For the design of the breakwater for the protection of Barra do Dande Ocean Terminal in Angola, a rock armor rubble mound structure was the obvious solution due to the proximity of a suitable quarry. For this type of breakwater there is a close relationship between damage resistance in terms of armor unit size and the required maintenance. Designing for small probability of damage generally infers high construction costs but lower maintenance costs. Breakwater roundheads are generally the most critical part of rubble mound breakwaters. In search of minimum lifetime costs, a stable low-cost solution for the breakwater head was investigated in terms of a three-layer rock armor solution applied in the most critical sectors of the roundhead. The aim was to avoid the production wise and construction wise costly large rock sizes while still maintaining a low probability of repairs. The three-layer rock armor solution applied in the critical roundhead sectors was studied in physical model tests at the Aalborg University Ocean and Coastal Engineering Laboratory, Denmark. This solution means that smaller rocks can be applied as failure occurs at significantly higher damage levels. The three-layer solution was a viable technical and economic solution for the port construction and operation.
The typical approach for generating nonlinear waves in physical models involves employing first- or second-order wave theory, requiring a large water depth at the wavemaker. When the prototype bathymetry shows a gentle slope, a large facility is required. However, practical constraints often make this unfeasible, leading to the use of steep transition slopes to obtain sufficient water depth at the generator. Incorporating a transition slope may generate unwanted free waves beyond the transition point, significantly impacting the wave parameters. The presence of these free waves causes the response of the tested structure to deviate from that found in the prototype. This paper offers guidelines for using transition slopes effectively while avoiding the generation of unwanted free waves after the transition point.
The stability formula for rock slopes under wave attack was revised in Van der Meer (2021), replacing the mean period Tm with the spectral period Tm-1.0. This rewritten formula closely resembles the Modified Van der Meer formula as in the Rock Manual (2007), with differences primarily in coefficients and the use of H2% in the Rock Manual and H1/3 in Van der Meer (2021).
The wave characteristics change significantly in shallow water due to nonlinearities and wave breaking. The result is a significant change in the wave height and period, especially when severe breaking occurs and infragravity waves become significant or even dominate the spectrum. This may lead to very large breaker parameters. At a certain point, existing stability formulas may thus become inaccurate, both the original and the Modified formula for shallow water. The primary objective of this paper is to identify when and where shallow water stability results deviate from established formulas and how these deviations can be described.
The analysis involves an in-depth examination of datasets from Van Gent et al. (2003), Eldrup (2019), and other relevant data to increase the understanding of waves in shallow water and how they affect rock slope stability.
The use of H2% in the Modified Van der Meer formula gives some difficulties as no reliable prediction method is available for that parameter when the relative depth is small, h/Hm0 depth < 1.5. The Van der Meer (2021) formula applies the significant wave height, and it may be chosen as either Hm0 or H1/3. These two parameters are almost identical in deep water for which the formula was derived, but significant differences may occur in shallow water. The application of the Van der Meer formula in shallow water indicates a preference for the use of Hm0 as it describes nonlinear waves better. The main conclusion is that the Van der Meer (2021) formula seems valid much further into the shallow water region than what the Rock Manual (2007) recommends and at least to relative water depths of h/Hm0 deep > 1.5. For shallow water with h/Hm0 depth < 1.5 no systematic trend with the energy period is observed anymore and constant combined stability numbers are given for guidance in preliminary design.
Monopiles are often the preferred foundation concept for an offshore wind turbine. The interaction between extreme waves and the large diameter monopile will in some cases result in a vertical jet of water uprush on the monopile (i.e., wave run-up) which subsequently may lead to large slamming loads on monopile appurtenances like the external working platform.
Extreme wave run-up interaction with an external working platform is often an area of concern during the design phase of an offshore wind project as an overly conservative assessment of the run-up loads may lead to unneeded costs in material and an increased project carbon footprint. An insufficient assessment of the run-up loads may lead to structural failure of the appurtenances and subsequent costly maintenance and repair works, further exacerbated by possibly difficult access to the damaged platform.
The practical process in the assessment of wave run-up on monopiles and associated loads on appurtenances can be a challenge to the designer due to lack of guidance on this topic in governing standards. The designer may then have to rely on several sources of available literature and must assess and include the effect of associated uncertainties like: Adjustment to site specific environmental conditions, unclear or unconcise terminology in the literature, lack of model test results representing the actual geometry and limited knowledge of spatial and temporal run-up load distribution on the appurtenances.
The aim of the present paper is to describe a complete methodology for assessment of wave run-up on monopiles and associated loads on appurtenances. The methodology, which will serve as a practical guide, is based on a collection of existing methods with new analysis to consider the pressure distribution on modern asymmetric grated platforms. This was based on experiences gained and challenges encountered during a detail design project of a monopile foundation for an offshore wind turbine in extreme environmental conditions. The sensitivity of the run-up assessment related to the design input (water depth, wave height and period, associated water level and current conditions) is discussed by considering a matrix with various environmental input combinations representing extreme environmental conditions.
