Design Of Marine Structures Research Articles

Statistical distribution of surface elevation by using quadratic forms of normal random variables

This paper is concerned with the statistical properties of surface elevation, which is crucial for the design and operation of marine and coastal structures and is helpful to the prediction of rogue waves. A semi-analytic quadratic model is proposed to describe the statistical distribution of surface elevation by using the theory of quadratic forms of normal random variables, in which the characteristic function and cumulants are given in analytical form, and the probability density is obtained by the numerical inversion of the characteristic function using the fast Fourier transform algorithm. Compared with Monte Carlo simulations, the quadratic model presents excellent performance in describing the probability density function of surface elevation, especially at the tails, for varying degrees of steepness, bandwidth, and directional spreading in both finite and infinite water depth. The effect of these parameters that characterize sea states on the statistical properties of surface elevation is also investigated. Through a comparative study, the quadratic model is superior to previously existing theoretical models.

Effects of submergence ratio on flow around a circular pier in combined wave–current flows using particle image velocimetry

The present study illustrates an experimental investigation of flow hydrodynamics in the vicinity of a submerged circular pier across various submergence levels under only current and wave–current combined flow conditions. The instantaneous velocity data are collected using particle image velocimetry for three distinct frequencies of waves to determine the influence of wave superimposition on the current-induced turbulence parameters. The distribution of phase averaged turbulence quantities, such as mean velocities, Reynolds shear stress, turbulent kinetic energy, flow patterns, and vorticity analysis by Q-criterion, are presented. The results provide insight into the impacts of wave frequency and submergence ratio on the formation of horseshoe vortices, trailing vortex, and reverse flow zones. From the results it is observed that a decrease in the submergence level of the structure causes the formation of strong horseshoe vortices and reverse flow zones in the absence of waves. Also, an increase in wave frequency intensifies the turbulence kinetic energy at the upstream of the pier and eddy generation behind the pier. The present findings highlight the effects of pier submergence and wave characteristics, such as frequency, wave height, and wave period, on flow patterns and turbulent flow characteristics and aid in the design of marine structures. Furthermore, experimental data serve as a valuable resource for validating theoretical or mathematical models related to combined wave–current environments.

Estimating metocean environments associated with extreme structural response to demonstrate the dangers of environmental contour methods

Extreme value analysis (EVA) uses data to estimate long-term extreme environmental conditions for variables such as significant wave height and period, for the design of marine structures. Together with models for the short-term evolution of the ocean environment and for wave–structure interaction, EVA provides a basis for full probabilistic design analysis. Alternatively, environmental contours provide an approximate approach to estimating structural integrity, without requiring structural knowledge. These contour methods also exploit statistical models, including EVA, but avoid the need for structural modelling by making what are believed to be conservative assumptions about the shape of the structural failure boundary in the environment space. These assumptions, however, may not always be appropriate, or may lead to unnecessary wasted resources from over design. We demonstrate a methodology for efficient fully probabilistic analysis of structural failure. From this, we estimate the joint conditional probability density of the environment (CDE), given the occurrence of an extreme structural response. We use CDE as a diagnostic to highlight the deficiencies of environmental contour methods for design; none of the IFORM environmental contours considered characterise CDE well for three example structures.

Advanced Analysis of Marine Structures

In the analysis and design of marine structures, one of the key issues is the accurate prediction of their strength under various load conditions, particularly impact and ultimate and fatigue strength [...]

On the role of curvature in the response of air-backed composites to hydrodynamic loading: An experimental study

Composite materials are increasingly utilized in high-performance naval structures, due to their superior properties over traditional materials like steel and aluminum. However, their widespread use is hindered by our limited understanding of their behavior when exposed to marine environments. One of the main loading conditions encountered during operations at sea is the hydrodynamic loading on the side in contact with water. Despite the practical significance of curved composite structures, the state-of-the-art on air-backed composites relies on the study of flat plates. Here, we use three-dimensional digital image correlation and planar particle image velocimetry to study the influence of curvature on the dynamic response of composite plates to hydrodynamic loading. Our findings reveal that curvature significantly influences both structural deformations and flow physics. The curved plate experiences localized vibrations with lower amplitude and higher frequency, caused by its increased stiffness. Additionally, the hydrodynamic pressure at the center of the plate decays faster in time for the curved configuration, highlighting the importance of curvature in shaping fluid–structure interactions. Our results advance the understanding of fluid–structure interactions in composite materials and highlight the importance of curvature in the design of resilient marine structures.

