Theoretical analysis of the interaction between blasting stress wave and linear interface crack under high in-situ stress in deep rock mass

Abstract

This study theoretically investigates the scattering characteristics of blasting stress waves, treaded as elastic waves, at a linear interface crack in a deep rock mass with an even compressive in-situ stress field. First, the basic equations of the deep rock mass theoretically treaded as a homogeneous isotropic medium with an initial stress field are derived based on the linear elastic, finite deformation, plane strain, isotropic, and small deformation hypotheses, and incremental stress theory. The linear interface crack is theoretically treaded as two displacement-free boundaries, of which the interpolation displacements are described by introducing two dislocation density functions. Next, the mathematical model of the blasting stress wave scattering at the linear interface crack is established through a set of singular integral equations of the first type for these two dislocation density functions with Cauchy kernels. Finally, the dislocating and opening displacements of the linear interface crack and the displacement and effective stress fields of the scattered stress wave are numerically calculated. The principal stress field of the scattered stress wave is compared with the experimental data to qualitatively verify the rationality and correctness of the mathematical model. Theoretically, it is found that even compressive in-situ stress with an amplitude of tens of megapascals significantly affects the displacement and effective stress fields of the scattered stress wave near the linear interface crack. In conclusion, considering even compressive in-situ stress is greatly significant when studying the wave and scattering behaviors of deep rock masses. This mathematical model provides a theoretical guidance for the study of stress wave energy transformation and crack propagation in the process of rock blasting and mineral mining.