Dispersion - Erosion Coupling in Landslides

Non-hydrostatic dispersive models can better describe the landslide motion. Following a dispersive wave equation and a mechanical erosion model for mass flows, here, we develop a novel dynamically coupled dispersion-erosion wave model that combines these two very essential complex processes. The newly developed model for landslide recovers the classical dispersive water waves and dispersive wave equation for landslide as special cases. We present several exact analytical solutions for the coupled dispersion-erosion model. These solutions are constructed for the time and spatial evolution of the flow depth. Solutions reveal that the dispersion and erosion are strongly coupled as they synchronously control the landslide dynamics. The results show that the wave dispersive wave amplifies with the increasing particle concentration, decreasing earth pressure, higher gravitational acceleration, increased slope angle and increased basal friction. The important novel understanding is that the intensity of the dispersive wave increases when erosion and dispersion are coupled. The results indicate the essence of proper selection of the initial and boundary conditions while solving applied and engineering problems associated with the dispersive - erosive mass transport. This provides the foundation for our understanding of the complex dispersion and erosion processes and their interplay.