Investigation of limit stress state in marginal zone of a seam by the methods of mechanics of granular media

The article presents the results of the problem solving on limit stress state in marginal zones of a coal seam. The problem assumes that mining is carried out at a sufficient depth, and the limit stresses a priori form in the marginal zones. The limit stress state criteria are the satisfied conditions of Mohr–Coulomb and Mohr–Kuznetsov in the seam and at the seam–side rock interface, respectively. It is assumed that the Mohr–Coulomb condition is fulfilled at all points of the limit stress state zone. Therefore, the stress–strain diagram is represented by the Prandtl stress function with horizontal branch of the ultimate strain. The problem is solved using the methods of mechanics of granular medium. The differential equation of the limit state of the seam is of hyperbolic type. It is solved numerically, and, subject to the boundary conditions set in each characteristic domain in the limit zone, three boundary problems of the limit equilibrium are solved in sequence. It is shown that the stress field components, both along the longitudinal axis of the seam and along the seam-and-rock contact, change by steps. With distance from the seam marginal zone in depth of rock mass, the size of a step decreases while the rate of the stress buildup soars. The calculation results on the stress state in the marginal zone of a seam are compared with the analogous results obtained from an exponential formula with an exponent represented by a set of strength characteristics of the seam and the seam–side rock interface. The dimension of a boundary seam zone inside which the results of the two approaches are close is found. In the problem solution on stress state of a seam, the stress curves in the marginal zone of the seam can by approximated by a polynomial with a maximal degree equal to the number of the analyzed domains. Using the values of stresses at the boundaries of these domains, the approximation polynomial coefficients are determined.

Cherdantsev N. V. Investigation of limit stress state in marginal zone of a seam by the methods of mechanics of granular media. MIAB. Mining Inf. Anal. Bull. 2020;(3):45-57. [In Russ]. DOI: 10.25018/0236-1493-2020-3-0-45-57.

Cherdantsev, Dr. Sci. (Eng.), Chief Researcher, e-mail: nvch2014@yandex.ru,
Federal Research Center of Coal and Coal Chemistry, Siberian Branch of Russian Academy of Sciences, 650065, Kemerovo, Russia.

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