Elasto-thermo-visco-plastic numerical modelling from a laboratory to geodynamic scale: implications for convergence-driven experiments

The development of a subduction zone, whether spontaneous or induced, encompasses a stage of strain localization and is epitomized by the growth of lithospheric-scale shear bands. Our aim in this paper, using a solid-mechanical constitutive description relevant for oceanic lithosphere, is to investigate factors that promote or inhibit localization of deformation in brittle and ductile regimes in convergence-driven numerical experiments. We used the Drucker-Prager yield criterion and a non-associative flow rule, allowing viscoplastic deformation to take directions independent of the preferred direction of yield. We present a step-by-step description of the constitutive law and the consistent algorithmic tangent modulus. The model domain contains an initial weak-zone on which localization can potentially nucleate. In solving the energy conservation problem, we incorporate a heat source term from the mechanical deformations which embodies the irreversible plastic work done. This work term couples the energy equation to the constitutive description, and hence hence the stress balance, via the evolving temperature field. On a sample-scale, we first conduct a series of isothermal benchmark tests. We then explore behavior including shear heating and volumetric work both separately and in concert. and thereby address the (in)significance of the latter, and hence assess their potential importance. We find that dilatational effects mostly enhance both shear band development and shear heating. We also observe that high temperature promotes shear band development whereas high confining pressure inhibits it, and infer that the competition between these factors is likely to be the major influence on the position within the lithosphere where shear bands nucleate

A Laboratory Earthquake‐Based Stochastic Seismic Source Generation Algorithm for Strike‐Slip Faults and its Application to the Southern San Andreas Fault

There is a sparse number of credible source models available from large‐magnitude past earthquakes. A stochastic source‐model‐generation algorithm thus becomes necessary for robust risk quantification using scenario earthquakes. We present an algorithm that combines the physics of fault ruptures as imaged in laboratory earthquakes with stress estimates on the fault constrained by field observations to generate stochastic source models for large‐magnitude (M_w 6.0–8.0) strike‐slip earthquakes. The algorithm is validated through a statistical comparison of synthetic ground‐motion histories from a stochastically generated source model for a magnitude 7.90 earthquake and a kinematic finite‐source inversion of an equivalent magnitude past earthquake on a geometrically similar fault. The synthetic dataset comprises three‐component ground‐motion waveforms, computed at 636 sites in southern California, for 10 hypothetical rupture scenarios (five hypocenters, each with two rupture directions) on the southern San Andreas fault. A similar validation exercise is conducted for a magnitude 6.0 earthquake, the lower magnitude limit for the algorithm. Additionally, ground motions from the M_w 7.9 earthquake simulations are compared against predictions by the Campbell–Bozorgnia Next Generation Attenuation relation, as well as the ShakeOut scenario earthquake. The algorithm is then applied to generate 50 source models for a hypothetical magnitude 7.9 earthquake originating at Parkfield, California, with rupture propagating from north to south (toward Wrightwood), similar to the 1857 Fort Tejon earthquake. Using the spectral element method, three‐component ground‐motion waveforms are computed in the Los Angeles basin for each scenario earthquake and the sensitivity of ground‐shaking intensity to seismic source parameters (such as the percentage of asperity area relative to the fault area, rupture speed, and rise time) is studied

On the importance of 3D stress state in 2D earthquake rupture simulations with off-fault deformation

During the last decades, many numerical models have been developed to investigate the conditions for seismic and aseismic slip. Those models explore the behavior of frictional faults, embedded in either elastic or inelastic mediums, and submitted to a far field loading (seismic cycle models), or initial stresses (single dynamic rupture models). Those initial conditions impact both on-fault and off-fault dynamics. Because of the sparsity of direct measurements of fault stresses, modelers have to make assumptions about these initial conditions. To this day, Anderson's theory is the only framework that can be used to link fault generation and reactivation to the three-dimensional stress field. In this work we look at the role of the three dimensional stress field in modelling a 2D strike-slip fault under plane-strain conditions. We show that setting up the incorrect initial stress field, based on Anderson's theory, can lead to underestimation of the damage zone width by up to a factor of six, for the studied cases. Moreover, because of the interactions between fault slip and off-fault deformation, initial stress field influences the rupture propagation. Our study emphasizes the need to set up the correct initial 3D stress field, even in 2D numerical simulations

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

A Micromechanics Based Constitutive Model for Brittle Failure at High Strain Rates

The micromechanical damage mechanics formulated by Ashby and Sammis, 1990, “The Damage Mechanics of Brittle Solids in Compression,” Pure Appl. Geophys., 133(3), pp. 489–521, and generalized by Deshpande and Evans 2008, “Inelastic Deformation and Energy Dissipation in Ceramics: A Mechanism-Based Constitutive Model,” J. Mech. Phys. Solids, 56(10), pp. 3077–3100. has been extended to allow for a more generalized stress state and to incorporate an experimentally motivated new crack growth (damage evolution) law that is valid over a wide range of loading rates. This law is sensitive to both the crack tip stress field and its time derivative. Incorporating this feature produces additional strain-rate sensitivity in the constitutive response. The model is also experimentally verified by predicting the failure strength of Dionysus-Pentelicon marble over strain rates ranging from ~10^(−6) to 10^3s^(−1). Model parameters determined from quasi-static experiments were used to predict the failure strength at higher loading rates. Agreement with experimental results was excellent

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