## Contents

Preface xvii

Acknowledgments xix

1 Soil aggregate, plasticity, and classification 1

1.1 Introduction 1

1.2 Soil: Separate size limits 1

1.3 Clay minerals 3

1.4 Nature of water in clay 6

1.5 Repulsive potential 9

1.6 Repulsive pressure 14

1.7 Flocculation and dispersion of clay particles 16

1.7.1 Salt flocculation and nonsalt flocculation 17

1.8 Consistency of cohesive soils 18

1.8.1 Liquid limit 19

1.8.2 Plastic limit 21

1.9 Liquidity index 24

1.10 Activity 24

1.11 Grain-size distribution of soil 26

1.12 Weight–volume relationships 29

1.13 Relative density and relative compaction 35

1.14 Relationship between emax and emin 36

1.15 Soil classification systems 38

1.15.1 Unified system 39

1.15.2 AASHTO classification system 42

1.16 Compaction 45

1.16.1 Standard Proctor compaction test 46

1.16.2 Modified Proctor compaction test 47

1.17 Empirical relationships for Proctor compaction tests 48

References 51

2 Stresses and strains: Elastic equilibrium 53

2.1 Introduction 53

2.2 Basic definition and sign conventions for stresses 53

2.3 Equations of static equilibrium 56

2.4 Concept of strain 61

2.5 Hooke’s law 63

2.6 Plane strain problems 64

2.6.1 Compatibility equation 65

2.6.2 Stress function 67

2.6.3 Compatibility equation in polar coordinates 68

2.7 Equations of compatibility for three-dimensional problems 71

2.8 Stresses on an inclined plane and principal

stresses for plane strain problems 73

2.8.1 Transformation of stress components from

polar to Cartesian coordinate system 74

2.8.2 Principal stress 75

2.8.3 Mohr’s circle for stresses 76

2.8.4 Pole method for finding stresses

on an inclined plane 78

2.9 Strains on an inclined plane and principal

strain for plane strain problems 82

2.10 Stress components on an inclined plane, principal

stress, and octahedral stresses: Three-dimensional case 84

2.10.1 Stress on an inclined plane 84

2.10.2 Transformation of axes 86

2.10.3 Principal stresses 88

2.10.4 Octahedral stresses 89

2.11 Strain components on an inclined plane, principal

strain, and octahedral strain: Three-dimensional case 93

3 Stresses and displacements in a soil mass:

Two-dimensional problems 97

3.1 Introduction 97

3.2 Vertical line load on the surface 97

3.2.1 Displacement on the surface (z = 0) 100

3.3 Vertical line load on the surface of a finite layer 102

3.4 Vertical line load inside a semi-infinite mass 102

3.5 Horizontal line load on the surface 104

3.6 Horizontal line load inside a semi-infinite mass 107

3.7 Uniform vertical loading on an infinite strip on the surface 108

3.7.1 Vertical displacement at the surface (z = 0) 113

3.8 Uniform strip load inside a semi-infinite mass 115

3.9 Uniform horizontal loading on an

infinite strip on the surface 116

3.9.1 Horizontal displacement at the surface (z = 0) 118

3.10 Triangular normal loading on an

infinite strip on the surface 121

3.10.1 Vertical deflection at the surface 122

3.11 Vertical stress in a semi-infinite mass

due to embankment loading 124

References 127

4 Stresses and displacements in a soil mass:

Three-dimensional problems 129

4.1 Introduction 129

4.2 Stresses due to a vertical point load on the surface 129

4.3 Deflection due to a concentrated point load at the surface 131

4.4 Horizontal point load on the surface 132

4.5 Vertical stress due to a line load of finite length 134

4.6 Stresses below a circularly loaded flexible

area (uniform vertical load) 137

4.7 Vertical displacement due to uniformly

loaded circular area at the surface 147

4.8 Vertical stress below a rectangular

loaded area on the surface 152

4.9 Deflection due to a uniformly loaded

flexible rectangular area 156

4.10 Stresses in a layered medium 160

4.11 Vertical stress at the interface of a

three-layer flexible system 162

4.12 Vertical stress in Westergaard material

due to a vertical point load 165

4.13 Solutions for vertical stress in Westergaard material 167

