Review on Advances in Research of Ice Loads on Ice-going Ships

TIAN Xi-min,ZOU Zao-jian,YU Ji-jun,WANG Fu-hua

(1.School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;2.Marine Design&Research Institute of China,Shanghai 200011,China)

0 Introduction

Geography of the arctic refers to the north of the Arctic Circle,with a total area of 21 million square kilometers including the Arctic Ocean,and about 8 million square kilometers island and mainland areas of the Arctic have been divided by the countries surrounding the Arctic.

According to the assessments made by the U.S.Geological Survey(USGS)in 2008,about 30%of the word’s undiscovered gas and 13%of the world’s undiscovered oil are stored in the North Arctic Circle[1],which is regarded as the Middle East of the future.

As the global warming became a global topic of interest,evidence reveals that the ice cap in the Arctic has been shrinking year by year.The Northern Sea Route(NSR),which was historically impassable,has been opened up for a small number of commercial ships during summer time.Recently,the USA government announced permitting further drilling in certain areas offshore Alaska.The Canada’s National Shipbuilding Purchasing Strategy(NSPS)has planned to purchase an Arctic icebreaker named‘John G Diefenbaker’,which will be put into service in 2017 and will play an important role in the Canada’s Northern Strategy.All these may imply the coming of another boom of Arctic development[2].

Arctic shipping and Arctic development face a variety of risks.The interaction between a ship and ice is a complex process.The magnitude of ice loads depends on the inherent characteristic of ice,the ice-structure interaction form,the structure’s geometry and dimension,the thick and velocity of ice,the ice failure model and other factors.

The prediction of ice loads plays an important role in the design of reliable and cost effective ice-going ships.The extreme forces exerted on the structures can cause severe damages.In many cases,accurate evaluations of the ice loads are the drives of optimal structure design.A conservative approach to estimate the ice loads can result in an extremely heavy penalty to the vessels or offshore structures when weight is a problem.When that happens,a reliable and accurate prediction method can be one of the most important issues for naval architects.

1 Description and definition of ice loads

When the ice sheet contacts the hull,crushing happens.The crushing force will keep growing with an increasing contact area until its vertical component is great enough to cause a bending failure of ice.After the ice floes have been broken from the ice sheet,the ship motion forces them to turn on edge until parallel with the hull.Then,the floes will become submerged and slide along the hull until they cannot maintain contact with the hull.In some hull zones,typically at the stern and at the shoulders which have large slope angles(almost vertical),crushing may be the only failure mode.Fig.1 shows the icebreaking process.

Fig.1 The icebreaking process

In order to reflect the magnitude of the ice loads,the hull can be divided into several areas[3].In the longitudinal direction,there are four regions:Bow,Bow Intermediate,Midbody and Stern.The Bow Intermediate,Midbody and Stern regions are further divided in the vertical direction into the Bottom,Lower and Icebelt regions.The extent of each Hull Area is illustrated in Fig.2.

Fig.2 Hull area extents

Ice loads may be conveniently categorized as local ice loads and global ice loads(ABS,2011)[4].Local ice loads are often defined as ice pressure acting on local areas(on shell plates and stiffeners).Global ice loads on ships are typically(vertical)bending moment on hull girder.With the recent progress of research,vibratory loads,iceberg impacts and propeller-ice interaction are also being dealt with.

1.1 Local ice loads

Local ice loads are one of the most important factors for determining ship hull’s scantling strength.The transmission of the ice load to a ship structure is through the local high pressure zones.High pressure zones are distributed in the interaction area during ice-ship interactions with ice in compression.Wells et al[5]performed laboratory indentation tests to study the pressure distribution at the ice-indenter interface.Isolated high pressure zones were found at the centre with very high pressures compared to the average pressures found during the tests.These high pressure zones were often seen to vary in intensity throughout the test,analogous to the behavior seen during medium and full-scale interactions.

Fig.3 Pressure-area values for ship-ice interaction data analyzed

Fig.4 Pressure-area values obtained from the crushing test

The average ice pressure is considered to be proportional to the contact area to the power of α,which can be defined asTaylor et al(2010)[6]examined several ship-ice interaction datasets using the‘event-maximum’method of local pressure analysis developed by Jordaan and co-workers.Local pressure analysis results for data from the USCGS Polar Sea,CCGS Terry Fox,CCGS Louis St.Laurent and Swedish Icebreaker Oden are presented.Fig.3 shows that the pressures follow a decreasing trend with increasing area,and each dataset has a distinct,well defined curve.This suggests that the pressure is dependent on some physical characteristic of the interaction,such as the ice type,thickness,or temperature.

