A Physics‐Based Rock Friction Constitutive Law: Steady State Friction

Aharonov, Einat; Scholz, Christopher H.

Experiments measuring friction over a wide range of sliding velocities find that the value of the friction coefficient varies widely: friction is high and behaves according to the rate and state constitutive law during slow sliding, yet markedly weakens as the sliding velocity approaches seismic slip speeds. We introduce a physics‐based theory to explain this behavior. Using conventional microphysics of creep, we calculate the velocity and temperature dependence of contact stresses during sliding, including the thermal effects of shear heating. Contacts are assumed to reach a coupled thermal and mechanical steady state, and friction is calculated for steady sliding. Results from theory provide good quantitative agreement with reported experimental results for quartz and granite friction over 11 orders of magnitude in velocity. The new model elucidates the physics of friction and predicts the connection between friction laws to independently determined material parameters. It predicts four frictional regimes as function of slip rate: at slow velocity friction is either velocity strengthening or weakening, depending on material parameters, and follows the rate and state friction law. Differences between surface and volume activation energies are the main control on velocity dependence. At intermediate velocity, for some material parameters, a distinct velocity strengthening regime emerges. At fast sliding, shear heating produces thermal softening of friction. At the fastest sliding, melting causes further weakening. This theory, with its four frictional regimes, fits well previously published experimental results under low temperature and normal stress.


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Journal of Geophysical Research: Solid Earth