Constitutive Behavior of Rocks During the Seismic Cycle

Abstract

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 rate, state, and temperature dependence of fault friction under the relevant sliding velocities and temperatures of the brittle lithosphere during seismic cycles. The competition between healing mechanisms, such as viscoelastic collapse, pressure‐solution creep, and crack sealing, 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. We calibrate the model using extensive laboratory data on synthetic albite and granite gouge, and on natural samples from the Alpine Fault and the Mugi Mélange in the Shimanto accretionary complex in Japan. The constitutive model consistently explains the evolving frictional response of fault gouge from room temperature to 600°C for sliding velocities ranging from nanometers to millimeters per second. The frictional response of faults can be uniquely determined by the in situ lithology and the prevailing hydrothermal conditions.

Constitutive Behavior of Olivine Gouge Across the Brittle‐Ductile Transition

“…The brittle-to-ductile transition involves an intermediate step characterized by semi-brittle deformation for a finite range of temperature of about a hundred degrees with the lower and upper bounds depending on the instantaneous slip-rate. The frictional regime can be explained by a rate-, state-, and temperature-dependent friction law with a power-exponent of 70 ± 10 and an activation energy of 40 ± 10 kJ/mol, compatible with other synthetic and natural gouges (Barbot, 2019a(Barbot, , 2022(Barbot, , 2023.…”

“…The brittle‐to‐ductile transition involves an intermediate step characterized by semi‐brittle deformation for a finite range of temperature of about a hundred degrees with the lower and upper bounds depending on the instantaneous slip‐rate. The frictional regime can be explained by a rate‐, state‐, and temperature‐dependent friction law with a power‐exponent of 70 ± 10 and an activation energy of 40 ± 10 kJ/mol, compatible with other synthetic and natural gouges (Barbot, 2019a, 2022, 2023). The semi‐brittle regime is characterized by a power exponent of 17 ± 3 and an activation energy of 240 ± 50 kJ/mol, sitting halfway between typical values for friction and the low power exponents of crystal plasticity.…”

“…The thermally activated power-law is characterized by a stress power exponent n 1 = 70 ± 10, the activation energy Q 1 = 40 ± 10 kJ/mol associated with the activation temperature 𝐴𝐴 T𝑇1 = 20 • C. The transition from steady-state velocity-strengthening at 100°C to velocity-weakening at 200°C can be explained by the competition between two healing mechanisms with activation energy H 1 = 10 kJ/mol and H 2 = 70 kJ/mol, activation temperature T 1 = 0°C and T 2 = 180°C, with power-law exponents p 1 = 2.2 m 1 and p 2 = 0.9 m 1 with a asperity-size exponent m 1 = 3.5. The thermodynamic parameters for healing are commensurate with those of other pure and synthetic gouge (Barbot, 2022(Barbot, , 2023. The friction-to-flow transition is captured by the activation of the rate-dependent creep mechanisms.…”

“…We describe a physical model that captures the three distinct mechanical regimes of Damaping olivine characterized by rate-and state-dependent friction at low temperatures with a velocity-strengthening to velocity-weakening transition between 100 and 200°C followed with increasing temperature by a friction-to-flow transition at about 300°C with increasing dependence on slip rate. This complex behavior can be described by the following constitutive law that combines frictional sliding and two thermally activated creep mechanisms related to semi-brittle and ductile flow (Barbot, 2023)…”

Transient and Steady‐State Friction in Non‐Isobaric Conditions

“…In Section 4, we compare the proposed physical model with previous friction laws. The constitutive model augments and complements previous formulations limited to isobaric conditions (Barbot, 2019a(Barbot, , 2022(Barbot, , 2023, enabling an increasingly comprehensive representation of fault mechanics during seismic cycles.…”