Project

SHIVER - Ice action on offshore wind turbines

Goal: Generation of a benchmark model-scale dataset for offshore wind turbines subject to sea or lake ice loading. Extension of an existing ice-structure interaction simulation model from one-dimensional to two-dimensional interaction. Investigation of the use of an active layer between ice and structure for mitigation of ice-induced vibrations.

Date: 1 October 2019 - 31 December 2024

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Project log

Hayo Hendrikse
added a research item
The manual application of universal (Rigsby) stage techniques is commonly used to determine the fabric of thin sections of ice viewed with crossed-polarized light. This process can require hours of focus in cold conditions to identify the c-axis of each grain in a thin section. Automated ice texture and fabric methods of several forms exist but are rarely implemented beyond the field of glaciology. The present study introduces a method based on the theory of interference coloration for automated ice texture and quarter fabric analysis by using in-plane conventional photography of an ice thin section as input. The method is compatible with universal stages and polariscopes, and is not restricted by the planar-face dimensions of the thin section, allowing for thin section analysis of any size when sufficient digital camera resolution is available. Light source color temperature and chromatic adaptation are considered in the interference coloration theory, and ice fabrics are simulated for reference in identifying ice types. Sample thin section texture and quarter fabric analyses from freshwater lake and laboratory-grown ice are presented to demonstrate the applications of the method. The method is compared with the Rigsby stage technique, which yielded mean (standard deviation of) azimuth and inclination errors of 2.9 (1.0) and 11.5 (8.0) degrees, respectively, thereby demonstrating accuracy sufficient for quantifying quarter fabrics when considering a mean standard deviation in inclination of 5.4 degrees with the Rigsby stage technique.
Hayo Hendrikse
added an update
As part of our attempts to study what goes on inside the ice Cody C. Owen worked on developing a tool for the determination of the fabric of thin sections of ice based on sets of photographs. Besides giving beautiful coloured pictures, we also attempted to use these techniques to study the processes at the grain size scale during ice-structure interaction. We hope to disseminate those results soon.
The publication of the theory and tool in Cold Regions Science and Technology brings back good memories from the start of the SHIVER project where we got a chance to go out onto the ice in the IJsselmeer to gather ice samples for analysis with Tim Christopher Hammer and Tom Willems . I hope we get to go again this year.
 
Hayo Hendrikse
added an update
Our first analysis of the offshore wind turbine results from the test campaign in 2021 is now published in Marine Structures. The main focus is on experimental validation of the different regimes of ice-induced vibrations that can develop. We found a multi-modal vibration regime and confirmed our suspicions that frequency lock-in would mainly develop for the second mode of the turbine. Some numerical simulation results are included as well to show which regimes are most relevant for design of support structures in a relative sense.
Congratulations to Tim Christopher Hammer and Tom Willems for this study.
As we did not get a chance to answer some of the reviewer comments we got in the final round of revision I like to take the opportunity here. We did indeed not mention the slope of the support structure in our paper. The monopiles we consider are near-vertical as written in the introduction and can also be seen in the pictures of the test campaign and the illustration of the turbine. Please note that our study concerned steel structures and not concrete ones, though we indeed did not mention that. And as it was suggested that everything we did is already known, I welcome some references to the literature we clearly missed. It is never too late to learn. In that spirit I would finally like to remark that editors can reject a paper, reviewers can only advise to do so.
 