A Novel Method for Estimating the Undrained Shear Strength of Marine Soil Based on CPTU Tests

The undrained shear strength is an essential parameter in the foundation design of marine structures. Due to the complex marine environment and technical limitations, it is difficult and costly to obtain offshore samples. Piezocone penetration tests (CPTU) are relatively low-cost compared to drilling and sampling methods. Therefore, based on the soil behavior type index (Ic) derived from CPTU results, a model for estimating cone factors (Nkt, Nke) is proposed to improve the accuracy of estimation of undrained shear strength. The result shows that the soil behavior type index (Ic) and cone factors take on a negatively correlated exponential relation. Incorporating a cone factor that varies with the soil behavior type index (Ic) significantly enhances the accuracy of undrained shear strength predictions compared to the conventional method of using a constant cone factor. This approach reduces the root mean square error (RMSE) for Nkt (Nke) from 0.124 (0.126) MPa to 0.056 (0.06) MPa, and the mean absolute error (MAE) from 0.0154 (0.016) MPa to 0.0032 (0.0036) MPa. The method was validated at an additional location and the predictions were in high agreement with the results of the consolidated quick direct shear test. The developed method can serve as an effective tool used in the design of foundations of marine structures.

Unleashing the Potential of a Hybrid 3D Hydrodynamic Monte Carlo Risk Model for Maritime Structures’ Design in the Imminent Climate Change Era

Submarine pipelines have become integral for transporting resources and drinking water across large bodies. Therefore, ensuring the stability and reliability of these submarine pipelines is crucial. Incorporating climate change impacts into the design of marine structures is paramount to assure their lifetime safety and serviceability. Deterministic design methods may not fully consider the uncertainties and risks related to climate change compared to risk-based design models. The latter approach considers the future risks and uncertainties linked to climate and environmental changes, thus ensuring infrastructure sustainability. This study pioneers a Hybrid 3D Hydrodynamic Monte Carlo Simulation (HMCS) Model to improve the reliability-based design of submarine pipelines, incorporating the effects of climate change. Current design approaches may follow deterministic methods, which may not systematically account for climate change’s comprehensive uncertainties and risks. Similarly, traditional design codes often follow a deterministic approach, lacking in the comprehensive integration of dynamic environmental factors such as wind, waves, currents, and geotechnical conditions, and may not adequately handle the uncertainties, including the long-term effects of climate change. Nowadays, most countries are developing new design codes to modify the risk levels for climate change’s effects, such as sea-level rises, changes in precipitation, or changes in the frequency/intensity of winds/storms/waves in coastal and marine designs. Our model may help these efforts by integrating a comprehensive risk-based approach, utilizing a 3D hydrodynamic model to correlate diverse environmental factors through Monte Carlo Simulations (MCS). The hybrid model can promise the sustainability of marine infrastructure by adapting to future environmental changes and uncertainties. Including such advanced methodologies in the design, codes are encouraged to reinforce the resilience of maritime structures in the climate change era. The present design codes should inevitably be reviewed according to climate change effects, and the hybrid risk-based design model proposed in this research should be included in codes to ensure the reliability of maritime structures. The HMCS model represents a significant advancement over existing risk models by incorporating comprehensive environmental factors, utilizing advanced simulation techniques, and explicitly addressing the impacts of climate change. This innovative approach ensures the development of more resilient and sustainable maritime infrastructure capable of withstanding future environmental uncertainties.

Experimental study of dynamic pressure and wave load on variform vertical cylinders under extreme waves

Extreme waves pose a significant threat to the proliferating marine structures, however, the impact on the vertical cylinder with different cross-sectional shapes remains inadequately evaluated. Herein, we carried out a physical experiment, comprising 45 scenarios generated by three water depths, three wave paddle velocities, and five vertical cylinder models, to measure the extreme wave-induced pressure and load on this type of structure. The wave load and dynamic pressure distribution in time and spatial domains under the influence of cross-sectional shapes and wave conditions have been fully discussed. The experimental results indicate that: 1) As the position turns from front to back side, the circumferential pressure of five models initially decreases and then increases. 2) The maximum differential pressure between the front and back side decreases with increased water depth and decreased velocity, and occurs earlier than the peak pressure on the front side. 3) The chamfered cross-section (round and right triangle) can significantly reduce the wave load compared to the rectangular section, and the circular section suffers the lowest force logically. The dynamic pressure and wave load in this experiment can serve to establish a more sophisticated load model and provide valuable insights for marine structural design and disaster prevention.

