Properties of ice from first-year ridges in the Barents Sea and Fram Strait

Journal Pre-proof Properties of ice from first-year ridges in the Barents Sea and Fram Strait

Victoria Bonath, Tommy Edeskär, Nina Lintzén, Lennart Fransson, Andrzej Cwirzen PII:

S0165-232X(17)30262-8

DOI:

https://doi.org/10.1016/j.coldregions.2019.102890

Reference:

COLTEC 102890

To appear in:

Cold Regions Science and Technology

Received date:

21 June 2017

Revised date:

15 July 2019

Accepted date:

12 September 2019

Please cite this article as: V. Bonath, T. Edeskär, N. Lintzén, et al., Properties of ice from first-year ridges in the Barents Sea and Fram Strait, Cold Regions Science and Technology(2018), https://doi.org/10.1016/j.coldregions.2019.102890

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© 2018 Published by Elsevier.

Journal Pre-proof

Properties of Ice from First-Year Ridges in the Barents Sea and Fram Strait Victoria Bonatha* , Tommy Edeskära, Nina Lintzéna, Lennart Franssona, Andrzej Cwirzena a

Luleå University of Technology (LTU), 971 87 Luleå, Sweden * Corresponding author: [email protected]

ABSTRACT

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First-year ice ridges are one of the main load scenarios that off-shore structures and vessels operating

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in ice-covered waters have to be designed for. For simulating such load scenarios, the knowledge gap

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on ice mechanical properties from the consolidated part of first-year ridges has to be filled. In total 410 small-scale uniaxial compression tests were conducted at different strain rates and ice temperatures on

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ice from the consolidated layer of 6 different first-year ridges in the sea around Svalbard. For the first

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time uniaxial tensile tests were performed on ice from first-year ridges using a new testing method. Ice strength was evaluated for different ice type, which are determined for each specimen based on a

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proposed ice classification system for ice from first-year ridges. 78% of all samples contained mixed

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ice with various compounds of brecciated columnar and granular ice. Ice strength of mixed ice showed isotropy, except for the samples containing mainly columnar ice crystals. For horizontal loading,

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mixed ice was stronger than columnar and granular ice. The residual strength of ductile ice depended on the strain rate. At 1.5% strain remained 70% of peak strength at 10-4 s-1 and 50% at 10-3 s-1. Ductile failure dominated for 75% of all mixed ice tests at 10-3 s-1 and -10°C. Ductile compressive strength was generally higher than brittle compressive strength for mixed ice. Brine volume was the main parameter influencing the tensile strength of the mixed ice which was between 0.14 MPa and 0.78 MPa measured at constant ice temperature of -10°C. Keywords: First-year ice ridges; Ice texture; Uniaxial compression strength; Tensile strength; Mechanical properties Victoria Bonath (corresponding author), Luleå Univ. of Technology, 971 87 Luleå, Sweden. E-mail: [email protected]. Phone number: +46 920 492934 Tommy Edeskär, Luleå Univ. of Technology, 971 87 Luleå, Sweden. E-mail: [email protected] Nina Lintzen, Luleå Univ. of Technology, 971 87 Luleå, Sweden. E-mail: [email protected] Lennart Fransson, Luleå Univ. of Technology, 971 87 Luleå, Sweden. E-mail: [email protected] Andrzej Cwirzen, Luleå Univ. of Technology, 971 87 Luleå, Sweden. E-mail: [email protected]

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1

Introduction

Sea ice ridges are ice features that form when two ice floes collide. Very often one ice floe is pushed below the other referred to as rafting. The ice gets crushed and broken into small pieces at the ice edges and piling of the broken ice up and downwards finally forms the ice ridge. From the beginning the ridge consists of loose ice blocks and pores filled with air, water, crushed ice, snow or watersoaked snow which is referred to as slush. The pores start to refreeze if temperatures are below freezing temperature. Freeze bonds built between single blocks and a refrozen layer grows within the

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ridge. At this point ice ridges can exert heavy loads to ships or offshore constructions, when they collide. Since ice ridges can be a high risk in this context, they have been studied for many years.

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Geometry, morphology and material properties such as strength and deformation are important for

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prediction and simulation of impact loads on structures.

