The weakness of earthquake faults

Bulletin of the Seismological Society of America, 2003

A 2D lattice particle model is used to simulate the dynamic rupture process of a normal fault. The system equations for the particle motions are solved numerically by the finite-difference method, under a given block boundary condition. The flexibility of the implementation of a 2D lattice particle model to simulate an earthquake dynamic process was demonstrated in previous modeling of a shallow angle thrust fault . Numerical results indicate that the particle motions (displacement, velocity, and acceleration) along the fault are discontinuous both in the fault-parallel and fault-normal directions, with a localized slip rupture and localized fault separation. In the vicinity of the fault outcrop (the position at which the fault intersects with the free surface), the particle velocity and acceleration increase rapidly, both on the hanging wall and the footwall. The particle motions on the hanging wall are larger than those on the footwall. These motions are amplified as the fault scarp develops (rupture breaks out at the surface), with strong asymmetry between the hanging wall and the footwall. Along the free surface, as the distance from the fault outcrop increases, the particle velocity and acceleration decrease rapidly on the footwall and less rapidly on the hanging wall. The asymmetrical particle motion results from the geometrical effect of the dip of the fault, the free surface, and the dynamic source rupture. The combination of all of these effects causes a strong asymmetry in stress when the rupture pulse approaches the free surface. The dynamically propagating rupture is characterized by a ramp slip time function accompanied with fault opening. The slip pulse becomes sharper when the rupture approaches the free surface; consequentially, the hanging wall in the vicinity of the fault exhibits a large vibration, which generates a strong surface wave propagating along the free surface away from the fault scarp on the hanging-wall side. This result is similar but significantly different from the numerical simulation of a normal fault with a moving double-couple dislocation source . In addition, the numerical result is qualitatively in agreement with recent foam-rubber experiments (Brune and Anooshehpoor, 1999) and similar to results from a finite-element simulation . Comparing with a 2D strike-slip fault and thrust fault, the particle motions in the vicinity of the normal fault on the free surface are smaller for a same-size rupture pulse.

A realistic numerical simulation model for all physical processes underlying the earthquake phenomenon on HPC's would provide a powerful tool to study fault behavior and earthquake nucleation. The microphysical particle-based Lattice Solid Model (LSM) currently being developed at QUAKES provides a basis on which to construct such a model. Presently, the model simulates stress transfer, seismic waves, fracture, friction, heat and gouge dynamics. Simulations show numerous features compatible with laboratory and field studies including shear localization, low-strength faults compatible with the Heat-Flow Constraint, slip pulses on faults, Gutenburg-Richter power law statistics and cycles of seismic activity exhibiting accelerating energy release prior to large events. Ultimately, when fully developed, it is envisaged that the LSM will be capable of simulating all physical processes underlying earthquakes including lubrication and dynamics of fluids, phase transformations, and chemical effects as well as all observable signals including strain, seismic, electric and magnetic. Increased computational capacity, a model refinement process involving feedback with laboratory and field observations, and integration with macroscopic simulation models would provide the means to study the earthquake cycle, and hence, to develop earthquake hazard quantification and forecasting methodology that best uses the incomplete recorded and incoming data. Recent LSM simulation results of patterns of accelerating energy release prior to large events suggest that earthquake statistics can evolve in a predictable way. These results demonstrate the potential utility of realistic numerical simulation models as a means to probe the earthquake cycle, and provide encouragement that earthquake forecasting is feasible, at least under certain conditions.