Energy Efficiency Analysis of a Deformable Wave Energy Converter Using Fully Coupled Dynamic Simulations

Deformable wave energy converters have significant potential for application as flexible material that can mitigate structural issues, while how to design the dimensions and choose an optimal deployment location remain unclear. In this paper, fully coupled computational fluid dynamics and computational solid mechanics were used to simulate the dynamic interactions between ocean waves and a deformable wave energy converter. The simulation results showed that the relative length to wave, deployment depth and aspect ratio of the device have significant effects on the energy conversion efficiency. By calculating the energy captured per unit width of the device, the energy efficiency was found to be up to 138%. The optimal energy conversion efficiencies were achieved when the structure length was 0.25, 0.5 or 0.75 of the dominating wavelength and submerged at a corresponding suitable depth. The aspect ratio and maximum stress inside the wave energy converter showed a nonlinear trend, with potential optimal points revealed. The simulation approach and results support the future design and optimisation of flexiable wave energy converters or other marine structures with notable deformations.

Effects of impact location on the dynamic response of repeatedly impacted aluminum alloy plates

This paper presents a numerical investigation of the effects of impact location on the dynamic response of aluminum alloy plates to repeated mass impacts. The numerical model was developed and validated against relevant test data. In the simulation, the strain hardening was adopted using existing published equations. A parametric study was performed by considering different impact locations while keeping impact energy (mass and velocity) identically for each impact. The results showed that the plate was deformed progressively, and the resulting impact forces increased, while its duration decreased when the plate was impacted repeatedly. While changing in impact location after each impact remarkably affected the response of impacted plates, i.e., less damage was observed. The study results are expected to be helpful for the design of marine structures including fishing boats subjected to repeated impacts arising from collisions or dropped objects. Keywords: Numerical simulation, aluminum alloy plate, repeated impacts, residual deformation.

3D SPH analysis of focused waves interacting with a floating structure

In recent years, the number of offshore floating structures has been growing and is expected to continue growing. Due to climate change, the frequency and severity of extreme waves are increasing. Numerical models can be a strategic tool in the reliable design and optimization of marine structures. However, the number of numerical parameters to be tuned plays a crucial role, as they could limit the model’s applicability and reliability. Furthermore, there are many challenges in modelling wave-structure interaction. Among these challenges, the simulation of one-dimensional tethers is of great concern when dealing with moored floating structures. In this study, a 3D numerical model is developed based on the Smoothed Particle Hydrodynamics (SPH) technique. This hydrodynamic model is coupled with a multi-body solver for the dynamic analysis of moorings and structures. In a three-dimensional numerical flume, focused ocean waves are generated with a piston-type wave-maker and propagated until impact with the floating structure. The developed model predicts the wave profile, impact forces, and structural dynamics, and is validated by comparing numerical results against experimental data.

A time-varying copula approach for describing seasonality in multivariate ocean data

Characterizing multivariate ocean variables is quite critical for reliability design and risk assessment of marine structures. A robust, precise, and practical multivariate statistic model is necessary for comprehending ocean characteristics. As the time-varying characteristics exist in the ocean data, it is unreasonable to employ a simple constant statistical model to characterize all the multivariate data at one time. Therefore, in this paper, a time-varying copula approach is developed for modeling time-varying multivariate ocean data. Considering climate variations, a time-varying formula for return period and environment contour is also derived. The developed approach is demonstrated based on a site-specific ocean dataset collected from a buoy on the US coast. The climate effects associated with the multivariate ocean variables are characterized. The developed time-varying copula approach is also compared to the conventional copula and the conditional model in estimating the return period. The results showed that the time-varying model is helpful to explore the most critical environmental conditions for marine structures.

