Derivation of XBIEM Kernels for Anti-plane/In-plane Problems and Implementation in Anti-plane Rupture Simulation Crossing Bimaterial Interface

Abstract:

We develop an extended boundary integral equation method (XBIEM) to analyse dynamic behavior of rupture crossing a medium interface in 2D. Many faults often lie near medium interfaces in the Earth’s heterogeneous crust consisting of various types of rocks. Some faults cross the interfaces, and the theoretical analysis of their dynamic behavior has been awaited. In the development, we focus on the extended parts of XBIEM in comparison to the conventional BIEM, and derive all the 2D displacement and stress kernels in response to a unit boundary traction in explicit discretized forms, which are the ingredients in the extension of BIEM. The final forms of kernels are compact and easy to evaluate numerically. They are implemented in simulating dynamic anti-plane rupture propagation across a bimaterial interface allowing secondary interfacial rupture. Our analysis shows a significant effect of an interfacial medium contrast on the control of dynamic rupture propagation.