Introduction

Task 4 was divided into the following sub-tasks:

• Subtask 4.1 - Investigations on Special Ice Mechanics Problems, 
• Subtask 4.2 - Dynamic Ice - Structure Interaction Model,
• Subtask 4.3 - Ridge Load Model,
• Subtask 4.4 - Fracture Dynamics Model,
• Subtask 4.5 - Probability Approach.

Objective

Description

Approaching the structure from the "frazzled" a unit volume of ice experiences, a stress increase and it's response is both elastic and viscoplastic. The relative weight of these two types of behaviour is controlled by the ice temperature and the strain rate. Elasticity is predominant at very low temperature and high velocity. Then the ice reacts as a brittle material. However, in general most interactions involve a viscoplastic component and the ice experiences "transient creep" corresponding to a work hardening phase. The stress concentrations which occur at grain boundaries can eventually lead to micro-cracking (at the grain scale). They can be induced either by grain boundary sliding or by dislocation pile-ups generated during the hardening phase. In these two cases the elastic and especially viscoplastic anisotropy of the ice grain is essential. The evolution of the cracking activity is influenced by the confining pressure which tends to oppose to the opening of cracks and in the ductile regime by parameters involved in the viscoplastic behaviour (i.e. temperature, strain-rate and stress level) which control crack nucleation as well as crack propagation. With increasing stresses, the increase of micro-cracking can lead to progressive damage which can be stabilised or which can end in slabbing. At the contact interface with the structure an increasing level of damage can result in the formation of crushed ice. The processes acting in the structure contact zone depend on the friction conditions at the interface.
 

Experimental Studies

The contribution aimed on a better understanding and modelling of the mechanisms involved in the damage of ice. It consisted of both experimental and theoretical studies on the following topics.

1. Micro-mechanisms responsible for crack nucleation at the grain scale

• The role of grain boundaries in the crack nucleation process in relation with the elastic and viscoplastic anisotropy of the ice crystal is studied by using the results of creep tests performed at the laboratory. Statistical treatment of the observations helped to improve the crack nucleation models and the models for damage evolution.

2. Mechanical behaviour of undamaged ice (transient creep)

• The strain incompatibilities between grains which arise during the polycrystal deformation can be relieved by micro-cracking. As these incompatibilities are responsible for work-hardening, from a macroscopic point of view the level of work hardening is likely to be an important parameter for modelling the process of damage. Transient creep models based on a description of hardening and recovery processes by means of internal state variables can provide such an indication. As they are of a phenomenological nature, they had to be tuned by using experimental results.

3. Mechanical behaviour of damaged ice

• The estimation of the energy dissipated by creep at a fixed damage level is essential to obtain a correct description of the damage evolution. A preliminary experimental study of the creep of damaged granular ice indicated that the apparent viscosity of damaged ice was several orders of magnitude less than for undamaged ice under the same conditions (stress, temperature). This study was extended to columnar ice.

4. Mechanical and physical processes occurring at the ice structure interface

• The experimental study and the modelling of the friction of ice over surface materials results in an interfacial behaviour law that being implemented in the numerical code for simulating ice - structure interaction. This law was used first as a slip-stick model to control the tangential contact forces. Secondly, it is used in the description of crushing and flaking failure of the ice sheet. This failure mode is associated to the dynamic problems and the highest global loads caused by level ice. Flaking failure originates from horizontal (cleavage) cracks that emanate from the ice edge into the ice sheet, forming a layered and damaged near field area at the ice edge. The velocity dependent friction at the ice - structure interface is believed to control the failure of these layers and the flaking failure mode. The partners LGGE and VTT  co-operated here to developed a model which can be used in Subtask 4.2.

5. Improvement of ice damage models

• The results from items 1 to 3 were used to improve the published damage models developed for ice. This part of the project which aims to a better understanding of crack nucleation, then damage evolution and bulk behaviour of the material, is complementary with the work in Subtask 4.4 which is devoted to the study of crack propagation. The complementarity lies also in the fact that the mechanical properties considered by the "crack cohesive model" are restricted to the local area ahead of the crack tip, as this investigation is focussed in the description of the ice properties at an intermediate scale, i.e. that of a small volume of ice containing a relatively large number of micro-cracks. The experimental work was done on both granular ice and natural or artificial columnar ice using the facilities of LGGE and the 3D testing machine available in the framework of the European Large Scale Facility programme at HSVA.

Deliverables

The results on these special mechanical properties of ice engaged in the measurements as well as on the improvements of the ice damage model were compiled in progress reports which were made available to the LOLEIF participants every 6 months and in the final report at the end of the project. These reports were disseminated to partners.
 

Interdependence and links with other tasks

The results provided by this task are primary used by the fracture dynamics modelling group within Subtask 4.4. Interdependence was established between LGGE and VTT in analysing ice failure processes as input information for the development of the ice - structure interaction model in Subtask 4.2. Fracture toughness tests were carried out in co-operation with HSVA (within the TMR Programme) which requires co-operation between LGGE and HSVA. Finally LGGE establishes fracture mechanisms of natural ice which is used by the fracture modelling group (Subtask 4.4).
 

