Modeling of granular column collapses with μ(I) rheology using smoothed particle hydrodynamic method

Abstract

In this paper, to simulate free surface flows of granular materials in a dense regime as a continuum media, a 2D SPH model is developed. The dense flow is characterized as a pressure dependent visco-plastic material based on a local constitutive law to calculate effective viscosity related to local pressure and the norm of strain rate tensor in the numerical method. A simple regularization technique is proposed to reproduce stopping condition and the free surface of a granular flow where the pressure vanishes. Pressure fluctuation as the main drawback of the weakly compressible SPH method leads to an inaccurate pressure distribution. This numerical instability increases at the free surface due to errors associated with the truncated kernels. In this work, a new algorithm is proposed to remove the nonphysical fluctuations by relating divergence of velocity to the Laplacian of pressure. The algorithm is validated for reproducing the dynamics and deposits of collapsing granular columns. The excellent agreement with experimental data is obtained. The maximum thickness of a granular flow on a rough inclined plane is obtained based on the local rheology model. The run-out distances and slopes of the deposits in the simulations also show good agreement with the values found in the experiments.