Distribution of individual wave overtopping volumes on mound breakwaters

Abstract

Conventional mound breakwaters are usually designed to withstand low mean wave overtopping discharges and a low proportion of overtopping waves (Pow). Existing formulas to estimate Pow and maximum individual wave overtopping volume are usually based on tests with high Pow; this study is focused on mound breakwaters subjected to Pow < 0.2. The performance of the 2-parameter Weibull and Exponential distributions is examined in order to describe individual wave overtopping volumes of mound breakwaters in non-breaking wave conditions. A new methodology is applied to 164 small-scale 2D physical tests to identify the number of overtopping waves, and the corresponding individual wave overtopping volumes. Utility functions are used to consider the relative relevance of the observed data: in this study, a quadratic utility function depending on all the individual wave overtopping volumes and step utility functions with 10%, 30% and 50% of the highest volumes are used to fit the Weibull and Exponential distributions. In this study, a new estimator of Pow is proposed to improve the predictions required to estimate the maximum individual wave overtopping volume. Existing estimators of Pow underpredict the largest values of Pow measured in the physical tests. The parameters fitted to the Weibull and Exponential distributions using the quadratic utility function provide estimations of the dimensionless maximum individual wave overtopping volume with relative mean squared errors rMSE = 10.4% and 10.6%, respectively. When CLASH Neural Network-estimated mean overtopping rates are used to predict the maximum individual wave overtopping with the quadratic utility function, the 2-parameter Weibull and Exponential distributions provide rMSE = 31.6% and rMSE = 33.3%, respectively. The new estimators proposed in this study improve the predictions of Pow and maximum individual wave overtopping volumes on conventional mound breakwaters designed for low wave overtopping rates.