Objectives

Description 

The physical reasons for the changes between simultaneous and non-simultaneous ice failure modes are not understood at present. This is one of the main reasons to the present inaccuracy in ice load predictions. 

The fracture dynamics modelling  in Subtask 4.4 clarified details of the various ice failure processes and contact phenomena occurring at the ice - structure interface. These results were used here in connection with a new working hypothesis, which states that a cyclic change between three ice failure modes, known as horizontal cleavage cracking, pure crushing and flaking, provide a key factor in explaining several important phenomena which have been observed in laboratory tests. These included a drop of the nominal crushing pressure at a critical ice velocity, a decrease of the ice load for stiff structures and the arise of steady state vibrations at intermediate ice velocities. The results from the full scale tests (Task 2) are used extensively to verify and quantify this hypothesis. Based thereon, a new physical model for the dynamic interaction between ice features and wide structures is being developed. 

The influence of the structural compliance is of special importance because the global load has been found to increase considerably in laboratory conditions if the structure compliance increases. In full scale conditions this load increase will be most likely impeded by the aerial randomness of sea ice strength. Therefore, the statistical variations in the local and aerial ice characteristics have been considered while building a new model for dynamic ice - structure interaction. 
 

Software development and verification

The new numerical model based on existing dynamic ice - structure interaction models developed by VTT and HUT. These existing physical models used in the numerical solutions were replaced by the new physical model. The quality and reliability of the computer program is tested by comparisons to all available laboratory measurements and field observations. Thereafter it is possible to design structures which are safe from severe ice induced vibrations. 

The new dynamic interaction model adopts a simplified version of the Ridge Load Model of Subtask 4.3 by using soil mechanical equations for ice rubble. Hence, the applicability of the dynamic model has been extended into ice ridges and rubble fields. The model was then used to simulate the global load as a combination of the load components due to the ridge keel, the consolidated layer and the sail. Cohesive and frictional load components at the keel and sail are treated separately in the time domain simulation. 
 

Deliverables

The progress of the numerical modelling of the dynamic ice - structure interaction is compiled in interim reports every 6 months and disseminated to all project participants including the Advisory Committee members and the European Commission. The final results were compiled in the final report at the end of the project.
 

Interdependence and links with other tasks

Co-operation was established between the Subtask's leader VTT and HUT who worked on the ridge load model (Task 4.3) as well as on the ridge properties (Subtask 2.2). Links were also established between this Subtask and all Subtasks under Task 2 (Full sale tests) as well as with Subtask 4.4 (Fracture dynamics model).

Objectives

Description

The risks to achieve this goal are normal. Reasonably accurate ridge mechanical properties full scale data were measured in Subtask 2.2. Non-linear finite element analysis (FEA) is matured and existing codes (e.g. ABAQUS or ANSYS) are used as a basis. There are several research reports on localised FEA but the above mentioned commercial finite element codes are presently lacking this feature even though they incorporate adaptive meshing for reducing the discretisation error. Thus, with relatively small extra efforts all the required capabilities for ridge - structure interaction simulation can be combined. With achievable adequate accuracy the developed FEA code could remove many uncertainties in ice force design and thus be a valuable design tool for the partners of this research.

NTNU further extend the theoretical modelling and included thermodynamics in the model:

A multi-year ridge has survived one or more summer melt seasons and is supposed to be highly consolidated. However, for first-year ridges the internal friction and consolidation are highly influenced by the thermal balance of the ridge from its birth. This means:

• External heat exchange such as convection to ambient fluid (air and water), long wave radiation, solar or short-wave radiation, condensation / sublimation (or evaporation in case of wet surface), melting of freezing and precipitation
• and internal heat transfer as well as melting and freezing.

The heat balance simulations were used to provide a bulk strength of the ice being used in a finite element model applicable to simulate the global load from a ridge.

This Subtask fits to university environment where theoretical work can be conducted along with postgraduate studies and as a part of a thesis work. In this conjunction the free computer resources are valuable in developing this kind of a non-linear numerical model.
 

Deliverables and Dissemination

Progress reports on the development of the ridge load model were delivered every six months, the final report 3 months before the end of the project. These reports were provided to the partners.
 

Interdependence and links to other tasks

HUT is the responsible partner. VTT gave a contribution to constitutive modelling and NTNU to consolidated layer thickness evolution by thermodynamic approach. This subtask was strongly related to the field measurements on ridge properties (Subtask 2.2) but also to the full scale tests conducted in subtasks 2.1, 2.3 and 2.4.

Objective

Description

The phenomena of splitting spalling and crushing is examined within a fracture mechanics framework. This subtask considered the following general influences:

• geometry, degree of confinement,
• contact crushing versus remote flexural failure,
• stability: crushing or splitting,
• splitting path stability,
• notch sensitivity versus strength failures,
• load path effects,
• crushing velocity
• and residual stress state and ice temperature.

