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In light of the recent increasing interest in the oil and gas developments in the arctic region, Huisman
Equipment B.V. started development of a drilling semi-submersible suited for arctic condition.
Model tests were performed by the Krylov Shipbuilding Research Institute to gain insight in the ice forces acting
on the structure. Based upon the data gathered during these model tests a mooring system was designed using
an ice loading model that was based on the means of the loads measured and assumed an ice-load
independent of vessel motions. For a more accurate design of the mooring system and a better understanding
of the dynamics, a dynamic model of the ice-loading and moored vessel motions is/was needed.
This thesis elaborates on a model that can model the dynamic interaction between the vessel motions and the
ice-loads. Based upon this model, the mooring system is optimized for the highest possible ice conditions.
During the model tests the model of the JBF Arctic was retained in a fixed position while being towed through
the ice. The main interest was in the interaction with level ice at operational draft. Three parameters were
varied during these tests: the ice thickness, the ice velocity and the trim angle of the vessel.
To model the ice loads, the first step was to create a model for the mean part of the ice loading. A very simple
ice model for the mean of the horizontal force had already been made by the Krylov Shipbuilding Research
Institute. This ice model only depends on the ice thickness and the ice velocity and is only valid within a certain
range. As part of this thesis the model was expanded so that it would be valid for the entire range of
parameters which are required during the time domain simulations. Next the transition between bending and
crushing was found to be dependent on the trim angle of the vessel. The mean loads in all other five DOF’s
were added based on correlations with the horizontal force or as separate entities. Several other ice
phenomenon were also added to the model, such as the initial transient interaction between the approaching
ice sheet and the vessel and a crude implementation of the interaction with ridges.
The second step to model the ice loads, was to add the fluctuating components of the ice loading. An extensive
study was done to analyze the frequency characteristics of the data gathered. The frequency characteristics of
the analyzed spectrums were random, and no correlation could be found with the variables that were varied
during the tests. A flat or white noise spectrum with the correct energy density was used to model the dynamic
part of the ice forces.
The moored vessel motions itself were modeled with AQWA DRIFT. The AQWA model was coupled with
MATLAB to incorporate the mean and dynamic ice forces. Eventually a model was delivered that can be used to
model the dynamics of a moored vessel in ice. This model was also used to do a comprehensive study to find
the optimal mooring configuration (material type, grade and, the anchor radius, the number of lines and their
layout etc.) for the JBF arctic.
The final mooring system can handle 3.1m thick ice moving at 0.5 m/s or 2.4m thick ice moving 1.5 m/s.

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Content uploaded by Chris Keijdener

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All content in this area was uploaded by Chris Keijdener on Jul 04, 2019

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... For large diameter structures, often circumferential cracks are initiated first that result in breaking off crescent-shaped pieces of ice. Their size depends on the ice thickness, with thicker ice generating cracks that wrap up to 135 • around the structure while thinner ice results in cracks that wrap 15-45 • [171]. This type of failure occurs more frequently in the central region than at the sides where the effective slope is smaller [172]. ...

... Model-scale experiments on the Kulluk were done by Matsuishi and Ettema [174]. Experiments on a similarly shaped floater are documented in Keijdener [171]. In both studies, it was found that the floater maintains a constant offset and had a slight trim angle but did not undergo cyclic motions. ...

... After the rubble reached its equilibrium size, the mean loads remained steady. Matsuishi and Ettema [174] found a linear dependence on the ice thickness while Keijdener [171] found a quadratic relation. However, the later model had a gradually increasing effective slope, which meant that as the trim of the vessel or the ice thickness increased, crushing become more dominant as a larger portion of the interaction took place with a part of the hull with a steeper slope. ...

