Wave Forces on Piling for Narrow-Band Spectra

The statistical distribution of peak forces for irregular linear ocean waves having a narrow-band spectrum is an exponential-type function, the form of which depends on the average relative balance between the drag and the inertial forces. The distribution is a function of two parameters determined by the drag and inertial coefficients and the physical dimensions characterizing the pile and the spectrum. Formulas and tables are developed for the first through the fourth moments, the median, the mode, the upper fractile, and the average of the highest p-th fraction of the peak forces. The method of moments and the method of maximum likelihood each provide procedures for estimating the parameters from the data. In addition, a graphical method consisting of plotting one minus the empirical distribution function on semi-log paper versus the peak force data and again versus the square of the data is developed. The theory is compared with wave forces measured near Davenport, California, in 50-ft water depths.