4.14 Distribution of contact stress over footings 169

4.14.1 Foundations of clay 169

4.14.2 Foundations on sand 170

4.15 Reliability of stress calculation using

the theory of elasticity 171

References 171

5 Pore water pressure due to undrained loading 173

5.1 Introduction 173

5.2 Pore water pressure developed due

to isotropic stress application 175

5.3 Pore water pressure parameter B 177

5.4 Pore water pressure due to uniaxial loading 177

5.5 Directional variation of Af 183

5.6 Pore water pressure under triaxial test conditions 183

5.7 Henkel’s modification of pore water pressure equation 185

5.8 Pore water pressure due to one-dimensional

strain loading (oedometer test) 189

References 191

6 Permeability 193

6.1 Introduction 193

6.2 Darcy’s law 193

6.3 Validity of Darcy’s law 196

6.4 Determination of the coefficient

of permeability in the laboratory 198

6.4.1 Constant-head test 199

6.4.2 Falling-head test 200

6.4.3 Permeability from consolidation test 201

6.5 Variation of the coefficient of permeability

for granular soils 202

6.5.1 Modification of Kozeny–Carman

equation for practical application 208

6.6 Variation of the coefficient of permeability

for cohesive soils 211

6.7 Directional variation of permeability

in anisotropic medium 215

6.8 Effective coefficient of permeability for stratified soils 218

6.8.1 Flow in the horizontal direction 219

6.8.2 Flow in the vertical direction 221

6.9 Determination of coefficient of permeability in the field 222

6.9.1 Pumping from wells 223

6.9.1.1 Gravity wells 223

6.9.1.2 Artesian wells 225

6.9.2 Auger hole test 227

6.10 Factors affecting the coefficient of permeability 229

6.11 Electroosmosis 230

6.11.1 Rate of drainage by electroosmosis 231

6.12 Compaction of clay for clay liners in waste disposal sites 234

References 238

7 Seepage 241

7.1 Introduction 241

7.2 Equation of continuity 241

7.2.1 Potential and stream functions 243

7.3 Use of continuity equation for solution

of simple flow problem 245

7.4 Flow nets 248

7.4.1 Definition 248

7.4.2 Calculation of seepage from a flow

net under a hydraulic structure 249

7.5 Hydraulic uplift force under a structure 253

7.6 Flow nets in anisotropic material 254

7.7 Construction of flow nets for hydraulic

structures on nonhomogeneous subsoils 257

7.8 Numerical analysis of seepage 261

7.8.1 General seepage problems 261

7.8.2 Seepage in layered soils 265

7.9 Seepage force per unit volume of soil mass 271

7.10 Safety of hydraulic structures against piping 273

7.11 Filter design 280

7.12 Calculation of seepage through an earth

dam resting on an impervious base 283

7.12.1 Dupuit’s solution 283

7.12.2 Schaffernak’s solution 284

7.12.3 L. Casagrande’s solution 286

7.12.4 Pavlovsky’s solution 289

7.12.4.1 Zone I (area agOf) 289

7.12.4.2 Zone II (area Ogbd) 290

7.12.4.3 Zone III (area bcd) 290

7.12.5 Seepage through earth dams with kx ≠ kz 291

7.13 Plotting of phreatic line for seepage through earth dams 294

7.14 Entrance, discharge, and transfer conditions

of line of seepage through earth dams 296

7.15 Flow net construction for earth dams 298

References 300

8 Consolidation 303

8.1 Introduction 303

8.2 Theory of one-dimensional consolidation 305

8.2.1 Constant ui with depth 310

8.2.2 Linear variation of ui 315

8.2.3 Sinusoidal variation of ui 315

8.2.4 Other types of pore water pressure variation 319

8.3 Degree of consolidation under time-dependent loading 324

8.4 Numerical solution for one-dimensional consolidation 328

8.4.1 Finite difference solution 328

8.4.2 Consolidation in a layered soil 330

8.5 Standard one-dimensional consolidation

test and interpretation 338

8.5.1 Preconsolidation pressure 339

8.5.1.1 Empirical correlations for

preconsolidation pressure 343

8.5.1.2 Empirical correlations for

overconsolidation ratio 344

8.5.2 Compression index 345

8.6 Effect of sample disturbance on the e versus log σ′ curve 347

