Modulation of fault strength during the seismic cycle by grain-size evolution around contact junctions

Earthquake prediction is fundamentally hampered by insufficient knowledge of the constitutive behavior of faults. Laboratory and theoretical work by Dieterich (1978) and Ruina (1983) formed the basis of rate-and-state friction, a constitutive framework that captures the healing and weakening of frictional contacts. The rate-and state law successfully explains the frictional behavior of a wide range of rocks and many phenomena associated with fault slip. The physics underlying the rate-and-state friction law is not fully understood, but it is generally accepted that several micro-mechanisms operate depending on the texture, maturity, fluid content, and other physical and kinematic conditions of the fault. Here, I formulate a constitutive framework that unifies a number of laboratory experiments on silicate rocks, and the gouges derived from these rocks, that describe the effect of grain-size, temperature, real area of contact, gouge thickness, and fault roughness. Fundamental to the model is that fault strength is controlled by the area of the interfacial contact junctions that support the shear and normal loads. The curvature of asperities weakly controls the area of their contact junction and the resulting fault strength. As a result, the dynamics of grain-size evolution around micro-asperities enables the seismic cycle. The model quantitatively explains the correlation between the characteristic weakening distance and the gouge thickness (Marone and Kilgore, 1993), the correlation of the static friction coefficient with the rate-dependence parameters (Ikari et al., 2011), the dependence of frictional resistance to sub-solidus temperatures (Chester, 1994), and predicts a range of grain sizes that is compatible with observations at exposed fault zones. However, the dynamics of grain-size evolution is still challenging to verify experimentally. The model features a regularization at vanishing slip speeds that implies distinct dynamics at low strength. For friction coefficients lower than 0.1, seismic cycle simulations predict the emergence of frictional instabilities with complex source time-functions. This is a significant departure from the predictions of rate-and-state friction that is most relevant to the dynamics of decollements, serpentinized shear zones, and other low-strength faults.