Field studies on ridge morphology from up to 45 sources and 300 first-year ridges are summarized by

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e.g. Timco and Burden (1997) and Strub-Klein and Sudom (2012). Equations for determination of uniaxial compressive strength of granular and columnar sea ice were suggested by e.g. Timco and

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Frederking (1990) and Moslet (2007) based on the results from small-scale compressive tests. Poplin

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and Wang (1994) studied the compressive strength of rafted ice containing various ice types and their

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results showed that rafted ice was generally stronger in horizontal loading direction than landfast ice with columnar ice crystals. Cox et al. (1984) presented strength data on ice from multi-year ridges, which showed a considerable scatter due to high variations in ice structure. The average strength of mixed multi-year ice was comparable to strength of granular or horizontally loaded columnar first-year ice. The residual ice strength, i.e. the ice strength left after the ductile peak ice strength is reached, of mixed multi-year ice was up to two third of the maximum ice strength. Uniaxial tensile strength on salt-water ice have been measured through direct tensile tests in a number of studies mainly on columnar ice (Dykins, 1970; Kuehn et al., 1990; Richter-Menge and Jones, 1993; Sammonds et al., 1998). So far there is no standard test method, since direct tensile tests on ice are challenging regarding sample preparation, alignment and clamping, consequently it is difficult to compare results from different studies. According to earlier studies strain-rate and temperature have a

Journal Pre-proof minor influence on tensile strength whereas it is strongly influenced by brine volume, Dykins (1970). The effect of temperature increases as ice salinity increases is due to temperature sensitivity of brine filled inclusions, Richter-Menge and Jones (1993). Load direction is essential for columnar sea ice because of anisotropic behavior. The strength grows by a factor of 2 to 4 when compared horizontal and vertical loading conditions of the columnar sea ice, Dykins (1970). A considerable knowledge gap was found for the mechanical properties of the consolidated part of first-year ridges. So far the most comprehensive studies on the uniaxial compressive strength of ice

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from first-year ridges have been published by Høyland et al. (2000), Høyland (2007) and Shafrova and

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Høyland (2008). Høyland (2007) performed 449 in-situ and laboratory compression tests on ice from

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first-year ridges. Shafrova and Høyland (2008) presented a 2D spatial strength distribution for two ridge cross-sections. Tensile strength of ice from pressure ridges is an essential material property from

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an engineering point of view since bending and splitting are common failure modes for ridge

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interactions with narrow structures (Bjerkås, 2006). Tensile strength tests require time, accuracy and a reliable test method. Tensile tests on mixed ice have only been performed by Cox and Richter-Menge

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(1985) for multi-year ice ridges, showing little variation with strain rate or temperature, but a

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considerable scatter in strength values due to high ice structure variations.

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The presented data on the ice from first-year ridges are crucial for developing reliable models and improving existing models to simulate the collision of first-year ridges against structures and ships. For this purpose, field investigations on in total 6 pressure ridges in the area of Svalbard took place during winters from 2011 to 2013. Details on the morphology of the ridges are not part of this paper. For this part of the study uniaxial compression and tensile tests were performed on the ice from the consolidated ridge parts at the laboratory of Luleå University of Technology. By studying the internal structure of ice from pressure ridges it was possible to relate different ice properties such as strength, porosity and salinity to ice structure. The ice loading history and ice behavior under uniaxial compression are described. Tensile tests were performed on the ice from first-year ridges using a new testing method.

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2

Field survey

Pressure ridges in the seas around Svalbard were investigated during the years 2011 to 2013 with help of the Norwegian Coast Guard vessel KV Svalbard. Bonath et al. 2018 describes field conditions and geometrical and morphological ridge data as well as measured in-situ ice temperatures. In order to study ice properties from the ridges, 20 cm thick ice cores were taken with a core drill. The transportation of the ice cores to the cold container on KV Svalbard was done instantaneously after coring to minimize brine drainage. The storage temperature was -20°C. For the pressure ridges from

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2012 and 2013, the exact position from the cores within the investigated ridge profiles is known, which made it possible to generate ice type and strength distribution graphs for the ridges. All 20 cm

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thick ice cores were shipped to Luleå University of Technology for laboratory testing, with a shipping duration of 2 weeks. Salinity profiles from the ridges and level ice were measured at random on 70

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mm-diameter ice cores. The cores were sliced with a handsaw into 10-20 cm thick pieces, which were

3

Laboratory tests

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stored and melted in room temperature for salinity measurements.

