An Approximation to the Statistical Characteristics of Wind Waves in Front and from the Toe of the Structure to the Toe of the Crown of Nonovertopped Breakwaters

Abstract

According to the main recommendations and technical criteria along the world, the design project of a breakwater must address the verification of the different failure modes that can affect the breakwater stability. This research focuses on the estimation of the statistical characteristics of the wind waves interacting with different breakwater types and their evolution from the toe of the structure to the toe of the crown. This knowledge is essential to calculate the reliability of the structure in its useful life. Partial standing wave patterns are likely to occur in front and along the section of the breakwater depending on their typology. Based on Rice's theory of envelope amplitude, we present an approximate solution of the total wave height distribution in front of the breakwater. The experimental results in 2D confirmed that the incident, the reflected and the total wave height in front of the breakwater followed a Rayleigh distribution in which the parameter is the root-mean-square total wave height. Its value depends on the modulus and phase of the reflection coefficient. The probability density function of the total wave height evolves from a Rayleigh to a Weibull distribution, whose scale and shape parameters vary from the toe to the crown of the structure, and depend on the breakwater type, the relative grain diameter, and the relative water depth. The largest deviation from the Rayleigh distribution occurs at the toe of the crown. These findings are weakly dependent on the incident wave steepness, and are valid for narrow-banded incident wave trains, impinging perpendicularly on nonovertopped breakwaters with a steep frontface, which ensures the rapid evolution of the wave train. Then, each mode of failure that might occur in the breakwater section can be formally checked against the same incident wave height, but verified (calculated) with the actual wave height, locally transformed by the specific typology.