theory and practice of foundation design (364-427) (1)

SOILM AND F5(j}!ANICS DATIONS

FOR A

CA

USE

SOIL MECHANICS AND FOUNDATIONS

MUNI BUDHU

JOHN WilEY & SONS, INC. "lew York / Chichestcr IlVeillheim I Brisballe I 5111gopore I TorOIlfO

Editor Wayne Anderson Marketing Manager Katherine Hepburn Semor Production Manager Lucille Buonocore Production Editor Leslie Surovick Cover Designer Lynn Rogan Illustration Editor Sigmund Malinowski Illustration Studio Radianl Illustration II:- Design Cover Photo CORBISlRogu Wood

Th is book was set in 10112 Times Ten by UG I GGS Informati pnnted and bound by RR DonnelJey/Wiliard . The cover was p Corporation.

This book is printed on acid-free paper. e The paper in this book was manufactu red by a include sustained yield harvesting of tts timbedan principles ensure that the numbers of tf'J''t';'

FPREFACE

Professor Hilary 1. Inyang, University of Massachusetts-Lowell Professor Derek Morris, Texas A&M University Professor Cyrus Aryani, California State University

111181 v

FO

vi PREFACE

Professor Shobha K. Bhatia, Syracuse University Major Richard L. Shelton, United States Military Academy Professor Colby C. Swan, University of Iowa Professor Panos I(jousis, University of Arizona Professor Carlos Santamarina, Georgia Institute of Tech Dr. William Isenhower, Ensoft, Inc.

Mr. Wayne Anderson and his staff, and Leslie S Sons were particularly helpful in getting this book done. to my wife and children who have contributed 1!mifican this book.

FO

NOTES for Instructors

I would like to present some guidance to assist you i graduate geotechnical engineering courses.

DESCRIPTION OF CHAPTERS

tlement is interpreted and the parameter required to determine time rate of settlement. The oedometer test is described and procedures to determine the various parameters for settlement calculations are presented.

Chapter 5 deals with the shear strength of soils and the tests (laboratory and field) required for its determination. The Mohr-Coulomb failure criterion is discussed using the student 's background in strength of materials (Mohr 's circle) and in statics (dry friction). Soils are treated as a dilatant-frictional material

vii

viii NOTES FOR INSTRUCTORS

rather than the conventional cohesive-fric tional materifll. Typical stress- strai n responses of sand and clay are presented and discussed. The implications of drained and undrained conditions on the shear strength of soil s are discussed. Laboratory and field tests to determine the shear strength of soils are described.

Chap ter 6 deviates from traditional undergraduate textboqk-topics by deal-ing with soil consolidation and strengt h as separate issues. I~'i. his chap\er, de-formation and strength are integrated within the framework 0 britical stilte soil mechanics using a simplifi ed version of the modified c m ay d!!!#fhe em-phasis is on understanding the mechanical behavior 0 ~ls ra her than present ing the mathematical form ul ation of critical state soil mec a~cs M the modified cam-clay model. The amoun t of mathematics is ke~o the ~!pjmum needed for un derstand ing and clarification of im portant co ceptS!--P rojection geomet ry is used to illustrate the different responses 0 soils wh the "'loading changes under drained and undrained loading. Althoug: thisap e eals with a simplification and an idealization of real soils, the real neftt i a simple framework, which allows the stlldent to think abou possJbte i sponses if can itions change from those originally conceive sis usuau n e gineeri ng ~tice It also allows them to bette r interpret soil test re ults. ,I

Chapter 7 deals wi bearing cae.aci1Y and seJ.t'ement of footings. Here bearing capacity and seuleme.pl are tteated as a in~e tO~iC. n the design of foundations. the geotechnical ngineer must be sa ' sfied at th earing capaci ty is sufficient and ~ttlem nl at working load is lera . In deed. for most shallow foo tings. it is settlf lT].ent that gover -Iii 1 n. ot bearing capaci ty. Limit equilibrium analysis is int roduced to illu trate th e method that has been used to fi n the pop~tieari ng cap}' Ity eq u~ion.s..and LO make use of the SIll-dent's ba'tgr nd in statics (equ ili rium) to mtrod uce a simple but powerful analytical t~o . Three sets of bearin capacity equations (Terzaghi as modified by Vesic, M~yerhof. and Sk pton) , lh inft uence of groundwater level , and

~ntric load't on bearing apacity are discussed. These equations are simpli fi ed b breaking them down 1m twi> catego ries-one relating to dra ined conditions. the o r er to undra ipe~ condi ons~laS{ic. one-dimensional consolidation. and a Sk: ~pton and Bj erQ!...nLs m thod'of determin ing settlement are presented . The elastic methodA~ findingSe-tt ement is based on work done by Gazettas (1985), ~ who descri1)ed p blems a ociated with the Janbu, Bjerrum , and Kj aernali (1956) m 1\od that conventionally quoted in textbooks. P ile fo dalio are described and discussed in Chapter 8. Methods for finding beari ng ~pacity and sett le ment of single and group piles are presented. Chapter 9 is about [wo-dimensional steady sta te flow th rough soils. Solu-

tions to two-dimensional flow using flow nets and the finite difference technique' are discussed . Emphases are placed on seepage. pore wate r pressure, and insta-bility. This chapter normally comes early in most current textbooks. The reason for placing this chapter here is because two-di mensional flow influences the sta-bility of earth structures (retaining walls and slopes), discussion of wh ich follows in Chapters 10 and 11. A student would then be able to make the practica l connection of two-di mensional flow and stability of geotechn ical systems readi ly.

Lateral earth pressures and their use in the analysis of earth retaining sys-tems and excavat ions are presen ted in Chapter 10. Gravit)' and flexible re laining walls. in addition \0 reinforced soil walls, arc discussed. Guidance is provided as to what strength parameters to use in d rained and undrained cond itions.

FNOTES FOR INSTRUCTORS ix

Chapter 11 is about slope stability. Here stability conditions are described based on drained or undrained conditions.

An appendix (Appendix A) allows easy access to frequently used typical soil parameters and correlations.

CHAPTER LAYOUT

dvent 0 ersonal computers, learning has become more visual. Some , studies hav epo[ ed that visual images have improved learning by as much as 400% . This tex-t ok is accompanied by a CD ROM that contains text, interactive animation, images, a glossary, notation, quizzes, notepads, and interactive prob-lem solving. It should appeal, particularly, to visual learners.

A quiz is included in appropriate chapters on the CD ROM to elicit per-formance and provide feedback on key concepts. Interactive problem solving is used to help students solve problems similar to the problem-solving exercises. When an interactive problem is repeated, new values are automatically gener-ated. Sounds are used to a limited extent. The CD ROM contains a virtual soils laboratory for the students to conduct geotechnical tests. These virtual tests are not intended to replace the necessary hands-on experience in a soil laboratory. Rather , they complement the hands-on experience, prepare the students for the real experience, test relevant prior knowledge of basic concepts for the interpre-

FO

X NOTES FOR INSTRUCTORS

tation of the test results, guide them through the evaluation and interpretation of the results, allow them to conduct tests that cannot otherwise be done during laboratory sessions, and allow them to use the results of their tests in practical applications.

ABET REQUIREMENTS

The United States Accreditation Board for Engi (ABET) has introduced new criteria for accreditation p this book has the author's judgment on how it satisfies ence (ES) and engineering design (ED) crit mended percentages allocated to ES and

COURSE MATERIAL

FO

NOTES for Students and Instructors

PURPOSES OF THIS BOOK

echanics and its appli-

technical engineering. The goals of this te

as follows:

o characterize soil properties,

cs to analyze and design simple geo-

ng this textbook you should be able to:

Descr be soi and determine their physical characteristics such as, grain size, wate~ ontent, and void ratio

Classify soils Determine compaction of soils Understand the importance of soil investigations and be able to plan a soil

investigation Understand the concept of effective stress Determine total and effective stresses and pore water pressures Determine soil permeability Determine how surface stresses are distributed within a soil mass Specify, conduct, and interpret soil tests to characterize soils

xi

FO

xii NOTES FOR STUDENTS AND INSTRUCTORS

Determine soil strength and deformation parameters from soil tests, for example, Young's modulus, friction angle and undrained shear strength

Discriminate between "drained" and "undrained" conditions Understand the effects of seepage on the stability of strucrure

Estimate the bearing capacity and settlement of structures unded on soils Analyze and design simple foundations

Determine the stability of earth structures, for examFi et ' in~ slopes

Distribution of Main Topi

Foundation and earth structures

Description 6 7 8 9 10

0 0 0 0 0

0

0 0 0 0 0 0 0

0 0 0 0 0 0 0

0 0

Stresses in soils D 0 0 0 0 0 0 0

Drained and undrained conditions U 0 0 0

Settlement and deformation C 0 0 O .

Shear strength T 0 0 0 0

Seepage 0

Bearing capacity and settlement of 0 0 foundations Stability of earth structures N 0

11

0

0

0

0

0

0

0

NOTES FOR STUDENTS AND INSTRUCTORS xiii

ASSESSMENT

You will be assessed aD how well you absorb and use the fundamentals of soil mechanics. Three areas of assessment are incorporated in the Exercise sections of this textbook. The first area called "Theory" is intended fog y-ou to demon strate your knowledge of the theory and extend it to uncovec1!Cwt elat ionships. The questions under "Theory" will help you later in your cf. ~eec to address un-conven tional issues using fundamental principles. The selon a cea ca~d " Prob-lem Solving" requires you to apply the fundamenta prin i les and--concepts to a wide variety of problems. These problems willtes our un erstandi ng and use of the fundamental principles and concep ts. The thirtl ea caUl d " Practical" is intended to create practical scenarios for you to use "a t 'o.n~y the subject matter in the specific chapter but prior mate rial/ i"h ya.u "havl' encountered. These problems try to mimic some aspects of r~tuatl \fls and give you a feel for how the materials you have studied so far t"~ be pplied 'o practice. Communications are. at leas!. as important as the technic detail~ 1n many 0 ese "Pract ica l" prob lems you are placed in a sit atlOn I co iv' ce stakeholders f you r technical competence. A quiz (multip) choice) on each chapter' dud~d in the CD \0 tcst you r general knowledge of t subj ct matter in that chapter: h,e questions on the quiz are re lated to the sec Ion Question.!J6 Guide Your eading,"' in-cluded in each chapter. ~ ~

SUGGESTIONS F R PRO.B EM SOL\lING~

,

Enginee ring is, ~ ,about propl em 5 "'I~n ~r most engineering problems, there i~~ nique method or procedure for fi nding solutions. Often, there is no unique .s~u Ion to an engineering~;~bl~~A suggested problem-solving pro-cedure is ~t1ined be low. ~

1. Rea/ the prObleJ.1l...ca ref~UY; ate or wrile down what is given and what you ~ required to find.

2. Draw clear diagrams or e tches wherever possible. 3. Devise trategy tOtn the solution. De termine what principles, concepts,

and.rqua tl ns a e needed to solve the problem. 4. p.lrfocm calcuJations making sure that you are using the correct units. 5. Chcc 'hethl r your results are reasonable.