The Arctic presents a great opportunity for two major industries. First, since the region is expected to contain a significant amount of hydrocarbon reserves, it is very attractive for the oil and gas industry. Second, the receding extent of sea ice is making the region more accessible for shipping and, therefore, an opportunity is emerging for the shipping industry. In order to exploit both economic opportunities in a safe and sustainable manner, a thorough understanding of the interaction between ice and floating structures is needed. The most common method for studying ice-floater interaction (IFI) is via numerical modeling, which the fluid is a major component of. As fluid-ice interaction is challenging to model, a wide range of simplified and sophisticated models are employed to meet the challenge. A literature study was performed on the usage of fluid models employed in IFI and it was found that they can be divided into four categories: hydrostatic models, models based on potential flow, models based on Reynolds-averaged Navier–Stokes or a similarly advanced method, and effective fluid models. The hydrostatic models are by far the most prevalent despite only accounting for buoyancy. Most IFI models that account for hydrodynamics make use of potential theory. These models account for fluid flow and surface waves, which together alter the dynamic behavior of floating ice, resulting in hydroelastic effects. The surface-wave-based coupling between ice and floater has not been studied before and there are still open questions regarding the effects of hydroelasticity on the bending failure of ice. The advanced fluid models are a recent trend in IFI and, consequently, most of those are still under development. These models are very promising and may be the future of IFI modeling. Finally, the effective models avoid the practical issues associated with hydrodynamic models in terms of development and calculation time by capturing hydrodynamics in an effective manner, employing, for instance, added mass and damping coefficients. While several studies investigated the efficacy of these models, currently no satisfactory effective fluid model exists. The main goal of this thesis is to further the understanding of how hydrodynamics affects the interaction between ice and a sloping structure and to assess whether it is possible to create an effective model that can replicate the observed effects. The full scope encompasses three smaller studies. First, the surface-wave-based coupling between an elastic ice sheet and nearby floater structure is investigated. This interaction has not been studied before and the solution method that is developed for this problem is also used in the subsequent two studies. Second, a thorough study of the effects of hydrodynamics on the interaction between a sloping structure and level ice is accomplished. This study resulted in the identification of the parameter range wherein hydrostatic models are valid, which is essential given that they constitute the majority of all models. In addition, this study improved the understanding of the effects of hydrodynamics by means of investigating the importance of various components such as the rotational inertia of the ice, axial compression, and the nonlinear hydrodynamic pressure. Furthermore, the relation was analyzed between the temporal development of the contact force and the velocity dependence of the breaking length. Lastly, based on the findings of the second study, an attempt was made to develop an effective fluid model for ice-slope interaction. The efficacy of this model was studied in this thesis for a range of parameters. The main findings of the three studies are summarized next. In the first part of this thesis, the interaction is investigated between an ice floe and a floater through surface waves. This problem is considered first as the Green's functions that are derived for this problem are required for the subsequent studies on ice-slope interaction. The floater is modeled in-plane as a thin rigid body that floats on the surface of a fluid layer of finite depth. On one side of the floater, an ice floe is present which is modeled as a semi-infinite Kirchhoff-Love plate. The floater is excited by external loads and the resulting motions generate waves. Those waves hitting the ice edge are partly transmitted into the ice floe and partly reflected back towards the floater. The reflected waves exert pressure on the floater, altering its response. The resulting motions of the floater were analyzed, revealing several interesting facts. The study showed that below a certain onset frequency, the waves are almost fully transmitted into the ice floe and, consequently, the response of the floater is unaffected by the presence of the ice. The susceptibility of a floater to the waves reflected by a nearby ice floe can thus be estimated by checking how much of its open water response occurs above or below the onset frequency. The onset frequency is sensitive to changes of the ice thickness and insensitive to changes of the Young's modulus and water depth. Above the onset frequency, the waves reflected by the ice have a pronounced effect on the response of the floater. In certain frequency ranges, quasi-standing waves occur within the gap between ice floe and floater. Within these frequency ranges, the response of the floater is significantly altered. Depending on the phasing between the reflected waves and the floater's motions, resonance or anti-resonance can occur which can greatly amplify or reduce the floater's motions when compared to the case when no ice is present. Even when there is no gap between ice and floater, the amplitude of the floater can still be amplified and its natural frequency somewhat increased. The second study of this thesis focuses on the effect of hydrodynamics on the bending failure of an elastic ice floe due to the interaction with a downward-sloping floater, i.e. the effects of hydrodynamics on ice-slope interaction (ISI). A novel, semi-analytical in-plane ISI model is proposed that is based on potential theory in conjunction with the nonlinear Bernoulli equation to describe the fluid pressure. The ice is modeled as a semi-infinite Kirchhoff-Love plate. The predictions of the hydrodynamic model are compared with those of a hydrostatic ISI model, thereby obtaining a quantitative measure of the effect of hydrodynamics on ISI. The comparison revealed several interesting facts. First, the importance of several components of the model was investigated to determine which ones are essential for ISI. It was found that the contribution of the rotational inertia of the ice, axial compression and the nonlinear hydrodynamic pressure is insignificant. Being able to ignore the last two components greatly simplifies the modeling of ISI as it removes all sources of spatial nonlinearity. The terms that were found to be essential for ISI, listed in the order of importance, are: bending of the ice floe, linear hydrodynamic pressure, hydrostatic pressure and the inertia of the ice floe. The contribution of the fluid's inertia is on average four to ten times bigger than that of the inertia of the ice. The study also demonstrated that the effect of wave radiation on ISI is minimal. Second, the relation between the temporal development of the contact force and the velocity-dependence of the breaking length was studied. The study showed that the breaking length has two regimes which are separated by a transition velocity. When the ice velocity is below the transition velocity, the ice fails during the initial impact. Alternatively, when the ice velocity is above the transition velocity, the ice floe survives the impact and fails with a breaking length that is close to the static breaking length. The transition velocity of the hydrodynamic model is much lower than the transition velocity of the hydrostatic model, 0.0725 m/s compared to 0.275 m/s. This major difference in transition velocity is the primary reason for the limited applicability of the hydrostatic model. The results show that the hydrostatic model should not be used when the ice velocity is higher than 0.6 times the transition velocity of the hydrodynamic model as its predictions will deviate significantly, with errors ranging from 30% to 100%. This upper bound corresponds to values between 0.02 m/s and 0.1 m/s for the parameters considered. Lastly, this study underlined the stochastic nature of the breaking length of the ice floe. When the floe fails, a relatively large segment of the floe is, in fact, close to failure. A defect in the ice can locally amplify the stresses, causing the ice to fail at the defect rather than at the location predicted by a homogeneous model. This can cause the breaking length to vary by 10% to 30%. The last part of this thesis builds on the knowledge gained in part two by attempting to create a simple effective fluid model (EFM) that captures the effects of hydrodynamics on ISI as observed in part two. Based on the observations, an EFM is proposed that uses frequency-independent added mass and damping coefficients. This EFM was added to the hydrostatic model, thereby obtaining an ISI model that contains all four essential components of the ISI model. The resulting effective ISI model is very simple and, consequently, its implementation is trivial compared to a true hydrodynamic model such as the one proposed in part two. Its simplicity should help to improve the adoption of hydrodynamics in ISI. The performance of the effective ISI model is assessed. Investigated are the velocity-dependent breaking length, the maximum contact force that occurred during the interaction, and the contact force as a function of time. The predictions of the effective model are far more accurate than those of the hydrostatic model. The coefficients of the EFM were found to be relatively insensitive to changes in the parameters, allowing the effective model to be used for a fairly broad range of parameters.

