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\begin{document}

\title{A microphysical model of rock friction and the brittle-ductile
transition controlled by dislocation glide and backstress evolution}



\author[1]{Christopher Thom}%
\author[2]{Lars Hansen}%
\author[3]{David Goldsby}%
\author[1]{Emily Brodsky}%
\affil[1]{University of California, Santa Cruz}%
\affil[2]{University of Minnesota-Twin Cities}%
\affil[3]{University of Pennsylvania}%


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  \date{May 18, 2024}


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\begin{abstract}
Rate-and state-friction is an empirical framework that describes the
complex velocity-, time-, and slip-dependent phenomena observed during
frictional sliding of rocks and gouge in the laboratory. Despite its
widespread use in earthquake nucleation and recurrence models, our
understanding of rate-and state-friction, particularly its time-and/or
slip-dependence, is still largely empirical, limiting our confidence in
extrapolating laboratory behavior to the seismogenic zone. While many
microphysical models have been proposed over the past few decades, none
have explicitly incorporated the effects of strain hardening,
anelasticity, or transient viscous rheology. Here we present a new model
of rock friction that incorporates these phenomena directly from the
microphysical behavior of lattice dislocations. This model of rock
friction exhibits the same logarithmic dependence on sliding velocity
(strain rate) as rate-and state-friction and predicts a dependence on
the internal backstress caused by long-range interactions among
geometrically necessary dislocations. Changes in the backstress evolve
exponentially with plastic strain of asperities and are dependent on
both the current backstress and previous deformation, which give rise to
phenomena consistent with interpretations of the `critical slip
distance,' `memory effect,' and `state variable' of rate- and
state-friction. Fault stability in this model is controlled by the
evolution of backstress and temperature. We provide several analytical
predictions for RSF-like behavior and the `brittle-ductile' transition
based on 2 microphysical mechanisms and measurable parameters such as
the geometrically necessary dislocation density and strain-dependent
hardening modulus.%
\end{abstract}%



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