Field data of armour damage in mound breakwaters is scarce, and experimental testing methods usually neglect the influence of pre-existing damage on subsequent damage increments. This study proposes a probabilistic framework, based on a dataset of 44 cumulative damage experiments, to estimate long-term damage progression in a full-scale, non-overtopped, cube-armoured mound breakwater located in the depth-induced wave breaking zone. A Gaussian copula-based Bayesian network is constructed to model the multivariate relationships between existing armour damage (S_e), the increment of armour damage (ΔS_e), the dimensionless water depth at the toe of the structure (h_s/H_m0), wave steepness (H_m0/L_0p), and the stability number (N_s). Each variable is modelled with a univariate parametric distribution, enabling inference of probabilities for values not directly observed in the experimental dataset. Model validation includes testing the Gaussian copula assumption, which is deemed a reasonable model, and assessing the defined graph with satisfactory results. The model is conditionalized using a historical wave dataset to generate synthetic damage curves, which are subsequently used to quantify a gamma process to model the survivability of the structure along its design life. A case study of a hypothetical breakwater with D_n=2 m close to the port of Tarragona (Spain) illustrates the methodology. According to the results of the model, the probability of observing a dimensionless damage S_e>5 corresponding to Initiation of Destruction after 10 years is 0.29. Overall, the obtained results are deemed conservative; this could be caused by the use of data from 2D experiments which do not take into account oblique wave attack. However, the approach is adaptable to other datasets with additional variables, breakwaters in different conditions or with other configurations, and can also be used in combination with simulations of synthetic wave data, making it relevant under changing climate conditions.

Extreme storms over the North Sea drive coastal flood risk in the Netherlands, causing high waves and extreme sea levels. Designing flood defenses requires accurate statistical extrapolation of hydraulic load conditions with return periods of 1,000 years or more. This is a challenging task given limited observational data. This study uses a large, simulated dataset (~9,000 years) to explore the statistical dependence between extreme wind speed u and surge height s. Storms were clustered using several techniques. Self-organizing maps (SOM) effectively captured physical relationships, such as the influence of wind direction and tidal offset on storm dynamics, however variability in statistical dependence between u and s for different clusters was better represented using manual clusters. Copula models were fitted to the cluster data, with the BB8 copula outperforming others. This study illustrates the potential of machine learning to identify patterns in large datasets while emphasizing the relevance of manual clustering approaches for revealing nuanced statistical dependencies critical to flood risk assessment.

Extreme sea level events pose significant risks to coastal regions, with non-tidal residuals (NTRs) being a primary driver in low-lying areas like the Netherlands, where shallow seas amplify their impact. This study investigates the spatial patterns of NTRs along the Dutch coast using time series clustering on historical NTR hydrographs. The design of hydraulic boundary conditions divides the Netherlands into three coastal regions. To evaluate whether this division sufficiently captures regional variability, three clustering scenarios (k = 3, k = 4, and k = 5) were explored. The analysis identified k = 5 as the optimal configuration based on the Davies-Bouldin index. This result emphasized the importance of fine-scale approaches to understanding regional spatial variations in NTR dynamics. Regional bathymetry and tide-surge interactions were explored as drivers of these spatial patterns. Southern stations near river systems and deeper waters displayed characteristics distinct from northern stations in the Wadden Sea, which are influenced by shallow tidal flats. Analysis of the M2 tidal constituent and the timing of NTR maxima relative to high tides underscored the role of tidal dynamics in shaping spatial clusters. Future research will focus on integrating spatio-temporal patterns and environmental drivers into clustering methodologies, providing deeper insights for coastal risk management and adaptation strategies.

