Foreword ...................................................... vii
Preface ........................................................ ix
1 INTRODUCTION ................................................. 1
1.1 SCOPE AND AIMS .......................................... 1
1.2 CAVITY EXPANSION THEORY ................................. 2
1.3 APPLICATION TO GEOMECHANICS ............................. 2
1.3.1 In-situ soil testing ............................. 2
1.3.2 Pile foundations and earth anchors ............... 3
1.3.3 Underground excavations and tunnelling ........... 4
1.3.4 Wellbore instability ............................. 4
1.4 SIGN CONVENTIONS ........................................ 5
1.5 SUMMARY ................................................. 5
REFERENCES ................................................... 6
Part I: Fundamental Solutions
2 ELASTIC SOLUTIONS ............................................ 9
2.1 INTRODUCTION ............................................ 9
2.2 ELASTIC SOLUTIONS IN ISOTROPIC MEDIA .................... 9
2.2.1 Expansion of a hollow sphere ..................... 9
2.2.2 Expansion of a thick-walled cylinder ............ 12
2.2.3 Cylindrical cavity subject to biaxial in-situ
stresses ........................................ 14
2.3 ELASTIC SOLUTIONS IN ANISOTROPIC MEDIA ................. 18
2.3.1 Expansion of a hollow sphere .................... 18
2.3.2 Expansion of a thick-walled cylinder ............ 21
2.4 ELASTIC SOLUTIONS IN A SEMI-INFINITE HALF-SPACE ........ 23
2.4.1 Cylindrical cavity in a half-space .............. 24
2.4.2 Spherical cavity in a half-space ................ 27
2.5 SUMMARY ................................................ 30
REFERENCES .................................................. 30
3 ELASTIC-PERFECTLY PLASTIC SOLUTIONS ......................... 32
3.1 INTRODUCTION ........................................... 32
3.2 SOLUTIONS FOR TRESCA CRITERION ......................... 32
3.2.1 Expansion of a spherical cavity in a finite
medium .......................................... 33
3.2.2 Expansion of a cylindrical cavity in a finite
medium .......................................... 38
3.2.3 Contraction of cavities in an infinite medium ... 43
3.3 SOLUTIONS FOR MOHR-COULOMB CRITERION ................... 50
3.3.1 Expansion of a spherical cavity in a finite
medium .......................................... 50
3.3.2 Expansion of a cylindrical cavity in a finite
medium .......................................... 57
3.3.3 Expansion of cavities in an infinite medium ..... 65
3.3.4 Contraction of cavities in an infinite medium ... 72
3.3.5 Expansion of cavities from zero initial
radius ........................................... 84
3.4 SUMMARY ................................................ 91
REFERENCES .................................................. 93
4 CRITICAL STATE SOLUTIONS .................................... 95
4.1 INTRODUCTION ........................................... 95
4.2 CAVITY EXPANSION FROM A FINITE INITIAL RADIUS .......... 95
4.2.1 Undrained expansion of cavities in clays ........ 95
4.2.2 Undrained contraction of cavities in clays ..... 112
4.2.3 Drained expansion of a cylindrical cavity in
NC clays ....................................... 116
4.2.4 Drained expansion of cavities in heavily ОС
clays .......................................... 121
4.3 CAVITY EXPANSION FROM ZERO INITIAL RADIUS ............. 125
4.3.1 Drained expansion of cavities in sands ......... 125
4.3.2 Undrained expansion of a cylindrical cavity
in a rate-type clay ............................ 131
4.4 SUMMARY ............................................... 136
REFERENCES ................................................. 137
5 FURTHER ELASTOPLASTIC SOLUTIONS ............................ 139
5.1 INTRODUCTION .......................................... 139
5.2 CAVITY EXPANSION IN HARDENING/SOFTENING SOILS ......... 139
5.2.1 Undrained expansion of a cylindrical cavity
in strain hardening/softening clays ............ 139
5.2.2 Undrained cavity expansion from zero radius
in clays ....................................... 142
5.3 CAVITY CONTRACTION IN BRITTLE/PLASTIC ROCK ............ 144
5.3.1 Cavity unloading in brittle-plastic rock
using the Mohr-Coulomb criterion ............... 145
5.3.2 Cavity unloading in brittle-plastic rock
using the Hoek-Brown criterion ................. 150
5.4 SOLUTIONS FOR РШСЕ-WISE MOHR-COULOMB CRITERION ........ 155
5.5 INVERSE CAVITY EXPANSION PROBLEMS ..................... 163
5.5.1 Cavity expansion in undrained clay ............. 163
5.5.2 Cavity expansion in cohesionless sand .......... 165
5.6 SUMMARY ............................................... 166
REFERENCES ................................................. 168
6 TIME-DEPENDENT SOLUTIONS ................................... 170
6.1 INTRODUCTION .......................................... 170
6.2 VISCO-ELASTIC SOLUTIONS ............................... 170
6.2.1 Visco-elastic models and method of stress
analysis ....................................... 170
6.2.2 Solutions for two simple cavity problems ....... 174
6.3 ELASTIC-VISCOPLASTIC SOLUTIONS ........................ 176
6.3.1 Elastic-viscoplastic stress-strain relations ... 177
6.3.2 Stresses and displacement in the initial
plastic zone ................................... 177
6.3.3 Stresses and displacement in the time-
dependent plastic zone ......................... 179
6.4 CONSOLIDATION SOLUTIONS ............................... 181
6.4.1 Consolidation of soil around an expanding
cavity ......................................... 181
6.4.2 Consolidation of soil around a contracting
cavity ......................................... 185
6.5 SUMMARY ............................................... 188
REFERENCES ................................................. 189
7 FINITE ELEMENT SOLUTIONS ................................... 190
7.1 INTRODUCTION .......................................... 190
