Conclusion

Although much attention has been given to the statistical formulations for extreme crest distribution in the context of the air gap problem for offshore platforms and for wave overtopping of coastal structures in shallow water, relatively little work has been done to investigate the wave overtopping for a fixed deck. In this paper, equations typically used to describe extreme crest ampitude distributions were extended to formulate a statistical model which would describe the exceedance probability for the normalized volume of water overtopping a fixed deck under extreme (nonlinear) wave conditions. The model relies on only a few parameters, notably the deck height, the root-mean-square of the incident waves, and a Weibull parameter representing the nonlinearity of the wave condition. Several assumptions were used to simplify the formulation. The most significant of these are the assumption of narrow banded spectra, locally sinusoidal wave profile, thin deck, and low deck.

To check these assumptions and to validate the statistical model, comparisons were made with small-scale laboratory measurements in a narrow (two-dimensional) wave flume. Typical JONSWAP wave spectra were used with over 3000 incident waves for each case. Measurements included the free surface variations seaward of the deck and the overtopping rate on the leading edge of the deck. The overtopping volume was normalized by $Q_{rms}$, $\eta_{rms}$ and $T_{1/3}$ from the total wave field measured seaward of the deck and were similar for both cases. The comparisons of the statistical model and measurements showed that

1. The Weibull distribution gives a better agreement of the exceedance probability for crest amplitudes seaward of the deck compared to the Rayleigh theory, and that the Weibull distribution gives a better agreement on the deck for lower deck heights (Fig. 10).
2. The modified Rayleigh overtopping distribution shows fair agreement with the experimental data for small values of $Q$, and the modified Weibull overtopping distribution gives excellent agreement for large values of $Q$ (Fig. 13).

Additional quantitative verification of the statistical model and extension of the theory to overtopping rate will be studied in the future. Upon further refinement, the model be useful to predict and understand the overtopping on the deck for engineering use.