A new average wave overtopping prediction formula with improved accuracy for smooth steep low-crested structures
Introduction
Wave overtopping is a key process in the design of sea defence structures. The overtopping events occurring during wave attack pose a threat to human lives, damage of property and infrastructure, and economic losses. A good knowledge of the wave overtopping process is necessary to improve the safety of sea defence structures. A type of sea defence structures which only recently became subject of investigation is the steep low-crested structures. This type refers to structures with slope angles from mild to vertical () and relative crest freeboards from small to zero ().
In a climate change context with sea levels rising globally and an increased storminess (i.e., more frequent and severe storms), the existing sea defence structures are becoming low-crested structures. Therefore, improved knowledge regarding the overtopping process is important to assess the safety of the existing coastal structures and to update the existing design guidelines. The steep and very steep structures are interesting to study as a limit case with vertical structures, which have been used widely as defence structures.
The steep low-crested structures are not only of importance as sea defence structures. The overtopping wave energy converter (OWEC) is a type of wave energy device that captures the overtopped water over a structure in a reservoir. The reservoir is emptied by a set of low-head turbines, generating electricity. Higher overtopping rates result in greater energy generation potential. The steep low-crested structures maximize the overtopping rates and therefore are of interest for OWECS applications (Gallach-Sánchez et al., 2018).
A knowledge gap of wave overtopping for steep low-crested structures was identified by Victor and Troch (2012a), which they partially filled by performing 2D physical model tests at Ghent University (Belgium), obtaining the so-called UG10 dataset (Victor and Troch, 2012b). The UG10 dataset includes overtopping data for slope angles , and relative crest freeboards . However, this dataset did not include tests for very steep slopes () and vertical structures (), combined with very small relative crest freeboards () and zero freeboards (). Based on the UG10 dataset and data available in the CLASH database (De Rouck et al., 2009), two average overtopping prediction formulae were obtained by Victor and Troch (2012a) and Van der Meer and Bruce (2014), the latter being included in the latest update of the EurOtop (2018) manual. The accuracy of these prediction formulae is good for the range of the UG10 dataset. However, an improvement of the prediction accuracy is still possible (Gallach-Sánchez et al., 2018) for very steep slopes to vertical structures with very small to zero relative crest freeboards, which is further proved in the present paper.
The aim of this research is to obtain a new average overtopping prediction formula that improves the accuracy of existing prediction formulae for the range of steep low-crested structures, especially the Van der Meer and Bruce (2014) prediction as it is the reference prediction in the EurOtop (2018) manual. To achieve this aim, 2D physical model tests were performed at Ghent University (Belgium), obtaining 939 overtopping tests resulting in the so-called UG13, UG14 and UG15 datasets. These tests were analysed and a new average overtopping prediction formula is obtained and presented in this paper. This new prediction formula is fitted through the new datasets and through relevant parts of the CLASH database (De Rouck et al., 2009). This paper is based on the outcomes of the doctoral research by Gallach-Sánchez (2018).
The definition ranges of slope angle and relative crest freeboard that are used in this paper are shown in Table 1 and Table 2, respectively.
Section 2 presents a literature review of the overtopping for steep low-crested structures including the existing prediction formulae valid for this type of structures. Section 3 explains the experimental setup and the test programme of the 2D physical model tests performed at Ghent University. Section 4 compares the new Ghent University overtopping data with the existing overtopping prediction formula for steep low-crested structures. Section 5 proposes a new average overtopping prediction formula for steep low-crested structures based on new and existing overtopping data. Finally, Section 6 presents the conclusions of this research.
Section snippets
Overview of average overtopping prediction formulae
While the study of the wave overtopping process for common types of coastal structures (i.e., mild slopes with large relative freeboards) is widely covered in the scientific literature, for some structural types like steep low-crested structures there are knowledge gaps to be addressed. A selection of the most relevant average wave overtopping prediction formulae are reviewed in this section.
Experimental setup and test programme
Three new wave overtopping datasets—UG13, UG14 and UG15—with a total of 939 tests were obtained to improve the knowledge of wave overtopping for steep low-crested structures. In this section, an overview of the experimental setup used in the model tests and a description of the test programme are presented.
Data analysis of average overtopping rates for steep low-crested structures
In this section, the average overtopping data of the UG13, UG14 and UG15 datasets are compared to the existing average overtopping prediction formulae for steep low-crested structures referred in Section 2: Victor and Troch (2012a) (Eq. (2)) and Van der Meer and Bruce (2014) (Eq. (3)).
New average overtopping prediction formula for steep low-crested structures
As stated in Section 4.2, it is possible to propose a new average overtopping prediction formula that improves the accuracy of the existing ones by including the new overtopping datasets UG13, UG14 and UG15 in the fitting of the prediction. In particular, a higher prediction accuracy is wanted for:
- i.
Vertical structures ();
- ii.
Very steep slopes (); and
- iii.
Very small and zero relative freeboards ().
The new prediction should maintain the accuracy achieved by Victor and Troch
Conclusions
A new average overtopping prediction formulae (Eq. (15)) for steep low-crested structures under non-breaking conditions is obtained by fitting a Weibull-type formula through selected subsets of the CLASH database, the existing UG10 datasets, and the new UG13, UG14 and UG15 datasets obtained at Ghent University. The range of application of this formula is for structures with slope angles and relative crest freeboards under non-breaking wave conditions. Only smooth and
Credit author statement
David Gallach-Sánchez: Conceptualization, Methodology, Formal analysis, Investigation, Data curation, Writing - original draft, Visualization. Peter Troch: Conceptualization, Methodology, Writing - review & editing, Supervision, Project administration. Andreas Kortenhaus: Conceptualization, Methodology, Writing - review & editing, Supervision.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
We thank the technicians at the Department of Civil Engineering of Ghent University for their help during the testing campaigns, and the master thesis students involved in the research. We also thank the anonymous reviewers of the paper for their very detailed review and constructive comments.
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