Experimentally Observed Strength Evolution in Rate and State Friction is Much Better Fit With a Slip Formulation Than an Aging Formulation

Pathikrit Bhattacharya, Allan M. Rubin, Terry E. Tullis, N. M. Beeler, & Keishi Okazaki

Submitted September 11, 2022, SCEC Contribution #12419, 2022 SCEC Annual Meeting Poster #158

Nearly all frictional interfaces strengthen as the logarithm of time when sliding at ultralow speeds. Observations of also logarithmic-in-time growth of interfacial contact area under such conditions have led to constitutive models that assume that this frictional strengthening results from purely time-dependent, and slip-insensitive, contact-area growth. The main laboratory support for such strengthening has traditionally been derived from increases in friction during “load-point hold” experiments, wherein a sliding interface is allowed to gradually self-relax down to subnanometric slip rates. In contrast, following step decreases in the shear loading rate, friction is widely reported to increase over a characteristic slip scale, independent of the magnitude of the slip-rate decrease—a signature of
slip-dependent strengthening. To investigate this apparent contradiction, we subjected granite samples to a series of step decreases in shear rate of up to 3.5 orders of magnitude and load-point holds of up to 10,000 s, such that both protocols accessed the phenomenological regime traditionally inferred to demonstrate time-dependent frictional strengthening. When modeling the resultant data, which probe interfacial slip rates ranging from 3 μm/s to less than 10 -5 μm/s, we found that constitutive models where low slip-rate friction evolution mimics log-time contact area growth require parameters that differ by orders of magnitude across the different experiments. In contrast, an alternative constitutive model, in which friction evolves only with interfacial slip, fits most of the data well with
nearly identical parameters. This leads to the surprising conclusion that frictional strengthening is dominantly slip-dependent, even at subnanometric slip rates. This suggests that instead of using the commonly used Aging formulation to describe frictional evolution in earthquake cycle simulations, the more computationally expensive Slip formulation should be used, even in the inter-seismic portion of the cycle. Of course, this argument for using the Slip formulation in earthquake simulations assumes that additional mechanisms, which are purely time dependent, are not dominantly operative on fault surfaces in the Earth just as they are not in our room temperature experiments on granite.

Key Words
fault friction, interseismic healing, earthquake cycle

Citation
Bhattacharya, P., Rubin, A. M., Tullis, T. E., Beeler, N. M., & Okazaki, K. (2022, 09). Experimentally Observed Strength Evolution in Rate and State Friction is Much Better Fit With a Slip Formulation Than an Aging Formulation. Poster Presentation at 2022 SCEC Annual Meeting.

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