Ian Jordaan

Mechanics of ice–structure interaction

Abstract The physical processes involved in the interaction of ice masses with offshore structures are described. For design purposes, two pressure-area relationships have been deduced, which take into account the randomness of data. The first is for local pressures, using ranked data from ship rams, resulting in a power-law decrease (≃−0.7) of pressure with design area. A second (global) pressure-area relationship with random parameters has been developed, also based on data from ship rams, with a power-law decrease (≃−0.4) of average global pressure with nominal contact area. Most of the force is transmitted through small areas termed “high-pressure zones”. Observations at the medium scale indicate an extremely regular cyclic load variation in a high-pressure zone over several cycles, superimposed on less regular fluctuations. The regular cyclic activity is ascribed to dynamic activity within a layer of damaged ice adjacent to the indentor or structure, and the other reductions in load to spalling activity. The main processes in the layer are recrystallization accompanied by microfracturing near the edges of the high-pressure zones (low confining pressures), and recrystallization accompanied by pressure softening at high confinements. These processes have been reproduced in triaxial tests on polycrystalline ice, and simulated in a finite element model that incorporates damage mechanics. Fractures, spalls, and splits lead to the global reductions in average pressure. Models of flexural failure are compared to data; the results confirm the trend of measurements but further full scale calibrations are needed.

Probabilistic Analysis of Local Ice Pressures

Extensive work in recent years has been carried out on the calculation of global ice loads on a probabilistic basis. An analysis method is presented for local ice pressures, which yields values of pressure for specific values of exceedance probability. In developing this method, particular attention has been paid to problems of exposure (length, position and number of impacts), as well as the area of exposure (area within area versus nominal contact area). The solution has been formulated for a series of discrete impacts, e.g., rams by a vessel, or a series of periods of continuous interactions. Data for the MV CANMAR Kigoriak and USCGC Polar Sea were ranked and curves were fitted through the tail of probability plots for three panel sizes. This allowed determination of exceedance probabilities of the design coefficients for pressure as a junction of area. The method developed was then applied to an example for a ship based on the data and expected number of rams per year. Formulas useful in the design of structures in ice are presented.

Application of damage mechanics to ice failure in compression

In this work some principles of viscoelastic theory as applicable to ice are reviewed. A multiaxial ice model, incorporating nonlinear damage, is presented based on the Burgers viscoelastic body with nonlinear dashpots in both the Kelvin and the Maxwell units. This mechanical ice model is found to be very efficient and accurate, especially for short loading periods. It includes the effects of microcracks and damage on the reduction in elastic modulus and the enhancement in creep deformation. Damage evolution is based on Schaperys approach using the generalized J integral theory. Volumetric deformation under compression is included which is mostly dilatation due to microcracking and other microstructural changes. Triaxial tests on laboratory-produced granular ice have been conducted to investigate the deformation of ice and the influence of cracks and damage. These tests have also been used to verify and calibrate the constitutive modelling. The damage model has been developed in FORTRAN code and implemented as a user subroutine in the ABAQUS finite element analysis program. The theoretical model provides good agreement with test results.

Microstructural change in ice : II. Creep behavior under triaxial stress conditions

This work investigates the deformation of ice under deviatoric stresses and confining pressures expected during ice-structure interaction. Granular ice was tested under a range of confining pressures (5-60 MPa) and deviatoric stresses (up to 25 MPa), with sample temperatures between -8° and -10°C. Samples were deformed to increasing end-levels of axial strain, and were thin-sectioned and photographed immediately following testing. At all confinement levels, the original texture of the sample is completely transformed within the first 10-15% strain, to a fine-grained matrix with a few larger, isolated grains. At low confinements, grain-size reduction is associated with extensive microcracking. At high confinements, few cracks are observed. Observations suggest that microcracking, melting and recrystallization are active at all levels of confinement, though the relative importance of each depends on the confinement, stress and accumulated strain. Deviatoric stress is a strong factor in controlling the creep, reflected in both the time required for the sample to reach accelerated creep and the tertiary creep rate itself. Two exceptions to this pattern were noted. First, some samples experienced strain localization and eventual rupture. These specimens tended to have higher creep rates even in the initial stages of strain. Second, prior damage resulted in rapid softening compared with the behavior of undamaged specimens. However, when strain rates are compared among all samples at a given level of cumulative axial strain, the creep behavior obeys a power law over the whole range of strain levels tested. Effective viscosity decreased from 10 7,8 to 10 6.4 MPa n s within the first 10% strain, during which the most substantial microstructural changes occurred, and then stayed relatively stable. The stress exponent, n, remained within the range 4.0-4.6. The dominant deformation mechanism appears to depend strongly on confining pressure (cracking at low pressure and dynamic recrystallization at high pressure). Creep rates at high confinement appear to increase relative to those at intermediate confinement, but the influence of temperature must be addressed further.

Disintegration of ice under fast compressive loading

During the interaction of ice with ships or other offshore structures, a compressive zone develops in the ice. This is the focus of the present work. An interpretation of field measurements shows that the compressive ice load is far from uniform; indeed, most of the load is transmitted through small areas of intense pressure characterized by a highly damaged layer. The processes leading to the formation of these zones include fractures, and in particular spalls near the edges of the zones, as well as a separate process of damage and microstructural change within the layer itself. In order to capture the essential points for deducing design requirements, we have formulated a probabilistic model of high-pressure zones. The mechanics of failure of ice in these zones is explored. Triaxial tests have been conducted. Mechanisms discussed include microcracking (shear banding), recrystallization and grain boundary melting. As pressures increase, the microcracking and recrystallization are suppressed and the strain rates decrease. At even higher pressures, the results show pressure softening with enhanced strain rates. Two state variables are used to model the ice deformation, corresponding to the hardening at lower pressures, and to the softening at higher pressures. Finite element analyses of the ice response incorporating these variables, corresponding to a medium scale indentation test have yielded promising results, showing the decline in load and the layer formation.