Kujala and Arughadhoss[7]summarized the available crushing pressure-nominal contact area relationships obtained through various ice crushing tests of IB Sampo,MT Uikku and gen-eral cargo ship-full scale as shown in Fig.4.All the measured results are below the envelope curve.By comparing model-scale data with full-scale measurements onboard of MS Arcturus and IB Sisu,p0=0.42 and α=0.52 were determined.It is taken as α=0.5 in DNV Rules and α=0.3 in IACS PC.

1.2 Global ice load on ships

The global ice load is an integrated effect of local ice loads over the hull area,and governs the ship’s overall performance in ice.Field measurements are considered as the most reliable basis for evaluating the magnitude of ice forces on ships since ice loading on ship hulls is rather complicated,and associated with the actual ice conditions,the hull geometry and the relative velocity between the ship and the ice.

Chernov(2009)[8]studied the global ice loads at the ship interaction with various types of ice formations in the expedition of‘Shtokman-2008’based on experiments.Some ice class rules(IACS PC)[3]also specify global ice loads.The global bending moment is dependent on ship operation(ship speed and power),ice conditions(ice concentration,thickness and floe size),and ship-ice interaction.

1.3 Iceberg-ship collision

The probability of collisions between ships and icebergs should be considered in Arctic and Antarctic regions.Fig.5 shows the collisions between icebergs and ship structure which caused significant structure damage and economic costs[9].The mechanics between icebergs and ship structures are different with the ice loads on a ship when breaking the ice.The crushing may be the only failure model in iceberg-ship collision and the flexural may be the main failure model when ice-going ships breaking the ice.

Fig.5 Damaged bow of Overseas Ohio after collision with iceberg

The knowledge about the iceberg mass and speed,the iceberg shape and a continuum mechanics model of icebergs is necessary for a realistic design against an accidental iceberg impact.At present,the rules and regulations for ice-going ships have not covered the shipice collision scenario.

2 Difficulties in the prediction of ice loads

For a designer or engineer,choosing a design ice load has always been a challenge because of the uncertainties of ice loads in nature.These uncertainties are partially due to the varying ice conditions and the complicated nature of ice-structure interaction process.

Techniques used to predict ice loads can be categorized into five groups:theoretical approaches,model experiments,empirical formulas,numerical simulations and shipboard measurement.At present,there is a lack of a commonly agreed method for calculating ice loads.To fully analyze the ice loads and resulting structural responses,various factors like ice failure model,the material property of ice,ship-ice interaction scenarios,etc.,must be modeled properly.

Additionally,since not all ice loads are stationary glancing impacts,this raises several important questions,e.g.whether the structural design/analyses based on stationary loads are valid when the loads are not stationary.Quinton and Daley have shown that moving ice loads incite a significantly different structural response in steel grillage structures than stationary ice loads do[10].

Semi-empirical formulations for ice resistance and ice loads are often limited to certain ship or structure types,such as the formulation of Lindqvist(1989)[11],which is validated against ice breakers.In von Bock und Polach(2010)[12],it is indicated that the formulation of Lindqvist(1989)is not necessarily applied to tankers or other ships,even though it is often used for those.

Model experiments are thought to be most reliable,but it can be costly and suffers from scale effect.Although the model experiments between structures and ice have developed for 50 years,there still faces how to scale down the strength of ice and correctly simulate the physical and mechanical properties of prototype ice.

There has been a considerable amount of research performed to measure sea ice properties,especially during the activity boom in the Canadian and American Beaufort Sea in the 1970s,1980s and early 1990s.Several review articles have been written to summarize these findings(e.g.Weeks and Assur,1967,1968;Schwarz and Weeks,1977;Mellor,1983,1986;Weeks and Ackley,1982,1986)[13].The reference[13]looks at the stage of knowledge and applications of the engineering properties of sea ice.The physical properties(microstructure,thickness,salinity,porosity,and density)and the mechanical properties(tensile,flexural,shear,uni-axial compression and multi-axial compression strength,borehole strength,failure envelope,creep,elastic and strain modulus,Poisson’s ratio,fracture toughness and friction)are explored.Timco and O’Brien(1994)[14]showed that the data for the first-year sea ice could be described by:

where σfis the flexural strength of the ice(in MPa)and the brine volume(vb)is expressed as a brine volume fraction(Fig.6).

