Article

Rafting and ridging of thin ice sheets

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Abstract

Rafting and pressure ridging are important processes in the deformation of sea ice that occur when two ice sheets are pushed together. In this study a two-dimensional computer model of the rafting and ridging process is used to simulate a situation in which two identical ice sheets are pushed together at constant speed. Each model ice sheet is composed of two thicknesses of ice. The ratio of the thicknesses is varied to obtain degrees of inhomogeneity. The accuracy of the simulations is assessed by comparison with a series of similar physical experiments performed in a refrigerated basin. Following this comparison, the computer model is used to perform an extensive series of simulations to explore the effect of the thickness and the thickness inhomogeneity of the model ice sheets on the likelihood of occurrence of ridging and rafting. During the simulations the energy consumption and forces are explicitly calculated. The energy consumed during the simulations is used to demonstrate the smooth transition between ridging and rafting that occurs when the homogeneity of the sheets is varied.

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... The external forces include buoyancy, gravitation and water drag. Implementation of the first two is straightforward, but the models used for drag are crudely simplified [22,[36][37][38]; rigorous modelling of hydrodynamics over even moderate time periods remains unattainable. The most elaborate drag model used is based on potential flow theory [32]. ...
... Even the simple simulations of floating ice blocks demonstrated the importance of describing the angularity of ice blocks and that the energy dissipation during ridging is higher than previously assumed. Ridging studies were later extended to model intact ice sheets and their failure into discrete blocks [36,39,43]. In the simulations of ridge formation from thin lead ice compressed between two thick floes, an increase of the friction coefficient of ice decreased the energy dissipation, while the dissipation increased with ice thickness [39]. ...
... However, not all ridges form from lead ice between thick floes, some form from two ice sheets compressed together. 2D DEM simulations of such ridging processes were verified through model-scale experiments [72] and used to study the parameters defining whether ridging or rafting dominates ice sheet deformation [36]. In these parallel experiments and simulations, it was also observed that rafting and ridging are not two different physical processes, but rafting is the precursor to ridging. ...
Article
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Sea ice loads on marine structures are caused by the failure process of ice against the structure. The failure process is affected by both the structure and the ice, thus is called ice–structure interaction. Many ice failure processes, including ice failure against inclined or vertical offshore structures, are composed of large numbers of discrete failure events which lead to the formation of piles of ice blocks. Such failure processes have been successfully studied by using the discrete element method (DEM). In addition, ice appears in nature often as discrete floes; either as single floes, ice floe fields or as parts of ridges. DEM has also been successfully applied to study the formation and deformation of these ice features, and the interactions of ships and structures with them. This paper gives a review of the use of DEM in studying ice–structure interaction, with emphasis on the lessons learned about the behaviour of sea ice as a discontinuous medium. This article is part of the theme issue ‘Modelling of sea-ice phenomena’.
... In the table, h is the ice thickness, and E and σ f are the elastic modulus and tensile strength, respectively. Other main parameters are given in Table 2 Hopkins et al. (1999) simulated ridge formation due to compression of ice floes of similar, but nonuniform, ice thickness and concluded that this nonuniform thickness mainly influenced the ratio of rafting and ridging. We accounted for the effect of varying ice thickness on frictional sliding by using an ice-ice friction coefficient of 0.6, which is at the high but realistic end for the values measured for ice (Sukhorukov and Løset, 2013). ...
... Formation of pressure ridges has been simulated earlier only by utilizing two-dimensional DEM models (Hopkins, 1994(Hopkins, , 1998Hopkins et al., 1999;Damsgaard et al., 2021). Since simulating pressure ridging in three-dimensions is a fairly complex effort, it is relevant to discuss how our results differ from two-dimensional simulations. ...
Article
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This study presents the first three-dimensional discrete element method simulations of pressure ridge formation. Pressure ridges are an important feature of the sea-ice cover, as they contribute to the mechanical thickening of ice and likely limit the strength of sea ice at large scales. We validate the simulations against laboratory-scale experiments, confirming their accuracy in predicting ridging forces and ridge geometries. Then we demonstrate that Cauchy–Froude scaling applies for translating laboratory-scale results on ridging to full-scale scenarios. We show that non-simultaneous failure, where an ice floe fails at distinct locations across the ridge length, is required for an accurate representation of the ridging process. This process cannot be described by two-dimensional simulations. We also find a linear relationship between the ridging forces and the ice thickness, contrasting with earlier results in the literature obtained by two-dimensional simulations.
... In further simulations by Hopkins (1994Hopkins ( , 1998, a thin, intact, lead ice was pushed against a thick ice floe and went through a continuous ice failure process to form a ridge. Hopkins et al. (1999) simulated the formation of a ridge due to compression of ice sheets of similar, but nonuniform, ice thickness. Importantly, these simulations suggested a relation F ∝ h 3/2 between the ridging force, F , and ice thickness, h, which has been used since in some Earth System Models to define the strength of ice of a given thickness (Lipscomb et al., 2007). ...
... Formation of pressure ridges has been simulated earlier only by utilizing two-dimensional DEM models (Hopkins, 1994(Hopkins, , 1998Hopkins et al., 1999;Damsgaard et al., 2021). Since simulating pressure ridging in three-dimensions is a fairly complex effort, it is relevant to discuss how our results differ from two-dimensional simulations. ...
Preprint
Full-text available
This study presents the first three-dimensional discrete element method simulations on pressure ridge formation. Pressure ridges are an important feature of the sea-ice cover, as they contribute to the mechanical thickening of ice and likely limit the strength of sea ice in large scale. We validate the simulations against laboratory-scale experiments, confirming their accuracy in predicting ridging forces and ridge geometries. Then we demonstrate that Cauchy-Froude scaling applies for translating laboratory-scale results on ridging to full-scale scenarios. We show that non-simultaneous failure, where an ice sheet fails at distinct locations across the ridge length, is required for an accurate representation of the ridging process. This process cannot be described by two-dimensional simulations. We also find a linear relationship between the ridging forces and the ice thickness, contrasting with earlier results in the literature obtained by two-dimensional simulations.
... It was found that sheets of uniform thickness tended to raft, whereas sheets of non-uniform thickness tended to ridge. Hopkins et al. [1999] developed a two-dimensional computer model to simulate rafting and ridging processes as a result of two identical sheets of ice being pushed together at constant speed. The degree of inhomogeneity was implemented by varying the ratio of thicknesses of the two ice sheets between 2/8 and 8/8 (uniform) in seven steps. ...
... Lower Ice Sheet layers gradually bonds the ice sheets together and the feature consolidates. Since rafting tends to be less prevalent than ridging, and tends to take place between thinner sheets of ice, it can be considered less of an engineering concern [Hopkins et al., 1999] and thus there is less research published on its consolidation. ...
Conference Paper
Over recent decades, there has been a continuing rise in commercial interest in the Arctic and its natural resources. Thick sea ice features, such as ridge keels and rafted ice, can generate some of the highest loads encountered by an offshore structure or marine vessel operating in the Arctic. Two important but closely associated properties that govern their initial strength are the degree of consolidation and the ice freeze-bond strength which are highly sensitive to a number of parameters, including space and time, the physical properties of the ice, the local meteorological and oceanographic conditions, and the loading conditions encountered. This thesis has focused on developing the understanding of the thermodynamics of consolidation, and the resultant mechanical properties of the freeze-bonds that form as a function of these parameters. Experiments have been undertaken from the micro-scale up to the metre-scale under both controlled laboratory and ice tank conditions, and Arctic field conditions. Results show that sea ice undergoing consolidation in the field is strongly influenced by the presence of oceanic heat fluxes, which acts to diverge the thermodynamic behaviour away from what is observed in the laboratory and ice tank. The shear freeze-bond strength also shows strong angular dependency, and under a significant degree of misorientation will approach the strength of level ice and samples instead fail in compression. This is significant as it indicates that there may be large local variations in the strength of a ridge keel due to geometry alone. Mechanical tests on the millimetre-scale conducted in-situ under a scanning electron microscope (SEM) have revealed that both solid and freeze-bonded ice exhibit the same failure modes that are typically observed on the centimetre-scale. The strength of solid ice and freeze-bonds at this scale also appears to be similar to what has been previously observed on larger scales.
