Rock Mechanics

Frontispiece Post-pillar mining in a jointed and faulted rock mass at the Dolphin Mine, King Island, Australia (photograph by permis­sion of King Island Scheelite and CSIRO Division of Geomechanics).

Rock Mechanics For underground mining Second edition

B.H.G. Brady Professor of Mining Engineering, University of Queensland, Australia

E.T. Brown Deputy Vice-Chancellor, University of Queensland, Australia

SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

A C.LP. Catalogue record for this book is available from the Library of Congress A catalogue record for this book is available from the British Library

ISBN 978-0-412-47550-4 ISBN 978-94-015-8129-5 (eBook) DOI 10.1007/978-94-015-8129-5

Printed on acid-free paper

All rights reserved First edition 1985

Second edition 1993 Reprinted 1994

Reprinted with corrections 1999. © 1985, 1992, 1999 B.H.G. Brady and E.T. Brown.

Originally published by Kluwer Academic Publishers in 1999 Softcover reprint of the hardcover 2nd edition 1999

No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical,

including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owners.

Typeset in 10/12 Times by AFS Image Setters Ltd, Glasgow, UK

Contents

Preface to the second edition xi Preface to the first edition xii Acknowledgements xiv

1 Rock mechanics and mining engineering 1

1.1 General concepts 1.2 Inherent complexities in rock mechanies 4 1.3 Underground mining 6 1.4 Functional interactions in mine engineering 11 1.5 Implementation of a rock mechanics programme 13

2 Stress and infinitesimal strain 17

2.1 Problem definition 17 2.2 Force and stress 18 2.3 Stress transformation 19 2.4 Principal stresses and stress invariants 23 2.5 Differential equations of static equilibrium 26 2.6 Plane problems and biaxial stress 27 2.7 Displacement and strain 29 2.8 Principal strains, strain transformation, volumetrie

strain and deviator strain 34 2.9 Strain compatibility equations 35 2.10 Stress-strain relations 35 2.11 Cylindrical polar co-ordinates 38 2.12 Geomechanics convention for displacement, strain and stress 40 2.13 Graphical representation of biaxial Strl;SS 42 Problems 44

3 Rock mass structure 48

3.1 Introduction 48 3.2 Major types of structural features 49 3.3 Important geomechanical properties of discontinuities 53 3.4 Collecting structural data 59 3.5 Presentation of structural data 69 3.6 The hemispherical projection 71 3.7 Rock mass classification 77 Problems 84

4 Rock strength and deformability 87

4.1 Introduction 87 4.2 Concepts and definitions 88

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CONTENTS

4.3 Behaviour of isotropie rock material in uniaxial compression 89

4.4 Behaviour of isotropie rock material in multiaxial compression 101

4.5 Strength criteria for isotropie rock material 106 4.6 Strength of anisotropie rock material in triaxial

compression 116 4.7 Shear behaviour of discontinuities 118 4.8 Models of discontinuity strength and deformation 128 4.9 Behaviour of discontinuous rock masses 132 Problems 137

5 Pre-mining state of stress 141

5.1 Specitication of the pre-mining state of stress 141 5.2 Factors influencing the in situ state of stress 142 5.3 Methods of in situ stress determination 146 5.4 Presentation of in situ stress measurement results 154 5.5 Results of in situ stress measurements 157 Problems 158

6 Methods of stress analysis 162

6.1 Analytical methods for mine design 162 6.2 Principles of classical stress analysis 163 6.3 Closed-form solutions for simple excavation shapes 171 6.4 Computational methods of stress analysis 176 6.5 The boundary element method 177 6.6 The finite element method 182 6.7 The distinct element method 189 6.8 Linked computational schemes 192

7 Excavation design in massive elastic rock 194

7.1 General design methodology 194 7.2 Zone of influence of an excavation 196 7.3 Effect of planes of weakness on elastic stress

distribution 199 7.4 Excavation shape and boundary stresses 204 7.5 Delineation of zones of rock failure 209 7.6 Support and reinforcement of massive rock 212 Problems 216

8 Excavation design in stratified rock 219

8.1 Design factors 219 8.2 Rock mass response to mining 220 8.3 Roof bed deformation mechanies 222 8.4 Roof design procedure for plane strain 225

