Hydraulic structures subject to bivariate hydrological loads: Return period, design and risk assessment.

During the recent years there has been an increasing interest in multivariate frequency analysis of hydrological variables, e.g. those describing extreme events like rainfall, floods or droughts. The multivariate analysis provides a better understanding of the phenomena under investigation and an additional insight about the interrelationships between the different variables (e.g. peak, volume and duration of the flood), exploiting the complete structure of the problem and making a full use of the available data. However, while the developments on multivariate analysis of hydrological data has produced a large body of literature, a clear assessment of the use of these methods in the design and risk assessment of hydraulic structures is still a matter of debate. In the present work we illustrate a general, structure-based framework for the design and/or risk assessment of hydraulic structures in a bivariate environment; we also compare it to recently proposed methods which are based on the assumption of hydrological design events (as is customary in the univariate context). For illustration purposes, both the structure-based and the design event-based approaches are applied to the design of an idealized structure, thus exploring the differences among the methods as function of the parameters involved. Our work highlights that the return period of structure failure in a multivariate environment strictly depends on the particular structure under design, and in most cases the design of an hydraulic structure cannot be based on a single, hydrological multivariate design event. This acts as a warning for practitioners against the use of design methods based on single hydrological events, as usually done in the context of univariate hydrology, thus neglecting the interplay between the structure and the hydrological loads acting on it.