Rate and State Friction as a Spatially Regularized Transient Viscous Flow Law

The theory of rate and state friction unifies field, laboratory, and theoretical analysis of the evolution of slip on natural faults. While the observational study of earthquakes and aseismic fault slip is hampered by its strong multi-scale character in space and time, numerical simulations are well-positioned to link the laboratory study of grain-scale processes to the scale at which rock masses move. However, challenges remain in accurately representing the complex and permanently evolving sub-surface fault networks that exist in nature. Additionally, the common representation of faults as interfaces may miss important physical aspects governing volumetric fault system behavior. In response, we propose a transient viscous rheology that produces shear bands that closely mimic the rate- and state-dependent sliding behavior of equivalent fault interfaces. Critically, we show that the expected tendency of the continuum rheology for runaway localization and mesh dependence can be halted by including an artificial diffusion-type regularization of anelastic strain rate in the softening law. We demonstrate analytically and numerically using a simplified fault transect that important aspects of the frictional behavior are not significantly affected by the introduced regularization. Any discrepancies with respect to the interfacial description of fault behavior are critically evaluated using one dimensional numerical velocity stepping and spring-slider experiments. Since no new physical parameters are introduced, our model may be straightforwardly used to extend the existing modeling techniques. The model predicts the emergence of complex patterns of shear localization and delocalization that may inform the interpretation of complex damage distributions observed around faults in nature.ISSN:2169-9313ISSN:0148-0227ISSN:2169-935