Numerical studies of quasi‐static tectonic loading and dynamic rupture of bi‐material interfaces

Abstract

SUMMARYDynamic simulations of homogeneous and bi-material fault rupture are modeled using different loading approaches. We demonstrate that a numerical method of quasi-static loading is capable of immediately loading bi-material interfaces to rupture without the iteration over multiple time steps. We show that our method is a computationally inexpensive approach to tectonic loading and is capable of loading a fault to failure. We observe earthquake rupture speed, slip distances and slip rates for homogeneous and bi-material faults for various applied stresses, friction properties and material contrasts across the bi-material interface. We comment on causes for unilateral rupture growth. The results are consistent with experimental results and highlight the importance of material heterogeneity in determining the rupture characteristics of earthquake faults.

Stress heterogeneities in earthquake rupture experiments with material contrasts

“…Uniaxial compression tests consisting of quasi-static loading and subsequent dynamic rupture are simulated using the Finite Element Method implemented in the esys.escript software (Gross et al, 2007;Langer et al, 2010). Triangular meshes are constructed using Gmsh (Geuzaine and Remacle, 2009) with variable mesh size ranging from 1 mm at the outer boundary to 500 µm along the fault.…”

“…In a first deformation step, the displacement of the top boundary is found by taking the average Young's modulus of the model domain and calculating the vertical displacement under compression with the pressure P . We obtain a solution for the elastic deformation equation σ ij,j = 0 as in Langer et al (2010). We determine the component σ 22 of the stress tensor in the model domain, which is aligned with the direction of P .…”

“…To model a dynamic slip on a fault we adapt Gmsh to contain contact joint elements (OlsenKettle et al, 2008;Langer et al, 2010Langer et al, , 2012 in a way that is similar to the traction-at-split-node method (e.g. Andrews, 1999).…”

“…Subshear ruptures have higher rupture velocities in the positive direction due to a tensile stress perturbation behind the rupture tip which follows the rupture front and promotes rupture (Weertman, 1980;Andrews and Ben-Zion, 1997;Rubin and Ampuero, 2007). Subshear ruptures therefore exhibit higher potencies in the positive direction and a preference for this direction in bilateral ruptures (Ben-Zion, 2001; Ampuero and Ben-Zion, 2008;Langer et al, 2010). Conversely, in the negative direction the sign of the normal stress change is reversed (compressive) behind the rupture tip leading to dynamic strengthening and lower rupture velocities for subshear rupture.…”

Proceedings of the 6th ACES Symposium, May 11–16, 2008, Cairns, Australia: Introduction to the Special Issue

“…A number of papers dealt with numerical simulations of earthquake faults and numerical methods including visualization [6][7][8][9][10][11][12].…”