... 1. Ridge formation models from Hopkins (1998) and Hopkins et al. (1991Hopkins et al. ( , 1999 showed that ridges first reach a maximum dynamic thickness and then continue to grow laterally. This lateral growth widens the ridge and therefore increases the relative occurrence of deformed ice with the maximum dynamic thickness, reducing the e folding. ...
... If the occurrence of rafting and ridging depends on the magnitude of deformation, this could establish a link between e folding and the deformation rate. Hopkins et al. (1999) identified that the relative likelihood of rafting increases with increasing homogeneity of the ice floes. Hence, regions like the Fast Ice zone that only experienced little deformation and with the ice still of relatively uniform thickness might have a higher portion of rafted ice and thus a different e folding than regions that experienced more ridging. ...
Article
Full-text available
An unusual, large, latent-heat polynya opened and then closed by freezing and convergence north of Greenland's coast in late winter 2018. The closing presented a natural but well-constrained full-scale ice deformation experiment. We observed the closing of and deformation within the polynya with satellite synthetic-aperture radar (SAR) imagery and measured the accumulated effects of dynamic and thermodynamic ice growth with an airborne electromagnetic (AEM) ice thickness survey 1 month after the closing began. During that time, strong ice convergence decreased the area of the refrozen polynya by a factor of 2.5. The AEM survey showed mean and modal thicknesses of the 1-month-old ice of 1.96 ± 1.5 m and 1.1 m, respectively. We show that this is in close agreement with modeled thermodynamic growth and with the dynamic thickening expected from the polynya area decrease during that time. We found significant differences in the shapes of ice thickness distributions (ITDs) in different regions of the refrozen polynya. These closely corresponded to different deformation histories of the surveyed ice that we reconstructed from Lagrangian ice drift trajectories in reverse chronological order. We constructed the ice drift trajectories from regularly gridded, high-resolution drift fields calculated from SAR imagery and extracted deformation derived from the drift fields along the trajectories. Results show a linear proportionality between convergence and thickness change that agrees well with the ice thickness redistribution theory. We found a proportionality between the e folding of the ITDs' tails and the total deformation experienced by the ice. Lastly, we developed a simple, volume-conserving model to derive dynamic ice thickness change from the combination of Lagrangian trajectories and high-resolution SAR drift and deformation fields. The model has a spatial resolution of 1.4 km and reconstructs thickness profiles in reasonable agreement with the AEM observations. The modeled ITD resembles the main characteristics of the observed ITD, including mode, e folding, and full width at half maximum. Thus, we demonstrate that high-resolution SAR deformation observations are capable of producing realistic ice thickness distributions.
... As for the phenomenon of rafting, several authors have investigated the physical process of rafting (e.g. Parmerter, 1975;Hopkins et al., 1999;Bailey et al., 2010), however none of these models attempt to predict the wave conditions required for rafting to occur. For example, Hopkins et al. (1999) modelled rafting by pushing two ice sheets together at constant speeds. ...
... Parmerter, 1975;Hopkins et al., 1999;Bailey et al., 2010), however none of these models attempt to predict the wave conditions required for rafting to occur. For example, Hopkins et al. (1999) modelled rafting by pushing two ice sheets together at constant speeds. This was to simulate the forces between much larger sheets of pack ice. ...
Thesis
The wave-induced collisions and rafting of ice floes are investigated experimentally and theoretically. Results from a series of wave basin experiments are presented. Ice floes are simulated experimentally using thin plastic disks. The first round of experiments focusses on measuring the oscillatory surge, heave, pitch and drift motions of solitary floes. The second and third rounds of experiments record the motions of two adjacent floes. Rafting is suppressed in the second round, and allowed in the third round. Collision and rafting regimes are identified, and collision behaviours are quantified over a range of incident wavelengths and wave amplitudes. Two mathematical models are proposed to model the wave-induced motions of solitary floes. The first is based on slope-sliding theory, and the second is based on linear potential-flow theory. Both models are validated using results from the single-floe experiments. Model-data comparisons show that the slope-sliding model is valid in the long-wavelength regime, and potential-flow model is more accurate in shorter wavelengths. A two-floe collision model is then developed to replicate the conditions of the two-floe experiments. Slope-sliding theory is used to model floe motions. A time-stepping algorithm is implemented to determine the occurrence of collision and rafting events. Predicted collision behaviours are compared with results from the two-floe experiments. Good agreement is attained in incident waves of intermediate to long wavelengths.
... Initial DEMs for sea ice utilized circular DEs moving in two dimensions (Babic et al., 1990;. Soon after, two-dimensional DEM with polygonal DEs was used to study pressure ridge formation (Hopkins, 1994(Hopkins, , 1998Hopkins et al., , 1999. Additionally, Hopkins et al. (2004) and Hopkins and Thorndike (2006) modeled Arctic pack ice in 2D, where ridge formation at floe-to-floe contacts was described using a contact interaction model developed by Hopkins (1996). ...
Article
Full-text available
Plain Language Summary Sea ice forms in cold climates and is susceptible to being easily fragmented by wind and currents, resulting in a dynamic landscape comprising solid fast ice, drift ice and pack ice. Pack ice, in particular, can pose challenges such as hindering shipping, causing damage to offshore structures, and complicating traditional fishing and hunting activities. Operational models for sea ice dynamics are currently utilized to optimize ship routes and the deployment of icebreakers. Although existing rheology‐based models perform well on large scales, they encounter difficulties in capturing the finer details that are often crucial. In this study, we utilize a high‐resolution Discrete Element Model computer code that is capable of simulating detailed sea ice dynamics at scales ranging from meters to kilometers. Our simulation results reveal insights that are not readily obtained from conventional large‐scale models, and we explore the potential for integrating these two approaches to create a hybrid model.
... Previous studies (e.g., Parmerter, 1975;Eicken and Lange, 1989;Worby et al., 1996;Toyota et al., 2007) demonstrate that when the ice thickness is over 0.3 m, ice trends to ridge rather than raft in compressional deformation. Since ridging requires more energy than rafting, thin ice can attain higher values of convergence than thick ice Hopkins et al., 1999). Regarding shear, thick ice has higher shear strength than thin ice (Flato and Hibler, 1995). ...
... For the current version, it is set to a simple percentage value, and if at least one of the floes exceeds this threshold, then ridging will take place. However, more complex probabilities can depend upon compressive stress and thickness (Damsgaard et al., 2021;Hibler, 1980;Hopkins, 1998;Hopkins et al., 1999;Tuhkuri & Lensu, 2002). When ridging occurs, the area of the floes is reduced as the mass is transferred toward increasing the thickness of one of the colliding floes. ...
Article
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Sea ice dynamics exhibit granular behavior as individual floes and fracture networks become particularly evident at length scales O(10–100) km and smaller. However, climate models do not resolve floes and represent sea ice as a continuum, while existing floe‐scale sea ice models tend to oversimplify floes using discrete elements of predefined simple shapes. The idealized nature of climate and discrete element sea ice models presents a challenge of comparing the model output with floe‐scale sea ice observations. Here we present SubZero, a conceptually new sea ice model geared to explicitly simulate the life cycles of individual floes by using complex discrete elements with time‐evolving shapes. This unique model uses parameterizations of floe‐scale processes, such as collisions, fractures, ridging, and welding, to simulate a wide range of evolving floe shapes and sizes. We demonstrate the novel capabilities of the SubZero model in idealized experiments, including uniaxial compression, the summer‐time sea ice flow through the Nares Strait, and winter‐time sea ice growth. The model naturally reproduces the statistical behavior of the observed sea ice, such as the power‐law appearance of the floe size distribution and the long‐tailed ice thickness distribution. The SubZero model could provide a valuable alternative to existing discrete element and continuous sea ice models for simulations of floe interactions.
... Figure 7b also shows that these three kinds of ice thicknesses varied almost synchronously-the c.c. for undeformed ice and deformed ice with total ice thickness are both 0.89-, suggesting that deformation processes play an essential role in determining the ice thickness distribution in Area S2. Although a high correlation between undeformed and deformed ice thickness might not be expected, it seems consistent because in this analysis undeformed ice includes rafted ice, and the rafting process is often accompanied by ridging (Hopkins et al., 1999). Higher values appeared during 1997, 2003-2005, 2011, 2013-2015, and 2018 with a somewhat decreasing trend. ...
