An exact solution for ideal dam-break floods on steep slopes

Dam-break floods on steep slopes occur in diverse settings. They may result from failure of either natural or man-made dams, and they have been responsible for the loss of thousands of lives [Costa, 1988]. Recent disasters resulting from dam-break floods on steep slopes include those at Fonte Santa mines, Portugal, in November 2006 and Taum Sauk, Missouri, USA, in December 2005. Numerical solutions of the shallow-water equations are generally used to predict the behavior of dam-break floods, but exact analytical solutions suitable for testing these numerical solutions have been available only for floods with infinite volumes, horizontal beds, or both. Computational models used to simulate dam-break floods commonly produce numerical instabilities and/or significant errors close to the moving front when steep slopes and/or irregular terrain are present in the flood path. In part these problems reflect the complex interaction of phenomena not included in model formulation (e.g., intense sediment transport under timedependent flow conditions), but in part they also reflect shortcomings in the numerical solution algorithms themselves. Therefore it is important to obtain exact analytical solutions of the shallow-water equations that can be used to test the robustness of numerical models when they are applied to floods of finite volume on steep slopes. This paper presents a new solution for this purpose.