The units of measurement used in this textbook follow the SI system. En-gineering calculations are approximations and do not result in exact numbe rs. All cal

Fxiv NOTES FOR STUDENTS AND INSTRUCTORS

provides animations, interactive problem solving, quizzes, virtual laboratories, special modules (for example, a computer program to find stresses within a soil) , spreadsheets, videos, a notepad, a glossary, a list of notations, and a calculator.

CD icons in the textbook have Inset numbers that are intend1...d to alert you to sp~cial features present on the CD-ROM. The numbers hv~ following meamng:

2. Virtual lab 1. Interactive animation ~

3. Interactive problem solving 4. Spreadsheet 5. Video 6. Computer program utility

PRESENTATION

normally given any projects, the

SHEAR STRENGTH OF SOILS

Resistance to shear forces Coulomb's law Now, let us start our study of soil mechanics and foundations.

FO

CONTENTS

CHAPTER 1 INTRODUCTION TO SOIL MECHANICS A

1.0 Introduction 1 1.1 Marvels of Civil Engineering-The Hi :d 1.2 Geotechnical Lessons from Failu es 4

CHAPTER 2 PHYSICAL CHARACTE INVESTIGATIONS 6

2.0 2.1 2.2 2.3

Introduction

22 oarse-Grained Soils 22

t ation of Soils Based on Particle Size 25 2.6 2.7

29 31

Fall Cone Method to Determine Liquid and Plastic Limits 32 2.7.4 Shrinkage Limit 33

2.8 Soil Classification Schemes 36 2.9 Engineering Use Chart 39 2.10 One-Dimensional Flow of Water Through Soils 42

2.10.1 Groundwater 42 2.10.2 Head 42 2.10.3 Darcy's Law 44 2.10.4 Empirical Relationships for k 45 2.10.5 Flow Parallel to Soil Layers 49 2.10.6 Flow Normal to Soil Layers 50

xv

FO

xvi CONTENTS

2.11

2.12

2.13

2.14

Dry Unit Weight-Water Content Relationship 2.12.1 Basic Concept 58 2.12.2 Proctor Compaction Test 58 2.12.3 Zero Air Voids Curve 59 2.12.4 Importance of Compaction 60 2.12.5 Field Compaction 60 2.12.6 Compaction Quality Control

2.12.2 2.13.3 2.13.4 2.13.5 2.13.6 2.13.7 2.13.8

2.12.6.1 Sand Cone 61 2.12.6.2 Balloon Test

6

Exercises

51

0 3. 3. 3.3 ~ 81 3.3.3 hear Stresses and Shear Strains 83

3.4 Idealized Stress-Strain Response and Yielding 84 3.4.1 Material Responses to Normal Loading and Unloading 84 3.4.2 Material Response to Shear Forces 86 3.4.3 Yield Surface 87

3.5 Hooke 's Law 88 3.5.1 General State of Stress 88 3.5.2 Principal Stresses 89 3.5.3 Displacements from Strains and Forces from Stresses 89

3.6 Plane Strain and Axial Symmetric Conditions 90 3.6.1 Plane Strain 90 3.6.2 Axisymmetric Condition 91

3.7 Anisotropic Elastic States 94

FO

CONTENTS xvii

3.8 Stress and Strain States 96 3.8.1 Mohr's Circle for Stress States 96 3.8.2 Mohr's Circle for Strain States 98

3.9 Total and Effective Stresses 100 3.9.1 The Principle of Effective Stress 100 3.9.2 Effective Stresses Due to Geostatic Stress Fie ' s 02 3.9.3 Effects of Capillarity 103 3.9.4 Effects of Seepage 104

3.10 Lateral Earth Pressure at Rest 109 3.11 Stresses in Soil from Surface Loads 110

3.11.1 Point Load 111

3.12

3.13

3.11.2 Line Load 112 3.11.3 3.11.4 3.11.5 3.11.6 3.11.7 3.11.8

4.0 ',on 141 4.1 Definitions of Key Terms 142 4.2 Questions to Guide Your Reading 143 4.3 Basic Concepts 144

4.3.1 Instantaneous Load 145

133

4.3.2 Consolidation Under a Constant Load-Primary Consolidation 145

4.3.3 Secondary Compression 146 4.3.4 Drainage Path 146 4.3.5 Rate of Consolidation 147 4.3.6 Effective Stress Changes 147 4.3.7 Void Ratio and Settlement Changes Under a Constant Load

148

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xviii CONTENTS

4.3.8 4.3.9 4.3 .10 4.3.11

Effects of Vertical Stresses on Primary Consolidation Primary Consolidation Parameters 149 Effects of Loading History 150 Overconsolidation Ratio 151

4.3.12 Possible and Impossible Consolidation Soil States 4.4 Calculation of Primary Consolidation Settlement 152

148

4.4.1 Effects of Unloading/Reloading of a Soil Samp e Taken am

4.5

4.6 4.7

the Field 152 4.4.2 Primary Consolidation Settlement of

Fine-Grained Soils 153 4.4.3 Primary Consolidation Settlement of 0 e

4.4.4 4.4.5

4.5.3

Grained Soils 153

173

~ O De rrnination of the Secondary Compression Index 79 ~ 4.8 R 1"a . nship Between Laboratory and Field Consolidation 182 4.9 Typica-:l al~J of Consolidation Settlement Parameters and Empirical ~ Relatio~ps 183

4.10 Sand Drains 184 4.11 Lateral Earth Pressure at Rest Due to Overconsolidation 188 4.12 Summary 188 Practical Examples 189 Exercises 195

CHAPTER 5 SHEAR STRENGTH OF SalLS 199

5.0 Introduction 199 5.1 Definitions of Key Terms 200

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CONTENTS xix

5.2 Questions to Guide Your Reading 200 5.3 Typical Response of Soils to Shearing Forces 201

5.3.1 Effects of Increasing the Normal Effective Stress 203 5.3.2 Effects of Overconsolidation Ratio 205 5.3.3 Cemented Soils 206

5.4 Simple Model for the Shear Strength of Soils Using 206

5.5 Interpretation of the Shear Strength of Soils 5.6 Mohr-Coulomb Failure Criterion 213 5.7 Undrained and Drained Shear Strength 2 5.8 Laboratory Tests to Determine Shear Streng

5.8.1 Shear Box or Direct Shear ' 21 5.8.2 5.8.3 5.8.4 5.8.5 5.8.6

5.9 Pore Water Pres sur 5.10

5.11

229

240

249

252

MODEL TO INTERPRET SOIL BEHAVIOR

6.0 6.1 Definitions of Key Terms 263 6.2 Questions to Guide Your Reading 264 6.3 Basic Concepts 264

6.3.1 Parameter Mapping 264 6.3.2 Failure Surface 265 6.3.3 Soil Yielding 266 6.3.4 Prediction of the Behavior of Normally Consolidated and

Lightly OverconsoJidated Soils Under Drained Conditions 267

6.3.5 Prediction of the Behavior of Normally Consolidated and Lightly Overconsolidated Soils Under Undrained Condition 269

XX CONTENTS

6.4

6.5

6.6 6.7

6.8

6.9 6.10

7.0 7.1 7.2 7.3

6.3.6 Prediction of the Behavior of HeaVIly Overconsolldated Soils 270

6.3.7 Critical State Boundary 271 6.3.8 Volume Changes and Excess Pore Water Pressures 271 6.3.9 Effects of Effective Stress Paths 272 Elements of the Critical State Model 273 6.4.1 Yield Surface 273 6.4.2 Critical State Parameters 273

6.4.2.1 Failure Line in (q, p') Spa 6.4.2.2 Failure Line in (q, e) Space.

Failure Stresses from the Critical Sta le Model 6.5.1 Drained Triaxial Test 277 6.5.2 Undrained Triaxial Test 1,9 Soi l Stiffness 287 Strains from the Cntical Stat 6.7. 1 Volumetric Strains 6.7.2 Shear Strains 91 Calculated Stress-51 81 ResponfF 296 6.8.1 Drained Compr~ '[tits 296 6.8.2 Undrain Compr n Tests 2f>7 K .. -Consoli ared i\ 'nse 304

27'3 275

Relatio~i Between Simple Soil Tests, ~itic S e Parameters, and Soil STrength 307

6.10. 1 ndrained Shear Strengt h6f'(~l'ays~ar-f e Liquid and Plastic bimi~ 307 .'-' "

FO

CONTENTS xxi

7.7 Allowable Bearing Capacity and Factor of Safety 329 7.7.1 Calculation of Allowable Bearing Capacity 329

7.8 7.9 7.10 7.11 7.12

7.13

7.7.2 Building Codes Bearing Capacity Values 330 Effects of Groundwater 330 Eccentric Loads 336 Bearing Capacity of Layered Soils 339 Settlement 340 Settlement Calculations 342 7.12.1 Immediate Settlement 343 7.12.2 Primary Consolidation Settlement Determination of Bearing Capacity and Sett e

Soils from Field Tests 350 7.13 .1

7.13.2 7.13.3

7.14 Horizontal Elastic Dis 7.15 Summary 358 Practical Examples 358 Exercises 365

CHAPTERS

8.0 8.1 8.2 8.3

8.7 8.8

1 374

8.9 Consolidation Settlement Under a Pile Group 400

oarse-Grained

8.10 Procedure to Estimate Settlement of Single and Group Piles 401 8.11 Piles Subjected to Negative Skin Friction 404 8.12 Pile-Driving Formula and Wave Equation 406 8.13 Summary 408 Practical Example 408 Exercises 411

CHAPTER 9 TWO-DIMENSIONAL FLOW OF WATER THROUGH SOILS 415

9.0 Introduction 415 9.1 Definitions of Key Terms 416

FO

xxii CONTENTS

9.2 9.3 9.4

9.S

Questions to Guide Your Reading 416 Two-Dimensional Flow of Water Through Porous Media Flow Net Sketching 419 9.4.1 Criteria for Sketching Flow Nets 419 9.4.2 Flow Net for Isotropic Soils 420 9.4.3 Anisotropic Soil 421 Interpretation of Flow Net 422 9.5.1 Flow Rate 422 9.5.2 Hydraulic Gradient 423 9.5.3 Static Liquefaction, Heaving, Boiling, 9.5.4 Critical Hydraulic Gradient 4 3 9.5.5 Pore Water Pressure Distribu(t ----.. ,-9.5.6 Uplift Forces 424

417

423

9.6 Finite Difference Solution for 'D 429 9.7 Flow Through Earth Dams 43 9.8 Summary 440 Practical Example 440 Exercises 442

CHAPTER 10

10.0 10.1 Definiti 10.2 10.3 10.4 10.5

fir Total Stress Analysis 462 art Pressures to Retaining Walls 465

nd Modes of Failure 467

10.10

10.11 Braced Excavation 496 10.12 Mechanical Stabilized Earth Walls 500

10.12.1 Basic Concepts 500

484

472

10.12.2 Stability of Mechanjcal Stabilized Earth Walls 502

482

FO

10.13 Summary 510 Practical Examples 510 Exercises 516

CHAPTER 11 SLOPE STABILITY 522

11.0 Introduction 522 11.1 Definitions of Key Terms 523 1l.2 Questions to Guide Your Reading 523

~ P.

