Stress State of Layered Rock Mass Containing A Mine Working of Round Cross-section

The elastoplastic problem of the stress state of layered rock mass containing an extended single mine working is solved in the following sequence. A stress field is built in the parts of mass adjacent directly to the mine working that form an extremely stressed area (the area of inelastic deformations). Then the area is spread into the rock mass, and the stress field is built in it in accordance with the characteristics method developed by V.V. Sokolovsky to be applied to the calculation of granular and coherent media. The method has been developed to solve problems of differential equations of the equilibrium of continuum mechanics jointly with general and special strength criteria of Coulomb–Mohr. This non-linear system belongs to hyperbolic equations. The characteristics method alternately solves three boundary value problems for a number of specific areas of the extremely stressed rock mass. Then, by substituting the extremely stressed area with stresses at its boundary, the elastoplastic problem is reduced to the boundary value problem of theory of elasticity for a medium with reinforced cutout, whose dimensions comply with dimensions of the extremely stressed area. The problem is solved by using the boundary element method and controlled by compliance with static boundary conditions at the boundary of plastic area and elastic region. The elastoplastic problem of the stress state of a layered array containing an extended single mine working is solved in the following sequence. First, a stress field is constructed in the parts of the array adjacent directly to the mine working, with from an extremely stressed zone (a zone of inelastic deformations). Further, this zone extends deep into the array, and the stress field in it is constructed by the method of characteristics developed by V.V. Sokolovsky in relation to the calculation of bulk medium. The method is designed to solve a system of differential equations of equilibrium of continuum mechanics together with general and special Coulomb — Mohr strength criteria. This nonlinear system belongs to hyperbolic equations. The method of characteristics alternately solves the boundary value problems for a number of characteristic sections of the extremely stressed zone of the array. Then, by replacing the extremely stressed zone with stresses at its boundary, the elastically plastic problem is reduced to the boundary value problem of the theory of elasticity for a medium with a reinforced cutout, the dimensions of which correspond to the dimensions of the extremely stressed zone. It is solved by the boundary element method and is controlled by the fulfillment of static boundary conditions at the boundary of the plastic zone and the elastic region.