Abstract
Most physical model tests carried out to quantify wave overtopping are conducted using a wave energy spectrum, which is then used to generate a free surface wave time series at the wave paddle. This method means that an infinite number of time series can be generated, but, due to the expense of running physical models, often only a single time series is considered. The aim of this work is to investigate the variation in the main overtopping measures when multiple wave times series generated from the same spectrum are used. Physical model tests in a flume measuring 15 m (length) by 0.23 m (width) with an operating depth up to 0.22 m were carried out using a stochastic approach on two types of structures (a smooth slope and a vertical wall), and a variety of wave conditions. Results show variation of overtopping discharge, computed by normalising the range of the discharges at a certain wave condition with the maximum value of the discharge in the range up to 10 % , when the same wave time series is used, but this range increases to 75 % when different time series are used. This variation is found to be of a similar magnitude to both the one found with similar experiments looking at the phenomena in numerical models, and that specified by the confidence bounds in empirical methods.
Highlights
The coastal region has significant global economic and societal importance, leading to the extensive construction of coastal structures to defend these areas from the effects of wave action and currents
Subsequent work, using numerical models, by [25,26] carried out an extensive Monte Carlo analysis, and concluded that higher uncertainty was observed in both the overtopping discharge and the individual overtopping volumes when the probability of overtopping was less than 5%, with uncertainty decreasing as overtopping increased
There is a larger increase in σ observed at a lower value of R∗ for the vertical wall; this is due to the lower overtopping discharges, and subsequent greater variability experienced by the vertical wall than the smooth slope for the same wave conditions and crest height
Summary
The coastal region has significant global economic and societal importance, leading to the extensive construction of coastal structures to defend these areas from the effects of wave action and currents. We are interested in one particular aspect that has recently gained attention, the quantification of the uncertainty induced by the generation of individual sequences of waves from the same energy density spectrum This uncertainty occurs due to the fact that from every energy spectrum an infinite number of different waves sequences can be generated, by changing the initial seeding of the random phase distribution. Evidence that this plays an important role in the variability of results of numerical models was first given in studies by [23] for the prediction of run-up and [24] for overtopping which used a limited number of tests and waves, but showed that the parameters of overtopping can vary significantly with the seeding used. Work by [27] investigated a similar problem in the study of breakwater failure due to wave–structure interaction
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