Pure and Applied Geophysics, 2006

Despite the insight gained from 2D particle models, and given that the dynamics of crustal faults occur in 3D space, the question remains, how do the 3D fault gouge dynamics differ from those in 2D? Traditionally, 2D modeling has been preferred over 3D simulations because of the computational cost of solving 3D problems. However, modern high performance computing architectures, combined with a parallel implementation of the Lattice Solid Model (LSM), provide the opportunity to explore 3D fault micromechanics and to progress understanding of effective constitutive relations of fault gouge layers. In this paper, macroscopic friction values from 2D and 3D LSM simulations, performed on an SGI Altix 3700 super-cluster, are compared. Two rectangular elastic blocks of bonded particles, with a rough fault plane and separated by a region of randomly sized non-bonded gouge particles, are sheared in opposite directions by normally-loaded driving plates. The results demonstrate that the gouge particles in the 3D models undergo significant out-of-plane motion during shear. The 3D models also exhibit a higher mean macroscopic friction than the 2D models for varying values of interparticle friction. 2D LSM gouge models have previously been shown to exhibit accelerating energy release in simulated earthquake cycles, supporting the Critical Point hypothesis. The 3D models are shown to also display accelerating energy release and good fits of power law time-to-failure functions to the cumulative energy release are obtained.

Pure and Applied Geophysics, 2011

The microstructural state and evolution of fault gouge has important implications for the mechanical behaviour, and hence the seismic slip potential of faults. We use 3D discrete element (DEM) simulations to investigate the fragmentation processes operating in fault gouge during shear. Our granular fault gouge models consist of aggregate grains, each composed of several thousand spherical particles stuck together with breakable elastic bonds. The aggregate grains are confined between two blocks of solid material and sheared under a given normal stress. During shear, the grains can fragment in a somewhat realistic way leading to an evolution of grain size, grain shape and overall texture. The 'breaking up' of the fault gouge is driven by two distinct comminution mechanisms: grain abrasion and grain splitting. The relative importance of the two mechanisms depends on applied normal stress, boundary wall roughness and accumulated shear strain. If normal stress is sufficiently high, grain splitting contributes significantly to comminution, particularly in the initial stages of the simulations. In contrast, grain abrasion is the dominant mechanism operating in simulations carried out at lower normal stress and is also the main fragmentation mechanism during the later stages of all simulations. Rough boundaries promote relatively more grain splitting whereas smooth boundaries favor grain abrasion. Grain splitting (plus accompanying abrasion) appears to be an efficient mechanism for reducing the mean grain size of the gouge debris and leads rapidly to a power law size distribution with an exponent that increases with strain. Grain abrasion (acting alone) is an effective way to generate excess fine grains and leads to a bimodal distribution of grain sizes. We suggest that these two distinct mechanisms would operate at different stages of a fault's history. The resulting distributions in grain size and grain shape may significantly affect frictional strength and stability. Our results therefore have implications for the earthquake potential of seismically active faults with accumulations of gouge. They may also be relevant to the susceptibility of rockslides since non-cohesive basal shear zones will evolve in a similar way and potentially control the dynamics of the slide.

Journal of Geophysical Research, 2009

We model ruptures on faults that weaken in response to flash heating of microscopic asperity contacts (within a rate-and-state framework) and thermal pressurization of pore fluid. These are arguably the primary weakening mechanisms on mature faults at coseismic slip rates, at least prior to large slip accumulation. Ruptures on strongly rate-weakening faults take the form of slip pulses or cracks, depending on the background stress. Self-sustaining slip pulses exist within a narrow range of stresses: below this range, artificially nucleated ruptures arrest; above this range, ruptures are crack-like. Natural earthquakes will occur as slip pulses if faults operate at the minimum stress required for propagation. Using laboratory-based flash heating parameters, propagation is permitted when the ratio of shear to effective normal stress on the fault is 0.2-0.3; this is mildly influenced by reasonable choices of hydrothermal properties. The San Andreas and other major faults are thought to operate at such stress levels. While the overall stress level is quite small, the peak stress at the rupture front is consistent with static friction coefficients of 0.6-0.9. Growing slip pulses have stress drops of $3 MPa; slip and the length of the slip pulse increase linearly with propagation distance at $0.14 and $30 m/km, respectively. These values are consistent with seismic and geologic observations. In contrast, cracks on faults of the same rheology have stress drops exceeding 20 MPa, and slip at the hypocenter increases with distance at $1 m/km.

