Effect of the parameters of the biaxial field of rock pressure on the shape of the fracture zone formed by an explosion of a cylindrical charge in a brittle medium

The effect of the biaxial field of external rock pressure on the deformation of the fracture zone formed by radial cracks in an elastic-brittle medium is studied. We consider cylindrical charges that are rather thin compared to the diameter of the explosive borehole. This allows one to exclude the grinding zone from consideration. At the initial moment of time, the system of emerging cracks originating at the boundary of the circular hole is assumed to be symmetric. To solve the problem, we use singular integral equations and the fracture criterion $\sigma_v$. The propagation trajectories of the system cracks are calculated in the quasistatic approximation in a step-by-step manner in relation to the parameters of the external compressive stress field. Two ideal variants of loading of the crack system are analyzed. In the first variant, gaseous detonation products penetrate into cracks, and the pressure in the explosion cavity and the cracks instantaneously equalizes. In the second variant, gases do not penetrate into the cracks of the system. The fracture zone is shown to become an ellipse whose long axis is oriented in the direction of the largest compressive stress in magnitude acting at infinity. The effect of the variants of loading of the crack system on the shape and dimensions of the deformed fracture zone is evaluated.