Introduction to Soil Mechanics

Preface xii

Dedication and Acknowledgments xiii

List of Symbols xiv

1 Soil Structure 1

1.1 Volume relationships 1

1.1.1 Voids ratio (e) 2

1.1.2 Porosity (n) 3

1.1.3 Degree of saturation (S_r) 3

1.2 Weight-volume relationships 6

1.2.1 Bulk densities 7

1.2.2 Dry densities 8

1.2.3 Saturated densities 8

1.2.4 Submerged densities (¿') 9

1.2.5 Density of solids (¿_s) 10

1.2.6 Specific gravity (G_s) 10

1.2.7 Moisture content (m) 11

1.2.8 Partially saturated soil 12

1.2.9 Relative density (D_r) 18

1.3 Alteration of soil structure by compaction 20

1.3.1 Laboratory compaction tests 21

1.3.2 Practical considerations 26

1.3.3 Relative compaction (C_r) 27

1.3.4 Compactive effort 27

1.3.5 Under- and overcompaction 28

1.3.6 Site tests of compaction 28

1.4 California bearing ratio (CBR) test 30

1.5 The pycnometer 35

Supplementary problems for Chapter 1 39

2 Classification of Cohesive Soils 43

2.1 Atterberg Limits 43

2.1.1 Liquid Limit (LL) 43

2.1.2 Plastic Limit 48

2.1.3 Shrinkage Limit 50

2.1.4 Swelling of cohesive soils 56

2.1.5 Saturation Limit (Z%) 56

2.1.6 Relationship between the limits 57

2.1.7 Linear shrinkage and swelling 59

2.2 Consistency indices 64

2.2.1 Plasticity index (PI) 64

2.2.2 Relative consistency index (RI) 64

2.2.3 Liquidity index (LI) 64

2.3 Classification of soils by particle size 69

2.3.1 Sieve analysis 69

2.3.2 Uniformity coefficient (U) 73

2.3.3 Filter design 74

2.3.4 Typical problems 77

2.3.5 Combination of materials 78

2.3.6 Sedimentation tests 85

Supplementary problems for Chapter 2 91

3 Permeability and Seepage 92

3.1 Coefficient of permeability (k) 93

3.2 Seepage velocity (u_s) 94

3.3 Determination of the value of k 96

3.3.1 Constant head test 96

3.3.2 Falling head test 98

3.4 Field pumping tests 102

3.4.1 Unconfined layer 102

3.4.2 Radius of influence (R) 104

3.4.3 Confined layer under artesian pressure (s_A) 106

3.5 Permeability of stratified soil 107

3.6 Flow nets 108

3.6.1 Flow lines (FL) 109

3.6.2 Head loss in a flow channel 111

3.6.3 Equipotential lines (EPL) 111

3.6.4 Flow net construction 113

3.6.5 Application of flow nets 114

3.6.6 Seepage flowrate (Q) 114

3.6.7 Seepage pressure 115

3.6.8 Seepage force (S) 119

3.7 Erosion due to seepage 121

3.8 Prevention of piping 128

3.9 Flow net for earth dams 129

Supplementary problems for Chapter 3 135

4 Pressure at Depth Due to Surface Loading 139

4.1 Concentrated point load 140

4.2 Concentrated line load 142

4.3 Uniform strip loading (Michell's solution) 144

4.4 Bulb of pressure diagrams 147

4.5 Vertical pressure under triangular strip load 151

4.6 Vertical pressure under circular area 156

4.7 Rectangular footing 159

4.8 Footings of irregular shape 163

4.9 Pressure distribution under footings 167

4.9.1 Influence of footing 167

4.9.2 Influence of loading 170

4.10 Linear dispersion of pressure 170

Supplementary problems for Chapter 4 173

5 Effective Pressure (s') 175

5.1 Unloaded state 175

5.2 Loaded state 177

5.3 Flooded state 180

5.4 Types of problem 182

5.5 Effect of seepage on shallow footings 194

5.6 Ground water lowering (at atmospheric pressure) 195

5.7 Reduction of artesian pressure 196

5.8 Capillary movement of water 199

5.8.1 Equilibrium moisture content (m_E) 204

