An advanced SPH model for protective constructions of debris flows adopting the modified HBP constitutive law

In many catchments prone to debris flows, prevention structures such as check dams and retention basins have been installed to prevent debris flows from impacting the nearby infrastructures. The SPH model adopting the Herschel–Bulkley– Papanastasiou (HBP) constitutive law has shown good potential in modeling the interaction between debris flow and prevention structures. However, the accuracy of this model is not fully satisfactory when modeling the deposition process of debris flow, because the original HBP law is a viscoplastic model which does not consider frictional dissipation. Therefore, in this paper, we proposed a novel SPH model for analyzing the interaction between debris flow and prevention structures, by incorporating a modified HBP law with frictional dissipation into the original SPH model. The proposed model is validated by column collapse and flume benchmark experiments first and then utilized to analyze a real debris flow and its interaction with the prevention structures in the Cancia catchment in northern Italian Alps. The results of the column collapse experiment show that our model exhibits a better performance in simulating the collapse process compared with the original SPH model, and the simulation results of the sand flume test illustrate that the proposed model can accurately predict the impact force of debris flow on the prevention structure. The simulation results of the Cancia debris flow demonstrate that the check dams can dramatically diminish the discharge and the frontal flow velocity of the debris flow, and the peak impact force of debris flow generally decreases with gentler channel slope. Furthermore, various prevention structures show different interaction mechanisms with debris flows: the flat deposition platform mainly dissipates the kinetic energy of the flow, the check dam mainly reduces the peak discharge of the debris flow and intercepts the debris mass, and the retention basin at the outlet contributes to the deposition of debris flow. The proposed novel SPH model is helpful for guiding the optimization design of multiple prevention structures in debris flow gullies.