Numerical Analysis of a Dam-Break Wave with a Non-Newtonian Fluid over an Erodible Bed

Landslides are a phenomenon that has often been studied and analyzed mainly due to their frequency and their dangerous potential. The word landslide covers a broad category of ground movements that can be caused both by nature and by human mistakes. The type of movements that are the focus of this thesis are mud flows and debris flows, two of the fastest types of ground movements, whose speed and amount of material often lead to a change in the topography of their bed. This modification of the bed upon which the movement occurs has not only effects on possible future events but even on the landslide itself. This change in topography can be seen as a form of entrainment of material from the bed into the landslide. This phenomenon of erosion can often increase the amount of overall material involved in the landslide and, therefore, a modification of the pathing and destructive potential of the same flow. A numerical study of this phenomenon has been performed in this thesis with a Lattice-Boltzmann Method, a relatively recent method whose main focal point is the numerical resolution of an appropriate Boltzmann equation instead of the more classical approach that usually solves the Shallow-Water equations. The material taken into consideration for the flow in the experiments was a Non-Newtonian fluid with a behavior that could be properly represented by a Herschel-Bulkley model. A rheology that presents both a stress threshold for plasticity and a shear-thinning behavior, both of which are phenomena encountered when talking about debris and mud flows. After an explanation of the mathematical model and a comparison with a simple case with an analytical solution, the code was used to perform simulations of a dam-break wave over an incline encountering an erodible bed and entraining material from it. The experiments were performed with varying parameters to study the influence of the size of the erodible layer and the inclination of the slope on the movement. Lastly, after an analysis of the obtained results, some examples of further studies are mentioned like the influence of space-time discretization.