11.3 Some Types of Slope Failure 524 11.4 Some Causes of Slope Failure 525

11.5 11 .6 11 .7 11.8

1l.4.1 Erosion 525 11.4.2 Rainfall 525 1l.4.3 Earthquakes 525 11.4.4 Geological Features 1l.4.5 External Loadin 11.4.6

11.4.7

550

551

CONTENTS xxiii

~APPENDIXB DISTRIBUTION OF SURFACE STRESSES WITHIN FINITE SOIL LAYERS 562

APPENDIXC LATERAL EARTH PRESSURE COEFFICIENTS (KERISEL AND ABSI, 1970) 566

ANSWERS TO SELECTED PROBLEMS 571

REFERENCES 573

INDEX 578

FNotation

Note: A prime (') after a notation for stress denotes effecti~ stress.

xxiv

A B Co

CC CSM D Df Dr

G

Area Width Cohesion Compression index Recompression index Horizontal coefficient of

consolidation

Critic Diam

Ending bearing stress Skin friction Factor of safety Mobilization factor for ct> Mobilization factor for 5" Shear modulus Specific gravity Pressure head Elevation head Head Height

o

o

Hydra cen ctivityor coefficient a ~eability ctive lateral ear

FO

5 51 5PT T

u

u

UC URL

v

w .. z ex

Temperature correction factor

Resultant lateral force Overconsolidation ratio with

respect to stress invariants Undrained shear strength Degree of saturation Sensitivity Standard penetration test Sliding force or resistance Time factor Pore water pressure Average degree of

consolidation Uniformity coefficient Unloading/reloading 1 Velocity

Dilation angle Slope angle Adhesion factor Skin friction coefficient for

drained condition

I:

Psc

cr

T

NOTATION XXV

Deflection or settlement Normal strain Volumetric strain Deviatoric stil'ain

Wall friction coefficient Poisson's ratio Elastic settlement Primary consolidation Secondary consolidation

settlement Normal stress Shear stress Critical state shear strength Shear strength at failure Peak shear strength Residual shear strength Velocity potential Rotation of principal plane

to the horizontal Plastification angle for piles Stream potential

FOR A

CADE

MIC

USE O

NLY

CHAPTER 1 INTRODUCTION TO SOIL MECHANICS AND FOUNDATIONS

1.0 INTRODUCTION Soil is the oldest and most cOIllp,le ' ngine ~ateri a1. o~anceslOrs used soils as construct ion material to%uild burial s es, fl ood prolt ctio ,and shellers. Western civilization credits tHe omans {or recogn izing the-imp~tance of soils in the stability of structures. Roma enjinee rs. espec alJy VhruviUs 0 served du ri ng the reign of Empt'fOr-A ugust In the first ce ury B.C pai great atten-tion to soil types (s nd, gr v';' e t;")and to the esign and co truction of solid founda tions. The as no tieore ical basis for design; ex rience from trial and error was relied upon. ,, ___ _

Coulomb tt 773) is credited as the iirst ftC rson to use mechanics to solve soil problems. H, as a/fllember of ~nch'~al Engineers, who were in-te rested rOlecting old fortresses that fen asHy from cannon fi re. To protect the (ortre es'fr~rtillery attack, loping maf scs of soil were placed in front of them (Fig..l). The enemy had to tu LbeMw the soi l mass and the fortress to attack. Of c rse, the ene then became an easy target. The mass of soil applies a ateral force to the fa s ;"at'!:cUld cause it to topple ove r or could cause it tCi:llifle--away from ~ sod ass. ulomb attempted to determine the lateral

ree so that he coifld evaluate th sta bi lity of the fortress. He postulated that a wedge of soil AB Fig. 1 would fa il along a slip plane Be and [his wedge wou ld push tlie II out or overtopple it as it moves down the slip plane.

Mo t'meot 0 the edge along the slip plane would occu r only if the soil resistan e ~ng the edge were overcome. Coulomb assumed that the soil re-sista nce is pro ided by friction between the particles and the problem became one of a wedge s wing on a rough (frictional) plane. which you may have analyzed in your physics or mechanics course. Cou lomb has tacitly defined a fail ure cri-lerion for soils. Today, Coulomb's failure criterion and method of analysis still preva il.

From the ea rly 20th century. the rapid growth of cities. industry, and com-merce required a myriad of building systems: for example, skyscrapers, large publ ic build ings. dams fo r electric power generation and reservoirs for water supply and irrigation. lUnnels. roads and railroads, pon and harbor facilities, bridges, airpo rts and runways, mining activities, hospita ls, sanitation systems, drainage systems, and towers for communication systems. These bui lding systems requ ire stable and economic fo undations and new questions about soils were asked. For example, what is the state of st ress in a soi l mass, how can one design safe and economic foundations, how much wou ld a bu ilding settle, and what is

1

FO

2 CHAPTER 1 INTRODUCTION TO SOIL MECHANICS AND FOUNDATIONS

A

Soil mass for protecti on of the fortress

Unprotected fortress that was felled easily by cannon fire

Slip plane

FIGURE 1.1 Unprotected and protected fortress .

1.1 MARVELS OF CIVIL ENGINEERING-THE HIDDEN TRUTH

ontinue to ask these v confronted us. Some of

The work that geotechnical engineers do is often invisible once construction is completed . For example, four marvelous structures-the Sears Tower (Fig. 1.2), the Empire State Building (Fig. 1.3), the Taj Mahal (Fig. 1.4), and the Hoover

FOR

1.1 MARVELS OF CIVIL ENGINEERING-THE HIDDEN TRUTH 3

FIGURE 1.4 Taj Mahal. ( Will & Deni Mclntyre/Photo Researchers.)

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4 CHAPTER 1 INTRODUCTION TO SOil MECHANICS AND FOUNDATIONS

1.2

r.e-alQ>-\?fJ;~eG la ~n~ron, U.S. Department of

F~OM FAILURES IS;. &t uctures that , e foun eel earth rely on our ability to design safe and r CQflomic founda-Gons. Becml e f the natural vagaries of soils, failures do occur. . orne failures hav bee ca strophic and caused severe damage to lives and properties thers hav be n insidious. Failures occur because of inadequate site and soil inves . ations unforeseen soil and water conditions; natural hazards; poor engineering n:} sis, design, construction, and quality control; postconstruc-tion activities; and usage outside the design conditions. When failures are inves-tigated thoroughly, we obtain lessons and information that will guide us to prevent similar types of failure in the future . Some types of failure caused by natural hazards (earthquakes, hurricanes, etc.) are difficult to prevent and our efforts must be directed toward solutions that mitigate damages to lives and properties.

One of the earliest failures that was investigated and contributed to our knowledge of soil behavior is the failure of the Transcona Grain Elevator in 1913 (Fig. 1.6). Within 24 hours after loading the grain elevator at a rate of about 1 m of grain height per day, the bin house began to tilt and settle. Fortunately, the structural damage was minimal and the bin house was later restored . No borings were done to identify the soils and to obtain information on their strength.

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1.2 GEOTECHNICAL LESSONS FROM FAILURES 5

more to the development of this science than is generally recognized ." We have come a long way in understanding soil behavior since its father-

hood by Terzaghi in 1925. We continue to learn more daily though research on and experience from failures and your contribution to understanding soil behav-ior is needed. Join me on a journey of learning the fundamentals of soil mechanics and its applications to practical problems so that we can avoid failures or, at least, reduce the probability of their occurrence.

CHAPTER 2 -------------------------, PHYSICAL CHARACTERISTICS OF SOILS AND SOIL INVESTIGATIONS

) ES ED 90 10

2.0 INTRODUCTION

6

The purpose of this chapter is to inLt u ~ou 115. You will learn some basic descriptions of sOLis and some fundamen,lal p.hysical soi l oper(ies that you should retain for fu ture use ;n this [ l(t a~dj,in geotechnical engmee g ractice. Soils. derived from the weathering of y, are \'ery cCf1 plex materia and va ry widely. There is no certain . ha a so I will have th arne pro rl ies within a few centimeters of its curre L at.i,9n. ,

One of the primary tasKS of a geotec hnical eng' eer a collect, classify, and investig'l le ttie PhYSiCa~1 pr Denies of sgil this apter, we will deal wit h descript ions of soil'S tests t dete rmine the J2.hYS~cal propert ies of soils, soil clas-sification, one-dime io flow of w er thrOugh o s, and methods of soi l in-vest igation ~all:t soils lnvestigati ns are c ndu ted only all a fraction of n proposed sit ea it would be prohl itively $.Xpensive to conduct an extensive Investigation f a whole sile. e then ha~ make est imates and judgmcnfs

sed on infor alion from lim 'ted set of observations and field and labora tory les \:lata.

n-.engineering, ~isasse bl omplex systems into parts and then study each p art and its re ationship to e wh ole. We will do the same for soils. Soils will,!)e dismantled in to th ree st ituents and we will exa mine how the propor-ions of eachl onstl ent s;.hllJ cterize soils. When you complete this chapter, you

"1' ... " should be ' Ie to: .........

Describe and classify soils Determme particle size distribution in a soil mass Determine the proportions of the main constituents in a soil Determine index properties of soils Detennine the rate of flow of water through soils Determine maximum dry unit weight and optimum water conlent

Plan a soi l investiga tion

Sample Practical Situation A highway is pl"Oposed to link the city of Nos-cu t to the village of Windsor Fores!. The highway rou te will pass through a terrai n Ihat is relallve!y flat and is expected to be flooded by a 100 year SlOrm even t.

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2.1 DEFINITIONS OF KEY TERMS 7

Degree of sa r (ion (5) is the ratio of the volume of water to the volume of void.

Bulk unit weight ('Y) is the weight density, that is , the weight of a soil per unit volume.

Saturated unit weight ('Ysat) is the weight of a saturated soil per unit volume. Dry unit weight ('Yd) is the weight of a dry soil per unit volume. Effective unit weight ('Y') is the weight of soil solids in a submerged soil per

unit volume. Relative density (Dr) is an index that quantifies the degree of packing between

the loosest and densest state of coarse-grained soils. Effective particle size (D10) is the average particle diameter of the soil at 10

percentile; that is, 10% of the particles are smaller than this size (diameter).

