Theoretical analysis of the scattering characteristics of blasting stress waves at an arc-shaped interface crack in a deep rock mass with high in-situ stress

Abstract

A mathematical model of blasting stress wave scattering at an arc-shaped interface crack is established to theoretically analyze and verify the scattering characteristics of blasting stress waves at an arc-shaped interface crack in a deep rock mass with high in-situ stress. Based on the continuum mechanics, finite deformation, and incremental stress theories and the geometric and physical characteristics of the arc-shaped interface crack, the mathematical model includes a set of the first class of singular integral equations with Hilbert kernels. The opening and dislocating displacements of the arc-shaped interface crack and the effective stress components of scattered stress waves are numerically calculated and discussed with the variation of the type, frequency, and incident angle of the blasting stress wave; the curvature radius and opening angle of the arc-shaped interface crack. The condition that the dynamic stress intensity factors and energy release rates at the upper and lower tips of the arc-shaped interface crack reach peak are also provided. It is found that when the frequency of the blasting stress wave and the curvature radius of the arc-shaped interface crack increase, the peaks of the above dynamic stress intensity factors will increase further, and the arc-shaped interface crack is more likely to expand or destabilize. Although the order of in-situ stress is much smaller than that of Young’s modulus of the deep rock mass, it increases the effective stress concentration of scattered stress waves and the opening and dislocating displacements of the arc-shaped interface crack. These findings will provide theoretical guidance for analyzing the cracking characteristics of blasting stress waves in deep rock masses with high in-situ stress.