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

Abstract

The crest elevation of mound breakwaters is usually designed considering a tolerable mean wave overtopping discharge. However, pedestrian safety, characterized by the overtopping layer thickness (OLT) and the overtopping flow velocity (OFV), is becoming more relevant due to the reduction of the crest freeboards of coastal structures. Studies in the literature focusing on OLT and OFV do not consider the bottom slope effect, even if it has a remarkable impact on mound breakwater design under depth-limited breaking wave conditions. Therefore, this research focuses on the influence of the bottom slope on OLT and OFV exceeded by 2% of incoming waves, hc,2% and uc,2%. A total of 235 2D physical tests were conducted on conventional mound breakwaters with a single-layer Cubipod® and double-layer rock and cube armors with 2% and 4% bottom slopes. Neural networks were used to determine the optimum point to estimate wave characteristics for hc,2% and uc,2% calculation; that point was located at a distance from the model toe of three times the water depth at the toe (hs) of the structure. The influence of the bottom slope is studied using trained neural networks with fixed wave conditions in the wave generation zone; hc,2% slightly decreases and uc,2% increases as the gradient of the bottom slope increases.

Individual wave overtopping volumes on mound breakwaters in breaking wave conditions and gentle sea bottoms

“…As exposed in Section 1, in depth-limited breaking wave conditions, the optimum point where wave characteristics are estimated is relevant for design and needs to be determined (Mares-Nasarre et al, 2020). Thus, G1 and G2 were calibrated considering wave characteristics at several distances from the structure toe in Q*= q/(g Hm0 T01).…”

“…Herrera et al (2017) pointed out that bottom slope directly influences mound breakwater design; the optimum point where wave characteristics are estimated needs to be determined when in depth-limited breaking wave conditions. Mares-Nasarre et al (2020) found a significant effect of bottom slope on the overtopping layer thickness (hc) and the overtopping flow velocity (uc). Mares-Nasarre et al (2020) also determined that the optimum point to estimate wave characteristics to calculate hc and uc was located at a distance of 3 times the water depth from the toe of the structure.…”

“…Mares-Nasarre et al (2020) found a significant effect of bottom slope on the overtopping layer thickness (hc) and the overtopping flow velocity (uc). Mares-Nasarre et al (2020) also determined that the optimum point to estimate wave characteristics to calculate hc and uc was located at a distance of 3 times the water depth from the toe of the structure. However, the influence of the bottom slope on Vmax has not yet been analyzed.…”

Armor Damage of Overtopped Mound Breakwaters in Depth-Limited Breaking Wave Conditions

“…It should be noted that depth-induced wave breaking takes place in the model zone, so the existing methods to separate incident and reflected waves are not reliable. Two extra wave gauges were placed in the middle of the breakwater crest (S10) and behind the breakwater model (S11); S10 was used to analyze the overtopping layer thickness [31] whereas S11 was used to detect possible phenomena of water piling-up. Overtopping discharges were recorded using a weighting system located behind the model [32].…”

Explicit Neural Network-derived formula for overtopping flow on mound breakwaters in depth-limited breaking wave conditions

“…Several predictors exist for OLT and OFV on dike crests (Schüttrumpf and Van Gent, 2003;van Bergeijk et al, 2019). However, few studies are focused on OLT and OFV on mound breakwater crests (Mares-Nasarre et al, 2020a. Mares-Nasarre et al (2020a) demonstrated that the bottom slope (m) is a significant variable for estimating OLT and OFV, but m is not considered as an explanatory variable in the estimators found in the literature.…”