5.8.2 Soil suction (S_s) 208

Supplementary problems for Chapter 5 214

6 Shear Strength of Soils 219

6.1 Coulomb-Mohr Theory 220

6.1.1 Stresses on the plane of failure 221

6.1.2 Friction and cohesion 223

6.1.3 Apparent cohesion 224

6.2 Stress path 224

6.2.1 Stress path failure envelope 225

6.2.2 Variation of stress path 231

6.3 Effect of saturation 234

6.3.1 Effective Mohr's circle 234

6.3.2 Effective stress path (ESP) 234

6.4 Measurement of shear strength 238

6.4.1 Triaxial tests 238

6.4.2 Variation of pore pressure 240

6.4.3 Total excess pore pressure 241

6.4.4 Unconsolidated-undrained tests 242

6.4.5 Quick-undrained test 248

6.4.6 Consolidated-undrained (CU) test 250

6.4.7 Consolidated-drained (CD) test 252

6.4.8 Unconfined compression strength of clays 253

6.4.9 Standard shear box test 256

6.4.10 The Vane shear test 259

6.4.11 Residual shear strength 261

6.5 Thixotropy of clay 263

6.6 Undrained cohesion and overburden pressure 263

Supplementary problems for Chapter 6 265

7 Consolidation and Settlement 268

7.1 Consolidation 268

7.2 The pressure-voids ratio curve 270

7.2.1 Analytical solution 270

7.2.2 Equation of the s'-e curve 271

7.2.3 Alternative conventional procedure 274

7.2.4 Graphical solution 276

7.3 Forms of the s'-e curve 279

7.3.1 Normally consolidated clay 280

7.3.2 Overconsolidated clays 280

7.4 Coefficient of Compressibility (a_v) 281

7.5 Coefficient of Volume Change (m_v) 282

7.5.1 Voids ratio method 282

7.5.2 Direct method 282

7.6 Estimation of settlement 284

7.6.1 Voids ratio method 286

7.6.2 Method Using m_v 288

7.6.3 Direct method 289

7.7 Rate of consolidation 291

7.7.1 Variation of excess pore pressure with time 292

7.7.2 Typical pore pressure distributions 293

7.7.3 Estimation of time 294

7.7.4 Coefficient of Consolidation (c_v) 295

7.8 Pore pressure isochrones 301

7.8.1 Average percentage consolidation 302

7.9 Coefficient of permeability (k) 310

7.10 Time from similarity 310

7.11 Total settlement 311

7.11.1 Initial compression 311

7.11.2 Primary consolidation 311

7.11.3 Secondary consolidation 312

Supplementary problems for Chapter 7 314

8 Lateral Earth Pressure 319

8.1 Resistance to active expansion 320

8.2 The value of K₀ 321

8.3 Stress path representation 322

8.4 Rankine's theory of cohesionless soil 324

8.4.1 Stress path representation (Lambe) 330

8.5 Rankine-Bell theory for c - f soil 334

8.5.1 Tension cracks 335

8.5.2 Effect of surcharge (q kN/m) on z₀ 336

8.5.3 Water in the cracks only 336

8.6 Rankine-Bell theory for c-soil 336

8.7 Pressure-force and its line of action 336

8.7.1 Triangular diagram for uniform soil 337

8.7.2 Triangular diagram for water 337

8.7.3 Rectangular diagram for surcharge only 338

8.8 Wall supporting sloping surface 342

8.9 General formulae for c - f soil 342

8.9.1 Active case 343

8.9.2 Passive case (with surcharge) 345

8.10 Formulae for pure clay (f = 0) 349

8.11 Height of unsupported clay 350

8.12 Wedge theories 350

8.12.1 Procedure for cohesionless soil 351

8.12.2 Procedure for cohesive soil 355

8.12.3 Point of application of P_a(x) 359

8.12.4 Effect of static water table 360

8.13 Stability of retaining walls 360

8.13.1 Gravity walls 360

8.13.2 Cantilever walls 361

8.13.3 Buttress and counterfort walls 361

