skip to main content

Title: Constitutive Behavior of Rocks During the Seismic Cycle

Establishing a constitutive law for fault friction is a crucial objective of earthquake science. However, the complex frictional behavior of natural and synthetic gouges in laboratory experiments eludes explanations. Here, we present a constitutive framework that elucidates the rate, state, and temperature dependence of fault friction under the relevant sliding velocities and temperatures of the brittle lithosphere during seismic cycles. The competition between healing mechanisms, such as viscoelastic collapse, pressure‐solution creep, and crack sealing, explains the low‐temperature stability transition from steady‐state velocity‐strengthening to velocity‐weakening as a function of slip‐rate and temperature. In addition, capturing the transition from cataclastic flow to semi‐brittle creep accounts for the stabilization of fault slip at elevated temperatures. We calibrate the model using extensive laboratory data on synthetic albite and granite gouge, and on natural samples from the Alpine Fault and the Mugi Mélange in the Shimanto accretionary complex in Japan. The constitutive model consistently explains the evolving frictional response of fault gouge from room temperature to 600°C for sliding velocities ranging from nanometers to millimeters per second. The frictional response of faults can be uniquely determined by the in situ lithology and the prevailing hydrothermal conditions.

more » « less
Author(s) / Creator(s):
Publisher / Repository:
DOI PREFIX: 10.1029
Date Published:
Journal Name:
AGU Advances
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    The empirical constitutive modeling framework of rate‐ and state‐dependent friction (RSF) is commonly used to describe the time‐dependent frictional response of fault gouge to perturbations from steady sliding. In a previous study (Ferdowsi & Rubin, 2020), we found that a granular‐physics‐based model of a fault shear zone, with time‐independent properties at the contact scale, reproduces the phenomenology of laboratory rock and gouge friction experiments in velocity‐step and slide‐hold (SH) protocols. A few slide‐hold‐slide (SHS) simulations further suggested that the granular model might outperform current empirical RSF laws in describing laboratory data. Here, we explore the behavior of the same Discrete Element Method (DEM) model in SH and SHS protocols over a wide range of sliding velocities, hold durations, and system stiffnesses, and provide additional support for this view. We find that, similar to laboratory data, the rate of stress decay during SH simulations is in general agreement with the “Slip law” version of the RSF equations, using parameter values determined independently from velocity step tests. During reslides following long hold times, the model, similar to lab data, produces a nearly constant rate of frictional healing with log hold time, with that rate being in the range of ∼0.5 to 1 times the RSF “state evolution” parameterb. We also find that, as in laboratory experiments, the granular layer undergoes log‐time compaction during holds. This is consistent with the traditional understanding of state evolution under the Aging law, even though the associated stress decay is similar to that predicted by the Slip and not the Aging law.

    more » « less
  2. Abstract

    The constitutive behavior of faults is central to many interconnected aspects of earthquake science, from fault dynamics to induced seismicity, to seismic hazards characterization. Yet, a friction law applicable to the range of temperatures found in the brittle crust and upper mantle is still missing. In particular, rocks often exhibit a transition from steady‐state velocity‐strengthening at room temperature to velocity‐weakening in warmer conditions that is poorly understood. Here, we investigate the effect of competing healing mechanisms on the evolution of frictional resistance in a physical model of rate‐, state‐, and temperature‐dependent friction. The yield strength for fault slip depends on the real area of contact, which is modulated by the competition between the growth and erosion of interfacial micro‐asperities. Incorporating multiple healing mechanisms and rock‐forming minerals with different thermodynamic properties allows a transition of the velocity‐ and temperature‐dependence of friction at steady‐state with varying temperatures. We explain the mechanical data for granite, pyroxene, amphibole, shale, and natural fault gouges with activation energies and stress power exponent for weakening of 10–50 kJ/mol and 55–150, respectively, compatible with subcritical crack growth and inter‐granular flow in the active slip zone. Activation energies for the time‐dependent healing process in the range 90–130 kJ/mol in dry conditions and 20–65 kJ/mol in wet conditions indicate the prominence of viscoelastic collapse of microasperities in the absence of water and of pressure‐solution creep, crack healing, and cementation when assisted by pore fluids.

