3D discrete numerical modelling of ridge keel punch through tests

Ridge keel punch through tests were simulated in 3D. In simulations unconsolidated ridge keel was modelled as a rubble pile of loose ice blocks. Combined finite–discrete element method (FEM–DEM) with rigid discrete elements representing ice blocks was used. Simulations were run in full scale. In total 47 simulations were run with various friction coefficients and keel depths. The failure process of simulated rubble piles was analysed and the shear strength of the rubble pile was derived from results. The effect of rubble porosity, keel depth and friction on shear strength of the pile was also analysed. The simulation results were compared to laboratory and full-scale punch through tests of unconsolidated ice rubble. Shear strength values achieved from simulations were in range for experimental results. Failure process was observed to be similar to laboratory experiments.     

Mechanical properties of model ice ridge keels

Rubble ice presents pressure dependent yield strength and its behaviour can be described by mathematical models based on several mechanical parameters. They are investigated for HSVA model rubble ice through the analysis of three different tests: the oedometer test, the pile test and the punch test. This last test is analysed with the non-linear Eulerian finite element method. The tests were performed on 4 ice ridges with two different submersion times. A 0.5 to 1.2 kPa model scale Mohr-Coulomb cohesion (0.6 to 1.5 kPa Drucker-Prager cohesion), depending on the ridge history, was used in the simulations of the model scale punch tests. The friction angle is estimated between 30 and 45° (40 and 50° Drucker-Prager friction angle). The upper value was used in the punch test simulations. A 0.9 MPa Young modulus was derived and the hydrostatic compressive yield curve was determined. The numerical model is able to estimate the rubble action during the entire penetration of the punch test in the keel and it is shown that a cohesive softening occurs in the rubble. In order to reproduce the experimental load time series for the short submersion time ridges it was necessary to use a vertical distribution of the cohesion representing the vertical distribution of the freeze-bond strength. A sensitivity analysis of the punch test shows that the keel depth and the ice density are the main parameters governing the keel frictional resistance. A precise determination of these parameters is therefore crucial for a correct determination of the rubble mechanical properties from the numerical simulation of experimental punch tests. The punch test is not appropriate for the determination of the friction angle due to the low confinement pressure at the failure plane. The numerical analysis of the punch test allows the estimation of different assumptions used in analytical models for the rubble failure: the cohesion averaging is an under-conservative approximation, and the non-simultaneity of the cohesive and shear resistance maximum values can be considered in the peak load estimation by the computation of their quadratic mean. The comparison with full scale values shows a reasonably good scaling of the cohesion for the model ice ridges with a long submersion time.     

Velocity effects in laboratory scale punch through experiments

Laboratory scale punch through tests on floating rubble consisting of plastic blocks were conducted. The motivation of using plastic blocks was to simplify the interpretation of results as the plastic blocks do not freeze together. The emphasis was on the methods used to derive the rubble material properties from results. In the experiments, a flat indentor platen penetrated the rubble. The indentor force as a function of its penetration was recorded. Different indentor velocities were used. The behavior of the rubble was related to the measured indentor force records. The results were compared with earlier laboratory scale punch through tests. The experiments showed, that punch through tests give results, that in some cases are difficult to interpret. The reason for this is mainly in the hydrodynamical effects arising with high indentor velocities. The results showed, that the existence of the rubble in the basin could change the hydrodynamical effects from the tests earlier used to capture them. It is shown that these effects can partly explain the shear rate dependency of the ice rubble observed in earlier work on punch through tests.     

Experiments on level ice loading on an icebreaking tanker with different ice drift angles

A series of tests was performed with a laboratory-scale model ship to simulate the effects of ice load parameters on an icebreaking tanker. A model of the icebreaking tanker Uikku was mounted on a rigid carriage and towed through an unbroken ice sheet in the ice tank of the Marine Technology Group at Aalto University. Two ice sheets and 11 different experimental configurations were used. The carriage speed, heading angle of the model ship, and ice thickness were varied, and the forces, accelerations, ice cusp sizes, carriage positions, and ice pile dimensions under the intact ice sheets were measured.This paper includes results for the measurements of ice rubble loads against the model hull in the horizontal plane. Phenomena such as ice failure modes and ice rubble accumulation on the upstream side of the hull beneath the ice sheet were observed in some tests. The icebreaking lengths and dimensions of ice rubble were analyzed for some tests. The effects of towing speed, heading angle under the intact ice sheet in front of the hull, and the accompanying ice loads on the formation and build-up of ice rubble were analyzed. In addition, the evolution of ice rubble geometry, in cross sections and the horizontal plane, was investigated. There was good agreement over several orders of magnitude between the measured and calculated values of the lateral ice forces. These results are relevant to the modeling of ice loading on hulls and the design of moored or dynamic positioned structures for operation in ice-covered waters. Some parameters obtained from these tests can be used as input for future numerical simulations.     

