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

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.