Hayo Hendrikse
added a research item
For offshore wind farms which are planned in sub-arctic regions like the Baltic Sea and Bohai Bay, support structure design has to account for load effects from dynamic ice-structure interaction. There is relatively high uncertainty related to dynamic ice loads as little to no load-and response data of offshore wind turbines exposed to drifting ice exists. In the present study the potential for the development of ice-induced vibrations for an offshore wind turbine on monopile foundation is experimentally investigated. The experiments aimed to reproduce at scale the interaction of an idling and operational 14 MW turbine with ice representative of 50-year return period Southern Baltic Sea conditions. A real-time hybrid test setup was used to allow the incorporation of the specific modal properties of an offshore wind turbine at the ice action point, as well as virtual wind loading. The experiments showed that all known regimes of ice-induced vibrations develop depending on the magnitude of the ice drift speed. At low speed this is intermittent crushing and at intermediate speeds is 'frequency lock-in' in the second global bending mode of the turbine. For high ice speeds continuous brittle crushing was found. A new finding is the development of an interaction regime with a strongly amplified non-harmonic first-mode response of the structure, combined with higher modes after moments of global ice failure. The regime develops between speeds where intermittent crushing and frequency lock-in in the second global bending mode develop. The development of this regime can be related to the specific modal properties of the wind turbine, for which the second and third global bending mode can be easily excited at the ice action point. Preliminary numerical simulations with a phenomenological ice model coupled to a full wind turbine model show that intermittent crushing and the new regime result in the largest bending moments for a large part of the support structure. Frequency lock-in and continuous brittle crushing result in significantly smaller bending moments throughout the structure.
Hayo Hendrikse
added an update
In a recent study Florian van der Stap conducted in collaboration with WoodThilsted we investigated the feasibility of monopile foundations in the Baltic Sea. His report can be found in the TU Delft repository:
With the current limitations to monopile design and knowledge of ice-structure interaction no mitigating measures are envisaged up to the latitudes of the Gulf of Finland. Thanks to Martin Bjerre Nielsen for the collaboration on this project. We will present the results at POAC'23 in Glasgow.
To improve our simulation tools we continue to study the experimental data gathered last year and are planning a new test campaign at Aalto University for the spring of 2023. There we will start focussing on the interaction between ice and steep cones, which may be used to mitigate ice-induced vibrations. We recently completed the analysis of our data for the effect of wind-ice misalignment on IIV which is now under review with a journal and Tim Christopher Hammer is starting the development of VANILLA 2.0 as we see a need to improve the model capabilities to both simulate the constraining effect of ice at the side of the turbines as well as potential damping effects from ice rubble and extrusion. Cody C. Owen is in the final phase of his PhD and processing our small-scale experimental data where the focus is on the change in material behaviour of the ice when the loading rate is changed from high to low, typical for a cycle of frequency lock-in. Similar results were obtained from the forced vibration basin tests for which the data analysis is almost complete and where we identified the dependence of the added mass and added damping on oscillation frequency and amplitude.
We aim to have all results publicly available in the course of 2023.
 
Hayo Hendrikse
added a research item
This study analyses the results from basin tests with a vertically sided cylindrical pile loaded by ice failing in crushing. Tests were performed with a ‘rigid’ structure and with structural models representing a series of single-degree-of-freedom (SDOF) oscillators covering a wide range of mass, frequency, and damping values. The structural models were represented by a real-time hybrid test setup, which combined physical and numerical components to measure real ice forces, apply the forces to a numerical structural model, and simulate the dynamics of the tested structural models in real-time. The test results are analysed and simple numerical simulations are performed to assess the relevance of several ice force characteristics observed from the ‘rigid’ structure tests to the ice-induced vibrations in the SDOF oscillators. The results from the rigid structure tests show that the median ice forcing frequency is linearly related to the ice drift speed. The mean and standard deviation of the ice forces on the rigid structure show a negative force-velocity gradient at low ice drift speeds and indications of a positive force-velocity gradient at higher ice drift speeds. The comparison of experimental results to the simulations of the single-degree-of-freedom oscillator tests shows that the positive force-velocity gradient at higher ice drift speeds allows to best capture the dynamics during continuous brittle crushing as observed in the experiments. Furthermore, the comparison shows that frequency lock-in initiation is primarily driven by the velocity-independent spatial frequency spectrum of the ice force signal. The added damping caused by the positive force-velocity gradient must be considered to capture the frequency lock-in initiation speeds measured in the constant deceleration experiments. The consideration of the negative force-velocity gradient at low relative velocities is not needed to capture these frequency lock-in initiation speeds as observed in the experiments. However, once frequency lock-in is initiated, the negative gradient is needed to correctly capture the dynamics during frequency lock-in. Analysis of the results shows that the peak forces during intermittent crushing at the end of the load build-up phase have a dependence on relative velocity equal to the load dependence on velocity of rigid structures at low speed. This indicates that intermittent crushing is not a purely brittle type of interaction.
Hayo Hendrikse
added an update
The first study made with the test campaign data by Marnix van den Berg has been published in Cold Regions Science and Technology. We focussed on how the ice load measurements on a rigid structure can tell something about ice-induced vibrations of a flexible structure, focussing on the onset of frequency lock-in, and showing that intermittent crushing is not a purely brittle phenomenon.
 
