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 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.

Unstable Slip Pulses and Earthquake Nucleation as a Nonequilibrium First-Order Phase Transition

“…We use constitutive functions f (|v|, φ) and g(|v|, φ) that capture the generic properties of frictional interfaces; first, we set g(|v|, φ) = 1 − |v|φ/D [1,4,34,[50][51][52], where φ represents the typical age/maturity of contact asperities that compose the spatially-extended interface, such that φ = t accounts for frictional aging/healing in the absence of slip, v = 0, and φ = D/|v| accounts for frictional rejuvenation over characteristic slip D in the presence of slip, v = 0. Second, we use the function f (|v|, φ = D/|v|) [20,34] plotted in Fig. 1; this N-shaped steady-state friction curve features a velocity-strengthening branch at extremely small v's, essentially representing quiescent/locked interfacial states, a velocity-weakening branch at intermediate v's and another velocity-strengthening branch beyond a high-v minimum [34, [53][54][55].…”

Spatiotemporal Dynamics of Frictional Systems: The Interplay of Interfacial Friction and Bulk Elasticity

“…To test this prediction over a broad range of H values, L c (H) has been theoretically calculated using the homogeneous linear stability analysis discussed in Sect. IV A [87]. Note, though, that the present problem is more complicated than the case discussed in Sect.…”

“…(b) Dependence of critical length L c on system height H. The lines show analytical predictions for a 2D analysis (solid line) and a small-H limit analysis (dashed line). The two agree for small H, while the former saturates at a finite value for large H. The circles show numerical results from and 2D finite-H FEM simulations [87]. Reasonable and non-trivial agreement between the theory, which is based on homogeneous linear stability of steady sliding, and the numerics, based on transient inhomogeneous simulations, is demonstrated (see [87] for additional discussion).…”

Finite element modeling of dynamic frictional rupture with rate and state friction

“…At a larger scale, rate and state friction has been extensively used to analyze and explain different aspects of earthquake scenarios [5,6,7]. Instability of rate and state friction and the corresponding critical nucleation length have been the topic of several recent works [8,9,10,11].…”