Current wind design codes incorporate turbulence through gust factors and rely on historical wind data, including tropical cyclones. While generally conservative, standard code wind profiles and spectra do not fully reproduce the vertical distribution and dynamic characteristics of hurricane winds, particularly in the supergradient region near the eyewall, and can sometimes underestimate tail risks, low-probability, high-impact events, as observed during Hurricane Otis in Acapulco (2023). This study probabilistically evaluates wind-induced vibrations in high-rise buildings with different lateral resisting systems equipped with fluid viscous dampers (FVDs), under non-tropical storm and tropical cyclone conditions. Along-wind loads were modeled in the time domain as stationary, multidimensional stochastic processes and analyzed using one million Monte Carlo simulations and Incremental Dynamic Analysis on the DelftBlue supercomputer. Statistical distributions of responses, bivariate dependence via copulas, and fragility curves were obtained. Results show that wind type, structural deformation mode, and damper properties significantly affect response distributions, correlation structures, and failure probabilities. FVDs effectively reduce structural dynamic response, improving serviceability, while increased shear stiffness further reduces fragility. Modeling hurricane winds as non-tropical storms can overestimate damper effectiveness. These findings provide insights for refining wind codes and designing high-rise buildings that remain safe and functional under extreme events.

This study explores the statistical dependence between wind speed and surge height along the Dutch coast using a large synthetic dataset. Storms were clustered based on wind direction, tidal offset, wind rotation, tidal peak, surge and wind exceedance duration, resulting in 16 clusters per wind direction and per location. Apart from wind direction, comparing clusters revealed a limited impact of clustering based on these storm characteristics on the choice of the best-fitting copula model, suggesting sub-clustering may not be necessary for accurately representing the statistical dependence between extreme wind speeds and surge heights. The BB8 copula generally provided the best fit to the data. However, the observed upper tail dependence did not decrease to zero, particularly for western to northern wind directions, indicating non-negligible dependence in joint extremes of wind speed and surge height. Therefore, applying the BB8 copula (or any other copula model without upper tail dependence) may lead to underestimation of the flood risk, when applied in probabilistic analyses. The findings from this study provide valuable insights for refining hydraulic load models for reliability assessments and design of flood defenses.

This study evaluates five scoring rules, or measures of statistical accuracy, for assessing uncertainty estimates from expert judgment studies and model forecasts. These rules — the Continuously Ranked Probability Score ((Formula presented.)), Kolmogorov-Smirnov ((Formula presented.)), Cramer-von Mises ((Formula presented.)), Anderson Darling ((Formula presented.)), and chi-square test — were applied to 6864 expert uncertainty estimates from 49 Classical Model (CM) studies. We compared their sensitivity to various biases and their ability to serve as performance-based weight for expert estimates. Additionally, the piecewise uniform and Metalog distribution were evaluated for their representation of expert estimates because four of the five rules require interpolating the experts' estimates. Simulating biased estimates reveals varying sensitivity of the considered test statistics to these biases. Expert weights derived using one measure of statistical accuracy were evaluated with other measures to assess their performance. The main conclusions are (1) (Formula presented.) overlooks important biases, while chi-square and (Formula presented.) behave similarly, as do (Formula presented.) and (Formula presented.). (2) All measures except (Formula presented.) agree that performance weighting is superior to equal weighting with respect to statistical accuracy. (3) Neither distributions can effectively predict the position of a removed quantile estimate. These insights show the behavior of different scoring rules for combining uncertainty estimates from expert or models, and extent the knowledge for best-practices.

Offshore floating structures are experiencing harsh environmental conditions risking their safety. Therefore, mooring lines are crucial for ensuring structures’ stability. Sudden increases in tensions after temporarily slack of the mooring line are called snap loads and are the most critical load states. These snap loads and their dependence to various factors are investigated in the present study. 12 study locations in the south-eastern North Sea are selected. For each location, wave and current variables are extracted from a three-dimensional large-scale numerical model covering the European Shelf. Mooring tensions at different rope positions are calculated via a Finite Element model for flexible mooring lines for different hydrodynamic conditions and used subsequently to obtain tension rates as indicator for snap loads. The dependence among 13 variables per study location is modelled via Gaussian copula-based Bayesian Networks (GCBN). This allows for spatial analysis of the relationships between hydrodynamic variables and tension rates, but also to determine the influence of hydrodynamic variables on expected tension rates. Furthermore, distributions of tension rates are obtained under specific constant hydrodynamic conditions. The results indicate that conditionalising on certain hydrodynamic variables can reduce the expected tension rates, as their marginal distributions are characterised by heavy tails. Still, mooring systems should be designed conservatively. However, once specific hydrodynamic information is available, uncertainties can be minimised, enhancing safety and reliability. Thus, accounting for the dependence among hydrodynamic variables and tension rates is crucial for improving the safety of structures under varying environmental conditions.

