Explicit Wave-Overtopping Formula for Mound Breakwaters with Crown Walls Using CLASH Neural Network–Derived Data

Abstract

Based on the CLASH Neural Network (CLASH NN), a new 16-parameter overtopping estimator (Q6) is developed for conventional mound breakwaters with crown wall, both with and without toe berm. Q6 is built-up using the overtopping estimations given by the CLASH NN and checked using the CLASH database. Q6 is compared to other conventional overtopping formulas, and the Q6 obtained the lowest predicting errors. Q6 provides overtopping predictions similar to the CLASH NN for CMBW but using only six explanatory dimensionless variables (Rc/Hm0, Ir, Rc/h, Gc/Hm0, Ac/Rc and a toe berm variable based on Rc/h) and two reduction factors (γf and γβ).Q6 describes explicit relationships between input variables and overtopping discharge and hence it facilitates use in engineering design to identify cost-effective solutions and to quantify the influence of variations in wave and structural parameters.

Influence of Parapets on Wave Overtopping on Mound Breakwaters with Crown Walls

“…Equation (10) is proposed to estimate the dimensionless mean wave overtopping discharge when there is a parapet (rMSE = 16.4%). Very low wave overtopping rates are not reliable because of the sensitivity of the measuring instruments and data analysis in both physical and numerical modeling; similar to the criterion used in the EU-CLASH Project (2001)(2002)(2003) and other publications, such as Molines and Medina [4], only tests with logQ p > −7 were used to calibrate the parameters of Equation (10). The dashed line in Figure 10 corresponds to the linear regression of the data given by Equation (10) fitted to 38 tests.…”

“…In this study, the variance was not considered constant. Thus, following the methodology given by Molines and Medina [4], the error (e) may be considered a variable with a Gaussian distribution with zero mean and a variance estimated by Equation (11): σ (e) = −0.035logQ − 0.1.…”

“…Wave overtopping on mound breakwaters with crown walls can be decreased by (1) increasing the size of the breakwater (e.g., higher crest elevation or wider crest berm), or (2) using a parapet (recurved wall or bullnose) on the crown wall. There is extensive literature focused on mean wave-overtopping discharges on mound breakwaters, q(m 3 /s/m), with several prediction tools, such as those given by EurOtop [1,2], Van Gent et al [3], and Molines and Medina [4,5]. However, the literature background on the influence of parapets on the overtopping of mound breakwaters is limited.…”

Influence of Mild Bottom Slopes on the Overtopping Flow over Mound Breakwaters under Depth-Limited Breaking Wave Conditions

“…Since overtopping is a highly nonlinear problem, NNs have been applied in research and practical applications such as CLASH NN [25]. NNs have also been applied with fewer input variables and smaller datasets, with satisfactory results, to define explicit overtopping formulae [5], to assess the influence of armor placement on hydraulic stability [26], or to identify the most relevant variables to estimate forces on the crown wall [27]. Thus, when the assumption of linear relationships between variables is not valid, acceptable and reliable results may be obtained when applying NNs rather than conventional methods, such as the case of the influence of bottom slope on the overtopping layer thickness and overtopping flow velocity on mound breakwaters in depth-limited breaking-wave conditions (a highly nonlinear problem).…”

“…There is extensive literature on q (see EurOtop 2018 [4] and Molines and Medina [5]) and individual wave overtopping volumes (see Nørgaard et al [6] and Molines et al [7]) on mound breakwaters. Nevertheless, few studies have focused on OLT and OFV on dikes (see Schüttrumpf and Van Gent [8]) or on mound breakwaters (see Mares-Nasarre et al [9]).…”