Cody C. Owen
added a research item
For the topic of predicting ice-induced vibrations of vertically sided offshore structures, the rate-dependent ductile-to-brittle transitional deformation and failure behavior of ice is critical but remains superficially understood. To investigate this knowledge gap, a test setup has been designed which allows for in-situ crossed-polarization imaging of passively confined ice thick sections subjected to compressive loading. The test setup is designed to recreate the scenario of a cross-section at the leading edge of an ice sheet which is laterally confined by surrounding ice and fails in crushing against a structure. The setup comprises a linear actuator which drives a flat plate into a confinement box containing the ice thick section, which is passively confined orthogonal to the plane of loading by thick fused silica glass plates. The ice is illuminated through the glass plates with crossed-polarized light, which highlights the microstructure of the ice. Freshwater ice of columnar grain structure is prepared in the ice laboratory at Delft University of Technology, and quantified in terms of its microstructure. The ice thick sections in the test setup are subjected to a range of deformation rates at different temperatures. While similar experiments have been performed, this setup provides novelty by accentuating the dynamic microstructural deformation in-situ with crossed-polarized light. Moreover, this microstructural deformation is observed for global deformation rates relevant for ice-induced vibrations of offshore structures. A description of the test setup is presented along with preliminary experimental results.
Hayo Hendrikse
added an update
Tim, Cody and Hayo will attend the OMAE 2022 conference in Hamburg next week presenting some of the first results from the SHIVER test campaign.
In our talks we discuss the results from analysis of the wind turbine specific test data and more general the scaling approach of the campaign and the cold model ice used during testing.
 
Hayo Hendrikse
added 2 research items
Ice-induced vibrations of offshore wind turbines on monopile foundations were investigated experimentally at the Aalto Ice Tank. A real-time hybrid test setup was developed allowing to accurately simulate the motion of a wind turbine in interaction with ice, incorporating the multi-modal aspects of the interaction and the effect of simultaneous ice and wind loading. Different vibration patterns were observed where some could be described based on the common terminology of intermittent crushing or continuous brittle crushing. However, not all resulting vibrations could be described accordingly. A combination of several global bending modes interacting with the ice resulted in high global ice loads and structural response. Such response is likely typical for an offshore wind turbine, owing to the dynamic characteristics of the structure. The type of interaction observed during the tests would be most critical for design as the largest bending moments in critical cross-sections of the foundations occur for this regime. A classification of ice-induced vibrations is proposed which encompasses the experimental observations for offshore wind turbines on the basis of the periodicity in the structural response at the ice action point.
With the recent surge in development of offshore wind in the Baltic Sea, Bohai Sea and other ice-prone regions, a need has arisen for new basin tests to qualify the interaction between offshore wind turbines and sea ice. To this end, a series of model tests was performed at the Aalto ice basin as part of the SHIVER project. The tests were aimed at modeling the dynamic interaction between flexible, vertically-sided structures and ice failing in crushing. A real-time hybrid test setup was used which combines numerical and physical components to model the structure. This novel test setup enabled the testing of a wide range of structure types, including existing full-scale structures for which ice-induced vibrations have been documented, and a series of single-degree-of-freedom oscillators to obtain a better understanding of the fundamental processes during dynamic ice- structure interaction. The tests were primarily focused on the dynamic behavior of support structures for offshore wind turbines under ice crushing loads. First results of the campaign show that the combination of the use of cold model ice and not scaling time and deflection of the structure can yield representative ice-structure interaction in the basin. This is demonstrated with experiments during which a scaled model of the Norströmsgrund lighthouse and Molikpaq caisson were used. The offshore wind turbine tests resulted in multi-modal interaction which can be shown to be relevant for the design of the support structure. The dataset has been made publicly available for further analysis.
Hayo Hendrikse
added an update
The Aalto University communications team made a nice movie about the first test campaign last year. You can watch it here:
 
Hayo Hendrikse
added an update
The raw data from our first series of ice tank tests is now available online. A description of the data and experiments can be found in our latest Data-In-Brief article. Some analysis papers have already been submitted to journals and while we wait for the outcome of the peer-review we are continuing to use the data to find answers to our research questions and validate our numerical tools. If you plan on using the data and have any questions please do not hesitate to reach out!
 
