Minimal model for slow, sub-Rayleigh, supershear, and unsteady rupture propagation along homogeneously loaded frictional interfaces

Abstract

In nature and experiments, a large variety of rupture speeds and front modes along frictional interfaces are observed. Here, we introduce a minimal model for the rupture of homogeneously loaded interfaces with velocity strengthening dynamic friction, containing only two dimensionless parameters;τ which governs the prestress, andᾱ which is set by the dynamic viscosity. This model contains a large variety of front types, including slow fronts, sub-Rayleigh fronts, super-shear fronts, slip pulses, cracks, arresting fronts and fronts that alternate between arresting and propagating phases. Our results indicate that this wide range of front types is an inherent property of frictional systems with velocity strengthening branches.

The moment duration scaling relation for slow rupture arises from transient rupture speeds

“…From each event we extract the displacement u and the fault length L, which is found from the position of the rightmost block that has ruptured. We run the simulations until all blocks are immobile or until the average velocity reaches 0.1% of the steady-state slip speed τ =α (Thøgersen et al, 2019). In dimensionless units the zeroth-order moment for rupture propagation along a line is…”

“…The system is sketched in Figure 1a. This model has previously been used to determine the steady-state rupture velocity which includes subshear, supershear, and slow rupture, as well as an arresting region at low τ and intermediate α (Thøgersen et al, 2019). The steady-state front speed v c;∞ can be found exactly when α ¼ 0 (Amundsen et al, 2015).…”

The Moment Duration Scaling Relation for Slow Rupture Arises From Transient Rupture Speeds

“…This simple model produces a large variety of slip, including slip pulses, cracks, sub‐Rayleigh rupture, supershear rupture, slow rupture, and arresting fronts (c). The color bars show the fault length of arresting fronts and the steady‐state rupture speed for given and (adapted from Thøgersen et al., ). Each event consists of a single simulation, which gives the block sliding velocity as a function of position and time (d), from which we extract the front position L (e).…”

“…From each event we extract the displacement and the fault length , which is found from the position of the rightmost block that has ruptured. We run the simulations until all blocks are immobile or until the average velocity reaches 0.1 % of the steady‐state slip speed (Thøgersen et al., ). In dimensionless units the zeroth‐order moment for rupture propagation along a line is where is the average displacement on a fault of length .…”

“…and (2) Can a difference in M 0 -T scaling relations alone be attributed to different physical mechanisms behind slow and fast rupture? We address both (1) and (2) through a Burridge-Knopoff-type model with Amontons-Coulomb friction with a velocity strengthening friction term that has previously been shown to contain a large variety of rupture phenomena, including subshear, supershear, and slow propagation (Thøgersen et al, 2019). Velocity strengthening friction has been shown to be a generic feature of dry friction (Bar-Sinai et al, 2014) and has been reported in Halite shear zones at low slip speeds or large confining pressures (Shimamoto, 1986).…”