Contents lists available at ScienceDirect Structural Safety journal homepage: www.elsevier.com/locate/strusafe Development of environmental contours for frst-year ice ridge statistics Wei Chai a,b,c, ⁎ , Bernt J. Leira c, ⁎ , Arvid Naess d , Knut Høyland e , Sören Ehlers f a Key Laboratory of High Performance Ship Technology (Wuhan University of Technology), Ministry of Education, Wuhan, China b Departments of Naval Architecture, Ocean and Structural Engineering, School of Transportation, Wuhan University of Technology, Wuhan, China c Department of Marine Technology, Norwegian University of Science and Technology, Trondheim, Norway d Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway e Sustainable Arctic Marine and Coastal Technology (SAMCoT), Centre for Research-based Innovation (CRI), Norwegian University of Science and Technology, Trondheim, Norway f Institute for Ship Structural Design and Analysis, Hamburg University of Technology, Hamburg, Germany ARTICLEINFO Keywords: Environmental contours Ice ridge Reliability-based design ABSTRACT Ice ridges represent a major threat to ships and ofshore structures in areas with sea ice but no icebergs, since they frequently determine and govern the structural design loads. This work focuses on the development of environmental contours for frst-year sea ice ridge statistics, which are able to represent the key parameters that will infuence the extreme loads that would be acting on ice-capable vessels sailing in Arctic regions. Based on the inverse frst order reliability method (IFORM), the development of environmental contours to be applied for the reliability-based design of ice-capable vessels in Arctic regions is elaborated. The number of relevant parameters and hence the dimension of the space containing the environmental contour will depend on the particular ice-vessel interaction model that is to be applied. Furthermore, the infuence from the degree of correlation between the environmental parameters as well as from the number of ship-ice ridge interaction during the voyage on the environmental contour shapes are studied. 1. 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 ofshore structures in order to explore natural re- sources and also for ice-capable vessels that are able to navigate along Arctic shipping routes [1]. For ice-capable vessels sailing in Arctic re- gions,anumberofdiferent ice types will be encountered, such as level ice, broken ice, rafted ice, ice rubble felds and ice ridges. The ice conditions along the Arctic shipping routes mostly consist of frst-year ice, but with rather few ice features appearing during the summer season. Among the aforementioned ice types, frst-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 regula- tions,suchastheFinnish-SwedishIceClassRules(FSICR),International Association of Classifcation 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 simplicityoftheirapplication.However,ice-inducedloadsonshiphulls 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 as- pects 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. Withintheframeworkofreliability-baseddesign,theUltimateLimit States (ULS) criteria which ensures that no signifcant structural da- mage 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 asso- ciated with a specifc exceedance probability (or a specifc 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 actingonthetransversframesinthebowregionduringtheshipandice https://doi.org/10.1016/j.strusafe.2020.101996 Received 23 December 2018; Received in revised form 29 November 2019; Accepted 4 June 2020 ⁎ Corresponding authors at: Departments of Naval Architecture, Ocean and Structural Engineering, School of Transportation, Wuhan University of Technology, Wuhan, China (W. Chai). E-mail addresses: chaiwei@whut.edu.cn (W. Chai), bernt.leira@ntnu.no (B.J. Leira), arvid.naess@ntnu.no (A. Naess), knut.hoyland@ntnu.no (K. Høyland), ehlers@tuhh.de (S. Ehlers). Structural Safety 87 (2020) 101996 0167-4730/ © 2020 Elsevier Ltd. All rights reserved. T