Finite Element Model of Branched Ruptures Including Off-Fault Plasticity

Fault intersections are a geometric complexity that frequently occurs in nature. Here we focus on earthquake rupture behavior when a continuous, planar main fault has a second fault branching off of it. We use the finite element method to examine which faults are activated and how the surrounding material responds for both elastic and elastic-plastic off-fault descriptions. Compared to an elastic model, a non-cohesive, elastic-plastic material, intended to account for zones of damaged rock bordering maturely slipped faults, will inhibit rupture on compressional side branches and promote rupture of extensional side branches. Activation of extensional side branches can be delayed and is triggered by continued rupture propagation on the main fault. We examine the deformation near the branching junction and find that fault opening is common for elastic materials, especially for compressional side branches. An elastic-plastic material is more realistic since elevated stresses around the propagating rupture tip and at the branching junction should bring the surrounding material to failure. With an elastic-plastic material model, fault opening is inhibited for a range of realistic material parameters. For large cohesive strengths opening can occur, but with material softening, a real feature of plastically deforming rocks, opening can be prevented. We also discuss algorithmic artifacts that may arise due to the presence of such a triple junction. When opening does not occur, the behavior at the triple junction is simplified and standard contact routines in finite element programs are able to properly represent the physical situation.Earth and Planetary SciencesEngineering and Applied Science

Influence of Material Contrast on Fault Branching Behavior

Material contrasts across faults are a common occurrence, and it is important to understand if these material contrasts can influence the path of rupture propagation. Here we examine models, solved numerically, of rupture propagation through one type of geometric complexity, that of a fault branch stemming from a planar main fault on which rupture initiates. This geometry, with a material contrast across the main fault, could be representative of either a mature strike-slip fault or a subduction zone interface. We consider branches in both the compressional and extensional quadrants of the fault, and material configurations in which the branch fault is in either the stier or the more compliant material and configurations with no material contrast. We find that there are regimes in which this elastic contrast can influence the rupture behavior at a branching junction, but there are also stress states for which the branch activation will not depend on the orientation of the mismatch. For the scenarios presented here, both compressional and extensional side branches are more likely to rupture if the branch is on the side of the fault with the more compliant material versus the stiffer material. The stresses induced on the branch fault, by rupture traveling on the main fault, are different for the two orientations of material contrast. We show how the interactions between rupture on the two faults determine which faults are activated.Earth and Planetary SciencesEngineering and Applied Science

Role of Fault Branches in Earthquake Rupture Dynamics

We analyze earthquake ruptures propagating along a straight “main” fault and encountering a finite-length branch fault. Such intersections are often observed in natural fault systems. The predicted effects of the interaction with the branch that we report can be remarkable; they can strongly perturb the propagation velocity on the main fault and, in some cases, even arrest that propagation. Earlier work (Kame et al., 2003; Bhat et al., 2004) emphasized the role of the fault pre-stress state, branch geometry (i.e., branching angle), and the incoming rupture velocity at the branching junction in determining whether the rupture would follow the branch or continue on the main fault or both, through simulations which did not let a rupture on the branch encounter a barrier or a fault end (called ‘infinite’ branch cases henceforth). In this study we look at “finite” branch cases, and study the effect also of branch length, with rupture being blocked from propagation beyond the branch end. It is known that sudden stoppage of a dynamic rupture front leads to the propagation of large dynamic stress perturbations in the medium. These have been known to nucleate or terminate ruptures on adjacent fault segments (Harris et al., 1991; Harris and Day, 1993, 1999; Harris et al., 2002; Fliss et al., 2005, among others). We thus anticipate interaction between the rupture on the main fault and the branched one at two stages, when the rupture is propagating on the branch and when it is suddenly blocked at the branch end. We show that in general rupture termination on a compressional branch little affects propagation on the main fault compared to the infinite branch cases. For branches on the extensional side, we show in some cases, that whereas an infinite' branch would have allowed (or stopped) rupture propagation on the main fault, a finite branch stops (or allows) propagation on the main fault. Such results have a dependence on branch length that we document. We also illustrate branch-related complexities in rupture velocity evolution which could be one of the sources of the high-frequency content of strong ground motion record. Complexities in the slip distribution, often associated with a presumed heterogeneous strength distribution along the fault, can also be observed when rupture is terminated on a branch.Earth and Planetary Science

Off-fault Damage Patterns Due to Supershear Ruptures with Application to the 2001 Mw 8.1 Kokoxili (Kunlun) Tibet Earthquake

We extend a model of a two-dimensional self-healing slip pulse, propagating dynamically in steady state with slip-weakening failure criterion, to the supershear regime in order to study the off-fault stressing induced by such a slip pulse and investigate features unique to the supershear range. Specifically, we show that there exists a nonattenuating stress field behind the Mach front that radiates high stresses arbitrarily far from the fault (practically this would be limited to distances comparable to the depth of the seismogenic zone), thus being capable of creating fresh damage or inducing Coulomb failure in known structures at large distances away from the main fault. We allow for both strike-slip and dip-slip failure induced by such a slip pulse. We show that off-fault damage is controlled by the speed of the slip-pulse, scaled stress drop, and principal stress orientation of the prestress field. We apply this model to study damage features induced during the 2001 Kokoxili (Kunlun) event in Tibet, for which it has been suggested that much of the rupture was supershear. We argue that an interval of simultaneous induced normal faulting is more likely due to a slip partitioning mechanism suggested previously than to the special features of supershear rupture. However, those features do provide an explanation for otherwise anomalous ground cracking at several kilometers from the main fault. We also make some estimates of fracture energy which, for a given net slip and dynamic stress drop, is lower than for a sub-Rayleigh slip pulse because part of the energy fed by the far-field stress is radiated back along the Mach fronts.Earth and Planetary SciencesEngineering and Applied Science

