Cavity Expansion Methods in Geomechanics by Hai-Sui Yu School of Civil Engineering, University of Nottingham, U. K. KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON
TABLE OF CONTENTS Foreword Preface vii 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 xi
xii Table of Contents 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 OC 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
Table of Contents xiii 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 PIECE-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
xiv Table of Contents 7.3 COUPLED CONSOLIDATION ANALYSIS 7.3.1 Finite element formulation 7.3.2 The modified Cam clay model 7.3.3 Finite element program 7.4 SUMMARY REFERENCES Part II: Geotechnical Applications 8 IN-SITU SOIL TESTING 8.1 INTRODUCTION 8.1.1 The principle of pressuremeter testing 8.1.2 Types of pressuremeter 8.1.3 Cone penetrometer testing 8.2 SELF-BORING PRESSUREMETER TESTS IN CLAY 8.2.1 Shear modulus 8.2.2 In-situ total horizontal stress 8.2.3 Undrained shear strength 8.2.4 Consolidation coefficient 8.2.5 Effects of finite pressuremeter length and initial stress state 8.3 SELF-BORING PRESSUREMETER TESTS IN SAND 8.3.1 Shear modulus 8.3.2 In-situ total horizontal stress 8.3.3 Drained shear strength 8.3.4 State parameter 8.3.5 Effect of finite pressuremeter length 8.4 CONE PRESSUREMETER TESTS IN CLAY AND SAND 8.4.1 Cone pressuremeter testing in clay 8.4.2 Cone pressuremeter testing in sand 8.5 CONE PENETRATION TESTS IN SOIL 8.5.1 Cone penetration in cohesive soils 8.5.2 Cone penetration in cohesionless soils 8.5.3 General remarks 8.6 SUMMARY
Table of Contents xv 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
xvi Table of Contents 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