Article
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The lowest latitude sea ice in the world (excluding coastal freezing) is in the southern Sea of Okhotsk (south of 46°N), where it has significant impacts on freshwater input and primary production. This region is subject to climate change, and accordingly the monitoring of sea ice conditions is important. However, the interannual variability of the region's sea ice is poorly understood due to its logistical challenges. Sea ice observations have been conducted in this region every winter for the period 1996–2020. The interannual variability of the ice conditions and the likely factors responsible for it were investigated using visual observations following the international ASPeCt protocol, combined with satellite SSM/I‐SSMIS ice concentration data (1988–2020). AMSR‐derived ice drift data sets and ERA5 meteorological reanalysis data sets were also analyzed to examine the effects of dynamic and thermodynamic processes. Our analysis revealed that (a) sea ice area in this region varies differently from that in the central and northern Sea of Okhotsk, where decreasing trends are reported, (b) sea ice volume has remarkable interannual variation and the peaks appeared much to more affected by dynamically deformed ice than freezing conditions, and (c) prominently deformed ice can be explained by taking shear components into account based on sea ice rheology. These results suggest the importance of including the proper sea ice rheology in numerical sea ice models to reproduce the realistic sea ice volume and deformation processes, for all seasonal ice zones.
... However, as ice rubble is modeled as a continuum, FEM cannot provide detailed granular properties of the rubble, and there is uncertainty in determining whether there are enough blocks to consider the rubble as a continuum [28]. The DEM was developed by Cundall et al. [29] and was introduced by Hopkins and Hibler into ice simulations [30][31][32]. In the DEM, large deformations and discontinuous properties of ice can be modeled using the movement of individual ice blocks within it [33]. ...
Article
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Freezing in ice rubble is a common phenomenon in cold regions, which can consolidate loose blocks and change their mechanical properties. To model the cohesive effect in frozen ice rubble, and to describe the fragmentation behavior with a large external forces exerted, a freeze-bond model based on the dilated polyhedral discrete element method (DEM) is proposed. Herein, imaginary bonding is initialized at the contact points to transmit forces and moments, and the initiation of the damage is detected using the hybrid fracture model. The model is validated through the qualitative agreement between the simulation results and the analytical solution of two bonding particles. To study the effect of freeze-bond on the floating ice rubble, punch-through tests were simulated on the ice rubble under freezing and nonfreezing conditions. The deformation and resistance of the ice rubble are investigated during indenter penetration. The influence of the internal friction coefficient on the strength of the ice rubble is determined. The results indicate that the proposed model can properly describe the consolidated ice rubble, and the freeze-bond effect is of great significance to the ice rubble properties.
... In order to elucidate this observation, Fig. 10 shows the load-displacement records in non-dimensional form. The data was made non-dimensional by following the analysis of ridging by Hopkins et al. [27]: ...
Article
Laboratory-scale experiments on ice-structure interaction process in shallow water were performed by pushing a ten-meter-wide ice sheet against an inclined structure of the same width. Seven experiments were performed in three series: In one of the series, the compressive and flexural strengths were both about 50kPa, in the two other test series the ice strength was two and four times higher. The ice thickness was about 50 mm in all experiments. The loading process showed two phases: the ice load on the structure (1) first increased linearly with a rate that was constant for all experiments, after which (2) the loading process reached a steady-state phase with approximately constant load. The magnitude of ice loads was not proportional to ice strength, as the weakest ice yielded higher loads than the ice having twice its strength. The ice rubble grounded in all experiments, but the bottom carried only a small portion of the load. The load records could be normalized by a factor combining the weight and the characteristic length of the intact ice. Based on the normalization, a model explaining the loading process was derived; the weight of the incoming ice has a dominant role during phase (1), while buckling explains the change in the process to phase (2) when the ice is strong enough. The loading process for the weakest ice was different from that for the other two ice types used. For example, instead of forming a rubble pile consisting of distinct ice blocks, weakest ice formed a dense pile of slush. The normalized ice load data highlighted the differences in the loading process.
... These results are in general agreement with field measurements that were later obtained by others (Tucker and Govoni 1981;Melling and Riedel 1996). More recently, discrete-particle numerical modelling and model-ice laboratory experiments have produced new insights on the sheet ice -rubble interaction (Hopkins 1998;Tuhkuri and Lensu 2002). While the above works provide some guidance on the characteristics of rubble fronts created by large ice sheets in lakes and oceans, more work needs to be done to apply a similar analysis to rivers. ...
Chapter
One of the most dynamic and complex events that can occur in a river is produced by the abrupt release of a major ice jam. The release generates a steep wave that travels ahead of the rubble from the jam, and can itself cause breakup and new rubble in downstream reaches. The complex and dynamic interaction between the forces generated by the wave, the highly variable competence of the intact ice cover, and the ever-changing river bathymetry and planform render measurement and prediction very difficult. Yet, much new understanding has been acquired in the past ten years, which is likely to form the foundation for a new generation of sophisticated numerical models. In this chapter, current understanding of the dynamic aspects of breakup is reviewed in detail within the context of what is already known about river waves. The emphasis is on the wave characteristics and on the role played by stationary and moving ice in the formation and motion of different types of breaking fronts.
... The 1 discrete nature of brash ice makes DEM more suitable for the simulation of ice blocks and structure interaction where separate noncontinuum elements are considered. The application of DEM to model ice rubble in ice ridges can be found in Hopkins et al. (1991), Hopkins et al. (1999), Polojärvi and Tuhkuri (2009), Polojärvi et al. (2012), and Polojärvi and Tuhkuri (2013). ...
Article
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The repeated passage of ships through ice-infested waters create a field of broken ice pieces. The typical size of the broken ice pieces is generally <2.0 m. This area might be referred to as a brash ice field. The movement of ships and vessels leads to the transportation and accumulation of broken ice pieces in a brash ice field. A better understanding of the properties and behavior of brash ice could improve the estimates of ice load that are associated with shipping in a brash ice field. An in situ test referred to in this study as a pull up test will be performed in Luleå harbor, Luleå, Sweden. An attempt will be made to estimate the mechanical and physical properties of a brash ice field based on the in situ test results. The test setup, procedure, and test results will be described in detail. Furthermore, the test will be simulated using the smoothed particle hydrodynamics (SPH) formulation. The numerical simulations will calibrate the numerical and material model of brash ice using the pull up test measurements. In this numerical model, a discrete mass-spring-dashpot model will be used to simulate buoyancy and drag. The continuous surface cap model (CSCM) will be used as a material model for the brash ice. The elastic modulus and the fracture energy of brash ice as a material model input will be estimated by an ad hoc scaling formula. The parameters, such as void fraction (Vf), cohesion (c), and angle of internal friction (φ) will be altered to assess their influence on the test data. The analysis of the in situ test results and the simulation results provide a preliminary approach to understand the brash ice failure process that could be further developed into modeling techniques for marine design and operations.
... (1) Ridge formation models from Hopkins (1998) and Hopkins et al. (1991Hopkins et al. ( , 1999 showed that ridges first reach a maximum thickness and then continue to grow laterally. This lateral growth widens the ridge and therefore increases the relative occurrence of deformed ice with the maximum thickness, and thereby reduces the -folding. ...
Preprint
Full-text available
An unusual, large polynya opened and then closed by freezing and convergence north of the coast of Greenland in late winter 2018. The closing corresponded to a natural, but well-constrained, full-scale ice deformation experiment. We have observed the closing of and deformation within the polynya with satellite synthetic-aperture radar (SAR) imagery, and measured the accumulated effects of dynamic and thermodynamic ice growth 5 with an airborne electromagnetic (AEM) ice thickness survey one month after the closing began. During that time strong ice convergence decreased the area of the former polynya by a factor of 2.5. The AEM survey showed mean and modal thicknesses of the one-month old ice of 1.96 ± 1.5 m and 0.95 m, respectively.We show that this is in close agreement with the modeled thermodynamic growth and with the dynamic thickening expected from the polynya area decrease during that time. In addition,we found characteristic differences in the shapes of ice thickness distributions in different regions of the closing polynya. These closely corresponded to different deformation histories of the surveyed ice that were derived from the high-resolution SAR imagery by drift tracking along Lagrangian backward trajectories. Results show a linear proportionality between convergence and thickness change that agrees well with ice thickness redistribution theory. In addition, the e-folding of the tails of the different ice thickness distributions is proportional to the magnitude of the total deformation experienced by the ice. Lastly, we developed a simple volume-conserving model to derive dynamic ice thickness change from high-resolution SAR deformation tracking. The model has a spatial resolution of 1.4 km and reconstructs thickness profiles in reasonable agreement with the AEM observations. The computed ice thickness distribution resembles main characteristics like mode, e-folding, and width of the observed distribution. This demonstrates that high-resolution SAR deformation observations are capable of producing realistic ice thickness distributions. The MYI surrounding the polynya had a mean and modal total thickness (snow + ice) of 2.1 ± 1.4 m and 2.0 m, respectively. The similar first- and multi-year ice mean thicknesses elude to the large amount of deformation experienced by the closing polynya.
