A Physics‐Based Rock Friction Constitutive Law: Steady State Friction. Issue 2 (17th February 2018) - Aharonov, Einat; Scholz, Christopher H.
Abstract: 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. Plain Language Summary: Experiments measuring friction over a wide range of sliding velocities find that the value of the friction coefficient varies widely: friction is high during slow sliding, yet markedly weakens as the sliding velocity rises to seismic slip rates. We introduce a physics‐based theory to explain this behavior. Our model assumes friction is controlled by creep at contacts that form between the sliding surfaces. It also assumes that when sliding is fast contacts heat up, and this affects friction profoundly. Our model is able to quantitatively predict, for the first time, reported experimental results for steady state friction at all experimentally measured slip rates. This is done using material parameters that are measured from other experiments, unrelated to friction. The new model may have far reaching implications for understanding friction in general and for earthquake physics in particular. Key Points: Friction of rocks depends on slip rate: it follows conventional rate and state during slow slip, yet markedly weakens as slip rates approach seismic speeds Using conventional microphysics of creep, we develop a physics‐based model for steady state friction at all slip rates The model uses independently determined parameters to predict quartz friction experiments at all slip rates