Distribution of individual wave overtopping volumes at rubble mound seawalls

For a safe design of a rubble mound seawall, overtopping characteristics such as the mean overtopping discharge (q) and the maximum individual overtopping volume (Vmax) should be limited. Unlike q, the estimation of Vmax is more complex and requires a wave-by-wave analysis of overtopping as well as a statistical analysis. The present study contributes to the knowledge of the distribution of individual overtopping volumes and the estimation of Vmax at rubble mound seawalls. A total of 135, small-scale 2D physical model tests were conducted across a practical range of crest freeboards and considered the slopes of 1:1.5 and 1:2. The well-known 2-parameter Weibull and Exponential distributions were first fitted to the experimental data to estimate the Vmax. Different approaches to sample the observed distribution of wave-by-wave overtopping volumes were evaluated including a threshold method using the top 10%, 30%, and 50% of individual overtopping volumes, and a method that applies a greater weighting to the larger events. For both Weibull and Exponential distributions, the weighted method was found to be the best one providing a 23% and 17% decrease in scatter index (SI) values compared to the best of existing methods. To facilitate the estimation of Vmax for design purposes, a simple empirical formula was developed as a function of the dimensionless mean overtopping discharge (q*) and the number of overtopping waves (Now). This formula with SI = 37% outperformed the distribution-based methods as well as the best of existing formulae for Vmax. In the case of the normalised bias (NBIAS), the distribution methods underestimated Vmax by −21% (Weibull) and −31% (Exponential) whereas the new formula yielded NBIAS = −6%.