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ArticleName Mathematical modeling of boundary problems in geomechanics
DOI 10.17580/gzh.2019.12.03
ArticleAuthor Gospodarikov A. P., Zatsepin M. A.

Saint-Petersburg Mining University, Saint-Petersburg, Russia:

A. P. Gospodarikov, Professor, Doctor of Engineering Sciences
M. A. Zatsepin, Associate Professor, Candidate of Physical-Mathematical Sciences,


Development of bedded deposits is associated with man-caused distortion of specific environment—rock masses, which are very complicated in their structure (specific character of texture: bedded, solid, etc.; specific character of structure: fragmental, granular–crystalline, etc.), can vary significantly in mechanical properties (strength, deformation, etc.) and are characterized with a wide variety of laws and techniques to assess their stress–strain behavior (elastic, elasto-plastic, elasto-viscous-plastic, viscous-plastic deformation, etc.). It is obvious that studying parameters of mechanical processes taking place in such environs cannot be methodologically restricted to separate application of real experiment data, laboratory data or analytical calculations. It should be noticed that the majority of applied problems in the stress–strain analysis of rock masses are impossible to be solved only with the application of classical continuous field analog techniques (theories of elasticity, plasticity, structural mechanics, etc.). The study object features inhomogeneity, jointing, anisotropy, geometrical irregularity, etc. Analytical description of cavity surfaces and setting boundary conditions for such objects are extremely complicated and, correspondingly, it is impossible to find closed-form solution to be convenient for engineering practice. Different numerical methods are known to be expedient (methods of finite elements, boundary elements, boundary integral equations, finite differences, etc.). This article is devoted to different geomechanical problems connected with the stress–strain analysis of rock masses containing different purpose and shape underground openings in the course of mineral mining.

keywords Underground mining, rock mass, stress–strain behavior, geomechanics, mathematical modeling, finite difference method, boundary element method, finite element method

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