Effects of inelastic off-fault deformation on the dynamics of earthquake rupture and branch fault activation

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We conducted a comprehensive investigation of the factors controlling the formation, location, and extent of inelastic deformation surrounding a fault during dynamic earthquake rupture with drained and undrained pore fluid response. This work was motivated by geologic observations of fault zone complexity and the damage patterns found in fault zones which indicate that fault geometry and structures in the damage zone can play an important role during dynamic earthquake rupture, serving as locations for rupture arrest and nucleation, causing variations in rupture propagation velocity, and controlling rupture path. Using 2D finite element analyses of mode II shear earthquake rupture in a homogeneous material under remote loading, we investigated how pressure-dependent inelastic deformation in the fault-bordering material develops during dynamic rupture and influences rupture dynamics. We find that the location, with respect to the fault, of the actively deforming plastic zone is controlled by direction, Ψ, of most compressive pre-stress to the fault. In modeling of a "dry," or drained, material, inelastic deformation occurs only on the extensional side for higher angles of most compressive stress, Ψ ≥ 45°, on both the extensional and compressional sides for 10° ≤ Ψ ≤ 45°, and only on the compressional side Ψ < 10°. Undrained pressure changes due to the poroelastic response, which oppose isotropic changes in stress and are proportional to the Skempton coefficient, B, strengthen the extensional side of the fault and weaken the compressional side against inelastic yielding. We also investigate how inelastic deformation controls the evolution of rupture velocity, branch path selection, and peak ground velocities and accelerations. Because the width of the plastic zone grows with increasing rupture length in a self-similar manner, the energy dissipated by inelastic deformation can limit the rupture velocity and result in self-similar rupture at a constant velocity finitely below the Rayleigh wave speed. Observed earthquake rupture speeds of 0.80 c R - 0.92 c R could be explained by a specific fracture energy with a linear dependence on crack length. When initial stresses are such that a transition to supershear would be possible in an elastic material, the transition to supershear is delayed or even prevented in some cases by inelastic off-fault deformation. Branch activation is more favorable at higher propagation velocities, but off-fault inelastic deformation reduces the likelihood of branch fault activation by slowing rupture velocity. Moderate reductions in radiated horizontal and vertical ground velocity and large reductions in accelerations occur when elastic-plastic off-fault response is incorporated during rupture.