Set-up and Solution of the Problem on the Transition of the Rock Layer, Located in the Soil of In-Seam Working, in the limit State
On the basis of the developed mathematical model of geomechanical state of the massif of the rocks, which are under the condition of the state of plane deformation, the problem is solved on the transition in a critical stressed state of the coal seat rock layer on which to the whole of its power the working of rectangular cross-section was excavated. The model is built based on the second outer boundary-value problem of elasticity theory for the Fredholm integral equation of the second kind. It takes into account the strength anisotropy of the rock massif, as well as the difference between the characteristics of the coal seam and the strength of the host rocks, which assumes the presence of critical stressed zones in the selvedge of the seam. Coal seam deformation diagram is taken in the form of an ideal Prandtl diagram. The bases of the algorithm of its realization are the boundary element methods, mechanical quadratures and the method of successive approximations. Based on the results of computational experiment presented are the dependencies of parameters of the bearing pressure in the vicinity of the working and the strength characteristics of the rock layer on a number of working laying depths, at which the layer is transferred to the limit state accompanied by its protrusion to the working.