Parallel channels' fracturing mechanism during ice management operations. Part I: Theory
Introduction
An important objective for a physical ice management operation is to reduce the size of drifting ice floes that will interact with downstream protected structures (e.g., platforms and drilling vessels). This can be achieved via different ice management strategies. Typically, several icebreakers are hierarchically deployed upstream and operated with different prescribed patterns to systematically breakdown the incoming large ice floes. The designed operational patterns include circular, elliptical, (linear/arched) racetrack, orbital, and linear patterns (Hamilton et al., 2011a; Hamilton et al., 2016). For all these different patterns, the icebreakers' tracks over ice usually form a series of parallel channels (see Fig. 1a) filled with newly broken ice rubble (i.e., brash ice). Notably, it was often observed that long cracks were formed between parallel channels, leading to a further reduction in ice floe sizes (Farid et al., 2014; Hamilton et al., 2011a). The term ‘long cracks’, as adopted herein, is to make a differentiation from conventional fracture patterns such as radial and circumferential cracks formed during interactions of level ice and sloping structure (e.g., the bow region of an icebreaker or an offshore structure with a sloping surface at the waterline/ice line). The differentiation follows a similar theoretical framework as laid down by Goldstein and Osipenko (1993, 1983), who separated fractures into outer and inner problems during ship – ice interactions. The long cracks studied in this paper fall into the category of the outer problem, which is largely influenced by the floe ice's boundaries and confinement (Goldstein and Osipenko, 1983). Fig. 1a illustrates one such long crack captured during the Oden Arctic Technology Research Cruise in 2015 (OATRC2015). An overview of OATRC2015 is given by Lubbad et al. (2016); Fig. 1b conceptually highlights the described fracturing phenomena during ice management operations.
Such ice fracturing phenomena are rather important while designing ice management operations. Hamilton et al., 2011a, Hamilton et al., 2011b developed a numerical simulator based on ship and ice field kinematics to quantify the performances of different ice management strategies. One critical assumption of the simulation is that ice floes with aspect ratios of 1:1 are ‘naturally’ generated between two parallel channels. Given the distance between two parallel channels, the downstream managed ice floe size is thus quantified. This assumption was mainly based on field observations, as there exist no theoretical explanations or experimental quantifications. This paper (i.e., Part I of two sequential papers) seeks to offer a theoretical explanation regarding such an observed ‘parallel channels’ fracturing mechanism’. The sequel paper (i.e., Part II) reports comparisons between the theoretical results and full-scale data collected by conducting well-controlled experiments in the field. The two papers address and answer practical questions regarding, for example, ‘optimised parallel channel spacing’ and ‘out-going floe size’ for specific ice management operations. Moreover, the theoretical formulations presented herein are useful to enhance the capacities of the numerical Simulator for Arctic Marine Structures (SAMS, 2018) so that it can be used to evaluate different ice management strategies. For a description of SAMS, its theoretical background and potential applications, the reader is referred to (Lu, 2014; Lubbad and Løset, 2011; Lubbad and Løset, 2015; Lubbad et al., 2018).
This paper starts with qualitative field observations regarding the ice fracturing phenomena between parallel icebreaker channels. Based on field observations and knowledge regarding ship – level ice interactions, a theoretical model is proposed to address one of the important contributors to the observed long cracks. The theoretical model entails an edge crack's propagation and kinking in the presence of a neighbouring free boundary. Extensive parametric studies were carried out on the theoretical model. All the analyses are carried out with an eXtended Finite Element Method (XFEM) based numerical scheme. The numerical results were further fitted to analytical closed-form formulae conforming to both existing analytical results in limiting scenarios (i.e., asymptotic solutions) and field experiments. In the sequel paper (Paper II), the developed analytical formulations will be verified against a series of well controlled parallel channel tests undertaken during OATRC2015.