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In the laboratory the storage temperature of the ice cores was -25°C. The storage duration in the

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laboratory until testing was 2- 6 weeks in 2011, 6 – 10 weeks in 2012 and 2 – 20 weeks in 2013. Unconfined compressive strength was tested on 410 specimens. The specimens’ shape was a rectangular prism with 170 mm height and a square base with 70 mm side length. For determining density of each specimen, the geometrical dimensions were measured with a sliding caliper and finally the sample weight was divided by the resulting sample volume. The total porosity, νt , which is the sum of the relative brine volume and the relative air volume, was calculated according to Cox and Weeks (1983). Salinity was measured after melting the tested specimen. To obtain detailed information about the ice texture, horizontal and vertical thin sections were prepared from each specimen. Ice structures were identified by studying the thin sections under cross polarized light.

Journal Pre-proof The test set-up is shown in Fig. 1. A customized cold chamber between the upper and the lower crosshead of the testing machine enables testing of ice samples at certain temperatures. A load cell is installed at the upper cross-head and deformation is measured by a differential transformer at the lower upwards moving piston, implying that sample deformation has to be adjusted for the system deformation according to Fig. 2. Steel plates are used as contact plates. Sample preparation was done carefully and the end surfaces were polished with a very fine sandpaper in order to provide parallel and smooth end surfaces and thus to reduce negative effects such as radial restraint from the steel

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plates; anyhow this affect cannot be completely eliminated.

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The compressive strength tests were conducted at nominal strain rates of 10-2 s-1 , 10-3 s-1 , 5·10-4 s-1 and

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10-4 s-1 , Table 1. Ice temperatures were chosen within the order of in-situ ice temperatures, whereof the samples from R1-2013 were tested at -3.5°C and all other samples were tested at -10°C. The sample

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temperature was reached by storing the specimen at the certain temperature minimum 2 hours before

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testing. The results are presented in engineering stress and engineering strain. The non-linear behaviour of mixed ice under compression, as shown in Fig. 3, makes it difficult to

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determine an elastic modulus by mechanical tests. Exact values for an elastic modulus can only be

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obtained by dynamic methods utilizing flexural vibration or elastic wave propagation Otherwise the

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obtained strain modulus would never refer to the purely elastic behaviour of ice; since always some delayed elasticity from grain boundary sliding (Sinha, 1978) would affect the result. In literature the elastic modulus can be referred to as the effective modulus or initial tangent modulus. Common relationships used for engineering problems are the tangent and secant modulus in order to express the elastic behaviour of non-linear materials. The tangent modulus was referred to the maximum curvegradient, which was determined through a step-wise determination of the gradient of the stress-strain curve in phase II (Fig. 3). The secant modulus is defined as the ratio of the peak strength σP and the failure strain εP , where failure strain is subjected to the total strain recorded from the moment where load recordings >0. Uniaxial tensile tests were performed on samples from 2012. The test rig was the same as for the compression tests, but custom-made wedge-shaped restraints were developed to fix the specimen in

Journal Pre-proof the testing machine. The specimen got wedged when load was applied. The contact edges of the restraints were rounded to eliminate load concentrations. A concave shaped web (Fig. 4) with a smallest cross-section in the middle of the specimen was used so that the failure will occur in that area. Since the wedges are moving in the restraints until they are fixed and the specimen itself has no constant cross-section, no information on deformation of the ice was recorded. The tensile strength is calculated by dividing the maximum load with the sample cross-sectional area at failure location. In total 35 Specimen were tested at loading rates of 1 mm/s and 0.1 mm/s, see Table 2. The ice

Physical properties and ice texture

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4.1

Results

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temperature was -10°C for all tensile tests.

Data for generating salinity profiles from the level ice and from ridges have been collected both during

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field and laboratory work. Salinity profiles are presented in Fig. 5. The maximum depth which could be drilled by the 70 mm core drill was approximately 2 m. The salinities profiles from in-situ

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measurements are in good agreement with the laboratory measurements.

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From a study of the ice texture three predominant ice types within the consolidated part of pressure

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ridges were investigated which are illustrated and described in Fig. 6 and Table 3. The three main groups are granular, columnar and mixed ice. Mixed ice is a mixture of the two former ice types, which built mainly through deformation and refreezing of the ice cover. The position within the ridge profile is known for all specimens from 2012 and 2013, enabling the visualization of ice type distribution within each ridge profile (Fig. 7). In total 52% of all tested specimen consisted of randomly mixed ice referred to as type IIIB and 26% came from ice classified as IIIA. The middle part of the ridge cross-sections was clearly classified as mixed ice containing both type IIIA and IIIB. Only 4% of pure granular ice was found. The 18% proportion of columnar ice was mainly concentrated on the border areas of the ridge cross-sections, close to level ice and scattered sparely within the middle part of the keel. 4.2

