Numerical simulation of elastic wave propagation in fractured rock with the boundary integral equation method

Abstract

This paper describes a boundary integral equation method for simulating two‐dimensional elastic wave propagation in a rock mass with nonwelded discontinuities, such as fractures, joints, and faults. The numerical formulation is based on the three‐dimensional boundary integral equations that are reduced to two dimensions by numerical integration along the axis orthogonal to the plane of interest. The numerical technique requires the assembly and solution of the coefficient matrix only for the first time step, resulting in a significant reduction in computational time. Nonwelded discontinuities are each treated as an elastic contact between blocks of a fractured rock mass. Across such an elastic contact, seismic stresses are continuous and particle displacements are discontinuous by an amount which is proportional to the stress on the discontinuity and inversely to the specific stiffness of the discontinuity. Simulations demonstrate that such formulated boundary element method successfully models elastic wave propagation along and across a single fracture generated by a line source.