The rapid changes in the shipping fleet during the last decades has increased the ship-induced loads and, thus, their impact on infrastructures, margin protections and ecosystems. Primary waves have been pointed out as the cause of those impacts, with heights that can exceed 2 m and periods around 2 minutes. Consequently, extensive literature can be found on their estimation mainly from a deterministic perspective with methods based on datasets limited to one location, making difficult their generalization. These studies propose either computationally expensive numerical models or empirical equations which often underestimate the extreme primary waves, hindering their use for design purposes. Moreover, a framework to allow the design of infrastructure under ship-wave attack based on probabilistic concepts such as return periods is still missing. In this study, a probabilistic model based on bivariate copulas is proposed to model the joint distribution of the primary wave height, the peak of the total energy flux, the ship length, the ship width, the relative velocity of the ship and the blockage factor. This model, a vine-copula, is developed and validated for four different deployments along the Savannah river (USA), with different locations and times. To do so, the model is quantified using part of the data in one deployment and validated using the rest of the data from this deployment and data of the other three. The vine-copula is validated from both a predictive performance point of view and with respect to the statistical properties. We prove that the probabilistic dependence of the data is preserved spatially and temporally in the Savannah river.

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Aquaculture at sea is gaining increasing importance, not only as a (local) food source but also due to its potential of being combined with other offshore activities such as wind parks. Nevertheless, experience of offshore aquaculture is limited. This study aims to provide a framework to evaluate offshore aquaculture suitability accounting for the probabilistic dependence between relevant variables. This framework is applied to obtain suitability maps of aquaculture for the North Sea for the blue mussel Mytilus edulis and the sugar kelp Saccharina latissima. For each of these species, three ecological variables are selected and the optimal growth and critical survival limits are defined. Here, suitability is defined as the probability of meeting these conditions. Data on the selected variables is extracted from a large-scale 3D hydrodynamic and ecological model of the northwest European Shelf, of which daily extremes are sampled. The probabilistic model is developed using bivariate copula models, which are fitted to each variable pair to describe their joint distribution function at each studied location. Empirical distribution functions are used to describe the univariate distribution function of each variable and location. Using Monte-Carlo simulations, the probability of meeting the optimal and critical limits is estimated and suitability maps accounting for the probabilistic dependence between the variables are generated. In addition, suitability maps disregarding the dependence are generated and compared to those accounting for the probabilistic dependence. It was found that considering the dependence between variables significantly improves the accuracy of the results for optimal and critical growth conditions for both species. The presented method allows to identify potential areas where blue mussel and sugar kelp cultivation is the most suitable. For instance, in this study, a north-south elongated area west of the German and Danish coast appears to be most suitable for blue mussels, while estuaries and rivers are found the most suitable for the sugar kelp.

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Rising sea levels caused by climate change are increasing the risk of overtopping on coastal structures. Moreover, there is a growing societal concern about the visual impact of these structures, which leads to the lowering of their crest freeboards. In previous studies, safety during overtopping events was assessed considering the overtopping layer thickness (h_c), the overtopping flow velocity (u_c) and the individual wave overtopping volume (V). Existing models in the literature to estimate h_c, u_c and V on mound breakwater crests are mainly deterministic, involve a chain of successive estimations leading to accumulated errors and/or do not account for the dependencies between h_c, u_c and V. This study proposes a model to describe the joint probability distribution of h_c, u_c and V based on bivariate copulas. Experimental data from small-scale 2D physical tests conducted on mound breakwaters with three armor layers (single-layer Cubipod®, and double-layer cubes and rocks) in depth-limited breaking wave conditions on two mild bottom slopes and dimensionless crest freeboards between 0.33 and 3.20 is used. Lognormal distribution functions are proposed for each variable and a multivariate dependence model is developed through a one-tree vine-copula. The parameters of this model are quantified directly using wave characteristics and the structure geometry minimizing the accumulated errors in the final predictions. The application of the model is illustrated by computing the probability of not fulfilling at least a tolerability limit for one of the studied variables (OR probability). The OR probability is computed both considering the dependence and assuming independence between the variables and a significant difference is obtained. It is concluded that by accounting for the multivariate dependence between the variables, it is possible to reduce the crest freeboard and, thus, achieve a more economic design within the required safety level.

