 describes seepage infilled discontinuities, while Table II.11 providesterms which describe seepage conditions in unfilleddiscontinuities. These observations will alsoindicate the position of the water table, or watertables in the case of rock masses containingalternating layers of low and high permeability rocksuch as shale and sandstone. In dry climates theevaporation rate may exceed the seepage rate and itmay not be possible readily to observe seepagelocations, while in cold weather icicles provide agood indication of even very low seepage rates. Theflow quantities will also help anticipate conditionsduring construction such as flooding and pumpingrequirements of excavations, and the likelyperformance of the foundation with respect toseepage.Using these terms outlined in this section, a typicaldescription for a rock material would be asfollows:

Grey, fine grained, crystalline, slightlyweathered, moderately strong basalt.

Note that the rock name comes last because this isless important then the engineering properties of therock.An example of a rock mass description is asfollows:

Columnar jointed with vertical columns andone set of horizontal joints, spacing ofvertical joints is very wide, spacing ofhorizontal joints wide, joints lengths are 3 to5 m (10 to 16 ft) vertically and 0.5 to 1 m (1.5to 3 ft) horizontally; joint aperture isextremely narrow and the discontinuityinfilling is very soft clay. The verticalcolumnar joints are smooth, while thehorizontal joints are very rough. No seepage.

4.2.2Discontinuity mapping

One of the most important components of anysurface mapping program is the definition of thestructural geology according to the parametersshown in Fig. 4.4. It is recommended, whereverpossible, that the mapping be carried out by the sameperson or engineering group that will carry out thedesign. This will help to ensure that the objectives ofthe mapping program are clearly identified and thedata collected are relevant to the design. Forexample, a large number of short, impersistentjoints that have little influence on the rock massstrength should be given much less attention duringmapping than one clay filled fault on which thewhole foundation could fail. A design engineeranalyzing the data who is not familiar with the site,may not be able to distinguish on a contoured stereonet the relative importance of the many impersistentjoints and the single fault.As discussed in Chapter 2, the most convenientmeans of expressing the orientation ofdiscontinuities for engineering purposes is in termsof the dip and dip direction. Special geologicalcompasses are available with which dip and dipdirection can be measured simultaneously anddirectly, with no need to make any conversions ofthe readings before plotting them on the stereo net.A compass made by the Showa Sokki company inJapan is specifically designed for discontinuitymapping and also has a built-in inclinometer(Fig. 2.4).(a) Mapping methods


The most common methods of structural mappingare line and window mapping, both of which can beused either on surface outcrops or in exploratoryadits. Line mapping comprises stretching a tapealong the face and mapping every discontinuity thatintersects the line; line lengths are normallybetween 50 and 100 m (150–300 ft). If the endpoints of the line are surveyed, then the location ofall the discontinuities can be determined. Windowmapping comprises mapping all discontinuitieswithin a representative segment or ‘win dow’ offixed size, spaced at regular intervals along theexposure. The intervening areas are examined forsimilarity of structure. The length of a windowwould normally be about 10 m (30 ft). Either ofthese mapping techniques may be used in the siteselection phase of a project, depending on theextent of the face available for mapping. Once thefinal site has been selected, it may be appropriate toconduct detailed mapping at the foundation location.For example, in one spillway foundation project,every discontinuity was numbered and its extent andlocation marked on a plan of the site. The propertiesof each discontinuity were then mapped andrecorded in a table which enabled the designers tostudy any individual feature that could have aninfluence on stability.(b) Corrections for discontinuity orientationAn important factor to consider in the interpretationof mapping results is the relative orientationbetween the face and the discontinuities. Thisrelative orientation introduces a bias to both thediscontinuity spacing and the number ofdiscontinuities that are mapped. The bias arisesbecause all discontinuities oriented at right angles tothe face will be visible on the face, while fewdiscontinuities oriented sub-parallel to the face willbe visible (Fig. 4.5). The bias in spacing can becorrected as follows (Terzaghi, 1965):

(4.3)where S is the true spacing between discontinuitiesof the same set, Sapp is the measured (apparent)spacing and ? is the angle between face and strikeof discontinuities.The number of discontinuities in a set can be

adjusted to account for the relative orientationbetween the face and the strike of the discontinuityas follows:

(4.4)

where N is the adjusted number of discontinuitiesand Napp is the measured number of discontinuities.For example, a vertical drill hole will inter sect fewsteeply dipping discontinuities and the Terzaghicorrection will calculate an appropriate increase inthe number of these surfaces. Furthermore, somestereonet programs will use the Terzaghi correctionto increase the number of discontinuities and allowfor the bias in sampling orientation; this moreaccurately represents the population ofdiscontinuities.(c) Roughness measurementsA component of the friction angle of mostdiscontinuities is the surface roughness, and animportant part of any mapping program ismeasurement of this parameter. During thepreliminary stages of an investigation program it isusually satisfactory to make a visual assessment ofthe roughness angle using the method described byBarton (1973) to determine joint roughnesscoefficient (JRC) values of typical discontinuities(see Section 3.4.2).If in the final design stage of a project a fewdiscontinuities having a significant effect onstability have been identified, there are a number ofmethods of accurately measuring the surfaceroughness of these critical surfaces. For example, amechanical profilometer can be used to measure thevariation in height of a rock surface relative to aplanar reference surface, with care being taken tomeasure the roughness in the direction of sliding.Tse and Cruden (1979) demonstrate that it ispossible to correlate these measurements with thestandard profiles proposed by Barton to define JRCvalues, and Yu and Vayassade (1991) describe thesensitivity of these measurements to the samplingfrequency.An alternative method of measuring roughnessdeveloped by Fecker and Rengers (1971) consistsof measuring the orientation of the discontinuity

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with a geological compass to which a series ofplates of different diameters are attached to the lid(Fig. 4.6(a)). If the diameter of the larger plates isabout the same dimensions as the wavelength of theroughness, then the measured orientation will beapproximately equal to the average orientation ofthe surface. However, the smaller diameter plateswill show a scatter in the orientation measurementsas the plates lie on irregularities with shorterwavelengths. If the orientation measurements areplotted on a stereo net, the degree of scatter in thepoles about the mean orientation is a measure of theroughness. Alternatively, a plot of plate diameteragainst roughness angle i will show that shortwavelength asperities ?1 have higher roughnessangles than those with longer wavelengths ?2(Fig. 4.6(b)).An important factor to consider in the measurementof roughness is the minimum wave-length of theasperities that should be used in design. As aguideline for design, it is suggested the selection ofa value for i depends on the dimensions of thebearing area relative to maximum wavelength. Forexample, in the case of a spread footing with abearing surface area not more than the wavelength ?2, a roughness angle corresponding to platediameters of 2d–3d for which the i value is about15° would be appropriate (Fig. 4.6(b)). However, inthe case of a structure with a bearing surface equalto several multiples of ?2, a roughness anglecorresponding to plate diameters of 6d–8d for whichthe i value is about 5° may be suitable. The scaleeffect results in some reduction in roughness anglewith larger samples such that the shorter wavelengthasperities seem to have less influence on overallfriction angle for in situ conditions where thesliding surface has a length of at least severalmeters (Patton and Deere, 1970; Barton andChoubey, 1977). In general, the total friction angle

used in design would normally not exceedabout 50°. The other factor to consider in theselection of i is the magnitude of the normal stresson the surface compared with the compressivestrength of the rock (see Section 3.4.2).

4.3Drilling

Detailed foundation design will usually requiremore information on the sub-surface characteristicsof the bearing material than can be extrapolatedfrom surface mapping. Methods of drilling that canbe used for subsurface investigations includediamond drilling, and occasionally percussion orlarge diameter drilling: calyx drilling. If exposuresfor bedrock mapping are limited, test pits may beexcavated to expose the underlying rock. However,test pits will not be able to penetrate to a significantdepth into the rock, unless it is very weak, so testpits will rarely provide information on subsurfacerock properties.

4.3.1Diamond drilling

Diamond drilling is the most common method ofsub-surface exploration for rock; it is used to obtainintact and undisturbed core samples that provideinformation on geological conditions, as well assamples for laboratory testing (see Section 10.2.1).Similarly to surface mapping, it is important to usestandard core logging procedures so that conditionsbetween sites can be compared (ISRM, 1981a).(a) Core loggingA typical core log in Fig. 4.7(a) shows commondata which are recorded on drill logs. Note that onthe logs that qualitative data—RQD anddiscontinuity frequency (number of discontinuities/unit length)—are plotted in the form of histogramssuch that zones of closely fractured or weak rockappear as wide bars that can be readily identifiedwhen scanning the log. Discontinuity frequency andRQD are defined as follows, with care being takento distinguish between natural discontinuities anddrill induced (mechanical) breaks in the core:

An RQD value of 100% means that every piece of


core has a length greater than 100 mm (4 in.) and isindicative of good quality rock. It is also importantto take a color photograph, complete with a legend,scale and color chart, of each core box (Fig. 4.7(b)). (b) Core recoveryAn important requirement for diamond drillingconducted for foundation engineering purposes is

complete recovery of the core. All zones and seamsof weak and fractured rock must be recovered whichrequires the use of techniques that minimizebreakage and loss of core. This can be achievedwith minimum N size core (45 mm, 1.775 in.diameter) because core breakage increases withdecreasing core size. Core quality is also enhancedwith the use of a triple tube core barrel in which the

Figure 4.6 Measurement of surface roughness values with plates of different diameters attached to the lid of ageological compass: (a) dip measurements with plates of differing diameters; and (b) relationship between roughnessmeasurements and plate diameters.

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inner tube is mounted on bearings that do not rotateduring drilling so there is little spinning or vibrationof the core. When the core barrel is recovered at theend of the drill run, the inner tube is pumped out ofthe core barrel rather than hammered out, as is thecase with a double tube barrel. The usual procedurefor logging the core is to lay the inner barrel, whichis split longitudinally, on a cradle, such as a length of L-section steel, so that the upper half of thebarrel can be removed without disturbing the core.This allows the core to be logged while it is still inthe barrel. A further refinement for drilling in verypoor rock is to use a transparent perspex inner tubein which the core can be logged once it is removedfrom the split triple tube. Careful drilling forfoundation investigations will usually require thatthe drillers work on an hourly rate; drillers workingon a footage basis with a production bonus will tendto sacrifice quality for quantity.In very closely broken rock standard drillingtechniques may not be adequate to obtain goodquality core and in these circumstances it may benecessary to use a procedure developed by Rocha(1967). This involves grouting a steel rod into a pilothole and then overcoring this to remove an integralsample comprising both the rod and the surroundingcore. If the rod is oriented before it is grouted inplace, then it is also possible to orient the core (seebelow).Core recovery values are usually used inconjunction with RQD measurements to assess therock mass quality. For example, a rock masscomprising a strong, slightly weathered rockcontaining wide, clay-filled seams may give theappearance of having a high RQD value if the clayis lost in the drilling. However, the core recoveryvalues would show the amount of missing core andallow a true value of the RQD to be calculated.(c) Core orientationA possible requirement of diamond drilling forfoundation engineering is orientation of the core sothat the dip and dip direction of the discontinuitiescan be determined. For example, it may benecessary to orient a drill core where there is apossibility of shear failure taking place on persistent

discontinuities, or settlement due to compression ofclay filled seams. In a vertical drill hole the dip ofall the discontinuities intersected by the hole can bedetermined, but there is no information on their dipdirection; in an inclined drill hole it is not possibleto determine either dip or dip direction ofdiscontinuities from examination of the core.Methods of orienting discontinuities during drillinginclude marking a line of known orientation on thecore and measuring the position of the discontinuityrelative to this line, and the use of the boreholecamera as described below.A simple and effective core orienting device is theclay impression core barrel (Fig. 4.8(a)) whichutilizes a modified inner core barrel withconventional wire-line diamond drilling equipment(Call et al., 1982). The barrel is eccentricallyweighted with lead and lowered into an inclinedborehole so that its orientation with respect to thevertical is known, i.e. the weight rotates to thebottom of the hole. Modeling clay protrudes fromthe downhole end of the inner barrel such that it alsoextends through the drill bit when the inner andouter tubes are engaged. The barrel assembly ispressed against the hole bottom which causes theclay to take an impression of the core stub left fromthe previous core run. The inner barrel is thenretrieved with the wire-line and a conventionalbarrel is lowered to continue coring. At thecompletion of the run, the recovered core is fittedtogether and the core is oriented by matching thepiece of core from the upper end of the core runwith the oriented clay imprint. A reference line,which represents the top of the core, is run from theoriented core stub along the length of the core. Allthe discontinuities in the core can then be orientedrelative to this line and their dip and dip directioncalculated if the dip and plunge of the hole areknown (Fig. 4.8(b)). Computer programs areavailable to convert core discontinuity anglesdirectly to dips/dip directions and plot them on astereo net.The clay impression barrel can only be used ininclined holes within the dip range 45°–70° wherethe weighted barrel will orient itself as it is lowered


down the hole. In shallow vertical holes, the corebarrel may be oriented by scribing an oriented

reference line down the side of the drill rods as theyare lowered down the hole. A disadvantage of the

Figure 4.7 Diamond drill core logging procedures: typical diamond drill core log and photograph of diamond drill corewith length scale and color reference scale.

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clay impression barrel method is that only the toppiece of each core run is oriented, and if there is azone of fractured rock in which it is not possible tofit all the core fragments together then theorientation line will be lost below this point.Another method of orientating core is theChristienson-Hugel technique that scribes threecontinuous, oriented longitudinal grooves down theside of the core as it enters the barrel during drilling

(Boart Longyear Co., 1996). The grooves are cut bythree tungsten carbide scribes located just behindthe bit, and the scribes are spacedaround thecircumference of the core such that it is possible todetermine the top of each piece of core. Thereference groove is fixed relative to the orientinglug, and the orientation of the lug is measured witha multi-shot directional survey instrument located inthe upper part of the non-magnetic core barrel. The

Figure 4.8 Clay impression core barrel orientation procedures: (a) core barrel used to orient diamond core in inclineddrill holes (Call et al., 1982); and (b) dip/dip direction measurements of discontinuity in oriented core.


multi-shot instrument takes photographs of the lugand a compass at any interval depending on therequired frequency of orientation measurements.Once the orientation of the reference groove hasbeen measured on the film, the orientation of eachdiscontinuity is determined using a goniometer, orthe technique illustrated in Fig. 4.8 (b).A disadvantage of these two core orientationtechniques is that they interrupt and slow down thedrilling, and the orientation measurements are madeon disturbed core. Alternative procedures tomeasure the orientation of discontinuities in situ arethe side scanning borehole video camera, or theimpression packer. The impression packer makes animprint of the discontinuities in the wall of the hole,while the video camera provides a continuous,colored, 360° record of features in the wall of the drillhole, including water and gas discharges. Thecamera housing also contains a compass todetermine the orientation of the camera in the hole,and the depth down the hole is precisely measuredwith a sensor on the cable on which the camera issuspended. Software that processes the recordedvideo image can rotate the ‘core’ so that it can beviewed from any direction, or can display anunwrapped view of the wall of the hole. Theunwrapped view shows each discontinuity in theform of a sine wave from which the orientation ofthe discontinuity, as well as its width, can bedetermined. The procedure is to use a mouse todigitize points along the trace of the discontinuitywhich are then fitted to a true sine wave from whichthe orientation is calculated (Fig. 4.9).An essential part of any oriented core measurementsis borehole surveying to determine the dip andplunge of the hole at selected intervals. With thisinformation, measured discontinuity orientationscan be corrected for the true inclination of the hole.Hole survey instruments include the Sperry Sun andEastman multi-shot tools that take photographs of acompass and dip circle at pre-set time intervals. Thetool is lowered down the hole on the wireline andthe depth recorded at the times that the photographsare taken. In this way the orientation of the hole at anumber of depths can be obtained. The Tro-Pari

instrument is a single shot tool that has the compassand dip circle mounted on gimbals that are locked inposition after a time interval that is sufficient tolower the instrument to the bottom of the hole.

4.3.2Percussion drilling

Percussion drilling using a pneumatic or hydraulicdrill is less expensive and has a faster penetrationrate than diamond drilling (see Section 10.2.2).However, because no core is obtained it will notprovide much more information than the depth tobedrock, and the approximate variation in rockstrength by observing changes in the penetrationrate and the color of the cuttings. This informationwould only suffice in the case of the design offoundations for structures with low bearingpressures. However, instrumentation is availablethat can be attached to percussion drill rigs to recordand produce plots of a number of differentgeological parameters continuously during drilling(Lutz and Morey, 1988). Typical parameters thatcan be recorded with this instrumentation include:

1. instantaneous feed rate which is related to themechanical properties of the rock such asmodulus and hardness;

2. tool thrust which supplements the feed rate datawhen cavities are encountered;

3. tool torque which can be used to identify graveland boulder zones;

4. drilling fluid pressure which is related to thepermeability of the formation being drilled;pressures are high in plastic deposits such asclay, and low in sands and gravel; and

5. drill string vibration which is related to the rockhardness.

Percussion drilling with automatic recordinginstruments could be used to back up a diamonddrilling program with the core being a reference tocalibrate the percussion results.

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4.3.3Calyx drilling

At locations where it is necessary to observe in siturock conditions and also obtain large diameter corefor testing purposes, core holes with diameters of 1–3 m (3–10 ft) can be drilled with a Calyx drill. Thiscomprises a steel barrel, equipped with tungstencarbide teeth, to which both a thrust and torque canbe applied. After the drill has advanced by about 1m (3 ft), the core is broken off either by drivingwedges into the annulus, or by an explosive methodusing a detonating cord placed at the bottom of theannulus. The core is removed by grouting a liftingeye into the top of the core and pulling it out with acrane.

4.4Ground water measurements

The main effects of ground water on foundation

performance are uplift pressures that reduce theshear strength resistance of discontinuity surfaces,and seepage that results in loss of storage water, andin extreme cases, scour of weak seams within therock mass. The relationship between the distributionof water pressures within the rock mass and the rateof seepage through it is given by Darcy’s Lawwhich states that (Fig. 4.10):

(4.5)where Qs is the seepage volume per unit time, k isthe coefficient of permeability, A is the cross-sectional area of the sample, and ih is the pressuregradient. The pressure gradient is given by

(4.6)

where is the head loss between the ends ofthe sample with length l. The head h is equal to thepressure P, at depth h, divided by the water density, ?w (Fig. 4.10).The relationships in equations 4.5 and 4.6 show that

Figure 4.9 Orientation of discontinuity in borehole using image from 360° scanning video camera: (a) core-like imageof drill hole showing elliptical intersection between hole and discontinuity; and (b) expanded (‘unwrapped’) view ofborehole wall with discontinuity displayed as sine wave (Colog Inc., 1995).


the definition of ground water conditions within afoundation requires information on at least two ofthe three parameters, namely the seepage rate perunit area Qs/A, the pressure gradient ih and thepermeability k, the usual units of which are m/s.This section describes methods of measuringground water pressure and rock mass permeability.(a) PermeabilityThe permeability of most intact rock (primarypermeability) is essentially zero and the flowof water in a rock mass (secondary permeability) isconcentrated in the discontinuities. Consequently,ground water conditions are highly dependent uponthe orientation, length, width and infillingcharacteristics of the discontinuities. In the designof investigation programs, as well as drainage andgrouting systems, drill holes should be oriented tointersect discontinuities that are expected to carrywater.In rock types such as sedimentary and metamorphicrocks, in which there is a predominant discontinuityorientation, ground water flow will be concentratedin a direction parallel to the predominantdiscontinuities, i.e. the bedding or foliation. Suchrock types will exhibit anisotropic permeability.That is, the permeability will be significantlygreater parallel to the bedding than perpendicular toit. A modified form of Darcy’s law can be used foranisotropic rock as follows:

(4.7)where k1 and k2 are the permeabilities parallel and

perpendicular to the predominant discontinuity set,respectively.The permeability of a rock mass is highlydependent upon the width of the discontinuities, andit has been shown that the permeability of an arrayof smooth, parallel discontinuities is proportional tothe cube of the opening width of the discontinuity(Louis, 1967). Therefore blasting and stress reliefthat result in opening of discontinuities can producea significant increase in seepage quantities. Anotherfactor to consider is that Darcy’s law is onlyapplicable for low velocity, laminar flowconditions. These conditions will usually apply inthe case of jointed rock and in fact no lower limit isknown to exist for Darcy’s law (Todd, 1959).However, Darcy’s law cannot be used for materialswith large diameter solution openings and verysteep gradients. A guideline on applicableconditions for Darcy’s law is when the Reynoldsnumber is less than 1. Reynolds number (Re) isgiven by

(4.8)

where ?w is the fluid density, v is the flow velocity,d is the diameter (of a pipe), and ? is the viscosity ofthe fluid.Because of the very great influence of thediscontinuities on the permeability of the rockmass, ground water studies should consist of in situmeasurements with as little disturbance of the rockmass as possible. Common investigation methodsdescribed below consist of the installation of

Figure 4.10 Definition of permeability in terms of Darcy’s law.

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piezometers in drill holes to measure waterpressure, and conducting falling head and pumptests to measure permeability.

4.4.1Water pressure measurements

A piezometer is a system installed in a drill hole tomeasure the water pressure existing at a point, orover a nominated interval, in a saturated material.Piezometers can also be used for ground watersampling, permeability testing, and as observationwells during pump tests. With careful installation,they will also allow long term monitoring of groundwater conditions. The measured pressure values canbe used directly in stability and seepage analyses.In planning a piezometer installation, two importantdecisions that have to be made are the location ofthe point of measurement, and the method ofmeasuring the piezometric level. First, the locationof the point of measurement is determined by thegeometry of the foundation, with the pressure beingmeasured in the vicinity of potential failure surfacewhere uplift pressures could cause instability. Also,the measurement zone must intersect discontinuitiesthat communicate hydraulically with the generaldiscontinuity pattern in the area; the appropriatelocation of the measurement zone is determined,where possible, from examination of drill core.The second factor to consider in piezometerinstallations is the method of measuring the changesin pressure in the piezometer. If the volume ofwater that is required to register a head fluctuationin a piezometer is large relative to the rate of entryat the intake, there will be a time lag introduced intothe piezometer readings. This factor is especiallypertinent to head measurements in low permeabilityformations (Freeze and Cherry, 1979). For thisreason, piezometers in rock usually consist of apressure-measuring device installed in a sealedsection of the drill hole. The volume change withinthis sealed section, caused by the operation of thepiezometer, should be very small in order that theresponse of the complete installation to pressurechanges in the surrounding rock is rapid. If a device

is used that requires a large volume change for itsoperation, the change in pressure induced by thischange in volume may give rise to significant errorsin measurement (Terzaghi and Peck, 1967).Ground water pressures may be monitored in openholes if the permeability of the rock mass is greaterthan about 10−6 m/s. Rock types such as coarsegrained sandstones and highly fractured rock mayhave permeabilities as high as 10−6 m/s, but mostcompetent rocks that would be suitable for thefoundations of large structures have permeabilitiesof less than 10−7 m/s. Therefore, open standpipesare rarely utilized in monitoring of ground waterpressures in rock and one of the types of piezometerinstallations discussed below are usually used.(a) Standpipe piezometersA standpipe piezometer consists of a length ofplastic pipe, with a perforated or porous section atthe lower end which is encased in clean gravel orsand to provide a good hydraulic connection withthe rock (Fig. 4.11). This section of the piezometer,which is the point where the water pressure ismeasured, is isolated from the rest of the hole with aseal(s) comprising filter layers to preventcontamination of the clean sand, and a layer ofbentonite. The bentonite is usually placed in theform of compacted balls that will fall a considerabledepth down a water-filled hole before they expand.In very deep holes the balls can be first soaked inoil to form a protective layer that delays theirexpansion. However, cement is preferred as a sealfor holes with depths greater than about 300 m(1000 ft).The water level in a standpipe piezometer can bemeasured with a well sounder consisting of agraduated electrical cable, with two bared ends,connected to an electrical circuit consisting of abattery and an ammeter. When the bared ends comeinto contact with the water the circuit is closed anda current is registered on the ammeter. Theadvantages of this type of piezometer are that it issimple and reliable, but has the disadvantages thatthere must be access to the top of the hole, and therecan be significant time lag in low permeability rock.(b) Pneumatic piezometers


A rapid response time can be achieved usingpneumatic piezometers which comprise a valveassembly and a pair of air lines that connect thevalve to the surface. The valve is placed in thesealed section of the piezometer to measure thewater pressure at that point. The operating principleis to pump air down the supply line until the airpressure equals the water pressure in the sealedsection and the valve opens to start air flowing inthe return tube. The pressure required to open thevalve is recorded on a pressure gauge at the surface.Pneumatic piezometers are suitable for lowpermeability rock installations and are particularlyuseful for foundation installations where pressuresare being measured under the structure and access tothe collar of vertical drill holes is not possible. Thedisadvantages of this type of piezometer are the risk

of damage to the lines either during construction oroperation, and the need to maintain a calibratedreadout unit. (c) Electronic transducersWater pressure measurements with electricaltransducers allow very rapid response time and theopportunity to record and process the results at aconsiderable distance from the structure. Commontypes of electrical transducers include strain gaugesand vibrating wire gauges that measure pressurewith a high degree of accuracy. It is recommendedthat all transducers be thoroughly tested andcalibrated before installation (Patton, 1987). Itshould also be kept in mind that the long termreliability of these sensitive electrical instrumentsmay not equal that of the structure and provisionshould be made for their maintenance and possible

Figure 4.11 Typical standpipe piezometer installation.

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replacement.(d) Multi-completion piezometersAt locations where there are rock types withdiffering permeabilities, it is possible that zones ofhigh ground water pressure may exist within agenerally depressurized area. In suchcircumstances, it may be desirable to measure theground water pressure at a number of points in adrill hole. This can be achieved by installingmultiple standpipe piezometers in a single drill holewith bentonite or cement seals between each sectionof perforated pipe. The maximum number of suchstandpipes that can be installed in an NX boreholeis three; with more pipes, placement of filter andeffective seals becomes very difficult.An alternative method of measuring water pressures

at a number of different points in a drill hole is touse a multi-port (MP) system which also allowsmeasurement of permeabilities and retrieval of watersamples (Black et al., 1986). The MP system is amodular multiple-level ground water . monitoringdevice employing a single, closed access tube withvalved ports (Fig. 4.12). The valved ports are usedto provide access to several different levels of adrill hole in a single well casing. The modulardesign permits as many monitoring zones as desiredto be established in a drill hole. The system consistsof casing components which are permanentlyinstalled in the drill hole, and pressure transducers,sampling probes and specialized tools that arelowered down the hole. The casing componentsinclude casing sections of various lengths, two

Figure 4.12 Multiple completion piezometer installation (MP System, Westbay Instruments) with probe positioned tomake pressure measurement (Black et al., 1986): (a) probe located at measurement port coupling; and (b) probemeasuring fluid pressure outside coupling.


types of valved port couplings with capabilitieseither to measure pressure or take samples. The portassemblies can be isolated in the drill hole bysealing the annulus between the monitoring zonesusing either pairs of packers, or by filling theannulus with a cement grout or bentonite seal. TheMP system has been used in drill holes up to 1200 m(4300 ft) deep.

4.4.2Permeability measurements

Permeability is the fundamental parametergoverning the flow and pressure distribution ofground water in the rock mass (Cedergren, 1989).Permeability values are required for a number offoundation design procedures, including seepage indam foundations, and the effect of drainage andgrouting on ground water pressure distributions.Because ground water flow in fractured rock takesplace predominately in the discontinuities, it isnecessary that permeability measurements be madein situ; it is not possible to simulate a fractured rockmass in the laboratory. The following is a briefdescription of the two most common methods of insitu permeability testing, namely variable headtests, and pumping tests. Detailed procedures forpermeability tests are described in the literature andthe tests themselves are usually conducted byspecialists in the field of hydrology.(a) Variable head testsThe principle of the variable head tests is tohydraulically isolate a section of a drill hole, eitherin a standpipe piezometer or in an open hole withinflatable packers. Water is then removed from thestandpipe or drill rods so that the water pressure inthe test section differs from the equilibrium groundwater pressure. This results in water flowing fromthe rock surrounding the test section untilequilibrium is re-established (rising head test).Permeability is determined by measuring the rate atwhich a known volume of water flows from therock under a known head. In the falling head test therate at which the water falls in the rods or pipe ismeasured, while in the constant head test the

volume of water required to keep the water in therods at a constant level is measured.Permeability tests carried out in piezometers arelimited to the section defined by the position andlength of the perforated portion of the piezometer.However, in an open hole the use of inflatablepackers allows tests to be carried out in any positionin the hole and over any length of hole so thepermeability of selected discontinuity zones can beinvestigated.Permeability measurements can be made duringdiamond drilling using a triple packer system that islowered through the rods so that the test isconducted in a portion of the hole below the bit(Fig. 4.13). The packer system consists of threeinflatable rubber packers, each 1 m (3 ft) long whichis sufficient to minimize the risk of leakage past thepacker. The lower two packers are joined by aperforated steel pipe, the length of which dependson the required test length, while the top and middlepackers are joined by a solid pipe. The wholepacker assembly is lowered down the drill hole onthe wire line through the drill rods and the lowertwo packers extend through the bit into the openhole, while the upper packer is located in the lowerend of the core barrel. The three packers are theninflated with nitrogen through a small diameterplastic tube that runs down the hole to seal thepacker assembly into the rods and isolate a length ofdrill hole below the bit. If water is introduced intothe drill rods it will flow through the perforated pipeinto the rock isolated by the two lower packers. Thisflow of water is measured by monitoring the changeof water level in the drill rods. The procedure for the variable head test is first toestablish the rest water level which is the staticequilibrium level of the water table at the drill holelocation (Fig. 4.14). The pumping of circulationwater during drilling will disturb this equilibriumand the permeability results will be in error ifinsufficient time is allowed for equilibriumconditions to be re-established. Once equilibriumhas been established, water is removed from thestandpipe (piezometer test) to lower the water levelby about 1–2 m (3–6 ft) and the rate at which the

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water level rises in the pipe is measured. For a test set up such as shown in Fig. 4.14, the permeability k

Figure 4.13 Triple packer arrangement for making falling-head permeability tests in conjunction with diamond drilling.


is calculated from the following relationship:

(4.9)

where A is the cross-sectional area of the standpipe is the internal radius of the standpipe; L

is the length of the uncased test section; t1 and t2 arethe times at which the water level has risendistances of h1 and h2 respectively above the newequilibrium level established by removing waterfrom the hole. The differential heads h1 and h2 aswell as the initial equilibrium head h0 are defined inFig. 4.14(a), while a typical semilog plot of the risein water level in the casing with time is shown inFig. 4.14(b).The different diameters of the drill hole andstandpipe are accounted for by the shape factor, Fwhich for this test arrangement is given by:

(4.10)

where R is the radius of the drill hole.

(b) Pumped wellsThe main limitations of permeability tests carriedout in drill holes are that only a small volume ofrock in the vicinity of the hole is tested, and it is notpossible to determine the directional anisotropy ofthe rock mass. Both these limitations are overcomeby conducting pump tests, as described brieflybelow.A pump test arrangement consists of a vertical wellequipped with a pump, and an array of piezometersin which the water table elevation can be measuredin the rock mass surrounding the well. Thepiezometers can be arranged so that the influence ofvarious geologic features on ground waterconditions can be determined. For instance,piezometers could be installed on either side of afault, or in directions parallel and perpendicular tosets of persistent discontinuities such as beddingplanes. Selection of the best location for both thepumped well and the observation wells requiresconsiderable experience and judgment and should

Figure 4.14 Method of calculating permeability for variable head test in cased observation well. (a) test arrangementshowing variable heads h and times t; and (b) plot of head increase against time.

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only be carried out after thorough geologicalinvestigations have been carried out.The test procedure consists of pumping water at asteady rate from the well and measuring the drop inwater level in both the pumped well and theobservation wells. The duration of the test can rangefrom as short as eight hours to as long as severalweeks depending the permeability of the rock mass.When the pumping is stopped, the water levels inall the wells are measured until a static water levelis determined—this is known as the recovery stageof the test. Plots of draw down (or recovery) againsttime can be used to calculate permeability valuesusing methods described by Cedergren (1989),Todd (1959), Jacob (1950) and Theis (1935).Because of the cost and time required for pumptests, they are usually only conducted for the designof major structures such dams where both seepageand uplift are of concern. For other structures,installation of piezometers to measure the groundwater table and conduct falling head tests usuallyprovides sufficient information on ground waterconditions for design purposes.

4.5In situ modulus and shear strength testing

In situ testing of deformation modulus and shearstrength is sometimes required for the design offoundations for major structures such as dams andbridges. Circumstances where this might be car riedout include foundations comprising closelyfractured and weak rock that could compress,resulting in settlement of the structure, orcontinuous, low strength discontinuities on whichsliding could take place. The need for in situ testingwould arise when it is not possible to obtainundisturbed samples, or sufficiently large samples,for laboratory testing.

4.5.1Modulus testing

While the modulus of intact rock can be determinedby laboratory tests on pieces of core, the modulus of

fractured rock masses, which depends upon bothstrain of intact rock, and closure and movement ofthe discontinuities, must be determined by in situmethods. With all in situ tests there will be somedisturbance of the rock, particularly where blastingmust be used to prepare the site, and the test mustbe designed to evaluate the extent of thisdisturbance. Furthermore, excavation of thefoundation may also involve some disturbance tothe rock and it is important to make an assessmentof the degree of disturbance at the test sitecompared with the likely condition in thefoundation.Three methods of in situ modulus testing aredescribed in this section, starting with tests on smallvolumes of rock at the periphery of a drill hole andprogressing to large scale tests conducted intunnels. The choice of the appropriate testingmethod will depend on such factors as the spacing ofthe discontinuities in comparison with the testvolume, the magnitude of the test load incomparison with the structural load, and, of course,time and budget constraints.(a) Borehole testsThe deformation modulus can be measured inboreholes using either a borehole dilatometer or aborehole jack. The advantages of borehole testingare that modulus measurements can be made remotefrom the surface as part of the exploration program,and different geological conditions at the site can beexamined. Also, the tests can be carried outrelatively quickly and at a lower cost compared withplate load and radial jacking tests. Thedisadvantages of borehole tests are that the volumeof rock tested is small and the measurements areonly in the direction at right angles to the boreholeaxis which may not coincide with the loadingdirection of the structure.The dilatometerThe dilatometer exerts a uniform radial pressure onthe walls of the drill hole by means of a flexiblerubber sleeve. The expansion of the borehole ismeasured by the oil or gas flow into the sleeve asthe pressure is raised (Goodman et al., 1968), or bypotentiometers or linear variable differential


transformers (LVDT) built inside the sleeve (Rochaet al., 1966). This latter type, in which themeasurement devices are arranged at right angles,has the advantage that the anisotropy of the rock canbe measured.Figure 4.15 shows the components of a ColoradoSchool of Mines (CSM) type flexible dilatometer.The expansion volume of the borehole is measuredwith a hand-operated screw pump in which thenumber of turns or part turns are preciselymeasured; this requires that the hydraulic system beof rigid construction to minimize errors inmeasuring dilation. Alternatively, the volumetricexpansion can be measured directly in the probe(Bourbonnais, 1985). Figure 4.16 shows typicalpressure-dilation graphs for a calibration test carriedout in a material of known modulus, and a testcarried out in rock. A complete test usually consistsof three loading and unloading cycles, with dilationand pressure readings being taken on both theloading and unloading cycles.The shear modulus Gd and the modulus of elasticityEd of the rock in the drill hole test section are givenby (ISRM 1987):

(4.11)

and(4.12)

where L is the length of test section (cellmembrane); d is the diameter of drill hole testsection; VR is Poisson’s ratio of the rock; ? is thepump con stant (the fluid volume displaced per turnof pump wheel). The stiffness of rock in test sectionkR is

(4.13)

where ks is the stiffness of hydraulic system(equation 4.16) and kT is the stiffness of overallsystem plus rock (ratio D/C in Fig. 4.16).The rock stiffness kR is calculated from calibrationof the hydraulic system and the results of a pressure-dilation test carried out in a calibration cyl inder ofknown modulus. The steps for calculating the rockstiffness are as follows. If the elastic modulus and

Poisson’s ratio of the calibration cylinder are Ec andvc respectively, then the shear modulus Gc of thecalibration cylinder is given by

(4.14)

and the stiffness of the calibration cylinder kc is

(4.15)

where , and ri, ro are the inside andoutside radii of the calibration cylinder respectively.The stiffness of the hydraulic system, ks, iscalculated from the stiffness of the calibrationcylinder and the slope of the calibration pressure-dilation curve, km (ratio B/A in Fig. 4.16) as follows:

(4.16)

It is also necessary to make a correction for pressurelosses due to the rigidity of the membrane. This isdetermined by inflating the dilatometer in the airwithout confinement to show the pressure requiredto inflate the membrane and the hydraulic system.

(4.17)where pi,corr is the corrected pressure; pi is theindicated pressure; n is the number of turns to attainpi, and mp is the slope of pressure-dilation curve fordilation in air (MPa/turn).Another correction is required to account for loss ofvolume in the hydraulic system that takes place ininflating and seating the membrane. For the testmeasurements shown in Fig. 4.16, the net correctednumber of turns ?ncorr is calculated from

(4.18)

(b) Borehole jackAs an alternative to the flexible dilatometer, theborehole jack can be used to measure rockdeformability in a drill hole. The jack exerts adirectional pressure by means of semi-cylindricalsteel loading platens, with the deformation beingmeasured with linear variable differentialtransformers (LVDTs) built into the cell.Calculation of the modulus is carried out in a

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similar manner to that of the dilatometer, exceptthat allowance must be made for the more difficultboundary conditions. It has been shown by finiteelement analysis that calculated values of rockmodulus should be corrected to account for thevariation in the ratio between the steel and the rockmoduli (Heuze and Salem, 1977). When the

modulus of the steel is much greater than that of theintact rock (Esteel/Erock>75), the correction factor isnegligible because there is little deformation of thesteel platens as the pressure is applied. However,when the rock modulus is high compared with thesteel modulus, the modulus value calculated fromthe jack test is less than the true rock modulus

Figure 4.15 Dilatometer for making modulus measurements in boreholes (ISRM, 1987): (a) components of adilatometer system; and (b) cross section showing fabrication details of CSM-type dilatometer.

1. Piston actuator.

2. Vernier.

3. Valve.

4. Pressure transducer.

5. Pressure readout.

6. High-pressure stainless-steel tubing.

7. Polyurethane rubber membrane.

8. Removable end cap.

9. High-pressure connection.

10. Pipe thread for insertion tool.

11. Fluid passage.


and the correction factors shown in Table 4.1 shouldbe applied.(c) Plate load testThe plate load test comprises application of acompressive stress normal to the rock surface andmeasuring the deformation of the rock as the load isapplied. The test can be carried out in an explorationadit where the opposite wall of the adit provides thereaction to the applied load, and with the loadoriented to coincide with the direction of thestructural load, such as the thrust of the abutment ofan arch dam. In low modulus rock where substantialdeformation is expected, the load can be applied bymeans of an hydraulic jack. However, the test canbe time consuming and expensive because of greatweight of the jack and an alternative means ofapplying the load is to use flatjacks placed between

the two reaction surfaces (Fig. 4.17). Althoughflatjacks are lighter and easier to handle thanhydraulic jacks, they have limited expansioncapacity (about 5 mm or 0.2 in.), and a series offlatjacks are required if substantial deformation isexpected. Where it is necessary to conduct a test atthe ground surface, the reaction can be applied bymeans of a cables anchored at some depth below thesurface using an arrangement such as that shown inFig. 4.18 (Pusch, 1993).Site preparation consists of removing all rock thatmay have been loosened by blasting duringexcavation of the adit and then using grout to createa uniform bearing surface normal to the loaddirection. The theoretical basis for the plate loadtest is that the load is applied to an infinite halfspace, a condition that is not met in a tunnel

Table 4.1 Correction factors for borehole jack modulus measurements

Erock/Ecalc Esteel/Erock

1.09 30.0

Figure 4.16 Typical pressure-dilation graphs for a CSM dilatometer test (ISRM, 1987).

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Erock/Ecalc Esteel/Erock

1.75 7.52.38 4.82.86 3.93.7 3.2which consists of a small hole in an essentiallyinfinite volume of rock. In order to minimize therestraining effect of the surrounding rock on thedeformation induced by the plate loading test, it hasbeen shown that the width of the tunnel should benot less than twice the diameter of the loaded plateas shown in Fig. 4.19 (Misterek et al., 1974).Deformation measurements are made with a tunneldiameter gauge that registers the increase in width ofthe tunnel, and with multi-position extensometers(MPBX) installed in holes drilled into the rockalong the load axis. The depth of the extensometerholes must be such that the deepest anchor isbeyond the zone of deformation, a distance of aboutsix times the flatjack diameter. With the use ofLVDTs to measure the relative displacementbetween the anchors and the heads at the rocksurface, a continuous reading of deformation can beobtained at some distance from the test location.The extensometer readings provide information onthe variation of modulus with depth, the location ofopen discontinuities and the extent of the blastdamage zone. The modulus is calculated from thedisplacement measurements using equationsdeveloped by Timoshenko and Goodier (1951),assuming that the rock is a homogeneous infinitehalf space of elastic isotropic material. For a testcondition in which the bearing plate is circular andhas a circular hole in the centre through which thedeformation measurements are made, thedeformation modulus Ez at any depth z is given bythe following expression (ISRM, 1981a and b)

(4.19)

where ?z is the measured deflection at depth z belowthe lower surface of the bearing plate; p is the

applied pressure on the bearing plate; v is thePoisson’s ratio; r1 is the radius of hole in the centreof the bearing plate; r2 is the outer radius of bearingplate; and C is a constant (see below). For a circular bearing plate with radius r and nocentre hole and deflection measurements made atdepths z below the rock surface, the deformationmodulus is given by

(4.20)

For measurements at the surface of the rock where this expression reduces to

(4.21)

The theoretical solution for a perfectly rigid plategives the constant C as p/2, or 1.57. However,allowance must be made for the slight flexibility ofthe plate through which the load is applied whichresults in the deformation being somewhat greaterthan the theoretical deformation. This results in thecalculated modulus being less than the true modulusand for this reason the constant C is usually giventhe value of 2.Heuze and Salem (1977) examined a number ofdifferent test conditions and give values forcorrection factors that should be applied to testsresults. These conditions include the ratio Esteel/Erock, the plate geometry, the anisotropiccharacteristics of the rock, and the effect of rockbreakage under the plate. These calculations showthat use of a value of 2 for the constant C isgenerally satisfactory. However, for anisotropicrock, the plate load test will tend to over-estimate themodulus where the load is applied at an oblique angleto the direction of greatest compression, or lowestmodulus. Under these conditions the constant C


may have a value as low as 1.0–0.8.(d) Radial jacking testThe plate load test has a number of limitations,namely that the load is applied along a single axisand, in the case of widely jointed rock, theloaded area may encompass few if anydiscontinuities in which case the rock mass is notbeing tested. These limitations are overcome to somedegree by the radial jacking test in which a uniformradial pressure is applied to a length of theperiphery of a tunnel, and radial deformations aremeasured along a number of axes. The results ofthis test will provide the deformation modulus of alarger volume of the rock mass than is possible withthe plate load test and, in the case of anisotropicrock, will show the variation of the modulus withrespect to the bedding or foliation orientation.Although more information on rock conditions is

provided by the radial jacking test than the plateload test, the high cost and time required forconducting the test means that very few will becarried out and thus the results may not berepresentative of the overall site.Details of the set up, testing and analysis proceduresare described by Wallace et al. (1969), Misterek(1969), Golze (1977), ISRM (1981a).The test set up consists of first carefully preparing alength of tunnel by removing all blast damaged rockand irregularities so that the rocksurface is as closeto a circular shape as possible. The tunnel diametershould be about 2.5 m (8 ft). The test length shouldat least equal to the diameter, and the length of thetunnel with a circular section should be about 1.5times the length of the test length to eliminatepossible end effects. A shotcrete or concrete liningis then placed to produce a smooth bearing surface

Figure 4.17 Typical set up for a uniaxial jacking test in which the load is applied through hydraulic flatjacks (Mistereket al., 1974, © ASTM, reprinted with permission).

1. Concrete pad. 2. 1 m diameter flatjack. 3. Particle board pad. 4. Top plate. 5. MPBX anchors-5 or more/hole. 6.MPBX sensor head. 7. Rubber sleeve over lead wires. 8. Transducer lead wire. 9. Hydraulic hoses. 10. Hydraulic pump,70 MPa. 11. Data-acquisition system MPa. 12. NX drill hole, depth=6 flatjack diameters. 13. Prepared diameter, 1.5 to2×flat jack diameter. 14. Base plate. 15. Screws for set up and removal. 16. Tunnel diameter gauge. 17. 254 mmdiameter aluminum columns. 18. Tunnel surface.

SITE SELECTION 129

for the jacks. If the purpose of the test is to measurethe rock modulus, then the lining should besegmented so that it produces no restraining effecton the radial strain of the rock. If the purpose of thetest is to examine the lining together with the rock,then the lining should not be segemented and itsproperties should be modeled according to those ofthe prototype.A series of radial holes are then drilled and multi-position extensometers installed with the longestanchor at a depth where no rock deformation willtake place. This depth is about two diameters fromthe loaded surface, which can be checked bycarrying out trial calculations of deformation versusdepth for typical test parameters. The number ofextensometers installed in the central plane of thetest section can vary from 4 to 16 equally spaced

around the circumference. Additional referenceextensometers arrays can be placed at distances of 0.5 and 1.0 times the test length along the tunnel tomeasure deformation remote from the pressure zone.Where the rock is anisotropic or contains apredominant discontinuity set, some extensometerscan be oriented parallel and perpendicular to thestructure.The pressure can be applied either using waterpressure (Fig. 4.20, Oberti et al., 1986), or a seriesof hydraulic flatjacks (Fig. 4.21; ISRM, 1981a orb). The advantage of using water pressure is thatuniform pressure can be applied over a considerablelength of the tunnel, but it is necessary that the rocksurface be completely sealed, which may bedifficult in low modulus rock. Details of the setupof a radial jacking test using flatjacks shown in

Figure 4.18 Typical arrangement of plate load test at ground surface (Pusch, 1992). 1. Hydraulic jacks. 2. Steel beamreaction head. 3. Steel lid. 4. Tie rods. 5. Concrete foundation. 6. Schistose gneiss. 7. 100 mm dia. anchor holes.


Fig. 4.21 illustrates the use of circular steel sets andshaped wooden lagging, located at a uniformdistance from the flatjacks, to provide reaction tothe applied pressure. The deformation is measuredwith short, single position extensometers referencedto a central, independently supported beam.The rock mass deformation modulus is calculatedalong any radius from the pressure-deformationmeasurements assuming that the test consists of acircular hole in an infinite elastic medium with auniform radial pressure applied to a finite length ofthe surface of the hole. An exact solution to thiscondition has been presented by Tranter and Craggs(1945) which assumes that the rock is continuous,homogeneous, isotropic and elastic. It is consideredthat these conditions are adequately satisfied for theradial jacking test because the discontinuities do notopen or fail by shear. The following calculationprocedure provides a reasonably accurate analysisof the test results; a more detailed analysis can becarried out by numerical methods.If flatjacks are used (Fig. 4.21), the applied load

values are first corrected to give an equivalentdistributed pressure p1 on the test chamber lining:

(4.22)

where p1 is the distributed pressure on the lining atradius r1; b is the width of the flat jack; r1 is theradius at flatjacks; pm is the manometric pressure inthe flatjacks.The equivalent pressure p2 at a measuring radius r2just beneath the lining and outside the zone ofirregular stresses beneath the lining and any looserock is calculated as follows:

(4.23)

Superposition of displacements for two ‘fictitious’loaded lengths is used to give the equivalentdisplacements A for an infinitely long test chamber(Fig. 4.22):

(4.24)where ?A1 is the measured deformation at the centerof the test chamber; and ?B is the measured

Figure 4.19 Required dimensions of adit for conducting uniaxial jacking tests (Misterek et al., 1974, © ASTM reprintedwith permission): (a) analysis condition—loading at boundary of semi-infinite elastic solid; and (b) site conditionsshowing required dimensions of tunnel. Note: R is the radius of the loaded area and the diagrams are not to scale.

SITE SELECTION 131

de formation at a distance L from the center of thetest chamber (where L is the length of the testchamber).The result of the long duration test ?d undermaximum pressure (max. p2) is plotted on thedisplacement graph (Fig. 4.23). Test data for eachcycle are proportionally corrected to give thecomplete long-term pressure-displacement curve.The elastic component ?e and the plastic component ?p of the total deformation ?t are obtained from thedeformation at the final unloading:

(4.25)The elastic modulus E and the deformation modulusof the rock mass, Em at radial distance r2 (Fig. 4.21)are obtained from the pressure-displacement curves(Fig. 4.23) using the following formulae based onthe theory of elasticity:

(4.26)

(4.27)

where p2 is the maximum test pressure; and v is theestimated value for Poisson’s ratio. As an alternative to equations 4.26 and 4.27, the

moduli of undisturbed rock may be calculatedtaking into account the effect of a fissured andloosened region by using the following formulae:

(4.28)

(4.29)

where r3 is the radius to the limit of the assumedfissured and fractured zone.

4.5.2Direct shear tests

Direct shear tests may be conducted in situ wherethere is a discontinuity that has a critical influenceon sliding stability, and which contains an infillingsuch as a sensitive clay that would be disturbed byremoving the sample for laboratory testing.Probably the most important purpose of an in situshear test is to determine the cohesion of the discontinuity infilling because this strength parametercan have a very significant effect on the stability. Itis difficult to obtain an intact, undisturbed sampleof a discontinuity containing a soft clay and

Figure 4.20 Radial jacking test: pressure applied with water pressure and extensometers aligned parallel andperpendicular to geological structure (Oberti et al., 1986).

1. Extensometer lead wires. 2. MPBX—total of four. 3. Steel tube. 4. Waterproof lining. 5. Reinforced concrete ring. 6.Inflatable rubber ring. 7. Roller to position tube.


determine the peak shear strength in the laboratory.However, if the infilling is thick enough, samplescan be dug out of the discontinuity and recompactedinto a laboratory shear box and the approximatecohesion determined in this manner. An effectivetest program would consist of a limited number ofin situ tests, backed up by extensive laboratorytesting.A typical in situ direct shear test set up is shown inFig. 4.24 (Saint Simon et al., 1979). In the case oftests conducted in adits, the reaction for the normalload is obtained from the opposite wall of the adit.Tests can be conducted on a rock surface usingcables anchored into the rock adjacent to the testsite to supply the normal reaction. The first task inthe test is to isolate a block of rock above thediscontinuity surface without disturbing theinfilling; in weak rock such as shales it may bepossible to use hand excavation methods, but in

stronger rocks, diamond saws would have to beemployed. Wherever possible, the direction of theshear load should be set up so that it is coincidentwith the likely direction of sliding. For example, onthe Nukui arch dam project in Japan, the shearstrength of a vertical fault in one abutment wastested in direct shear by setting up both the normaland shear load acting horizontally.The test procedure would be similar to that of thelaboratory direct shear test in that a constant normalload is applied and the shear load is graduallyincreased until sliding takes place. The normal andshear displacements are measured with dial gauges.If there are two shear load jacks operating inopposite directions, the sample can be reset aftereach test, in order to conduct tests at a number ofdifferent normal loads and obtain values of both thepeak and residual strengths.4.6 References

Figure 4.21 Details of the arrangement of flat jacks in a radial jacking test (ISRM, 1981).

1. Circular steel set. 2. Wedge to expand steel set. 3. Central reference beam. 4. Expansion measuring surface, radius r2 .5. Flatjack radius r1. 6. Steel rod. 7. Dial gauge extensometer. 8. Hardwood lagging. 9. Flatjack. 10. Shotcrete lining.11. Rock surface. 12. Extensometer drill hole.

SITE SELECTION 133

Barton, N.R. (1973) Review of a new shear strengthcriteria for rock joints. Engineering Geology, 7,189– 236.

Barton, N.R. and Choubey, V. (1977) The shear strengthof rock joints in theory and practice. Rock Mechanics,10(1–2), 1–54.

Black, W.H., Smith, H.R. and Patton, F.D. (1986) Multi-level ground water monitoring with the MP System.Proc. NWWA-AGU Conf. on Surface and BoreholeGeophysical Methods and GroundwaterInstrumentation, Denver, CO, pp. 41–61.

Boart Longyear Co. (1996) Oriented core drilling servicetechnical literature.

Bourbonnais, J. (1985) New developments in rock testingand monitoring equipment for tunneling projects. Proc.5th Annual Canadian Tunneling Conference, Montreal,pp. 106–125.

Call, R.D., Savely, J.P. and Pakalnis, R. (1982) A simplecore orientation device. In Stability in Surface Mining(ed. C.O.Brawner), SME, AIME, New York,pp. 465–81.

Cedergren, H.R. (1989) Seepage, Drainage andFlownets, 3rd edn, Wiley, New York.

Colog Inc. (1995) Borehole Image Processing System

(BIP), Golden, Colorado and RaaX Co. Ltd, Australia.Davis, J.L. and Annan, A.P. (1989) Ground penetrating

radar for high resolution mapping of soil and rockstratigraphy. Geophysical Prospecting, 37, 531–51.

Deere, D.U. and Miller, R.P. (1966) EngineeringClassification and Index Properties of Intact Rock.Technical Report No. AFWL-TR-65–116. Air ForceWeapons Laboratory, Kirkland Air Force Base, NewMexico.

Fecker, E. and Rengers, N. (1971) Measurement of largescale roughness of rock planes by means ofprofilometer and geological compass. Proc. Symp. onRock Fracture, Nancy, Paper 1–18.

Freeze, R.A. and Cherry J.A. (1979) Groundwater,Prentice-Hall, New Jersey, p. 234.

Geological Society Engineering Group Working Party(1970) The logging of rock cores for engineeringpurposes. Q. J. Eng. Gel., 3, 1–24.

Geological Society Engineering Group Working Party(1977) The description of rock masses for engineeringpurposes. Q. J. Eng. Gel., 10, 355–88.

Golze, A.R. (ed.) (1977) Handbook of Dam Engineering.Van Nostrand Reinhold, New York, pp. 235–40.

Goodman, R.E. (1976) Methods of Geological

Figure 4.22 Method of superposition to give displacements for equivalent uniformally distributed loading—eliminationof end effects (ISRM, 1981).


Engineering. West, St. Paul, pp. 102–22.Goodman, R.E., Van, T.K. and Heuze, F.E. (1968) The

measurement of rock deformability in boreholes. Proc.10th Symp. on Rock Mechanics, AIME, Austin, Texas,pp. 523–55.

Griffiths, D.H. and King, R.F. (1988) Applied Geophysicsfor Geologists and Engineers, (2nd edn), PergamonPress, Oxford.

Heuze, F.E. and Salem, A. (1977) Rock deformabilitymeasured in situ—problems and solutions. Int. Symp.on Field Measurements in Rock Mechanics, Zurich,pp. 375–87.

Hiltscher, R., Carlsson, A. and Olsson, T. (1984)Determination of the deformation properties of bedrockunder turbine foundations. Rock Mech., 17, 37–49.

Horslev, M.S. (1951) Time lag and Soil Permeability inGround Water Measurements. US Corps of EngineersWaterways Experiment Station, Bulletin No. 36.

International Society for Rock Mechanics (ISRM)(1981a) Rock Characterization, Testing andMonitoring; ISRM Suggested Methods. (ed.E.T.Brown). Pergamon Press, Oxford.

International Society for Rock Mechanics (ISRM) (1981b)Basic geological description of rock masses. Int. J.Rock Mech. Min. Sci. & Geomech. Abstr., 18, 85–110

International Society for Rock Mechanics (ISRM)

(1981c) Suggested Methods for the QuantitativeDescription of Discontinuities in Rock Masses (ed. E.T.Brown), Pergamon Press, Oxford.

International Society for Rock Mechanics (ISRM) (1987)Suggested methods for deformability determinationusing a flexible dilatometer. Int. J. Rock Mech. Min.Sci. & Geomech. Abstr., 24(2), 123–34.

Inkster, D.R., Rossiter, J.R., Goodman, R., Galbraith, M.and Davis, J.L. (1989) Ground penetrating radar forsubsurface environmental applications. 7th ThematicConference on Remote Sensing for ExplorationGeology, Calgary, Alberta, Canada, pp. 127–40.

Jacob, C.E. (1950) Flow of ground water, in EngineeringHydraulics (ed. H.Rouse), Wiley, New York,pp. 321–86.

Lo, K.Y. and Yung, T.C. B. (1987) A field method for thedetermination of rock mass modulus. Can. Geotech. J.,24, 406–413.

Louis, C. (1967) A study of Groundwater Flow in JointedRock and its Influence on the Stability of Rock Masses.Doctorate Thesis, University of Karlsrue (in German).English translation Imperial College (London) RockMechanics Research Report No. 10, Sept. 1969.

Lutz, J. and Morey, J. (1988) Utilization andComputerization Processing of Exploratory DrillingParameter Recordings. JEAN LUTZ S.A. Technical

Figure 4.23 Typical pressure-displacement curves for radial jacking test (ISRM, 1981).

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Literature No. 88–136.Misterek, D.L. (1969) Analysis of data from radial

jacking tests. Determination of the in situ modulusof deformation of rock, ASTM STP 477, Am. Soc. forTesting and Materials. pp. 27–38.

Misterek, D.L., Slebir, E.J. and Montgomery, J.S. (1974)Bureau of Reclamation procedures for conductinguniaxial jacking tests. Field testing and instrumentationof rock, ASTM, STP 554, Am. Soc. Testing andMaterials, pp. 35–51.

Oberti, G., Bavestrello, F. and Rossi, R.P. (1986) Rockmechanics investigations, design and construction ofthe Ridracoli Dam. Rock Mech. and Rock Eng., 19,113–42.

Patton, F.D. (1987) Personal communication.Patton, F.D. and Deere, D.U. (1970) Significant

geological factors in rock slope stability. Proc. Symp.on Planning Open Pit Mines, Johannesburg, SouthAfrica. Balkema, Amsterdam, pp. 143–51.

Peterson, J.E., Sullivan, J.T. and Tater, G.A. (1982) Theuse of computer enhanced satellite imagery forgeologic reconnaissance of damsites. ICOLD, 14thCong. on Large Dams, Rio de Janiero, Q53, R26, Vol.II, pp. 449–71.

Rocha, M. (1967) A method of integral sampling of rock

masses. Rock Mech. 3(1), 1–12.Rocha, M., DaSilveira, A., Grossman, N. and DeOliveira,

E. (1966) Determination of the deformability of rockalong boreholes. Proc. 1st ISRM Cong., Lisbon, Vol. 1,pp. 697–704.

Saint Simon, P.G. R., Solymar, Z.V. and Thompson, W.J.(1979) Damsite investigation in soft rocks of PeaceRiver Valley, Alberta, Canada. Proc. 4th Int. Conf. onRock Mechanics, Montreux, Vol. 2, Int. Soc. RockMechanics, pp. 553–60.

Skermer, N.A. (1984) M Creek debris flow disaster.Canadian Geotechnical Conference: Canadian CaseHistories, Landslides, Toronto, pp. 187–94.

Stahl, R.L. (1973) Detection and Delineation of Faults bySurface Resistivity Measurements—Gas Hills Region,Wyoming. US Bureau of Mines, RI 7824.

Terzaghi, R. (1965) Sources of errors in joint surveys.Geotechnique, 15, 287.

Terzaghi, K. and Peck, R.P. (1967) Soil Mechanics inEngineering Practice (2nd edn), Wiley, New York,pp. 660–73.

Theis, C.V. (1935) The relation of the lowering of thepiezometric surface, and the rate and duration ofdischarge of a well using ground water storage. Trans.Amer. Geophysical Union, 16, 519–24.

Figure 4.24 Typical set up for an in situ direct-shear test in an adit (Saint Simon et al., 1979).

1. Rock anchor. 2. Hand-placed concrete. 3. WF beam. 4. Hardwood. 5. Steel plates. 6. 30 ton jack. 7. Dial gauge. 8.Steel rollers. 9. Reinforced concrete. 10. Bearing plate. 11. Styrofoam. 12. 50 ton jack. 13. Steel ball.


Timoshenko, S. and Goodier, J.N. (1951) Theory ofElasticity, (2nd edn), McGraw-Hill, New York.

Todd, D.K. (1959) Ground Water Hydrology. Wiley, NewYork, pp. 47–9 and pp. 78–114.

Tranter, C.J. and Craggs, J.W. (1945) The stressdistribution in a long circular cylinder when adiscontinuous pressure is applied to the curved surface.Phil. Mag., 36, 241–50.

Tse, R. and Cruden, D.M. (1979) Estimating jointroughness coefficients. Int. J. Rock Mech. Min. Sci. &Geomech. Abstr., 16, 303–7.

VanDine. D.F. and Lister, D.R. (1983) Debris torrents -a

new natural hazard? The British ColumbiaProfessional Engineer, 34(12), 9–12.

Wallace, G.B., Slebir, E.J. and Anderson, F.A. (1969) Insitu methods for determining deformation modulusused by the Bureau of Reclamation.

Determination of the in situ modulus of deformation ofrock, ASTM STP 477, Am. Soc. for Testing andMaterials, pp. 3–26.

Yu, X. and Vayassade, B. (1991) Joint profiles and theirroughness parameters. Int. J. Rock Mech. Min. Sci. &Geomech. Abstr., 28(4), 333–6.

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5Bearing capacity, settlement and stress distribution

5.1Introduction

Two types of rock foundations, each requiringdifferent design procedures, are illustrated inFig. 5.1. The upper photograph shows spreadfootings for a cut and cover structure founded on aninterbedded sequence of very weak sandstone andshale. With each footing surrounded by aconsiderable extent of intact rock, the primarydesign task for these foundations is determinationof the allowable bearing pressure and the magnitudeof the settlement. The lower photograph shows abridge foundation located near the crest of a verticalslope in very strong granite. The rock has adequatebearing capacity for the applied loads andsettlement will be elastic and negligible. Therefore,the primary design task is to ensure that blocks ofrock in the foundation formed by continuous jointsare stable against toppling and sliding.This chapter describes methods for determining thebearing capacity and settlement of footings onfractured rock, while Chapter 6 discussesfoundation stability. Most foundations consist ofsquare or rectangular reinforced concrete structuresthat are sized to ensure that the rock can support thestructural loads without excessive settlement.A particular feature of spread footings on rock isthat the bearing surface need not be normal to thedirection of the applied load because rock hassignificant shear strength, and it is possible toinstall anchors to provide additional shear resistanceif required. Thus, vertical loads can be supported onsloping rock faces, or inclined loads on horizontalsurfaces. Where external loads such as wind, water

and seismic forces act on a structure, overturningmoments and uplift forces may be developed andthe foundation design must accommodate theseconditions. When uplift forces are developed it maybe necessary to install tie-down anchors (seeChapter 9).The majority of foundations on rock are spreadfootings at the ground surface, but there areconditions for which this type of footing may not besuitable. These conditions include locations wherethe available bearing area is insufficient resulting inexcessive contact pressure, or where suitablebearing surfaces occur at a considerable depth and itis uneconomical to excavate the overlying weakmaterial. In these cases socketed piers would berequired (see Chapter 8).The design of surface footings on rock encompassesthe following three tasks that examine differentaspects of foundation performance:

1. the bearing capacity of the rock to ensure thatthere will be no crushing or creep of thematerial within the loaded zone;

2. settlement of the foundation which will resultfrom both elastic and inelastic strain of the rock,and possibly compression of weak seams within the volume of rock compressed by theapplied load;

3. sliding and shear failure of blocks of rockformed by intersecting discontinuities withinthe foundation. This condition usually occurswhere the foundation is located on a steep slopeand the orientation of the discontinuities is suchthat the blocks can slide out of the open face.

Figure 5.1 Photographs of foundations on rock showing different geometrical and geological conditions:

(a) spread footings for a cut and cover structure founded on very weak, horizontally bedded rock; and

(b) bridge footing on very strong rock containing continuous vertical discontinuities (photograph by MarkGoldbach).

BEARING CAPACITY OF FRACTURED ROCK 139

with respect to all three of these conditions becausethey are independent of each other. For example, afooting on very strong rock with ample bearingcapacity and minimal settlement may still fail ifblocks formed by persistent discontinuities can slidefrom the foundation. Also, a footing on a thin slab ofstrong rock may exhibit excessive settlement as aresult of compression of an underlying soft seamdespite the upper layer having adequate bearingcapacity and there being no open face on which asliding failure could take place.

5.2Bearing capacity

The usual method of determining allowable bearingpressures is to use published tables or buildingcodes relating allowable values to rock type.However, in circumstances where the rockconditions do not match descriptions in the codes, itis more appropriate to use limit equilibrium ornumerical methods incorporating appropriate rockmass strength parameters. The method used willdepend on such factors as movement tolerances andthe complexity of geological conditions at the site.Thus, for a low rise building located on a uniformrock type it is common to use the codes todetermine the allowable bearing pressure, while fora dam or large bridge on fractured rock containingseams of compressible rock, more detailed analysismay be required (Rawlings and Wyllie, 1986).For rock foundations where the rock is stronger thanthe concrete from which the footing is constructed,the bearing capacity of the rock will be of noconsequence. It is found that bearing capacityproblems usually relate to details of the structuralgeology. This section describes methods ofdetermining the bearing capacity of foundations inthe following geological conditions:

1. fractured and weathered rock;2. shallow dipping bedding planes;3. layered formations;4. karstic formations.

5.2.1Building codes

For many structures, the required dimensions of thefooting bearing area can be determined frompublished tables or building codes which listallowable bearing pressure for various rock types.Table 5.1, from the building code for the city ofRochester, New York, gives allowable bearingpressures for three classes of rock defined by theirstrength, and describes the influence ofdiscontinuities on bearing capacity (Goodman,1980). Table 5.2 lists allowable bearing pressuresfor a variety of geological conditions defined byrock type and age.The bearing pressures listed in Table 5.2 have beendeveloped from observations of existing stablestructures and incorporate a substantial factor ofsafety, so settlement should be minimal. However,the values given are related mainly to the rockstrength, and must be reduced where the rock isweathered, fractured, or is non-homogeneous andcontains seams of weak and decomposed rock.Usually allowable bearing pressures are determinedfrom the allowable settlement, which in rock ismainly related to the discontinuity characteristics.Settlement results from closure of opendiscontinuities, and compression of seamscontaining low strength infillings. Where the rock issound but fractured, the bearing pressures given inTable 5.2 can be modified to ensure that settlementis minimal. The effect of fracture intensity onbearing capacity can be estimated from the RQD ofdrill core as follows (Peck et al., 1974):

• RQD>90%–no reduction;• RQD>50%, <90%–reduce bearing pressure by

factor of about 0.25–0.7; • RQD<50%–reduce bearing pressure by a factor

of about 0.25–0.1; reduce bearing pressurefurther if extensive clay seams present.

The application of the allowable bearing values inTable 5.2 and these reduction factors requiresinformation on sub-surface conditions and theapplication of some judgment. If it is considered that

140 BEARING CAPACITY, SETTLEMENT AND STRESS DISTRIBUTION

The performance of a foundation must be checked

the actual rock properties do not meet the generalconditions applicable to Table 5.2, or for the designof structures such as dams or nuclear power plantswhere a particularly high degree of reliability isrequired, there are a number of methods ofcalculating the allowable bearing capacity asdescribed below.Shown on Table 5.3 are actual bearing pressuresused on a number of projects reported in theliterature, as well as the type of structure and thegeology. The bearing pressures quoted are notnecessarily the limiting value for the site because itis likely that the design bearing pressures aredependent on such factors as the type of structureand its tolerance for settlement, and the requiredsize of the bearing surface to accommodate thestructure. The bearing pressures in Table 5.3 rangefrom a high of 7.2 MPa for very strong granitic rockon the Canadian shield for a comparatively lightly

loaded structure, to a low of 0.2 MPa for a bridgeconstructed on shale in Spain. These values can becompared with those prescribed by Building Codesin Table 5.2.

5.2.2Bearing capacity of fractured rock

Figure 5.2(a) shows a foundation bearing on ahorizontal rock surface. At bearing pressures wellbelow the ultimate bearing capacity the rock willbehave elastically and the settlement of the footingcan be calculated from equation 5.18 inSection 5.4.1. However, at increased loads wherethe pressure approaches the ultimate bearingcapacity of the rock, fractures will be initiatedwhich will grow and coalesce forming wedges andareas of crushed rock (Fig. 5.2(a)). These conditionswill result in dilatancy of the rock and the formation

Table 5.1 Provisions of the Building Code for Rochester, New York (dates given in parenthesis)

*The 1.5 m (5 ft) depth limit for weak seams is a guideline that may not be applicable under all conditions. An estimateon the volume of rock influenced by a foundation load can be obtained by assuming that the stress in the rock isinsignificant once the stress level is less than 10% of the applied stress. For isotropic, elastic rock, the stress distributionin the foundation takes the form of a cone, with a side slope angle of 1H:2V, defining the rate at which the foundationstress diminishes with depth. Under these conditions, the 10% stress level occurs at a depth equal to about twice the widthof the footing.


Table 5.3 Allowable bearing pressures (qa) for completed projects

Number Project Location Rock type qa MPa (ksf) Reference

1 Museum Sudbury, Canada Igneous-quartziteconglomerate

7.2 (150) Franklin andPearson (1985)

2 Steel arch bridge–220 m span

Grand Canyon, USA Dolomitic limestone 2.4 (50) Cannon and Turton(1994)

3 Apartment building New Jersey, USA Diabase, fractured;till (30 blows/ft)

2 (40); 0.6 (12) Kaufman and Brand(1991)

4 Steel truss bridge–760 m long

West Virginia, USA Sandstone; shale 1.5 (30); 1(20) Kaufman and Brand(1991)

5 Humber suspensionbridge

UK Chalk 1.25 (26) Simm (1984)

Table 5.2 Allowable bearing pressures for fresh rocks according to typical building codes. Reduce values to account forweathering, unrepresentative fracturing or non-homogeneous rock*. Values from Thorburn (1966), Woodward et al.(1972) and Ontario Ministry of Transport and communications (1983)


Number Project Location Rock type qa MPa (ksf) Reference

6 Bridge Galacia, Spain Shale and schist 1.0 (20) Serrano and Olalla(1995)

7 Suspension bridge–1990 m span

Kobe, Japan Sedimentary—softclaystone andsandstone

0.88 (18) Yamagata et al.(1995)

8 Concrete box girderbridge– 260 m span

Brisbane, Australia Sedimentary—coal,shale, siltstone

0.8 (17) Williams (1989)

9 Nuclear powerstation

Lancashire, UK Sandstone,mudstone

0.63 (13) Thompson andLeach (1991)

10 Viaduct bridge Galacia, Spain Granite—weathered 0.72(15) Serrano and Olalla(1995)

11 Cable stayed bridge Badajoz, Spain Gneiss—highlyweathered

0.43 (9) Serrano and Olalla(1995)

12 Bridge River Lagos Spain Shale andquartzshale

0.3 (6) Serrano and Olalla(1995)

of radial fractures that expand outwards and caneventually reach the surface to create a wedge ofrock. Displacement of such a wedge can result insudden failure of the footing.The diminished strength of the rock under thefooting (zone A) compared with the unfracturedsurrounding rock (zone B) is illustrated in the Mohrdiagram (Fig. 5.2(b)). This diagram demonstratesthat the rock under the footing is in a state oftriaxial compression with the major principal stressequal to the bearing pressure (q) and the minorprincipal stress equal to the confinement applied bythe surrounding rock. The maximum stress that thesurrounding rock can sustain is the uniaxialcompressive strength of the rock mass σu(m) in zoneB, assuming that the footing is at the ground surface.These conditions apply where there are nopredominant discontinuities that can form preferredfailure surfaces, or where the rock is porous, such aschalk, that can compress under the foundationloading. Calculation of the bearing capacity of closelyfractured, or very weak rock based on the failuremechanism illustrated in Fig. 5.2, can be carried outin a manner similar to soil mechanics. Thisprocedure, as developed by Bell and extended byTerzaghi (1943), is a simplified and conservativeanalysis which approximates the curved shearfailure surfaces that develop in the foundation

because no exact mathematical solution has beenderived for analyzing such a failure. The simplifiedanalysis assumes straight lines for the failuresurfaces, and ignores the weight of the rock in thefoundation as well as the shear stresses that developalong the vertical interface between the twowedges.The analysis is based on the assumption that activeand passive wedges, defined by straight lines, aredeveloped in the rock under the footing, and theshear strength parameters of these sur faces arethose of the rock mass (Fig. 5.3(a)). For a footing ofinfinite length bearing on a horizontal rock surface,the rock under the foundation is assumed to be incompression similar to a specimen in a triaxialcompression test. The major principal stress in zoneA, s1A, is equal to the footing pressure q, if theweight of the rock beneath the footing is neglected.Zone B is like a triaxial compression test with themajor principal stress s1B acting horizontally, and theminor principal stress s3B acting vertically. If thefooting is at the ground surface s3B is zero, while ifthe footing is below the rock surface, the surchargeqs is equal to the average vertical stress produced bythe rock weight above the footing level.At the moment of foundation failure both zonesshear simultaneously and the minor principal stressin zone A, s3A, equals the major principal stress inzone B, s1B. The minor principal stress in zone A is


produced by the resistance of zone B to beingcompressed, which is the uniaxial compressivestrength of the rock mass (Fig. 5.3(b)). The strengthof rock in triaxial compression (s1, s3) can definedas a curved envelope (Hoek-Brown strengthcriterion) as described in Section 3.3.3. Using thiscriterion, the strength of a fractured rock mass is

(5.1)where m and s are constants which depend upon thetype of rock and the degree to which the rock isfractured (see Table 3.7); su(r) is the unconfinedcompressive strength of intact rock, and s1, s3 arethe major and minor principal stresses respectively.Equation 5.1 gives the major principal stress actingon zone A, s1A. The minor principal stress on zoneA, s3A, is the strength of the rock in zone B, and isequal to the uniaxial strength of the rock mass whenthe surcharge is zero. The uniaxial compressivestrength of a fractured rock mass is

(5.2)

and the bearing capacity is equal to the majorprincipal stress in zone A which is given by

(5.3)

The plot in Fig. 5.3(b) shows the relationshipbetween the strength s1A and the confining stressesprovided by the surrounding rock s3A. Thisillustrates that a very significant increase in thebearing capacity is produced by a small increase inthe confining pressure.The allowable bearing pressure qa is related to therock mass strength by the factor of safety FS andthe correction factor Cf1:

(5.4)

The factor Cf1 is applied to the calculated allowablebearing pressure to account for the shape of thefoundation and has the values given in Table 5.4

Figure 5.2 Bearing capacity of foundation bearing on rock surface: (a) formation of fractured rock (A) beneath footingcontained by wedges of intact rock surrounding footing (B); and (b) Mohr diagram of stresses in bearing rock.


(Sowers, 1970).A more comprehensive procedure for calculatingthe ultimate bearing capacity of fractured rock isdescribed by Serrano and Olalla (1994) in which therock mass strength is defined by the Hoek andBrown strength criteria as above. The method ofanalysis can accommodate recessed footings,inclined loads and foundations located on slopingground surfaces.For most loading conditions on sound rock thefactor of safety will be in the range 2–3 for whichthere is little risk of settlement. A factor of safety of3 is used for the dead load plus the maximum liveload. If part of the live load is temporary such aswind and earthquake, then a factor of safety of 2 canbe used (US Department of the Navy, 1982).In the equations to calculate the allowable bearingcapacity for a fractured rock mass with the strength

defined by curved strength envelopes, it isimportant to distinguish between the compressivestrength of the intact rock and that of the rock mass.The intact rock strength su(r) is determined fromlaboratory tests on rock cores, while for fracturedrock the strength is defined by equation 5.1 with thedegree of fracturing of the rock mass beingaccounted for by the constants m and s.

5.2.3Recessed footings

In the case of a footing which is recessed into therock surface, it is necessary to modify equation 5.4to account for the increase in the stress s1s as aresult of the confining stress qs applied at theground surface. That is, the minor principal stress

Figure 5.3 Analysis of bearing capacity of fractured rock: (a) active A and passive B wedges in foundation; and (b)curved rock mass strength envelope. Allowable bearing pressure=qa, strength of bearing rock=s1A, factor of safety


Table 5.4 Correction factors for foundation shapes

Foundation shape Cf1 Cf2

Strip 1.0 1.0Rectangular

1.12 0.91.05 0.95

Square 1.25 0.85Circular 1.2 0.7s3B is equal to qs and the modified value of theallowable bearing pressure is as follows. Curvedstrength envelope:

(5.5)

where(5.6)

5.2.4Bearing capacity factors

For weak rock with little fracturing, an expressionfor the allowable bearing capacity is the Bellsolution , which is developed using the sameprinciples as described in Section 5.2.2. Thisbearing capacity analysis takes into account theweight of the rock in the active wedge, as well asthe confinement provided by the surrounding rockwhere the footing is recessed below the surface. TheBell solution for the allowable bearing capacity fora strip, square or circular footing is

(5.7)

where B is the footing width (for strip or squarefooting) or diameter (for circular footing); ?r is therock density; D is the depth of embedment; and c isthe rock mass cohesion. The correction factors Cf1and Cf2 which account for the footing shape aregiven in Table 5.4. The terms Nc, N? and Nq arebearing capacity factors defined as follows (Lambeand Whitman, 1969):

(5.8)

where The factor Nc showsthe influence of the cohesion, the factor N? showsthe influence of the soil weight and foundationwidth, and the factor Nq shows the influence of thesurcharge.As discussed in Section 5.2.2 above, the active-passive wedge analysis is a simplified and conservative method of analysis. Furthermore, values forthe bearing capacity factors determined fromlaboratory experiments show that the actual valuesare higher than the theoretical values, particularlyfor rough bearing surfaces and high friction angles.Figure 5.4 shows values for the three bearingcapacity factors in relation to the friction anglebased on the trial wedge method developed byTerzaghi (1943). These experimental values areknown to underestimate actual values infoundations and can differ from values calculated inthe Bell solution (equation 5.8).The conditions for which equation 5.7 and thebearing capacity factors given by Fig. 5.4 can beused are as follows:

1. loading is vertical and concentric;2. depth of embedment D is less than or equal to

B;3. foundation rock is uniform to depth below the

maximum expected shear surface;4. water level is lower than depth of the shear

surface;5. foundation rock has strength parameters


defined by friction angle and cohesion;6. friction and adhesion on the vertical sides of the

footing are neglected.

Note that equation 5.7 can be simplified if theweight of the wedge of rock in the foundation isignored, and the footing is at the surface Itis justified to ignore the weight of the rock where itis a small proportion of the foundation load. Underthese conditions, equation 5.7 reduces to

(5.9)

5.2.5Foundations on sloping ground

For conditions where the foundation is located on asloping ground surface, it is necessary to modify thebearing capacity factors to account for the reducedlateral resistance provided by the smaller mass ofrock on the downslope side of the footing. Onshallow slopes where the slope angle is less than , bearing capacity or settlement will usually controlthe allowable working load on the footing. Forslopes angles greater than , it is seldomnecessary to check bearing capacity because thestability of the slope will be the controlling factor(Hong Kong Geotechnical Engineering Office,1981).For foundations on sloping ground surfaces, theallowable bearing pressure is calculated as follows:

(5.10)

where Ncq and Nc? are bearing capacity factors givenin Fig. 5.5, and Cf1 and Cf2 are correction factorswhich account for the footing shape and are given inTable 5.4. The value of the factor Ncq depends onthe stability number No which is defined as

(5.11)

where ?r is the rock density, c is the rock masscohesion and H is the slope height as shown inFig. 5.5.The calculation of allowable bearing capacity using

the bearing capacity factors given in Fig. 5.5 andequations 5.10 and 5.11 assumes that the water tableis at a depth at least equal to the width of the footingbelow the base of the footing. Where the water tableis higher than this level, stability analyses should becarried out including the effect of water pressures inthe foundation.For foundations located on level ground at the crestof a slope, the allowable bearing pressure will bereduced if the foundation is at a distance less thanabout six footing widths behind the crest. Thestability of slopes with foundations located close tothe crest can be checked by the methods of stabilityanalysis described in Chapter 6 using a factor ofsafety of 2–3 so that deformation will be minimal.

5.2.6Bearing capacity of shallow dipping beddedformations

In the methods of calculating bearing capacitydescribed in Section 5.2.2, the failuremechanism involved development of a passivewedge of rock that induced a confining stress on theactive wedge of rock beneath the footing. Themagnitude of this confining stress depends on thestrength of the rock mass composed of either intactrock, or interlocking fragments of intact rock.However, if the rock contains sets of discontinuitiesthat form one or more of the surfaces of this wedge,the bearing capacity of the foundation may bereduced for two reasons. First, the shape of thewedge will be defined by the orientation of thediscontinuities and the dimensions and surface areaof the wedge may be limited and second, thestrength of the discontinuities is usuallysignificantly less than that of the rock mass. Theseconditions could result in failure of the foundationdue to displacement of the passive wedge.Figure 5.6 shows a foundation containing two sets ofconjugate joints dipping at angles ?1 and ?2 whichform the base surfaces of an active wedge (A) and apassive wedge (B) respectively. The minimumprincipal stress s3A acting horizontally on the activewedge A can be calculated from equation 5.12 as


follows (Ladanyi and Roy, 1971):(5.12)

Figure 5.4 Bearing capacity factors for footings located on horizontal ground surface (US Dept of the Navy, 1982).


from which the allowable bearing pressure is

(5.13)

where B is the width of foundation; ?1 is the dip ofdiscontinuity set 1; c1, c2 are the cohesions ofdiscontinuity sets 1 and 2 respectively;

Figure 5.5 Values for bearing capacity factors for footings located on sloping ground surface (US Dept of the Navy,1982).


and and are the friction angles ofdiscontinuity sets 1 and 2 respectively.If the rock surface around the footing is subjected toa surcharge pressure qs, as might be the case if thefooting were recessed into the ground surface, thenthe bearing capacity is significantly increased due tothe confinement provided to the passive wedge. Thesurcharge qs is incorporated into the analysis of thebearing capacity by modifying equation 5.12 as

follows(5.

14)One method of improving the bearing capacity of afoundation on a layered formation is to install rockbolts that are anchored below the level of thepassive wedge and then tensioned against the rocksurface. This has the effect of applying an artificialsurcharge at the ground surface; equation 5.14 canbe used to calculate the magnitude of the boltingforce required to achieve the required bearingcapacity.

EXAMPLE 5.1

BEARING CAPACITY

The following is an example comparing the allowable bearing capacities calculated by the alternativemethods described in this section.

Consider a 2 m wide strip footing bearing on the surface of a fair quality limestone in which theaverage discontinuity spacing is 400 mm and the discontinuities contain some clay. The strengthproperties of the rock are as follows:

1. unconfined compressive strength of intact rock, MPa or 11 000 p.s.i. (Table 3.6);2. curved strength envelope parameters: , (Table 3.7);3. rock density, .

