Bifurcation of collinear crack system under dynamic compression

Abstract

The evolution pattern of collinear crack array plays a very important role in the final failure pattern of rock and predicting earthquake. Crack interactions lead to the nonhomogeneous pseudo-traction, then result in bifurcation of crack growth pattern. Bifurcation condition of crack growth pattern can be expressed by the crack growth length/spacing ratio. For collinear cracks loaded by dynamic compressive loads, uniform crack growth pattern yields to non-uniform crack growth pattern when the crack growth length/spacing ratio is larger than a critical value. In this paper, crack interactions are studied using stress superposition principle and the Chebyshev polynomials expansion of the pseudo-traction. The analytical solution of the critical value for two collinear cracks and infinite collinear cracks is given out. The critical value is sensitive to pre-existing crack length, the friction coefficient, the orientation of pre-existing crack, crack growth velocity.