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Aquaculture is gaining importance in the current context of continuous growth population as a source of (local) food resources and its potential of being combined with other uses at sea (e.g.: offshore energy production or tourism). Consequently, within the European Horizon 2020 project UNITED, the combination of mussel and seaweed cultivation together with wind energy production in the German North Sea is investigated. Here, the feasibility of the mussel Mytilus edulis and seaweed Saccharina latissima based on their ecological needs is analysed. Ecological data from a three-dimensional hydrodynamic and ecological model covering the northwest European continental shelf is used. For each of the two species, three variables are selected as relevant, including in both of them the water temperature. In addition, chlorophyll-a and dissolved oxygen are considered for mussels, and dissolved inorganic nitrogen and phosphorus are selected for seaweed. Temperature is selected as dominant variable so its daily maxima for the growing months are selected together with the concomitants of the other variables. Gaussian Mixture distributions (see McLachlan and Peel (2000)) and truncated Gaussian kernel distributions (see Bowman and Azzalini (1997)) are used to model the marginal distributions of the random variables. Bivariate copulas are fitted for each pair of variables to describe their dependence structure. Finally, probabilities of being within the optimal ranges of the relevant variables are calculated. Chlorophyll-a concentration and temperature are the most limiting variables for mussels and seaweed, respectively. Relatively low probabilities are obtained, since ranges for optimal growth are considered. Generally, it is feasible to cultivate mussels and seaweed at this location based on the selected ecological variables, as the probability of variables reaching values outside growth limits for the species is low. @en

Teaching sustainability and ethics to engineering students is a challenging but necessary task that has been increasingly investigated during the last few years. In this research, a systematic method to identify the level of awareness in students about sustainability and ethics is developed. Here, it is applied to students studying the Civil Engineering bachelor’s degree at the School of Civil Engineering of Universitat Politècnica de València (UPV), though this method is potentially applicable to equivalent ABET and EUR-ACE accredited bachelor’s degrees. A survey was performed, and data was analyzed using Analytical hierarchical process technique; this technique determines the relative importance of each criterion, as well as the consistency of the emitted judgements, in an objective manner. These results allowed to discover that students do not have a robust opinion related to sustainability and ethics, except those students with previous experience in the construction sector. Environmental and social dimensions of sustainability and ethics were identified as the main focuses to emphasize in the civil engineering curriculum. Finally, actions to boot these principles are also proposed; potential courses where sustainability and ethics concepts could be explicitly included were selected and the inclusion of an environmental budget in the bachelor thesis was recommended, among others suggestions. @en

Before the year 1519, the Valley of Mexico was a closed basin and at the bottom of the valley, an extensive system of shallow lakes was formed. Within this lacustrine system, the capital of the Aztec empire, Tenochtitlan, was built. The Aztecs were known for their impressive constructions and complex hydraulic structures, of which the most impressive structure was the Nezahualcoyotl dike. This structure was constructed across Lake Texcoco. Its principal function was to protect the city of Tenochtitlan from high water levels at the lake. However, there is not enough information about the reliability of this dike. Mainly due to two reasons, today there are no remains left of the dike and most of the lacustrine system is drained. In this paper, we present a method to study the reliability of the Nezahualcoyotl dike under two failure modes, overturning and sliding. This is done by following up on the work presented by Torres-Alves & Morales-Nápoles (2020) where they developed a hydrological characterization of the lacustrine system and studied the dike under one failure mode, overflow. The proposed analysis aims to provide a more realistic assessment of the reliability of the dike as a flood defense mechanism. @en

An accurate estimation of wind and wave variables is key for coastal and offshore applications. Recently, copulas have gained popularity for modelling wind and waves multivariate dependence, since accounting for the hydrodynamic relationships between them is needed to ensure reliable estimations of the required design values. In this study, copula-based Bayesian networks (BNs) are explored as a tool to model extreme values of significant wave height (Hs), wave period, wave direction, wind speed and wind direction. The model is applied to a case study located in the Alboran sea, close to the Spanish coast, using ERA5 database. Extreme values of Hs are sampled using Yearly Maxima and concomitant values of the missing variables are used. K-means clustering algorithm is applied to separate the different wave components and a BN is built for each of them. The assumption of modelling the dependence between the variables using Gaussian copulas and the structure of BNs are supported with the d-calibratioson score. Fitted marginal distributions are introduced in the nodes of the BNs and their performance is assessed using in-sample data and the coefficient of determination. The BN models proposed present high performance with a low computational cost proving to be powerful tools for modelling the variables under investigation. Future research will include different locations and databases. @en

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.

