Slip- and time-dependent fault constitutive law and its significance in earthquake generation cycles

By integrating effects of microscopic interactions between statistically self-similar fault surfaces, we succeeded in deriving a slip- and time-dependent fault constitutive law that rationally unifies the slip-dependent law and the rate- and state-dependent law. In this constitutive law the slip-weakening results from the abrasion of surface asperities that proceeds irreversibly with fault slip. On the other hand, the restoration of shear strength after the arrest of faulting results from the adhesion of surface asperities that proceeds with contact time. At the limit of high slip-rate the unified constitutive law is reduced to the slip-weakening law. At the limit of low slip-rate it shows the well-known log t strengthening of faults over the wide range of contact time t. In the steady state with a constant slip-rate V the shear strength has the negative log V dependence, known as the velocity-weakening. Another important property expected from the unified constitutive law is the gradual increase of the critical weakening displacement D, with stationary contact time. We numerically examined behavior of a single degree of freedom elastic system following the slip- and time-dependent constitutive law, and found that the periodic stick-slip motion is realized when the adhesion rate is high in comparison with the loading rate. If the adhesion rate is very low, behavior of the system gradually changes from stick-slip motion to steady sliding with time.