Dynamic weakening is limited by granular dynamics

Earthquakes are the result of the frictional instability of faults containing fine rock powders called gouge derived from attrition in past fault motions. Understanding the frictional instability of granular matter in terms of constitutive laws is thus important. Because of the importance of granular matter for industries and engineering, the friction of granular matter has been studied in the field of solid earth science and other fields, such as statistical physics. In solid earth science, the rate- and state-dependent friction law was established by laboratory experiments at a very low sliding velocity (μm/s to mm/s). Recent experiments conducted at sub-seismic to seismic sliding velocities (mm/s to m/s), however, show that frictional properties are much richer than those predicted by the rate- and state-dependent friction law. One of the most important findings in such experiments is the remarkable weakening due to mechano-chemical effects by frictional heating [Tullis, 2007]. In statistical physics, another empirical law holds for much faster deformation than the former, showing positive shear-rate dependence. Until Recently, friction of granular matter has been investigated independently in the fields of solid earth science and statistical physics, and thus the relation between these distinct constitutive laws is not clear. Recently, some experimental studies have been reported to connect the achievements in these two fields. For example, a laboratory experiment on dry glass beads under very low normal stress (0.02 to 0.05 MPa) in which the frictional heat is negligible reveals the transition from velocity-weakening friction at low sliding velocities to velocity-strengthening friction at high sliding velocities [Kuwano et al., 2011]. Importantly, the velocity-strengthening nature at high sliding velocities is quantitatively the same as those observed in simulations. The inelastic deformation of the grains therefore plays a vital role at high sliding velocities. In this study, we report a friction experiment under higher pressure (0.1 to 0.9 MPa), in which the frictional heat is significant. To clarify the effect of frictional heat in high-speed friction systematically, we investigated both the pressure and the velocity dependence of the friction coefficient over a wide range of sliding velocities ranging from aseismic to seismic slip velocities. We observed considerable weakening, described well by a flash-heating theory, above the sliding velocity of 1 cm/s regardless of pressure. At higher velocities, the velocity strengthening behavior replaced the velocity weakening behavior. This strengthening at higher velocities agrees with data from numerical simulations on sheared granular matter and is therefore described in terms of energy dissipation due to the inelastic deformation of grains. We propose a unified steady-state friction law that well describes the velocity and pressure dependence of the steady-state friction coefficient.