Hayo Hendrikse
added 2 research items
Basin tests were performed at the Aalto Ice Tank to gather data on ice-structure action and interaction in May and June, 2021. The Aalto Ice Tank is an indoor testing facility that is part of the Department of Mechanical Engineering at Aalto University. A real-time hybrid test setup was mounted to a carriage on a bridge spanning the ice tank. A vertically sided cylindrical pile was moved through the ice by moving the carriage along the bridge. The dynamic response to the measured ice loads was simulated by the real-time hybrid test setup for a range of test structures including offshore wind turbines, a series of single- and multi-degree-of-freedom oscillators, the Norströmsgrund lighthouse and the Molikpaq caisson structure. In addition, ice loads were measured in forced vibration tests and while moving the rigid pile through the ice with a constant speed. The data can be accessed from the 4TU.ResearchData repository: http://dx.doi.org/10.4121/17087462.v1
Basin tests were performed at the Aalto Ice Tank to gather data on ice-structure action and interaction from ice failing against a vertically sided cylindrical pile. The tests were performed with a real-time hybrid test setup, which combined physical and numerical components to simulate a range of test structures in real-time. The dataset includes results from tests with offshore wind turbine structures, structural models representing a series of single- and multi-degree-of-freedom oscillators, and scaled dynamic models of the Norströmsgrund lighthouse and the Molikpaq caisson structure. In addition, forced vibration tests and rigid structure tests were performed. Ice loads and structural response were measured with accelerometers, displacement sensors, potentiometers, strain gauges and load cells and the ice-structure interaction process was filmed from three different camera angles. The resulting raw data have been categorized and stored as unfiltered time series. A total of 259 different tests are included in the dataset. The model ice formation procedure and the test temperature were aimed at creating model ice that mimics the material behaviour of full-scale saline ice during crushing failure, with a specific focus on the transition from brittle to ductile behaviour. The data can be used for validation of models for dynamic ice-structure interaction. The offshore wind turbine data can be used to study the effect of wind loading on the interaction with ice and the effect of the specific dynamic properties of wind turbine structures with monopile foundations on the ice-structure interaction process. The forced-oscillation data can be used to quantify the time and speed dependent aspects of ice loading. The Norströmsgrund lighthouse and the Molikpaq data can be used as a reference comparison to full-scale data on ice loads.
Hayo Hendrikse
added a research item
Much attention has been given to the dynamic ice-structure interaction of the Molikpaq caisson which resulted in severe, almost catastrophic, structural vibrations during the winter of 1985-1986 at Amauligak I-65 in the Canadian Beaufort Sea. In this study, specific focus is given to the scientific literature describing the ice-induced vibration event on May 12, 1986 over the observed range of ice conditions and drift speeds. While considering the limitations of the measurement data available for the event, the scenario is reviewed and a recent phenomenological model is implemented to simulate the ice-induced vibrations observed. A simplified model of the Molikpaq caisson is simulated to interact with an ice floe and the results are compared with the full-scale observations from the event. Limitations of the modeling with respect to the available full-scale data are discussed and modeling results are compared to previous simulations attempting to explain the event on May 12, 1986. It is concluded that this ice-induced vibration event should be treated with caution and detailed considerations of the scenario, including a comprehensive structural model, must be implemented for accurate simulation of the event on May 12, 1986. Models and theories derived exclusively from this event should be scrutinized in light of its uncertain and complex conditions and thus treated skeptically.
Tim Christopher Hammer
added a research item
With the ongoing development of offshore wind in cold regions where the foundations are exposed to sea ice, there is a strong need for data to validate the numerically predicted dynamic interaction between ice and structure used for design. Full-scale data is non-existent and only a limited number of experimental campaigns in ice tanks have been conducted for this specific problem. When compared to traditional structures subjected to sea ice loading like lighthouses and oil and gas platforms, the motion of the turbines at the ice action point is both in line with the ice drift direction but also significantly across due to the interaction of the turbine with the wind. Furthermore, the structure being slender overall and having a large top mass results in a very particular set of modes of oscillation where at least both the first and second global bending mode are expected to interact with the ice. To capture this complexity, a real-time hybrid test setup has been designed for basin tests in the SHIVER project and is presented in this paper. The setup uses two integrated linear actuators to control the motion of a rigid pile in two dimensions. Loads at the ice-action point are measured and used in a numerical model where these are combined with virtual loads, for example wind loading, to determine the response of the structure which is then applied in the physical setup by the actuators. The system allows to test a wide range of combinations of structural stiffness, mass, and damping, including structural properties typically associated with the relevant modes of oscillation of offshore wind turbines.
Hayo Hendrikse
added an update
In June we completed our first series of basin tests at the Aalto ice tank. We managed to create a large benchmark dataset for offshore wind turbines in ice including interaction with sea ice during idling, power-production and under misaligned wind-ice conditions.
We conducted our tests using a new real-time hybrid test setup.The setup uses two linear actuators to control the motion of a test structure. We measure the ice load which is then transferred to software to calculate the structural response of a structure of interest. The structural response is then imposed on the physical test structure by the actuators.
This way we have tested several vertical structures, ranging from rigid piles, theoretical single-degree-of-freedom oscillators, multi-modal models of offshore wind turbines, and the Norströmsgrund lighthouse and Molikpaq platform.
During the campaign we crushed 2.2 km of (model) ice. We went for a particular hard and cold type of ice to stay as close to reality as possible (400 to 500 kPa bending strength, above 500 kPa compressive strength).
Thanks to Tim Christopher Hammer , Marnix van den Berg , Cody C. Owen , Tom Willems , Nick Ebben, Arttu Polojärvi , Otto Puolakka, Teemu Päivätinta, Lasse Turja, Jeroen Koning and Kees van Beek for their amazing effort in making this campaign happen.
All data will become publicly available by December, stay tuned for more info!
 