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CONTENTS

8.5 Roof design for square and rectangular excavations 230 8.6 Improved design procedures 232

9 Excavation design in jointed rock 234

9.1 Design factors 234 9.2 Identification of potential failure modes 235 9.3 Symmetrie triangular roof prism 238 9.4 Asymmetrie triangular roof prism 242 9.5 Roof stability analysis for a tetrahedral wedge 245 9.6 Pragmatic design in jointed rock 247

10 Energy, mine stability and rockbursts 251

10.1 Mechanical relevance of energy changes 251 10.2 Mining consequences of energy changes 255 10.3 Energy transmission in rock 257 10.4 Spherical cavity in a hydrostatic stress field 265 10.5 General determination of released and excess energy 270 10.6 Mine stability and rockbursts 273 10.7 Instability due to pillar crushing 275 10.8 Thin tabular excavations 280 10.9 Instability due to fault slip 283 10.10 Seismic event parameters 285

11 Rock support and reinforcement 288

11.1 Terminology 288 1l.2 Support and reinforcement principles 289 11.3 Rock-support interaction analysis 293 11.4 Pre-reinforcement 298 1l.5 Support and reinforcement design 300 11.6 Materials and techniques 314

12 Mining methods and method selection 326

12.1 Mining excavations 326 12.2 Rock mass response to stoping activity 328 12.3 Orebody properties influencing mining method 331 12.4 Underground mining methods 334 12.5 Mining method selection 347

13 Naturally supported mining methods 350

13.1 Components of a supported mine structure 350 13.2 Field observations of pillar performance 352 13.3 Tributary area analysis of pillar support 354 13.4 Design of a stope-and-pillar layout 360 13.5 Bearing capacity of roof and floor rocks 366 13.6 The Elliot Lake room-and-pillar mines 367

VII

CONTENTS

13.7 Stope-and-pillar design in irregular orebodies 13.8 Open stope-and-pillar design at Mount Charlotte 13.9 Yielding pillars Problems

14 Artificially supported mining methods

14.1 Techniques of artificial support 14.2 Backfill properties and placement 14.3 Design ofmine backfill 14.4 Cut-and-fill stoping 14.5 Backfill applications in open stoping 14.6 Reinforcement of open stope walls

15 Longwall and caving mining methods

15.1 Classification of longwall and caving mining methods 15.2 Longwall mining in hard rock 15.3 Longwall coal mining 15.4 Sublevel caving 15.5 Block caving Problems

16 Mining-induced surface subsidence

16.1 Types and effects of mining-induced subsidence 16.2 Chimney caving 16.3 Sinkholes in carbonate rock 16.4 Discontinuous subsidence associated with caving

methods of mining 16.5 Continuous subsidence due to the mining of

tabular orebodies

17 Blasting mechanics

17.1 B lasting processes in underground mining 17.2 Explosives 17.3 Elastic models of explosive-rock interaction 17.4 Phenomenology of rock breakage by explosives 17.5 Computational models of blasting 17.6 Perimeter blasting 17.7 Transient ground motion 17.8 Dynamic performance and design of underground

excavations 17.9 Evaluation of explosive and blast performance

18 Monitoring rock mass performance

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18.1 The purposes and nature of monitoring rock mass performance

371 374 377 378

380

380 382 386 388 392 396

399

399 399 404 414 425 434

438

438 440 448

449

456

466

466 466 469 471 475 476 480

484 486

491

491

CONTENTS

18.2 Monitoring systems 18.3 Examples of monitoring rock mass perfonnance

492 505

Appendix ABasie constructions using the hemispherieal projection 518

A.l Projection of a line A.2 Projection of the great circle and pole to aplane A.3 Detennination of the line of intersection of two planes A.4 Detennination of the angle between two lines in a plane A.5 Detennination of dip direction and true dip A.6 Rotation about an inclined axis

Appendix B Stresses and displacements induced by point and infinite line loads in an infinite, isotropie, elastie continuum

B.l A point load (the Kelvin equations) B.2 An infinite line load

Appendix C Calculation sequences for rock-support interaction analysis

C.1 Scope C.2 Required support line calculations C.3 Available support line calculatio]ls