Experiments on the damage process in ice under compressive states of stress

During ice-structure interaction, ice will fail in a brittle manner dominated by two processes. The first corresponds to the formation of macrocracks and the consequent spalling-off of large ice pieces. The second includes an intense shear-damage process in zones, termed critical zones, where high pressures are transmitted to the structure. The shear-damage process results in microstructural changes including microcrack formation and recrystallization. A range of tests on laboratory-prepared granular ice have been conducted to determine the fundamental behaviour of ice under various stress states and stress history, particularly as it relates to changes in microstructure. The test series was designed to study three aspects: the intrinsic creep properties of intact, undamaged ice; the enhancement of creep and changes in microstructure due to damage; and the effects of different stress paths. Tests on intact ice with triaxial confining pressures and low deviatoric stresses, aimed at defining the intrinsic creep response in the absence of microcracking, showed that an accelerated creep rate occurred at relatively low deviatoric stresses. Hence, a minimum creep rate occurred under these conditions. Recrystallization to a smaller grain-size and void formation were observed. Ice damaged uniaxially and triaxially prior to testing showed enhancement of creep under both uniaxial and triaxial loading conditions. Creep rates in triaxially damaged ice were found to be non-linear with high deviatoric stresses, corresponding to a power-law dependence of creep rate. Uniaxially damaged specimens contained microcracks parallel to the stressed direction which tended to close under triaxial confinement. Damage under triaxial conditions at low confining pressures produced small recrystallized grains near zones of microcracking. At high confining pressures, a fine-grained recrystallized structure with no apparent cracking was observed uniformly across the specimen. The recrystallization process contributes significantly to the enhanced creep rates found in damaged specimens.

The Flow Properties of Crushed Ice

The flow properties of crushed ice under plane-strain conditions are examined. The analysis is based on a set laboratory experiments. The geometric configuration provided a wide range of pressures and material behaviors. At the early stages of the extrusion, and near the exit, where pressures are low, models based on Mohr-Coulomb flow theory describe the extrusion of crushed ice satisfactorily. At more advanced stages of the tests, high pressures developed, crushed ice became fused, and its behavior was similar to that of highly damaged polycrystalline ice. An extrusion model based on a nonlinear viscous flow is presented. This formulation is appropriate for the pressure ranges encountered in ice-structure interaction. After the initial compaction of the material, the dynamic force characteristics similar and cracking are not necessary to produce the dynamic effect in the ice-structure interaction. The vibrations appear to be related to variations in the width of the fused zone of ice.

Ice fracture and spalling in ice-structure interaction

The role of fracture and spalling in ice-structure interaction is described. The most likely regions in which fractures will be initiated from flaws are shear zones with low confining pressure and tensile zones. Flaws of different lengths and of different locations are investigated numerically in terms of strain energy release rate at crack tips. The open crack of Kendalls double cantilever beam theory has also been investigated theoretically and numerically. Such flaws are less likely to propagate and have to be located in specific planes. Since flaws in ice are random in nature, a probabilistic modelling is necessary for the future study of ice fracture and spalling.

Localized pressures during ice–structure interaction: relevance to design criteria

Abstract Crushing is a prevalent mode of ice failure during ice–structure interaction. This failure mode frequently occurs with vertical structures and over local areas on sloping structures. During ice crushing, the interaction zone is characterized by three distinct regions of pressure; critical zones, regions of background pressure, and areas of recently spalled ice. Critical zones may be defined as local regions of ice where intense pressures occur over short time periods. Critical zones influence significantly the crushing process. The parameters associated with critical zones are quantified by examining three types of field-scale interactions; medium-scale indentation tests, ship ramming trials of the Louis S. St. Laurent and CanMar Kigoriak, and an ice–structure interaction with the offshore structure Molikpaq. Critical zones occur regardless of the scale or type of interaction. Despite the highly random nature of critical zones, basic parameters such as zonal size, force, pressure, and spatial density are quantified. Critical zones are found to be approximately 0.10 m 2 in area and may exert forces ranging from 0.1–4 MN. Spatial densities of the critical zones, defined as the number of zones per unit meter, range from about 0.6 to 0.8 zones/m 2 and appear to be influenced by confining pressure and scale effects. Critical zones provide an explanation for the exhibited reduction in average pressure with increasing contact area. Two kinds of pressure–area relationships are presented; one in which the contact area increases over time, the other in which large, unconfined contact areas contain smaller, highly confined regions. The importance of aspect ratio in relation to the pressure–area trend is discussed. Reduction in contact area due to spalling and the orientation of the critical zones within an impacted area are examined with respect to the aspect ratio.

Analysis of medium scale ice-indentation tests

A medium-scale ice-indentation test program was conducted on Hobsons Choice Ice Island in May, 1990. This test series was performed as an extension to a similar program conducted the previous year. A description of the 1990 test program along with a description of the observed failure surface is presented. Ice samples, both undamaged multi-year sea ice and ice from the pulverized layer, were collected and transported to the Ice-Structures Laboratory of Memorial University of Newfoundland. Uniaxial compression tests, including constant strain rate tests and creep tests, were conducted. Estimates of peak stress, elastic strain, delayed elastic strain and permanent viscous creep were determined and comparisons were made between undamaged, laboratory-damaged and pulverized ice. Finite element simulations were conducted and compared to field observations. This finite element analysis focused on the behaviour of an intermediate layer of highly damaged ice at the ice-structure interface. The results of the finite element simulation indicate that deformation of the intermediate layer is dominated by viscous behaviour.