Effects of pore pressure-dependent friction laws on supershear earthquakes

We study how heterogeneous rupture propagation affects the coherence of shear and Rayleigh Mach wavefronts radiated by supershear earthquakes. We address this question using numerical simulations of ruptures on a planar, vertical strike‐slip fault embedded in a three‐dimensional, homogeneous, linear elastic half‐space. Ruptures propagate spontaneously in accordance with a linear slip‐weakening friction law through both homogeneous and heterogeneous initial shear stress fields. In the 3‐D homogeneous case, rupture fronts are curved owing to interactions with the free surface and the finite fault width; however, this curvature does not greatly diminish the coherence of Mach fronts relative to cases in which the rupture front is constrained to be straight, as studied by Dunham and Bhat (2008a). Introducing heterogeneity in the initial shear stress distribution causes ruptures to propagate at speeds that locally fluctuate above and below the shear wave speed. Calculations of the Fourier amplitude spectra (FAS) of ground velocity time histories corroborate the kinematic results of Bizzarri and Spudich (2008a): (1) The ground motion of a supershear rupture is richer in high frequency with respect to a subshear one. (2) When a Mach pulse is present, its high frequency content overwhelms that arising from stress heterogeneity. Present numerical experiments indicate that a Mach pulse causes approximately anω−1.7high frequency falloff in the FAS of ground displacement. Moreover, within the context of the employed representation of heterogeneities and over the range of parameter space that is accessible with current computational resources, our simulations suggest that while heterogeneities reduce peak ground velocity and diminish the coherence of the Mach fronts, ground motion at stations experiencing Mach pulses should be richer in high frequencies compared to stations without Mach pulses. In contrast to the foregoing theoretical results, we find no average elevation of 5%‐damped absolute response spectral accelerations (SA) in the period band 0.05–0.4 s observed at stations that presumably experienced Mach pulses during the 1979 Imperial Valley, 1999 Kocaeli, and 2002 Denali Fault earthquakes compared to SA observed at non‐Mach pulse stations in the same earthquakes. A 20% amplification of short period SA is seen only at a few of the Imperial Valley stations closest to the fault. This lack of elevated SA suggests that either Mach pulses in real earthquakes are even more incoherent that in our simulations or that Mach pulses are vulnerable to attenuation through nonlinear soil response. In any case, this result might imply that current engineering models of high frequency earthquake ground motions do not need to be modified by more than 20% close to the fault to account for Mach pulses, provided that the existing data are adequately representative of ground motions from supershear earthquakes.

We incorporate shear strain localization into spontaneous elastodynamic rupture simulations using a shear transformation zone (STZ) friction law. In the STZ model, plastic strain in the granular fault gouge occurs in local regions called STZs. The number density of STZs is governed by an effective disorder temperature, and regions with elevated effective temperature have an increased strain rate. STZ theory resolves the dynamic evolution of the effective temperature across the width of the fault zone. Shear bands spontaneously form in the model due to feedbacks amplifying heterogeneities in the initial effective temperature. In dynamic earthquake simulations, strain localization is a mechanism for dynamic fault weakening. A shear band dynamically forms, reduces the sliding stress, and decreases the frictional energy dissipation on the fault. We investigate the effect of the dynamic weakening due to localization in generating pulse‐like, crack‐like, and supershear rupture. Our results illustrate that the additional weakening and reduction of on‐fault energy dissipation due to localization have a significant impact on the initial shear stress required for supershear or pulse‐like rupture to propagate on a fault.

Effect of real-world frictional strengthening layer near the Earth's free surface on rupture characteristics with different friction laws: Implication for scarcity of supershear earthquakes

Field investigations suggest that supershear earthquakes occur on geometrically simple, smooth fault segments. In contrast, dynamic rupture simulations show how heterogeneity of stress, strength, and fault geometry can trigger supershear transitions, as well as other complex rupture styles. Here we examine the Fang and Dunham (2013) ensemble of 2‐D plane strain dynamic ruptures on fractally rough faults subject to strongly rate weakening friction laws to document the effect of fault roughness and prestress on rupture behavior. Roughness gives rise to extremely diverse rupture styles, such as rupture arrests, secondary slip pulses that rerupture previously slipped fault sections, and supershear transitions. Even when the prestress is below the Burridge‐Andrews threshold for supershear on planar faults with uniform stress and strength conditions, supershear transitions are observed. A statistical analysis of the rupture velocity distribution reveals that supershear transients become increasingly likely at higher stress levels and on rougher faults. We examine individual ruptures and identify recurrent patterns for the supershear transition. While some transitions occur on fault segments that are favorably oriented in the background stress field, other transitions happen at the initiation of or after propagation through an unfavorable bend. We conclude that supershear transients are indeed favored by geometric complexity. In contrast, sustained supershear propagation is most common on segments that are locally smoother than average. Because rupture style is so sensitive to both background stress and small‐scale details of the fault geometry, it seems unlikely that field maps of fault traces will provide reliable deterministic predictions of supershear propagation on specific fault segments.

Application of finite element simulations for data reduction of experimental friction tests on rubber–metal contacts

The adoption of advanced high-strength steels is growing in the automotive industry due to their good strength-to-weight ratio. However, the frictional contact conditions differ from the ones arising in mild steels due to the high values of contact pressure. The objective of this study is the detailed numerical analysis of the frictional contact conditions in the hole expansion test. The Coulomb friction law is adopted in the finite element model, using different values for the (constant) friction coefficient, as well as a pressure dependent friction coefficient. The increase of the friction coefficient leads to an increase of the punch force and a slight decrease of the hole expansion. The results show that increasing the friction coefficient postpones the onset of necking, but the localization does not change.

Industrial storage of granular material using silos is common, however, improved understanding of silo flow is needed. Various continuum models attempt to describe the velocity of dense granular flow in silos. Kinematic, and recently, stochastic models, based upon the diffusion of some quantity, perform well when there is a single orifice, and when the yield criterion is satisfied. However, if system stresses are insufficient to satisfy the yield criterion, or if there is a second orifice, these models fail to capture the entire flow behaviour. Advances in granular rheology have allowed a pressure dependent friction law to be defined which can capture the behaviour of granular silo flow including un-yielded zones, flow-rate independence of fill height, the Beverloo flow-rate, and various other phenomena. We performed silo discharge experiments in a flat bottomed planar silo with a single and two adjacent orifices, for two grain types. The velocity was measured using Particle Image Velocimetry. Results were compared to a mathematical model based on the μ (I) rheology which was shown to qualitatively capture the observed phenomena including plug-like zones where the yield criterion is not satisfied. These preliminary results strongly encourage future investigations into the effect of friction parameters and numerical boundary conditions.

Elasto–plastic behavior of the third generation Fortiform 1050 steel has been analysed using cyclic tension–compression tests. At the same time, the pseudo elastic modulus evolution with plastic strain was analysed using cyclic loading and unloading tests. From the experiments, it was found that the cyclic behavior of the steel is strongly kinematic and elastic modulus decrease with plastic strain is relevant for numerical modelling. In order to numerically analyse a U-Drawing process, strip drawing tests have been carried out at different contact pressures and Filzek model has been used to fit the experimental data and implement a pressure dependent friction law in Autoform software. Finally, numerical predictions of springback have been compared with the experimentally ones obtained using a sensorized U-Drawing tooling. Different material and contact models have been examined and most influencing parameters have been identified to model the forming of these new steels.