Geochemistry Geophysics Geosystems, 2021

Seismically active faults pose a major threat to many communities worldwide. Therefore, it is vital to make appropriate predictions on the probability of large earthquakes and their associated effects, such as tsunamis and mass movements. Several factors contribute to the difficulties to estimate seismic hazard in the vicinity of such faults. Besides the vulnerability of structures and the societal impact, geological factors play an important role in seismic hazard assessment and the development of models that describe fault activity (Zöller & Hainzl, 2007). Current models for earthquake recurrence incorporate mathematical models of earthquake statistics (Gutenberg-Richter, Omori-Utsu-Aftershocks, Brownian-First-Passage-Time), numerical models of earthquakes and rupture processes (Rate-and-State-Friction), interseismic stress built-up and the interaction of multiple faults over a larger area via stress transfer (e.g.,

Journal of Geophysical Research, 2000

We investigate the impact of variations in the friction and geometry on models of fault dynamics. We focus primarily on a three-dimensional continuum model with scalar displacements. Slip occurs on an embedded two-dimensional planar interface. Friction is characterized by a two-parameter rate and state law, incorporating a characteristic length for weakening, a characteristic time for healing, and a velocity-weakening steady state. As the friction parameters are varied, there is a crossover from narrow, self-healing slip pulses to crack-like solutions that heal in response to edge effects. For repeated ruptures the crack-like regime exhibits periodic or aperiodic systemwide events. The self-healing regime exhibits dynamical complexity and a broad distribution of rupture areas. The behavior can also change from periodicity or quasi-periodicity to dynamical complexity as the total fault size or the length-to-width ratio is increased. Our results for the continuum model agree qualitatively with analogous results obtained for a one-dimensional Burridõe-Knopoff model in which radiation effects are approximated by viscous dissipation. context of a three-dimensional continuum model and a one-dimensional Burridge-Knopoff model. In our studies, dynamical complexity refers to observations of a

2008

A number of recent studies suggest that dynamic slip on earthquake faults may trigger consistent frictional weakening or lubrication, a feature enhanced at relatively high slip rates (of the order of 1 m/s). Here we present the first clear seismological evidence of a progressive fault weakening under dynamic earthquake slip. The weakening increases with the estimated amount of heat rate (and resulting temperature increase) generated on the fault by frictional heating, indicating the presence of some thermally-activated weakening processes. The observed effect seems stronger for less mature slip systems, suggesting that confinement of heat or fluids is less effective on faults which possess a wider damage zone.

Journal of Geophysical Research, 2005

Field observations of pseudotachylites and experimental studies of high-speed friction indicate that melting on a slipping interface may significantly affect the magnitude of shear stresses resisting slip. We investigate the effects of rock melting on the dynamic friction using theoretical models of shear heating that couple heat transfer, thermodynamics of phase transitions, and fluid mechanics. Results of laboratory experiments conducted at high (order of m/s) slip velocities but low (order of MPa) normal stresses suggest that the onset of frictional melting may give rise to substantial increases in the effective fault strength, presumably due to viscous effects. However, extrapolation of the modeling results to in situ conditions suggests that the efficiency of viscous braking is significantly reduced under high normal and shear stresses. When transient increases in the dynamic fault strength due to fusion are not sufficient to inhibit slip, decreases in the effective melt viscosity due to shear heating and melting of clasts drastically decrease the dynamic friction, resulting in a nearly complete stress drop ("thermal runaway"). The amount of energy dissipation associated with the formation of pseudotachylites is governed by the temperature dependence of melt viscosity and the average clast size in the fault gouge prior to melting. Clasts from a coarse-grained gouge have lower chances of survival in a pseudotachylite due to a higher likelihood of nonequilibrium overheating. The maximum temperature and energy dissipation attainable on the fault surface are ultimately limited by either the rock solidus (via viscous braking, and slip arrest) or liquidus (via thermal runaway and vanishing resistance to sliding). Our modeling results indicate that the thermally activated fault strengthening and rupture arrest are unlikely to occur in most mafic protoliths but might be relevant for quartz-rich rocks, especially at shallow (<5-7 km) depths where the driving shear stress is relatively low.

