The landslide velocity

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 (nonlinear advection) and externally applied forces, consisting of the net driving force and the viscous resistant. From the physical point of view, the model represents a novel class of nonlinear advective–dissipative system, where classical Voellmy and inviscid Burgers' equations are specifications of this general model. We show that the nonlinear 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, most cost-effective, and 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 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 the steady state has been explained. We reveal the fact that shifting, uplifting, and stretching of the velocity field stem from the forcing and nonlinear 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 uplift, and nonlinear advection. We disclose the fact that the domain translation and stretching solely depend 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 practitioners with key information for instantly and accurately estimating the impact force that is very important in delineating hazard zones and for the mitigation of landslide hazards.