Figure 5.6 Bearing capacity of foundation on rock containing inclined bedding planes and orthogonal joint sets.


Note that for a strip footing, the correction factors Cf1 and Cf2 are equal to 1.

BUILDING CODES

From Tables 5.1 and 5.2, a bearing capacity of about 1– 2 MPa (21–42 kips ft-2) can be interpretedfor rock which is moderately strong and has a moderate discontinuity spacing.

HOEK-BROWN STRENGTH CRITERION

The allowable bearing pressure for a rock mass with the strength properties defined by a curvedstrength envelope is calculated using equation 5.4. For a factor of safety of 3, and the values of m, s andsu(r) given above, the allowable bearing pressure is calculated to be 1.14 MPa (23.8 ksf).

BELL SOLUTION

Application of equation 5.7 to calculate allowable bearing capacities from the bearing capacity factorsrequires values for the rock mass friction angle and cohesion. These two parameters are obtained fromequations 3.16–3.19. For an average pressure on the foundation of 2 MPa, the instantaneous values forthe friction angle cohesion are 25° and 0.54 MPa respectively and the value of the factor is 2.47.From equations 5.8 the bearing capacity factors are:

From equation 5.7, the allowable bearing pressure, assuming a strip footing of width 2 m, is:

This calculation shows that the weight of the rock wedge (the second term in equation 5.7) in thefoundation has little influence on the allowable bearing pressure.

If the foundation were recessed a depth of 1 m below the ground surface, the third term in equation 5.7 becomes 0.14. Therefore, recessing the footing to a depth of only 1 m has little influence on thebearing capacity.

Values for the bearing capacity values can also be obtained from Fig. 5.4 from which the allowable bearing capacity calculated from equation 5.7 is 3.7 MPa (77 ksf).

As discussed in Section 5.2.4, the Bell solution (equation 5.7) is a conservative method of calculatingbearing capacity, and the use of bearing capacity factors given in Fig. 5.4 will give higher bearingcapacities. Furthermore, the low bearing capacities given by the building codes are an indication of theconservatism that is built into the building codes to account for the range of geological conditions thatthe codes can accommodate.

SHALLOW DIPPING BEDDED FORMATIONS

If the rock contains two sets of orthogonal joints which dip at and the allowablebearing capacity is calculated from equation 5.13. Assume that the friction angle of both these jointsurfaces is 25° so that the factors If the cohesion of both joint sets is zero, theallowable bearing capacity is 0.03 MPa (0.54 ksf), and if the cohesion is 0.5 MPa (72.5p.s.i.), the allowable bearing capacity increases to 1.8 MPa (38 ksf). This result shows that persistent


discontinuities oriented approximately parallel to the surfaces of the active and passive wedge in thefoundation will significantly reduce the allowable bearing capacity.

5.2.7Bearing capacity of layered formations

Where a footing is located on a thin slab of strongrock overlying a considerable thickness of muchweaker rock, there are three possible failuremechanisms. The footing may punch through thestronger, upper layer, or the upper layer could fail ineither buckling or bending (Fig. 5.7). In all thesecases, failure of the upper layer of rock is likely toresult in a sudden and substantial settlement of thefoundation if the material in the lower layer haslittle load bearing capacity. Hoek and Londe (1974)quote a case of a footing for a high-rise buildingwith a load of 2000 MN (225 000 ton) that punchedthrough a 10 m (33 ft) thick sound limestone bed.

Another possible failure mode is that of settlementof the combined two layer system; calculation ofsettlement is described in Section 5.3.With the upper layer of rock having a significantlyhigher modulus than the lower layer, the upper layerwill carry most of the load and foundation stabilitywill depend primarily on the capacity of this layer.The usual procedure in the initial stages of designwould be to assume that the upper layer carries allthe load since this will produce a conservativedesign. If the deformation moduli of the twomaterials can be accurately defined, then finiteelement analysis, for example, may be carried out todetermine the stress distribution between the layersmore precisely and the foundation design could bemodified accordingly.

Figure 5.7 Spread footings on layered rock formations with rigid upper layer and weaker lower layer and weaker lowerlayer (Sowers, 1976): (a) punching failure; (b) buckling failure; and (c) bending failure.


The mode of failure of the upper layer will dependon the rock mass properties of each layer, and theratio of the thickness of the upper layer H to the widthB of the footing. If the ratio H/B is low and thelower layer is compressible such as weathered orporous rock, then a punching type failure may takeplace. However, if the lower layer is plastic andincompressible such as clay or soft shale, then theupper layer may buckle (Sowers, 1976). For highervalues of the ratio H/B and if the lower layer iscompressible, then the upper layer may fail inbending.For a punching type failure, the bearing capacity ofthe foundation is found by multiplying the shearstrength of the rock in the upper layer by the surfacearea of the failure surface. This surface can beassumed to be cylindrical in shape with an areaequal to the product of the perimeter of the footingand the thickness of the bed. Sowers (1977)describes punching failures of a spread footinglocated on porous Miami oolite overlying a thickbed of considerably weaker porous oolite and sand.One failure occurred under a 1.5 m (5 ft) thick fill,and another under a spread footing which had beenrecessed into the upper bed thus diminishing thesurface area available to resist punching failure. Thecalculated perimeter shear in the upper oolite crustwas about 90 kPa (1.87 ksf). Remedial measures forthese punching failures comprised grouting thelower bed to improve its bearing capacity, and inother locations cavities in the oolite were cleaned ofsand and then filled with concrete.The shear strength of the rock in the upper layermay be determined by direct shear testing, if amachine with sufficient capacity to fail intact rockis available. An alternative means of determiningshear strength is to construct a Mohr’s envelopefrom the tensile and compressive strengths of theintact rock (Kaderabek and Reynolds, 1981).Where the mode of failure comprises bending andtension, the stability of the foundation is assessed bycomparing the tensile strength of the rock with thetensile stress level in the lower side of the slab. Thetheoretical tensile stresses in the lower side of theupper layer can be calculated using the methods of

Roark and Young (1970), assuming the bearing slabis circular in shape, is simply supported around theedges and no support is provided by the underlying,compressible material. The tensile stress st in thecenter of the lower surface of a circular slab loadedwith uniform load Q acting over an area with radiusB/2 is (Fig. 5.7(c)):

(5.15)

where M is the maximum moment at the center ofthe slab under the applied load given by

(5.16)

where r is the radius of circular slab supporting theload, H is the thickness of the slab and v is thePoisson’s ratio of the rock. The value of theparameter r0 depends on the relative dimensions ofthe diameter of the loaded area B and the thicknessof the slab:

(5.17)

In applying this equation, a decision has to be madeon the appropriate value for the radius of the slab rif this is not defined by the geology or topography ofthe site. A sensitivity analysis will show that thestress level reaches an approximate maximum valueas the radius increases and this will give anindication of the likely stress level that should beused in design.Kaderabek and Reynolds (1981) report that fullscale load tests were carried out to try and induce abeam tension failure, but none occurred despite thetheoretical maximum tensile stress exceeding thelaboratory tensile strength by a factor of 2. There hasbeen no reported failure of this type in the southFlorida area (Kaderabek and Reynolds, 1981).

5.3Bearing capacity of karstic formations

The design of foundations in karstic formations isone of the most challenging tasks in rock foundation


engineering and there are unfortunately instances offailures related to solution of lime-stones and theformation of sink holes (Sowers, 1975; Costopolous,1987). These failures are the result of both thelocation of structures on undetected solutionfeatures, and the development of sink holes afterconstruction because of pumping to dewater nearbyexcavations. Successful foundation design in theseconditions requires first the location of solutioncavities so that the structure is suitably sited, andsecond, the determination of appropriate bearingvalues and construction procedures (Knott et al.,1993).

5.3.1Characteristics of solution features

The formation of solution features is the result ofchemical solution of limestone by percolatingground water containing dissolved carbon dioxidewhich makes the water slightly acidic. During theearly stages of solution, cavities will tend to formon joints and bedding along which the water flow isconcentrated and the cavities may follow areasonably regular pattern. As the solution processdevelops and the cavities enlarge, their size,location and shape become impossible to predictwith any certainty, and careful and detailedinvestigation programs are required when designingfoundation in these formations. The following is abrief description of common karst features.• Slots and pinnacles Slots are narrow, linearfeatures dissolved along a guiding structural featuresuch as a joint or bedding plane, with pinnacles ofrock remaining between the slots (Fig. 5.8(a)).These features are formed by dissolution alongvertical fractures or by downcutting due to lateralground water flow along the bottom of slots. Theslots usually have maximum widths of about 1–2 m(3–6 ft) but their depths can be as great as 10 m (30ft) and their lengths can be traced for hundreds ofmeters. The peaks of the pinnacles are oftenrounded and streamlined. Slots and pinnacles havealso been observed in tilted and folded rock withdips as great as 45°, in which the upper parts of the

slots are vertical, while in the lower part of the slotsthe control of inclined features becomes morenoticeable. Where the limestone contains a morechemically resistant bed, overhangs or even bridgesmay form in the slots as the less resistant rock isdissolved more rapidly on each side of this bed.Slots appear to have poorly developed internaldrainage systems with infiltrating ground waterbeing collected and moved laterally from minorslots to master slots under the residual soil blanket.Therefore, piping and sediment transport are lesseffective than in solution cavities and there is oftena thick layer of soil overlying and masking the slotsthat may eventually collapse into the slot. Voids inthe soil zone occur due to migration of soil particlesinto the underlying drainage cavities, and usuallyoccur near the top of rock and enlarge until theycollapse and form sink holes.• Karst valleys In karst regions the surface drainageis typically diverted into underground routesresulting in the disruption of the surface drainage.For example, tributary streams end abruptly inswallow holes and high-order streams emerge fromkarst springs. Most large scale drain-age basinshave both fluvial (surface) and karst (underground)drainage components, and when all the flow isunderground a dry valley is created.• Negative relief landforms Karst regions typicallyhave low areas, or sinkholes, which slope down intoclosed depressions in which the only ground waterexit is underground; sinkholes may developsuddenly with collapse of the soil layer, or maysettle slowly over time (Fig. 5.8(b)). Solutioncavities form where high permeability pathwaysaccelerate dissolution of the rock and enlargedrainage paths into which soil and insolubleresidue, and eventually boulders and rockfragments, are transported by piping, washing andgravitational collapse. These flow pathways formchimneys which may have vertical, sloping andhorizontal sections and are controlled by resistantbeds that concentrate the water flow. Sinkholes areusually bowl shaped depressions that may be barelyperceptible or have diameters as large as 1000 m(3000 ft). Where a resistant caprock bed limits the


horizontal development of the solution cavity it mayhave steep sides and greater depth than a cavity inmore uniform rock.• Positive relief landforms Some positive karsticlandforms include pinnacles in the form of isolatedspires above the surrounding terrain, and residualhills shaped as cones (near vertical sides) andtowers (vertical sides) where resistant caprockprotects the limestone from dissolution while thesurrounding rock is dissolved. • Caves Caves can be either single conduits orinterconnected mazes which can be categorized bytheir shape as follows. A linear passage is a straightsegment that follows a well defined discontinuity,an angulate passage has straight sections connectedby sharp bends formed as the water flow follows theregional joint pattern, and a sinuous passageconsists of broad sweeping curves and typicallyoccurs in flat lying rocks. Interconnected mazes cancomprise a network of passages formed on theregional joint pattern.• Residual soil Residual soil is the material thatremains after the carbonate rock has been dissolvedand carried away, and typically occupies only a tinyfraction of the original volume of rock. It comprisesthe insoluble materials of the rock such as silica inthe form of chert or quartz, clay minerals and otherclastics, and often iron oxide which remain after thelimestone is dissolved (Sowers, 1976a). The residualsoil forms a blanket over the rock surface andpartially or entirely fills cavities and seams that areeroded into these openings by seeping water.Eventually, channels may become clogged by theeroding residual soil which will halt further solutionand result in increased dissolution at other points.The strength of residual soils often decreases withdepth because of the migration of soil particles andthe higher moisture content, with the soil close tothe contact with the rock being much softer andoften pasty. Generally, the soil is structureless dueto the great reduction in volume during itsformation and subsequent transportation. The rock-soil interface is well defined and sharp, usually withsome limestone or chert boulders floating in the soilmass above the boundary. However, in highly sandy

or shaley limestones with high proportions ofimpurities, some relic structure may be seen and therock interface may comprise a zone of highlyweathered limestone. In many areas, sedimentary,colluvial or glacial deposits may overlie the residualsoil.

5.3.2Detection of solution features

The detection and location of solution featuresusually involves application of a number ofintegrated techniques starting with collection of pastexperience and historical records, as well as aerialphotography for site reconnaissance, followed bygeophysics for site specific studies, and finallydrilling for detailed design. In locations wheresolution cavities are suspected, it is usual to locatedrill holes at each footing or pier position.Aerial photographs can be used to detect karsticterrain which is shown by such topographic featuresas basin-studded plains, narrow U-shaped valleyswith vertical sides, rolling topography, andscalloped effect around river systems, with streamsentrenched in bedrock on rectangular patterns. It isoften useful to examine photographs over anextended time period which may show, forexample, the progressive development ofsolutioning, or that sinkholes have been obscured byhuman activities.Geophysical methods suitable for the detection ofsolution cavities are ground penetrating radar(GPR), microgravity surveys and electricalresistivity (see Section 4.1.2). The selection of themost appropriate technique(s) for each site willdepend on the particular site conditions, with thedecision being made by personnel with experiencein the area. For example, GPR has been usedsuccessfully in Florida where the cavities areoverlain by sand (Benson, 1984), but is lesssuccessful in Pennsylvania where the overburden isa clayey soil with a high moisture content. Thereliability of geophysics to detect solution cavitiesand predict their shape is limited because thesefeatures often occur at variable depths, have


irregular shapes and can be filled with materialswhich can include air, water, clay and boulders. For

this reason drilling is often carried out for finaldesign.

Figure 5.8 Diagram of sink hole development: (a) section showing stages of ravelling into enlarged joints by roofspalling and soil erosion; and (b) plan showing development of sink holes along alignment of joint sets (adapted from Knottet al., 1993).


Diamond drilling is the most reliable method ofinvestigating karstic terrain because it is possible todistinguish between bedrock, boulders and soilinfilling, and to obtain samples for laboratorystrength testing. Percussion drilling, which is fasterand less expensive than diamond drilling, may alsobe used as a supplementary investigation methodwhere, for example, there is a need to examine alarge number of lightly loaded footings. Percussiondrilling needs full-time inspection (or recordingdevices) to note changes in penetration rates and thenature of the cuttings. As a guideline on the numberof drill holes that may be needed to investigate afoundation, it can be shown that if a solution cavityoccupies 10% of the surface of the bearing area,then 16 uniformly spaced drill holes are required tobe certain of detecting this feature, and if only fiveholes are drilled, the probability of detection dropsto 50% (Benson et al., 1982).

5.3.3Foundation types in karstic terrain

The types of foundations suitable for karstic terrainmay be grouped under the three headings: shallowfoundations, foundation treatment and deepfoundations. These are discussed briefly below andtheir advantages and limitations are described inTable 5.5.(a) Shallow foundationsShallow foundations are used where the rock is at ashallow depth of less than about 3 m (10 ft), orsuitable bearing soils are available at the surface.They can also be used in conjunction withfoundation treatments such as pressure grouting,compaction grouting, jet grouting or over-excavation and backfill of soft areas with concrete orgranular material. For small cavities where there issound rock around the periphery, it is often possibleto enlarge and reinforce the foundation to bridgeover the solution feature, using a conservativebearing capacity, or to construct pedestals bearingon prepared surfaces. If the arrangement of theholes or footings results in some eccentricity of thefoundation it may be necessary to combine one or

more footings to form a strap or mat foundation.Figure 5.9 shows a number of different designs for aseries of foundations where the load is carried onthe peripheral rock (Katzenbach and Romberg,1987).With shallow foundations there may be a risk ofsettlement, particularly where the footing is bearingon the overburden soil. Settlement, which can ariseas the result of compression and consolidation ofthe soil, may be irregular and depend more on thethickness of the soil overlying pinnacles and slotsrather than on the magnitude of the foundationsloads. In the more highly stressed areas of the soilabove the pinnacles, compression may result in thesoil punching into the areas of deeper, softer soil.Furthermore, the soil may also consolidate underthe increased loads and this may occur at a slowerrate than the compression and continue for a year ormore. These processes may be accelerated bylowering of the water table, by constructiondewatering for example. Probably the most frequentcause of settlement is raveling and erosion of thesoil into underlying solution cavities where theparticles are carried away by the ground watersystem. These processes may occur slowly andprogressively if the cavities are of limited size, orrapidly if an arch or bridge were to collapse. Wherefootings are located on rock, there may be a riskthat the bearing material is a pinnacle that couldmove under the increased loading, or an underlyingcavity could collapse.(b) Foundation treatmentFoundation treatment for shallow foundationsconsists of filling cavities and placing the footing onthe fill. Shallow, cone shaped cavities are cleaned asdeep as possible and plugged with lean concreteforming a plug that is at least 1.5 times thicker thanits width. If drilling with a jack hammer shows thatthe rock around the pit is sound, then the bearingcapacity of the foundation will not be impaired. Fillmethods that have been used include graded gravelfor low capacity loads (Couch, 1984), mixtures of70% cement, 25% sand and 5% bentonite pumpedinto voids (Klopp, 1969), grouting of sand filledseams (Sowers, 1977), lean ‘dental’ concrete


(Antes, 1981) and mass concrete fill in cleaned outvoids to support a mine hoist (Wagener, 1984).Grouting is usually carried out where the footingbears on rock containing voids, to both strengthenthe rock and prevent migration of soils into the opencavities. The procedure is to drill a pattern of holes

into the bearing rock and inject grout at lowpressure; successive series of holes are then drilledat progressively closer split spacing (primary,secondary and tertiary holes) until the grout takediminishes. The grout may be either neat cement, orcontain fillers such as sand (e.g. mix ratio 2 parts

Table 5.5 Foundation types in karstic terrain (Knott et al., 1993)

Foundation type Advantages Limitations

I Shallow foundationsSpread footings:on soil;on granular padon soil

Low cost foundations; granular padsimproves shallow soil bearingcapacity.

Susceptible to settlement damage dueto consolidation, desiccation ormigration of soil particles, or if lowstrength soil present. Collapse ofunderlying cavities could alsodamage footing. Use with extremecaution.

Spread footings bearing on rock Low cost foundation; potentialeliminated for settlement due toconsolidation, desiccation ormigration of soil particles.

Potential for differential settlement ifsoft seams are not removed fromjoints in underlying rock. Footingcould also be damaged by settlementof weathered rock or collapse ofcavities below bearing surface.Grouting may be required to fill voidsin rock.

Footing supported by pedestalsbearing on rock

Less costly than deep foundations;allows flexibility during construction

Depth to bedrock must be reasonablywell known before construction.Same limitations apply as to spreadfootings on rock.

Spread footings bearing on leanconcrete pad over rock

Reduced risk of settlement due toconsolidation, desiccation ormigration of soil particles. Caneliminate visible soil filled slots.

Higher cost than spread footings onrock. Footings can be damaged bysettlement of underlying weatheredzones or collapse of cavities. Mayrequire grouting to fill voids.

II Foundation treatmentSpread footings on rock or soil withgrout cap to fill voids in soil and rock

Low cost foundations; grouted padimproves shallow soil bearingcapacity, and modulus of rock.

Susceptible to settlement damage dueto consolidation, desiccation ormigration of soil particles, or if lowstrength soil present. Collapse ofunderlying cavities could alsodamage footing. Use with extremecaution.

Spread footings with vibra-replacement (stone columns)

Potentially cheaper than some otherdeep foundation treatments

Provides pathway for water to seepinto underground karst drainagenetwork, resulting in potential forparticle migration and increasedsolution activity. Generally not agood approach for karst areas.

Deep dynamic compaction Voids in soil can be collapsed.Potentially less costly than some

Does not work well in clayey soil.Does not eliminate potential for


Foundation type Advantages Limitationsother deep treatment techniques. particle migration. Generally not a

good approach for karst areas.Pressure injected footings (PIF) onrock.

Adaptable to variable rock surfacesand ground water conditions. Abilityto break through voids in soil due toimpacts. Impacts also load tests PIFas it is being driven.

Ability to break through voids needsto be verified. Cannot evaluateconditions below pile tip. Similarlimitations to spread footings onuntreated rock. Foundation type notcommonly used.

III Deep foundationsDrilled shafts in rock Adaptable to variable depths, can

assess the presence of cavities bydrilling probe holes, can drill throughweathered zones and voids.

Experienced personnel needed on siteto determine shaft depth. Relativelyhigh cost. Ground water can be aproblem. Hard rock drilling can be aproblem overcome by correctequipment.

H-piles to rock Low cost for deep foundations ifactual lengths are known. Easy todrive. Additional piles can be addedto provide redundancy. Hardened tipscan help to reduce tip damage.

Capacity uncertain due to potentialfor pile damage from driving, voidsmay be present under pile and poortip contact on sloping rock. Variablelengths may result in differentialsettlement due to elastic shortening.Difficult to estimate pile lengthrequirements.

Mini-piles or pin piles into rock Successful in areas where othermethods failed. Can verify capacityby drilling probe hole or test loading,or by providing long bond zonebelow top of rock. Suitable for highlyvariable rock surfaces, voids in soilor rock, high ground water tables.

May have to telescope holes severaltimes to penetrate boulders, fracturedrock. Pregrouting of overburden mayby necessary to penetrate soft orcollapsed zones and stabilize voids.Lateral stability should be evaluated,particularly for voids in soil. Mustassure capacity of rock using longbond zone in rock if voids or soilfilled slots may exist. Load tests maybe required where rock quality isquestionable based on drilling. Costlypile type.

sand to 1 part water) or fly ash, depending on cost,required strength and the widths of the voids (seealso Section 7.6). Possible limitations of groutingare that the grout could preferentially flow into, butnot necessarily fill, a single open cavity andpenetrate minimally into tighter cavities. Diamonddrilling would often be required to confirm thequality and extent of the grouting.Another means of increasing the bearing capacitywhere the vertical depth of the solution cavities islimited, is to use dynamic compaction to break upand consolidate the upper layer. Couch (1984)

reports the use of a 15 tonne weight dropped from aheight of 18 m (60 ft) to consolidate the upper 8–10m (25–30 ft) of the foundation by collapsing thecavities. The limitations of dynamic compaction arethat it does not reduce the potential for soilmigration into underlying cavities, and the resultscan be difficult to quantify.(c) Deep foundationsDeep foundations are those with their depth at leasttwice their width, and include drilled shafts, H-pilesand pin piles; they are used where the depth tosound rock exceeds the depth of normal excavating


equipment. The following is a brief description ofeach foundation type (Knott et al., 1993).• Drilled shafts, or caissons These are formed bydrilling a large diameter hole (up to about 1 m or 40in) to a depth where there is a rock stratum capableof supporting the load on the shaft; the hole is thenfilled with concrete. Drilled shafts are typically usedwhere the rock surface is very irregular andconsequently their lengths are often variable acrossa site which requires suitable contractual terms toaccommodate this condition (Brown, 1991). Thecapacity of the shaft is usually based on end bearingon rock and very high bearing capacities can beachieved in sound rock, but the rock below the shaftshould be probed for cavities, clay seams andweathered rock by drilling exploratory holes.Additional capacity can be obtained by drilling asocket into rock and accounting for the rock-concrete shear strength (see also Chapter 8).The hole is usually drilled with an auger through thesoil and weathered rock to form a uniform bearingsurface on sound rock. The augering may need to besupplemented with DTH percussion drilling, coring,or drilling and blasting to remove protruding soiland rock. During these operations care must bebeing taken that the air used to lift the cuttings doesnot blow out soil seams and that the blasting doesnot open new seepage paths. Where clay filled seamsare encountered in the base, they could be cleanedout and filled with concrete, or rock bolts could beinstalled from the base of the caisson into soundrock to tie the caisson to the shaft. Alternatively, apipe pile or H-pile could be driven through thebottom of the shaft into the seam, provided that theseam is not so deep that an excessive length of pileis required to achieve satisfactory bearing. Wherethe caisson hangs up above a cavity, it may bepossible to install pin piles from within the shaft topass through the cavity into sound rock (Sowers,1984).Inflow of ground water into the drill hole can be asignificant problem and pumping should only becarried out if there is no risk that this will producesettlement in nearby structures due to the removalof the underlying soils. Furthermore, the pumping

volume may be significant; Wagener (1982) reportsthat a pump with a capacity of 27 000 liters per hour(7100 gal/h) was not able to dewater an 18 m (60 ft)deep shaft. If dewatering is not possible, then thetremie method (pipe extending to lower end ofshaft) or bottom dump buckets can be used to placethe concrete through the water. Some of theconcerns with this situation are that segregation ofthe concrete may occur, and that flowing groundwater may wash fines from the concrete as it sets.The quality of the concrete should be checked bycoring, with grouting carried out if necessary, to fillvoids.The drainage of limestone foundations can have anumber of detrimental effects on stability. First, theincreased seepage gradients can result in faster ratesof solution with consequent enlargement of solutioncavities which increases the stress on the adjacentrock. Second, the increase in the effective unitweight of the rock has the effect of increasing theloading on the rock. Third, the flow of water maydislodge loosely consolidated infilling material.• End bearing piles Piles are the most commontype of deep foundation because they are cheaper toinstall than drilled shafts and additional piles canreadily be driven to account for piles that do nothave the full bearing capacity. The piles are drivento top of rock or into the rock to penetrate theweathered rock and cavities. The piles are usuallyequipped with hardened tips and stiffened ends tominimize tip damage and provide capacity topenetrate the rock. Where tip damage is particularlysevere, damage can be minimized by pre-drilling alarge diameter hole through any obstructions intosound rock and then concreteing the pile into thehole. H-piles are used more frequently than pipepiles, and compact sections, such as HP 12×57instead of HP 12×53, are used to help resistbuckling.The bearing capacity of piles will depend on therock conditions at the tip; piles may enter pits oropen joints with the result that they will bend andtwist and have a lower bearing capacity, for aspecified deflection, than shorter piles (Fig. 5.10).Piles will also have reduced bearing capacity where


they are end bearing on a hard seam above a

Figure 5.9 Examples of construction procedures for spread footings on karstic terrain (after Katzenbach and Romberg,1987): (a) concrete-plug; (b) partial replacement of collapse material with concrete; (c) footing supported byunderground bridge; (d) shallow foundation with screw jacks for adjustment; (e) driven pile in collapse material, withsocketed pier in rock.


compressible seam, where they strike a sharpprojection and the end is split, or where they punchinto porous rock. Furthermore, piles may stop on aweak pinnacle that resists impact from driving, butmay gradually move under applied load. If thesolution cavity is very deep and end bearing pilescannot be used effectively, then batter piles may berequired to locate areas of sound rock.In assessing the bearing capacity of piles driven incavernous limestone, some precautions that may betaken are as follows. Where the irregular rockbearing surface results in the pile lengths differingby more than about 10%, an elastic analysis isrequired to estimate each pile’s share of the totalload and assess the need for additional piles(Sowers, 1975). Furthermore, the load capacity maybe reduced, compared with end bearing on soundrock, by as much as 25% to account for theuncertain bearing conditions (Daly, 1990). Finally,where the quality of the bearing rock is uncertain,the bearing capacity can be checked by pre- or post-drilling holes with an airtrack to check that

approximately 3m (10ft) of sound rock exists belowthe bearing level (Wagener, 1982). Methods ofassessing the capacity of piles include specifying arefusal limit, and dynamic pile monitoring (Rojas-Gonzalez et al., 1993).• Pin piles (micro or mini piles) These consist ofsmall diameter, typically about 180 mm (17 in)diameter, grouted pipe sections inserted into anoversized hole that has been drilled to a specifieddistance into rock (Fig. 5.11). Conventional drillingequipment is used but telescoping holes may berequired in poor ground in order to install severalstages of casing. This allows piles to be installedthrough soil into a wide variety of rock conditions,inclined at a variety of angles, and located wherethere is restricted access for larger drills or piledriving equipment, and where piling vibrations arenot permitted (Bruce and Nicholson, 1989).The grout may be neat cement grout or asandcement mix which is placed with a tremie tubeextending to the bottom of the pipe. When the pipeis full, a pressure fitting is attached to the top of the

Figure 5.10 Influence of karstic structure on pile support (after Sowers, 1976).

1. Long, supported pile.

2. Pile bent and wedged in crack.

3. Pile tip damaged on sloping rock surface.

4. Pile bearing on pinnacle.

5. Pile bent and not supported.

6. Short, supported pile.


pile and further grout is injected until it returns atthe annulus.Pin piles in rock can be designed for load transferby end bearing, skin friction, or a combination ofboth. Skin friction in the soil portion of the pile isnot considered in the capacity calculations, but it isdeveloped in the rock portion and can be animportant component of the capacity where thereare voids below the tip and end bearing is uncertain.The overall load capacity of the pile is limited bythe small cross-sectional area of the steel and groutand their resistance to bursting, buckling andcracking, as well as shear failure along theperiphery, particularly where the drill hole hasintersected cavities in the rock.Pin piles have been used in the renovation andexpansion of the Orchestra Hall in Chicago, wherelimited head room precluded the use of driven pilesand hand excavated caissons would have been tooexpensive. The construction procedure was to usean hydraulic rotary drill to advance holes to a depthof 30 m (100 ft) through clay and hard pan andpenetrate to a depth of about 0.5 m into thelimestone bedrock. The drill rod was a 180mm (7 in)diameter, 13mm (0.5in) wall thickness steel pipe,fitted with a sacrificial carbide cutting shoe, thatremained in the hole as the pin pile. After drilling, arebar cage was placed at the tip of the pile and atremie tube was used to fill the pile with neat cementgrout (28 day unconfined compressive strength of41MPa or 6000p.s.i.). Finally, additional grout waspumped down the pile under pressure to fill the tiparea and the drill hole annulus. Load tests onselected pin piles showed load capacities of between1.87 and 2.45 MN (420 and 550 kips) with apermanent deformation of 24 and 2.5 mm (0.95 and0.1 in) respectively, with 100% of the load beingcarried at the pile tip and none in skin friction(Scherer et al., 1996).

5.4Settlement

For many foundations on rock, the bearing materialcan be considered to be elastic and isotropic so

settlement occurs as the load is applied, and there isno time dependent effect. Under these conditions,settlement can be calculated using elastic theorywith appropriate values for the modulus andPoisson’s ratio of the rock mass. The mechanism ofsettlement of foundations on rock depends on thecombined properties of the intact rock and thediscontinuities, and depending on these properties,four different types of settlement can be identified:

1. settlement resulting from a combination ofstrain of the intact rock, slight closure andmovement of discontinuities, andcompression of any minor clay seams. If therock is strong and elastic, and any clay seamspresent are thin (less than a few millimetersthick), it can be assumed that the settlementwill also be elastic, and elastic theory can beused to calculate settlement. Elastic theory canbe applied to the calculation of settlement offoundations on isotropic, homogeneousformations, layered formations and transverselyisotropic materials.

2. settlement resulting from the movement ofblocks of rock due to shearing of discontinuitysurfaces. This will most often occur wherefoundations are located at the crest of a steepslope and potentially unstable blocks of rockare formed in the face. In hard rock where thereis little difference between the peak and residualstrength of the discontinuities, a small amountof displacement may be followed by suddencollapse.

3. time dependent settlement which includesfoundations on ductile rocks such as salt whichstrain continuously at any stress level, andbrittle rocks if the applied stress exceeds theyield stress (see Table 3.10). Time dependentsettlement may also occur if the rock containssubstantial seams of clay or other plastic rock.

4. settlement due to subsidence of the underlyingstrata which can occur in coal mining areaswhere collapse of the openings occursfollowing extraction of the coal resulting in theformation of a trough shaped depression at the


ground surface (see Section 5.4.4).

The following is a summary of methods ofcalculating settlement; for complex geologicalconditions where none of these methods apply,numerical analysis may be required.

5.4.1Settlement on elastic rock

Elastic theory can be used to calculate settlementfor a range of geological conditions which includehomogeneous, isotropic rock, layered formationsand transversely isotropic rock (Fig. 5.12). The datarequired for these analyses comprise the rockproperties expressed in terms of the modulus and

Figure 5.11 Typical pinpile installed in hole drilled into karstic bedrock (adapted from Knott et al., 1993).


Poisson’s ratio of each formation, the position andthickness of each layer, where applicable, and thefoundation shape and bearing pressure. Whencalculating settlement using the proceduresdescribed in the following sections, it is advisable tocarry out sensitivity analyses to determine theinfluence of the layer dimensions and elasticproperties of the rock mass on settlement. Rockmass moduli can rarely be determined withprecision, so it is important to calculate thesettlement for the range of moduli and dimensionsthat may exist at the site.(a) Homogeneous, isotropic rockWhere the rock mass is homogeneous and isotropic(Fig. 5.12(a)), the vertical settlement dv is given byequation 5.18 for a foundation approximated as oneor more uniformly distributed loads acting oncircular or rectangular areas near the surface of arelatively deep stratum (Schleicher, 1926):

(5.18)

where q is the uniformly distributed bearingpressure; B is the characteristic dimension of theloaded area, which for a circular area is thediameter, and for a rectangular area is the smallerdimension; Cd is a parameter which accounts for theshape of the of the loaded area and the position ofthe point for which settlement is being calculated; vis Poisson’s ratio and E is Young’s modulus.Table 5.6 gives values for parameter Cd for circular,square and rectangular footings bearing on uniform,elastic rock. The use of equation 5.18, together withthe appropriate shape and rigidity factor Cd, allowscalculation of settlement for a wide range offoundation shapes.(b) Layered formationsThe settlement of footings on layered formations,where the upper layer is relatively thin comparedwith the footing dimensions, can be calculated usingelastic theory in a similar manner to that of isotropicrock. This section demonstrates the application ofthis method to the following three geologicalconditions (Fig. 5.12(b, c, d)):

Table 5.6 Shape and rigidity factors Cd for calculating settlements of points on loaded areas at the surface of an elastichalf space (after Winterkorn and Fang, 1975)

Shape Center Corner Middle of short side Middle of long side Average

Circle 1.00 0.64 0.64 0.64 0.85Circle (rigid) 0.79 0.79 0.79 0.79 0.79Square 1.12 0.56 0.76 0.76 0.95Square (rigid) 0.99 0.99 0.99 0.99 0.99Rectangle:Length/width1.5 1.36 0.67 0.89 0.97 1.152 1.52 0.76 0.98 1.12 1.303 1.78 0.88 1.11 1.35 1.525 2.10 1.05 1.27 1.68 1.8310 2.53 1.26 1.49 2.12 2.25100 4.00 2.00 2.20 3.60 3.701000 5.47 2.75 2.94 5.03 5.1510000 6.90 3.50 3.70 6.50 6.60

1. a compressible layer overlying a rigid base,such as a surface layer of weathered rockoverlying fresh rock;

2. a relatively thin bed of compressible rockwithin a formation of stiffer rock;

3. a bed of stiff rock beneath which there is amuch thicker bed of more compressible rock.

These conditions are most likely to be encounteredin sedimentary formations where, for example, there


is a bed of low modulus clay shale within a stiffersandstone. Where the actual conditions at a site donot exactly match any of the models shown inFig. 5.12(b, c, d), or the moduli are not knownaccurately, a sensitivity analysis would be carriedout to examine the influence of modulus ratios andbed thickness on the settlement magnitude. In mostcases the calculated settlement will be sufficientlyaccurate when compared with the estimates made ofthe modulus values and the allowable settlementtolerance of the structure. Where the models are notsufficiently accurate, as may be the case for inclinedbeds of varying thickness (Fig. 5.12(e)), numericalanalysis will be required.(c) Compressible layer on rigid baseThe model shown in Fig. 5.12(b) of a compressiblelayer overlying a rigid base can be used, forexample, where there is a zone of weathering overfresh rock extending to a considerable depth. Theeffect of the rigid base is to diminish the settlementas compared with that produced where theweathered rock extends to a considerable depth.Settlement is calculated using equation 5.18, withshape factor replacing Cd. Table 5.7 gives valuesfor the factor for a variety of foundation shapesbearing on an elastic layer of thickness H underlainby a rigid base; the values given in the Table areapplicable to the center of the footing (Fig. 5.12(b)).The assumptions made in the calculation of thefactor are that, at the interface between thecompressible upper layer and the rigid base, thereare no horizontal shear stresses acting and nohorizontal displacement.(d) Compressible bed within stiff formationSettlement of a formation consisting of a relatively

thin bed of compressible rock underlying a bed ofstiffer rock (Fig. 5.12(c)) can be calculated in asimilar manner to that of a compressible layeroverlying a rigid base. The calculation procedureassumes that the lower bed is infinite and acts as arigid base, and that the middle and upper beds act asa single, compressible bed. Using theseassumptions, the shape factor can be obtained from Table 5.7, and the settlement is calculatedusing the modulus of the weighted average of thetwo beds. Thus the effective modulus of the twolayers is (E1H1+E2H2)/(H1+H2), and the value of Happlied in Table 5.7 is (H1+H2). Equation 5.18 isthen used to calculate the settlement.This calculation method tends to over-estimate thesettlement amount because it does not account forthe load distributing effect of the upper stiff layer.The upper layer supports a significant portion of theload and there is less load distributed into the lower,compressible bed (see Fig. 5.23).(e) Stiff layer overlying compressible formationAnother geological condition that may beencountered is that of layer of stiff rock overlying aless stiff material of infinite depth. For thiscondition, the surface settlement dv of a uniformlyloaded circular footing with diameter B is calculatedas follows:

(5.19)where a is a correction factors given in Table 5.8determined by the relative moduli of the twomaterials (E1/E2) and the ratio H/B, where H is thethickness of the upper layer (Fig. 5.12(d)). The termd8 is the settlement calculated assuming that thefoundation material is entirely composed of

Table 5.7 Values of the shape factor for settlement of the center of a uniformly loaded area on an elastic layerunderlain by a rigid base (Winterkorn and Fang, 1975)

H/B Circle Rectangle shape

infinite strip

0.1 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.090.25 0.24 0.24 0.23 0.23 0.23 0.23 0.23 0.230.5 0.48 0.48 0.47 0.47 0.47 0.47 0.47 0.471.0 0.70 0.75 0.81 0.83 0.83 0.83 0.83 0.83



infinite strip

1.5 0.80 0.86 0.97 1.03 1.07 1.08 1.08 1.08

Figure 5.12 Methods of settlement calculation for foundations on isotropic, layered and transversely isotropicrock.



infinite strip

2.5 0.88 0.97 1.12 1.22 1.33 1.39 1.40 1.403.5 0.91 1.01 1.19 1.31 1.45 1.56 1.59 1.605.0 0.94 1.05 1.24 1.38 1.55 1.72 1.82 1.838 1.00 1.12 1.36 1.52 1.78 2.10 2.53 8the lower material (elastic properties E2, v2) with the factor Cd determined from Table 5.6.

EXAMPLE 5.2

SETTLEMENT-ELASTIC ROCK

This example demonstrates the use of the settlement calculations described in this section andillustrates the effect of the different geological formations on settlement magnitudes.

Consider a 2m by 3 m (6 by 10 ft) rectangular footing supporting a applied load of 40 MN (9000 kips)so that the uniform applied bearing pressure is 6.7 MPa (150 ksf). Settlement is calculated as follows:

(a) If the foundation is composed of a uniform bed of isotropic rock, the shape factor is determinedfrom Table 5.6. The length to width ratio of the footing is 1.5 and the value of Cd at the center of the footingis 1.36. If the modulus is 2 GPa (0.29×106p.s.i.) and the Poisson’s ratio is 0.25, the settlement calculatedfrom equation 5.18 is

(b) If the relatively compressible material occurs in a bed that is 3 m (10 ft) thick andthe underlying material is relatively stiff and extends to a considerable depth, settlement iscalculated using shape factor From Table 5.7 has a value of 0.97 for and Substituting this value in equation 5.18 gives a settlement of 6 mm (0.24 in), a reduction of about40% as compared with the isotropic case.

(c) Where the foundation material is predominantly a moderately stiff rock, but contains a 3 m (10 ft)thick bed of compressible rock at a depth of 2 m (6 ft), settlement is calculated as follows. If the moduliof the two materials are 10 GPa and 2 GPa respectively, the Poisson’s ratios are both 0.25, the weightedaverage modulus of the two upper beds is 5.2 GPa (0.75×106 p.s.i.). The combined thickness of the twoupper beds is 5 m so the ratio H/B is 2.5 and the value of from Table 5.7 is 1.12. Equation 5.18 givesa settlement of 2.7 mm (0.11 in).

(d) Where the foundation comprises a layer of relatively stiff rock with modulus 10 GPa (1.45×106

p.s.i.) overlying a considerable thickness of more compressible rock settlement is calculated using the correction factors on Table 5.8 and equation 5.19. If the upper bed is 3m thick, the ratio H/B is 1.5 and the correction factor a is 0.357 (by interpolation) for a modulus ratio of5.0. The value of 600 is 8.5 mm from (a) above, so the settlement of the layered system is


(f) Inclined, variable thickness bedsThe settlement calculation methods described in this

section only apply to horizontal beds of uniformthickness. For conditions such as that shown

Table 5.8 Elastic distortion settlement correction factor a, at the center of a circular uniformly loaded area on an elasticlayer E1 underlain by a less stiff elastic material E2, of infinite depth; (Winterkorn and Fang, 1975)

H/B E1/E2

1 2 5 10 100

0 1.0 1.00 1.00 1.00 1.000.1 1.0 0.972 0.943 0.923 0.760.25 1.0 0.885 0.779 0.699 0.4310.5 1.0 0.747 0.566 0.463 0.2281.0 1.0 0.627 0.399 0.287 0.1212.5 1.0 0.55 0.274 0.175 0.0585.0 1.0 0.525 0.238 0.136 0.0368 1.0 0.500 0.200 0.100 0.010in Fig. 5.12(e) where the foundation contains aninclined, variable thickness bed, it is necessary touse numerical methods, such as finite elementanalysis or finite difference analysis, to calculatesettlement. These methods allow the inclination,thickness, position and properties of one or morebeds to be accurately modeled, as well as theincorporation of non-vertical loads. An example ofnumerical analysis is the calculation of settlementfor a series of bridge piers founded, at differentlevels, on a massive but very weak rock (Fig. 5.13).Both the horizontal and vertical movements arecalculated, as well as the stresses at any point in thefoundation. Calculation of the stresses, andcomparing them with the rock strength, allows areasof potential rock failure to be identified. Theanalysis shown in Fig. 5.13 was performed usingthe program FLAC—Fast Lagrangian Analysis ofContinua (Itasca Corp., 1995) which is a finitedifference analysis that simulates the behavior ofmaterials such as rock and soil that behaveaccording to linear or non-linear stress/strain laws inresponse to the applied forces or boundaryconditions. Some of the other features of theprogram include interface elements to simulateplanes along which slip can occur, ground waterpressures, structural elements to simulate rock boltsand dynamic analysis.

A method of modeling a jointed rock mass inwhich displacement and opening of the

discontinuities occurs is to use the program UDEC— Universal Distinct Element Code (Itasca Corp.,1986). Figure 7.11 in Chapter 7 shows an exampleof the use of the three-dimensional version ofUDEC (3DEC) to model the foundation of an archdam. Chapter 7 describes the functions of UDEC;however, detailed description of numerical analysisis beyond the scope of this book.

5.4.2Settlement on transversely isotropic rock

The calculation of settlement of foundations ontransversely isotropic uniform rock, such assandstones, shales and schists, free of beds ofcompressible rock, can be carried out usingequations developed by Kulhawy andGoodman (1980), Kulhawy (1978) and Gerrard andHarrison (1970). These equations give the value ofthe vertical settlement of a rigid circular load placedon the horizontal surface of a transversely isotropicrock mass in which the load axis is coincident withthe vertical modulus axis z. The properties of therock are defined by the vertical and horizontaldeformation modulus (Ez and Eh respectively), theshear modulus between the horizontal and verticalplanes (Ghv) and the following values of Poisson’sratio.

Vhh Poisson’s ratio for horizontal stress on the


complimentary horizontal strainVhz Poisson’s ratio for horizontal stress on

vertical strainvzh Poisson’s ratio for vertical stress on the

horizontal strain

The settlement dv is given by one of three equations

depending on the value of the factor ß2 which isgoverned by the properties of the rock mass. Theequations for settlement are as follows: ß2 positive:

(5.20a)

Figure 5.13 Example of numerical analysis using FLAC to calculate displacement vectors in a series of steppedfoundations on homogeneous, isotropic, very weak rock (model by U.Atukorala and M.Kelly).

Figure 5.14 Model of a fractured rock mass with three orthogonal joint sets for calculation of settlement of circularfooting with vertical applied load.


ß2 negative:

(5.20b)

(5.20c)

The appropriate equation to use is defined by:

(5.21)

The factors a, c', d, and e2 are defined by thefollowing equations:

(5.22a)

(5.22b)

(5.22c)

(5.22d)

where Q is the load applied to the footing; and b isthe radius of the loaded area. In the case of squareor rectangular footings, an equivalent radius can becalculated from the area of the footing, i.e.

for square footing of side length B.Note that Gerrard and Harrison give solutions forsettlement of strip footings on orthorhombic rock,and for other loading cases on transversely isotropicrock.The deformation and shear moduli, and thePoisson’s ratio of the rock mass model illustrated inFig. 5.14 can be calculated from the elasticproperties of the intact rock, the spacing of thediscontinuities, and their normal and shearstiffnesses. The equations for the rock mass elasticparameters are as follows:

(5.23)

(5.24)

(5.25)

for subscripts with and

The elastic properties of the intact rock and thediscontinuities are defined by the followingparameters:Er is the intact rock deformation modulus;vr is the intact rock Poisson’s ratio;Gr is the intact rock shear modulus, and

(5.26)

Sx, y, z is the spacing of each of the three sets of

discontinuities; kni is the normal stiffness of thediscontinuities of discontinuity set i; and ksi is theshear stiffness of discontinuity set i.A survey of joint stiffnesses determined by bothlaboratory and in situ testing shows the followingtypical range of normal stiffness kn and shearstiffness ks (Kulhawy, 1978).

1. For sandstone, dry sawed joint:

2. For marly, sand filled joint, 1–2 mm thickness:

3. For shale interbed, wet, 2–5 mm thickness:

The horizontal deformation modulus Eh, and theshear modulus Ghz, used in the calculation ofsettlement are found from equations 5.23 and 5.24as:

(5.27)

(5.28)

From equation 5.25, the values for the Poisson’sratios used in the settlement calculation are:

(5.29)

and the ratio of the vertical to horizontaldeformation moduli is given by


(5.30)

EXAMPLE 5.3

SETTLEMENT OF FRACTURED ROCK

The following example illustrates the method of calculating settlement of foundations bearing onfractured rock.

Consider a vertical bridge pier with a load Q of 40 MN and a footing area of 2 m by 2 m bearing on a moderately weak sandstone. Laboratory tests conducted on pieces of

core show that the elastic properties of the intact rock are as follows:

From equation 5.26 the shear modulus Gr of the intact rock is found to be 4 GPa.If the rock contains horizontal bedding planes with a clay infilling, and two sets of vertical joints

which are clean and tight, the effect of these discontinuities on settlement is as follows. The spacings ofthese discontinuity sets, and their normal and shear stiffnesses determined from in situ direct shear tests,are:

Bedding planes:

Joints:

From equations 5.23, 5.24 and 5.25, the deformation and shear moduli, and the Poisson’s ratio ofthe rock mass are calculated to be:

and

From equation 5.21, the factor ß2 is found to be 1.48 and the settlement from equation 5.20b is 34.1


mm.The influence of the ratio of the horizontal Eh to vertical Ez moduli on the settlement of the

foundation is shown in Fig. 5.15. With increasing thickness of the clay infilling in the bedding planes, thereis a corresponding decrease in the normal and shear stiffnesses (i.e. more compression under appliedload). If the properties of the vertical joints and the value of Eh are unchanged, the ratio Eh/Ez willincrease. Figure 5.15 shows that the settlement varies between 10.5 mm when the rock is isotropic

to about 62.5 mm when Equations 5.20–5.22 can also be used to determine the effect of differing properties of the vertical

discontinuities on settlement. For example, consider a rock mass comprising a series of horizontal slabseach 0.25 m thick, and the horizontal bedding planes forming these slabs have normal and shearstiffnesses of 2 and 1 GPa respectively. The vertical modulus is 0.48 GPa. The horizontal slabs can besimulated by setting and with the vertical joints having the same stiffness values as in theprevious example. The horizontal modulus is 9.1 GPa, and the ratio the shear modulus

GPa. The settlement is calculated to be 27.7 mm, which compares to a settlement of 34.1mm when the spacing of all the discontinuities is 0.25m. This shows that the relatively stiff, horizontalslabs have some effect in limiting settlement.

The settlement of an isotropic rock foundation can be calculated using equations 5.20 or equation 5.18. For example, Fig. 5.15 shows that when the ratio the settlement is 10.5 mm. Incomparison, using equation 5.18 with a shape factor Cd of 0.79 for a rigid, circular footing, a modulus of2 GPa and a Poisson’s ratio of 0.05, the calculated value of the settlement is 9 mm.

5.4.3Settlement on inelastic rock

For footings on elastic rock, the total settlement willoccur as the load is applied. However, timedependent settlement is likely where the foundation

contains seams of compressible material such asclay, or ductile materials such as salt or tar sand.Other conditions where time dependent effects maytake place include weathering resulting in decreasedbearing capacity, swelling due to stress relief,changes in internal stress conditions, or chemical

Figure 5.15 Influence of modulus ratio on settlement of a uniformly loaded circular area bearing on transversely isotropicrock.


reactions in the rock. Time dependent properties ofrock are discussed in more detail in Section 3.6.Where the foundation contains compressible seamsof soil, settlement due to compression of the soilcan be determined using conventional soilmechanics principles. Compression is a three stageprocess comprising distortion, consolidation andsecondary compression. Distortion occurs as theload is applied and is assumed to be elastic.Consolidation settlement determines the time rate ofsettlement and depends on the rate at which water isexpelled from the void spaces in the soil. Thus,water flows readily through clean sands soconsolidation settlement will be essentiallyinstantaneous, while the consolidation of clays maytake place over a period of months. Secondarycompression occurs as the result of yielding andcompression of the soil skeleton and is also timedependent.In computing the rate of compression, the stresslevel in the soil seam(s) can be determined using themethods described in Section 5.5 which give thestress distributions in both homogeneous andlayered formations. Where the foundationconditions cannot be modeled by one of themethods given in Section 5.5 it will be necessary touse numerical analysis to determine the stressdistributions (see Fig. 5.13).Foundations on ductile rocks, or rocks stressedabove the brittle to ductile transition stress (seeSection 3.6.3) will settle (creep), with the rate ofcreep dependent upon the level of the appliedstresses, and the time for which the load is applied.As shown in Fig. 3.23(c), during primary creep thestrain rate diminishes with time so that after acertain period settlement will cease. However, if thebearing stress is greater than that which induces theonset of secondary creep, settlement will continueindefinitely.The finite difference analysis program FLAC(Itasca, 1995), which can analyze stress and strainconditions in foundations, as shown in Fig. 5.13,can incorporate plastic materials and calculate time-dependent settlement. For example, the rock couldbe modeled as a visco-elastic material defined by

equation 3.23 which gives the axial strain with timeof a Burger substance subjected to a constant axialstress.

5.4.4Settlement due to ground subsidence

In coal mining areas where structures are locatedabove active or abandoned mines there is a risk thatcollapse of the underground openings can inducesubsidence or sink holes at the ground surface. It isusual practice in coal mines that the collapse is partof the extraction sequence. For example, inlongwall mining where as much as 90% of the coalis mined, the roof caves as the continuous miner andthe shield supports advance and no attempt is madeto maintain stable openings. This can result intrough subsidence at the surface which takes theform of a shallow, dishshaped depression formed bysagging and downwarping of the overlying rockformations into the mined out area (Karfakis, 1993).The dimensions of a subsidence trough are relatedto the thickness of the seam and the width ofextraction, and the depth of the seam below thesurface, with an approximate horizontal limit for thetrough width defined by lines inclined at angles of35° from the vertical at the edges of the extractionarea (Fig. 5.16). Charts have been developed whichrelate the shape of the subsidence trough to thedimensions D, W and M, and which show, forexample, that the maximum subsidence at the centerof the trough is about 80–90% of the seam thicknesswhen the extraction width exceeds the mining depth

, and drops to 10% of the seam thicknesswhen (National Coal Board, 1975).Much of the early work on subsidence above coalmines was undertaken in Britain, although it hassubsequently been found that the same principlesapply in most other coal mining areas. Factors thatmay influence the magnitude and characteristics ofthe subsidence are the type of rock above the minedseam, faulting and seam inclination, surfacetopography and the extent of ground waterinfiltration into the disturbed rock mass (Whittakerand Reddish, 1989).


Structures located on the surface within thesubsidence trough will experience horizontal andvertical displacement, tilt and bending, as well astensile (+e) or compressive (-e) strain depending ontheir position within the trough. Typical strain anddisplacement profiles are shown in Fig. 5.16.Another factor to consider is the change insubsidence with time. For example, a highwaybridge constructed in a sink hole area above aflooded salt mine was designed to accommodatefuture settlements of as much as 600 mm verticallyand 150 mm horizontally over 50 years (Matthewset al., 1998).In room and pillar operations, the pillars are sized sothat they can support the weight of the entireoverlying rock above both the pillars and the rooms.However as the workings are abandoned and thecoal in the pillars and the rock in the roof of therooms deteriorates, due to flooding or changes inmoisture content, the openings eventually collapse.This can result in the formation of a ‘chimney’ ofbroken rock that can eventually reach the surface toform a sink hole. The formation of such sinkholesdepends on such factors as the width of the room,the depth below the surface, the nature of theoverlying strata and the drainage of water into thecaved ground. Remedial action that may be taken tolimit the damage caused by sinkholes includecontrol of surface water infiltration, and backfillingthrough a hole drilled from the surface.

5.5Stress distributions in foundations

Most rock foundations will behave as linear elasticmaterials so it is possible to use elastic theory tocalculate stress distributions that are induced in therock. The reasons for using elastic theory are first,the availability of solutions for linear elastic mediawith boundary conditions that approximate those ofactual engineering situations. Second, studies haveshown that elastic theory will predict reasonablywell actual stresses measured in the field (Morganand Scala, 1968; Bozozuk, 1972).For the design of rock foundations it is necessary to

have a means of determining stress distributions forboth isotropic and transversely isotropic rock.Typical uses of stress distributions are in thecalculation of settlement of layered formationswhere it is necessary to determine the stresses ineach layer and the resulting consolidation that willtake place.Another use of stress distribution calculations is inthe examination of the interaction between thestress fields induced, for example, by two nearbyfoundations, or a foundation and a nearby tunnel.Using superposition, it is possible to add thestresses induced by each structure and determinewhether there is any portion of the rock that isoverstressed. The method of determining whetherthe rock is overstressed is shown in Fig. 5.3 wherethe strength of an isotropic fractured rock mass isplotted as a curved envelope in terms of the majorand minor principal stresses (referenceSection 3.3.2).The actual principal stresses acting at any point inthe foundation s1 and s3 are plotted on this diagramand the factor of safety FS is then the ratio betweenthe strength s1A at the applied minor principal stresss3, and the applied major principal stress s1, that is

(5.31)

where m and s are constants defined in Table 3.7;and su(r) is the unconfined compressive strength ofintact rock.Contours of the factor of safety can be plotted toshow areas that may be overstressed.

5.5.1Stress distributions in isotropic rock

The distribution of stresses within an elastic half-space resulting from a point load applied normal tothe surface and for small strains, as illustrated inFig. 5.17, is given by Boussinesq (1885). Theequations are as follows:


Figure 5.16 Subsidence of ground surface across longwall extraction based on European coal mining observations andpredictions. (a) subsidence profile; (b) strain profile; and (c) displacement profile (Whittaker and Reddish, 1989).


where v is Poisson’s ratio and, r, z and R aredimensions defined in Fig. 5.17.These stresses are those that would occur in aweightless linear elastic medium; they must besuperimposed upon the pre-existing stresses due tothe weight of the material. It should be noted fromthese equations that the stresses are independent ofthe elastic constants.(a) Distributed loadsThe Boussinesq equations can be applied to thestress analysis of foundations if they are modified toobtain the stresses under a distributed load. This canbe achieved by superposition, in which the forceacting on a differential area is integrated over theentire loaded area. Thus the vertical stress at depth zat any point beneath a distributed load applying apressure q is given by

(5.33)where Iz is an influence factor, the value of whichdepends upon the shape of the applied load and thelocation of the point at which the stress is measured

(Winterkorn and Fang, 1975). Figures 5.18 and5.19 give the values for influence factors for thevertical normal stress for any combination of depthz and radial distance r under circular andrectangular uniformly loaded areas. The stressdistribution for a square footing can beapproximated by a circular distributed load of thesame area. For example, the vertical stresses at anumber of points in the foundation rock arecalculated as follows.A 2 m by 2 m square footing (equivalent circulardimension, is loadedto 40 MN, the applied pressure At a depth belowthe edge of the footing the influence factor

and the vertical stress For a rectangular footing with thevalue of Therefore, at a depth of 3 m

the influencefactor is 0.095. Under the corner of the footing, thevertical stress Plotting the stress distributions calculated from the

Figure 5.17 Stresses in an elastic half space due to a point load at the surface (Winterkorn and Fang, 1975).


influence factors as stress contours provides auseful visual representation of both the stresses atany point in the foundation, and the shape of thestress ‘bulb’. Figure 5.20 shows two vertical stressprofiles, one under the center of the loaded area andthe other at a distance of the width of the footingfrom the center of the footing. Figure 5.21(a) showsthe contours of the vertical normal stress beneath auniformly loaded circular area, and illustrates howthe stresses are distributed in the rock beneath thefoundation.(b) Line loadsIn the case of a line load on an isotropic, linearelastic foundation (Fig. 5.21(b), the principalstresses at any point consist only of a radial stress srgiven by equation 5.34, with the tangential and shearstresses s? and tr? both being zero (Goodman, 1980):

(5.34)

where Q is the line load (MN/m), ? is the angle from

the vertical, and r is the radial distance from thepoint of application of Q.The stresses consist of a series of vectors radiatingfrom Q, with the length of the vectors beingproportional to the magnitude of the stress, andbeing constant along any stress contour. Thecontours of radial stress for a line load consist of aseries of circles tangent to the point of applicationof the load and centered at a depth Q/(pr) (Fig. 5.21(b)). Stress contours produced by distributed andline loads are compared in Figs. 5.21 (a) and (b).Equation 5.34 can also be used to determine thestress distributions beneath a line load inclined at anangle to the ground surface (Fig. 5.22). Under theseconditions, two sets of circular stress contours aredeveloped, one set for tensile stresses and the otherfor compressive stresses. In intact rock this stresscondition will be of little concern because the rockwill be able to withstand a small tensile stresswithout extensive fracturing of the rock. However,if the rock contains sets of discontinuities that formwedges in the foundation oriented approximately

Figure 5.18 Influence diagram for vertical normal stress sz at various points within an elastic half space under a uniformlyloaded circular area (Winterkorn and Fang, 1975).


normal to the stress directions, then this conditionmay result in movement of these wedges and failureof the foundation. A stability analysis of the wedgecould be carried out using the XSTABL method ofanalysis in which the failure surface can be modeledas a series of straight lines, anisotropic strengths canbe defined, andthe external load applied in anydirection (see Section 6.5).

5.5.2Stress distributions in layered formations

In layered formations where a stronger rock overliesa much weaker rock, the upper formation will carrythe majority of the load and the stress levels in thislayer will be considerably higher than those in thelower layer. Stress distributions in layered systemsfor elastic materials have been developed primarily

Figure 5.19 Influence diagram for vertical normal stress at a point within an elastic half space beneath the corner of auniformly loaded rectangular area (Winterkorn and Fang, 1975).


for pavement structures (Peattie, 1962; Burminster,1965) and the results can be applied to geologicalformations. Figure 5.23 shows how the verticalstress distribution in a two layer system varies withthe relative moduli of the two layers; at a modulusratio of 100 virtually all the load is carried in theupper layer (Winterkorn and Fang, 1975).The limitations of stress distribution calculationmethods developed for pavements are that thelayers must be both horizontal and of uniformthickness. In the many geological situations wherethese conditions are not applicable, numericalanalysis must be used to calculate stresses in thelayers.

5.5.3Stress distributions in transversely isotropic rock

The stress distributions determined by elastic theoryfor isotropic rock are modified, in transverselyisotropic rock, by the presence of sets ofdiscontinuities such as bedding planes, joints andfoliation. The orientation of the discontinuities andthe friction angle of these surfaces , limit the

range of directions that the stresses can take.According to the definition of interlayer friction, theabsolute value of the angle between the direction ofthe radial stress and the normal to the planes mustbe equal to or less than (Fig. 5.24). Therefore, thebulb of pressure cannot extend beyond the linesdrawn at an angle with the normal to the layers.Because the bulb of pressure in anisotropic rock isconfined more narrowly than in isotropic rock, itmust continue more deeply, meaning that thestresses are higher at a given depth below the loadthan would be the case for isotropic rock (Goodman,1980).The model used to calculate the stress distributionconsists of a half space containing a set ofdiscontinuities inclined at an angle ? to the loaddirection, loaded by a line load Q which can beinclined at any angle (Fig. 5.25). The stress in therock for these load conditions is entirely radial srwith the tangential and shear stresses being zero. Ifthe line load is decomposed into components Qx andQY parallel and perpendicular to the discontinuities

(5.35)The radial stress at any point defined by the radial

Figure 5.20 Distribution of vertical stress due to a loaded circular area on linear elastic half-space: (a) along verticallines; (b) along horizontal lines (after Winterkorn and Fang, 1975).


distance r, and angle ß with respect to thediscontinuity orientation, is given by

(5.36)

where h and g are dimensionless quantities

describing the properties of a transversely isotropicrock mass and are given by:

(5.37)

Figure 5.21 Stress contours for footings located on isotropic linear elastic half-space: (a) vertical normal stressesbeneath uniformly loaded circular area, radius b; and (b) radial stresses beneath line load.

Figure 5.22 Stress contours beneath inclined line load showing zones of compressive and tensile stress.


(5.38)

where E and v are the modulus and Poisson’s ratioof the intact rock respectively; S is the discontinuityspacing; kn, ks are the normal and shear stiffness ofthe discontinuities respectively which define theanisotropy of the rock mass; and ß is the anglebetween discontinuity orientation and radial stressdirection.These equations can be used to calculate contoursof equal radial stress within the foundation.Twoplots of the radial stresses are shown in Fig. 5.25which demonstrates the influence on the stressconcentrations of both discontinuity orientation andstiffness ratio. For the particular conditions shown,the contours are elongated when the stiffness ratio

(kn/ks) is as great as about 100, and are nearlycircular at a stiffness ratio of 10. These equationswere first developed by Bray (1977) and werechecked against model tests previously carried outby Gaziev and Erlikhman (1971). Applications ofthese equations would be in the study of interactingstress fields from adjacent footings, or for example,stress fields produced by a footing and a tunnelbelow the structure.

5.5.4Stress distributions in eccentrically loaded footings

On tall structures, horizontal forces produced bysuch conditions as earthquakes, wind and centrifugaltraffic loads, induce moments at the foundation levelwhich modify the pressure distribution beneath thefooting. For a strip footing of width B with loadscomprising a vertical load Q and an overturning

Figure 5.23 Vertical normal stress beneath center of uniformly loaded circular area at the surface of two-layer elasticsystem (after Winterkorn and Fang, 1975).


moment M, the resultant force will lie a distance efrom the axis of the footing. The term e is theeccentricity of the loading condition and is given by(Merritt, 1976):

(5.39)

If the distance e is less than B/6, that is, theresultant force is within the middle third of the baseof the footing, then the maximum and minimumpressures (q1 and q2) at the edges of the footings are(Fig. 5.26(a)):

(5.40)

(5.41)

while for a rectangular footing with length L andwidth B and the moment applied about thelong axis of the footing, the maximum andminimum pressures will be

(5.42)

(5.43)

where Q is the applied vertical load, M is theapplied moment and e is the loading eccentricity.Under these conditions, the pressure under thefooting is entirely compressive and it is necessary tocheck that the allowable bearing capacity is notexceeded in the high stress area at the edge ofthe footing. However, this calculation assumes thatthe footing is rigid, and the flexibility of standardreinforced concrete footings means that actualpressures will be less than those given in equations5.40–5.43.If the resultant lies outside the middle third, that is

the bearing is only on a portion of thefooting and tensile forces develop along one side(Fig. 5.26(b)). For this condition on a strip footing

Figure 5.24 Narrowing and deepening of the bulb of pressure due to limited shear stress along discontinuities(Goodman, 1980).


the pressure distribution is triangular and extendsover a width of 3(B/2–e), with the maximumpressure being:

(5.44)

While for a rectangular footing of width B andlength L, the maximum pressure is

(5.45)

For footings on rock where the loading condition

Figure 5.25 Contours of radial stress under line loads on transversely isotropic rock calculated by equations 5.36 to 5.38: (a) geological structure aligned horizontally (90° to vertical load); and (b) geological structure aligned at -30° tovertical load.


results in stability can be improved byinstalling tie-down anchors around the edge of thefooting. The anchors, which introduce a stabilizingmoment to counteract the overturning moment M,are designed with sufficient length to develop acone of rock in the foundation. The overturningresistance provided by this cone comprises both theweight of the cone and the strength of the rock onthe surface of the cone. Methods of rock anchordesign are discussed in Section 9.3.4.

5.6References

Antes, D.R. (1981) Footings and piles: a practicalfoundation solution in cavernous Leithsville carbonateformation. Proc. Design and Construction ofFoundations on the Carbonate Formations of NewJersey and Pennsylvania, New Jersey Institute ofTechnology, Newark, NJ, pp. 79–97.

Benson, R.C. (1984) Evaluation of differential settlementor collapse potential. Presentation to TransportationResearch Board, Annual Conference, Washington, DC.

Benson, R. C, Glaccum, R.A. and Noel, M.R. (1982)Geophysical Techniques for Sensing Buried Wastesand Waste Migration. Environmental Protection

Agency, National Water Well Association, Dublin, OH.Boussinesq, M.J. (1885) Applications des potentials, a

l’etude de l’equilibre et du movement des solideselastique. Gauthier-Villars, Paris.

Bozozuk, M. (1972) The Gloucester Test Fill, PhD thesis,Purdue University.

Bray, J. (1977) Unpublished notes, Imperial College,London.

Brown, A.D. (1991) Construction and design of drilledshafts. Hard Pinnacle Limestones, RecognizingSolutions to Today’s Problems and DefiningTomorrow’s Challenges. Deep Foundation Institute,Chicago, IL, pp. 123–40.

Bruce, D.A. and Nicholson, P.J. (1989) The practice andapplication of pin piling. ASCE FoundationEngineering Conference, Northwestern University,Evanston, IL, pp. 1–19.

Burmister, D.M. (1965) Influence Diagrams for Stressesand Displacements in a Two Layer Pavement Systemfor Airfields. Contract NBY 13009, Dept of the Navy,Washington, DC.

Cannon, J.A. and Turton, R.D. (1994) Spanning theGrand Canyon. Civil Engineering, New York,November, pp. 38–41.

Canadian Geotechnical Society (1978) CanadianFoundation Engineering Manual. Montreal, Section 2,pp. 6–9.

Figure 5.26 Stress conditions produced by footings subjected to overturning: (a)


Costopolous, S.D. (1987). Geotechnical engineering workfor the restoration of the Temple of Apollo Epicurius,Bassae. Sixth Int. Con. on Rock Mechanics, Montreal,ISRM, 327–30.

Couch, F.B. (1984) Solutions to special problems inkarstic limestone bedrock. Presentation toTransportation Research Board Symposium,Washington, DC.

Daly, P. (1990) Review of pile driving records at threesites in Yuen Long. Karst Geology in Hong Kong, (edsR.L.Langford, A.Hansen and R.Shaw), GeologicalSociety of Hong Kong, Bulletin No. 4, Hong Kong,pp. 123–34.

Fang, H-Y., ed. (1991) Foundation EngineeringHandbook, (2nd edn), Chapman & Hall, New York.923 pp.

Franklin, J.A. and Pearson, D (1985) Rock engineering forconstruction of Science North, Sudbury, Ontario.Canadian Geotechnical J., 22, 443–55.

Gaziev, E. and Erlikhman, S. (1971) Stresses and strainsin anisotropic foundations. Proc. Symp. on RockFracture, ISRM, Nacy, Paper II–1.

Gerrard, C.M. and Harrison, W.J. (1970) Circular loadsapplied to a cross-anisotropic half-space, and Stressesand displacements in a loaded orthorhombic half-space. Technical papers 8 and 9, Division of AppliedGeomechanics, Commonwealth Scientific andIndustrial Research Organization, Australia, 1970.(Reproduced as Appendices A and B in Poulos andDavis, 1974.)

Goodman, R.E. (1980) Introduction to Rock Mechanics,Wiley, New York, pp. 305–8.

Hoek, E. and Londe, P. (1974) The design of rock slopesand foundations. Third Int. Cong. on Rock Mechanics,ISRM, Denver, pp. 2–40.

Hong Kong Geotechnical Engineering Office (1981)Geotechnical Manual for Slopes, Hong Kong,pp. 129–34.

Itasca Consulting Group (1987) Fast Lagranian Analysisof Continua (FLAC), Version 2.00. Minneapolis.

Itasca Consulting Group (1996) Universal DistinctElement Code (UDEC), Version 3.0. Minneapolis,Minnesota.

Jaeger, J.C. and Cook, N.G. W. (1976) Fundamentals ofRock Mechanics. Chapman & Hall, London.

Kaderabek, T.J. and Reynolds, R.T. (1981) Miamilimestone foundation design and construction. ASCE,107(GT7) 859–72.

Karfakis, M.G. (1993) Residual subsidence over

abandoned coal mines. Comprehensive RockEngineering, Pergamon Press, Oxford, Vol. 5,pp. 451–76.

Katzenbach, R. and Romberg, W. (1987) Foundation ofhigh valley bridges in triassic sediments., Sixth Int.Con. on Rock Mechanics, Montreal, ISRM,pp. 419–23.

Kaufman, J.L. and Brand, A.H. (1991) Foundation studiesin a fault zone and a steep valley slope. Proc. Symp. onDetection of, and Construction at, the Soil/ RockInterface, Orlando, Florida. Geotechnical SpecialPublication, No. 28, ASCE, New York, pp. 73–90.

Klopp, R. (1969) Engineering geological problems duringthe foundation of the Biggetal power plant on karstifiedDevonian reef limestones in the Sauerland, and theirsolution (in German). Rock Mechanics, 1, 145–156.

Knott, D.L., Rojas-Gonzalez, L.F. and Newman, F.B.(1993) Current Foundation Engineering Practice forStructures in Karst Areas. Federal HighwayAdministration, Washington DC and PennsylvaniaDepartment of Transportation, Harrisburg, PA, Reportnumber FHWA-PA-91–007+90–12.

Kulhawy, F.H. (1978) Geomechanical model for rockfoundation settlement. ASCE, 104(GT2), 211–27.

Kulhawy, F.H. and Goodman, R.E. (1980) Design offoundations on discontinuous rock. Proc. Int. Conf. onStructural Foundations on Rock, Sydney, pp. 209–20.

Ladanyi, B. and Roy, A. (1971). Some aspects of thebearing capacity of rock mass. Proc. 7th CanadianSymp. Rock Mechanics, Edmonton.

Lemos, J.V. (1995) Experimental study of an arch dam ona jointed rock foundation. Proc. 8th Int. Cong. on RockMechanics, Tokyo, Vol. 3, Balkema, Rotterdam,pp. 1263–66

Lambe, T.W. and Whitman, R.V. (1969) Soil Mechanics.John Wiley, New York.

Matthews, S.L., Matzat, J.W. and Walker, S.E. (1998)Losing ground. Civil Engineering, ASCE, Washington,DC, April, 59–60.

Merritt, F.S. (1976) Standard Handbook for CivilEngineers. McGraw-Hill, New York, pp. 7–24.

Morgan, J.R. and Scala, A.J. (1968) Flexible pavementbehavior and application of elastic theory—a review.Proc. 4th Conf. of the Australian Road Research Board,Melbourne 4, Part 2, p. 1201.

National Coal Board (1975). Subsidence Engineer’sHandbook. London, UK.

Ontario Ministry of Transport and Communications(1983) Ontario Highway Bridge Design Code,


Highways Engineering Division, Toronto, p. 147.Peattie, K.R. (1962) Stress and Strain Factors for Three-

layer Elastic Systems. Highway Research BoardBulletin, No. 342.

Peck, R.B., Hanson, W.E. and Thornburn, T.H. (1974)Foundation Engineering, Wiley, New York,pp. 361–3.

Poulos, H.G. and Davis, E.H. (1974) Elastic Solutions forRock and Soil Mechanics, Wiley, New York,pp. 138–64.

Rawlings, G.E. and Wyllie, D.C. (1986) Bridgeabutments on rock. Transportation Geotechnique,Vancouver Geotechnical Society, Vancouver.

Roark, R.J. and Young, W.C. (1970) Formulas for Stressand Strain, McGraw-Hill, New York, pp. 325–67.

Rojas-Gonzalez, L.F., Knott, D.L. and Newman, F.B.(1993) Current Practice for Dynamic Pile Monitoringin the United States. Research Project 90–12,Commonwealth of Pennsylvania Department ofTransportation, Office of Research and SpecialStudies.

Scherer, S.D., Walter, W.H. and Johnson, R. (1996)Chicago’s micropile debut. Civil Engineering, ASCE,66(8), 51–3.

Schleicher, F. (1926) Zur theorie des Baugrundes. DerBauingenieur, 48, 49.

Serrano, A. and Olalla, C. (1994) Ultimate bearingcapacity of rock masses. Int. J. Rock Mech. MiningSciences & Geomech. Abstr., 31(2), 93–106.

Serrano, A. and Olalla, C. (1995) Allowable bearingcapacity of typical rock masses depending on RMR andcompression strength of intact rock. Proc. Int.Workshop on Rock Foundation, Tokyo, Japan,Balkema, Rotterdam, pp. 321–5.

Simm, K.F. (1984) Engineering solutions to geologicalproblems in the design and construction of the HumberBridge. Q. J. Eng. Geol., 17, 301–6.

Sowers, G.F. (1970) Introductory Soil Mechanics andFoundations, Macmillan New York, pp. 395–6.

Sowers, G.F. (1975) Failures in limestone in humidsubtropics. ASCE, 101(GT8), 771–87.

Sowers, G.F. (1976) Foundation bearing in weatheredrock. Proc. of Specialty Conf. on Rock Eng. forFoundations and Slopes, ASCE, Geotech. Eng. Div.,Boulder CO., Vol. II, pp. 32–41.

Sowers, G.F. (1977) Closure to failures in limestone inhumid subtropics. ASCE, 103(FT7), Proc. Paper 11521,807–13.

Sowers, G.F. (1976a) Settlement in terrains of well-

indurated limestone. Analysis and Design of BuildingFoundations (ed. H.Y.Fang) Envo Publishing Co.,pp. 701–25.

Sowers, G.F. (1984) Correction and protection inlimestone terrain. Sinkholes: their Geology,Engineering and Environmental Impact, Proc. FirstMulti-disciplinary Conf. on Sinkholes (ed. B.Peck),Balkema, Rotterdam, pp. 373–8.

Terzaghi, K. (1943) Theoretical Soil Mechanics. JohnWiley, New York.

Thompson, R.P. and Leach, B.A. (1991) Settlementprediction and measured performance of Heysam IIPower Station. Proc. 10th European Conf. SoilMechanics and Foundation Engineering, Florence,Italy, Balkema, Rotterdam, pp. 609–14.

Thorburn, S.H. (1966) Large diameter piles founded inbedrock. Proc. of Symposium on Large Bored Piles,Inst. of Civil Eng., London, pp. 95–103.

US Department of the Navy (1982) Foundations andEarth Structures, Design Manual 7.2, Alexandria, VA,pp. 72–130.

Wagener, F.M. (1982) Engineering construction indolomite. Ph. D. thesis, University of Natal, publishedby Geotechnical Div., SAICE, Johannesburg, SouthAfrica.

Wagener, F.M. and Day, P.W. (1984) Construction ondolomite in South Africa. Sinkholes: their Geology,Engineering and Environmental Impact, Proc. FirstMulti-disciplinary Conf. on Sinkholes (ed. B.Beck),Balkema, Rotterdam, pp. 403–11.

Whittaker, B.N. and Reddish, D.J. (1989) SubsidenceOccurrence, Prediction and Control. Elsevier,Amsterdam.

Williams, D.J. (1994) Geotechnical input to major bridgeproject. J. Geotechnical Eng., 115(3), 322–39.

Winterkorn, H.F. and Fang, H-F. (1975) FoundationEngineering Handbook. Van Nostrand Reinhold, NewYork, pp. 148–66.

Woodward, R.J., Gardner, W.S. and Greer, D.M. (1972)Drilled Pier Foundations, McGraw-Hill, New York.

Yamagata, M., Nitta, A. and Yamamoto, S. (1995) Designand its evaluation through displacement measurementfor the Akashi Kaikyo Bridge foundation. Proc. Int.Workshop on Rock Foundation, Tokyo, Japan,Balkema, Rotterdam, pp. 35–46.


6Stability of foundations

6.1Introduction

The significant affect of structural geology on thestability of rock foundations has been illustrated inthe examples of foundation failures discussed inSection 1.1. For foundations on strong but jointedrock, bearing capacity failures and excessivesettlement rarely occur, and a more frequent causeof instability is the movement of blocks of rock.The design information required on structuralgeology consists of the orientation, length andspacing of discontinuities, and their surface andinfilling characteristics (see Chapter 2). The firstthree parameters define the shape and size of blocksin the foundation and the direction in which theycan slide, while the last two parameters determinethe shear strength and settlement properties.Blocks formed by geological structure can bedivided into three distinct categories—planar,wedge and toppling blocks (Fig. 6.1(a-c)). Incontrast, in rock which is either closely or randomlyfractured so there is no dominant direction of thestructure, a large radius, shallow curved slip surfaceis usually formed (Fig. 6.1(d)). Typical stereonetsdepicting each of these four geological conditionsare shown in Fig. 2.10, while Figs 2.11 and 2.12illustrate methods of determining whether theblocks are potentially unstable. It is important todistinguish between the different failure typesbecause each requires a different method of stabilityanalysis. This chapter describes the main features ofeach of these failures and the corresponding methodof stability analysis. Also shown in Fig. 6.1 are twogeological conditions which generally form stable

foundations. Where the main geological structure iseither parallel to the face (Fig. 6.1(e)) or dippinginto the face (Fig. 6.1(f)), sliding is not possible.However, for the conditions shown in Fig. 6.1(e),there is a slight risk of buckling failures if the slopeis high and the beds have an outward convex shape(Cavers, 1981). Where the beds dip into the face,the foundation will be stable, but settlement mayoccur if the beds contain a compressible infilling.The methods of stability analysis presented in thischapter are primarily the limit equilibriumtechnique that are introduced in Section 1.6. Thistechnique was developed by Hoek and Bray (1981)and has now been adapted to a wide range ofgeotechnical conditions.

6.2Stability of sliding blocks

A planar failure is formed where a discontinuity isaligned approximately parallel to the face, and dipsout of the face, i.e. the discontinuity ‘daylights’ inthe face. If the dip of the discontinuity is steeperthan the face so that the discontinuity does notdaylight, or if the dip is somewhat flatter than thefriction angle of the surface, then the foundation islikely to be stable (Fig. 6.2). However, failure mayoccur on planes dipping out of the face at a flatterangle than the friction angle when destabilizingforces such as ground water pressures, non-verticalfoundation loads and seismic forces act on thefoundation. Release surfaces are required at eitherside of the block before move ment will take placeand these may be formed by a conjugate joint set

striking at right angles to the face, or by the

Figure 6.1 Effect of geological structure on foundation stability and settlement: (a) planar sliding failure on singlediscontinuity; (b) wedge sliding failure on two intersecting discontinuities; (c) toppling failure of steeply dipping slabs;(d) circular failure in closely fractured rock; (e) stable condition with no daylighting discontinuities; and (f) stablecondition, but compressible seam may result in settlement.

190 STABILITY OF FOUNDATIONS

geometry of the face itself if it forms an isolatedridge.This section discusses both the commonly useddeterministic analysis to calculate the factor ofsafety (Section 6.2.1), and the probabilistic analysis(Section 6.2.2).

6.2.1Deterministic stability analysis

Consider a strip footing with an applied load Qinclined at an angle ?Q, bearing on a steep rock face(Fig. 6.3). If the rock contains a continuous jointdipping out of the face, a planar block is formedthat may fail by shear failure on this surface. Thestability of this block is defined by the relativemagnitude of two forces acting parallel to thesliding surface: the resisting force fr acting up thesurface that resists failure, and an oppositedisplacing force fd acting down the surface. Theratio of these two forces is termed the factor ofsafety FS:

(6.1)

The forces fr and fd are calculated by resolving all

forces acting on the sliding plane into componentsacting parallel and perpendicular to this surface,assuming that the forces act through the center ofgravity of the block so that no moments aredeveloped. To facilitate resolution of the forces intotheir two components, a convention is adopted forthe direction in which they act such that positivenormal forces act to increase the compressive forceon the sliding plane, and positive shear forces actdown the plane to increase the driving force(Fig. 6.3 inset). A method of resolving the forcesinto their normal and shear components whichautomatically determines the correct sign of thecomponent is described in the followingparagraphs. The first step in calculating thecomponents is to draw up the foundation and itsload such that the following two conditions are met.

1. The face is drawn sloping down from left toright;

2. The direction in which a force acts is definedby an angle measured in a clockwise direction(0° to 360°) from a horizontal axis to the rightof the force.

Figure 6.2 Stability of sliding block related to dip of sliding surface.