Simple-shear box experiments with floating ice rubble

A simple-shear box was used to study the shear strength characteristics of floating layers of vertically unconstrained ice rubble comprised of parallelpiped ice blocks. A comparative set of experiments was also performed using floating layers of parallelpiped plastic blocks in order to determine the origin of cohesion in ice rubble. Experiments were also performed using mushy ice. However, the shear-box proved not to be useful for determining the shear testing of mushy ice.The shear strength of a layer of ice rubble was found to depend on normal stress, which in turn was found to depend on rubble thickness, layer porosity, and shear rate. The dependence on shear rate of normal stress and, as a consequence, of shear strength of a layer of floating ice rubble is attributed to the development of freeze-bonds between the ice blocks comprising the rubble layer. It is argued that, at slower shear rates, more and stronger freeze-bonds develop than at higher shear rates, thus enabling the layer to withstand larger normal stresses and, consequently, shear strengths that increase with decreasing shear rates. If the influence of freeze-bonding on normal stress is taken into account, and if a Mohr-Coulomb failure criterion is used to characterize shear strength, it is found that a floating layer of ice rubble undergoing continuous-shear deforms as a cohesionless material; or at least as a material with unique cohesive properties.     

Grounded rubble fields adjacent to offshore structures

A continuum model of grounded ice rubble fields is developed in which bulk rubble is treated as a Mohr-Coulomb material at critical equilibrium. The surrounding ice sheet is considered to form a rigid boundary. Approximate stress distributions are obtained using the method of integral relations. Loads on an offshore structure adjacent to a rubble field are related to maximum stresses exerted by the floating ice sheet. The influence of field geometry, grounding resistance, and rubble properties is examined.     

Ice rubbling and ice interaction with offshore facilities

In the context of this paper, ice rubbling is the term given to the process of ice interacting with itself and creating ice rubble. In nature, ice rubbling is most common in ridge-building in pack ice, but also occurs in the creation of stamukhi and ice pileups at shorelines. In ice interaction with platforms, the process of ice rubbling can have a significant influence on ice loads and other issues such as ice encroachment and platform access and egress. It is also well known that ridge-building in pack ice represents a limit to ice pressure within an ice field and has a significant influence on ice circulation models, ice forecasting and ship transits. In this paper, knowledge of ridge-building and pack ice pressures is briefly reviewed together with methods for applying this knowledge to ice interaction with platforms. The early work in investigating ridge-building forces by Parmerter and Coon is one of the starting points. The way rubbling limits can be used to assess Limit Force ice loads is well known, but uncertainties are implicit in the methodology which is largely based on empirical treatment of very limited measured data. Because of the limited measured data and ignorance of associated ice conditions, a factor of 5 (between lower and upper bounds) is included in the methodology for Limit Force ice loads in ISO 19906. This paper reports on new work to narrow this uncertainty by using ice mechanics theories originally developed for ice interacting with sloping platforms; and which (to a large extent) have been verified by field observations and measurements of ice loads on platforms.     

Model tests on ice-rubble size and ship resistance in ice rubble

Described here are the results of model tests on resistance to ship-hull motion through a thick layer of ice rubble; layer thickness was 45% of hull draft. The tests were aimed to elucidate the influences of ice-rubble size on ice-rubble resistance. It was found that as ice-rubble size increased so did the resistance encountered by the test hull. However, it was also found that a layer of mush ice produced a greater resistance than did layers comprised of ice blocks. A layer comprised of both mush ice and ice blocks produced a resistance intermediate to layers comprised of either mush ice or ice blocks.Ship resistance generally increased with increasing ship speed. However, the influences of ship speed and ice-rubble size on the contributing resistance processes were found to be somewhat more complex. For example, the frictional resistance experienced by the parallel midbody of the test hull initially decreased with increasing ship speed, when the ice rubble was comprised of ice blocks which were small compared to layer thickness and hull size. The frictional resistance subsequently increased then decreased again with increasing ship speed. When the layer was comprised of relatively large ice blocks, frictional resistance increased to a maximum value then decreased with increasing ship speed. Generally, larger frictional resistance occurred for the layers comprised of larger ice rubble. In accordance with the relative sizes of ice rubble and ship hull, and with hull speed, the variations in frictional resistance can be explained in terms of a layer behaving as either a granular medium or as a viscous fluid.An additional aim of the study was to verify the existence of a thrust due to the ascension of submerged ice at a hull's stern. The existence of a stern thrust had been postulated by Kitazawa and Ettema (1985). The present study indicates that a relatively weak stern thrust may occur, but its magnitude is negligibly small compared to other resistance forces.     