Appendix 0 Limiting equilibrium analysis of progressive hangingwall caving

ix

D.l Derivation of equations D.2 Calculation sequence

Answers to problems References Index

518 518 519 520 521 522

524

524 525

525

525 526 530

533

533 537

539 542 559

Preface to the second ed ition

Since the publication of the first edition, several developments in rock mechanics have occurred which justified a comprehensive revision of the text. In the field of solid mechanics, major advances have been observed in understanding the fun­damental modes of deformation, failure and stability of rock under conditions where rock stress is high in relation to rock strength. From the point of view of excavation design practice, a capacity for computational analysis of rock stress and displace­ment is more widely distributed at mine sites than at the time of preparing the first edition. In rock engineering practice, the development and demonstration of large­sc ale ground control techniques has resulted in modification of operating conditions, particularly with respect to maintenance of large stable working spans in open exca­vations. Each of these advances has major consequences for rock mechanics practice in mining and other underground engineering operations.

The advances in solid mechanics and geo-materials science have been dominated by two developments. First, strain localisation in a frictional, dilatant solid is now recog­nised as a source of excavation and mine instability. Second, variations in displacement­dependent and velocity-dependent frictional resistance to slip are accepted as controlling mechanisms in stability of sliding of discontinuities. Rockbursts may involve both strain localisation and joint slip, suggesting mitigation of this pervasive mining problem can now be based on principles derived from the goveming mechanics. The revision has resulted in increased attention to rockburst mechanics and to mine design and operating measures which exploit the state of contemporary knowledge.

The development and deployrnent of computational methods for design in rock is illustrated by the increased consideration in the text of topics such as numerical meth­ods for support and reinforcement design, and by discussion of several case studies of numerical simulation of rock response to mining. Other applications of numerical methods of stress and displacement analysis for mine layout and design are weIl estab­lished. Nevertheless, simple analytical solutions will continue to be used in prelimi­nary assessment of design problems and to provide a basis for engineering judgement of mine rock performance. Several important solutions for zone of influence of exca­vations have been revised to provide a wider scope for confident application.

Significant improvements in ground control practice in underground mines are represented by the engineered use ofbackfill in deep-Ievel mining and in application of long, grouted steel tendons or cable bolts in open stoping. In both cases, the engin­eering practices are based on analysis of the interaction between the host rock and the support or reinforcement system. Field demonstration exercises which validate these ground control methods and the related design procedures provide an assurance of their technical soundness and practical utility.

In the course of the revision, the authors have deleted some material they con­sidered to be less rigorous than desirable in a book of this type. They have also cor­rected several errors brought to their attention by a perceptive and informed readership, for wh ich they record their gratitude. Their hope is that the current ver­sion will be subject to the same rigorous and acute attention as the first edition.

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B. H. G. B. E.T.B.

Preface to the first edition

Rock mechanics is a field of applied science which has become recognised as a coherent engineering discipline within the last two decades. It consists of a body of knowledge of the mechanical properties of rock, various techniques for the analysis of rock stress under some imposed perturbation, a set of established principles ex­pressing rock mass response to load, and a logical scheme for applying these notions and techniques to real physical problems. Some of the areas where application of rock mechanics concepts have been demonstrated to be of industrial value include surface and subsurface construction, mining and other methods of mineral recovery, geothermal energy recovery and subsurface hazardous waste isolation. In many cases, the pressures of industrial demand for rigour and precision in project or pro­cess design have led to rapid evolution of the engineering discipline, and general improvement in its basis in both the geosciences and engineering mechanics. An in­tellectual commitrnent in some outstanding research centres to the proper develop­ment of rock mechanics has now resulted in a capacity for engineering design in rock not conceivable two decades ago.

Mining engineering is an obvious candidate for application of rock mechanics principles in the design of excavations generated by mineral extraction. A primary concern in mining operations, either on surface or underground, is loosely termed 'ground control', i.e. control of the displacement of rock surrounding the various ex­cavations generated by, and required to service, mining activity. The particular con­cern of this text is with the rock mechanics aspects of underground mining engineering, since it is in underground mining that many of the more interesting modes of rock mass behaviour are expressed. Realisation of the maximum economic potential of a mineral deposit frequently involves loading rock beyond the state where intact behaviour can be sustained. Therefore, underground mines frequently represent ideal sites afwhich to observe the limiting behaviour of the various ele­ments of a rock mass. It should then be clear why the earliest practitioners and re­searchers in rock mechanics were actively pursuing its mining engineering applications.