STABILITY OF SLIDING BLOCKS 191

Using these conventions, the normal and shearcomponents, on a plane dipping at angle ?p, of anyforce Q at an angle ?Q from the horizontal axis aregiven by:

(6.2)

(6.3)where ?p is the dip of sliding surface

This procedurecan be applied to the conditionshown in Fig. 6.3 to calculate the resisting force frwhich is the shear strength of the sliding surface.For a Mohr-Coulomb material, the shear stress onthe sliding plane is given by:

(6.4)

or(6.5)

where t is the shear stress on sliding surface, c is thecohesion, is the friction angle, A is the surfacearea of sliding surface and ?N is the sum of normalforces.For the foundation shown in Fig. 6.3, ?N is the sumof the normal components of the weight of thefoundation rock and the footing load, both of whichare positive. The weight W of the block of rock isdetermined from the cross-sectional area of the

block and the unit weight of the rock. W can beexpressed in terms of force per unit length offoundation or as a total weight. The total normalforce acting on this plane is

(6.6)The displacing force fd is the sum of thecomponents of all forces acting parallel to thefailure plane. In the case shown in Fig. 6.3, theshear component of Q acts up the plane and isnegative, while the shear component of W actsdown the plane and is positive. The total displacingforce is given by

(6.7)

and the factor of safety is given by equation 6.1.Note that for a vertical foundation load no other external loads and a cohesion of zero, aswould be the case for a clean, open fracture, thefactor of safety is given by:

(6.8)

That is, the limiting stability condition occurs whenthe dip of the sliding plane equals the friction angleof this surface, and is independent of the weight ofthe foundation and the footing load. If the calculation is carried out on a unit length of

Figure 6.3 Resolution of forces in foundation to determine normal N and shear S components on potential failuresurface.


foundation, all the forces are expressed in units of N/m (kips/ft) and the calculation method is appropriatefor strip footings with uniform geologicalconditions along their length. In the case of spreadfootings, it is necessary to select a length of thefoundation, which may be longer than the footinglength, on which to carry out the stability analysis.The appropriate analysis length of the foundationwill depend on the spacing of discontinuities thatform the side faces of the sliding block, and theweight would be calculated from the cross-sectionalarea of the block, its length and the rock unitweight.The principle of calculating the factor of safety of ablock of rock in a foundation by resolving forces todetermine the resisting and displacing forces can beextended to more complex conditions as shown inFig. 6.4. The range of forces that can beaccommodated in this analysis is as follows:

1. Foundation loads (Q1, Q2) Each force is thevector sum of the dead and live loads, plusexternal horizontal forces acting on thestructure such as wind, ice, water andearthquake loads.

2. Water forces (U, V) The uplift force U acts onthe potential sliding plane, while the thrustforce V acts in the tension crack; both theseforces act in directions normal to thediscontinuities:

(6.9)

(6.10)

where hw is the head of ground water at thebase of tension crack; L is the length of tensioncrack along strike; ?w is the unit weight ofwater; ?v is the dip angle of water force V; and

Figure 6.4 Forces acting on foundation containing planar discontinuity dipping out of slope face.


A is the area of sliding plane.3. Earthquake force (aW) The effect of

earthquakes is simulated by a ‘pseudo-static’hori zontal force aW equal to a fraction of theweight of the block. The earthquakeacceleration a is expressed as a portion of thegravity acceleration appropriate to the seismiczone for the project location.

4. Artificial support force (T) These forces arecommonly applied by installing rock bolts orcables anchored in sound rock below thepotential sliding plane and then tensioning themagainst the rock face to apply compressive andshear forces on the sliding plane.

Figure 6.4 shows a typical foundation whichcontains a planar discontinuity on which slidingcould take place, and is subjected to the loadconditions described above. Resolution of theseloads into their shear and normal components andexamination of the directions in which they act,

shows the influence that each has on stability. Theforces U, V, Q1H and aW all have negative (upward)normal components, that diminish the frictionalcomponent of the shear strength, and positive(downslope) shear components. Therefore all theseforces reduce the factor of safety. However, thefoundation weight W, the reinforcing force T andthe foundation load Q2 have positive (donwnward)normal components and negative (upslope) shearcomponents that improve the factor of safety.These equations also show that the support providedby the tensioned bolts varies significantly with theangle at which they are installed, and savings inbolting quantities of up to 50% can be achieved byinstalling bolts at the optimum angle. Bolts installednormal to the sliding plane will increase the normalforce only, but at a flatter angle than the normalthey will both increase normal force and diminishthe displacing force. The approximate optimumplunge ?Topt for the support force is

(6.11)

EXAMPLE 6.1

STABILITY ANALYSIS FOR PLANAR FAILURE

The stability of the foundation shown in Fig. 6.4 with respect to sliding failure can be calculated usingequations 6.1–6.10. The sliding surface comprises a planar fault with gouge infilling (refer to Fig. 3.17).The following values for the forces and force directions are assumed:

Forces:

Angles:

Slope dimensions:

Shear strength parameters:

The water forces U and V are calculated as follows:


The resisting force is calculated from equations 6.4 and 6.6 as follows:

The displacing force is calculated from equation 6.7 as follows:

The factor of safety is found from

The effect of the bolting force T on the factor of safety can be determined by setting , fromwhich the new factor of safety is

There are a number of limitations to the method ofanalysis described in Section 6.2, namely, thesliding surface must be planar and the strengthproperties uniform throughout the foundation, andall forces must act through the center of gravity ofthe block. If these conditions do not apply, then amore versatile analysis method can be used asdescribed in Section 6.6.It is important to note that in calculating the factor ofsafety of either a unit length or a specified length offoundation using the method described in thissection, it is assumed that no support is provided bythe two surfaces at the ends of the block. This isusually a conservative assumption except where therock contains sets of discontinuities at right anglesto the face and oriented such that they act as release

surfaces at either end of the block. Because of thisgeometric limitation, the planar method of stabilityanalysis is best suited to strip foundations where thestructural geology is consistent over the full lengthof the foundation. Stability analysis of a block ofrock supporting a single footing can also be carriedout using the three-dimensional wedge analysis(Section 6.3).

6.2.2Probabilistic stability analysis

The coefficient of reliability against sliding of thebridge foundation shown in Fig. 6.4 can becalculated using the Monte Carlo analysis methoddescribed in Section 1.6.4 (Chapter 1). Figure 6.5shows the results of a probabilistic analysis using

*W is calculated from the cross-sectional area of the sliding block, multiplied by the rock unit weight, 0.025 MN/m3. Ifthe total length of the foundations is 5 m, then the minimum length of the foundation block to be used in stability analysisis 5 m, and the values of W and A are:


the same design parameters as those inExample 6.1, but they are now expressed asprobability density functions, rather than discretevalues. The end-product of the probabilistic analysisis a distribution of the factor of safety whichquantifies the degree of uncertainty in the inputvalues. The example also shows the probabilitydensity function of each of the input parameters,and a sensitivity chart identifying which of theparameters has most influence on the coefficient ofreliability.This example shows the relationship between thedeterministic and probabilistic analyses. In thedeterministic analysis the factor of safety iscalculated from the mean or most likely values ofthe input variables, and for the unsupportedfoundation, the factor of safety has a value of 1.28.However, the probabilistic analysis shows that thefactor of safety can range from a minimum value of0.38 to a maximum value of 3.99 (Fig. 6.5). Theproportion of this distribution with a value greaterthan 1 is 0.78, which represents the coefficient ofreliability of the foundation. Also shown in Fig. 6.5is the distribution of the margin of safety for whichthe coefficient of reliability is 0.78. This exampleillustrates that, for these particular conditions, thecoefficient of reliability is well below the targetlevel for foundations shown in Fig. 1.9. This lowvalue for the coefficient of reliability is a functionof both the low factor of safety, and the wide rangesof uncertainty in the input parameters. The MonteCarlo analysis was performed using the computerprogram Crystal Ball (Decisioneering, 1994).

6.3Stability of wedge blocks

For a footing of limited areal extent on the crest of asteep face, it is often more appropriate to calculatethe stability of a three-dimensional wedgeshapedblock rather than the two-dimensional planar blockas described in the Section 6.2. A wedge failure isformed by two intersecting discontinuities whichboth dip out of the face, but are aligned at anoblique angle to the face (Fig. 6.6(a)). Sliding takes

place on both planes simultaneously in the directionof the line of intersection between the planes. Thefoundation is likely to be stable if the line ofintersection is either steeper than the face so that itdoes not daylight, or if it is flatter than the frictionangle in a similar manner to the stability conditionsof planar failures.The method of stability analysis of a wedge-shapedblock follows the same principles of that of theplanar block, except that it is necessary to resolveforces on both the sliding planes. The analysisprocedure is to calculate the weight of the wedge,and the area of each face. The weight, as well as allexternal forces such as the foundation load, waterand support forces, are then resolved into theirnormal and shear components acting oneach of thetwo sliding surfaces of the wedge. The basicequation for the factor of safety of a wedge is

(6.1)

where(6.12)

and

The function f' denotes the shear component ofthese four forces; N1, N2 are the effective normalforces on planes 1, 2; A1, A2 are the area of planes1, 2; , are the friction angles of planes 1, 2; c1,c2 are the cohesions of planes 1, 2; W is the weightof wedge; T is the tension in support force; E is theexternal load; V is the water force in the tensioncrack.A detailed procedure for calculating the factor ofsafety of a three-dimensional foundation block isgiven in Hoek and Bray (1981). The data requiredfor this analysis is as follows.

1. The shape of the wedge is defined by fivesurfaces: the face of the slope, the upper slope,the tension crack and the two intersecting planesforming the sides of the wedge. The orientationof these surfaces is defined by their dip and dipdirection.


2. The dimensions of the wedge are defined by two lengths: the vertical height H from the apex

Figure 6.5 Results of probabilistic analysis of stability using Monte Carlo analysis to calculate coefficient of reliabilityCR for foundation shown in Fig. 6.4: (a) probability distributions of design parameters; (b) probability distribution ofmargin of safety; and (c) sensitivity of input parameters to calculated margin of safety distribution.


of the wedge to the intersection of plane 1 withthe crest of the cut, and the distance L of thetension crack (if any) behind the face asmeasured along the trace of plane 1.

3. The shear strength of the rock is defined by thecohesion and friction angle of the two slidingplanes. The shear strengths of the two planescan have different values as would be the case

Figure 6.6 Stability of three-dimensional foundation block: (a) isometric view of wedge; and (b) cross section of wedgethrough line of intersection of planes 1 and 2.


where one discontinuity is a fault with a clayinfilling, and the other a clean joint.

4. The weight of the wedge is calculated from theunit weight of the rock and the calculatedvolume.

5. Water pressures acting on the wedge aredetermined by assuming that the slope is fullysaturated and that the forces U and V aredeveloped by a full head of ground water in thetension crack (Fig. 6.6 (b)). The effective normal force N' is the sum of the normalcomponents of W, E, V and T minus the upliftforce U. By varying the unit weight of thewater, it is possible to simulate varying levels ofthe water table.

6. External loads on the block consist of thefoundation load and a support force; theorientations of both these forces are defined bytheir trend and plunge.

An important component of this analysis is thecalculation of the normal forces acting on eachplane. This may show that there is no contact onone of the planes with the result that all the shearresistance will be generated on the other plane. Thisinformation is required in the calculation of both thefactor of safety, and the support force necessary toproduce a specified factor of safety. For a wedgewhich slides on both planes simultaneously, thesupport force is minimized if it is installed at theoptimum orientation. The support force optimum

trend is parallel to the trend of the line ofintersection between the two planes, and theoptimum plunge is equal to , where is theaverage friction angle of the two planes and ?i is theplunge of the line on intersection.The stability analysis of the three-dimensionalwedge block is very versatile and can be applied toa wide range of foundation conditions such asbridge piers located on steep slopes, and the hold-down capacity of uplift anchors. If there are anumber of external loads such as seismic forces andboth vertical and horizontal foundation loads, thesecan all be combined into a single vector. Situationswhere this analysis may not produce an accuratesolution are where the forces do not act through thecenter of gravity of the wedge and moments areproduced.A limitation of the Hoek and Bray algorithms is thatthe calculation method requires that the line ofintersection of the wedge intercepts the upper slopesurface. However, where the line of intersection isflatter than the upper slope, a wedge can still beformed if there is a tension crack that defines theback surface of the wedge. An analysis method thatdoes not have this geometric restriction has beendeveloped using vector algebra (Kielhorn, 1996). Afeature of this program is that a rotatable wire framedrawing of the wedge is produced as well as a three-dimensional paper cut out model, these are usefulaids in checking wedge geometry and the directionof forces.

EXAMPLE 6.2

WEDGE FAILURE STABILITY ANALYSIS

The following is an example of a stability analysis of a wedge block forming the foundation of abridge pier which applies a vertical external load of 4 MN (900 kips) to the wedge. It is assumed that thegeological conditions are those shown on the stereo net in Fig. 2.9 and that the wedge is formed by thefoliation and joint set B, and that the intersection of these two planes is along line I2 (dip 61.8° and dipdirection 208°). The orientation and shear strength properties of the planes forming the wedge are shownin Table 6.1.

The vertical height of the wedge is 25 m (82 ft), the distance to the tension crack along the line of the


foliation on the upper surface is 6 m (20 ft), and the rock density is 25 kN/m3 (160 lb/ft3). It is assumedthat the foundation is dry.

With no foundation load acting on the wedge, the factor of safety is 1.73, and with the verticalfoundation load applied the factor of safety drops to 1.2. Tensioned rock bolts can be installed toincrease the factor of safety to 1.75. The optimal orientation for the bolts is at a trend of 28° and a dipangle of 34° above the horizontal. For bolts installed at this orientation the required bolt force is 2.4 MN(540 kips). However, if the bolts are installed at an angle of 10° below the horizontal, the required boltforce increases to 3.2 MN (720 kips), showing the value of installing bolts at the

Table 6.1Properties of wedge block

Plane

Dip

Dipdirection

Frictionangledegrees

CohesionkPa(p.s.i)

Foliation

65 245

35 100(14.5)

Joint

85 135

20 50(7)

Upperslope

0 200

Slopeface

75 200

Tensioncrack

80 180

Lineofintersect

61 20


Plane

Dip

Dipdirection

Frictionangledegrees

CohesionkPa(p.s.i)

ion .8 8

optimum orientation. In practice, bolts are usually installed at a plunge angle slightly below thehorizontal to facilitate grouting.

6.4Three-dimensional stability analysis

In conditions where the shape of a block of rock in afoundation cannot be defined by the five surfaces asshown in Fig. 6.6, there are two other methods ofexamining the stability of three-dimensional blocks.Details of the analysis procedure of both thesemethods is beyond the scope of this book, but theirbasic principles are discussed below.Goodman and Shi (1985) have developed the ‘keyblock theory’ that is a generalized three-dimensional analysis of blocks defined bydiscontinuity surfaces. The basis of this theory isthe definition of blocks, on the basis of their shape,that can slide from the surface of an excavation, or

are ‘removable’. For example, in Fig. 6.7 blocks 2,3 and 4 in a dam foundation cannot slide becausethey are constrained by block 1—the key block. Ifblock 1 were to move, then blocks 2, 3 and 4 couldalso move resulting in failure of the foundation. Astereographic projection method showing the dipand dip direction of the discontinuities and theexcavation faces can be used to determine the shapeof the blocks and to identify the key block.A generalized three-dimensional slope stabilityanalysis has been developed by Hungr (1987) whichis based on Bishop’s method of two-dimensionalstability analysis. Instead of dividing the slope intoslices as used by Bishop, the three- dimensionalanalysis divides the slope into columns. Theanalysis procedure consists of calculating the

Figure 6.7 Identification of removable key block in the foundation of a dam (Goodman and Shi, 1985. Adapted bypermission of Richard E.Goodman).


vertical force equilibrium equation for each columnand summing the moment equilibrium for the entireassemblage of columns. These two equilibriumequations, which neglect the vertical shear forcesacting on the vertical faces of the columns, aresufficient conditions to determine all the unknownforces and calculate the factor of safety of the slope.Figure 6.8 shows a slope with a surcharge at thecrest. A conventional two-dimensional analysis ofthis slope gives a factor of safety of 1.09, while athree-dimensional analysis gives a factor of safetyof 1.25.

6.5Stability of toppling blocks

Toppling failures of foundations may be formedwhere discontinuities dip into the face and formeither a single block, or a series of slabs, such thatthe center of gravity of the block falls outside thebase (Fig. 6.9). These conditions for toppling areonly met where the dip angles of both the face andthe discontinuities are steep, and the discontinuitiesare aligned parallel to the face (Goodman and Bray,1976). Experience has shown that considerablemovement may take place as the slabs move

horizontally, but that overall failure of the slopewill not occur until there is shear failure of blocks atthe toe that act as keystones to constrain the slope.It is likely that the amount of movement prior tooverall slope failure will exceed the displacementtolerance of most structures so it is important toidentify geological structure that is susceptible totoppling.The analysis of foundations containing blockswhich could undergo toppling movement consistsof examining the stability conditions of each blockin turn starting at the top of the slope. A block willhave one of three stability modes: stable, sliding ortoppling (Fig. 6.9). The stability mode depends onthe dimensions of the block, the shear strengthparameters of its faces and the external forces actingon it. For example, short blocks at the crest (blocks7, 8, 9) for which the center of gravity falls insidethe base will be stable, provided that the frictionangle of the base is greater than the dip of the base.However, taller blocks in which the center ofgravity lies outside the base may topple (blocks 4,5, 6), depending on the restraint provided by theshear forces on the two sides of the block. If theblock does topple, it produces a thrust force againstthe block below it on the slope. If this next block is

Figure 6.8 Three-dimensional analysis of a slope with a foundation load at the crest (Hungr, 1987).


also tall it may topple as a result of this thrust force,even though its center of gravity lies inside thebase. At the toe of the slope where the blocks areshort and will not topple (blocks 1, 2, 3), the thrustforce produced by the upper toppling blocks may begreat enough to cause these blocks to slide with theresult that the overall slope will be unstable.However, if the toe blocks do not slide or topple,the upper blocks may undergo considerabledisplacement, but there will be no overall failure.If a footing is located on the slope, this load has theeffect of increasing the height of the block. Thismay cause a stable block to topple, or exacerbate anexisting toppling condition by increasing the thrustforces on the lower blocks.The first step in the stability analysis is to determinethe dimensions of all the blocks as defined by theirwidth ?x and their height yn (Fig. 6.10). Then,starting at the top of the slope, the forces acting oneach block are calculated. These forces comprise allor some of the following:

1. block weight Wn of block n;2. foundation load Q on the top surface;3. force Pn produced as a result of toppling of the

next higher block (n+1) in the foundation;4. restraint Pn-1 provided by the next lower block

(n-1) in the foundation;5. shear forces developed on the sides of the

blocks;6. normal and shear forces Nn and Sn respectively

acting on the base of the block;7. water pressures acting on the sides and base of

the blocks, the magnitudes of which aredenoted by the dimensions yw and zw.

The method of calculating whether a block willtopple or slide, or be stable, is as follows. First, byresolving all forces acting on a block intocomponents perpendicular and parallel to the base,the normal and shear forces acting on the base are:

Figure 6.9 Stability of foundation containing toppling blocks (adapted from Goodman and Bray, 1976).


(6.15)

(6.16)

where Wn is the weight of block is the dip angle of the base of the blocks; ?Q is theinclination of the load measured in a clock-wisedirection from a horizontal axis to the right of theforce (the slope is drawn sloping down from left toright); is the friction angle on the sides of theblocks; yw and zw are the heights of the groundwater on the upper and lower sides of the blockrespectively; Q is the foundation load in units offorce per unit length of slope; ?r is the rock unitweight; and ?w is the water unit weight.Considering rotational equilibrium, it is found thatthe force Pn-1,t which is just sufficient to preventtoppling of block n has the value

where Mn and Ln define the points of application ofthe forces Pn and Pn-1 respectively. The water forcesV1 and V3 acting on the sides of the blocks are

(6.18)

(6.19)Assuming that the blocks are in a state of limitingequilibrium so that equations 6.15 and 6.16 apply,the force just sufficient to prevent sliding of block nhas the value

(6.20)

Figure 6.10 Forces acting on a toppling block.


where is the friction angle on the base of theblocks, and the water pressure acting on the base ofthe block is

(6.21)The stability analysis procedure is to examine thestability condition of each block in turn, starting atthe top of the slope. The stability condition of eachblock is established according to the followingcriteria.

1. For sliding will not occur on the baseof the blocks, provided that no external forcesact, i.e.

2. For short blocks near the crest of the slopewhere the blocks will bestable.

3. Where this defines the uppertoppling block, and the forces Pn-1,t and Pn-1,sare calculated.

4. Calculate the forces Pn-1,t and Pn-1,s anddetermine stability conditions by the followingtests:

If the block is on the pointof toppling and Pn-1 is set equal to Pn-1,t;

If the blockswill not slide.

5. In the lower part of the slope where the blocksare short and toppling does not occur, the thrustproduced by the upper toppling blocks may besufficient to cause the toe blocks to slide, i.e.

(a) If the block is on the point ofsliding and Pn-1 is set equal to Pn-1,s;

(b) If the block will be stable, or(c) If , the block will slide.

If the bottom block slides, then the overallfoundation slope will be unstable. However, even ifthe bottom block(s) are stable and there is nooverall slope failure, considerable displacement ofthe toppling blocks higher in the slope may still takeplace.Having calculated the forces acting on each block,it is possible to determine the factor of safety of thefoundation by an iterative process as follows. The

friction angles are progressively changed untillimiting equilibrium conditions are reached and thelowest block is just on the point of sliding. Thefriction angle required for limiting equilibrium is , and if the friction angle of the base of the blocks is

, then the factor of safety is given by

(6.22)

Methods of stabilizing foundations that can undergotoppling movements can be divided into twocategories, namely modifying the shape of theblocks, or installing support (Wyllie, 1980). Ifpotential instability is recognized beforeconstruction, the blocks can be shortened byexcavating the upper part of the slope so that centerof gravity of the blocks falls inside the base.Alternatively, it may be possible to install rock boltsthrough a number of blocks to increase theireffective width, or the toe of the slope can besupported with tensioned rock bolts anchored instable rock below the zone of movement. Thecalculation of the required bolt force can be carriedout using equations 6.15–6.22 in which the supportis an external force, acting into the slope, on anynumber of toe blocks.The data required for the evaluation of stabilityconditions of a foundation with a potential fortoppling type movement are as follows.

1. The geology of the foundation is defined by thedip ?p and spacing ?x of the set of discontinuities that dips into the face of the slope. It isalso assumed that there is a set of orthogonaldiscontinuities that dip out of the face to formthe base of each block.

2. The dimensions of slope are defined by the dipangles of the face and the upper slope, and thevertical distance between the crest of the slopeand the lowest sliding block.

An important parameter in defining theheight of each block is the angle ß (Fig. 6.9)which must be selected from an inspection ofthe geological conditions and slopedimensions. It cannot be determinedanalytically, and its value is critical to stability.


If ß is large, the blocks will be short and notoppling will occur, while if ß is small, theblocks will be tall and most blocks will topple.

3. From the geology and the slope dimensions, theheight of each block yn can be calculated.

4. The shear strength of the rock is defined by thefriction angles of the base and sides of theblocks and respectively). This conditionmay arise where one set of discontinuities is, forexample, a set of clay filled bedding planes andthe other is a set of joints with rough surfaces.

5. The weight of each block is the product of itscross-sectional area and the rock unit weight.

6. Water pressures act on the sides and base ofeach block with values defined by the elevationof the water table.

7. The foundation load Q can act on any block(s)and can be inclined at any angle; it should benoted that all forces are expressed as a forceper unit length of the foundation.

6.6Stability of fractured rock masses

Where the rock mass contains no dominantgeological structure, but is randomly or closelyfractured, a rupture surface with an approximatelycircular shape may develop in a similar manner tofailures in soil. This surface will pass partiallythrough intact rock and partially along existingdiscontinuities to form a shallow, large radiussurface. This is in contrast to more deep seated, smallradius failures that occur in exca vations made inlow friction, cohesive soils. The stability analysis ofcut slopes in both soil and rock using limitequilibrium methods is well developed (Bishop,1955; Janbu, 1954; Nonveiller 1965; Morgensternand Price, 1965; Sarma, 1979) and these methodscan be applied to wide range of geological andgeometric conditions.The method of stability analysis for curved rupturesurfaces is similar to that for sliding blocksdescribed in Section 6.2 in that a unit thickness ofslope is studied and the factor of safety is given bythe ratio between the moments of the resisting and

driving forces on the rupture surface. The analysisprocedure is to divide the slope into a series ofslices, with vertical or non-vertical sides, and thenfind the effective normal force on the base of eachslice, from which the resisting force is given byequations 6.4 and 6.5. The total resisting moment iscalculated as the product of the radius of the rupturesurface and the sum of the resisting forces on thebase of the slices. The moment of the driving forceis the sum of the downslope components of theweight of each slice, together with any external andwater forces, multiplied by the moment arms. Thesimplified methods of analysis neglect the effect ofnormal and shear forces on the sides of the sliceswithout any significant loss of accuracy.The stability analysis program XSTABL (Sharma,1991), which uses the modified Bishop or Janbumethods of analysis for circular rupture surfaces,can be readily used in the examination of stabilityof rock foundations. An important feature of thisprogram is the ability to calculate the factor ofsafety for a variety of surface shapes, and find thesurface with the minimum factor of safety. Therupture surfaces, within specified ranges for theshape and position of the surface, are defined by arandom number generator. This search routine forthe minimum f actor of safety surface is notrequired if the position of the rupture surface isdetermined by a pre-existing geological feature.Figure 6.11 shows a foundation on a steep cut facesupporting two vertical loads (Q1 and Q2) and aninclined tie-back force T. The slope is made up ofthree geologic materials—overburden, schistoserock with the foliation dipping at 70° into the face,and a fault zone at the toe, and contains a singlewater table. The stability analysis of this foundationusing the program XSTABL involves the followingsteps.

1. The ground surface is defined by a series ofstraight line segments given by x and y co-ordinates.

2. The subsurface boundaries between materialtypes are also defined by straight linesegments.


3. The strength properties of the materials canbe defined by Mohr-Coulomb isotropic oranisotropic parameters, or curved (Hoek-Brown) envelopes. For anisotropic materials,different strengths can be defined for ranges ofdip angles as indicated by the inset onFig. 6.11. Curved strength envelopes, asdefined by the parameters m, s (Table 3.7) andsu, are used in the analysis in the followingmanner: the effective normal stress acting on thebase of each slice is determined, and thecorresponding instantaneous friction angle andcohesion is calculated from equations 3.16–3.19. This approach results in the shear strengthvarying along the rupture surface.

4. Water pressures can be defined by a phreaticor piezometric surface comprising a series ofstraight line segments, or as a pore waterpressure grid, or as an ru factor which definesthe pore water pressure as a fraction ru of thetotal vertical earth pressure .

5. External forces are defined in terms of theirmagnitude, position on the slope and inclination

in the plane of the section.6. Earthquake forces are simulated as

pseudostatic horizontal and vertical seismiccoefficients. For example, if a horizontalseismic coefficient of 0.09 is specified, then ahorizontal force equal to 0.09 times the weightof the slice is applied to each slice.

7. The rupture surface can be defined as acircular arc, or a series of straight linesegments, and a search routine finds the surfacewith the minimum factor of safety. For acircular surface, limits to the shape and positionof the surface are specified by ranges for theinitiation and termination points of the surface,and for angular limits for the lower end of thesurface. For surfaces comprising straight linesegments, a search rectangle can be defined foreach junction point between segments.

The following example illustrates the use ofXSTABL in the stability analysis of the foundationshown in Fig. 6.11.

EXAMPLE 6.3

Figure 6.11 Stability analysis of foundation using XSTABL program.


STABILITY ANALYSIS USING XSTABL

For the foundation shown in Fig. 6.11 the geological conditions consist of overburden with athickness of about 15 m overlying a moderately fractured schist in which the schistosity dips into theface at a dip of about 70°. At the toe of the slope there is a fault which has the same orientation as theschistosity and contains a weak, low permeability, crushed rock gouge. The properties of these threematerials are defined by their cohesion, friction angle and unit weight. The anisotropic strength of theschist is expressed by assigning a lower strength value in a direction aligned parallel to the schistosity(see inset). The table on Fig. 6.11 lists these input parameters.

The input parameters comprise x and y co-ordinate pairs defining the ground surface, materialboundaries and ground water surface elements, as well as material strength properties and magnitudesand positions of the external loads. The external loads consists of two foundations simulated bypressures acting vertically and positioned on the two cut benches: Atied-back anchor support force T is simulated as a third external pressure acting at an angle of 20° belowthe horizontal and positioned on the face below the lower foundation load Q2.

Earthquake forces are simulated by pseudo-static horizontal and vertical accelerations of 0.12g and 0.04g respectively.

XSTABL allows the general shape of the rupture surface to be defined, as well as the range overwhich the initiation and termination points intersect the excavation surface. In this case a Bishopanalysis has been carried out for a rupture surface comprising a circular arc with the lower end of thesurface at the toe of the slope and the upper end existing at any point at or above the level of load q2. InFig. 6.11 the rupture surface with the minimum factor of safety is indicated showing that the criticalcondition is the lower bench containing the low strength fault zone, and supporting the major foundationload.

The results of the analysis for a variety of conditions are:(A) Excavated slope with no foundation loads or support, static loading:

(B) Excavated slope with foundation loads: , no tie-backs, staticloading

(C) Excavated slope with foundation loads and support force:, static loading:

(D) Excavated slope with foundation loads: ,earthquake accelerations,

These analyses show the effect of both external loads and material properties on the stability of thefoundation slope. An analysis could also be carried out to simulate the effect of heavy blasting inthe excavation of the benches for the footings. If the blasting is heavy enough to loosen and shatterthe rock, the cohesion may be reduced from 200 to 50 kPa. This reduction in strength results in thefactor of safety of the foundation being diminished from 1.48 to 1.07 showing the importance ofcontrolling blasting operations.


6.7External effects on stability

The following is a discussion of two types ofexternal forces, ground motion due to earthquakesand turbulent water flow, that can have a significanteffect on stability, depending on the site conditions.

6.7.1Seismic design

Ground motion due to earthquakes induces forcesthat act on both the structure and the foundation,and it is necessary to examine the combined effectof these forces to determine the overall stabilityconditions of the foundation. Earthquake forces canbe assumed to act horizontally, or have bothhorizontal and vertical components. The forcesacting on the structure induce a base shear and anoverturning moment at the foundation level. Addedto these loads are the seismic forces acting on thefoundation itself. These forces are significant ifthere is a steep slope below the structure because itis possible that the whole foundation could slide ona shear plane inclined out of the slope. Examples ofslope failures induced by earthquakes are describedby Youd (1978), Horner et al. (1987) and Harp andJibson (1995), while the 1989 Loma Prietaearthquake in California is estimated to have causedbetween 2000 and 4000 rock, soil and debris fallsthat blocked many roads (Transportation ResearchBoard, 1996).Design of foundations subjected to seismic forcesconsists first of anchoring the structure to thefoundation, and second ensuring that the foundationitself is stable. Anchoring the structure is required toprevent both shear displacement and uplift resultingfrom overturning moments acting on the structure.The calculation of these forces is usually part of thestructural design and are considered to be additionalexternal loads acting on the foundation.The second stage of the design involvesexamination of the stability conditions of thefoundation under the combined loads imposed by thestructure and the seismic forces acting on thefoundation itself. The method of analysis consists of

calculating the factor of safety assuming that theearthquake is equivalent to a static force acting outof the slope. This technique is termed pseudo-staticanalysis. For example, if the design earthquakeacceleration is 15% of gravity, then a horizontalforce equal to 0.15 times the weight of thefoundation block is incorporated into the stabilityanalysis as an additional external force acting on theblock. In circumstances where the vertical andhorizontal earthquake motions may be in phase, avertical pseudo-static force could also be applied tothe foundation. The resultant of the twopseudostatic forces is resolved into componentsperpendicular and parallel to the sliding surface.The direction of these forces usually has the effectof decreasing the normal force and increasing thedisplacing force, which reduces the factor ofsafety. Earthquake accelerations used in design arespecified in building codes which divide the countryinto a number of zones of probable seismicintensity. These zones are based on both historicalearthquake records, and the theory of plate tectonicswhich relates the occurrence of earthquakes torelative movement of crustal plates. Mostearthquakes occur along the margins of these plates,with few earthquakes being recorded in the centralareas. Therefore, the higher risk seismic zones aresituated along the edges of the plates such as theperiphery of the Pacific Ocean— the west coasts ofNorth and South America, Japan, the Philippines,New Guinea and New Zealand. The magnitude ofthe earthquake for design purposes is expressed interms of an acceleration as a percentage of gravity.The pseudo-static method of stability analysis iswidely used in design because it is a simpletechnique and tends to produce a conservativeresult. However, in special cases the earthquake ismore accurately modeled as a dynamic transientforce which is used to determine displacement ofthe foundation. Methods of calculatingdisplacement of foundations under earthquakeloading are described in Section 7.4.


6.7.2Scour

The analyses presented in this chapter assume thatboth the geometry of the foundation and thecondition of the rock remain constant over the lifeof the project. However, where foundations aresubmerged in flowing water or are subject to waveaction, scour may result in steepening orundermining of the rock face below the footing.Another effect of both flowing and still water isweathering or dissolution of the rock (seeSection 3.6). The following is a discussion onmethods of predicting scour related to both the rockcharacteristics and the water flow conditions. Thistopic is also discussed in Section 7.6, Rehabilitationof dam foundations, while Section 10.4 discussesmethods of stabilizing foundations.The susceptibility of a foundation to scour can beestimated from the following relationship betweenthe erosive power of the water P and the resistanceof the rock to scour Kr (Annandale et al., 1996):

(6.23)Scour will occur when the power exceeds athreshold value that depends on the characteristics ofthe rock mass as defined by Kr. As discussed below,P is a function of water flow characteristics aroundthe foundation, while Kr is a function of fourquantifiable properties of the rock mass.(a) Scouring action of waterScour can result where water flow over irregularsurfaces is accompanied by eddies and turbulenceresulting in fluctuating pressures at the surface overwhich it is flowing. The action of these forces,together with the hydrostatic forces in the cracks,causes a tugging and pulling of the rock which canloosen and remove blocks from the foundation. Theerosive power of water P can be related to themagnitude of fluctuating pressures and the resultingrate of energy dissipation, or stream power, by thefollowing equation:

(6.24)where ?w is the unit weight of water; q is the unitdischarge and ?E is the energy loss (Smith andAnnandale, 1996).

A pier is an obstruction to flow which causessecondary currents and vortices to be developed asthe flow is deflected downwards in front of the pier,and then contracts and accelerates around the pier.This turbulence produces fluctuating pressuresaround the pier which is characteristic of energydissipation and erosive power. The erosive power isgreatest around a pier for flat bed flow conditionwhen the turbulence is most intense. If a scour holedevelops, the turbulence intensity, and erosivepower, diminishes as the scour hole increases indepth. Thus, scour will continue until an equilibriumcondition is reached where the energy dissipationdue to turbulence results in the erosive powerequaling the resistance of the rock. Furthermore,sorting of the scoured material will cause the largerrock fragments to remain in the scour holeproviding a protective layer in the base of the hole.Another factor that may limit scour is the increasingerosive resistance of the rock as scour developswhere, for example, the degree of weathering andthe fracture intensity decreases with depth.The complex flow patterns and related shearstresses at bridge piers are affected by the pierwidth, shape and alignment to the flow, as well asthe depth and velocity of the approach flow and thedepth and shape of the scour hole. Of these factors,the pier width is the most influential parameter.Measurements have shown that the shear stressaround the pier may be six to eight times that in theflat bed approach flow (Parola, 1993). However, thecomplexity of the actual flow conditions precludes,at present (1998), the development of an analyticalexpression for shear stress levels in turbulent flow.The stream power per unit area P, which is theproduct of the shear stress t and the approachvelocity V, for fully developed, turbulent flow can becalculated from:

(6.25)where ?w is the water unit weight; y is the flowdepth and d is the medium particle diameter on thestream bed. Equation 6.25 can be used to calculatethe stream power upstream of the pier which canthen be multiplied by a factor in the range 5–15 togive the approximate stream power or energy


dissipation in the more turbulent flow at the pier.This value of the stream power can then be used inequation 6.23 to assess the susceptibility of the rockto scour.(b) Scour resistance of rockIn order to quantify the susceptibility of rockmasses to scour, an erodibility index Kr has beendeveloped in which the relevant character of therock mass is calculated as the product of fourparameters (Annandale, 1995):

(6.26)This method of calculating the erodibility index is amodification of the Q-system for assessing supportrequirements for tunnels (Barton et al., 1974), thatuses properties of the rock mass that are readilymeasured in the field. The following is a discussionof each of the four parameters.1. Ms, the rock mass strength number represents thematerial strength of an intact representative samplewithout regard to its geologic heterogeneity within

the rock mass. The value of Ms is the product of theuniaxial compressive strength of the rock (unitsMPa) and its unit weight relative to a standard of 27kN/m3. For example, a rock with a uniaxialcompressive strength of 60 MPa and a unit weight of25 kN/m3 will have an Ms value of 56 [60×(25/27)].2. Kb, the particle-block size number is the meansize of block of rock as determined by jointspacing. Values for Kb can be calculated from thefollowing relationship:

(6.27)where RQD is the rock quality designation (seeSection 4.3.1) and Jn is the joint set number. Therelationship between Jn and the number ofdiscontinuity sets in the rock mass is shown inTable 6.2. The possible range of values for Kb is 1–100.3. Kd, the discontinuity or interparticle bond shearstrength number is calculated from the ratio

(6.28)Table 6.2 Relationship between number of discontinuity sets and joint set number Jn

Number of discontinuity sets Joint set number Jn

Intact, no or few joints, fissures 1.0One discontinuity set 1.2One discontinuity set plus random 1.5Two discontinuity sets 1.8Two discontinuity sets plus random 2.2Three discontinuity sets 2.7Three discontinuity sets plus random 3.3Four discontinuity sets 4.1Multiple discontinuity sets 5where Jr is the joint roughness number related to thecondition of the discontinuity surfaces, and Ja is thejoint alteration number related to the strength of the

material forming the surfaces of the discontinuities.Values for these two parameters are given in Tables6.3 and 6.4 respectively.

Table 6.3 Relationship between discontinuity surface shape and joint roughness number Jr

Discontinuity separation Conditions of rock surface Joint roughness number Jr

Tight discontinuities Impersistent discontinuities 4.0Rough or irregular, undulating 3.0Smooth, undulating 2.0Slickensided, undulating 1.5Rough or irregular, planar 1.5Smooth, planar 1.0


Discontinuity separation Conditions of rock surface Joint roughness number Jr

Slickensided, planar 0.5Open discontinuities Open discontinuities, or contain weak infilling that prevents

rock wall contact1.0

Shattered or micro-shattered clays 1.0

Table 6.4 Relationship between discontinuity surface condition and joint alteration number Ja

Description of infilling Joint alteration number Ja for joint width (mm)

1.0* 1.0–5.0† 5.0‡

Tightly healed, hard, nonsoftening impermeable infilling 0.75 – –Unaltered discontinuity walls, surface staining only 1 – –Slightly altered, non-softening, non-cohesive rock or crushed rockinfilling

2 2 2

Non-softening, slightly clayey non-cohesive infilling 3 6§ 10§

Non-softening, strongly overconsolidated clay infilling, with orwithout crushed rock.

3* 6** 10

Softening or low friction clay coatings and small quantities ofswelling clays

4 8§ 13§

Softening moderately overconsolidated clay infilling, with or withoutcrushed rock

4* 8** 13

Shattered or micro-shattered (swelling) clay gouge, with or withoutcrushed rock.

5* 10** 18

* Discontinuity walls effectively in contact.† Discontinuity walls come in contact after about 100 mm shear.‡ Discontinuity walls do not come into contact on shearing.§ Values added to Barton et al. (1974) data.** Also applies when crushed rock occurs in clay gouge without rock wall contact.4. Js, the relative ground structure numberrepresents the effective dip of the least favorablediscontinuity set with respect to the flow, andaccounts for the shape of the blocks of rock and theease with which the stream can penetrate the rocksurface and dislodge blocks. In general, rock masses

are more resistant to scour if they are slabby ratherthan blocky, and if the slabs dip upstream ratherthan downstream. These conditions are quantified inTable 6.5 which relates values for Js to theorientation and spacing of the discontinuity sets.

Table 6.5 Relationship between discontinuity orientation and spacing and relative ground structure number Js

Orientation of closer spaced discontinuityset

Dip of closer spaced discontinuity set(degrees)

Ratio of discontinuity spacing

1:1 1:2 1:4 1:8

VerticalDiscontinuities dip in direction of streamflow

90 1.1 1.2 1.2 1.3

80 0.7 0.6 0.6 0.570 0.6 0.5 0.5 0.460 0.5 0.5 0.4 0.450 0.5 0.5 0.4 0.4


Orientation of closer spaced discontinuityset

Dip of closer spaced discontinuity set(degrees)

Ratio of discontinuity spacing

1:1 1:2 1:4 1:8

40 0.5 0.5 0.5 0.530 0.6 0.6 0.6 0.520 0.8 0.8 0.7 0.710 1.3 1.1 1.0 0.90 1.1 1.1 1.1 1HorizontalDiscontinuities dip upstream

10 0.7 0.7 0.8 0.8

20 0.6 0.6 0.7 0.730 0.5 0.6 0.6 0.640 0.5 0.5 0.6 0.650 0.5 0.6 0.6 0.660 0.6 0.7 0.7 0.770 0.8 0.9 1 180 1.3 1.4 1.5 1.6(c) Stream power-scour resistance relationshipThe relationship between the scour resistance ofrock and soil materials and the energy dissipation ofwater flowing over a variety of hydraulic structureshas been determined empirically by studying fieldconditions. The results of 137 such observationsdistinguished between sites where scour did and did

not occur (Fig. 6.12). The dashed line is theapproximate threshold of scour for this data, and theapproximate relationship between the erodibilityindex Kr and the rate of energy dissipation per unitwidth of flow P(kW/m) is:

(6.29)Equation 6.29 and the information presented in

Figure 6.12 Relationship between erodibility index of rock and soil materials and rate of energy dissipation, showingerosion threshold (Annandale, 1995).


Fig. 6.12 can be used as a guideline in assessing thesusceptibility of a facility to scour. Where there is arisk of scour, preventative measures includemodifying the designs to reduce turbulent flows toacceptable levels, or protecting the rock withreinforced concrete aprons or rip rap.6.8 ReferencesAnnandale, G.W., Smith, S.P., Nairns, R. and Jones,J. S.

(1996) Scour power. ASCE, Civil Engineering, NewYork, July, pp. 58–60.

Annandale, G.W. (1995) Erodibility. J. HydraulicResearch, 33(4), 471–93.

Barton, N.R., Lien, R. and Lunde, J. (1974) Engineeringclassification of rock masses for the design of tunnelsupport. Rock Mechanics, 6(4), 189–236.

Bishop, A.W. (1955) The use of the slip circle in thestability analysis of earth slopes. Geotechnique, 5,7– 17.

Cavers, D.S. (1981) Simple method to analyze buckling ofrock slopes. Rock Mech., 14, 87–104.

Decisioneering Inc. (1994) Crystal Ball, Release 3.0.1.Boulder, CO.

Goodman, R.E. and Bray, J.W. (1976) Toppling of rockslopes. Proc. Specialty Conf. on Rock Engineering forFoundations and Slopes, Boulder, Colorado, ASCE,Vol. 2, 201–34.

Goodman, R.E. and Shi, G. (1985) Block Theory and itsApplication to Rock Engineering. Prentice-Hall,Englewood Cliffs, New Jersey.

Harp, E.L. and Jibson, R.W. (1995) Inventory ofLandslides Triggered by the 1994 Northridge, Cali-fornia Earthquake. US Geological Survey, Denver,Open-File Report 95–213, pp. 17.

Hoek, E. and Bray, J. (1981) Rock Slope Engineering,2nd edn, IMM, London.

Horner, R.B., Lamontagne, M. and Wetmiller, R.J. (1987)Rock and roll in the North West Territoriesthe 1985

Nahanni earthquakes. Geos, Dept. Energy Mines andResources, Ottawa, pp. 1–4.

Hungr, O. (1987) An extension of Bishop’s simplifiedmethod of slope stability analysis to three dimensions.Geotechnique, 37, 113–17.

Janbu, N. (1954) Application of composite slip circles forstability analysis. Proc. European Conf. on Stability ofEarth Slopes, Stockholm, Vol. 3, pp. 43–9.

Kielhorn, W. (1996) The Physics of Yet Another WedgeCalculator (YAWC). Coyote Software, Vancouver,Canada.

Morgenstern, N.R. and Price, V.E. (1965) The analysis ofthe stability of general slip surfaces. Geotechnique, 15,79–93.

Nonveiller, E. (1965) The stability analysis of slopes witha slip circle of general shape. Proc. 6th Int. Conf. SoilMech. Foundation Engineering, Montreal, Vol. 2,pp. 552.

Parola, A.C. (1993) Stability of rip rap at bridge piers. J.Hydraulic Eng., 119(10), 1080–93.

Sarma, S.K. (1979) Stability analysis of embankmentsand slopes. J. Geotech. Eng. Div., ASCE, 105, GT12,pp. 1511–1524.

Sharma, S. (1991) XSTABL, An Integrated Slope StabilityAnalysis Method for Personal Computers, Version 4.00.Interactive Software Designs, Inc. Moscow, ID, USA.

Smith, S.P. and Annandale, G.W. (1996) Scour inerodible rock II: erosive power at bridge piers. NorthAmerican Water and Environmental Congress, ASCE.

Transportation Research Board (1996) Landslides—Investigation and Mitigation, Chapter 4, LandslideTriggering Mechanisms, National Research Council,Washington, DC, pp. 673.

Wyllie, D.C. (1980) Toppling of rock slopes: examples ofanalysis and stabilization. Rock Mech. 13, 89–98.

Youd, T.L. (1978) Major cause of earthquake damage isground failure. Civil Engineering-ASCE, April,pp. 47–51.


7Foundations of gravity and embankment dams

7.1Introduction

Dam foundations typically require significantlymore extensive investigation and design programsthan do buildings, and most bridges. These programswill often comprise driving exploration adits in thefoundations and abutments, comprehensivelaboratory and in situ soil and rock strength testing,and a detailed analysis of gravity and seepage forcesinduced in the foundation. Such detailed programsare conducted for one or more of the followingreasons.

1. The consequences of failure of a dam areusually very severe and can result in loss of lifeand property damage. Furthermore, most damsare a vital part of the infrastructure of acommunity.

2. The loads on dams can be high compared withmost other structures, and are also non-vertical.For concrete dams, the shear component of thisload acting parallel to the dam foundation in adownstream direction can cause the dam toslide, and the vertical component can result inexcessive deformation.

3. The loads are cyclic due to fluctuations inreservoir level and the foundations must be ableto withstand these changing stress conditionswith no deterioration in their strength.

4. With the large size of most dams it is possiblethat they will be founded on materials ofdiffering strengths and deformation moduli,causing differential movement to occur; this ismost critical for concrete dams.

5. High hydraulic gradients and water pressuresare developed in dam foundations andmeasures must be taken to ensure that thefoundation can withstand these pressures, whilemaintaining seepage quantities at acceptablelevels.

The photograph in Fig. 7.1 shows the RevelstokeDam on the Columbia River in British Columbia,Canada. The dam comprises a concrete gravity damin the river channel with an earthfill embankmentsection on the right bank. The maximum height ofthe gravity section is 175 m (575 ft) made up of 23separate blocks ranging in width from 13 to 26 m(43 to 87 ft). The earthfill dam is 1160 m (3800 ft)long and has a maximum height of about 126 m(413 ft); it is located on a terrace comprising sand,gravel and cobbles at an elevation about 50 m (164ft) above the foundation of the gravity dam.Preparation of the foundation for the gravity damrequired extensive excavation, partly to locate thedownstream end of the highest dam blocks below amajor shear. The earthfill dam is founded on thegranular materials but a core trench was excavatedthrough this material to found the dam core directlyon bedrock (Forster, 1986).The discussion of dam foundations in this chapter isrestricted to gravity and embankment dams; thedesign of foundations for arch dams is beyond thescope of this book. Gravity and embankment damsare the two most common types of dams and thegeneral design procedures are well established.However, each project has its unique set of sitecharacteristics that must be considered in

investigation, design and construction. The chapterdiscusses design and construction of rockfoundations, as well as improvement techniques forexisting foundations where deterioration hasoccurred (Section 7.6). Deterioration of dams andtheir foundations is becoming increasinglyimportant in most developed countries with few newdams being constructed, and existing damsincreasing in age.

7.1.1Dam performance statistics

An analysis of dam performance provides a usefulinsight into the reliability of dams, and the causesand types of foundation deteriorations and failuresthat occur. A detailed study of a total of 178 failuresof concrete, masonry and earth dams in 31 countriesshowed that 25, or 14%, of these failures occurredas the result of deterioration of rock foundations(ICOLD, 1995). An earlier study (Kaloustian, 1984)of a total of 4489 concrete dams on rockfoundations as reported between 1900 and 1978 byICOLD (1979), and supplemented by additional

cases, shows similar results regarding failures, anddeteriorations that required significant repair toprevent failure.The primary conclusions of these analyses are asfollows.

1. The percentage of failures of large dams hasbeen falling over the four decades since 1950,with 2.2% of dams built before 1950 failing andless than 0.5% failing since that time.

2. The ratio (height H of failed dams/built height)varies little with height showing that largedams fail as often as small dams. However,failures of small dams (100 ft))are the most common because there is thelargest number of these dams.

3. Approximately 80% of the failures were ofearthfill and rockfill dams.

4. Most failures involve newly built dams: 59(33%) of the failures occurred either duringconstruction or within the first year ofoperation, while 108 (61%) of the failuresoccurred in the first ten years.

5. Foundation problems are the most common

Figure 7.1 Revelstoke Dam on the Columbia River in Canada, a combined concrete gravity and earthfill dam(photograph courtesy of B.C.Hydro).

216 INTRODUCTION

cause of failure of concrete dams: of the 178failures, 35 were due to foundations, of which25 were rock foundations. Internal erosion andinsufficient shear strength accounted for 15 ofthese failures. These figures can be expressedin terms of probabilities which show that theprobability of failure of rock foundations hasdropped from about 10-4 per dam year in theearly 1900’s to about 10-5 per dam year in the1980’s (see also Fig. 1.9). As there has been ahuge increase in the number of dams during

this period, these figures demonstrate asignificant improvement in safety.

6. The types of concrete dams that failed, togetherwith the average age of each type at failure, areas follows:

Gravity—six dams with average age of 3.7 years

Arch—three dams with average age of1.3 years

Buttress—one dam with age of 1 year.Table 7.1 Failures and deteriorations of concrete dams on rock foundations (Kaloustian, 1984)

Reservoir filling External effects Total

Floods Seismic events Others

Permeability: seepage uplift 30 4 2 1 3728 2 – – 30Heterogeneous deformation 20 – 1 – 21Shear failure of foundation or abutments 10 2 – 3 15Erosion of downstream pool due to surface flow 1 6 – – 7Totals 89 14 3 4 110Of the 110 failures and deteriorations recorded byICOLD (1979), the causes can be divided into fourmain categories of external effects: reservoir filling,floods, seismic events, and other assorted causes.Table 7.1 shows the distribution of these incidentsaccording to both the external effects and the typeof failure or deterioration. These figures show thatground water effects in the foundation, i.e. seepageand uplift (totaling 61% of the incidents) are themost common. Of the cases shown in Table 7.1,81% occurred during filling of the reservoir whichdemonstrates that this is a critical time in the life ofa dam when both the structure and its foundation areundergoing rapidly changing gravity and seepagestresses.The dam performance statistics (ICOLD, 1974)have also been analyzed to show the time of failureor deterioration after completion of the dam(Fig. 7.2). Deterioration due to loss of foundationstrength usually occurred within the first two yearsof operation (curve 1), while dam failures generallyoccurred within four years (curve 2). Deteriorationdue to seepage and uplift occurred later in the life ofthe dam but still took place within approximately

the first five years.Two significant rock foundation failures are theMalpasset Dam in France and the Teton Dam in theUSA. The Malpasset Dam, a 61 m (200 ft) highconcrete arch structure completed in 1954, failed in1959 as the result of a wedge of rock in the leftabutment sliding following build up of excessiveuplift water pressures (Jaeger, 1963). The TetonDam, a 93 m (305 ft) high central-core earthfillstructure, failed in 1976 during filling of thereservoir partly as the result of erosion of fill in thekey trench by water flowing from open joints in therock foundation (US Department of the Interior,1980).

7.1.2Foundation design for gravity and embankmentdams

The general requirements for the design of rockfoundations for gravity and embankment dams arestability against sliding and overturning, acceptablelevels of differential deformation, and control ofseepage and erosion. Depending on the type of dam

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS 217

and the geological conditions of the foundation, it isusual that differing levels of effort are directed tothese design tasks (Bieniawaski and Orr, 1976).Stability against sliding, both within the foundation,and at the interface between the dam and thefoundation, is usually of more concern for gravitydams than earthfill dams. Overturning is only ofconcern for gravity dams, together with thedevelopment of tensile stresses at the heel and highcompressive stresses at the toe induced by themoments. Methods of calculating the factor ofsafety against sliding and overturning, andexamples of remedial measures taken to preventsliding are discussed in Section 7.2 and 7.3.Deformation of the rock foundations is usually notof concern for embankment dams because thestructure can accommodate some differentialdeformation that may occur at the boundarybetween materials with different moduli. However,in concrete dams, differential deformation of thefoundation and abutments may be of concern if thisinduces excessive stress levels in the concrete (seeFig. 3.2 and Section 3.2).

Seepage in foundations, and particularly at thecontact between the dam and the foundation, is ofmost concern in embankment dams whereuncontrolled seepage can result in scour of the corematerial. Methods of preparing rock foundationsurfaces are discussed in Section 7.5, andprocedures for grouting and drainage are presentedin Section 7.7.

7.1.3Loads on dams

The resultant of the wide variety of loads that mayact on a dam must be resisted by the foundationwith no risk of sliding or overturning, and withoutexcessive deformation. The following is a summaryof typical load conditions, with particular emphasison gravity dams.

1. The dead weight consists of the dam structureplus appurtances such as intakes, gates andbridges. For concrete dams, the unit weight ofconcrete is approximately 23 kN/m3 (146 lb/

Figure 7.2 Time of dam deteriorations and failures after completion of construction (after Kaloustian, 1984): (1)deteriorations due to loss of strength; (2) dam failures; and (3) deteriorations due to seepage and uplift.

218 INTRODUCTION

ft3).2. Water exerts both external forces on the dam,

and internal forces in the foundation andabutments. The external water forces are madeup of the head of water acting on the upstreamface (either normal operating level or peakmaximum flood), the tail water where water isponded downstream of the dam, and loads onsloping or horizontal surfaces. The water forcesare modified by wave action, reservoir set updue to steady winds blowing up the reservoir,ice loading at the crest of the dam, andthe possible accumulation of silt behind the dam(Thomas, 1976). Horizontal silt pressure,including the effect of the water, is equivalentto a fluid with a density up to 13.5 kN/m3 (86lb/ft3); verticalsilt pressure is equivalent to asoil with a wet density up to 19 kN/m3 (121 lb/ft3). Themagnitude of ice forces, which act atthe dam water surface level, should beappropriate for the climatic conditions at thesite, and will depend on such factors as thethermal expansion of the ice and the wind drag.

3. Internal water forces comprise uplift forces inthe foundation and abutments, the magnitude ofwhich depends on the characteristics of the damand the foundation, as well as condition of thedam-rock contact. The uplift pressures will alsobe influenced by any provisions for groutcurtains and drainage, and their long termreliability.

4. Thermal expansion in concrete gravity damswhere the monolith joints are grouted, cancreate a thrust across the joints and result intwist effects and additional loading of thefoundation. These conditions are usually mostsevere during construction (Jansen, 1988).

5. The effect of seismic forces in foundationdesign is accounted for, as a firstapproximation, by applying an additionalexternal force to the structure acting throughthe center of gravity of the section in adownstream direction. This force is equal to theproduct of the weight of the dam and a seismiccoefficient, the value of which depends on the

seismicity of the site. An additional seismicforce is the hydrodynamic force produced by thereaction of the water on the dam. Thistechnique is known as pseudo-static seismicanalysis and is used to assess the overturningand sliding stability of gravity dams.

7.1.4Loading combinations

In selecting loads for design purposes, combinationsof loads are used that have a reasonable probabilityof simultaneous occurrence. Combinations oftransitory loads, each of which has only a remoteprobability of occurrence at any given time, andhave negligible probability of simultaneousoccurrence are not considered as a reasonable basisfor design (US Department of the Interior, 1976).The following load combinations are normallyconsidered for the design of concrete gravity dams(Jansen, 1988), with factors of safety as discussed inSection 7.2.5.

• Case I—construction condition: damcompleted but no water in the reservoir and notailwater; wind load on the downstream face.

• Case II—construction condition withearthquake: earthquake acceleration in thedownstream direction; no reservoir, tailwater orwind loads.

• Case in—normal operating condition: poolelevation at top of closed spillway gates or atspillway crest where spillway is ungated;minimum tailwater; dead load and uplift. Earth,silt and ice pressures, as applicable; temperatureload if monolith joints are grouted.

• Case IV—flood condition: reservoir and tailwater at maximum flood pool elevations.Tailwater pressures against spillway sectionsshould be based on the discharge height againstthe dam expected with the type of energydissipater provided (however, full tailwaterpressure should be used in uplift determination);dead load and uplift, earth, silt and temperatureloads are considered where applicable. Normally


all spillway gates will be open during themaximum design flood, but some gates may beclosed during lesser floods, depending on theoperating plan.

• Case V—normal operating condition withearthquake: earthquake acceleration in theupstream direction; other normal operatingloads, except no ice pressure.

7.2Sliding stability

The water impounded in a reservoir induces ahorizontal force on the dam structure that must beresisted by the shear strength of the rock in thefoundation to prevent sliding type failure (Fig. 7.3).Other structures that may be subjected to slidingfailure are spillways and gravity intake structureswhich are often perched high on the abutment of themain dam where the topography drops off steeplydownstream. A powerhouse located immediatelydownstream may require a deep excavation forminga high face below the intake structure, and theremay be a potential for a sliding failure ifdownstream dipping geological features daylight inthis face. Possible stabilization measures includeexcavating additional rock to lower the foundation

as could be done for the structure shown in Fig. 7.3,or joining the intake structure to the powerhouse toform a unit with a greater resistance to thehorizontal thrust of the reservoir water (Deere,1976). If these conditions cannot be met, anunderground powerhouse may be required.The following discussion on sliding stability mainlyrelates to gravity dams because this is often animportant design aspect for this dam type.

7.2.1Geological conditions causing sliding

The ability of the rock in the foundation to resistsliding failure depends on the orientation andcontinuity of faults, joints and bedding planes in thefoundation, the shear strength of thesediscontinuities, and the uplift pressures generated bythe head of water in the reservoir (Wahlstrom,1974; Rescher, 1981). Examples of geologicalconditions in which sliding is possible are shown inFig. 7.4.The examples in Fig. 7.4 show that there are a widevariety of geological conditions that can result insliding failure of dams. The one common conditionin all six cases is the presence of a weak plane thatdaylights at the ground surface downstream of thedam. However, the presence of low strength, near-

Figure 7.3 Foundation for spillway structure containing a fault plane that dips downstream and daylights in thedownstream excavation (after Nieble and Neto, 1983).

220 INTRODUCTION

horizontal discontinuities that do not daylightdownstream of the dam may result in excessivedisplacement of the foundation; Fig. 7.8 showsexamples of stabilization measures undertaken inthese geological conditions. In general, stabilityconditions are unfavorable if the discontinuities arecontinuous and planar, contain a low strength orbrittle infilling, and have positions and orientationsthat form a wedge of rock that can slide from thefoundation.

7.2.2Shear strength

The shear strength of a potential sliding surface isexpressed in terms of the cohesion and frictionangle of the surface (see equation 3.12). Thestability analysis should examine the shear strengthproperties of planes of weakness in the rock, as wellas the rock-concrete interface.

• Rock shear strength Shear strength parametersare determined either by laboratory or in situtesting as described in Section 4.5.2. However,reliable measurement of cohesion values of lowstrength infilling material will usually require insitu testing where the tests can be made of theundisturbed discontinuity. The shear strengthvalues used in design may include or excludecohesion, and may be either the peak or residualfriction angles. It would be appropriate to use thepeak friction angle if the discontinuity had nohistory of displacement, and the constructionprocess would not result in any significantrelaxation and movement of the surface. Also,the friction angle may include the effect ofsurface roughness i, if it is considered that theroughness of the discontinuity will contribute tothe total friction angle, (see Section 3.4).The most conservative strength parameterswould be to assume cohesion of zero and aresidual friction angle (Hoek and Londe, 1974).Deere (1976) suggests that the factor of safetyagainst sliding should be checked for both peakand residual values and recommends that the

factor of safety should be not less than 1.1 for theresidual friction angle.

• Rock-concrete shear strength The shape of theMohr envelope for these surfaces has been foundto be significantly non-linear with some tensilestrength (for intact surfaces) and a decreasingfriction angle at higher normal stress values. Thedevelopment of this envelope requires testing ofcores containing the rock-concrete interface indirect tension, triaxial extension and triaxialcompression (Lo et al., 1991a). Sampling of therock-concrete contact was carried out on sevenexisting dams founded on rock in Ontario andthe following shear strength parameters obtainedfor 16 sets of samples (Lo et al., 1991b):

Tension 0–450 kPa (65 psi)Cohesion 0–900 kPa (130 psi)Friction angle 32°–54°.

Stability analyses of the dams were carried outand in some cases it was found that the factor ofsafety against sliding was less than 1.0 ifcohesion was assumed to be zero. As all thedams were operating satisfactorily it wasconcluded that a tensile strength and cohesionwere operative over a significant portion of thebearing area.

7.2.3Water pressure distributions

Uplift water pressure on potential sliding surfaces inthe foundation will vary from the full reservoir headat the upstream end of the foundation, to zero, or thetailwater head, if any, at the downstream end. Thedistribution of this head along sliding surface willdepend on the presence and performance of groutcurtains and drain holes in the foundation, as well asthe stress condition on the plane. Measurement ofactual uplift pressures in foundations of a number ofUS Bureau of Reclamation dams where drains areoperational, shows that the values are often less thanthe theoretical distribution assumed for design (USDepartment of the Interior, 1951).


Uplift pressures used in design are based onobservations of piezometric measurements made inexisting dams, which show that drains are usuallyeffective in reducing the uplift pressure at the rowof drains to a value equal to between one half andone third of the head difference between theupstream and downstream ends of the foundation.

Therefore, a reasonable assumption for the pressuredistribution would be two straight line segments(lines a in Fig. 7.5). A more conservativeassumption, for the condition of the drains beinginoperative, would be a constant decrease in head(line b in Fig. 7.5).The uplift water pressure head ux along the line of

Figure 7.4 Geological conditions in dam foundations that can result in sliding failures (after Wahlstrom, 1974): (a)brittle jointed sandstone containing beds of clay shale dipping upstream and daylighting beyond the toe of the dam;(b) horizontally bedded limestone with clay shale seams that daylight downstream of the dam; (c) fracturedcrystalline rock containing a fault with low strength clay infilling that dips upstream; (d) conjugate joint sets withorientations that will result in easy shear dislocation of the rock mass; (e) sedimentary rocks dipping downstreamintersected by a fault that daylights beyond the toe of the dam; and (f) folded sequence of sedimentary rockscontaining clay shale beds.

222 INTRODUCTION

the foundation drains is

(7.1)

where ut and uh are the pressure heads respectivelyat the downstream (toe) and upstream (heel) ends ofthe foundation with width B; x is the distance of thedrains from the heel, and R is the proportionalreduction in head at the drains. Having calculatedthe value of ux, the total uplift force U per unitlength of the foundation is

(7.

2)

The structure shown in Fig. 7.5 is a spillway withthe gate closed; water forces external to thestructure comprise the driving forces on the gate and

upstream face of the apron D, D', a vertical force onthe apron V, and an inclined force on the ogee D?.The direction of all these forces is at right angles tothe face on which they act, and they are resolvedinto their vertical and horizontal components fordesign purposes. Note that when the gate is open thedriving force is diminished to D', D?, but flow overthe spillway can produce negative (uplift) pressuresalong the crest of the ogee.

7.2.4Stability analysis

The analysis of stability conditions of a slidingfailure of a gravity dam foundation follows theprinciples of the limit equilibrium analysis ofsliding blocks as described in Section 6.2. Limitequilibrium analysis consists of calculating the


resisting and displacing forces acting on the slidingsurface, with the ratio of these two forces being thefactor of safety of the foundation. Figures 7.6(a) and(b) show two different sliding failure modes thatmay take place in a dam foundation. In both cases,the dam length is much greater than its width and soa two-dimensional analysis can be carried out on aunit length of the dam. The equations defining thefactor of safety for each condition are as follows(Nicholson, 1983).In Fig. 7.6 (a) sliding can take place either along thehorizontal base of the dam (1), or along a planardiscontinuity that daylights in a face downstream ofthe dam (2). The factor of safety FS against slidingon any horizontal plane (surface 1) is

(7.3)

where c is the cohesion and is the friction angle

of the sliding surface, and A1 is its surface area; ?V1is the vertical force comprising the weight of thestructure, u1 is the water uplift force; ?H1 is the nethorizontal force due to the reservoir, and tailwaterpressures if any, acting on the upstream anddownstream faces of the dam respectively, plusother external forces such silt, ice and wind loads asappropriate.The water uplift force is calculated from equation 6.9 where hw is the total head between the reservoirlevel and the sliding surface. For a dam with avertical upstream face, the water produces only ahorizontal force while for a slopingupstream dam face, the water force acting on thisface has a vertical component which increases thenormal force on the sliding plane and improves theshear resistance.For a non-horizontal sliding surface (Fig. 7.6(a),

Figure 7.5 Spillway structure showing external water pressures acting on the ogee and gate, drainage and grout holes,and uplift pressure distributions in the foundation.

224 INTRODUCTION

surface (2) with dip of—?p) the factor of safety iscalculated using equation 7.4 in which the totalvertical and horizontal forces are resolved intonormal and shear forces acting on the slidingsurface. The uplift force u2 acts normal to thesliding plane and must be resolved into its verticaland horizontal components. The factor of safety FSagainst sliding is

(7.4)

Note that the angle ?p is positive if the foundationdips upstream, and negative if it dips downstream.In Fig. 7.6(b) the dam has been recessed into thefoundation so that there is a passive wedge of rockat the toe of the dam which provides a resistingforce in addition to the shear strength of the base ofthe dam. Using limit equilibrium methods, the factor of safety of the combined surface is given by:

(7.5)

where i is the subscript associated with n planarsegments making up the critical potential failure surface, each with dip ?i and area Ai; Hi and Vi arerespectively the horizontal and vertical componentsof any forces acting on plane i; ui is the uplift waterforce on segment i; and

(7.6)

Because ??i is a function of FS, calculation of thefactor of safety is an iterative process requiring firstan initial estimate of FS, which is refined with eachsuccessive iteration. Calculation of the factor ofsafety is facilitated by drawing a free body diagramof each wedge showing the magnitude and directionof all the applied and resulting forces acting on it.

Figure 7.6 Modes of sliding failure in foundations of gravity dams (after Underwood and Dixon, 1976): (a) slidingfailure on continuous planes in a foundation; and (b) sliding failure with passive wedge at the toe of the dam.


Where the dam is recessed dam into rock containingwell defined sets of discontinuities, the dip angle ?2of the base of the passive wedge may be defined bythe structural geology. However, in closelyfractured rock, for example, where the sliding planeis not defined by a pre-existing plane of weakness, ?2 is given by

(7.7)

The angle is the developed angle of internalfriction which is equal to

(7.8)

Note that, for the failure condition shown in Fig. 7.6(b), the two components of the resisting force maynot be additive if the two surfaces have differentshear stiffnesses. For example, if the base of the damis a rough rock surface with good cohesion betweenthe rock and the concrete, while the base of thepassive wedge is a continuous smooth joint, thenthe base of the dam will have a greater shearstiffness than the joint (see inset Fig. 7.6(b)).Therefore, a small shear displacement d willdevelop most of the shear resistance along the baseof the dam, with relatively little shear resistancebeing developed on the base of the wedge (i.e.

. Where the sliding surfaces havesignificantly different stiffnesses, considerationshould be given to ignoring the shear strength of theless stiff surface. For foundations comprising a number of polygons

formed by sets of discontinuities, a method ofanalysis method has been developed in whichsliding takes place both on the base and the sides ofeach block. This analysis method allows theincorporation of differing shear strength parameterson each sliding surface, and external water uplift,foundation loads and reinforcement forces atspecified locations and inclinations (US ArmyCorps of Engineers, 1989).Figure 7.7 shows a dam recessed into a horizontallybedded foundation rock where resistance to slidingis provided by the buckling strength of these slabs ofrock, in addition to the shear strength of the base ofthe dam. From the Euler formula for bucklingbeams, the approximate buckling resistance fr isgiven by (Underwood and Dixon, 1976):

(7.9)

where E is the deformation modulus of the intactrock; A is the cross-sectional area of the strut (for aunit length of the foundation, A equals the thicknessof the strut); L is the length of the strut; and D/2 isthe least radius of gyration or half strata thickness.The approximate overall factor of safety of slidingfor the condition shown in Fig. 7.7 is

(7.10)

where c and are the shear strength components onthe base of the dam, and A1 is the area of thefoundation. The magnitude of the buckling

Figure 7.7 Sliding failure in horizontally bedded foundation with buckling of slab at toe (after Underwood and Dixon,1976).

226 INTRODUCTION

resistance will be very sensitive to any fractures inthe strut that would open as soon as the strut startedto buckle. Therefore, if the rock contains verticaljointing it is likely that fr will be significantlydiminished from that given in equation 7.9 andsome judgement will be required to determine arealistic value for the length of the strut L, and theeffect of relative stiffnesses as discussed above (seeFig. 7.6(b)).Note that for the conditions shown in both Figs. 7.6(a) and (b) an improvement in sliding resistance canbe achieved by installing tensioned rock anchordownstream of the toe of the dam. For example, thefactor of safety against sliding of the spillway of theElkhart Dam in Indiana in the United States wasincreased by installing an anchored thrust block atthe toe of the structure. The rock anchors wereinstalled at a dip of 70° in an upstream direction andtensioned against the top of the thrust block toprovide both a vertical and horizontal force. Thesliding stability was calculated by considering thehorizontal component of the anchor force as apassive force that was added to the numerator(shear resistance) of equation 7.3 (Jansen, 1988).Where practical, installation of the reinforcementsuch that the dam is tied directly to the foundation,rather than downstream of the dam, will allow theperformance of the reinforcement to be morereliably predicted.

7.2.5Factor of safety

In using limit equilibrium analysis to calculate thesliding stability of a gravity dam, it is necessary toselect a factor of safety to which to design thefoundation. One of the factors that may influencethe selection of an appropriate factor of safety for aparticular dam is the degree of uncertainty in theload and strength values that are used in the design.The design values that are often least well definedare the cohesion on either the rock-concrete contactor a geological feature, uplift forces in thefoundation, and earthquake accelerations. Theinfluence of the variation in design parameters can

be studied by carrying out sensitivity analyses todetermine, for example, that a factor of safety of 2.0under static conditions does not drop below 1.3under seismic loading conditions. This issue can bestudied in more detail using reliability analysis inwhich all the variable parameters are defined asdistribution functions in order to calculate adistribution function for the coefficient of reliability,or probability of failure (see Sections 1.6 and6.2.2). As discussed in Section 7.1.1 and shown inFig. 1.9, analysis of dam failures indicates that thepresent probability of failure for rock foundations isabout 10−5 per dam year and foundation designscarried out using probabilistic methods should aimto achieve this level of reliability. This informationcan then be used in risk analysis to evaluate theconsequence of failure for various options, andselection of an appropriate design.The US Army Corps of Engineers (1981) hasestablished a factor of safety of 2.0 for normal staticloading conditions, and 1.3 for seismic loadingconditions. These factors of safety are acceptedprovided that a monitoring system is installed tomeasure structural movements and uplift pressures,and that the instrumentation and drainage ismaintained. In circumstances where the long termmaintenance of the dam is less certain than thoseunder the jurisdiction of the Corps of Engineers, theuse of higher factors of safety may be considered.

7.2.6Examples of stabilization

The following are examples of dams whereremedial work, in addition to drainage and grouting,has been carried out to prevent sliding in thefoundation. In all these cases the analysis principlesdemonstrated in Fig. 7.6 can be applied, with thedetails of the stabilization procedure varied to suitconditions at each site (Fig. 7.8).• Concrete shear keys The 180 m (590 ft) highItaipu Dam in Brazil is a hollow concrete gravitydam founded on a series of basalt flows. Within thefoundation there occurs a series of sub-horizontalflow contacts containing contact breccia. In order to


prevent sliding failure on these contacts, concreteshear keys were constructed to increase both theshear strength and the shear stiffness of thecontacts. They were formed by excavating eighttunnels at about 16 m (52 ft) centers, both paralleland normal to the dam axis, and filling them withconcrete. The tunnels were 2.5 m (8.2 ft) wide and3.5–7 m (11.5–23 ft) high so as to cut through theweak layer and into sound rock above and below. Across section is shown in Fig. 7.8(a). The total areaof the shear key is 125m×150m (410×490 ft). Asystem of drainage tunnels surrounds the squaregrid of shear keys to minimize the build up of waterpressure (Abrahao et al., 1983).• Bored concrete piles The spillway structure of theGezouba Project in China is a 35 m (115 ft) highconcrete gravity structure founded on a horizontallybedded sequence of sandstones, siltstones andclaystone (Fig. 7.8(b)). These rock types are all oflow strength and highly deformable. The shearstrength of the foundation was improved byinstalling a pattern of 20 m (65.6 ft) deep boredconcrete piles downstream of the dam (Xu et al.,1983).• Concrete ballast The Morris Shepard Dam Texasis a 57 m (187 ft) high, flat slab buttress damfounded on low permeability shale. In 1986movement monitoring results and observations ofcracks in the upstream and downstream spillwayfoundations showed that the structure had slid adistance of about 115 mm (4.53 in) sinceconstruction in 1941. Remedial work consisted ofinstalling 145 pressure relief wells because therehad been no drainage in the original construction,and placement of 60000m3 (78500yd3) of concretein the hollow core of the spillway. The combinationof reduced uplift pressures and increased weight ofthe dam had the effect of increasing the net verticalforce and thus the shear strength of the slip planes inthe foundation (ENR, 1988).• Excavation and concreting The Liu-Jia-Xia damon the Yellow River in China is a 147 m (482 ft)high concrete gravity dam founded on anextensively faulted and folded micaceous andhornblende schist. During construction of the

foundations selective excavation andconcreting was carried out in a number of faultzones to improve both the bearing capacity andshear strength of the rock mass. On the rightabutment, poor rock was excavated to a depth of 25m (82 ft), and in the main fault zone a 3×4 m(10×13 ft) shaft, 15m (50 ft) deep was excavatedand then back-filled with concrete followed byextensive grouting (Fu et al., 1983).• Tensioned anchors The Inguri Dam in Russia is a271.5 m (891 ft) high arch dam founded onlimestone and dolomite with the beds dippingdownstream at an angle of 50°–70°. The founda tionrock also contains six sets of closely spaced joints.Stabilization of the foundation consisted ofexcavating a network of tunnels in the fault zonesand back-filling these with concrete. A concrete slabwas then poured on the rock surface at the toe of thedam and tensioned anchors installed to provide anadditional restraining force (Mgalobelov andLomov, 1979).Tensioned anchors were also used in theconstruction of the Karakaya Dam in Turkey whichis a 173 m (568 ft) high concrete arch damconstructed in a narrow gorge with approximately60° side slopes. The foundation rock is a highlymetamorphosed gneiss containing faults andschistosity that dip out of the sides of the gorge atangles of between 40° and 80° to form a series ofpotentially unstable wedges in the abutments. Thesewedges were stabilized by installing multistrandanchors each stressed to 170 t. In the right abutmenta total of 1200 anchors where installed and a fewernumber in the left abutment where the geologicalconditions were more favorable to stability (Gavardand Gilg, 1983).Tensioned anchors have also been installed in anumber of concrete gravity dams to improve theirstability in the event of earthquake loading (seeSection 7.6).

7.3Overturning and stress distributions in

228 INTRODUCTION

foundations

In concrete gravity dams the resultant load on thefoundation is inclined in the downstream directionwhich induces both an overturning moment, and anon-uniform stress distribution in the foundationrock. Consequently, two components of the designof gravity dams are analysis of the stability of thestructure against overturning, and a comparison ofthe stress levels in the foundation with the allowablebearing capacity of the rock.A further component of the stress analysis is to

examine the deformation of the foundation underthe action of the applied loads, and to determine ifthese deformations result in the development ofexcessive stress levels in the concrete. Thiscondition may be most severe if the foundationcontains rocks of significantly different deformationmoduli resulting in the development of high stressgradients in the concrete at the boundaries of rocktypes (see Fig. 3.2).

Figure 7.8 Examples of methods of preventing sliding failure of gravity dam foundations: (a) concrete shear key inbrecciated zone of foundation of Itaipu Dam (Abrahao et al., 1983); (b) concrete bored piles installed across low-strength beds in dam foundation (Xu et al., 1983). 1. Grout curtain 2. Drain holes 3. Consolidation grouting 4. Good-quality basalt 5. Brecciated and faulted zone 6. Concrete shear key 7. Low-strength bed 8. Bored concrete piles.


7.3.1Overturning

Stability against overturning is determined bycalculating the resultant of the forces acting on thefoundation, and ensuring that this resultant actswithin the middle third of the base (Fig. 7.9). Theresultant acts through the centre of gravity CG ofthe structure and is the vector sum of the verticaland horizontal forces. The total vertical force ∑V isthe sum of the weight of the structure, the verticalcomponents of water forces acting on inclinedsurfaces, and uplift forces. The total horizontal force∑H is the sum of the water forces on the upstreamand downstream faces together with silt, ice andwind forces as appropriate. These forces are used tocalculate the overturning moment M and the loadingeccentricity, e equal to

(7.11)

from which the stress distribution in the foundationcan be estimated (see Section 7.3.2 below).The effect of earthquakes on overturning can bedetermined by adding a pseudo-static force to theresultant force vector. The horizontal pseudostatic

force is equal to the product of the weight of thedam and the seismic coefficient, and the verticalupwards pseudo-static force can be taken as onethird of the horizontal force (see Section 7.4). Thiswill have the effect of decreasing the vertical forceand increasing the moment, resulting in an increasein the eccentricity, e. For stability againstoverturning under earthquake loading conditions, itis usually considered satisfactory that the resultantlie within the base of the structure (Jansen, 1988).In practice, it is unlikely that bodily overturning of agravity dam will occur because other failures willoccur before this can take place. These failures willcomprise crushing of the toe material and crackingof the upstream material resulting in increaseduplift pressure and a reduction in shear resistance.

7.3.2Stress and strain in foundations

The stress distribution along a dam foundation canbe calculated, as a first approximation, from the sumof the stress produced by the weight of thestructure, and the stresses due to the moments. Thismethod gives a straight line distribution between the

Figure 7.9 Approximate method of calculating overturning stability and foundation stress distributions for concretegravity dams (after Underwood and Dixon, 1976).

230 INTRODUCTION

toe and the heel of the dam. Assuming that thelength of the dam is considerably greater than thewidth, the maximum and minimum stresses aredefined as:

(7.12a)

and

(7.12b)

where ?V is the sum of vertical forces, e is theeccentricity of foundation loading and B is the widthof foundation.If the resultant load lies within the middle third ofthe base the stresses are entirelycompressive, while if the resultant lies outside themiddle third tensile stresses are inducedat the heel (see also Section 5.5.4). If the stress atany portion on the foundation bearing surface istensile, it is usually assumed that over this portionof the base of the dam the uplift pressure is the fullhydrostatic head, and the cohesion is zero. Thestress levels defined by equations 7.12a and 7.12bcan be compared with allowable bearing capacity ofthe rock to estimate if excessive deformation willoccur (see Section 5.2.2). This analysis wouldinvolve defining the strength of the rock mass interms of the compressive strength of the intact rock,and rock mass strength parameters m and s(Table 3.7). In general it is found that the verysignificant loads produced by the weight of the damand the impounded water can induce stress changesin the foundation rock to a depth about equal to theheight of the dam. Section 5.5.3 provides someguidelines as to how structural geology mayinfluence the distribution of induced stresses in thefoundation. This information would be ofimportance, for example, in determining the depthto which an inverted pendulum should be installedin order to ensure that the lower end was in rockundisturbed by the structure.The assumptions made in equations 7.12 are that thefoundation is homogeneous, elastic and planar andthat the dam is rigid, which may be realistic in somecircumstances. However, at dam sites with complexgeological conditions and/or irregular topography, it

is not possible to use elastic theory to calculate thestress distributions and deformations. In thesecircumstances numerical methods are usually usedto identify areas of either tensile stress, or highcompressive stress, which exceed the allowablestresses in the concrete or rock (Itasca Corp., 1996;Zienkiewicz, 1988; Wittke et al., 1972). Animportant feature of numerical modeling of rock isthe ability to include discontinuities and determinewhether there will be shear movement or seperationas a result of the applied structural loads. Thefollowing are a number of examples of studies ofstress and strain in dam foundations where thegeological structure was incorporated in theanalysis. (a) Finite element analysis of stress distributionFinite element analysis was used to determine thestresses in the foundation of a gravity dam(Fig. 7.10). The calculated stress levels werecompared with the rock mass strength, as defined bycohesion and friction angle, to determine a factor ofsafety for each element. The analysis showed asignificant zone where the factor of safety was lessthan the required value of 1.5. Remedial work forthe foundation consisted of installing fully grouted,untensioned steel dowels which were assumed tohave the effect of increasing the cohesion of therock mass.(b) 3DEC analysis of displacement in jointedrockAnalyses were carried out to examine the influenceof discontinuites in the foundation on theperformance of the Cambambe Dam and the FunchoDam in Portugal (Lemos, 1996). Fig. 7.11 showsthe model of the 85 m high Cambambe concretearch dam founded on siltstones and sandstoneswhich contain three joint sets, with slightlydifferent orientations in the left and right banks. Ofparticular importance to deformation behavior ofthe foundation was a set of sub-horizontal, clayfilled joints with friction angles in the range 12–16°.These foundation conditions and the dam weremodeled using the program 3DEC, a three-dimensional version of the UDEC program


(Universal Distinct Element Code) (Itasca, 1996)with the purpose of comparing the computeddeflection of the structure with that measured in aphysical model. The dam was modeled using174 three-dimensional quadratic finite elementswhich allowed the shape of the curved shell to beaccurately defined, and to reproduce the bendingbehavior for elasto-plastic analysis. The foundationwas modeled as 904 discrete elements, with theirshapes and orientation defined by thediscontinuties. In the analysis the elements wereassumed to be deformable in order to model therock mass deformability and its effect on stressesinduced in the dam. The element sizes were fourtimes those in the physical model and in order tomodel the deformation accurately the stiffnesses

were reduced by a factor of four. Compatibility atthe interface between the dam and its foundationwas achieved by dividing the quadratic elementsinto eight triangles and by adding a slave node atthe face centres. The properties of the materialsmaking up the model are listed in Table 7.2.The effect of water pressure in the foundation,which influences sliding behavior, can be modeledin 3DEC by assuming that the blocks areimpervious and all flow takes place in the joints(Damjanac, 1996). However, this is demanding ofcomputer time, and for the model in Fig. 7.11 asimplified procedure was used based on anequivalent continuum model using rock masspermeability values from in situ tests.The displacement of the dam calculated by 3DEC,

Figure 7.10 Results of finite element analysis to calculate stress levels and factors of safety in foundation of a gravitydam (Egger and Spang, 1987).