8.13.4 Stability check 362

8.14 Sheet piles 368

8.14.1 Cantilever sheet pile walls 369

8.14.2 Factor of safety 370

8.14.3 Bending of sheet piles 374

8.14.4 Sheet pile in cohesive soils 375

8.15 Anchored sheet pile walls 375

8.15.1 Free-earth support method 376

8.15.2 Fixed-earth support method 384

8.15.3 Anchorage 390

8.15.4 Length of tie rod (L) 390

8.15.5 Stability of anchors 390

8.16 Effect of ground water 393

8.17 Stability of deep trenches 400

8.17.1 Horizontal bracing 400

8.18 Bentonite slurry support 406

8.18.1 Trench in clay 407

8.18.2 Trench in sand 408

Supplementary problems for Chapter 8 413

9 Bearing Capacity of Soils 420

9.1 Terminology 420

9.1.1 Foundation pressure (s) 420

9.1.2 Net foundation pressure (s_n) 421

9.1.3 Effective overburden pressure (s'₀) 421

9.1.4 Ultimate bearing capacity (q_u) 421

9.1.5 Net ultimate bearing capacity (q_n) 421

9.1.6 Safe net bearing capacity (q_sn) 422

9.1.7 Safe bearing capacity (q_s) 422

9.1.8 Allowable foundation pressure (s_a) 422

9.1.9 Presumed bearing values 424

9.2 Shallow strip footing 424

9.2.1 Terzaghi's equation for q_u 425

9.2.2 Effect of static water table 428

9.3 Influence of footing shape 435

9.4 Shallow rectangular footing 436

9.4.1 Method of Fellenius 438

9.5 Deep foundations 439

9.5.1 Moderately deep foundations 439

9.6 Standard penetration test (SPT) 443

> 445

9.7.1 Types of pile 446

9.8 Some reasons for choosing piles 449

9.9 Some reasons for not choosing piles 451

9.10 Effects necessitating caution 451

9.11 Negative skin friction 453

9.12 Stress distribution around piles 455

9.13 Load-carrying capacity of piles 455

9.13.1 Static formulae 456

9.13.2 End-bearing resistance (Q_e) 456

9.13.3 Shaft resistance (Q_s) 457

9.13.4 Ultimate carrying capacity of pile 458

9.13.5 Allowable carrying capacity of piles (Q_a) 458

9.13.6 Negative skin friction (Q_f) 458

9.14 End bearing resistance and SPT 464

9.15 Influence of pile section on Q_u 465

9.16 Group of piles 465

9.16.1 Eccentrically loaded pile group 468

9.16.2 Settlement of pile groups 471

9.16.3 Raking piles 472

Supplementary problems for Chapter 9 474

10 Stability of Slopes 479

10.1 Short-term and long-term stability 479

10.2 Total stress analysis (cohesive soils) 480

10.2.1 Homogeneous, pure clay (f_u = 0) 480

10.2.2 Increasing the value of F_s 481

10.2.3 Minimum value of F_s 482

10.2.4 Potential slip surface 482

10.2.5 Determination of the factor of safety 483

10.2.6 Homogeneous c - f soil (total stress analysis) 497

10.2.7 Stratified slopes 500

10.2.8 Slopes under water 501

10.2.9 Taylor's stability numbers 505

10.3 Effective stress analysis (cohesive soils) 513

10.3.1 Method of slices (radial procedure) 513

10.3.2 Bishop's conventional method 518

10.3.3 Bishop's rigorous iterative method 519

10.4 Stability of infinite slopes 523

Supplementary problems for Chapter 10 528

11 Eurocode 7 530

11.1 Introduction 530

11.2 Recommended units 530

11.3 Limit states 531

11.4 Design procedures 531

11.5 Verification procedures 532

11.6 Application of partial factors 534

Appendices

Appendix A Mass and Weight 552

Appendix B Units, Conversion Factors and Unity Brackets 556

Appendix C Simpson's Rule 562

Appendix D Resultant Force and Its Eccentricity 567

Appendix E References 570

Index 572