Rupture dynamics with energy loss outside the slip zone

Abstract

[1] Energy loss in a fault damage zone, outside the slip zone, contributes to the fracture energy that determines rupture velocity of an earthquake. A nonelastic two-dimensional dynamic calculation is done in which the slip zone is modeled as a fault plane and material off the fault is subject to a Coulomb yield condition. In a mode 2 crack-like solution in which an abrupt uniform drop of shear traction on the fault spreads from a point, Coulomb yielding occurs on the extensional side of the fault. Plastic strain is distributed with uniform magnitude along the fault, and it has a thickness normal to the fault proportional to propagation distance. Energy loss off the fault is also proportional to propagation distance, and it can become much larger than energy loss on the fault specified by the fault constitutive relation. The slip velocity function could be produced in an equivalent elastic problem by a slip-weakening friction law with breakdown slip D c increasing with distance. Fracture energy G and equivalent D c will be different in ruptures with different initiation points and stress drops, so they are not constitutive properties; they are determined by the dynamic solution that arrives at a particular point. Peak slip velocity is, however, a property of a fault location. Nonelastic response can be mimicked by imposing a limit on slip velocity on a fault in an elastic medium.

Off‐fault plasticity favors the arrest of dynamic ruptures on strength heterogeneity: Two‐dimensional cases

“…[9] We checked that in mode II, considering the homogeneous properties, we retrieved the same slip velocity limitation, the same asymmetric lateral extension of the plasticity after 2 km of propagation and the same linear dependency of the off-fault fracture energy with rupture length as found by Andrews [2005].…”

“…That is the reason why the constitutive law on the fault has been changed to a higher fracture energy and lower loading stress. This modification decreases the crack instability (increase of both S and d c ) before the strength change, compared to the original values of Andrews [2005]. We found that this combination of parameters, used for the homogeneous case study, leads to a too unstable rupture (for instance, the terminal velocity is reached very quickly), that is not likely to be stopped only by a small change of friction on the main rupture plane (considering that our fault is very smooth before the friction change, hence far from the critical state when reaching this point).…”

“…Below the limit, the medium behaves as a perfect elastic body, and above it, the energy is lost for off-fault rupturing. This formulation has been described and used by Andrews [2005]. For the method validation, we used almost the same parameter set to compute homogeneous cases, except the time step that was chosen 4 times smaller.…”

“…The rupture initiation zone is located at the center of the fault, and spans over 200 m (just above the critical crack length for the given parameters and same value used by Andrews [2005]). The small initial perturbation grows dynamically on this patch, where the static resistance is equal to the initial loading stress, and finally proceeds spontaneously into a dynamic crack that is able to propagate outside the nucleation zone.…”

“…For instance, Templeton and Rice [2008] found that off-fault plasticity was delaying the supershear transition. Previously, Andrews [2005] showed that the total fracture energy, including the energy dissipated inelastically, is increasing linearly with rupture propagation distance.…”