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The rupture of dry frictional interfaces occurs through the propagation offronts breaking the contacts at the interface. Recent experiments have shownthat the velocities of these rupture fronts range from quasi-static velocitiesproportional to the external loading rate to velocities larger than the shearwave speed. The way system parameters influence front speed is still poorlyunderstood. Here we study steady-state rupture propagation in a one-dimensional(1D) spring-block model of an extended frictional interface, for variousfriction laws. With the classical Amontons--Coulomb friction law, we derive aclosed-form expression for the steady-state rupture velocity as a function ofthe interfacial shear stress just prior to rupture. We then consider anadditional shear stiffness of the interface and show that the softer theinterface, the slower the rupture fronts. We provide an approximate closed formexpression for this effect. We finally show that adding a bulk viscosity on therelative motion of blocks accelerates steady-state rupture fronts and we givean approximate expression for this effect. We demonstrate that the 1D resultsare qualitatively valid in 2D. Our results provide insights into thequalitative role of various key parameters of a frictional interface on itsrupture dynamics. They will be useful to better understand the many systems inwhich spring-block models have proved adequate, from friction to granularmatter and earthquake dynamics.

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