A coupled algorithm for numerical analysis of an undermined rock massif stress–strain state

The purpose of the research is to develop a coupled algorithm of numerical modeling for solving practical problems of mechanics, in the case when there is a transition of a continuous medium part into a discrete one. As an example, the article considers the solution of the actual geo-mechanics problem on stress–strain state of the undermined rock massif from the mining depth to the earth's surface modeling. This problem is characterized by the fact that a part of the rock massif in the vicinity of the undermined space transforms into a discrete (block) state, while the rest of the rock massif remains solid. A special feature of the developed algorithm is the introduction of special type block elements in the form of elastic or viscoelastic bonds system into the numerical modeling procedure based on the finite element method. In the course of the study, it was shown that when mining depths are large, starting from a certain depth, their impact on the earth's surface decreases. This fact is confirmed by the results of field observations, but it is not confirmed by calculations according to engineering methodologies. The use of the developed approach of numerical modeling allows to model geo-mechanical processes throughout the entire depth of the rock massif during underground mining operations more correctly and adequately.