Journal of Geophysical Research, 2006

1] We investigate the role of frictional heating and thermal pressurization on earthquake ruptures by modeling the spontaneous propagation of a three-dimensional (3-D) crack on a planar fault governed by assigned constitutive laws and allowing the evolution of effective normal stress. We use both slip-weakening and rate-and state-dependent constitutive laws; in this latter case we employ the Linker and Dieterich evolution law for the state variable, and we couple the temporal variations of friction coefficient with those of effective normal stress. In the companion paper we investigate the effects of thermal pressurization on the dynamic traction evolution. We solve the 1-D heat conduction equation coupled with Darcy's law for fluid flow in porous media. We obtain a relation that couples pore fluid pressure to the temperature evolution on the fault plane. We analytically solve the thermal pressurization problem by considering an appropriate heat source for a fault of finite thickness. Our modeling results show that thermal pressurization reduces the temperature increase caused by frictional heating. However, the effect of the slipping zone thickness on temperature changes is stronger than that of thermal pressurization, at least for a constant porosity model. Pore pressure and effective normal stress evolution affect the dynamic propagation of the earthquake rupture producing a shorter breakdown time and larger breakdown stress drop and rupture velocity. The evolution of the state variable in the framework of rate-and state-dependent friction laws is very different when thermal pressurization is active. In this case the evolution of the friction coefficient differs substantially from that inferred from a slip-weakening law. This implies that the traction evolution and the dynamic parameters are strongly affected by thermal pressurization. Citation: Bizzarri, A., and M. Cocco (2006), A thermal pressurization model for the spontaneous dynamic rupture propagation on a three-dimensional fault: 1. Methodological approach,

Journal of Geophysical Research, 2008

Frictional properties of natural kaolinite-bearing gouge samples from the Median Tectonic Line (SW Japan) have been studied using a high-velocity rotary shear apparatus, and deformed samples have been observed with optical and electron (scanning and transmission) microscopy. For a slip velocity of 1 m s À1 and normal stresses from 0.3 to 1.3 MPa, a dramatic slip-weakening behavior was observed. X-ray diffraction analysis of deformed samples and additional high-velocity friction experiments on pure kaolinite indicate kaolinite dehydration during slip. The critical slip-weakening distance D c is of the order of 1 to 10 m. These values are extrapolated to higher normal stresses, assuming that D c is rather a thermal parameter than a parameter related to a true characteristic length. The calculation shows that dimensionally, D c / 1/s n 2 , where s n is the normal stress applied on the fault. The inferred D c values range from a few centimeters at 10 MPa normal stress to a few hundreds of microns at 100 MPa normal stress. Microscopic observations show partial amorphization and dramatic grain size reduction (down to the nanometer scale) localized in a narrow zone of about 1 to 10 mm thickness. Fracture energy G c is calculated from the mechanical curves and compared to surface energy due to grain size reduction, and energies of mineralogic transformations. We show that most of the fracture energy is either converted into heat or radiated energy. The geophysical consequences of thermal dehydration of bonded water during seismic slip are then commented in the light of mineralogical and poromechanical data of several fault zones, which tend to show that this phenomenon has to be taken into account in most of subsurface faults and in hydrous rocks of subducted oceanic crust.

1999

The particle-based lattice solid model developed to study the physics of rocks and the non-linear dynamics of earthquakes is motivated by the molecular dynamics methods and is comparable to the discrete element method. In order to allow large scale simulations to be performed, a high performance must be obtained when implementing the model. This is achieved by re ning the model according to the computer architecture and by developing algorithms that use the full potential of the given parallel super-computer. Particles in the model represents grains of rocks where interactions are computed via a neighbors table updated only when new contacts occur. An adaptative time step increment is implemented to minimize the total compuational time for a simulation. To compute the frictional force between particles, a non-linear system is resolved at each time step using a modi ed Newton algorithm. Except for the computation of the frictional forces, parallelism is obtained by distributing the work load of each loop of the program on the processors. However this involves time consuming communications and on average the program is 90% parallel. To obtain a better speedup, the particle data must be explicitly distributed on the processors where calculations on the di erent subsets of the model are done separately with a minimum of communications (as is the case for the compuation of frictional forces). Once this is done, it is expected that a parallelism of 98% at least in average would be achieved. The continuous re nement of the model and its ongoing adaptation to parallel computers as these evolve will allow large scale 3D simulations to be perfomed.

