Two-layer multi-state SPH modelling of momentum growth and its feedback in viscous debris flow on wet bed sediment

Flow-momentum growth and resultant feedback from bed-sediment entrainment significantly influence the mobility of debris flows and valley topography. Existing models inadequately capture the mass and momentum growth regulated by scale-sensitive, time-dependent pore water pressure in erodible beds, which exhibit pronounced anisotropy and nonlinearity. In this study, we propose a three-dimensional, two-layer, multi-state smooth particle hydrodynamics (TLMS-SPH) model to assess the flow-momentum growth of debris flows on wet beds. Herein, an enhanced Drucker-Prager (DP) yield criterion is integrated into the Herschel-Bulkley-Papanastasiou (HBP) rheology to mitigate particle collapse induced by gravitational perturbations in steep terrains. Particularly, an efficient hydro-poro-mechanics-based pore water pressure algorithm is presented and embedded in the SPH scheme to simulate the pore pressure response. To address the size effect, we rigorously tested the method through a series of full-scale, well-documented entrainment experiments. The results demonstrate that the model effectively captures and reproduces the complex dynamics of flow-momentum growth, manifesting in erosion-induced excessive volume and mobility changes. Our method establishes a clear link between volumetric water content and pore pressure response, further underscoring its capability to delineate levee-channel and deposition morphology. This study represents the first attempt to model debris flow on beds of varying wetness from a particulate perspective. [Display omitted] •A TLMS-SPH model for debris flow entrainment on varied wet sediments is developed.•Stable phase transition of erodible bed sediment on steep terrains is achieved.•A novel hydro-poro pressure algorithm is embedded in SPH scheme.•Momentum growth and feedback effects are adequately captured by the proposed method.•Levee-channel and depositional morphologies are qualitatively replicated.