DEVELOPMENT OF A MATHEMATICAL MODEL OF THE FORMATION OF THE STRESS STATE OF THE SUPPORT OF PARALLEL MINE WORKINGS CONSTRUCTED IN AREAS OF TECHNOLOGICALLY HETEROGENEOUS ROCKS
The paper includes a description of the developed mathematical model of the interaction of elements of a single deformable geomechanical system "rock mass - zones of technologically heterogeneous rocks - support parallel workings - inclined earth surface" under the action of gravitational forces in the array. The model allows us to take into account the influence on the stress-strain state of underground structures and the surrounding rock mass of factors such as the angle of inclination of the earth's surface; the number of parallel workings and their mutual location; the dimensions of the concentric zones of the rock mass previously hardened or weakened during the excavation; deformation characteristics of the rock mass in its natural state, technologically heterogeneous rocks and the material of the excavation support. Since sufficiently extended linear objects are considered, the calculation scheme, formulation and boundary conditions of the plane problem of elasticity theory on the equilibrium of a weighty linearly deformable semi-infinite region with an inclined boundary weakened by circular holes reinforced by rings are used. Concentric areas with different deformation characteristics are identified around the holes, modeling zones of technologically weakened rocks. The rigorous analytical solution of the problem is based on the application of the mathematical apparatus of the theory of functions of a complex variable - kolosov-muskhelishvili potentials characterizing the stress-strain state of the selected regions. Using the modified method of aramanovich i.g. Allows us to reduce the solution of the problem to a well-converging iterative process, at each step of which the problem of an infinite medium weakened by one reinforced hole in a concentric region with different characteristics is considered. In the future, the proposed mathematical model will be modified in order to take into account the impact on the stress state of underground structures of the weight of objects on the surface, as well as internal pressure.