Modeling repeated slip failures on faults governed by slip-weakening friction

Abstract

The single-body mass-spring analog model has been largely used to simulate the recurrence of earthquakes on faults described by rate- and state-dependent rheology. In this paper, the fault was assumed to be governed by the classical slip-weakening (SW) law in which the frictional resistance linearly decreases as the developed slip increases. First, a closed-form fully analytical solution to the 1D elastodynamic problem was derived, expressing the time evolution of the slip and its time derivative. Second, a suitable mechanism for the recovery of stress during the interseismic stage of the rupture was proposed, and this stress recovery was shown quantitatively to make possible the simulation of repeated instabilities with the SW law. Moreover, the theoretical predictions were shown to be compatible with the numerical solutions obtained by adopting a rate and state constitutive model. The analytical solution developed here is, by definition, dynamically consistent and nonsingular. Moreover, the slip velocity function within the coseismic time window found here can be easily incorporated into slip inversion algorithms.