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Contents

Preface to the Fourth Edition 1

ix

Rock as a Material 1.1 1.2 1.3 1.4 1.5

Introduction Joints and faults Rock-formingminerals The fabric of rocks The mechanical nature of rock

2 Analysis of Stress and Strain 2.1 Introduction 2.2 Definition of traction and stress 2.3 Analysis of stress in two dimensions 2.4 Graphical representations of stress in two dimensions 2.5 Stresses in three dimensions 2.6 Stress transformations in three dimensions 2.7 Mohr’s representation of stress in three dimensions 2.8 Stress invariants and stress deviation 2.9 Displacement and strain 2.10 Infinitesimal strain in two dimensions 2.11 Infinitesimal strain in three dimensions 2.12 Determination of principal stresses or strains from

measurements 2.13 Compatibility equations 2.14 Stress and strain in polar and cylindrical coordinates 2.15 Finite strain 3 Friction on Rock Surfaces 3.1 Introduction 3.2 Amonton’s law 3.3 Friction on rock surfaces 3.4 Stick-slip oscillations

9 9 10 17 23 27 32 35 38 41 43 49

55 56 57 60 65 65 66 67 70

3.5

Sliding on a plane of weakness

73

3.6

Effects of time and velocity

76

vi

CONTENTS

4

5

6

Deformation and Failure of Rock 4.1 Introduction 4.2 The stress-strain curve 4.3 Effects of confining stress and temperature 4.4 Types of fracture 4.5 Coulomb failure criterion 4.6 Mohr’s hypothesis 4.7 Effects of pore fluids 4.8 Failure under true-triaxial conditions 4.9 The effect of anisotropy on strength

80

80 80 85 87 90 94 97 100 103

Linear Elasticity 5.1 Introduction 5.2 Stress-strain relations for an isotropic h e a r elastic solid 5.3 Special cases 5.4 Hooke’s law in terms of deviatoric stresses and strains 5.5 Equations of stress equilibrium 5.6 Equations of stress equilibrium in cylindrical and spherical coordinates 5.7 Airy stress functions 5.8 Elastic strain energy and related principles 5.9 Uniqueness theorem for elasticity problems 5.10 Stress-strain relations for anisotropic materials

106

Laboratory Testing of Rocks 6.1 Introduction 6.2 Hydrostatic tests 6.3 Uniaxial compression 6.4 Triaxial tests 6.5 Stability and stiff testing machines 6.6 True-triaxial tests 6.7 Diametral compression of cylinders 6.8 Torsion of circular cylinders 6.9 Bending tests 6.10 Hollow cylinders

145

7 Poroelasticityand Thermoelasticity 7.1 Introduction 7.2 Hydrostatic poroelasticity 7.3 Undrained compression 7.4 Constitutive equations of poroelasticity 7.5 Equations of stress equilibrium and fluid flow 7.6 One-dimensional consolidation 7.7 Applications of poroelasticity 7.8 Thermoelasticity

106 107 111 115 116 122 126 128 135 137

145 146 148 150 152 157 158 161 162 165 168

168 169 175 178 183 189 195 197

CONTENTS

vii

8 Stresses around Cavities and Excavations 8.1 Introduction 8.2 Complex variable method for two-dimensional elasticity

205

problems Homogeneous state of stress Pressurized hollow cylinder Circular hole in a rock mass with given far-field principal stresses Stresses applied to a circular hole in an infinite rock mass Stresses applied to the surface of a solid cylinder Inclusions in an infinite region Elliptical hole in an infinite rock mass Stresses near a crack tip Nearly rectangular hole Spherical cavities Penny-shaped cracks Interactions between nearby cavities

206 211 214

8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11 8.12 8.13 8.14 9

Inelastic Behavior 9.1 Introduction 9.2 Plasticity and yield 9.3 Elastic -plastic hollow cylinder 9.4 Circular hole in an elastic - brittle -plastic rock mass 9.5 Perfectly plastic behavior 9.6 Flow between flat surfaces 9.7 Flow rules and hardening 9.8 Creep 9.9 Simple rheological models 9.10 Theory of viscoelasticity 9.1 I Some simple viscoelastic problems

205

216 22 1 225 228 23 1 237 242 244 247 250 252

252 252 255 257 260 263 266 268 271 276 279

10 Micromechanical Models 10.1 Introduction 10.2 Effective moduli of heterogeneous rocks 10.3 Effect of pores on compressibility 10.4 Crack closure and elastic nonlinearity 10.5 Effective medium theories 10.6 Sliding crack friction and hysteresis 10.7 Griffith cracks and the Griffith locus 10.8 Linear elastic fracture mechanics 10.9 Griffith theory of failure

28 1

11 Wave Propagation in Rocks 11.1 Introduction 11.2 One-dimensional elastic wave propagation 11.3 Harmonic waves and group velocity 11.4 Elastic waves in unbounded media

321

281 281 284 292 295 301 307 311 314

321 322 327 332

viii

CONTENTS

11.5 Reflection and refraction of waves at an interface 11.6 Surface and interface waves 1 1.7 Transient waves 11.8 Effects of fluid saturation 1 1.9 Attenuation 1 1.10 Inelastic waves 12

Hydromechanical Behavior of Fractures Introduction Geometry of rock fractures Normal stiffness of rock fractures Behavior of rock fractures under shear Hydraulic transmissivity of rock fractures Coupled hydromechanical behavior Seismic response of rock fractures Fractured rock masses

12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8

337 343 347 353 355 360 365 365 365 369 375 377 386 388 394

13 State of Stress Underground 13.1 Introduction 13.2 Simple models for the state of stress in the subsurface 13.3 Measured values of subsurface stresses 13.4 Surface loads on a half-space: two-dimensional theory 13.5 Surface loads on a half-space: three-dimensionaltheory 13.6 Hydraulic fracturing 13.7 Other stress-measurementmethods

399 399 400 403 404 408 41 1 415

14 Geological Applications 14.1 Introduction 14.2 Stresses and faulting 14.3 Overthrust faulting and sliding under gravity 14.4 Stresses around faults 14.5 Mechanics of intrusion 14.6 Beam models for crustal folding 14.7 Earthquake mechanics

419 419 419 423 425 428 431 434

References

439

Index

469