7.2 UNCOUPLED DRAINED AND UNDRAINED ANALYSIS .............. 190
7.2.1 Finite element formulation ..................... 190
7.2.2 Plasticity models for soils .................... 193
7.2.3 Finite element program ......................... 201
7.3 COUPLED CONSOLIDATION ANALYSIS ........................ 202
7.3.1 Finite element formulation ..................... 202
7.3.2 The modified Cam clay model .................... 204
7.3.3 Finite element program ......................... 205
7.4 SUMMARY ............................................... 205
REFERENCES ................................................. 206
Part II: Geotechnical Applications
8 IN-SITU SOIL TESTING ....................................... 209
8.1 INTRODUCTION .......................................... 209
8.1.1 The principle of pressuremeter testing ......... 209
8.1.2 Types of pressuremeter ......................... 209
8.1.3 Cone penetrometer testing ...................... 210
8.2 SELF-BORING PRESSUREMETER TESTS IN CLAY ............... 211
8.2.1 Shear modulus .................................. 212
8.2.2 In-situ total horizontal stress ................ 213
8.2.3 Undrained shear strength ....................... 213
8.2.4 Consolidation coefficient ...................... 223
8.2.5 Effects of finite pressuremeter length and
initial stress state ........................... 224
8.3 SELF-BORING PRESSUREMETER TESTS IN SAND ............... 227
8.3.1 Shear modulus .................................. 227
8.3.2 In-situ total horizontal stress ................ 228
8.3.3 Drained shear strength ......................... 228
8.3.4 State parameter ................................ 233
8.3.5 Effect of finite pressuremeter length .......... 243
8.4 CONE PRESSUREMETER TESTS IN CLAY AND SAND ............. 245
8.4.1 Cone pressuremeter testing in clay ............. 245
8.4.2 Cone pressuremeter testing in sand ............. 247
8.5 CONE PENETRATION TESTS IN SOIL ........................ 255
8.5.1 Cone penetration in cohesive soils ............. 256
8.5.2 Cone penetration in cohesionless soils ......... 260
8.5.3 General remarks ................................ 266
8.6 SUMMARY ............................................... 267
REFERENCES ................................................. 267
9 PILE FOUNDATIONS AND EARTH ANCHORS ......................... 275
9.1 INTRODUCTION .......................................... 275
9.2 AXIAL CAPACITY OF DRIVEN PILES IN CLAY ................ 276
9.2.1 Shaft capacity of piles: effect of the
installation on soil stress .................... 276
9.2.2 End bearing capacity of driven piles ........... 282
9.2.3 Increase in capacity of piles with time:
effect of consolidation ........................ 283
9.3 AXIAL CAPACITY OF DRIVEN PILES IN SAND ................ 285
9.3.1 End bearing capacity of piles in sand .......... 285
9.3.2 End bearing capacity of piles in crushable
sands .......................................... 289
9.4 LATERAL CAPACITY OF PILES ............................. 289
9.4.1 Limiting lateral pressures in clay ............. 289
9.4.2 Limiting lateral pressures in sand ............. 290
9.4.3 Limiting lateral pressures in rock ............. 291
9.5 BEARING CAPACITY OF SAND WITH A SURCHARGE ............. 293
9.6 UPLIFT CAPACITY OF PLATE ANCHORS IN SOILS ............. 295
9.6.1 Plate anchors in clay .......................... 296
9.6.2 Plate anchors in sand .......................... 300
9.7 SUMMARY ............................................... 303
REFERENCES ................................................. 305
10 UNDERGROUND EXCAVATIONS AND TUNNELLING ..................... 309
10.1 INTRODUCTION .......................................... 309
10.2 EXCAVATION DESIGN IN MASSIVE ROCK ..................... 310
10.2.1 Elastic stress analysis ........................ 311
10.2.2 Elastic-plastic (fracture) stress analysis ..... 316
10.3 ROCK SUPPORT IN UNDERGROUND EXCAVATIONS ............... 319
10.3.1 The principle of rock support and
reinforcement .................................. 319
10.3.2 Ground response curves ......................... 321
10.4 TUNNELS IN COHESIVE SOILS ............................. 324
10.4.1 Settlements due to tunnelling - total stress
analysis ....................................... 327
10.4.2 Settlements due to tunnelling - effective
stress analysis ................................ 332
10.4.3 Stability of tunnels ........................... 346
10.5 TUNNELS IN COHESIVE-FRICTIONAL SOILS .................. 348
10.5.1 Settlements due to tunnelling .................. 348
10.5.2 Stability of tunnels ........................... 352
10.6 SUMMARY ............................................... 354
REFERENCES ................................................. 356
11 WELLBORE INSTABILITY ....................................... 360
11.1 INTRODUCTION .......................................... 360
11.2 ELASTIC ANALYSIS OF WELLBORE INSTABILITY .............. 361
11.2.1 Stress analysis using constant stiffness
elasticity ..................................... 362
11.2.2 Analysis using pressure-dependent elasticity ... 364
11.2.3 Effect of stress-induced anisotropy on
wellbore instability ........................... 366
11.3 POROELASTIC ANALYSIS OF WELLBORE INSTABILITY ......... 369
11.3.1 Semi-analytical solutions ...................... 369
11.3.2 Application to wellbore instability
prediction ..................................... 372
11.4 PLASTIC ANALYSIS OF WELLBORE INSTABILITY .............. 376
11.4.1 Stability criteria ............................. 376
11.4.2 Stability analysis using critical state
models ......................................... 377
11.5 SUMMARY ............................................... 379
REFERENCES .................................................... 380
INDEX ......................................................... 383
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