Section snippets
Ice fracturing during ship – Level ice interactions
Before we present the ship – ice interactions under the presence of an adjacent parallel channel, it is beneficial to take a retrospective look into the theory of ship – level ice interactions. This is because the theory can be further extended to the observed ‘parallel channels’ fracturing mechanism’. Particularly, it is the ice breaking/fracture patterns that are of interest here. It is generally accepted that during ship – level ice interactions, aside from local crushing and potential
Methods
With the proposed edge crack model in Fig. 6b, we are to establish the relationship among geometrical factors (i.e., h and A0), crack propagation criteria related terms (i.e., SIFs KI and KII) and the eventual crack propagation path. Ultimately, we shall address practical questions such as 1) what is the maximum channel spacing hmax beyond which the long crack ceases to develop and 2) what is the maximum floe size Lmax that can be produced between two parallel channels with a given spacing. In
Benchmark tests
Before we apply the proposed methods and numerical scheme to our problem, relatively simplified benchmark tests were conducted to validate the numerical model. The benchmark test results are presented herein.
Results
After the satisfactory benchmark tests conducted in the previous section, the developed numerical scheme was applied to the proposed test setup in Fig. 11 to study the edge crack's propagation.
Discussion
This paper offers a theoretical explanation of the observed long cracks that frequently develop between two parallel channels during ice management operations. After revisiting the theories concerning ship – level ice interactions and corresponding ice fracture patterns, the theoretical model shown in Fig. 6, i.e., an edge crack scenario, has been proposed to explain the observed parallel channels' fracturing mechanism. The theoretical model was extensively studied using a separately developed
Conclusions
Based on a review and discussion of the theories regarding level ice – ship interactions, the physics behind parallel channel fracture mechanisms were presented. The observed long cracks between two parallel channels are considered to be caused by the presence of a nearby free boundary. In lieu of this, a theoretical model involving the splitting of an edge crack has been proposed in this paper. The model was extensively studied using a separately and purposely developed eXtended Finite Element
Acknowledgements
The Oden Arctic Technology Research Cruise 2015 (OATRC2015) was supported by the ExxonMobil Upstream Research Company and performed by the Norwegian University of Science and Technology (NTNU) in cooperation with the Swedish Polar Research Secretariat (SPRS) and the Swedish Maritime Administration (SMA). In addition, OATRC2013, which was sponsored by Statoil, is also acknowledged because part of the data was used for this paper. The research is also funded by VISTA – a basic research program in
References (69)
Analysis for splitting of ice floes during summer impact
Cold Reg. Sci. Technol.
(1988)- et al.
Weight function for an edge-cracked rectangular plate
Eng. Fract. Mech.
(2014) - et al.
Asymptotic analysis of crack interaction with free boundary
Int. J. Solids Struct.
(2000) Stress intensity factor calculations based on a conservation integral
Int. J. Solids Struct.
(1978)- et al.
Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements
Cem. Concr. Res.
(1976) - et al.
Mixed mode cracking in layered materials
Adv. Appl. Mech.
(1991) - et al.
In-plane fracture of an ice floe: a theoretical study on the splitting failure mode
Cold Reg. Sci. Technol.
(2015) - et al.
Out-of-plane failure of an ice floe: radial-crack-initiation-controlled fracture
Cold Reg. Sci. Technol.
(2015) - et al.
Fracture of an ice floe: local out-of-plane flexural failures versus global in-plane splitting failure
Cold Reg. Sci. Technol.
(2016) - et al.
A numerical model for real-time simulation of ship-ice interaction
Cold Reg. Sci. Technol.
(2011)
A numerical method for the prediction of ship performance in level ice
Cold Reg. Sci. Technol.
Comment on the spalling and edge-cracking of plates
Scr. Metall. Mater.
The edge cracking and spalling of brittle plates
Acta Metall.
Finite elements for determination of crack tip elastic stress intensity factors
Eng. Fract. Mech.
Fracture Mechanics: Fundamentals and Applications
Scaling of sea ice fracture-part I: vertical penetration
J. Appl. Mech.
Scaling of sea ice fracture-part II: horizontal load from moving ice
J. Appl. Mech.
Fracture and Size Effect in Concrete and Other Quasibrittle Materials
Elastic crack growth in finite elements with minimal remeshing
Int. J. Numer. Methods Eng.
Failure analysis of impacting ice floes
Journal of Offshore Mechanics and Arctic Engineering
360 Camera System for Mornitoring Ice Conditions
The fracture toughness of ice
Ice-Structure Interaction
Splitting of ice floes
Radial cracking with closure
Int. J. Fract.
Scale effects on the in-situ tensile strength and fracture of ice. Part II: first-year sea ice at Resolute, NWT
Int. J. Fract.
