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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.

On one approach to the numerical modeling of the strain-stress state of layered rock mass