232 INTRODUCTION

using the rock mass properties listed in Table 7.2,closely matched those in the physical model and

showed that sliding on the low strength joints didnot occur until the loads were well in

Table 7.2 Rock and concrete properties used in 3DEC analysis of arch dam (Lemos, 1996)

Parmeter Concrete Rock/Concrete interface Intact rock Joint Clay infilling

Young’s modulus (GPa) 31 – 51 – –Poisson’s ratio 0.2 – 0.2 – –Cohesion (MPa) 12 10 – 0 0Tensile strength (MPa) 10 6 – – –Friction angle (°) 37 30 – 30 15Dilation angle (°) 0 – 0 –Normal stiffness (GPa/m) – – 1.0 –Shear stiffness (GPa/m) – – – 0.50 –excess of the design load. A similar modelingtechnique was used for the 43 m high Funcho archdam which is founded on interbedded shale andgraywacke striking parallel to the valley anddipping at about 40–60°. The deformation moduliof the foundation rock varied from 1 GPa (145 ksi)

for the shale in the right bank to 25 GPa (3600 ksi)for the graywacke in the left bank. Both the 3DECmodel and the monitoring of the structure showedstrains of up to 10 mm in a direction towards thelower modulus rock in the right bank.A feature of the 3DEC analysis, which was not an

Figure 7.11 Three-dimensional 3DEC analysis of concrete arch dam, and foundation containing three joint sets, tocompare calculated displacement with physical model (Lemos, 1996).


issue in the studies reported by Lemos (1996)because arch dams cannot withstand large motions,is the ability to model displacement resulting fromshearing and separation of the discontinuities.(c) Finite element analysis of abutments injointed workThe Cannelles concrete arch dam in Spain isconstructed in a steep sided canyon on a limestonefoundation. The limestone is strong, but contains apersistent set of discontinuities that have a nearvertical dip, strike parallel to the canyon walls andhave an infilling of clay and irregular limestone

concretions with widths of between 10 and 300 mm(0.4 and 11.8 in). An extensive in situ testingprogram was carried out to determine the shearstrength parameters of the infilled discontinuities.Stability analysis of the abutments was carried outusing of two-dimensional finite element model in ahorizontal plane assuming plane strain con ditions(Fig. 7.12). The analysis required a detaileddescription of the shear behavior of thediscontinuities, the input parameters being the peakand residual shear strengths, the change in strengthwith shear displacement, and the normal and shear

Figure 7.12 Two-dimensional finite element model of a horizontal section of Cannelles Dam showing the orientationsof the principal joint sets and the stabilization of the abutments (Alonso and Carol, 1985).

234 INTRODUCTION

stiffnesses. The analysis investigated the stability ofthe abutments and stabilization measures required toprevent movement along the joints. Thesestabilization measures consisted of tunnels filledwith concrete at a number of levels in theabutments, and a counterfort wall on the rightabutment (Alonso and Carol, 1985).(d) Three-dimension finite element analysis ofarch dam abutmentsA three-dimensional finite element analysis ofjointed rock was used in the design of the Longton220 m (722 ft) high arch dam in China (Carrere etal., 1987). The model incorporated the dam and thetopography, as well as the major geological featuressuch as gouge-filled faults with low friction angles.The stress analysis showed that it was necessary tostiffen certain faults in the abutments with concretefilled galleries to keep stresses and strains in thedam within acceptable limits.(e) Open joints in foundation upstream of damThe Albigna concrete gravity dam in Switzerland isfounded on a strong granite which contains a set ofpersistent, healed discontinuities that dipdownstream at an angle of about 60° (Fig. 7.13). Itwas discovered from monitoring of the deflection of

the crest of the dam, as well as seepagemeasurements, that the foundation was undergoingelastic-plastic deformation as a result of the openingof the downstream dipping discontinuities.Measurements with a sliding micrometer showedthe extent to which the two discontinuities closest tothe heel of the dam opened when the reservoir levelwas raised by 30 m (98 ft) to full storage level.Remedial work for this condition comprisedemptying the reservoir, cleaning of rock surfacesupstream of the dam, and sealing the discontinuitieswith a neoprene sheet 240 m long and 12 m wide(790 by 40 ft) (Kovari and Peter, 1983).

7.4Earthquake response of dams

7.4.1Introduction

The three main hazards to dams from earthquakesare:

1. fault movement in the dam foundation;

Figure 7.13 Strain measurements along boreholes M1 and M2 showing opening of discontinuities in the heel of the damas a result of increase in water level from 2137 to 2161 m (Kovari and Peter, 1983).


2. ground motion in the foundation;3. wave action in the reservoir.

Displacement of a fault running through thefoundation is likely to result in severe damageor even collapse of the dam. For this reason,detailed geological investigations are carried out fordams in seismic regions to identify potentiallyactive faults and site the dam at a safe distance fromsuch features, or design the dam to accommodatedisplacement. Both numerical and physical modelshave been used to study fault displacement in damfoundations. For example, a 1:250 physical model ofa 185 m high arch dam in Greece whichincorporated a joint system showed that up to 1 mof movement could occur without damage to thestructure. There are at least two dams, the MorrisDam in California and the Clyde Dam in NewZealand, in which the plane of an underlying faulthas been extended through the entire dam section inthe form of a sliding joint. In both cases the jointsare vertical and are designed for displacements ofup to 2 m, although up to 1990 no movement hadbeen detected (National Research Council, 1990).Ground motion can induce excessive stresses anddisplacements in both the dam and its foundationresulting in slope failures of embankment dams, andcracking of concrete dams. For dams founded onrock it is important to analyze the structural geologyto identify blocks of rock in the foundation orabutments that may move when subjected toearthquake loading. A third cause of damage is theoccurrence of landslides or rock falls into thereservoir that create water waves (seiche) resultingin a rise in water level that may overtop the dam.The following are two examples of earthquakeinduced dam failures. The San Fernando Dam inCalifornia is a 44 m high hydraulic earthfill dam. In1971 a 6.5 Richter magnitude earthquake centeredapproximately 8 km from the dam caused arotational slip failure of the downstream face andpart of the crest; fortunately, enough of the upstreamhalf of the dam remained in place to contain thewater (Jennings, 1971). The Konya Dam in India isa 91 m high concrete gravity dam which was

damaged by a Richter magnitude 6.5 earthquake thatgenerated in the dam a peak acceleration ofapproximately 50% of gravity. The dam sustained ahorizontal crack near the upper third point and manyof the appurtenances were damaged (Housner,1970; Chopra and Chakrabati, 1973).The San Fernando Dam in California is in an areaof high seismicity where extensive studies ofearthquakes have been made. The experience gainedfrom the San Fernando Dam and other welldocumented seismic events, have been used tosignificantly improve the design and constructionprocedures for all structures, including dams, inareas where earthquakes are common. However, theKonya Dam in India is in an area of low seismicactivity and it is believed that the earthquake wasrelated to reservoir filling. Other dams in lowseismic areas have also recorded earthquakes duringreservoir filling. For example, the 128 m (420 ft)high Kariba Dam Dam on the Zambezi River incentral Africa, which is in a nonseismic area,recorded nine earthquakes with Richter magnitudes5.1–6.1 over a three month period as the reservoirreached full impoundment (Rothe, 1969). Also, theHsinfengkiang Dam in China, which is a 91 m (300ft) high buttress dam, was damaged by a magnitude6.1 earthquake in 1962; the damage consisted of ahorizontal crack about 15 m (50 ft) below the crest(Sheng et al., 1970). These events show that thepossible occurrence of earthquakes in areas of lowseismicity should be considered in the design ofmajor dams.

7.4.2Measured motions of foundation rock

For dams located in mountainous terrain, seismicdesign should take into account the possible spatialvariation in the ground motions from the valley floorto high in the abutments. Although there are fewground motion records on the walls of canyons andmost were of low intensity, many of the records thatdo exist show significant variation in the motions.For example, during a 1984 earthquake in Japan,ground motions were measured for the Nagawado

236 INTRODUCTION

(arch) Dam which is 155 m high and has a crestlength of 355.5 m. The following are some of theaccelerations measured at different points on thedam and in its foundation and abutments:

1. foundation at depth of 17 m below base of dam—0.029g at right angles to the dam axis and 0.016g parallel to the dam axis;

2. deep in right abutment at elevation of 25 mabove base of dam—0.021g at right angles todam axis and 0.018g parallel to dam axis;

3. deep in right abutment at elevation of crest ofdam—0.026g at right angles to dam axis and 0.031g parallel to dam axis;

4. crest of dam at midspan—0.197g peak radialacceleration;

5. crest of dam at quarter point from left abutment—0.245g peak radial acceleration.

Other records have shown that the ratio of thehorizontal peak velocity at the crest level of the damto that at the base of the dam is generally greaterthan unity. Motions recorded at the Ambiesta (arch)Dam in Italy in 1976 showed a base to crest velocityratio of 3.1–1.9, at the Chirkey (arch) Dam inRussia the base to crest velocity ratio was 1.6, and atthe Pacoima Dam in California the acceleration atthe crest level was about twice that at the base. Suchnon-uniform motions can have a significant effecton the stresses generated in the concrete damcompared with uniform motions (National ResearchCouncil, 1990). However, these are all low intensitymotions and it is not known if there will be adifferent response in the case of stronger motions.

7.4.3Sliding stability and overturning under seismicloads

For concrete gravity dams the stability againstsliding can be determined by limit equilibriummethods, and the stress distribution in thefoundation can be estimated by taking moments (seeSection 7.3). As a first approximation, the effect ofearthquake loading on sliding stability and stress

distribution can be determined by pseudo-staticanalysis, but this is only applicable for particularlystiff dams with heights less than 30 m (100 ft). Whereapplicable, the analysis procedure consists ofapplying a constant force as an external load actingthrough the center of gravity of the structure. Thisforce can be applied in a horizontal direction only,but if it is considered that the horizontal and verticalmotions will be in phase, then both horizontal andvertical forces could be applied to the structure.This can produce a resultant force acting in adownstream direction, above the horizontal, whichis the direction most detrimental to stability.The magnitude of the inertial force Qi is given by(Jansen, 1988):

(7.13)where a is the seismic coefficient expressed as afraction of the gravitational acceleration; and W isthe weight of the dam.A significant component of the forces influencingthe stability of a gravity dam is the pore waterpressure in the foundation. However, it is usuallyassumed that the pore water pressure is constant forboth static and seismic loading for the followingreasons. During seismic events, as the dam movesupstream, the upstream portion of the dam carriesthe inertia load in compression resulting in higherpore pressures, while the stresses in the downstreamportion of the dam tend towards tension causingreduction in pore pressures. When the movement ofthe dam reverses, pore pressures tend to be reducedin the upstream portion and increased in thedownstream portion. Since the increase in porepressures in the compressive zones is usuallyaccompanied by a larger increase in total stress,higher pore pressures do not significantly affectstability during seismic loading. Should crackingoccur in the upstream face during an earthquake, itis usually assumed that the oscillations occurquickly enough that there is no significantpenetration of water into the cracks (NationalResearch Council, 1990).In addition to the force due to acceleration of thedam, it is necessary to add a hydrodynamic forceresulting from the reaction of the impounded water


on the dam. This hydrodynamic force can becalculated from the Westergaard formula as follows(Westergaard, 1933):

(7.14)

(7.15)

where Qe is the horizontal hydrodynamic forcedown to depth y; Me is the moment at depth y due toQe; hw is the total height of water at the dam face; Ceis the factor depending principally on the height ofthe dam and the earthquake period te in seconds (teis often assumed as 1 s) and is equal to

(7.16a)

(7.16b)

The factor ke accounts for any slope on the face of

the dam and varies from 1 for a vertical face to 0 fora horizontal face (Fig. 7.13).Pseudo-static analysis is an approximation forexamining stability conditions of a foundationsubjected to earthquake motions. It will usuallyproduce a conservative design because the shortduration transient earthquake force is modeled as aconstant, uni-directional force. Advantages ofpseudo-static analysis are that the accelerationvalues are taken directly from the building codes,and the calculation method is relatively straightforward.

7.4.4Finite element analysis

Dynamic response of dams can be carried out usingfinite element analysis to calculate stresses andstrains in the dam and its foundation, induced byearthquake accelerations in the foundation.Figure 7.15 shows an example of a three-dimensional dynamic analysis of a concrete gravitydam using the program ABAQUS (Hibbitt,Karlsson and Sorensen, Inc., 1987). The modelincorporates the foundation and abutments of the

Figure 7.14 Value of hydrodynamic pressure coefficient ke for sloping dam faces (Jansen, 1988).

238 INTRODUCTION

dam so as to account correctly for the differingproperties of the soil in the right abutment and therock in the foundation and left abutment. The mainpurpose of this analysis was to determine the stresslevels in the concrete which were found to behighest at the crest where the greatest strains wereinduced. Stress levels in the foundation rock weresubstantially less than the rock strength, and therewas no significant displacement of the foundationrock.Details of the dynamic finite element analysismethod, which are beyond the scope of this book,are described by Chopra (1978), Fenves and Chopra(1984, 1987), Fok et al., (1986) and Jansen (1988).A component of these analyses that is ofsignificance to the calculated stresses in the dam isthe interaction between the dam and thedeformation of the foundation rock. This is becausedams, and particularly arch dams, partly resist thereservoir water pressures as well as thermal andearthquake forces by transmitting these forces to thefoundation and the canyon walls. The effect ofincluding the dam-foundation interaction, incomparison with modelling the dam with a rigidfoundation, is to reduce the maximum principalstresses throughout the dam monolith. It is usuallyassumed that the deformation modulus of thefoundation rock is constant for both static andseismic loading conditions.Finite element analysis was also used to determinethe displacement of a wedge of rock in a dam foundation when subjected to a Richter magnitude 6.5 earthquake represented by three syntheticaccelerograms (Scott and Dreher, 1983). The factorof safety at each time step was calculated by limitequilibrium methods and was only found to dropbelow 1.0 on two occasions during the earthquakefor durations of 0.05 s (Fig. 7.16). If the maximumdam loads and the peak inertial forces had beenused in a pseudo-static analysis,the factor of safetywould have been less than 1.0 and the conclusionmight have been that the foundation was unstable.The displacement of the rock wedge during this 0.05 s period was calculated to be 7.9 mm (0.31 in).The analyses can account for the effect of the rate

of shear displacement on the shear strength of therock discontinuities (Crawford and Curran, 1982).The analysis results shown in Fig. 7.16 are based onwork done at the proposed Auburn Dam inCalifornia, where the foundation contains apotentially active fault (US Department of theInterior, 1978).

7.4.5Earthquake displacement analysis

Calculation of the factor of safety against sliding bypseudo-static limit equilibrium methods forearthquake loading conditions (see Section 7.4.2) isusually a conservative method of analysis. Failuredoes not necessarily occur when the dynamictransient stress reaches the strength of the rock, andif the factor of safety drops below 1.0 at some time,and on some portions of the foundation, it does notnecessarily imply a serious problem. What reallymatters is the magnitude of permanent displacementcaused at the times that the factor of safety is lessthan 1.0 (Lin and Whitman, 1986). A method ofcalculating displacement as the result of earthquakemotions has been developed by Newmark (1965).The principle of Newmark’s method is illustrated inFig. 7.17 which shows the displacement of a blockwhen the base is subjected to a uniform horizontalacceleration pulse of magnitude ag and duration t0.The velocity of the foundation is a function of thetime t and is designated y(t), and its velocity at timet is y. Assuming a frictional contact between theblock and the base, the velocity of the block will bex, and the relative velocity between the block and thebase will be u where

(7.17)The resistance to motion is accounted for by theinertia of the block. The maximum force that can beused to accelerate the block is theshearing resistance on the base of the block whichhas a friction angle of . This limiting force isproportional to the weight of the block W and is ofmagnitude , corresponding to a yieldacceleration ay of , as shown by thedashed line on the acceleration plot (Fig. 7.17(b)).


The shaded area shows that the ground acceleration

Figure 7.15 Example of dynamic, three-dimensional analysis of a concrete gravity dam (B.C.Hydro, Sandwell Inc.): (a)dam model from downstream perspective; and (b) vertical section through crest of dam showing deflected shape underdynamic loading (deflection at magnification of 44).

240 INTRODUCTION

pulse exceeds the acceleration of the block,resulting in slippage.Figure 7.17(c) shows the velocities as a function oftime for both the ground and the block acceleratingforces. The maximum velocity for the groundaccelerating force has a magnitude v which remainsconstant after an elapsed time of to. The magnitudeof the ground velocity vg is given by

(7.18)while the velocity of the block vb is

(7.19)After time tm the two velocities are equal and theblock comes to rest with respect to the foundation,that is, the relative . The value of tm iscalculated by equating the ground velocity v to thevelocity of the block to give the followingexpression for the time tm:

(7.20)

The displacement dm of the block relative to the

Figure 7.16 Calculation of factor of safety against time for a rock wedge in a dam foundation under earthquake loads(Scott and Dreher, 1983): (a) geology of foundation; and (b) variation of factor of safety with ground motion history.


ground at time tm is obtained by computing the areaof the shaded region on Fig. 7.17(c) as follows:

(7.21)

Equation 7.21 gives the displacement of the block inresponse to a single acceleration pulse (duration to,magnitude ag) that exceeds the yield acceleration

, assuming infinite ground displacement.The equation also shows that the displacement isproportional to the square of the ground velocity.

While equation 7.21 applies to a block on ahorizontal plane, a block on a sloping plane will slipat a lower yield acceleration and show greaterdisplacement depending on the direction of theacceleration pulse. For a cohesionless surface wherethe factor of safety of the block FS is equal to

and the applied acceleration ishorizontal, Newmark shows that the yieldacceleration ay, is given by

(7.22)where is the friction angle of sliding surface, and ?p is the dip angle of this plane. Note that for

. Also equation 7.22 shows

Figure 7.17 Displacement of rigid block on moving base (Newmark, 1965): (a) block on moving base; (b) accelerationplot; and (c) velocity plot.

242 INTRODUCTION

that for a block on a sloping surface, the yieldacceleration is higher when the acceleration pulse isin the downdip direction compared with the pulse inthe updip direction.The displacement of a block on an inclined planecan be calculated by combining equations 7.21 and7.22 as follows:

In an actual earthquake, the pulse would befollowed by a number of pulses of varyingmagnitude, both positive and negative, which willproduce a series of displacement pulses. Thismethod of displacement analysis can be applied tothe case of a transient sinusoidal acceleration (a(t)g)illustrated in Fig. 7.18 (Goodman and Seed, 1966).If during some period of the acceleration pulse theshear stress on the sliding surface exceeds the shearstrength, displacement will take place.Displacement will, of course, take place much morereadily in a down slope direction, which isillustrated in Fig. 7.18 where the shaded areas arethe portion of each pulse in which movement takesplace. For the conditions illustrated in Fig. 7.18, it isassumed that the yield acceleration diminishes withdisplacement, that is, Integration of the yield portions of the accelerationpulses give the velocity of the block. It will start tomove at time t1 when the yield acceleration isexceeded, and the velocity will increase up to timet2 when the acceleration drops below the yieldacceleration. The velocity drops to zero at time t3 asthe acceleration direction begins to change from upslope to down slope. Integration of the velocitypulses gives the displacement of the block, with theduration of each displacement pulse being (t3—t1).The simple displacement models shown in Figs7.17 and 7.18 have since been developed to modeldisplacement due to actual earthquake motionsmore accurately. For example, Sarma (1975) usedseveral non-rectangular pulses to model groundmotion. Also, Franklin and Chang (1977) examinedthe effect of erratic ground motion on predicteddisplacement, and have drawn up a series of design

charts from which displacement of embankmentscan be calculated. In addition, Jibson et al. (1998)have developed maps showing the probabilistichazard from landslides induced by earthquakes,based on the shaking intensity and groundacceleration, slope angle and rock mass strength.Where these techniques are used to evaluate thepossible permanent deformations of embankmentdams and soil slopes, they are applicable where thesoils are not vulnerable to major strength loss, or tothe development to high excess pore waterpressures at the anticipated level of shaking.

7.5Preparation of rock surfaces

An important aspect of dam construction is thecareful preparation of the bearing surface to ensurethat the contact is watertight and that the rock hasadequate bearing capacity. Exposure of the finalrock surface should also be an opportunity to carryout detailed geological mapping to check oninterpretations made during the investigation anddesign phases of the project.For embankment dams the importance of goodsurface preparation cannot be over emphasizedbecause this may be the main path for water seepageonce impoundment begins. The bearing surfaceshould be free of irregularities to minimize the riskof localized arching in the fill, and differential strainand cracking in the embankment. Also, opendiscontinuities underlying erodible material in thefill should be sealed to prevent erosion. It isbelieved that a cause of failure of the Teton Dam inIdaho was inadequate sealing of opendiscontinuities in the foundation (US Dept. of theInterior, 1980). For concrete dams, foundationtreatment is required to remove material withinsufficient bearing capacity or shearing resistance,and to seal discontinuities to prevent eitherexcessive seepage or erosion of weak infillingmaterials. The following are some examples ofpreparation work that may be required to the surfaceof a rock foundation prior to starting construction ofthe dam (Fig. 7.19).


7.5.1Shaping

For earthfill dams it is desirable to have areasonably uniform rock surface that is free ofirregular knobs, cavities and overhangs, orexcessive changes in slope (Pratt et al., 1972).The shaping work can involve both dental concreteto fill voids or overhangs, and careful blasting forrock removal. In general, slopes should be trimmedto maximum angles in the range of 1:1 to 2V:1H.Where possible, it is desirable to shape both thefoundation and the abutments so that dam is pressedinto rather than pulled away from the contactsurfaces under the reservoir load. If blasting isrequired for any of this work, extreme care must beexercised to prevent damage to the foundation rockfrom excessive explosive charges (controlledblasting is discussed in Chapter 10).As an example of quantifying shaping work, at theCat Arm earthfill dam in Newfoundland, Canada,the specifications including the following

provisions in the foundation preparation(Humphries, 1987; Thomas, 1976).

1. General abutment slope should not be steeperthan 4H:3V.

2. For steps up to 3 m high, slope should not besteeper than 3V:1H.

3. For steps up to 5 m high, slope should not besteeper than 2V:1H.

4. For (1) and (2), when normal to the dam axis,the foundation must not present a smoothcontinuous surface for more than 30% of thecore width.

For concrete dams, the foundation should bereasonably level and if the natural surface dipsdownstream it may be necessary to cut a series ofsteps, dipping upstream, to improve the shearingresistance of the surface. Surfaces that have beenpolished by glacial action, for example, should beroughened by light blasting or chipping. Steps orabrupt changes in elevation of the foundation should

Figure 7.18 Integration of accelerograms to determine downslope movement (Goodman and Seed, 1966).

244 INTRODUCTION

not be located close to block joints so as to avoidcreating thin wedges under a portion of the block(Jansen, 1988).

7.5.2Cleaning and sealing

The final foundation surface should be cleaned ofall loose and broken rock with particular attentionpaid to zones and seams of weak rock. This usuallyrequires the use of air and water jets with sufficientpressure to break up and move unsuitable materials.For embankment dams, faults and seams of weak orweathered rock are usually cleaned out to a depth ofnot less than three times their width and thenbackfilled with concrete or slush grout. Theconcrete should be highly plastic, and the aggregatedimensions not more than about one third of thecrack width. Placement of the concrete should becarried out using a tremie pipe extending to thebottom of the fracture, and not poured or brushed infrom the surface.As an example of sealing deep fractures, at theNormandy Dam in Tennessee, four open jointsextending to 30 m (100ft) below the surface were

sealed by drilling a series of closely spaced, 0.92 m(3 ft) diameter holes which were then filled withconcrete. In addition, all weathered rock at thesurface was removed and the exposed discontinuitiescarefully sealed (Spearman, 1976). Another methodto seal narrow, continuous fractures, that has beenused at the Mintang Project in Taiwan, is to washout low strength infillings with high pressures waterjets to depths of several tens. of meters, and then fillthe open seams with grout (Hoek, 1986; Cheng,1987).Cutoff trenches are frequently used to controlseepage in the foundation of embankment dams.Where blasting must be used for excavation of a keytrench, carefully aligned blast holes, light chargesand appropriate detonation sequences must be usedto prevent fracturing and loosening of thesurrounding rock (see Chapter 10). Heavy blastingcould result in increased permeability of thefoundation rock and limit the effectiveness of thecutoff. The base width of a cutoff trench is usuallybetween one half and one quarter of the height ofthe dam, and the slopes should be flat enough toensure that there is no arching in the fill (Jansen,1988).

Figure 7.19 Preparation of rock foundation surfaces for embankment dam.


Rocks, such as shales, which deteriorate onexposure to the atmosphere, and to wetting anddrying cycles, should be protected duringfoundation preparation. One means of doing this isto make the overall excavation to just above finalgrade and then to remove the remainingrock progressively as the dam is constructed.Alternatively, the rock could be shotcreted as soonas it is exposed. In rockfill dams, air and water willcontinue to circulate in the voids in the fill at thefoundation level, and soft rocks may continue todeteriorate after completion of the dam. In thesecircumstances, the rock surface can be sealed withshotcrete.For concrete gravity dams, the US Bureau ofReclamation provides the followingrecommendation for the required depth ofexcavation of steeply dipping, transverse (upstream-downstream aligned) discontinuities in thefoundations of concrete dams (Golze, 1977):

or(7.22a)

or

or(7.22b)

where d is the depth cleaning; b is the width offracture; and H is the height of dam above generalfoundation level.

7.5.3Rebound

Geological processes such as erosion, or excavationas part of the construction work, can result inrebound of the foundation. Rebound occurspredominantly in weak rock such as shales, and theopen discontinuities may be filled with weatheringproducts or river silt. Another cause of rebound ishigh horizontal stress in the rock that is relievedwhen the excavation for the foundation reduces thevertical stress. The effects of rebound can includedifferential movement of the structure, as well as

the creation of fractures in the foundation with lowshear strength and high permeability.The following are three examples of remedial workcarried out in the case of rebound. At the PeaceCanyon Project in British Columbia the workcomprised excavation and structural grouting(Lauga and Taylor, 1983), at the Garrison Dam inNorth Dakota periodic regrouting was performed(Lane, 1955), and at the Oahe Dam in South Dakotadeep rock anchors were installed and the damredesigned with increased articulation toaccommodate movement (Underwood et al., 1964).

7.5.4Solution cavities

Cavities may exist in the foundations of damsconstructed on soluble rocks such as limestone,gypsum, anhydrite, and calcium carbonate (Jamesand Kirkpatrick, 1980). Such cavities can causeexcessive leakage as occurred at the Keban inTurkey (Bosovic et al., 1981), or solution of thesematerials can result in failure such as is suspected tohave occurred at the Quail Creek reservoir in Utahwhere gypsum was found in the foundation (ENR,1989).Solution cavities can be sealed with cement grout orconcrete, provided that the exploration program hasadequately defined the extent of the cavities (seealso Section 5.3). For example, at the Keban Dam,the large size of the cavities required that they firstbe filled with rock, gravel, sand and clay beforeinjecting grout.The Zimapan Dam in Mexico was constructed inkarstic terrain and mapping carried out in a systemof tunnels driven into the abutments identifiednearly 2100 discontinuities, of which about 9%were open with an average width of about 500 mm(Fig. 7.20). The grouting procedure was first toclean clay infilling material from the solutioncavities, and then seal the outlet in the wall of thetunnel with a grout plug before filling the cavitywith grout using an injection hose. Following thiswork, additional grout holes were drilledsurrounding the karstic zone to treat the rock mass,

246 INTRODUCTION

and to create the grout curtain (Foyo et al., 1997).The design of the grout curtain was based on theprinciple of the grout intensity number GIN whichis defined as the product of the final grout pressure(bars) and the maximum cement absorption (litersper linear meter), or (Lombardi andDeere, 1993). For this project a GIN of 2000 barlm-1 was used which balanced the requirements togrout open discontinuities with low pressure, andfine discontinuities with high pressure whileavoiding the risk of hydrofracturing.

7.6Foundation rehabilitation

As increasing numbers of dams reach or exceedtheir design life, there is a corresponding need forinspections to identify deterioration, and then tocarry out required rehabilitation work, as well asupgrading to meet new operating and safetystandards. As an example of the scope of such

inspection and remediation programs, the CaliforniaDivision of Safety of Dams carried out anevaluation of the seismic stability of more than 1200 dams under their jurisdiction (Babbitt, 1993).It was found that there was a need for upgrading ofa total of 94 dams, of which eight required groutingand drainage of the foundation. Other types ofremediation ranged from increasing freeboard,buttressing of both concrete gravity andembankment dams, and in nine cases constructingreplacement dams.There will often be some uncertainty in thecondition of dams with ages of several decadesbecause, for example, the design and as-builtdrawings, as well as the maintenance records maybe missing or incomplete. Furthermore, a visualinspection of the dam, together with an examinationof the instrumentation records, if any, may notprovide much definitive information on thedistribution of water uplift pressures on the base ofthe dam, or weathering of rock in the foundation. In

Figure 7.20 Grouting procedures of Zimapan Dam: (a) layout of grouting tunnels in abutments and typical curtain groutholes; and (b) grouting of solution cavities intersected in tunnel (Foyo et al., 1997). 1. Access tunnel 2. Shaft 3.Diversion tunnel 4. Grout tunnel 5. Bedding 6. Karst feature 7. Grout hole 8. Grout curtain 9. Drain hole 10. Cementplug 11. Injection hose


order to quantify this uncertainty, prob abilisticmethods of analysis have been developed whichaddress both the stability mechanics and the degreeof uncertainty in the design parameters (ICOLD,1993). Section 1.6.4 discusses methods ofcalculating the probability distribution of the factorof safety of a structure from which the coefficient ofreliability can be calculated. This analysis may showfor example, that two structures have the samedeterministic factor of safety. However, if thestability of one is less certain as shown by a lowercoefficient of reliability CR then this would havethe higher priority for remedial work. A similarprocedure has been used to evaluate the stability ofconcrete gravity navigation structures, in which areliability index was calculated in order to ranktheir stability conditions (Wolff, 1993). It is alsoimportant that the safety of the dam with respect toboth its probability of failure and the consequence offailure meet the general standard of the industry.Figure 1.9 shows that dams are generally designedso that the annual probability of failure causingdamage is in the range, or better, of 10−4 for a loss oflife of 10, and 10−5 for loss of life of 100.The following are some examples of remedial workthat has been undertaken for dam foundations.

7.6.1Monitoring

The most common instrumentation that is installedin dam foundations are piezometers to measure thedistribution of water uplift pressures, andinstruments such as extensometers, inclinometersand tiltmeters to measure displacement. Animportant development regarding dam safety isautomation which allows readings to be taken atspecified intervals and the results transmitted to aremote location for interpretation and analysis(Myers and Marilley, 1997; Elliott, 1997). If areading exceeds a pre-determined threshold, thesystem controlling the instrumentation can bedesigned to set off alarms and increase thefrequency of the readings. Factors to consider in thedesign of automated monitoring systems include the

power availability (solar, power grid), distance ofmonitoring personnel from site (travel time to checkalarmed condition), site security (vandalism, wildanimal interference), natural hazards (snowavalanches, forest fires) and consequences of failure(facilities in downstream flood path).There are a number of manufacturers of automatedmonitoring systems and it is generallyrecommended that well-proven commercialinstrumentation be used rather than one-off customequipment. Instrumentation in dams is oftensubjected to a wide range of temperature andhumidity and even the best systems require ongoingmaintenance by experienced personnel in order toproduce reliable readings over a long time period. Ifthere is a tendency for the system to produce falsealarms, its credibility will be slowly eroded andthere is the danger that a real emergency will beignored.

7.6.2Grouting, sealing and drainage

Dams designed with a grouting/inspection gallery inthe lower part of the structure will allow a groutingprogram to be carried out during the operation ofthe dam in order to decrease the permeability or toimprove the rock modulus. However, drilling holesfrom the crest of the dam into a small target in thefoundation, which will require accurate drilling withclose control of deviation, may not be feasible,particularly in embankment dams with slopingcores.One of the difficulties in grouting a foundationunder full head conditions is that high gradients andflows in the rock may carry away the grout before ithas time to set, even if fast setting grout is used. Forexample, at the Stewartville Dam in Ontario,Canada which is founded on limestone containingmicaceous material it was necessary to carry outremedial work 1, 18, 20, 34 and 41 years after thereservoir was first filled. This work comprisedcement and cement-asphalt grouting, and placing anupstream low permeability blanket (Lo et al.,1991b). Similarly, at the Albigna Dam in

248 INTRODUCTION

Switzerland it was necessary to drain the reservoirin order to place a neoprene sheet on the foundationimmediately upstream of the structure to controlwater pressure induced movement (seeSection 7.3.2). If possible, it is preferable tolower the water in the reservoir to below the levelthat is being treated.Because grouting of the foundation of an existingdam is likely to reduce the effectiveness of thedrains, these should be re-drilled at the end of thegrouting operation.Monitoring of piezometers in the foundation, aswell as seepage rates, may also show that waterpressures in the foundation are rising tounacceptable levels indicating that the effectivenessof the drains is diminishing. Under thesecircumstances remedial work could include drillingnew holes from the drainage gallery, or cleaning theexisting holes with water jets or brushes.

7.6.3Anchoring

Permanent post-tensioned anchors have been usedin the United States since the 1970’s to help existingdams meet contemporary safety standards. Themost common usage of anchors has resulted fromdam safety re-analysis based on new criteria for thePMF (Peak Maximum Flood) and the MCE(Maximum Credible Earthquake) (Powell andPearson, 1993). Dams designed in the first half ofthis century generally do not meet the newstandards and owners are required by law to takeappropriate remedial action. Anchors have beenused in dam-raising operations where they haveproved more economical in resisting the increasedoverturning moments than placing additionalconcrete mass. Typical application of anchorsinclude resistance to overturning, sliding andearthquake forces (Bruce, 1993a).Details of anchor design and construction arediscussed in Chapter 9; particularly importantfeatures of anchors for dams are corrosionprotection of all components and a comprehensiveand well documented testing program.

A typical application of post-tensioned anchors is atthe Stewart Mountain in Arizona which is a thinarch concrete dam with a maximum height of 64.6m (212 ft) and a width varying from 10.4 m (34 ft)at the base to 2.4 m (8 ft) at the crest (Bianchi andBruce, 1993; Bruce et al., 1991). The damfoundation is a strong pre-Cambrian quartz dioritecut by irregular but strong granite dykes. Three-dimensional finite element stability analysis ofseismic loading conditions showed that there was aneed to improve the strength of the arch dambecause of the poor quality of the horizontalconstruction joints between concrete pours. Inaddition, it was necessary to install anchors tostabilize the left thrust block to prevent slidingfailure at or just below the structure/foundationcontact where the rock was fractured, sheared andweathered.The anchors installed in the concrete archcomprised a bundle of 22, 15.2 mm (0.6 in) diameterepoxy coated strands each with a design load of 2.8MN (630 kips) which was about 50% of theguaranteed ultimate tensile strength (GUTS). Thebond lengths varied from 9.1 to 14 m (30–46 ft) andthe free stressing length varied up to 67.7 m (222ft). A total of 62 tendons were installed at 2.4 m (8ft) centers along the crest of the dam in 254 mm (10in) diameter holes drilled with a down-the-holehammer (Fig. 7.21). Of particular importance forthe drilling was accurate hole alignment which wasachieved by first installing a carefully aligned 1.5 m(5 ft) long guide tube at the collar, and thenmeasuring the hole deviation at 3 m (10 ft)intervals.

7.6.4Scour protection

High velocity, turbulent flow such as occurs duringspillway operation can result in scour that canloosen and remove blocks from spillway chutes,tunnels and foundations, possibility resulting insteepening and eventually undermining of thestructures (Burgi and Eckley, 1987; Annandale etal., 1996a; Perlea et al., 1997). The susceptibility of


a foundation to scour can be estimated from acomparison between the erosive power of the waterand the resistance of the rock to scour, such that thethreshold of scour is when the erosive power justequals the scour resistance. As discussed below, theerosive power is a function of the water flowcharacteristics in plunge pools and spillway chutes,while the erosion resistance is a function of fourquantifiable properties of the rock mass. This matter is also discussed in Section 6.7.2regarding the scour of bridge piers.(a) Erosive power action of waterScour can result where water flow over irregularsurfaces is accompanied by eddies and turbulenceresulting in fluctuating pressures at the surface overwhich it is flowing. The action of these forces,together with the hydrostatic forces in the cracks,causes a tugging and pulling of the rock which canloosen and remove blocks from the surface overwhich the water is flowing. The erosive power ofwater per unit flow width P can be related to themagnitude of fluctuating pressures and the resultingrate of energy dissipation, or stream power, by thefollowing equation:

(7.23)where ?w is the unit weight of water; q is the unitdischarge and ?E is the energy loss (Annandale,1995).Examples of turbulent flow resulting in energydissipation are headcuts where a spillwaydischarges over a drop structure into a plunge pool,hydraulic jumps where flow undergoes an abruptchange in slope, where there are changes in bedslope causing separation of the flow from the bed,and open channel flow. In all four cases, theoreticalrelationships backed-up by experimental data, havebeen developed between the energy loss, and theflow characteristics and bed geometry. Details ofthese relationships, which are beyond the scope ofthis book, will depend on the particular conditions ateach site and should be verified by specialists in thefield of hydraulic engineering.(b) Scour resistance of rockIn order to quantify the susceptibility of rockmasses to scour, an erodibility index Kr has been

developed in which the relevant character of therock mass is calculated as the product of fourparameters (Annandale, 1995):

(7.24)This method of calculating the erodibility index is amodification of the Q-system for assessing sup portrequirements for tunnels that uses properties of therock mass that are readily measured in the field. Thefour properties of the rock mass that are used toassess its resistance to scour are the strength of theintact rock Ms, the mean block size as determined bythe joint spacing Kb, the shear strength of thediscontinuity surfaces Kd and the shape of theblocks and the dip of the discontinuity set relative tothe flow direction Js. Section 6.7.2 describes indetail the method of calculating Kr, and providestables relating properties of the rock mass to valuesfor these dimensionless parameters.(c) Stream power-scour resistance relationshipThe relationship between the scour resistance ofrock and soil materials and the energy dissipation ofwater flowing over a variety of hydraulic structureshas been determined empirically by studying fieldconditions. The results of 137 such observations areshown in Fig. 6.12 in which the sites where scourdid and did not occur are distinguished. The dashedline is the approximate threshold of scour for thisdata, and the relationship between the erodibilityindex Kr and the rate of energy dissipation per unitwidth of flow p (kW/m2) is:

(7.25)Equation 7.25 and the information presented inFig. 6.12 can be used as a guideline in assessing thesusceptibility of a facility to scour. Where there is arisk of scour, preventative measures includemodifying the designs to reduce turbulent flows toacceptable levels, or protecting the rock withreinforced concrete aprons or rip rap.

7.7Grouting and drainage

Grouting of dam foundations to reduce thepermeability of the rock, and sometimes to improve

250 INTRODUCTION

the modulus, is widely practised and for manystructures it is essential for both safety andeconomic performance. Grouting involves theinjection of liquids into discontinuities and voids inthe rock which then set to form a stable andresistant component of the rock mass. By suitablelocation of injection drill holes, injection pressures

and the properties of the injection fluid, it ispossible to form a continuous curtain, blanket orbulb of grouted rock and improve the properties ofthe rock mass by a desired amount. Figure 7.22shows an example of the use of grouted zones undera buttress dam (Jaoui et al., 1982), while Fig. 7.20shows a more extensive grouting operation of both

Figure 7.21 Section through arch of Stewart Mountain Dam showing typical multi-strand anchor installation (Bianchiand Bruce, 1993).

1. Full reservoir level. 2. Normal tailwater. 3. Arch section. 4. Silt. 5. Alluvium and fill. 6. Bedrock foundation. 7. 22Strand bundled tendon. 8. Bond length (9–14 m).


the foundation and the abutments.

7.7.1Grouting functions

Grouting can fulfill one or more of the followingfunctions, depending on the use of the dam and thegeological conditions of the foundation(Casagrande, 1961).(a) Consolidation groutingImprovement of the modulus of the rock will reducedeformation under load. Since the modulus of therock mass is highly dependent on the closure anddisplacement of discontinuities, filling these with astable grout will have a significant effect on themodulus (Kikuchi et al., 1995). Consolidationgrouting is most commonly used in the foundationof concrete dams, which are sensitive to differentialmovement. Consolidation grouting was carried outin the abutments of the Cabril arch dam in Portugalwhich was founded on strong, unaltered granite butwas experiencing deformation of the cantilevers.The grouting was successful in reducing themaximum deflection from 65 mm to 50 mm (2.6–2in), an improvement of nearly 25% (Serafim, 1964).(b) Permeability controlThis is used to reduce seepage quantities and upliftpressure. For rocks in which the intact rock isimpervious, seepage is concentrated in thediscontinuities and filling the discontinuities with astable grout will substantially reduce the rock masspermeability. This may involve the formation of acontinuous curtain over the full length of the damand into the abutments, and the curtain maycomprise a single row, or multiple rows of holes.(c) Uplift controlA low permeability grout curtain in combinationwith a line of drain holes downstream of the curtainwill significantly reduce uplift pressures in thefoundation. Reduced uplift pressures will im provethe factor of safety against sliding. Reference toFig. 7.5 shows the range of uplift water pressuresthat may exist depending on the efficiency of thegrout curtain and drain holes.(d) Erosion control

High pressure gradients and seepage velocities thatdevelop in dam foundations can erode low strength,unconsolidated infillings, as well as closelyfractured or weak rock at the base of the core. Thisis an unstable situation because as erosion occursthe seepage quantities and scour will increase, andeventually the integrity of the dam may bethreatened. Grouting for erosion control will requirethat the holes be carefully placed to intersect thediscontinuities that are of concern and to ensure thatthe consolidation of the infilling is as continuous aspossible.For grouting to fulfill these four functions, thereneeds to be:

1. complete filling of discontinuities and voids;2. high mechanical strength of the grout;3. good bond to rock;4. resistance of the grout to chemical leaching;5. predictability of the grouting process;6. limited travel of the grout to avoid losses.

The following is a general description of usualgrout practices that will produce the desired results.There are no standard grouting procedures becausefor each installation, procedures must be modifiedto suit the geological conditions at the site.

7.7.2Grout types

This discussion of grouting methods is mainlyconcerns cement-water grouts because these are thematerials most often used in rock foundations.However, a wide variety of other grouts areavailable for special applications. For example, hotasphalt has been used to seal solution cavities in thelimestone foundation of the Stewartville Dam inOntario under full head conditions in which the flowquantities were so high that cement grout could notbe retained long enough to set in the large cavities(Lukajic et al., 1985). Also, sealing of large cavitieswith high turbulent flows has been achieved usingorganic foams containing polyurethane (Cambefort,1977), and fine (0.05–0.1 mm wide) cracks have

252 INTRODUCTION

been sealed with silicate based grouts in thefoundation of a landfill containment facility whereacid leachate would have dissolved cement grout(Graf et al., 1985). It is likely that chemical groutswill become common in sealing containmentfacilities for hazardous wastes where leakagetolerances are very low and fine discontinuities haveto be sealed.The use of cement grout is not appropriate wherethe discontinuity width is less than about 0.25 mm,or three times the maximum particle size of thecement, otherwise rapid blinding of thediscontinuity occurs (Karol, 1986). Under theseconditions, it may be possible to use ultra-finecements together with a superplasticizer to keep the

cement particles dispersed and prevent theformation of flocs (Weaver, 1993). Alternatively,chemical grouts such as silicates, resins andacrylamides may be used; these grouts willpenetrate fine fractures, are resistant to acid attack,have fast set times, and will set without shrinkage.Their main disadvantage is high cost.

7.7.3Mechanism of grouting

When grout is pumped down a drill hole thatintersects a series of discontinuities, the extent towhich they are filled with grout will depend onphysical properties of the grout, namely the

Figure 7.22 Example of consolidation and curtain grouting installations in the foundation of a buttress dam (Jaoui etal., 1982).

1. Consolidation grouting. 2. Grout curtain. 3. Drain holes. 4. Grouting and drainage gallery.


cohesion (or yield point of visco-plastic fluid) andviscosity of the grout mix. Viscosity determines therate at which grout flows from a hole under a givenpressure (the time required to fill the fracture), andcohesion determines how far the grout will traveland limits the extent of the grouted zone (Deere andLombardi, 1985). These two properties have to bebalanced to produce the properties most suitable tothe site conditions. For example, when grouting finefractures, a low cohesion grout (with high watercontent) will flow a considerable distance from thehole, but the grout may be discontinuous and of lowstrength, and form an ineffective seepage barrier.Once a cement grout has been pumped into a crackit should form a solid that entirely fills the spacewith no shrinkage. However, while the chemicalaction of cement hydration requires a water:cementratio of 0.45:1 by volume (or 0.3:1 by weight), waterin excess of this is required for making the groutworkable and transporting and placing it. Some ofthis excess water will be retained in the set grout,but much of it must be removed as the grout sets.This process is known as bleeding. It takes place asthe movement of the grout in a crack slows so thatthe cement particles settle and water collects abovethe surface of the cement. Unless this bleed watercan be removed and replaced with more cement, aneffective seal will not be formed. Figure 7.23 showsthree stages of grout penetration in a horizontalcrack. At the start of grouting (a), the grout travelsfrom the hole freely along the open crack under thepressure from the grout hole. As the pressure in thegrout builds up, the limit of penetration is reachedand there is no further motion of the grout (b). Atthis time, bleed starts in a lateral direction, becausebleeding in a vertical direction is limited, to form adiscontinuous grout filling (c). The diagramdemonstrates that vertical fractures, in which thebleed water can rise to the surface, can be morereadily grouted than horizontal fractures (Houlsby,1985).The extent to which grouts bleed is related to thewater:cement (w:c) ratio of the placement mix. At aw:c ratio of 2:1 (by volume) which is commonlyused in grouting operations, after a period of about

one hour 35% of the volume is filled with water,with only 65% of the fracture containing grout. Formuch thinner mixes with w:c ratios of 12:1,bleeding takes place within 15 minutes and thebleed water volume occupies about 85% of thevolume of the fracture. In order to minimizesettlement of the cement, bentonite is often added tothe mix in the proportion of 2–4% bentonite byweight of cement (see Section 7.7.6).

7.7.4Drilling method

Grout holes can be drilled by either percussion ordiamond methods. Percussion drilling is faster andcheaper than rotary drilling and producessatisfactory results as long as precautions are takenthat the holes are parallel so that there are no gaps inthe curtain caused by excessive hole deviation. Ifthe length of the holes exceeds about 8–10 m (26–33 ft) it is recommended that the orientation of theholes be measured and if deviation is excessive,modified drilling methods could be used.The advantages of diamond drilling are thatfractures in the core can be examined which can beuseful in the planning of grouting operations, and acleaner and straighter hole is obtained. It is usualthat a minimum of 10% of grout holes are diamonddrilled to obtain geological information. Holediameters have little effect on the results of groutingand they are usually in the range 40– 50 mm (1.5–2in).It is most important that the walls of the drill holesare thoroughly cleaned of drill cuttings that blockfractures intersected in the walls and would preventgrout penetration. It has been found that water issignificantly better than air in cleaning cuttings fromdrill holes, so water circulation is preferable to aircirculation for removing cuttings. Also, if the holeintersects a fracture into which the circulation wateris lost, the drilling should be stopped as soon aspossible to minimize the risk of the fracturebecoming clogged with cuttings. Grouting wouldthen be carried out to seal the fracture beforerecommencing drilling (Weaver, 1991).

254 INTRODUCTION

Additional information on drilling methods isdiscussed in Sections 4.3 and 10.2.

7.7.5Hole patterns

The two categories of grouting to seal seepage,namely blanket and curtain grouting, requiredifferent patterns of holes which depend on thegeometry of the dam, the geology of the foundationand the degree of water tightness that must beachieved. Figure 7.24 shows the arrangement ofdrill holes for blanket and curtain grouting used toseal the fractured and faulted sandstones, siltstones,mudstones and shales in the foundation of theWimbleball Dam in the UK. In total, the blanketand curtain grouting involved almost 94 000 m (310000 ft) of drilling and the injection of 3500 t ofgrout (Bruce and George, 1982).For both curtain and blanket grouting, the firstrequirement of laying out grout holes is that they beoriented to intersect the main water bearingdiscontinuity set(s) in the foundation. For example,if there is a set of persistent, steeply dippingdiscontinuities aligned at right angles to the damaxis, the grout holes would be drilled at a dip ofabout 60° to 70° and a trend parallel to the dam axis.Vertical grout holes would be appropriate for sets ofhorizontal discontinuities in the foundation. (a) Blanket groutingThe rock immediately under the dam may be morepermeable than the rock at depth as the result ofblasting damage during surface preparation, andstress relief causing opening of discontinuities. Thisis also the area where high hydraulic gradients aredeveloped, so particular attention is required tosealing this region of the foundation. Forembankment dams, blanket grouting consists ofdrilling holes on a square pattern to cover the entirearea of the core so that the combination of the blanketand curtain grouting form a ‘T’ under the dam(Sherard et al., 1963). This minimizes the risk ofseepage paths being developed over the top of thegrout curtain which can result in scour of the corematerial.

(b) Curtain groutingIn theory, the effectiveness of a grout curtain inreducing uplift pressures is improved if it is inclinedat about 15° upstream so that the seepage path islengthened compared with a vertical curtain.However, this does require more careful control ofdrill hole alignment to ensure that the holes areparallel and lie in the same plane.The following is a general plan for laying outcurtain grout holes, the details of which woulddepend on the geological condition and degree ofwater tightness needed (Deere, 1976).

1. Drill exploration holes using coring equipmentto a depth equal to the full head H on about 30m (100 ft) spacing. The core will provideinformation on the general geology of thefoundation from which the details of thegrouting plan can be drawn up. Conductpermeability measurements to assess thegrouting requirements and methods.

2. Drill primary grout holes to a depth of H/2 to2H/3; hole spacings may range from 3–20 m(10–65 ft).

3. Drill secondary grout holes on split spacing sothere is progressive closure of the curtain.These holes may be drilled to a shallower depththan the primary holes if the rock becomestighter with depth.

4. If additional grouting is needed, tertiary andpossibly quartenary holes are drilled on splitspacings (Bruce and George, 1982).Alternatively, a second row of grout holes isdrilled at a distance of about 2m (6 ft)downstream following the same layout as theprimary and secondary holes.

Close spacing will be required in low permeabilityrock because the grout will penetrate a shorterdistance in the narrow fractures. Generally, thewider fractures are grouted with the primary andsecondary holes, while the finer fractures aregrouted with the tertiary holes. The final spacing ofthe grout holes will depend on the permeabilitycriterion established for the foundation, and the


development of a continuous curtain or blanket. Thegrouting operation is evaluated by conductingvariable head tests in open holes to measure thepermeability of the rock mass (see Section 4.4.2), ormonitoring grout takes. Selection of an acceptablepermeability criterion for the foundation depends onboth the value of the water lost by leakage, as wellas the type of dam (see Fig. 7.26 andSection 7.7.10). As shown in the proceduredescribed in the previous paragraphs, the generalapproach to effective grouting is to drill holes at aprogressively closer spacing, or to drill multiplerows of holes, until the permeability criterion is

achieved.

7.7.6Grout mixes

Where cement grouts are used, the possible mixesthat can be used range from 1:1 to as high as 10:1(water:cement ratio). The low-ratio, thick grouts areused to fill wide fractures and voids, while very thin,high ratio grouts have been used when sealing finefractures where there is concern regarding thepenetration of thicker grouts.The use of thick grouts to seal tight fractures will

Figure 7.23 Grout penetration of horizontal fractures: ph is the pressure in the grout hole; d is the distance along crack(Houlsby, 1985): (a) start of grouting; (b) grout reaches limit of penetration for the particular pressure and water:cementratio used; and (c) grout stiffens, radius of pressure transmission contracts and bleed pockets develop.

256 INTRODUCTION

result in little penetration into the rock surroundingthe hole because of the high cohesion of the mix.However, it is likely that the grout that doespenetrate the fracture will be of good quality, so apattern of closely spaced holes would be required toseal a tight rock mass effectively. Conversely, lowcohesion, high w:c ratio grouts will penetrategreater distances in tight fractures, but a continuousseal may not be formed. As discussed inSection 7.7.3, thin grouts have a high proportion ofexcess water when they set and so much of thevolume filled by the mix will consist of water whichmust be bled off to form a tight seal. Both Deereand Houlsby (1982) recommend the use of thicker,‘stable’ mixes in which there is minimal settling ofthe cement grains. Houlsby’s criteria for groutmixes are as follows. A starter mix is selected based on previousexperience, permeability tests and information onfracture width and orientation. Once grouting hasstarted, successively thicker mixes may be useddepending on how well the hole has accepted thegrout.At most sites, a ratio of 2:1 w:c ratio (by volume) issuitable for a starter mix, except in the followingcases:

• For fractures with widths of 0.75 mm (0.03 in) orfiner, start with a mix of 3:1.

• For fractures with widths of 1.2–2.5 mm (0.5– 0.1 in), start with a mix of 1:1.

Note, equivalent water:cement (w:c) ratios are:

• (2:1) by volume=(1.3:1) by weight;• (1:1.5) by volume=(1:1) by weight; and• (1:1) by volume=(0.67:1) by weight.

Bentonite is often used in cement grouts to reducethe sedimentation of the cement particles so thatthere is less tendency for fractures to be partiallyfilled with poor quality grout. The proportion ofbentonite added to the mix is usually in the range of2–4% of the weight of cement. It has also beenfound that the main effect of bentonite is to increase

the cohesion which limits the penetration distance.However, the use of fluidizers such as Intraplast(Sika) enhances the penetration of grout into finefractures without the w:c ratio having to beincreased (Deere and Lombardi, 1985).

7.7.7Grout strength

It is considered that a minimum strength of about 9MPa (1300 p.s.i.) is required for grout to be able toresist high hydraulic gradients without scour orpiping (Deere, 1982). This strength range isapproximately equivalent to that of weak concrete.It is likely that this minimum strength will also berequired for consolidation grouting where the groutis being employed to improve the modulus of therock mass.While bentonite is used to reduce the sedimentationof cement grouts, it has the disadvantage that it willreduce the strength of the grout. Laboratory studiesof grout strengths show that for thin mixes at a w:cratio of about 6:1 by volume, the bentonite loweredthe strength by about 50–75% , while for thickermixes at a w:c ratio of about 2:1, the strength wasreduced by about 25% (Burgin, 1979). Sampleswith a w:c ratio of 1.5:1 gave 28 day strengths ofabout 9 MPa (1300 p.s.i.), at bentonite contents ofbetween 2% and 8% . At this w:c ratio there waslittle influence of the bentonite content on the groutstrength.

7.7.8Grout pressures

Pressures used for grouting should be sufficient toinject grout into the fractures in the foundationrock, and achieve some radial penetration. Thispressure should be less than that required to fracturethe rock because it is not desirable to create newfractures that may not then be completely fil ledwith grout. One of the factors that determines thequantity of grout take is the pressure drop in thegrout along the fracture. Once this pressure dropequals the applied pressure in the hole, there will be


no further take and grouting is halted becauseprogressively increasing the pressure to inducefurther grout take may force open fractures in therock. In tight rock it is unnecessary to maintain thepressure while the grout sets because the grout willnot flow out of the fracture once it has been injectedto refusal. However, if open voids are being groutedthe pressure should be maintained until the grouthas taken its initial set.

A chart relating grout pressure to depth below theground surface and the strength of rock is given inFig. 7.25 (Houlsby, 1977a). This chart shows thatpressures as great as two or three times theoverburden pressure can be used in strong rock(lines 3 and 4 on Fig. 7.25). However, groutpressures should be less than the overburdenpressure in very weak and fractured rock tominimize the development of new fractures, and in

Figure 7.24 Arrangement of blanket and curtain grouting for buttress dam (Bruce and George, 1982): (a) plan andelevation along line of grout curtain; and (b) section through typical buttress showing relative location of blanket andcurtain grouting, and pressure relief wells.

258 INTRODUCTION

horizontally bedded rock where the grout couldcause heaving at the surface. It is possible to applysufficient pressure to open fractures and increase thedistance of grout penetration without causinghydrofracturing of the rock. This approach is basedon the ‘rule of thumb’ that the maximum pressure isequal to one bar per meter of depth (line 1 inFig. 7.25), and has been used successfully ingrouting strong rock. A more conservative approachwith respect to prevention of hydrofracturing is touse a maximum pressure of one p.s.i. per foot ofdepth (line 5 in Fig. 7.25) which may limit the groutpenetration (Weaver, 1993).Another factor to consider in determining groutpressures is increasing pressure with each stage ofgrouting. Deere and Lombardi (1985) suggest thatthe pressures p used in each stage of grouting couldbe as follows, depending on site conditions:

1. primary: p;2. secondary: 1.5p;3. tertiary: 2p;4. quartenary: 2.5p.

7.7.9Grouting procedures

Grouting is usually carried out in stages usinginflatable or expansion packers to isolate sections ofthe hole. This procedure ensures that the full lengthof the hole is grouted and avoids the situation thatmay develop if the full length of the hole were to begrouted in one operation, where most of the grout ispumped into one open fracture and no grout isinjected into the tighter fractures. The length of holethat is grouted in any stage is determined bypositioning the packer so that individual fracturescan be grouted as desired. Grouting lengths varyfrom as short as 3m (10 ft) to as long as 10 m (33ft), with shorter lengths being used closer to therock surface and in more fractured rock.The grout is injected into the hole at thepredetermined pressure and grouting is continueduntil there is ‘refusal’ in grout take. That is,grouting should not be stopped until there has been

no measurable take over a five to ten minute periodso that the grout that has been injected into thefracture has been packed tight. This procedure willpromote and maintain the full penetration of thegrout, particularly if the applied pressure has beensufficient to open the fractures, which may not bethe case if the pressure was cut off while the holewas still taking grout.Grouting can either be carried out from the topdown, or the bottom up depending on the conditionof the rock. In poor rock where the drill holes willnot stay open, grouting is carried out from the topwhich requires that the hole be progressivelydeepened with each stage of grouting. A packer isused to isolate each section of the hole so thathigher pressures can be used at depth withoutfracturing the near-surface rock. The disadvantageof this procedure is that the drilling costs are highbecause the drill rods have to be removed and thegrout tubes and packers lowered into the hole foreach section of grouting. The advantage is that thegrouting can be stopped if the rockpermeability increases with depth to a value lessthan the minimum required value. In good qualityrock, the grout hole can be drilled to full depth andthen grouted from the bottom up using packers toisolate successive sections of the hole (Bruce,1993b).

7.7.10Permeability criteria for grouted rock

When planning a grouting program it is important todetermine the level of permeability that is requiredto suit both the function of the dam, and its safeoperation. For example, where the function of thedam is flood control, seepage through thefoundation is acceptable as long as it does notcompromise the safety of the structure due to scouror piping of loose discontinuity infillings. Wherethere is a significant economic value to the waterstored in the reservoir, and particularly where wateris pumped into the reservoir, seepage losses aremuch less acceptable. The permeability of the rockmass after grouting can be measured either by


conducting variable head tests in test holes andcalculating the permeability (Section 4.4.2), or bymonitoring the grout take expressed in weight ofcement per unit length of hole.Permeability criteria, as suggested by Houlsby(1977a), for grout curtains in the foundations of avariety of dam types are shown in Fig. 7.26.Permeability values can be expressed in units ofboth lugeons and m/s, assuming 1 lugeon isequivalent to 1.3×10−7 m/s. Lugeon values varyfrom less than 1 for rock with occasional tightfractures, to as much as 100 for rock containingfractures with widths up to approximately 6 mm (0.25 in). Details of field test methods to measure

permeability are provided in Section 4.4. As shownin Fig. 7.25, the permeability criteria range from 1lugeon where seepage must be minimized, to ashigh as 5 to 7 lugeons where seepage is permittedand the foundation comprises sound rock in whichthere is no risk of piping.The original lugeon test was conducted at a pressureof 10 bar (150 p.s.i.) and 1 lugeon equals a watertake of 1 liter/m length of hole/minute (Houslby,1977b). This pressure level is now considered to betoo high because fracturing of the rock may occur atthese pressures. For tests conducted at lowerpressures, a modified lugeon value can be calculatedby multiplying the measured water take by the ratio:

1. One bar per meter depth2. pB=4D3. pB=3D4. pB=2D5. One p.s.i per foot depth6. pB=1.5D7. pB=1DpB=is the pressure at the bottom of the stage

Figure 7.25 Typical permissible grout pressures for various foundation condition (after Houlsby, 1977a).

260 INTRODUCTION

10 bar/Test pressure.An alternative permeability criterion is based ongrout take expressed in weight of cement take perunit length of drill hole. Deere (1976) suggests thatgrout take should be no more than 12.5– 25 kg/m(8–16 lb/ft) to achieve adequate sealing of highdams. The advantage of using grout take as thepermeability criterion is that the effectiveness of thegrout seal can be determined during groutingoperations with no need to perform additional tests.However, the disadvantage is that the grout takedepends to some degree on injection pressures andmix ratios, and more closely controlled permeabilitymeasurements can be made using permeability testsemploying water.

7.7.11Monitoring grouting operations

The installation of an efficient grout curtaindepends to a large degree on precise control andmonitoring of the grouting process. Precise controlof the grout mix and injection pressure will allow,for example, the water:cement ratio and pressure tobe decreased if a wide fracture is encountered inwhich take would be excessive at high injectionpressure and water:cement ratio. Similarly, accuraterecords of grout take, preferably plottedgraphically, provide information that can be used toevaluate the grouting program and determine whereextra holes are required to produce an effective seal.Equipment is now available to control and monitorautomatically the following functions of groutingoperations in up to six holes simultaneously(Demming et al., 1985):

1. cement weight per hour;2. pressure;3. flow;4. flow/pressure; 5. total bag rate for the hole;6. water take in volume per minute during water

pressure test.

Water:cement ratios can be keyed into the

computer, and nuclear densometers and magneticflow meters on the line monitor actual densities andquantities allowing close control of the groutingoperation. The system also has the capability togenerate reports showing, in the form ofhistograms, results of all the units listed above. Thecontrol and monitoring equipment, together with themixers and pumps, is contained in a steel shippingcontainer that can readily be moved around the site.In many installations, the pumping equipment is onthe surface and the grouting operation is in a tunnelor gallery deep in the foundation with a telephonefor communication.

7.7.12Leaching

Because grouts are subject to chemical leaching,their long term stability must be considered indesign, and their performance monitored duringoperations. Leaching corrosion of cement grout iscaused by the dissolution and removal of hardenedcement compounds by seepage water (Petrovsky,1982). The main component of hydrated cement islime (CaO) which can comprise 60– 65% of thetotal cement volume in the form of free calciumhydroxide (Ca(OH)2) and hydrated calciumcompounds such as silicates, aluminates andalumino-ferrites. These hydrated compounds remainstable in the calcium hydroxide solution atconcentrations of about 1300 mg CaO/l and a pH of12.0. Leaching of calcium hydroxide isaccompanied by the hydrolysis of the hydratedcement compounds and the release of lime to theseepage water. The reduction of CaO content in thecement grout leads to gradual decomposition of thecement binder and deterioration of the grout. Theremoval of 25% of the lime from the grout canreduce its strength by as much as 50%.In permeable cement grout, there are three stages ofleaching as follows.

1. First, the rapid dissolution of the free calciumhydroxide. This occurs at the onset of theleaching process and the concentration of


calcium in the seepage water is at its highestpoint.

2. Second, lime is liberated from the hydratedcalcium compounds by the hydrolytic action of

the seepage water, and the calciumconcentration in the seepage water diminishes.

3. Third, the calcium hydroxide and the hydratedcompounds are dissolved from the deeper

Figure 7.26 Suggested permeability criteria for rock foundations (after Houlsby, 1977a).

262 INTRODUCTION

zones in the grout. During this leaching stage,the concentration of the calcium in the seepagewater is low and remains relatively constant.

Petrovsky describes a nine year monitoring programof grout curtains on three concrete gravity dams inRussia. By measuring the calcium content of thewater flowing in the drain holes it was possible tocalculate the weight of calcium lost from thecurtains. The gradients of the grout loss lines inFig. 7.27 show that the rate of loss was significantlyhigher at dam 2 which was 4 years old, than indams 1 and 3 which were between 12 and 16 yearsold. This indicates that the leaching rate decreaseswith time, and that leaching process was in thesecondary stage (as defined in the previousparagraphs) at dam 2, while it was in the tertiarystage at dams 1 and 3. While it was considered thatthe rate of loss was not significant when comparedwith the quantity of grout in the curtains, if theleaching were to be concentrated in a few high flowzones, the grout curtain could be weakened at thesepoints.

In any foundation where a grout curtain is installedto control seepage and/or uplift, it is important thatthe performance of the curtain is monitored bymeasuring seepage volumes in the drainage system,and by installing piezometers to measure waterpressures in the foundation. If increases in upliftpressures and seepage quantities can be attributed todeterioration in the grout curtain, then additionalgrouting can readily be carried out if there aregalleries in the foundation or base of the dam.

7.7.13Drainage

When grout curtains are installed in damfoundations, they usually incorporate drains holeslocated downstream of the curtain. The functions ofthese holes are to provide a low pressure outlet forseepage water, and to provide a monitoring point ofpressures and seepage quantities in the foundation.Pressures can be measured by fitting pressuregauges to pipes sealed into the collars of the holes,and seepage quantities can be monitored by V-notch

Figure 7.27 Leaching intensity for dam grout curtains (Petrovsky, 1982).

Dam 1:36 m high, 513 m long; 6 m deep grout curtain with holes on 1.5 m centres. Total grout take=51 tonnes.

Dam 2:124 m high, 1072 m long; 60 m deep grout curtain with holes on 3–5 m centers. Total grout take=2500 tonnes.

Dam 3:65 m high, 391 m long; 40 m deep grout curtain with holes on 0.5–1.4 m centers. Total grout take= 12 000tonnes.


weirs at the discharge point in the gallery.Drain holes are, of course, drilled after grouting iscomplete to minimize the risk of filling the holeswith grout, and are oriented such that they inter sectthe water bearing discontinuities. The holes may bealigned either vertically, or dipping downstream sothat they are not drilled into the grout curtain. Thedrain hole diameter should be a minimum of about75 mm (3 in) and the spacing of may be in the range1.5–5 m (5–16 ft), with narrower spacing beingused in rock containing impersistent discontinuities.As a general rule, hole depths vary from 20 to 40%of the water head, and from 35 to 70% of the groutcurtain depth (Golze, 1977). Another factor thatmay be considered in planning the location of thedrain holes, particularly for arch dams, is that thecompressive stresses induced in the foundation bythe weight of the dam may close discontinuities andreduce permeability resulting in the development ofincreased uplift pressures towards the downstreamtoe of the dam. Under these conditions the drainholes may be inclined upstream but should notintersect open discontinuities at the upstream toewhere the water thrust on the dam may producetensile stresses in the rock (ICOLD, 1993).The drain holes may be uncased in sound rock, orcased with perforated plastic casing in fracturedrock. The casing will keep the hole open andcontrol loosening of the rock in the walls of thehole. Provision should also be made for cleaning orredrilling holes in the event they become blocked bybacterial growth, for example.7.8 ReferencesAbrahao, R.A., Silveira, J.F. and de Barros, F.P. (1983)

Itaipu main dam foundations: design and performanceduring construction and preliminary filling of thereservoir. 5th Int. Cong. on Rock Mech., Melbourne,ISRM, pp. C191–7.

Annandale, G.W. (1995) Erodibility. J. HydraulicResearch, 33(4), 471–93.

Annandale, G.W., Abt, S.R., Ruff, J. and Wittler, R.(1996a) Scour damage. The Military Engineer, Soc. ofAmerican Military Eng., 88(580), 34–5.

Alonso, E.E. and Carol, I. (1985) Foundation analysis ofan arch dam. Comparison of two modelling techniques:no tension and jointed rock material. Rock Mech. and

Rock Eng., 18(3), 187–204.Babbitt, D.H. (1993) Improving seismic safety of dams in

California. Proc. Specialty Conf. onGeotechnical Practice in Dam Rehabilitation, ASCEGeotech. Special Pub. No. 35, Raleigh, NC,pp. 365–72.

Bianchi, R.H. and Bruce, D.A. (1993) Use ofposttensioned anchorages on the arch portion of theStewart Mountain Dam, Arizona. Proc. Specialty Conf.on Geotechnical Practice in Dam Rehabilitation,ASCE Geotech. Special Pub. No. 35, Raleigh, NC,pp. 791–802.

Bieniawski, Z.T. and Orr, C.M. (1976) Rapid siteappraisal for dam foundations by the geomechanicsclassification. ICOLD, Trans. 12th Int. Congress onLarge Dams, Mexico, Vol. II, Q46, R32, ICOLD(www.icold-cigb.org.1) pp. 483–500.

Bosovic, A., Badanur, H., Nonveiller, E. and Pavlin, B.(1981) The Keban Dam foundation on karstifiedlimestone. Bull. Int. Assoc. of Eng. Geol., 24, 45–51.

Bruce, D.A. (1993a) Stabilization of concrete dams bypost-tensioned rock anchorages: the state of Americanpractice. Proc. Specialty Conf. on GeotechnicalPractice in Dam Rehabilitation, ASCE Geotech.Special Pub. No. 35, Raleigh, NC, pp. 320–32.

Bruce, D.A. (1993b) Review of drilling and groutingmethods of existing embankment dams. Proc. SpecialtyConf. on Geotechnical Practice in Dam Rehabilitation,ASCE Geotech. Special Pub. No. 35, Raleigh, NC,pp. 803–19.

Bruce, D.A., Fiedler, W.R. and Triplett, R.E. (1991)Anchors in the desert. Civil Engineering, 61(12),40–43.

Bruce, D.A. and George, C.R. F. (1982) Rock grouting atWimbleball Dam. Geotechnique, 32(4), 323–48.

Burgi, P.H. and Eckley, M.S. (1987) Repairs at GlenCanyon Dam. Concrete International, March, 24–31.

Burgin, C.R. (1979) Investigations of the PhysicalProperties of Cement-bentonite Grouts forImprovement of Dam Foundations. Thesis, Universityof Florida, partial requirement for MSc degree.

Cambefort, H. (1977) The principles and applications ofgrouting. Q. J. Eng. Geol., 10, 57–95.

Carol, I. and Alonso, E.E., (1985) A new joint elementfor the analysis of fractured rock. Proc. 5th Int. Cong.on Rock Mech., Melbourne, ISRM, pp. F147–51.

Carrere, A., Nury, C. and Pouyet, P. (1987) Thecontribution of a non-linear, three dimensional finiteelement model to the evaluation of the appropriateness

264 INTRODUCTION

of a geologically complex foundation for a 220 m higharch dam in Longton, China (in French). Proc. 6th Int.Cong. Rock Mech., Montreal, ISRM, pp. 305–311.

Casagrande, A. (1961) Control of seepage throughfoundations and abutments of dams. Geotechnique, XI,161–182.

Cheng, Y. (1987) New development in seam treatment ofFeitsui Arch Dam foundation, Taiwan. Proc. 6th Int.Cong. Rock Mech., Montreal, ISRM, pp. 319–326.

Chopra, A.K. (1978) Earthquake resistant designs ofconcrete gravity dams. J. Structural Div. ASCE, 104(ST6), 953–971.

Chopra, A.K. and Chakrabati, P. (1973) The KonyaEarthquake and the damage to Konya Dam. Bull. of theSeismological Soc. of Amer., 63(2), 381–97.

Crawford, A.M. and Curran, J.H. (1982) The influence ofrate- and displacement-dependent shear resistance ofrock slopes to seismic loads. Int. J. Rock Mech. Min.Sci. & Geomech. Abstr., 19, 1–8.

Deere, D.U. (1976) Dams on rock foundations—somedesign questions. Specialty Conf. on Rock Eng. forFoundations and Slopes, Boulder, CO, ASCE,Geotechnical Eng. Div., Vol. 2, pp. 55–86.

Deere, D.U. (1982) Cement-bentonite grouting for dams.Grouting in Geotechnical Engineering, Proc. of Conf.sponsored by Geotechnical Eng. Div., ASCE, NewOrleans, pp. 279–300.

Deere, D.U. and Lombardi, G. (1985) Grout slurries thickor thin? Proc. of Session ‘Issues in Dam Grouting’,Denver, Colorado, ASCE, Geotechnical Eng. Div.,pp. 156–164.

Demming, M., Rogers, J.L. and Tula, A. (1985)Computer applications in grouting. Proc. of SessionIssues in Dam Grouting, Denver, Colorado, ASCE,Geotechnical Eng. Div., pp. 123–131.

Egger, P. and Spang, K. (1987) Stability investigationsfor ground improvement by rock bolts at a large dam.Proc. 6th Int. Cong. Rock Mech., Montreal, ISRM,pp. 349–354.

Elliott, J.F. (1997) Monitoring pre-stressed structures.Civil Engineering, ASCE, New York, July, 61–3.

Engineering News Record (1988) Brakes put on slippingspillway. ENR, June, 24–6.

Engineering News Record (1989) Foundation problemsare blamed for reservoir embankment failure. ENR,January, 10–11.

Fenves, G. and Chopra, A.K. (1984) EAGD-84: AComputer Program for Earthquake Analysis ofConcrete Gravity Dams. Report No. UCB/EERC-84/

11, Earthquake Engineering Research Center,University of California, Berkeley, CA.

Fenves, G. and Chopra, A.K. (1987) Simplifiedearthquake analysis of concrete dams. ASCE, J.Structural Eng., 113(8), 1688–708.

Fok, K.L., Hall, J.F. and Chopra, A.K. (1986)EACD-3D: A Computer Program for ThreeDimensional Earthquake Analysis of ConcreteDams. Report No. UCB/EERC-86/09, EarthquakeEngi neering Research Center, University ofCalifornia, Berkeley, CA.Forster, J.W. (1986) Geological problems overcome at

Revelstoke. Water Power and Dam Construction, July,53–8, August, 42–5.

Foyo, A., Tomillo, C., Maycotte, J.I. and Willis, P. (1997)Geological features, permeability and groutabiltycharacteristics of the Zimapan Dam foundation,Hidalgo State, Mexico. Engineering Geology, 46,157–74.

Franklin, A.G. and Chang, F.K. (1977) EarthquakeResistance of Earth and Rock-fill Dams. Report 5:Permanent Displacement of Earth Embankments byNewmark Sliding Block Analysis. US Army EngineerWaterways Experiment Station, Vicksburg, Miss.,Miscellaneous Paper S-71–17.

Fu, B.-J., Zhu, Z.-J. and Li, G.-Z. (1983) Analyticalexperience on the stability of the high dam foundationof the Liu-Jia-Xia hydropower station. 5th Int. Cong.on Rock Mech., Melbourne, ISRM, pp. C199–203.

Gavard, M. and Gilg, B. (1983) Stability analysis of theexcavation of the Karakaya arch dam and power plant.5th Int. Cong. on Rock Mech., Melbourne, ISRM,pp. C219–25.

Golze, A.R. (1977) Handbook of Dam Engineering. VanNostrand Reinhold, New York.

Goodman, R.E. and Seed, H.B. (1966) Earthquakeinduced displacements of sand embankments. ASCE,92, SM2, 125–46.

Graf, E.D., Rhoades, D.J. and Faught, K.L. (1985)Chemical grout curtains at Ox Mountain dams. Proc. ofSession Issues in Dam Grouting, Denver, Colorado,ASCE, Geotechnical Eng. Div., pp. 92–9.

Hibbitt, Karlsson and Sorensen, Inc. (1987) ABAQUSThree Dimensional Finite Element Analysis.Providence, Rhode Island.

Hoek, E. (1986) Personnel communication.Hoek, E. and Londe, P. (1974) Surface workings in rock.

Proc. 3rd Int. Cong. on Rock Mech., Denver, ISRM,Vol. 2, pp. 613–54.


Houlsby, A.C. (1977a) Engineering of grout curtains tostandards. ASCE, Geotech. Div., 103(GT9),pp. 953–71.

Houlsby, A.C. (1977b) Routine interpretation of thelugeon water-test. Q. J. Eng. Geol., 9, 303–13.

Houslby, A.C. (1982) Optimum water:cement ratios forrock grouting. Grouting in Geotechnical Engineering,Proc. of Conf. sponsored by the GeotechnicalEngineering Division, ASCE, New Orleans,pp. 317–31.

Houlsby, A.C. (1985) Cement grouting: water minimizingpractices. Proc. of Session on Issues in Dam Grouting,Denver, Colorado, ASCE, Geotechnical Eng. Div.,pp. 34–75.

Housner, G.W. (1970) Seismic events at Konya Dam,rock mechanics theory and practice. Proc. 11th Symp.on Rock Mech. American Institute of Mining,Metallurgical and Petroleum Engineers, New York.

Humphries, R.W. (1987) Filter design, foundationtreatment and hydraulic fracturing of dams founded onrock. Proc. South-east States GeotechnicalConference, Nashville, TN.

ICOLD (1979) Deterioration cases collected and theirpreliminary assessment. Trans. ICOLD, 1, 2.

ICOLD (1993) Rock foundations for dams. ICOLDBulletin, 88, Paris.

ICOLD (1995) Dam failures statistical analysis.International Commission on Large Dams (ICOLD),Bulletin 99, Paris.

Itasca Consulting Group (1996) Universal DistinctElement Code (UDEC), Version 3.0. Minneapolis,Minnesota.

Jaeger, C. (1963) The Malpasset Report. Water Power, 15(2), 55–61.

James, A.N. and Kirkpatrick, I.M. (1980) Design offoundations of dams containing soluble rocks and soils.Q. J. Eng. Geol., 13, 189–98.

Jansen, R.B. (1988) Advanced Dam Engineering forDesign, Construction, and Rehabilitation. VanNostrand Reinhold, New York.

Jaoui, A., Islah, M., Garnier, G., Gavard, M. and Gilg, B.(1982) The Tamzaourt-Dam, a buttress dam withparticular foundation problems. 14th Cong. on LargeDams, Rio de Janiero, ICOLD, Vol. II, Q53, R3,pp. 37–48.

Jennings, P.C. (Ed.) (1971) Engineering Features of theSan Fernando Earthquake. California Institute ofTechnology, Pasadena, California.

Jibson, R.W., Harp, E.L. and Michael, J.A. (1998) A

Method for Producing Digital Probabilistic SeismicLandslide Hazard Maps: An Example from the LosAngeles, California, Area. US Geological Survey,Denver, Open-File Report 98–113, pp. 17.

Kaloustian, E.S. (1984) Statistical analysis of distributionof concrete dam foundation failures. Proc. Int. Conf. onSafety of Dams, Coimbra, Portugal, Balkema,Rotterdam, pp. 311–319.

Karol, R.H. (1986) Chemical and Microfine Grouting.Workshop on Remedial Seepage Control, US ArmyEngineer Waterways Experiment Station, October.

Kikuchi, K., Mito, Y. and Adachi, T. (1995) Case studyof the mechanical improvement of rock masses bygrouting. Proc. Int. Workshop on Rock Foundation,Tokyo, Japan, Balkema, Rotterdam, pp. 393–7.

Kovari, K. and Peter, G. (1983) Continuous strainmonitoring in the rock foundation of a large dam. RockMech. and Rock Eng., 16, 157–71.

Lane, K.S. (1955) Designing for foundation movementsat Garrison Dam. 5th Congress on Large Dams,ICOLD, Paris.

Lane, R.G.T. (1963) The jetting and grouting of fissuredquartzite at Kariba. Conf. on Grouts, British NationalSociety on Soil Mechanics, London, pp. 85–90.

Lauga, H. and Taylor, H. (1983) Gravity dam onhorizontally bedded sedimentary rock. Proc. 7th PanAmerican Conf. on Soil Mechanics and FoundationEng., Vancouver, pp. 77–91.

Lemos, J.V. (1996) Modelling of arch dams on jointedrock foundations. Proc. ISRM Int. Symp. Eurock ‘96,Turin, September, ed. G.Barla, Balkema, Rotterdam,Vol. 1, pp. 519–26.

Lin, J.-S. and Whitman, R.V. (1986) Earthquake induceddisplacement of sliding blocks. J. Geotech. Eng. Div.,ASCE, 112(1), 44–59.

Lo, K.Y., Ogawa, T., Lukajic, B. and Dupak, D.D.(1991a) Measurement of strength parameters ofconcrete-rock contact at the dam-foundation interface.Geotechnical Testing J., 14(4), 383–94.

Lo, K.Y., Ogawa, T., Lukajic, B., Smith, G.F. and Tang,J.H.K. (1991b) The evaluation of stability of existingconcrete dams on rock foundations and remedialmeasures. Proc. 17th Int. Cong., Int. Commission onLarge Dams, Vienna, Austria, pp. 963–90.

Lombardi, G. and Deere, D. (1993) Grouting design andcontrol using the GIN principle. Water Power DamConstruction, Sutton, UK, June, 15–22.

Lukajic, B., Smith, G. and Deans, J. (1985) Use ofasphalt in treatment of dam foundation leakage,

266 INTRODUCTION

Stewartville Dam. Specialty Conf. on Rock Eng. forFoundations and Slopes, Boulder, CO, ASCE,Geotechnical Eng. Div., Vol. 2, pp. 76–91.

Mgalobelov, Y.B. and Lomov, I.E. (1979) Stabilizationof the Inguri arch dam rock foundation. 4th Int. Cong.on Rock Mech., Montreux, ISRM, pp. 433–8.

Myers, B.K. and Marilley, J.M. (1997) Automatedmonitoring of Tolt Dam. Civil Engineer, ASCE, March,44–6.

National Research Council (1990) EarthquakeEngineering for Concrete Dams: Design, Performanceand Research Needs. National Academy Press,Washington, DC.

Newmark, N.M. (1965) Effect of earthquakes on damsand embankments. Geotechnique, 15(2), 139–60.

Nicholson, G.A. (1983) Design of Gravity Dams on RockFoundations: Sliding Stability Assessment by LimitEquilibrium and Selection of Shear StrengthParameters. Technical Report GL-83–13,Geotechnical Laboratory, US Army EngineerWaterways Experiment Station, Vicksburg, MS.

Nieble, C.M. and Neto, S.B. (1983) Conceptualgeomechanical models: their evolution during thedesign and construction of dams. Proc. 5th Int. Cong.Rock Mech., Melbourne, ISRM, pp. C213–17.

Perlea V.G., Mathews, D.L. and Walberg, F.C. (1997)Rock erosion of unlined spillway chute. Int.Commission on Large Dams 19th Congress, Florence,Q. 75, R. 11, pp. 153–72.