    more » « less
  3. Abstract

    Rate‐ and state‐friction (RSF) is an empirical framework that describes the complex velocity‐, time‐, and slip‐dependent phenomena observed during frictional sliding of rocks and gouge in the laboratory. Despite its widespread use in earthquake nucleation and recurrence models, our understanding of RSF, particularly its time‐ and/or slip‐dependence, is still largely empirical, limiting our confidence in extrapolating laboratory behavior to the seismogenic zone. While many microphysical models have been proposed over the past few decades, none have explicitly incorporated the effects of strain hardening, anelasticity, or transient elastoplastic rheology. Here we present a new model of rock friction that incorporates these phenomena directly from the microphysical behavior of lattice dislocations. This model of rock friction exhibits the same logarithmic dependence on sliding velocity (strain rate) as RSF and displays a dependence on the internal backstress caused by long‐range interactions among geometrically necessary dislocations (GNDs). Changes in the backstress (internal stress) evolve exponentially with plastic strain of asperities and are dependent on both the current backstress and previous deformation, which give rise to phenomena consistent with interpretations of the “critical slip distance,” “memory effect,” and “evolution effect” of RSF. The rate dependence of friction in this model is primarily controlled by the evolution of backstress and temperature. We provide several analytical predictions for RSF‐like behavior and the “brittle‐ductile” transition based on microphysical mechanisms and measurable parameters such as the GND density and strain‐dependent hardening modulus.

    more » « less
  4. Abstract

    Localized frictional sliding on faults in the continental crust transitions at depth to distributed deformation in viscous shear zones. This brittle‐ductile transition (BDT), and/or the transition from velocity‐weakening (VW) to velocity‐strengthening (VS) friction, are controlled by the lithospheric thermal structure and composition. Here, we investigate these transitions, and their effect on the depth extent of earthquakes, using 2D antiplane shear simulations of a strike‐slip fault with rate‐and‐state friction. The off‐fault material is viscoelastic, with temperature‐dependent dislocation creep. We solve the heat equation for temperature, accounting for frictional and viscous shear heating that creates a thermal anomaly relative to the ambient geotherm which reduces viscosity and facilitates viscous flow. We explore several geotherms and effective normal stress distributions (by changing pore pressure), quantifying the thermal anomaly, seismic and aseismic slip, and the transition from frictional sliding to viscous flow. The thermal anomaly can reach several hundred degrees below the seismogenic zone in models with hydrostatic pressure but is smaller for higher pressure (and these high‐pressure models are most consistent with San Andreas Fault heat flow constraints). Shear heating raises the BDT, sometimes to where it limits rupture depth rather than the frictional VW‐to‐VS transition. Our thermomechanical modeling framework can be used to evaluate lithospheric rheology and thermal models through predictions of earthquake ruptures, postseismic and interseismic crustal deformation, heat flow, and the geological structures that reflect the complex deformation beneath faults.

    more » « less
  5. Abstract

    Rate‐ and state‐dependent friction (RSF) equations are commonly used to describe the time‐dependent frictional response of fault gouge to perturbations in sliding velocity. Among the better‐known versions are the Aging and Slip laws for the evolution of state. Although the Slip law is more successful, neither can predict all the robust features of lab data. RSF laws are also empirical, and their micromechanical origin is a matter of much debate. Here we use a granular physics‐based model to explore the extent to which RSF behavior, as observed in rock and gouge friction experiments, can be explained by the response of a granular gouge layer with time‐independent properties at the contact scale. We examine slip histories for which abundant lab data are available and find that the granular model (1) mimics the Slip law for those loading protocols where the Slip law accurately models laboratory data (velocity‐step and slide‐hold tests) and (2) deviates from the Slip law under conditions where the Slip law fails to match laboratory data (the reslide portions of slide‐hold‐slide tests), in the proper sense to better match those data. The simulations also indicate that state is sometimes decoupled from porosity in a way that is inconsistent with traditional interpretations of “state” in RSF. Finally, if the “granular temperature” of the gouge is suitably normalized by the confining pressure, it produces an estimate of the direct velocity effect (the RSF parametera) that is consistent with our simulations and in the ballpark of lab  data.

    more » « less