Solution of a boundary-value problem which arises in determining the state of stress of solid rock

Abstract

Gritsko [1] and Vlasenko [2] formulated an experimental-analytical method of determining the stresses in the solid rock by means of field measurements of the displacements of the roofs of coal seams during working. Vlasenko and Senuk [3] formulatedtheplane cases of problems in the theory of elasticity which arise in determining the state of stress of the rock. By the method of Muskhelishvili [4], these problems can be reduced to the determination of a piecewise-holomorphie function if(z) which is related to the true stresses by the well-known formulas of Kolosov and Muskhelishvili [4], which satisfy the following boundary condition on the real axis Im z = 0:where ++(t) and +-(t) are the boundary values of the unknown function on approaching the upper and lower halfplanes, the piecewise-constant function G(t) is a coefficient of the problem, and g(t) is an independent term.In this article we propose a method of solving the boundary problem of Riemann (1). with the special features of boundary conditions specified from experimental data.Problem A. I, 5* of [3]. Let us consider this, which is the most general and characteristic problem of the experimental-analytical method. In this ease the functions G(t) and g(t) take the form O(t) = 1, t 6 L,= (a', a) + (o, 03 -1, t ( (a, b)e2.to -~) outside (a', b')