A mathematical study on the influence of particle concentration in the dynamics of drag and associated landslide motion

Landslides down a mountain slope involve highly complex processes, and accurately predicting their dynamics is crucial for effective hazard assessment. Among the various aspects influencing the dynamics, drag also has a dominant role, that accounts for the complex interaction between constituent phases, especially when the phases have different velocity. Here, we study the dynamics of three different drag models: Simple drag, generalized drag and enhanced drag. We incorporate these drags in a two-phase mass flow model so as to have a unified model for different drags. Then, we perform the numerical experiments for the mixture flows akin to the flow of hyperconcentrated sediments and water saturated debris flow where particle concentration varies substantially. Among the flows with different drag models, simple drag results in the highest drag intensity producing less relative motion between the phases, leading to reduced mass advection, increased reverse flow, and slower movement of the mass at the rear. The results show that the simple and generalized drags become infinitely large as the solid volume fraction approaches unity, which is not naturally admissible. In contrast, the enhanced drag remains smooth and applicable across all solid volume fractions, from dilute to dense flows. With the varying density ratios of the fluid to solid phase, drag varies linearly whereas the generalized drag varies strongly nonlinearly and enhanced drag varies weakly nonlinearly. This study provides us further insights on the role of drag in multiphase mass flows and the necessity to choose an appropriate expression for drag to access geohazards.