Formula of Overtopping Discharge of Vertical Seawall with A Form Similar to Solitary Wave Function

An empirical formula to predict overtopping discharge of vertical wall is presented, in which an expression similar to the solitary wave function is proposed to describe the rule of the influence of relative water depth. The formula is derived from performing an investigation to the well-known overtopping graphs of Goda, and for the sake of interest, the process of the derivation is detailed. To make clear the formula's performance, relevant test datasets in the CLASH database are extracted to examine the error levels of the formula. As a result, an overall good agreement has been found between the predictions of the formula and the extracted datasets in a wide range outside the extreme shallow region, i.e., the range of relative water depth smaller than 0.6, in which the water depth near the wall is so shallow that nearly all the incoming waves have been broken before reaching the wall.