Scale effects on the in-situ tensile strength and fracture of ice part I: large grained freshwater ice at Spray Lakes reservoir, Alberta
Int. J. Fract.
The ship-ice interaction
Dynamics of continuous-mode icebreaking by a polar-class icebreaker hull
J. Ship Res.
Indentation spalling of edge-loaded ice sheets
Sea ice management trials during oden Arctic technology research cruise 2013 offshore north East Greenland
Some aspects of fracture mechanics of ice cover
Fracture mechanics in modeling of icebreaking capability of ships
J. Cold Reg. Eng.
Ice management for support of arctic floating operations
Simulation of ice management fleet operations using two decades of Beaufort Sea ice drift and thickness time histories
Cited by (17)
Numerical simulation of heterogeneous ice sheet-structure interaction based on cohesive element method
2024, Applied Ocean ResearchInvestigation of the fracture mechanism of level ice with extended finite element method
2022, Ocean EngineeringCitation Excerpt :Lu et al. (2012) firstly applied extended finite element method to simulate the failure of ice wedge, and the results showed that the bending fracture could be well presented by this method. After that, Lu et al. (2017, 2018) established a numerical scheme for simulating splitting cracks of ice floe and investigated the fracture mechanism of sea ice between parallel channels. The feasibility of using this approach to study splitting cracking was verified by comparing the numerical results with full-scale ship tests and ice floe fracture tests.
Dynamic bending of an ice wedge resting on a winkler-type elastic foundation
2022, Cold Regions Science and TechnologyCitation Excerpt :Because of the simplicity of Eq. (13), fast calculations can be easily achieved given different ice wedge bending scenarios. Comparing the numbers in Table 5 with an actual engineering case with the icebreaker Otso, Frej and Oden in Fig. 26(a) (taken from (Johansson and Liljestrom, 1989)), we see that for the case with the ice thickness h = 1 m, all three ice breakers' full transit speeds vary from around 3 m/s to 4.5 m/s; whereas in Table 5, Eq. (13) can accommodate the ship speed as an input ranging from 0.1 m/s to 10 m/s. Moreover, Fig. 26(b) shows that in this particular case, the icebreakers can offer a maximum net thrust (i.e., used to overcome the ice resistance) in the range from around 1.2 MN to 1.8 MN, whereas in Table 5, the range of fb can be up to 2.07 MN for only one ice breaking event (normally there are several ice breaking events taking place simultaneously around the ship hull for ice – going ships transiting in level ice (Enkvist et al., 1979, Lu et al., 2018)). With this concrete example, we demonstrated that there is a large margin for the use of Eq. (13) when it comes to its engineering applications.
Performance quantification of icebreaker operations in ice management by numerical simulations
2022, Cold Regions Science and TechnologyA review for numerical simulation methods of ship–ice interaction
2020, Ocean EngineeringCitation Excerpt :For example, an analytical solution regarding an infinite wedge beam on the support of an elastic foundation was broadly employed in calculating the ice-breaking load for level ice–ship interactions numerically tabulated the results of an infinite ice wedge’s flexural failure (Kotras, 1983; Lubbad and Løset, 2011; Milano, 1973). This continuous bending behavior creates an identifiable fragmentation pattern, i.e. the consecutive arrangements of cusps (or small blocks in shape of half-moon) and wedges along the waterline of ship stem (Naegle, 1981; Lu et al., 2018b). Empirical formulae were used to estimate an ice wedge’s flexural failure and to construct numerical tools to study level ice–ship interactions (Su et al., 2010a; Liu et al., 2006).
An overview of the Oden Arctic Technology Research Cruise 2015 (OATRC2015) and numerical simulations performed with SAMS driven by data collected during the cruise
2018, Cold Regions Science and TechnologyCitation Excerpt :In regard to the validation of SAMS, the OATRC2015 expedition provides ample cases and data sets to validate each module separately and collectively. For example, within this special issue, Tsarau et al. (2018) utilised the OATRC2015 data to validate the developed propeller wash model within the hydrodynamic module, and Lu et al. (2018a, 2018b) developed and validated analytical formulas to account for the kinking behaviour of long splitting cracks, and these analytical formulae became a further enrichment to the existing fracture module. The following text, on the other hand, focuses on the overall validation of SAMS using OATRC2015 full-scale data.