8.7 Secondary consolidation 349

8.8 General comments on consolidation tests 352

8.9 Calculation of one-dimensional consolidation settlement 356

8.10 Coefficient of consolidation 358

8.10.1 Logarithm-of-time method 358

8.10.2 Square-root-of-time method 359

8.10.3 Su’s maximum-slope method 360

8.10.4 Computational method 361

8.10.5 Empirical correlation 362

8.10.6 Rectangular hyperbola method 362

8.10.7 ΔHt − t/ΔHt method 364

8.10.8 Early-stage log t method 364

8.11 One-dimensional consolidation with viscoelastic models 367

8.12 Constant rate-of-strain consolidation tests 373

8.12.1 Theory 373

8.12.2 Coefficient of consolidation 377

8.12.3 Interpretation of experimental results 378

8.13 Constant-gradient consolidation test 380

8.13.1 Theory 381

8.13.2 Interpretation of experimental results 383

8.14 Sand drains 384

8.14.1 Free-strain consolidation with no smear 386

8.14.2 Equal-strain consolidation with no smear 388

8.14.3 Effect of smear zone on radial consolidation 394

8.15 Numerical solution for radial drainage (sand drain) 394

8.16 General comments on sand drain problems 398

References 400

9 Shear strength of soils 403

9.1 Introduction 403

9.2 Mohr–Coulomb failure criterion 403

9.3 Shearing strength of granular soils 405

9.3.1 Direct shear test 405

9.3.2 Triaxial test 409

9.3.3 Axial compression tests 411

9.3.4 Axial extension tests 413

9.4 Critical void ratio 413

9.5 Curvature of the failure envelope 415

9.6 General comments on the friction

angle of granular soils 417

9.7 Shear strength of granular soils under

plane strain conditions 417

9.8 Shear strength of cohesive soils 422

9.8.1 Consolidated drained test 423

9.8.2 Consolidated undrained test 428

9.8.3 Unconsolidated undrained test 431

9.9 Unconfined compression test 435

9.10 Modulus of elasticity and Poisson’s

ratio from triaxial tests 436

9.11 Friction angles ϕ and ϕult 439

9.12 Effect of rate of strain on the undrained shear strength 440

9.13 Effect of temperature on the undrained shear strength 443

9.14 Stress path 445

9.14.1 Rendulic plot 445

9.14.2 Lambe’s stress path 448

9.15 Hvorslev’s parameters 455

9.16 Relations between moisture content, effective

stress, and strength for clay soils 458

9.16.1 Relations between water content and strength 458

9.16.2 Unique effective stress failure envelope 458

9.16.3 Unique relation between water

content and effective stress 461

9.17 Correlations for effective stress friction angle 462

9.18 Anisotropy in undrained shear strength 465

9.19 Sensitivity and thixotropic characteristics of clays 467

9.20 Vane shear test 472

9.20.1 Correlations with field

vane shear strength 477

9.21 Relation of undrained shear strength (Su)

and effective overburden pressure (p′) 478

9.22 Creep in soils 482

9.23 Other theoretical considerations: Yield

surfaces in three dimensions 490

9.24 Experimental results to compare the yield functions 496

References 503

10 Elastic settlement of shallow foundations 509

10.1 Introduction 509

10.2 Elastic settlement of foundations on

saturated clay (Poisson’s ratio ν = 0.5) 509

10.3 Elastic settlement of foundations on granular soil 511

10.4 Settlement calculation of foundations on granular

soil using methods based on observed settlement

of structures and full-scale prototypes 512

10.4.1 Terzaghi and Peck’s method 512

10.4.2 Meyerhof’s method 514

10.4.3 Method of Peck and Bazaraa 514

10.4.4 Method of Burland and Burbidge 515

10.5 Semi-empirical methods for settlement

calculation of foundations on granular soil 518

10.5.1 Strain influence factor method 518

10.5.2 Field tests on load–settlement

behavior: L1−L2 method 524

10.6 Settlement derived from theory of elasticity 526

10.6.1 Settlement based on theories of

Steinbrenner (1934) and Fox (1948) 526

10.6.2 Improved equation for elastic settlement 534

References 539

11 Consolidation settlement of shallow foundations 541

11.1 Introduction 541

