Modeling of unsaturated granular flows by a two-layer approach

Flows of partially saturated grain-fluid mixtures over complex curved topography are commonly observed in nature. However, comprehensive understanding of the physics behind them is to date out of reach. To investigate their dynamic process, a two-layer approach is proposed, in which the fluid-saturated granular layer is overlaid by the pure granular material. More specifically, the lower layer is described by a two-phase mixture theory of density preserving solid and fluid constituents. For the upper layer, the single-phase granular mass is treated as a frictional Coulomb-like continuum, and the dilation effect and the influence of the interstitial air are ignored. The capillarity effects and grains-size segregation are not considered in both the layers. The lower and upper layers interact at an interface which is a material surface for the fluid phase, but across which the mass exchange for the granular phase may take place. The granular mass exchange across the layer interface is parameterized by an entrainment type postulate. In addition, the classical jump conditions are employed to connect both layers at the interface dynamically. Furthermore, we perform the depth-averaged technique for the saturated grain-fluid mixture lower layer and the pure granular upper layer, respectively, to simplify the governing equations established. It is demonstrated that the resulting model equations can be reduced to most of the existing single-layer pure granular flow models and saturated two-phase single-layer debris flow models. Numerical solutions demonstrate that the present two-layer model can describe flows of partially saturated grain-fluid mixtures and the transition process of a saturated grain-fluid mixture into an under-saturated state.