The calculation of the parameters of disc-shaped hydraulic fracturing crack propagating in hard rock roofs of a coal seam near the in-seam working

Abstract

The model of geomechanical state of the disc-shaped hydraulic fracturing crack that propagates in hard rocks near the in-seam working was developed. The peculiarity of the model is in non-homogeneous stress field which is conditioned by the presence of the working. This field plays an important role in calculating the trajectory of the crack propagation and under certain conditions it drastically changes the direction of the initial crack. The problem of the rock massif stress state in the vicinity of the in-seam working is narrowed to the second exterior boundary value problem of the elasticity theory for integrated singular equation. It can be reached by substituting limit stress coal seam marginal zones by their acting stresses. Analyzing the results it is defined that when the ratio of the working liquid pressure to the gravitational hard rock pressure equals four units the trajectory of the crack is linear and coincides with the direction of the initial crack. If the ratio of the working liquid pressure to the gravitational pressure changes from three to four units the trajectory of the crack looks as a gently sloping curve that insignificantly changes its direction towards the initial crack.