A Comparison between Classical, Power-Law Rate-and-State Friction, and CNS Models Based on Numerical Simulations of Seismic Cycles

The insufficient knowledge of frictional sliding fundamentally hampers us to understand earthquake dynamics and predict seismic hazards. To uncover the underlying physics of fault instability and extrapolate the observations in nature and experiments, Dieterich (1978) and Ruina (1983) proposed the classical rate-and-state friction (RSF) laws based on laboratory observations, Barbot (2019) suggested a power-law RSF law based on the grain-size evolution around contact junctions, and Chen et al. (2016) developed a CNS (Chen-Niemeijer-Spiers) model governed by rate-strengthening intergranular sliding and contact creep by pressure solution. The CNS model incorporates a more detailed description of microphysical process and, as a result, requires specification of more parameters. All three models are rate-dependent and incorporate a single internal variable and they have successfully captured the healing and frictional behaviors for various rock types. We use a spring-slider model to simulate a wide range of fault slip behaviors ranging from stable sliding, attenuated oscillations, self-sustained oscillations, to periodic stick slips, particularly emphasizing the evolution of frictional properties, shear stress, and slip velocity in different seismic cycles. Subsequently, we analyze the numerical results for the three models and evaluate them with the published experimental data. Through this numerical and theoretical work, we make a direct comparison between simulations exhibiting the classical and power-law RSF-controlled fault slip behaviors, and simulations dictated by the CNS model. Our results indicate that three models behave similarly in stable sliding and attenuated oscillations when friction parameters and stress conditions are the same. However, some noticeable differences (e.g., slip velocity, stress drop, recurrence interval) are observed for self-sustaining oscillations and periodic stick slips. Compared with the other two models, the CNS model may exhibit a more stable fault slip behavior. The comparison of numerical simulations in three models may provide an alternative and valuable way to simulate the fault frictional sliding and contribute to a better understanding of natural and induced seismicity.