Rock Rheology

1. Introduction.- 2. Mechanical Properties of Rocks.- 2.1. Diagnostic tests.- 2.2. Unconfined uniaxial compressive tests.- 2.3. Other mechanical tests.- 2.4. Triaxial tests.- Exercises.- 3. Creep of Rocks.- 3.1. History of creep tests.- 3.2. Uniaxial creep.- 3.3. Mathematical model.- 3.4. Examples.- 3.5. Creep in triaxial stress-state.- Exercises.- 4. Volume Deformation.- 4.1. Dilatancy and/or compressibility.- 4.2. Volume compressibility.- 4.3. Mathematical models for the hydrostatic compressibility of volume.- 4.4. Volume dilatancy.- 4.5. Rock dilatancy during creep.- Exercises.- 5. Classical Constitutive Equations.- 5.1. The linear elastic model.- 5.2. Plane strain elasticity in cylindrical coordinates.- 5.3. Thick-walled tube subjected to internal and external pressures.- 5.4. The general linear viscoelastic model.- Exercises.- 6. Rock ‘Elasticity’ at High Pressures.- 6.1. The elastic moduli.- 6.2. Determination of elastic moduli by dynamic procedures.- 6.3. Longitudinal and shear waves in the case of high stresses and finite strains.- 6.4. Restrictions concerning the elastic parameters.- Exercises.- 7. Rock Plasticity.- 7.1. Historical outline.- 7.2. Constitutive hypotheses.- 7.3. Constitutive equation.- 7.4. Yield function and plastic potential.- 7.5. Example for a dilatant rock.- 7.6. Example of compressible/dilatant rock.- 7.7. Generalization of the model for finite rotations.- Exercises.- 8. Elastic/Viscoplastic Constitutive Equations.- 8.1. General considerations.- 8.2. Experimental foundation.- 8.3. Constitutive hypotheses.- 8.4. Constitutive equations.- 8.5. An example for a compressible/dilatant hard rock.- 8.6. Examples for softer rocks.- 8.7. A uniaxial example.- 8.8. Acoustic emission.- Exercises.- 9. Damage and Failure of Rocks.- 9.1. Classicalshort-time failure-strength criteria.- 9.2. Some experimental evidence.- 9.3. The energetic damage parameter.- 9.4. Numerical examples.- Exercises.- 10. Stress states In-Situ.- 10.1. Primary stress-state.- 10.2. Secondary and relative stress fields.- 10.3. Initial stresses and strains for the linear elastic model.- 10.4. Primary states for the elasto-plastic constitutive equation.- 10.5. Primary states for the linear viscoelastic model.- 10.6. Primary states for the elastic/viscoplastic model.- 10.7. Stresses and strains around underground openings.- Exercises.- 11. Creep and Dilatancy/Compressibility of Rocks Around Vertical Shafts and Oil Wells.- 11.1. Formulation of the problem.- 11.2. The linear elastic solution.- 11.3. The linear viscoelastic rock.- 11.4. The elastic/viscoplastic rock.- 11.5. Dilatancy/compressibility and damage around a well.- 11.6. A more general primary stress-state.- Exercises.- 12. Creep and Dilatancy/Compressibility of Rocks Around Horizontal Tunnels.- 12.1. Formulation of the problem.- 12.2. The elastic approach.- 12.3. Creep around a tunnel according to a linear viscoelastic model.- 12.4. Creep according to an elastic/viscoplastic model.- 12.5. Creep, dilatancy/compressibility, damage, and failure around a tunnel.- Exercises.- 13. Tunnel Support Analysis.- 13.1. Formulation of the problem.- 13.2. Linear elastic support; linear viscoelastic rock.- 13.3. Non-linear self-adjusting supports; linear viscoelastic rock.- 13.4. Non-linear self-adjusting support; elastic/viscoplastic rock.- Exercises.- Appendix 1. A Short Introduction to Fracture Mechanics.- A1.1. Introduction.- A1.2. The fundamental relations of the plane theory of elasticity.- A1.4. The main boundary-value problems.- A1.5. The influence functions corresponding to the elementary crack.- A1.6. The Griffith crack in the plane problem.- A1.7. Stress intensity factors and criteria for the propagation of the crack.- A1.8. Systems of rectilinear cracks.- A1.9. Application to the crack kinking problem.- A1.10. Some numerical and experimental results.- Appendix 2. Creep and Stress Variation Around a Well or a Tunnel. A Numerical Approach.- References.- Author Index.