Soil Mechanics for Unsaturated Soils

Soil Mechanics for Unsaturated Soils......Page 1
Foreword......Page 3
Preface......Page 4
Table of Contents......Page 7
1.1 Role of Climate......Page 19
1.2.1 Construction and Operation of a Dam......Page 21
1.2.2 Natural Slopes Subjected to Environmental Changes......Page 23
1.2.4 Stability of Vertical or near Vertical Excavations......Page 24
1.2.6 Bearing Capacity for Shallow Foundations......Page 25
1.2.7 Ground Movements Involving Expansive Soils......Page 26
1.3 Typical Profiles of Unsaturated Soils......Page 27
1.3.1 Typical Tropical Residual Soil Profile......Page 28
1.3.2 Typical Expansive Soils Profile......Page 29
1.4 Need for Unsaturated Soil Mechanics......Page 30
1.5 Scope of the Book......Page 31
1.6.2 Air-Water Interface or Contractile Skin......Page 32
1.7 Terminology and Definitions......Page 33
1.8 Historical Developments......Page 34
2.1 Properties of the Individual Phases......Page 38
2.1.1.3 Air Phase......Page 39
2.1.2 Viscosity......Page 41
2.1.3 Surface Tension......Page 42
2.2 Interaction of Air and Water......Page 43
2.2.2 Water Vapor......Page 44
2.2.3 Air Dissolving in Water......Page 45
2.2.3.2 Diffusion of Gases through Water......Page 46
2.3.1 Porosity......Page 47
2.3.3 Degree of Saturation......Page 48
2.3.4 Water Content......Page 49
2.3.6 Basic Volume-Mass Relationship......Page 50
2.3.7 Changes in Volume-Mass Properties......Page 51
2.3.8.1 Piston-Porous Stone Analogy......Page 52
2.3.8.2 Conservation of Mass Applied to a Mixture......Page 54
2.3.8.4 Air-Water Mixture......Page 55
3.1.1 Effective Stress Concept for a Saturated Soil......Page 56
3.1.2 Proposed Effective Stress Equation for an Unsaturated Soil......Page 57
3.2.1.1 Normal and Shear Stresses on a Soil Element......Page 60
3.2.2 Stress State Variables......Page 61
3.2.2.1 Other Combinations of Stress State Variables......Page 62
3.2.4 Dry Soils......Page 63
3.3 Limiting Stress State Conditions......Page 64
3.4.1 The Concept of Axis Translation......Page 65
3.4.3 Other Experimental Evidence in Support of the Proposed Stress State Variables......Page 66
3.5.1 In Situ Stress State Component Profiles......Page 67
3.5.1.1 Coefficient of Lateral Earth Pressure......Page 70
3.5.1.2.3 Vegetation......Page 71
3.5.2 Extended Mohr Diagram......Page 72
3.5.2.1 Equation of Mohr Circles......Page 73
3.5.2.2 Construction of Mohr Circles......Page 74
3.5.3 Stress Invariants......Page 76
3.5.5 Stress Paths......Page 77
3.6 Role of Osmotic Suction......Page 81
4.1.1 Components of Soil Suction......Page 82
4.1.2 Typical Suction Values and Their Measuring Devices......Page 84
4.2.1 Capillary Height......Page 85
4.2.2 Capillary Pressure......Page 86
4.2.3 Height of the Capillary Rise and Radius Effects......Page 87
4.3.1.2 Peltier Effects......Page 88
4.3.1.3 Peltier Psychrometer......Page 89
4.3.1.4 Psychrometer Calibration......Page 91
4.3.1.5 Psychrometer Performance......Page 92
4.3.2.2 Measurement and Calibration Techniques (Filter Paper Method)......Page 95
4.3.2.3 The Use of the Filter Paper Method in Practice......Page 97
4.4 Measurements of Matric Suction......Page 98
4.4.1 High Air Entry Disks......Page 99
4.4.2 Direct Measurements......Page 100
4.4.2.1 Tensiometers......Page 101
4.4.2.2 Servicing the Tensiometer Prior to Installation......Page 102
4.4.2.5 Small Tip Tensiometer......Page 104
4.4.2.7 Tensiometer Performance for Field Measurements......Page 106
4.4.2.8 Osmotic Tensiometers......Page 108
