The landslide drag

Abstract

Drag is one of the most important energy dissipation mechanisms in nature, including landslides and debris flows. To satisfactorily reproduce laboratory or field data in simulating landslides, often empirical relations or convenient numerical values are used for the drag force coefficient. However, this is just a parameter calibration rather than a physical reality. Why should the drag coefficient be a constant for a dynamically evolving landslide? Which drag coefficient represents the physical reality? So, what exactly is the drag remains an open question. As the landslide is a deformable body, the drag-deformation-flow must be interconnected. Empirical drag coefficients lack important dynamical aspects. As the drag coefficient is less likely to be measurable, it must be described with some mechanical models. Yet, there exists no analytical model for the drag coefficient. Here, we postulate that the drag coefficient must be a function of the evolving landslide velocity, as it must contain information constituting the landslide acceleration in relation to the net driving acceleration. We develop an innovative, evolutionary drag coefficient that adjusts automatically during the landslide motion. The drag coefficient is described by a dimensionless acceleration number as it is regulated by the physics and dynamics of the flow. Formal derivation shows that the drag coefficient is the measure of energy inefficiency. This settles down the deliberation on the drag force in landslide dynamics, reshaping the concept of drag. Simulation results highlight the essence, mechanical strength and functionality of the proposed analytical drag as it demonstrates the inherent frictional behaviour of granular debris flows. As the dynamical drag coefficients appeared to be around the often calibrated values, the new drag potentially well reproduces natural event dynamics, but now with clear physical basis.