Crack growth resistance and dynamic rupture arrest under slip dependent friction

The slip-strengthening behavior observed in fracture and friction experiments is considered as a possible candidate for crack growth resistance and dynamic rupture arrest. The peak shear stress τp and the strengthening slip Ds play a role in the crack growth resistance. Depending on this resistance, the rupture may be stopped by a strengthening barrier. In such a case, we show that the residual shear stress at the end of the dynamic process is not grid-size dependent, suggesting that the static shear stress will not exhibit any singularity at the crack tip. Hence, rupture arrest by a strengthening barrier is compatible with a criterion based on finite shear stress threshold. Considering a finite weak zone bounded by two strengthening barriers, we investigate the modalities of the rupture arrest. Despite the presence of the barriers, the size of the rupture event is not controlled a priori but rather depends on both the strength of the barrier and the seismic energy released in the weak zone. Depending on the parameters of the strengthening, two mechanisms are possible for the rupture arrest. The first one is associated with a negative stress drop inside the resisting zone. This mechanism is independent from the size of the weak zone. The second mechanism is associated with a positive stress drop inside the resisting zone, and is crack-size dependent. In both cases, we show the existence of a crack-arrest zone characterized by small amount of slip and shear stress concentration and associated with a self-healing slip pulse. This model, with weak zones and resisting zones is consistent with recent strong motion inversions and offers a possible mechanism for the fault length increase over geological times through progressive barrier damaging.