Three-dimensional simulation of spontaneous rupture: The effect of nonuniform prestress

abstract

We use a finite difference method to study crack propagation in a three-dimensional continuum, for conditions of both uniform and nonuniform prestress. The rupture criterion employed satisfies two fundamental physical requirements: it ensures finite stresses in the continuum and finite energy dissipation in crack extension. The finite stress numerical simulations exhibit abrupt jumps in rupture velocity when sharp changes in prestress are encountered on the crack plane, behavior analogous to that predicted theoretically for two-dimensional, singular cracks. For uniform prestress conditions, the slip velocity function is approximately a low-pass filtered version of that of a singular, constant rupture velocity crack. For nonuniform prestress, spatial variations of peak slip velocity are strongly coupled to spatial variations of rupture velocity.

For uniform prestress and low cohesion, rupture velocity is predicted to exceed the S-wave velocity in directions for which mode II (inplane) crack motion dominates. A subshear rupture velocity is predicted for directions of predominantly mode III (antiplane) crack motion. Introduction of stress heterogeneities is sufficient, in each of the three cases studied, to reduce average rupture velocity to less than the S velocity, but local supershear rupture velocities can still occur in regions of high prestress. Rupture models with significant segments of supershear propagation velocities may be consistent with seismic data for some large earthquakes, even where average rupture velocity can be reliably determined to be subshear.