BREACH: An erosion model for earthen dam failures

A physically based mathematical model (BREACH) to predict the breach characteristics (size, time of formation) and the discharge hydrograph emanating from a breached earthen dam is presented. The earthen dam may be man-made or naturally formed by a landslide. The model is developed by coupling the conservation of mass of the reservoir inflow, spillway outflow, and breach outflow with the sediment transport capacity of the unsteady uniform flow along an erosion-formed breached channel. The bottom slope of the breach is assumed to be essentially that of the downstream face of the dam. The growth of the breach channel is dependent on the dam’s material properties (D50 size, unit weight, friction angle, cohesive strength). The model considers the possible existence of the following complexities: 1) core material having properties which differ from those of the outer portions of the dam; 2) the necessity of forming an eroded ditch along the downstream face of the dam prior to the actual breach formation by the overtopping water; 3) the downstream face of the dam can have a grass cover or be composed of a material of larger grain size than the outer portion of the dam; 4) enlargement of the breach through the mechanism of one or more sudden structural collapses due to the hydrostatic pressure force exceeding the resisting shear and cohesive forces; 5) enlargement of the breach width by slope stability theory: 6) initiation of the breach via piping with subsequent progression to a free surface breach flow; and 7) erosion transport can be for either noncohesive (granular) materials or cohesive (clay) materials. The outflow hydrograph is obtained through a time-stepping iterative solution that requires only a few seconds for computation on a mainframe computer. The model is not subject to numerical stability or convergence difficulties. The model’s predictions are compared with observations of a piping failure of the man-made Teton Dam in Idaho, the piping failure of the man-made Lawn Lake Dam in Colorado, and a breached landslide-formed dam in Peru. Also, the model has been used to predict possible downstream flooding from a potential breach of the landslide blockage of Spirit Lake in the aftermath of the eruption of Mount St. Helens in Washington. Model sensitivity to numerical parameters is minimal; however, it is sensitive to the internal friction angle of the dam’s material and the extent of grass cover when simulating man-made dams and to the cohesive strength of the material composing landslideformed dams.