4.4.2.9 Axis-Translation Technique......Page 109
4.4.3 Indirect Measurements......Page 111
4.4.3.1 Thermal Conductivity Sensors......Page 113
4.4.3.3 Calibration of Sensors......Page 115
4.4.3.5 The MCS 6000 Sensors......Page 117
4.4.3.6 The AGWA-II Sensors......Page 118
4.5 Measurements of Osmotic Suction......Page 122
4.5.1 Squeezing Technique......Page 123
5.1 Flow of Water......Page 125
5.1.1 Driving Potential for Water Phase......Page 126
5.1.3.1 Fluid and Porous Medium Components......Page 128
5.1.3.4 Relationship between Coefficient of Permeability and Degree of Saturation......Page 129
5.1.3.6 Relationship between Water Coefficient of Permeability and Volumetric Water Content......Page 131
5.1.3.7 Hysteresis of the Permeability Function......Page 134
5.2.2 Fick\'s Law for Air Phase......Page 135
5.2.3 Coefficient of Permeability with Respect to Air Phase......Page 137
5.2.3.2 Relationship between Air Coefficient of Permeability and Matric Suction......Page 138
5.3.1 Air Diffusion through Water......Page 139
5.4 Summary of Flow Laws......Page 141
6.1.1.1.1 Steady-State Method......Page 142
6.1.1.1.2 Apparatus for Steady-State Method......Page 143
6.1.1.1.4 Presentation of Water Coefficients of Permeability......Page 144
6.1.1.1.6 Instantaneous Profile Method......Page 145
6.1.1.1.7 Instantaneous Profile Method Proposed by Hamilton et al......Page 146
6.1.1.1.8 Computations for the Instantaneous Profile Method......Page 147
6.1.1.1.10 In Situ Instantaneous Profile Method......Page 148
6.1.1.1.11 Computations for the In Situ Instantaneous Profile Method......Page 149
6.1.2.1 Tempe Pressure Cell Apparatus and Test Procedure......Page 151
6.1.2.2 Volumetric Pressure Plate Extractor Apparatus and Test Procedure......Page 152
6.1.2.3 Test Procedure for the Volumetric Pressure Plate Extractor......Page 153
6.1.2.6 Computation of K_w Using the Soil-Water Characteristic Curve......Page 154
6.2 Measurement of Air Coefficient of Permeability......Page 156
6.2.2 Triaxial Permeameter Cell for Air and Water Permeability Measurements......Page 158
6.3 Measurement of Diffusion......Page 161
6.3.2 Measurements of the Coefficient of Diffusion......Page 162
6.3.2.1 Procedure for Computing Diffusion Properties......Page 163
6.3.3.2 Diffused Air Volume Indicator (DAVI)......Page 164
6.3.3.4 Computation of Diffused Air Volume......Page 166
6.3.3.5 Accuracy of the Diffused Air Volume Indicator......Page 167
7.1 Steady-State Water Flow......Page 168
7.1.1.2 Heterogeneous, Anisotropic Steady-State Seepage......Page 169
7.1.2 One-Dimensional Flow......Page 170
7.1.2.1 Formulation for One-Dimensional Flow......Page 171
7.1.2.2 Solution for One-Dimensional Flow......Page 172
7.1.2.4 Head Boundary Condition......Page 173
7.1.2.5 Flux Boundary Condition......Page 174
7.1.3.1 Formulation for Two-Dimensional Flow......Page 177
7.1.3.2 Solutions for Two-Dimensional Flow......Page 178
7.1.3.3 Seepage Analysis Using the Finite Element Method......Page 179
7.1.3.4 Examples of Two-Dimensional Problems......Page 182
7.1.3.5 Infinite Slope......Page 189
7.1.4 Three-Dimensional Flow......Page 191
7.2.1 One-Dimensional Flow......Page 193
7.2.2 Two-Dimensional Flow......Page 194
7.3 Steady-State Air Diffusion through Water......Page 195
8.1 Compressibility of Pore Fluids......Page 196
8.1.3 Compressibility of Air-Water Mixtures......Page 197
8.1.4 Components of Compressibility of an Air-Water Mixture......Page 199
8.1.5 Other Relations for Compressibility of Air-Water Mixtures......Page 200