... Взаимодействие льдин на границе между припаем и паковым льдом приводит к их разламыванию, нагромождению и образованию торосов. В результате продолжительного воздействия сил сжатия происходит скопление и объединение фрагментов льда в ледяные глыбы, протяжённость которых может достигать сотен километров (Hopkins et al., 1999). Часто вдоль кромки припая образуются целые пояса торосов (Бушуев и др., 1974). ...
... One of the approaches to the mathematical modeling of ice hummock formation was the discrete element method which allows presenting the drifting ice cover in the form of the set of the great number of ice floes with specified properties. The numerical solutions to the two-dimensional problems allowed obtaining the realistic forms of ice ridges and the distribution of ice blocks [20,21]. ...
Article
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A method for studying stamukhas using the modern field equipment is considered. The peculiarities of morphometric characteristics and parameters of the internal structure of stamukhas are analyzed. The interrelation between the consolidated layer thickness and the accumulated freezing degree days is derived for different seas. The comparative analysis of morphometric characteristics and the consolidated layer in the ice-covered seas of Russia is carried out. It is shown that the formation of stamukhas in different regions has specific features depending on the depth, bottom topography, drift characteristics, ice thickness, and dates of fast ice formation. The maximum thickness of the consolidated layer is registered in the Kara and Laptev seas. https://rdcu.be/b5unn
... The benefits of FEM-DEM analyses in ice mechanics are its ability to account for a high number of individual ice blocks and to account for the granular behavior of ice rubble. Methods that account for such features have been used in several studies on ice mechanics (Williams et al., 1986;Hopkins and Hibler III, 1991;Hopkins, 1992Hopkins, , 1998Hopkins et al., 1999;Barker and Croasdale, 2004;Liferov, 2005;Tuhkuri and Polojärvi, 2005;Polojärvi and Tuhkuri, 2009, 2013a, 2013bKonuk et al., 2009;Polojärvi et al., 2012Polojärvi et al., , 2015Metrikin and Løset, 2013;Metrikin et al., 2015;Shunying et al., 2015;van den Berg et al., 2018). A recent review by Tuhkuri and Polojärvi (2018) describes how such methods have been used in studies on ice loads in various ice loading scenarios. ...
Article
This paper studies the ice-structure interaction process on a wide, inclined, offshore structure in shallow water. In such a process, the ice rubble pile that forms in front of the structure may reach the seabed, or in other words, the rubble pile may ground. A grounded rubble pile is often assumed to protect the structure from high peak ice loads. The study is based on two-dimensional combined finite-discrete element method simulations and it focuses on the effect of water depth and ice thickness on peak ice load magnitudes. In order to obtain a better understanding of the physical phenomena behind the peak ice load events in shallow water, we analyse the probability of rubble pile grounding, the rubble pile geometries, and the load transmission from the intact ice sheet to the structure through the ice rubble pile. We also discuss the parameter effects and the probability and severity of ice encroachment in shallow and deep water. Our simulations suggest that an interaction process in shallow water may lead to higher peak ice load magnitudes than an interaction process in deep water. This is at least the case when there is no pre-existing, partially consolidated ice rubble pile in front of the structure. We also observed that the ice thickness influences the probability of rubble pile grounding: For a given ice thickness to water depth ratio, thin ice appears to ground with higher probability than thick ice.
... Resistance on a ship penetrating a sea ice ridge is a key design parameter of ice breaking ships and has important implications on marine transport in polar seas, where ridges are common ice features. Ridges are accumulations of broken ice blocks resulting from compression and shear failure of sea ice sheets under loading from winds and currents (Parmerter and Coon, 1972;Hopkins et al., 1999;Tuhkuri and Lensu, 2002). A ridge can be so large that a ship cannot pass through it but either gets stuck, or needs to ram several times into the ridge to get through. ...
Article
Resistance on a ship penetrating a sea ice ridge is a key design parameter of ice breaking ships. The resistance of a ship in an unconsolidated ridge has been studied by using a three dimensional discrete element method. Ridges of equal thickness but different widths were used and it was observed that the ridge width has a major effect on the ridge resistance: The ridge resistance increases with increasing ridge width, until the ridge width is of the same order as the ship length. The ridge resistance was decomposed into a frictional force and a deformation force. The deformation force is due to the ridge deformation by the ship bow and it was shown that the deformation force is related with the mass of ice blocks accelerated by and moving with the ship.
... There were periods of strong noise, but a downward trend in amplitude began early in 2017. By that point, the area had already been covered with ice for more than a month, but it takes time for keels and other features under the ice (which tend to scatter energy out of the ocean acoustic waveguide) to develop during fracturing, drifting, rafting, and ridging [26][27][28][29][30] . Evidence of these processes appears in the images in Figs 9 and 10, which were obtained during a helicopter flight from Barrow to the vicinity of the array on March 18, 2017. ...
Article
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Acoustic data from the Canada Basin Acoustic Propagation Experiment are discussed. These recordings were obtained under seasonally varying sea ice to the north of Alaska during a period of 154 days. They contain signals from sources that were deployed at ranges of 17.5, 29.6, and 237.8 km and ambient sounds from marine mammals and ice-related events. After the area was covered with ice, the amplitude of receptions from the most distant source gradually decreased as scattering features on the underside of the ice developed during fracturing, drifting, ridging, and rafting events. Improvements are presented for an Arctic acoustic model that is based on the parabolic equation method, and the approach is applied to a problem in which variable ice thickness acts as a loss mechanism by scattering energy out of the waveguide. Some of the recordings have a harmonic signature that is believed to be associated with the resonances of ice floes rubbing together, but variations in the harmonics over short time scales cannot be explained in terms of the resonances of an isolated floe. This behavior may be related to the coupling of vibrations at contact points that vary during the relative motions of floes.
... The strength of FEM-DEM in ice mechanics resides in its ability to account for numerous individual ice floes and blocks and for the granular behavior of ice rubble. Models accounting for these features have been used in several studies on ice mechanics [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. Fig. 1a-f describe simulations that had an ice sheet of thickness h pushed against an inclined rigid structure. ...
Article
A R T I C L E I N F O Keywords: ice loads Offshore structures Arctic engineering Ice-structure interaction Finite-discrete element method Discrete element method Ice mechanics A B S T R A C T This paper focuses on mechanisms that limit the sea ice loads on offshore structures. It introduces a probabilistic limit load model, which can be used to analyze peak ice load events and to estimate the maximum peak ice load values on a wide, inclined, offshore structure. The model is based on simple mechanical principles, and it accounts for a mixed-mode ice failure process that includes buckling and local crushing of ice. The model development is based on observations on two-dimensional combined finite-discrete element method simulations on the ice-structure interaction process. The paper also presents a numerical limit load algorithm, which is an extension of the probabilistic limit load model and capable of yielding a large number of stochastic peak ice load values. The algorithm is compared to simulation-based and full-scale observations. Analyzing peak ice load events is challenging as sea ice goes through a complex mixed-mode failure process during such events. The algorithm is an effective tool for this analysis, and it shows that distinguishing between the buckling and local crushing failure is virtually impossible if the only data available from a peak load event is the value of the peak ice load. The algorithm shows potential in improving estimates of maximum peak ice load values on offshore structures.
... Second, rafting likely occurred. Hopkins et al. (1999) showed that during thin ice ridging, rafting was often observed. Bonnemaire et al. (2003) also found a large variation in ice-block thicknesses in one Barents Sea ridge (20-190 cm) and separated the variations into three block thickness groups, which were 1, 2 and 3 times the level ice thickness from which the ridge was formed. ...
