Simulation of quasi-static and dynamic collapses of rectangular granular columns using smoothed particle hydrodynamics method

The quasi-static collapse of granular material where the effect of particle inertia is negligible is an important topic of interest in various natural phenomena and industrial processes. However, less focus has been placed on experimental and numerical studies of this type of collapse. To provide a better understanding of the quasi-static and dynamic collapses of granular materials and the transitional behavior between these two collapses, a three-dimensional (3D) smoothed particle hydrodynamics (SPH) model was developed and used to investigate the collapse of rectangular sand columns with aspect ratios ranging from 0.26 to 11. To model the sand under flow-type failure, the Drucker- Prager constitutive model with nonassociated flow rule was implemented in the SPH formulations. The quasi-static collapse was initiated by slowly moving one of the side walls, and dynamic collapse was modeled by suddenly removing the wall. The SPH results reveal that both quasi-static and dynamic collapses show qualitative similarities and primarily depend on the initial aspect ratio of the column, resulting in two deposit morphologies, including a truncated wedge-like final deposit with a flat surface at the top for small aspect ratios and a wedge-like deposit with a tip for large aspect ratios, which is consistent with experimental observations in the literature. For quasi-static collapse, the final deposit profile (e.g., final height, runout distance) and energy dissipation were theoretically derived and were found to be in close agreement with SPH simulations and experiments. The sensitivity of the deposit profile to the wall velocity was also investigated to provide useful insight into the transitional behavior between quasi-static and dynamic collapses. This sensitivity analysis revealed that the transition between quasistatic and dynamic collapses occurs within a small range of Midi numbers.