A numerical three-dimensional non-cohesive earthen dam breach model

A numerical three-dimensional dam breach model is developed for the non-cohesive earthen dam overtopping breach problem. The breach location can be anywhere along the dam. The topography of the entire dam site is considered. Three kinds of phenomena are modeled: vertical erosion of the dam face or breach channel where the flow surface is above the eroded soil surface; undercutting of the breach channel sides followed by sudden collapse of the undercut soil; and possible sudden collapse of sides of breach channel entrances upon loss of local stability. Transport of sediment is limited to the transport capacity.; A hybrid-type of the total variation diminishing finite-difference scheme with first-order in time and second-order in space is proposed to calculate outflow through a varying-geometry breach channel by solving two-dimensional shallow water equations. The source term is formulated to represent the bottom and side slopes, and a flux limiter is proposed. This scheme is shown to accurately reproduce supercritical, subcritical, and transcritical flows for the following analytical or experimental cases: one-dimensional theoretical dam break with initially dry and initially wet beds; steady flow over a bump; hydraulic jump; one-dimensional dam break with a bottom slope; and two-dimensional dam break with bottom and side slopes. Results show that our scheme has a good capability to calculate dam-breach outflows from a varying-geometry breach channel.; The model is tested using one field test from the IMPACT project funded by the European Commission and data from two historically breached dams. Results show that our three-dimensional model accurately predicts the peak breach discharge rate and the final breach width for these cases. Both the breach location and reservoir shape have a significant effect on the peak breach discharge and the outflow hydrograph shape. The real shape of the breach channel during the breach process is successfully modeled.; The overtopping dam-breach problem with multiple breach locations under wind and wave actions is modeled. Intermittent wave overtopping and erosion are simulated. The dam initially breaches at one location and in some cases may breach at additional locations. Both the wind speed and wind direction can change the final breach shape and breach outflow hydrograph and the number of breaches for a particular reservoir.