Probability distribution of individual wave overtopping volumes for smooth impermeable steep slopes with low crest freeboards

Abstract

Several studies showed that the probability distribution of the wave-by-wave (individual) overtopping volumes of traditional sea defense structures is described by a Weibull distribution with a shape factor b=0.75. Those structures typically feature relatively large crest freeboards. For the particular design applications of overtopping wave energy converters and smooth dikes in severe storm conditions, knowledge is required on the probability distribution of the individual overtopping volumes of smooth structures with relatively low crest freeboards. This study contributes to a better knowledge on that distribution by analyzing the individual overtopping volumes obtained from new experiments on smooth structures with relatively small crest freeboards (0.10<Rc/Hm0<1.69) and relatively steep slopes (0.36<cotα<2.75). Furthermore, the characteristics of the corresponding probability distributions are compared to the existing formulations for traditional sea defense structures and submerged dikes or levees. The probability distribution of the individual overtopping volumes for the tested structures also appears to be well described by a Weibull distribution. However, the shape factor b and probability of overtopping Pow (related to the scale factor of the Weibull distribution) are both dependent on the relative crest freeboard and the slope angle. Both b and Pow increase for decreasing relative crest freeboard: b reaches values up to 1.5, while Pow approaches the value of 1.0 (all waves overtop the crest of the structure). Moreover, both the shape factor and probability of overtopping decrease for increasing slope angle. Therefore, two new prediction formulae are proposed for b and Pow based on the new experiments. Finally, based on the relation between the relative 2% run-up height Ru2%/Hm0 and the probability of overtopping Pow, a new prediction formula for Ru2%/Hm0 is proposed, bridging the gap between steep slopes and vertical walls adjacent to relatively deep water.