Rock Armour Slope Stability under Wave Attack in Shallow Water

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 formulae 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 formulae 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 deep < 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 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 deep < 1.5no systematic trend with the energy period is observed anymore and constant combined stability numbers are given for guidance in preliminary design.