Hybrid FEM-Peridynamic Modelling of Supershear Earthquake Ruptures

During earthquakes, seismic ruptures propagate (V_r) along faults as mode II-III cracks, approaching the shear wave speed V_s (i.e., sub-Rayleigh or V_r ~ 0.9 V_s), or, in at least 15% cases, at V_r faster than V_s (i.e., supershear or V_r ~ √2V_s ) (Bao et al., 2022). Since ground shaking increases with rupture speed, the transition from sub-Rayleigh to supershear speeds is critical in seismic hazard studies. This transition may occur (1) directly, due to dynamic stress perturbations associated with stress and strength heterogeneities along the fault, presence of fault step-overs and damage zones, etc., or (2) in-directly, where the stress peak ahead of the main crack tip (mother crack) nucleates a secondary crack (daughter crack) once the local fault strength is exceeded (Burridge-Andrews model).

Here we employ a newly-conceived 2-dimensional hybrid Finite Element Method and Peridynamic (FEM/PD-2D) model to simulate crack propagation and investigate the transition from sub-Rayleigh to supershear in dry and fluid-saturated media, where the Finite Element Method is used to simulate fluid flow, while Peridynamics is used to describe solid deformation. The model also incorporates a novel bond failure criterion based on critical rotation deformation (i.e., deflection angle of the Peridynamic bonds before and after shear deformation) for mode II fracture propagation.

First, we validate the FEM/PD-2D model against previous results from (1) numerical simulations with ABAQUS by Yolum et al. (2021), and (2) physical experiments with PMMA by Svetlizky et al. (2015). In case (1), the FEM/PD-2D model accurately reproduces rupture propagation in a dry Homalite plate with a pre-notch subjected to impact shear loading. Supershear rupture is recognized by the emergence of shear Mach waves observed in the particle velocity magnitude contours. In agreement with Yolum et al. (2021), the stable supershear crack velocity lies between √2V_s and V_p (compressional wave speed). In case (2), the model reproduces the shear loading experiments of PMMA blocks with a frictional interface, and yields crack growth curves and supershear propagation consistent with the measurements of Svetlizky et al. (2015).

Subsequently, we apply the FEM/PD-2D model to explore rupture propagation along both dry and fully saturated media under shear loading. Supershear crack speeds and the emergence of shear Mach cones are observed in both the dry and fluid-saturated cases. Supershear rupture can be achieved through either the in-direct (Burridge-Andrews mechanism) or a direct transition. Notably, the presence of the fluid phase enhances the sub-Raileigh to supershear transition due to poroelastic effects at the rupture front. The findings from this model, beyond their implications for earthquake hazard assessment, may also explain the formation mechanisms of hundred-meter-thick rock damage zones adjacent to seismogenic faults.