Design Sea States Research Articles

Experimental analysis of extreme wave loads on a containership

Model-scale experiments were conducted to investigate the non-linearities associated with the Vertical Bending Moment (VBM) of a rigid container vessel in irregular waves. Long-duration runs ( ≃ 25 hours of data in full scale) were performed to allow the calculation of statistically meaningful extreme values of hogging and sagging on five different sea-states (from Hs = 6 m up to Hs = 17 m).The model tests are presented in detail, and sampling errors are estimated. It is found that the ratio between linear and non-linear VBM (the so-called non-linear factor) can be modeled as a function of the linear value only. For a given linear value, the non-linear correction is the same, whatever the sea state. This observation, new in the fully non-linear case, is very valuable as it opens the door to efficient design assessment methodologies such as increased design sea state or design waves.

Study of the wet-towing transportation of an FPSO with elastomeric-supporting topside modules

This study focuses on the wet-towing transportation of an FPSO with elastomeric-supporting topside modules. In the study, an approximation method is utilized to calculate the wet-towing resistance in the design sea state for determining the wet-towing configuration. Meanwhile, the study successfully achieves to simulate the hydrodynamic responses and structural interactions synchronously for the complex wet-towing system. This numerical method is applied to the feasibility analysis of the wet-towing configuration in the design sea state, which indicates that the mean wet-towing resistance, peak towline tension, and dynamic responses of the FPSO are all within the design scope, proving that the wet-towing configuration is feasible. A parameter sensitivity analysis is performed for the wet-towing transportation, which reveals that the increase in towing speed and severity of sea state results in larger towing resistance. Extending the towline length has a significant dampening effect on both peak towline tension and its fluctuation during extreme sea state. The excursions of wind, wave, and current incident directions from the towing route can lead to the offsets of the FPSO, so an auxiliary tug is necessary to keep the FPSO in the planned route, and the wet tow in head sea is recommended.

Wave-in-deck loads: an assessment of present design practice given recent improvements in the description of extreme waves and the nature of the applied loads

This paper contributes to the on-going discussion of how best to calculate the reliability of a fixed offshores structure. This discussion has been driven, in large part, by improved physical understanding of waves arising in realistic design sea-states, with a growing appreciation that many ‘design wave events’ will be breaking, irrespective of water depth. As such, it is increasingly acknowledged that some aspects of present design practice are non-conservative. In re-assessing older structures, the accurate calculation of horizontal wave-in-deck (WID) loads is often the most important and least tractable part. This paper explains the underlying reason, highlights the wider implications for identifying an appropriate design point, and raises fundamental questions in the assumptions underpinning present practice. Specifically, a large laboratory data base of WID events is used to assess the success of available models. These comparisons confirm that recommended practice, including recent updates, consistently under-predict the maximum WID loads on which reliability calculations should be based. In contrast the recently developed Lagrangian Momentum Absorption (LMA) model (Ma and Swan, 2020b), a simple but complete load model that combines fully-nonlinear wave inputs and the openness/porosity of a structure, provides highly accurate predictions. This is achieved without empirical coefficients/calibrations and therefore ideally suited to design/re-assessment applications.

A practical design procedure for initial sizing of heaving point absorber wave energy converters

Designing a wave energy converter with the proper size has always been challenging since it is a trade-off between many factors including cost, practicality, and energy output. In this paper a practical design procedure for sizing of heaving point absorbers wave energy converters is presented. Size can be represented by the body volume. Budal power bounds are deployed to obtain the body volume and annual mean absorbed power of the wave energy converter. Budal power bounds are determined for each sea state. Aiming a specific power capture ratio, several sets of design sea states with related design volume and annual mean absorbed power are defined. With the design objective of maximizing the ratio of mean power to submerged volume, and considering suitable design constraints, the best size is obtained. The proposed procedure will be then deployed for a case study and the design will be compared with an existing similar point absorber. The results show that the mean absorbed power does not depend on the size but is a function of selected sea states. Furthermore, the comparison study reveals that the proposed design procedure yields reasonable power characteristics.

