Geometric reliability analysis applied to wave overtopping of sea defences

Surge levels and waves are mutually dependent random variables, and this is reflected in their joint confidence regions or probability density contours (PDCs). The PDC generalises the concept of confidence intervals of a single variable in order to deal with multiple quantiles, so that the contour implies a geometric bound of observations falling inside it. This study introduces an efficient numerical scheme for quantifying the reliability index of a sea defence using a distance ratio of two PDCs, i.e., a dispersed PDC that just reaches the limit state surface and a one-standard-deviation PDC. The joint PDCs are defined in the original space of random variables and represented via a series of discrete vertices, which do not necessarily need to be smooth or elliptical in shape in order to fit different scattering patterns of the observations. Two numerical examples involving coastal wave overtopping problems indicate that the proposed contour-based expanding method (CBEM) provides flexibility to adopt various parametric or non-parametric joint distributions. The numerical implementation of the proposed algorithm graphically demonstrates an intuitive interpretation of the reliability index, which makes the relation between the joint PDCs and the limit state function more explicit.