The application of spectral analysis in the determination of wave loads on vertical breakwaters

Abstract

Vertical breakwaters are used in the design of harbours to create a protective area. This protective area can be an approach channel or the harbour itself. Because of large new projects, such as Maasvlakte 11 in the Netherlands and the increasing sizes of ships, many harbours have to be placed in deep water. Deep water requires higher breakwaters. For many years, in Europe the only breakwaters built were rubble mound breakwaters. They consists of rock material and have a more or less trapezoidal shape. With increasing depth this type of breakwaters becomes expensive and the vertical breakwaters seem to be the better alternative. To create new and better design tools for vertical breakwaters a research program has been initiated with financial support of the European Union. European research institutes and universities are doing extensive research in this program. This report presents the results of the research of an alternative method to determine horizontal wave forces on a vertical breakwater. Due to the horizontal wave forces many failure mechanisms, such as sliding and overturning, can occur. The alternative method, presented in this report, calculates with a given wave spectrum the wave force spectrum. A wave spectrum describes a wave field, by giving for a range of frequencies the contribution of each frequency (actually a regular wave with that frequency) to the total energy of the wave field. The waves that are subject of this study are long-crested, non-breaking waves, that approach the breakwater at a right angle. The wave spectrum is transferred into the wave force spectrum by multiplication with the so called transfer function. For this calculation it is assumed that there exists a linear relation between the incoming waves and the wave forces on the breakwater. This, however, is not entirely true. The transfer function is determined by calculating for a large number of regular waves with various periods the wave forces on the breakwater. The choice of the height for the regular waves poses difficulties which have been given extensive research. The pressure diagram on the front wall of the vertical breakwater at a wave crest can be divided into two parts: one part from the wave crest to mean water level and one part from mean water level to the bottom or, often, the top of the berm. From the latter part a linear behaviour can be recognised, however, the former part introduces a non-linearity. There remains a dependency on the size of the height for the regular waves. Therefore in the determination of the transfer function this wave height cannot be chosen arbitrarily. It can be stated that for a low wave height water depth ratio the non-linearity is small and the transfer function can be used easily, however for a large ratio the influence of the size of the chosen wave height cannot be neglected. Therefore two ways of calculating the transfer function are introduced in this study. One is a constant height for all regular waves in the determination of the transfer function. The other way takes the wave steepness constant over the frequency range. Some features of the latter way are that for low frequencies the values for the transfer function become unrealistically high and that for higher frequencies the influence of the non-linearity decreases. To study the transfer function and its application many comparisons have been made with results of model tests and with the General Wave Spectrum Model (GWSM). The model test are tests performed in the design of the Eastern Scheldt Storm Surge Barrier and model tests with caissons, both performed at Delft Hydraulics. The General Wave Spectrum Model enables the generation of a wave spectrum by chosing parameters (e.g. for energy, peak frequency and left and right flank). The generated wave spectrum allows to make calculations with different types of wave spectra. The model tests with caissons cannot give conclusive results to confirm the method of the transfer function. The tests give results for the transfer function that match the theoretical transfer function. The course of the measured transfer function seems to be best described by the transfer function with constant wave steepness. However the choice of which constant wave height or which wave steepness to use remains very difficult. The comparison with the model tests performed in the design of the Eastern Scheldt Storm Surge Barrier show that, also, the transfer function calculated with the constant wave steepness follows the course of the model test results better in a large frequency range. The values of the test results and the theoretical results deviate a lot, but that is probably due to the schematisation made for the theoretical results. Another comparison is made with the use of the GWSM. Beside the influence of the non-linearity of the transfer functions the influence of the shape of the spectrum is studied. The reason for this is the fact that other methods of determining the wave force neglect the influence of the shape of the wave spectrum, which appears to be not correct. Calculations with double-peaked wave spectra and wave spectra with varying steepness of the right flank prove the influence on the wave force. A method, that is widely used to determine the wave forces on vertical breakwaters, is the method of Goda. It is a method that includes both breaking and non-breaking waves. The calculation of the wave force is made by using a representative wave height and period. Various comparisons have been made between the method of the transfer function and Goda's method. The method of the transfer function takes the influence of the shape of the wave spectrum into account, opposite to the method of Goda. From comparative calculations with the method of Goda it shows that the influence of the shape of the wave spectrum is of importance. When more energy of a wave spectrum can be found at higher frequencies, because of a second, high frequency, peak or because of a less steep right flank, Goda gives relative high wave forces.