Hayo Hendrikse
added an update
We are happy to announce that Marnix van den Berg joined the SHIVER project as a postdoctoral researcher in June. Marnix joined the project at the start of the first basin test campaign at the Aalto Ice Tank and will work on the data analysis of that campaign and closely with Tim Christopher Hammer on preparation for our second series of experiments in September 2022.
 
Hayo Hendrikse
added an update
We faced some delays in the project due to COVID-19 so I skipped the quarterly update for April. We have now adjusted to the situation so it is time to share some news.
We reached a major milestone in growing first ice in the cold rooms at TU Delft. Though still just a gigantic ice cube, this is a big step towards the small-scale indentation tests Cody C. Owen will perform later this year. Currently, we are gathering all bits and pieces to practice the controlled growth of ice. The test setup sketches will be completed by September, based on the earlier works by Toyama et al. who managed to capture dynamic ice-structure interaction at the small-scale.
Tim Christopher Hammer has been working on the design of an offshore wind turbine with SGRE to be used as a reference structure for our theoretical studies and a basis for the basin testing at Aalto University in January 2021. He is now in the process of defining representative met ocean conditions for the Southern Baltic which we will use to compare the loads resulting from ice-structure interaction between a fully-coupled approach and the approach used often in the industry of pre-defining the ice load time series. The results of this study will become available around October.
Our first basin tests at Aalto University have been postponed by a couple of months as we did not make much progress on the design of the test setup since March. We aim to present the first design by September, where the choice has been made to go for a hardware-in-the-loop type setup to be able to obtain the low natural frequencies of an offshore wind turbine at the basin scale. Pre-testing is ongoing at Aalto to quantify how the model ice can be made brittle and stiff for the purpose of indentation testing.
We will update again right after the first annual workshop which is planned for the 1st of October.
 
