Stress–strain behavior model of disturbed rock mass with regard to anisotropy and discontinuities

Strength estimation of underground structures is an important problem in mine planning. Such computation involves mathematical modeling. This article proposes the mathematical model of the stress–strain behavior of disturbed rock mass with regard to its anisotropic properties. The model is also effective in rock mass with comparatively small discontinuities and internal stresses. The modeling uses the stochastic theory of potential and the mathematical theory of elasticity. An integrated stochastic potential of the stress–strain behavior of the anisotropic medium is constructed and used to formulate the boundary problems to find stresses and strains. The algorithm of the problem solution is developed. Unlike the boundary problems in classical elasticity, the determinate boundary conditions in the newly formulated problems are replaced by the stochastic conditions. As a result, it is possible to extend the model application range to rocks which are not absolutely uniform. Furthermore, the proposed integrated stochastic potential allows including the internal stresses of rocks in the solution. The capabilities of numerical methods grow. Efficiency of the algorithm is illustrated by solving the basic problem of elasticity for an anisotropic medium with a weakening in the form of an elliptical hole.

Adigamov A. E., Yudenkov A. V. Stress–strain behavior model of disturbed rock mass with regard to anisotropy and discontinuities. MIAB. Mining Inf. Anal. Bull. 2021;(8):93103. [In Russ]. DOI: 10.25018/0236_1493_2021_8_0_93.

A.E. Adigamov, Cand. Sci. (Eng.), Assistant Professor, National University of Science and Technology «MISiS», 119049, Moscow, Russia,e-mail: arckad.adigamow@yandex.ru,
A.V. Yudenkov, Dr. Sci. (Phys. Mathem.), Professor, Smolensk State Academy of Physical Culture, Sport and Tourism, 214018, Smolensk, Russia, e-mail: aleks-ydenkov@mail.ru.

A.E. Adigamov, e-mail: arckad.adigamow@yandex.ru.

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