Static and sliding contact of rough surfaces: effect of asperity-scale properties and long-range elastic interactions

Friction in static and sliding contact of rough surfaces is important in numerous physical phenomena. We seek to understand macroscopically observed static and sliding contact behavior as the collective response of a large number of microscopic asperities. We develop an efficient numerical framework that can be used to investigate how the macroscopic response of multiple frictional contacts depends on long-range elastic interactions, different constitutive assumptions about the deforming contacts and their local shear resistance, and surface roughness. We approximate the contact between two rough surfaces as that between a regular array of discrete deformable elements attached to a elastic block and a rigid rough surface. The deformable elements are viscoelastic or elasto/viscoplastic with a range of relaxation times, and the elastic interaction between contacts is long-range. We find that the model reproduces main macroscopic features of evolution of contact and friction for a range of constitutive models of the elements, suggesting that macroscopic frictional response is robust with respect to the microscopic behavior. Viscoelasticity/viscoplasticity contributes to the increase of friction with contact time and leads to a subtle history dependence. Interestingly, long-range elastic interactions only change the results quantitatively compared to the meanfield response. We find that sustained increase in the static friction coefficient during long hold times suggests viscoelastic response of the underlying material with multiple relaxation time scales. We also find that the experimentally observed proportionality of the direct effect in velocity jump experiments to the logarithm of the velocity jump points to a complex material-dependent shear resistance at the microscale.Comment: 33 pages, 17 figure

Stable creeping fault segments can become destructive as a result of dynamic weakening

Faults in Earth’s crust accommodate slow relative motion between tectonic plates through either similarly slow slip or fast, seismic-wave-producing rupture events perceived as earthquakes. These types of behaviour are often assumed to be separated in space and to occur on two different types of fault segment: one with stable, rate-strengthening friction and the other with rate-weakening friction that leads to stick-slip. The 2011 Tohoku-Oki earthquake with moment magnitude M_w = 9.0 challenged such assumptions by accumulating its largest seismic slip in the area that had been assumed to be creeping. Here we propose a model in which stable, rate-strengthening behaviour at low slip rates is combined with coseismic weakening due to rapid shear heating of pore fluids, allowing unstable slip to occur in segments that can creep between events. The model parameters are based on laboratory measurements on samples from the fault of the M_w 7.6 1999 Chi-Chi earthquake. The long-term slip behaviour of the model, which we examine using a unique numerical approach that includes all wave effects, reproduces and explains a number of both long-term and coseismic observations—some of them seemingly contradictory—about the faults at which the Tohoku-Oki and Chi-Chi earthquakes occurred, including there being more high-frequency radiation from areas of lower slip, the largest seismic slip in the Tohoku-Oki earthquake having occurred in a potentially creeping segment, the overall pattern of previous events in the area and the complexity of the Tohoku-Oki rupture. The implication that earthquake rupture may break through large portions of creeping segments, which are at present considered to be barriers, requires a re-evaluation of seismic hazard in many areas

Spatiotemporal Properties of Sub‐Rayleigh and Supershear Ruptures Inferred From Full‐Field Dynamic Imaging of Laboratory Experiments

Many earthquakes propagate at sub‐Rayleigh speeds. Earthquakes propagating at supershear speeds, though less common, are by far more destructive. Hence, it is important to quantify the motion characteristics associated with both types of earthquake ruptures. Here we report on the spatiotemporal properties of dynamic ruptures measured in our laboratory experiments using the dynamic digital image correlation technique. Earthquakes are mimicked by the frictional rupture propagating along the interface of two Homalite plates. Digital images of the propagating ruptures are captured by an ultrahigh‐speed camera and processed with digital image correlation in order to produce sequences of evolving displacement and velocity maps. Our measurements reveal the full‐field structure of the velocity components, bridge the gap between previous spatially sparse velocimeter measurements available only at two to three locations, and enable us to quantify the attenuation patterns away from the interface

Microseismicity on Patches of Higher Compression During Larger-Scale Earthquake Nucleation in a Rate-and-State Fault Model

While many large earthquakes are preceded by observable foreshocks, the mechanism responsible for the occurrence of these smaller‐scale seismic events remains uncertain. One physical explanation of foreshocks with growing support is that they are produced by the interaction of slow slip with fault heterogeneity. Inspired by the suggestion from laboratory experiments that foreshocks occur on fault asperities (bumps), we explore rate‐and‐state fault models with patches of higher normal stress embedded in a larger seismogenic region by conducting 3‐D numerical simulations of their behavior over long‐term sequences of aseismic and seismic slips. The models do produce smaller‐scale seismicity during the aseismic nucleation of larger‐scale seismic events. These smaller‐scale events have reasonable stress drops, despite the highly elevated compression assigned to the source patches. We find that the two main factors contributing to the reasonable stress drops are the significant extent of the rupture into the region surrounding the patches and the aseismic stress release just prior to the seismic events. The smaller‐scale seismicity can only occur if a sufficient separation in nucleation scales between the foreshock‐like events and mainshocks is achieved. Our modeling provides insight into the conditions conducive for generating foreshocks on both natural and laboratory faults

Nearly magnitude‐invariant stress drops in simulated crack‐like earthquake sequences on rate‐and‐state faults with thermal pressurization of pore fluids

