Abstract
The article considers the problem of determining the thermoelastic stresses that arise when drilling a coal seam with a depth of at least 800 m. The stress-strain state is a term that has penetrated from the mechanics of a deformable solid body into various areas, both natural and technological. Usually, three types of stress-strain state are distinguished: the first type of elastic work - up to 35% of the breaking load; the second type of elastic-plastic work - up to 75% of the breaking load, while cracks appear and their number increases with increasing load; the third type of destruction - cracks appear like an avalanche and every detail is destroyed. For the first time, we succeeded in solving analytically the Stefan problem for a cylinder of finite dimensions, with a moving interface, by selecting an integral transformation. A similar solution for a well in coal seams (as well as for other applications) gives an analytical solution to the deformation-wave process in a rock mass, discovered experimentally in the late 70s of the last century (scientific discovery of 1985, priority of 1978). Our experimental and theoretical results fit into the model of macroscopic localization of plastic flow. This model shows that the localization of plastic flow in solids (and in a coal seam) has a pronounced wave character. At the same time, at the stages of easy slip, linear and parabolic strain hardening, as well as at the stage of preliminary destruction, the observed patterns of localization are different types of wave processes.