In absence of sufficient data, structured expert judgment is a suitable method to estimate uncertain quantities. While such methods are well established for individual variables, eliciting their dependence in a structured manner is a less explored field of research. We tested the performance of experts in constructing and quantifying a nonparametric Bayesian network, describing the correlation between river tributary discharges. Specialized software was provided to assist the experts. Expert performance was investigated using the dependence calibration score (a correlation matrix distance metric) and the likelihood of the joint distribution. Desirable properties of the dependence calibration score were investigated theoretically. Individual expert judgments were combined based on performance into a group opinion aka decision maker. All experts were able to create and quantify a correlation matrix between 10 variables that resembled the correlations between observed discharges well. The decision makers performed similarly to the best expert. Based on the metrics investigated, it mattered little which expert opinions and with what weight were combined in a decision maker. This is partly because all experts performed well. Adding a bad performing expert increased the positive effect of performance-based weighting, underscoring the importance of developing scoring rules for dependence elicitation. The overall results are promising: Aided by specialized graphical software, the experts in this study were able to quickly create and quantify dependence structures.

Base isolation of high-rise buildings has growing popularity to limit peak floor accelerations under seismic loads; however, it may increase susceptibility to wind-induced vibrations due to the increase in fundamental vibration period. This study presents an equivalent coupled-two-beam (CTB) model incorporating base isolation (BI) and a tuned mass damper inerter (TMDI) to evaluate passive vibration control under lateral wind loads for various lateral resisting systems. A 144-meter-tall building was analyzed under along-wind and across-wind loads simulated as Gaussian processes, considering six isolator-damper configurations: (1) fixed-base (FB), (2) FB with a top TMDI (FB-TTMDI), (3) BI, (4) BI with a top TMDI (BI-TTMDI), (5) BI with a bottom TMDI (BI-BTMDI), and (6) BI with double TMDI (BI-DTMDI). TMDIs were compared to traditional tuned mass dampers (TMDs) to assess mass amplification under varying base isolator damping. Optimization strategies were explored to enhance vibration control: for FB-TTMDI, the TMDI placement minimized RMS accelerations, while for BI-TTMDI, it was optimized to reduce peak displacement. Finally, design guidelines are provided for ultimate and serviceability limit states. Results indicate hybrid control systems are most effective when lateral deformation resembles pure bending, making them suited for shear wall-frame and tubular systems.

Immersed tunnels are positive buoyant structures during installation and negative buoyant after installation. A tunnel is composed of sequential immersed elements that are coupled to each other in joints. Tunnel elements consist of segments which are compressed to each other by longitudinal post-tensioning. After immersion the tunnel is supported by the seabed and the longitudinal post-tension is cut at the joints between segments. Therefore, the structure is a segmented lining which is sensitive for settlements due to non uniform circumstances over the length of the tunnel. An uneven response of the bedding underneath the tunnel introduce shear forces in joints of an immersed tunnel. Because immersed tunnels need to be buoyant during installation, they have limitations on weight and geometry, the size and therefore the capacity of these shear keys is limited because the height of the tunnel, as shear keys are applied in the walls of the tunnel. The foundation response is influenced by many factors related to subsoil but also to construction and dredging tolerances. The shear forces were derived as a function of different covariance lengths for subsoil stiffness and dredging tolerances for different tunnel layouts. In reliability analyses, using two different probabilistic methods, exceedance probabilities of maximum shear forces are derived for one lay out using Non Parametric Bayesian Networks and Vine Copulas. The analyses give more insight in to the magnitude of the shear forces in joints both in conditioned and unconditioned situations and this can be used for the design of immersed tunnels.

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.