Steady-state solutions of rupture propagation in an earthquake simulator governed by rate and state dependent friction

Abstract

Earthquake simulators become increasingly important with respect to seismic hazard assessment. It is, therefore, a crucial ques- tion whether the imposed simplifications, e.g. reducing fully dynamic to quasi-dynamic rupture propagation, may lead to unrealistic results. In the present study, we focus on the role of rupture velocity vr in an earthquake simulator governed by rate-and-state dependent friction as proposed by (8). In particular, we investigate the range of possible val- ues of vr within the model. As an end-member scenario, we consider the existence of a steady-state solution of a one-dimensional rupture front propagating with vr on an idealized two-dimensional fault of infi- nite dimension discretized into uniform cells. We find that, in principle, values of vr between 0 and ∞ are possible depending on the values of slip speed ˙ δ0 and pre-stress τ0 ahead of the rupture front. In this view, values of ˙ δ0 close to the slip speed during an earthquake ˙ δEQ lead to small values of the time-to-failure and can thus generate ruptures with unrealistic high values of vr, if the model is close to the steady-state conditions. These results are useful to provide constraints for the pa- rameter space of a reasonable earthquake simulator.