Convex environmental contours for non-stationary processes

Environmental contours are tools frequently used in the early design of marine structures. They provide a description of critical design conditions and serve as a means for simplifying expensive long-term response calculations. Here, we consider convex contours based on the assumption of convex failure sets. We provide a rigorous foundation for the existence of such contours when the underlying environmental factors are modelled by a general, possibly non-stationary, process. This constitutes a generalisation of existing theory and is done to properly account for empirically observed increases in extreme sea-states.Two definitions are proposed, based respectively on averages or quantiles of exceedence times, along with minimal conditions on the environmental processes to guarantee existence. In order to illustrate these methods we give two examples, including an empirical study containing a method for constructing contours based on the presented theory.

Statistical Modeling and Applications of Joint Distributions for Significant Wave Height, Spectral Peak Period, and Peak Direction of Propagation: A Case Study in the Norwegian Sea

The estimation of long-term extreme response is a crucial task in the design of marine structures. The target extreme responses are typically defined by annual exceedance probabilities of 10−2 and 10−4. Various approaches can be employed for this purpose, with preference given to statistical long-term analysis, which involves aggregating the exceedance probabilities of all potential sea states contributing to the exceedance of the target extremes. A joint model encompassing important metocean parameters such as wind, waves, and current is often necessary. This study specifically focuses on waves and wave-induced responses. In characterizing short-term sea state conditions, significant wave height (Hs), spectral peak period (Tp) and peak direction of propagation (Φp) are identified as the most important sea state characteristics. The objective of this work is to present the results of the joint model for the three sea state parameters, i.e., Hs, Tp and Φp, at an offshore site in the Norwegian Sea. The conditional modeling approach is applied using long-term hindcast data, and different statistical models are discussed for fitting the marginal and conditional distributions. The fitted parameters for all directional sectors are provided, offering a comprehensive representation of the joint model for direct use in long-term response analysis. Two case studies are included to illustrate the application of the fitted joint model in long-term response analyses. The case studies identify the governing wave directions and the most important combinations of short-term sea state characteristics regarding the estimation of long-term extreme responses.

Comparing linear damage hypothesis to linear elastic fracture mechanics in the estimation of fatigue life in a high speed light craft

Linear elastic fracture mechanics methods provide a more comprehensive representation of crack propagation compared to traditional methods such as the linear damage hypothesis (or SN curve approach). These techniques have been widely adopted in the aerospace industry, however, their usage in the design of marine structures remains limited. The presented research uses full-scale trial data measured onboard a 111 m wave-piercing catamaran to compare the results obtained from linear elastic fracture mechanics and SN curve-based methods. The results reveal significant differences in estimated fatigue life between SN curve-based methods and fracture mechanics methods. These differences are likely due to limitations in the fracture mechanics model during the crack initiation phase. Changes in fracture mechanics parameters also had a significant effect on fatigue life, suggesting that if accuracy is important then material specific parameters are required. Despite the limitations shown, linear elastic fracture mechanics methods have a higher level of tailor-ability when compared to SN curve based methods and could offer benefits in situations such as the tracking of known flaws or in the assessment of changes to vessel configuration, or usage profiles.

Long-term assessment of wave conditions and wave energy resource in the Arctic Ocean

It was recently shown that the Arctic has been warming much faster than the rest of the globe during the last decades. This warming has reduced the ice extent significantly, which will strongly impact the wave climate in the Arctic regions, thus affecting the design of marine structures, operations, and energy resources. This study focuses on the higher latitudes, and uses the advanced wave hindcast NORA3, which covers a big part of the North Atlantic and the whole Arctic Ocean, to analyze the spatio–temporal properties of wave height and wave energy flux during the last three decades. The most energetic waves in the Arctic Ocean are observed in the Greenland Sea and the Barents Sea. The study shows that the substantial diminishing of sea ice in the Arctic induces local and regional changes in both mean and extreme wave conditions. In the Arctic Ocean the changes in extreme wave height are more pronounced compared to changes in mean wave conditions. The results also indicate a strong positive trend in the extreme wave heights in the Arctic regions of the Barents Sea, the Kara Sea, the Laptev Sea, the East Siberian Sea, the Chukchi Sea, and the Beaufort Sea.