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8 CHAPTER 2 PHYSICAL CHARACTERISTICS OF SOILS AND SOIL INVESTIGATIONS

2.2

A verage particle diameter (Dso) is the average particle diameter of the soil. Liquid limit (wLd is the water content at which a soil changes from a plastic

state to a liquid state. Plastic limit (WPL) is the water content at which a soil changes fro ,

to a plastic state . Shrinkage limit (wsd is the water content at which a soil c a

to a semisolid state without further change in volun . Groundwater is water under gravity in excess of th

pores. Head (H) is the mechanical energy per unit weig 1. Coefficient of permeability (k) is a propo

flow velocity of water through soils.

soil tests required to characterize soils? l4'? 1'b';/ Ul,V'" t ?

U. What is a s 1 investigation? 13. How do you plan a soil investigation? 14. What are the effects of water on the unit weight of soils? 15. What factors affect the compaction of soils?

2.3 COMPOSITION OF SOILS

2.3.1 Soil Formation Soils are formed from the physical and chemical weathering of rocks. Physical weathering involves reduction of size without any change in the original com-position of the parent rock. The main agents responsible for this process are

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2.3 COMPOSITION OF SOILS 9

exfoliation, unloading, erosion , freezing, and thawing. Chemical weathering causes both reductions in size and chemical alteration of the original parent rock. The main agents responsible for chemical weathering are hydration, carbonation, and oxidation. Often, chemical and physical weathering take place in concert.

Soils that remain at the site of weathering are called resid R soils. These soils retain many of the elements that comprise the parent r ck. Alluvial soils, also called fluvial soils, are soils that were transported by river and strea s. The composition of these soils depends on the environmen del' hich t ey were transported and is often different from the parent r k. rofil of alluvial soils usually consists of layers of different soils. Muc our ities has been and is occurring in and on alluvial soils. 01 'al ils are soils that were transported and deposited by glaciers. M oils deposited in a marine environment.

2.3.2 Soil Types

Glacial till is a soil that consists mainly of coarse particles. Glacial clays are soils that were deposited in ancient lakes and subsequently

frozen. The thawing of these lakes reveals a soil profile of neatly stratified silt and clay, sometimes called varved clay. The silt layer is light in color and was deposited during summer periods while the thinner, dark clay layer was deposited during winter periods. Gypsum is calcium sulphate formed under heat and pressure from sedi-ments in ocean brine.

Lateritic soils are residual soils that are cemented with iron oxides and are found in tropical regions.

F10 CHAPTER 2 PHYSICAL CHARACTERISTICS OF SOilS AND SOil INVESTIGATIONS

Loam is a mixture of sand, silt, and clay that may contain organic material. Loess is a wind blown, uniform fine-grained soil. Mud is clay and silt mixed with water into a viscous fluid.

2.3.3 Clay Minerals

and 0 = Silicon

(a) Single (b) A tetrahedral

Aluminum o and = Oxygen or Hydroxyl 0 = Aluminum

(c) Single octahedrons (d) Octahedral sheet FIGURE 2.2 (a) Silica tetrahedrons, (b) silica sheets, (c) single aluminum octahedrons, and (d) aluminum sheets.

soil.

F2.3 COMPOSITION OF SOILS 11

'+- Sili ca sheet '---'

- Alumina sheet Silica sheet L-l""'_~:':"-. Hydrogen bonds ~-"""""", Silica sheet ~-=:a::::::E!I~ Potassium ions

(a) Kaolinite (b) Illite (c) FIGURE 2.3 Structure of kaolinite, illite, and montmoril

O per gram while ar of 45 gram 0 i.s -... their large sur ac s, surface forces significantly influence the behavior of fine-grained so l~ compa d to coarse-grained soils. ~ Th s fa ce charges on fine-grained soils are negative (anions). These neg-ative surface rge attract cations and the positively charged side of water molecules from surrounding water. Consequently, a thin film or layer of water, called adsorbed water, is bonded to the mineral surfaces. The thin film or layer of water is known as the diffuse double layer (Fig. 2.4). The largest concentration of cations occurs at the mineral surface and decreases exponentially with distance away from the surface (Fig. 2.4) .

Drying of most soils, with the exception of gypsum, using an oven for which the standard temperature is 105 5C, cannot remove the adsorbed water. The adsorbed water influences the way a soil behaves. For example, plasticity, which we will deal with in Section 2.6, in soils is attributed to the adsorbed water. Toxic chemicals that seep into the ground contaminate soil and groundwater. The sur-face chemistry of fine-grained soils is important in understanding the migration, sequestration, re-release, and ultimate removal of toxic compounds from soils.

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Mineral surface

Diffuse double layer

c .2

~ c

'" u c o (.)

FIGURE 2.4 Diffuse double layer.

(a) Flocculated structure--saltwater environment (b) Flocculated structure-freshwater environment

(c) Dispersed structure FIGURE 2.5 Soil fabric.

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2.3 COMPOSITION OF SOILS 13

parallel to each other. A flocculated structure, formed under a freshwater envi-ronment, results when many particles tend to orient perpendicular to each other. A dispersed structure is the result when a majority of the particles orient parallel to each other.

00 a -bearing capacities and good drainage qual-i . an their stren an ' olum change characteristics are not significantly

)

flected by chang 111 oistu l' c nditions. They are practically incompressible w en dense, b '/? Sl . C n ol

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14 CHAPTER 2 PHVSICAL CHARACTERISTICS OF SOILS AND SOIL INVESTIGATIONS

The essential points are: 1. Soils are derivedfrom the weathering of rocks and are commonly de-

scribed by textural terms such as gravels, sands, silts, and clays. 2. Particle size is used to distinguish various soil textures. 3. Clays are composed of three main types of mineral-kaolinite, illite,

and montmorillonite. 4. The clay minerals consist of silica and alumina sheets that are com-

bined to form layers. The bonds between layers play a very important role in the mechanical behavior of clays. The bond between the layers in montmorillonite is very weak compared with kaolinite and illite. Water can easily enter between the layeJ'S in montmorillonite, causing swelling.

5. A thin layer of water is bonded to the mineral surfaces of soils and significantly influences the physical Jlnd mechanical characteristics of fine-grained soils.

6. Fine-grained soils have much larger surface areas than coarse-grained soils and are responsible for the major physical and mechallical dif-ferences between coarse-grained andfine-grained soils.

7. The engineering properties of fine-grained soils depend mliinly on mineralogical factors.

Soil is composed of solids, liquids, and gases (Fig. 2.6a). The solid phase may be mineral , organic matter, or both. As mentioned before, we will not deal with organic matter in this textbook. The spaces between the solids (soil particles) are called voids. Water is often the predominant liquid and air is the predominant gas. We will use the terms water and air instead of liquids and gases. The soil water is commonly called pore water and it plays a very important role in the behavior of soils under load. If all the voids are filled by water, the soil is satu-rated. Otherwise, the soil is unsaturated. If all the voids are filled with air, the soil is said to be dry.

We can idealize the three phases of soil as shown in Fig. 2.6b. The physical properties of soils are influenced by the relative proportions of each of these

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Idealization

(a) Soil

FIGURE 2 .6 Soil phases.

where

2.4 PHASE RELATIONSHIPS 15

(b) Idealized soil

= w" x 100% W,

(2.1)

(2.2)

(2.3)

The water con nt o~r1 is found by weighing a sample of the soil and then placing 'o( in an ov aNifO ::t: SOC until the weight of the sample remains constant; that is, all e abso bed water is driven out. For most soils, a constant weight is achieved in u 4 hours. The soil is removed from the oven, cooled, and then weighed. Example 2.2 illustrates the measurements and calculations required to determine the water content.

2. Void ratio (e) is the ratio of the volume of void space to the volume of solids. Void ratio is usually expressed as a decimal quantity.

(2.4)

3. Specific volume (V') is the volume of soil per unit volume of solids:

I V' = f = 1 + e I (2.5)

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This equation is useful in relating volumes as shown in Example 2.3 and in the calculation of volumetric strains (Chapter 3).

solids to the

(2.8)

Let m 1 be the mass of the container; m2 be the mass of the container and dry soil; m 3 be the mass of the container, soil, and water; and m 4 be the mass of the container and water. The mass of dry soil is ms = m2 - mi , the mass of water displaced by the soil particles is m s = m4 - m 3 + ms> and Gs = m ) m s.

6. Degree of saturation (5) is the ratio, often expressed as a percentage, of the volume of water to the volume of voids:

or Se = wG. I (2.9) If 5 = 1 or 100%, the soil is saturated. If 5 = 0, the soil is bone dry. It is practically impossible to obtain a soil with 5 = O.

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TABLE 2.1 Typical Values of Unit Weight for Soils

Soil type 'Y.at (kN/m3 ) 'Yd (kN/m3 )

Gravel 20-22 15-17 Sand 18-20 13-16 Silt 18-20 14-18 Clay 16-22 14-21

7. Unit weight is the weight of a soil per unit vol bulk unit weight, 'Y, to denote unit weight:

(2.10)

Special Cases

(a)

(2.11 )

(b) Dr;

(2.12)

of a saturated soil, sur-

(2.13)

8. Rela! e de sity (Dr) is an index that quantifies the degree of packing between the loosest and densest possible state of coarse-grained soils as deter-mined by experiments:

(2.14)

where emax is the maximum void ratio (loosest condition), emin is the minimum void ratio (densest condition), and e is the current void ratio.

The maximum void ratio is found by pouring dry sand, for example, into a mold of volume (V) 2830 cm3 using a funnel. The sand that fills the mold is weighed. If the weight of the sand is W, then by combining Eqs. (2.10) and (2.12) we get emax = Gs'Yw(VIW) - 1. The minimum void ratio is determined by vibrating the sand with a weight imposing a vertical stress of 13.8 kPa on top of the sand. Vibration occurs for 8 minutes at a frequency of 3600 Hz and amplitude of 0.064

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18 CHAPTER 2 PHYSICAL CHARACTERISTICS OF SOilS AND SOil INVESTIGATIONS

TABLE 2.2 Description Based on Relative Density

Dr (%) Description

0-15 Very loose 15-35 Loose 35-65 Medium dense 65-85 Dense 85-100 Very dense

Prove the

(a)

Strategy he proo s of these equations are algebraic manipulations. Start with the basic ni ,. n and then manipulate the basic equation algebraically to get the desired form.

Solution 2.1 (a) For this relationship, we proceed as follows:

Step 1: Write down the basic equation,

Step 2: Manipulate the basic equation to get the desired equation. You want to get e in the denominator and you have V v . You know that Vv = eVs and Vw is the weight of water divided by the unit

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weight of water. From the definition of water content, the weight of water is wWs' Here is the algebra:

(b) For this relationship, we proceed as follows :

Step 1: Write down the basic equation,

Step 2:

ap ipulate the b Sle equation-to get the new form of the equation.

