Evolution of Cracks at the Edge of a Gas-Bearing Coal Seam under Stationary Mining

In this paper, we consider the conditions under which the gas enclosed in a main crack located at the edge of a coal or rock formation can produce fracture of the formation. Kinetic theory is developed for two competing physical processes: formation unloading due to rock pressure and gas filtration from the crack cavity into the surrounding rock. The first process promotes fracture, and the second leads to a decrease in the gas pressure causing the fracture. The evolution of the crack is determined by the ratio of the rates of these processes. It is found that a modified Griffith's criterion is a necessary but not sufficient condition for fracture. For formation fracturing, it is also necessary that the ratio of the unloading rate to the filtration rate exceed a certain threshold value.