Flexure failure of the consolidated layer on conical structures may result in either pile-up of broken ice rubble in front of the structure or ride-up of the consolidated layer on the slope of the cone. These phenomena can increase the load significantly and affect the failure mechanism of the ice. For the last eight years, there has been a full-scale in-situ monitoring Programme to examine the interaction between ice features and the Confederation Bridge piers (Brown, 2006). Using the data from the Confederation Bridge Monitoring Programme, observations pertaining to rubble pile-up and ride-up will be presented. The study concentrates especially on the effect of ice velocity, consolidated layer thickness, keel depth and slope angles of the pile-up and ride-up on the height of interaction of both phenomena. A detailed statistical analysis has been carried out, resulting in relations between the dependent and independent variables.

This paper reviews progress during the past decade in understanding the brittle compressive failure of ice. Evidence is presented for the frictional crack sliding-wing mechanism and for the role of localized fragmentation. The ductile-to-brittle transition is explained in terms of the suppression of crack growth and is modeled in terms of Ashby−Hallam wing crack mechanics and Riedel−Rice crack-tip creep. The brittle compressive strength is related to ice−ice friction. Modeling and experiment suggest that the transition strain rate of cracked ice scales as (crack size)-1.5 and that its brittle strength scales as (crack size)-0.5, at least for small specimens. Possible size effects are noted.

This book describes the stochastic method for ocean wave analysis. This method provides a route to predicting the characteristics of random ocean waves - information vital for the design and safe operation of ships and ocean structures. Assuming a basic knowledge of probability theory, the book begins wuith a chapter describing the essential elements of wind-generated random seas from the stochastic point of view. The following three chapters introduce spectral analysis techniques, probabilistic predictions of wave amplitudes, wave height and periodicitiy. A further four chapters discuss sea severity, extreme sea state, directional wave energy spreading in random seas and special wave events such as wave breaking and group phenomena. Finally, the stochastic properties of non-Gaussian waves are presented. Useful appendices and an extensive reference list are included. Examples of practical applications of the theories presented can be found throughout the text. This book will be suitable as a text for graduate students of naval, ocean and coastal engineering. It will also serve as useful reference for research scientists and engineers working in this field.

Most probable maximum-an explanation

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Dynamics, Slender Structures and an Introduction to Continuum Mechanics

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Metrikine, A. (2006). Dynamics, Slender Structures and an Introduction to Continuum Mechanics. Delft: TUDelft
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Wikipedia: Rodrigues' rotation formula

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Rodrigues, O. (sd). Wikipedia: Rodrigues' rotation formula. Opgehaald van Wikipedia:
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Mooring Analysis -Time Domain

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BDA. (2011). Mooring Analysis -Time Domain.

DNV-OS-E301 Position Mooring

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DNV. (Oct 2008). DNV-OS-E301 Position Mooring. DNV.