David Place

Simulation of the frictional stick-slip instability

A lattice solid model capable of simulating rock friction, fracture and the associated seismic wave radiation is developed in order to study the origin of the stick-slip instability that is responsible for earthquakes. The model consists of a lattice of interacting particles. In order to study the effect of surface roughness on the frictional behavior of elastic blocks being rubbed past one another, the simplest possible particle interactions were specified corresponding to radially dependent elastic-brittle bonds. The model material can therefore be considered as round elastic grains with negligible friction between their surfaces. Although breaking of the bonds can occur, fracturing energy is not considered. Stick-slip behavior is observed in a numerical experiment involving 2D blocks with rough surfaces being rubbed past one another at a constant rate. Slip is initiated when two interlocking asperities push past one another exciting a slip pulse. The pulse fronts propagate with speeds ranging from the Rayleigh wave speed up to a value between the shear and compressional wave speeds in agreement with field observations and theoretical analyses of mode-II rupture. Slip rates are comparable to seismic rates in the initial part of one slip pulse whose front propagates at the Rayleigh wave speed. However, the slip rate is an order of magnitude higher in the main part of pulses, possibly because of the simplified model description that neglected intrinsic friction and the high rates at which the blocks were driven, or alternatively, uncertainty in slip rates obtained through the inversion of seismograms. Particle trajectories during slip have motions normal to the fault, indicating that the fault surfaces jump apart during the passage of the slip pulse. Normal motion is expected as the asperities on the two surfaces ride over one another. The form of the particle trajectories is similar to those observed in stick-slip experiments involving foam rubber blocks (Bruneet al., 1993). Additional work is required to determine whether the slip pulses relate to the interface waves proposed by Brune and co-workers to explain the heat-flow paradox and whether they are capable of inducing a significant local reduction in the normal stress. It is hoped that the progressive development of the lattice solid model will lead to realistic simulations of earthquake dynamics and ultimately, provide clues as to whether or not earthquakes are predictable.

Numerical simulation of earthquake faults with gouge: Toward a comprehensive explanation for the heat flow paradox

The particle-based lattice solid model is used to simulate transform faults with and without fault gouge. Stick-slip frictional behavior is observed in two-dimensional numerical experiments of model faults both with and without gouge. When no gouge is present, the fault is strong, and the heat generation and stress drops are correspondingly high, in disaccord with observations surrounding the heat flow paradox. In contrast, when a gouge is specified, the fault is weak, and the heat generation as well as stress drops are low, in quantitative agreement with observational constraints. The heat flow is low on average and during short periods of aseismic creep. Seismic efficiencies are compatible with observationally based bounds. Counter intuitively, the fault strength decreases as the intrinsic friction between particles is increased beyond a given threshold. The mechanism for low fault strength and heat is rolling and jostling of fault gouge grains during slip. This allows macroscopic movement of the fault with only minimal slip between surfaces of the gouge grains. As this dynamical mechanism operates during seismic and aseismic slip, it provides an explanation for the lack of a heat flow anomaly in both the seismic and creeping parts of the San Andreas fault. The simulation results provide the first comprehensive and quantitative possible explanation of the heat flow paradox and suggest that fault gouge plays a fundamental role on the dynamics of earthquake faults. Whether rolling and jostling of fault gouge particles provides the explanation for the heat flow paradox in nature remains to be validated by observation evidence.

A LATTICE SOLID MODEL FOR THE NONLINEAR DYNAMICS OF EARTHQUAKES

A lattice solid model is presented that is capable of simulating the nonlinear dynamical processes (friction and fracture) associated with earthquakes. It is based on molecular dynamics principles to model interacting particles by numerically solving their equations of motion. Particles represent indivisible units of the system such as grains and interactions are described through effective potential functions. In this initial work, particles interact through radial pairwise potentials and the solid is made of particles arranged in a two–dimensional triangular lattice which corresponds to an isotropic elastic medium in the macroscopic limit. Simple and tractable potentials are specified to model brittle and ductile material. Numerical experiments of flawed brittle and ductile blocks subjected to uni–axial compression yield mode II fracturing behavior and characteristic stress–strain curves. In another experiment involving brittle blocks with rough surfaces being dragged past one another, stick–slip frictional behavior is observed. These results suggest that earthquakes can be simulated using the particle based modeling approaches even when the particles and their interactions are highly simplified.