Petrovsky, M.B. (1982) Monitoring of grout leaching atthree dam curtains in crystalline rock foundations.Proc. Conf. on Grouting in Geotechnical Engineering,New Orleans, ASCE, Geotechnical Eng. Div.,pp. 105–19.

Powell, C. and Pearson, R. (1993) Coolidge Damabutment stability and stabilization. Proc. SpecialtyConf. on Geotechnical Practice in Dam Rehabilitation,ASCE Geotech. Special Pub. No. 35, Raleigh, NC,pp. 834–49.

Pratt, H.K., McMordic, R.C. and Dumas, R.M. (1972)Foundations and Abutments—Bennett and Mica Dams.J. Geotech. Div., ASCE, 98, SM 10, 1053–72 .

Rescher, O.J. (1981) GeomechanischeModelluntersuchungen fur die Grundung vonTalsperren (Foundation problems of large dams—geomechanical model tests), Rock Mech., 14, 117–66.

Rocha, M. (1974) Present possibilities of studyingfoundations of concrete dams. Proc. 3rd Int. Cong.Rock Mech., Denver, pp. 879–97.

Rothe, J.P. (1969) Earthquake and reservoir loadings.Proc. 4th World Conf. on Earthquake Engineering,International Association for Earthquake Engineering.

Sarma, S.K. (1975) Seismic stability of earth dams andembankments. Geothechnique 25(4), 743–61.

Scott, G.A. and Dreher, K.J. (1983) Dynamic stability ofconcrete dam foundations. Proc. 5th Int. Cong. RockMech., Melbourne, ISRM, pp. C227–33.

Seed, H.B., Duncan, J.M. and Idris, I.M. (1975) Criteriaand methods for static and dynamic analysis of earthdams. In Naylor, D.J., Stagg, K. and Zienkiewicz, O.C.(eds), Criteria and Assumptions for Numerical Analysisof Dams, Swansea, University College, pp. 564–88.

Serafim, J.L. (1964) The behaviour of arch dams andtheir foundations. Proc. 8th Int. Cong. on Large Dams,Edinburgh, ICOLD, Discussion on Q.29, Vol. V.

Sheng, C.-K., et al. (1970) Earthquakes induced byreservoir impounding and their effects on theHsinfengkiang Dam. Proc. 10th Int. Conf. on LargeDams, Madrid, ICOLD.

Sherard, J.L., Woodward, R.J., Gizienski, S.F. andClevenger, W.A. (1963) Earth and Earth-Rock dams.Wiley, New York, pp. 509–62.

Spearman, E.L. (1976) Foundation investigation andtreatment for TVA dams. Proc. of Specialty Conf. onRock Eng. for Foundations and Slopes, Boulder, CO,ASCE, Geotechnical Eng. Div., pp. 101–13.

Thomas, H.H. (1976) The Engineering of Large Dams.Wiley, New York, pp. 55–8.

Underwood, L.B. and Dixon, N.A. (1976) Dams on rockfoundations. Specialty Conf. on Rock Eng. forFoundations and Slopes, Boulder, CO, ASCE,Geotechnical Eng. Div., Vol. 2, pp. 125–46.

Underwood, L.B., Thorfinnson, S.T. and Black, W.T.(1964) Rebound in redesign of Oahe Dam hydraulicStructures. J. Soil Mech. and Foundation Div., ASCE,90, SM3.

US Army Corps of Engineers (1981) Sliding Stability ofConcrete Structures. Technical Letter No. 1110–2–256.

US Army Corps of Engineers (1989) Re-evaluation of theSliding Stability of Concrete Structures on Rock withEmphasis on European Experience. US Army Eng.Waterways Experiment Station, Vicksberg, MS,Technical Report REMR-GT-12.

US Department of the Interior, Bureau of Reclamation(1951) Design Criteria for Concrete Gravity and ArchDams. Eng. Monograph No. 19.

US Department of the Interior, Bureau of Reclamation,


(1976) Design Manual for Concrete Gravity Dams. AWater Resources Technical Publication.

US Department of the Interior, Bureau of Reclamation(1978) Foundation Studies (Design and Analysis ofAuburn Dam, Vol. II).

US Department of the Interior, Teton Dam Failure ReviewGroup (1980) Failure of Teton Dam, Final Report. Supt.of Documents, US Govt Printing Office, Washington,DC.

Wahlstrom, E.E. (1974) Dams, dam foundations andreservoir sites. (Developments in GeotechnicalEngineering, Vol. 6), Elsevier S.P. C., Amsterdam,Oxford, New York.

Weaver, K.D. (1991) Dam Foundation Grouting. ASCE,New York.

Weaver, K.D. (1993) Some considerations for remedialgrouting for seepage control. Proc. Specialty Conf. onGeotechnical Practice in Dam Rehabilitation, ASCEGeotech. Special Pub. No. 35, Raleigh, NC, 256–67.

Westergaard, H.M. (1933) Water pressures on damsduring earthquakes. Trans, ASCE, 98, 418–33.

Wittke, W., Rodatz, W. and Wallner, M. (1972) Threedimensional calculation of the stability of caverns,slopes and foundations in anisotropic, jointed rock, bymeans of the finite element method. DeutscheGeotechnik, 1(1).

Wolff, T.F. (1993) Reliability analysis of navigationstructures. Proc. Specialty Conf. on GeotechnicalPractice in Dam Rehabilitation, ASCE Geotech.Special Pub. No. 35, Raleigh, NC, pp. 159–73.

Xu, L.X., Gong, Z.X. and Lin, W.P. (1983) Slidingstability of foundation rock with shear zones. 5th Int.Cong. on Rock Mech., Melbourne, ISRM,pp. C205– 208.

Zienkiewicz, O.C. (1988) The Finite Element Analysis inEngineering Science, 3rd edn, McGraw Hill, NewYork.

268 INTRODUCTION

8Rock socketed piers

8.1Introduction

Socketed piers are constructed in drill holesextending below the structure to depths wheresound rock, that can sustain the applied loads, isencountered. They are used where there is nosuitable bearing material at the surface and it isuneconomical to excavate this low strengthmaterial, and for conditions where structural loadsare substantial and permissible settlements small.Loads on drilled piers are usually vertical andcompressive. However, inclined and uplift loads canbe accommodated with the use of suitable designsand construction methods.Figure 8.1 shows a worm’s eye view of commonapplications of deep foundations where one highrise building is supported by belled caissons andanother by piles bearing on, or socketed into thebedrock. In both these cases, the load is supportedin a combination of side-wall shear and end bearingand the full length of the pier is utilized. Anotherapplication for drilled piers is to transfer thestructural load to a specified depth by ensuring thereis no side-wall shear developed. Figure 8.2 showsan example of this type of construction to transferthe building load in piers adjacent to the tunnel to adepth below the invert and avoid inducing stresseson to the tunnel lining. A similar application isshown in Fig. 1.2(c).

8.1.1Types of deep foundations

The essential difference between piles and drilled

piers is in the method of construction. Piles areinstalled by driving or vibrating the structuralmember and displacing the ground, while piers areinstalled by drilling a hole which is then filled withconcrete. Drilled piers may be installed entirely instiff, cohesive soil, or drilled through the soil to endbearing on rock, or drilled (socketed) to some depthinto the rock.

8.1.2Investigations for socketed piers

Drilling large diameter holes in rock is expensiveand it is important for economy that the length anddiameter of the socket are minimized. This willusually require that a thorough investigation ofsubsurface conditions be carried out to determinethe depth to sound rock and the quality of the rockwhich will be supporting the load. Of particularimportance is the identification of geologicalfeatures such as zones of shattered or weak rock,and clay-filled seams. Where piers are beinginstalled in karstic formations, drilling will usuallybe required at most or all pier locations to locatepossible solution features. These exploration drillholes would have to extend as far as 3 m (10 ft), ortwo to three times the socket diameter, below theplanned bearing level for the end of the socket toensure that there are no cavities in the bearing area.On one highway project, in a narrow gorge wherethe rock type was a strong limestone, the piers hadto be extended to depths as great as 60 m (200 ft)below the planned depth before competent rock wasencountered in which to drill a 2 m (6 ft) deep

socket (Kay, 1989). Foundation construction inkarstic formations is also discussed in Section 5.3.

Information is also required on the compressivestrength of the rock to determine the bearing

Figure 8.1 Typical installations of belled and rock socketed drilled piers (Macaulay, 1976. Reprinted by permission ofHoughton Mifflin Co.).

270 ROCK SOCKETED PIERS

capacity, and the modulus to determine thesettlement characteristics. Compressive strength canbe measured with laboratory tests on rock coresfrom which design values for bearing capacity andshear strength can be determined. However,modulus values used in design are the rock massmodulus and it may be necessary to carry out in situtesting, such as pressuremeter tests, to establishdesign values. Alternatively, a method of relatingrock mass modulus to geological characteristics isdescribed in Section 3.2.Information on ground water is also useful inassessing likely construction conditions. Theposition of the water table will determine whetherthe shaft will be wet or dry, and the permeability ofthe rock will determine whether wet shafts can bepumped dry. This information should be evaluated

during design because if it is likely that the shaftwill be flooded, then inspection and cleaning of thewalls and base of the shaft will be difficult.Consequently, conservative side-wall strengthvalues would be used to account for possibleaccumulations of cuttings and drill mud on bearingsurfaces.

8.2Load capacity of socketed piers in compression

Drilled piers can be designed to support the appliedload in:

1. side-wall shear comprising adhesion or skinfriction on the wall of the socket; or

2. end bearing on the material below the tip of the

Figure 8.2 End-bearing drilled pier transfers applied load to rock below tunnel invert.

LOAD CAPACITY OF SOCKETED PIERS IN COMPRESSION 271

pier; or3. a combination of both.

Situations where support is provided solely in side-wall shear are where the base of the drilled holecannot be cleaned so that it is uncertain that any endbearing support will be developed. Alternatively,where sound bed rock underlies low strengthoverburden material, it may be possible to achievethe required support in end bearing on the rockonly, and assume that no support is developed in theoverburden. However, where the pier is drilledsome depth into sound rock, a combination of side-wall shear and end bearing can be assumed(Kulhawy and Goodman, 1980).

8.2.1Mechanism of load transfer

The relative magnitude of the support developed inside-wall shear and end bearing depends on thefollowing factors. First, the moduli of the materialsin which the pier is socketed and that of the pier itself,second, the magnitude of loading in relation to theside-wall shear strength, and third, the method ofconstruction. The mechanism of load transfer andsettlement of a socketed pier, and the distribution ofsupport between the sidewalls of the shaft and endbearing is illustrated in Fig. 8.3. In this model allthe shaft resistance is replaced by a spring withstiffness ks, and all the end bearing is replaced witha second spring of stiffness kb. The support providedin side-wall shear Qs and end bearing Qb are eachequal to the product of the displacement and thespring stiffness, i.e. (Winterkorn andFang, 1975). In the first case, much of the support is developed inthe upper part of the pier, that is, the side-wallresistance per unit displacement is much greaterthan the end bearing force developed for the samedisplacement. Thus the spring constant ks is stifferthan the spring constant at the base kb. Thedeflection of the pier is a combination of elasticshortening of the pier and deflection of the tip.Because most of the deflection occurs in the upper

part of the pier, that is, ds is greater than db, theportion of support developed in side-wall shear ismuch greater than that developed in end bearing.In the second case, material with very low bearingcapacity occurs at the base of the pier, such that thespring constant kb is much less stiff than the springconstant ks. Provided that the applied load does notexceed the shear strength of the side-walls, most ofthe displacement will occur in the upper part of thepier and the major portion of the load will be carriedin side-wall shear.In the third case, the pier has been drilled throughmaterial with a low modulus to end bearing onmaterial with much higher modulus, so the springconstant kb is much greater than the spring constantks. In this case, much of the displacement will occurdue to elastic shortening of the pier, and a relativelysmall amount due to deflection of the high modulusmaterial below the base of the pier. Under theseconditions, most of the load is carried in endbearing.

8.2.2Shear behavior of rock sockets

Both theoretical and field studies of theperformance of rock-socketed piers show that themajor portion of the applied load is usually carriedin side-wall shear. The peak shear stress t developedon the walls of the shaft is assumed to behave as aMohr-Coulomb material as follows:

(8.1)where c is the cohesion between the rock and theconcrete, a is the normal stress at the rock-concreteinterface, and is the friction angle of the rocksurface.If the displacement of the pier exceeds the elasticlimit of the interface so that the cohesion is lost andthe friction angle is diminished to the residual value

, the available shear strength is now given by(8.2)

Normal stress at the rock-concrete interface isinduced by two mechanisms. First, application of acompressive load on the top of the pier results in


elastic dilation of the concrete, and second, sheardisplacement at the rough surface of the drill holeresults in mechanical dilation of the interface. If thestiffness of the material surrounding the socket withrespect to normal displacement is constant, then thenormal stress will increase with increasing appliedload, and there will be a corresponding increase inthe shear strength.The degree of mechanical dilation that occurs is

related to the roughness of the walls of the socket,as well as the strength of the rock that forms theirregularities. As shown in equation 3.13, theseirregularities tend to be sheared off as the normalstress increases. Therefore, for rock that issignificantly weaker than concrete, the roughness ofthe surface may have little influence on the shearstress developed on the walls of the pier.Simulations of the behavior of rock sockets have

Figure 8.3 Simplified support mechanism for socketed piers showing components of load carried in side shear (Qs andend bearing (Qb) (Winterkorn and Fang, 1975).


been carried out in laboratory tests using a constantstiffness direct shear machine (Ooi and Carter,1987). The test samples consisted of 76 mm (3 in)diameter sandstone cores with concrete cast on oneend. The interface between the rock and theconcrete consisted of either a smooth surface cutwith a diamond saw, or a series of asperities withwavelengths ranging from 10 to 15 mm (0.4–0.6 in)and an amplitude of 2.5 mm (0.1 in). The equivalentroughness angle i of the asperities ranges from 18°to 28°. The uniaxial compressive strengths of thesandstone and concrete were respectively 15–20MPa (2200– 2900 p.s.i.) and 40 MPa (5800 p.s.i.).The effect of bonding of the concrete to the rock wasexamined by casting the concrete directly to therock surface on some of the samples, and by placinga plastic film on the surface of other samples whichacted as a bond breaker.Two plots of Ooi and Carter’s test results show (a)typical shear stress-shear displacement curves, and(b) a summary of the relationship between shear andnormal stresses for both peak and residual strengthsfor all rough surfaces, both bonded and unbonded(Fig. 8.4). Note that in Fig. 8.4(b) the ratio ofnormal and shear stress scales is about 3.5. Theconclusions that can be drawn from the test resultsare as follows.

1. There is a distinct peak shear stress that occursat a shear displacement of less than 1 mm (0.04 in) and the residual shear strength occurs ata displacement of about 2–5 mm (0.08–0.2 in).

2. Cohesive bonding between the concrete and therock has a significant effect on the peak andresidual shear strengths as indicated by curve 1(bonded) and 2 (unbonded).

3. A rough rock-concrete interface has aconsiderably higher shear strength than asmooth interface (compare curves 1 and 3).

4. The peak shear strength, at low normalstresses, is almost an order of magnitude higherthan the residual shear strength (Fig. 8.4(b)),indicative of the significant loss of support thatoccurs when the bond is broken.

8.2.3Factors affecting the load capacity of socketed piers

Figure 8.5 shows the results of load tests carried outon a socketed pier installed through hard silty clayinto highly weathered siltstone at a site in Singapore(Chang and Wong, 1987). These results illustratetypical performance of socketed piers. That is, thedistribution of the axial load is highly non-uniform,and the larger portion of the load is carried in thestronger rock while the portion of the load carried inend bearing is relatively small.The performance of rock socketed piers has beenstudied in laboratory tests, in analytical studiesusing finite element analysis and in full scale loadtests. The laboratory work has studied model piersand has tested the rock-concrete interface todetermine the factors that influence the shearresistance (Ladanyi and Domingue, 1980; Pells etal., 1980). The finite element analyses haveinvestigated the influence of socket geometry(length to diameter ratio), and the relative modulibetween the concrete and the rock in the walls andbase of the socket on both load capacity anddisplacement (Rowe et al., 1978; Donald et al.,1980; Rowe and Pells, 1980). In many of the fullscale load tests, measurements have been made ofthe portion of the load carried in side shear and thatin end bearing. This had been achieved byconstructing piers with soft material such asstyrofoam at the base to eliminate end bearing, andby casing the socket to eliminate side-wall shear(Seychuck, 1970; Glos and Briggs, 1983).The results of this investigation work have shownthat the following factors have a significantinfluence on the load capacity and settlement of thepier:

(a) the geometry of the socket as defined by thelength to diameter ratio;

(b) the modulus of the rock both around the socketand below the base;

(c) the strength of the rock in the walls of thesocket and below the pier;

(d) the condition of the side-walls with respect toroughness, and the presence of drill cuttings or


bentonite cakes;(e) the condition of the end of the pier with respect

to the removal of drill cuttings and other loosematerial from the bottom of the socket;

(f) layering in the rock and the presence of seamswith differing strengths and moduli.

(g) settlement of the pier in relation to the elasticlimit of side-wall shear strength.

(h) creep of the material at the rock-concreteinterface resulting in increasing settlement withtime.

Figure 8.4 Shear behavior of rock-concrete joints tested in constant normal stiffness apparatus (Ooi and Carter,1987): (a) typical shear stress-displacement curves; and (b) peak and residual strength envelopes.


(a) Effect of socket geometryThe geometry of a rock socket, which is defined bythe length to diameter ratio, has a significant effecton the load capacity of the pier. As the ratioincreases from 0, the portion of the load carried inend bearing diminishes and progressively more ofthe load is carried in side-wall shear. This isillustrated in Fig. 8.6 where, for the condition thatthe rock has a higher modulus than the pier, almostall the load is carried in side-wall shear at an L/Bratio of 4, while only 50% of the load is carried inside-wall shear at an L/B ratio of 1 (Osterberg andGill, 1973). The implication of this behavior is thatshort sockets rely on sound rock at the base of thepier to provide a substantial portion of the supportwhereas, in long rock sockets, little of the loadreaches the base.The typical distributions of load shown in Fig. 8.6have been confirmed by instrumenting productionpiers and measuring the stress both at the base and atintervals down the socket for installations is veryweak shale (Horvath et al., 1989) and in karsticdolomite (Tang et al., 1994). Section 8.2.3(g)discusses how the loads in the base and socket

change with time after completion of construction.(b) Effect of rock modulusAs shown in equations 8.1 and 8.2 the shear stressdeveloped on the side-walls of a socket is partiallydependent on the normal stress acting on the rocksurface, with the magnitude of this normal stressbeing directly related to the stiffness ofthe surrounding rock. Loading of the pier results insome displacement at the rock-concrete interfaceand for a rough interface surface, where the strengthof the rock is such that the asperities are not shearedoff, dilation occurs which increases the normalstress at the surface. This increase in normal stress ?s is given by the following equation (Seidel andHaberfield, 1994):

(8.3)

where E(m) and v(m) are respectively the rock massmodulus and Poison’s ratio and r and ?rrespectively are the radius of the pier and thechange in radius due to dilation. Another possiblemethod of increasing the normal stress is to use non-shrink cement in the pier to eliminate the shrinkagethat occurs as normal cement sets.

Figure 8.5 Typical distributions of socket Qs and base Qb loads in rock-socketed piers (Chang and Wong, 1987).


The relationship in equation 8.3 is illustrated inFig. 8.6 which shows the distribution of shear stressalong the walls of the socket. Where the rock has ahigher modulus than the concrete thesocket is confined and high normal stresses aredeveloped on the side-wall. As a consequence, amajor portion of the load is carried in the upper partof the socket. In contrast, where the rock has alower modulus than the concrete thenormal stresses are diminished and less of the loadis carried in shear on the sides of the socket. For theconditions shown in Fig. 8.6, the effect of areduction in the modulus by one order of magnitudecauses the shear stress to be more uniformlydistributed down the socket and the base load toincrease from about 8% to 30% of the appliedload.

The stress distribution down the socket is alsoinfluenced by the deformation modulus of the rockat the base of the pier. If the rock has a very lowmodulus then it will support a negligible portion ofthe load. Figure 8.7 illustrates two different stressdistributions depending on the relative modulus ofthe rock in the socket, and that below the base. Thepier with the low modulus rock in the base has areduced bearing capacity compared with the pierwith sound rock in the base.(c) Effect of rock strengthThe shear strength developed on the side-walls ofsockets and the bearing capacity of the rock belowthe base of the pier are related to the strength of therock mass. Where the rock is weaker than theconcrete, shear zones will develop down the sidesof the socket at a diameter slightly greater than the

Figure 8.6 Distribution of side-wall shear stress in relation to socket length and modulus ratio (after Osterberg and Gill,1973).


asperities on the walls of the hole. With increasingstrength of the rock, the shear strength that can besustained in the walls of the socket is increased, andwhen the rock is stronger than the concrete, thelimiting shear strength is the strength of theconcrete. Figure 8.8 shows the results of load testson full scale piers. The full line shows the relationship between the ultimate average shearstress tult developed in the side-wall and the uniaxialcompressive strength su(r) of the rock, and thedashed line shows the same relationship with afactor of safety of 2.5 applied to the shear stress.The capacity of the walls of the shaft to sustain theapplied vertical load is expressed in terms of theadhesion factor a which is given by the ratio t/su(r).For piers installed in the very weak to moderatelyweak sedimentary rocks, the adhesion factor forultimate shear stress conditions was found to be

(Fig. 8.8). Application of afactor of safety of 2.5 to these results provides anapproximate allowable adhesion factor of

Further information on the valueof allowable adhesion values is provided by testresults of full scale piers in weathered sedimentaryand granitic rocks in Singapore. It was found that for

rock with compressive strengths in the range 1–5MPa (145–725 p.s.i.) the allowable adhesion factorwas given by (Lueng, 1996)(note: adhesion values given for compressivestrength in MPa).The bearing capacity of the base of the pile isrelated to both the rock strength and the geometryof the socket (Fig. 8.9). Where the base of the pieris at, or close to, the ground surface (Fig. 8.9(a)), awedge type of failure is developed and the pierundergoes both vertical displacement and rotation.Where the depth of embedment is greater than twicethe diameter of the socket (Fig. 8.9(b)) a punchingtype failure occurs and a truncated conical plug offractured rock is formed below the base (Williams etal., 1980).Allowable side-wall and end-bearing stress valuesfor use in design of piers are given in Section 8.3.(d) Condition of side wallsThe laboratory tests of rock-concrete shear strengthbehavior (Fig. 8.4) clearly show the difference in

Figure 8.7 Effect of rock modulus at base of pile on distribution of side-wall shear stress (Osterberg and Gill, 1973).


shear strength of rough and smooth sockets. Sample1 in which grooves had been cut on the rock surfaceshows higher peak and residual stresses than sample3 which was a saw-cut surface. Similar results hadbeen found in full-scale tests as shown in Fig. 8.10(Horvath et al., 1983). These tests were conductedin very weak mudstones with uniaxial compressivestrengths of about 7 MPa (1000 p.s.i.); RQD valuesranged from 29% to 88% and occasional clay seamsup to 37 mm (1.5 in) thick were encountered. Thesockets were 710 mm (28 in) in diameter and 1.37 m(4.5 ft) long. The sockets were drilled with an augerto produce a relatively smooth side-wall surface. Inhalf of the test sockets grooves were cut which werebetween 10 and 30 mm (0.4–1.2 in) deep (in theradial direction) and about 10 mm (0.4 in) long (inthe axial direction). The load-displacement curvesin Fig. 8.10 show that the effect of the grooves is toreduce the displacement by a small amount in theelastic range, but there is significantly less totaldisplacement. In general, the effect of grooving thewalls of the socket is to reduce brittle failure, thatis, the large displacement that occurs once theelastic range has been exceeded.In production shafts grooves can be cut with a

grooving tool suitable for the rock conditions. Forexample, the sockets in a very weak sequence ofmudstones, siltstones and sandstones withcompressive strengths ranging from 3.2 to 11.6MPa (460–16700 p.s.i.) for the NorthumberlandStraight bridge in Canada were roughened withrectangular grooves 240 mm (9.45 in) high and 110mm (4.3 in) deep on a vertical spacing of 1 m (3.3ft) (Walter et al., 1997).Another significant effect on shear strength ofsockets is the presence of loose drill cuttings andbentonite cakes on the side walls of the sockets(Fig. 8.11). Drill cuttings may be removed bywashing the socket with water jets, but bentonitecakes are more difficult to dislodge. Wherebentonite is used to stabilize the walls of the socket,there is likely to be a cake of bentonite between therock surface and the concrete. The cake was foundto be as thick as 40 mm in sockets excavated inmudstone, while in other cases, the cake was paperthin and did not effect pier performance (Williamsand Pells, 1981). To take into account the possibleeffect of bentonite on the walls of the socket, thesetests indicate that the design bond strength shouldbe reduced to about 25% of the value assumed for a

Figure 8.8 Relationship between compressive strength of rock in socket and side-wall shear resistance, or adhesionfactor (Williams and Pells, 1981, courtesy of Research Journals. National Research Council Canada). su(r): rockunconfinedcompressive strength; tult: ultimate side-wall shear stress.



Figure 8.9 Typical failure mechanism for end-bearing piles (Williams et al., 1980): (a) base of pier bearing at groundsurface; and (b) socketed pier with length/diameter>2.

1. Original position of pier. 2. Position of pile after failure of base. 3. Original ground surface. 4. Heave and cracking to1–1.6 m from pier. 5. Passive zone containing heaved slabs. 6. Plastic zone showing intense fracturing with slickensidedsurfaces. 7. Conical zone relatively unsheared. 8. Intact rock. 9. Truncated conical plug. 10. Loading column with baseplate. 11. Steel casing with concrete base plate.

load tests to verify performance.An alternative to bentonite slurries for maintainingwall stability is to use polymer slurries. Polymers donot form mudcakes and so there is improved loadtransfer at the rock-concrete interface comparedwith shafts drilled with bentonite. The action ofpolymer slurries is to increase the effective stress atthe borehole wall by increasing the viscosity of thefiltrate while a hydraulic gradient is maintainedbetween the slurry column and the water in the rockdiscontinuities. This action enhances hole stabilityas long as the pressures in the slurry column exceedthe hydrostatic ground water pressure in theformation. However, a possible detrimental effectof polymer slurries is the deposition of drill cuttingsin the base of the pier if the suspended solids arenot in stable suspension, and settle after clean out iscompleted (O’Neill and Hassan, 1994).(e) Condition of end of socketIf it is assumed in design that load is carried in endbearing, it is essential that the end of the socket bethoroughly cleaned of all drill cuttings and looserock. If there is a low modulus material in the baseof the socket, considerable displacement of the pier

will have to take place before end bearing ismobilized. It is likely that this displacement willcause the peak side-wall shear strength to beexceeded so that the actual bond strength will bethe residual shear strength resulting in a diminishedload capacity of the pier.Where it is not possible to clean and inspect the endof the socket, it may be necessary to assume thatthere is no end bearing; this requires that the socketbe made long enough to carry the full load in side-wall shear.(f) Layering in the rockLayers of weak, low modulus rock both in thesocket and below the base of the pier may influencethe load bearing capacity of the pier. In some casesoccasional layers may be beneficial to theperformance of the pier if they form grooves thatincrease the effective roughness of the walls of thesocket. However, the other effect of low-moduluslayers is to reduce both the shear strength and themodulus of the rock mass which will reduce theload capacity of the pier. The effective side-wallshear resistance t* and modulus E* of the layeredrock mass can be calculated as the weighted average

Figure 8.10 Comparison of load-displacement behavior for augered and grooved sockets (Horvath et al., 1983, courtesyof Research Journals. National Research Council Canada).


of the two materials as follows (Rowe andArmitage, 1987; Thorne, 1980):

(8.4)(8.5)

where p is the proportion of the shaft which consistsof low strength material; ts, Es are the side-wallshear resistance and modulus of low strengthmaterial; and tr, Er are the side-wall shear resistanceand modulus of the higher strength material.Where the pier will be loaded partially or totally inend bearing, it is important that any low strengthlayers below the end of the socket are identified. Insome cases it may be necessary to drill explorationholes at some or all pier locations to determine theposition and thickness of such seams, and alsoestablish criteria for acceptable rock below thesocket (Gill, 1980). Soft seams located at distancesgreater than about three socket diameters below theend of the socket, will probably have little effect onbearing capacity. However, the effect of seamslocated in the immediate end bearing area of the

socket should be evaluated by the use of equations8.4 and 8.5, or numerical analysis to examine thespecific effect of such layers.(g) CreepOne of the few available records of the load anddisplacement performance over time of socketedpiers is provided by Tang et al. (1994) and Drumm(1998). This study examined three piers drilledthrough residual soil with thickness ranging from 3.07 m to 17.8 m (10.1–58.7 ft) and socketed intohard, grey dolomite containing enlarged joints andetched pits which formed extremely irregularpinnacles. The depth of the rock sockets rangedfrom 8.97 to 6.4 m (29.5–21 ft) and the axial designload varied from 10 600 to 12 600 kN (2380–2830kips) (Fig. 8.12).Figure 8.12 (a) shows the stresses at the top andbase of one pier for a period of 2000 days andFig. 8.12(b) shows the change in the distribution ofstresses down the shaft over the same time period.The proportion of the load carried in end loading

Figure 8.11 Influence of side-wall condition on socket shear strength (Williams and Pells, 1981, courtesy of ResearchJournals. National Research Council Canada).


varied from 14% to 19% of the load at the top of thepier. While the strain gauges in shaft showedincreasing load with time, the load cell at the baseshowed mininal load increase after construction wascomplete.Similar performance has been reported by Ladanyi(1977) for a 0.89 m (35 in) diameter pier socketedto a depth of 4.57 m (15 ft) in horizontally bedded,fractured shale. The total applied load was 9.15 MN(2060 kips) and the design values for side-wallshear resistance and end bearing were 1.035 MPa(150 p.s.i.) and 4.83 MPa (700 p.s.i.) respectively.The load in end bearing was monitored over aperiod of nearly four years and the results showedthat this load increased by about 65% after the endof construction. However, at the end of this periodonly about 10% of the applied load was beingcarried in end bearing.The likely mechanism for the change in load withtime is the gradual shedding of the side-wallresistance in the more highly stressed upper part ofthe socket, with a corresponding increase in the baseload. This load adjustment takes place at stresseswhich are well below the peak stress so there is nosignificant displacement of the pier.

8.2.4Socketed piers in karstic formation

Where socketed piers are to be installed in karsticformations, the detailed geology must beinvestigated to ensure that the end is not bearing ona rock pinnacle, or thin seam of rock above acavity. If cavities are suspected, exploration drillholes would be required, with a hole at every pier,extending to below the planned bearing level, ifconditions vary across the site. This may result indifferent designs being prepared for each pier to suitthe local geological conditions.If the bearing surface at the tip is sloped, the bearingcapacity may be improved by cutting a bench, or byinstalling steel dowels into holes drilled into soundrock (Sowers, 1976). Alternatively, the hole can beextended to more competent rock. Cutting a benchwill often require dewatering of the caisson, which

may be difficult where the upper part of the holepasses through soil which could blow in if a steephydraulic gradient is developed.See also Section 5.3 for more detailed discussionson foundation construction in karstic terrain.

8.3Design values: side-wall resistance and end

bearing

Rock socketed piers can be designed to carrycompressive loads in side-wall shear only, or endbearing only, or a combination of both. The mostimportant factors that influence the designprocedure are the strength, degree of fracturing andmodulus of the rock, the condition of the walls andbase of the socket, and the geometry of the socket.

8.3.1Side-wall shear resistance

In determining the load capacity in side-wall shear,the simplifying assumption is made that the shearstress t is uniformly distributed down the walls ofthe socket and the allowable load capacity is givenby the following equation:

(8.6)where Q is the total applied load; ta is the allowableside-wall shear stress; B is the diameter of socket,and L is the length of socket.The diameter of the socket is usually determined bythe type of drilling equipment that is available, andthe length is selected so that average side-wall shearstress is not greater than the allowable shear stress,and that the design settlement is not exceeded.An approximate correlation between the observedside-wall shear stress, expressed in terms of theadhesion factor and the strength of the rock in the sockets of test piersis shown in Fig. 8.8. These results, together withadditional tests, have been used to develop thefollowing equations relating the approximateallowable side-wall resistance ta (in MPa) andunconfined compressive rock strength su(r) (in MPa)for smooth and grooved sockets (Rowe and


Armitage, 1987).For clean sockets, with side-wall undulationsbetween 1 mm and 10 mm deep and less than 10

mm wide (0.04–0.4 in deep, <0.4 in wide):

Figure 8.12 Variation in load distribution in socketed pier with time: (a) shaft stress versus time in relation toconstruction progress; and (b) vertical stress distribution and geological profile of socketed pier (data provided by E.Drumm, University of Tennessee, 1998).


(8.7a)

or

(8.7b)

For clean sockets, with side-wall undulationsgreater than 10 mm deep and 10 mm wide (>0.4 indeep, >0.4 in. wide):

(8.8)

Values for the adhesion factor a (t/(su(r)) as definedin Fig. 8.8, may be available from test piers at thesite or from tests in similar geological conditions.The factor of safety FS included in equations 8.7and 8.8 relates the ultimate to the allowable shearresistance, and takes into account the many factorsthat can influence the side-wall shear resistance asdiscussed in Section 8.2.3, as well as uncertainty inthe construction quality. As shown in Fig. 8.8, afactor of safety of 2.5 relates the ultimate toallowable stress values in these test piers. However,where the rock is closely fractured so that the rockmass in the walls of the socket tends to be loose andhave a low deformation modulus, the values for tashould be reduced from the value given in equations8.7 and 8.8. This will allow for the lower confiningpressures developed around the socket. A limitedamount of test data indicates that ta should bereduced by as much as 40% where the modulus ofthe rock mass is approximately one fifth of themodulus of the intact rock (Williams and Pells,1981).Use of equations 8.7 and 8.8 with an appropriatefactor of safety will usually result in the pierbehaving elastically with minimal risk of excessivesettlement. The small difference between these twoequations shows that the roughness of the side-wallshas little influence on the shear resistance when theapplied shear stresses are well within the elasticlimit (see Fig. 8.10). The main value of roughenedsockets is in minimizing settlement if this is criticalto performance of the pier.At sites where there are a large number of piers tobe installed, or in geological conditions where there

is little previous experience in this type ofinstallation, load tests are often justified to determineactual design values for side wall shear strength.The tests may save significant construction costs ifthe test strength is shown to be higher than theconservative value assumed in the design. Forexample, load tests using an Osterburg hydrauliccell to apply the load were carried out on a 0.91 m(3 ft) diameter pier installed in a very weaksequence of mudstones, siltstones and sandstones forthe Northumberland Strait bridge (Walter et al.,1997) In order to test two rock types within a singlepier, the pier was cast with a styrofoam plug in thebase and the Osterburg cell was located between theupper and lower test sections of the concrete pier.The procedure was to first test the upper, shortertest section, then to cast an additional concrete plugon the top of the socket and re-apply the load to testthe lower section. Tests were carried out to find theworking and ultimate shear strengths, as well ascyclic tests to check that there was no loss ofadhesion with expected ice loading conditions.The test results confirmed that the workingstrengths were close to those found for similarmaterials, and the final design socket length wasabout 55% of the length calculated in thepreliminary design.

8.3.2End-bearing capacity

As illustrated in Fig. 8.9, a highly loaded, end-bearing socket may fracture a cone of rock beneaththe end of the pier which will result in excessivesettlement. However, tests piers have been loaded tobase pressures as high as three and even ten timesthe compressive strength of the rock withoutcollapse (Williams, 1980). Test results demonstratethat allowable load capacity Qa, which includes afactor of safety of about 2–3, at the base of the pieris (Rowe and Armitage, 1987):

(8.9)

where su(r) is the uniaxial compressive strength ofrock at the base of pier; and B is the diameter of


base of pier.Equation 8.9 is applicable provided that thefollowing three conditions are met:

1. The base of the socket is at least one diameterbelow the ground surface.

2. The rock to a depth of at least one diameterbelow the base of the socket is either intact ortightly jointed (no compressible or gouge filledseams).

3. There are no solution cavities or voids belowthe base of the pier.

For conditions where the rock below the base of thepier contains horizontal or near horizontal seamsinfilled with material of lower strength than thebearing rock, the allowable end-bearing capacity isreduced from that given in equation 8.9 and can befound from:

(8.10)where

(8.11)

and for socket length L, diameter B,

(8.12)

The characteristics of the seams are defined by theirspacing S and thickness t if filled with rock debrisor soil. The term K' is applicable for , and .The factor K' includes anominal factor of safety of 3 against the lower-bound bearing capacity of the rock foundation(Canadian Geotechnical Society, 1992).

8.4Axial deformation

8.4.1Settlement mechanism of socketed piers

This section describes procedures for calculating thevertical settlement of socketed piers for threedifferent construction methods:

1. side-wall resistance only;2. end bearing only;3. combined side-wall resistance and end bearing.

The design methods can accommodate rock withdiffering moduli in the socket and base of the pier,as well as sockets which are recessed below thesurface. The settlement calculations have beendeveloped from finite element analyses (Pells andTurner, 1979; Rowe and Armitage, 1987), theresults of which have been checked againstsettlements of full scale load tests (Horvath et al.,1989; Chiu and Donald, 1983).Axial deformation of a socketed pier, withincreasing load, is a three stage process as follows.

1. Deformation starts with elastic compression ofthe pier where it is not bonded to the rock, andelastic shear strain at the rock-grout interface.Under these conditions the deformation issmall and the major portion of the applied loadis carried in side-wall shear. The pier exhibitselastic behavior during this stage of theloading.

2. Slippage starts at the rock-concrete interfaceand an increasing portion of the load istransferred to the base of the pier.

3. At increasing displacement, the rock-concretebond is broken and a constant frictional shearresistance is developed on the walls of thesocket; an increasing load is carried in endbearing. At this level of displacement, slipoccurs on the wall of socket and the side-wallresistance exhibits plastic behavior.


Although methods of calculating verticaldisplacement have been developed for both elasticand plastic behavior of socketed piers (Rowe andArmitage, 1987), the usual design practice is toassume elastic conditions that occur at smallsettlements. In calculating elastic settlement it isassumed that the pier consists of an elastic inclusionwelded into the surrounding rock and that no slipoccurs at the rock-concrete interface. Under theseconditions, the displacements are small, and endbearing resistance is not fully mobilized.As illustrated in Fig. 8.13, there are a number ofdifferent socket conditions depending on thegeology of the site and the construction method ofthe pier. The condition of the socket determines theload transfer mechanism from the head of the pier tothe side walls and base, and calculation of settlementrequires the use of influence factors appropriate foreach condition. Influence factors are provided for thefollowing four socket conditions:

1. side-wall shear resistance only (Figs. 8.14,8.15);

2. end bearing only (Fig. 8.16);3. side-wall resistance and end bearing for a

socket in a homogeneous rock (Fig. 8.17);4. side-wall resistance and end bearing where the

rock in the walls and the base have differingmoduli (Fig. 8.17).

8.4.2Settlement of side-wall resistance sockets

Socketed piers that support the applied load in side-wall resistance only may be constructed where thebase of the drill hole cannot be cleaned outeffectively, or where the rock in the base has littlebearing capacity, such as karstic limestone or veryweak shale. The general equation for settlement d ofthe top of a socketed pier with side shear resistance,at the surface of a semi-elastic half space is:

(8.13)

where Q is the applied load; B is the diameter ofsocket; Em(s) is the modulus of deformation of rock

mass in the shaft; and I is the settlement influencefactor given in Fig. 8.14. Values of the rock massdeformation modulus have been back-analyzed fromobservations of the settlement of socketed piers andthe following correlation between the modulus andthe uniaxial compressive strength of the rock su(r),incorporating a factor of safety of approximately 2,has been proposed (Rowe and Armitage, 1987):

(8.14)Note that in making an assessment of the value ofthe rock modulus, the degree of fracturing of therock mass must be considered. Reference toFig. 3.10 shows the relationship between thecharacteristics of the rock mass and the modulus ofdeformation; more highly fractured rock will beable to deform more readily and there will be lessconfinement on the socket. Where the rock is highlyfractured, judgment will be required to assesswhether it is necessary to reduce the rock massmodulus calculated using equation 8.14.Settlement calculated using equation 8.13, with thevalue of the influence factor I being related to thesocket geometry L/B and the modulus ratio R, givenin Fig. 8.14. These values have been calculated for aPoisson’s ratio of 0.25; it has been found thatvariations in the Poisson’s ratio in the range 0.1–0.3for rock and 0.15–0.3 for the concrete have littleeffect on the influence factors.The values for the influence factors shown inFig. 8.14 assume that the socket is fully bondedfrom the rock surface. However, influence factorswill be reduced where the pier is recessed below theground surface because the rock around the socketis more confined and the normal stress at theconcrete surface is increased. Recessed sockets areformed by casing the upper part of the hole, or forconditions where the socket passes through a layerof weathered rock where there is little or no side-wallshear resistance developed. For a recessed socket,the settlement is given by

(8.15)

where RF is a reduction factor given in Fig. 8.15.


8.4.3Settlement of end loaded piers

Where the shaft of the pier is cased such that no

side-wall shear is developed and the load is entirely

Figure 8.13 Summary of methods of calculating elastic settlement of side-wall sockets, end bearing piers and completesocketed piers.


supported in end bearing, the settlement iscalculated in a similar manner to that of a footing onthe surface. However, the settlement of the pier willbe less than that of a footing at the surface becausethe rock in the bearing area below the base of thepier is more highly confined than the surface rock.This confinement is accounted for by applying areduction factor to the settlement equation. Thevalue of the reduction factor depends on the ratio ofthe depth of embedment D to the diameter of thepier B, and the relative stiffness of the pier and therock. If the ratio of the pier modulus to the rockmodulus is greater than about 50 , thenthe pier can be considered to be a rigid footing,while if the ratio is less than 50, the pier can beconsidered as a flexible footing. Values of thesocketed piers: reduction factor are given inFig. 8.16 for both flexible and rigid circularfootings; these reduction factors are for the averagesettlement of the footing.Using the reduction factors given in Fig. 8.16, theequation for the settlement of an end bearing pier,including the elastic compression of the pier itself is

(8.16)

where Ec is the concrete modulus; RF' is the

reduction factor for an end bearing socket; D is thedepth of pier; Cd is the shape and rigidity factor asgiven in Table 5.6 (since piers are usually circular inshape, the values for Cd for average settlement are 0.85 of flexible footing, and 0.79 for a rigid footing).Q is the foundation load; Em(b) is the deformationmodulus of the rock mass in the pier base; B is thepier diameter, and v is the rock mass Poisson’sratio.

8.4.4Settlement of socketed, end bearing piers

Reference to Fig. 8.6 shows that a portion of theload on a socketed pier is carried in end bearing,and that the end bearing load is related to the socketgeometry and the rock modulus. For theseconditions, settlement is calculated using equation 8.13, using influence factors for an end bearingsocketed pier given in Fig. 8.17. These curves havebeen developed for elastic behavior with no slipalong the side-walls (Rowe and Armitage, 1987).The three sets of curves in Fig. 8.17 show the effecton the influence factors of differing moduli betweenthe rock in the base, and the rock in the socket (Em(b)/Em(s)). Comparison of Fig. 8.17 (for

Figure 8.14 Elastic settlement influence factors for side-wall resistance socketed pier (Pells and Turner, 1979, courtesyof Research Journals. National Research Council Canada).


with Fig. 8.14 shows that the influence factor for aside-wall shear/end-bearing socket has a largervalue than a socket with no end bearing whichdemonstrates that a pier with end bearing on a

clean, sound rock surface will settle less than a pierwith side-wall resistance only. The three sets ofcurves in Fig. 8.17 also show that settlement willdiminish with increasing modulus of the rock at the

Figure 8.15 Reduction factors for calculation of settlement of recessed sockets (Pells and Turner, 1979, courtesy ofResearch Journals. National Research Council Canada).

Figure 8.16 Reduction factors for calculation of average settlement of end bearing sockets (Pells and Turner, 1979,courtesy of Research Journals. National Research Council Canada).


base.Where a portion of the applied load is carried in endbearing, it is necessary to check that this load doesnot exceed the bearing capacity of the rock in the

base. The percentage of the load carried in endbearing can be determined from the lower half ofFig. 8.17, from which the pressure on the rock inthe base of the pier can be calculated.

EXAMPLE 8.1

DESIGN OF ROCK SOCKETED PIERS

The following are examples of the design procedures for the different types of socketed piersdiscussed in this chapter. Consider a pier with a diameter B of 1.5 m and a vertical compressive load Qof 10 MN. Assume that the concrete has a modulus Ec of 20 GPa, and that the compressive strengths ofthe rock in the socket and base of the pier are as follows:

socket compressive strength=2 MPabase compressive strength=20 MPabase Poisson’s ratio=0.25.

SIDE-WALL SHEAR RESISTANCE ONLY

Assume that the hole is drilled with an auger and that the rock is sufficiently massive that it is notrequired to use bentonite to stabilize the walls of the hole. Furthermore, equipment is not available togroove the walls so the drill hole has no significant roughness. For the

condition that the base of the socket cannot be cleanedso that no end bearing will be developed, it isnecessarythat the socket be long enough to carry the full appliedload in side-wall shear. Fromequation 8.7 the workingbond stress for rock with a compressive strength of 2MPa and a smooth,clean socket is 0.35 MPa. The required socket length L is calculated from equation 8.6as follows,assuming that the average bond stress developed over the full length of the socket is 0.35 MPa:

The settlement of the head of the pier, assuming elastic behavior is calculated from equation 8.13,using Fig. 8.14 to determine the influence factor I and equation 8.14 to determine the rock modulus

. In Fig. 8.14 the ratio and the length-to-diameterratio L/B is , which gives an influence factor of 0.26. The settlement is given by:

where


If the pier is cased through an upper 3 m thick layer of soil (new total length=9 m), then thesettlement calculation is modified as follows. A reduction factor RF is applied to the elasticsettlement of the socket as given in

Fig. 8.15. For a value of D/B of and a modulus ratio, , the valuefor RF is approximately 0.8. Therefore the elastic settlement of the socket is:

To this settlement must be added the elastic compression of the recessed, 3 m length of the pierwhich is equal to 0.9 mm.

END BEARING PIER

Assume that the purpose of the pile is to transfer the applied load to the rock at a depth of 6 m belowthe ground surface as shown, for example, in Fig. 8.2. In these circumstances the socket would be casedthrough the rock and the entire load would be carried in end bearing. The applied bearing pressure s onthe end of the pier is:

Figure 8.17Elastic settlement influence factors and end-bearing ratios for complete socketed piers (after Rowe andArmitage, 1987, courtesy of Research Journals. National Research Council Canada).


As shown in equation 8.9, the allowable bearing pressure, including a factor of safety againstfracture of the rock of about 3, for an end bearing pier is equal to the uniaxial compressive strengthof the rock. The compressive strength of the rock below the base of the pier is 20 MPa so the entireapplied load of 10 MN can be safely carried in end bearing.

The settlement of an end bearing pile is calculated from equation 8.16, using Fig. 8.16 to determine thereduction factor RF. The ratio of the concrete modulus to the modulus of the rock below the base

is i.e. less than 50, so it can be assumed that the base ofthe pier will act as a flexible footing. The reduction factor for a flexible footing on a rock with aPoisson’s ratio of 0.25 and a depth to diameter ratio, , is 0.7. The settlement iscalculated as follows

These calculations show that settlement due to compression of the pier is small compared with thecompression of the rock below the base.

SOCKETED AND END-BEARING PIER

For a pier fully socketed into the rock, the end of which is bearing on a clean, sound rock surface, theload will be supported in both side-wall shear and end bearing. Under these conditions the socket lengthcan be significantly shorter than where the load is supported only in side-wall shear. A design procedurefor this type of pier is first to select a socket length which is less than that required to carry the fullapplied load in side-wall shear resistance, and then use Fig. 8.17 to determine the settlement influencefactor and the end-bearing load.

For a socket length of 4 m, L/B is 2.7 and from the upper half of Fig. 8.17(a) the influence factor I is about 0.18 when .

The settlement is calculated from equation 8.13 as:

The portion of the load carried in end bearing can also be determined from Fig. 8.17(a). Byextending a vertical line from the point on the horizontal axis where down to intersectthe line representing the ratio the ratio Qb/Q is found to have a value of about 40%.Therefore, the load carried in end bearing is 4 MN and the load carried in side-wall shear is 6 MN.Having determined the socket length to achieve a specified settlement, the final task is to ensurethat the side-wall and end bearing stresses do not exceed allowable values as specified by equations8.7 and 8.9 respectively.

An alternative design procedure is to calculate an influence factor from an allowable settlement valueand then use Fig. 8.17 to determine the required socket length. Inspection of Fig. 8.17 shows that it willnot always be possible to achieve an intersection between the Ec/Em(s) lines and the horizontal line drawnfrom the required value of the influence factor. If there is no intersection between the horizontal line


drawn from the I axis and the modulus ratio curve Ec/Em(s), then the design value for the influence factorcannot be achieved. It is then necessary to modify the design as follows.

For conditions where the design influence factor is too small for an intersection point, it would benecessary to increase the allowable settlement, or decrease the pier load by installing more piers. Forconditions where the design influence factor is too high for an intersection point, this would indicate thatthe allowable settlement is high and slip will occur along the shaft. If the load on the pier is high enoughto cause slip, then the pier will no longer behave elastically and plastic shear will occur along the socket.If the value for I is too low to achieve an intersection, then the required settlement is too small for theconditions and either a greater settlement must be accepted or a larger pile diameter used.

8.4.5Socketed piers with pre-load applied at base

The application of a pre-load stress at the base of anend bearing socketed pier has the effect of reducingsettlement, and this technique may be used wherethe rock is poor or where settlement tolerances areminimal. The upward movement of the pier whenthe pre-load is applied at the base causes a reductionof the load supported by shaft resistance and a moreuniform distribution of load down the shaft, theeffect of which is to improve the load-settlementbehavior. Pre-loading the base of a pier will have nosignificant effect on the load capacity unlessconsolidation grouting of the rock below the base ofthe pier is carried out.Pre-loads have been produced by installing a loadcell at the base of test piers (Horvath et al., 1983;Meyer and Schade, 1995), and by pressure groutingthe base (Simons, 1963; Taylor, 1975). In theproject described by Meyer and Schade, anOsterburg hydraulic cell was placed in the base ofpiers up to 1.32 m (52 in) diameter drilled into soilwhich were then loaded to compress the materialbeneath the base of the pier. This procedure alsotested the side-wall shear of the piers which showedthat it was possible to reduce the length of thesocket by about 10 m (30 ft) from that assumed inthe design. Furthermore, the piers supported the 8.9MN (2000 kip) service load with only 12 mm (0.5in) of settlement.In the project described by Taylor, pressure groutingwas used at a site where six out of a total of 22 pierswere socketed into a volcanic agglomerate

comprising basalt gravel and boulders in a matrix ofweathered ash, while the remainder were endbearing on sound basalt. The piers in theagglomerate were belled to increase the bearingcapacity and then the base was pressure grouted tolimit settlement. The pressure grouting procedurewas to place a layer of clean gravel at the base ofeach pier, and then cast the concrete with grout pipesextending through the pier to the base. Grout waspumped into the gravel at the base, beforeapplication of the structural load, at a pressure equalto the maximum calculated bearing stress, includingearthquake loading. Some uplift of the piers wasobserved during grouting, but this was limited bythe side-wall shear resistance of the socket. Theobjective of this procedure was to induce settlementin the base of the pier prior to application of thestructural load. This was considered to besuccessful in that settlements of the piers socketedinto the agglomerate was no greater than that of thepiers founded on sound basalt.

8.5Uplift

Uplift loads on socketed piers can result whereelevated structures are subjected to horizontal loads.Examples of structural uplift loads are talltransmission towers where the tower forms a pointof intersection between two sections of tangent line,and some members of dock structures that mustwithstand ship impacts.Another condition where uplift forces may be


developed are piers drilled through expansive soilsand then socketed into rock. Swelling of the soil cangrip and lift the shaft developing tensile stresses inthe pier. Swelling pressures in clay can be as highas 2 MPa (300 p.s.i.), and free swell of such a soilmay amount to 20% or more of the thickness of thezone of active heaving. There are examples ofunreinforced pier shafts breaking in tension in areaswhere swelling soils are prevalent, with the breakoften occurring immediately above the base orunderream (Woodward et al., 1972). Figure. 8.18shows a design suitable for use in areas of swellingclays. The reinforcement for the pier consists of aconcrete-filled steel pipe which has the capacity tocarry the applied compressive load. The outside ofthe pipe down to the bottom of the expansive layeris coated with bituminous mastic. When the pier isgripped and lifted by the expansive clay, the masticcoating flows and the upward force in the pier islimited to the shear strength of the mastic.In many circumstances where substantial uplift loadsoccur, the most economical design is often theinstallation of tensioned anchors as described inChapter 9. The advantage of the use of tensionedanchors is that they can be installed in smallerdiameter holes than socketed piers and by applyinga pre-load, the uplift displacement can be controlled.Socketed piers can be designed to resist uplift forceseither by enlarging or belling the base, or bydeveloping sufficient side-wall shear resistance.While belling the base of a pier is common in soils,this can be an expensive and difficult operation inrock. Moreover, since a significant amount of side-wall shear resistance is developed in rock sockets, itis usually more economical to deepen the socketthan to construct a shorter, belled socket

8.5.1Uplift resistance in side-wall shear

Uplift load tests have been performed on side-wallresistance socketed piers to determine their loaddisplacement behavior and the ultimate loadcapacity (Webb and Davies, 1980; Kulhawy, 1985;Garcia-Fragio et al., 1987). The results of tension

tests conducted by Webb and Davis on concretepiers socketed into very weak sandstone have beencompared with the results of compression tests (referto Fig. 8.10). The two sets of curves have similarshapes within the linear elastic range. However, asthe uplift load increases and the side-wall bondbegins to break down, the tension pier undergoeslarge deformations and eventually fails, comparedwith the compression pier where settlement islimited because an increasing proportion of the loadis taken in end bearing.The results of load-displacement tests performed ontension piers can be used to calculate the shearstress developed on the side-wall, and the actualdisplacement can be compared with the theoreticaldisplacement calculated from elastic theory forcompression piers. The tests by Webb and Daviesindicate that equation 8.7 can be used to estimateside-wall shear strength for tensile loads providedthat there is no tendency for a cone of rock at thesurface to break out around the pier; this requires alength:diameter ratio of at least two (seeSection 9.3.4).The measured displacements of the piers tested intension by Webb and Davies have been comparedwith theoretical settlements for compression testscalculated from elastic theory using equation 8.13(for fully bonded sockets), and equation 8.15 (forrecessed sockets), and the influence factors given inFigs 8.14 and 8.15 respectively. It is found that themeasured displacement of the socket, taking intoaccount the elongation of the shaft, is within about30% of the displacements calculated by elastictheory for compression piers.An example of a full scale testing program of upliftcapacity of concrete piers socketed into rock isdescribed by Yoshii (1995) for a transmission lineproject constructed in steep, mountainous terrain.The towers were 110 m (360 ft) high and the foursupporting piers were each 20 m (66 ft) deep and upto 3.5 m (11.5 ft) in diameter. The sockets wereexcavated by pipe clamshell and manual labour.The loads on the foundations were due to the towerand cable weights, the cable tension and windforces which produced a combination of


compressive, uplift and lateral loading. Part of thedesign work comprised uplift tests on test piers 8 m(26 ft) long and 2.5 m (8.2 ft) in diameter, with theload applied with a hydraulic jack installed withinthe base of the pier. The rock in the socket was aweathered granite with a cohesion of 2–20 kPa (0.3–2.9 p.s.i.) and a friction angle of about 45°.The tests showed that the socket behaved elasticallyup to the design load of 11 MN, and achieved anultimate load of 17 MN (3820 kips). The averageshear stresses generated on the walls of the socketat these two loads were 175 kPa and 270 kParespectively (25 and 39 p.s.i.). These stresses forpiers in very weak rock can be compared withallowable and ultimate shear stresses presented inFig. 8.8 (compression) and Table 9.2 (tension).In conclusion, it is suggested that preliminarydesign of tension piers, or piers that are onlyoccasionally subjected to tensile loads, can becarried out using the equations that have beendeveloped for the design of compression piers.

However, for piers with substantial tensile loads, ordynamic tensile loads, full scale load tests may beperformed to determine the allowable side-wallshear resistance and the load-displacementbehavior.

8.5.2Uplift resistance of belled piers

In weak rock it is possible to bell the base of thepier either to increase the bearing capacity of acompression pier, or to resist uplift in the case of atension pier. The uplift capacity of a socketed pier iscalculated as follows (FHWA, 1988) and is basedon the breakout theory for discs (Vesic, 1971).The side-wall shear resistance above the bell shouldbe discounted, and the pier should be designed as ananchor, for which the net upward bearing capacityis

(8.17)where Ab, the area of bearing surface of the bell is

Figure 8.18 Design of belled pier for relief or uplift due to expansion of upper clay layer; the outer layer of concrete isexpected to break in tension near the bottom of the expansive layer. (by Raba-Kistner Consultants Inc. (Woodward etal., 1972)).

Note: Pipe must develop sufficient bond below rock level to transfer column load and uplift forces to concrete shaft andfooting.


given by

(8.18)

Bb is the diameter of bell, Bs is the diameter ofshaft, Nu is the uplift bearing capacity factor and tbis the shear strength of rock mass (seeequation 3.15). The value of the uplift bearingcapacity factor Nu depends on the ratio z/Bb, wherethe dimension z is defined in Fig. 8.19. Thisassumes that the base of the layer of expansive soilacts as a free surface:When

and when

These values for Nu are for intact or slightlyfractured rock; for closely fractured rock Nu shouldbe reduced by an appropriate amount determined bythe designer (FHWA, 1988).

8.6Laterally loaded socketed piers

Lateral loads on socketed piers may be derived fromwind pressures, current forces from flowing water,wave action, earthquakes, and in the case ofbridges, centrifugal forces and braking forces frommoving vehicles (Fig. 8.20). Other causes of lateralloading are impacts from ships in the case of docksand dolphins, and rock and soil pressures where thepier is used to reinforce a slope (Oak-land andChameau, 1989). The capacity of a socketed pier towithstand lateral loads depends on the rigidity of thepier, as well as the load-deformation characteristicsand formation thicknesses of the rock and soil inwhich the pier is socketed (Carter and Kulhawy,1992).For a pier that passes through a soft soil and is thensocketed in sound rock, even a short embedmentlength in the rock can have a significant effect onthe lateral deformation. Poulos (1972) describes amethod of calculating the displacement of laterallyloaded piles using elastic theory. This analysisexamines the difference in deflection betweenpinned-tip piles that bear on the rock surface and are

free to rotate but not translate, and fixed-tip pilesthat are socketed into the rock and neither rotate ortranslate. The analysis shows that the lateraldeflection for fixed-tip piles can be considerablyless than that of pinned-tip piles.For a pier that is fully embedded in rock with ahigher modulus than that of the pier material, thelateral deformation at the rock surface will beprimarily a function of the pier modulus anddeformation is likely to be minimal. This isgenerally a stable condition, except where the rockcontains shallow dipping fractures forming blocksthat could move under the application of thehorizontal load (refer to Fig. 8.25). The forceexerted on the blocks of rock can be calculatedusing p-y curves (see Section 8.6.1). The results canbe used to determine the required capacity of rockanchors that should be installed to preventmovement.

8.6.1Computing lateral deflection with p-y curves

The most widely used procedure for designinglaterally loaded piers is the p-y method. Thefollowing is a description of the principle of thismethod; analyses usually involve the use ofcomputer programs such as COM624 (FHWA,1986) and LATPILE (University of BritishColumbia, 1985) which use similar algorithms.Details of the analysis procedure and applications ofthese programs, which is beyond the scope of thisbook, are provided in the program documentation.Application of a lateral load to a socketed pier mustresult in some lateral deflection. The lateraldeflection will, in turn, cause a reaction in thesurrounding rock and soil that acts in the oppositedirection to the deflection. The magnitude of thereaction in the rock or soil is a function of thedeflection, and the deflection is dependent on thesoil-rock reaction. Thus, calculating the behavior ofa socketed pier under lateral load involves thesolution of a soil-rock-structure interactionproblem. In this solution, two conditions must besatisfied: the equations of equilibrium, and


compatability between deflection and soil-rockreaction.This method of analysis can be extended beyond theelastic range to analyze movements where the soilor rock yields plastically and ultimately fails inshear. This can be modeled using p-y curves whichrepresent:

1. the lateral deformation y of the soil and rock atany given depth below the ground surface; and

2. horizontally applied rock and soil reactions p(units kN/m or lbf/ft) ranging from zero to thestage of yielding of the rock-soil in ultimateshear when the deformation increases withoutany further increase in the load.

The p-y curves are independent of the dimensions,shape and stiffness of the pier and represent thedeformation of a discrete slice of the soil and rocksurrounding the pier that is unaffected by loadingabove and below it (Tomlinson, 1977).A model for a laterally loaded socketed pier

demonstrating the concept of p-y curves is shown inFig. 8.21. Each layer of soil and rock has beenreplaced with a spring, and the load-deformationbehavior of each spring is represented by a p-ycurve (Fig. 8.21(b)).The rock or soil reaction p (force per unit lengthdown the socketed pier) is a function of the lateraldeflection y. The p-y curves in Fig. 8.21(b) show theyielding and increasing modulus of the soil in theportion of the pier drilled through soil, and thehigher modulus, elastic behavior of the rock in thesocket. The deflected shape of the pier is super-imposed on the p-y curves, and the deformationmodulus of the soil is given by the secant to the p-ycurve at the corresponding deflection. Figure 8.21(c) shows that the modulus is defined as the ratio

and the modulus increases with depth.The deflection of the pier can be modeled mostaccurately by defining a p-y curve at the top andbottom of each layer since the program interpolatessoil behaviour between each pair of given points.The general behavior of a socketed pier under lateral

Figure 8.19 Belled piers to resist uplift forces due to (a) expansive soils, (b) tensile loads.


load can be obtained by solving the followingdifferential equation (Hetenyi, 1946):

(8.19)

where Qx is the axial load on the pier; y is the lateraldeflection of the pier at a point x along the length ofthe shaft; p is the lateral soil reaction per unit lengthof pier; EI is the flexural rigidity of pier withmodulus E and moment of inertia I; I equals pr4/4for circular pier with radius r; and W is thedistributed horizontal load along the length of theshaft.Other beam formula which are used to calculate theshear stress in the pier V, the bending moment M,and the slope of the elastic curve S are

(8.20)

(8.21)

(8.22)

Calculation of the deflected shape of a laterallyloaded pier, as well as the shear andbending moment in the pile involves an iterativeprocess comprising the following steps.

1. The deflected shape of the pier is assumed bythe computer.

2. The p-y curves are entered with the deflectionsand a set of modulus values is obtained.

3. With the modulus values, the differentialequations defining the behavior of the pier aresolved to obtain a new set of deflections.

4. Steps 2 and 3 are repeated until the deflectionsobtained are within the given tolerances of thevalues obtained from the previous computation.

5. Bending moment, shear and other aspects of thebehavior of the pier are then computed.

Figure 8.20 Typical conditions resulting in lateral loads on socketed piers: (a) socketed piers installed to stabilizefailing slope; and (b) loadings on single-column support for a bridge (FHWA-IP-84–11).


The procedure for constructing p-y curves for claysand granular soils, above and below the water table,for both static and dynamic loading, as well as forweak rock, has been developed by Reese (Reese etal., 1974; FHWA, 1986; Reese, 1997). Theprocedure consists of first calculating the ultimateresistance pult of the soil and rock, and thencalculating the modulus from laboratory tests,orusing empirical relationships between rock masscharacteristics and modulus (Fig. 3.10).Alternatively, p-y curves can be obtained from theresults of in situ pressuremeter tests (Atukorala etal., 1986; Briaud et al., 1982, 1983), and frominclinometer measurements (Brown and Zhang,1994).

8.6.2p-y curves for rock

There are few records of p-y curves for rock,probably because once the rock strength is greaterthen that of the concrete, the pier is essentially fixed

at the top of rock and the design issue relates to thestability of the rock socket rather than the modulus(see Section 8.6.3). However, the results of a limitednumber of tests of installations in very weak rockhave been used in the development of a preliminaryprocedure for drawing up p-y curves for weak rockbased on the following concepts and procedures(Reese, 1997).

1. The geological structure of the rock mass cansignificantly influence its behavior, which mustbe taken into account in the application of theprocedures described in this section.

2. The p-y curves for rock and the bendingstiffness EI for the pile must both reflect non-linear behavior in order to predict loadings atfailure.

3. The initial slope of the p-y curves must bepredicted because small lateral deflections ofpiles in rock can result in resistances of largemagnitudes. For a given value of compressivestrength, is assumed to increase withdepth below the ground surface.

Figure 8.21 Model of a socketed pier under lateral load showing the concept of soil response: (a) reaction of rock andsoil layers replaced by springs; (b) stress-strain curves; (c) increase in modulus with depth.


4. The modulus of the rock mass Em, forcorrelation with may be taken from theinitial slope of a pressuremeter curve. Othercorrelations between the rock mass rating RMRfor rock masses and the in situ modulus ofdeformation are shown in Fig. 3.10 andequation 3.5.

5. The ultimate resistance pult for the p-y curveswill rarely, if ever, be developed in practice,but the prediction of pult is necessary in order toreflect non-linear behavior.

6. The component of the resistance related to thedepth below the surface is considered to besmall in comparison with that from thecompressive strength, and therefore the weightof the rock is neglected.

7. The compressive strength of the intact rockused for computing the value for pult may beobtained from tests of intact samples.

8. The assumption is made that fracturing willoccur at the rock surface under smalldeflections. Therefore, the compressivestrength of the intact rock is reduced by a factorar to account for the fracturing. The value for aris assumed to be 0.33 for RQD values of 100%and to increase linearly to 1.0 at RQD of 0%.This relationship between ar and RQD accountsfor the likely brittle failure and significant lossof strength of massive rock when strained,compared with the greater amount ofdeformation that may occur prior to failure forfractured rock (i.e. low RQD). If the RQD is 0%the compressive strength may be taken directlyfrom the pressuremeter curve.

(a) Ultimate resistance of rockThe ultimate resistance pult of the rock when subjectto lateral loading in a drilled socket is based uponlimit equilibrium and increases in value with depthbelow the surface of the rock. The value for pult isgiven by (Reese, 1997):

(8.23)

or

(8.24)where ar is the strength reduction factor; su(r) is thecompressive strength of the intact rock, usuallylower bound and will vary with depth as appropriatefor site conditions; xr is the depth below the surfaceof the rock; and B is the pier diameter.(b) Slope of initial portion of p-y curveFor a beam resting on an elastic, homogeneous,isotropic solid, the relationship between themodulus of the rock mass Emi over the initial part ofthe p-y curve, and the initial slope of the curve is given by

(8.25)where ki is a dimensionless constant derived fromexperiment and assumes that the depth below therock surface has a similar effect on ki as for pult. Forthe initial portion of the p-y curve up to point A (seeFig. 8.22), values for ki are given by:

(8.26)

or(8.27)

Equations 8.26 and 8.27 which have been developedfrom experimental data show that the initialportions of the p-y curves are very stiff, which isconsistent with the very low deflections observedduring the initial loads.(c) Calculation of p-y curvesThe p-y curves for weak rock have three portions asshown in Fig. 8.22. The procedure for devel opingthese curves is to calculate first pult using equation8.23 or 8.24 appropriate for the depth, and then theinitial slope of the curve using equation 8.26 or8.27. The three portions of the p-y curve are definedby the following equations. The initial straight lineportion is given by:

(8.28)while the curved portion is given by

(8.29)

and the horizontal portion by(8.30)


where(8.31)

and km is a constant ranging from 5E–4 to 5E–5.Based on the very limited number of case studies, ithas been found that km has values of 5E–4 for vuggylimestone, and 5E–5 for sandstone containing veryclosely spaced discontinuities. These tests aredescribed in more detail in (d) below. The value for the deflection yA defining the limit ofthe linear portion of the p-y curve is found bysolving for the intersection of equations 8.28 and8.29 and is given by

(8.32)

The equations described in this section are based onlimited data and should be used with an appropriatefactor of safety for conditions where the geologydiffers significantly from that at the test sites.Where possible, full-scale load tests should becarried out to confirm these calculations. Also, theassumed linear relationship between p and y shouldbe valid for static loading and if resistance is duelateral stresses only (Reese, 1997).(d) Examples of p-y curves from full scale tests

Figure. 8.23 shows the results of two lateral loadtests on pier socketed into very weak rock, and thegeneral trend of the p-y curves for these materialscalculated using the procedures discussed inSection 8.6.2 (a), (b) and (c) above. For each test, p-y curves for depths below the top of bedrock (xr) of1 m and 3 m (3.28 and 6.56 ft) are shown toillustrate the effect of depth on the lateral resistanceof these materials. That is, both the ultimate lateralresistance pult and the initial modulus increasewith depth. A summary of test methods and siteconditions, and values for the design parameters, isas follows.

1. 1.22 m (48 in) diameter pier drilled to a totaldepth of 17.53 m (57.7 ft), with a 13.32 m (43.7ft) long socket into brittle, vuggy lime-stone;the RQD was assumed to be close to zero. Themaximum horizontal load was 670 kN (150kips) and the deflection of the pier wasmeasured at the point of application of the loadand at the top of rock (FHWA, 1984; Reese,1997). The maximum deflection was 18 mm (0.71 in) at the point of load application (3.5 m(11.5 ft) above the rock level), and 0.54 mm (0.0213 in) at rock level. The design parameters

Figure 8.22 Typical p-y curve for weak rock.


defining the p-y curves are shown in Fig. 8.23(a).

2. 2.25 m (88.6 in) diameter piers drilled to adepth of 12.5 and 13.8 m (41 and 42.3 ft) intodense, fractured sandstone with RQD rangingfrom 0 to 80%. An inclinometer casing wascast into the pier to measure the deflection asthe horizontal load was applied, and thedeflected shape was then used to derive p-ycurves by making a best fit to the data using apreselected analytical function for the p-yrelationship (Brown and Zhang, 1994; Reese,1997). The maximum applied load was 6450kN (1450 kips) and the maximum deflection atthe top of the pier was 6 mm (0.24 in). Thedesign parameters defining the p-y curves areshown in Fig. 8.23(b).

(e) Example of analysis of laterally loadedsocketed pierThe results of an analysis of a laterally loadedsocketed pier using the program LATPILE areshown in Fig. 8.24. The depth of the overburden is 6m, and the socket depth in rock is 2 m, for a totalpier depth of 8 m. The p-y curves at the top and bottom of the overburden, and inthe rock show the significantlydifferent resistance provided by the overburden andthe rock. The three pairs of curves in the lower partof Fig. 8.24 show the displacement, moment andshear force distributions down the pier, and theeffect on these parameters of the 2 m long socket.For these particular conditions, the overburden issufficiently stiff to provide considerable resistanceto the lateral loads, and the socket has only a minoreffect in reducing the displacement, moment andshear.

8.6.3Socket stability under lateral load

An important aspect of the design of rock socketedpiers under lateral load is the stability of the rock inthe socket. Figure 8.25 shows two examples of rockwedges formed (a) by a single pier located on a

slope face, and (b) at the base of a vertical wallsupported by a row of piers. The stability of rocksocket will be highly dependent on the structuralgeology of rock because this will define the shapeand dimensions of the wedge, as well as the shearstrength parameters of the sliding surfaces. Ofparticular importance is the presence ofdiscontinuities that are oriented to form the base ofthe wedge. In Fig. 8.25(a) a joint that dips eitherinto or out of the slope could develop an unstablewedge, and this condition is exacerbated if the rockcontains a vertical conjugate joint set that formsrelease surfaces on the sides of the wedge. In fullscale load tests (Maeda, 1983; Yoshii, 1995) inwhich the pier was socketed into a weathered,rhyolitic tuffy breccia with no continuous joints, thedip angle of the base of the wedge ψp was found tobe (Fig. 8.25(a)):

(8.33)

where ψf is the dip of the slope face and is thefriction angle of the rock in the socket.Note that a negative value for ψp indicates that thebase of the wedge is inclined above the horizontal.The tests by Maeda also showed that the angledefining the width of the wedge is approximatelyequal to 45°.Figure 8.25(b) shows a vertical wall with ahorizontal surface at the base. In this casediscontinuities dipping away from the wall will not‘daylight’ and a potentially unstable wedge will notbe formed. However, joints dipping towards thewall do form a wedge and stability calculations byGreenway et al. (1986) showed that the capacity ofthe socket to sustain lateral loads is a minimumwhen the dip of the fractures ψp is in the range ofabout 5° to 30°.The stability of the rock sockets with the geometriesshown in Fig. 8.25 can be analyzed using theprinciples described in Chapter 6. This analysisinvolves resolving all forces acting on the wedgeinto vectors parallel and normal to the slidingsurface, from which the resisting and displacingforces and the factor of safety are calculated. In thecase of the wedge in Fig. 8.25(a) a conservative


assumption would be that no shear stresses aredeveloped on the two sides of the wedge and thatthe resistance would be developed solely on thebase. The normal stress on the base would becalculated for the weight of the entire wedge. Incontrast, for the wedge in Fig. 8.25(b), the factor ofsafety could be calculated for a unit length of thewedge, again assuming that no shear resistance isdeveloped on the end faces. Potentially unstablewedges in the socket area could be reinforced withtensioned rock bolts anchored below the base of thesocket. The shear force determined by the programLATPILE would be used to determine themagnitude of the displacing force acting on thewedge and calculate the reinforcing force requiredto retain the wedge of rock.

8.7References

American Petroleum Institute (1979) Recommendedpractice for planning, designing and constructing fixedoffshore platforms. Report No. API-RP2A,Washington, DC, 10th Edition.

Atukorala, U.D., Byrne, P.M. and She, J. (1986)Prediction of ‘p-y’ Curves from Pressuremeter Tests.Soil Mechanics Series 108, Civil EngineeringDepartment, University of British Columbia.

Barton, Y.O. and Pande, G.N. (1982) Laterally loadedpiles in sand: centrifuge tests and finite elementanalyses. Numerical Models in Geomechanics,Balkema, Rotterdam, pp. 749–58

Briaud, J.-L., Smith, T.D. and Meyer, B.J. (1982)Pressuremeter gives elementary model of laterallyloaded piles. Int. Symp. on in situ Testing of Rock andSoils, Paris, May.

Briaud, J.-L., Smith, T.D. and Meyer, B.J. (1983)Laterally loaded piles and the pressuremeter:comparison of existing methods. ASTM SpecialTechnical Publication on the Design and Performanceof Laterally Loaded Piles and Pile Groups, June.

Brown, D.A. and Zhang, S. (1994) Determination of p-ycurves in fractured rock using inclinometer data. Proc.Int. Conf. Design and Construction of DeepFoundations, US Federal Highway Administration,Orlando, FL, pp. 857–71.

Canadian Geotechnical Society (1985) Canadian

Foundation Engineering Manual, 2nd edn, BiTechPublishers, Vancouver, British Columbia.

Carter, J.P. and Kulhawy, F.H. (1992) Analysis oflaterally loaded shafts in rock. J. Geotechncial Eng.,118(6), ASCE, 839–55.

Chang, M.F. and Wong, I.H. (1987) Shaft friction ofdrilled piers in weathered rock. Proc. 6th Int. Conf. onRock Mech. Montreal, ISRM, pp. 313–18.

Chiu, H.K. and Donald, I.B. (1983) Prediction of theperformance of side resistance piles socketed inMelbourne mudstone. Proc. International Cong. onRock Mech., Melbourne, ISRM, pp. C235–243.

Donald, I.B., Chiu, H.K. and Sloan, S.W. (1980)Theoretical analysis of rock socketed piles. Proc.International Conf. on Structural Foundations onRock, Sydney, pp. 303–16.

Drumm, E.C. (1998) Personal communication.Federal Highway Administration (US) (1986) Behavior

of Piles and Pile Groups Under Lateral Load. FHWA/RD-85–106, Federal Highway Administration, Dept. ofResearch, Development and Technology, McLean,Virginia.

Federal Highway Administration (US) (1988) Drilledshafts: Construction Procedures and Design Methods.FHWA-HI-88–042, Federal Highway Administration,Dept. of Research, Development and Technology,McLean, Virginia.

Garcia-Fragio, A., James, E., Romana, M. and Simic, D.(1987) Testing the Axial Capacity of Steel PilesGrouted into Rock. Int. Soc. Rock Mechanics,Montreal, pp. 267–71.

Gill, S.A. (1980) Design and construction of rocksockets. Proc. International Conf. on StructuralFoundations on Rock, Sydney, pp. 241–52.

Glos, G.H. and Briggs, O.H. (1983) Rock sockets in softrock. J. Geotech. Eng. Div., ASCE, 109(4), 525–35.

Greenway, D.R., Powell, G.E. and Bell, G.S. (1986)Rock-socketed caissons for retention of an urban road.Proc. of Conf. on Rock Engineering and Excavation inan Urban Environment, Hong Kong, Inst. Mining andMet., pp. 173–80.

Hetenyi, M. (1946) Beams on Elastic Foundations. TheUniversity of Michigan Press, Ann Arbor, Michigan.

Horvath, R.G., Kenney, T.C. and Kozicki, P. (1983)Methods of improving the performance of drilled piersin weak rock. Can. Geotech. J., 20, 758–72.

Horvath, R.G., Schebesh, D. and Anderson, M. (1989)Load-displacement behaviour of socketed piers—Hamilton General Hospital. Canadian Geotechnical


Journal, 26, 260–8.

Figure 8.23 p—y curves for very weak rocks determined from lateral load tests on rock socketed piers (adapted fromReese, 1997).


Kay, G.B. (1989) Personal communication.Kulhawy, F.H. (1985) Drained uplift capacity of drilled

shafts. Proc. XI Int. Conf. on Soil Mech. andFoundation Eng., San Francisco, pp. 1549–52.

Kulhawy, F.H. and Goodman, R.E. (1980) Design offoundations on discontinuous rock. Proc. InternationalConf. on Structural Foundations on Rock, Sydney,Australia, pp. 209–220.

Figure 8.24 Illustration of a laterally loaded pier showing deflection, moment and shear force computed by programLATPILE.


Ladanyi, B. (1977) Friction and end bearing tests onbedrock for high capacity socket design: Discussion.Can. Geotech. J., 14, 153–5.

Ladanyi, B. and Domingue, D. (1980) An analysis ofbond strength for rock socketed piers. Proc. Int. Conf.on Structural Foundations on Rock, Sydney,pp. 363–73.

Lueng, C.F. (1996) Case studies of rock socketed piles. J.

Southeast Asian Geotechnical Soc., 27(1), 51–67. Macaulay, D. (1976) Underground. Houghton Mifflin

Co., Boston, MA.Maeda, H. (1983) Horizontal behavior of pier foundation

on a soft rock slope. Int. Congress of Rock Mechanics,Melbourne, ISRM, pp. C181–4.

Matlock, H. (1970). Correlations for laterally loaded pilesin soft clay. Proc. 2nd Annual Offshore Technology

Figure 8.25 Stability of rock sockets under lateral loading: (a) wedge formed by single laterally loaded socket locatedon slope (after Maeda, 1983); and (b) wedge formed at base of vertical wall supported by a row of socketed piers (afterGreenway et al., 1986).


Conf., Paper 1204, Vol. 1, Houston, pp. 577–94.Meyer, B.J. and Schade, P.R. (1995) Touchdown for the

O-cell test. Civil Engineering, ASCE, February, 57–9.Oakland, M.W. and Chameau, J.-L. (1989) Analysis of

drilled piers used for slope stabilization. TransportationResearch Record 1219, Transportation ResearchBoard, Washington, DC, pp. 21–32.

O’Neill, M.W. and Hassan, K.M. (1994) Drilled shafts:effects of construction on performance and designcriteria. Proc. Int. Conf. Design and Construction ofDeep Foundations, US Federal HighwayAdministration, Orlando, FL, pp. 137–87.

Ooi, L.H. and Carter, J.P. (1987) Direct shear behavior ofconcrete-sandstone interfaces. Proc. 6th Int. Conf. onRock Mech., Montreal, ISRM, pp. 467–70.

Osterberg, J.O. and Gill, S.A. (1973) Load transfermechanisms for piers socketed in hard soils or rock.Proc. 9th Canadian Sym. on Rock Mech., Montreal,pp. 235–62.

Pells, P.J. N., Rowe, R.K. and Turner, R.M. (1980) Anexperimental investigation into side shear for socketedpiles in sandstone. Proc. Int. Conf. on StructuralFoundations on Rock, Sydney, pp. 291–302.

Pells, P.J. N. and Turner, R.M. (1979) Elastic solutions forthe design and analysis of rock socketed piles. Can.Geotech. J., 16, 481–7.

Poulos, H.G. (1972). Behavior of laterally loaded piles: III—socketed piles. J. Soil Mech. and Foundation Div.,ASCE, 98, SM4, 342–60.

Reese, L.C. (1997) Analysis of laterally loaded piles inweak rock. J. Geotechnical and GeoenvironmentalEng., 123(11), ASCE, 1010–17.

Reese, L.C., Cox, W.R. and Koop, F.D. (1974) Analysis oflaterally loaded piles in sand. 6th Annual OffshoreTechnology Conference, Houston, Texas, Paper, No.2079.

Rowe, R.K. and Armitage, H.H. (1987) Theoreticalsolutions for the axial deformation of drilled shafts inrock. Can. Geotech. J., 24, 114–25 and 126–42.

Rowe, R.K., Booker, J.R. and Balaam, N. (1978)Application of the initial stress method to soilstructureinteraction. Int. J. of Numer. Meth. in Eng., 12(5),873–80.

Rowe, R.K. and Pells, P.J. N. (1980) A theoretical studyof pile-rock socket behavior. Proc. Int. Conf. onStructural Foundations on Rock, Sydney, pp. 253–64.

Seidel, J.P. and Haberfield, C.M. (1994) A new approachto the prediction of drilled pier performance in rock.Proc. Int. Conf. Design and Construction of Deep

Foundations, US Federal Highway Administration,Orlando, FL, pp. 556–85.

Seychuck, J.L. (1970) Load tests on bedrock. Can.Geotech. J., 7, 464–70.

Simons, H. (ed.) (1963) The Bridge Spanning LakeMaracaibo in Venezuela. Bauverlag GmbH.,WeisenBaden, pp. 22–59.

Sowers, G.F. (1976). Foundation bearing in weatheredrock. Proc. of Specialty Conf. on Rock Eng. forFoundations and Slopes, Boulder, CO., ASCE,Geotech. Eng. Div., Vol. II, pp. 32–41.

