Conventionally, allowable mean overtopping discharge is used as a design criterion for coastal structures. The mean overtopping discharge needs to be limited to ensure structural stability as well as the safety of people, vehicles, and properties behind the structure. Nowadays, limits for the maximum individual overtopping volumes are also specified in the design manuals, which requires the study of wave overtopping in wave-by-wave form. In some cases, in order to achieve more reliable safety for pedestrians and vehicles or to assess the stability of the inner slope, the maximum velocity and thickness of the overtopping flow need to be considered as well. The present paper aims to review the basic concepts of the individual wave overtopping such as the estimation of the probability of overtopping and the statistical methods to study the distribution of individual overtopping volumes. The temporal evolutions of the overtopping flow thickness / velocity along with the calculation of the overtopping discharge are discussed. Moreover, since the continuous recording of parameters is required for the study of individual wave overtopping, the most common experimental measurement and data analysis techniques with an emphasis on their advantages and limitations are discussed.@en

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%.@en

During storms, ensuring the protection of people, vehicles and infrastructure on the crest of coastal structures from wave overtopping hazards is crucial. The thickness of the wave overtopping layer is a key variable used for assessing safety and maintaining a secure design. Traditionally, this parameter is associated with the height difference between the fictitious wave run-up level exceeded by 2% of waves and the crest freeboard of coastal structures. This study aims to investigate the wave overtopping layer thickness on the crest of rubble mound seawalls. To achieve this, a series of 125 small-scale 2D physical model tests were conducted on a two-layer rubble mound seawall with an impermeable core and slopes of 1:1.5 and 1:2. The obtained results indicated that the existing empirical formulas, originally developed for dikes, underestimate the overtopping layer thickness on the studied seawall. Therefore, modifications were made to the formulas found in the literature specifically tailored for rubble mound seawalls. The newly proposed formulas for estimating overtopping layer thickness at both the seaward edge and the middle of the crest showed improvements compared to the existing formulas.@en

Estimation of the mean overtopping discharge is a major task in the design and assessment of the crest level of rubble mound structures such as breakwaters and seawalls. The tolerable mean overtopping rates are given based on the associated risk and wave characteristics. Several empirical formulas have been developed for the prediction of mean overtopping discharge at coastal structures. These formulas can be applied to a wide variety of coastal structures, but have limited accuracy and/or do not reflect the physics of the phenomena. The main aim of this study is to overcome these issues for rubble mound structures by considering the physics of the process in the formula development. To achieve this, first, the references used in the extended CLASH database (also called the EurOtop-2018 database), were scrutinized, the reported wave characteristics were corrected (if required) and the rubble mound structure subset was extended using a recent study. Then noting that overtopping occurs when the wave runup exceeds the freeboard, the difference between the maximum wave runup and crest freeboard was considered as the governing parameter in the mean overtopping discharge formula. In the developed formula, a semi-empirical relationship between the mean overtopping and wave runup has been established. The performances of the developed formulas and existing ones were evaluated both qualitatively and quantitively. Accuracy metrics such as RMSE and BIAS indicated the superiority of the developed simple formula. Finally, a design formula to consider uncertainty and some guidelines are provided for practitioners.@en

Seawalls play a significant role in protecting coastal areas against wave attack and flooding. The accurate estimation of wave overtopping at seawalls is therefore crucial to adequately protect people and infrastructure in these regions. In this study, the mean wave overtopping rate at rubble mound seawalls was investigated through 140 small-scale physical model tests which adds to the limited existing data for this structure type in the extended CLASH database called EurOtop (2018). The combined dataset is used to evaluate the prediction skill of existing empirical formulae and to identify their limitations. The role of wave steepness on the mean overtopping rate is closely examined as it has not yet been considered properly in the EurOtop (2018) formulation. A new formula was derived using dimensional analysis and physical justifications of the overtopping phenomenon. The formula was found to provide a 40% decrease in RMSE in comparison to that of the EurOtop (2018). In addition, the new formula yields a BIAS ≈0, a significant improvement compared to −0.38 (non-dimensional discharge) of the EurOtop (2018) formula. The proposed formula has a simple form where non-dimensional overtopping discharge depends only on the relative crest freeboard and wave steepness, which were found to be the most important variables based on a sensitivity analysis.@en