SPH-DEM Modeling of Debris and Mud Flows

Gravitational mass movements, such as debris and mud flows, are among the most destructive natural hazards, leading to substantial fatalities and extensive economic damage worldwide. Improving our understanding and modeling of these processes is essential for developing effective risk management and early warning strategies. When debris and mud flows pass through a curved channel, centrifugal forces may cause a difference in flow height between the inner and outer banks of the channel. This height difference, known as superelevation, can be described using analytical models that establish a relationship between the superelevation height and the flow velocity.

Analytical models often employ a forced vortex approach, incorporating parameters such as the cross-sectional slope of the flow surface, flow width, and bend radius. These models, however, rely on assumptions such as a linear flow surface between mud deposits on the banks, a rectangular cross-section, and neglect both complex rheological behaviors and solid-fluid interactions. As a result, an empirically determined correction factor is required within the formula. The absence of a clear mechanical rationale for this correction factor presents challenges, as it is currently derived only through field investigations and laboratory experiments.

This study presents an enhancement to the existing forced vortex approach by incorporating insights from numerical modeling. A coupled SPH-DEM numerical model is employed, where DEM particles represent coarse solid particles, and SPH accounts for the fluid phase, comprising fines and water. The SPH-DEM coupling is based on the no-slip interaction model, with simulations performed using a GPU-based solver to ensure enhanced computational efficiency. To validate the approach, a parametric test is conducted, initially back-calculating laboratory-scale experiments. The study further involves varying the water content in debris and mud flows to examine its impact on flow behavior and superelevation. Larger water contents lead to an increased superelevation angle. Results from the parametric test reveal a clear correlation between water content and the flow surface shape in curved channels. Specifically, mud flows are characterized by convex upward surface shapes, whereas more granular debris flows typically exhibit concave downward shapes.

The distribution of material within the cross-section of the flow is governed by the equilibrium between boundary forces and centrifugal forces acting on the flow, which directly influences the superelevation. Numerical investigations are conducted to determine a correction factor and assess the extent to which inertial effects contribute to this correction factor for different material mixtures. Furthermore, we demonstrate that the effect of the flow surface shape is significant and is currently only accounted for by the empirical correction factor. This study offers new physical insights for the back-calculation of debris flow velocities in curved sections marked by mud deposits. Large-scale SPH-DEM simulations of a real debris flow event at Illgraben (Switzerland) are performed, showing good agreement with field data and its potential for further real-scale modeling.