Tang, Q., Drumm, E.C. and Bennett, R.M. (1994)Response of drilled shaft foundations in karst duringconstruction loading. Proc. Int. Conf. Design andConstruction of Deep Foundations, US FederalHighway Administration, Orlando, FL, pp. 1296–309.

Taylor, P.W. (1975) Pre-loaded pier foundations for citybuilding. New Zealand Eng. 15, pp. 320–5.

Thorne, C.P. (1980) The capacity of piers drilled in rock.Proc. Int. Conf. on Structural Foundations on Rock,Sydney, pp. 223–33.

Tomlinson, M.J. (1977) Pile Design and ConstructionPractice. ICE, Cement and Concrete Association,London.

University of British Columbia (1985) Deflections ofLaterally Loaded Piles, LATPILE.PC. CivilEngineering Program Library, UBC, Vancouver.

Vesic, A.S. (1971) Breakout resistance of objectsembedded in the ocean bottom. J. Soil Mech. andFoundation Div., ASCE, 97, SM9 (Proc. Paper 8372),1183–205.

Walter, D.J., Burwash, W.J. and Montgomery, R.A.(1997) Design of large-diameter drilled shafts for theNorthumberland Straight bridge project. CanadianGeotech. J., 34, 580–7.

Webb, D.L. and Davies, P. (1980) Ultimate tensile loadsof bored piles socketed into sandstone rock. Proc. Int.Conf. on Structural Foundations on Rock, Sydney,pp. 265–70.

Williams, A.F. (1980) The Design and Performance ofPiles Socketed in Weak Rock. PhD Thesis, MonashUniversity, Melbourne.

Williams, A.F., Johnston, I.W. and Donald, I.B. (1980)The design of socketed piles in weak rock. Proc. Int.Conf. on Structural Foundations on Rock, Sydney,pp. 327–47.

Williams, A.F. and Pells, P.J. N. (1981) Side resistancerock sockets in sandstone, mudstone and shale. Can.Geotech. J., 18, 502–13.


Winterkorn, H.F. and Fang, H.-F. (1975) FoundationEngineering Handbook. Van Nostrand Reinhold, NewYork, pp. 601–15.

Woodward, R.J., Gardner, W.S. and Greer, D.M. (1972)Drilled Pier Foundations. McGraw-Hill, New York,pp. 84–91.


9Tension foundations

9.1Introduction

In contrast to that of soil, the relatively high shearand tensile strengths of rock allows rockfoundations to support substantial tension (uplift)loads. These loads are transferred from the structureto the foundation rock by steel anchors, comprisingrigid bars or flexible strands. The anchors aresecured with cement or epoxy grout in a hole drilledinto the foundation, and the head of the anchor isthen embedded in, or bolted to, the structure. Inapplications where movement of the structure mustbe limited, the anchors are prestressed. This methodof support, which mobilizes a mass of rock in thefoundation to resist the uplift, is often a moreefficient support method for tensile loads thanattaching the structure to a mass of concrete with aweight equal to the applied load.Figure 9.1 shows the main support towers of asuspension bridge, and an internal view of one ofthe anchor chambers. Each cable consists of 20strands which are anchored with 12 m (40 ft) longanchors installed into a pattern of holes drilled intothe rock. The anchors are secured with mechanicalexpansion shells, and then pretensioned against thereaction plate in the anchor chamber so that therewould be no movement of the anchorage when thesuspension cables were loaded. At the completionof installation, the anchor holes were fully groutedto protect the cables against corrosion. Note thatthis installation was carried out in the 1960’s;although the anchors are performing satisfactorily,present practice would be to use grout anchoragesrather than mechanical expansion shells, and to use

a more reliable method of corrosion protection.Figure 9.2 as well as Fig. 1.2(d) show otherapplications of rock anchors to support tensile loadsand demonstrates the wide range of loadingconditions that can be accommodated by rockanchors. In all these applications, the general designand construction procedure comprises drilling ahole, or holes, where possible in a direction parallelto the direction of the applied load to a depth whererock is encountered, and then anchoring a rigid steelbar or cable in the hole. This installation can be assimple as a length of reinforcing steel fully groutedinto the hole, or as complex as a bundle of highstrength steel cables with two layers of corrosionprotection which is anchored in the lower part of thehole with cement grout and then tensioned. Thechoice of anchor type will depend on such factors asthe magnitude and duration of the load, thepotential for corrosion, the rock conditions in theanchor zone, and physical constraints such asconstruction access.The examples shown in Fig. 9.2 illustrate somedifferent conditions for anchor installations. InFig. 9.2(a) the anchors to secure the rock fallprotection roof would have to be of low capacitybecause it would be necessary to use a lightweightdrill that could be lifted into position on the slopeface, and a cable anchor that could be readilyinserted in the uphole. In contrast, the anchorsthrough the gravity dam (Fig. 9.2(b)) could be ofmuch larger capacity because a barge-mounted drillcould be used to drill large diameter holes, and ahigh capacity cable anchor assembly could be liftedinto place using a helicopter or crane.

This chapter discusses the following four aspects ofthe design and construction of tensioned anchors:

1. the different types of anchors and anchoragesystems that are available on the market, andtheir applications;

2. design methods to determine the load capacityof anchors;

3. causes of corrosion and methods of corrosionprotection for permanent protection;

4. test methods used during construction to verifyanchor performance and capacity.

The anchors described are mainly suitable forinstallations in rock. Descriptions of anchorssystems suitable for installation in soil, whichusually require the use of such techniques as belledor pressure grouted anchors, may be found in publications by Hanna (1982) and Federal HighwayAdministration (1982).

9.2Anchor materials and anchorage methods

The anchors used for the typical applications shownin Figs 9.1 and 9.2 are generally fabricated fromrigid steel bars or strand, and anchored with cementor epoxy grout. This section describes the materialsthat are available from some specialistmanufacturers of anchor products and theconditions in which they are most often used. Theseproducts are suitable for ‘permanent’ anchors,the performance of which must meet the followingcriteria.

1. A high degree of reliability is required for boththe materials from which the tieback and headcomponents are fabricated and the completedinstallation.

2. The applied structural loads may be either staticor cyclic, and may be as high as 5 MN (≈1000kips).

3. Deformation tolerances are low and must bepredictable.

4. The service life should not be less than about

50 years.

In order to meet these requirements, the materialsmust be of very high quality and the installation andtesting procedures be designed so that theperformance of every anchor can be verified. Thereason for this high level of quality control is thatonce the anchors are installed, it is virtuallyimpossible to inspect or replace them withoutexcavating the foundation.There are many types of rock bolts available on themarket that are used in the mining industry and fortemporary support in tunnels. These productsinclude various types of rigid bolts with wedge typeanchorages, and bolts such as Swellex (Atlas Copco)and Split Set (Ingersoll Rand) which are malleableand deform as they are installed. Generally thesebolts have lengths up to about 3 m, are not corrosionprotected and are designed to yield at high loads.While these properties are suitable for theconditions for which they are designed, theirperformance will not meet the requirements forpermanent anchors listed in the previous paragraph.Consequently they are not discussed in this book.

9.2.1Allowable working loads and safety factors

The allowable working load of an anchor is thedesign load that the anchor is required to sustainunder normal service conditions; higher loads maybe acceptable as long as they only occurinfrequently and are within limits as specified below.The allowable working load is expressed as apercentage of the specified characteristic strength ofthe steel. The characteristic strength is theguaranteed limit below which not more than 5% ofthe test results fall; none of the test results are lessthan 95% of the characteristic strength.The characteristic strength of the steel may be eitherthe guaranteed ultimate tensile stress (GUTS) or theyield stress. The yield stress is the stress at which thepermanent strain reaches 0.1% (known as the 0.1%offset stress), and is equivalent to about 85% of theultimate tensile stress. These values are supplied by

ANCHOR MATERIALS AND ANCHORAGE METHODS 311

the tendon manufacturer as part of the product

Figure 9.1 Suspension bridge across the Peace River in northern British Columbia, Canada (courtesy of the BritishColumbia Ministry of Transportation and Highways): (a) view of bridge with anchor chamber in foreground; and (b)interior view of anchor chamber showing connections between the 20 individual strands and the head of the rockanchors.

312 TENSION FOUNDATIONS

specification, and it is usually possibly to obtain amill certificate which gives the strength results forthe particular batch of steel from which the bar ortendon was manufactured. Figure 9.3 shows typicalload extension curves for a seven-wire strand and aprestressing bar and defines both the yield andultimate loads.The allowable working load is generally taken to bebetween 50% and 62.5% of the ultimate tensilestrength, i.e. the factor of safety against failure ofthe anchor material is between 2 and 1.6. Littlejohnand Bruce (1975b) provide an extensive review ofsafety factors used in practice and specified in codesby such countries as Britain, France, Germany andSwitzerland. The factors of safety used and

specified vary from as low as 1.43 to as high as 2.27, but the trend appears to be to use a factor ofsafety of 2 for most permanent applications. Asdescribed in Section 9.5, the procedure for testingthe performance of anchors requires the applicationof an overload which can readily be accommodatedif the working load is 50% of the ultimate strength;the maximum test load should not exceed the yieldload of the steel. This margin of safety also allowsthe application of occasional overloads during theservice life to stress levels up to about 60% of theultimate strength.

Figure 9.2 Typical applications of rock anchors to support tension loads: (a) anchored roof to protect roadway fromrock falls; (b) permanent tie-downs installed to improve overturning resistance of dam; and (c) rock anchors providingsupport for tensioned cable.


9.2.2Steel relaxation

A property of steel which may be of significance tothe performance of tensioned anchors is stressrelaxation. Tensioned anchors may lose loadwith time as a result of both steel relaxation, asdescribed in this section, and creep of the anchorageas described in Section 9.3.7.The factors that influence steel relaxation are thestress level, the service temperature, time afterstressing, and in the case of strand, the tendency ofthe strand to unwind. At stress levels up to 50% ofthe ultimate strength, relaxation is negligible and ifan overload is applied during testing this will reducethe tendency of the strand to relax during service.For stress levels of 75% of the ultimate strength andtemperatures of 20° C, a load loss of 5–10% of theapplied stress occurs in ordinary stress relievedsteel, while in ‘stabilized’ strand the load loss isreduced to 1.5%.Figure 9.4 shows the relationship between the stress

relaxation, as a percentage of the initial stress, andtime for steel bar, wire and strand. This graphshows that the major part of the relaxation takesplace in the first 100 hours. However, the relaxationwill continue with time, although at a decreasingrate, and the relative relaxations ?t at times t of 1,100, 1000 and 250 000 hours are

The equation defining the loss of stress due torelaxation at normal ambient temperatures is asfollows (Libby, 1977):

(9.1)

where ?sr is the relaxation stress loss at time t hoursafter stressing; si is the initial stress, and sy is the 0.1% offset stress.Note that this equation is only applicable when theratio si/sy is equal to or greater than 0.55, becausewhen the initial stress is less than 0.55 of the 0.1%offset stress, relaxation is negligible.In situations where these levels of relaxation are

Figure 9.3 Typical stress-strain curves for 32 mm diameter prestressing bar and 13 mm diameter strand (after Libby,1977).


unacceptable, restressing at a time of 1000 hourswill reduce the further relaxation to about onequarter of its normal value at an initial stress of 70%of GUTS. Another method of reducing relaxation isto overload the anchor at the time of initial stressingand hold this stress for a period of up to 10 minuteswhich disposes of the rapid initial relaxation(Littlejohn and Bruce, 1976). It is also found thatthe relaxation rate increases rapidly at temperaturesover 20° C which may be of significance in someapplications.

9.2.3Strength properties of steel bar and strand

The properties of steel bar and strand anchors thatare required for design are the yield stress, theultimate tensile stress, the elastic modulus and therelaxation characteristics. While the manufacturer’sspecifications should be checked for the actualproperties of any product, the information given inTable 9.1, which lists the properties for somewidely distributed products, can be used as aguideline for preliminary design.

9.2.4Applications of rigid bar anchors

The types of steel bars used as rock anchors includedeformed reinforcing steel, continuously threadedbar such as Dywidag Threadbar or Williams all-thread bar, and hollow core rock bolts such asWilliams bar. In almost all applications, deformedbar is used because of the improved steel-groutbond strength in comparison with smooth bar.Figure 9.5 shows two typical installations of baranchors and illustrates both mechanical wedge andgrout type anchorages. The Dywidag threadbar hasa smooth plastic sheath on its upper end where nobond is developed (Fig. 9.5(a)). When the bar isfully grouted this arrangement forms an bondlength lb over which a rock-grout-steel bondoperates, and a free stressing length lf whichallows strain in the bar during tensioning. Thefeatures of continuously threaded bar are that it canbe cut to any desired length and the threads canwithstand rough handling in the field withoutdamage. The cement grouted anchorage can be usedin both weak and strong rock with the length of theanchorage being adjusted according to the strengthof the rock (see Section 9.4). The value of the free

Figure 9.4 Relaxation of tendon steel and bar from initial stress of 0.7 ultimate tensile strength (after Littlejohn and Bruce,1975a).

1. Range of values for stress relieved wires. 2. Alloy steel wires. 3. Range of values for stress relieved strands. 4. Rangeof values for 19-wire strand (not stress relieved). 5. Stabilized strand.


stressing length is the ability of this length of thebar to strain in response to changing loads in theanchor. Note that this type of installation would notbe considered to have sufficient corrosion protectionfor most permanent installations.The hollow core bolt (Fig. 9.5(b)) is anchored witha mechanical rock anchor. This type of anchor is setby drilling a hole with a diameter that is just largeenough to grip the cone, and then torquing the bar todraw the cone into the shell and force the two

halves of the shell against the wall of the drill hole.The advantage of mechanical anchors is that thebolt can be installed and tensioned in one operation,which is in contrast to grouted anchors that cannotbe tensioned until the grout has set after a period ofseveral days. The hole through the center of the baris used to grout the bolt either immediately before,or after tensioning. In a down hole, the grout ispumped

Table 9.1 Properties of common types of bar used for permanent rock anchors

Product Yield stress (1% offset)MPa (kips/in2)

Ultimate tensile stressGUTS MPa (kips/in2)

Elastic modulusGPa (p.s.i)

Reinforcing steel 400 grade 400 (58) 600 (87) 201 (29×106)Dywidag 420/500 grade 420 (61) 500 (72) 201 (29×106)Dywidag 835/1030 grade 835 (121) 1030 (149) 205 (29.7×106)Williams hollow core bar 371 (54) 501 (73) 207 (30×106)Prestressing strand, 7-wire. 15 mm dia. 1570 (228) 1770 (257) 193 (28×106)down the bar until grout return is obtained at thecollar of the hole, while in an uphole, the grout ispumped up a tube sealed into the collar until returnis obtained through the center hole. This groutingsystem eliminates the use of grout tubes attached tothe bar which can be damaged during installation ofthe bar. For permanent installations, the anchors arealways grouted because the mechanical anchor willslip in time as a result of corrosion of the wedge andcreep of the highly stressed rock around the anchor.A significant difference between the two types ofanchor shown in Fig. 9.5 is the manner in which thetensioning force is retained in the bar. In the fullybonded Williams bar, the nut and reaction plate areeffectively superfluous once the grout has reachedits full strength because the steel is bonded to therock over the full length of the anchor. In contrast,for bars with a free stressing length (in the case ofthe Dywidag bar) the maintenance of the prestressdepends on the integrity of the anchor nut and platebecause there is no bond developed in the freestressing length. Therefore it is important that goodcorrosion protection be provided for the heads ofanchors with free stressing lengths. Moreover, therock under the bearing plate should be protectedfrom weathering, where appropriate, because if the

highly stressed rock under the plate were to breakdown, the tension in the bolt would be lost.Reinforcing steel is used where the primary functionof the anchors is to secure a footing to a rocksurface and the loading conditions consist of purelycompressive loads, or uplift and/or shear loads onlyoccur infrequently. The installation procedurewould be to drill a pattern of holes in the rockfoundation, anchor the reinforcing bar with cementgrout, and then cast the footing with the exposedpart of the anchors embedded in the concrete. In theexample shown in Fig. 9.2(c), the anchors couldeither be embedded in the concrete to form apassive anchor, or they could be sleeved through theconcrete and then pre-stressed against the topsurface of the concrete footing. For a discussion onthe performance of passive and prestressedfoundations see Section 9.3.Rigid bar anchors are commonly installed where thedesign working load is in the range of about 100–600 kN (22–135 kips), and where the requiredlength is less than about 8 m (25 ft). The advantagesof bar anchors are the ease of handling short lengthswhich can be coupled together as required, andlocking off the applied stress using a threaded nutwhich can be reset if the bar is later retensioned.


The disadvantages of bar anchors are their limitedload capacity (it is impractical to bundle bars toform higher capacity anchors), and the difficulty ofhandling long, continuous lengths. Where longanchors are required and access space is restricted,couplings can be used to join short sections of bar.However, for long anchors, continuous strand maybe preferred to coupled rigid bars because of the time

required during installation to couple the bars andinstall corrosion protection on the couplings.

9.2.5Applications of strand anchors

Figure 9.6 shows the components of a multistrandtendon with a corrosion protection system

Figure 9.5 Typical bar anchors with grout and mechanical anchors (courtesy Dywidag Systems Int. and Williams FormHardware and Rock Bolt Co.): (a) Dywidag continuous threadbar with grouted anchor and smooth sheath on freestressing length; and (b) Williams hollow core bar with mechanical anchor showing alternative grouting methods forupholes and downholes.


comprising a grouted corrugated sheath on the bondlength, and polypropylene sheaths with a corrosioninhibiting grease on each strand in the unbondedlength. In the bond length, the strands are separatedby spacers and the entire anchor assembly iscentered in the drill hole with centering sleeves sothat all components of the anchorage assembly arefully encased in grout. The usual procedure is togrout the corrugated sheath on to the strand in anassembly yard and then transport the assembledanchor to the site for installation. Care is taken notto bend the bonded length which would result incracking and weakening of the grout. Where it isnecessary to bend the anchor during installationbecause of space limitations, grouting both insideand outside the sheath can be performed after theassembly has been placed in the hole. This requiresthat the anchor be fabricated with two grout tubes,one inside and one outside the corrugatedsheathing, or both inside the sheathing but with oneextending through the end cap for grouting theannulus.The tensioned strand is secured at the head of theanchor by pairs of tapered wedges that grip thecable with a serrated inner surface and are held inplace by tapered holes in the anchor plate (Fig. 9.7).The wedges are pushed into the holes in the anchorplate once the strand has been tensioned to the lock-off load.The required load capacity of the anchor is obtainedby assembling a bundle of strands as shown inFig. 9.6. An upper limit for the number of strandsthat can be readily made into a bundle is about 25strands which has an ultimate load capacity inexcess of 4 MN (900 000 lb), and requires a drillhole with a diameter of at least 200 mm (8 in).Because it is not possible to join lengths of strand,the entire anchor assembly, with the corrosionprotective sheaths, has to be fabricated in one piece,the weight of which can be considerable. Therefore,when determining the number of strand to make upa bundle, an important consideration is the methodof installation. For example, in vertical or steeplyinclined down-holes, a heavy anchor can often belowered into the hole using a crane or helicopter,

while in horizontal or up-holes it would bepreferable to use a greater number of anchors, eachwith fewer strands to facilitate their being pushed upthe hole.

9.2.6Cement grout anchorage

Anchorage methods for tie-backs includemechanical wedges, resin grout and cement grout,of which cement grout is the most common for permanent installations and is used for a wide variety ofapplications. Epoxy resin and mechanical wedgeanchors can be used to secure low capacity rockbolts, that is loads of up to about 200 kN (45 000lb), and with lengths not more than about 8 m (25ft). The advantages and disadvantages of these threetypes of anchorages are discussed in the followingsections.The advantages of cement grout anchorage are theavailability and low cost of the materials, simpleinstallation procedures, and its suitability for a widerange of soil and rock conditions. In addition,cement provides an environment that protects thesteel bar or strand from corrosion, and whenproperly installed the strength of the grout willimprove rather than deteriorate with time. Thedisadvantages are that careful quality control isrequired during mixing and placing, that in fracturedrock it may flow into even fine fractures (widthgreater than about 0.25 mm) resulting in anincompletely filled hole, and the set grout is brittleand can be damaged by movement duringinstallation and stressing.The procedure for the design and installation of agrout anchor is as follows.(a) Hole diameterFor economy, the hole diameter must be as small aspossible, while providing a sufficiently thickannulus of grout to transmit the shear stresses fromthe steel to the surrounding rock. The hole diametershould also be large enough that the anchor can bereadily inserted without having to resort tohammering or driving. In fractured rock, fragmentsof rock may be dislodged from the walls of the hole


as the anchor is pushed forward and the anchor could become jammed part way into the hole if the

Figure 9.6 Typical multi-strand anchor with corrosion protection comprising grouted corrugated sleeve, polypropylenesheath and full grout embedment (courtesy Lang Tendons).


hole diameter is too small. Usual practice in theselection of the drill hole diameter is to ensure thatthe ratio of the diameters of the anchor da and holedh falls within the following approximate range:

(9.2)

The low end of this range would be used in strong,massive rock while the high end would be usedin fractured rock. For example, a bundled anchorwith a diameter of 100 mm could be installed in a200 mm diameter hole in fractured rock, or a 150mm diameter hole in massive rock. The use of ratioshigher than 2.5 is possible, but the larger holediameter will be more costly to drill, and require ahigher compressed air quantity to flush the cuttingsfrom the hole.(b) Bond lengthThe most important factors influencing the selection

of the bond length is the strength and fracturecharacteristics of the rock in the bond zone. Theresults of load tests on anchors installed in a widevariety of rock conditions have providedapproximate values for the allowable working bondstress at the rock-grout interface. The working bondstress, which is related to the unconfinedcompressive strength of the rock, has values whichrange from about 350 kPa (50 p.s.i.) for weak rockto a high of 1400 kPa (200 p.s.i.) for strong rock. Ifit is assumed that the shear stress is uniformlydistributed along the full length of the anchor, therequired bond length can be calculated from theworking bond stress and the area of the periphery ofthe drill hole in the bond zone.Further details on the procedure for calculating therequired bond length is given in Section 9.3.2 whichdescribes the design of rock anchors.

Figure 9.7 Head of multi-strand anchor showing tapered wedges gripping the strand and seated in tapered holes in thebearing plate.


(c) Grout mixThe required properties of grout used to anchortensioned bars are first that it is strong enoughto withstand the high stresses that are developedaround the anchor, second that it does not degradewith time, and third that it is non-corrosive so that itdoes not affect the properties of the steel. Anotherconsideration is that it must be of a consistency thatwill permit it to be readily placed in long, smalldiameter holes. In designing a grout mix to meetthese requirements, the factors to consider are thewater:cement ratio (w:c), the required setting time,and the use of additives to reduce shrinkage andsegregation, and to improve workability (see (d)below). The use of grout mixes containing sand orfine aggregate is usually not recommended becausethese granular materials tend to block grout tubes.The cement used in grouts can be ordinary Portlandcement (Type I), sulphate resisting cement (TypeII), or hi-early (rapid setting) cement (Type III)(Bruce et al., 1996). Type I is used for mostapplications, with the following possibleexceptions. If the rock contains sulfide mineralssuch as pyrite, or if the anchor is exposed to seawater, sulfate resisting Type II cement would berequired. Where the sulfate content exceeds 2000ppm, Type V cement should be used which has ahigh resistance to sulfate.Type III cement would be used where support mustbe provided shortly after installation; the setting timecan be reduced from about five or six days for TypeI cement, to three or four days for Type III. One ofthe difficulties in using Type III cement is that itsworking time is limited in warm weather. Highalumina cement should be avoided because a highwater:cement ratio is required for pumpabilitywhich may produce a low quality grout.Water used in grout should generally meet drinkingwater standards, except for the presence of bacteria.Contaminants that can be harmful to theperformance of grout are sulfates, sugars andsuspended matter (e.g. algae), and chlorides shouldbe avoided where the grout will be in direct contactwith the steel. The concentrations of thesesubstances should be less than 0.1% in the case of

sulfates, and less than 0.5% in the case of chlorides.The water:cement ratio (by weight) used in the groutmix has a significant influence in the performance ofgrout: high water contents result in reduced strengthsand durability, increased shrinkage and excessivebleed as shown in Fig. 9.8. These properties relateto both the bond strength of the grout and theprotection it provides against corrosion of the steel.For example, excessive grout bleed will result insegregation and the presence of water in the upperpart of the anchor zone. It is found that a w:c ratioof between 0.4 and 0.45 will produce a grout thatcan be readily pumped down small diameter grouttubes and will produce a strong, continuous groutcolumn.The setting time of grout is important in schedulingtensioning operations, and in quickly providingsupport in emergency situations. Figure 9.9 showsthe comparative setting times for a number of groutproducts. On projects where a substantial number ofanchors are being installed, crushing tests on 50 mm(2 in) cubes of grout can be carried out to determinethe compressive strength at 7 and 28 days. Strengthsof 20 MPa (3000 p.s.i.) at 7 days, and 30 MPa (4300p.s.i.) at 28 days are generally required, and aminimum strength at the time of stressing of 20MPa (3000 p.s.i.) is recommended. On smallerprojects where there is insufficient time to carry outsuch testing, the strength of the grout is effectivelydetermined by load-deformation measurementsmade during tensioning of the anchor.(d) AdmixturesWhile grout mixes comprising only cement andwater are generally satisfactory for anchoringprojects, non-shrink grouts formulated by groutmanufacturers specifically for anchor installationsare also available. These pre-mixed products willprovide a more uniform and higher quality groutthan may be produced by field mixing of theingredients, and the non-shrink properties willenhance both the bond strength and theencapsulation of the anchor.The use of admixtures is usually restricted tocompounds that control bleed, improve flowabil


ity, reduce water content and retard set; a commonnon-shrink agent is Intraplas N (Sika Products) thatis added to the mix at about 1% of the cementweight. However, accelerators, expansion agentsand admixtures containing chlorides or sulfides, oraluminum powder should be avoided. Admixturesshould only be used where tests have shown thatthey will have no long term effect on theperformance of the anchor system, such asdegradation of the grout or corrosion of the steel.Expanding grouts should only be used to fill voidssuch as under the trumpet at the head of the anchor.Where the expansion of the grout is due to thegeneration of gases during setting, the grout is likelyto be porous and may then not be an effective barrierto water and moisture.In mixing grouts containing additives, the materialsshould be added in the following order: water-cement-additives. Mixing should be carried outcontinuously using a high speed shear type mixerequipped with a recirculating chamber. Grout which

has not been used within 30 minutes after mixing isunsuitable because the process of setting hasproceeded too far and the additives are no longereffective.(e) Grout pressuresRock anchors are usually grouted at atmosphericpressure. Pressure grouting is only used where therock is sufficiently loose and fractured that thegrout will be forced into the rock mass toconsolidate and strengthen it, and form a mass ofgrouted rock integral with the anchor zone.Depending on the degree to which the rock isfractured, the effect of pressure grouting may be toincrease the capacity of the anchorage by as muchas 100%.A common procedure for pressure grouting is toinstall the anchor with two sets of grout tubes. Thetube for primary grout extends to the distal end ofthe anchor zone and is used to fill the entire holewith grout as shown by the return of grout at thevent tube sealed in the collar of the hole. The tube

Figure 9.8 Effect of water content on the compressive strength, bleed and flow resistance of grout mixes (Littlejohn andBruce, 1975b).


for pressure grouting, known as a tube en machette,is usually about 8–10 mm in diameter with holesdrilled through it at regular intervals in the anchorzone. The holes are covered with a flexible rubbersleeve and fixed to the pipe to form a one-way valvesystem. Once the primary grout has attained aninitial set, the secondary grout is pumped throughthe secondary grout tube to fracture the primarygrout and penetrate the rock. This operation can berepeated a number of times and produce asignificant improvement in anchor capacity.The pressure used for secondary grouting woulddepend on the grout take and the pressure shouldonly be sufficient to cause the grout to penetrateexisting fractures in the rock. Care should beexercised that the pressure does not exceed theconfining pressure of the rock surrounding theanchor zone, because this could result in fracture ofthe rock and reduction in the strength of the rock

mass.(f) CentralizersIt is important that the bar (or strand bundle) befully embedded in a continuous and uniform groutcolumn to develop a high strength bond in theanchor zone, and provide corrosion protection forthe steel. This is achieved by installing centralizersleeves at intervals along the bond zone which holdthe anchor away from the walls of the drill hole andachieve a minimum grout cover of about 15 mm (0.6 in). These centralizers are plastic ‘springs’attached to the anchor with wire that are able todeform as they are pushed into the drill hole toaccommodate variations in drill hole diameter(Fig. 9.10). The spacing between centralizers isusually between 0.5 and 3 m (1.5–10 ft), dependingon the flexibility of the anchor and curvature of thedrill hole.

Figure 9.9 Relationship between grout compressive strength and time of curing for various anchor grouts (OceanConstruction Products).


9.2.7Resin grout anchorage

Resin anchorages are used for the installation ofrigid bars with maximum lengths of about 7–8 m(23–26 ft), and maximum tensile loads of about 200kN (45000lb). The anchorage is a two componentsystem usually consisting of a viscous liquid resinand a catalyst that are packaged together in plastic‘sausage’ cartridges about 200 mm (8 in) long and20 mm (0.75 in) in diameter (Fig. 9.11). When the

two components are mixed by driving and spinningthe bolt through the cartridges and shredding theplastic sheath, they set to form a rigid, non-degrading solid that anchors the steel bar in the hole.The setting time for the resin varies from about 1minute to as much as 90 minutes depending on thereagents. The setting time is dependent on thetemperature; fast setting resin sets in 4 minutes at atemperature of -5°C (23°F), and 25 seconds at 35°C(95°F). The resins have a limited shelf life and theexpiry date should be checked at the start of the

Figure 9.10 Dywidag bar anchor and corrugated sheathing, with two types of centralizer sleeves to hold bar from wallsof drill hole.


project. The principal advantage of the resin anchorage isthe simplicity and speed of installation, withsupport being provided within minutes of spinningthe bolt. The disadvantages are the limited lengthand tension load of the bolt, and the fact that onlybars can be used. Another disadvantage is thatcorrosion protective sheaths cannot be used with aresin anchorage because they will be damaged whenthe bar is spun to mix the resin. The corrosionresistance of resin grouted anchors is limitedbecause it is not possible to ensure that the bar iscompletely encapsulated in resin. Also, the shreddedplastic sleeve may be a pathway for water to reachthe unprotected bar. The corrosion protectionsystems for permanent anchors discussed inSection 9.4.4 provide a more reliable level ofprotection than that of resin anchorages.The installation procedure is to place in the drillhole a sufficient number of resin cartridges to fillthe annular space around the anchor. It is importantthat the hole diameter is within the tolerancesspecified by the cartridge manufacturer because ifthe hole is too large mixing of the resin will beinadequate. This usually precludes the use ofcoupled bolts because the hole size required toaccommodate the couplings will be too large for

complete resin mixing. This drawback may beovercome by reducing the hole diameter in the bondzone to be anchored with resin, and then usingcement grout in the upper part of the hole with thelarger diameter. Test have shown that the optimumannulus thickness for resin grout is about 3 mm (1/8in) (Ulrich et al., 1990).The bar is spun as it is driven through thecartridges, and the spinning is continued for about30 seconds after the bar has reached the end of thehole. The speed of rotation should be at least 60revolutions per minute to achieve full mixing of theresin, and shred the plastic cartridges. This isaccomplished by coupling the bolt to the drill chuckwith a dolly and rotating the bolt with the drill, orusing a torque wrench. When using fully threadedbars, the direction of rotation should auger the resininto the anchor zone; the opposite rotation mayresult in the distal end of the bolt being ungroutedas the resin is augered out of the hole. With boltlengths greater than about 7–8 m (23–26 ft), mostdrills cannot rotate a fully embedded bolt at therequired speed which limits the maximum boltlength.If the bolt is fully embedded in fast setting resin, itcannot be tensioned and the bolt acts as a passiveanchor, or dowel. However, a tensioned bolt can be

Figure 9.11 Resin cartridges; the white strip down the side of the cartridges is the hardener.


installed by using a fast setting resin (2–4 minutesetting time) in the distal end of the hole, and aslower setting resin (15–30 minute setting time) inthe remainder of the hole. The bolt is tensionedafter the fast resin has set but before the slower resinhas hardened. When all the resin has set, a fullygrouted tensioned anchor is created which willcontinue to function even if the plate and nut at thesurface are lost.

9.2.8Mechanical anchorage

The photograph in Fig. 9.12 shows the details of aWilliams mechanical anchor, and the fullinstallation is shown in Fig. 9.5(b). The componentsof the mechanical anchor are a pair of wedges thatslide over a tapered cone threaded on the end of thebar. The installation procedure is to drill a hole to aspecified diameter so that the wedge is gripped bythe walls of the hole. When the bolt is torqued, thecone moves up the bar and expands the wedgesagainst the walls of the hole to anchor the bar. Notethat the surfaces of the wedges are smooth becausethis produces a uniform pressure on the rock, incomparison with serrated surfaces which crush andbreak the rock possibly resulting in reduced loadcapacity of the anchorage.The advantage of mechanical anchors is thatinstallation is rapid, although not as rapid as resinanchors, and tensioning can be carried out as soonas the anchor has been set. They can also be usedwhere flowing water precludes the use of cementanchorages. The disadvantage of the mechanicalanchor is that it can only be used in medium tostrong rock in which the anchor will grip, and themaximum working tensile load is in the range 150–300 kN (35 000–70 000 lb). Mechanical anchors forpermanent installations must always be fullygrouted because creep and corrosion of theanchorage will result in loss of support with time.Grouting can be carried out either using a grout tubeattached to the bar before installation, or in the caseof the Williams bar, through the center hole untilthere is grout return at the collar.

9.3Design procedure for tensioned anchors

When a tensile load is applied to a rock anchor, thisload is supported by the mass of rock in which theanchor is embedded (see the three examples inFig. 9.2). The mechanism by which the load istransmitted from the steel bar or strand to thesurrounding rock depends upon the followingfactors.

1. The applied load is transmitted from the steelanchor to the rock in the walls of the drill holeby the shear stresses developed at the steel-grout and grout-rock interfaces.

2. Stresses are developed between the rock in theimmediate vicinity of the anchor and thesurrounding rock. The capacity of the rock towithstand these stresses is significantlyinfluenced by the orientation of discontinuitiesin the rock.

3. If the applied load acts in a direction above thehorizontal, the mass of rock in which the bolt isanchored acts as a gravity restraining force(Figs 9.2(b) and (c)). Where the load acts belowthe horizontal (Fig. 9.2(a)), the cone of rockmust be self supporting.

The following is a description of these componentsof anchor performance.

9.3.1Mechanics of load transfer mechanism betweenanchor, grout and rock

When a tensile load is applied to a steel bar or cablethat is anchored in rock with a column of grout(either cement or epoxy resin), shear stresses aredeveloped at both the steel-grout and grout-rockinterfaces (Fig. 9.13). The distribution of thesestresses along the length of the anchor has beenstudied in laboratory model tests (Farmer, 1975),full-scale field tests (Golder Associates, 1983), andnumerical analysis (Russell, 1968; Coates and Yu,1971; Wijk, 1978). All these results show that underelastic conditions, the shear stress distribution is


non-linear with high stresses concentrated at the topof the bond length which diminish rapidly down thehole.The shear stress distribution tx at the steel-groutinterface along a fully bonded tensioned anchor,assuming that the steel, grout and rock all behaveelastically and there is no slippage at the interface,can be defined by the following equation (Farmer,1975):

(9.3)

where r1 is the radius of bolt; s0 is the normal stressapplied at the proximal end (closest to the rocksurface) of bond length; x is the distance from theproximal end of bond length;

(9.4)

for i.e. thin grout annulus, or

(9.5)

for i.e. thick grout annulus; is the elastic modulus of the grout,

Eb is the elastic modulus of bolt, and r2 is the radiusof the drill hole.

The curve in Fig. 9.13 shows a typical distributionfor the shear stress in terms of the dimensionlessratios tx/s0 and x/r1. This curve has been developedfor a 30 mm (1.2 in) diameter bar grouted withepoxy resin resin into a 40 mm (1.6 in) diameterdrill hole. The elastic moduli of the epoxy and steelare 2 GPa and 200 GPa (0.29×106 and 29×106 p.s.i.)respectively. Equation 9.3, which defines anexponential decay in the shear stress, can be used asa guideline to determine the length of bond requiredto dissipate the full applied tension within theanchorage. The shear stress is diminished to 1 % ofits value at the top of the anchorage when ? is equalto 4.6, so the bond length lb to effectively dissipatethe applied stress is equal to

(9.6)

Integration of equation 9.3 allows calculation of thetotal load Q carried by the anchorage between anytwo points (x1 and x2) along the bond length asfollows:

Figure 9.12 Wedge-type mechanical anchor (courtesy of Williams Form Hardware and Rockbolt Co.).


(9.7)

Equation 9.7 can be used to calculate the loadcarried between any two points along the bondlength, x1 and The load carried by thefull length of the bond length, i.e. and

is approximately equal to the product of theapplied tensile stress and the cross-sectional area ofthe bar, assuming that the term is small when

A value of the parameter ? has been found from a

series of tests on bar anchors in which strain gaugeswere attached on the bond length at values of xequal to 0.3, 1.52, 3.05, 5.18 and 7.62 m (1– 25 ft).The anchors were installed in rock comprisingalternating layers of closely fractured argillite andmoderately fractured quartzite. With reference toFig. 9.13, the values for the loads, stresses anddimensions were as follows:

The strain gauges showed a typical highly non-linearstress distribution along the bond length with thestress in the bar diminishing to zero at 2.1 and 3.7 mat the lowest and highest test loads respectively. Itwas found that values for the parameter ? of about 0.

Figure 9.13 Distribution of shear stress along the length of the anchor zone of a tensioned anchor (after Farmer, 1975).


03–0.05 gave a close match between the measuredloads along the bond zone and those predicted byequation 9.7.The shear stress distribution curve shown inFig. 9.13 assumes no slippage at the interface andelastic behavior over the full length of theanchorage. However, as the applied stress isincreased, the shape of the shear stress distributioncurve becomes more linear and a greater portion ofthe load is carried at the distal end of the anchor(Fig. 9.14). As the load is further increased, thebond at the proximal end of the bond length willstart to fail. Once the bond has been broken, theshear strength will be equal to the friction of thesurface. General design practice is to select acombination of applied load and anchoragedimensions such that there is no slippage, and thatthe shear stress does not reach the distal end of theanchorage. That is, the applied load for theconditions shown in Fig. 9.14, would be betweenQ1 and Q2.The shear stresses developed at the steel-grout-rockinterfaces along the bond length will result in achange in the stress field in the material around theanchorage. Figure 9.15 shows the results of modeltests of a tensioned anchor in sand where the bondlength is at some distance below the ground surface

(Hobst and Zajic, 1977). The contours of verticalstress show that there is a zone of compression atthe proximal end and above the bond length, and azone of dilation at the distal end and below theanchor. This stress distribution shows the value ofhaving the bond length embedded at some depthbelow the surface to contain the zone of compressedrock. An anchor with the top of the bond length atthe ground surface would have diminished capacitybecause the compressed rock would not be confined.Also,the zone of dilated rock shows how nearbystructures may be influenced by a tensioned anchor.

9.3.2Allowable bond stresses and anchor design

The typical distributions of shear stresses along theanchor length shown in Figs 9.13 and 9.14demonstrate the non-linear nature of thisdistribution. However, the exact form of thisdistribution is difficult to predict for the wide rangeof conditions that may exist within a tensionedanchor. For this reason a simplifying assumption ismade for design purposes, namely that theshear stress is uniformly distributed along the bondlength. The magnitude of this average shear stressfor both the rock-grout and grout-steel interfaces

Figure 9.14 Variation in distributions of tensile stress along length of anchor zone with increasing applied load.


has been established empirically from the results oftests on full-scale and laboratory anchors.Calculation of the bond length is a two stageprocess that ensures that the working bond stressesare not exceeded at either the rock-grout or thegrout-steel interfaces. First, the bond length anddrill hole diameter are selected such that the averageshear stress at the rock-grout interface is less than orequal to the working bond strength. Second, thelength of the anchor is checked against the requireddesign development length of the steel which is thelength of embedment required to support the appliedtensile load.Assuming that the shear stress is uniformlydistributed on the surface of the drill hole forming

the bond length, the bond length lb is calculatedfrom

(9.8)

where Q is the applied tensile load at the head ofanchor; d is the diameter of drill hole, and τa is theworking bond strength of rock-grout interface.From equation 9.8 a combination of bond lengthand drill hole diameter is selected such that theshear stress at the rock-grout interface is less than orequal to the working bond stress. Equation 9.8indicates that in design, the average bond stress canbe matched to the working bond stress by increasingthe bond length, or the hole diameter as required.

Figure 9.15 Results of model tests of tensioned anchor in cohesionless sand showing distribution of vertical stresscontours and zones of compression and dilation (Hobst and Zajic, 1977).


However, a practical limit on the bond length is inthe range 8–10 m (26–33 ft), with usual rockdrilling equipment limiting the drill hole diameter toabout 150 mm (6 in). If a longer bond length than 8–10 m is required, additional, lower capacity anchorsshould be installed. The reason for this restriction isthat the peak stress is developed at the proximal endof the bond and if this stress is greater than theultimate bond strength, failure of the grout in theproximal end of the bond will occur regardless ofthe bond length.An approximate relationship between the rockgroutbond strength and the uniaxial compressive strengthof the rock has been developed from the results ofload tests on anchors installed with cement groutanchorages in a wide range of rock types andstrengths (Littlejohn and Bruce, 1977). Values forthe design, or working τa, and ultimate τu bondstrengths for cement grout are given by equations 9.9 and 9.10 respectively:

(9.9)and

(9.10)where σu(r) is the uniaxial compressive strength ofthe rock in the bond zone, or that of the weakestrock in the bond zone if the rock is layered.Values of τa, assuming a factor of safety of 3applied to τu, which have been used for a variety ofrock types and rock strengths for cement grout areshown in Table 9.2 (PTI, 1996; Littlejohn andBruce; 1977).Some judgement should be used in the applicationof equation 9.8 and Table 9.2 to ensure that thebond stress value is suitable for the actualconditions that may be encountered. Unfavourableconditions necessitating a low value of τa wouldinclude a smooth hole surface produced by rotarydrilling

Table 9.2 Approximate relationship between rock type and working bond shear strength for cement grout anchorages

Rock type Working bond stress τa at rock-grout interface

MPa p.s.i.

Granite, basalt 0.55–1.0 80–150Dolomitic limestone 0.45–0.70 70–100Soft limestone 0.35–0.50 50–70Slates, strong shales 0.30–0.45 40–70Weak shales 0.05–0.30 10–40Sandstone 0.30–0.60 40–80Concrete 0.45–0.90 70–130Weak rock 0.35–0.70 50–100Medium rock 0.70–1.05 100–150Strong rock 1.05–1.40 150–200compared with percussion drilling, a zone of loose,fractured rock in the bond length, drill cuttingssmeared on the walls of the hole, holes from whichthe drill cuttings cannot be completely cleaned, orflowing water. Favorable bond conditions may occurwhere the rock comprises strong rock with narrowlayers of weaker rock, or in strong basalt containingvesicles; in both conditions irregularities in the wallof the hole enhance bonding. Because the actualconditions in the hole are likely to be unknown,

usual practice is to conduct performance tests onselected anchors to ensure that the anchor meetsspecified acceptance criteria (see Section 9.5).For the resin products that are widely available,ultimate rock-resin bond strengths vary from about4.8 MPa (700 p.s.i.) for installations in very stronggranite with compressive strengths in the range of80–100 MPa (12 000–15 000 p.s.i.) to 1 MPa (150p.s.i.) in weak mudstones and siltstones withcompressive strengths in the range 5–5.5 MPa (700–


800 p.s.i.). Based on these values, it is possible toproduce ultimate anchorage strengths ofapproximately 200 kN (45 000 lb) with bondlengths of 0.3 m (12 in) and 1.4 m (55 inches)respectively for these two classes of rock strengths.The second step in the anchor design is to checkthat the shear stress developed at the steel-groutbond interface does not exceed the working bondstress (British Standards Institution, 1985). Valuesfor bond stresses have been derived from pull-outtests conducted in concrete to determinedevelopment lengths of bar and strand. Developmentlengths, which are the embedment lengths requiredto develop the full strength of the bar are defined bythe following equations (Canadian Portland CementAssociation, 1984).

1. For 35 mm diameter bars and smaller:

(9.11)

but not less than(9.12)

2. For 45 mm diameter bars:

(9.13)

3. For 55 mm diameter bars:

(9.14)

4. For prestressing strand

(9.15)

where ld is the development length (mm); Ab is thecross-sectional area of bar (mm2); sy is the specifiedyield strength of non-pre-stressed reinforcement(MPa); suc is the specified compressive strength ofgrout (MPa); and db is the nominal diameter of baror strand (mm). The relationship between bardiameter and working development length asdefined by equations 9.11–9.15 is shown inFig. 9.16.Equations 9.11–9.15 define working developmentlengths which should be suitable for most anchoring

projects, although a factor of safety up to about 1.5may be used in poor anchoring conditions. Suchconditions include variable grout thickness in theannulus where the anchor cannot be accuratelycentered in the hole, or a low strength grout becauseof flowing water in the bond zone or where the groutis contaminated with drill cuttings.

9.3.3Prestressed and passive anchors

Where rock anchors are used to support tensionloads, there are two different design methods thatcan be used—prestressed or passive anchors(Fig. 9.17). The advantages of using prestressedanchors are that the deflection of the head of theanchor is minimal on the application of thestructural load, and they can have a somewhatgreater load capacity. This is of particularimportance in the case of anchors subjected tocyclic loads which could experience fatigue failureif not prestressed.Figure 9.17 demonstrates the mechanism by whichtie-down anchors support tensile loads. In Fig. 9.17(a), the anchor comprises two components: a bondlength lb and a free stressing length lf. Over the bondlength, bond is developed between the steel and thecement grout which secures the tie-down in thehole, while in the free stressing length, which isungrouted or encased in a smooth plastic sheath, nobond is developed. When a reaction plate isinstalled at the rock surface and a tensile load isapplied to the head of the anchor, a zone of rockbetween the reaction plate and the bond length iscompressed. This also develops shear stresses at theboundary between the compressed zone and thesurrounding rock. Under these conditions, thecapacity of the anchor to sustain pull-out forcesdepends on the shear stress in the bond length, aswell as the shear strength of the rock at theboundaries of the zone of compressed rock(Fig. 9.17(a)). In the case of anchors installed belowthe horizontal, there is additional uplift capacity inthe weight of the rock mobilized between the bondlength and the reaction plate. Also, the capacity of


the anchor is enhanced where the most highlystressed portion of the rock mass at the upper end ofthe bond zone is below the ground surface and isconfined by the surrounding rock.Figure 9.17(b) shows an anchor which is bondedover its full length and no prestress is applied—thisis sometimes referred to as a passive anchor. In thiscase, the application of the structural load causesshear stresses to be developed in the bond zone atthe ground surface. Since this rock is unconfined,and may also be weathered and/or fractured byblasting in the preparation of the foundation, itscapacity to withstand the concentrated stresses atthe upper end of the anchor is less than that of theembedded anchor. The result is likely to be partialdebonding of the anchor and displacement as theload is applied.Another important difference between theprestressed and passive anchors is the displacementof the head of the anchor on the application of thestructural load. This is illustrated in the model shownin Fig. 9.18, where the bond is replaced with aspring of stiffness kb and the shear strength of therock in which the anchor is embedded is replacedwith a spring of stiffness kr. The tensile load Qsupported by the anchor is equal to the product ofthe spring stiffness and the displacement d. In thecase of a prestressed anchor (Fig. 9.18(a)), thedisplacement of the head of the anchor, at loads up

to the level of the pre-load Qp, will be limited to thesmall deformation of the surrounding rock,

. Once the structural load exceeds theprestress load, the displacement of the head of theanchor will be equal to elastic elongation of the free-stressing length plus the small amount ofdeformation in the rock surrounding the bond zone.The displacement db of a passive anchor (Fig. 9.18(b)) will be primarily the result of strain of theupper end of the bond zone at the ground surface.Because the upper end of the bond zone isunconfined, the displacement db will exceed thedisplacement dr of the more highly confinedprestressed anchor, i.e. . As the load isincreased, a progressively longer portion of theanchor zone is stressed and the displacement dbincreases. The relative load-displacement behaviorof prestressed and passive anchors is illustrated inFig. 9.19.

9.3.4Uplift capacity of rock anchors

Figure 9.20 illustrates two common uplift loadingconditions for rock anchors—a pure tension load(a), and a combination of tension and moment (b).An example of an anchor loaded in pure tension isthe support for a guy wire where the wire andthe anchor are co-linear, while a combination of

Figure 9.16 Working development lengths for steel bar and strand anchored in cement grout; lengths calculated fromequations 9.11–9.15.


Figure 9.17 Mechanism of support of tension loads by (a) prestressed and (b) passive anchors.


tower subjected, for example to wind loads, isanchored with bolts in a circular or square patternaround the base. Much of the work in developingdesign procedures for these loading conditions hasbeen carried out by electrical utilities for the designof foundations for transmission towerss (EPRI,1983; Ghosh, 1976). These are tall structures that donot produce high bearing pressures, but mustwithstand significant moments induced by windloads and tension in the conductors, particularlywhen they are coated with ice. The different designprocedures used for these two loading conditions isdescribed in the following sections.(a) Pure tension loadingThere are several possible failure modes for anchorsloaded in pure tension (Fig. 9.20(a)). Failure mayoccur in the steel, or in the bond at either the rock-grout or the grout-steel interfaces, or a cone of rockwith its apex near the mid-point of the anchor zone

may be pulled out. Design against failure of theanchor at the grout interfaces requires that thelength of the bond zone, and the diameters of thebar and drill hole are proportioned such that theaverage shear stress is less than the working bondshear strength. Values for working rock-grout bondshear strength are given in Table 9.2 and formulaefor development lengths of embedded bars andstrand are given by equations 9.11–9.15.After the bond length required to resist bond failurehas been determined, the next step is to check thatthe anchor will mobilize a sufficient volume of rockto support the applied load. The results of uplifttests on rock anchors show that the mass of rockmobilized around the anchor is approximatelyconical, with the dimensions and shape of the conebeing dependent on the structural geology of thesite. A simplifying assumption can be made that theapex angle is 90°, and that the position of the apex

Figure 9.18 Simplified model of support mechanism of (a) prestressed and (b) passive anchors.


is at the mid-point of the bond length (Fig. 9.20(a)).The weight of the cone can be calculated from thesedimensions, but test results show that the maximumuplift load that is actually supported is as low asseven and as high as 56 times the weight of the cone(Saliman and Schaefer, 1968; Littlejohn et al.,1977a). The difference between the cone weight andthe actual uplift capacity is that the support isprovided by the strength of the rock on the surfaceof the cone. This clearly demonstrates that usingonly the weight of the cone for uplift resistance

produces a very conservative design. A precise design method for the capacity of upliftanchors cannot readily be developed because thedimensions of the wedge, as well as the strength ofthe rock on the surface of the cone are difficult todefine. Littlejohn and Bruce (1975a) have made asurvey of cone dimensions used on about twentyprojects around the world which shows that theapex angle varies from 60° to 90°, and that theposition of the apex varies from the top to thebottom of the bond length. Narrow apex angles

Figure 9.19 Typical relative load-deflection performance of prestressed and passive anchors.

Figure 9.20 Types of loading conditions for uplift anchors: (a) pure uplift load; and (b) combined compression andmoment load.


(60°) are used in weak rock, and in strong rock thatthe apex angle may be as great as 120°(Radhakrishna and Klym, 1980). The shape of therock cone is also strongly influenced by thestructural geology in the bond length as illustratedin Fig. 9.21. The most favorable case is that ofcontinuous structure aligned at right angles totheanchor (Fig. 9.21(a)), and the least favorableangle is where the structure is aligned parallel to theanchor (Fig. 9.21(b)). It is considered that the mostlikely location of the apex of the cone is the mid-point of the bond because the shear stress isconcentrated in the upper half of the bond length.The rock strength that operates on the surface of thecone can only be estimated because the failuremechanism consists of a complex combination ofshear and tensile movements related to the details ofthe geological structure relative to the direction ofthe applied load. The range of rock fracture

mechanisms that may occur is illustrated inFig. 9.21. As it would not be possible to simulatethis failure mechanism in laboratory scale tests, thestrength developed on the surface of the cone is bestdetermined from the results of full-scale uplift tests.Where load tests are not possible, the strength of therock under these load conditions can be estimatedfrom equation 9.16 which gives the tensile strengthof fractured rock (Hoek, 1983) (st is a negativenumber):

(9.16)

where st is the working tensile strength on surfaceof cone, su(r) isthe unconfined compressive strengthof rock; m, s are rock mass strength constants (seeTable 3.7) and FS is the factor of safety applied tothe rock strength. A limited number of results oftests on uplift anchors (Saliman and Schaefer, 1968;Littlejohn et al., 1977a; Ismael, 1982) indicates that

Figure 9.21 Influence of structural geology on the shape of cones of rock mobilized by uplift anchors: (a) wide coneformed in horizontal bedded formation; (b) narrow cone formed along vertical joints; and (c) surface of cone formedalong conjugate joints.


equation 9.16 gives reasonable values for thestrength of fractured rock in tension.The value assumed for the factor of safety inequation 9.16 would depend on the fractureintensity of the rock and the orientation of thediscontinuities with respect to the anchor. It isestimated that the value of FS may vary from 2 formassive rock with the predominant discontinuity setat right angles to the anchor, to 4 for closelyfractured rock, or where the discontinuities areparallel to the anchor. Where a large number ofanchors are to be installed on a project and there aresubstantial savings to be realized in having the bondlength as short as possible, it would usually beappropriate to conduct a test program to verify therock strength. The capacity of an anchor loaded in tension againstfailure of the cone of rock depends upon thecombined weight of rock in the cone and the rockstrength on the surface of the cone (Fig. 9.22). Thebuoyant weight Wc of the cone is

(9.17)

and the resisting force f(r) developed on the curvedsurface area of the cone is

(9.18)

The capacity of the rock cone to resist the tension

force Q depends on the direction of the force. If Qacts vertically upwards the weight improves theload capacity, while if Q acts vertically downwardsthe weight diminishes the load capacity. Therefore,the uplift capacity Q is given by

(9.19)

In equations 9.17–9.19, ? is the apex angle of cone,D is the depth of apex below ground surface, Dw isthe depth of water table below ground surface, ?r isthe rock unit weight, ?w is the water unit weight, ?cis the angle between vertical upwards direction andload direction, and FS is the factor of safety appliedto the load. (b) Combined moment and tension loadingThe load condition shown in Fig. 9.20(b) comprisesa combination of a moment M, and an vertical forceQ applied to the tower structure which is anchoredwith a group of bolts arranged in a circular patternaround the base (Fig. 9.23). A full scale test of thisloading condition has been carried out byRadhakrishna and Klym (1980) and the method ofcalculating the support has been reported by Ismail(1982).A structure subjected to vertical and moment loadsinduces a distribution of stresses in the foundationwhich can be approximated by the method shown inFig. 9.23. The moment applied to the structure isresisted by a force couple composed of tension T

Figure 9.22 Cone of rock mobilized by tie-down anchor to resist uplift load.


and compression C forces. The tensile force ismobilized by the rock anchors and the compressionforce is mobilized by the rock on which the tower isfounded. The distance between these forces isdefined by a lever arm am which depends upon theload distribution in the foundation and the geometryof the anchor layout. Where the bolts are laid out ina circular pattern and the distribution of the stressesacross the base of the tower is triangular, the leverarm is found to be about 0.7 times the diameter ofthe anchor bolt circle. This value for the lever armis in agreement with the theoretical value for thecase of a triangular stress distribution in a steel ringsubjected to bending.The stability of the structure is calculated from theweight of the truncated cone of rock mobilized inthe foundation, and the strength of the rock on aportion of the cone surface that is subjected touplift. Assume that the apex angle of the rock coneis 90° so that the truncated cone has the dimensionsshown in the lower diagram on Fig. 9.23. Theweight of the mass of rock in the truncated cone isgiven by

(9.20)

for , where D is depth of the truncated coneand d is the diameter of the circle of anchor bolts.For a symmetrical distribution of the tension andcompression forces in the foundation, only the rockon the surface of the uplift half of the cone will bemobilized to resist the applied loads. The surfacearea of one half of the truncated cone, ignoring the

horizontal base of the cone, is

(9.21)

and the resisting force generated on this surface is(9.22)

where st is the tensile strength of the rock on thesurface of the cone as defined by equation 9.16.The vertical force on the wedge is the total of theapplied vertical force Q and the tension force Tinduced by the moment. The magnitude of the forceT is determined by taking moments about the axisof rotation such that

(9.23)

Therefore the load capacity of the tower foundationis given by

(9.24)

Note that the sign of the force Q depends on itsdirection and is defined as follows:

+Q vertical force upwards in same direction astension force induced by the moment;

-Q vertical force downwards.

Equation 9.24 can be solved to find the length ofbolt required to mobilize a cone of rock withdimensions sufficient to support the combinedloads, with the required capacity of the boltsdepending on the bolt pattern selected. It is alsonecessary to check that the compressive stressesinduced on the outer edge of the foundation do notexceed the bearing capacity of the rock.

EXAMPLE 9.1

VERTICAL UPLIFT LOADING

Consider an anchor loaded with a vertical uplift force of 250 kN (56.2 kips) installed in a horizontally


bedded limestone with a uniaxial compressive strength of 30 MPa (4350 p.s.i.) (moderately weak rock)

Figure 9.23 Truncated cone of rock mobilized by group of anchors to resist combined uplift and moment loading: (a)dimensions of truncated cone; (b) plan of anchors; (c) triangular stress distribution; and (d) section through upliftportion of cone.


and a fracture spacing of about 0.5 m (1.6 ft). The load is coincident with the axis of the bolt so there areno moments generated in the anchor. The water table is 0.5 m below the ground surface

. Determine the length of passive, fully grouted anchor required to support thisload.

The first step in the design is to determine the diameter of the steel bar that will have a working loadof 250 kN. A 25 mm (1 in) diameter, continuously threaded bar with an ultimate tensile stress of 1030MPa (150 k.s.i.) will have an ultimate strength of 506 kN (114 kips) and a working strength, at 50% ofthe ultimate strength, of 253 kN (57 kips) (see Table 9.1). This bar will support the uplift force.

From equation 9.9 and Table 9.2, the working bond strength at the rock-grout interface for limestonewith a compressive strength of 30 MPa (4350 p.s.i.) will be in the range 700 kPa-1 MPa (100–145p.s.i.). Assume a value for the working bond strength of 800 kPa (116 p.s.i.) for design purposes.

If the 25 mm diameter bar da is installed in a 50 mm (2 in) diameter drill hole dh, the value of the ratiodh/da is 2 (see equation 9.2). Assuming that the bolt is anchored with cement grout, and the shear stressis uniformly distributed along the bond, it can be determined from equation 9.8 that the required bondlength is 2 m (6.6 ft). From equation 9.11 the required development length is 1.75 m (5.75 ft). This showsthat the rock-grout bond strength, which is less than the grout-steel bond, governs the bond lengthdetermination.

The uplift capacity is the sum of the weight of the cone of rock mobilized by the anchor, and thestrength developed on the surface of the cone as defined by equation 9.19. If the density of the rock is 25kN/m3 (160 lb/ft3) and the apex angle is 90°, and the depth is 1 m (apex at mid-point of bond), thebuoyant weight of the cone is 24.9 kN (5.6 kips). The surface area is 4.4m2 (47.4 ft2). From table 3.7, theconstants m, s defining the rock mass strength are and and fromequation 9.16, the working rock strength in tension on the surface of the cone, assuming FS equals 2 isabout 10 kPa (1.5 p.s.i.). The total uplift resistance is the sum of cone weight of 24.9 kN (5.6 kips) andthe tensile strength of the cone surface of 44 kN (9.9 kips) which is less than the design load of 250 kN.If the bolt length is increased to 4m (13.1 ft) so that the cone depth is 2 m (6.6 ft), then the cone weightincreases to 186 kN (41.8 kips) and the surface area of the cone increases to 17.7m2 (190.5ft2). The totalresistance is 363 kN (82 kips) which exceeds the design load.

These figures show that the very low tensile strength generates more uplift capacity than the weight ofthe cone of rock.

EXAMPLE 9.2

UPLIFT-MOMENT LOADING

To illustrate the design of a combined uplift and moment loading, consider a tower with an uplift loadof 250 kN (56.2 kips) and a moment of 500 kNm (369 kip-ft). The base of this tower has a diameter of 2m (6.6 ft) and is anchored with eight bolts equally spaced around the base. The rock propertiesare identical to those described in Example 9.1.

The first step is to calculate the depth of the truncated rock cone that must be mobilized to supportthis loading condition. The tension force is calculated from equation 9.23 to be 750 kN (168.6 kips) andthe total uplift force is 1000 kN (224.8 kips). If it is assumed that the depth below the surface of thetruncated cone is 3.0 m and the water table is again 0.5 m below ground surface


then the weight of the 45° truncated cone is calculated from equation 9.20 to be 1219 kN (274 kips).From equation 9.21 the surface area of one half of the truncated cone is 33 m2 (355 ft2), and the resistingforce due to the tensile strength of the rock is 330 kN (74 kips). From equation 9.24 the total resistingforce exceeds the uplift force by a factor of safety of 1.47 [(1219+250)/1000].

The load on each bolt is calculated as follows. The applied uplift load is uniformly distributed on eachbolt and is equal to (7 kips). The uplift force generated by the moment is concentratedon the edge of the foundation and is distributed between three bolts (Fig. 9.23(b)). The load on each boltis approximately (56 kips) and the total force on each bolt is 281 kN (63 kips). Forsteel with an ultimate tensile strength of 1030 MPa (150 k.s.i.), a 30 mm diameter bar will have anultimate strength of 728 kN (164 kips). If the maximum working load is 364 kN (82 kips) at 50% of theultimate strength, a 30 mm bar has adequate capacity for these loads, with allowance for some non-uniformity in loading. The load on each anchor can be more accurately calculated by integrating to findthe portion of the force supported by each bolt.

9.3.5Group action

Where a number of anchors are required to supportthe structural load, the combined effect of the groupof anchors must be evaluated. As shown inFig. 9.23, the cones of rock mobilized byeach anchor interact where the bolts are closelyspaced to form a single truncated cone. In order toprevent excessive stress concentrations beingdeveloped around the anchors that could fracture therock, and minimize the risk of drills holesintersecting, it is usual practice to specify both aminimum spacing and a stagger between the bondzones. While there are no codes defining spacingand stagger, one commonly used criteria for theminimum spacing is that it should be the lesservalue of four times the diameter of the bond zone or1.2 m (4 ft) (PTI, 1996). Also, the South AfricanCode of Practice (1972) recommends that foranchors spaced at less than 0.5 times the bondlength, the stagger between alternate anchors shouldbe 0.5 times the anchor length.Anchors can also be staggered by installing them atdifferent angles. This is particularly importantwhere there is a persistent set of discontinuities; theanchors should be oriented so that they cross thediscontinuities and are not all aligned either parallelor perpendicular to the discontinuity sets.

9.3.6Cyclic loading of anchors

Conditions that could result in cyclic loading ontensioned anchors may include tidal movement, andwind and traffic loading (Madhloom, 1978; AlMosawe, 1979). Where the anchorage is in closelyfractured rock, the cyclic loading may causeloosening and dilation of the rock mass, andeventual reduction in the capacity of the anchor.The installation of prestressed anchors under theseconditions will maintain the interlock between theblocks of rock in the anchor zone and minimize therisk of movement of the anchorage. In addition,placement of the top of the bond zone at some depthbelow the rock surface will provide confinement tothe rock in the most highly stressed area of the rockand minimize the risk of loosening of the rockmass. Section 9.3.3 discusses the applications ofprestressed and passive anchors.

9.3.7Time-dependent behavior and creep

On many projects that rely on tensioned anchors forpermanent support, there is a requirement for longterm monitoring of both the load in selectedanchors, and the deformation of the structure. Thesetwo sets of information will be of value indetermining the cause of any displacement or


change in load. For example, movement in adirection that lengthens the anchor together with anincrease in load would indicate that the anchor isholding, but there is insufficient anchoring force toprevent movement of the structure.A monitoring specification has been prepared by theBureau Securitas (1972) which specifies both thenumber of anchors that must be monitored and themonitoring frequency as follows.

1. Number of anchors to be monitored10% of total anchors installed for 1–50

anchors7% of total anchors installed for 51–500

anchors5% of total anchors installed for >500

anchors2. Frequency of monitoring

First year, every three monthsSecond year, every six monthsThird to tenth year, once a year

3. Load change toleranceA change in load greater than 20% of the

design should be investigated.

Time-dependent behavior of rock anchors willresult from both relaxation of the steel bar or strand,and creep of the grout and rock in the bond length.As discussed in Section 9.2.2, relaxation of the steel

will be negligible if the applied load is not morethan about 50% of the ultimate strength. At appliedloads in excess of 50% of the ultimate strength,relaxation will be limited if the anchor is restressedat a time of 1000 hours.Figure 9.24 shows a typical plot of load loss againsttime for anchors comprising 12×15.2 mm (0.6)diameter Dyform strand with an 8 m (26 ft) longbond zone in a 140 mm (5.5 in) diameter drill hole.The design loads were in the range 2172–2337 kN(488–525 kips) (Littlejohn and Bruce, 1979). Inanother test, monitoring was carried out over aperiod of five years (248 weeks) of the load in anumber of cement grouted, 36 mm diameter baranchors loaded to 80% of the ultimate strength of thebar. The results showed a relatively rapid loss ofload of about 5-7% of the applied load in the firstsix months, followed by a decreased rate of loadloss in the subsequent months with a total loss ofload of 7–9% at the end of five years (Benmokraneand Ballivy, 1991). Additional tests have shownthat the load is generally stable or decreases veryslowly after the first six months, with the majority ofthe load being lost in the first one or two months(FHWA, 1982; Golder Associates, 1989).In comparison with the creep rates for bare strandshown in Fig. 9.24, it has been found that epoxy-coated filled strand exhibits creep rates that are anorder of magnitude higher, although the total

Figure 9.24 Long-term load monitoring of anchors (Littlejohn and Bruce, 1979).


elongation was within acceptable limits (Bruen etal., 1996). A possible cause of this creep movementmay be deformation of the epoxy between thestrands (see Section 9.5.3, Acceptance Criteria).

9.3.8Effect of blasting on anchorage

Blasting may sometimes take place close totensioned anchors and it will be necessary to designthe blasting procedure so that there is no damage tothe anchors. Damage that can be caused by blastingmay include fracture of the grout in the bond zone,overstressing of the bar of strand, and disturbanceof the head of the anchor. Methods of protectinganchors against these causes of damage aredescribed below.(a) Blast damage to bondDetonation of an explosive confined in a drill holewill generate a shock wave in the surrounding rockthat will have sufficient energy within a distance ofabout 40–50 borehole diameters to fracture the rock(refer to Fig. 10.13). At greater distances, the shockwave will generate ground vibrations that may havesufficient magnitude to fracture the grout in theanchorage zone. The resilience of cement groutedanchors to blasting is demonstrated in hard rockmining operations where it is common practice tomine upwards through pre-placed passive anchors.Despite the high level of explosive energy to whichthese anchors are subjected, they are still effectivein supporting the mine roof.A specific testing program of the performance ofresin anchored rock bolts located close to blasts hasbeen carried out in a tunnel in Wales (Little-john etal., 1989; Rodger et al., 1996). The tests showedthat all deformations in the bolts were elastic andthere was no resin-bolt debonding or loss of loadfor ground accelerations in the range 10–640 g.These accelerations were developed by explosiveloads per delay in the range 16.5–35.8 kg (36–79lb) detonated at distances as close as 1 m (3.3 ft)from the bolts. Section 10.3.4 discusses methods ofcalculating blast vibration levels. While grouted bolts are able to sustain load when

subjected to blast induced vibrations, it is likely thatthe grout, which is brittle, is cracked by the groundmotion and may then be more susceptible tocorrosion. Where corrosion of the steel is ofconcern, the provision of a grouted sheath that ismore resilient than the grout alone, will improvecorrosion resistance.(b) Overstressing of bar or strandPassage of the shock wave through the rock causesdilation and compression of the rock mass whichwill alter the strain in the anchor. This strain will betransient if the rock behaves elastically. However, ifthe magnitude of the shock wave is sufficient topermanently open discontinuities which areintersected by the anchor, there will be acorresponding permanent increase in the stress inthe anchor.In the tunnel blasting tests described in (a) above, itwas found that the dynamic stress induced in thebolts was about twice the level for fully grouted,untensioned bolts than for prestressed boltsanchored with two speed resin. This indicates thatconfinement of the rock by the tensioned bolts helpsto limit the deformation of the rock mass andcorresponding strain in the steel. For example, in a 6m (19.7 ft) long bolt tensioned to 100 kN (22.5kips) subjected to a peak particle acceleration of 345mm/sec (13.5 in/ sec) and a maximum accelerationof 130g, the peak dynamic stress in the boltsreached a level of 13% in excess of the prestress.An approximate relationship between the peakdynamic load (expressed as a percentage of theprestress load) and the blast parameters for thetunnel in Wales was found to be

(9.25)

where R is the distance between the blast (m) and thebolt and W is the explosive weight detonated perdelay (kg) (Littlejohn, 1993).Another example of stresses induced in tensionedanchors by blasting is given by Littlejohn et al.(1977b) where both the transient and permanentstress in anchors installed in the footwall of a coalmine were monitored. The anchors had working


loads of 1500 kN (337 kips) and free stressinglengths of 12 m (39 ft), and were located parallel tothe rows of blast holes. A row of nine blast holes,each loaded with 32 kg (70 lb) of explosive andlocated 5 m (16 ft) from the row of anchors, wasdetonated on a single delay. Detonation of thisexplosive charge caused an instantaneous increasein anchor load of 100 kN (7%) and a permanentincrease of load of 64 kN (4%).(c) Flyrock damageWhere there is a possibility of damage to the headof a prestressed anchor from flyrock, either the blastshould be covered with blasting mats or the headprotected in an appropriate manner. This isparticularly important in the case of strand becausethe wedges are highly stressed and sensitive todamage.

9.3.9Anchors in permafrost

Extensive rock bolting has been carried out inpermafrost using both cement and resin anchor-ages. The general method used in all theseinstallations is to heat the ground around the bondlength sufficiently to melt the permafrost during thetime that the cement or resin is setting. When thepermafrost reforms, the ground expands to developa contact pressure between the ground and the groutthat enhances the bond strength (Kast and Skermer,1986). Using this method the cement or resin setsnormally and the bond strengths developed arecomparable to those obtained in unfrozen ground.Tests have been conducted in 8 m (26 ft) deep holesin sound, frozen rock using a neat Ciment Fondu-water grout mix heated to about 13°C (55°F);Ciment Fondu has a high heat of hydration whichcounteracts the cooling effect of the ground. Thebar was heated prior to installation and thepermafrost around the hole was melted bycirculating steam. It was found that the temperaturein the grout was maintained above freezing for up to18 hours, which compared with a setting time of thegrout of about 5 hours. Pull tests indicated that anultimate rock-grout bond strength of about 1 MPa

(145 p.s.i.) was developed, while the steel-groutbond strength was as high as 7 MPa (1015 p.s.i.).These bond values are similar to those for anchorsin weak rock (see Table 9.2).Resin has also been used for anchors installations inpermafrost with ground temperatures down to −30°C. The procedure was to circulate hot water in thehole to melt the ice around the hole, and to heat thebar and resin to about 35°C (95°F). The bar wasthen installed in the normal manner and the resinsets before the temperature of the ground adjacent tothe resin dropped below the freezing level (Kast,1989).A detailed testing program of anchors installed inpermafrost has also been carried out by Johnstonand Ladanyi (1972). The material in the bond zonecomprised varved silt and clay, containing icelenses 2–8 mm (0.8–0.3 in) thick, at an overallground temperature of about −0.5°C (31°F). Thegrout mix used for the anchorage consisted of highearly strength cement (Type III), sand and watermixed in the proportions 1:1:0.5. The grouttemperature when placed was between 5 and 14°C(40–55°F). At the completion of the test program allthe anchors were recovered and is was found thatthe grout was hard and the particles well bonded,and the surface in contact with the frozen soil wasnot flaky or powdery. Although the primary purposeof this program was to conduct creep tests, itappears that the working bond strength for theseconditions was about 0.1 MPa (14.5 p.s.i.).

9.4Corrosion protection

The protection of permanent anchors, andsometimes temporary anchors, against corrosion isone of the most important aspects of their designand construction. Current practice is to provide acorrosion protection system, appropriate for the siteconditions, for all permanent anchors, as well as fortemporary anchors where the environment iscorrosive and there is a chance of failure duringtheir service life. Permanent anchors are defined asthose with a service life exceeding 24 months (PTI,


1996). The importance of corrosion protection isdemonstrated in the results of a survey of failure ofanchorage systems caused by corrosion (Littlejohn,1987). A total of 35 cases of corrosion failure havebeen reported in the literature, of which 11 weretemporary anchors; the time to failure varied fromsix months to 31 years. These failures could bedivided into the following three categories:

1. corrosion of the bond zone (2 failures);2. corrosion of the free stressing length (21

failures);3. corrosion of the head (19 failures).

While these failures are only a small fraction of themillions of anchor projects that have been installed,corrosion is just about the only cause of failure oncethe system has been installed and tested. Researchon corrosion of rock bolts in Finland and Swedenhas shown that there can be defects in the groutencapsulation of cement grouted anchors,particularly in and under the head area where thecorrosion protection may be incomplete (Baxter,1997). Furthermore, for resin anchored boltsencapsulation of the steel can be incomplete due topoor mixing, the presence of the shredded plasticsheath in the resin and the inability to center the barin the hole.The process of corrosion is complex and not clearlyunderstood, particularly in the highly variableconditions that may occur below the groundsurface. For this reason corrosion protectionmeasures are almost always provided on permanentanchors.

9.4.1Mechanism of corrosion

The mechanism of corrosion of prestressing steel ispredominantly an electrolytic reaction in whichthree conditions must be present. First, the steelstrand or bar must be in contact with an electrolyte,which in rock anchors is usually water. Second, theelectrolyte must be in contact with an anode and acathode, and third, there must be direct metallic

connection between the anode and cathode(Fig. 9.25). A film of water is sufficient to developcorrosion, and the corrosion risk increases inflowing water where the corrosion products arecarried away to expose a new surface to attack.Humidity is an even more dangerous conditionbecause of the ample supply of oxygen to thecorrosion site (Littlejohn and Bruce, 1977).Where these three conditions exist, corrosion willoccur if a current flows between the anode and thecathode. The rate of corrosion is proportional to themagnitude of the current, and corrosion occurs asthe metal ions go into solution at the anode. Thereare two mechanisms which will develop a currentflow. First, a galvanic micro-cell is set up where thecathode has a higher electrical potential relative tothe electrolyte than the anode resulting in thedevelopment of a potential difference between theanode and the cathode (Fig. 9.25(a)). Second, wherestray direct currents are present in the soil, the steeloffers a low resistance path and a portion of thecurrent may leak into the anchor (Fig. 9.25(b)).Where the current leaves the steel and dischargesback into the soil or electrolyte, an anode is formedand corrosion pits will firm at this point (FHWA,1982). Potential stray current sources are electrifiedrailways, welding operations, cathodic protectionrectifiers and electroplating plants.Galvanic micro-cells may develop under a varietyof circumstances, all of which meet the threeconditions for corrosion listed in the previousparagraphs. Any one, or a combination of theconditions described below may occur around ananchor and result in corrosion (Hanna, 1982).

1. Inhomogeneities within the metal Impuritiesand regions of varying composition will havedifferent electric potentials with the result that acurrent flow is generated between differentregions within the metal.

2. Defects at the metal surface Cracks in themetal surface, which may develop when thesteel is stressed, form discontinuities in anyprotective layer and the crack becomes ananodic zone where corrosion may initiate.


3. Bimetallic cells Where two metals are incontact, the difference in electric potential between the metals generates a current. Themorereactive cell acts as the anode and, undertheright conditions, corrosion occurs at theanode.

4. Oxygen supply Where there is a high oxygenconcentration at the surface, the metal becomescathodic and sites of low oxygen concentrationbecome anodic. The magnitude of the currentgenerated is related to the difference in oxygenconcentration.

5. Hydrogen concentration A variation inhydrogen ion concentration, or pH, produces anelectrical differential and the formation of agalvanic micro-cell.

9.4.2Types of corrosion

Corrosion can occur as general corrosion on theentire surface of the steel, as local corrosionforming pitting and crevices, and as hydrogenembrittlement. General corrosion results where theanode and cathode are approximately equal in area,and can be beneficial where it forms a thin,continuous and stable coating that protects the steelfrom further attack. Local corrosion is associatedwith defects and inhomogeneities in the steel, andalso where stressing produces breaks in a protectivesurface layer. Hydrogen embrittlement occurswhere the steel molecular structure is disrupted andweakened by the absorption into the metal lattice ofatomic hydrogen. The conditions under which thesetypes of corrosion develop are discussed below(FHWA, 1982; Reeves, 1987).(a) Pitting corrosionPitting corrosion results from intense local attack inan electrolyte. It is one of the most destructiveforms of corrosion because the pit will reduce thecross-sectional area of the highly stressed steelmember. Furthermore, once initiated, the corrosionprocess within the pit produces a condition thatstimulates further corrosion. The galvanic cellshown in Fig. 9.25(a) shows the conditions that

produce pitting corrosion. The chloride ions locallyweaken the passive film protecting the steel and ananodic zone is developed where metal ions go intosolution. These ions react with the water to producea variety of iron oxide corrosion products (rust). Asthe process continues, the pH of the cathodeincreases due to the accumulation of hydroxyl ions.Simultaneously, the pH is lowered within the pitbecause corrosion products retard the diffusion ofoxygen into the pit, while chloride ions migrate intothe pit. The rate of corrosion increases as the pHdecreases.(b) Stress corrosionStress corrosion cracking is an anodic corrosionprocess with the crack forming at anodic sites. Theformation of a crack in a steel under high tensileload exposes a fresh metal surface to attack and thereduction in cross-sectional area may eventuallyresult in brittle failure of the anchor. There is someindication that high strength steels with a yieldstress above 1240 MPa (180 000 p.s.i.), or aRockwell C hardness greater than 40 are susceptibleto stress corrosion cracking (Uhlig, 1971).(c) Hydrogen embrittlementHydrogen embrittlement occurs when atomichydrogen resulting from a corrosion reaction orcathodic polarization enters the metal lattice atcathodic zones. At a void in the metal, the atomichydrogen will combine to form molecular hydrogenin a process that generates internal stresses andreduces the ductility of the steel. Sulfide ions at thecathode zone accelerate hydrogen embrittlement by‘poisoning’ the steel surface enabling the atomichydrogen to penetrate the metal more easily.Hydrogen embrittlement may not be visible on thesteel surface, and can occur slowly resulting infailure of the anchor long after installation.(d) Bacterial corrosionWet clays, marshes and organic soils below thewater table often contain sulfate-reducing anaerobicbacteria that will accelerate steel corrosion in de-aerated soils. These bacteria exist where sulfates,moisture and organic matter are present, and aremost active at pH levels between 6.2 and 7.8. Theydo not survive at high pH levels. The bacterial


corrosion process involves the reduction of sulfatesto sulfides with hydrogen supplied by the steel andthe formation of rust and weak, porous ferroussulfide. This corrosion may be general, or local toform pits.

(e) Corrosion in groutEmbedding an anchor in grout produces alkaline,high-pH conditions and the formation of a galvanicmicro-cell involving oxygen. Local concentrationsof oxygen at the anode lead to general corrosion and

Figure 9.25 Representation of corrosion mechanisms: (a) galvanic micro-cell developed at steel surface (Hanna, 1982);and (b) stray-current corrosion (FHWA, 1982).


the formation of a layer of hydrous ferrous oxide.This is a passive layer that is insoluble in solutionswith a pH above 4.5. As the pH of the grout isabove 12.5, the ferrous oxide inhibits furthercorrosion. However, the protective environmentprovided by the grout will be diminished if thegrout is cracked or porous allowing penetration ofchemicals, such as chloride (Cl−), sulfite (SO),sulfate (SO3) and carbonate (CO3) ions that willneutralize the alkaline conditions. Studies ofdiffusion rates of chlorides through cement grout,with subsequent corrosion of the steel, can be usedto estimate the service life of anchors protectedsolely with cement grouts (Chakravorty et al.,1995). Protective systems comprising both cementgrout, and plastic sheathes that are resistant tocracking and prevent moisture infiltration of themore brittle grout, are discussed in Section 9.4.4.Steel corrosion within a grout column is adangerous condition because the products ofcorrosion occupy a greater volume than the originalmetal and large bursting pressures are developed.These pressures may be great enough to break upthe grout column and can lead to loss of bonding.

9.4.3Corrosive conditions

Investigation programs for anchoring projects willusually include a study of the potential for corrosionof the anchors. Because there are many differenttypes of corrosion as described in the previoussection, there are also many different geological andground water conditions that cause corrosion.Furthermore, conditions may change with time as aresult of changes in land use and such events aschemical spills. Consequently it is difficult todetermine definitively the corrosive nature of a siteand general practice is to provide corrosion for allpermanent anchor systems.The following list describes conditions that willusually create a corrosive environment (Hanna,1982; PTI, 1996):

1. soils and rocks which contain chlorides;

2. seasonal changes in the ground water table;3. anchorages in marine environments where they

are exposed to sea water which containschlorides and sulfates;

4. fully saturated clays with high sulfate content;5. anchorages passing through different ground

types which possess different chemicalcharacteristics;

6. peat bogs, organic fills containing humic acid;7. acid mine or industrial waste.

The corrosive environments described above can bequantified in terms of the pH value and theresistivity of the site. In highly acidic ground (pH<4),corrosion by pitting is likely, while in a slightlyalkaline ground (pH between 6.2 and 7.8), sulfate-reducing bacteria flourish. Soil resistivity is relatedto corrosion potential by the magnitude of thecurrent that can flow between the steel and the soil.The lower the resistivity of a soil, the larger thecurrent flow and the greater the corrosion potential.In general the degree of corrosiveness decreases asfollows (King, 1977):

As a guideline on corrosive conditions, groundshould be considered aggressive and permanentanchors should be protected against corrosion if ithas one or more of the following conditions (PTI,1996):

1. pH<4.5;2. resistivity<2000 ohm cm;3. sulfides present;4. stray currents present;5. chemical attack has occurred to other buried

structures.

The type of steel used for the anchor also has aninfluence on corrosion potential. It is found thatquenched and tempered prestressing steels aresusceptible to hydrogen embrittlement corrosionand should not be used for permanent anchors.