Experimental and numerical study on the hydrodynamic loads on a single floating hydrocarbon storage tank and its dynamic responses

An innovative floating hydrocarbon storage facility (FHSF) has recently been proposed. The facility consists of several modular floating hydrocarbon storage tanks (FHSTs) surrounded by floating barges with compliant mooring system. Hydrodynamic loads on the FHST and its dynamic response are important for the global design. To validate the concept of the single FHST, model tests at 1:48.7 scale is performed in the coastal basin in National University of Singapore. Two models of single FHST with different bottom slab shapes are tested, one of which has bottom skirts. The mooring fenders to support the model were mimicked by a flexible beam system. Fresh water is used to fill the tank at different filling ratios. Decay tests, regular wave tests and irregular wave tests under design sea states are performed. The rigid body motions in six degrees of freedom and the sum fender reaction forces were measured. Numerical model of the single FHST is established and analyzed in frequency domain and time domain. The effect of the bottom skirt, internal liquid, and the fender system were considered. Viscous damping is calculated based on the empirical formula and adjusted by comparing with measured results. Numerical results are comparative to the experimental results. This paper shows the motions of the tested FHSTs are mild even in the 100-year storm, and the bottom skirts effectively reduce the hydrodynamic responses.

Fast random wave generation in numerical tanks

Generating and absorbing random waves in numerical models is a challenging problem, in particular when meaningful wave statistics should be generated to meet design sea-state requirements. The methodology presented herein allows for the generation of random wave fields (free surface elevation and velocities) to be reconstructed in time and in space by using window processing from a reference time series. It is demonstrated that the methodology is efficient in reproducing long non-repeating wave sequences by using only O(101)–O(102) wave components, rather than O(103)–O(104) required by a direct reconstruction from a single spectrum. This reduces the computational times required for the development of wave-train time-series elements by 40 times. Errors in instantaneous surface elevation and particle velocity between windowed and non-windowed reconstruction techniques were less than 0·4 and 0·2%, respectively, in the cases considered. The technique was combined with the relaxation zone method typically used in numerical wave tanks for generating waves. The simulations were performed using Proteus, a rapidly developing CFD−FEM toolkit for modelling fluid−structure interaction cases. The use of windowed reconstruction reduced the overall computational time associated with the simulation of waves in a numerical wave tank by ∼40 and ∼70% for serial and parallel execution. Results of the study show windowed reconstruction to be suitable for the representation of long-duration wave trains. Wave height and peak period are conserved within 2 and 1%, respectively.

Eliciting features of 2D greenwater overtopping of a fixed box using modified dam break models

Greenwater overtopping of a 2D fixed rectangular box due to focused wave groups is investigated using Computational Fluid Dynamics (CFD). Simulations span a wide parameter space, such that a range of overtopping types previously observed in experiments - including dam-break, plunging plus dam-break and hammer fist events - are observed. For each greenwater event the horizontal momentum flux and overtopping volume are computed, as these represent integrated quantities linked to damage potential on offshore facilities. These values are compared to simplified predictions based on the classical dam-break model with the dam height based on a run-up calculation on the box. It is found that these predictions deviate from measurements made in the CFD simulations because the classical model omits physics evident during overtopping events. Modifications to the classical dam-break model are presented to account for (i) the finite duration of an overtopping event; (ii) the finite quantity of water in the crest of a wave which exceeds the freeboard; (iii) the local geometry at the edge of the box; and (iv) the horizontal momentum in the crest of a wave which exceeds the freeboard. Insight gained from the first of these corrections leads to a new parameter- the relative overtopping duration T', defined as the ratio of the duration for which fluid exceeds the freeboard to the natural time scale for runout of a dam with height equal to maximum run-up above freeboard. It is found that this new parameter dramatically reduces scatter in the integrated quantities. The results suggest that this new parameter, which combines freeboard exceedance and overtopping duration, may be an efficient indicator for screening metocean conditions to identify design sea states.

Design loads and long term distribution of mooring line response of a large weathervaning vessel in a tropical cyclone environment

The mooring design of a floating offshore structure requires the estimation of mooring responses corresponding to annual exceedance probabilities of 10−2 (extreme event) and sometimes 10−4 (survival event). The most straightforward method to determine the extreme design response under a specified design sea state, is to carry out N time domain simulations, so as to capture the inherent randomness of this sea state and use the N maximum values to estimate the most probable maximum response for design. However, this requires typically 30–40 time-domain analyses of the same design sea state, which is computationally extensive. In this paper it is shown that the required number of time domain simulations can be reduced significantly by utilising the peaks of the mooring tension time series, obtained from time domain simulations, to derive a distribution for the maxima. Different variations of using these peaks are explored and a “best practice” for this technique is proposed. In order to establish a robust benchmark for evaluating and validating this “best practice”, extensive time domain simulations have been carried out for a large permanently connected, weathervaning vessel, with catenary mooring system, in a tropical cyclone environment. Both extreme and survival conditions are explored, by running 170 3-h simulations for each condition, thereby representing in detail the random nature of each sea state. It is shown that a reliable distribution for the maxima, (within ±4% from the benchmark) can be obtained in a manner which is simple and computationally efficient, based on just 4–7 time domain analyses. Thus by using more peaks from the time domain analyses, there is a significant gain in terms of accuracy and efficiency. The above “best practice” is used to calculate the most probable maximum mooring line response and the variability of this maximum (short term variability) within a 3-h sea state for environmental conditions with annual exceedance probabilities of 10−2 and 10−4. It is shown that the short term variability is not invariant but may be described in terms of a Gumbel distribution whose parameters depend on the magnitude of the response. These expressions provide a means of calculating the long term distribution of mooring line load, accounting for the short term variability, which can be used to address the reliability of a mooring system.