大尺度圆锥结构的冰力计算

大尺度圆锥结构的冰力计算不同于小尺度圆锥结构的冰力计算,它必须考虑堆积冰的影响。Maattanen教授根据他在波斯尼亚湾Kemi-Ⅰ灯塔试验圆锥上所取得的经验,建立了大尺度圆锥结构冰力分析有限元模型。但在他的文献中,对许多关键性细节(如堆积尺度)都未给出明确表达。在本文中,作者以清晰的思路分析推导了该模型的这些细节,最后,应用该模型对JZ-93锥体平台作了冰载分析,分析结果得到设计部门的认可。     

Comparison and analysis of experimental and virtual laboratory scale punch through tests

Laboratory scale punch through tests on floating rubble consisting of plastic blocks were conducted and simulated with a 3D discrete numerical model. The purpose was to analyse the experimental method and to validate the model. The motivation of using plastic blocks instead of ice was to simplify the interpretation of results as the plastic blocks do not freeze together. The indentor force and the lateral force induced by the rubble on one of the basin walls were recorded as a function of indentor penetration. Further, the experiments were recorded with a video camera and a motion tracking software was used to analyse the rubble deformation. The force records and deformation patterns from the experiments and simulations were in agreement. The evolution of the deformation patterns could be closely linked to the indentor force records, which demonstrates the need for the numerical model to correctly represent the rubble deformation. The experiments and the simulations showed, that the lateral force within the pile increased considerably during a punch through experiment. This makes the interpretation of punch through experiment results for material modelling challenging: the friction angle of the rubble can become overestimated making the punch through test unsuitable for achieving accurate values for friction angle. Consequently, no value for the rubble friction angle was derived here.     

Structure-rubble field interaction

Analytical aspects of interaction between an unconsolidated or poorly consolidated rubble field and a conical-type, massive, ice-resistant, bottom-founded offshore structure are presented in the paper. This matter is a substantial part of an analysis of global ice loading imposed on an offshore structure in the transition zone of the Arctic Seas. The paper contains analytical formulation of the problem and relevant analytical results which describe the geometrical aspects of the ice-structure interaction along with the global ice load which can be imposed on the structure. The results can be generalized and used for structures with arbitrary cone angles up to 90°. All results are presented in tabulated and graphical forms convenient for practical engineering applications.     

The structure and strength of first-year ice ridges in the Baltic Sea

Sea ice ridges are typical features in the Baltic Sea ice pack accounting for on average up to one-third of the total ice mass. They are difficult obstacles to winter navigation and cause large forces on ships and offshore structures. However, the internal structure and strength properties of ice ridges are quite poorly known. This paper presents the results of an experimental project on the structure and strength of first-year ice ridges in the Baltic Sea carried through during 1987–1989. Altogether, six freely floating ridges were investigated. Their total thickness ranges from 4 to 17 m. Valuable field data about the size and shape of ridges, consolidated and unconsolidated parts, block size and porosity have been obtained by drilling and sampling. Divers and underwater video cameras have been used for observing the ridge keel structure. The totally consolidated layer within the ridges was 1–2 times the thickness of the surrounding level ice. The average porosity was 29%. The strength of the keel part has been measured with a full scale loading test. The force required to shear the keel was determined as a function of the normal force, the settlement rate, and the porosity of the keel. The shear strength of the ridge keels was from 1.7 up to more than 4.0 kPa. Also small scale tests were conducted in an ice tank giving results in agreement with the full scale tests.     

Offshore pipeline protection against seabed gouging by ice: An overview

Offshore operators in the Arctic will rely on seafloor installations, notably pipelines, to manage and transport hydrocarbons. In icy waters, these structures are at risk of being damaged by gouging ice features, either icebergs or sea ice ridges. This phenomenon generally occurs when an ice feature drifts into shallower areas and its keel starts plowing the seabed over considerable distances. It is generally agreed that adequate protection against these events can be achieved by burying the pipeline below the seafloor. The question is: what constitutes a safe and economical burial depth for any given location? An answer to this question requires adequate knowledge of material properties (soil, ice keel and pipeline), a reliable handle on the processes taking place during gouging and a consensus on what constitutes acceptable risks. Research on this subject has been on-going for the past few decades, along several fronts. One is by means of field studies, including replicating gouging scenarios in a natural environment, in situ ice characterization, seabed mapping and on-land relict gouge investigations. Another is through laboratory studies, either at single gravity or in a centrifuge. Theoretical analyses and numerical simulations have also contributed to our current understanding of gouging phenomena. Several research groups proposed some form of guidelines for estimating gouging parameters—examples are presented. These methodologies are instructive in that they represent an integrated approach to an improved understanding of gouging phenomena. They point the way to what one may expect in terms of future guidelines to a safe and cost-effective burial depth.     