8.1.5.1 Limitation of Kelvin\'s Equation in Formulating the Compressibility Equation......Page 201
8.2 Derivations of Pore Pressure Parameters......Page 202
8.2.1 Tangent and Secant Pore Pressure Parameters......Page 203
8.2.2 Summary of Necessary Constitutive Relations......Page 204
8.2.3 Drained and Undrained Loading......Page 206
8.2.4 Total Stress and Soil Anisotropy......Page 208
8.2.5 K_0-Loading......Page 209
8.2.6 Hilf\'s Analysis......Page 210
8.2.7 Isotropic Loading......Page 212
8.2.8 Uniaxial Loading......Page 214
8.2.9 Triaxial Loading......Page 215
8.2.10 Three-Dimensional Loading......Page 217
8.2.11 Alpha Parameters......Page 218
8.3.1 Secant B\'_h Pore Pressure Parameter Derived from Hilf\'s Analysis......Page 219
8.3.2 Graphical Procedure for Hilf\'s Analysis......Page 220
8.3.3 Experimental Results of Tangent B Pore Pressure Parameters for Isotropic Loading......Page 222
8.3.4 Theoretical Prediction of B Pore Pressure Parameters for Isotropic Loading......Page 224
8.3.5 Experimental Results of Tangent B and A Parameters for Triaxial Loading......Page 233
8.3.6 Experimental Measurements of the Alpha Parameter......Page 234
9.1 History of Shear Strength......Page 235
9.1.1 Data Associated with Incomplete Stress Variable Measurements......Page 242
9.2.1 Failure Criteria......Page 243
9.2.2 Shear Strength Equation......Page 245
9.2.3 Extended Mohr-Coulomb Failure Envelope......Page 246
9.2.4 Use of (Sigma - u_w ) and (u_a - u_w ) to Define Shear Strength......Page 248
9.2.5 Mohr-Coulomb and Stress Point Envelopes......Page 249
9.3 Triaxial Tests on Unsaturated Soils......Page 254
9.3.2 Constant Water Content Test......Page 256
9.3.3 Consolidated Undrained Test with Pore Pressure Measurements......Page 258
9.3.4 Undrained Test......Page 261
9.3.5 Unconfined Compression Test......Page 263
9.4 Direct Shear Tests on Unsaturated Soils......Page 265
9.5.1 Background on Strain Rates for Triaxial Testing......Page 266
9.5.2 Strain Rates for Triaxial Tests......Page 268
9.5.3 Displacement Rate for Direct Shear Tests......Page 272
9.7 Nonlinearity of Failure Envelope......Page 273
9.8 Relationships between Phi^b and Chi......Page 276
10.1.1 Axis-Translation Technique......Page 278
10.1.2 Pore-Water Pressure Control or Measurement......Page 281
10.1.3 Pressure Response below the Ceramic Disk......Page 284
10.1.4 Pore-Air Pressure Control or Measurement......Page 290
10.1.5 Water Volume Change Measurement......Page 291
10.1.7 Overall Volume Change Measurement......Page 293
10.1.8 Specimen Preparation......Page 294
10.1.9 Backpressuring to Produce Saturation......Page 295
10.2 Test Procedures for Triaxial Tests......Page 297
10.2.1 Consolidated Drained Test......Page 298
10.2.3 Consolidated Undrained Test with Pore Pressure Measurements......Page 299
10.3 Test Procedures for Direct Shear Tests......Page 300
10.4.1.1 Consolidated Drained Triaxial Tests......Page 302
10.4.1.3 Nonlinear Shear Strength versus Matric Suction......Page 304
10.4.1.4 Undrained and Unconfined Compression Tests......Page 306
10.4.2 Direct Shear Test Results......Page 307
11.1 Earth Pressures......Page 315
11.1.1 At Rest Earth Pressure Conditions......Page 316
11.1.2 Estimation of Depth of Cracking......Page 318
11.1.3 Extended Rankine Theory of Earth Pressures......Page 319
11.1.3.1 Active Earth Pressure......Page 321
11.1.3.5 Active Earth Pressure Distribution (Linear Decrease in Matric Suction to the Water Table)......Page 322
