Dynamics and Properties of the Cohesive Zone in Rapid Fracture and Friction

How frictional slip evolves

Earthquake-like ruptures break the contacts that form the frictional interface separating contacting bodies and mediate the onset of frictional motion (stick-slip). The slip (motion) of the interface immediately resulting from the rupture that initiates each stick-slip event is generally much smaller than the total slip logged over the duration of the event. Slip after the onset of friction is generally attributed to continuous motion globally attributed to 'dynamic friction'. Here we show, by means of direct measurements of real contact area and slip at the frictional interface, that sequences of myriad hitherto invisible, secondary ruptures are triggered immediately in the wake of each initial rupture. Each secondary rupture generates incremental slip that, when not resolved, may appear as steady sliding of the interface. Each slip increment is linked, via fracture mechanics, to corresponding variations of contact area and local strain. Only by accounting for the contributions of these secondary ruptures can the accumulated interface slip be described. These results have important ramifications both to our fundamental understanding of frictional motion as well as to the essential role of aftershocks within natural faults in generating earthquake-mediated slip.

Static friction coefficient depends on the external pressure and block shape due to precursor slip

Amontons' law states that the maximum static friction force on a solid object is proportional to the loading force and is independent of the apparent contact area. This law indicates that the static friction coefficient does not depend on the external pressure or object shape. Here, we numerically investigate the sliding motion of a 3D viscoelastic block on a rigid substrate using the finite element method (FEM). The macroscopic static friction coefficient decreases with an increase in the external pressure, length, or width of the object, which contradicts Amontons' law. Precursor slip occurs in the 2D interface between the block and substrate before bulk sliding. The decrease in the macroscopic static friction coefficient is scaled by the critical area of the precursor slip. A theoretical analysis of the simplified models reveals that bulk sliding results from the instability of the quasi-static precursor slip caused by velocity-weakening local friction. We also show that the critical slip area determines the macroscopic static friction coefficient, which explains the results of the FEM simulation.

Earthquake Nucleation Along Faults With Heterogeneous Weakening Rate

The transition from quasistatic slip growth to dynamic rupture propagation constitutes one possible scenario to describe earthquake nucleation. If this transition is rather well understood for homogeneous faults, how the friction properties of multiscale asperities may influence the overall stability of seismogenic faults remains largely unclear. Combining classical nucleation theory and concepts borrowed from condensed matter physics, we propose a comprehensive analytical framework that predicts the influence of heterogeneities of weakening rate on the nucleation lengthL c for linearly slip-dependent friction laws. Model predictions are compared to nucleation lengths measured from 2D dynamic simulations of earthquake nucleation along heterogeneous faults. Our results show that the interplay between frictional properties and the asperity size gives birth to three instability regimes (local, extremal, and homogenized), each related to different nucleation scenarios, and that the influence of heterogeneities at a scale far lower than the nucleation length can be averaged.