Two-phase SPH-DEM modeling of the superelevation phenomenon of debris and mud flows

When debris and mud flows pass through curved channels, centrifugal forces lead to a height difference – known as superelevation – between the inner and outer banks. Analytical models describe this phenomenon by relating the superelevation angle to flow speed. However, these models assume simplified flow dynamics, a linear flow free surface, and do not explicitly account for solid–fluid interactions, requiring an empirical correction factor. In this study, we perform fully depth-resolved SPH-DEM numerical experiments to investigate the influence of water content on superelevation in curved channels. DEM represents the coarse solid particles, while SPH models the fluid phase, including both fines and water. The model is first validated against laboratory-scale experiments of debris flow superelevation. A parametric study is then conducted by varying the water content in debris and mud flows. The results show that increased water content leads to higher flow velocity and thus greater superelevation. The transverse flow surface depends strongly on material composition: mud flows typically exhibit convex-downward profiles, whereas granular flows display concave-downward profiles. By balancing centrifugal forces with basal normal stresses, we establish a correlation between the empirical correction factor, water content, and flow-surface curvature. However, the numerical experiments also reveal significant spatial variability in the correction factor along the bend, indicating additional mechanisms – specifically, a run-up impact that promotes superelevation, and subsequent alternating transverse motions – that limit the applicability of this analytical approach. Finally, SPH-DEM simulations of a real debris flow event at Illgraben successfully reproduce the observed field data, demonstrating the ability of the model for large-scale applications.