Bivariate Statistical Approach to Check Adequacy of Dam Spillway

The problem of selecting the appropriate design flood is a constant concern to dam engineering and, in general, in the hydrological practice. Overtopping represents more than 40% of dam failures in the world. The determination of the design flood is based in some cases on the T-year quantile of flood peak, and in other cases considering also the T-year quantile of flood volume. However, flood peak and flood volume have a positive (strong or weak) dependence. To model properly this aspect a bivariate probability distribution is considered using the concept of 2-Copulas, and a bivariate extreme value distribution with generalized extreme value marginals is proposed. The peak–volume pair can then be transformed into the correspondent flood hydrograph, representing the river basin response, through a simple linear model. The hydrological safety of dams is considered checking adequacy of dam spillway. The reservoir behavior is tested using a long synthetic series of flood hydrographs. An application to an existing dam is given.