A constitutive model for fault gouge deformation in dynamic rupture simulations

In the context of numerical simulations of elastodynamic ruptures, we compare friction laws, including the linear slip-weakening (SW) law, the Dieterich-Ruina (DR) law, and the Free Volume (FV) law. The FV law is based on microscopic physics, incorporating Shear Transformation Zone (STZ) Theory which describes local, non-affine rearrangements within the granular fault gouge. A dynamic state variable models dilation and compaction of the gouge, and accounts for weakening and re-strengthening in the FV law. The principal difference between the FV law and the DR law is associated with the characteristic length scale L. In the FV law, LFV grows with increasing slip rate, while in the DR law LDR is independent of slip rate. The length scale for friction is observed to vary with slip velocity in laboratory experiments with simulated fault gouge, suggesting that the FV law captures an essential feature of gouge-filled faults. In simulations of spontaneous elastodynamic rupture, for equal energy dissipation the FV law produces ruptures with smaller nucleation lengths, lower peak slip velocities, and increased slip required for friction to fully weaken to steady sliding when compared to ruptures governed by the SW or DR laws. We also examine generalizations of the DR and FV laws that incorporate rapid velocity weakening. The rapid weakening laws produce selfhealing slip pulse ruptures for low initial shear loads. For parameters which produce identical net slip in the pulses of each rapid weakening friction law, the FV law exhibits a much shorter nucleation length, a larger slip-weakening distance, and less frictional energy dissipation than corresponding ruptures obtained using the DR law.