Underground mining continues to provide strong motivation for the advancement of rock mechanics. Mining activity is now conducted at depths greater than 4000 m, although not without some difficulty. At shallower depths, single mine excavations greater than 350 m in height, and exceeding 500 000 m3 in volume, are not uncom­mon. In any engineering terms, these are significant accomplishments, and the natu­ral pressure is to build on them. Such advances are undoubtedly possible. Both the knowledge of the mechanical properties of rock, and the analytical capacity to pre­dict rock mass performance under load, improve as observations are made of in-situ rock behaviour, and as analytical techniques evolve and are verified by practical ap­plication.

This text is intended to address many of the rock mechanics issues arising in underground mining engineering, although it is not exclusively a text on mining applications. It consists of four general sections, viz. general engineering mechanics relevant to rock mechanics; mechanical properties of rock and rock masses;

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PREFACE TO THE FIRST EDITION

underground design and design of various types and associated components of a mine structure; and several topics related to rock mechanics practice. The material presented is an elaboration of a course of lectures originally prepared for undergrad­uate rock mechanics instruction for mining students at the Royal School of Mines, Imperial College, London. Some subsequent additions to this material, made by one of the authors while at the University of Minnesota, are also included. The authors believe that the material is suitable for presentation to senior undergraduate students in both mining and geological engineering, and for the initial stages of post-graduate instruction in these fields. It should also be of interest to students of other aspects of geomechanics, notably civil engineers involved in subsurface construction, and en­gineering geologists interested in mining and underground excavation design. Prac­tising mining engineers and rock mechanics engineers involved in mine design may use the book profitably for review purposes, or perhaps to obtain an appreciation of the current state of engineering knowledge in their area of specialisation.

Throughout the text, and particularly in those sections concerned with excavation design and design of amine structure, reference is made to computational methods for the analysis of stress and displacement in a rock mass. The use of various compu­tation schemes, such as the boundary element, finite element imd distinct element methods, is now firmly and properly embedded in rock mechanics practice. The authors have not listed computer codes in this book. They are now available in most program libraries, and are transported more appropriately on magnetic storage media than as listings in text.

The preparation of this book was assisted considerably by the authors' colleagues and friends. Part of the contribution of Dr John Bray ofImperial College is evident in the text, and the authors record their gratitude for his many other informal contribu­tions made over aperiod of several years. Dr John Hudson of Imperial College and Gavin Ferguson of Seltrust Engineering Ltd read the text painstakingly and made many valuable suggestions for improvement. Professor Charles Fairhurst supported preparation activities at the University of Minnesota, for which one of the authors is personally grateful. The authors are also indebted to Moira Knox, Carol Makkyla and Colleen Brady for their work on the typescript, to Rosie and Steve Priest who pre­pared the index, and to Laurie Wilson for undertaking a range of tedious, but import­ant, chores. The authors are also pleased to be able to record their appreciation of the encouragement and understanding accorded them by the publisher's representatives, Roger Jones, who persuaded them to write the book, and Geoffrey Palmer, who ex­pertly supervised its production. Finally, they also thank the many individuals and organisations who freely gave permission to reproduce published material.

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B. H. G. B. E. T. B.

Acknowledgements

We would like to thank the following people and organisations for permission to re­produce previously published material:

