This study presents a new explicit empirical formula to estimate wave transmission on Cubipod Homogeneous Low-Crested Structures (HLCS) under depth-limited breaking wave conditions. The formula was derived using Artificial Neural Networks (ANN) to identify and quantify the influence of nineteen candidate explanatory variables on the squared wave transmission coefficient, (Formula presented). A total of 210 two-dimensional physical model tests conducted at the Universitat Politècnica de València (Spain) were used to calibrate the formula. The dimensionless crest freeboard using the nominal diameter (R_c/D_n50) and the dimensionless incident wave height at the structure toe using the water depth (H_m0,I/h_s) were identified as the most relevant explanatory variables. A new two-variable formulation with 3 fitting-parameters was found to estimate the proportion of transmitted energy, (Formula presented), with a coefficient of determination R² = 0.89. The proposed formula was also applied to an external dataset of experimental tests on Cubipod HLCS previously reported in the literature. The results demonstrated a significantly better agreement than existing empirical formulas confirming the robustness and applicability of the new formula. The proposed formula is a reliable and easy-to-apply new tool for the preliminary design of emerged and submerged undamaged HLCS in depth-limited breaking wave conditions. The new explicit formula is particularly suited for low-crested structures aimed at combining coastal protection and ecosystem enhancement, such as artificial reefs in coral environments.

Homogeneous Low-Crested Structures (HLCS) with pre-cast concrete units are a new coastal structure to protect beaches from wave attack. HLCS are a natural based solution which can be used to restore degraded coral reefs areas where not only the coastal protection is important but also the regeneration of the ecosystem. The placement grid of HLCS plays a relevant role on their hydraulic performance affecting the wave transmission and hydraulic stability. Within the Project HOLOBREAK, 5-layer Cubipod HLCS trunks with H/V≈2:1 were tested in the wave flume of the Laboratory of Ports and Coasts (30 x 1.2 x 1.2 m) at the Universitat Politècnica de València. The 5-layer Cubipod HLCS was constructed following a triangular equilateral placement grid with porosity p[%]=50 on a 4% bottom slope. The model showed a total height around 20 cm with Cubipods with nominal diameter D_n[cm]=3.79 In total, 100 tests were carried out with four wave steepnesses (s_0p=0.01, 0.02, 0.03 and 0.04) and four crest freeboards (R_c[cm]=-3, 0, 5, 10 cm). The tests measured the layer thickness, armor stability, wave reflection and wave transmission of the structure. The wave height (H_m0) and wave period (T_p) at the toe of the structure were obtained using the SwanOne model. In this study, Neural Network models are used to create a new wave transmission estimator valid for 5-layer Cubipod HLCS with R²=0.91 within the ranges-2<R_c/H_m0<3.6 and 0.008<s_0p<0.035.

The retreat of coral reefs during decades, and their progressive degradation, is a clear indicator of the poor health of coastal ecosystems, which in turn affects the stability of nearby beaches protected by these reefs. In addition to their importance in the resilience of coastal ecosystems, coral reefs also produce on average 1,000 m³/km² of biogenic sediment per year, which is key for the long-term stability of neighbouring sandy beaches. Sea-sand-sun tourism is critical for the social and economic development of many coastal communities worldwide and often this is directly related to the quality of the natural resources. The focus of the HOLOBREAK Project is the study of Homogeneous Low-Crested Structures (HLCS), a new type of coastal structure composed of large rocks or pre-cast concrete units. These are similar to low-crested structures (LCS) but without a core, mimicking the protection provided by coral reefs to adjacent beaches. HLCS also provide an increased porous substrate that allows colonization of the structure by local species. The placement grid of the HLCS is significant in economic, logistic and functional perspectives; affecting the feasibility of construction, the costs involved and its effectiveness as beach protection. In this study, various placement grids were analysed. The results of the physical 3D tests were calibrated and validated against numerical placement tests, based on a Bullet Physical Engine (BPE). Good agreement was found, with a global mean relative error of 2.75%, indicating that the BPE model is a valuable tool for the feasibility analysis of different placement grids.

Armor erosion due to wave attack has been studied intensively since it is considered the main failure mode of mound breakwaters. Cube-armored mound breakwaters in depth-limited breaking wave conditions are common in practice but have received limited attention in the literature. In this study, 2D physical tests were performed on non-overtopped double-layer randomly-placed cube-armored mound breakwater models with armor slope cotα = 1.5 and bottom slope m = 2% in breaking wave conditions. Using the experimental results, a new hydraulic stability formula was derived with a coefficient of determination R² = 0.85 based on a power relationship between the armor damage and the stability number and the dimensionless water depth. A lower hydraulic stability was found for the front slope of non-overtopped cube-armored structures in breaking wave conditions when compared to formulas given in the literature.