The weakness of earthquake faults

Numerical experiments using: the particle based lattice solid model produce simulated earthquakes. Model faults with a thin gouge layer are sufficiently weak relative to those without gouge to explain the heat flow paradox (HFP). Stress drop statistics are in agreement with field estimates. Models with a thick granular fault zone exhibit a strong evolution effect. Results are initially similar to those of laboratory experiments but after a sufficient time, the system self-organizes into a weak state. The long time :required for self-organization could explain why weak gouge has not been observed in the laboratory. The new results suggest an HFP explanation without the so called fatal flaws of previously proposed solutions. They demonstrate that fault friction potentially undergoes a strong evolution effect and could be dependent on gouge microstructure. This raises questions about the extent to which laboratory derived friction laws can be used in macroscopic domain earthquake simulation studies.

Parallel simulation system for earthquake generation: fault analysis modules and parallel coupling analysis

Solid earth simulations have recently been developed to address issues such as natural disasters, global environmental destruction and the conservation of natural resources. The simulation of solid earth phenomena involves the analysis of complex structures including strata, faults, and heterogeneous material properties. Simulation of the generation and cycle of earthquakes is particularly important, but such simulations require the analysis of complex fault dynamics. GeoFEM is a parallel finite‐element analysis system intended for solid earth field phenomena problems. This paper describes recent development in the GeoFEM project for the simulation of earthquake generation and cycles. Copyright

Extension of the Lattice Solid Model to Incorporate Temperature Related Effects

Abstract—The elastic and frictional properties of solids are temperature-dependent. Thus, heat has without doubt a major influence on the dynamics of earthquakes, particularly considering the high temperatures generated during large slip events. In order to provide a foundation for the study of these heat related effects, the Lattice Solid Model for the study of earthquake dynamics is extended to incorporate the generation and transfer of heat. The thermal and elastic properties of 2- and 3-D lattice solids in the macroscopic limit are derived. To verify the numerical implementation of heat transfer, a simulation has been performed in a simple case and the results compared to a known analytical solution for the same problem. Thermal expansion and a simple approximation of a temperature-dependent pore fluid pressure are implemented in the 2-D Lattice Solid Model. Simulations confirm that these effects influence the dynamics of the slip of a fault with fault gouge. Whereas thermal expansion only minor influences the dynamics of fault rupture, the influence of the increase in the pore fluid pressure generated by slip heating is more significant. The simulations show that the temperatures generated during slip events accord with those expected for real earthquakes as inferred from geologic evidence.

Numerical Simulation of Localisation Phenomena in a Fault Zone

A lattice solid model was developed to study the physics of rocks and the nonlinear dynamics of earthquakes and is applied here to the study of fault zone evolution. The numerical experiments involve shearing a transform fault model initialised with a weak and heterogeneous fault zone. During the experiments, a fault gouge layer forms with features that are similar to those observed in recent laboratory experiments involving simulated fault gouge (Beeler et al., 1996). This includes formation of Reidel (R 1) shears and localisation of shear into bands. During the numerical experiments, as in the laboratory experiments, decreases of the gouge layer strength correlate with decreases in gouge layer thickness. After a large displacement, a re-organisation of the model fault gouge is observed with slip becoming highly localised in a very narrow basal shear zone. This zone is such that it enhances the rolling-type micro-physical mechanism that was responsible for the low heat and fault strength observed in previous numerical experiments (Mora and Place, 1998, 1999) and proposed as an explanation of the heat flow paradox (HFP). The long time required for the self-organisation process is a possible reason why the weak gouge layers predicted by the numerical experiments, and which could explain the HFP, have not yet been observed in the laboratory. The energy balance of a typical rupture event is studied. The seismic efficiency of ruptures of the gouge layer is found to be low (approximately 4%), substantially lower than previous estimates and compatible with typical field-based estimates.