A methodology for the bivariate hydrological characterisation of the overtopping failure for river levees

This research presents a methodology for the hydrological characterisation of the overtopping failure for an existing river levee. Conventional procedures usually consider only one variable for the hydrologic forcing, e.g. peak discharge Q. Such an approach might fail if also the volume of the hydrograph V is a significant factor.  The proposed procedure is based on the generation of a set of plausible hydrographs. Each hydrograph has a couple of Q and V resulting from an approximated bivariate distribution. The shapes of the hydrographs are classified according to their tendency to produce overtopping, introducing the new Overtopping Hydrograph Shape Index (OHSI). The levee of a river reach located in Tuscany Region, Italy, was tested. As a preliminary result, it was found that the hydrographs that produce overtopping failure lay in a zone in the Q-V space, delimited by the Critical Overtopping Flood Hydrograph (COFH) curve. The existence of the COFH demonstrates that overtopping failure is not determined by a unique variable Q but rather by the combination of both Q and V. The limiting case corresponds to a family of hydrographs with varying Q and V values. The COFH allows dividing the Q-V space into two zones: the no-failure zone and the failure zone, which simplify the evaluation of the failure probability for a river levee.  This procedure is based on tools that are widely known and it is replicable by the public administrations or public entities that are interesting in the hydrologic and hydraulic risk assessment.