11.2 One-dimensional primary consolidation

settlement calculation 541

11.3 Skempton–Bjerrum modification for

calculation of consolidation settlement 550

11.4 Settlement calculation using stress path 558

11.5 Comparison of primary consolidation

settlement calculation procedures 564

11.6 Secondary consolidation settlement 565

11.7 Precompression for improving foundation soils 566

11.8 Precompression with sand drains 572

References 573

Appendix: Calculation of Stress at the Interface

of a Three-Layered Flexible System 575

## Preface

This textbook is intended for use in an introductory graduate level course

that broadens (expands) the fundamental concepts acquired by students in

their undergraduate work. The introductory graduate course can be followed

by advanced courses dedicated to topics such as mechanical and

chemical stabilization of soils, geoenvironmental engineering, finite element

application to geotechnical engineering, critical state soil mechanics,

geosynthetics, rock mechanics, and others.

The first edition of this book was published jointly by Hemisphere

Publishing Corporation and McGraw-Hill Book Company of New York

with a 1983 copyright. Taylor & Francis Group published the second and

third editions with 1997 and 2008 copyrights, respectively. Compared to

the third edition, the text is now divided into 11 chapters. Stresses and

displacements in a soil mass are now presented in two chapters with twodimensional

problems in Chapter 3 and three-dimensional problems in

Chapter 4. Permeability and seepage are now presented in two separate

chapters (Chapters 6 and 7). Similarly, the settlement of shallow foundations

is now presented in two chapters—elastic settlement in Chapter 10

and consolidation settlement in Chapter 11. Several new example problems

have been added. SI units have been used throughout the text.

Some major changes in this edition include the following:

• In Chapter 1, “Soil aggregate, plasticity, and classification,” a

more detailed description of the relationships between the maximum

and minimum void ratios of granular soils is provided. The

American Association of State Highway and Transportation Officials

(AASHTO) soil classification system has been added to this chapter.

Sections on soil compaction procedures in the laboratory, along with

recently developed empirical relationships for maximum dry unit

weight and optimum moisture content obtained from Proctor compaction

tests, have been summarized.

• Chapter 4, “Stresses and displacements in a soil mass: Threedimensional

problems,” has new sections on vertical stress due to a

line load of finite length; vertical stress in Westergaard material due

to point load; line load of finite length; circularly loaded area; and

rectangularly loaded area.

• The fundamental concepts of compaction of clay soil for the construction

of clay liners in waste disposal sites as they relate to permeability

are discussed in Chapter 6, “Permeability.”

• Several new empirical correlations for overconsolidation ratio and

compression index for clay soils have been added to Chapter 8,

“Consolidation.”

• Chapter 9, “Shear strength of soils,” provides additional discussion

on the components affecting friction angle of granular soils, drained

failure envelopes, and secant residual friction angles of clay and clay

shale. Also added to this chapter are some new correlations between

field vane shear strength, preconsolidation pressure, and overconsolidation

ratio of clay soils.

• Chapter 10, “Elastic settlement of shallow foundations,” has been

thoroughly revised and expanded.

• Discussion related to precompression with sand drains has been added

to Chapter 11, “Consolidation settlement of shallow foundations.”

• The parameters required for the calculation of stress at the interface

of a three-layered flexible system have been presented in graphical

form in the Appendix, which should make interpolation easier.