Timco and Frederking(1990,1991)[15-16]developed a model to predict the full thickness strength by dividing the ice sheet into nine separate layers and then calculating the compressive strength of each layer based on the temperature,salinity,density and grain structure.Fig.7 shows a plot of the compressive strength of a 1 m thick sheet of sea ice as a function of air temperature.The figure shows that the compressive strength is a strong function of loading strain rate(ε˙)and less dependent upon the temperature until close to the melting point.Compressive strength values ranged from 0.4 MPa to about 5 MPa.

For a more accurate prediction,a method involving complete determination of the loads based on scientific principle rather than empirical procedures is needed.These oversimplified approaches cannot give a designer the comprehensive information.In the next section,the theoretical methods and numerical simulations for the ice loads problems are reviewed.

Fig.6 Flexural strength versus the square root of the brine volume for first-year sea ice

Fig.7 Plot of the compressive strength of the ice as a function of temperature

3 Development of ice loads theories and simulations

Due to the lack of field observations and the insufficient understanding of the physics of icebreaking especially by moving structures,studies are usually done by combining rational theoretical analysis with empirically obtained information,i.e.,semi-empirical methods.Numerical simulation of ice loads has been used as a research tool for decades.With the increase of computational power available,it became possible to use fine discretization,model large volumes of ice and,especially,to use non-linear methods to analyze ice failure process with large displacements.In general,the numerical simulation methods can be divided into probabilistic approach,FEM(finite element method),DEM(discrete element method)and energy approach.Of course,other methods are also used to predict the ice loads,e.g.Sayed and Kubat(2011)[17]using Particle in Cell method studied ice pressures of the Canadian Coast Guard vessel,CCGS Louis S.St-Laurent.

3.1 Probabilistic approach

The ship hull interaction with ice is of random nature,therefore,it is reasonable to apply probabilistic rather than deterministic method for estimating the ice loads acting on the ship hull[18].

According to the current literature,Kheysin[19-20]was the first to use a probabilistic approach for ice loads on ships.He used a Poisson distribution for the number of impacts in an arbitrary interval of time,based on measurements by Likhomanov[21].Maes et al(1984)[22]performed a study on probabilistic methods for fixed structure in ice and the methodology has been reviewed by Nessim et al(1987)[23],Nessim and Jordaan(1991)[24],and Blanchet(1990)[25].Daley and his co-workers formulated the ASPEN model over several years and it culminated in the publication by Daley et al(1991)[26].Kujala(1991)[27]used the results of probabilistic methods to study the safety of ships in the Baltic Sea with respect to ice induced loads.Jordaan et al(1993)[28]presented a probabilistic approach to the local ice pressure based on test data of ship ramming trials.Zou(1996)[29]proposed a design curve for the estimation of extreme ice loads,which was based on the design area and extreme value theory.The design area was modeled as a random number of critical zones,each with a random force.

To estimate probabilistic design loads,the designer must first identify distributions for the input parameters for the ice loading scenarios.Ice forces for different interaction scenarios may depend on many parameters.A general flow diagram outlining the approach for loads analysis and design is illustrated in Fig.8 by Ralph and Jordaan(2013)[30].

The probabilistic method is not appropriate in the design of a structure for a rare event.

Fig.8 Example flow chart for probabilistic model development

3.2 Finite element method

Finite element method,especially the commercial software has been widely used to calculate the ice loads in recent years.

Sawamura et al(2008)[31]studied with a numerical simulation of the dynamic bending behavior of a floating ice-sheet subjected to the dynamic force by using ABAQUS/Explicit.Wang et al(2008)[32]developed a collision model for nonlinear dynamic finite element analysis on a LNG ship and a crushable ice using commercial code DYTRAN.

Liu[9]used nonlinear finite-element analysis,a commercial code LS-DYNA,to assess the internal mechanics of both icebergs and ship structures.However,due to the difficulties of simulating ice,NLFEA(Nonlinear finite-element analysis)is not straightforward.To facilitate such simulations,a plasticity-based material model for icebergs was developed in this thesis.Iceberg crack propagation was simulated by element erosion.An empirical failure criterion for detecting those failed ice elements is proposed.

