Critical Nucleation Length for Accelerating Frictional Slip

Abstract

AbstractThe spontaneous nucleation of accelerating slip along slowly driven frictional interfaces is central to a broad range of geophysical, physical, and engineering systems, with particularly far‐reaching implications for earthquake physics. A common approach to this problem associates nucleation with an instability of an expanding creep patch upon surpassing a critical length Lc. The critical nucleation length Lc is conventionally obtained from a spring‐block linear stability analysis extended to interfaces separating elastically deformable bodies using model‐dependent fracture mechanics estimates. We propose an alternative approach in which the critical nucleation length is obtained from a related linear stability analysis of homogeneous sliding along interfaces separating elastically deformable bodies. For elastically identical half‐spaces and rate‐and‐state friction, the two approaches are shown to yield Lc that features the same scaling structure, but with substantially different numerical prefactors, resulting in a significantly larger Lc in our approach. The proposed approach is also shown to be naturally applicable to finite‐size systems and bimaterial interfaces, for which various analytic results are derived. To quantitatively test the proposed approach, we performed inertial Finite‐Element‐Method calculations for a finite‐size two‐dimensional elastically deformable body in rate‐and‐state frictional contact with a rigid body under sideway loading. We show that the theoretically predicted Lc and its finite‐size dependence are in reasonably good quantitative agreement with the full numerical solutions, lending support to the proposed approach. These results offer a theoretical framework for predicting rapid slip nucleation along frictional interfaces.