Development of environmental contours for first-year ice ridge statistics
Introduction
The reduction of both the extent and the thickness of ice in the Arctic during the recent decades has resulted in an increasing demand for development of offshore structures in order to explore natural resources and also for ice-capable vessels that are able to navigate along Arctic shipping routes [1]. For ice-capable vessels sailing in Arctic regions, a number of different ice types will be encountered, such as level ice, broken ice, rafted ice, ice rubble fields and ice ridges. The ice conditions along the Arctic shipping routes mostly consist of first-year ice, but with rather few ice features appearing during the summer season. Among the aforementioned ice types, first-year sea ice ridges are assumed to pose a major threat to ships in Arctic regions since they frequently determine and govern the design loads on the ship hull [2].
Current Arctic ship designs are mainly based on rules and regulations, such as the Finnish-Swedish Ice Class Rules (FSICR), International Association of Classification Societies (IACS) Polar Class rules, International Maritime Organization (IMO) Polar code, DNV rules and so on. These rules for ship structural design primarily rely on experience and deterministic solutions [3] and are attractive due to the simplicity of their application. However, ice-induced loads on ship hulls are random by nature [4], [5]. The randomness is caused by the variation of ice conditions (e.g., the physical and mechanical properties) in the Arctic regions and by the complexity of the ship and ice interaction process with respect to the various force components. Therefore, probabilistic methods should be applied to describe the stochastic aspects of ice loads, and a reliability-based design method that takes into consideration the randomness and uncertainties of the ice conditions and ice loads could enrich current rule-based design methods.
Within the framework of reliability-based design, the Ultimate Limit States (ULS) criteria which ensures that no significant structural damage occurs during the design life of a structure, represent essential requirements. For the design of Arctic ships, the ULS criteria implies that the vessel should be able to withstand the ice load actions associated with a specific exceedance probability (or a specific return period), both for the local and global actions on the vessels. In this study, the local ice loads are considered, which determine e.g. the loads acting on the transvers frames in the bow region during the ship and ice ridge interaction process. Generally, the most appropriate and accurate approach to estimate extreme ice loads is the full long-term response analysis that accounts for the contribution from each ice condition with specific physical and mechanical parameters and the probability of occurrence for each specific ice condition. However, such a long-term analysis is usually time-consuming for cases where numerical simulations with a high accuracy are required [6].
In order to improve the efficiency of the ULS design procedures which are applied at an early design stage, the environmental contour method is commonly applied as an alternative to the full long-term analysis and it has been widely used for the design of ships and offshore structures subjected to wave, and (or) wind loads, such as offshore platforms [7], wave energy converters [8], [9] and wind turbines [10], etc. In this work, the concept of environmental contours is firstly introduced for first-year ice ridge statistics and the environmental contour is defined as a collection of ice ridge conditions that correspond to a given return period [11]. Then, the desired extreme ice loads for the same return period can be estimated with a good accuracy on the basis of ice loads from the worst combination of ice ridge parameters along the generated environmental contour. Numerical load (or experiments) are accordingly only required for some selected ice conditions located along the environmental contour in order to calculate ice ridge loads and to find the worst ice condition.
Traditionally, the environmental contour for a given return period is established by the inverse first order reliability method (IFORM) and the joint probability distributions of the environmental parameters [12]. In addition to the IFORM, there are other methods that can be applied to generate environmental contours, such as Monte Carlo simulation [13], the copulas [14], the inverse second order reliability method (ISORM) [15] and the principal component analysis method [16].
The main focus of this work is on the development of environmental contours based on ice ridge statistics which can be used for reliability-based design. Specifically, the key parameters for characterization of ice ridges, which determine the ice loads on ship hulls, are identified according to the mechanisms behind the ice ridge and ship interaction process. Subsequently, probabilistic models are applied in order to represent these key parameters. On the basis of the IFORM and distributions of the key parameters for ice ridges, different dimensions of environmental contours for a given return period are generated corresponding to different models for the interaction process.
Section snippets
Background
Among the various ice conditions along Arctic shipping routes, first-year ice ridges are regarded to be a major threat that should be accounted for at the design stage. A typical example of a ship in an ice ridge field is presented in Fig. 1. Basically, a ridge is a line or wall of broken sea ice features that are forced upwards by pressure or shear [17]. When level ice floes are compressed and/or sheared by environmental driving forces, e.g. due to wind and current forces, ice ridges are
Environmental contour method
In this section, the principle of the environmental contour method used for reliability-based design and the generation of the environmental contour based on the IFORM are introduced. The ULS criteria can in general be expressed in the following form:where G(∙) denotes the failure function and the n-dimensional vector S = (S1, S2, …, Sn)T represents the environmental variables with the joint probability density function (PDF), fS(s). Y(S) represents the extreme loads acting on
Statistical models for key parameters
Based on the descriptions of the ship and first-year ice ridge interaction process provided in Section 2.2, the ice forces can be separated into two components, i.e. from the consolidated layer part and from the unconsolidated keel part. The consolidated layer is generally considered as a thick level ice. From the ISO standard [22], the experiments in Ref. [32] and numerical studies in Refs. [26], [41], [42], it is shown that the thickness of ice feature and ice flexural strength are key
Development of environmental contours
Based on the probabilistic models for the key parameters representing the ice ridge properties and the IFORM, different forms of environmental contours, such as two-dimensional contour lines, three-dimensional contour surfaces and four-dimensional manifolds are developed in this Section. Application of the environmental contour method for the purpose of extreme ice load estimation is available as illustrated in Section 5.1, while prediction of ice loads for the models proposed in 5.2
Conclusions and future work
Based on the ship and ice ridge interaction process, four parameters which characterize the first-year sea ice ridges are identified as the key quantities for determining the ice ridge loads on a ship hull. Probabilistic models are applied to represent the collected data for the key parameters. The principle underlying the environmental contour method is applied for the purpose of reliability-based design of Arctic ships. By applying the IFORM, different forms of environmental contours are
CRediT authorship contribution statement
Wei Chai: Original idea, Main draft, Coding, Analysis. Bernt J. Leira: Original idea, Draft revision, Supervision, Project manager. Arvid Naess: Draft review. Knut Høyland: Draft review, Supervision. Sören Ehlers: Draft review.
