Development of static and kinematic approaches in geomechanical problems

Abstract

Abstract The hypothesis of a linear stress field of a rock mass undisturbed by driving workings underlies the solution to many problems of rock mechanics. The problem of rock pressure control requires knowledge of the stress-strain state of the rock mass in the vicinity of workings, which causes the development of analytical and numerical methods for calculating the deformation. When the methods of numerical calculation were not sufficiently developed, the analytical capabilities of the selection of stress functions were used, which satisfied the conditions of small strain elasticity theory. The greatest success in this direction was achieved for the areas with angular points. The development of numerical methods shifted the point of influence of investigations to calculating the deformation of specific cases arising in a rock mass with workings. It is established in the work that analytical solutions for the areas with angular points are incorrect, and numerical solutions of Cauchy problems are also incorrect if an additional problem is not considered.