Rock Anisotropy and the Theory of Stress Measurements

ISBN-13: 9783540123880 / Angielski / Miękka / 1983 / 482 str.

Bernard Amadei

Opis

Any undisturbed rock mass is subject to natural stresses inclu ding gravitational stresses due to the mass of the overburden and possibly tectonic stresses due to the straining of the earth's crust and remanent stresses due to past tectonism. Knowledge of the in situ stress field must be integrated into any rock engineering design along with general rock mass characteristics such as de for mability, strength, permeability and time dependent behavior. For example, the choice of optimum orientation and shape of deep underground caverns or complex underground works will be controlled by the orientation and the magnitude of the in situ stress @ield if it is necessary to minimize stress concentration problems. Long term variation of the in situ stress field may also help to evaluate the potential hazard of earthquake occurences. The magnitude and orientation of the stress field ata point within a rock mass can be measured but there is no known method by which the state of stress at a point can be accurately determined by instruments located remotely. In general, measurements are made inside boreholes, on outcrops or on the internal surfaces of under ground cavities. Most of the measuring techniques intentionally disturb the state of stress in the rock and then measure consequent strains and displacements. Measured strains or displacements are then related to the stresses through assumptions of material behavior. A common procedure is to assume that the rock mass is linearly elastic, isotropic, continuous and homogeneous."

Spis treści

1: Introduction.- 2: Deformability of Anisotropic Rocks.- 2.1 Introduction.- 2.2 Constitutive Relations.- 2.2.1 Generalized Hookers Law.- 2.2.2 Stratified Media.- 2.2.3 Regularly Jointed Rocks.- 2.2.4 Effective Stress Laws.- 2.2.5 Transformation of Elastic Constants.- 2.3 Testing of Anisotropic Rocks.- 2.3.1 Laboratory Testing.- 2.3.2 In Situ Testing.- 3: Strength of Anisotropic Rocks.- 3.1 Introduction.- 3.2 Experimental Observations.- 3.2.1 Laboratory Testing.- 3.2.2 In Situ Testing.- 3.3 Analytical Models.- 3.3.1 Discontinuous Models.- 3.3.2 Continuous Models.- 4: Elastic Equilibrium of an Anisotropic Homogeneous Body Bounded Internally by a Cylindrical Surface of Arbitrary Cross Section.- 4.1 Introduction.- 4.2 Geometry and Definition of the Problem.- 4.3 Formulation of the Problem.- 4.3.1 Basic Equations.- 4.3.2 Sign Conventions.- 4.3.3 Beltrami Michell Equations of Compatibility.- 4.3.4 Boundary Conditions.- 4.3.5 The General Expressions for the Stress Functions.- 4.3.6 The General Expressions for the Components of Stress and Displacement.- 4.4 Special Case of Anisotropy: A Plane of Elastic Symmetry Perpendicular to the Hole Axis.- 4.5 Plane Strain and Plane Stress Formulations.- 4.5.1 Plane Problems of the Theory of Elasticity.- 4.5.2 Plane Strain Formulations.- 4.5.3 Plane Stress Formulations.- 4.5.4 Remarks.- 4.6 Particular Solution for an Infinite Cylinder with a Circular Cross Section.- 4.6.1 Fourier Series Boundary Conditions.- 4.6.2 General Expressions for the Analytic Functions Øk (zk) (k = 1,2,3).- 4.6.3 Special Cases of Fourier Distributions.- 4.6.4 Closed Form Solutions.- 4.6.5 Remarks.- 4.6.6 Numerical Examples.- 5: Elastic Equilibrium of an Anisotropic Homogeneous Body Bounded Internally by an Isotropic Inclusion of Circular Cross Section.- 5.1 Introduction.- 5.2 Geometry and Definition of the Problem.- 5.3 Formulation of Problem (A).- 5.3.1 Basic Equations.- 5.3.2 Beltrami Michell Equations of Compatibility.- 5.3.3 Fourier Series Boundary Conditions.- 5.3.4 Formulation of the Plane Problem.- 5.3.5 Formulation of the Antiplane Problem.- 5.4 Formulation of Problem (B).- 5.5 Condition of Continuity.- 5.6 Closed Form Solutions.- 5.7 Remarks.- 5.7.1 Rigid Body Translations.- 5.7.2 Variations in Length of Oblique Distances.- 5.7.3 Induced Stress Field within the Anisotropic Body.- 5.7.4 Limiting Cases.- 5.8 Numerical Examples.- 5.8.1 Isotropic Solution.- 5.8.2 Anisotropic Solution.- 6: Influence of Rock Anisotropy on Stress Measurements by Overcoring Techniques.- 6.1 Introduction.- 6.2 In Situ Determination of Stress by Relief Techniques.- 6.3 Information Obtained from Measuring Techniques.- 6.4 General Formulas for Overcoring and Undercoring Techniques.- 6.4.1 Overcoring Techniques.- 6.4.2 Undercoring Techniques.- 6.4.3 Absolute Stresses — Changes in Stress.- 6.5 General Results for Overcoring in Anisotropic Media.- 6.5.1 Introduction.- 6.5.2 Isotropic Solution.- 6.5.3 Anisotropic Solution; Literature Review.- 6.5.4 Anisotropic Solution; Present Analysis.- a) Number of Independent Measurements in a Single Borehole.- b) Number of Boreholes.- c) Influence of Rock Anisotropy on the Determination of the In Situ Stress Field.- 7: Summary and Conclusions.- References.- Appendix 2.1.- Appendix 4.1.- Appendix 4.2.- Appendix 4.3.- Appendix 4.4.- Appendix 4.5.- Appendix 4.6.- Appendix 4.7.- Appendix 4.8.- Appendix 5.1.- Appendix 5.2.- Appendix 5.3.- Appendix 5.4.- Appendix 6.1.- Appendix 6.2: Program Berni 1.- Appendix 6.3: Program Berni 2.- Appendix 6.4: Program Berni 3.- Appendix 6.5: Program listings.