Mathematical modeling of the problem of compression of a rock sample with friction at the end

Abstract

Analytical solutions of the problem of the stress-strain state of the environment around the workings with non-uniform compression in the elastic-plastic formulation, with account for transboundary deformation are few. Some solutions of the problem under the conditions of Tresk and Coulomb plasticity are obtained. In these solutions, there are simplifying assumptions that the area of inelastic deformations cover the entire contour of the mine, the angle of internal friction is zero, etc. The features of the post-limit deformation of rock masses near underground mines consist on the formation of destruction zones around the mine workings, zones of plastic and elastic deformation, covering the part of contour or the entire contour depending on the boundary conditions and contour profiles, and a given law of the state of the environment. The mathematical description of the process of formation of inelastic deformations areas near the workings and obtaining a solution by the analytical method is rather difficult. Due to the lack of knowledge of this problem to date, it is advisable to use numerical methods of mathematics and mechanics using modern information technology and technology. The article presents mathematical models and results of solving a geomechanical problem based on information technology and the finite element method. The developed procedures and programs allow solving with the help of modern computers a wide class of mining tasks in which it is required to determine the stress-strain state of the rock mass weakened by mine workings in different mining and geological conditions. tasks, field structures, mathematical models, array heterogeneity, rock properties, rock samples.