Hayo Hendrikse
added an update
Hayo Hendrikse
added 2 research items
Interaction of sea or lake ice with vertically sided offshore structures may result in severe structural vibrations commonly referred to as ice-induced vibrations. With the surge in offshore wind developments in sub-arctic regions this problem has received increased attention over the last decade, whereas traditionally the topic has been mainly associated with lighthouses and structures for hydrocarbon extraction. It is important for the safe design of these offshore structures to have the ability to predict the interaction between ice and structure in an expected scenario. A model for simulation of the interaction between a drifting ice floe and a vertically sided offshore structure is presented. The nonlinear speed dependent ductile and brittle deformation and local crushing of ice are considered phenomenologically. A one-dimensional sea ice dynamics model is applied to incorporate the effects of floe size, wind and current. The structure is modelled by incorporating its modal properties obtained from a general-purpose finite element software package. Alternatively, the model can be coupled to in-house design software for fully coupled simulations. Examples of application of the model to simulate dynamic ice-structure interaction are provided. Simulation results are validated with public data from forced vibration experiments, small-scale intermittent crushing and frequency lock-in, and full-scale interaction with the Norströmsgrund lighthouse. Effects of floe size and environmental driving forces on the development of ice-induced vibrations in full-scale are studied. It is shown that sustained frequency lock-in vibrations of the structure can only develop for very specific combinations of environmental driving forces and ice floe size. In all other cases, the ice floe slows down and comes to a stop, or accelerates to a drift speed which exceeds the range where frequency lock-in develops. This results in only a few cycles of vibration per interaction event, such as observed for the Norströmsgrund lighthouse in the Baltic Sea.
Hayo Hendrikse
added an update
We started the project in October 2019 with a kick-off meeting at the Aalto University ice basin to investigate possibilities for scale model tests to be performed late 2020:
I have been working with Tom Willems , Arttu Polojärvi and Otto Puolakka to define the test setup, which has proven to be, and still is, a challenge given our aim to not scale the natural frequencies of the first global bending modes compared to a full-scale offshore wind turbine.
Much time went into the refinement of the definition of the three PhD projects and we are happy to announce that Cody C. Owen and Tim Christopher Hammer joined the project as PhD students. There is currently one open position remaining:
Cody C. Owen is working on scaling of ice-induced vibrations based on existing model-scale data and is currently at Aalto University to get experience with cold room work.
Tim Christopher Hammer is working on familiarising himself with offshore wind simulation software and the ice load model with the aim of making a detailled comparison between different approaches to include ice loading in offshore wind and identifying potentially governing ice loading scenarios from fully coupled analysis.
We further worked on the design and construction of two cold rooms at TU Delft which are now planned to be completed and ready for use early April 2020. The next project update will follow around that time.
 
Hayo Hendrikse
added a research item
Ice-induced vibrations have to be considered in the design of vertically sided offshore structures which may encounter drifting sea or lake ice during their lifetime. One particular aspect is the contribution of ice-induced vibrations to the fatigue of such structures. Estimation of the duration of events is often difficult, due to limited available data on ice drift, leading to conservative assumptions. In this paper, the approach followed for assessing the fatigue resulting from frequency lock-in vibrations in the design stage of a recent offshore wind project is presented. The project concerned offshore wind turbines with jacket support structures consisting partly of vertical structural members. The severity of ice-induced vibrations for the structures is first assessed using a simulation model. Following this, ice drift is included in the assessment to obtain an estimate of the number of cycles of frequency lock-in over the lifetime of the structure. Results show that site-specific combinations of ice floe size and driving forces significantly influence the expected number of cycles of frequency lock-in. It is concluded that for this project limited conditions exist in which sustained vibrations can develop and that the contribution of frequency lock-in to structural fatigue is therefore limited as well.
Hayo Hendrikse
added a research item
Offshore wind turbines at locations where sea or lake ice is present need to be designed to withstand ice-induced loading. For vertical-sided support structures, such as monopiles, the effects of ice-induced vibrations need to be considered in the design. Current practice is either to use approaches provided in design standards, or for example to apply pre-generated ice load time series in the wind turbine aeroelastic model. These approaches have the drawback that the coupling between ice failure behavior and structural motion is not included. The effect of omitting this coupling on predictions for fatigue and ultimate limit states is currently not known. To enable fully coupled simulations in the design of offshore wind turbines, an existing simulation model for ice crushing has been recently coupled ("VANILLA") to the in-house aeroelastic software package BHawC. In this paper this fully coupled model is applied to simulate ultimate limit state design load cases (DLCs) for a recent design of an offshore wind turbine on a monopile foundation. The project that is chosen for this case study is situated in the Southern Baltic Sea. The loads obtained for ice-and wind loading with the VANILLA model are compared to wind-and wave-induced loading. It is found that intermittent crushing is the governing ice interaction mode for offshore wind turbine support structures and rotor-nacelle-assembly components.
Hayo Hendrikse
added a project goal
Generation of a benchmark model-scale dataset for offshore wind turbines subject to sea or lake ice loading. Extension of an existing ice-structure interaction simulation model from one-dimensional to two-dimensional interaction. Investigation of the use of an active layer between ice and structure for mitigation of ice-induced vibrations.