An Extended Microphysical Friction Model for Variable Normal Stress Conditions

Variations in effective normal stress (${\sigma }_n$) disrupt the proportionality between normal stress and shear resistance. Understanding this is crucial for advancing studies of earthquake triggering. However, rate-and-state-dependent friction laws often fall short in describing friction under variable ${\sigma }_n$. This study extends a microphysical friction model, originally developed for granular gouge friction at constant ${\sigma }_n$, to accommodate variable ${\sigma }_n$. We incorporate the effects of gouge elasticity, alongside granular flow and grain scale plasticity, and test the model against four distinct types of gouge shearing experiments that simulate varying-${\sigma }_n$ conditions. Our modified model captures all key frictional responses observed in the experiments, with qualitative agreement. Importantly, it captures the ${\sigma }_n$-effect through a physically based plastic deformation term, thus eliminating the need for an empirical sensitivity factor (the α-value proposed by Linker & Dieterich, 1992, https://doi.org/10.1029/92jb00017). The model indicates that changes in ${\sigma }_n$ induce instantaneous and transient adjustments in shear stress and gouge dilatation state, alongside slight variations in steady-state friction. We show that the emergence of an apparent elastic loading stage during imposed perturbations arises from an accompanying velocity excursion, and we derive a physics-based expression for the empirical α-value. The model has significant implications for the dynamic triggering of earthquakes, for correlations between local earthquakes and solid tides or remote seismic waves, and for the assessment of seismic hazards associated with reservoir depletion and injection activities.