On the Sensitivity of Optimal Wave Energy Device Geometry to the Energy Maximizing Control System

Wave energy converters (WECs) are traditionally designed independently of control systems. This usually involves matching the device frequency response to the predominant sea spectrum of a specific site. Energy maximizing control systems are subsequently employed to improve the energy conversion of the device for sea states other than the design sea state. It is well known that some control techniques have the ability to change the characteristics of a wave energy device, allowing it to improve the power absorption for frequencies other than the device natural frequency. However, while the controllers do their best to broaden the device frequency response, they can be limited in their capability to produce an overall optimal system. A different approach is studied in this paper, where iteration is performed between geometry optimization and control design. The aim is to investigate the implications of geometry optimization in the absence of control and the ultimate effect of incorporating the control design at the geometry optimization stage. Unconstrained control strategies are considered, namely, latching, declutching, and a model predictive control-like algorithm. It is shown that different optimal WEC geometries can be obtained depending on whether the device is controlled or not and the type of controller employed. The differences in overall power absorption characteristics of the optimized geometries are presented.

Soil-structure interaction analysis of jack-up platforms subjected to monochrome and irregular waves

As jack-up platforms have recently been used in deeper and harsher waters, there has been an increasing demand to understand their behaviour more accurately to develop more sophisticated analysis techniques. One of the areas of significant development has been the modelling of spudcan performance, where the load-displacement behaviour of the foundation is required to be included in any numerical model of the structure. In this study, beam on nonlinear winkler foundation (BNWF) modeling—which is based on using nonlinear springs and dampers instead of a continuum soil media—is employed for this purpose. A regular monochrome design wave and an irregular wave representing a design sea state are applied to the platform as lateral loading. By using the BNWF model and assuming a granular soil under spudcans, properties such as soil nonlinear behaviour near the structure, contact phenomena at the interface of soil and spudcan (such as uplifting and rocking), and geometrical nonlinear behaviour of the structure are studied. Results of this study show that inelastic behaviour of the soil causes an increase in the lateral displacement at the hull elevation and permanent unequal settlement in soil below the spudcans, which are increased by decreasing the friction angle of the sandy soil. In fact, spudcans and the underlying soil cause a relative fixity at the platform support, which changes the dynamic response of the structure compared with the case where the structure is assumed to have a fixed support or pinned support. For simulating this behaviour without explicit modelling of soil-structure interaction (SSI), moment-rotation curves at the end of platform legs, which are dependent on foundation dimensions and soil characteristics, are obtained. These curves can be used in a simplified model of the platform for considering the relative fixity at the soil-foundation interface.

A new approach to environmental contours for ocean engineering applications based on direct Monte Carlo simulations

The environmental contour concept is often applied in structural ship design in conjunction with the inverse first order reliability method (IFORM). It allows the great advantage of considering the environmental loads independently of the structural response of the ship. In this way, design sea states may be identified along the contour and time consuming response calculations are only needed for a limited set of design sea states. The traditional way of establishing such environmental contour lines is by applying the Rosenblatt transformation and identify the circle (in two dimensions) with radius equal to the reliability index βr. The points along this circle are then transformed back to the original environmental space, specifying the closed contour. In this paper, an alternative approach for establishing environmental contour lines in the original environmental space is proposed, eliminating the need for any transformations. For a given failure probability, Pf, the resulting contour line encloses a convex region in the environmental space. For any design with a convex failure region not intersecting this region, the probability of failure is at most Pf. Thus, the contour line can be used to obtain an upper bound on the failure probabilities of a large class of designs. This approach utilizes Monte Carlo simulations of the joint environmental model and is generally found to perform well. Advantages are that it yields a more precise interpretation and allows for more flexible modeling of the environmental parameters. In addition, possible over- or underestimation of failure probabilities due to the Rosenblatt transformation inherent in the traditional approach can be avoided with the proposed method.

