Steady-state propagation speed of rupture fronts along one-dimensional frictional interfaces

TL;DR

This paper investigates the steady-state propagation speed of rupture fronts along one-dimensional frictional interfaces using a spring-block model, deriving analytical expressions and exploring effects of interface properties on rupture dynamics.

Contribution

It provides analytical formulas for rupture velocity considering different friction laws, interface stiffness, and bulk viscosity, enhancing understanding of rupture dynamics in 1D and 2D models.

Findings

Softer interfaces slow rupture fronts.

Bulk viscosity accelerates rupture propagation.

Derived closed-form expressions for rupture velocity.

Abstract

The rupture of dry frictional interfaces occurs through the propagation of fronts breaking the contacts at the interface. Recent experiments have shown that the velocities of these rupture fronts range from quasi-static velocities proportional to the external loading rate to velocities larger than the shear wave speed. The way system parameters influence front speed is still poorly understood. Here we study steady-state rupture propagation in a one-dimensional (1D) spring-block model of an extended frictional interface, for various friction laws. With the classical Amontons--Coulomb friction law, we derive a closed-form expression for the steady-state rupture velocity as a function of the interfacial shear stress just prior to rupture. We then consider an additional shear stiffness of the interface and show that the softer the interface, the slower the rupture fronts. We provide an approximate closed form expression for this effect. We finally show that adding a bulk viscosity on the relative motion of blocks accelerates steady-state rupture fronts and we give an approximate expression for this effect. We demonstrate that the 1D results are qualitatively valid in 2D. Our results provide insights into the qualitative role of various key parameters of a frictional interface on its rupture dynamics. They will be useful to better understand the many systems in which spring-block models have proved adequate, from friction to granular matter and earthquake dynamics.