Article
In this study, four first-year ice ridges (R1, R2, R3 and R4) were measured during the transition from the “main” phase to the “decay” phase. The measurements were conducted on two ice floes in the Arctic Ocean northwest of Svalbard during May and June 2015. Ice ridge R1 was approximately 13 m thick and 200 m long, R2 was 5 m thick and 500 m long, R3 was 6 m thick and 75 m long, and R4 was 9 m thick and 150 m long. The objective of this study was to investigate the rubble macroporosity evolution, ridge drilling resistance and consolidated layer small-scale strength in the decaying ridges. The ice rubble macroporosity and ridge drilling resistance values were obtained through mechanical drilling. The drilling resistance was measured by the drill operator, which was defined as hard, medium or soft. The small-scale strength was measured in the field via uniaxial compression with a nominal strain rate of 10⁻³ s⁻¹. The rubble macroporosities in R1, R2, R3 and R4 ranged from 10% to 27%, and the temporal macroporosity variation was the result of seasonal developments. The rubble macroporosity in R2 decreased from 25% (27 days old) to 16% (34 days old, 4 days before breakup). In R1, which was larger, colder and older than R2, the rubble macroporosity remained constant (11%–10%) over a ten-day period. Because ridges R3 (22% rubble macroporosity) and R4 (27% rubble macroporosity) were only mapped once, no temporal development was measured. We suggest that the ice rubble macroporosity in saline, first-year ridges continuously decreases over time and that this decrease accelerates during the decay phase. Furthermore, both the consolidated layer uniaxial compressive strength (measured in R1, R2 and R3) and the ridge drilling resistance (measured in R1, R2, R3 and R4) decreased during the transition from the main phase to the decay phase, due to an increase in ice temperatures. After the ridges reached an isothermal state, the drilling resistance and strength remained constant, and the brine volume (microporosity) increased. The ice cores collected from the decaying ice exhibited ductile failure modes when subjected to uniaxial compression.
... Discrete approaches, where individual blocks of ice rubble are accounted for, have been used in a number of studies on ice mechanics (see e.g. Williams et al., 1986;Hopkins and Hibler III, 1991;Hopkins, 1992Hopkins, , 1998Hopkins et al., 1999;Barker and Croasdale, 2004;Liferov, 2005;Tuhkuri and Polojärvi, 2005;Tuhkuri, 2009, 2013a,b;Polojärvi et al., 2012Polojärvi et al., , 2015. ...
Article
This paper analyses peak ice loads on an inclined, rigid marine structure by using data from 2D combined finite-discrete element method simulations. The aim is look for answers to the questions: what type of distributions do peak ice loads follow, what type of data is needed for their analysis, and how should the data on peak ice loads be collected? In the simulations, an initially continuous ice sheet, modeled as a floating beam, breaks into smaller ice blocks as the sheet is pushed against the structure. Statistical tools were used to analyse the peak ice load distributions, error estimates, and peak ice load occurrences. Load distributions appeared to be right-skewed and thus non-normal. Gumbel distribution appeared to describe the data well. The results show that the large scatter in the ice load data is due to the ice-structure interaction process itself. Due to the scatter, a large number of observations are needed for studying peak ice load statistics: To reliably observe a 15% difference in peak loads due to a single parameter would require more than 80 observations in total. The results showed that high peak loads may occur even in the early stage of the ice-structure interaction process.
... During the interaction process, the initially intact ice sheet fails into a rubble pile of ice blocks, which then interact with each other and the structure. Similar approaches, where individual ice features are accounted for with some level of accuracy, have been used in a number of studies on ice mechanics (Williams et al., 1986;Hopkins and Hibler III, 1991;Hopkins, 1992Hopkins, , 1998Hopkins et al., 1999;Barker and Croasdale, 2004;Liferov, 2005;Tuhkuri and Polojärvi, 2005;Tuhkuri, 2009, 2013a,b;Konuk et al., 2009;Polojärvi et al., 2012Polojärvi et al., , 2015Metrikin and Løset, 2013;Metrikin et al., 2015;Shunying et al., 2015;van den Berg, 2016). ...
Article
This paper focuses on the mechanisms and limits for the peak ice load values on inclined marine structures, and presents a buckling model, which explains well the phenomena behind the maximum peak ice loads. The study is based on two-dimensional combined finite-discrete element method simulations of the failure process of level ice against a structure. The simulations yield ice load records, which show consecutive peak ice load events. The complexity of the failure process makes the analysis on the mechanical phenomena behind the peak ice load events extremely challenging. The introduced buckling model assumes that the ice sheet breaks into separate ice floes in front of the structure before the maximum peak ice loads occur. The model is demonstrated to be able to quantify the effect of force chains, which have an important role in the ice-structure interaction process.
... x Number of keels LEGEND thickness favour rafting (Hopkins et al., 1999). Simple rafting, where the ice thickness is doubled, is likely to occur between uniform ice sheets while multiple layering occurs between non-uniform ice sheets. ...
Conference Paper
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We developed a quantitative scheme for identifying Antarctic first year ridge sails and keels from 204 drill profiles obtained from the Weddell, Ross, Amundsen and Bellingshausen Seas. A sail is defined as a non-level section on the top surface which has at least one point which is >0.3m above the surrounding level top surface. A keel is defined as a non-level section on the bottom surface which has at least one point which is >2.25 times as thick as the surrounding mean level ice thickness. From nearly 19km of drill data we identified 48 ridges. Almost 65% of them are not associated with any sails, while a small proportion overlap with two sails. The ratio between maximum snow sail height and maximum ice keel depth is 1:3.6. Estimating the volume of a ridge by assuming it has the same thickness as the surrounding level ice, underestimates by approximately 40%. Estimation of mass contained within keels from snow sail statistics must take into account the probability of a keel being associated with a sail and the ratios between the snow sail and ice keel.
... Marko & Thomson [9] suggested that these lineaments are analogous to strike-slip faults in the Earth's crust. Friction plays a key role in ice rafting and ridging [10]. Stick-slip friction has been observed in laboratory experiments on multiyear sea ice [7], and one can deduce that it plays a key role in sea ice dynamics and explains behaviour observed in ice tank experiments [11]. ...
Article
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We have conducted a series of high-resolution friction experiments on large floating saline ice floes in an environmental test basin. In these experiments, a central ice floe was pushed between two other floes, sliding along two interfacial faults. The frictional motion was predominantly stick-slip. Shear stresses, normal stresses, local strains and slip displacement were measured along the sliding faults, and acoustic emissions were monitored. High-resolution measurements during a single stick-slip cycle at several positions along the fault allowed us to identify two phases of frictional slip: a nucleation phase, where a nucleation zone begins to slip before the rest of the fault, and a propagation phase when the entire fault is slipping. This is slip-weakening behaviour. We have therefore characterized what we consider to be a key deformation mechanism in Arctic Ocean dynamics. In order to understand the micromechanics of sea ice friction, we have employed a theoretical constitutive relation (i.e. an equation for shear stress in terms of temperature, normal load, acceleration, velocity and slip displacement) derived from the physics of asperity-asperity contact and sliding (Hatton et al. 2009 Phil. Mag. 89, 2771-2799 (doi:10.1080/14786430903113769)). We find that our experimental data conform reasonably with this frictional law once slip weakening is introduced. We find that the constitutive relation follows Archard's law rather than Amontons' law, with tau proportional to sigma(n)(n) (where tau is the shear stress and sigma(n) is the normal stress) and n=26/27, with a fractal asperity distribution, where the frictional shear stress, tau = f(fractal) T(ml)w(s), where f(fractal) is the fractal asperity height distribution, T-ml is the shear strength for frictional melting and lubrication and w(s) is the slip weakening. We can therefore deduce that the interfacial faults failed in shear for these experimental conditions through processes of brittle failure of asperities in shear, and, at higher velocities, through frictional heating, localized surface melting and hydrodynamic lubrication. This article is part of the themed issue 'Microdynamics of ice'.
... was 70 @BULLET . Hopkins et al. (1999), (2009, 2013a,b), and Poloj?rvi et al. (2012Poloj?rvi et al. ( , 2015). 42 Figure 1shows an example of a simulated ice-structure interaction process and illustrates an 43 important advantage of FEM-DEM modeling. ...
