Scaling theory for the statistics of slip at frictional interfaces

TL;DR

This paper develops a scaling theory for slip events at frictional interfaces, incorporating disorder effects, and predicts how avalanches and fractures behave, with validation from a minimal model.

Contribution

It introduces a novel scaling framework that accounts for disorder in slip statistics and predicts the transition from avalanches to system-spanning fractures.

Findings

Derived scaling relations for slip avalanches.

Identified a cut-off length for avalanches influenced by disorder.

Validated predictions using a minimal frictional interface model.

Abstract

Slip at a frictional interface occurs via intermittent events. Understanding how these events are nucleated, can propagate, or stop spontaneously remains a challenge, central to earthquake science and tribology. In the absence of disorder, rate-and-state approaches predict a diverging nucleation length at some stress $\sigma^*$, beyond which cracks can propagate. Here we argue for a flat interface that disorder is a relevant perturbation to this description. We justify why the distribution of slip contains two parts: a powerlaw corresponding to `avalanches', and a `narrow' distribution of system-spanning `fracture' events. We derive novel scaling relations for avalanches, including a relation between the stress drop and the spatial extension of a slip event. We compute the cut-off length beyond which avalanches cannot be stopped by disorder, leading to a system-spanning fracture, and successfully test these predictions in a minimal model of frictional interfaces.