Prediction of Overtopping Dike Failure: Sediment Transport and Dynamic Granular Bed Deformation Model

Earth dike failure due to overtopping flow produces a significant displacement of bed-sediment mass. While sediment dynamics typically prevails as a nonequilibrium condition, the bed deformation is resulted from the simultaneous bed erosion and dike body displacement. However, most of the existing shallow water erosion models do not resolve the dynamic bed deformation. In this study, a depth-averaged nonequilibrium sediment transport model is developed and coupled with a set of Savage-Hutter type equations to characterize the dynamic bed deformation, leading to an innovative approach to tackle flows over erodible/deformable beds. The one-sided first-order upwind finite-volume method was adopted for the solution of the system of conservation laws of flow and bed deformation (granular mass transport). A static resistance condition for granular mass was thoroughly defined to preserve the numerical stability of the equations representing the bed deformation component of the model. The model was tested against the experimental data sets for dike overtopping flow, dam-break flow of dry granular mass on a slope, and the analytical solutions. The proposed model enhances the prediction capability by the existing shallow water equations-based equations due to the dynamic bed deformation modeling.