Fundamentals of Rock Mechanics

1.1 Introduction.

1.2 Joints and faults.

1.3 Rock-forming minerals.

1.4 The fabric of rocks.

1.5 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 principle 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.

3.5 Sliding on a plane of weakness.

3.6 Effects of time and velocity.

4. 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.

5. Linear Elasticity.

5.1 Introduction.

5.2 Stress-strain relations for an isotropic linear 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.

6. 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.

7. Poroelasticity and 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.

8. Stresses around Cavities and Excavations.

8.1 Introduction.

8.2 Complex variable method for two-dimensional elasticity problems.

8.3 Homogeneous state of stress.

8.4 Pressurised hollow cylinder.

8.5 Circular hole in a rock mass with given far-field principal stresses.

8.6 Stresses applied to a circular hole in an infinite rock mass.

8.7 Stresses applied to the surface of a solid cylinder.

8.8 Inclusions in an infinite region.

8.9 Elliptical hole in an infinite rock mass.

8.10 Stresses near a crack tip.

8.11 Nearly rectangular hole.

8.12 Spherical cavities.

8.13 Penny-shaped cracks.

8.14 Interactions between nearby cavities.

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.

9.11 Some simple viscoelastic problems.

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 Griffith theory of failure.

10.9 Linear elastic fracture mechanics.

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.

11.5 Reflection and refraction of waves at an interface.

11.6 Surface and interface waves.

11.7 Transient waves.

11.8 Effects of fluid saturation.

11.9 Attenuation.

11.10 Inelastic waves.

12. Hydromechanical Behavior of Fractures.

12.1 Introduction.

12.2 Geometry of rock fractures.

12.3 Normal stiffness of rock fractures.

12.4 Behaviour of rock fractures under shear.

12.5 Hydraulic transmissivity of rock fractures.

12.6 Coupled hydro-mechanical behavior.

12.7 Seismic response of rock fractures.

12.8 Fractured rock masses.

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-dimensional theory.

13.6 Hydraulic fracturing.

13.7 Other stress measurement methods.

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.

References