On the speed of fast and slow rupture fronts along frictional interfaces

Abstract

The transition from stick to slip at a dry frictional interface occurs through the breaking of the junctions between the two contacting surfaces. Typically, interactions between the junctions through the bulk lead to rupture fronts propagating from weak and/or highly stressed regions, whose junctions break first. Experiments find rupture fronts ranging from quasi-static fronts with speeds proportional to external loading rates, via fronts much slower than the Rayleigh wave speed, and fronts that propagate near the Rayleigh wave speed, to fronts that travel faster than the shear wave speed. The mechanisms behind and selection between these fronts are still imperfectly understood. Here we perform simulations in an elastic 2D spring--block model where the frictional interaction between each interfacial block and the substrate arises from a set of junctions modeled explicitly. We find that a proportionality between material slip speed and rupture front speed, previously reported for slow fronts, actually holds across the full range of front speeds we observe. We revisit a mechanism for slow slip in the model and demonstrate that fast slip and fast fronts have a different, inertial origin. We highlight the long transients in front speed even in homogeneous interfaces, and we study how both the local shear to normal stress ratio and the local strength are involved in the selection of front type and front speed. Lastly, we introduce an experimentally accessible integrated measure of block slip history, the Gini coefficient, and demonstrate that in the model it is a good predictor of the history-dependent local static friction coefficient of the interface. These results will contribute both to building a physically-based classification of the various types of fronts and to identifying the important mechanisms involved in the selection of their propagation speed.

29 pages, 21 figures

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• A 2-D Model for friction of complex anisotropic surfaces
• Steady-state propagation speed of rupture fronts along one-dimensional frictional interfaces
• Tuning friction with composite hierarchical surfaces
• Correlation between slip precursors and topological length scales at the onset of frictional sliding
• A minimal model for slow, sub-Rayleigh, super-shear and unsteady rupture propagation along homogeneously loaded frictional interfaces
• Nature of the high-speed rupture of the two-dimensional Burridge-Knopoff model of earthquakes
• Transition between Macroscopic Steady Slippage and Creep Motion in a System with Velocity-Dependent Friction Stress
• Deriving the slip front propagation velocity with the slip- and slip-velocity-dependent friction laws via the use of the linear marginal stability hypothesis