A MATHEMATICAL MODEL OF PROGRESSIVE EARTH DAM FAILURE

The need to predict and understand the characteristics of dam failure has become an important subject in the past few years. In this work a mathematical model is developed by combining unsteady flow equations with sediment transport and continuity to represent the erosive process that occurs in an earth dam failing under the action of escaping waters.;The breach geometry is assumed to follow Lane's model for stable channels. Several modifications are introduced to allow the inclusion of the effect of the position of the breach upon the characteristics of the outflow hydrograph. The outflow hydrograph provides the necessary boundary conditions for downstream propagation of the flood wave produced by the failing dam.;The resulting partial differential equations are discretized using the finite difference approach and then integrated by solving the corresponding set of algebraic equations. The solution domain has unique characteristics: it stretches itself as time progresses and its boundaries are curved. A discretization scheme is proposed and developed to make the discretization of the governing equations at irregular mesh points near the boundary totally compatible with the internal grid. The algebraic system of equations was solved in a coupled form.;Model validation was sought by simulating the failure of the Mantaro Natural Dam in Peru. The numerical results reproduced quite well the basic characteristics of the resulting flood event.;The proposed model is analyzed by considering the magnitude and behavior of the system eigenvalues. The nature of these eigenvalues indicates the inadequacy of the available sediment transport equations in the supercritical flow regime. Their relative magnitude serves as a guide in suggesting some approximations that may be used and their solution technique.;Sensitivity analysis was undertaken, using the Mantaro Dam characteristics. The results indicate that the outflow hydrograph is greatly affected by resistance to flow and the location of the breach. Its proximity to a non-erodible side wall tends to amplify the peakedness of the outflow hydrograph. The effect of several other physical parameters, such as porosity, angle of friction, the representative grain size, on the characteristics of the outflow hydrograph was also considered and analyzed.