Bayesian Inversion of Rate-and-State Parameters from Frictional Sliding Experiments on Quartz Gouge

Taeho Kim, Nadia Lapusta, Daniel Faulkner, & John Bedford

Published September 8, 2024, SCEC Contribution #13869, 2024 SCEC Annual Meeting Poster #141

Despite the ubiquity of fine granular gouge in fault cores, small grain sizes are often avoided in experiments due to their propensity for unstable frictional sliding and the corresponding difficulty to infer their friction properties. In this study, we develop a Bayesian inversion framework based on a spring-slider model of the experiment to infer rate-and-state friction properties for both stable and unstable (stick-slip) responses of fine-grained quartz gouge. The gouge shows a complex history of deformation, such as the development of unstable events with the accumulation of slip and long-term changes in the average friction coefficient. The inversion framework is first applied to a stable velocity step data and infers friction parameters with superior precision to conventional methods based on non-linear least squares. Applying the inversion framework to stick-slip data shows that the evolution of friction parameters from stable sliding to stick-slip is more consistent with the physical interpretations of the parameters for the slip law than for the aging law. Testing the same gouge material under the same effective normal stress but different pore pressure additionally shows that the presence of pressurized pore fluids significantly changes the frictional stability of the gouge. The best fitting spring-slider model of the experimental stick-slip events shows a lower tendency to stick during the arrest phase and to creep during the nucleation phase than observed. Furthermore, the spring-slider models have a stronger dependence of the stress drop on the loading rate than the experiment. We additionally develop a quasi-static finite-element model which suggests that slip during the loading and nucleation phases is uniform in space and that the discrepancy between the experiments and spring-slider models is not obviously due to finite-fault effects. Furthermore our modeled maximum slip rates during stick-slip suggest that slip is minimally affected by dynamic weakening mechanisms such as flash heating. Hence the discrepancy implies that the rate-and-state formulation needs to be adjusted, either by a new state-evolution law or by varying rate-and-state parameters over the earthquake cycle, i.e., making them dependent on slip rate. The developed inversion framework allows quantitative analysis of unstable material in the laboratory, opening new doors for further validation of constitutive relationships for friction beyond the stable regime of sliding.

Key Words
Frictional stability of granular gouge, Bayesian inversion, rate-and-state friction

Citation
Kim, T., Lapusta, N., Faulkner, D., & Bedford, J. (2024, 09). Bayesian Inversion of Rate-and-State Parameters from Frictional Sliding Experiments on Quartz Gouge. Poster Presentation at 2024 SCEC Annual Meeting.

Related Projects & Working Groups
Fault and Rupture Mechanics (FARM)