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

TLDR

Floods from failures of natural and constructed dams pose a widespread hazard to people and property. The study seeks rapid methods to assess flood hazards from dam failures, especially sudden natural dams. The authors use a simple physically based breach‑formation model showing that peak discharge depends on a dimensionless parameter η = kV₀/(g l/2 d⁷/²), with distinct asymptotic forms for slow (η≪1) and fast (η≫1) breach growth. Although traditional statistical relations between peak discharge and water volume or lake level are limited, the proposed model accurately predicts peak discharge and offers a rapid way to estimate its plausible range when water volume and dam‑face depth are known.

Abstract

Floods from failures of natural and constructed dams constitute a widespread hazard to people and property. Expeditious means of assessing flood 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 η= kV 0 / g l/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 η takes asymptotically distinct forms depending on whether η ≪ 1 (relatively slow breach formation or small lake volume) or η ≫ 1 (relatively fast breach formation or large lake volume). Theoretical predictions agree well with data from dam failures for which k , and thus η, 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.