New Physical Insights and Design Formulas on Wave Overtopping at Sloping and Vertical Structures

Mean wave overtopping discharge is a key design parameter for many coastal structures, typically designed to limit overtopping discharge to below a chosen admissible value. Dutch, German, and British design guidance from the 1990s was updated using results of research projects supported by the European Commission, and subsequently unified with the publication of the European Manual for the Assessment of Wave Overtopping, or EurOtop [EurOtop. (2007). European Manual for the Assessment of Wave Overtopping, T. Pullen, et al., eds.], now used all over the world. This paper explores five technical issues that were not well covered in the unified manual. (1) For sloping structures, overtopping at low and zero freeboard conditions: new analysis brings together the conventional exponential formulas with the few reliable datasets including very low and zero freeboard. In doing so, early Dutch work from the 1970s was revisited. Weibull-type formulas are proposed, describing wave overtopping at slopes for the whole range $R_c/H_{m0}\ge 0$. (2) For vertical walls, the manual distinguishes overtopping responses depending upon whether wave breaking occurs, with nonbreaking and breaking conditions described by exponential and power law formulas, respectively. Here, the governing equations are manipulated in such a way as to reunify the methods, enabling direct and intuitive comparison. (3) For overtopping at vertical walls under nonimpulsive conditions, early Italian/Dutch and British formulas of the 1990s diverge significantly for higher freeboards. This paper explores why these two reliable studies arrived at two such different predictors. By reanalysis of the original datasets augmented by further data drawn from the international database on wave overtopping, a physical distinction based on the nature of the foreshore is proposed and tested. (4) The prediction method for overtopping at composite vertical structures is reworked to enable the influence of the mound to be apparent and to align with plain vertical wall formulas for smaller mounds. A new scheme is proposed that treats composite structures via a small adjustment to the new vertical wall approach proposed earlier. (5) There is vast literature on overtopping response at mildly sloping structures and substantial literature on vertical walls, but in the intervening range (approximately $1V:1.5H$ to $5V:1H$), there is a paucity of reported tests. Recently published Belgian data have enabled the development of a continuous prediction scheme spanning mild slopes, steep slopes, and vertical structures without foreshore.