Simulation of spontaneous rupture based on a combined boundary integral equation method and finite element method approach: SH and P-SV cases

Abstract

We present a hybrid approach for solving the dynamic rupture problem in an anelastic medium. It combines the advantages of the boundary integral equation method (BIEM), which is capable of representing accurately the solution near a crack tip, with those of the domain finite element method (FEM), which can handle conveniently heterogeneous materials, as well as the traction-free condition on a free surface and the continuity of traction across interfaces. When applied jointly, the proposed BIEM and the FEM can be used to solve efficiently spontaneous rupture problems in heterogeneous media, provided the rupture surface is contained within a homogeneous portion of the domain. The proposed method, BIEM-FEM approach (BDM, for Boundary/Domain Method), is verified for several antiplane (SH) and in-plane (P-SV) 2-D cases, in which the slip is prescribed along the fault (kinematic rupture). For spontaneous rupture, we examine the performance of the BDM by computing its convergence rate for an example in a homogeneous half-space with a slip-weakening friction law on the fault. By including the boundary integral representation on the fault, without using any refinement near the crack tips, the solution converges with the same rate as problems that do not exhibit any stress concentrations; that is, for the piecewise linear elements used here, the rms of the slip-rate distribution and of the traction distribution on the fault converge as O(Δx), whereas the slip distribution converges as O(Δx2), in which Δx is the mesh size of the finite element mesh. Additional 2-D spontaneous rupture simulations are performed for an inclined fault in a half-space for different values of the dip angle and for a folded layer system in a half-space, focusing only the P-SV case. The results show that the waves generated at the free surface and within the layers contribute to the propagation of the fault rupture and have a visible and sometimes strong effect on the ensuing ground motion. © 2010 The Authors Geophysical Journal International © 2010 RAS.