Article
This paper analyses peak ice load data from 2D combined finite-discrete element method simulations. In these simulations, an initially continuous ice sheet, modeled as a floating beam, breaks into smaller ice blocks as the sheet is pushed against an inclined structure. Multivariate linear regression modeling and the variable elimination method were used in the analysis of the data. The analysis gave valuable insight into the peak ice load data in a simulated ice-structure interaction process. It was found that the peak ice load data can be estimated with good accuracy using only five parameters: the ice thickness, the inclination angle of the structure, the shear strength of ice, the ice-structure, and ice–ice friction coefficients. The ice thickness and the structure’s inclination angle had the strongest relative effects, with their importance changing during the process. The results also showed that the stage of the ice-structure interaction process should be taken into account in ice load models. The results of this paper underline the importance of the statistical analysis of ice load data and give valuable suggestions for future work.
... Data of the morphology and width distribution of ridges and rafts as a function of the size of the combining ice floes are scarce, though there are indications that rafts can be substantially larger than ridges (Hopkins et al., 1999). We crudely define the width of the contact zone in ridging to be 5 m, or the size of the smaller of the two combining floes, whichever is smaller: δ ridge (r 1 , r 2 ) = min(5 m, r 1 , r 2 ). ...
Article
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Sea ice exhibits considerable seasonal and longer-term variations in extent, concentration, thickness, and age, and is characterized by a complex and continuously changing distribution of floe sizes and thicknesses, particularly in the marginal ice zone (MIZ). Models of sea ice used in current climate models keep track of its concentration and of the distribution of ice thicknesses, but do not account for the floe size distribution and its potential effects on air–sea exchange and sea-ice evolution. Accurately capturing sea-ice variability in climate models may require a better understanding and representation of the distribution of floe sizes and thicknesses. We develop and demonstrate a model for the evolution of the joint sea-ice floe size and thickness distribution that depends on atmospheric and oceanic forcing fields. The model accounts for effects due to multiple processes that are active in the MIZ and seasonal ice zones: freezing and melting along the lateral side and base of floes, mechanical interactions due to floe collisions (ridging and rafting), and sea-ice fracture due to wave propagation in the MIZ. The model is then examined and demonstrated in a series of idealized test cases.
... These results are in general agreement with field measurements that were later obtained by others (Tucker and Govoni 1981;Melling and Riedel 1996). More recently, discrete-particle numerical modelling and model-ice laboratory experiments have produced new insights on the sheet ice -rubble interaction (Hopkins 1998;Tuhkuri and Lensu 2002). While the above works provide some guidance on the characteristics of rubble fronts created by large ice sheets in lakes and oceans, more work needs to be done to apply a similar analysis to rivers. ...
Preprint
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Large-scale modeling of sea ice dynamics assumes scale-invariance that is used to calibrate and validate current models. Validity of this assumption, particularly its lower spatial limit, remains poorly understood. Identifying when, where, and why scale-invariance does not apply is essential for linking meter-scale sea ice mechanics with large-scale sea ice dynamics and climate models. Here we address this challenge by employing unique high-resolution ship radar imagery from MOSAiC expedition in an analysis based on novel deep learning-based optical flow technique. Together these allow capturing sea ice kinematics consistently at unprecedented 20-meter spatial and 10-minute temporal resolutions over an entire winter season and into summer over a 10-kilometer spatial domain. We show that the sea ice within this domain remains largely quiescent for extended periods, with distinct events revealing a 102-meter lower limit for scale-invariance that endures as the ice cover undergoes seasonal evolution. This threshold remains stable throughout the winter, even as deformation features become more localized and distinct, suggesting an intrinsic mechanical constraint that is invariant under varying external conditions. Once the ice transitions to a floe-dominated configuration in summer, no comparable scaling signature emerges. Our results give a limit under which continuum models fail to capture critical fine-scale processes, highlighting the need for approaches accounting for detailed description of discontinuous spatial and temporal behavior of sea ice.
Article
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Model for describing a three-dimensional continuous failure process of an ice sheet is introduced. The presented model is based on the combined finite-discrete element method. The ice sheet consists of polyhedral rigid discrete elements joined by a lattice of Timoshenko beam elements, which go through cohesive softening upon sheet failure. The contact model accounts for inter-particle friction and local failure of ice in contacts. The model is carefully validated against a laboratory experiment, where an ice sheet is pushed against an inclined plane. Convincing agreement between the modelled and experimental failure process is found. The effect of ice sheet tessellation and element size is tested and found to be only moderate. The model compares favorably to earlier ones: The modelling and the experimental results agree, the domain sizes used can be large, and the modelled failure processes are long in duration. Requirements for numerical modelling of ice failure processes are discussed.
Thesis
This thesis is concerned with the study of sea ice cover deformation caused by the processes in the atmosphere and ocean. Only a modest number of studies has addressed the cross-scale analysis of the ice deformation. The aim of the present research has two foci: to investigate the variability of ice deformations and identify mechanisms responsible for their generation, and to explore the relationships of the ice deformation in the range of spatial scales. Two types of ice, the multi-year pack ice in the central Arctic and the seasonal ice in the northern Baltic Sea, are studied. The research includes a field experiment, observation analysis and modelling. Stresses in the ice generated by non-uniform drift of ice, ocean waves, and ice deformation due to variations in the ambient air temperature are considered. To separate thermal and motion induced deformation on the floe scale a thermo-mechanical non-linear viscous-elastic model has been developed. The results from these simulations are compared with the observations from the field experiment. To study the aggregate behaviour of the ice cover the mesoscale deformations are analysed along with the local ice strain. The continuum anisotropic and granular ice models are employed to simulate the highly inhomogeneous spatial structure of the deformation fields observed. The wave emission due to ice failure is also investigated. A comparison of field observations and laboratory tests in an ice tank and asymptotic analysis allow us to identify mechanisms of the wave emission at frequencies between 0.2 Hz and 1.0 Hz. The scaling formalism for the ice deformation and stress is suggested. The results of the data analysis and modelling have converged into a coherent scheme describing the spatial and temporal variability of the sea ice cover deformation from the local scale through the single floe scale to the mesoscale.
Article
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The mechanical interactions between ice floes in the polar sea‐ice packs play an important role in the state and predictability of the sea‐ice cover. We use a Lagrangian‐based numerical model to investigate such floe‐floe interactions. Our simulations show that elastic and reversible deformation offers significant resistance to compression before ice floes yield with brittle failure. Compressional strength dramatically decreases once pressure ridges start to form, which implies that thicker sea ice is not necessarily stronger than thinner ice. The mechanical transition is not accounted for in most current sea‐ice models that describe ice strength by thickness alone. We propose a parameterization that describes failure mechanics from fracture toughness and Coulomb sliding, improving the representation of ridge building dynamics in particle‐based and continuum sea‐ice models.
Article
This paper represents the state-of-the-art in the field of ice tank numerical simulation methods. It gives a comprehensive review of existing commercial and prototype numerical methods in the ship–ice interaction, including aspects such as features, capabilities, and presents a discussion in terms of their characteristics. The numerical simulation techniques are categorized as discrete element method, finite element method, cohesive element method, smoothed particle hydrodynamics method, peridynamics method, lattice Boltzmann method, and some coupled models of these methods, mainly depending on what the numerical methods are implemented to simulate the behavior of ice. One purpose is to classify the chosen methods and evaluate their efficiency and accuracy, and to enable potential readers to quickly grasp the main numerical methods and the development of their applications in the ship–ice interaction scenarios. We assess their practicability and validity from both perspectives of practice and physics and discuss challenges in existing numerical simulation methods. We highlight the significance of interdisciplinary applications for developing the research in fluid–structure interactions. Instead of elaborating on the numerical simulation techniques theoretically, their applications in ship–ice interaction scenarios are focused and presented.
Article
Purpose This paper aims to simulate a punch shear test of partly consolidated ice ridge keel by using a three-dimensional discrete element method. The authors model the contact forces between discrete ice blocks with Hertz–Mindlin contact model. For freeze bonds between the ice blocks, the authors apply classical linear cohesion model with few modifications. Based on punch shear test simulations, the authors are able to determine the main characteristics of an ice ridge from the material parameters of the ice and freeze bonds. Design/methodology/approach The authors introduced a discrete model for ice that can be used for modelling of ice ridges. The authors started with short introduction to current status with ice ridge modelling. Then they introduced the model, which comprises Hertz–Mindlin contact model and freeze bond model with linear cohesion and softening. Finally, the authors presented the numerical results obtained using EDEM is commercial Discrete Element Modeling software (EDEM) and analysed the results. Findings The Hertz–Mindlin model with cohesive freeze bonds and linear softening is a reasonable model for ice rubble. It is trivial that the ice blocks within the ice ridge are not spherical particles, but according to results, the representation of ice blocks as spheres gave promising results. The simulation results provide information on how the properties of freeze bond affect the results of punch shear test. Thus, the simulation results can be used to approximate the freeze bonds properties within an ice ridge when experimental data are available. Research limitations/implications As the exact properties of ice rubble are unknown, more research is required both in experimental and theoretical fields of ice rubble mechanics. Originality/value Based on this numerical study, the authors are able to determine the main characteristics of an ice ridge from material parameters of ice and freeze bonds. Furthermore, the authors conclude that the model creates a promising basis for further development in other applications within ice mechanics.