11.1.3.6 Active Earth Pressure Distribution When the Soil has Tension Cracks......Page 323
11.1.3.9 Passive Earth Pressure Distribution (Constant Matric Suction with Depth)......Page 325
11.1.3.11 Deformations with Active and Passive States......Page 326
11.1.4 Total Lateral Earth Force......Page 327
11.1.4.1 Active Earth Force......Page 328
11.1.4.2 Passive Earth Force......Page 329
11.1.5 Effect of Changes in Matric Suction on the Active and Passive Earth Pressure......Page 330
11.1.6 Unsupported Excavations......Page 331
11.1.6.1 Effect of Tension Cracks on the Unsupported Height......Page 332
11.2.1 Terzaghi Bearing Capacity Theory......Page 333
11.2.2.1 Stress State Variable Approach......Page 335
11.2.2.2 Total Stress Approach......Page 336
11.2.3 Bearing Capacity of Layered Systems......Page 337
11.3.1 Location of the Critical Slip Surface......Page 338
11.3.2 General Limit Equilibrium (GLE) Method......Page 339
11.3.2.1 Shear Force Mobilized Equation......Page 341
11.3.2.3 Factor of Safety with Respect to Moment Equilibrium......Page 342
11.3.2.5 Interslice Force Function......Page 343
11.3.2.6 Procedures for Solving the Factors of Safety Equation......Page 345
11.3.2.7 Pore-Water Pressure Designation......Page 346
11.3.3 Other Limit Equilibrium Methods......Page 348
11.3.4 Numerical Difficulties Associated with the Limit Equilibrium Method of Slices......Page 350
11.3.5.1 The \"Total Cohesion\" Method......Page 351
11.3.5.2.1 Example No. 1......Page 352
11.3.5.2.2 Example No. 2......Page 356
11.3.5.3.1 General Layout of Problems and Soil Properties......Page 358
11.3.5.3.2 Initial Conditions for the Seepage Analysis......Page 360
11.3.5.3.3 Seepage and Slope Stability Results under High-Intensity Rainfall Conditions......Page 362
12.1 Literature Review......Page 364
12.2.1 Continuity Requirements......Page 367
12.2.2 Overall Volume Change......Page 368
12.3.1 Elasticity Form......Page 369
12.3.1.2 Change in the Volume of Air......Page 371
12.3.1.5 Triaxial Loading......Page 372
12.3.1.6 K_0-Loading......Page 374
12.3.2 Compressibility Form......Page 375
12.3.4 Use of (Sigma - u_w ) and (u_a - u_w ) to Formulate Constitutive Relations......Page 376
12.4 Experimental Verifications for Uniqueness of Constitutive Surfaces......Page 378
12.4.2 Verification of Uniqueness of the Constitutive Surfaces Using Small Stress Changes......Page 379
12.4.3 Verification of the Constitutive Surfaces Using Large Stress State Variable Changes......Page 381
12.5 Relationship among Volumetric Deformation Coefficients......Page 383
12.5.1 Relationship of Volumetric Deformation Coefficients for the Void Ratio and Water Content Surfaces......Page 384
12.5.3 Laboratory Tests Used for Obtaining Volumetric Deformation Coefficients......Page 385
12.5.4 Relationship of Volumetric Deformation Coefficients for Unloading Surfaces......Page 387
12.5.6 Constitutive Surfaces on a Semi-Logarithmic Plot......Page 388
13.1 Literature Review......Page 392
13.2 Test Procedures and Equipments......Page 394
13.2.1 Loading Constitutive Surfaces......Page 395
13.2.1.1 Oedometer Tests......Page 396
13.2.1.2 Pressure Plate Drying Tests......Page 397
13.2.1.4 Determination of Volume Change Indices......Page 398
13.2.1.5 Determination of Volume Change Indices Associated with the Transition Plane......Page 400
13.2.1.6 Typical Results from Pressure Plate Tests......Page 404
13.2.1.8 \'\'Constant Volume\'\' Test......Page 406
13.2.1.10 Correction for the Compressibility of the Apparatus......Page 407
