Equilibrium approach for modeling erosional failure of granular dams

Abstract

Erosional failure of granular dams by an overtopping body of water is investigated using a depth-averaged morphodynamic model. The transport of sediment by the flow assumes the sediment flux to remain in equilibrium with the local bed shear stress. Accordingly, the shallow-water hydrodynamic equations are coupled with the Exner equation for mass conservation of the sediment. The system of equations is solved using a fully coupled well-balanced finite volume method, second-order accurate in time and space. The effect of the steep bed slope of a dam face is incorporated into both the hydrodynamics and sediment transport equations, leading to improved predictions. Comparison with results obtained from nonequilibrium sediment transport models indicates that such models perform poorly while predicting the bed evolution near the toe of an eroding dam. Observations from experimental studies demonstrate that the amount of sediment entrained by the flow is not significant, except during the initial moments of failure. This suggests that the vertical exchange of mass between the bed and the flow layer, as assumed by the nonequilibrium models, may not be completely valid during the failure. The equilibrium model results, reproducing the key flow features of the overtopping failure process, are validated by experimental measurements. The study provides fresh insights into the sediment transport processes associated with the erosion of a granular dam by overtopping, establishes the appropriateness of the equilibrium approach for its numerical modeling, and proposes a well-balanced second-order accurate solution technique for solving the resulting coupled equations of flow and sediment transport.