Three-dimensional analytical solution of free vibrations of a simply supported composite plate in contact with a fluid

Background:The quantification of fluid–structure interactions is critical for the design and optimization of marine structures. As composite materials gain more traction in naval construction, there is a dire need of modeling tools to detail the dynamic response of composites in contact with fluids. Current structural theories and finite-element simulations offer promising pathways, but their strong hypotheses on through-the-thickness deformations and high computational cost challenge their practical feasibility. Methods:We propose an analytical three-dimensional solution to the free vibration of a bidirectional composite, separating a fluid column from vacuum. We leverage Pagano’s method to describe the three-dimensional displacement field in each ply of the composite plate and the fluid potential in the form of a Fourier series. Results:An analytical solution to the coupled fluid–structure problem is derived by imposing the continuity of displacement and stress at the ply interfaces, as well as boundary conditions on dry and wetted plies. We specialize the solution to sandwich structures of naval interest, offering insight on how the interactions with water can dramatically affect mode shapes and through-the-thickness profiles of displacement and stress. Discussion:The proposed approach provides the foundations for the design of thick composite plates for use in marine structures.

An efficient hybrid collocation scheme for vibro-acoustic analysis of the underwater functionally graded structures in the shallow ocean

In this paper, a novel hybrid collocation scheme based on the generalized finite difference method (GFDM) and the Burton–Miller singular boundary method (BMSBM) is developed to study the vibration and acoustic radiation characteristics of an underwater functionally graded (FG) structure immersed in the shallow ocean. By utilizing the individual strengths of both methods, the GFDM is adopted for the vibration analysis of the FG structures, while the BMSBM is applied for the acoustic wave radiation analysis. Numerical examples verify the accuracy and efficiency of the proposed hybrid collocation scheme for the natural frequency and acoustic radiation behavior of the underwater structures consisting of the functionally graded materials (FGMs). The influences of the material parameters, structural geometries and shallow ocean environment on the natural frequencies of the structural vibration and the underwater acoustic wave radiation field are investigated in detail. Numerical study shows that the variation trend of the natural frequencies of the structural vibration is consistent with that of the resonance peak frequencies of the underwater acoustic radiation field. The present results may provide valuable references for the design and application of underwater marine structures consisting of the FGMs.

Multivariate probability analysis of wind-wave actions on offshore wind turbine via copula-based analysis

Floating structures in service encounter extreme natural hazards, such as correlated extreme wind-wave loads. This study aims to provide realistic multivariate models of environmental parameters to accurately describe the statistical characteristics of metoceanic conditions, which are essential for the reliability-based design of marine structures. The multiload analysis method includes three major steps: (1) to identify the best-fit univariate marginal distributions of the wind-wave parameters. Mixed models composed of a set of single-mode parametric distributions were found to be more suitable for the measured variables. (2) To construct joint probability distributions of multiple variables using copula-based models, the performance of various models namely, trivariate metaelliptical copulas, Archimedean copulas, and vine copula models. It was observed that joint distributions can be best modelled using vine copula models with considerable flexibility. The final process involves establishing environmental surfaces and contours based on the inverse first-order reliability method. The most unfavourable combination of extreme design conditions can be defined on the environmental surface which is useful for evaluating the response characteristics of offshore wind turbines. These expressions provide a preliminary assessment of wind-wave loads on offshore structures.

Hydrodynamic analysis of the combined structure of offshore monopile wind turbine foundation and aquaculture cage

Reliable prediction in hydrodynamics is crucial for the design of marine structures, especially for columnar structures such as offshore wind turbine foundations. A combined structure of fixed monopile wind turbine foundation and bottom-seated circular aquaculture cage is proposed for efficiently utilizing the offshore space and reducing the wave forces on the monopile wind turbine foundation. A further developed volume-averaged numerical model is adopted to simulate the pressure drop due to clean and fouled cages by introducing the porous media theory, in which the coefficients of source terms are determined by the least square method based on hydrodynamic force on cage from existing experimental data. The Stokes fifth-order wave theory is considered reliable in simulating the nonlinear waves on slopes and corresponding inline wave force by comparing with multiple existing experimental data. Then the effects of incident wave steepness, seabed bottom slopes and cage diameters on simulation results are analyzed. Results reveal the fouled cage can effectively reduce inline wave forces relative to the clean cage of the combined structure, accompanying a significant resonance effect of wave motion inside the cage.