Extended landslide velocity and analytical drag

TL;DR

This paper introduces an extended landslide velocity model incorporating hydraulic pressure gradient forces, revealing a pressure-inertia paradox and proposing a novel analytical viscous drag model for landslide dynamics.

Contribution

It develops a comprehensive velocity model including hydraulic pressure effects and introduces the first analytical viscous drag model with a new dimensionless drag number.

Findings

The extended model shows a pressure-inertia paradox with upstream and downslope motion.

Viscous drag significantly influences landslide dynamics and differs for expanding and contracting motions.

The new drag model aligns with empirical values and offers a physically-based analytical approach.

Abstract

The landslide velocity plays a dominant role in estimating impact force and devastated area. Here, based on Pudasaini and Krautblatter (2022), I develop a novel extended landslide velocity model that includes the force induced by the hydraulic pressure gradient which was neglected by all the existing analytical landslide velocity models. By a rigorous conversion between this force and inertia, I develop two peer systems expecting to produce the same results. However, this contradicts with our conventional wisdom. This raises a question of whether we should develop some new balance equations. I compare the two velocity models that neglects and includes the force induced by the hydraulic pressure gradient. Analytical solutions produced by the two systems are different. The new model is comprehensive, elegant, and yet an extraordinary development as it reveals serendipitous circumstances resulting in a pressure-inertia-paradox. Surprisingly, the mass first moves upstream, then it winds back and accelerates downslope. The difference between the extended and simple solution widens strongly as the force associated with the hydraulic pressure gradient increases, demonstrating its importance. Viscous drag plays an important role in controlling the landslide dynamics. However, no explicit mechanical and analytical model exists for this. The careful sagacity of the graceful form of new velocity equation results in a mechanically extensive, dynamically evolving analytical model for viscous drag, the first of this kind. A dimensionless drag number is constructed. Contrary to the prevailing practices, I have proven that drags are essentially different for the expanding and contracting motions, an entirely novel perception. Drag coefficients are close to the often used empirical or numerical values. But, now, I offer an innovative, physically-founded analytical model for drag in mass flow simulation.