Wave overtopping at vertical and battered smooth impermeable structures

Highlights

• A simple formula set was derived to predict the mean wave overtopping rate at vertical and slightly battered, smooth, impermeable structures.

• The formula derivation and validation were performed using small-scale, large-scale and field measurements datasets, including the EurOtop database and other most recent studies.

• Accuracy metrics were used to show the superiority of the formula sets compared to the existing approaches.

• The applicability of the formula set is extended for probabilistic design purposes.

Abstract

Coastal structures play a major role in protecting people and property given the increasing threat of climate-change-induced flooding. Hence, an accurate prediction of wave overtopping for each structure is required to protect both people and properties on the structure's lee side. In this study, a formula set is developed for predicting the mean wave overtopping rate for vertical and slightly battered smooth impermeable structures. The formula set is derived using available datasets of small-scale laboratory experiments and further validated using large-scale laboratory and prototype tests and field measurements. The developed formula set for vertical structures is simple, physically sound, and contains consistent functional forms for deep and shallow water conditions, making it unique among other existing formulas. More importantly, its performance based on several accuracy metrics, is superior to existing prediction methods, including over a wide range of environmental conditions and structural characteristics. Correction factors are proposed for applications to slightly battered structures, as well as obliquely attacking waves. Finally, the formula for probabilistic design is also suggested to account for safety margins in practical applications.

Introduction

Coastal defense structures have become an inevitable part of coastline design and development. Between the many different types and intended purposes, seawalls and vertical breakwaters are among the most common defense structures. Such structures are used when there is still a chance for relatively large incoming waves to generate a significant run-up across the defense structure face, reach the top and perhaps run over the crest and fall on the lee side. Accordingly, overtopping is a critical phenomenon which involves risk for authorities and the general public (Allsop et al., 1995). Of the various types of models (i.e., analytical, empirical, numerical and physical) used to predict the wave overtopping rate for particular wave sets and structural characteristics, empirical models are the most commonly used method, as they do not encompass many of the issues found in the other methods (van der Meer et al., 2009a). For instance, the numerical modeling of this phenomenon has been found quite challenging (e.g., from a computational point of view), and hence has been used in limited studies (e.g. by Xiao et al., 2009; Vanneste et al., 2014; and Suzuki et al., 2017). Hence, most studies have used laboratory measurements to develop widely applicable empirical formulas. However, choosing an appropriate modeling scale and approach has been a challenging task in preparing a suitable dataset for further analysis (De Rouck et al., 2005). Likewise, due to the natural complexity of this phenomenon, the important underlying parameters have been a debated topic for a long time. For instance, Owen (1980) measured various parameters to investigate their importance in altering the overtopping volume. Following that, Allsop et al. (2005) presented a summary of formulas and tests for vertical, battered and composite seawalls. Their proposed formulas were later considered as the basis for many other approaches (e.g. van der Meer and Bruce, 2014; EurOtop, 2018). However, depending on the (limited) dataset used, differing degrees of generalization and ranges of applicability limit the use of a particular formula (Williams et al., 2019; Liu et al., 2020). Furthermore, the performance of the empirical formulas has not been thoroughly compared with that of soft computing models such as Zanuttigh et al. (2016).

The authors, who previously studied the wave overtopping formulas (i.e., Etemad-Shahidi et al., 2016), set out to re-visit their approaches and assumptions to update their formula using a larger dataset and improved analysis methods. The authors also noted the complexity and performance of some of the existing approaches (including Etemad-Shahidi et al., 2016) and the inevitable shortcomings of soft computing tools. In this paper, the available databases of wave overtopping measurements are introduced and discussed. Then some of the most widely used wave overtopping prediction formulas and an ANN-based approach are presented and their performances are investigated. These lead to the rationale for developing a new set of formulas, using non-dimensional parameters and physical reasoning, which offers an enhancement by more precisely predicting the mean wave overtopping rate for shallow and deep-water cases in front of a vertical or slightly battered smooth impermeable structure.