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| rate-and-state friction | |
|---|---|
| Name | Rate-and-state friction |
| Field | Fracture mechanics, Seismology, Geophysics |
| Introduced | 1970s |
| Key people | Keiiti Aki; James R. Rice; Alan B. Scholz; John R. Rice; Tom A. N. V. Dieterich; Christopher H. Scholz |
rate-and-state friction is a phenomenological framework used to describe how frictional resistance on fault surfaces depends on sliding velocity and the history (state) of contact. It synthesizes laboratory experiments, theoretical mechanics, and observational constraints to model time- and velocity-dependent shear strength on fractures and faults. The formulation has been influential in earthquake source physics, rock mechanics, and numerical simulations of fault slip.
Rate-and-state friction emerged from efforts in the 1970s and 1980s to reconcile laboratory results on rock friction with field observations of earthquake recurrence and slow slip. Key contributors include Tom A. N. V. Dieterich, James R. Rice, Alan B. Scholz, and Keiiti Aki, whose work linked microscale contact processes to macroscale fault behavior. The framework seeks to capture phenomena such as velocity-weakening and velocity-strengthening behavior, transient healing, preseismic slip, and seismic nucleation observed in experiments by groups at institutions like U.S. Geological Survey, California Institute of Technology, and Massachusetts Institute of Technology.
Rate-and-state friction expresses shear stress as a function of slip rate and one or more internal state variables. The canonical formulation couples a constitutive equation for friction coefficient to a state evolution law; foundational theoretical treatments were advanced by John R. Rice and Tom A. N. V. Dieterich and later elaborated by Christopher H. Scholz. These equations are embedded in continuum mechanics frameworks used by researchers at Scripps Institution of Oceanography and Woods Hole Oceanographic Institution to link fault strength to elastic loading from crustal deformation measured by agencies such as United States Geological Survey and observatories like Parkfield Observatory.
Typical friction laws take the form μ = μ0 + a ln(V/V0) + b ln(θV0/Dc), with state variable θ and characteristic slip distance Dc; this formulation was popularized by studies at Brown University and Stanford University. Variants include the ageing (Dieterich) law and the slip (Ruina) law, developed in work involving Harvard University and University of California, Berkeley laboratories. The parameters a and b control instantaneous velocity dependence and evolution toward steady state; experiments at Los Alamos National Laboratory and Lawrence Berkeley National Laboratory constrained ranges used in models of earthquake cycles applied by groups at Seismological Society of America and European Geosciences Union.
Laboratory studies using biaxial and rotary shear apparatuses at Geological Survey of Japan, ETH Zurich, and Institut de Physique du Globe de Paris revealed direct effects, transient healing, and scale dependence of Dc. Observations at Lamont–Doherty Earth Observatory and Geophysical Institute, University of Alaska Fairbanks showed temperature, humidity, and gouge mineralogy influence parameters—a focus of collaborations with National Aeronautics and Space Administration and National Science Foundation-funded programs. High-pressure, high-temperature experiments conducted by teams at Imperial College London and University of Tokyo connected frictional behavior to metamorphic reactions studied in conjunction with Royal Society grants and international workshops like those organized by International Association of Seismology and Physics of the Earth’s Interior.
Rate-and-state laws underpin models of earthquake nucleation, afterslip, slow slip events, and earthquake sequences simulated for regions including Parkfield, California, the San Andreas Fault, and the Japan Trench. They inform seismic hazard assessments performed by institutions such as United States Geological Survey and regional agencies, and are integrated into inversion studies using data from networks like Incorporated Research Institutions for Seismology and observatories including Japan Meteorological Agency. The framework has been applied to induced seismicity studies tied to operations by companies like Chevron Corporation and policy considerations debated in forums hosted by European Commission and United Nations scientific panels.
Numerical implementations embed rate-and-state constitutive laws in finite-element and boundary-element codes developed at Los Alamos National Laboratory, California Institute of Technology, and ETH Zurich. Codes such as those used in community platforms supported by Geoscience Australia and research groups at University of California, Santa Barbara handle stiffness-dependent nucleation, rupture propagation, and dynamic weakening mechanisms. Computational challenges addressed by teams at National Superconducting Cyclotron Laboratory and Argonne National Laboratory include stiffness of the ODE system, spatial heterogeneity, and coupling to viscoelastic earth models used in seismic cycle simulations by Purdue University and University of Oxford.
Limitations include uncertain scaling of Dc from laboratory to crustal scales, parameter trade-offs identified in studies at German Research Centre for Geosciences (GFZ) and Seismological Laboratory, Caltech, and gaps linking microscale physics to macroscopic laws—a topic of work at Max Planck Institute for Geosciences and Planetary Science Institute. Extensions incorporate thermal pressurization, pore-fluid effects, and damage rheologies pursued by teams at Columbia University and University of Leeds. Alternative frictional descriptions include empirical slip-weakening laws used by United States Navy sponsored projects, rate-dependent plasticity models from Massachusetts Institute of Technology mechanics groups, and micromechanical approaches developed at Czech Academy of Sciences.