Three-dimensional non-cohesive earthen dam breach model. Part 1: Theory and methodology

"An erosion and force/moment equilibrium based 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 model considers the topography of the entire dam site. Three-dimensional slope stability along the main direction of flow in the breach channel is checked. A second order hybrid-type of total variation diminishing finite-difference scheme is proposed to simulate the dam breach outflow by solving the two-dimensional shallow water equations. The 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 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. Applications to a simple breach channel show that calculated flows match the broad-crested weir formula and reasonably fit the grids."