Methods for predicting peak discharge of floods caused by failure of natural and constructed earthen dams

Floods from failures of natural and constructed darns constitute a widespread hazard to people and property. Expeditious means of assessing hood hazards are necessary, particularly in the case of natural dams, which may form suddenly and unexpectedly. We revise statistical relations (derived from data for past constructed and natural dam failures) between peak discharge (Q(p)) and water volume released (V-0) or drop in lake level (d) but assert that such relations, even when cast into a dimensionless form, are of limited utility because they fail to portray the effect of breach-formation rate. We then analyze a simple, physically based model of dam-breach formation to show that the hydrograph at the breach depends primarily on a dimensionless parameter eta = kV(0)/g(1/2)d(7/2), where k is the mean erosion rate of the breach and g is acceleration due to gravity. The functional relationship between Q(p) and eta takes asymptotically distinct forms depending on whether eta less than or equal to 1 (relatively slow breach formation or small lake volume) or eta much greater than 1 (relatively fast breach formation or large lake volume). Theoretical predictions agree well with data from dam failures for which k, and thus eta, can be estimated. The theory thus provides a rapid means of predicting the plausible range of values of peak discharge at the breach in an earthen dam as long as the impounded water volume and the water depth at the dam face can be estimated.