# The Theory of Strata Mechanics

**Edited By**

- H. Gil, Silesian Technical University, Gliwice, Poland

During the last thirty years, the increasing need for extracting coal from new mining fields, especially from unmined protective pillars and seams that are threatened with rock bursts and rock-gas eruptions, has accelerated the development of research in the fundamental mining discipline known as rock mass mechanics or geomechanics. Generally, rock mass mechanics is concerned with rock mass movements and with the phenomena accompanying them. Extensive theoretical, laboratory, and in-situ investigations have resulted in considerable achievements in the field of rock mass mechanics. It is impossible to include all these achievements in a single monograph, and therefore in the present book the author has attempted to contruct a synthetic mathematical description of the rock mass movements and of the strain and stress state induced by mining, in particular when extracting mineral deposits.

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### Book information

- Published: May 1991
- Imprint: ELSEVIER
- ISBN: 978-0-444-98761-7

### Reviews

..a thorough, well-written, rigorously mathematical treatment of interest to mining engineers and engineering geologists working with tunnels and other underground openings...Professor Gil has written a comprehensive, well-organized treatise on strata mechanics.

Bulletin of the Association of Engineering Geologists

### Table of Contents

(abbreviated) **Introduction.** Development of rock mass mechanics. Interrelation between the mechanics of rock masses and the mechanics of continuous media. **1. Rock Masses Disturbed by Mining.** General characteristics of rock masses. Idealization of the rock mass. Primary stress state. The equation of continuity. The equation of motion. Concept of weightlessness of a rock. **2. The Elastic State of Rock Around Excavations.** The elastic properties of a rock mass. Effect of rock layering upon the form of the equations of state. Equation of equilibrium in terms of displacements. Plane state of strain in a rock mass. Systems operating in a plane state of strain. Three-dimensional states of displacement and stress in the vicinity of excavations. **3. The Viscoelastic State of Rock Around Excavations.** Rheological properties of rock masses. Differential form of the state equations. Integral form of the state equations. The displacement equation of equilibrium. Plane strain state. Plane strain- and stress distributions around excavations. Three-dimensional stress state around excavations. **4. Geometrical Theories of Rock Mass Movements.** Introduction. The effect of an excavation upon a point isolated on the ground surface. The relation between the surface of influence and the subsidence profile. The plane profile of a full subsidence trough. Inclination and curvature of the plane profile ofa subsidence trough. Determining the horizontal component of displacement and strain. Variation of the shape of a subsidence trough with time. Three-dimensional profile of a subsidence trough with two-parameter surface of influence. Three-dimensional profile of a subsidence trough described by a three-parameter influence function. Differential equations for displacements in a rock mass. **5. Elastic-Plastic Model of an Inhomogeneous Rock Mass.** Introduction Elastic-plastic properties of rocks. The mechanism of elastic-plastic deformation of rocks and the concept of dislocation. Dislocation energy. Dislocation movement and macroscopic plastic strains. Differential equation describing the average dislocation displacement vector. Dislocation model of a dry rock mass. Equations of the dislocation model. General solution of the equations of the dislocation model with account of the anisotropy and inhomogeneity of the rock mass. Solution of the equations of the dislocation model for an isotropic, uniformly elastic rock mass. Separating the elastic stress field from the total stress field. One-dimensional distribution of displacement and stress in a rock mass. Estimate of the distribution of stress in a coal seam. Generalization of the dislocation model. Dislocation model of a water-saturated rock mass. Effect of local rock swelling. Effect of local stowing. **6. Theoretical Foundations of Controlling Movements of a Rock Mass**. Introduction. Minimization of surface deformations by mining two rectilinear faces simultaneously. Minimization of surface deformations developed in a rock mass around the lining of a shaft. Minimization of surface deformations around the outcrop of a fold. Method for continuously controlling rock mass movements. References. Subject Index.