MATHEMATICAL MODELING OF DISPLACEMENTS OUTSIDE THE ELASTIC LIMITS IN TRANSVERSALLY ISOTROPIC MASSIF NEAR THE WORKING
M. E. Eskaliev1, S. Malgazhdarov2
1Kazakh National Women’s Teacher Training University, Almaty, Republic of Kazakhstan
2Military Engineering Institute of Radio Electronics and Communications, Almaty, Republic of Kazakhstan
Keywords: Упругость, пластичность, параметр, комплексный потенциал, перемещения, алгоритм, система, Elasticity, plasticity, parameter, complex potential, displacements, algorithm, system
Abstract
The development of limiting states near a mine in a transversally isotropic (layered) massif of complex structure is considered. In the elastic zone, the massif has an anisotropic structure and obeys the generalized Hooke’s law, and in the plastic zone it is assumed isotropic. When determining the plastic zones, the Hoek-Brown failure criterion was used for the first time. The problem is solved approximately by the P.I. Perlin’s semi-inverse method using an iterative scheme. A system of algebraic equations is constructed to find the unknown coefficients of the complex potential. The values of displacements in a plastic zone are found using the characteristics method.
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