W s + Ww Ws + wWs V s + Vv Vs + V v

W,( l + SetGs ) "I = VsU + e)

Gs'Yw(1 + Se/G,) Gs'Yw(1 + w) 1 + e 1 + e

or

_ (0., + se) "I - 1 + e "I,.

EXAMPLE 2.2

A sample of saturated clay was placed in a container and weighed. The weight was 6 N. The clay in its container was placed in an oven for 24 hours at lOSOC. The weight reduced to a constant value of 5 N. The weight of the container is 1 N. If Gs = 2.7, determine the (a) water content, (b) void ratio, (c) bulk unit weight, (d) dry unit weight, and (e) effective unit weight.

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Strategy Write down what is given and then use the appropriate equations to find the unknowns. You are given the weight of the natural soil , sometimes called the wet weight , and the dry weight of the soil. The difference between these will give the weight of water and you can find the water content by using Eq. (2.3). You are also given a saturated soil, which means that S

Solution 2.2 Step 1: Write down what is given.

Step 2:

Step 3:

Step 4:

Weight of sample + container = 6 N. Weight of dry sample + container =

Determi

or

t.; f dry soil:

, =6 5=14N~ i _ 5-1~~

00 =! x 10As% 4

(see Example 2.1)

( Gs ) _ 2.7 _ 3 -- '/w - x 9.8 - 15.8 kN/m 1 + e 1 + 0.675

'I 19.7 'I = = = 15.8 kN/m3

d (1 + w) 1 + 0.25 Step 7: Determine the effective unit weight.

'I' = (~s: e1 )'/w = (12; ~6~5) x 9.8 = 9.9 kN/m3 or

'I' = '/sat - '/W = 19.7 - 9.8 = 9.9 kN/m3

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C 2.4 PHASE RELATIONSHIPS 21

EXAMPLE 2.3 An embankment for a highway is to be constructed from a soil compacted to a dry unit weight of 18 kN/m3 . The clay has to be trucked to the site from a borrow pit. The bulk unit weight of the soil in the borrow pit is 17 kN/m 3 and it natural water content is 5% . Calculate the volume of clay from the borrow p.' re uired for 1 cubic meter of embankment. Assume Gs = 2.7.

Solution 2.3 Step 1:

pit and embankment. Let

oid ratio, respectively, of borrow pit clay

17 _ 3 1 + 0.05 - 16.2 kN/m

But

and therefore

'Yw ( 9.8 ) eJ = Gs - - 1 = 2.7 -6- - 1 = 0.633 'Yd 1 .2

Similarly,

ez = Gs ~: - 1 = 2.7(~.:) -1 = 0.47

F22 CHAPTER 2 PHVSICAL CHARACTERISTICS OF SOILS AND SOIL INVESTIGATIONS

Step 3: Determine the volume of borrow pit material. V; 1 + e1 Vz 1 + e2

Therefore

V' = V' 1. + e1 = 1(1 + 0.633) 1 2 1 + e2 1 + 0.47

EXAMPLE 2.4


Step 2:

is a is ribution of particles with various sizes. ces t response of soils to loads and to flow

d n the laboratory to find particle sizes in

2.5.1 Particle Size of Coarse-Grained Soils The distribution of particle sizes or average grain diameter of coarse-grained soils-gravels and sands-is obtained by screening a known weight of the soil through a stack of sieves of progressively finer mesh size. A typical stack of sieves is shown in Fig. 2.7.

Each sieve is identified by a number that corresponds to the number of square holes per linear inch of mesh. The particle diameter in the screening process, often called sieve analysis, is the maximum particle dimension to pass through the square hole of a particular mesh. A known weight of dry soil is placed on the largest sieve (the top sieve) and the nest of sieves is then placed on a vibrator, called a sieve shaker, and shaken. The nest of sieves is dismantled, one sieve at a time. The soil retained on each sieve is weigh ed and the percentage of soil retained on each sieve is calculated. The results are plotted on a graph of

2.5 DETERMINATION OF PARTICLE SIZE Of SOILS 23

FIGURE 2.7 Stack of sieves.

~~E~~~~,:~~~~.~e;,~:e"t re aUled) as the Fig. 2.8. The re-,,~~;t;:::;.I::;, the gradation i( sca le for particle {(c~:U'""~~~t the smallest in a soil

ilh sieve (rom the top of the ,;:~':..'-",-~~:,.:~~lt-~,,:!p~e~,~c."e~n~t weight retained is

100 (2.15)

;

2: (% Retained on ith sieve) (2.16) ,.,

weight. The unit of mass is grams or kilograms.

100 90 t ,I 80 + 70

, 60 0

" 50

'. 3. 2. 10

100 PartIc le SIze tmm) -qal"llllmlc sea%!

FIGURE 2.8 Particle size distribution curves.

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2.5.2 Particle Size of Fine-Grained Soils

w+""--t- Hydromeler

FIGURE 2.9 Hydrometer in soil-water suspension .

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2.5 DETERMINATION OF PARTICLE SIZE OF SOILS 25

sophisticated methods are available (e.g., light scattering methods). The dashed line in Fig. 2.S shows a typical particle size distribution for fine-grained soils.

2.5.3 Characterization of Soils Based on Particle Size

(2.18)

which 60% of the particles are

(2.19)

f the soil particles for which 30% of the particles are

TABLE 2.3 Soil ype, Descriptions, and Average Grain Sizes According to uses

Soil type

Gravel

Sand

Silt

Clay

Description

Rounded and/or angular bulky hard rock

Rounded and/or angular bulky hard rock

Particles smaller than 0.075 mm. exhibit little or no strength when dried Particles smaller than 0.002 mm. exhibit significant strength when dried; water reduces strength

Average grain size

Coarse: 75 mm to 19 mm Fine: 19 mm to 4 mm Coarse: 4 mm to 1.7 mm Medium: 1.7 mm to 0.380 mm Fine: 0.380 mm to 0.075 mm 0.075 mm to 0.002 mm

< 0.002 mm

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The essential points are: 1. A sieve analysis is used to determine the grain size distribution of

coarse-grained soils. 2. For fine-grained soils, a hydrometer analysis is used to find the parti-

cle size distribution.

FOR

2.5 DETERMINATION OF PARTICLE SIZE OF SOILS 27

3. Particle size distribution is represented on a semilogarithmic plot of % finer (ordinate, arithmetic scale) versus particle size (abscissa, log-arithm scale).

4. The particle size distribution plot is used to delineate the different soil textures (percentages of gravel, sand, silt, and clay) in a soil.

5. The effective size, D 10, ;s the diameter of the particle$ of which 10% of the soil is finer. D 10 is an important value in tegulatitrg flow through soils and can significantly influence the mechanical behavior of soils.

6. D50 is the average grain size diameter pi the soil. 7. Two coefficients-the uniformity coefficient and the coefficient of cur-

vature-are used to characterize the particle size distribution. Uni-form soils have uniformity coefficients 4, coefficients of cur-vature between 1 and 3, lind flat gradtuion curves. Gap-graded soils have coefficients of curvature 3, and one or more humps on the gradation curves.

90.1 181.9 108.8

6.1

par cle size distribution curve. Determin (1) the effective size, (2) the average particle size, (3) the uni-formity coefficient, and (4) the coefficient of curvature.

(c) Determine the textural composition of the soil (i.e., the amount of gravel, sand, etc.).

(d) Describe the gradation curve.

Strategy The best way to solve this type of problem is to make a table to carry out the calculations and then plot a gradation curve. Total mass of dry sample (M) used is 500 grams but on summing the masses of the retained soil in column 2 we obtain 499.7 grams. The reduction in mass is due to losses mainly from a small quantity of soil that gets stuck in the meshes of the sieves. You should use the "after sieving" total mass of 499.7 grams in the calculations.

28 CHAPTER 2 PHVSICAL CHARACTERlsnCS OF SOilS AND SOIL INVESTIGATIONS

Solution 2.5 Step 1: Tabulate data 10 obtain % fi ner.

Mass retained % Retained Sieve no. (grams) M, IM,IM ) x 100 I.(% Retained}

4 0 0 0 10 14.8 3.0~ 3.0 20 98.0 19.6 22.6 40 90.1 18.0

100 181.9 36.4 200 108.8 21.8 p," 6. 1 1.2

TOl al mass M '" 499.7 100

Slep 2: PIOl the gradalion curve.

Slep 3:

Slep 4:

Step 5:

80 10

~ 60 50 40

30 20 10 0 0.001

See Fig. E2.5 for a plo

Gravel 3% ) Sand = 9 -.&% SilL -n~(= 1.2% Cal u1ate'iiC and Cc.

~c Dw = 0.45 = 4.5 '~ 01 C \f~JIJ)2 = 0.182 = 0.72 ._,.;,. DloD6iJ 0.1 x 0.45

Sand~ Gravels

0.01 Partlc.~ s,ze (mm) - logarithmIC !.Cll1e

FIGURE E2.S Pa rticle size distr ibut ion cu rve.

~ Frner

l ob\: 0 - 100

- 22.6 77.4 1 00 ~.6 = 59.4 00 T77 = 23.0

- 98.8 - 1.2

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2.6 PHYSICAL STATES AND INDEX PROPERTIES OF FINE-GRAINED SOILS 29

2.6 PHYSICAL STATES AND INDEX PROPERTIES OF FINE-GRAINED SOILS

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Table 2 .4 Description of Soil Strength Based on Liquidity Index

Values of IL

IL < 0

0 < h < 1

h > 1

Description of soil strength

Semisolid state-high strength, brittle (sudden) fracture G is expected Plastic state-intermediate strength, soil deforms like a plastic material Liquid state-low strength, soil deforms like a v' cou fluid

lp A =--------'.---Clay fraction (% )

(2.21)

You should recall that the clay fraction is the amount of particles less than 2 f.lm.

TABLE 2.5 Typical Atterberg Limits for Soils

Soil type WLL(%) WPL (%) Ip (%)

Sand Nonplastic Silt 30-40 20-25 10-15 Clay 40-150 25-50 15-100

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2.7 DETERMINATION OF THE LIQUID, PLASTIC, AND SHRINKAGE LIMITS 31

5 2.7 DETERMINATION OF THE LIQUID, PLASTIC, AND SHRINKAGE LIMITS

2.7.1 Casagrande Cup Method

'0 small differences in apparatus.

Hard rubber base

\SlJ H

2 mm

Cam

FIGURE 2.11 Cup apparatus for the determination of liquid limit. (photo courtesy of Geotest.)

