Cavity Expansion Methods in Geomechanics

Transcription

1 Cavity Expansion Methods in Geomechanics by Hai-Sui Yu School of Civil Engineering, University of Nottingham, U. K. KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON

2 TABLE OF CONTENTS Foreword Preface vii ix 1 INTRODUCTION SCOPE AND AIMS CAVITY EXPANSION THEORY APPLICATION TO GEOMECHANICS In-situ soil testing Pile foundations and earth anchors Underground excavations and tunnelling Wellbore instability SIGN CONVENTIONS SUMMARY 5 REFERENCES 6 Part I: Fundamental Solutions 2 ELASTIC SOLUTIONS INTRODUCTION ELASTIC SOLUTIONS IN ISOTROPIC MEDIA Expansion of a hollow sphere Expansion of a thick-walled cylinder Cylindrical cavity subject to biaxial in-situ stresses ELASTIC SOLUTIONS IN ANISOTROPIC MEDIA Expansion of a hollow sphere, Expansion of a thick-walled cylinder ELASTIC SOLUTIONS IN A SEMI-INFINITE HALF-SPACE Cylindrical cavity in a half-space Spherical cavity in a half-space SUMMARY 30 xi

3 xii Table of Contents REFERENCES 30 3 ELASTIC-PERFECTLY PLASTIC SOLUTIONS INTRODUCTION SOLUTIONS FOR TRESCA CRITERION Expansion of a spherical cavity in a finite medium Expansion of a cylindrical cavity in a finite medium Contraction of cavities in an infinite medium SOLUTIONS FOR MOHR-COULOMB CRITERION Expansion of a spherical cavity in a finite medium Expansion of a cylindrical cavity in a finite medium Expansion of cavities in an infinite medium Contraction of cavities in an infinite medium Expansion of cavities from zero initial radius SUMMARY 91 REFERENCES 93 4 CRITICAL STATE SOLUTIONS INTRODUCTION CAVITY EXPANSION FROM A FINITE INITIAL RADIUS Undrained expansion of cavities in clays Undrained contraction of cavities in clays Drained expansion of a cylindrical cavity in NC clays Drained expansion of cavities in heavily OC clays CAVITY EXPANSION FROM ZERO INITIAL RADIUS Drained expansion of cavities in sands Undrained expansion of a cylindrical cavity in a rate-type clay SUMMARY 136 REFERENCES FURTHER ELASTOPLASTIC SOLUTIONS INTRODUCTION CAVITY EXPANSION IN HARDENING/SOFTENING SOILS Undrained expansion of a cylindrical cavity in strain hardening/softening clays 139

4 Table of Contents xiii Undrained cavity expansion from zero radius in clays CAVITY CONTRACTION IN BRITTLE/PLASTIC ROCK Cavity unloading in brittle-plastic rock using the Mohr-Coulomb criterion Cavity unloading in brittle-plastic rock using the Hoek-Brown criterion SOLUTIONS FOR PIECE-WISE MOHR-COULOMB CRITERION INVERSE CAVITY EXPANSION PROBLEMS Cavity expansion in undrained clay Cavity expansion in cohesionless sand SUMMARY 166 REFERENCES TIME-DEPENDENT SOLUTIONS INTRODUCTION VISCO-ELASTIC SOLUTIONS Visco-elastic models and method of stress analysis Solutions for two simple cavity problems ELASTIC-VISCOPLASTIC SOLUTIONS Elastic-viscoplastic stress-strain relations Stresses and displacement in the initial plastic zone Stresses and displacement in the time-dependent plastic zone CONSOLIDATION SOLUTIONS Consolidation of soil around an expanding cavity Consolidation of soil around a contracting cavity SUMMARY 188 REFERENCES FINITE ELEMENT SOLUTIONS INTRODUCTION UNCOUPLED DRAINED AND UNDRAINED ANALYSIS Finite element formulation Plasticity models for soils Finite element program 201

5 xiv Table of Contents 7.3 COUPLED CONSOLIDATION ANALYSIS Finite element formulation The modified Cam clay model Finite element program 7.4 SUMMARY REFERENCES Part II: Geotechnical Applications 8 IN-SITU SOIL TESTING 8.1 INTRODUCTION The principle of pressuremeter testing Types of pressuremeter Cone penetrometer testing 8.2 SELF-BORING PRESSUREMETER TESTS IN CLAY Shear modulus In-situ total horizontal stress Undrained shear strength Consolidation coefficient Effects of finite pressuremeter length and initial stress state 8.3 SELF-BORING PRESSUREMETER TESTS IN SAND Shear modulus In-situ total horizontal stress Drained shear strength State parameter Effect of finite pressuremeter length 8.4 CONE PRESSUREMETER TESTS IN CLAY AND SAND Cone pressuremeter testing in clay Cone pressuremeter testing in sand 8.5 CONE PENETRATION TESTS IN SOIL Cone penetration in cohesive soils Cone penetration in cohesionless soils General remarks 8.6 SUMMARY

6 Table of Contents xv REFERENCES PILE FOUNDATIONS AND EARTH ANCHORS INTRODUCTION AXIAL CAPACITY OF DRIVEN PILES IN CLAY Shaft capacity of piles: effect of the installation on soil stress End bearing capacity of driven piles Increase in capacity of piles with time: effect of consolidation AXIAL CAPACITY OF DRIVEN PILES IN SAND End bearing capacity of piles in sand End bearing capacity of piles in crushable sands LATERAL CAPACITY OF PILES Limiting lateral pressures in clay Limiting lateral pressures in sand Limiting lateral pressures in rock BEARING CAPACITY OF SAND WITH A SURCHARGE UPLIFT CAPACITY OF PLATE ANCHORS IN SOILS Plate anchors in clay Plate anchors in sand SUMMARY 303 REFERENCES UNDERGROUND EXCAVATIONS AND TUNNELLING INTRODUCTION EXCAVATION DESIGN IN MASSIVE ROCK Elastic stress analysis Elastic-plastic (fracture) stress analysis ROCK SUPPORT IN UNDERGROUND EXCAVATIONS The principle of rock support and reinforcement Ground response curves TUNNELS IN COHESIVE SOILS Settlements due to tunnelling - total stress analysis 327

7 xvi Table of Contents Settlements due to tunnelling - effective stress analysis ' Stability of tunnels TUNNELS IN COHESIVE-FRICTIONAL SOILS Settlements due to tunnelling Stability of tunnels SUMMARY 354 REFERENCES WELLBORE INSTABILITY INTRODUCTION ELASTIC ANALYSIS OF WELLBORE INSTABILITY Stress analysis using constant stiffness elasticity Analysis using pressure-dependent elasticity Effect of stress-induced anisotropy on wellbore instability POROELASTIC ANALYSIS OF WELLBORE INSTABILITY Semi-analytical solutions Application to wellbore instability prediction PLASTIC ANALYSIS OF WELLBORE INSTABILITY Stability criteria Stability analysis using critical state models SUMMARY 379 REFERENCES 380 INDEX 383