Simulation of velocity and shear stress distributions in granular column collapses by a mesh-free method

Abstract

To describe granular flows in the dense regime, the μ(I) rheology model was proposed. It has been proven to be effective in reproducing flow dynamics in the dense regime caused by dry granular materials. For continuum modeling, the mesh-free method can easily handle flows with interface such as free surface, which commonly exists in most granular flows. In this study, the μ(I) rheology model is coupled with a mesh-free method, Moving Particle Semi-implicit method (MPS). The coupled model is used to analyze velocity and shear stress distributions in granular column collapses. To validate the model, velocity measurements were conducted on two aspect ratios a = 1.25 and 5.0. The coupled model is verified by the measured velocity profiles. Both horizontal and vertical velocity distributions are examined in the validation. A linear relationship on the velocity distribution is observed in the flowing region in the collapses both experimentally and numerically. Another larger aspect ratio a = 7.0 were then simulated and a similar linear velocity distribution was obtained. On the basis of the velocity analysis, the tangential shear stress was analyzed and discussed in the three collapses. It showed that the distribution of the shear stress is symmetrical with the opposite direction. In the core quasi-static region, the shear stress was larger than that in the flowing region. In the free fall of the upper portion for the large aspect ratios such as a = 7.0, there was very small shear stress. In the center of the column in the collapses, the shear stress almost remains zero with some fluctuations.