MATHEMATICAL MODELING OF EARTH DAM BREACHES

At the present state-of-the-art every dam which impounds water has a potential of failure and there is an urgent need for predicting the magnitude, shape, duration, and other parameters of the outflow hydrograph which results from such dam failure. A mathematical model has been developed in order to predict the outflow hydrograph of earth dam breaches. The model is based on the water continuity and motion equations, the sediment continuity equation, a sediment transport equation and a breach form equation. In addition, another simple model was developed considering the Corps of Engineers - Schoklitsch discharge formula and Cristofano's approach for embankment erosion.;The mechanism responsible for the breach formation is studied considering a section of greatest efficiency from the erosional standpoint, in which the geometric characteristics are functions of a new parameter: the embankment angle of repose.;The second-order quasilinear hyperbolic system that includes continuity and motion equations, is implicitly solved by a four-point scheme in the space-time plane, considering the reservoir and a rating curve as boundary conditions upstream and downstream respectively.;The spatial and temporal variations of the breach are combined with the unsteady water model yielding discharge and area along the embankment in each time step. The total sediment transport is explicitly calculated resulting in a new embankment profile, taking into consideration the updated boundary conditions.;The sediment transport discharge is considered according to two different approaches. A method combining DuBoys' model of bed load transport with Einstein's suspended load method is used to calculate the total sediment transport. A second approach is derived to express a transport function as dependent on duration of failure, erodibility index, and water velocity.;The validity of the mathematical models was checked by applying them to two actual earth dam failures: the Teton Dam and the Mantaro Dam. The discharge variation intensity increased the unsteadiness of the flow and numerical instabilities were generated. This influence caused by inertia terms in the motion equation led to difficulties in calibrating the model. Experiments have shown that loops are almost absent for slopes greater than 0.001 and consequently this parameter was not taken into consideration since most dams have S(,0) >> 0.1. When the Manning's coefficient is increased, damping in discharge peak occurs and opens the loop of unsteadiness.;Good agreement was obtained between the model and the observed data, except for the Einstein-DuBoys model that presented high instabilities.