On a new approach in assessing the behavior of a large number parallel galleries

Abstract

The problem of assessing the behavior of a large number of underground structures such as parallel tunnels, characteristic of mines for the extraction of minerals, including coal, is considered. Traditionally, studies are performed for a single object, and then the parameters found are accepted for all other objects. At the same time, the multiplicity of such objects can lead to another factor of strength impairment associated with the possibility of localization of the stress-strain state in one of the zones of the structure, leading to excess of the planned strength parameters. In this paper, the theory of calculation of strength properties of such objects is based on the example of underground structures.

The research is based on the block element method based on factorization approaches. The problem is reduced to a system of integral equations of the first kind with a difference kernel, which is reduced to a system of Fredholm integral equations of the second kind. By calculating the integrals describing the nuclei of these equations according to the theory of deductions, it is possible to reduce the integral equations to a system of algebraic equations available for analytical analysis, which allows to identify the localization of stresses or displacements. The long-range approach made it possible to find a connection between these equations with the Riemann problem for a set of pairs of analytic functions, the number of which coincides with the number of galleries. In earlier works, the resulting stress-strain state was characterized by calculating only the vertical contact stresses on the supports and the vertical displacements of roof slack charges. In this paper, it is possible to construct an approach that allows us to calculate all three components of the stresses on the supports and all three components of the roof sagging displacement.