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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.

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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.

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Armor damage due to wave attack is the principal failure mode to be considered when designing conventional mound breakwaters. Armor layers of mound breakwaters are typically designed using formulas in the literature for non-overtopped mound breakwaters in non-breaking wave conditions, although overtopped mound breakwaters in the depth-induced breaking wave zone are common design conditions. In this study, 2D physical tests with an armor slope H/V = 3/2 are analyzed in order to better describe the hydraulic stability of overtopped mound breakwaters with double-layer rock, double-layer randomly-place cube and single-layer Cubipod® armors in depth-limited breaking wave conditions. Hydraulic stability formulas are derived for each armor section (front slope, crest and rear slope) and each armor layer. The front slope of overtopped double-layer rock structures is more stable than the front slope of non-overtopped mound breakwaters in breaking wave conditions. When wave attack increases, armor damage appears first on the front slope, later on the crest and, finally, on the rear side. However, once the damage begins on the crest and rear side, the progression is much faster than on the front slope, because more wave energy is dissipated through the armored crest and rear side.@en

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.

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Rubble mound breakwaters usually present a crest wall to increase the crest freeboards without a large increase of the consumption of material. Methods in the literature to design crest walls are based on estimates of the wave loads. These methods are focused on the maximum loading that attacks a single position of the crest wall. In practice, crest walls have a finite length. Since the maximum loading does not occur at the same instant over the entire length of the crest wall for oblique waves, these methods overestimate the loading in the situation of oblique waves. Wave loads under oblique wave attack have been measured in physical model tests. A method to account for the effect of the finite length of crest walls has been developed, and design guidelines have been derived. The results of this study in combination with the existing methods in the literature to estimate the wave forces enable a more advanced design of crest walls.@en

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.@en

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.

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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).

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Mound breakwater design is evolving owing to rising sea levels caused by climate change and social concern regarding the visual impact of coastal structures. The crest freeboard of coastal structures tends to decrease while overtopping hazard increases over time. Pedestrian safety when facing overtopping events on coastal structures has been assessed considering the overtopping layer thickness (OLT) and overtopping flow velocity (OFV). This paper proposes a new method to estimate the OLT and OFV on mound breakwater crests during extreme overtopping events, based on 123 2D small-scale physical tests of conventional low-crested mound breakwaters with a single-layer Cubipod® and double-layer rock and cube armors. The new method to estimate OLT exceeded by 2% of incoming waves is based on formulas given in literature for dikes, but adapted and calibrated for mound breakwaters. The formula to estimate the OFV exceeded by 2% of incoming waves is based on the correlation between the statistics of the OLT and OFV, considering an empirical coefficient calibrated for each type of armor layer. Exponential and Rayleigh distribution functions are proposed for estimating the OLT and OFV with exceedance probabilities under 2%. Although the statistics of OLT and OFV depend on similar variables, contrary to intuition, specific OLT and OFV corresponding to the same overtopping event appear to be independent.@en

In recent years, mound breakwater design has had to consider social concerns about the visual impact of coastal structures as well as the rise in sea levels due to climate change. Additionally, mound breakwater design must consider pedestrian safety when facing overtopping loads and the subsequent hazards. The overtopping hazard on dikes has been studied considering the overtopping velocity and the overtopping layer thickness on the crest. This paper proposes a new method to estimate the overtopping layer thickness on the crest of mound breakwaters based on 123 physical tests of conventional low-crested mound breakwaters with three different armors. The new method is based on formulas given in the literature to estimate wave run-up for mound breakwaters and overtopping layer thickness on the crest of dikes which was exceeded by 2% of the incoming waves, but using the roughness factors 0.33 (Cubipod ®-1L), 0.48 (rocks-2L) and 0.35 (cubes-2L) and the empirical coefficients 0.51 and 0.89. The new method explained 79% of the variance in the observed overtopping layer thickness exceeded by 2% of the incoming waves (rMSE=0.21).@en