Rupture dynamics along bimaterial interfaces: a parametric study of the shear-normal traction coupling
Résumé
Earthquake ruptures often develop along faults separating materials with dissimilar elastic properties. Due to the broken symmetry, the propagation of the rupture along the bimaterial interface is driven by the coupling between interfacial sliding and normal traction perturbations. We numerically investigate in-plane rupture growth along a planar interface, under slip weakening friction, separating two dissimilar isotropic linearly elastic half-spaces, and we perform a parametric study of the classical Prakash-Clifton regularization, for different material contrasts. In particular the mesh-dependence and the regularization-dependence of the numerical solutions are analysed in this parameter space. When the regularization involves a slip-rate dependent relaxation time, a characteristic sliding distance is identified below which numerical solutions no longer depend on the regularization parameter, that is, they are physically well-posed solutions. Such regularization provides an adaptive high-frequency filter of the slip-induced normal traction perturbations, following the dynamic shrinking of the dissipation zone during the acceleration phase. In contrast, a regularization involving a constant relaxation time leads to numerical solutions that always depend on the regularization parameter since it fails in adapting to the shrinking of the process zone. Dynamic regularization is further investigated using a non-local regularization based on a relaxation time that depends on the dynamic length of the dissipation zone. Such reformulation is shown to provide similar results as the dynamic timescale regularization proposed by Prakash-Clifton when the slip rate is replaced by the maximum slip rate along the sliding interface. This leads to the identification of a dissipative length scale associated with the coupling between interfacial sliding and normal traction perturbations, together with a scaling law between the maximum slip rate and the dynamic size of the process zone during the rupture propagation. Dynamic timescale regularization provides mesh-independent and physically well-posed numerical solutions during the acceleration phase towards an asymptotic speed. When generalized Rayleigh wave does not exist, numerical solutions are shown to tend towards an asymptotic velocity higher than the slowest shear wave speed. When the generalized Rayleigh wave speed exists, numerical solutions tend towards this velocity becoming noisier and noisier as the rupture progresses. In this regime regularization dependent, unstable finite-size pulses may be generated.
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