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60

55

~ C 50 2 c 0 '-'

\ I I \ c- Best-fit straight line I called the liquid state line l

-. --'- '

\ : , w LL = 46.2% 2 45 '" ~

40

- \ \. \ ! 35

10 20 25 30 40 50 60 708090 100 Number of blows - logarithmic scale

FIGURE 2.12 Typical liquid limit results fro

2.7.2 Plastic Limit Test

FIGURE 2.13 Fall cone apparatus.

e cup method.

FOR

2.7 DETERMINATION OF THE LIQUID. PLASTIC, AND SHRINKAGE LIMITS 33

60 I

55

~ 50 c

~ c 4 5 :3 2 '"

40 3:

35

I 80 gram co~e ~

Best-fit straignt line )' V V ~ 24 gram cone

WLL = 40% 11 / ) V / / 30

10 20 30 40 50 60 70 Penetration of cone (mm) - logari thmic scale

FIGURE 2 .14 Typical fall cone test resul .

water co 1: liquid sta 80 gram c

~ (2.22)

The shrinkage limit is determined as follows. A mass of wet soil, m l , is placed in a porcelain dish 44.5 mm in diameter and 12.5 mm high and then oven-dried . The volume of oven-dried soil is determined by using mercury to occupy the vacant spaces caused by shrinkage. The mass of the mercury is determined and the volume decrease caused by shrinkage can be calculated from the known density of mercury. The shrinkage limit is calculated from

(2 .23)

where m l is the mass of the wet soil, m 2 is the mass of the oven-dried soil , VI is the volume of wet soil, V2 is the volume of the oven-dried soil, and g is the acceleration due to gravity (9.8 m/s2).

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The essential points are: 1. Fine-grained soils can exist in one of four states: solid, semisolid,

plastic, alld liquid 2. Water is the agent that is responsible for changing the stat~ of soils. 3. A soil gets weaker if its water content increases. 4. Three limits are defined based on the water content that causes a

change of state. These are the liquid limit-the water content that caused the soil to change from a liquid to a plastic state; the plastic limit-the water content that caused the soil to change f rom a plastic to a semisolid; and the shrinkage limit-the water content that caused the soil to change from a semisolid to a solid state. A ll these limiting water contents are found from laboratory tests.

5. The plasticity index defines the range of water content for which the soil behaves like a plastic maltrial.

6. The liquidity index gives a measure of strength.

EXAMPLE 2.6, A liquid limit test c results:

iquid limit , you must make a semi-logarithm plot of water content versus n of blows. Use the data to make your plot, then extract the liquid limit (water content on the liquid state line corresponding to 25 blows). Two determinations of the plastic limit were made and the differences in the results are small. So, use the average value of water content as the plastic limit.

Solution 2.6 Step 1: Plot the data .

See Fig. E2.6. Step 2: Extract the liquid limit.

The water content on the liquid state line corresponding to a terminal blow of 25 gives the liquid limit.

WLL = 38%

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2.7 DETERMINATION OF THE LIQUID, PLASTIC, AND SHRINKAGE LIMITS 35

6C ~------~----~--.--r-r-.-'" 55 .

~ 501---~ c ~ 45 ~-----~~----r-~r-~-r-r~~

8 40 I--~~~.:j::~=-IIIIIIIt1 iii ~ ~ 35

30~-------~~'--~~r-~-r-r~~ 25L-______ ~~ __ L-~~~_L_L~~

10 20 25 30 40 50 60 708090100 Number of blows - logarithmic scale

FIGURE E2.6 cup method.

Step 3:

Step 4:

Step 5:

Step 6:

Calculate plastic limit. The plastic limit is

Calculate lp.

2Q. + 0.8 L i PL = 2 = 20.6"1~

Parameter 80 gram cone 240 gram cone

Penetration (mm) Water content (%)

5.5 39.0

7.8 44.8

14.8 52.5

22 60 .3

32 67

8.5 36.0

15 45.1

21 49.8

35 58.1

Determine (a) the liquid limit, (b) the plastic limit, (c) the plasticity index, and (d) the liquidity index if the natural water content is 36%. Strategy Adopt the same strategy as in Example 2.6. Make a semilogarithm plot of water content versus penetration. Use the data to make your plot, then extract the liquid limit (water content on the liquid state line corresponding to 20 mm). Find the water content difference between the two liquid state Jines at any fixed penetration. Use this value to determine the plastic limit.

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70

65 .

~ 60 C 55 2 c 0 u

(;j 50 ro s: 45

40

35 1 10 20 100

Solution 2.7 Step 1: Plot the data.

See Fig. E2. 7. Step 2:

Step 3:

10 = 17%

~.:#,--W.....:P--"L 36 - 17 = 0.45 42

1 2.8 SOIL CLASSIFICATION SCHEMES A classification scheme provides a method of identifying soils in a particular group that would likely exhibit similar characteristics. Soil classification is used to specify a certain soil type that is best suitable for a given application. There are several classification schemes available . Each was devised for a specific use. For example, the American Association of State Highway and Transportation

2 . SOIL CLAS$JFI(AnON SCHEMES 37

Officials (AAS HTO) developed one scheme that classifies soi ls according to thei r use fulness in roads and highways while the Un ified SOl i Classifica llon System (USeS) was originally developed for use in airfield construcllon but was later modified fo r genera l use .

We will study on ly the uses because it is neither too ela rate nor 100 simplistic. The uses uses symbols for the particle size grou s. These symbols and their represe ntations are : G- gravel, S- sand. M-sih, lay. Tr ese are combincd with other symbols expressing gradation charlcten ics- for well graded and P for poorly graded- and plasticity characteri ics-H': or high and L for low, and a sy mbol. 0, indicating the presence 0 ganic- aterial . A typical classification of CL means a clay soi! wi th low plasticit)': hile S.P means a poorly graded sand. The flowcharts shown in Figs. - ,0 pro ide ystematlc means of classifying a SOl i accord ing 10 the USCS. A

Expe ri menta l results from soi ls lesttcl fn m di rent parts of the world were plotted on a grap h o[ plasticity index 0 in te) r s liq uId ill}lit (abscissa) . It was fou nd that clays. silts, and o r i 501 ' lie ' distinct regions of the graph. A line defi ned by the eq uation

~;;-:;:;;- (2.24)

Soll 11 111le "allied PToc;eed 10 1l0000hart 01 Fli. 2.15b

Between 5% and 12%?

PIII$llc tl.yey"non Non -pl~1C $Illy s.cond Jettei' C t,non

Second lett ... M

1I1,,~lt!tt ... ~G.U-C:il:4 ."d lSec s3 second l.n_ os W. 0Ihe!w!,. YCond lett ... ~ P

II IusllltiefosS,VC}'6 end lSec...:3 l!(:ond lett_ 1$ W. 01 ......... " second letter ~ P

'" IS clay "ilCtlon > SIlt tractIon?

Yes No

11 "1"$1 Ifll.f "G. UC;t4 .nd 1 !i:CC!i:3

CIess,loellion IS: GW...(IC "' ....... CI_,Ioc:'-:1OII OS: GP GC

"'''$Ilttttf .. S. UC~6 .ndl~ct$3

Ct-.'WIOll ~: SW-SC "' ........ CIa5,loeallOll ~: SP -sc

1",rsll"Ie, IS G. UC~4."dlsCCs3

CluSI'it.lton IS: GW-GM Oth_,H. Classll't.Ioon Is: GP...(IM 11',rsI (.tt ... " S, UC2'6 ,"d I SCC!i:3

Clnsrt'ClI,on 15 SW-SM

"'--. CI,ultIClt,O" 05. SP-5M

FIGURE 2.15. Unified Soil Classification flOWChart for coarse-grained soils.

FO


Is

Are 50% of particles < 0.075 mm?

"'LL (ovendried) IVLL (not dried)

----'---No

< 0.75%

daries between clays (above the line) and silts and org ic soils (below e line) n in Fig. 2.16. A second line, the

-Hne expre~ed as Ip = 0 (WL - 8) , defines the upper limit of the correlation be een plasticity index .frt ligilfc Ii it. If the results of your soil tests fall above 0 ' 50 - , e, you sho of your cesults and ,epea! younes!s,

,

50 I--t--t-~~

~ 40 I--t--+--t---+--+/ C-.-+--+ / -1--+--1 >< OJ

-0

.!: 30 f----f--+---\---bo''---l---V''-:-.~ u ~ '" 20 I--t--+--Y-'---+--:>"'f--+--r-'--II--t--i n::

OL-~~~L~_~_L-~_~_-L_-L_~~ o 10 20 30 40 50 60 70 80 90 100

Liquid limi t (%) FIGURE 2.16 Plasticity chart.

FO

2.9 ENGINEERING USE CHART 39

2.9 ENGINEERING USE CHART

You may ask: "How do I use a soil classification to select a soil for a particular type of construction, for example, a dam?" Geotechnical engineers have pre-pared charts based on experience to assist you in selecting a soi 0 particular construction purpose . One such chart is shown in Table 2.6. Th numerical values 1 to 9 are ratings with No.1 the best. The chart should 0 y used to rovide guidance and to make a preliminary assessment of the tabi1' of a oil for a particular use. You should not rely on such descriR strength or "negligible" compressibility to make fin decisions. We will deal later (Chapters 4 and 5 with determine strength and compressibility propei-t" .. "'--

EXAMPLE 2.8

Particle size analyses were carried 0 particle size distribution curves l e s the two soils are:

Soil

A B

il Classification Scheme .

.. ....: . ~~"'.e two soils is a better material for

ntageo g a? ,

Cla~ Silt l 100 90 80 70

'" 60 c:

u:: 50 if!. 40

30 20 10

I .-.... -

-- .

if

o 0.001

I ;: / 111

So il A

V

,

I /' I I L ...... I I .t" I 0 .01 0.1

se t e partlc e

Sand Gravel

'I

/ I /

Soil B

10 Particle size (mm) - logarithmic scale

FIGURE E2.8

FO


TABLE 2 .6 Engineering Use Chart (After Wagner, 1957)

Workability as a

Group Permeability construction Typical names of soil groups symbols when compacted

Well-graded gravels, gravel-sand GW Pervious mixtures, little or no fines Poorly graded gravels, gravel - GP Very pervious Negligible sand mixtures, little or no fines Silty gravels, poorly graded GM Negligible gravel-sand-silt mixtures Clayey gravels, poorly graded GC gravel-sand-clay mixtures Well-graded sands, gravelly SW Excellent sands, little or no fines Poorly graded sands, gravelly SP sands, little or no fines Silty sands, poorly graded sand- SM Low silt mixtures Clayey sands, poorly graded ~ Low sand-clay mixtures Inorganic silts and very fine ML Medium sands, rock flour, silty or clayey fine sands with slight pi as ieit\! Inorganic clays of low to Medium medium plastici ty , gravelly c sandy clays, silky clays, lean clays

Poor Medium

Fair to High poor

Poor High

, Organic clays of medium Impervious Poor High plasticity

.!lat and other highly organic soils

the different percentages of each soil type and then follow the flowchart. To determine whether your soil is organic or inorganic, plot your Atterberg limits on the plasticity chart and check whether the limits fall within an inorganic or organic soil region.