Article
Biogeochemical cycling of trace metals in sea ice is important to the productivity of the Arctic Ocean. Unfortunately, the processes by which trace metals accumulate into sea ice are poorly understood. To gain a clearer understanding of the mechanisms behind trace metal accumulation, dissolved (D, <0.2 μm), and labile particulate (LP = Total Dissolvable – Dissolved) iron (Fe), manganese (Mn), and cadmium (Cd) concentrations were compared to the structure observed in sea ice. Samples were pre-concentrated via solid-phase extraction on NOBIAS Chelate PA-1 resin and analyzed on a Graphite Furnace Atomic Absorption Spectrometer. Using photographic analysis for the percentage of pore microstructure and δ¹⁸O analysis, sea ice structure was determined to be snow ice, granular ice (frazil ice), mixed ice (granular and columnar ice) and columnar ice. Salinity and nutrients were low, indicating brine drainage and multi-year ice. High trace metal concentrations in snow ice indicated meteoric snow was a source of trace metals to sea ice. High concentrations of LPFe in granular ice indicated entrainment of suspended particulate trace metals by frazil ice during the formation of the granular ice structure. Whereas the high concentrations of DFe and DMn in granular ice may have been due to reduction from LPFe and LPMn after particle entrainment, indicating chemical transformation processes. Low dissolved and labile particulate trace metal concentrations in mixed and columnar ice indicated a release due to brine drainage. Our study clearly indicates that the differences observed in trace metals among sea ice structures, showed that sea ice formation, chemical reduction and brine release were the processes driving trace metal accumulation and release in the Arctic sea ice.
Article
Failure of level ice against an inclined marine structure has been simulated using a two-dimensional finite-discrete element method. The simulation model is deterministic, but very sensitive to initial conditions. This allowed us to create ice load data and to study the evolution of the ice failure process. The mean load, the standard deviation, and the maximum load increased during the ice failure process. Ice thickness had a strong effect on the ice load and also the plastic limit of ice had an effect, especially when the ice was thick. The coefficient of variation of the ice load was initially high and then continuously decreased during the ice failure process. This suggests that the ice failure process did not reach a stationary stage, showed high probability of extreme peak loads, and that distributions with a constant coefficient of variation should not be used for this kind of ice loading processes. Extreme value analysis, with the assumption that the ice load follow a log-normal distribution on each time step, fitted the data well and suggested that the maximum ice load increases with sample size. Further, it appears that the peak ice loads are bounded by the crushing capacity of the ice even in the case of an inclined structure. The statistical analysis of simulated ice load data further suggests that observations from short interaction processes, or with small sample sizes, may lead to very inaccurate ice load estimates.
Article
Arctic landfast sea ice is widely utilized for transportation by local communities and industry, with trafficability largely governed by ice roughness. Here, we introduce an approach to evaluate ice roughness that can aid in routing of ice roads and assessment of spatial variability and long-term changes in trafficability. Drawing on synthetic aperture radar (SAR) polarimetry, SAR interferometry (InSAR), and other remote sensing techniques, we integrated approaches into the trafficability assessment that had rarely been applied over sea ice in the past. Analysis of aerial photogrammetry obtained through structure-from-motion helped verify cm-scale accuracy of X-band InSAR-derived ridge height and link L-band polarimetric classification to specific roughness regimes. Jointly, these approaches enable a km-scale evaluation of ridge topography and cm- to m-scale roughness—both critical for the assessment of trafficability. A trafficability index was derived from such SAR data in conjunction with analysis of ice trail routing and ice use near Utqiaġvik, Alaska. The index identifies areas of reduced trafficability, associated with pressure ridges or rubble ice, and served to delineate favorable trail routes for different modes of transportation, with potential uses ranging from ice road routing to emergency evacuation. Community outreach is needed to explore how this approach could assist different ice users in reducing risk, minimizing trail or ice construction efforts, and improving safety.
Chapter
Two types of ice cover deformation processes have been studied: compression of ice fields made up of small floes and compression of two identical ice sheets. While these processes have differences, they also show common features. It is suggested that the ice cover deformation should be described as a single process with different phases. In this context, the fact that an ice cover can have several different morphological features (rafted ice, ridges, rubble) is not an indication of different processes, but an indication of different stages in a single process.
Chapter
A model of a single ice ridge is constructed based on the laws of mass, impulse and energy balance and on the representation of a ridge as a discontinuity line. Self-oscillations of the ice cover induced by the buildup of two ridges are investigated. The approach to the modeling of an ice cover with numerous ridges in the onedimensional case is formulated.
Article
The ice rafting is familiar in Bohai sea. Studying its forming characters is important in analyzing the reliability of ice design parameters on offshore structure. Theoretical analysis and numerical simulation has been applied to discuss the problem of the ice rafting in Bohai sea. Assuming the sea ice to be viscous-elastic material, the process of ice rafting on the force of wave, current and wind is simulated by using the discrete element method. The analysed results show that the ice is easily fractured on the action of wave, and the ice thickness is thin, the rafting is more easily occurred. The rafted ice length is increased with the ice thickness decreasing and the enhancive force of ocean current and wind.
Article
The ice pack in Arctic and sub-Arctic seas is characterized by granularity from the pancake ice formed in the waves of marginal ice zones, rubble fields that border coastlines, ice blocks in the sails and keels of pressure ridges that criss-cross the ice pack, to the Arctic Basin floes that range from sub-kilometer size to large plates that extend for tens of kilometres. The granularity of the pack is formed from fracture and driven by wind driven deformation. Traditionally, the pack ice and its dynamic processes have been modelled using an Eulerian continuum approach by capturing the average behavior of a sufficient volume of material. Rapidly increasing computational power has made it possible to directly simulate the ice pack and capture the granularity that governs sea ice dynamics. The discrete element modelling (DEM) technique, used for modelling systems of discrete particles, is ideally suited to modelling granular sea ice problems. This article gives an overview and description of some of this work.
Article
This is the first complete account of the physics of the creep and fracture of ice, and their interconnectivity. It investigates the deformation of low-pressure ice, which is fundamental to glaciers, polar ice sheets and the uppermost region of icy moons of the outer Solar System. The book discusses ice structure and its defects, and describes the relationship between structure and mechanical properties. It reviews observations and measurements, and then interprets them in terms of physical mechanisms. The book provides a road-map to future studies of ice mechanics, such as the behaviour of glaciers and ice sheets in relation to climate change and the dating of deep ice cores. It also highlights how this knowledge is transferable into an understanding of other crystalline materials. Written by experts in the field, it is ideal for graduate students, engineers and scientists in Earth and planetary science, and materials science.
Article
Unusual thrust structures in thin sea ice sheets were observed in Labrador and Greenland. These structures are the result of thin ice sheets being of wind and waves. When thicker pack ice is subjected to these same forces pressure ridges result.
Article
A two-dimensional particle simulation model of the sea-ice ridging process is developed. In this model, ridges are formed from a floating layer of rubble compressed between converging multiyear floes. The energy consumed in ridge growth, including dissipation, is explicitly calculated. A series of experiments are performed to establish the dependence of the energy consumed in ridging on the velocity of the multiyear floes and on the shape, the friction coefficient, and the inelasticity of the rubble blocks. The experiments show that shape and friction between ice blocks are the most significant factors in determining the energy required to ridge ice. In large-scale sea ice modeling, using a variable thickness approach, it is convenient to parameterize total ridging work in terms of the increase of potential energy. The results of the ridging simulations with block-shaped rubble suggest that the total ridging work may be 4–5 times the increase in potential energy. At the same time, an analytical model of the ridging process is developed from classical Mohr-Coulomb-Rankine theory for a cohesionless granular material. The predictions of this model, using values of porosity and the passive pressure coefficient derived from the ridge simulations, are in fair agreement with the numerical experiments. However, several violations of the basic assumptions underlying the Mohr-Coulomb-Rankine model are noted in the ridge simulations.