Ice ridge keel characteristics and distribution in the Northumberland Strait

Ice ridges impacts are a major design consideration for offshore structures in the Arctic. Consequently, field programs on the frequency and characteristics of ridges can provide valuable empirical information for the design of future offshore structures. The Confederation Bridge ice force monitoring program monitors ice ridge keels through sonar instrumentation at the bridge. A total of 3199 keel cross-sections were identified during the 2007 and 2008 ice seasons using a new processing method. Of the 3199 keels identified, 137 keels caused loads over 1 MN. The shape of each keel was visually identified and classified as one of four shapes: triangular, trapezoidal, w-shaped, and multiple peak keels. Triangular and trapezoidal keels made up more than 60% of the keels that cause loads over 1 MN. Four of the five largest loads had keels that were trapezoidal. For the 3199 keel cross-sections, the depth, width, leading and trailing keel angles, bottom width and area were identified and distributions of these keel properties were developed. The distribution was then compared to the design keel depth distribution from the Confederation Bridge. The observed 2007 and 2008 keel depth distributions was slightly lower than the design distribution likely due to the significant number of multiple peak and w-shaped keels. Additionally, the maximum keel depth suggested by the observed distribution was shallower than the maximum predicted keel depth.     

Ice loads on the caisson structures in the Canadian Beaufort Sea

This paper presents a comprehensive overview of the characteristics, instrumentation and measured ice loads on the caisson structures that were used for exploratory drilling in the Canadian Beaufort Sea in the 1970s and 1980s. Details are presented on the Tarsiut Caisson, the Single-Steel Drilling Caisson (SSDC), the Caisson-Retained Island (CRI), and the Mobile Arctic Caisson (MAC) Molikpaq. The global loads on the structures are presented as a Line Load (Global Load per unit width of the structure) and the Global Pressure (Line Load per unit ice thickness). Over 170 loading events are documented. There is excellent agreement amongst the measured loads on all of the structures if factors such as ice rubble and ice thickness are considered. Global loads are shown to be a function of the ice macrostructure (level first-year sea ice, multi-year ice, first-year ridges, hummock fields, isolated floes) and failure mode of the ice (bending, creep, mixed mode, crushing). The analysis shows that there is a general increase in the Line Load with increasing ice thickness. Empirical equations are presented to predict the global load in terms of the ice thickness and structure width for different ice failure modes. The most significant result of the analysis shows that the maximum Global Pressure measured for all types of ice loading events never exceeded 2 MN/m², with the vast majority less than 1.5 MN/m².     

Model test study of the nonsimultaneous failure of ice before wide conical structures

From 2007 to 2008, a series of model tests were performed to observe the ice failure before wide conical structures. The variable testing parameters include the water line diameter of the model cone and ice speed. When D/h > 25, the failures of ice wedges around the cone start to behave nonsimultaneously in these tests. The rubble piece size and the ride-up height were found to have linear relationships with the ratio of D/h in the tests. Several independent zones of bending were found in the nonsimultaneous failure process of ice. With the increasing of the ratio of D/h and the number of independent zones, the total ice force was found being reduced by degrees.     

A new composite energy absorbing system for aircraft and helicopter

In this paper, an innovative lightweight composite energy-absorbing keel beam system has been developed to be retrofitted in aircraft and helicopter in order to improve their crashworthiness performance. The developed system consists of everting stringer and keel beam. The sub-floor stringers were designed as everting stringer to guide and control the failure mechanisms at pre-crush and post-crush failure stages of composite keel beam webs and core. Polyurethane foam was employed to fill the core of the beam to eliminate any hypothesis of global buckling. Quasi-static axial crushing behaviour of the composite keel beam is investigated experimentally. The results showed that the crushing behaviour of the developed system is found to be sensitive to the change in keel beam web thickness. Laminate sequence has a significant influence on the failure mode types, average crush loads and energy absorption capability of composite keel beam. The desired energy absorbing mechanism revealed that the innovated system can be used for aircraft and helicopter and meet the requirements, together with substantial weight saving.     