Sea level rise due to climate change, as well as social pressure to decrease the visual impact of coastal structures, have led to reduced crest freeboards, and this increases the overtopping hazard. In previous studies, pedestrian safety during overtopping events was assessed considering the overtopping layer thickness (OLT) and the overtopping flow velocity (OFV). This study analyzed the statistics of OLT and OFV on mound breakwaters without crown walls during severe wave storms. Small-scale 2D physical tests were conducted on mound breakwaters with dimensionless crest freeboards between 0.29 and 1.77, testing three armor layers (single-layer Cubipod®, and double-layer cubes and rocks) in depth-limited breaking wave conditions and with two bottom slopes. Neural Networks were used to develop new estimators for the OLT and OFV exceeded by 2% of the incoming waves with a high coefficient of determination (0.866 ≤ R² ≤ 0.876). The best number of significant figures in the empirical coefficients of the new estimators was determined according to their variability. The 1-parameter Exponential and Rayleigh distribution functions were proposed to estimate the extreme values of OLT and OFV with 0.803 ≤ R² ≤ 0.812, respectively.

Mound breakwaters are usually designed to limit the mean wave overtopping rate (q) or the maximum individual wave overtopping volume (V_max). However, rarely do studies focus on wave overtopping volumes on breakwaters in depth-limited breaking wave conditions. This study analyzes 2D physical tests on mound breakwaters with relevant overtopping rates (0.33 ≤ R_c/H_m0 ≤ 2.83) and three armor layers (Cubipod®-1L, rock-2L and cube-2L) in depth-limited breaking wave conditions (0.20 ≤ H_m0/h_s ≤ 0.90) and with two bottom slopes (m = 1/25 and m = 1/50). The 2-parameter Weibull distribution was used to estimate V_max* = V_max/(gH_m0T₀₁ ²) with coefficient of determination R² = 83.3%. In this study, the bottom slope (m = 1/50 and m = 1/25) did not significantly influence V_max or the number of overtopping events, N_ow. During the design phase of a mound breakwater, q is required to use the methods given in the literature to estimate V_max. Thus, q must be estimated for design purposes when measured q is not available. In this study, CLASH Neural Network (CLASH NN) was used to estimate q with R² = 63.6%. If the 2-parameter Weibull distribution proposed in this study is used to estimate V_max with q estimated using CLASH NN, the prediction error of V_max* is R² = 61.7%. With the method presented in this study, the ratio between estimated and measured V_max* falls within the range 1/2 to 2 (90% error band) when q is estimated with CLASH NN. The new estimators derived in this study provide good predictions of N_ow and V_max with a method simpler than those in the literature on overtopped mound breakwaters in depth-limited breaking wave conditions on gentle sea bottoms (1/50 ≤ m ≤ 1/25).

In many countries, the health of the marine ecosystems and the sun-sand-sea tourism depend on the coral reefs, which have been retreating around the world during the last decades. Homogeneous Low-Crested Structures (HLCS), made of large rocks or pre-cast concrete units, can be placed to mimic the functions of beach protection and eventually serve as a refuge for species. HLCS is a type of multi-purpose green infrastructure which is functionally similar to conventional low-crested structures but have higher porosity and are more easily dismantled for re-use. Contrary to conventional low-crested structures, the functionality of HLCS protecting beaches depends on the selected placement grid; this paper describes physical and numerical placement tests on horizontal bottom used to characterize the layers coefficients of Cubipod^® HLCS. The Bullet Physic Engine (BPE) numerical model used in the gaming industry, which is based on the rigid body method, is calibrated using the physical placement tests. The layer coefficients of Cubipod^® HLCS measured in the physical placement tests were similar to those obtained with the BPE numerical model, which could be used to optimize placement grids of HLCS on specific sea bottom conditions. Finally, the influence of the placement grid of Cubipod^® HLCS on the structure height, crest freeboard and wave transmission is analyzed.

A method has been developed to estimate wave overtopping discharges for a wide range of coastal structures. The prediction method is based on Neural Network modelling. For this purpose use is made of a data set obtained from a large number of physical model tests (collected within the framework of the European project CLASH, see e.g. [Steendam, G.J., Van der Meer, J.W., Verhaeghe, H., Besley, P., Franco, L. and Van Gent, M.R.A. (2004). The international database on wave overtopping. World Scientific, Proc. 29th ICCE, vol. 4, pp. 4301-4313, Lisbon, Portugal.]). Moreover, a method was developed to obtain confidence intervals for the overtopping predictions of the neural network.

A method has been developed to estimate wave overtopping discharges for a wide range of coastal structures. The prediction method is based on the technique of Neural Network modelling. For this purpose use is made of a data set obtained from a large number of physical model tests. Moreover, a method was developed to obtain the confidence intervals around these predictions.