Riemann vector equation in the problem of strength of the set of tunnels

Abstract

The study of factors affecting the strength properties of changing underground structures is performed, but for various reasons this study is small. The set of parallel underground structures considered as a block structure consisting of the upper linearly elastic layer and the formation modeled by Kirchhoff plate is being examined. The stratum containing the extracted minerals lies on the layers, which environment mechanical characteristics are soil-like and allow you to model it asWinkler’s bed. It is assumed that the thickness of the reservoir is much smaller than the thickness of the upper layer, which takes place in the real conditions of extraction of many minerals. In contrast to the approaches made in the works of various authors, in this paper, despite the presence of multiplicity of galleries, a method is created to describe the behavior of parameters of each tunnel. This is achieved by reducing the problem to the vector Riemann boundary value problem, for which a factorization method is being developed.