A simplified method to downscale wave dynamics on vertical breakwaters

A coastal structure is usually designed with the final objective to guarantee its functionality and stability throughout its life cycle. Regarding stability, the three main failure modes are sliding, overturning and failure of the foundations. To accomplish the design objectives, a design sea state is usually used when calculating the loads and scour around the structure. This design sea state corresponds to a certain sea state with specific return period values of a significant wave height. However, the combination of different simultaneous sea state parameters can produce other critical situations compromising the stability of the structure which then require the calculation of long time series of wave forces corresponding to long-term historical wave situations. Moreover, a design force associated to a certain return period can be defined from the time series of the stability parameters. The most accurate techniques which can be used to estimate structure stability are based on numerical and physical models, but these are very time consuming and the calculation of long time series is therefore unfeasible. Here, we propose a hybrid methodology to transform wave conditions into wave forces acting upon vertical structures and scour around it. The methodology consists of a selection of a subset of sea states representative of wave climate at the structure location, using a maximum dissimilarity algorithm, The wave forces acting upon the structure and scour around it, for the wave situations selected, are then estimated as is the reconstruction of the calculated parameters corresponding to historical sea states using an interpolation technique based on radial basis function. The validation of the results, through a direct comparison between reconstructed series and analytically (semi-empirical formulations) calculated ones, confirms the ability of the developed methodology to reconstruct time series of stability parameters on vertical breakwaters. This methodology allows its application to numerical and physical models.

Endurance Wave Analysis (EWA) and its application for assessment of offshore structures under extreme waves

The aim of this paper is to introduce a novel approach, called Endurance Wave Analysis (EWA), for non-linear dynamic analysis and assessment of offshore structures subjected to irregular wave forces. This is, in fact, an extension of the Endurance Time Analysis (ETA) already presented by previous researchers for the seismic assessment of onshore structures. With the EWA method, the offshore structure is simulated under a predefined Intensifying Wave Train Function (IWTF), corresponding to a gradually deteriorating sea state at a specific site. The function is designed so that the roughness of the sea state represented by them increases over the time and even goes well beyond the design sea state. The IWTF is then used for the non-linear dynamic analysis of the structure. Using EWA, damage indices or any other desirable parameters, from the linear elastic range of behavior to permanent deformation or complete collapse level, can be studied directly in terms of the sea state roughness. Structural integrity can then be evaluated based on the EWA results. In this paper the concept of the EWA is presented and the method is examined on sample offshore platforms. Different irregular IWTFs are generated and employed to evaluate the integrity of the three two-dimensional example steel jacket type platforms. The results clearly show that the proposed method is very effective for the dynamic non-linear analysis and assessment of offshore structures subjected to sea loads.

The Effect of Declustering in the r-Largest Maxima Model for the Estimation of HS-Design Values

A major problem often encountered in design sea-state prediction is the limited amount of available extreme- type wave data. The Annual Maxima model is consistent with the conditions of the mathematical background of Extreme Value Theory, yet its application raises statistical uncertainties in cases where the initial data population is limited. Due to this, alternative models of similar theoretical background have been developed to describe extreme values, including the maxima method. A main problem in applying this model refers to the appropriate selection of a sample com- prising the r independent maxima within each year of the available time series: since in nature environmental extremes tend to appear in clusters, the native time series under examination should be appropriately de-clustered to satisfy the independency assumption. Some established declustering procedures refer to: a) the selection of a Standard Storm Length, b) the combination of a run length k and a relatively high threshold value u (Runs declustering), c) the estima- tion of wave energy reductions between consecutive sea-state systems (DeClustering Algorithm) and d) the selection of the three largest monthly maxima of each year of the initial significant wave height time series (triple annual maximum series). The aim of this paper is to assess the effect of the aforementioned declustering procedures on the numerical results obtained by the r-largest model.

역 일계이차 모멘트법을 이용한 설계 해상상태의 결정에 관한 연구

Response-based approach is getting more preferred in determining the design sea-state for offshore structures because traditional environment-based approach is known to yield a much conservative design condition. This paper introduces the inverse first-order second-moment (IFOSM) method as a response-based approach, which is expected to give a more feasible design condition at the cost of reasonable number of motion analyses. The IFOSM method is based on the theory of probability and adopts an optimization scheme to determine the design point. Both the design maximum response and design sea state can be obtained straightforwardly from the optimum. The IFOSM method has been applied to a turret-moored FPSO's design problem and showed its effectiveness in practical use.