The influence of directional spreading of waves is significant for wave-induced loads, wave breaking and nonlinearity of the waves. For physical model testing performed at test facilities such as the Ocean and Coastal Engineering Laboratory at Aalborg University, it is crucial to validate if the test conditions match the target sea states by measurement and analysis of the generated directional wave field. Most of the existing methods assume a double summation sea state to be present which is valid in the prototype. However, waves in the laboratory are usually generated by single summation. The current paper presents a method to analyze short-crested waves generated by the single summation method. Compared to similar methods oblique reflections are considered instead of only in-line reflections. The results show that the method successfully decomposes the incident and reflected wave fields in the time domain. Thus, for example the incident wave height distribution may be obtained. The sensitivity of the new method to additional reflective directions, noise, calibration errors and positional errors of the wave gauges was found small.
In hydraulic model tests, it is common practice to relate the response of the tested structure to the incident wave parameters at the toe. Estimation of the incident wave parameters at the toe is thus an essential part of the analysis of hydraulic model testing. In many cases, the design conditions at the toe are given by waves that are highly nonlinear or even depth limited. Modelling such conditions requires reproducing the prototype foreshore slope in the model. The present paper provide guidelines on the accuracy of a nonlinear reflection separation algorithm when applied to nonlinear waves over sloping foreshores. A simple methodology has been established to estimate the expected errors on the incident wave parameters.
This paper investigates the influence of a crown wall on wave overtopping on rubble mound breakwaters. Existing data is used to modify the EurOtop overtopping formula updated by Eldrup et al. (2022) to cover the influence of the crown wall. The effect of raising the wall above the armor crest (elevated wall) or lowering the wall below the armor crest (lowered wall) is investigated. A crown wall at the armor crest level is considered as the reference case. By increasing the elevation of either the armor crest or the crown wall, overtopping is reduced and by lowering either of them, overtopping increases. The influence of the crown wall height, elevated or lowered compared to the armor crest, is not considered accurately in the present design guidelines and thus corrections are suggested. For an elevated wall, a modified crest width has been defined, to better describe the presence of the armor crest in front of the wall. For the lowered wall the effective freeboard might be taken as the average of the wall and armor freeboards. The improvement compared to existing methods is significant, especially for breakwaters with a large elevated wall. The proposed modifications to the EurOtop Manual increase the range of applicability with respect to the wall configuration.
The present paper deals with overtopping prediction for berm breakwaters in line with the EurOtop methodology. The basis for the paper is the recent advances proposed for EurOtop for conventional breakwaters with respect to the influence of the wave steepness and the crest width. New model tests have been performed to investigate the applicability of these influence factors to berm breakwaters. To cover a white spot in existing data for berm breakwaters, the model tests included wave conditions with very low wave steepness. The results show that the recently developed influence factors for conventional breakwaters also improve predictions for berm breakwaters. Based on this, an additional influence factor for the dimensionless berm width is established. The berm width was in previous studies made dimensionless by the wave height, but the present study indicates that the wavelength is more appropriate.
For design validation of offshore structures and conceptualisation of wave energy converters, physical model testing performed in wave basin laboratories is often applied. In such cases, knowledge about the wave conditions is of great significance. For validation of the wave condition in such tests, different methods for estimation of the directional wave spectra may be applied. However, different assumptions are imposed in the methods and deviations here from providing uncertainties in the results. The following paper quantifies the influence of nonlinear effects on the accuracy of the estimated directional wave spectra. This is done by analysis of idealised, synthetically generated waves based on second order wave theory and secondly with simplified amplitude dispersion included. The present analyzes show that the uncertainties of the directional wave spectra are proportional to the level of nonlinearity present in the wave field.
In this paper existing guidelines to predict wave overtopping on rubble mound breakwaters and coastal structures are modified and improved with respect to the influence of the roughness and crest width. Data from recently made model tests and existing data are combined to demonstrate the need for modifying these formulations in EurOtop. A new reduction factor γcw for the crest width is established and is an improvement of the method by Besley. The influence of the roughness of the slope normally also includes an influence of the breaker parameter when it is larger than a certain limit (EurOtop suggest ξm-1.0 > 5). The present study shows that the breaker parameter is not the ideal dimensionless parameter describing the influence of the wave period for breakwaters with steep slopes, as for such structures the front slope has much less influence on the overtopping than the wave steepness. Thus slope angle and wave steepness have been uncoupled to describe the influence of the armor roughness on wave overtopping. The improvement in the overtopping prediction compared to EurOtop is significant, specifically for the new data sets that have data outside the range of the calibration data used for influence of roughness in EurOtop. The proposed improved methods enlarge the range of applicability with respect to crest width and wave steepness.