Stress drops, inferred to be magnitude‐invariant, are a key characteristic used to describe natural earthquakes. Theoretical studies and laboratory experiments indicate that enhanced dynamic weakening, such as thermal pressurization of pore fluids, may be present on natural faults. At first glance, magnitude invariance of stress drops and enhanced dynamic weakening seem incompatible since larger events may experience greater weakening and should thus have lower final stresses and higher stress drops. We hypothesize that enhanced dynamic weakening can be reconciled with magnitude‐invariant stress drops due to larger events having lower average prestress when compared to smaller events. We conduct numerical simulations of long‐term earthquake sequences in fault models with rate‐and‐state friction and thermal pressurization, and in the parameter regime that results mostly in crack‐like ruptures, we find that such models can explain both the observationally inferred stress drop invariance and increasing breakdown energy with event magnitude. Smaller events indeed have larger average initial stresses than medium‐sized events, and we find nearly constant stress drops for events spanning up to two orders of magnitude in average slip, comparable to approximately six orders of magnitude in seismic moment. Segment‐spanning events have more complex behavior, which depends on the properties of the arresting velocity‐strengthening region at the edges of the faults

Three-dimensional earthquake sequence simulations with evolving temperature and pore pressure due to shear heating: Effect of heterogeneous hydraulic diffusivity

A new methodology for three-dimensional (3-D) simulations of earthquake sequences is presented that accounts not only for inertial effects during seismic events but also for shear-induced temperature variations on the fault and the associated evolution of pore fluid pressure. In particular, the methodology allows to capture thermal pressurization (TP) due to frictional heating in a shear zone. One-dimensional (1-D) diffusion of heat and pore fluids in the fault-normal direction is incorporated using a spectral method, which is unconditionally stable, accurate with affordable computational resources, and highly suitable to earthquake sequence calculations that use variable time steps. The approach is used to investigate the effect of heterogeneous hydraulic properties by considering a fault model with two regions of different hydraulic diffusivities and hence different potential for TP. We find that the region of more efficient TP produces larger slip in model-spanning events. The slip deficit in the other region is filled with more frequent smaller events, creating spatiotemporal complexity of large events on the fault. Interestingly, the area of maximum slip in model-spanning events is not associated with the maximum temperature increase because of stronger dynamic weakening in that area. The region of more efficient TP has lower interseismic shear stress, which discourages rupture nucleation there, contrary to what was concluded in prior studies. Seismic events nucleate in the region of less efficient TP where interseismic shear stress is higher. In our model, hypocenters of large events do not occur in areas of large slip or large stress drop

Connecting depth limits of interseismic locking, microseismicity, and large earthquakes in models of long-term fault slip

Thickness of the seismogenic zone is commonly determined based on the depth of microseismicity or the fault locking depth inferred from geodetic observations. The relation between the two estimates and their connection to the depth limit of large earthquakes remain elusive. Here we explore the seismic and geodetic observables in models of faults governed by laboratory-based friction laws that combine quasi-static rate-and-state friction and enhanced dynamic weakening. Our models suggest that the transition between the locked and fully creeping regions can occur over a broad depth range. The effective locking depth, D_(elock), associated with concentrated loading and promoting microseismicity, is located at the top of this transition zone; the geodetic locking depth, D_(glock), inverted from surface geodetic observations, corresponds to the depth of fault creeping with approximately half of the long-term rate. Following large earthquakes, D_(elock) either stays unchanged or becomes shallower due to creep penetrating into the shallower locked areas, whereas D_(glock) deepens as the slip deficit region expands, compensating for the afterslip. As the result, the two locking depths diverge in the late interseismic period, consistent with available seismic and geodetic observations from several major fault segments in Southern California. We find that D_(glock) provides a bound on the depth limit of large earthquakes in our models. However, the assumed layered distribution of fault friction and simple depth estimates are insufficient to characterize more heterogeneous faults, e.g., ones with significant along-strike variations. Improved observations and models are needed to illuminate physical properties and seismic potential of fault zones

Rupture-dependent breakdown energy in fault models with thermo-hydro-mechanical processes

Substantial insight into earthquake source processes has resulted from considering frictional ruptures analogous to cohesive-zone shear cracks from fracture mechanics. This analogy holds for slip-weakening representations of fault friction that encapsulate the resistance to rupture propagation in the form of breakdown energy, analogous to fracture energy, prescribed in advance as if it were a material property of the fault interface. Here, we use numerical models of earthquake sequences with enhanced weakening due to thermal pressurization of pore fluids to show how accounting for thermo-hydro-mechanical processes during dynamic shear ruptures makes breakdown energy rupture-dependent. We find that local breakdown energy is neither a constant material property nor uniquely defined by the amount of slip attained during rupture, but depends on how that slip is achieved through the history of slip rate and dynamic stress changes during the rupture process. As a consequence, the frictional breakdown energy of the same location along the fault can vary significantly in different earthquake ruptures that pass through. These results suggest the need to reexamine the assumption of predetermined frictional breakdown energy common in dynamic rupture modeling and to better understand the factors that control rupture dynamics in the presence of thermo-hydro-mechanical processes