Solution 2.8 Step 1: Determine the percentages of each soil type from the particle size

distribution curve.

material

Excellent

Good

Good

Good

Excellent

Fair

Fair

Good

Fair

Good to fair

Fair

Poor

Poor

Poor

2.9 ENGINEERING USE CHART 41

Con$tituent Soil A Soil B

Percent o f particle greater than 0.075 mm 12 80 Gravel fraction (%) 0 16 Sand fraction (".) 12 64 Sill fraction 1%1 59 20 Clay fraction 1%) 29 0

F1 4


Step 2: Use the flowchart. Following the flowchart, Soil A is ML and Soil B is SM.

Step 3: Plot the Atterberg limits on the plasticity chart.

Step 4: Use Table 2.6 to make a preliminary assess Soil B with a rating of 5 is better than Soil B dam core.

from two-dimensional flo

2.10.2 Head Darcy 's law governs the flow of water through soils. But before we delve into Darcy's law, we will discuss an important principle in fluid mechanics- Ber-noulli 's principle-which is essential in understanding flow through soils.

If you cap one end of a tube, fill the tube with water, and then rest it on your table (Fig. 2.17), the height of water with reference to your table is called the pressure head (hp ). Head refers to the mechanical energy per unit weight. If you raise the tube above the table, the mechanical energy or total head increases.

FO

2.10 ONEOIMENSIONAL FLOW OF WATER THROUGH SOILS 43

Pressure head

FIGURE 2.17

Datum-top of table

hp = ufy",

Pressure head

You now have two components 0: elevation head (hJ. If water ere to a under steady state condition, tH given as u2!2g. The total head (so to Bernoulli's principle i

(2.25)

(2.26)

w, ere u = hp is pore w er pressure. Consider a lind~;'('~taining a soil mass with water flowing through it at

a consta t'G-ate as piMi~ Fig. 2.18. If we connect two tubes, A and B, called piezomete , t a dis ance I apart, the water will rise to different heights in each of the tubes. 19ht of water in tube B near the exit is lower than A. Why? As the water flows through the soil, energy is dissipated through friction with the soil particles, resulting in a loss of head. The head loss between A and B, assum-

Tube A Tube B

I- I ---+j FIGURE 2.18 Head loss due to flow of water through soil.


ing decrease in he~d is posi tive and our _d

FOR

2.10 ONE-DIMENSIONAL FLOW OF WATER THROUGH SOILS 45

pervious" clays are in dam construction to curtail the flow of water through the dam and as barriers in landfills to prevent migration of effluent to the surrounding area. Clean sands and gravels are pervious and can be used as drainage materials or soil filters.

2.10.4 Empirical Relationships for k For a homogeneous soil, the coefficient of permeabilit on its void ratio. You should recall that the void ra i is

The essential points are: 1. The flow 0/ water through soils is governed by Darcy's law, which

states that the average flow velocity is proportional to the hydraulic gradient.

(2.31)

2. The proportionality coefficient in Darcy's law is called the coefficient of permeability or hydraulic conductivity, k.

3. The value of k is influenced by the void ratio, particle size distribu-tion, and the wholeness of the soil mass.

4. Homogeneous clays are practically impervious while sands and grav-els are pervious.

n diameter is placed in a tube 1 m long. A constant supply of water is a 1 e flow into one end of the soil at A and the outflow at B is collected by a bell er (Fig. E2.9). The average amount of water collected is 1 cm3 for every 10 seconds. The tube is inclined as shown in Fig. E2.9. Determine the

Table

FIGURE E2.9

FO

46 CHAPTER 2 PHVSICAL CHARACTERISTICS OF SOILS AND SOIL INVESTIGATIONS

(a) hydraulic gradient, (b) flow rate, (c) average velocity, (d) seepage velocity, if e = 0.6, and (e) coefficient of permeability.

Solution 2.9 Step 1: Define the datum position. Select the to Step 2: Find the total heads at A (inflow) a d

Step 3:

Step 4:

Step 6:

collected, Q = 1 cm3 , t = 10 seconds

u = Au 'IT X (diam)2 'IT X 102 2

A = = = 78.5 cm 4 4

u = qu = ~ = 0.0013 cmJs A 78.5

Determine seepage velocity.

u u =-

S n

e 0.6 n = -- = --- = 0.38

1 + e 1 + 0.6 0.0013

Us = 038 = 0.0034 cmJs Step 7: Determine the coefficient of permeability. From Darcy's law u = ki.

v 0.0013 . k = - = -- = 10.8 X 10-4 cm/s i 1.2

2.10 ONEDIMENSIONAL flOW OF WATER THROUGH SOILS 47

EXAMPLE 2.10 A drainage pipe (Fig. E2.lOa) became complete ly blocked during a srorm by a plug of sand , 1.5 In long, followed by another plug of a mixture of clays, silts. and sands, 0.5 m long. When the storm was over. the wa ter level above ground was l m. The coefficient ofpenneability of the sa nd IS 2 t lmet t ~ the mlxtUie of days. SlitS, and sands

(a) Plot the variation of pressure , e levlltlon, and rot s a ver the l ength of rhe pipe.

(b) Calculate the pore water pressure al (J) the e e r 0 t~sand plug and (2) the center of the mixture of clays, siits, and an~s. ,

(c)

Step L:

Step 2:

Select te exit j t datum . .........,

drainage pipe as the

ermine heads at A aqd B. (h,)7= 0 m , th)A - 0 2 + :: 33m, HA = 0 + 3.3 == 3.3 m h')B - 0 ~:~\.. = 0 m, Hn - 0 m

Determine t~~~.ll 6sS In each plug. Head 10 wee~A al).d B - IHe - H ... I = 33 m (decrease 10 head taken a positive.}. be I1HI! LJ> 1

FO


~

Step 4:

3.5

3

2.5 E 2 " ro 1.5 CI) I

0.5

flow in the sand; let I:l.H2 , L 2 , k2 , and q2 be the head loss, length, coefficient of permeability, and flow in the mixture of clays, silts, and sa nds. Now,

D.H\ D.H\ ql = Akl -- = A X 2k2 --L\ Ll

D.H2 M-I2 q2 = Ak2 -- = A X k2 --L2 L2

From the continuity equation, ql = q2

Solving, we get

(1)

(2)

tiD = 2.31 x 'Yw = 2.31 x 9.8 = 22.6 kPa

Distance (m) FIGURE E2.10b Variation of elevation, pressure, and total heads along pipe.

FO

2.10 ONEDIMENSIONAL FLOW OF WATER THROUGH SOILS 49

Let E be the center of the mixture of clays, silts, and sands.

UE = 0.66 x 9.8 = 6.5 kPa

Step 7: Find the average hydraulic gradients.

~ Horizontal !low l Vertical flow kl

~ k 2 ? ~ k3 ?

FIGURE 2 .19 Flow through stratified layers.

(2.33)

50 CHAPTER 2 PHVSICAL CHARACTERISnCS OF SOILS AND SOIL INVESTIGATIONS

2.10.6 Flow Normal to Soil layers For flow norma1to the soil layers, the head loss in the soil mass is the sum of the head losses in each layer:

(2.34)

whe re I1H is the total head loss. and I1hl to I1h" are (he head sses in et ch of the n layers. The velocity in each layer is the same. The anilogx to electr city is flow of curren t through resistors in series. From Darcy's aw we o~

wherc k t(cq) is the eq uivalent permeability i k :" are the vertical permeabilities of the fir and (2.35) leads to

Values of k t(cq\ arc gener less.

(2.35)

(2.36)

EXAMPLE 2.1 A canal is cur into so il .! a st rati gr PI1Y.:$how~n iFig. E2.11 . Assuming flow takes plac laterally and vertically th,i0ugh n,} id970f the ca nal and vertically below the ~. ~ermine the eq uivalent pe eability in the horizontal and vert ical direC{lons. Calculate the ratio N he;.Auivalent horizontal permeability 10 the equiva'p r vertical7 e-ability [or flow through the sides of the canal .

Strate'" Use ~d t~ eq uivalent horizontal permeabili ty over ,-I. til depth of the -?then use Eq . (2.36) to find the equivalent

anal. To make the calculations easier, convert

T Canal 3.0m

1 k=0_3"10~~

k=0.8)( tolc~

FIGURE E2 .11

2 .11 DETERMINATION OF THE CO EFACIENT OF PERMEABIUTY 51

Solution 2.11 Step 1: Find k. cq) and k* "l) for flow through the sides of the canal.

SICp 3:

From Eq. (2.33), I

H .. = 3 m

k.(.q) = - (z l k .. 1 + z2k n ... ... + z .k , ~) Ho - ~( l x 0.23 x LO G -j j.5 xS.2 = 3 x 10- 6 cmls

Fro m Eq . (2.36).

3 10.61 (

1 1.5 0.5) ()- 6 0.23 + ""2 + 2

~_. 49 ) 5.7

x IO-~ emts

What's next . . .In or~t ca1 (f ate flow, we need to know the coefficient of per-m'eal5i rity k. We ih discuss how this coefficient is determined in the laboratory and in the fie ld .

2 2 .11 DETERMINATION OF THE COEFFICIENT OF PERMEABILITY

2 .11 .1 Constant-Head Test The consta nt -head lest is used to de termine the coefficient of permeability of coarse.grained soils. A typical constant-head apparatus is shown in Fig. 2.20. Water is allowed to flow through a cylindrical sam ple of soil under a constant head (II) . The outflow (Q ) is collected in a graduated cylinder at a convenient duration (t ).

FO


T h

Mariotte bottle

Coarse-grai ned soil

FIGURE 2 _20 A constant-head apparatus_

With reference to Fig. 2.20,

uantity of water

(2.37)

(2.38)

ter, T is the temperature in DC at which the mea-T = fL7"c/fL2fPC is the temperature correction factor

! RT = 2.42 - 0.475 [neT) I (2.39)

2.11.2 Falling-Head Test The falling-head test is used for fine-grained soils because the flow of water through these soils is too slow to get reasonable measurements from the constant-head test. A compacted soil sample or a sample extracted from the field is placed in a metal or acrylic cylinder (Fig. 2.21). Porous stones are positioned at the top and bottom faces of the sample to prevent its disintegration and to allow water to percolate through it. Water flows through the sample from a standpipe at-tached to the top of the cylinder. The head of water (h) changes with time as flow occurs through the soil. At different times, the head of water is recorded.

FOR

2.11 DETERMINATION OF THE COEFFICIENT OF PERMEABILITY 53

T h

~ dh T

I+- Standpipe

/T L

...... 1.

Fine-grained soil

-::: :~To beaker

FIGURE 2_21 A falling-head apparatus.

