Rock Rheology: (7 Mechanics of Elastic and Inelastic Solids)

The present book is the result of work carried out over a period of about ten years by the author and his co-workers in order to describe more accurately the slow irreversible deformation in time of the rocks surrounding underground openings. To begin with, our efforts were directed toward a better under­ standing of the mechanical behaviour of rocks and to the formulation of more precise mathematical models for their dominant mechanical properties, mainly irreversible dilatancy and/or compressibility during creep. Subsequent efforts were focused on finding improved solutions to important mining and oil engineering problems, such as, for instance, the creep of rocks around wells and tunnels, short-term failure which may occur around an underground opening, damage and failure which take place after long-time intervals, the tunnel support analysis incorporating rock creep, etc. The book is the result of a great number of questions posed either by mining engineers or by the author himself, and of the corresponding answers (unfor­ tunately often only partial answers). This dialogue must certainly be continued in order to improve the models and to formulate models for other kinds of rocks, or, ultimately to obtain solutions for other important engineering problems. It is hoped that the book will also contribute to a better description, by means of mathematical models, of the mechanical behaviour of rocks.

Table of Contents:
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.

Review :
'This book is of interest to rock mechanics researchers especially those in the geotechnical field.' Pageoph