An Eulerian-Eulerian two-phase model based on a collisional-frictional law for the granular stress is proposed for the description of underwater granular flows and is applied to the collapses of immersed granular columns, which can be viewed as an idealized physical model of submarine landslides. In the mathematical model, the kinetic theory for dry granular flows is extended to take into account the particle-fluid interaction when formulating the collisional stress in the granular material, while the frictional stress is modeled based on an existing relation obtained by statistically averaging the individual contact forces among cohesionless particles. The drag force and the virtual-mass force are considered to represent the inter-phase interaction. The two-phase model is then employed to simulate the laboratory experiments of the collapses of granular columns immersed in an ambient liquid with an emphasis on the effect of the initial packing condition of the granular particles. It has been shown that the computed collapsing process of granular columns is in very good agreement with the experimental observations, and the proposed model can well capture the dynamic features of underwater granular flows. The effects of fluid pressure, drag force, and particle and fluid properties on the granular collapse are also discussed. It is demonstrated that the interstitial fluid flow plays a significant role in the collapsing process.

It has been reported that, in submarine landslides down a slope, only a small part of the landslide momentum was transferred to the tsunami while most was lost in the further propagation over the flat bed. The high momentum of landslides off a slope meant a long run-out and a great impact on underwater infrastructure. Nevertheless, little attention has been paid to the variation of momentum of deformable submarine landslides off a slope, i.e. the loss of momentum when the slides flow away from the slope over a flat bottom. In this paper, the translational momentum of deformable submarine granular landslides running down a non-erodible inclined bed is investigated with a two-phase smoothed particle hydrodynamics model. After flowing down the slope, the transport rate and flux of the landslide translational momentum along the propagation over the flat bottom are examined. The effects of physical variables of the slide, particularly the grain size, the initial compaction and the front intrusion angle on the variation of the translational momentum, are explored. Accordingly, scaling relations of the spatial-temporal maximum transport rate and flux of the landslide translational momentum, as well as those of the slide final run-out and the generated leading wave height, are proposed. These scaling relations, although based on numerical data of small-scale granular landslides, demonstrate a preliminary attempt to develop practical expressions in the framework of momentum for estimating the run-out of real submarine landslides and the impact on underwater infrastructure.