Journal of Geophysical Research, 2010

1] Despite the importance of hydromechanical effects in fault processes, not much is known about the interplay of chemical and mechanical processes, in part because the conditions are difficult to simulate in the laboratory. We report results from an experimental study of simulated fault gouge composed of rock salt sheared under conditions where pressure solution is known to operate. At sliding velocities above 10 mm/s and high shear strains (>5), friction measurements show that layers of rock salt weaken significantly and ultimately slide unstably (i.e., stick-slip). Microstructural observations show the presence of a zone of comminuted grains along shear zone boundaries, forming boundary-parallel Y shears at high sliding velocities. Samples deformed at low sliding velocities do not show boundary-parallel shear but rather exhibit low porosity passive regions isolated by dilational zones in the Riedel shear orientation. We posit that the significant strain weakening observed at high sliding velocities is caused by severe grain size reduction as shear localization develops, i.e., by frictional wear, ultimately leading to the development of a throughgoing boundary parallel Y shear. Unstable slip is probably related to rupture on this Y shear surface with intermittent healing of the asperities by pressure solution. Furthermore, the data show that the weakening and subsequent unstable slip can be delayed (i.e., occur at higher strains) by lower sliding velocities, larger initial grain sizes, lower normal stresses, and the presence of fluids. This suggests a competition between mechanical wear and chemical processes. Our data highlight the importance of hydrothermal processes in tectonic faulting.

As a result of the comminution that takes place over numerous earthquake cycles, mature faults are characterized by thick layers of pulverized gouge with finite porosity that is saturated with water at seismogenic depths. The heat generated during earthquakes raises the gouge temperature and thermal expansion of the pore fluid, and surrounding solids produce elevated pore pressures that cause fault strength to decrease in the process known as thermal pressurization. Building upon this framework, we describe a model that imposes a plane-strain configuration and shows that the stress variations caused by porothermoelasticity promote the Mohr-Coulomb failure of previously undeformed regions. Except in special cases where the friction is rate strengthening, we find that the frictional strength must vary throughout the post-failure region, which we identify in our model with the shear zone. We introduce a strain rate function that describes the overall influence of distributed slip on energy dissipation and fault strength as the shear zone thickness expands. Using typical fault parameters at 7 km depth, the shear zone reaches several millimeters of thickness after 1 s sliding at an overall rate of 1 m/s. The expansion of the shear zone limits the temperature rise to several hundred degrees Celsius, and the average fault strength falls to about a tenth of the static frictional strength.

Journal of Geophysical Research: Solid Earth, 1999

During earthquake rupture, faults slip at velocities of cm/s to m/s. Fault friction at these velocities strongly influences dynamic rupture but is at present poorly constrained. We study friction of simulated fault gouge as a function of normal stress (•,, = 25 to 70 MPa) and load point velocity (V = 0.001 to 10 mm/s). Layers of granular quartz (3 mm thick) are sheared between rough surfaces in a direct shear apparatus at ambient conditions. For a constant •,,, we impose regular step changes in V throughout 20 mm net slip and monitor the frictional response. A striking observation at high velocity is a dramatic reduction in the instantaneous change in frictional strength for a step change in velocity (friction direct effect) with accumulated slip. Gouge layers dilate for a step increase in velocity, and the amount of dilation decreases with slip and is systematically greater at higher velocity. The steady state friction velocity dependence (a-b) evolves from strengthening to weakening with slip but is not significantly influenced by V or •,,. Measurements of dilation imply that an additional mechanism, such as grain rolling, operates at high velocity and that the active shear zone narrows with slip. Data from slow (gm/s) and fast (mm/s) tests indicate a similar displacement dependent textural evolution and comparable comminution rates. Our experiments produce a distinct shear localization fabric and velocity weakening behavior despite limited net displacements and negligible shear heating. Under these conditions we find no evidence for the strong velocity weakening or low friction values predicted by some theoretical models of dynamic rupture. Thus certain mechanisms for strong frictional weakening, such as grain rolling, can likely be ruled out for the conditions of our study.