Let dh be the drop in head over a tim loss in the tube is

the cross-sectional area, s length of the soil sample, and h is t. The continuity condition requires that (qu)in =

dh h -Q - = Ak-

dt L

and the solution for k in the vertical direction is

The essential points are: 1. The constant-head test is used to detennine the coefficient ofpenne-

ability of coarse-grained soils.

(2.40)

2. The falling-head test is used to detennine the coefficient of permeabil-ity of fine-grained soils.

FO


EXAMPLE 2.12

A sample of sand, 5 cm in diameter and 15 cm long, was prepared at a porosity of 60% in a constant-head apparatus. The total head was kept constant at 30 cm and the amount of water collected in 5 seconds was 40 cm3 . The tesr,.,temperature was 20C. Calculate the coefficient of permeability and the seep' ~elocity.

Strategy From the data given, you can readily apply D t cy


Step 2: Calcula

Initial head = 90 em Final head = 84 cm Duration of test = 15 minutes Diameter of tube = 6 mm Temperature = 22C

Determine k.

cm/s

ki 0.2 x 2 - = --- = 0.67 cmls n 0.6

Strategy Since this is a falling-head test, you should use Eq. (2.40). Make sure you are using consistent units.

FO


Solution 2 .13 Step 1: Calculate the parameters required in Eq. (2.40).

Step 2:

12 - tl = 15 X 60 = 900 seconds

a = 'IT X ~6110? = 0.28 cm2 G A = 80 cm2 (given)

Calculate k.

k = aL In(hl) = 0.28 X 10 In 6:\.= 27 A(lz - t l ) h2 80 X 900 ~lb.... .

What's next . .. In the constant-head

ell penetrates through the water-bearing stratum and is per-the section that is below the groundwater level.

2. The soil mass is homQgeneous, isotropic, and of infinite size. 3. Darcy's law is valid. 4. Flow is radial toward the well. 5. The hydraulic gradient at any point in the water-bearing stratum is constant

and is equal to the slope of groundwater surface (Dupuit's assumptions) .

Let dz be the drop in total head over a distance dr. Then according to Dupuit's assumption the hydraulic gradient is

. dz [=-

dr

FO


Observation wells I Pumping well ------~----e-----~-- --- -------------I l--- r 1------. !-'2 ' ,

...---__ -, I ,--_-,

The area of flow

where z is

O need to rearrano

an 'f, and hl an Ii ' ation and integrate it between the limits rj

" Completing th

k = qo In(r2Ir[) TI(h~ - hi) (2.41)

With measurements of rl> r2 , h1' h2' and qv (flow rate of the pump), k can be calculated from Eq. (2.41). This test is only practical for coarse-grained soils.

Pumping tests lower the groundwater, which then causes stress changes in the soil. Since the groundwater is not lowered uniformly as shown by the draw-down curve in Fig. 2.22, the stress changes in the soil will not be even. Conse-quently, pumping tests near existing structures can cause them to settle unevenly. You should consider the possibility of differential settlement on existing struc-tures when you plan a pumping test. Also, it is sometimes necessary to tempo-rarily lower the groundwater level for construction. The process of lowering the groundwater is called dewatering.

FO


Observation wells I Pumping well ------~----e-----~------------------! !-15m~ ~30m +

FIGURE E2.14

EXAMPLE 15 m and the

center

Step 1:

15 m

Impervious

soil bed of thickness ate of pumping was 10.6

cated at 15 m and 30 m from the .4

e measurements to directly apply Eq. (2.41) to ketc f the pump test to identify the values to be

tch of the pump test with the appropriate dimensions-see

Step 2: Substitute given values in Eq. (2.41) to find k. 1'2 = 30 m , 1'1 = 15 m, h 2 = 15 - (1.9 + 1.4) = 11.7 m, hI = 15 - (1.9 + 1.6) = 11.5 m k = qu In(rzlr1) = 10.6 X 10-3 In(30/15) = 50 X 10-2 I

1T( h~ - hD 1T(1l.72 - 11.52) 1 04' em s

What's next . .. Water, although regarded as the "foe" in geotechnical engineering, can be used to improve soil strength, reduce soil deformations under loads, and reduce the permeability. Next, we will study how water can assist in the improvement of soils.

58 CHAPTER 2 PHVSlCAl CHARACTERISTICS Of SOILS ANO SOlllNVESTlGATIONS

2.12 DRY UNIT WEIGHT- WATER CONTENT RELATIONSHIP

2 .12.1 Basic Concept Let 'S examine Eq . (2.12) for dry unit weight, that IS ,

'1" = (~)'Y .. = C + ~.'G~S)'Yw (2.42) The extreme righthand side term was obtained by rc la ci n~ b~ e = wGjS. How can we increase the dry unit weight? Examination iE . (2~) reveals [hat we have to reduce the void ratio; tha i is, wlS mllsLbe r du .' T he theoret iea! maximum dry unit weight is ob tained W7.:. 1 tha is

e~ (2.43 )

2 .12.2 Proctor Compact) n Te A laboratory test . ca lled the Proci was developed to delive landa rd amou nt of mechanical ener (comp~c i e effort) t i:lelermine th maximum d ry unit weight of a soi l. In the fi and,V'd Proctor te a r soi l s~imen is mixed with water and com acted a c:tlmdrical mold vOlu 044 x 10- m) (sta ndard Procto mold) by r Beated blows from th ass a hammer, 2.5 kg, falling freely (fa a height jpf 05 mm (Fig ..... 2. ). . IS compacted in th ree layers, each of w his su iected to 2~s.

A nfodified Pr test was de eloped or c paction of airfields to sup-port hea aire f I ads. In the modified Pro tor tesl, a hamme r with a mass 4.54 kg falls eely om a height of 4 mm. e SOil is compacted in five layers with 25 blo per layer in l)Atandard Proctor mold.

Fou r or ore tests ar~o~ducted on the soil using different water con tents. Th last test is idenl lf\e w e addit ional water causes the bulk uni t weight of

e soil fO decrease fThe resul ared,lo!led as dry unit weight (ordinate) versus wa r'content (ab ssa). T ieal dry unit weighl- water content plots are shown in f ig. 2.24.

Clays usually yjeld l=shaped curves. Sands do nOl often Yield a clear bell ;

Yo) Moltl (b) Hamme. FIGURE 2.23 Compaction apparatus . (photo courtesy of Geotesr.)

FOR

2.12 DRY UNIT WEIGHT-WATER CONTENT RELATIONSHIP 59

12

10L---------~L---------~----~~~~~~~----~ 4 6

FIGURE 2 .24

un aturated at the maximum dry unit weight, that is, can det mine the degree of saturation at the maximum dry unit weight

using q. ( -A2). We. know 'Yd = ('Yd)max and W = Wop I from our Proctor test results . If Gs is know w. an solve Eq. (2.42) for 5. If Gs is not known, you can substitute a value of 2.7 with little resulting error in most cases. Equation (2.42) can be used to plot a series of theoretical curves of dry unit weight versus water content for different degrees of saturation (Jines of constant degree of saturation) as shown in Fig. 2.24 for 5 = 100% and 5 = 80%. You plot these curves as follows:

1. Assume a fixed value of 5, say, 5 = 1 (100 % saturation). 2. Substitute arbitrarily chosen values of w, approximately within the range

of water content on your graph. 3. With the fixed value of 5 and either an estimated value of Gs (= 2.7) or a

known value, find 'Yd for each value of W using Eq . (2.42) and plot the results of 'Yd versus w.

4. Repeat for a different value of 5.

FO


,

OJ

"

Increasing compaction

1 Water content

FIGURE 2.25 Effect of increasing compaction efforts on water content relationship .

The curve corresponding to S = 1 is k voids line. This line represents the mini ... _-.: .... _ ._ water content [Eq. (2.43)].

The achievement of zero Proctor test, using higher leve.l mum dry unit weight at a lower 0 (Fig. 2.25). The degree 0 aturation i than the standard compactIDlnii"'t,~I"""".i

2.12.5 Field Compaction

a uration line or zero air ble at a given

A variety of mechanical equipment is used to compact soils in the field. You may have seen various types of rollers being used in road construction . Each type of roller has special mechanical systems to effectively compact a particular soil type. For example, a sheepsfoot roller (Fig. 2.26a) is generally used to compact fine-grained soils while a drum type roller (Fig. 2.26b) is generally used to compact coarse-grained soils.

2.12.6 Compaction Quality Control A geotechnical engineer needs to check that field compaction meets specifica-tions. Various types of equipment are available to check the amount of compac-

FOR


FIGURE 2.26 Two types of machinery for field compaction. (Photos courtesy of Vibromax America, Inc.)

tion achieved in the field . Three popular apparatuses are (1) the sand cone, (2) the balloon, and (3) nuclear density meters.

2.12.6.1 Sand Cone A sand cone apparatus is shown in Fig. 2.27. It consists of a glass or plastic jar with a funnel attached to the neck of the jar.

The procedure for a sand cone test is as follows:

1. Fill the jar with a standard sand-a sand with known density-and deter-mine the weight of the sand cone apparatus with the jar filled with sand

FO


FIGURE 2 .27

2. 3.

Jar

Ottawa sand

D . . h W" ry umt welg t: 'fd = 11

STM) recom-

2 . 12.6.2 Balloon Test The balloon test apparatus (Fig. 2.28) consists of a graduated cylinder with a centrally placed balloon. The cylinder is filled with water. The procedure for the balloon test is as follows:

1. Fill the cylinder with water and record its volume, VI' 2. Excavate a small hole in the soil and determine the weight of the excavated

soil (W). 3. Determine the water content of the excavated soil (w).

FO


Air re lease va lve

Balloon

Pump

FIGURE 2.28 Balloon test device.

4. 5. Record the volume of wat 6. Calculate the unit weigb;

nt of a soil at a particular site.

FIGURE 2.29 Nuclear density meter. (Photo courtesy of Seaman Nuclear Corp.)

FO


The essential points are: 1. Compaction is the densijication of a soil by the expulsion of air and

the rearrangement of soil particles. 2. The Proctor test is used to determine the maximum dry unit weight

and the optimum water content and serves as the reference for field specijications of compaction.

3. Higher compactive effort increases the maximum dry unit weight and reduces the optimum water content.

4. Compaction increases strength, lowers compressibility'; and reduces the permeability of soils.

5. A variety of field equipment is used to check the dry unit weights achieved in the field Popular fiel!1 equiwnent includes the sand cone apparatus, the balloon apparatus.., an the nu lear density eter.

EXAMPLE 2.15

The results of a standard

Bulk unit Water weight content (%) (kN/m3)

6.2 16.9 8.1 18.7 9.8 19.5

11.5 20.5 12.3 20.4 13.2 20.1

theory and practice of foundation design (364-427) (1)

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