Modelling Flows Involving Highly Dynamic Interactions Between Granular Material and Water with SPH

A SPH multi-phase formulation combined with a granular rheological model is applied to the modelling of flows involving highly dynamic interactions between granular material and water. The granular material is treated as a continuum and is assumed to behave as a shear-thinning fluid. A rheological law similar to the rheology (Jop et al., 2006) is used. The material effective viscosity is thus a function of the mean scalar rate of strain, and of the yield stress. The latter is calculated according to the pressure-dependent Drucker-Prager criterion. Therefore, it depends on the internal friction angle and on the effective stress in the material. Under the lithostatic assumption, effective stress is computed solving a Laplace problem within the granular material domain (Ghaïtanellis et al., 2018).

The water and the granular phases are treated as immiscible continua, discretized in two distinct sets of SPH particles with different mass and behaviour laws. In all other respects, both phases are treated similarly. The multi-phase Weakly-Compressible SPH formulation is based on Hu and Adams’ (2006) model, improved so that it can also handle a free-surface.

The model is implemented within the open-source code GPUSPH that runs entirely on GPUs with CUDA. With a high level of optimization and of the multi-GPU capability, GPUSPH can be applied to real-world 3D cases involving several millions of particles with a reasonable computational time. In this paper, the model is first validated on a 2D experimental case of dam-break on movable bed (Spinewine and Zech, 2007). It is then used to simulate the 2007 Chehalis Lake landslide.