Post-Katrina performance of a turret-moored floating storage and offloading unit in the Gulf of Mexico

Conventional design of ships and offshore platforms relies on performing a short-term response analysis for metocean conditions with a 100-year return period. This approach is efficient but not necessarily conservative when compared with a comprehensive long-term response analysis that considers platform responses for storms encountered over the lifetime of the platform. Turret-moored floating production, storage and offloading systems are sensitive to non-collinear wind, waves, and current conditions. During hurricanes in the Gulf of Mexico such conditions frequently occur and, depending on the resulting weathervaning characteristics of a turret-moored tanker, they may have a strong impact on vessel motions, mooring line loads, and riser performance. In recent years some very strong hurricanes have occurred in the Gulf of Mexico, e.g. Katrina and Rita in 2005. When including these recent storm data in the long-term response analysis they have a marked effect on the extrapolated 100-year long-term responses. The post-Katrina long-term responses of a generic turret-moored floating storage and offloading unit are evaluated and compared against pre-Katrina analysis results. The results of the analysis are used to stipulate response-based design criteria which are simple short-term design sea states that can reproduce a given long-term response (e.g. roll).

Design Loads Used for Direct Strength Assessment of Merchant Ship Structures

This paper summarizes the results of extensive research on the design loads used for strength assessment of merchant ship structures such as tankers, bulk carriers, and container ships. The main aim of the research was to develop practical estimation methods of design loads having rational technical backgrounds acting on primary structural members of tankers, bulk carriers, and container ships. During this study we will do the following. (1) The design sea states that closely resemble the actual sea states which are considered as the most severe for hull structures are proposed. (2) The practical estimation methods of the design sea states are proposed by parametric studies using the results of series calculation of representative merchant ships. (3) The practical estimation methods of design regular waves resulting in the same level of stresses as that induced in irregular waves under the design sea states are proposed. (4) The practical estimation methods of the design loads such as ship motions, accelerations, hull-girder bending moments, and hydrodynamic pressures that are induced under design regular waves are briefly introduced. The findings in this study have been summarized and implemented in the new design standards for tanker, bulk carrier, and container ship structures (“Guidelines for Tanker Structures,” 2001, Nippon Kaiji Kyokai; “Guidelines for Bulk Carrier Structures,” 2002, Nippon Kaiji Kyokai; “Guidelines for Container Carrier Structures,” 2003, Nippon Kaiji Kyokai).

Design sea state assessment using genetic algorithm approach

Two major statistical issues can be distinguished in the procedure of wave extreme prediction. The first issue is that predicted extreme values must be based on data collected in a relatively short time. The second issue is extrapolation of the observed data into its extreme region, typically lying well beyond from even the most extreme available observation. The process of extrapolation plays a fundamental role in this area of analysis and therefore it is essential to fit empirically a convenient probability distribution that describes the available data as closely as possible. Determination of extreme values probability distribution parameters by genetic algorithm is applied to improve the methodology of extreme sea state prediction. Illustrative applications of the method are given for a North Atlantic sea environment. The results are presented as crest height maximum values occurring with a given probability or in a design storm that has a specified return period.

Extensive study on the design loads used for strength assessment of tanker and bulk carrier structures

ClassNK has undertaken wide-ranging basic research covering many aspects related to the safety of ship structures, including design loads, structural analysis, strength assessment of buckling, collapse, and fatigue, and rational corrosion margins to develop new design standards which have transparency and consistency. Among the wide-ranging basic research, this article summarizes the results of extensive work on the design loads used for strength assessments of tanker and bulk carrier structures. The main aim of the research was to develop practical estimation methods of design loads with rational technical backgrounds relating to the actual loads acting on the primary structural members of tankers and bulk carriers. During this study, we proposed the following methodology. Design sea states that closely resemble the actual sea states which are considered to be the most severe for hull structures. Find practical estimation methods for the design sea states by parametric studies using the results of series calculations on representative tankers and bulk carriers. Find practical estimation methods for design regular waves which will result in the same level of stresses as those induced in irregular waves under the design sea states. We also briefly introduced some practical estimation methods for the design loads, such as ship motions, accelerations, hull-girder bending moments, and hydrodynamic pressures that are induced under design regular waves. The findings in this study have been summarized and implemented in the new design standards for tanker and bulk carrier structures.

Long term prediction of non-linear vertical bending moments on a fast monohull

An assessment is made of the maximum wave induced bending moment expected to occur during the operational lifetime of a fast monohull, based on long term distribution calculations of the non-linear vertical bending moment at mid-ship. The ship is assumed to operate in the Northern North Sea, with an operational life of 25 years. A succession of short-term stationary ship responses represented by Rayleigh distributions of peaks results in the long-term distribution of the structural loads. Non-linear pseudo transfer functions are used in the procedure to calculate the variances of the short-term responses. The amplitudes of these transfer functions are calculated by a non-linear time domain seakeeping program. The results are compared with rules minimum required values and also with results from simpler calculation procedures such as adopting design sea states.