The evolution of rock friction is more sensitive to slip than elapsed time, even at near-zero slip rates

Abstract

Nearly all frictional interfaces strengthen as the logarithm of time when sliding at ultra-low 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 . μ m · s − 1 . to less than 10 − 5 μ m · s − 1 , 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.

A Rate‐, State‐, and Temperature‐Dependent Friction Law With Competing Healing Mechanisms

“…where the parameters play a similar role as in Equation 5. The aging and slip laws for a single healing mechanism in isothermal conditions exhibit various advantages and drawbacks to explain velocity-step experimental data (e.g., Beeler et al, 1994;Bhattacharya et al, 2017Bhattacharya et al, , 2022) so we consider them as possible end-member formulations. In Equation 4, the direct effect of temperature is opposite to the direct effect of velocity, leading to an instantaneous reduction in frictional resistance for a finite increase in temperature (Blanpied et al, 1995(Blanpied et al, , 1998Chester, 1994Chester, , 1995Chester & Higgs, 1992).…”

“…Multiple healing mechanisms can also be described with an evolution law that falls within the slip law end‐member, as follows $$$\frac{\dot{d}}{d}=\frac{\lambda V}{2h}\ln \left\{\frac{2h}{\lambda V}\sum\limits _{k=1}^{N}\frac{{G}_{k}}{{p}_{k}{d}^{{p}_{k}}}\mathrm{exp}\left[-\frac{{H}_{k}}{R}\left(\frac{1}{T}-\frac{1}{{T}_{k}}\right)\right]\right\}\hspace*{.5em}$$$ where the parameters play a similar role as in Equation 5. The aging and slip laws for a single healing mechanism in isothermal conditions exhibit various advantages and drawbacks to explain velocity‐step experimental data (e.g., Beeler et al., 1994; Bhattacharya et al., 2017, 2022) so we consider them as possible end‐member formulations. In Equation 4, the direct effect of temperature is opposite to the direct effect of velocity, leading to an instantaneous reduction in frictional resistance for a finite increase in temperature (Blanpied et al., 1995, 1998; Chester, 1994, 1995; Chester & Higgs, 1992).…”

Rate and State Simulation of Two Experiments With Pore Fluid Injection Under Creep Conditions

“…Recent experiments Bhattacharya et al. (2022) have indicated that the slip law describes data better than the aging law even at very low sliding velocities (3μm/s to less than 10 −5 μm/s). Nevertheless, I have used the aging law.…”

A Spectral Boundary‐Integral Method for Faults and Fractures in a Poroelastic Solid: Simulations of a Rate‐and‐State Fault With Dilatancy, Compaction, and Fluid Injection

“…However, the initial rupture may be well explained by linear slip weakening, provided its parameters are chosen to account for pre-slip healing (which changes the effective slip-weakening behavior, e.g., the peak friction), and those methods would work well to understand, for example, how far the rupture propagates. Note, however, that there are alternative formulations of rate-and-state friction, with different state-variable evolution laws such as the slip law (Ruina, 1983) as well as various composite laws, and the formulation that best describes various laboratory experiments is a topic of ongoing research (Bhattacharya et al, 2015(Bhattacharya et al, , 2022. The slip law, in particular, results in non-linear effective slip weakening of friction at the rupture tip (e.g., Ampuero & Rubin, 2008).…”