New insights in the probability distributions of wave-by-wave overtopping volumes at vertical breakwaters

Advances in the development of prediction tools for wave overtopping allow now for overtopping volumes to be estimated with good accuracy, with the combined use of mean overtopping rates and maximum wave by wave overtopping volumes in a sequence of wave overtopping events. While previous literature has tended to focus on mean overtopping rates at coastal structures, limited studies have investigated the wave by wave overtopping volumes at coastal sea defences; in particular, a paucity of studies have focussed on the prediction of the shape parameter in the Weibull distribution (i.e., Weibull b) of overtopping volumes. This study provides new insights on the probability distribution of individual wave overtopping volumes at plain vertical seawalls by analysing the measured Weibull b values derived from a series of laboratory experiments on seawalls performed on a wide range of wave conditions and crest freeboards. The influence of wave conditions (wave steepness, significant wave height), structural parameters (crest freeboard, toe water depth), impulsiveness, probability of overtopping waves, and overtopping discharge on Weibull b parameter were examined, and then compared with the well-established empirical formulae. For the conditions covered within this study, it was found that the probability distribution of wave-by-wave overtopping volumes follow a 2-parameter Weibull distribution. No apparent differences in Weibull b values were reported with the variation of incident wave steepness and impulsiveness parameter. Results of this study revealed that Weibull b values at vertical walls, subjected to non-impulsive wave conditions, can be predicted reasonably well using relative freeboard and relative overtopping rates. A new unified formula is proposed for the estimation of Weibull b values at vertical walls under impulsive and non-impulsive wave attack.