Parameter effects on simulated ice rubbling forces on a wide sloping structure

Based on numerical simulations, this paper investigates parameter effects on the ice rubbling forces on a wide sloping structure. Ninety simulations were made with a two dimensional combined finite–discrete element method and five parameter values were varied. Two level factorial designs were used to analyze these simulation results. The main interest of the study was on the ice forces when there was floating ice rubble in front of the structure. The results indicated that the mean peak force on the structure depends on different parameters during different phases of the rubble formation process. Ice thickness was seen to be affecting the forces during all of these phases. Studied parameters were usually interacting with each other, thus indicating that their effects cannot be considered separately.     

Internal strength properties of river ice jams

River ice jams can cause extreme flood events with major consequences to infrastructure, riverside communities, and aquatic life. The emerging issue of climate change and the growing appreciation of related ecological linkages underscore the need for process-based predictive capability, such as theoretical advances and numerical modelling. A key element of such capability is the internal strength of the rubble comprising an ice jam, which is quantified by a few empirical constants, most notably the angle of internal friction, φ. Though this angle is considered a material property, there is considerable variation in reported values, which derive from applications of established theoretical concepts to actual case studies. The source of this discrepancy is identified by re-examining the theoretical formulations of ice jam stability and noting certain restrictive assumptions that were made in early literature. A less restrictive analysis takes into account the three-dimensional state of stress within an ice jam and leads to a more correct formulation. The resulting φ-values are consistent with experimental data obtained with specially-designed experimental setups. Relevant information can also be gleaned from more recent developments, intended to describe the dynamic evolution of ice accumulations into ice jams, via adaptations of constitutive laws that were originally developed for sea and lake ice. Analysis of the constitutive equations indicates that it is only when full lateral confinement occurs and the static (ice jam) condition is approached that φ can be considered a material constant. For this late phase of ice jam formation, the constitutive law appears to under-predict the value of φ while over-predicting the ratio of lateral-to-streamwise stresses.     

A comprehensive analysis of the morphology of first-year sea ice ridges

A review of the morphological properties of over 300 full-scale floating first-year sea ice ridges has been made, including measurements from 1971 until the present time. Ridges were examined from the Bering and Chukchi Seas, Beaufort Sea, Svalbard waters, Barents Sea and Russian Arctic Ocean for the Arctic regions; and from the Canadian East Coast, Baltic Sea, Sea of Azov, Caspian Sea and Offshore Sakhalin for the Subarctic (or temperate) regions. Grounded ridges were excluded. A wide catalogue comprising the ridge thicknesses (sail, keel and consolidated layer), widths and angles as well as the macroporosity and the block dimensions is provided. The maximum sail height was found to be 8 m (offshore Sakhalin), and the mean peak sail height was 2.0 m, based on 356 profiles. The mean peak keel depth is 8.0 m, based on 321 profiles. The relationship between the maximum sail height, h_s, and the maximum keel depth, h_k, for all ridges is best described by the power equation h_k = 5.11h_s^0.69. The correlation differs depending on the region. For Arctic ridges a linear relationship was found to be the best fit (h_k = 3.84h_s), while for the Subarctic ridges a power relationship (h_k = 6.14h_s^0.53) best fit the data. The ratio of maximum keel to maximum sail is 5.17 on average (based on 308 values), and has also been calculated for each region mentioned above. Arctic ridges generally have a lower keel-to-sail ratio than those in Subarctic regions. The statistical distribution of keel-to-sail ratios is best represented by a gamma distribution. The average sail and keel widths were 12 and 36 m, respectively. The relationships between the sail and keel widths and other geometrical parameters were also determined. Variation of sail and keel thicknesses within individual ridges has been compared with the variability of all ridges. Ridge cross-sectional geometry can vary greatly along the length of a ridge, even over a short distance. A study was made on sail block thicknesses, and it was found that they correlate well with the sail height with a square root model. The typical macroporosity for a first-year ice ridge is 22% (based on 58 values) with an average sail macroporosity of 18% (based on 49 values) and average keel rubble macroporosity of 20% (based on 44 values). The average ridge consolidated layer thickness was 1.36 m based on 118 values. The variation of the consolidated layer was examined, and it was found that the layer tends to grow evenly with time over the width of the ridge cross section. A greater spacing between the measurements seemed to affect the variation, as it decreased with an increasing distance between each borehole. A statistical analysis based on 377 measurements of the consolidated layer of ridges in the Barents Sea showed that the gamma distribution well describes the distribution of the consolidated layer thicknesses in that area.