APPLICATIONS OF THEORY OF ELASTICITY IN （应用弹性理论的）.pdf

APPLICATIONS OF THEORY OF ELASTICITY IN ROCK MECHANICS 1. INTRODUCTION 2. CLOSED-FORM SOLUTIONS VS. NUMERICAL METHODS 3. TWO-DIMENSIONAL FORMULATION 3.1 Plane Strain Analysis 3.2 Plane Stress Analysis 3.3 Generalized Plane Strain Analysis 3.4 Analysis in Polar or Cylindrical Coordinates 4. EXAMPLES 4.1 Hollow Cylinder under Pressure 4.2 Circular Hole Drilled Under a Triaxial Principal Stress Field at Infinity 4.3 Circular Hole Drilled Under a Triaxial Stress Field-General Solution 5. USING STRESSES IN ROCK ENGINEERING 6. REFERENCES Recommended Readings: 1) Chapter 4 in Rock Mechanics and the Design of Structures in Rocks, by Obert, L. and Duvall, W.I., Wiley, New York, 1967. CVEN 5768 - Lecture Notes 6 Page 1 © B. Amadei 1. INTRODUCTION The theory of elasticity is used widely in rock mechanics to predict how rock masses respond to loads and excavation (surface and underground). The assumptions inherent to the theory of elasticity are: C the material is elastic (linear or non-linear) which implies an immediate response during loading and a fully reversible response upon unloading, C the material behaves as a continuum. If time is involved (time-deferred response), the theory of viscoelasticity should be used instead. In classical linear elastic theory, it is assumed that no distinction needs to be made between the Lagrangian and Eulerian descriptions of strain. The six components of stress, the six components of strain and the three components of displacement must satisfy some basic equations called field equations, e.g. 3 equations of equilibrium, 6 equations relating strains to displacement and 6 equations relating stresses to strains. Thus, a total of 15 equations are available to solve for 15 unknowns, i.e. 6 stresses, 6 strains, and 3 d