A two-phase SPH model for massive sediment motion in free surface flows

Massive sediment motion in water with a free surface is an important kind of geophysical flows such as hyper-concentrated sediment laden river flows discharging into estuarine delta and turbidity currents generated by subaqueous landslides. One of the key and common characteristics of such flows is that interactions between water and sediment as well as those among sediment particles are equally important in affecting the sediment motion and the fluid flow. This paper presents a numerical model that builds on and extends an earlier two-phase SPH model based on a continuum formulation of solid-liquid mixtures (Shi et al., 2017) to provide a unified description of massive sediment motion in free surface flows. In the model, a constitutive law based on the rheology of dense granular flow is introduced to express the intergranular stresses while the interphase drag force is determined by combining the Ergun equation for dense solid-fluid mixtures and the power law for dilute suspensions. The proposed model is firstly applied to the study of collapse of loosely or densely packed granular columns submerged in water. The computed surface profiles of the granular column are found to be in good agreement with the experimental data. It shows that the loosely packed and the densely packed columns behave rather differently due to the differences in water-sediment interaction processes. The model is then used to simulate a dam-break flow over a mobile sediment bed. The computed configurations of the flow and the movable bed also agree well with the measured data. The predicted position on the leading edge of the flow has a mean error of 0.8% while the mean error for the maximum bed height is 12.9%. To further identify the dynamic processes involved, effects of water-sediment interactions on the motion of bed materials are investigated by examining the spatial and temporal variations of pressure and flow velocity. As shown in the applications, the proposed two-phase SPH model can successfully represent both the gravity-driven underwater granular flows and the shear flow driven intense sediment transport, implying its potential use in practical scenarios in which the two kinds of flows exist simultaneously, such as landslides triggered by storm in shallow sea and flows resulted in barrier or dam breaks.