Article
A theory describing evolution of the ice thickness distribution (the probability density of ice thickness) was proposed by Thorndike et al. (1975) and has been used in several sea ice models. The advantage of this theory over the widely used two-level formulation is that it treats ridging explicitly as a redistribution of ice thickness, and ice strength as a function of energy losses incurred by ridge formation. However, the parameterization of these processes remains rather speculative and largely untested, and so our purpose here is to explore these parameterizations using a numerical model based on this theory. The model uses a 160-km resolution grid of the Arctic and 7 years of observed atmospheric forcing data (1979-1985). Monthly oceanic heat flux and current fields are obtained from a 40-km resolution coupled ice-ocean model run separately with the same forcing. By requiring the computed monthly mean ice drift to have the same magnitude as observed buoy drift, we estimate the primary strength parameter: the ratio of total to potential energy change during ridging. This ratio depends on the value of other parameters; however, the standard case has a ratio of 17 which is within the range estimated by Hopkins (1994) in simulations of individual ridging events. The effects of ridge redistribution and shear ridging parameters are illustrated by a series of sensitivity studies and comparisons between observed and modeled ice thickness distributions and ridge statistics. In addition, these comparisons highlight the following shortcomings of the thickness distribution theory as it is presently implemented: first, the process of first-year to multiyear ridge consolidation is ignored; and second, the observed preferential melt of thick ridged ice is not reproduced.
Article
Unusual thrust structures in thin sea ice sheets were observed in Labrador and Greenland. These structures are the result of thin ice sheets being forced into each other by a combination of wind and waves. When thicker pack ice is subjected to these same forces pressure ridges result.
Article
A mechanical model is developed to describe the rafting of ice sheets of equal thickness. Rafting is one of the important deformation mechanisms in thin ice. The model predicts the force required to initiate rafting. This force is an upper bound for the force in pack ice. The model is also used to calculate the bending stress developed by rafting. The stress increases in proportion to the square root of ice thickness. Thus for a given ice strength there is a maximum thickness of ice which can raft without fracturing. For typical young ice properties the calculated value of 17 cm is in good agreement with field observation.
Article
A kinematic model of pressure ridge formation is presented, in which the lateral and vertical motion of ice blocks is combined with a force balance and breaking stress calculation. A computer program encompassing several physical processes has been used to simulate ridge formation in ice with thicknesses from 20 cm to 2 meters. The resulting profiles are compared with measured profiles of other authors. A lower bound to the force required to form ridges is calculated from an energy balance and found to be of the order of the forces that may result from wind loading on the ice. When the ridge model proceeds through many steps, a limit cycle is established that provides a limiting height for ridges. This height depends on the thickness and strength of the ice. Limiting height calculations are made for ice sheets from 20 cm to 4 meters thick. The most striking features of the ice in the Arctic Ocean are the ridges, which are linear accumulations of ice caused by the compressional and shearing interactions of ice floes. These ridges rise several meters above the ocean surface and may extend from several meters to tens of meters below the surface. Knowledge of ridge size, distribution, and formation mechanisms is important for several reasons. Because of their size and distribution, ridges present formidable obstacles to both surface and submarine transportation systems. Ridges affect the rheological behavior of pack ice, since the compressibility of the pack is determined, in part, by its ability to form ridge'like structures. The ridging process constantly alters the proportions of pressured ice, open water, and young ice, and these altered proportions in turn influence the thermal interaction
Article
The pressure ridging process is simulated using a two-dimensional particle model. Blocks are broken from an intact sheet of relatively thin lead ice pushed against a thick, multiyear floe at a constant speed. The blocks of ice rubble accumulate to form the ridge sail and keel. During the simulations the energy consumed in ridge growth, including dissipation, is explicitly calculated. On the basis of the results of simulations performed with the model, the ridging process can be divided into four distinct stages. The first stage begins with an intact sheet of lead ice impacting a floe and ends when the sail reaches its maximum height. In the second stage the ridge keel deepens and widens. The stage ends when the maximum keel draft is reached. In the third stage the direction of growth is leadward creating a rubble field of more or less uniform thickness. The third stage ends when the supply of thin ice is exhausted. In the fourth stage the rubble field is compressed between converging floes. The results of simulations establish the dependence of ridging energetics in the first and second stages on the thickness of the ice sheet and the amount of ice pushed into the ridge. The average profiles of the simulated ridges delineate the growth process in the first, second, and third stages. The energetics and profiles of the fourth stage were described by Hopkins et al. [1991]. Lead ice extents of up to 1300 m are pushed into ridges to determine maximum sail heights, keel drafts, and ridging forces.
Article
The sea ice pressure ridging process is modeled using a two-dimensional particle simulation technique. In this model, blocks are broken from an intact sheet of relatively thin lead ice driven against a thick, multiyear floe at a constant speed. The blocks of ice rubble accumulate to form the ridge sail and keel. The energy consumed in ridge growth, including dissipation, is explicitly calculated. A series of numerical experiments are performed to establish the dependence of the energetics on the thickness of the ice sheet and the friction between blocks. The results suggest that the total energy required to create a pressure ridge is an order of magnitude greater than the potential energy in the ridge structure. A typical sea ice cover in the polar regions contains a variety of ice thicknesses that evolve in response to both dynamic and thermodynamic forcing. The variable thickness of the ice cover is created by deformation, which simultaneously causes formation of thick ice through ridge building and thin ice through lead creation. Since the energy expended in deformation is largely determined by the ridging process, an understanding of the energetics of pressure ridging is critical in the determination of ice strength on a geophysical scale.
Measurements of curvilinear ridges in the Bay of Bothnia during the ZIP-97 experimentRep. M-231, 64Ship Lab
  • M Lensu
  • J Tuhkuri
  • M Hopkins
  • M Lensu
  • J Tuhkuri
  • M Hopkins
Ice tank tests on ridging of non-uniform ice sheetsRep. M-236Ship Lab
  • J Tuhkuri
  • M Lensu
  • J Tuhkuri
  • M Lensu
Models of pressure ridge formation in sea ice Ice tank tests on ridging of non-uniform ice sheets, Rep. M-236
  • R R Parmerter
  • M D Coon
  • J Tuhkuri
  • M Lensu
Parmerter, R. R., and M.D. Coon, Models of pressure ridge formation in sea ice, J. Geophys. Res., 77, 6565-6575, 1972. Tuhkuri, J., and M. Lensu, Ice tank tests on ridging of non-uniform ice sheets, Rep. M-236, Ship Lab., Helsinki Univ. of Technol., Espoo, Finland, 1998.
Army Cold Regions Research and Engineering Laboratory, 72 Lyme Road, Hanover, NH 03755. (hopkins@crrel. usace.army.mil)
  • M A Hopkins
  • U S M Lensu
  • J Tuhkuri
M. A. Hopkins, U.S. Army Cold Regions Research and Engineering Laboratory, 72 Lyme Road, Hanover, NH 03755. (hopkins@crrel. usace.army.mil) M. Lensu and J. Tuhkuri, Ship Laboratory, Helsinki University of Technology, Tietotie 1, FIN 02150, Espoo, Finland. (Received June 15, 1998; revised January 25, 1999; accepted January 29, 1999.)
Lensu Ice tank tests on ridging of non-uniform ice sheets Espoo
  • J M Tuhkuri
Tuhkuri, J., and M. Lensu, Ice tank tests on ridging of non-uniform ice sheets, Rep. M-236, Ship Lab., Helsinki Univ. of Technol., Espoo, Finland, 1998.
Hopkins Measurements of curvilinear ridges in the Bay of Bothnia during the ZIP-97 experiment Espoo
  • M J Lensu
  • M Tuhkuri
Hopkins Measurements of curvilinear ridges in the Bay of Bothnia during the ZIP-97 experimentRep. M-231 64Ship Lab
  • M J Lensu
  • M Tuhkuri
Lensu Ice tank tests on ridging of non-uniform ice sheetsRep. M-236Ship Lab
  • J M Tuhkuri
On pressure ridgesCRREL Rep
  • W F A Weeks
  • Kovacs