FUNDAMENTALS AND APPLICATIONS OF ROCK MECHANICS

By G. LAVIL

CONTENTS 1 INTRODUCTION AIMS ROCK FRACTURES NOTATION AND BASIC CONCEPTS SOME DEFINITIONS FROM STRUCTURAL GEOLOGY HOW TO SOLVE FRACTURE PROBLEMS ACCURACY, SIGNIFICANT FIGURES, AND ROUNDING SUMMARY MAIN SYMBOLS USED WORKED EXAMPLES EXERCISES REFERENCES AND SUGGESTED READING 2 STRESS SOME BASIC DEFINITIONS THE CONCEPT OF STRESS PRINCIPAL STRESSES STRESSES ON AN ARBITRARY PLANE MOHR’S CIRCLES SPECIAL STRESS STATES STRESS FIELDS 3 DISPLACEMENT AND STRAIN BASIC DEFINITIONS DISPLACEMENT STRAIN DEFORMATION OF A ROCK BODY MEASURING STRAIN 4 RELATION BETWEEN STRESS AND STRAIN ONE-DIMENSIONAL HOOKE’S LAW THREE-DIMENSIONAL HOOKE’S LAW ELASTIC CONSTANTS ROCK STRESS CRUSTAL STRESS AND STRAIN FIELDS STRAIN ENERGY 5 LOADING OF BRITTLE ROCKS TO FAILURE BEHAVIOUR OF ROCK UNDER LOADING THE EXPERIMENTAL STRESS–STRAIN CURVE THE MAIN STAGES LEADING TO BRITTLE FAILURE THE BRITTLE–DUCTILE TRANSITION 6 STRESS CONCENTRATION ANALOGIES AND ELLIPTICAL HOLES CIRCULAR HOLES AND STRESS MEASUREMENTS CAVITIES HOLES CLOSE TO A FREE SURFACE HOLES IN ANISOTROPIC ROCKS 7 THEORIES OF BRITTLE FAILURE OF ROCKS FAILURE AND STRENGTH THE COULOMB MATERIAL THE COULOMB CRITERION FOR ROCKS SOME EMPIRICAL CRITERIA THE THEORY OF GRIFFITH THE GRIFFITH CRITERION FOR ROCKS A COMBINED ROCK-FAILURE CRITERION TRESCA AND VON MISES CRITERIA REFERENCES AND FURTHER READING 8 EXTENSION FRACTURES AND SHEAR FRACTURES BASIC TYPES OF ROCK FRACTURES TENSION FRACTURES HYDROFRACTURES SHEAR FRACTURES 9 DISPLACEMENTS AND DRIVING STRESSES OF FRACTURES CRACK GEOMETRIES DISPLACEMENT MODES OF CRACKS DIP-SLIP FAULTS STRIKE-SLIP FAULTS 10 TOUGHNESS AND FRACTURE MECHANICS TOUGHNESS FRACTURE MECHANICS TOUGHNESS OF ROCK CORE, DAMAGE ZONE, AND PROCESS ZONE BASIC EQUATIONS OF K AND G TOUGHNESS IN TERMS OF FRACTURE DISPLACEMENTS 10 10 WORKED EXAMPLES 10 11 EXERCISES 11 FIELD ANALYSIS OF EXTENSION FRACTURES TYPES OF EXTENSION FRACTURES JOINTS MINERAL VEINS DYKES INCLINED SHEETS SILLS MAN-MADE HYDRAULIC FRACTURES 11 10 FIELD MEASUREMENTS OF FRACTURES 11 11 SUMMARY 11 12 WORKED EXAMPLES 11 13 EXERCISES 12 FIELD ANALYSIS OF FAULTS SLICKENSIDES AND OBLIQUE-SLIP FAULTS 13 EVOLUTION OF EXTENSION FRACTURES DEVELOPMENT OF TENSION FRACTURES PROPAGATION OF HYDROFRACTURES HYDROFRACTURE DEFLECTION AND ARREST HYDROFRACTURE APERTURE AND OVERPRESSURE TIP STRESSES AND SURFACE DEFORMATION 13 10 EXERCISES 14 EVOLUTION OF FAULTS INITIATION OF FAULTS FAULT GROWTH FAULT DAMAGE ZONE AND CORE LOCAL STRESSES IN FAULT ZONES FRACTURE DEFLECTION AND ARREST EVOLUTION OF FAULT SLIP 14 10 WORKED EXAMPLES 14 11 EXERCISES 15 FLUID TRANSPORT IN ROCKS – THE BASICS FLUID TRANSPORT IN POROUS AND FRACTURED ROCKS DARCY’S LAW THE CUBIC LAW FLUID TRANSPORT IN A SINGLE SET OF FRACTURES FLUID TRANSPORT IN TWO ORTHOGONAL SETS OF FRACTURES FRACTURES AND PERMEABILITY 15 10 WORKED EXAMPLES 15 11 EXERCISES 16 FLUID TRANSPORT IN FAULTS OVERVIEW GROUND-WATER FLOW TO FAULT ZONES GROUND-WATER FLOW ALONG FAULT ZONES APERTURE AND FLUID PRESSURE FLUID TRANSPORT IN THE DAMAGE ZONE FLUID TRANSPORT IN THE CORE PERMEABILITY DEVELOPMENT 16 10 MAIN SYMBOLS USED 16 11 WORKED EXAMPLES 16 12 EXERCISES 17 FLUID TRANSPORT IN HYDROFRACTURES DRIVING PRESSURE AND VOLUMETRIC FLOW RATE VERTICAL HYDROFRACTURES (DYKES) INCLINED HYDROFRACTURES (CONE SHEETS) 17 10 EXERCISES