Park, S.-H.; Choi, J.-G., and Cho, Y.-J., 2021. Development of a probability model for the transmission coefficient of Low Crested Breakwaters (LCB). In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 484–488. Coconut Creek (Florida), ISSN 0749-0208.
Low Crested Breakwaters (LCB) have been the most preferred structural type among many countermeasures against beach erosion. The extent of shore protection by LCB depends on transmittance coefficients, which are random due to the variability inherent in the marine environment. However, a probability model for transmittance coefficients is hard to find in the literature, indispensable for the reliability-based optimal design of LCB. In this rationale, first, a probability model of transmission coefficients is empirically developed. In doing so, transmittance characteristics of LCB were examined using the situ-wave data at the up-wave and down-wave sides of LCB at Bong-Po and Sok-Cho from 2019.8.6 to 2019.8.21 in order to identify the pertinent random variables affecting LCB transmittance. It turns out that sea wave conditions significantly affect the transmittance coefficients, and the roughness of sea wave conditions can be quantified in terms of wave height and its associated wave slope. Wave height and its associated wave slope are highly correlated in the mild sea, but they behave independently as wave heights get more enhanced. These complicated interrelations between wave height and wave slope can be described using the joint distribution of wave amplitude and its associated period by Longuet-Higgins (1983). In this rationale, we analytically derived a probability model for transmittance coefficients of LCB from the joint distribution of wave amplitude and its associated period by Longuet-Higgins (1983) and d'Angremond, van der Meer, and de Jong (1996) model using the standard technique of transformation of random variables (Papoulis, 1984). Numerical simulation shows that as sea wave conditions are getting harsh, a non-negligible probability mass shifts toward the low transmittance coefficients due to long waves appearing in the random wave field by sub-harmonic resonance wave-wave interaction, which is well-known after the studies of Hasselmann(1967) and Phillips(1980) on the development of wind waves. It was also shown that the probability mass shift toward the low transmission coefficients is accompanied by the probability mass shift toward higher transmission coefficients, which also comply with the studies of Hasselmann (1967) and Phillips (1980).