Thermal weakening friction during seismic slip: experiments and models
with heat sources and sinks
Abstract
Recent experiments systematically explore rock friction under crustal
earthquake conditions revealing that faults undergo abrupt dynamic
weakening. Processes related to heating and weakening of fault surface
have been invoked to explain pronounced velocity weakening. Both contact
asperity temperature $T_a$ and background temperature $T$ of the
slip zone evolve significantly during high velocity slip due to heat
sources (frictional work), heat sinks (e.g. latent heat of decomposition
processes) and diffusion. Using carefully calibrated High Velocity
Rotary Friction experiments, we test the compatibility of thermal
weakening models: (1) a model of friction based only on $T$ in an
extremely simplified, Arrhenius-like thermal dependence; (2) a flash
heating model which accounts for evolution of both $V$ and $T$; (3)
same but including heat sinks in the thermal balance; (4) same but
including the thermal dependence of diffusivity and heat capacity. All
models reflect the experimental results but model (1) results in
unrealistically low temperatures and models (2) reproduces the
restrengthening phase only by modifying the parameters for each
experimental condition. The presence of dissipative heat sinks in (3)
significantly affects $T$ and reflects on the friction, allowing a
better joint fit of the initial weakening and final strength recovery
across a range of experiments. Temperature is significantly altered by
thermal dependence of (4). However, similar results can be obtained by
(3) and (4) by adjusting the energy sinks. To compute temperature in
this type of problem we compare the efficiency of three different
numerical solutions (Finite differences, wavenumber summation, and
discrete integral).