9.4.4Corrosion protection methods

A number of rock bolt and rock anchormanufacturers have developed proprietary rockcorrosion protection systems that have beenthoroughly tested in a wide range of applicationsand can be used with confidence for permanentanchors. A partial list of these manufacturersinclude Dywidag, Freyssinet and Williams FormHardware and Rock Bolt Co. While the basicmethod of protection for all these systems is verysimple, installa tion requires close attention to detailto ensure that every part of the anchor will bepermanently protected.PTI (1996) classifies corrosion protection systemsas either Class I or Class II. For Class I anchors thebond length is encapsulated in a grout-filled sheathor is coated with epoxy, while for Class II anchorsthe bare strand or bar is embedded in grout. In bothcases the unbonded length is encapsulated in asheath filled with a corrosion inhibitor or a heatshrink sleeve, and the head comprises a trumpetfilled with corrosion inhibitor and the exposed headis covered for permanent anchors. Figure 9.26illustrates an anchor with Class I corrosionprotection, while Fig. 9.5 illustrates anchors withClass II corrosion protection. Table 9.3 lists theconditions under which anchors with Class I and IIprotection systems may be used.The general requirements of a corrosion protectionsystem are as follows.

1. There will be no break down, cracking ordissolution of the protection system during theservice life of the anchor.

2. The fabrication of the protection system can becarried out either in a plant or on site in such amanner that the quality of the system can beverified.

3. The installation and stressing of the anchor canbe carried out without damage to the protectionsystem.

4. The materials used in the protection systemmust be inert with respect to both the steelanchor and the surrounding environment.

The material most commonly used for corrosionprotection is cement grout, primarily because itcreates a high pH environment that passivates thesteel by forming a surface layer of hydrous ferrousoxide. In addition, cement grout is inexpensive,simple to install, has sufficient strength for mostapplications, and has a long service life. Thegreatest drawback to grout is its tendency to crack,particularly when loaded in tension or bending.Because of the brittle nature of grout, it is usual thatthe protection system comprises a combination ofgrout and a plastic sleeve. In this way, the groutproduces the high pH environment around the steel,while the plastic sleeve provides protection againstcracking of the grout. In order to minimize theformation of shrinkage cracks that would reduce thecorrosion resistance of the grout, it is commonpractice to incorporate additives in the grout mix toeliminate shrinkage and reduce bleed (seeSection 9.2.6).A corrosion protection system that can be used forboth bar anchors and strand is shown in Fig. 9.26;the components and installation procedure are asfollows.

Table 9.3 Conditions for which Class I and II corrosion protection systems may be used (modified from PTI, 1996)

Class IDouble corrosion protection

Class IISingle corrosion protection

Permanent anchors (working life>24 months); andground conditions aggressive or unknown; and seriousconsequences of failure;

Temporary anchors (working life<24 months); andground conditions aggressive;

or orPermanent anchors (working life>24 months); andground conditions aggressive or unknown; andconsequences of failure not serious; and incremental

Permanent anchors; and ground conditions non-aggressive; and consequences of failure not serious; andincremental placement costs expensive.


Class IDouble corrosion protection

Class IISingle corrosion protection

placement costs inexpensive.1. A corrugated sheath made of high density

polyethylene (HDPE) is grouted over the fulllength of the bar. This operation can be carriedout before the bar is inserted in the hole byplacing the bar on an inclined surface with thehead up and then pumping grout through thegrout cap so that the sheath is filled from the

bottom upwards. Alternatively, the sheath canbe grouted after installation in the hole througha grout tube sealed inside the sheath. In thebond zone the corrugated sheath transmits theshear stresses from the steel through the twolayers of grout to the rock.

2. A smooth plastic sheath, coinciding with the

Figure 9.26 Corrosion protection system for anchors comprising two grout layers, a corrugated plastic sheath, and agrease-filled sleeve for the head (courtesy Dywidag Systems Int.).


free stressing length, is placed over thecorrugated sheath. The ends of the smoothsheath are sealed with heat shrink tubing toprevent grout from entering the annular spacebetween the sheaths.

3. Any couplings in the bar are protected withheat shrink tubing.

4. Centralizing sleeves are attached to the bondzone at intervals of about 1 m to produce auniform thickness of grout in the annulus.

5. Two tubes are attached to the sheathing. In anuphole the grout tube is attached to the headwhile the vent tube extends to the top (distal) ofthe anchor. In a down hole, the grout tubeextends to the lower (distal) end of the anchorand the vent tube is attached to the head. Thecompleted assembly is lowered into the drillhole, taking care not to bend the bar or crackthe grout by using a rigid cradle set at the sameinclination as the drill hole.

6. The reaction plate with holes for the grout andvent tubes is installed. Attached to the underside of the plate is a steel tube with a sealbetween the plate and the plastic sheathing.

7. The hole is grouted through the grout tube untilgrout return is obtained in the vent tube.

8. After stressing, an anti-corrosion grease ispumped through a nipple in the plate to protectthe length of the bar between the plate and theplastic sheathing. Also, a cap filled with greaseis installed to protect the nut or wedges fromcorrosion.

The corrosion protection system shown in Fig. 9.26will provide three layers of protection—two layersof grout and the plastic sheathing. However, theportion of the anchor immediately below the head isespecially vulnerable to corrosion because, in orderto permit stressing and installation of the locking nutor strand wedges, it cannot be grouted prior tostressing. Protection of the head is particularlyimportant because this portion of the anchor is oftenexposed to the atmosphere, and on marine and riverstructures the heads will be subjected to fluctuatingwater levels and humid air. The head is protected

with an anti-corrosive grease which canaccommodate movement of the head due totemperature fluctuations and cyclic loading; groutwould crack under these conditions. An alternative to a grouted corrugated sleeve overthe full length of a strand anchor is to encase thefree stressing length in a polypropylene sheathpacked with anti-corrosion grease which is thenembedded in grout (see Fig. 9.6). This system willprovide the same level of protection as that shownin Fig. 9.26 but the light weight and flexibility ofthe polypropylene sheath facilitates handling in thefield.Corrosion protection systems other than grout arealso available. For example, stainless prestressingsteels are available (George Clark Ltd, SheffieldUK), but their cost would prohibit their use exceptin highly corrosive atmospheres with seriousconsequences for failure. Galvanized or epoxycoated bars are also available. Epoxy coatings willmeet requirements for Class I protection where thecoating thickness for the bar is in the range 0.18–0.3mm (ASTM A775), or 0.64–1.14 mm for strand(ASTM A882). Fiberglass bars may be analternative in highly corrosive conditions.Rock bolts anchored with resin cartridges arewidely used in civil engineering projects (seeSection 9.2.7), but the corrosion protection providedby the in situ mixed resin is likely to be inferior tothat of cement grout encapsulation (Baxter, 1997).The reason for this situation is that the resin does notprovide a high-pH environment such as cementgrout, and it is not possible to center the bar in thehole and to have control over the uniformdistribution of resin within the annulus between thewalls of the hole and the bar. Moreover, the plasticsheath in which the resin components are packagedare shredded, but remain mixed with the resin andare likely to be a conduit for the passage of waterfrom the rock to the steel.

9.3.5Corrosion monitoring

For installations supported with permanent anchors,


particularly where there is a serious consequence offailure, it is useful to have a means of monitoringcorrosion of the steel. At present (1998) corrosionmonitoring is rarely carried out. The requirementsfor a system for long term corrosion monitoring arethat it must be stable, compact so that an oversizehole is not required for installation, and is notdestructive to the anchor. One monitoring systemthat should meet these requirements is manufacturedby Vetek Corporation. The system comprises anelectrode of silver-silver chloride inside a plasticbraid that is wrapped around the steel anchor, but isnot electrically connected to it. The bolt with theelectrode can then be installed in the HDPE plasticsheath in the normal manner. The condition of thesteel is monitored by measuring the electricpotential between the anchor and the electrode usinga remote readout unit. The system can be automatedto trigger an alarm if the potential drops below apre-set limit.

9.5Installation and testing

The materials from which the anchor is fabricated,and procedures used for installation and testing, areusually specified in the contract documents. Thesespecifications must strike a balance between a‘method’ specification that defines all the materialsand procedures that must be used by the contractor,and a ‘performance’ specification that simplydefines the end product. If only specialist anchorcontractors are invited to bid, then a performancespecification can be prepared that specifies thecapacity of the anchor, the minimum free stressinglength, the level of corrosion protection, and theacceptance criteria with respect to load testing. Thisgives the contractor the flexibility to select thedrilling method, anchor materials and length ofanchorage that will be both economical, and achievethe required performance. If there is open biddingon the contract so that inexperienced contractorsmay perform the work, it would be necessary towrite a method specification that defines all aspectsof the contract. A successful anchoring project can

require the use of special drilling, grouting andtesting equipment, as well as close attention to allthe details of the installation, and for these reasonsspecialist contractors are preferred on largeanchoring projects.Components of an anchoring project that are usuallyspecified are the free stressing length and theworking load, the permeability of the rock in thebond length, the load testing requirements, and theacceptance criteria for these tests. This sectiondiscusses the testing procedures used to verify theperformance of the anchor, while methods ofdrilling and grouting are usually left to thediscretion of the contractor, and are discussed inChapter 10.

9.5.1Water testing

It is important that the grout does not leak into therock surrounding the anchor hole because this mayresult in a partially grouted anchor. Cement groutmay flow into fractures with apertures greater thanabout 0.25 mm (0.01 in) and it will be necessary toseal such fractures prior to installing the anchor.The water tightness of the drill hole can be tested byfilling the hole with water and subjecting it to apressure of 35 kPa (5 p.s.i.) in excess of thehydrostatic head as measured at the top of the hole.The rate at which the water level falls in the hole isobserved and the hole is acceptable if the seepagerate does not exceed 9.5 l (2.5 gal) over a 10 minuteperiod (PTI, 1996); time should be allowed for therock in the walls of the hole to be saturated. If thisrate is exceeded, then it is necessary to grout thehole using a low water: cement ratio grout or asanded grout, let the grout set for a period of about8–24 hours, and then redrill the hole. Drillingshould be carried out while the grout strength is stillconsiderably less than that of the rock so that thedrill steel will not deviate off the hole alignment.The water tightness test would then be repeated toensure that the fractures had been sealed, and ifnecessary the hole is regrouted and redrilled.As an alternative to filling the entire hole with


water, packers could be used to isolate the bond zoneto determine seepage conditions only in this areawhere complete grouting is required. This procedurewould be required where the rock is fractured in theportion of the hole where the free stressing length islocated and complete grouting may not benecessary.Holes that are flowing under artesian pressures mayalso need sealing after drilling if it is not possible tocontrol the flow by applying a back pressure duringgrouting of the anchor. Failure to seal a flowinghole may result in grout being washed from the holeand the formation of a poor quality anchorage. Theprocedure for grouting a flowing hole would be toseal a pair of tubes into the collar, with the grouttube extending to the bottom of the hole and a venttube at the ground surface. A grout pressure inexcess of the water inflow pressure could bemaintained until the grout had set by extending thegrout tubes vertically to develop the requiredhydrostatic head. Alternately, drain holes could bedrilled to lower the water pressure prior to installingthe anchor. A more difficult circumstance toovercome is where ground water flow through therock around the bond zone is fast enough to carryaway the grout before it has time to set. Where suchconditions are possible, a careful ground waterinvestigation may be justified because rapid waterflow may preclude the use of grouted anchors.

9.5.2Load testing

The stressing procedure for all permanent anchorsincorporates tests to evaluate their performance andensure that they meet specified acceptance criteria.The tests comprise applying a load to the bar orstrand with a hydraulic jack, and monitoring theextension of the anchor by measuring themovement of the head. Figure 9.27 shows a typicalset up for a load test of a bar anchor. The testequipment comprises a coupling and extension rodwhich passes through the hollow ram jack, and issecured with a nut on the top of the jack. The lowerpart of the jack has a hydraulic wrench to tighten

the nut when the design load has been reached.Prior to starting testing, the hydraulic system shouldbe calibrated in a compression testing machine torelate gauge pressure to applied load.Movement of the head of the anchor is measured, tothe nearest 0.025 mm (0.001 in), with a dial gaugemounted on a reference point which is independentof the anchor. If the dial gauge is mounted on thebearing plate, the measured movement may be inerror due to the displacement of the plate as the loadis applied. The usual procedure is to mount the dialgauge on a tripod set up on the ground at a distanceof about 1 m (3 ft) from the head of the anchor(Fig. 9.27).The purpose of making load-extensionmeasurements is to ensure that the anchor isbehaving elastically, that there is no loss of loadwith time, and that the required volume of rock tosupport the applied load is being mobilized by theanchor. This behavior is evaluated by carrying outfour types of tests (PTI, 1996):

1. performance tests;2. proof tests;3. creep tests;4. lift-off tests

The performance and creep tests are a detailedexamination of the load-extension behavior. Theyare carried out on the first two to five anchors, andon a minimum 2% of the remaining anchors. Proofand creep tests are carried out on all remaining theanchors. For any anchor that fails either test, anadditional two performance tests are performed, andthe failed anchor is either improved to meet therequired load, or is replaced. A lift-off test isperformed on every anchor.(a) Performance testsThe performance test comprises a cyclic loadingprocedure in the following sequence with anextension measurement being made at eachincrement (Fig. 9.28):

AL, 0.25P, AL,0.25P, 0.5P, AL,


0.25P, 0.5P, 0.75P, AL,0.25P, 0.5P, 0.75P, P, AL,0.25P, 0.5P, 0.75P, P, 1.2P, AL,0.25P, 0.5P, 0.75P, P, 1.2P, 1.33P—hold forcreep test, AL,P—lock-off.

where AL is the alignment load required to take outslack out of the system, and P is the design (lock-off) load.The application of an overload is an important partof checking that the anchor has capacity in excessof the design load. However, the value of themaximum load must be compared with the yieldstrength of the steel to ensure that it does not exceed80% of the elastic limit of the steel.(b) Proof testsThe loading sequence for a proof test is as follows:

AL, 0.25P, 0.5P, 0.75P, P, 1.2P, 1.33P,

–hold for creep test, AL(optional), P—lockoff

This loading sequence is equivalent to the last cycleof the performance test shown on Fig. 9.28. (c) Creep testsAt the applied maximum load of 1.33P in both theperformance and proof tests, creep extensionreadings are taken at intervals of 1, 2, 3, 4, 5, 6 and10 minutes. If the total creep movement between 1and 10 minutes exceeds 1 mm (0.04 in), the testload should be maintained for an additional 50minutes and the extension recorded at 20, 30, 40, 50and 60 minutes.(d) Lift-off testsWhen the anchor has been locked off at the designload, the jack pressure is reduced to zero and thenreapplied to determine the load at which the nut orwedges are lifted off the bearing plate. This test isperformed on every anchor.

Figure 9.27 Hydraulic jack set up for stressing a bar anchor; the jack incorporates a wrench for tightening the nut. Thedial gauge to measure displacement of the head is mounted on a tripod which is an independent reference point.


9.5.3Acceptance criteria

An anchor is acceptable if the results of theperformance, proof, creep and lift-off tests meetthree acceptance criteria recommended by the PTI(1996) for permanent anchors; these are as follows:

1. The total elastic extension measured inperformance or proof tests should exceed 80%of the theoretical elastic elongation of the freestressing length, and be less than the theoreticalelastic elongation of the free stressing lengthplus 50% of the bond length (Fig. 9.29).

2. The creep extension should not exceed 1 mm(0.04 in) during the period of 1–10 minutes. Ifthis value is exceeded, then the total creepextension within the period 6–60 minutesshould not exceed 2 mm (0.08 in) (Fig. 9.30).

3. The lift-off should be within 5% of thespecified transfer load.

The first criterion ensures that the rock massbetween the head and the bond length is mobilizedby the applied load, and that the major portion ofthe bond stress is developed in the top half of the

anchorage. This criterion is shown graphically inFig. 9.29 where the elastic ?e and permanent ?pportions of the measured extension are plottedagainst load for the performance test shown inFig. 9.28. An anchor meets the acceptance criterionif the elastic extension line falls between the twodashed lines designated (a) and (b). The acceptancecriteria extension limits are calculated using theelastic modulus of the steel (see Table 9.1) and thecross-section area of the bar or strand bundle,together with the appropriate bond and freestressing lengths.It is generally found that creep in rock anchors issmall and that conducting long term creep tests isnot warranted. If creep exceeds the limit in criterion2, the anchor is unacceptable because this is anindication of failure of the bond rather than thecreep of the surrounding rock. Where an anchorfails to meet the acceptance criterion, it may bepossible to improve the bond if there are secondarygrout tubes through which pressure grouting can becarried out. If this is not possible a replacementanchor would have to be installed. As discussed inSection 9.3.7, creep of epoxy filled strand may begreater than that of bare strand, and the acceptancecriterion should be adjusted accordingly. At a test

Figure 9.28 Results of anchor performance test showing load-displacement measurements, and permanent (?p) andelastic (?e) displacement.


load of 80% of the ultimate strength, creepmovements are estimated to be 0.015% , or higher,of the apparent free stressing length during the 6–10minute log cycle.When conducting lift-off tests on strand anchors,care should be taken not to loosen the wedges andre-grip the strand at a different position. Properseating of the wedges requires that they beembedded into the steel, and indentations in the steelwill act as stress concentrators that should not belocated below the bearing plate.9.6 ReferencesAl-Mosawe, M.J. (1979) The Effect of Repeated and

Alternating loads on the Behaviour of Dead andPrestressed Anchors in Sand. Thesis, University ofSheffield, England.

Baxter, D.A. (1997) Rockbolt corrosion under scrutiny.Tunnels and Tunnelling International, London, July,35–8.

Benmokrane, B. and Ballivy, G. (1991) Five yearmonitoring of load losses on prestressed cement-grouted rock anchors. Can. Geotech. J., 28, 668–77.

British Standards Institution (1985) The Structural Use of

Concrete. BS 8110, Part 1, London.Bruce, D.A., Greene, B. and Schaffer, A. (1996) Unique

cofferdam construction: Pt. Marion Lock and Dam,Pennsylvania. Ground Engineering, April, 41–4.

Bruen, M.P., Pansic, N. and Schwartz, M.I. (1996)Creeping suspicion. ASCE, Civil Engineering, May,60–3.

Bureau Securitas (1972) Ground Anchors. French Codeof Practice, Editions Eyrolles, RecommendationsTA72.

Canadian Portland Cement Association (1984) ConcreteDesign Handbook. CPCA, Ottawa, pp. 178–81.

Chakravorty, M., Frangopol, D.M., Mosher, R.L. andPytte, J.E. (1995) Time-dependent reliability of rock-anchored structures. Reliability Eng. and SystemSafety, 47, 231–36.

Coates, D.F. and Yu, Y.S. (1971) Rock Anchor DesignMechanics. Canada Dept. of Energy Mines andResources, Research Report No. R233.

Dywidag Canada, Ltd (1993) Dywidag RockAnchorMono-bar, Bundle Anchor, Epoxy Anchor.Dyckerhoff & Widmann AG, Munich, W. Germany.

Electric Power Research Institute (1983) TransmissionLine Structure Foundations for Uplift-compression

Figure 9.29 Permanent and elastic displacement of anchor in comparison with acceptance criteria.


Loading. EPRI EL-2870, Project 1493–1 EPRI, PaltoAlto, CA.

Farmer, I.W. (1975) Stress distribution along a resingrouted anchor. Int. J. Rock Mech. &; Geomech.Abstr., 12, 347–51.

Federal Highway Administration (US) (1982) Tiebacks.Report No. FHWA/RD-82/047, Washington, DC.

Ghosh, R.S. (1976) Reinforced Concrete Footing -Anchored in Rock. Ontario Hydro Research DivisionReport No. S76–4-K, Toronto, Canada.

Golder Associates (1983) Project files: full scale loadtests on instrumented anchors.

Golder Associates (1989) Project files: long termmonitoring results.

Hanna, T.H. (1982) Foundations in Tension—GroundAnchors. Trans Tech/McGraw-Hill, Clausthal-Zellerfeld, Germany.

Hobst, L. and Zajic, J. (1977) Anchoring in Rock.Elsevier, Amsterdam, pp. 38–43.

Hoek, E. (1983) Strength of jointed rock masses.Geotechnique 33, 3, 187–223.

Ismael, N.F. (1982) Design of shallow rock-anchoredfoundations. Can. Geotech. J., 19, 463–71.

Johnston, G.H. and Ladanyi, B. (1972) Field tests ofgrouted rock anchors in permafrost. Can. Geotech. J.,9, 176–94.

Kast, G. (1989) Personal communication.Kast, G, and Skermer, N. (1986) DEW Line anchors in

permafrost. Geotech. News, 4(4), 30–3.King, R.A. (1977) A Review of Soil Corrosiveness with

particular Reference to Reinforced Earth. Transportand Road Research Laboratory, Crowthorne, UK,Supplementary Research Report No. 316.

Libby, J.R. (1977) Modern Prestressed Concrete. VanNostrand Reinhold, New York.

Littlejohn, G.S. (1987) Ground anchorages: corrosionperformance. Proc. Inst. of Civil Eng., Part 1, Vol. 82,pp. 645–62.

Littlejohn, G.S. (1993) Overview of rock anchorages.Comprehensive Rock Engineering, Pergamon Press,UK, Vol. 4, Ch. 15, pp. 413–50.

Littlejohn, G.S. and Bruce, D.A. (1975a) Rock anchors —

Figure 9.30 Results of creep test showing measured extension over a 10 minute period compared with acceptancecriterion of 1 mm.


state of the art. Part 1: Design. Ground Eng., 8(4),41–8.

Littlejohn, G.S. and Bruce, D.A. (1975b) Rock anchors -state of the art. Part 2: Construction. Ground Eng., 8(4),36–45.

Littlejohn, G.S. and Bruce, D.A. (1976) Rock anchors —state of the art. Part 3: Stressing and testing. GroundEng., 9(5), 331–41.

Littlejohn, G.S. and Bruce, D.A. (1977) Rock anchors -design and quality control. Proc. 16th Symp. on RockMechanics, U. of Minnesota, pp. 77–88.

Littlejohn, G.S. and Bruce, D.A. (1979) Long-termperformance of high capacity rock anchors atDevonport. Ground Eng., 12(7), 25–33.

Littlejohn, G.S., Bruce, D.A. and Deppner, W. (1977a)Anchor field tests in carboniferous strata. SpecialtySession No. 4, 9th International Conf. on SoilMechanics an Foundation Eng., Tokyo, pp. 82–6.

Littlejohn, G.S., Norton, P.J. and Turner, M.J. (1977b) Astudy of rock slope reinforcement at Westfield(Scotland) open pit and the effect of blasting onprestressed anchors. Proc. Conf. on Rock Eng.University of Newcastle upon Tyne, Vol. 1,pp. 293–310.

Littlejohn, G.S., Rodger, A.A., Mothersille, D.K. V. andHolland, D.C. (1989) Dynamic response of rock bolts.Proc. 2nd Int. Conf. on Foundations and Tunnels, (2),Engineering Technics Press, pp. 57–64.

Madhloom, A. (1978) Repeated loading of piles in sand.Thesis, University of Sheffield, England. Post-Tensioning Institute (1996) Recommendations forPrestressed Rock and Soil Anchors, 3rd edn, Phoenix.,AZ.

Radhakrishna, H.S. and Klym, T.W. (1980) Behavior ofrock anchored foundations subject to shear andmoment loads. IEEE Trans. on Power Apparatus andSystems, Vol. PAS-99, No 2, pp. 760–4.

Reeves, R.B. (1987) Corrosion protection of permanenttiebacks. Speciality Conf. on Rock Fall Mitigation,Region 10, Federal Highway Administration, Portland,Oregon.

Rodger, A.A., Littlejohn, G.S., Xu, H. and Holland,D. C.(1996) Instrumentation for monitoring the dynamic andstatic behaviour of rock bolts in tunnels. Proc. Inst. CivilEng., 119, 146–55.

Russell, J.R. (1968) Stress distributions around rockbolts: elastic stresses. Proc. 10th Symp. on Rock Mech.,Austen, Texas, pp. 661–6.

Saliman, R. and Schaefer, R. (1968) Anchored footingsfor transmission towers. ASCE Annual Meeting andNational Meeting on Structural Engineering,Pittsburgh, PA, Sept. 3-Oct. 4, Preprint 753.

South African Code of Practice (1972) Lateral Support inSurface Excavations. The South African Institution ofCivil Engineers, Johannesburg.

Uhlig, H.H. (1971) Corrosion and Corrosion Control.Wiley, New York, p. 134.

Ulrich, B.F., Wuest, W.J. and Stateham, R.M. (1990)Relationship between annulus thickness and theintegrity of resin-grouted roof bolts. Report ofInvestigations 9253, United States Bureau of Mines,Washington, DC.

Wijk, G. (1978) A theoretical remark on the stress fieldaround prestressed rock bolts. Int. J. Rock Mech. &Geomech. Abstr. 15, 289–294.


10Construction methods in rock

10.1Introduction

The construction of foundations on rock will usuallyinvolve one or more of the following three tasks.

1. First, there is likely to be some rock excavationeither by blasting, or a non-explosive methodsuch as ripping or splitting, which must be donewith care to avoid damaging the bearing rock.

2. Second, some reinforcement of the foundationmay have to be installed to ensure the long-termstability of the structure.

3. Third, a suitable bearing surface or excavationfor the structure will have to be prepared.

Often these construction tasks will be performed byan independent contractor whose performance willdepend to some degree on the specifications towhich he is working. Therefore, the construction ofa stable foundation will depend not only on thepreparation of reliable designs, but also on contractdocuments that clearly define the work required andthe rights and responsibilities of the owner andcontractor, and provide a fair level ofcompensation. It is also important that theassumption of risk in the performance of the workshould be appropriately apportioned between theowner and the contractor. For example, if anexcavation is to be made below the water tablewhere subsurface conditions are uncertain,requesting a lump sum price would probably resultin high bids because the contractors would have toinclude contingencies to cover their risk. Analternative would be to obtain unit prices for spec

ified work items and then pay for the work actuallycarried out.This chapter describes common constructionmethods for rock excavations, and discusses theprinciples involved in the preparation of contractdocuments.

10.2Drilling

On most rock foundation projects there is arequirement to drill holes for such purposes asgeological investigation, blasting, the installation ofanchors or socketed piers, and the set up ofinstrumentation. An example of the versatility indrilling equipment is shown in Fig. 10.1 where a‘bencher’ is drilling holes for rock bolts in a verticalcliff face. The bencher comprises a pneumaticpercussion drifter mounted on a boom equippedwith a chain feed; the boom is attached to the cliffface with a rock anchor. The drillers are suspendedon heavy duty canvas belts attached with carabinersto steel core, hemp ropes which are specificallydesigned for this type of work. Their supplies arecarried in a ‘spider’ (in the foreground) which is analuminium basket equipped with a pneumatic hoistmotor; a steel hoist rope attached to a pin above thecrest of the cliff allows the spider to be raised andlowered on the face.Drilling methods that are commonly used on rockconstruction projects are diamond, percussion,rotary and auger drilling, with diameters rangingfrom 50 mm (2 in) to 1.2 m (48 in). In selecting thedrilling equipment appropriate for the site

conditions, the following factors should beconsidered:

1. recovery of intact samples;2. length of hole;3. diameter of hole;4. directional tolerance;5. site access;6. strength and degree of fracturing of the rock;7. depth and condition of overburden;8. availability of drilling water;9. condition of wall of hole;

10. drilling rates and costs.

This section describes common drilling methodsand the conditions in which they may be used;information on drilling equipment and methods maybe obtained from handbooks (ADITC, 1997) andproduct literature published by drill manufacturerssuch as Atlas Copco, Boyles Bros. Drilling Co.,Gardner-Denver, Longyear, Sandvik and Tamrock.General descriptions of drilling equipment andoperations are included in publications by theFederal Highway Administration (1982) andSociety of Mining Engineers (1973).

Figure 10.1 Rock bolt holes being drilled in the face of a vertical cliff with a pneumatic bencher drill (photograph byD.Wood).

CONSTRUCTION METHODS IN ROCK 361

10.2.1Diamond drilling

The primary use of diamond drilling is investigationwork to recover intact core for the study of sitegeology, and to obtain samples for laboratorystrength testing (see Section 4.3). Diamond drillsmay also be used in construction where it isnecessary to drill long, accurately aligned holes, orwhere access space is limited and it is not possibleto use percussion drills. Because diamond drills relyon rotational speed and thrust rather than impactforce to cut the rock, diamond drills have smallerdimensions than percussion drills, and are capable ofdrilling to greater depth. Diamond drill holes canreach depths in excess of 1000 m (3000 ft). Thedeviation of diamond drilled holes is less than thatof percussion drilled holes because diamond drillrods are stiffer than percussion drill rods, anddiamond drills develop a steady thrust comparedwith the impact forces in a percussion drill. Withthe use of appropriate casing and drilling muds,

diamond drill holes can be put down in highlyfractured ground which would cave if drilled with apercussion drill.The disadvantages of diamond drilling are the lowadvance rates and high cost relative to percussiondrills. Also, the diamond bit cuts a hole with asmooth wall surface which will result in a lowerbond strength for rock anchors compared with therelatively rough surface produced by percussiondrills.The main components of a diamond drill comprise apower unit which may be a diesel or compressed airmotor, and a drill head that is powered from themotor through a gear box and gear train (Fig. 10.2).The function of the drill head is to rotate the drillstring, supply thrust to the drill bit and to advancethe rods as the drill bit cuts the hole. The drill stringcomprises lengths of drill rod which are flushcoupled and have a diameter slightly smaller thanthe hole diameter, a core barrel which retains thedrill core as the hole advances, and the drill bit onthe lower end of the core barrel. The cutting face of

Figure 10.2 Diesel-powered surface diamond drill (courtesy of JKS Boyles, 1989).

362 DRILLING

the drill bit is impregnated with diamonds set in ametal alloy matrix, and the cutting action isachieved by applying a high rotational speed (about2000 rpm) and low thrust (30–70 kN, or 6700–16000 lb).During drilling it is essential that the bit is flushedcontinually with water or drilling mud to cool thebit, remove the cuttings and reduce friction betweenthe drill string and the walls of the hole. Wheredrilling fluid circulation is lost, casing or muds areused to seal fractures and zones of broken,permeable ground. Usual practice is to advancecasing through the overburden and seat the casingshoe in bedrock to form a watertight seal throughthe permeable upper formations. If the drill fluid islost in a fracture intersected in the bedrock, varioustypes of muds can be used to form a cake on thewalls of the hole, or the fracture can be sealed withgrout. However, if it is later planned to conductpermeability tests in the hole, it is necessary to

employ muds that will break down a few days afteruse, and can be washed out of the hole to leave thewalls of the hole uncontaminated.In North America, diamond coring equipmentdimensions are designated by letters as shown inTable 10.1. For example, NQTT refers to: N sizecore, Q designates wire line equipment, and TTdesignates a triple-tube core barrel. Wire lineequipment, which is used for deep drill holes, has adouble tube core barrel consisting of an inner corebarrel that is retrieved with an overshot assemblylowered down the hole on a steel cable, or wireline(Fig. 10.3). This system allows the core barrel to beretrieved at the end of every drill run without thetime-consuming process of pulling the rods. Atriple-tube core barrel contains a split inner tubethat is pumped out of the core barrel withoutdisturbing the core. The split tube is placed on acradle and the top half of the tube is

Table 10.1 Dimensions of diamond drilling equipment (Boart Longyear Inc.)

Hole diameter Core diameter Casing OD* Drill rod OD

mm (in) mm (in) mm (in) mm (in)

AQ 48.0 (1.89) 26.9 (1.06) 57.1 (2.25) 44.5 (1.75)BQTT 60.0 (2.36) 33.5 (1.32) 73.0 (2.87) 55.6 (2.19)NQTT 75.7 (2.98) 45.1 (1.78) 88.9 (3.5) 69.9 (2.75)HQTT 96.0 (3.78) 61.1 (2.41) 114.3 (4.5) 88.9 (3.5)PQTT 122.7 (4.83) 83.0 (3.27) – 117.5 (4.63)*Wire line series dimensions, AW, BW, NW, HW.removed, making it possible to log the core withminimal disturbance. In comparison, the core isremoved from a double-tube core barrel by pumpingor hammering, which inevitably results indisturbance to the core.In very weak, fractured rock a system can be used inwhich the inner tube of the triple-tube barrel is linedwith a clear plastic sleeve. The core slides into thesleeve as the drill advances. When the inner tube isopened, the core is contained in the plastic tubewhere it can be logged, photographed, and storedwith minimal disturbance.

10.2.2Percussion drilling

Percussion drilling is the most common method ofrock drilling because of its relatively low cost, andthe high production rates that can be achieved(Fig. 10.4). While the predominant use of thisequipment is for drilling blast holes, it is also usedto drill holes for rock anchors, socketed piers anddrainage. The two main categories of percussiondrills are pneumatic and hydraulic, with the driftereither being on the surface (conventional jackhammer or airtrac), or in the hole (down-the-hole(DTH) drills). The common range of hole diametersfor this equipment is from 35 mm (1.5 in) to 150


mm (6 in) for surface drills, and from 100 mm (4in) to 200 mm (8 in) for DTH drills. The maximumlength of holes drilled with surface mounted driftersis limited to about 30–40 m (100–120 ft), althoughefficiency starts to diminish at depths greater thanabout 20 m (65 ft). This depth limitation is theresult of the difficulty in flushing cuttings from thehole, the reduction in efficiency as a result of loss ofenergy in the drill string, as well as the excessivedeviation. However, DTH drills can drill holes todepths of about 300 m (1000 ft), because there is noloss of energy in the drill string.(a) Surface percussion drillsThe principle of percussion drilling is to apply aseries of impact forces to a tungsten carbide drill bitwith sufficient energy to crush and break the rock.With each impact, the bit is rotated to expose a newface to the bit, while the cuttings are continuouslyflushed from the hole with air or water. Theminimum flushing or bailing velocity for cleaningthe cuttings is 1000–2000 m/min (3000–7000f.p.m.). Thus the drilling rate depends on thefollowing factors: the impact energy, the thrust onthe drill rods, the rotation speed, the rate at whichthe cuttings are flushed from the hole, the conditionof the rock, and the hole dimensions. All thesefactors are considered in the selection of the mostappropriate method of drilling for each project.In both pneumatic and hydraulic percussion drills,impact is applied by means of a reciprocating pistonwhich strikes the bit or drill steel and produces aseries of high-energy stress waves that aretransmitted to the bit. The impact rate is in the range2000–3500 blows per minute. The reciprocatingaction of the piston is controlled by valves thatintroduce compressed air or hydraulic fluidalternately at each end of the cylinder(Fig. 10.5). The shock wave travels down the drillsteel at a speed of about 5000 m/s (the speed ofsound in steel), and the shape of the shock wavedepends on the shape and impact velocity of thepiston. A pneumatic drill produces a shock wavethat has a high peak stress, while the shock waveproduced by a hydraulic drill is more uniform(Fig. 10.6). The result is that a hydraulic drill can

produce a shock wave with higher total energy, andtherefore a higher penetration rate, than a pneumaticdrill. If a pneumatic drill were to produce a shockwave with the same total energy as the hydraulicdrill, overstressing and breakage of the drill rodswould occur.Rotation of the drill steel is either dependent orindependent of the movement of the piston. Withdependent rotation, the drill rod is rotated on thebackstroke of the piston by a rifle bar. A system ofratchet and pawls allows the piston to travel forwardwithout rotation on the forward stroke while thefluted rifle bar is positioned for the next stroke(Fig. 10.7). Therefore the speed of rotation, which isusually in the range of about 50–100 rpm, cannot bechanged to suit varying rock conditions.Independent rotation is achieved by a motor thatoperates independently of the movement of thepiston, and is both reversible and has variabletorque.The advantages of hydraulic drills over pneumaticdrills are the greater penetration rates (up to 50%higher), greater control of the drilling functions, andreduced noise and exhaust mist. However, thedisadvantages of hydraulic drills are their highercapital cost and more expensive maintenance.(b) Down-the-hole (DTH) drillsDrills with the drifter mounted at the surface requirethat the impact energy produced by the piston betransmitted down the drill rods to the bit. There is asignificant loss of energy in the drill string thatbecomes greater as the hole depth increases. Theefficiency of the drill can be significantly improvedby mounting the drifter in the hole immediatelybehind the bit which allows both larger diameterand deeper holes (at least 300 m, or 1000 ft) to bedrilled. Other advantages of the DTH drills arelower noise levels, and reduced wear on the drillrods. However, the disadvantages are that theminimum hole diameter is limited by the cylinderdimensions to about 100 mm (4 in). Also, in shortholes the penetration rate of a DTH drill is less thanthat of a surface mounted drill because of thesmaller cylinder diameter of the DTH drifter. Inhighly fractured rock, DTH drills should be used

364 DRILLING

with care because caving of the hole can result inloss of the drifter.

10.2.3Rotary drills

Rotary drilling is a versatile drilling method that canbe used to drill holes from 75 mm (3 in) to 560 mm(22 in) in diameter, and, in the case of oil wells, upto several thousand meters deep. The components

of a rotary drill are a surface drive unit, which maybe a standard diamond drill or a larger truckmounted diesel unit, that applies a torque and thrustto the drill string and bit. The thrust applied to thebit may be as high 500 kN (110 000 lb) in hard rockin order to achieve contact pressures which are highenough to break the rock. The rotation of the bit, ata speed of between 30 and 120 rpm, continuouslyexposes the bit to a fresh rock face.Rotary drills can be employed in very soft rock

Figure 10.3 Diagram of wire-line core barrel. (courtesy of JKS Boyles).


using drag bits, and in very hard rock using rollercone bits equipped with tungsten carbide inserts(Fig. 10.8). In soft rock the bit scrapes the rock,while in hard rock the torque and thrust applied tothe bit produces a crushing and chipping action. The

cuttings are cleaned from the hole by either air orwater which is forced down the drill rods andexhausted up the annulus between the drill rods andthe wall of the hole.The primary applications of rotary drills are in oil

Figure 10.4 Tracked drill equipped with surface mounted hydraulic drifter (Tamrock Drills).

Figure 10.5 Working principle of a hydraulic drifter (Tamrock (1983)). The piston is shown at the front end of itsstroke. Oil enters drifter through the high-pressure port (1) and flows to the front part of cylinder (2). The piston isforced backwards and at the same time oil enters the distribution chamber (3), pushing the distributor (4) to the rearposition. A portion of the oil enters the high-pressure accumulator (5) that is filled with nitrogen. The nitrogen iscompressed and accumulates energy. The oil in the rear of the cylinder escapes through port (6) to the return port (7).The low-pressure accumulator (8) prevents shock loads in the return hose.

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wells, and for large diameter blast holes in open pitmines. They may be used in geological explorationto advance the hole through materials such asboulder till and rock where there is no requirementto obtain intact samples. Examination of thecuttings and recording the advance rate will give anindication of the geological conditions, but wouldnot be a substitute for continuous sampling.

10.2.4Overburden drilling

Where holes must be advanced through aconsiderable thickness of overburden overlying thebedrock, it is often necessary to install casing toprevent the hole from caving. Where the over-burden is soft soil, the casing can be pushed ordriven, but in situations where the overburden isdense soil or contains boulders, it will be necessaryto advance the casing by drilling. Drillingeconomies can be realized if the casinginstallation and rock drilling can be carried out inone operation using the same drill rig. Drillingsystems that can perform these dual operations arediamond drilling, or two percussion methods,namely the Tubex system manufactured bySandvik, and drills manufactured by the Klemm andBarber companies.

The Tubex bit, which is used with either surfacemounted or down-the-hole percussion drills,comprises a reamer mounted on a cam behinda tungsten carbide insert pilot bit (Fig. 10.9). Whena torque is applied to the drill rods the reamerexpands the pilot hole to a diameter just larger thanthe casing and the shoulder on the guide advancesthe casing. When the casing has been seated inbedrock and the torque is reversed, the reamercontracts and the bit can be withdrawn through thecasing. Hole diameters drilled with Tubex bits areshown in Table 10.2.The Klemm and Barber drills use a two-tubedrilling system to advance the casing and the drillstring independently. The Barber drill uses a rotarycasing driver to advance the casing equipped with atungsten carbide studded shoe through materialsranging from sand and gravel to boulders. A topdrive simultaneously advances a drill stringequipped with a down-the-hole hammer, drag bit orroller cone bit that drills either inside or ahead ofthe casing. Once the casing has been seated in thebedrock and the overburden drilling is complete, thehole in the rock can be drilled to depths of severalhundred meters. Cuttings are cleaned from the holeusing air or water pumped down the drill rods andreturned in the space be

Figure 10.6 Impulse curves for (a) hydraulic and (b) pneumatic drifters (Atlas Copco).


Table 10.2 Drill hole diameters for Tubex drilling

Drill bit number Casing ID (overburden) Hole diameter (rock)

mm (in) mm (in)

Tubex 90 102 (4) 85 (3.34)Tubex 115 126 (5) 110 (4.31)Tubex 140 152 (6) 128 (5)Tubex 165 181 (7.1) 152 (6)Tubex 190 205 (8.1) 165 (6.5)Tubex 215 241 (9.5) 203 (8)Tubex 240 260 (10.25) 229 (9)Tubex 365 387 (15.25) 356 (14)tween the rods and the casing. Holes can be drilledwith diameters up to 1 m (40 in).

10.2.5Large diameter drilling

Large diameter (in the approximate range 0.6–3 mor 2–10 ft) drill holes may be required for suchpurposes as detailed in situ inspections of dam

Figure 10.7 Pneumatic, surface mounted, rifle-bar rotated percussion drill showing rotation mechanism comprisingratchet and pawls (courtesy Ingersoll-Rand Co. and Society of Mining Engineers, 1973).

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foundations, or the installation of rock socketedpiers. Holes of these dimensions can be drilled withaugers (in soft rock) or percussion methods whereno core recovery is required, or by the Calyxmethod if there is a need to recover core.

Augers are used in overburden and soft rock withcompressive strengths up to 30 MPa (4350 psi)where the material is strong enough for the walls ofthe hole to stand unsupported. The advantages ofaugering are the high penetration rates, the low

Figure 10.8 Rotary tricone drill bits: (a) soft-formation, (b) medium-formation, (c) hard-formation, (d) tungsten carbideinserts for very hard formation (courtesy Hughes Tool Co. and Society of Mining Engineers, 1973).


noise levels, and that no flushing medium isrequired to remove cuttings from the hole. In shortholes, continuous flight augers are used where theexcavated material is brought to the surface by therotating flights and the drill string is not brought tothe surface until the hole is complete. For largerholes, the 2–3 m (6–10 ft) long auger is loweredinto the hole on the drill string (Fig. 10.10). Whenthe hole has been advanced a short distance theauger is retracted with the excavated material anddischarged by reversing the rotation direction.For large diameter holes in strong rock, a specialtydrill called the ‘super drill’ can be used(Fig.10.11). This is a large size DTH hammerequipped with a button bit that can drill holes withdiameters up to about 0.75 m (30 in) and to depthsof several hundred meters. This drill can be used toinstall rock socketed piers and holes for highcapacity multi-strand tensioned anchors.Where core samples are required, the Calyx drillingsystem provides core with a diameter up to 3 m (10ft), and a clean hole that is suitable for geologicalmapping. The drill consists of a blunt nosed steelbarrel that is rotated in the hole. The cutting medium

is steel shot which is poured or injected into thehole and is trapped beneath the blunt bottom of thebarrel. The tumbling and rolling action of the shotcuts the rock. Alternatively, the lower edge of thebarrel can be equipped with tungsten carbide teeththat can cut even strong rock, although the rate ofadvance will be slow. The core, which is removedabout every meter, must be broken off the bottom ofthe hole. This can be accomplished by driving awedge between the core and the wall of the hole, orby detonating a ring of primacord around the lowerend of the core. The core, or pieces of core, are thenremoved by drilling a hole in the top and installingan eye so that the core can be lifted out with acrane.

10.2.6Directional drilling

An important advance in drilling technology is theability to control the direction of drill holes.Directional drilling allows holes to be drilled inboth rock and soil with lengths of up to about 2000m (5500 ft) in which both the path that the drill

Figure 10.9 Tubex drilling system for setting casing through overburden (courtesy Atlas Copco).

1. Shoulder. 2. Bit tube. 3. Guide. 4. Reamer. 5. Pilot bit.

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follows, and the end point, can be specified to

Figure 10.10 Auger drilling holes for rock-socketed piers for a bridge foundation (diagram courtesy of Atlas Copco).


tolerances of about 1% of the length of the hole.This allows, for example, curved holes to be drilledto bypass obstructions, or long straight holes to bedrilled which would otherwise wander off line.Applications of directional drilling includecontrolling the direction of deep investigation anddrainage holes, drilling multiple holes from a singleset up, and some instrumentation installations.Directional drilling could also be used where thereis no access to a location where a straight hole canbe drilled, where a precise exit point is required, orto place instrumentation cables in a secure holeunder a structure (National Research Council,1994).Directional drilling technology was developed inthe oil industry where several production wells arefrequently drilled from the same surface location.Figure 10.12 shows an example of an oil welldrilling rig being used to drill a 500 m (1650 ft)long hole for a telephone cable under a majorhighway. The entry point for the hole is at an angle

of 60° and is located on a steep valley slope, whilethe exit point is horizontal and located in the floorof the valley.The components of the directional drilling systemused with the drill rig shown in Fig. 10.12 are asfollows.

1. A roller cone drill bit (refer to Fig. 10.8).2. A head assembly containing a low speed (70–

150 rpm), high torque rotary motor whichdirectly drives the bit. Behind the motor there isa bent sub which allows a bend of up to 2° tobe set between the head and the drill string. Thedirection of the hole is controlled by setting thedirection and angle of the bend in the sub.

3. A string of standard drill rods. The rods do notrotate during drilling but are used to apply athrust to the bit, to convey drilling mud to therotary mud motor and the drill bit, and to setthe direction of the bent sub. The rotary motoris powered by the mud pumped down the drill

Figure 10.11 0.6 m (2 ft) diameter superdrill for drilling socket holes in hard rock (Ingersoll Rand Co.)

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rods, which then passes through the bit to cleanthe cuttings from the hole.

An efficient and accurate method of detecting theposition of the drill hole is the MWD (measurementwhile drilling) method. The MWD system comprisesa 10 m (31 ft) long, non-magnetic stainless steeldrill collar located behind the head assembly andbent sub. Within this collar are housedmagnetometers, which detect the azimuth of thecollar relative to the earth’s magnetic field, andaccelerometers which detect dip of the collarrelative to the earth’s gravitational field. Electricaloutput from the magnetometers and accelerometersis encoded into a binary signal that is pulsed up themud column to the surface. By frequent monitoringof the azimuth and dip readings, it is possible tocalculate the position of the end of the drill hole andits position relative to the required alignment. If achange in direction is required, the drill string is

rotated to reset the orientation of the bent sub.The precision with which a hole can be directedalong a specified path depends on the accuracy withwhich its position can be determined, and theminimum radii through which it can be turned. Theminimum radius for a 75 mm (3 in) diameter drillhole is about 100 m (300 ft) and the hole can bedrilled as a continuous curve, or a series of curvesand tangents. Experience has shown that it ispossible to achieve directional control of ±2–3 m (6–10 ft) over a hole length of 500 m (1650 ft).

10.3Blasting and non-explosive rock excavation

Rock excavation is often required on rockfoundation projects to remove, for example, materialthat may not have sufficient bearing capacity, or toform a level bearing surface. While blasting is themost common rock excavation method because of

Figure 10.12 Directional drilling system drilling 200 mm (8 in) diameter hole under highway to exit in valley floor(Sierra Drilling).


its relatively low cost, non-explosive excavationmethods such as ripping, splitting and the use ofhydraulic breakers are suitable where the rock isweak, or there is a need for very precise control ofeither excavation limits, and/or ground vibrationlevels.The requirements of any excavation method are theuse of procedures that break the rock efficiently,while controlling damage to the rock in the bearingsurface, of the slopes above and below thefoundation, and any nearby structures. This sectiondescribes the basics mechanics of blasting, and howthey may be applied to the design of blasts wherethere is a need to control rock fragmentation andground vibrations. Also discussed are non-explosiveexcavation techniques suitable for rock foundationprojects.

10.3.1Rock fracture by explosives

Blasting operations comprise the following threetasks:

1. drilling blast holes which have an appropriatediameter, and are laid out in a regular pattern asdefined by the burden and spacing;

2. loading the holes with a suitable type andquantity of explosive;

3. detonating the holes in a precise sequence.

The design of all these parameters depends on themechanism by which rock is broken by explosives,and an understanding of the rock fracturemechanism as described below is essential to thedesign of blasts.When an explosive is detonated, it is convertedwithin a few microseconds from a solid to a hightemperature gas. When confined in a blasthole, thisvery rapid reaction causes pressures that can reach100 000 atmospheres to be exerted against the wallsof the borehole. The explosive energy is transmittedinto the rock mass in the form of a shockwavewhich travels at a velocity of several thousandmeters per second. Rock breakage, which depends

on both the energy of the shock wave, and to agreater extent on the gas pressure, is a three stageprocess as follows: first, crushing occurs in theimmediate vicinity of the borehole; second, radialfractures are developed; and third, movement of thefractured rock mass takes place towards the freeface (Fig. 10.13).The following is a more detailed description of therock fracture mechanism illustrated in Fig. 10.13(FHWA, 1985; Hemphill, 1981). As the shock waveenters the rock surrounding the borehole, thematerial is crushed in compression for a distance ofone to two borehole diameters (Fig. 10.13(a)).However this effect is limited because, with theexpansion of the compressive wave front, the stresslevel quickly decays below the dynamiccompressive strength of the rock. At this stage thehigh gas pressure and the expansion of the boreholedevelops fractures aligned parallel to the boreholeaxis in the form of a series of radial cracks that mayextend to distances up to 40–50 borehole diameters(Fig. 10.13(b)). If there is a free face within adistance of about 30 borehole diameters of the hole,a portion of the shock wave is reflected from theface and this results in some spalling of rock on thefree face (Fig. 10.13(b)). Furthermore, the reliefprovided by the free face, combined with the forceexerted by the expanding high pressure gas, causesmovement of the rock that has been weakened andbroken into wedge shaped pieces by the formation ofthe radial cracks. This movement of the rock massextends the radial cracks to the free face resulting infragmentation of the rock mass (Fig. 10.13(c)).This mechanism of rock fracture clearly shows theimportance of the presence of a free face, at thecorrect distance from the blast hole, for efficientblasting operations. If the hole is located in a largevolume of rock with no free face, there will be nobreakage other than the crushing and formation ofthe radial cracks, and possibly some cratering at thesurface. On the other hand, if the hole is too close tothe face, the explosive energy will not be confinedby the rock, resulting in venting of the high pressuregases and the creation of excessive flyrock andnoise.

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The distance between the nearest free face and theblast hole is termed the burden, which isapproximately related to the explosive diameter bythe following empirical relationship (FHWA,1985):

(10.1a)

where Be is the burden distance in meters; SGe is theexplosive specific gravity; SGr is the rock specificgravity; and de is the explosive diameter in mm.

Figure 10.13 Mechanism of rock breakage by explosives: (a) crushing and formation of radial fractures; (b) rockspalling on free face; and (c) movement of fractured rock at free face.


Alternatively,

(10.1b)

where Be is in feet and de is in inches.In a blast consisting of a number of multi-holerows, it is necessary that the holes be detonated in asequence starting with the holes closest to the freeface. With a suitable delay interval between rows,there is sufficient time for fracture anddisplacement of the rock in each row to form a freeface for the succeeding row. If this interval is tooshort, the result is excessive airblast and rockfracture behind the blast holes, while if the intervalis too long, the muck pile is scattered. Anappropriate delay interval in milliseconds is about10–12 times the burden in meters (i.e. 30 ms delaysfor a 3 m burden).

10.3.2Controlled blasting

In making a rock excavation for a foundation it isoften necessary to use controlled blastingprocedures that limit damage to the rock in thebearing surface and any surrounding rock cuts.Excessive blast damage can result in reducedbearing capacity, and instability of slopes above orbelow the foundation. Figure 10.14 shows aphotograph of a rock cut in very strong granite inwhich excessive blasting energy in the upper part ofthe cut has severely fractured the rock, whilecontrolled blasting in the lower half has formed avertical, stable face.Controlled blasting involves drilling closely spaced,carefully aligned drill holes, which are loaded witha light explosive charge, and detonated in aspecified sequence with respect to the main blast.The principle of controlled blasting is closelyrelated to the mechanism of rock fracture describedin Section 10.3.1. An explosive load is used thatgenerates a shock wave and gas pressure that is justsufficient to break the rock between drill holes, butnot cause crushing or develop radial fractures in therock behind the face. This is achieved by twomethods. First, an explosive is used with a relatively

low detonation velocity of about 2800 m/s (9200 ft/s) which is approximately one half the velocity ofhigh strength nitroglycerin based gelatin dynamites.Second, the explosive diameter is less than that ofthe drill hole so there is an air gap between theexplosive and the rock in the walls of the drill hole.The dimensions of the air gap are given by thedecoupling ratio which is the ratio of the boreholediameter to the explosive diameter. At a decouplingratio of 2, the pressure level in the borehole is aboutan order of magnitude less than that when theexplosive is packed into the hole, i.e., at adecoupling ratio of 1.Rock fracture along a required design line isachieved when a low energy shock wave producedby a low strength, decoupled explosive intersects anearby drill hole. The hole acts as a stressconcentrator, and is reflected from this free face.Under the right conditions this will result in theformation of a clean fracture between the holes withno cracking of the rock behind the face (Langeforsand Kihlstrom, 1967). There is some flexibilityallowed in the detonation of the final line holes:they can be detonated on the same delay, or ondifferent delays without significantly effecting thefinal result. Also, they can be detonated before orafter the holes in the main blast (see below).Where there is a need for very closely controlledblasting, one or more unloaded holes can be drilledbetween the loaded holes to ‘guide’ the fracturealong the required line. The general objective in thedesign of a controlled blast is for the distribution ofexplosive energy on the face to be as uniform aspossible. This is achieved by drilling accuratelyaligned and evenly spaced holes, and by distributingthe explosive up the full length of the hole usingsmall diameter and/or spaced charges. To minimizepoor results caused by deviation of the drill holes,the maximum depth of drill holes is usually limitedto about 8 m (26 ft).Three common methods of controlled blasting arepreshearing, trim blasting and line drilling. Themain features of these three methods are describedbelow, together with approximate equations for thehole spacing and explosive charge. These equations

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should be considered as guidelines because it isessential that the strength of the rock mass andcharacter of the discontinuities be taken intoaccount when designing a blast.(a) PreshearingIn preshearing, the row of holes along the final faceare detonated before the main blast, or on the firstdelay interval of the main blast. This forms afracture, coincident with the final row of drill holes,which inhibits the extension of the radial cracksfrom the main blast. The row of preshear holes caneither be detonated on the same delay, or onseparate delays if there is a need to control groundvibrations in the area outside the blast.

The approximate explosive load per unit length ofdrill hole we to produce a clean presplit line withoutdamage to the wall is given by equation 10.2. Theactual explosive load should be adjusted to accountfor the rock strength and degree of fracturing:

(10.2)

where dh is the drill hole diameter (mm or in).Using this explosive load, the appropriate holespacing on the preshear line is about 10–12 timesthe hole diameter.(b) Trim blasting

Figure 10.14 Comparison of rock conditions on presheared (lower) and heavily blasted (upper) rock faces.


In trim blasting, the final row of holes is detonatedlast in the sequence, either as the last row in aproduction blast, or after the production blast. Thusthe trim blast removes rock broken by the main blastand forms a stable face along the trim line. Thespacing between trim blast holes can be slightlygreater than that for presplit holes because in thecase of trimming there is a free face to providerelief for the blast. In the layout of trim blast holes,approximate dimensions for the spacing and burdenare 16 and 20 times the drill hole diameterrespectively. The explosive load can be estimatedfrom equation 10.2.The choice between the use of preshear and trimblasting is often decided by operational conditions.First, for a preshear the total burden should be atleast 2–3 times the hole depth to ensure there is anadequate mass of rock to confine the explosiveforce; instances of displacement of the entire by thepreshear have been recorded. Second, the groundvibration levels at some distance from the blastproduced by preshearing can be greater than thoseproduced by trim blasting because of the greaterconfinement of the final line explosive. Third, trimblasting is often preferred in closely fractured rock;in preshear blasting the minimal relief for theexplosive gases can cause damage to the rockbehind the final line.(c) Line drillingLine drilling involves drilling a line of closelyspaced, carefully aligned holes along the final wallline, and loading every second or third hole withexplosive. The unloaded holes act as stressconcentrators causing a fracture to formpreferentially between the holes during the passageof the shock wave produced by adjacent loadedholes. Although this method of controlled blastingis expensive because of the quantity of carefuldrilling required, it can produce stable rock facescut to close-dimensional tolerances.A particular use of line drilling is for the excavationof tight corners (Fig. 10.15). In the case of bothconvex and concave slopes, unloaded line holes aredrilled in the corner area to act as guides for theshock wave produced by the presplit holes. On the

concave slope (Fig. 10.15(a)), a loaded hole isrequired to break the confined rock in the corner,while on the convex slope (Fig. 10.15(b)) all theholes in the corner are unloaded because there isample relief in this situation (Du Pont, 1964).

10.3.3Blasting horizontal surfaces

A common operation on rock foundation projects isexcavation to create a level bearing area for thestructural footing. The two main requirements of theblasting operation under these conditions are thatthe final surface be within close elevationtolerances, and that there be minimal damage to thebearing rock. If there is excessive overblasting,cleaning of the rock surface of broken rock will be atime-consuming operation, and extra concrete willbe needed to fill the overbreak. On the other hand,under-excavation will require expensive trimblasting of the high points to bring the surface tograde.One method of producing a stable bearing surfaceclose to the required grade is to use inclined, ratherthan vertical blast holes (Fig. 10.16). Usual blastingpractice is to use vertical holes which are sub-drilledto below the required final excavation level. Thecratering effect at the bottom of each blast hole thenproduces a rock surface that is at no point higherthan the required grade. The sub-drill depth forvertical holes is about one third of the burdendistance. However, with the use of holes inclinedtowards the free face, the sub-drill depth can bereduced and the irregularity of the rock surfacediminished. In addition, there is greater relief oninclined holes than vertical holes with the result thatthere is less damage to the rock in the foundationarea. The disadvantages of inclined holes are theslight extra drilling length, the greater difficulty incontrolling hole direction, and the increasedpossibility of hanging the drill steel in the hole,especially when drilling broken ground.

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10.3.4Ground vibration control

As the shock wave produced by the detonation of anexplosive spreads out into the rock in the direction

away from the free face, its energy will diminishbelow that required to break the rock. However, theenergy level will still be sufficient to generateground vibrations that may propagate toconsiderable distances from the blast. Any

Figure 10.15 Layout of preshear and line holes to excavate rock in tight corners: (a) pattern when excavation is insidepreshear plane; and (b) pattern when excavation is outside preshear plane.


structures located within this vibration area will besubjected to this motion and may be damaged if thevibration levels exceed certain thresholds. Inaddition, humans are very sensitive to groundvibrations and may be disturbed at distancesconsiderably greater than those which cause damageto structures. This section describes methods ofdetermining ground vibration levels and providesdamage thresholds for a number of types ofstructures.(a) Calculation of ground vibrations

The detonation of an explosive charge near a freesurface generates two body waves and onesurface wave as a result of the elastic response ofthe rock. The faster of the two waves propagatedwithin the rock is called the primary or P wavewhich is a compressive wave that produces particlemotion in the direction of propagation. The slowerbody wave is called the secondary or S wave whichis a shear wave that produces motions perpendicularto the direction of propagation. The surface wave,which is slower than either the P or S wave, isnamed after Rayleigh who proved its existence, and

Figure 10.16 Comparison of extent of over-excavation when using vertical and inclined blast holes to excavatefoundation: (a) inclined blast holes; and (b) vertical blast holes.

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is known as the R wave. In terms of vibrationdamage, the R wave is the most important becauseit propagates along the ground surface, and becauseits amplitude decays more slowly with distancetravelled than either the P or S wave.The wide variations in geometrical and geologicalconditions on typical blasting sites preclude thecalculation of ground vibration levels by means ofelastodynamic equations. Therefore, the mostreliable predictions are given by empiricalrelationships developed from the measurement ofvibration levels produced by full-scale blasts.The potential of damage to a structure from blastvibrations is related to the response of the structureto passing vibrations. Damage occurs whendifferential movement between structural membersor between different points in the same structuralmember causes strains to develop which, in turn,cause cracking (Dowding, 1985). The strain inducedin a structure is related to both the magnitude, andto the frequency of the vibration.Numerous studies have examined the level ofground vibrations that induces damage in structures,and particularly residential structures. These studieshave shown that damage potential can be mostreadily correlated with the particle velocity (Siskindet al., 1976; Siskind et al., 1980; Stagg et al., 1984).The particle velocity is a measure of the velocity ofparticles of ground during passage of the shockwave, and not the propagation velocity of the shockwave itself.The stress wave has three components—vertical,longitudinal and transverse—and it is necessary tomeasure all three components and use the greatest,termed the peak particle velocity (PPV), to assessdamage potential. The magnitude of the PPV isrelated to the both the radial distance from the blastRe and the explosive weight detonated per delay Wby:

(10.3)

where ke and ße are constants which have to bedetermined by measurements of vibrations at eachparticular blast site; the term is known as

the scaled distance.Equation 10.3 plots as a straight line on log-logpaper in which ke is the intercept on the velocityaxis at a scaled distance of 1.0, and ße is the slopeof the line (Fig. 10.17). The results of vibrationmeasurements for surface blasts show that values ofthe constants ke and ße are as follows (Oriard,1971):

Units: PPV—mm/s; Re—m; We—kg

Units: PPV—in/s; Re—ft; We—lb.For preshear blasts where the explosive is morehighly confined, the constant ke can reach values6400 (metric) or 800 (imperial).Equation 10.3 can be solved to predict groundvibration levels for a particular blast. Alternatively,the maximum allowable explosive weight per delaycan be calculated to minimize the risk that vibrationlevels will exceed a certain thresh old level at aspecified distance from the blast. Whereequation 10.3 shows that vibrations will be close tocritical levels, it is preferable to measure actualvibrations to establish reliable values for theconstants ke and βe.(b) Vibration damage thresholdsVibration measurement programs have determinedthe threshold vibrations levels that may result indamage to structures of various types, as well as thevibration levels that are perceptible andobjectionable to humans (Table 10.3).The velocity of 50 mm/s (2 in/s) is used as adamage threshold for a wide range of structures andis accepted as a practical limit in many blastingoperations. For the results shown in Fig. 10.17, inorder to maintain the PPV below 50 mm/s it isnecessary that the scaled distance exceed 6.35 m/kg½. That is, at a distance of 20 m (65 ft) from theblast, the maximum explosive weight detonated perdelay should be 9.9 kg (22 lb).The frequency of the ground vibrations is also ofimportance in assessing damage potential. If theprincipal frequency, that is, the frequency of greatestamplitude pulse, is approximately equal to the


natural frequency of the structure, then there is agreater risk of damage than if the principal andnatural frequencies are significantly different(Dowding, 1985). The natural frequency of two-storey residential buildings is in the range 5–20 Hz,and the natural frequency decreases with increasing

height of the structure. The principal frequency of ablast will vary with such factors as the type of blast,the distance between the blast and the structure, andthe material through which the ground vibrationstravel. Typical construction

Table 10.3 Peak particle velocity damage threshold levels

Threshold velocity Description of effect of ground vibrations due to blasting

mm/s (in/s)

3–5 (0.12–0.2) Vibrations perceptible to humans33–50 (1.3–2) Vibrations objectional to humans50 (2) Limit below which risk of damage to structures, even old buildings, is very slight (<5%). Also,

no damage to underground utilities.250 (10) Damage to restrained, monolithic concrete walls.blasts produce vibrations with principal frequencies in the range of about 50–100 Hz. It is found that

Figure 10.17 Typical plot of measured peak particle velocity versus scaled distance for a series of blasts.

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large quarry blasts produce vibrations with lowerprincipal frequencies than construction blasts, thatprincipal frequencies decrease with increasingdistance due to frequency attenuation, and thatvibrations measured on rock have higherfrequencies than those measured in soil.

10.3.5Vibrations in uncured concrete

On some construction projects there may be a needto carry out blasting operations close to uncuredconcrete. Under these circumstances, explosivecharge weights per delay should be designed to keepground vibrations to within limits which aredetermined by the age of the concrete, the distanceof the concrete from the blast, and the type ofstructure. Figure 10.18 and Table 10.4 show anapproximate relationship between allowable peakparticle velocity levels and the concrete age (Oriardand Coulson, 1980). At ages less than four hours,the concrete has not yet set and somewhat highervibration levels are permissible than during theperiod of between 4 and 24 hours when the concreteis taking its initial set. The two sets of vibrationlimits shown in Fig. 10.18 also show that massconcrete (i) is able to withstand higher vibrationsthan structural walls and slabs (ii); structural wallsof freshly poured concrete are particularly sensitiveto vibrations.Figure 10.18 shows that, for the same time afterbatching, allowable vibration levels are greater fordistances of 0–15 m (50 ft)—lines marked ‘a’—than for distances greater than 75 m (250 ft)—linesmarked ‘b’. The reason for this is that concrete can Table 10.4 Illustration of particle velocity and distance criteria for blasting near uncured concrete

Time from batching (hours) Nonstructural fill and mass concrete mm/s(in/s)

Structural walls, structural concrete slabsmm/s (in/s)

0–4 100 (4) df 50 (2) df

4–24 25 (1) df 6 (0.25) df

24–72 40 (1.5) df 25 (1) df

72–168 75 (3) df 50 (2) df

168–240 200 (8) df 125 (5) df

over 240 375 (15) df 250 (10) df


Time from batching (hours) Nonstructural fill and mass concrete mm/s(in/s)

Structural walls, structural concrete slabsmm/s (in/s)

df=distance factor to account for frequency attenuation=1.0 when distance is 0–15 m (0–50 ft)=0.8 when distance is 15–50 m (50–150 ft)=0.7 when distance is 50–80 m (150–250 ft)=0.6 when distance is over 80 m (over 250 ft)better withstand high frequency vibrations becauselow frequencies induce greater deflections in thestructure. Vibration frequencies decrease as thedistance from the blast increases because there isattenuation of frequency with distance. The result ofthis frequency attenuation is that, at equal curingtimes, higher vibration levels are permitted at closerdistances as shown by the two series of linesmarked ‘a’ and ‘b’ on Fig. 10.18.

In critical conditions it is recommended thatvibrations and strength tests be conducted toconfirm the performance of the concrete and therelationships given in Fig. 10.18.

10.3.6Non-explosive excavation

Where an excavation must be made to close

Figure 10.18 Approximate maximum allowable vibration levels in uncured concrete (Oriard and Coulson, 1980): (i)non-structural fill, mass concrete; and (ii) structural concrete walls and slabs.

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dimensional tolerances, or where vibration levelsmust be restricted to very low levels, it may beappropriate to use non-explosive excavationmethods rather than blasting. Four commonmethods are ripping, impact hammers, hydraulicsplitters, and expansion compounds.Ripping with a ripping tooth mounted on abulldozer is the most efficient non-blastingexcavation method, but can only be used in areasthat are large enough, such as a dam foundation, forthe equipment to operate. Also, the degree offracturing and strength of the rock must be suitablefor the equipment to be used. A common method ofassessing the suitability of ripping as an excavationmethod is to compare the seismic velocity of therock (see Section 4.1.2) with rippability charts for arange of bulldozer sizes (Caterpillar Inc., 1997).These charts have been developed from extensivefield testing, and show, for example, that a D-8Rdozer (228 kW or 305 hp) can rip rock with seismicvelocities up to 1500–1800 m/s (5000 to 6000 ft/s),while for a D-10R dozer (425 kW or 570 hp) theupper limit for ripping is a seismic velocity of about2100–2400 m/s (7000 to 8000 ft/s).A more comprehensive method of assessingrippability is to determine the excavatability indexwhich is the product four parameters related to therock strength Ms, the block size Kb, the orientationand spacing of the discontinuities Kd, and the shearstrength of the discontinuities Js (Kirsten, 1982).The excavatability index Kr is calculated from

(10.4)These four parameters are identical to those used toassess the susceptibility of rock to scour asdiscussed in Section 6.7.2. This is appropriatebecause the mechanisms of scour and ripping are

similar in that they involve the application of a forceto remove particles of in situ rock. Magnitudes forthe four parameters can be determined fromTables 6.2–6.5 which assign numerical values togeological characteristics of the rock mass. Forexample:

1. for a moderately weak rock,

2. with three joints sets and an RQD of 50%,

3. with tight but smooth planar discontinuities andslightly altered rock surfaces,

4. with the closer joint spacing dipping in thedirection of ripping at 45° and slabby rock withan aspect ratio of 1:4,

5.

Field tests have shown that the limits to ripping interms of the Kr values for equipment with thefollowing flywheel powers are as in Table 10.5.It is suggested that these categories of Kr be used asa guideline in selecting excavation methods to suitdifferent sizes of equipment, and that the procedureshould be calibrated to suit local conditions.In contrast to ripping, an hydraulic impact hammermounted on an excavator boom can operate in morerestricted areas and excavate to very closetolerances with minimal damage to the rock beyondthe excavation limits. Impact hammers can breakeven very strong rock provided that it containsdiscontinuities which can be exploited by the chiselto loosen and move blocks. Section 10.5.3 discussesthe relationship between rock mass strengthcharacteristics and the appropriate method ofexcavation.

Table 10.5 Limits to ripping in terms of excavatability index Kr

Kr Limits to ripping

0.1–10 Can be ripped by dozers with flywheel powers in the range 100–150 kW (135–200 hp), e.g. CaterpillarD6D/D7G;

10–1000 Can be ripped by dozers with flywheel powers in the range 225–300 kW (300–400 hp), e.g. CaterpillarD8K/D9H;

>1000 Extremely difficult ripping even by dozers with flywheel powers of 520 kW (700 hp), e.g. Caterpillar D10.Excavation with both hydraulic splitters and expansion agents involves drilling closely spaced


holes (about 150–200 mm, or 6–8 in, spacing) alongthe required excavation .line, and then applying ahigh internal pressure to the boreholes. In the case ofthe hydraulic splitter the internal pressure isgenerated by a wedge that is pushed by hydraulicsbetween two tapered platens. In the case ofexpansive cement, the pressure is developed whenthe cement is mixed with water and confined in aborehole. This pressure is sufficient to generatefractures that will preferentially form between thedrill holes that act as stress concentrators. Thesemethods produce the best results in massive rock orconcrete; in fractured rock it can be difficult tocontrol the direction of the cracks.The advantages of hydraulic splitters and expansionagents are lack of noise and vibration, and thegenerally precise control over excavation limits.The disadvantages are that both these methods areslow and costly and are not suitable for theexcavation of large volumes of rock. Most chemicalexpansion agents require a period of about 5–12hours to break the rock.

10.4Bearing surface improvement and rock

reinforcement

Prior to construction of a footing it may benecessary to take steps, depending on the geologicaland geometrical conditions at the site, to prepare asuitable bearing surface, and reinforce the bearingrock. The purpose of this work would be to ensurethat the rock has adequate bearing capacity, and thatthere is no excessive movement or weathering ofthe foundation rock during the design life of thestructure. In addition to stabilization work carriedout at the time of construction, remedial work mayalso be necessary during operation of the structure.Remedial work is most often required in climateswhere the rock is subjected to frequent freeze-thawcycles, heavy precipitation, or where the rock issusceptible to weathering.Figure 10.19 shows examples of a variety of surfacepreparation and reinforcement measures that may beapplicable on rock construction projects (Wyllie,

1979, 1991, 1995; Cheng, 1987; Romana andIzquierdo, 1987; FHWA, 1982). In Fig. 10.19 thefooting is located on a bench cut into a steep rockface. The rock contains a set of joints that dips out ofthe slope face at an angle of about 30° and there is apotential for sliding failures on these surfaces. Therock also contains a fault that is parallel to themajor joint set, and weathering of the broken rockbelow the fault has formed a cavity in the rock face.In the bearing area there is a seam of crushed andsheared rock that dips at an angle of about 65° intothe face. The block formed by the intersection of thefault and the seam of sheared rock will bepotentially unstable under the loads applied by thestructure. The following is a brief description of thestabilization work ((1)–(9)) illustrated in Fig. 10.19;design procedures for this work are provided inChapters 5, 6 and 9.

10.4.1Trim blasting (1)

The formation of a planar, level bearing surfacemay require controlled blasting or a non-explosiveexcavation method. Where possible, thebearing surface should be at right angles to thedirection of the applied load so there is no tendencyof the footing to slide. Also, there should be noirregular protrusions or cavities so that the bearingpressure will be uniform across the full area of thefooting, with no stress concentrations induced in thefooting.

10.4.2Surface preparation (2)

Following excavation of the rock, the bearingsurface should be thoroughly cleaned of all broken,loose and weathered rock using high pressure air orwater hoses. Levelling of the base of a blastedexcavation with a dozer will rarely produce anadequate structural bearing surface because cavitiesin the excavated surface will be filled with brokenrock that cannot be compacted by the low bearingpressure of the tracks.

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In some circumstances it may be necessary toroughen smooth and planar bearing surfaces if thereis a risk of the footing sliding on this surface. Anhydraulic impact hammer may be an appropriatemeans of removing blocks of rock to roughen the

surface.

Figure 10.19 Surface preparation and reinforcement of rock foundation.

1. Trim blast to create level bearing surface. 2. Loose and broken rock cleaned from bearing surface. 3. Lean concretefill in seam of weak rock. 4. Shotcrete with drain holes to control rock weathering and frost action. 5. Pins to preventloosening and movement of jointed rock. 6. Tensioned rock anchors to reinforce crest of foundation. 7. Tensioned,multi-strand anchors installed to prevent shear failure on fault dipping out of slope face. 8. Concrete buttress to supportcavity. 9. Drain hole to prevent build up of water pressure behind buttress.


10.4.3Dental concrete (3)

If the bearing surface is intersected by a seam ofcrushed or faulted rock, this can be sub-excavated toa depth equal to at least twice its width and thenback filled with lean concrete. This procedure willprobably be satisfactory where the fault width is notmore than about one quarter to one third of thefooting width. If the fault width is greater than onethird of the footing width, the design bearingpressure should be reduced accordingly, and a moreextensive dental concreting program may berequired. Alternatively, the footing could bereinforced to bridge over the low bearing pressurearea.

10.4.4Shotcrete (4)

Shotcrete is pneumatically applied, fine aggregatemortar (less than 13 mm or 1/2 in aggregate size)that is usually placed in a 75–100 mm (3–4 in) thicklayer (ACI, 1996). When applied on surfaceexcavations, the primary functions of shotcrete areto prevent loosening and weathering of the surfacerock; negligible support of the overall slope isprovided. The effectiveness of shotcrete depends toa large degree on the condition of the rock surfaceto which it is applied. The surface should be free oforganic matter, soil and broken rock, and shouldalso be damp to ensure good adhesion between theshotcrete and the rock. The shotcrete applicationsshown in Fig. 10.19 will prevent the seepage of run-off water and frost heave under the footing, and alsoprevent loosening of the rock along the crest of thebench on which the footing is located. It is importantthat there be holes through the shotcrete to preventbuild up of water pressures. In massive rock thedrain holes should be drilled before the shotcrete isapplied so that the holes can be located to intersectdiscontinuities along which seepage water isflowing. The holes are plugged with rags or woodenplugs while the shotcrete is applied.For all permanent applications shotcrete should bereinforced to reduce the risk of cracking and

spalling. The two most common types ofreinforcement are welded wire mesh and steelfibers. Wire mesh is the more commonreinforcement method, but the advantages of usingsteel fiber reinforcing are the faster application timeand production of a superior product on irregularrock surfaces.(a) Wire mesh reinforcingWelded wire mesh is usually fabricated from 3.5mm (0.13 in or 10 gauge) diameter wire onminimum 100 mm (4 in) centers and is attached tothe rock surface with threaded pins, complete with anut and washer. The pins are grouted into holesdrilled in the rock on about 1–2 m (3–6 ft) centers,and located at low points to hold the mesh close tothe rock face so that the mesh will be entirelyencased in shotcrete. Wire mesh can only be usedon reasonably uniform surfaces because its stiffnessprevents it from being closely attached to irregularsurfaces. Weld mesh is generally preferable to themore flexible chain link mesh because the 50 mm (2in) opening size of chain link mesh is too small forcomplete penetration of the aggregate with theresult that voids may be formed behind the mesh.An alternative method of installing mesh is to placeit between two layers of shotcrete, with the firstlayer creating a smoother surface to which the meshcan be closely attached.(b) Steel fiber reinforcingThe installation of mesh on to rock faces to providereinforcement for shotcrete is time consuming andlabor intensive. In comparison, shotcrete containingsteel fibers as the reinforcement medium can beapplied in a single pass. For applications onirregular surfaces the extra cost of the fibers andwear to the pump and hoses usually more thancompensates for the saving in installation time ofmesh. Fibers are manufactured from high strengthcarbon steel with lengths of 30–38 mm (1.2–1.5 in)and an equivalent diameter of 0.5 mm (0.02 in), andare deformed or have crimped ends to resist pull-out. The principal function of the fibers is toincrease significantly the tensile and post-crackstrength of the shotcrete compared with non-reinforced shotcrete (Fig. 10.20).

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Shotcrete properties are specified as follows.

1. Compressive strength is usually about 20 MPa(2900 p.s.i.) at 3 days and 30 MPa (4350 p.s.i.)at 7 days.

2. First crack flexural strength is 4.5 MPa (650psi) at 7 days.

3. The toughness index determines the post-crackstrength. The procedure for calculating thetoughness indices I5 and I10 is shown onFig. 10.20; toughness indices of

are suitable for mostapplications.

Shotcrete is tested by cutting samples from a 0.6 m(24 in) square by 0.1 m (4 in) thick test panel that isshot at the same time and with the same mix andpump as the production shotcrete. The samples aretested in a compression machine to determine thecompressive strength, and in bendingto determinethe flexural strength and the I5 and I10 toughnessindices (ASTM, 1985).Steel fiber reinforced shotcrete can be applied usingstandard shotcrete equipment, although the wear to

the pump and hose is somewhat greater than whenused to place non-fiber mix. Pumping of steel-fibermix requires that the fibers be uniformly distributedin the shotcrete mix to avoid balling that wouldblock the pump or produce a partially reinforcedproduct. The usual procedure is to add the fibers inthe ready mix plant, either to wet mix in a mixertruck, or to dry mix which is packaged in bags.The properties of shotcrete are enhanced by the useof micro-silica which is added to the mix as apartial replacement for cement (USBM, 1984).Silica fume is an ultra fine powder with a particlesize approximately equal to that of cigarette smoke.When added to shotcrete, silica fume reducesrebound, allows thickness of up to half a meter to beapplied in a single pass, and covers surfaces onwhich there is running water. There is also anincrease in the long term strength in most cases.Typical shotcrete mixes for wet and dry processesare shown in Table 10.6. The wet mix is used wherethe shotcrete can be supplied to the site in ready-mix trucks, while dry mix is supplied in bags (1 m3

capacity) and the water is added at the nozzle underthe control of the nozzleman. When using dry mix,better results are achieved if the mix is pre-

Figure 10.20 Load-deformation characteristics of steel-fiber reinforced shotcrete. 1. without fibers 2. 1% vol. fibers 3.2% vol. fibers 4. 3% vol. fibers


moisturized to about 4% water content before it isplaced in the pump.

10.4.5Shear keys (5)

Where there is a possibility of blocks sliding ondiscontinuties dipping out of the slope face, theslope can be stabilized with shear keys installed atthe toe of the blocks. The function of the keys is toprevent movement of blocks on the face because

progressive loosening and loss of interlock on thediscontinuity surfaces could result in a much largerfailure. The required size of a key to support ablock, which depends upon the block dimensions,the dip and shear strength properties of the slidingplane, can be determined by limit equilibriummethods (see Chapter 6). In these calculations it canbe assumed that the key supplies a resisting force,acting up the sliding plane, that is equal to the shearstrength of the steel. The

Table 10.6 Typical shotcrete mix proportions, at the nozzle (Wood, 1998)

Material Wet mix Dry mix

Plain Silica fume Plain Silica fume

kg/m3 (lb/ft3) % by wt. kg/m3 (lb/ft3) % by wt. kg/m3 (lb/ft3) % by wt. kg/m3 (lb/ft3) % by wt.

Portlandcement,Type 10

400 (25) 17.0 350 (22) 15.0 425 (26) 18.0 375 (23) 16.0

Silicafume

– – 0.0 47 (2.9) 2.0 – – 0.0 50 (3.1) 2.1

Coarseaggregate, <10mm*

460 (28) 19.6 485 (30) 20.8 495 (31) 21.0 490 (30) 20.9

Concretesand*

1260 (78) 53.7 1215 (75) 52.1 1215 (75) 51.5 1205 (75) 51.4

Steelfibers

57 (3.5) 2.4 57 (3.5) 2.4 60 (3.7) 2.5 60 (3.7) 2.6

Water 170 (10.5) 7.2 177 (11) 7.6 165 (10.2) 7.0 165 (10.2) 7.0Waterreducingadmixture

Yes – Yes – – – – – – –

Superplasticizer

– – – Yes – – – – – – –

Air-entrainingadmixture

Yes – Yes – – – – – – –

Total 2347 100.0 2331 100.0 2360 100.0 2345 100.0* Proportions based on “specific surface dry” aggregates.working strength of steel in shear is about 25% ofthe yield tensile strength.The keys comprise a row of steel reinforcing barsfully grouted into holes drilled to a depth of about 0.3–0.6 m (1–2 ft). The diameter of the bars may rangefrom about 25 to 50 mm (1–2 in) and the spacing

depends on the support force required. The bars arefully encased in concrete, both to protect the steelfrom corrosion, and to provide continuous supportthat will prevent movement of the block. Shear keysare usually only used to support blocks up to about2 m (6 ft) thick; it is more efficient to support larger

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blocks with tensioned rock bolts which provide botha resisting force and normal force on the slidingplane.

10.4.6Rock bolts (6)

The rock bolts shown in Fig. 10.19 are installed justbelow the crest of the bench on which the footing islocated. The function of these bolts is to preventloosening and movement of the rock in this areawhich is both highly stressed, and susceptible torelaxation because of its proximity to the verticalface. Movement of the rock in this area could resultin loss of support along the outer edge of thefooting.These bolts could be either tensioned or untensioneddepending on the geological conditions. If the rockcontains sets of joints dipping out of the face andthere has already been some movement on thesejoints, tensioned bolts would probably be requiredto increase the shear strength of the surface.However, if the rock is generally massive andundisturbed, the installation of untensioned, fullygrouted bolts to minimize long term loosening ofthe rock may be satisfactory. Details of design andinstallation procedures for rock bolts are given inChapter 9.

