Earthquake nucleation in intact or healed rocks

Earthquakes are generated because faults lose strength with increasing slip and slip rate. Among the simplest representations of slip-dependent strength is the linear slip-weakening model, characterized by a linear drop to a residual friction. However, healed fault rocks often exhibit some slip strengthening before the onset of weakening. Here we investigate the effect of such a slip-hardening phase on the initial growth of a slip patch and on the nucleation of rupture instabilities. We assume a piecewise linear strength versus slip constitutive relation. We compute stress and slip distributions for in-plane or antiplane rupture configurations in response to an increasing, locally peaked (parabolic with curvature kappa) stress profile. In contrast with the strictly linear slip-weakening case, our calculations show that the curvature of the loading profile and the level of background stress strongly influence the nucleation size. Even for small amounts of slip hardening, we find that the critical nucleation size scales with 1/root kappa for kappa -> 0, i.e., crack growth remains stable up to very large crack sizes for sufficiently smooth loading profiles. Likewise, when the background stress tau(b) is very close to the initial strength tau(c), the critical crack size scales with 1/root tau(c)-tau(b). An eigenvalue analysis shows that the nucleation length increases as the proportion of the crack undergoing slip hardening increases, irrespective of the details of the loading profile. Overall, our results indicate that earthquake nucleation sizes can significantly increase due to slip hardening (e.g., in healed fault rocks), especially when the background loading is smooth.