Flow rule of dense granular flows down a rough incline

Abstract

We present experimental findings on the flow rule for granular flows on a rough inclined plane using various materials including sand and glass beads of various sizes and four types of copper particles with different shapes. We characterize the materials by measuring $h_s$ (the thickness at which the flow subsides) as a function of the plane inclination $θ$ on various surfaces. Measuring the surface velocity $u$ of the flow as a function of flow thickness $h$, we find that for sand and glass beads the Pouliquen flow rule $u/\sqrt{gh} \sim βh/h_s$ provides reasonable but not perfect collapse of the $u(h)$ curves measured for various $θ$ and mean particle diameter $d$. Improved collapse is obtained for sand and glass beads by using a recently proposed scaling of the form $u/\sqrt{gh} =β\cdot h \tan^2θ/h_s\ \tan^2θ_1$ where $θ_1$ is the angle at which the $h_s(θ)$ curves diverge. Measuring the slope $β$ for ten different sizes of sand and glass beads, we find a systematic, strong increase of $β$ with the divergence angle $θ_1$ of $h_s$. The copper materials with different shapes are not well described by either flow rule with $u \sim h^{3/2}$.