Acknowledgments
This work is supported by Research Council of Norway (RCN project number: 249272/O80). Financial support from The Joint Center of Excellence for Arctic Shipping and Operations, which is funded by the Lloyd's Register Foundation (grant number: GA\100077, project number at NTNU: 650263) is also acknowledged. The Lloyd's Register Foundation helps to protect life and property by supporting engineering-related education, public engagement and the application of research. This article is the last
References (57)
A comparison of stochastic process models for definition of design contours
Struct Saf
(2008)- et al.
Combining contours of significant wave height and peak period with platform response distributions for predicting design response
Mar Struct
(2010) - et al.
Modified environmental contour method for predicting long-term extreme responses of bottom-fixed offshore wind turbines
Mar Struct
(2016) - et al.
Alternative environmental contours for structural reliability analysis
Struct Saf
(2015) - et al.
Multivariate environmental contours using C-vine copulas
Ocean Eng
(2016) - et al.
Environmental contours based on inverse SORM
Mar struct
(2018) - et al.
Application of principal component analysis (PCA) and improved joint probability distributions to the inverse first-order reliability method (I-FORM) for predicting extreme sea states
Ocean Eng
(2016) - et al.
A comprehensive analysis of the morphology of first-year sea ice ridges
Cold Reg Sci Technol
(2012) - et al.
A numerical method for the prediction of ship performance in level ice
Cold Reg Sci Technol
(2010) - et al.
A six-degrees-of-freedom numerical model for level ice–ship interaction
Cold Reg Sci Technol
(2013)
Ice loads on inclined marine structures-Virtual experiments on ice failure process evolution
Mar struct
An engineering method for simulating dynamic interaction of moored ship with first-year ice ridge
Ocean Eng
Simulating transverse icebreaking process considering both crushing and bending failures
Mar struct
A comparison study on the estimation of extreme structural response from different environmental contour methods
Mar struct
Development of environmental contours using Nataf distribution model
Ocean Eng
A numerical model for real-time simulation of ship–ice interaction
Cold Reg Sci Technol
Numerical modeling of ice load on an icebreaking tanker: comparing simulations with model tests
Cold Reg Sci Technol
Effect of dynamic bending of level ice on ship's continuous-mode icebreaking
Cold Reg Sci Technol
A review of the engineering properties of sea ice
Cold Reg Sci Technol
Flexural strength equation for sea ice
Cold Reg Sci Technol
On the decay of first-year ice ridges: Measurements and evolution of rubble macroporosity, ridge drilling resistance and consolidated layer strength
Cold Reg Sci Technol
Mechanics of ice–structure interaction
Eng Fract Mech
Multivariate distribution models with prescribed marginals and covariances
Probab Eng Mech
Model tests of a submerged turret loading concept in level ice, broken ice and pressure ridges
Cold Reg Sci Technol
Assessment of uncertainty in environmental contours due to parametric uncertainty in models of the dependence structure between metocean variables
Appl Ocean Res
Estimating operability of ships in ridged ice fields
Cold Reg Sci Technol
Numerical Prediction of Ship-Ice Interaction: A Project Presentation
Cited by (5)
Ice ridge evolution: Investigation in-situ and computer simulations
2024, Polar ScienceAn investigation on the speed dependence of ice resistance using an advanced CFD+DEM approach based on pre-sawn ice tests
2022, Ocean EngineeringCitation Excerpt :During a simulation, the solver calculates the tensile and shear stresses between particles; if the stress exceeds its maximum limit, the bond breaks and the particles separate. This may be particularly useful to model phenomena containing ice breakups, such as a ship operating in level ice, large ice floes, and ice ridges (Ni et al., 2020; Chai et al., 2020; Li et al., 2021; Jeong et al., 2021). The maximum limit of stresses can also be set as a function of load and loading time, which is useful when the bond can be damaged under a continuous load (brittle fracture growth), e.g. ice in waves (Dolatshah et al., 2018; Huang et al., 2019; Passerotti et al., 2021; He et al., 2022).
A simplified calculation method of ice–structure–water dynamic interaction under earthquake action
2021, Extreme Mechanics LettersCitation Excerpt :The service environment of the offshore elevated pile structures is complex and affected by many factors [7,8]. From the perspective of design, sea ice is probably among the foremost factors to influence offshore structures, potentially compromising its structural integrity [9,10]. Understanding ice–structure interaction is critical for an efficient and safe design of offshore structures in ice-covered waters [11].
Structural design considerations for ships operating in arctic regions
2022, Chinese Journal of Ship ResearchRisk reasoning from factor correlation of maritime traffic under arctic sea ice status association with a bayesian belief network
2021, Sustainability (Switzerland)