Issue 49

A. Baryakh et alii, Frattura ed Integrità Strutturale, 49 (2019) 257-266; DOI: 10.3221/IGF-ESIS.49.25 257 Focused on Russian mechanics contributions for Structural Integrity On one approach to the numerical modeling of the strain-stress state of layered rock mass Alexander Baryakh Perm Federal Research Center of Ural Branch of Russian Academy of Science, director, corresponding member of Russian Academy of Science, Russia bar@mi-perm.ru, http://www.permsc.ru/ Sergey Lobanov Mining Institute of the Ural Branch of the Russian Academy of Science, Russia LSerg@mi-perm.ru , https://www.mi-perm.ru/ A BSTRACT . According to the principle of virtual work for a system of elastic layers, a semi-analytical scheme for constructing the finite-dimensional analog of the variational equation was developed based on the well-known analytical solution in the Fourier series for a single layer. The solution of a test problem shows that the constructed numerical procedure of mathematical modeling ensures fairly accurate calculations and highly effective computer-aided realization. It was demonstrated that the proposed semi-analytical scheme for constructing the finite-dimensional analog of the variational equation can be effectively used for the assessment of safety conditions of the potash salt development within the Upper Kama salt deposit. K EYWORDS . Mathematical modeling; Finite elements; Strains; Stresses; Rocks. Citation: Baryakh, A., Lobanov., S., On one approach to the numerical modeling of the strain-stress state of layered rock mass, Frattura ed Integrità Strutturale, 49 (2019) 257-266. Received: 29.04.2019 Accepted: 21.05.2019 Published: 01.07.2019 Copyright: © 2019 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. I NTRODUCTION edimentary rock masses, the interior of which often contains salt deposits, are characterized by a thin-layered structure. The analysis of their strain-stress state and failure as a result of mining operations is of considerable importance in ensuring the protection of mines against flooding [1,2]. In certain cases such rock masses can be represented as a system of plane-parallel layers. In solving the problems of this class, it is common practice to use both the traditional numerical finite and boundary element methods and special computational techniques, which are based on the "sequential stiffness" and "sequential compliance" procedures [3], the Fourier series expansion [4], and combinations of various computational procedures [5.6]. These methods were thoroughly discussed and analyzed in work [7]. S