30 Nov 2021

30 Nov 2021

Review status: this preprint is currently under review for the journal ESurf.

The Landslide Velocity

Shiva P. Pudasaini1,2 and Michael Krautblatter1 Shiva P. Pudasaini and Michael Krautblatter
  • 1Technical University of Munich, Chair of Landslide Research Arcisstrasse 21, D-80333, Munich, Germany
  • 2University of Bonn, Institute of Geosciences, Geophysics Section Meckenheimer Allee 176, D-53115, Bonn, Germany

Abstract. Proper knowledge of velocity is required in accurately determining the enormous destructive energy carried by a landslide. We present the first, simple and physics-based general analytical landslide velocity model that simultaneously incorporates the internal deformation (non-linear advection) and externally applied forces, consisting of the net driving force and the viscous resistant. From the physical point of view, the model stands as a novel class of non-linear advective – dissipative system where classical Voellmy and inviscid Burgers' equation are specifications of this general model. We show that the non-linear advection and external forcing fundamentally regulate the state of motion and deformation, which substantially enhances our understanding of the velocity of a coherently deforming landslide. Since analytical solutions provide the fastest, the most cost-effective and the best rigorous answer to the problem, we construct several new and general exact analytical solutions. These solutions cover the wider spectrum of landslide velocity and directly reduce to the mass point motion. New solutions bridge the existing gap between the negligibly deforming and geometrically massively deforming landslides through their internal deformations. This provides a novel, rapid and consistent method for efficient coupling of different types of mass transports. The mechanism of landslide advection, stretching and approaching to the steady-state has been explained. We reveal the fact that shifting, up-lifting and stretching of the velocity field stem from the forcing and non-linear advection. The intrinsic mechanism of our solution describes the fascinating breaking wave and emergence of landslide folding. This happens collectively as the solution system simultaneously introduces downslope propagation of the domain, velocity up-lift and non-linear advection. We disclose the fact that the domain translation and stretching solely depends on the net driving force, and along with advection, the viscous drag fully controls the shock wave generation, wave breaking, folding, and also the velocity magnitude. This demonstrates that landslide dynamics are architectured by advection and reigned by the system forcing. The analytically obtained velocities are close to observed values in natural events. These solutions constitute a new foundation of landslide velocity in solving technical problems. This provides the practitioners with the key information in instantly and accurately estimating the impact force that is very important in delineating hazard zones and for the mitigation of landslide hazards.

Shiva P. Pudasaini and Michael Krautblatter

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on esurf-2021-81', Anonymous Referee #1, 21 Dec 2021
  • RC2: 'Comment on esurf-2021-81', Anonymous Referee #1, 22 Dec 2021
  • RC3: 'Comment on esurf-2021-81', Anonymous Referee #2, 06 Jan 2022

Shiva P. Pudasaini and Michael Krautblatter

Shiva P. Pudasaini and Michael Krautblatter


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Short summary
We present first physics-based general landslide velocity model incorporating internal deformation & external forces. Voellmy & inviscid Burgers’ equation are specifications of the novel advective-dissipative system. Our unified analytical solutions constitute new foundation of landslide velocity, provide practitioners key information in instantly estimating impact forces. Solutions describe breaking wave & folding, revealing landslide dynamics are architectured by advection, reigned by forcing.