Abstract
AbstractEarthquakes 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 κ) 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 for κ→0, i.e., crack growth remains stable up to very large crack sizes for sufficiently smooth loading profiles. Likewise, when the background stress τb is very close to the initial strength τc, the critical crack size scales with . 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.
Highlights
Within the Earth’s brittle crust, deformation is localized along narrow shear faults
Even for small amounts of slip hardening, we find that the critical nucleation size scales with 1∕ κ for κ → 0, i.e., crack growth remains stable up to very large crack sizes for sufficiently smooth loading profiles
Our results indicate that earthquake nucleation sizes can significantly increase due to slip hardening, especially when the background loading is smooth
Summary
Within the Earth’s brittle crust, deformation is localized along narrow shear faults. Slip along faults can be slow and stable but is very sudden and dynamic during earthquakes. Laboratory experiments [e.g., Ohnaka and Shen, 1999; Ohnaka, 2000] and theoretical analyses [e.g., Campillo and Ionescu, 1997; Rubin and Ampuero, 2005; Ampuero and Rubin, 2008] have shown that periods of stable slip occur over some area along the fault immediately prior to dynamic slip, showing the existence of a nucleation phase of earthquake rupture. We focus our attention to earthquake nucleation along faults which are initially healed and locked. Faults can be viewed as interfaces across which displacement discontinuities accumulate. “slip” on a fault should be viewed as an integrated strain across the fault core
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