13.2.1.11 Correction for Sampling Disturbance......Page 408
13.2.2.1 Unloading Tests After Compression......Page 410
13.2.2.2 Pressure Plate Wetting Tests......Page 411
13.2.2.3 Free-Swell Tests......Page 412
13.2.2.4 Determination of Volume Change Indices......Page 413
14.1 Literature Review......Page 415
14.1.1 Factors Affecting Total Heave......Page 419
14.2 Past, Present, and Future States of Stress......Page 421
14.2.1 Stress State History......Page 422
14.2.2 In Situ Stress State......Page 423
14.3 Theory of Heave Predictions......Page 424
14.3.1 Total Heave Formulations......Page 425
14.3.3 Example of Heave Calculations......Page 426
14.3.4.1 Slab-on-Grade Floor, Regina, Saskatchewan......Page 428
14.4 Control Factors in Heave Prediction and Reduction......Page 429
14.4.1 Closed-Form Heave Equation When Swelling Pressure is Constant......Page 430
14.4.2 Effect of Correcting the Swelling Pressure on the Prediction of Total Heave......Page 431
14.4.3 Example with Wetting from the Top to a Specified Depth......Page 432
14.4.4 Example with a Portion of the Profile Removed by Excavation and Backfilled with a Nonexpansive Soil......Page 433
14.5 Notes on Collapsible Soils......Page 435
15.1 Literature Review......Page 437
15.2 Physical Relations Required for the Formulation......Page 438
15.3 Derivation of Consolidation Equations......Page 440
15.3.1 Water Phase Partial Differential Equation......Page 441
15.3.1.3 Special Case of an Unsaturated Soil Condition......Page 442
15.3.2 Air Phase Partial Differential Equation......Page 443
15.3.2.3 Special Case of an Unsaturated Soil......Page 444
15.4 Solution of Consolidation Equations Using Finite Difference Technique......Page 445
15.5.1.1 Presentation of Results......Page 447
15.5.1.2 Theoretical Analyses......Page 448
15.5.2.1 Presentation of Results......Page 451
15.5.2.2 Theoretical Analysis......Page 454
15.6 Dimensionless Consolidation Parameters......Page 455
16.1.1 Unsteady-State Seepage in Isotropic Soil......Page 458
16.1.2 Unsteady-State Seepage in an Anisotropic Soil......Page 459
16.1.2.1 Anisotropy in Permeability......Page 460
16.1.2.2 Water Phase Partial Differential Equation......Page 461
16.1.2.3 Seepage Analysis Using the Finite Element Method......Page 462
16.1.2.6 Example of Groundwater Seepage below a Lagoon......Page 465
16.1.2.7 Example of Seepage within a Layered Hill Slope......Page 467
16.2.1 Constitutive Relations......Page 474
16.2.1.1 Soil Structure......Page 479
16.2.1.2 Water Phase......Page 481
16.2.2.1 Equilibrium Equations......Page 490
16.3.1 Air Phase Partial Differential Equation......Page 491
16.3.3 Heat Flow Equation......Page 492
16.3.4.2 Surface Boundary Conditions for Water Vapor Flow......Page 493
16.3.4.3 Surface Boundary Conditions for Heat Flow......Page 495
Appendix A: Units and Symbols......Page 496
B.2 Total or Overall Equilibrium......Page 500
B.3 Independent Phase Equilibrium......Page 501
B.3.3 Contractile Skin Equilibrium......Page 502
B.4 Equilibrium of the Soil Structure (i.e., Arrangement of Soil Particles)......Page 505
B.5 Other Combinations of Stress State Variables......Page 506
References......Page 507
A......Page 525
B......Page 527
C......Page 528
D......Page 534
E......Page 536
F......Page 538
H......Page 540
I......Page 542
M......Page 543
N......Page 546
P......Page 547
R......Page 552
S......Page 553
T......Page 560
U......Page 563
V......Page 564
W......Page 565
Z......Page 567