Finite Element Simulations of Dynamic Shear Rupture Experiments and Dynamic Path Selection along Kinked and Branched Faults

We analyze the nucleation and propagation of shear cracks along nonplanar, kinked, and branched fault paths corresponding to the configurations used in recent laboratory fracture studies by Rousseau and Rosakis (2003, 2009). The aim is to reproduce numerically those shear rupture experiments and from that provide an insight into processes which are active when a crack, initially propagating in mode II along a straight path, interacts with a bend in the fault or a branching junction. The experiments involved impact loading of thin Homalite-100 (a photoelastic polymer) plates, which had been cut along bent or branched paths and weakly glued back together everywhere except along a starter notch near the impact site. Strain gage recordings and high-speed photography of isochromatic lines provided characterization of the transient deformation fields associated with the impact and fracture propagation. We found that dynamic explicit 2-D plane-stress finite element analyses with a simple linear slip-weakening description of cohesive and frictional strength of the bonded interfaces can reproduce the qualitative rupture behavior past the bend and branch junctions in most cases and reproduce the principal features revealed by the photographs of dynamic isochromatic line patterns. The presence of a kink or branch can cause an abrupt change in rupture propagation velocity. Additionally, the finite element results allow comparison between total slip accumulated along the main and inclined fault segments. We found that slip along inclined faults can be substantially less than slip along the main fault, and the amount depends on the branch angle and kink or branch configuration.Earth and Planetary SciencesEngineering and Applied Science

Finite element simulations of dynamic shear rupture experiments and dynamic path selection along kinked and branched faults

We analyze the nucleation and propagation of shear cracks along nonplanar, kinked, and branched fault paths corresponding to the configurations used in recent laboratory fracture studies by Rousseau and Rosakis (2003, 2009). The aim is to reproduce numerically those shear rupture experiments and from that provide an insight into processes which are active when a crack, initially propagating in mode II along a straight path, interacts with a bend in the fault or a branching junction. The experiments involved impact loading of thin Homalite‐100 (a photoelastic polymer) plates, which had been cut along bent or branched paths and weakly glued back together everywhere except along a starter notch near the impact site. Strain gage recordings and high‐speed photography of isochromatic lines provided characterization of the transient deformation fields associated with the impact and fracture propagation. We found that dynamic explicit 2‐D plane‐stress finite element analyses with a simple linear slip‐weakening description of cohesive and frictional strength of the bonded interfaces can reproduce the qualitative rupture behavior past the bend and branch junctions in most cases and reproduce the principal features revealed by the photographs of dynamic isochromatic line patterns. The presence of a kink or branch can cause an abrupt change in rupture propagation velocity. Additionally, the finite element results allow comparison between total slip accumulated along the main and inclined fault segments. We found that slip along inclined faults can be substantially less than slip along the main fault, and the amount depends on the branch angle and kink or branch configuration

Effects of Pre-Stress State and Rupture Velocity on Dynamic Fault Branching

We consider a mode II rupture which propagates along a planar main fault and encounters an intersection with a branching fault. Using an elastodynamic boundary integral equation formulation, allowing the failure path to be dynamically self-chosen, we study the following questions: Does the rupture initiate along the branch? Does it continue? Is the extensional or compressional side most favored for branching? Does rupture continue on the main fault too? Failure is described by a slip-weakening law for which the strength at any amount of slip is proportional to normal stress

Finite Element Modeling of Branched Ruptures Including Off-Fault Plasticity

Fault intersections are a geometric complexity that frequently occurs in nature. Here we focus on earthquake rupture behavior when a continuous planar main fault has a second fault branching off of it. We use the finite element (FE) method to examine which faults are activated and how the surrounding material responds for both elastic and elastic–plastic off-fault descriptions. Compared to an elastic model, a noncohesive elastic–plastic material, intended to account for zones of damaged rock bordering maturely slipped faults, will inhibit rupture on compressional side branches and promote rupture of extensional side branches. Activation of extensional side branches can be delayed and is triggered by continued rupture propagation on the main fault. We examine the deformation near the branching junction and find that fault opening is common for elastic materials, especially for compressional side branches. An elastic–plastic material is more realistic because elevated stresses around the propagating rupture tip and at the branching junction should bring the surrounding material to failure. With an elastic–plastic material model, fault opening is inhibited for a range of realistic material parameters. For large cohesive strengths, opening can occur, but with material softening, a real feature of plastically deforming rocks, open- ing can be prevented. We also discuss algorithmic artifacts that may arise due to the presence of such a triple junction. When opening does not occur, the behavior at the triple junction is simplified and standard contact routines in FE programs are able to properly represent the physical situation.Engineering and Applied Science