Mount Isa Mines Limited (Cover photograph); King Island Scheelite and CSIRO Division of Geomechanics (Frontispiece); Soc. Min. Met. & Expl. (Figures 1.4 & 5, 13.16, 19,20 & 21, 15.13, 15, 16,27,28,29 & 32, 16.10, Tables 12.1 & 15.2); Canadian Inst. Min. Metall. (Figures 13.17 & 18); G.V. Borquez (Figure 1.4); J. C. Folinsbee (Figure 1.5); M. H. de Freitas (Figure 3.2); Elsevier (Figures 3.3, 4.8); Goldfields of S. Afr. (Figure 3.5); Pergamon Press (Figures 3.7, 8, 9, 10, 11, 12, 16, 17 & 21, 4.11, 12, 13, 19,21,43,46 and 50, 11.1, 15.19,21,22, 17.3); Z. T. Bieniawski (Figure 3.30, Tables 3.5 & 6); Instn Min. Metall. (Figures 3.31, 4.17, 8.8 & 9,11.13 & 30,16.13 & 14, 18.5,6,7,8 & 19, A3.5, Tables 3.8 & 9,11.2); ELE Int. (Figure 4.14). Figure 4.20 reprinted from Q. Colo. School Mines, 54(3), 177-99 (1959), L. H. Robinson, by permission of the Colorado School of Mines. Figure 4.31b--d reproduced from 1. Engng Inaustry, 89, 62-73 (1967) by permission of R. McLamore, K. E. Gray and Am. Soc. Mech. Engrs. Australasian Inst. Min. Metall. (Figures 4.34 & 36); Thomas Telford (Figures 4.35 & 37); R. E. Goodman (Figures 4.42, 43 & 45); N. R. Barton (Figure 4.46); E. Hoek (Figure 4.48); J.R. Enever (Figure 5.8); Association of Engineering Geologists (Figure 8.6); G. E. Blight and Am. Soc. Civ. Engrs (Figures 1O.5c and d, 14.3a); N. G. W. Cook (Figure 10.24); J. R. Rice and Birkhauser Verlag (Figure 10.25); A. McGarr and South Afr. Inst. Min. & Metall. (Figure 10.26); Elsevier (Figures 11.17, 18, 19,20 and 22, 14.11); W. D. Ortlepp (Figure 11.32); Chamber of Mines of South Africa (Figure 11.33); H. O. Harnrin and Soc. Min. Metall. & Expl. (Figures 12.1,2,5,6, 7, 8, 9, 10, 11 & 12); Dravo Corp (Figure 12.3); H. Wagner and South Afr. Inst. Min. & Metall. (Figure 13.9); D. G. F. Hedley (Figures 13.15, 17, 18, 19 & 20); LA. Goddard (Figure 13.21); M. F. Lee (Figures 13.22 & 23, 18.19); G. Swan (Figures 14.3b & 14.4); v. A. Koskela (Figure 14.9); P. Lappalainen (Figure 14.10); J. A. Ryder (Figure 15.1 & 2); M.D.G. Salamon (Figures 15.4, 18.13 & 14, Table 18.2); Instn Min. Engrs (Figures 15.5 & 9, 16.24); B.N. Whittaker (Figures 15.5,9 & 12); National Coal Board and A. H. Wilson (Figures 15.6 & 7, Table 15.1); National Coal Board (Figures 15.8,16.17, 18,19,20 & 23); L. J. Thomas (Figures 15.10 & 11); Figure 15.25 reproduced from Storage in Excavated Rock Caverns, (ed. M. Bergman) by peimission of Pergamon Press. Figure 15.30 is reproduced from Proc. 4th CanadianRock Mech. symp. (1968) by permission of the Minister of Supply and Services Canada. Mining Journal and G. A. Ferguson (Figure 15.31); University of Toronto Press (Figures 4.48, 16.8); D. S. Berry (Figure 16.21); C. K. McKenzie and Julius Kruttschnitt Mineral Research Centre (Figures 17.14, 15 & 16); C. K. McKenzie (Figure 17.17); K. Kovari and A. A. Balkema, Rotterdam (Figure 18.4); P. Londe and Am. Soc. Civ. Engrs (Figure 18.5); Glotzl Gesellschaft fur Baumesstechnik mbH (Figure 18.6); Am. Min. Congr. (Figure 18.9); H. F. Bock (Figure 18.18); D. H. Laubscher (Tables 3.8 and 3.9, 3.31, 11.3, 12.1, 15.2); Mining Journal (Table 11.4); E. G. Thomas and the Australian Mineral Foundation (Tables 14.1 & 2); A. A. Balkema (Tables 3.5 and 3.6, 5.8, 13.22 & 23, 14.3b, 4, 9 & 10, 15.1 & 2, 17.17)

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