Lubbad et al(2011)[33]described a numerical model to simulate the process of ship-ice interaction in real-time.New analytical closed form solutions are established and used to represent the ice breaking process.PhysX is used for the first time to solve the equations of rigid body motions in 6 degree of freedom for all ice floes in the calculation domain.

3.3 Discrete element method

With rapid advance of numerical techniques and computation hardware,numerical analysis and,in particular,the Discrete Element Method(DEM)has evolved into a very powerful simulation tool for complementing analytical and experimental works.Applications of the DEM arise in mechanical,geotechnical and structural engineering and include,but are not limited to,simulations of particle motion,granular assemblies,ice-structure interaction,fracturing rocks,silo filling,impact problems,and so on.

Cundall(1971)[34]first proposed the distinct element method as a means for simulating the behavior of jointed rocks.The details of the procedure were outlined by Cundall and Strack(1978)[35].The method was generalized in a subsequent paper by Williams et al(1985)[36]who presented the DEM.

The theoretical basis of DEM is the conservation of mass and energy and balance of momentum and moment of momentum.DECICE,an acronym for Discrete Element Code for ice-related problems,is a commercial code owned by O-ceanic Consulting Corporation which is currently in use by the National Research Council’s Institute for Ocean Technology(NRC-IOT)to study a variety of problems.Zhan et al(2010)[37]simulated the ship maneuvering in ice covered waters using the Ship Maneuvering Laboratory(SML)program and DEM code DECICE(Fig.9).Lau et al(2011)[38]used DECICE to compute forces and moments by considering a 1:21 scale model of the Canadian icebreaker Terry-Fox moving forward and turning in level ice.The three-dimensional numerical model created within DECICE consists of(1)A rigid moving element representing the Terry-Fox icebreaker,(2)A free-floating ice plate,(3)A rigid boundary and(4)A water foundation.

Sawamura et al(2011)[39]developed a 2D model and a 3D model to simulate the interaction between ice floe and ship,respectively.The motions of the broken ice floes were described by 3 DOFs in 2-dimentional simulation and 6 DOFs in 3-dimentional one.

Paavilainen et al(2009,2011)[40-41]have developed a 2D combined FEM-DEM method to study ice sheet failure and rubble pile formation process against a wide inclined structure.The method was used to study rubble pile formation and deformation,as well as the extreme ice load events.

Fig.9 Ship maneuvering model using DECICE

3.4 Energy approach

Energy methods provide a simple method of determining forces,and have long been used to do so[42].Daley(1999)[43]summarized the general energy approach and derived some old and new cases and provided examples.It is assumed that one body is initially moving(the impacting body)and the other is at rest(the impacted body).This concept is applied to a ship striking an ice edge,or ice striking an offshore structure.The energy approach is based on equating the available kinetic energy with the energy expended in crushing and potential energy:

where KEeis available kinetic energy,IE is crushing energy,PE is potential energy.The detail of each item can be referenced to Ref.[43].

The energy approach to compute the ice loads needs a variety of ice force equations in different ship-ice collision scenarios.The impact idealization is essentially one-dimensional,the actual collision is three-dimensional.Nevertheless,the energy solutions give insight into the process,particularly for cases in which the energy balance governs the outcome.

4 Conclusions and recommendations

The safe and economical operation of marine structures in ice conditions demands accurate estimation of ice loads.Main types of theories developed are identified in recent years.The ice failure model and the material property of ice are not understood completely.Existing ice class rules have focused on vessel performance and responses of hull and machinery.These rules only provide a minimum set of requirements that must be supplemented by more comprehensive considerations of a wider range of topics.

A risk-based or probabilistic approach could result in more rational design methodologies that insure safety while simultaneously improve the efficiency of the resulting designs.The first step in this process would be definition of specific load cases,and the probabilities of occurrence for these load cases for each of the ice-condition categories.Since the probabilistic approach needs the actual full-scale ice loads data,a possible future research is collection and correlation of the full-scale data.

An effective approach to obtain pressure distribution and force history is nonlinear numerical simulation.In the numerical simulations of ship-ice interactions,the ship structure can be treated as a rigid body or deformable one,and the sea ice as continuum media or discrete materials.The DEM models can be applied to level ice or pancake ice and ice parameters,such as floe shapes,size,frictions,and concentrations can be modeled appropriately.Effective numerical tools should be developed with reliable computational parameters.

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