Two-phase two-layer SPH modeling of surge waves generated by debris flows

Debris flows, characterized by high speeds and long run-out distances, can trigger a series of destructive events when entering reservoir areas, even leading to severe secondary geological disasters due to the generated huge surge waves. Therefore, accurately modeling the debris flow dynamics and the complicated interactions with the water body is crucial in engineering applications. In this work, the debris flow was conceptualized as a solid-liquid mixture and a numerical method based on two-phase two-layer smooth particle hydrodynamics (SPH) model was proposed to perform 2D simulations of surge waves generated by debris flows. In this method, two layers of SPH particles, representing the liquid and solid phases respectively, can overlap and move independently governed by their respective equations: the Navier–Stokes equations for the liquid phase and Newton's second law for the solid phase, with interactions between these phases characterized by drag force and buoyancy force during particle overlap. To validate the proposed numerical method and analyze the influence of composition of debris flows, three laboratory experiments were conducted: surge waves generated by a water column, a dry granular column, and a saturated granular column collapse into water. The established model was applied to these experiments and all simulated results demonstrate the robustness and versatility of the proposed method in effectively modeling the generation of the surge waves due to solid-liquid mixtures collapse into water. The effects of the granular internal friction angle, the baffle lifting speed, the initial saturation (defined as the initial depth ratio of water to granular material), the dynamic viscosity of pore water, and the downstream water depth on the generated wave amplitude and the front end of the granules are also investigated. It indicates that these factors have significant influence on the wave amplitude, which suggests that the composition of debris flows and downstream water depth are the important parameters in the surge wave generation.