Abstract
Seismic processes under the influence of tectonic forces in the earth’s crust generate shock waves, often leading to deep cracks, and, as a result, to catastrophic phenomena. A model of an elastic medium with a crack is often used for various contact conditions on its cracks. There is elastic medium (not thermoelastic) in connection with the complexity of solutions of the system of equations of motion of a thermoelastic medium, which belongs to systems of mixed hyperbolic-parabolic type. In this paper, a mathematical model of rock mass dynamics has been developed using a model of coupled thermoelasticity taking into account its thermoelastic properties with crack of an arbitrary geometry on its surface. Based on the method of generalized functions for elastic media with a crack of arbitrary shape, a generalized solution of the thermoelastic problem is constructed for given jumps of the relative velocity of displacements of the crack edges and stress jumps on the crack, its regular integral representation is given. The problem is solved in a 3D case in space of Laplace transforms in time.