10.4.7Tensioned rock anchors (7)

The tensioned rock anchors shown in Fig. 10.19 areinstalled to prevent a sliding type failure of thewedge of rock formed by the intersection of thefault dipping out of the slope face, and thesubvertical seam of fractured rock. Because of thehigh probability of movement of this wedge underthe applied structural loads, it would be necessarythat the anchors be installed and tensioned prior toconstruction of the footing. This procedure wouldprestress the foundation by providing normal andshear stresses on the potential sliding plane andprevent movement when the structural load isapplied. A very important aspect of the design of

these anchors is the determination of the lengthrequired to ensure that they are anchored below thedepth of the deepest potential failure plane. Thiswould require both careful mapping of the rock faceand a vertical diamond drill hole to identify allpossible faults with this orientation.

10.4.8Concrete buttress (8)

The concrete buttress shown in Fig. 10.19 has beenconstructed to fill a cavity in the rock face that hasdeveloped as the result of weathering of thefractured rock below the fault plane. The buttressfulfills two functions: first to retain and protect thearea of weak rock, and second to support theoverhang. The loads on the buttress are low so it isnot necessary that the concrete be reinforced.However, in order that the buttress preventrelaxation of the rock, it should be founded on aclean rock surface and anchored to the base usingsteel pins to prevent sliding. Also, the top should bepoured so that it is in continuous contact with theunderside of the overhang. In order to meet thissecond requirement, it may be necessary to placethe last pour through a hole drilled downwards intothe cavity from the rock face, and use a non-shrinkagent in the pour.

10.4.9Drain holes (9)

It is possible that ground water seepage will beconcentrated at the fault zone and the underlyingarea of fractured rock. If this is the case, drain holeswould be required through the buttress to ensure thatwater pressures do not build up behind the concrete.It is usual for drain holes to be cased with aperforated plastic pipe to prevent caving. Theorientation and position of the drain holes should beselected so that they intersect the majordiscontinuities that are carrying the water. Sincemost intact rock has essentially zero permeability,holes which do not intersect discontinuities will notbe effective drains. For the conditions shown in


Fig. 10.19, drain holes inclined at the same angle asthe fault would produce limited drainage comparedwith the flatter hole shown which intersects anumber of these features.

10.5Contracts and specifications

The success of a construction project can oftendepend as much on the contract and specificationsthat define the work, as the design of the projectitself. The importance of contracts is first that theydefine the work to be performed, and second thatthey are legal documents that prescribe the rightsand responsibilities of the owner and the contractor.The contract must also comply with all laws whichmay be applicable to the project. While mostconstruction contracts have the same basic format,every project requires a set of documents thatspecifically addresses the particular conditions ofthe work. Some of the basic decisions that arerequired in preparing the documents are the type ofcontract, i.e., unit or fixed price contracts, whetherbids will be open to all contractors or only toselected contractors (prequalification), and whetherend-product or method specifications will beprepared. This section discusses these aspects ofcontract specifications with particular reference toprojects involving rock excavation. Also, thediscussion is mainly directed to North Americancontracting practices (Berman and Crossland, 1972;Crimmins et al., 1972).

10.5.1Components of contract documents

Contract documents usually consist of the followingprincipal components (Merritt, 1976):

1. advertisement for bids;2. information to bidders;3. proposal form;4. contract-agreement form5. bond forms;6. general provisions;

7. special provisions;8. technical specifications.

All these items, apart from the last two, willgenerally have similar formats regardless of theconstruction project and the type of contract. As aguideline in preparing contracts, most governmentagencies, utilities and corporations have drawn upstandard documents which they have found to beapplicable to the type of work in which they areinvolved. The following is a summary of the itemsthat are included in the general and specialprovisions, and the technical specifications.(a) General and special provisionsThe general provisions set out the rights andresponsibilities of the parties to the contract (ownerand contractor) and the surety, the requirementsgoverning their business and legal relationships, andthe authority of the engineer. Where the generalconditions are standard documents that arepublished by the contracting agency, and it isnecessary to make modifications, additions ordeletions to suit the requirements of the project,these items constitute the special provisions.Particular items that are usually included in thegeneral provisions are as follows:

1. Definitions and abbreviations of terms used inthe specifications.

2. Bidding requirements which includeprequalification, delivery of proposal, bondingand, for public agencies, a noncollusionaffidavit. Prequalification is documentaryevidence of capability and financial standing,or particular experience in a portion of the worksuch as socketed piers or high tension anchors.

3. Contract and subcontract procedure whichincludes award and execution of the contract,requirements for contract bond, submission ofprogress schedule, recourse for failure toexecute the contract, and provisions forsubletting contracts.

4. Scope of work is a description of the work to beperformed, and such items as work spaceavailable for equipment and materials, final site

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clean up, and maintenance of traffic whererequired. Also, a limit is set on the deviation ofactual quantities from estimated quantitieswithout change in the contract price (seeSection 10.5.3(d)).

5. Control of work which includes the authority ofthe engineer, the plans, specifications andworking drawings. Also included areprocedures for inspection and testing of thework, handling of defective work, contractor’sclaims for change orders, and final acceptanceof the completed work.

6. Legal and public relations covers all provisionsfor legal relations between the contractor andowner, and between the contractor and thegeneral public. Also covered are liability andinsurance provisions, and compliance withapplicable laws such as public safety,explosives and blasting, accident prevention,public safety, public utilities and pollutionabatement.

7. Prosecution and progress includes provisionsfor commencement and completion of the work,suspension of the work, unavoidable delays,default of the contract, liquidated damages andextension of time.

8. Measurement and payment includes provisionsfor measurement of quantities, scope ofpayment, payment for changes in plans,procedures for partial and final payment,termination of contractor’s responsibility, andguarantee against defective work.

(b) Technical specificationThe technical specifications give details of thegeneral and special conditions affecting theperformance of the work, materials to be used,construction details, measurement of quantitiesunder the scheduled items of work, and the methodof payment for these items.

10.5.2Types of contract

Factors to consider in the selection of the most

appropriate type of contract for a project are thecertainty with which site conditions and quantitiescan be defined, the required flexibility in theconstruction work, and the time available to prepareand negotiate a contract. Fundamental to theselection of the appropriate type of contract isdetermining how the risk should be shared betweenthe owner and the contractor; this depends on theuncertainties that may be encountered during thecourse of the work. The basic contract types areunit-price and lump sum, with various types ofnegotiated contracts that may be used under specialcircumstances. The following are descriptions ofcommon types of contract and the conditions inwhich they may be applicable for foundationprojects involving rock excavation and support.(a) Unit-price contractThis is the most common type of contract for rockexcavation work, and is used when it is not possibleto delineate on the drawings the exact quantities tobe included in the contract. The terms of thiscontract provide that the owner will pay to thecontractor a specified amount of money for eachunit of work completed. The units of work may beany items whose quantities can be measured such ascubic meters of rock, lineal meter of rock bolt, orcubic meters of grout. Payments are usually madeby the owner at specified intervals duringconstruction, with the amount of each paymentdepending on the value of the work completedduring the prior time period.(b) Lump-sum contractIf the owner knows exactly the quantities of work tobe accomplished, and these quantities can beaccurately shown on the drawings, a lump-sumcontract can be let. Payments are usually made on amonthly basis with the amount of each paymentdepending on the value of work completed in theprior time period. Note that a lump-sum contractcan be let with a portion of the work such asgrouting awarded on a unit price basis.While the majority of projects involving rockexcavation are bid as either unit price or lump sumcontracts, some major infrastructure projects are bidon the basis of design-build or build-operate-


transfer (BOT) as discussed below.(c) Design-build contractIn design-build projects the owner will define suchcriteria as the location of a bridge, its requiredcapacity, the construction schedule and the designstandards that it should meet. The contractors thenform teams with engineering companies to producethe designs that meet both the project requirements,and suit their experience and available equipment.The advantages of the design-build process are thatoverall procurement time is reduced and that thereshould be cost savings in that the constructionmethod and materials are not restricted to thoseselected by an independent designer. However, forsuccessful design-build projects it is essential thatthe criteria are carefully defined and that they arethen fulfilled in the actual construction.(d) BOT contractsBOT projects, and their many variations, expand thescope of the design-build concept and require theconstruction consortium to finance, design, buildand then operate the facility while collecting a fee(such as a toll on a bridge). The fee must cover thetotal of the capital cost of construction as well asoperating costs, and return a reasonable profit. Themagnitude of the fee, which may be limited in thecontract terms, must be set at a level that will attracta sufficient number of users; this often requiresvariable pricing depending on demand. At the endof a specified concession period, which may be inthe range 20–30 years, ownership of the facility istransferred back to the government agency (Levy,1996).

10.5.3Rock excavation and reinforcement specifications

The specifications for projects involving rockexcavation and reinforcement must includeprovisions for the uncertainties inherent in theseprojects. Typical of the uncertainties in thegeotechnical aspects of a project are the depth tobedrock, ground water inflow quantities, and thepresence of seams of weak or fractured rock. It isunlikely that a representative sampling of these

conditions will be provided by surface mapping andsome investigative drilling. Some of the methodswhich can be used to address these uncertainties inthe contract are discussed in this section.(a) Geotechnical dataThe technical specifications for a rock excavationproject should include a geotechnical reportdescribing the geology, ground water and materialproperties of the site. This information is sometimesdivided into factual data and interpretative data asfollows. Factual data comprise surface mappingresults, drill logs and the results of in situ andlaboratory tests, with no projections orinterpretation of the data. Interpretative data mayshow such information as projection of databetween drill holes, a range of possible ground waterinflow rates, stable slope angles of excavations andthe support methods that may be required. Thepurpose of providing two sets of data is todifferentiate clearly between data that have beenverified, and interpretations of this data based onjudgement and previous experience at this andsimilar sites. The reports should clearly state thelimitations of the data provided. For example,freezing temperatures and heavy rain may changeconditions from those described in the report, andinterpolations of data between drill holes may notbe precise.(b) Definition of rock and soilThe ratio of excavation costs between rock and soilmay vary from as low as 2 for bulk excavation, to ashigh as 15 for sites with small rock quantities to beexcavated to tight tolerances. Although somecontracts classify all materials to be excavated as‘common’, frequently there are different unit ratesfor excavation quantities of rock and soil and thisrequires that the contract contains a definition ofthese materials for payment purposes. This canreadily be accomplished at sites where overburden(soil) overlies sound bed rock and the boundarybetween the two materials can be determined bymapping, drilling and geophysics. However, wherethere is a continuous gradation between ‘rock’ and‘soil’, or the boundary is highly irregular; it is oftendifficult to draw up an unambiguous definition that

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clearly distinguishes between the two materials.The ease with which rock can be excavated dependson both the strength of the intact material and thedegree of fracturing, so both these properties shouldbe incorporated in any definitions of materials thatare included in the contract. Figure 10.21 shows anapproximate relationship between the method ofexcavation—digging, ripping or blasting—and thematerial properties as defined by the strength of theintact rock and the fracture frequency (seeSection 4.3.1). This chart shows, for example, thateven very weak rock may need to be blasted if thediscontinuities are very widely spaced so that thereare no blocks that can be loosened and removed bythe excavating equipment. The boundaries shownon this chart depend, of course, on the excavationequipment used by the contractor, and some

calibration in local conditions will be requiredbefore it can be used with confidence to definematerials for payment purposes. Section 10.3.6discusses a more comprehensive method ofclassifying rock in relation to the method ofexcavation.An alternative material classification, that definesthe material according to the equipment with whichit can be excavated, has been drawn up by the USBureau of Reclamation. This classification, which isgiven in full below, can be used as a guideline inpreparing a classification to suit local conditions.

‘Except as otherwise provided in thesespecifications, material excavated will bemeasured and classified in excavation, to thelines shown on the drawings or as provided in

Figure 10.21 Possible excavation methods related to strength and degree of fracturing of rock (modified from US Deptof Navy, 1982).

Note: Rock strength classifications refer to ranges listed in Table 3.6.


these specifications, and will be classified forpayment as follows:

Rock excavation. For purposes ofclassification of excavation, rock is defined assound and solid masses, layers or ledges ofmineral matter in place and of such hardnessand texture that it:

1. Cannot be effectively loosened or brokendown by ripping in a single pass with alate model tractor-mounted ripperequipped with one digging point ofstandard manufacturer’s designadequately sized for use with andpropelled by a crawler type tractor ratedbetween 210- and 240-net flywheelhorsepower, operating in low gear, or

2. In areas where it is impractical to classifyby use of a ripper described above, rockexcavation is defined as sound materialof such hardness and texture that itcannot be loosened and broken down by a6-pound drifting pick. The drifting pickshall be class D, Federal SpecificationGGG-H-506d, with handle not less than34 inches in length.

3. All boulders or detached pieces of solidrock more than 1 cubic yard in volumewill be classified as rock excavation.

Common excavation. Common excavationincludes all material other than rock excavation. Allboulders or detached pieces of solid rock less than 1cubic yard in volume will be classified as commonexcavation.’ (c) RiskOn most projects involving rock excavation there islikely to be some uncertainty as to the conditionsthat will be encountered: a single persistentdiscontinuity may cause failure of a slope designedat a steep angle, or a zone of faulted rock may beencountered in the bearing area of a foundation. It isusually considered that is beneficial, to both thecost and progress of the project, that there is anapportionment of risk for these uncertainties

between the owner and the contractor.The sharing of risk is most convenientlyaccommodated by the type of contract that is usedon the project. For example, in circumstances wherethere is uncertainty as to the conditions that may beencountered, the contractors will submit high bids ifthey have to assume all the risk for constructioncosts regardless of the conditions encountered.However, if the owner is prepared to cover some ofthe risk by paying specified unit prices for items forwhich the quantities are uncertain, the total cost ofthe project is likely to be lower. For example, thedocuments may simply state that a foundationexcavation shall have certain minimum dimensionsand consist of ‘sound rock’, for which a lump sumpayment will be made. In these circumstances, thecontractors assume all the risk and their bid mustcover contingencies for such factors as dewatering,slope support and improvement of the rock if it hasinadequate bearing capacity. However, if unit pricesare paid for approved quantities of all these items,the total contract price is likely to be lower becausethe contractors have greater assurance that they willbe paid for the work performed.(d) Variation in quantitiesIt is rarely possible to define precisely in thecontract the quantities of all items on the project.Quantities that are often difficult to define are rockand common excavation, rock bolt lengths, andshotcrete and grouting volumes. While the use of aunit price contract allows flexibility in payment foractual quantities, it is also desirable to have amechanism for protection against ‘unbalanced’bids.An unbalanced bid is a high unit price with asubstantial profit margin that is bid for an item thatonly has a small quantity in the contract. Therefore,the price of this item will not significantly affect thetotal bid price. However, if during construction theactual quantity of this unit becomes much greaterthan that originally estimated, there may besubstantial increases in the overall project cost.Protection against unbalanced bids can be providedby including a clause in the contract that requiresthat the unit prices be renegotiated if the actual

396 DRILLING

quantity differs from the estimated quantity by morethan say 20%. This clause will also protect thecontractor in the event that the actual quantity issubstantially less than the estimate and the bid priceis insufficient to cover the mobilization costs.(e) PrequalificationOn rock excavation projects it may be desirable tohave the work performed by a contractor who isexperienced, for. example, in presplit blasting andcontrol of ground vibrations. This may be achievedby including in the bidding requirements a clausespecifying that the contractor supplies documentaryevidence of previous experience in this work, andthat the personnel with this experience will beworking on the project. This process ofprequalification may not be possible on projects forsome government agencies who have to accept bidsfrom all contractors. In these circumstances it maybe necessary to prepare specifications that aresomewhat more detailed than on contracts whereonly experienced contractors are invited to submitbids.An additional type of prequalification involves onlyinviting selected contractors with particularexperience in certain specialist operations to bid ona project. For example, there are only a limitednumber of contractors experienced in the

installation of high tension anchors, and only thesecontractors may be invited to submit bids for thework. However, in these circumstances thecontractor may also be given the responsibility ofdetermining the bond length and the procedures forachieving the required load capacity, while thedesigner only specifies the minimum working loadand the free stressing length. In this way thecontractor assumes some risk on the project inreturn for not having to bid on an open contract.Other specialist operations that may not be put outto open bidding are shotcreting, grouting and highscaling.(f) End-product and method specificationsA factor to consider in the preparation of a contractis the extent to which the methods to be used by thecontractor will be prescribed in the documents. Thatis, whether ‘end-product’ or ‘method’ specificationswill be prepared. In most cases it is preferable toprepare end-product specifications, which specifythe structure that is to be built, so that theconstruction methods and equipment that areemployed by the contractors are left to theirdiscretion. Method specifications would only berequired where an unusual structure is to be built,and/or where the contractors have little experiencein the required construction procedures. Method


specifications result in the majority of the risk beingassumed by the designer and the owner. (g) Dispute Review BoardIn order to reduce the often lengthy and costlyresolution of construction claims in the courts, thereis increasing support for an alternative method usinga Dispute Review Board (Coffee, 1988; ASCE,1989). The Board is usually composed of threemembers, one chosen by the owner, one by thecontractor and a third who chairs the group, who ischosen by the two members themselves. The Boardmeets at the site once every three monthsapproximately, and also receives copies of progressreports in order to stay informed about the job andareas of potential dispute.Figure 10.22 shows the mechanism for resolution ofa dispute involving the DRB, together with themaximum times permitted for each of the activities.The operation and functions of the Board aredefined in the contract documents. The objective ofthis process is to resolve disputes as they occur,when the facts and the personnel involved arereadily available. Furthermore, the work continueswhile the dispute is resolved, so the schedule ismaintained, the job is completed and final paymentmade promptly. (h) Partnering

Partnering is not a contract, but a culture andmanagement style that requires a particularapproach to reduce the effects of any disputes(Atkinson and Knowles, 1996). The aim is toproduce teamwork between the participants andreduce confrontation, together with a disputeresolution process that develops trust between theall the stakeholders involved on the project. Thestages in implementing a partnering program are asfollows.

1. Pre-bid meeting A pre-bid meeting instigatedby the owner sets out the procedures for thepartnering process, and engenders a trust andcommitment to the process by all parties.

2. Audit An audit of all the stakeholders’management systems is carried out to produce aProject Quality Plan, and evaluate whethertheir culture will allow them to participate fullyin the partnering process.

3. Specification The owner’s commitment topartnering needs to be reflected in the biddocuments. This will include a clear statementof the objectives of the process, a schedule ofmeetings and workshops and a description ofthe Dispute Resolution process.

4. Award of contract Following the award of the

Figure 10.22 Process for resolution of construction disputes involving a Disputes Review Board, DRB (Stanley, 1989).

398 DRILLING

contract, the owner and contractor each appointa partnering leader, partnering workshops areorganized, and a facilitator who will help toimplement partnering is named.

5. Partnering workshops Early in the project alldecision making personnel from the mainorganizations are involved in workshops inwhich the potential problems are examined andan agreed Project Mission Statement isdeveloped.

6. Partnering agreements The result of theworkshops is the preparation of a PartneringAgreement that states the objectives of theproject, and defines the communication anddispute resolution processes. The agreementcan then be used to evaluate the performance ofthe partnering as the project proceeds.

7. Dispute resolution The resolution of disputesas described in (g) above is a well provenprocedure for rapidly and economically settledisputes and avoid claims. Projects involvingexcavations and construction in rock areinherently uncertain because of the naturalvariability in rock characteristics, and it isbeneficial to use a system to resolve conflictsefficiently to the satisfaction of all parties.

10.6 ReferencesAmerican Concrete Institute (1996) Specification for

Shotcrete. ACI 506.2–95.American Society of Civil Engineers, (1989) Avoiding

and resolving disputes in underground construction.ASCE Technical Committee on Contracting Practices,Underground Technology Research Council, June.

ASTM (1985) Flexural Toughness and First-crackStrength of Fiber-reinforced Concrete (Using Beamwith Third-point Loading). ASTM standards Vol. 04.02, C 1018–85.

Atkins, K.P. and Sowers, G.F. (1984) Tunneling underbuilding with thin rock cover. J. Geotech. Eng., ASCE,110(3), 311–17.

Atkinson, D. and Knowles, J.R. (1996) Partnering: thestakeholder ethos. Tunnels and Tunnelling, May, 45–6.

Atlas Copco (1978) Product Manual, 3rd edn, AtlasCopco AB, Stockholm.

ADITC (Australian Drilling Industry Training CommitteeLtd) (1997) Drilling—Manual of methods, applications

and management. CRS Lewis Publishers, BatonRouge, FL.

Berman, T. and Crossland, S.H. (1972) ConstructionBusiness Handbook, McGraw-Hill, NewYork, Ch.14.

Boyles Bros Drilling Co. (1988) Product data.Caterpillar Inc. (1997) Caterpillar Performance

Handbook, Edition 28. Peoria, IL.Cheng, Y. (1987) New development in seam treatment of

the Feitsui arch Dam foundation. Proc. of Int. Conf.,Montreal, Int. Soc. of Rock Mechanics, pp. 319–26.

Coffee, J.D. (1988) Dispute review boards in WashingtonState. Amer. Arbitration Assoc. J., December.

Crimmins, R., Samuels, R. and Monahan, B.P. (1972)Construction Rock Work Guide. Wiley-Interscience,New York.

Dowding, C.H. (1985) Blast Vibration Monitoring andControl. Prentice-Hall, Englewood Cliffs, NJ.

Du Pont of Canada (1964) Controlled Blasting.Wilmington, Delaware.

Federal Highway Administration (US) (1982) Tiebacks.FHWA, US Department of Transportation, Report No.FHWA/RD-82/047.

Federal Highway Administration (US) (1985) RockBlasting. FHWA, US Department of Transportation,Contract No. DTFH 61–83-C-00110.

Federal Highway Administration (US) (1989) RockSlopes: Design, Excavation, Stabilization. FHWA, USDepartment of Transportation.

Golder Associates (1989) Project files.Hemphill, G.B. (1981) Blasting Operations. McGraw-

Hill, New York.Kirsten, H.A. D. (1982) A classification system for

excavation of natural materials. The Civil Engineer inSouth Africa, July, 292–303.

Langefors, U. and Kihlstrom, B. (1967) The ModernTechnique of Rock Blasting, Wiley, New York.

Levy, S.M. (1996) Build, Operate, Transfer. Wiley, NewYork.

McGregor, K. (1967) The Drilling of Rock. CR Books,London

Merritt, F.S. (ed.) (1976) Standard Handbook for CivilEngineers, McGraw-Hill, New York, Ch. 3–4.

National Research Council (1994) Drilling andExcavation Technologies for the Future. NationalAcademy Press, Washington, DC.

Oriard, L.L. (1971) Blasting effects and their control inopen pit mining. Proc. Second Int. Conf. on Stability inOpen Pit Mining, Vancouver, AIME, New York,pp. 197–222.


Oriard, L.L. and Coulson, J.H. (1980) TVA BlastVibration Criteria for Mass Concrete. MinimizingDetrimental Construction Vibrations, ASCE, Preprint80–175, pp. 103–23.

Romana, M. and Izquierdo, F.A. (1987) Reinforcement ofslopes under Denia Castle, Spain. Proc. of Int. Conf.,Montreal; Int. Soc. of Rock Mech., pp. 485–9.

Siskind, D.E., Stachura, V.J. and Raddiffe, K.S. (1976)Noise and Vibrations in Residential Structures fromQuarry Production Blasting. US Bureau of Mines,Report of Investigations 8168.

Siskind, D.E., Stagg, M.S., Kopp, J.W. and Dowding,C.H. (1980) Structure Response and Damage Producedby Ground Vibrations from Surface Blasting. USBureau of Mines, Report of Investigations 8507.

Society of Mining Engineers (1973) Mining EngineeringHandbook, Vol. 1. SME of AIME, New York, Ch. 11.

Stagg, M.S., Siskind, D.E., Stevens, M.G. and Dowding,C.H. (1984) Effects of Repeated Blasting on a WoodFrame House. US Bureau of Mines, Report ofInvestigations 8896.

Stanley, E.M. (1989) Dispute review boards, a betterway. Civil Engineering ASCE, New York, December,pp. 58–60.

Tamrock, (1983) Handbook of Underground Drilling,Tamrock Drills, Finland

US Bureau of Mines (1984) Selected Pneumatic Gunitesfor use in Underground Mines: a ComparativeEngineering Analysis. USBM, Dept. of the Interior,Information circular 8984.

US Department of Navy (1982) Design Manual 7.1, SoilMechanics, NAVFAC DM-7.1, Alexandria, Virginia.

Wood, D.F. (1998) Personnal communication.Wyllie, D.C. (1979) Fractured bridge supports stabilized

under traffic. Railway Track and Structures, Jully,pp. 29–32.

Wyllie, D.C. (1991) Rock slopes stabilization andprotection measures. 34th Ann. M. AEG, Chicago,October.

Wyllie, D.C. (1995) Stability of foundations on jointedrock—case studies. Proc. Int. Workshop on RockFoundations, Japan, A.A.Balkema, pp. 253–8.

400 DRILLING

APPENDIX IStereonets for hand plotting of structural geology data

I.1Introduction

Analysis of the orientation of structural geologydata involves first plotting poles representing thedip and dip direction of each discontinuity. Thisplot will help to identify discontinuity sets, forwhich both the average orientation and the scatter(dispersion) can be calculated. The second step inthe analysis is to plot great circles representing theaverage orientation of each set, majordiscontinuities such as faults, and the dip and dipdirection of the cut face. Hand plotting of structuraldata can be carried out on the stereonets provided inthis Appendix. Figure I.1 shows a polar net whileFig. I.2 is equatorial net and Fig. I.3 shows therelationship between these two projections.

I.2Plotting poles

Poles can be plotted on the polar stereonet (Fig. I.1)on which the dip direction is indicated on theperiphery of the circle, and the dip is measuredalong radial lines with zero degrees at the center.The procedure for plotting poles is to lay a sheet oftracing paper on the printed polar net and mark thenorth direction and each quadrant position aroundthe edge of the outer circle. A mark is then made toshow the pole which represents the orientation ofeach discontinuity as defined by its dip and dipdirection. Poles for shallow dipping discontinuitieslie close to the center of the circle, and poles ofsteeply dipping discontinuities lie close to theperiphery of the circle.

I.3Plotting great circles

Great circles are plotted on the equatorial net(Fig. I.2), but they cannot be plotted directly on thisnet because the true dip can only be scaled off thehorizontal axis. The plotting procedure for greatcircles consists of the following steps in whichshallow dipping planes plot close to the peripheryof the net, and steeply dipping planes plot as largerradius circles close to the center.

1. Lay a piece of tracing paper on the net with athumb tack through the center point so that thetracing paper can be rotated on the tracingpaper.

2. Mark the north direction of the net on thetracing paper.

3. Locate the dip direction of the plane on thescale around the circumference of the net andmark this point on the tracing paper. Note thatthe dip direction scale on the equatorial net forplotting great circles starts at the north point atthe top of the circle and increases in aclockwise direction.

4. Rotate the tracing paper until the dip directionmark coincides with the horizontal axis of thenet, that is the 90° or 180° points of the dipdirection scale.

5. Locate the arc on the net corresponding to thedip of the plane and trace this arc on tothe paper. Note that a horizontal plane has agreat circle at the circumference of the net, anda vertical plane is represented by a straight linepassing through the center of the net.

6. Rotate the tracing paper so that the two northpoints coincide and the great circle is orientedcorrectly.

I.4Lines of intersection

The intersection of two planes is a straight linewhich defines the direction in which a wedgeformed by these two planes will slide. The

procedure for determining the orientation of the lineof intersection between two planes is as follows.

1. Locate the line of intersection between the twoplanes which is represented by the point atwhich the two great circles intersect.

2. Draw a line from the center of the net throughthe point of intersection and extend it to thecircumference of the net.

3. The trend of the line of intersection is given by

Figure I.1 Polar equal area stereonet for plotting poles (drawn by C.M. St John, Royal School of Mines, London).

402 APPENDIX I

the position where the line drawn in Step 2intersects the scale on the circumference of thenet.

4. Rotate the tracing paper until the line drawn inStep 2 lies over one of the horizontal axes ofthe net (dip directions 90° or 180°).

5. The plunge of the line of intersection is read offthe scale on the horizontal axis with a

horizontal plunge having a point of intersectionat the circumference and a vertical plunge at thecenter of the net.

I.5Reference

Hoek, E. and Bray, J. (1981) Rock Slope Engineering, 3rdedn, IMM, London.

Figure I.2 Equatorial equal area net for plotting poles and great circles (drawn by C.M. St John, Royal School ofMines, London).

APPENDIX I 403

Figure I.3 Polar and equatorial projections of a sphere (Hoek and Bray, 1981).

404 APPENDIX I

APPENDIX IIQuantitative description of discontinuities in rock masses

II. 1Introduction

This appendix provides details of the parametersused in geological mapping and diamond drillingfor the quantitative description of rock masses. Theinformation provided is based entirely on theprocedures drawn up by the International Society ofRock Mechanics (ISRM, 1981), and which arediscussed in more detail in Sections 4.2 and 4.3 ofthis book. The objective of using the ISRMprocedures for geological mapping and drill corelogging are as follows. First, these procedures arequantitative, so that each parameter is measured andthe results can be used either directly, orinterpreted, for use in design. Second, the use ofstandardized procedures allows different personnelto work to the same standards, and to producecomparable information.The following is a description of the parameters thatdescribe the rock mass, together with tables listingvalues used to quantify these parameters. Alsoprovided are mapping forms that can be used torecord both geological mapping and oriented corelogging. Further information on geologicalcharacterization and methods of data collection arediscussed in Chapter 4.

II.2Rock mass characterization parameters

Figure II.1 illustrates the parameters thatcharacterize the rock mass, and Fig. II.2 shows howthey can be divided into six classes related to therock material and its strength, the discontinuity

characteristics, infilling properties, the dimensionsand shape of the blocks of rock, and ground waterconditions. Each of the parameters in Fig. II.2, (A)to (M), is discussed below.

II.2.1Rock material description

(A) Rock typeThe value of including the rock type in describing arock mass is that this defines the process by whichthe rock was formed. For example, sedimentaryrocks such as sandstone usually contain wellordered sets of discontinuities because they are laiddown in layers, and are medium to low strengthbecause they have usually only been subject tomoderate heating and compression. Also, the rocktype gives an indication of the properties of the rockmass from general experience of their engineeringperformance. For ex ample, granite tends to bestrong and massive and resistant to weathering, incomparison to shale which is often weak and fissile,and can weather rapidly when exposed to wettingand drying cycles.The three primary characteristics of rock that areused to define its type are (see Table II.1):

1. color, as well as whether light or dark mineralspredominate;

2. texture or fabric ranging from crystalline,granular or glassy;

3. grain size that can range from clay particles togravel (Table II.2).

(B) Rock strengthThe compressive strength of the rock comprisingthe walls of a discontinuity is an importantcomponent of shear strength and deformability,especially if the walls are in direct rock to rockcontact as in the case of unfilled joints. Slight sheardisplacement of individual joints caused by shearstresses within the rock mass often results in verysmall asperity contact areas and actual stresseslocally approaching or exceeding the compressionstrength of the rock wall materials, hence theasperity damage. The wall strength is quantified inthe determination of shear strength as the jointcompressive strength (JCS) as discussed in

Section 3.4.2(b).Table II.3 defines ranges of rock material strengthwith a corresponding grade (R6 etc.) related tosimple field identification procedures.(C) WeatheringRock masses are frequently weathered near thesurface, and are sometimes altered by hydrothermalprocesses. The weathering (and alteration) generallyaffects the walls of discontinuities more than theinterior of rock blocks. This results in a wallstrength some fraction of what would be measuredon the fresher rock found in the interior of the rockblocks, for example that sampled by drill core. Adescription of the state of weathering or alteration

Figure II.1 Diagram illustrating rock mass properties.

406 APPENDIX II

both for the rock material and for the rock mass is

Figure II.2 List of parameters describing rock mass characteristics.

APPENDIX II 407

therefore an essential part of the description of wallstrength.There are two main results of weathering: onedominated by mechanical disintegration, the otherby chemical decomposition including solution.Generally, both mechanical and chemical effects acttogether, but, depending on climatic regime, one orother of these aspects may be dominant. Mechanicalweathering results in opening of discontinuities, theformation of new discontinuities by rock fracture,the opening of grain boundaries, and the fracture orcleavage of individual mineral grains. Chemicalweathering results in discoloration of the rock and

leads to the eventual decomposition of silicateminerals to clay minerals: some minerals, notablyquartz, resist this action and may surviveunchanged. Solution is an aspect of chemicalweathering which is particularly important in thecase of carbonate and saline minerals.The relatively thin ‘skin’ of wall rock that affectsshear strength and deformability can be tested bymeans of simple index tests. The apparent uniaxialcompression strength can be estimated both fromSchmidt hammer tests and from scratch andgeological hammer tests, since the

Table II.1 Rock type classification

Note: Numbers can be used to identify rock types on data sheets (see Appendix III).Reference: Geological Society Engineering Group Working Party (1977)

Table II.2 Grain size scale

Description Grain size

mm (in)

Boulders 200–600 (7.9–23.6)Cobbles 60–200 (2.4–7.9)Coarse gravel 20–60 (0.8–0.24)Medium gravel 6–20 (0.2–0.8)Fine gravel 2–6 (0.1–0.2)Coarse sand 0.6–2 (0.02–0.1)Medium sand 0.2–0.6 (0.008–0.02)Fine sand 0.06–0.2 (0.002–0.008)Silt, clay <0.06 (<0.002)

Table II.3 Classification of rock material strengths


MPa (p.s.i)

R6 Extremely strong rock Specimen can only be chipped withgeological hammer.

>250 (>36000)

R5 Very strong rock Specimen requires many blows ofgeological hammer to fracture it.

100–250 (15 000–36 000)

R4 Strong rock Specimen requires more than one blowwith a geological hammer to fractureit.

50–100 (7000–15 000)

R3 Medium weak rock Cannot be scraped or peeled with apocket knife; specimen can befractured with single firm blow of

25–50 (3500–7000)

408 APPENDIX II


MPa (p.s.i)geological hammer.

R2 Weak rock Can be peeled with a pocket knife;shallow indentations made by firmblow with point of geological hammer.

5–25 (725–3500)

R1 Very weak rock Crumbles under firm blows with pointof geological hammer; can be peeledby a pocket knife.

1–5 (150–725)

R0 Extremely weak rock Indented by thumbnail. 0.25–1 (35–150)S6 Hard clay Indented with difficulty by thumbnail. >0.5 (>70)S5 Very stiff clay Readily indented by thumbnail. 0.25–0.5 (35–70)S4 Stiff clay Readily indented by thumb but

penetrated only with great difficulty.0.1–0.25 (15–35)

S3 Firm clay Can be penetrated several inches bythumb with moderate effort.

0.05–0.1 (7–15)

S2 Soft clay Easily penetrated several inches bythumb.

0.025–0.05 (4–7)

S1 Very soft clay Easily penetrated several inches byfist.

<0.025 (<4)

latter have been roughly calibrated against a largebody of test data.Mineral coatings will affect the shear strength ofdiscontinuities to a marked degree if the walls areplanar and smooth. The type of mineral coatingsshould be described where possible. Samples shouldbe taken when in doubt.Table II.4 defines grades of rock weathering.

II.2.2Discontinuity description

(D) Discontinuity typeThe discontinuity type is useful in the description ofthe rock mass because each type has properties

Table II.4 Weathering and alteration grades

Grade Term Description

I Fresh No visible sign of rock material weathering; perhaps slight discoloration on majordiscontinuity surfaces.

II Slightly weathered Discoloration indicates weathering of rock material and discontinuity surfaces. Allthe rock material may be discolored by weathering and may be somewhat weakerexternally than in its fresh condition.

III Moderately weathered Less than half of the rock material is decomposed and/or disintegrated to a soil.Fresh or discolored rock is present either as a continuous framework or ascorestones.

IV Highly weathered More than half of the rock material is decomposed and/or disintegrated to a soil.Fresh or discolored rock is present either as a discontinuous framework or ascorestones.

V Completely weathered All rock material is decomposed and/or disintegrated to soil. The original massstructure is still largely intact.

VI Residual soil All rock material is converted to soil. The mass structure and material fabric aredestroyed. There is a large change in volume, but the soil has not been significantlytransported.

APPENDIX II 409

that influence the behavior of the rock mass. Forexample, faults can have lengths of severalkilometers and contain low strength gouge, whilejoints lengths usually do not exceed a few metersand they often contain no infilling. Section 2.1.1describes the characteristics of the most commontypes of discontinuities which include faults,bedding, foliation, joints, cleavage and schistosity.(E) Discontinuity orientationThe orientation of a discontinuity in space isdescribed by the dip of the line of steepestdeclination measured from horizontal, and by thedip direction measured clockwise from true north.Example: dip direction (α)/dip (ψ) (025°/45°).The orientation of discontinuities relative to anengineering structure largely controls the possibilityof unstable conditions or excessive deformationsdeveloping. The importance of orientation increaseswhen other conditions for deformation are present,such as low shear strength and a sufficient numberof discontinuities or joint sets for slip to occur.The mutual orientation of discontinuities willdetermine the shape of the individual blockscomprising the rock mass.(F) RoughnessThe wall roughness of a discontinuity is apotentially important component of its shearstrength, especially in the case of undisplaced andinterlocked features (e.g. unfilled joints). Theimportance of wall roughness declines as aperture,or infilling thickness, or the degree of any previousdisplacement increases.In general terms the roughness of discontinuitywalls can be characterized by undulations andasperities. Large scale undulations, if interlockedand in contact, cause dilation during sheardisplacement since they are too large to be shearedoff. Asperities are small scale roughness that tendsto be damaged during shear displacement unless thediscontinuity walls are of high strength and/or thestress levels are low, so that dilation can also occuron these small scale features.In practice, undulations affect the initial direction ofshear displacement relative to the mean discontinuity plane, while asperities affect the shear

strength that would normally be sampled in alaboratory or medium scale in situ direct shear test.If the direction of potential sliding is known,roughness can be sampled by linear profiles takenparallel to this direction. In many cases the relevantdirection is parallel to the dip (dip vector). In caseswhere sliding is controlled by two intersectingdiscontinuity planes, the direction of potentialsliding is parallel to the line of intersection of theplanes. In the case of arch dam abutment stability,the direction of potential sliding may have a markedhorizontal component.If the direction of potential sliding is unknown, butnevertheless of importance, roughness must besampled in three dimensions instead of two. Thiscan be done with a compass and disk-clinometer(Fig. 4.6). Dip and dip direction readings can beplotted as poles on equal-area nets. Alternatively,discontinuity surfaces can be contoured relative totheir mean planes using photogrammetric methods.This can be a useful technique if the criticalsurfaces are inaccessible.The purpose of all roughness sampling methods isfor the eventual estimation or calculation of shearstrength and dilation. Presently available methodsof interpreting roughness profiles and estimatingshear strength include measuring the i value (orinclination) of the irregularities, or the jointroughness coefficient JRC of the surface (Fig. II.3).The contribution of the surface roughness to thetotal friction angle of a surface is discussed in moredetail in Section 3.4.2.Descriptive terms that can be used to defineroughness are a combination of small scale features(several centimeters dimensions): rough, smooth,slickensided, and larger scale features (severalmeters dimensions): stepped, undulating, planar.These terms can then be combined to describedecreasing levels of roughness as in Table II.5.(G) ApertureAperture is the perpendicular distance separatingthe adjacent rock walls of an open discontinuity, inwhich the intervening space is air or water filled.Aperture is thereby distinguished from the

410 APPENDIX II

Figure II.3 Roughness profiles and corresponding range of JRC values associated with each one (ISRM, 1981).

APPENDIX II 411

Table II.5 Descriptive terms for roughness

Level Description

I Rough, steppedII Smooth, steppedIII Slickensided, steppedIV Rough, undulatingV Smooth, undulatingVI Slickensided, undulatingVII Rough, planarVIII Smooth, planarIX Slickensided, planarwidth of a filled discontinuity. Discontinuities thathave been filled (e.g. with clay) also come underthis category if filling material has been washed outlocally.Large aperture can result from shear displacementof discontinuities having appreciable roughness andwaviness, from tensile opening, from outwash, andfrom solution. Steep or vertical discontinuities thathave opened in tension as a result of valley erosionor glacial retreat may have very large apertures.In most sub-surface rock masses apertures are smalland will probably be less than half a millimeter,compared to the tens, hundreds or even thousandsof millimeters width of some of the outwash orextension varieties. Unless discontinuities areexceptionally smooth and planar it will not be ofgreat significance to the shear strength that a‘closed’ feature is 0.1 mm wide or 1.0 mm wide.However, indirectly as a result of hydraulicconductivity, even the finest may be significant inchanging the effective normal stress and thereforealso the shear strength.Unfortunately, visual observation of small aperturesis inherently unreliable since, with the possibleexceptions of drilled holes and bored tunnels,visible apertures are bound to be disturbedapertures, either due to disturbance by blasting, ordue to surface weathering effects. The influence ofapertures is best assessed by water permeabilitytesting.Apertures are recorded from the point of view ofboth their loosening and conducting capacity. Jointwater pressure, inflow of water and outflow of

storage products (both liquid and gas) will all beaffected by aperture.Apertures can be described by the terms listed inTable II.6.

II.2.3Infilling description

(H) Infilling type and widthInfilling is the term for material separating theadjacent rock walls of discontinuities, e.g. calcite,chlorite, clay, silt, fault gouge, breccia etc. Theperpendicular distance between the adjacent rockwalls is termed the width of the filled discontinuity,as opposed to the aperture of a gapped or openfeature.Owing to the enormous variety of occurrences,filled discontinuities display a wide range ofphysical behavior, in particular as regards their shearstrength deformability and permeability. Short-termand long-term behavior may be quite different suchthat it is easy to be misled by favorable short-termconditions.The wide range of physical behavior depends onmany factors of which the following are probablythe most important:

1. mineralogy of filling material (Table II.1);2. grading or particle size (Table II.2);3. over-consolidation ratio;4. water content and permeability (Table II.11);5. previous shear displacement;6. wall roughness (Fig. II.3 and Table II.5);

412 APPENDIX II

7. width (Table II.6); 8. fracturing or crushing of wall rock.Table II.6 Aperture dimensions

Aperture(mm)

Description

<0.1 Very tight0.1–0.25 Tight ‘Closed’ features0.25–0.5 Partly open0.5–2.5 Open2.5–10 Wide Moderately ‘Gapped’ features>10 wide1–100 Very wide100–1000 Extremely wide ‘Open’ features>1 m CavernousEvery attempt should be made to record the abovefactors, using quantitative descriptions wherepossible, together with sketches and/or colorphotographs of the most important occurrences.Certain index tests are suggested for a closerinvestigation of major discontinuities considered tobe a threat to stability. In special cases the results ofthese field descriptions may warrant therecommendation for large scale in situ testing, atleast in the case of dam foundations or majorslopes.

II.2.4Rock mass description

(I) SpacingThe spacing of adjacent discontinuities largelycontrols the size of individual blocks of intact rock.Several closely spaced sets tend to give conditionsof low mass cohesion whereas those that are widelyspaced are much more likely to yield interlockingconditions. These effects depend upon the

persistence of the individual discontinuities.In exceptional cases a close spacing may change themode of failure of a rock mass from translational tocircular or even to flow (e.g. a ‘sugar cube’ shearzone in quartzite). With extremely close spacing theorientation is of little consequence as failure mayoccur through rotation or rolling of the small rockpieces.As in the case of orientation, the importance ofspacing increases when other conditions fordeformation are present, i.e. low shear strength anda sufficient number of discontinuities or joint setsfor slip to occur.The spacing of individual discontinuities andassociated sets has a strong influence on the masspermeability and seepage characteristics. In general,the hydraulic conductivity of any given set will beinversely proportional to the spacing, if individualjoint apertures are comparable.Spacing can be described by means of terms listedin Table II.7.

Table II.7 Spacing dimensions

Description Spacing, mm

Extremely close spacing <20Very close spacing 20–60Close spacing 60–200Moderate spacing 200–600Wide spacing 600–2000Very wide spacing 2000–6000

APPENDIX II 413

Description Spacing, mm

Extremely wide spacing >6000(J) PersistencePersistence implies the areal extent or size of adiscontinuity within a plane. It can be crudelyquantified by observing the discontinuity tracelengths on the surface of exposures. It is one of themost important rock mass parameters, but one ofthe most difficult to quantify in anything but crudeterms.The discontinuities of one particular set will oftenbe more persistent than those of the other sets. Theminor sets will therefore tend to terminate againstthe primary features, or they may terminate in solidrock.In the case of rock slopes and dam foundations it isof the greatest importance to attempt to assess thedegree of persistence of those discontinuities thatare unfavorably orientated for stability. The degreeto which discontinuities persist beneath adjacentrock blocks without terminating in solid rock orterminating against other discontinuities determinesthe degree to which failure of intact rock would beinvolved in eventual failure. Perhaps, more likely, itdetermines the degree to which ‘down-stepping’would have to occur between adjacentdiscontinuities for a failure surface to develop.Persistence is also of the greatest importance totension crack development behind the crest of aslope.Frequently, rock exposures are small compared withthe area or length of persistent discontinuities, andthe real persistence can only be guessed. Lessfrequently it may be possible to record the diplength and the strike length of exposeddiscontinuities and thereby estimate theirpersistence along a given plane through the rock

mass using probability theory. However, thedifficulties and uncertainties involved in the fieldmeasurements will be considerable for most rockexposures encountered (see also Section 2.6.2).Persistence can be described by means of termslisted in Table II. 8.(K) Number of setsBoth the mechanical behavior and the appearance ofa rock mass will be dominated by the number ofsets of discontinuities that intersect one another.The mechanical behavior is especially affectedsince the number of sets determines the extent towhich the rock mass can deform without involvingfailure of the intact rock. The appearance of the rockmass is affected since the number of sets determinesthe degrees of overbreak that tends to occur withexcavation by blasting (Fig. II.4).The number of sets of discontinuities may be adominant feature of rock slope stability, thoughtraditionally the orientation of discontinuitiesrelative to the face is considered of primaryimportance. However, a large number of sets havingclose spacing may change the potential mode ofslope failure from translational or toppling torotational/circular.In the case of tunnel stability three or more sets willgenerally constitute a three-dimensional blockstructure having a considerable more ‘degrees offreedom’ for deformation than a rock mass with lessthan three sets. For example, a strongly foliatedphyllite with just one closely spaced joint set maygive equally good tunneling conditions as a massivegranite with three widely spaces joint sets. Theamount of overbreak in a tunnel will usually bestrongly dependent on the number of sets.

Table II.8 Persistence dimensions

Persistence Dimensions, m

Very low persistence <1Low persistence 1–3Medium persistence 3–10High persistence 10–20Very high persistence >20

414 APPENDIX II

The number of joint sets occurring locally (forexample along the length of a tunnel) can bedescribed according to the following scheme:

I massive, occasional random joints;II one joint set;

III one joint set plus random;IV two joint sets;V two joint sets plus random;

VI three joint sets;VII three joint sets plus random;VII

Ifour or more joint sets;

IX crushed rock, earth-like.

Major individual discontinuities should be recordedon an individual basis.(L) Block size and shapeBlock size is an extremely important indicator ofrock mass behavior. Block dimensions aredetermined by discontinuity spacing, by the numberof sets, and by the persistence of the discontinuitiesdelineating potential blocks.The number of sets and the orientation determinethe shape of the resulting blocks, which can take theapproximate form of cubes, rhombohedrons,

Figure II.4 Examples illustrating the effect of the number of joint sets on the mechanical behavior and appearance ofrock masses (ISRM, 1981).

APPENDIX II 415

tetrahedrons, sheets etc. However, regulargeometric shapes are the exception rather than therule since the joints in any one set are seldomconsistently parallel. Jointing in sedimentary rocksusually produces the most regular block shapes.The combined properties of block size andinterblock shear strength determine the mechanicalbehavior of the rock mass under given stressconditions. Rock masses composed of large blockstend to be less deformable, and in the case ofunderground construction, develop favorablearching and interlocking. In the case of slopes, asmall block size may cause the potential mode offailure to resemble that of soil (i.e. circular/rotational) instead of the translational or topplingmodes of failure usually associated withdiscontinuous rock masses. In exceptional cases‘block’ size may be so small that flow occurs, aswith a ‘sugar-cube’ shear zone in quartzite.Rock quarrying and blasting efficiency are likely tobe largely a function of the natural in situ block size.It may be helpful to think in terms of a block sizedistribution for the rock mass in much the same waythat soils are categorized by a distribution ofparticle sizes.Block size can be described either by means of theaverage dimension of typical blocks (block sizeindex Ib), or by the total number of jointsintersecting a unit volume of the rock mass(volumetric joint count Jv, Table II.9).Rock massesRock masses can be described by the followingadjectives, to give an impression of block size andshape (Fig. II.5):

I massive=few joints or very wide spacing;II blocky=approximately equidimensional;

III tabular=one dimension considerably smallerthan the other two;

IV columnar=one dimension considerably largerthan the other two;

V irregular=wide variations of block size andshape;

VI crushed=heavily jointed to ‘sugar cube’.

II.2.5Ground water

(M) SeepageWater seepage through rock masses results mainlyfrom flow through water conducting discontinuities(‘secondary’ permeability). In the case of certainsedimentary rocks the ‘primary’ permeability of therock material may be significant such that aproportion of the total seepage occurs through thepores. The rate of seepage is roughly proportional tothe local hydraulic gradient and to the relevantdirectional permeability, proportionality beingdependent on laminar flow. High velocity flowthrough open discontinuities may result in increasedhead losses due to turbulence.The prediction of ground water levels, likely seepagepaths, and approximate water pressures may oftengive advance warning of stability or constructiondifficulties. The field description of rock massesmust inevitably precede any recommendation forfield permeability tests so these factors should becarefully assessed at this early stage.Irregular ground water levels and perched watertables may be encountered in rock masses that arepartitioned by persistent impermeable features suchas dykes, clay filled discontinuities or impermeablebeds. The prediction of these potential flow-barriersand associated irregular water tables is ofconsiderable importance, especially for engineeringprojects where such barriers might be penetrated atdepth by tunneling, resulting in high pressureinflows.Seepage of water caused by drainage into anengineering excavation may have far reachingconsequences in cases where a sinking groundwater level would cause settlement of nearbystructures founded on overlying clay deposits.The approximate description of the localhydrogeology should be supplemented with detailedobservations of seepage from individualdiscontinuities or particular sets, according to theirrelative importance to stability. A short commentconcerning recent precipitation in the area, ifknown, will be helpful in the interpretation of theseobservations. Additional data concerning ground

416 APPENDIX II

water trends, and rainfall and temperature recordswill be useful supplementary information.In the case of rock slopes, the preliminary designestimates will be based on assumed values ofeffective normal stress. If, as a result of fieldobservations, one has to conclude that pessimisticassumptions of water pressure are justified (i.e. atension crack full of water with zero exit pressure atthe toe of the unfavorable discontinuity) then thiswill clearly have the greatest consequences for

design. So also will the field observation of rockslops and tunnel portals through ice wedging and/or increased water pressure caused by ice-blockeddrainage paths are serious seasonal problems inmany countries.Seepage from individual unfilled and filleddiscontinuities or from specific sets exposed in atunnel or in a surface exposure can be assessedaccording to the following descriptive terms inTable II.10 and II.11.

Figure II.5 Sketches of rock masses illustrating block shape. (a) blocky; (b) irregular; (c) tabular; and (d) columnar(ISRM, 1981).

APPENDIX II 417

In the case of a rock engineering construction whichacts as a drain for the rock mass, for example atunnel, it is helpful if the overall flow into individual

sections of the structure are described. This shouldideally be performed immediately after excavationas ground water levels, or the rock

Table II.9 Block dimensions

Description Jv (joints/m3)

Very large blocks <1.0Large blocks 1–3Medium-sized blocks 3–10Small blocks 10–30Very small blocks >30

Table II.10 Seepage quantities in unfilled discontinuities

Seepage rating Description

I The discontinuity is very tight and dry, water flow along it does not appear possible.II The discontinuity is dry with no evidence of water flow.III The discontinuity flow is dry but shows evidence of water flow, i.e. rust staining etc.IV The discontinuity is damp but no free water is present.V The discontinuity shows seepage, occasional drops of water, but no continuous flow.VI The discontinuity shows a continuous flow of water. (Estimate liters/min and describe pressure i.e.

low, medium, high).

Table II.11 Seepage quantities in filled discontinuities


I The filling materials are heavily consolidated and dry, significant flow appears unlikely due to verylow permeability.

II The filling materials are damp, but no free water is present.III The filling materials are wet, occasional drops of water.IV The filling materials show signs of outwash, continuous flow of water (estimate liter/min).V The filling materials are washed out locally, considerable water flow along out-wash channels

(estimate liter/min and describe pressure, i.e. low medium, high).VI The filling materials are washed out completely, very high water pressures experienced, especially

on first exposure (estimate liter/ min and describe pressure).

Table II.12 Seepage quantities in rock mass (e.g. tunnel wall)


I Dry walls and roof, no detectable seepage.II Minor seepage, specify dripping discontinuities.III Medium inflow, specify discontinuities with continuous flow (estimate liter/min/ 10 m length of

excavation).IV Major inflow, specify discontinuities with strong flows (estimate liter/ min/10 m length of

excavation).V Exceptionally high inflow, specify source of exceptional flows (estimate liter/min/10 m length of

excavation).

418 APPENDIX II

mass storage, may be depleted rapidly. Descriptionsof seepage quantities are given in Table II.12.A field assessment of the likely effectiveness ofsurface drains, inclined drill holes, or drainagegalleries should be made in the case of major rockslopes. This assessment will depend on theorientation, spacing and apertures of the relevantdiscontinuities.The potential influence of frost and ice on theseepage paths through the rock mass should beassessed. Observations of seepage from the surfacetrace of discontinuities may be misleading infreezing temperatures. The possibility of ice-blocked drainage paths should be assessed from thepoint of view of surface deterioration of a rockexcavation, and from the point of view of overallstability.

II.3Field mapping sheets

The two mapping sheets included with thisappendix provide a means of recording thequalitative geological data described in Section II.2above.Sheet 1 Rock mass description sheet describes therock material in terms of its colour, grain size andstrength, the rock mass in terms of the block shape,size, weathering and the number of discontinuitysets and their spacing.Sheet 2 Discontinuity survey data sheet describesthe characteristics of each discontinuity in terms ofits type, orientation, persistence, aperture/width,filling, surface roughness and water flow. Thissheet can be used for recording both outcrop (ortunnel) mapping data, and oriented core data(excluding persistence and surface shape).

II.4References

International Society for Rock Mechanics (1981b)Suggested Methods of the Quantitative Description ofDiscontinuities in Rock Masses (ed. E.T.Brown),Pergamon Press, Oxford, UK.

APPENDIX II 419

420 APPENDIX II

APPENDIX II 421

APPENDIX IIIConversion factors

Imperial unit SI unit SI unit symbol Conversion factor (Imperialto SI)

Conversion factor (SI toImperial)

Lengthmile kilometer km 1 mile=1.609 km 1 km=0.6214 milefoot meter m 1 ft=0.3048 m 1 m=3.2808 ft

millimeter mm 1 ft=304.80 mm 1 mm=0.003 281 ftinch millimeter mm 1 in=25.40 mm 1 mm=0.039 37 inAreasquare mile square kilometer km2 1 mile2=2.590 km2 1 km2=0.3861 mile2

hectare ha 1 mile2=259.0 ha 1 ha=0.003 861 mile2

acre hectare ha 1 acre=0.4047 ha 1 ha=2.4710 acresquare meter m2 1 acre=4047 m2 1 m2=0.000 247 1 acre

square foot square meter m2 1 ft2=0.092 90 m2 1 m2=10.7643 ft2

square inch square millimeter mm2 1 in2=645.2 mm2 1 mm2=0.001 550 in2

Volumecubic yard cubic meter m3 1 yd3=0.7646 m3 1 m3=1.3080 yd3

cubic foot cubic meter m3 1 ft3=0.028 32 m3 1 m3=35.3150 ft3

liter liter 1 ft3=28.32 1 1 liter=0.035 31 ft3

cubic inch cubic millimeter mm3 1 in3=16 387 mm3 1 mm3=61.024×10−6 in3

cubic centimeter cm3 1 in3=16.387 cm3 1 cm3=0.061 02 in3

liter 1 in3=0.016 39 1 1 liter=61.02 in3

Imp. gallon cubic meter m3 1 gal=0.004 56 m3 1 m3=220.0 galliter l 1 gal=4.546 l 1 liter=0.220 gal

pint liter l 1 pt=0.568 l 1 liter=1.7606 ptUS gallon cubic meter m3 1 US gal=0.0038 m3 1 m3=263.2 US gal

liter l 1 US gal=3.8 l 11=0.264 US galMasston tonne t 1 ton=0.9072 tonne 1 tonne=1.1023 tonton (2000 lb) (US) kilogram kg 1 ton=907.19 kg 1 kg=0.001 102 tonton (2240 lb) (UK) = 1016.1 kg = 0.000 984 ton

Imperial unit SI unit SI unit symbol Conversion factor (Imperialto SI)


kip kilogram kg 1 kip=453.59 kg 1 kg=0.002 204 6 kip

pound kilogram kg 1 lb=0.4536 kg 1 kg=2.2046 lbMass densityton per cubic yard (2000lb) (US)

kilogram per cubic meter kg/m3 1 ton/yd3=1186.49 kg/m3 1 kg/m3=0.000 842 8 ton/yd3

tonne per cubic meter t/m3 1 ton/yd3=1.1865 t/m3 1 t/m3=0.8428 ton/yd3

ton per cubic yard (2240lb) (UK)

1 ton/yd3=1328.9 kg/m3 1 kg/m3=0.000 75 ton/yd3

pound per cubic foot kilogram per cubic meter kg/cm3 1 lb/ft3=16.02 kg/m3 1 kg/cm3=0.062 42 lb/ft3

tonne per cubic meter t/m3 1 lb/ft3=0.01602 t/m3 1 t/m3=62.42 lb/ft3

pound per cubic inch gram per cubiccentimeter

g/cm3 1 lb/in3=27.68 g/cm3 1 g/cm3=0.036 13 lb/in3

tonne per cubic meter t/m3 1 lb/in3=27.68 t/m3 1 t/m3=0.036 13 lb/in3

Forceton force (2000 lb) (US) kilonewton kN 1 tonf=8.896 kN 1 kN=0.1124 tonf (US)ton force (2240 lb) (UK) =9.964 kN =0.1004 tonf (UK)kip force kilonewton kN 1 kipf=4.448 kN 1 kN=0.2248 kipfpound force newton N 1 lbf=4.448 N 1 N=0.2248 lbftonf/ft (2000 lb) (US) kilonewton kN/m 1 ton f/ft=29.186 kN/m 1 kN/m=0.034 26 tonf/ft

(US)ton f/ft (2240 lb) (UK) per meter =32.68 kN/m =0.0306 tonf/ft (UK)pound force per foot newton per meter N/m 1 lbf/ft=14.59 N/m 1 N/m=0.068 53 lbf/ftHydraulic conductivitycentimeter per second meter per second m/s 1 cm/s=0.01 m/s 1 m/s=100 cm/sfoot per year meter per second m/s 1 ft/yr=0.9665×10−8 m/s 1 m/s=1.0346×108 ft/yrfoot per second meter per second m/s 1 ft/s=0.3048 m/s 1 m/s=3.2808 ft/sFlow ratecubic foot per minute cubic meter per second m3/s 1 ft3/min=0.000 471 9

m3/s1 m3/s=2119.093 ft3/min

liter per second l/s 1 ft3/min=0.4719 l/s 1 l/s=2.1191 ft3/mincubic foot per second cubic meter per second m3/s 1 ft3/s=0.028 32 m3/s 1 m3/s=35.315 ft3/s

liter per second l/s 1 ft3/s=28.32 l/s 1 l/s=0.035 31 ft3/sgallon per minute liter per second l/s 1 gal/min=0.075 77 l/s 1 l/s=13.2 gal/min

Imperial unit SI unit SI unit symbol Conversion factor(Imperial to SI)


Pressure, Stresston force per squarefoot (2000 lb) (US)

kilopascal kPa 1 tonf/ft2=95.76 kPa 1 kPa=0.01044 ton f/ft2

ton force per square 1 tonf/ft2=107.3 kPa 1 kPa=0.00932 ton/ft2

423

Imperial unit SI unit SI unit symbol Conversion factor(Imperial to SI)


foot (2240 lb) (UK)pound force per pascal Pa 1 lbf/ft2=47.88 Pa 1 Pa=0.020 89 lbf/ft2

square foot kilopascal kPa 1 lbf/ft2=0.047 88 kPa 1 kPa=20.89 lbf/ft2

pound force per pascal Pa 1 lbf/in2=6895 Pa 1 Pa=0.000 1450 lbf/in2

square inch kilopascal kPa 1 lbf/in2=6.895 kPa 1 kPa=0.1450 lbf/in2

Weight density*pound force per cubicfoot

kilonewton per cubicmeter

kN/m3 1 lbf/ft3–0.157 kN/m3 1 kN/m3=6.37 lbf/ft3

Energyfoot lbf joules J 1 ft.lbf=1.355 J 1 J=0.7376 ft.lbf* Assuming a gravitational acceleration of 9.807 m/s2

424

Index

Acid leachate 234Active/passive wedges 137Adit 93, 122, 128Air photograph 93, 95Alignment studies 94Allowable bearing pressures 135

see also Bearing capacityAnhydrite 83, 228Anisotropic rock 59, 126Anode 320Aperture 102, 328, 381Artesian pressure 328Arylamide grout 235fcAsperities 69, 76, 102, 106

rock socket 253Asphalt 234Attenuation

blasting 353, 355seismic waves 97

Atterburg limits 83Australia 136

Back analysis 50, 65, 76Basalt 69, 211, 272Base shear 9Bearing capacity 131, 133, 138

bedded formations 142building codes 133dipping formations 140fractured rock 136karstic formations 144layered formations 143recessed footing 139, 142slab 144sloping ground 139wedge 141

Bearing capacity factors 139

Bearing surface improvement 225, 356Bedding 25, 94, 95, 113, 119, 125Bell solution 139, 142Bending failure 143Bentonite 71, 114, 116, 151, 239, 258Beta distribution 20Bieniawaski, Z.T. 60, 203Blasting 7, 194, 226, 227, 345

burden 347preshear 348controlled blasting 347corners 349damage 113, 347damage thresholds 353free face 346ground vibration control 349horizontal surfaces 349line drilling 349modulus test 119, 122preshearing 348rock anchor damage 318rock fracture mechanism 345, 346scaled distance 352shockwave 346sub-drill 349trim blasting 348, 356vibration frequency 353vibration particle velocity 352vibrations in uncured concrete 353

Blasting mats 319Block size/shape 103, 385Borehole surveying 111Borehole video camera 111Boussinesq equations 166Brazilian tension test 71, 80Breccia 71, 211Bridge

425

arch 1exploration 93foundation failure 5scour of foundations 195settlement 12calculations of 159suspension 11, 131, 136, 287

Britain 136, 164, 290Buckling failure 143Building

codes 133, 142foundation design, seismic 9loads 8

Bulk modulus 97Burger substance 85, 164

Calcite 71, 82Calcium carbonate 5, 228Calcium hydroxide 243California 10, 58, 194, 219, 220, 223, 229Canada 9, 16, 53, 83, 136, 200, 226, 230, 258Carbonation 82, 83Cathode 320Cement

grout 234leaching 243piezometer 114, 117

Centre of gravity 188Centrifugal force 173, 274Chalk 69China 88, 211, 218, 219Chloride 298, 323Chlorite 83 Clay 71, 83, 144, 215, 217, 272, 324

classification 378Claystone 82, 211Cleavage 26Coal 319Coal mining 164Coecient of reliability 18, 23, 230Cohesion 66, 70, 71, 76, 192, 194, 215

grout 237in situ test 128sliding stability 180wedge 186

Com624, 275Compass 110, 111

geological 29, 104, 105, 370Compressive strength 48

asperities 70bearing capacity 137classification 61, 375fractured rock 64intact rock 63point load strength 63rock anchor bond 306rock socket 257, 264shotcrete 359testing 51

Compressive wave 97Concrete

arch dam 231bearing surface improvement 227blasting damage 353buttress 361dam abutment reinforcement 218properties 217scour protection 199, 233

Conglomerate 69Consolidation 163Contracts

blasting 364build-operate-transfer 363components of contract documents 362definition of rock and soil 364design-build 363

Dispute Review Board 367end product 362, 367factual data 364general and special provisions 362interpretative data 364lump-sum 363measurement and payment 363method specifications 361, 367partnering 368prequalification 366ripping 364risk 366rock excavation and reinforcement 364technical specification 363types of contract 363unit price 363variation in quantities 366

Correction factorborehole jack 121footing shape 138settlement 158

Corrosion 7

426 INDEX

bacterial corrosion 323cables 287hydrogen embrittlement 323in grout 323monitoring 327pitting corrosion 321rock anchors 320stress corrosion 322

Corrosive environment 323Creep 80, 83, 87

carbonate 84components (four) 84constants 88ductile rock 5heave 83in situ measurement 86long term 88mechanisms 84modulus test 54rock anchors 332rock sockets 261salt 85sandstone 85shale 85shear loading 88stress dependent 5, 163weathering 48

Curved shear strength envelope 79Cut and cover 131Cyclic loading 50, 89, 317

Dam 1, 2arch 200, 202, 215, 216buttress 202dam-foundation interaction 221earthquake response 218, 220

see also Pseudo-static analysisfactor of safety 210

and sliding 207, 210failures and deteriorations 4, 201finite element analysis 221gravity 202overturning 213stress distribution 214, 215hydrodynamic force 220ice forces 204, 208in situ testing 119loading combinations 204loads 203

probability analysis 230reliability 201reservoir filling 219seismic upgrading 229silt forces 204, 208sliding joint 219stability against sliding/overturning 203, 220tailwater 204, 208thermal expansion 204water forces 203wind forces 204, 208

Dam failurefloods 202reservoir filling 202seepage and uplift 203seismic events 202time of failure 203

Dam foundationsblasting 227bored concrete piles 211buckling strength 210cleaning and sealing 226concrete ballast 211concrete shear keys 211, 217, 218cuto trench 227displacement (earthquake) 221, 224drainage 207, 211, 244drains, bacterial growth 244dynamic pore pressure 220erosion 202, 225excavation and concreting 211factor of safety 215finite element analysis 215, 218flow net 13grout 229, 233internal water forces 204investigation/design 200monitoring 230neoprene sheet 218open joints 218, 227permeability 116

Dam foundations (contd.)preparation of rock surfaces 218, 225rebound 228recessed foundation 209rehabilitation 229rock anchor 210, 212, 228, 231rock-concrete shear strength 205, 207, 216rock shear strength 205

INDEX 427

seepage 218seismic forces 204seismic ground motion 219shaping 225sliding failure 204, 207, 208slush grout 227solution cavities 228stabilization 211water pressure 207, 214, 244

Dam performance statistics 201Dam rehabilitation

anchoring 231grouting 230monitoring 230scour protection 231

DamsAlbigna dam 218, 230Ambiesta dam 220Auburn dam 223Cabril arch dam 233Cambambe dam 215Cannelles dam 217Cat Arm dam 226Chirkey dam 220Clyde dam 219Elkhart dam 210Funcho dam 216Garrison dam 228Gezouba project 211Ghe Zhou gravity dam 88Gordon dam 51Hsinfengkiang dam 219Inguri dam 212Itaipu dam 211Karakaya dam 213Kariba dam 219Keban dam 228Konya dam 219Liu-Jia-Xia dam 211Long Valley dam 10Longton arch dam 218Malpasset dam 5, 203Mintang project 227Morris dam 219Morris Shepard dam 211Nagawado dam 219Normandy dam 227Nukui arch dam 128Oahe dam 228

Pacoima dam 220Peace Canyon project 228Quail Creek 228Revelstoke gravity dam 200San Fernando dam 219Stewart mountain 231Stewartville dam 230, 234Teton dam 203, 225Wimbleball dam 236Zimapan dam 228

Darcy’s law 112Debris flow 95Deere, D.U. 205, 206Deformation modulus 48, 50, 56, 216

anisotropic rock 58back analysis 51borehole jack 121definition 51dilatometer 120fractured rock 57, 58in situ testing 119intact rock 51, 57plate load test 122radial jacking test 125rock mass 58, 60rock socket 256settlement 160, 162size eect 56weak rock 55

Degree of fracturing 97Delphi panel 18Dental concrete 226, 358Deterministic analysis 15, 179Development length 307Diamond drilling 93, 106, 109, 117, 361Dilation angle 217Dilatometer 86Diorite 231Dip 28, 102, 104, 379, 381Dip direction 28, 102, 104, 379, 381Direct shear test 74–6, 128Discontinuity

aperture 381daylight 27, 38, 40, 177, 205, 280dispersion 40displaced 73frequency 106infilling 71, 205length (probability distribution) 42

428 INDEX

mapping 44number of sets 103, 385orientation 28, 379

and scour 198orthogonal 26, 33, 95, 100persistence 103, 383roughness 69sets 33, 196spacing 46, 58, 103, 105, 383

probability distribution 43type 378undisplaced 73–4

Dolomite 82, 212, 261Dowels 215Drainage 116, 244, 328, 361

shotcrete 358Drill core 111, 133

orientation 109photograph 106recovery 107

Drilling 106, 334auger 342bencher 334calyx 106, 111, 342cased holes 342Christienson-Hugel 110clay impression core barrel 109diamond drilling 106, 107, 109, 147, 335directional drilling 343down-the-hole (DTH) drill 337, 338drill string vibration 111drilling mud 336feed rate 111fluid pressure 111hole alignment 231integral sample 109large diameter drilling 342overburden drilling 340percussion drilling 111, 147, 235, 334, 337rotary drill 340super drill 343tool thrust 111tool torque 111triple tube core barrel 107, 336Tubex system 341

Dynamic compaction 151Dywidag threadbar 292, 324

Earthquake 56, 173, 182, 231, 274

building foundation 9displacement analysis 195, 223fault displacement 218force modification factor 9ground motion variation 219hydrodynamic force 220importance factor 10reservoir filling 219seismic response factor 9stability analysis 194zonal velocity ratio 9see also Pseudo-static seismic analysis

Eccentricity 173Elastic material 53Elastic modulus 120Electrolyte 320Epoxy 231Erodibility index 232Erosion 225, 228Expansion agents (rock breakage) 356Explosives 112, 346, 352Extensometer 230

Factor of safety 15, 663-d slope 188dam foundations 211bearing capacity 138design values 16deterministic 23planar failure 179rock sockets 263, 264toppling failure 191uplift 313wedge failure 185

Failure typecircular 36, 191planar 36, 38, 177sliding 205, 206toppling 36, 38, 188wedge 25, 35, 36, 38, 183, 283

Fatigue 89Fault 94, 95

bridge foundation 1dam foundation 212, 218, 219definition 25geophysics 97ground water 119infilling 71, 103mapping 104

INDEX 429

Fibre glass rock anchors 327Fill loads 9Finite dierence analysis 163Finite element analysis

borehole jack 121dam foundation 217, 231dynamic 221layered foundation 143rock socket 254, 265settlement 160

FLAC 159, 163Flatjack 122, 126Flexural strength, shotcrete 359Flood 231Flow net 15Flyrock 319Flysch 55Foliation 26, 113Foundation failures 4, 201France 5, 203, 290Friction angle

back analysis 76dam foundation 215infilling 71limit equilibrium 40Mohr-Coulomb material 66Newmark analysis 223residual 71rock type 66sliding stability 180stability analysis 192stress distribution 171toppling failure 191wedge 186

Friction cone 40

Geological mapping 99, 104, 374Geophysics 96, 147

explosive 97ground penetrating radar 99, 147resistivity 98seismic 97

Germany 29, 290Gneiss 53, 69, 213Goodman, R.E. 159, 171, 187, 188, 225Goodman jack tests 53Grain size 85, 375Granite 69, 82, 99, 131Graywacke 216

Great circle 30, 35, 370Ground water 13, 112

mapping 104, 387rock socket 251tension crack 181, 186toppling 190

Grout 7, 82, 116, 228, 230, 233blanket grouting 236bleeding 235cohesion 237consolidation grouting 233curtain grouting 237drilling method 235erosion control 234fluidizers 239grouting procedures 240hole patterns 236, 237leaching 243mechanism of 235mixes 237monitoring 241overburden pressure 239permeability

control 233criteria 241

pressure 239strength 239types of 234uplift control 233viscosity 235

Gypsum 5, 82, 83, 228

Halite 5, 82Heat shrink tubing 326Heave 83, 83Helicopter 287Hoek

back analysis 76dam foundation 205foundation failure 143tensile strength 80, 313wedge failure 186

Hoek-Brown strength criterion 65, 76, 137, 142Hong Kong 140Hydration 82, 83Hydraulic impact hammer 7, 355Hydraulic jack 122Hydraulic splitter 7, 356Hydrofracture 239

430 INDEX

Hysteresis 52

Illite 83Impression packer 111In situ testing 93, 119, 217Inclinometer 230Industrial waste 324Inelastic rock 163 Infilling 70, 71

classification 382dam foundation 227in situ test 128mapping 103normally-, over-consolidated 74permeability 113scour 197

Instrumentation 230International Society of Rock Mechanics 100, 374Italy 220

Japan 29, 95, 128, 136, 195, 219Joint 26Joint compressive strength (JCS) 70, 376Joint roughness coecient (JRC) 70, 102, 105

Kaolinite 82, 83Karst 94Karstic formation 4, 144

characteristics 145dam foundation 228deep foundations 151foundation type 148, 149foundation treatment 151geophysics 96ground penetrating radar 99rock socketed pier 6, 249, 263sealing 228

Key block theory 187Kinematic analysis 38Kulhawy, F.H. 159

Landfill 234Landslide 94, 95, 219LATPILE 275Leaching 243Lime 243Limestone 13, 55, 69, 71, 82, 145, 152, 212, 217, 228,

230, 234, 249Limit equilibrium analysis 179, 207, 210

Limit states design 16Line mapping 104Line of intersection 35, 40, 183, 372, 381Linear variable dierential transformer (LVDT) 52, 74, 120Load

dead load 138highway bridge 10impact 10live load 138railway bridge 10

Load factor 17Load-deformation behaviour, fractured rock 53Lognormal distribution 43Lugeon 241

Mapping 93Mapping sheets 388, 389Margin of safety 20Marl 55, 68Mexico 228Mica 59, 68, 82Modulus of elasticity 120Mohr diagram 71Mohr-Coulomb material 66, 180, 253Monitoring 230Monte Carlo analysis 21, 40, 183Montmorillonite 71, 83Mudstone 83, 258Multi-position extensometers 122, 125

Negative exponential distribution 43Neoprene 230New York 133Newmark, N.M. 223Nitrogen 117Non-explosive excavation 345, 355Non-shrink grout 298Normal distribution 20

Olivine 83Oolite 144Orthogonal joint sets 26Osterburg hydraulic cell 264, 272Overturning moment 173Oxidation 82, 83

Packer 117, 240, 328Peck, R.B. 133Permanent deformation 54

INDEX 431

Permeability 13anisotropic rock 113Darcy’s law 112discontinuity aperture 102drainage 361drilling 111falling head tests 237infilling 103mapping 104measurement 116piezometers 113primary permeability 112pump test 119secondary permeability 113shape factor 118UDEC 215variable head test 117

Persistenceclassification 384mapping 44

Perspex 109Photograph 110Phyllite 59Piezometer 113, 117, 230, 231

electrical transducers 115multiple standpipe 115multi-port (MP) 115pneumatic 114standpipe 114time lag 114

Piles 88, 152, 249Pin piles 153Pins (rock reinforcement) 360Plate load test 53, 55, 87, 122

correction factor 124Plate tectonics 195Plunge 29, 373Point load test 63Poisson’s ratio 52, 53, 97, 120, 160Pole density 32Pole plot 31, 370Polyethylene (HDPE) 326Polypropylene 327Polyurethane 234Porosity 97Portugal 215, 217Potentiometer 120Pre-load 272Pressure gradient 112

Probabilistic analysis 18, 183Probability 40, 385

density function 183detection of sink holes 147distributions 19, 42of failure 18, 21, 36, 202, 230

Pseudo-static seismic analysis 194bridge 182, 192dam 223gravity dam 204, 213, 220, 221

Punching failure 143p-y curves 275Pyrrotite 82

Radial stress 172Railway 10Rayleigh wave 97, 351Rebound 228Recessed footing 138, 209Reconnaissance 93Reinforcement of rock 7, 356Release surface 177, 183Reliability analysis 18Residual soil 147Resin anchor 301, 304Resin grout 235Resistivity 98Retaining-wall instability 6Reynolds number 113Rigidity factor 155Rip rap 199, 233Ripping 355River hydraulics 95Rock anchor 1, 182, 361

acceptance criteria 330allowable working load 290anchor materials 289bearing capacity 142bond length 297cement admixtures 298cement grout anchorage 292, 296cement grout mix 297centralizers 300Ciment Fondu 319corrosion failure 302, 320mechanism 320protection 293, 324types 321corrosive conditions 323

432 INDEX

creep 302, 317, 330, 332cyclic loading 317dam 210, 228, 231displacement of the head 308drilling 335eect of blasting 318embedment length 307failure 7galvanized 327group action 316grout bleed 298grout pressures 300guaranteed ultimate tensile strength 290hole diameter 296lift-o test 330load transfer mechanism 303load-extension measurement 329mechanical anchor 292, 302moment/tension loads 314optimum plunge angle 186passive 308performance test 329permafrost 319polypropylene sheath 294pre-stressed 307proof test 330resin anchor 300, 320rock cone 310, 313seepage 328shear stress distribution 303Split Set bolts 290stagger 4steel relaxation 290, 317steel/grout bond 307strand anchors 293strength properties 292Swellex bolts 290tie-down 174toppling 191tube en machette 300uplift capacity 308water testing 328working bond strength 306, 320yield stress 290

Rock mass 65Rock mass rating (RMR) 60Rock mass strength 48Rock socketed pier 3

belling 273, 274

bentonite 258condition of end of socket 260condition of side walls 258creep 261eect of rock modulus 255eect of rock strength 257eect of socket geometry 255end-bearing capacity 264factor of safety 263failure 6influence factors 265, 269investigation 249karstic formation 151, 263lateral load 274, 280lateral stability 280load capacity 251, 254load transfer 251pre-load 272p-y curve 276, 277recessed socket 267reduction factor 267rock layering 261settlement end bearing 267socketed 269settlement mechanism 265settlement side wall 265side-wall shear resistance 253, 263, 265uplift load 272, 273, 274

Rock type 100, 374Roughness

angle 74classification 381discontinuity 102infilling 103measurement 105rock socket 253scour resistance 197

RQD 106, 133, 196, 258, 278, 279, 280, 355Russia 212, 220, 244

Salt 163Sandstone 53, 69, 80, 83, 131, 156, 159, 211, 215, 253,

273Saponite 83Sarma 225Schist 55, 59, 68, 159, 211Schistosity 26Scour 4, 112, 198

dam foundation 203, 231

INDEX 433

energy dissipation 232erosive power of water 195, 232foundation stability 5, 195grout strength 239Q-system 232resistence of rock 196rock susceptibility 355sealing grout 234water action 13

Sculpting (of rock) 7Sea water 298, 323Seed 225Seepage 13, 15, 112, 116

blasting 148classification 386, 387dam failure 202

Seepage (contd.)embankment dam 225grouting 233, 236leaching 243mapping 34, 104permeability criteria 241weathering 82

Seiche 219Seismic codes 195Seismic upgrading 229Sensitivity analysis 17Serpentine 83Settlement 4, 131

allowable 11arch bridge 1bridges 12, 50buildings 50compressible bed within sti formation 156compressible layer on rigid base 156deformation modulus 28dierential 11, 50elastic 54elastic rock 155geological conditions 133ground subsidence 164homogeneous, isotropic rock 155inclined, variable thickness beds 159layered formation 155sliding 154sti layer overlying compressible formation 158time dependent 154, 163transversely isotropic rock 159

Shale 55, 59, 68, 82, 83, 131, 144, 156, 159, 216, 227,

228, 261Shape factor

permeability 118settlement 156

Shear modulus 58, 97, 120, 121, 161Shear strength 48, 66, 69, 112, 119

discontinuities 66fractured rock 75steel 360

Sheeting joint 6Shotcrete 82, 228, 358

mix 359silica fume 359steel fibre reinforcing 358wire mesh reinforcing 358

Silicate grout 234Siltstone 69, 211, 215, 254Sine wave 111Singapore 254, 257Site selection 93Size eects 56, 64Slate 69Sliding stability 133Solution cavity detection 147Sowers, G.F. 144, 153Spacing (of discontinuities), classification 384Spain 135, 136Spread footing 2, 62Stability of foundations 2, 5, 13, 27, 177Stainless prestressing steels 327Stereo net 31, 38, 104, 106, 109, 370

data selection 33Stereographic projection 29Stiness 58, 120, 161, 216, 218Stiness ratio 172Stochastic model (discontinuities) 36Strain gauges 52Strength testing

in situ 49–50laboratory 49

Stress distribution 164distributed loads 167eccentrically loaded footings 173elastic isotropic rock 166layered formations 168line load 168transversely isotropic rock 171

Stress field 83Stress relief 83, 113, 228

434 INDEX

Strike 28Structural geology 7, 93, 177, 312, 370Styrofoam 9, 264Subsidence 164Sulphates 298Sulphide 83Survey 110Swelling 82

chemical reaction 83clay 82hydration 82pressures 82

Switzerland 218, 230, 290Sylvite 82

Talus 95Tar sand 163Tensile strength 48, 79–80, 144, 217

fractured rock 313Tension crack 95Tension foundation 4Terrestrial photograph 95Terzaghi, K. 137Terzaghi correction 105Test pit 106Texture 375Three-dimensional stability analysis 187Tiltmeter 230Time-dependent properties 80Toppling 188

see also Failure typeTransmission tower 11, 272, 309Trend 29, 372Triangular distribution 20Tunnel 125, 249

seepage 389

UDEC 159, 215United States of America 8, 136, 203, 210, 231University of California, Berkeley 50

Variable head test 116Vermicullite 83

Visco-elastic material 87, 163Viscous flow 85V-notch weir 244

Wall strength 102Water jets 227Water sampling 115Water table 97, 118Weathering 4, 48

bearing capacity 135, 163chemical 376, 379classification 80, 379decomposition 82disintegration 80geophysics 96mapping 102mechanical 376, 379settlement 156

Wedgerock socket, lateral load 283see also Failure type

Well sounder 114Williams all-thread bar 292Williams hollow core bar 302Window mapping 104Wire-line 109Worked examples

bearing capacity 142rock anchor (uplift, moment loading) 315settlement

elastic rock 158fractured rock 162

socketed piers 269stability analysis

planar failure 182wedge failure 187XSTABL 193

XSTABL stability analysis 193

Yield acceleration 224Young’s modulus 53

INDEX 435