Critical nucleation length for accelerating frictional slip

Abstract

The 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 $L_c$. The critical nucleation length $L_c$ 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 $L_c$ that features the same scaling structure, but with substantially different numerical pre-factors, resulting in a significantly larger $L_c$ 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 $L_c$ 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.

arXiv commentAdded discussion about nonlinearity, new results for the slip law & different background strength (Fig. 3)

References in corpus (5)

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Cited by in corpus (7)

• Earthquake Nucleation along Faults with Heterogeneous Weakening Rate
• Unstable slip pulses and earthquake nucleation as a non-equilibrium first-order phase transition
• Finite element modeling of dynamic frictional rupture with rate and state friction
• The emergence of crack-like behavior of frictional rupture: The origin of stress drops
• Velocity-driven frictional sliding: Coarsening and steady-state pulse trains
• Onset of sliding across scales: How the contact topography impacts frictional strength
• A finite geometry, inertia assisted coarsening-to-complexity transition in homogeneous frictional systems