Constitutive behavior of rocks during the seismic cycle in non-isothermal, non-isobaric conditions

Establishing a constitutive law for fault friction is a crucial objective of earthquake science. However, the complex frictional behavior of natural and synthetic gouges in laboratory experiments eludes explanations. Here, we present a constitutive framework that elucidates the slip-rate, state, temperature, and normal stress dependence of fault friction under the relevant sliding velocities and temperatures of the brittle lithosphere during seismic cycles. The competition between healing mechanisms explains the low-temperature stability transition from steady-state velocity-strengthening to velocity-weakening as a function of slip-rate and temperature. In addition, capturing the transition from cataclastic flow to semi-brittle creep accounts for the stabilization of fault slip at elevated temperatures. The brittle behavior is controlled by the real area of contact, which is a nonlinear function of normal stress, leading to an instantaneous decrease of the effective friction coefficient upon positive normal stress steps. The rate of healing also depends on normal stress, associated with an evolutionary response. If these two effects do not compensate exactly, steady-state friction follows a nonlinear dependence on normal stress. We calibrate the model using extensive laboratory data covering various relevant tectonic settings. The constitutive model consistently explains the evolving frictional response of fault gouge from room temperature to 600 for sliding velocities ranging from nanometers to millimeters per second, and normal stress from atmospheric pressure to gigapascals. The frictional response of faults can be uniquely determined by the in situ lithology and the prevailing hydrothermal conditions.