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

David Skålid Amundsen*, Jørgen Kjoshagen Trømborg, Kjetil Thøgersen, Eytan Katzav, Anders Malthe-Sørenssen, Julien Scheibert

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

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 quasistatic 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.

Original languageAmerican English
Article number032406
JournalPhysical Review E
Volume92
Issue number3
DOIs
StatePublished - 21 Sep 2015

Bibliographical note

Publisher Copyright:
© 2015 American Physical Society.

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