Quaking in sand -- Dynamics of granular shear flow at the "quasi-static" limit

We propose a minimal model that produces repetitive quaking of soft particles under steady shearing in numerical experiments. As opposed to using fixed Columb friction, we include a characteristic velocity above which the tangential force weakens. Our study at the non-inertial limit, where granular flows would inevitably be rate-independent in conventional treatments, establishes a state diagram spanned by two axes: the mean contact per particle versus a dimensionless shear rate with the grain size and the velocity weakening taken into account. Quaking behaviors reported previously with our prior laboratory experiments are now justified with values of this dimensionless shear rate, indicative of a transition between fully frictional “solid” and free slipping “liquid”. The mean contact number links the packing density to the mechanical stability. The sign of jumps in mean contact number divides the quaking states into two types and reveals a switch of the underlying mechanism. Our amendment to the conventional model renders the non-inertia limits of granular flow rate-dependent and produces intriguing dynamics, that might shed light on understanding the buildup of earthquakes and their precursors.