The Entire Landslide Velocity
Abstract. The enormous destructive energy carried by a landslide is principally determined by its velocity. Pudasaini and Krautblatter (2022) presented a simple, physics-based analytical landslide velocity model that simultaneously incorporates the internal deformation and externally applied forces. They also constructed various general exact solutions for the landslide velocity. However, previous solutions are incomplete as they only apply to accelerating motions. Here, I advance further by constructing several new general analytical solutions for decelerating motions and unify these with the existing solutions for the landslide velocity. This provides the complete and honest picture of the landslide in multiple segments with accelerating and decelerating movements covering its release, motion through the track, the run-out as well as deposition. My analytical procedure connects several accelerating and decelerating segments by a junction with a kink to construct a multi-sectoral unified velocity solution down the entire path. Analytical solutions reveal essentially different novel mechanisms and processes of acceleration, deceleration and the mass halting. I show that there are fundamental differences between the landslide release, acceleration, deceleration and deposition in space and time as the dramatic transition takes place while the motion changes from the driving force dominated to resisting force dominated sector. I uniquely determine the landslide position and time as it switches from accelerating to decelerating state. Considering all the accelerating and decelerating motions, I analytically obtain the exact total travel time and the travel distance for the whole motion. Different initial landslide velocities with ascending or descending fronts result in strikingly contrasting travel distances, and elongated or contracted deposition lengths. Time and space evolution of the marching landslide with initial velocity distribution consisting of multiple peaks and troughs of variable strengths and extents lead to a spectacular propagation pattern with different stretchings and contractings resulting in multiple waves, foldings, crests and settlements. The analytical method manifests that, computationally costly numerical solutions may now be replaced by a highly cost-effective, unified and complete analytical solution down the entire track. This offers a great technical advantage for the geomorphologists, landslide practitioners and engineers as it provides immediate and very simple solution to the complex landslide motion.
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