Linear-elastic fracture mechanics (LEFM) is in its own way as confining an idealisation as plasticity. It would be a pity to drop one narrow idealisation only to be limited by another. Real ice is more complicated and the interaction between fracture and creep is important. This subtask explored the applications of modern approaches to creep fracture. 

Further, research in this subtask analyses the interaction between different modes on a more rational and fundamental basis, properly based on identifiable material and geometric parameters and on dimensional analysis. A cohesive crack model was used to link quantitatively the measured load versus crack-opening displacements measured in the field with the fracture energy, and to extrapolate in quantitative terms the influence of specimen size on this fracture resistance. A feature of cohesive crack modelling is the assumption that a significant portion of the non-linear deformation can be expected to localise on a crack band ahead of the crack. As the rate of loading is reduced, bulk deformation can be expected to become significant if not dominant, and indeed at a slow enough loading rate bulk creep would occur without fracture. This facet of the modelling requires a constitutive law for the sea ice in bulk, and both the cohesive crack and the bulk creep needs to be modelled. The field tests include cyclic and other load history effects for the purpose of defining the necessary constitutive behaviour more thoroughly. A pragmatic approach is through a non-linear visco-elastic model which treats the ice sheet as a two-dimensional elastic continuum, and the properties represent the response of a typical first-year ice sheet. The work initiated at Clarkson University including comparisons was extended by full-scale measurements carried out as part of the field program and to extend the comparison to the extensive sets of data from Canadian measurements.

Adequate physically based constitutive models of sea ice are not yet available. Thus this subtask applied a phenomenological model with its base in the non-linear theory of visco-elasticity. It incorporated the non-linear visco-elastic characterisation of ice under tensile loading for stress magnitudes from very small to almost tensile strength for long times and complex loading histories, the change in characterisation parameters between different scales, and the ability to predict the rate dependency of fracture through visco-elastic theory in conjunction with an applicable fracture theory.

Knowledge of the fracture energy variation with scale and constitutive behaviour is essential if the time dependent loading on the structure was modelled adequately, and the impact of ice impact velocity was incorporated. The cohesive crack model, combined with a visco-elastic description of the bulk ice, plays a significant role in deciding whether failure will be by splitting or crushing.

A final objective is once and for all to resolve the much disputed question of "scale effects", which has bedevilled ice force research for many years. Scale effects in other areas of mechanics and physics have always responded to a more complete physical understanding and there is no reason why this should not also apply to ice. An important consequence is to derive at a clear position about which kinds of model scale experiments can be applied directly to full-scale predictions, and which require correction.
 

General

The American specialist Prof. John Dempsey (Clarkson University) is involved in this subtask as Visiting Professor at CU. He is one of the leading authorities in ice fracture mechanics and the project benefited strongly from his contributions.
 

Deliverables

A progress report on this activity was submitted every six months. The subtask's final deliverable was a soundly based documented ice force prediction model which takes account of fracture, consistent with measurements taken in other activities. The results were communicated to the industry by conference papers, papers in scientific articles and popular articles.
 

Interdependence and links to other tasks

Fracture dynamics modelling needed input from actual ice structure interaction and ice fracture processes obtained in Subtasks 2.3 and 2.4. Representatives of this group observed the full scale measurements at the lighthouse. Of great importance is the co-operation with LGGE who carried out the experiments on fracture toughness of ice as well as basic ice fracture tests on small-scale for formulation of an advanced ice damage model within Subtask 4.1.

Objectives

Description

For the probabilistic approach a probabilistic description of the ice conditions near the structure was needed first. The parameters of the probabilistic model included at least ice thickness, ice strength, temperature, ice velocity, salinity, porosity, direction of ice movement and also different forms of ice features, such as level ice, rafted ice, ridged ice, etc. Probabilities of encountering these features were incorporated as well.

The "Achilles heel" of such a model is its ability to distinguish between parameter combinations which induce different ice failure modes. The distinction is important because different ice failure modes can induce very different ice forces. A load model describes the ice force in each different interaction scenario. Using a load model in conjunction with the probabilistic description of the ice regime a probability density function for the total ice force can be calculated. This function can then be used to define a characteristic design load to be compared with the results of a deterministic approach.
 

Deliverables

The approach described above is written as software. Initially it comprises a research tool but it is intended later to make it accessible as a user friendly software package developed as part of a separate program / activity. 

Progress of the study and the final results were compiled every 6 months in interim reports (six monthly management and progress reports and annual reports) and at the end of the project in the final report within Task 6. These reports were disseminated to all project participants including the European Commission and the Advisory Committee. Key results were communicated to the industry by conference papers and journal articles.
 

Interdependence and links to other tasks

CU, NTNU and VTT co-operated closely on this task. Also versatile input from all other partners of the project into the probability approach was provided. Prof. K. Shkhinek of St. Petersburg State Technical University substantially contribute to this task. Special links were established to the full scale measurement groups (Task 2) and all it's subtasks) which provided the input to the probability function. Further, a link was established to Subtask Subtask 4.2 where a new load combination formula is developed for the probability model.