The role of compressional dynamics in setting the scale-dependent rheology of granular flows: Application to the emergence of thin layer stability

Abstract

One great challenge of modeling granular systems lies in capturing the rheologic dependencies on scale. For example, there are marked differences between quasi-static, intermediate, and rapid flow regimes. In this study, we demonstrate that assumptions for infinite stiffness of rigid particles, an assumption upon which the state-of the-art ($μ(I)$-rheology) modeling approaches are constructed, must be relaxed in order to recover the physical mechanisms behind many scale-dependent and non-local rheological effects. Any relaxation of the infinite stiffness assumption allows for particles to compress in series, whereby the number of simultaneously compressed particles controls the extent to which end-member particles experience a modified coefficient of effective friction, analogous to reduced stiffness for springs in series. To demonstrate the importance of such a mechanism in setting the dynamics for dense rigid granular systems, we show that modifying simple models to include the kinematics introduced by compression in series captures the emergence of thin layer stability, a widely observed yet incompletely explained non-local granular phenomenon. We also discuss, in general, how knowledge of the contact network and softness provides a potential physical basis for the diffusion of granular temperature.