Compressive strength for first-year ridges

Journal Pre-proof The results from uniaxial compressive tests are summarized in Tables 4 to 6. Table 4 specifies strength values for the ice types defined in Table 3. The average strength values and total porosities were listed for horizontal and vertical load direction separately and the ratio between vertical and horizontal compressive strength is given for each ice type. In Table 5 compressive strength and total porosity are summarized for different ice temperatures. The compressive strength measured for different nominal strain rates is shown in Table 6. Independent of load direction or ice type, maximum compressive strength was achieved at a nominal

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strain rate equal to 10-3 s-1 and decreased both for higher and lower strain rates. The strength decrease

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is remarkably 30% for mixed ice at a nominal strain rate of 10-4 s-1 , but only 10% for a nominal strain

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rate of 10-2 s-1 .

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The frequency of the uniformly distributed strength values obtained from all compression tests disregarding ice type, loading direction or strain rate are shown in Fig. 8. The mean values and

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standard deviations for all tested samples are equal to 5.0 MPa and 2.1 MPa at -10°C and 3.5 MPa and

4.3

Failure behavior

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0.6 MPa at -3.5°C.

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In the present study only ductile failures occurred for specimens tested at -3.5°C. In the case of ice

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temperatures of -10°C, all specimens failed in a brittle manner at nominal strain rates higher than 10·s-1 while for lower strain rates only ductile failure occurred. The specimens load tested at the nominal

strain rate of 10-3 s-1 and -10 °C showed both brittle and ductile failure and are presented in Table 7 and Table 8 for respective failure type. The salinity, ice density and sample numbers for respective load direction are added for further analysis. A higher compressive strength at ductile failure was observed for mixed and granular ice, whereas columnar and rafted ice was stronger at brittle failure. 4.4

Stress-strain characteristics for ice from first-year ridges

The complete load history of an ice sample under uniaxial compression can be illustrated by stressstrain diagrams. Within structural design it is well established to use the 95th percentile for strength data, meaning that only 5% of all samples have strength higher than the percentile value. P95-

Journal Pre-proof diagrams were generated representing the 95th percentile for respective load condition as presented in Fig. 9 to Fig. 12. The curves are generated by taking the 95th percentile of stress values at each strain values with 0.015 % strain -steps. The lines for the stress-strain curves only base on the experimental results and are not completely smooth. One reason is that if too few samples are tested within one load configuration already small differences between the stress-strain curves can lead to unevenness in the representative curve. The diagram in Fig. 9 shows a P95- diagram for mixed ice. The histograms show the distribution from all tested samples within that load condition resulting in a normal distribution for

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peak strength and residual strength at 1.5% strain and lognormal distribution for the failure strain.

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Significant values derived from the stress-strain diagrams, e.g. the peak strength σP (95%) and the

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corresponding strain value ε P (95%) for respective curve, are summarized in Tables 9 and 10. Since a

σ1.5(95%) at 1.5% strain is presented in Table 10.

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ductile material often has a significant residual strength after reaching the peak strength, the strength

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Calculated tangent moduli values are presented in Table 11 while the average values for secant moduli are shown in Table 12. The tangent modulus is plotted as a function of the total porosity in Fig. 13,

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where tangent moduli values for all specimens of respective ice type are located within the respective

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data region. A trend of dependency between tangent modulus and total porosity is visible for all ice

4.5

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types, but the dependency is differently strong. Tensile strength

The average tensile strength and material data for 33 specimens was 0.44 MPa with a standard deviation of 0.15 MPa. The strength values ranged from 0.14 MPa to 0.79 MPa. Tensile tests were performed at two different load velocities but from the results presented in Table 13 no obvious impact of load rate on ice strength was observed.

5 5.1

Analysis and Discussion Physical properties and ice structure

Journal Pre-proof The salinity profiles from the ridges do not show any characteristic trend, and values oscillate mainly between 3 psu and 6 psu (Fig. 5). Similar profiles were observed also by e.g. Høyland (2007). Ridge salinity profiles in the field were measured just beside the position of the cores taken for mechanical testing. This procedure enabled to control whether brine drainage during coring and transportation had a high impact on the final result. The in-situ salinity profile for R2-2013 was taken close to three different sample points (distance approximately 30 cm). For the upper 40 cm the salinity measured insitu is in some cases higher than the results from the laboratory, especially for cores S6 and S7.

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Therefore brine drainage has to be considered here, but other reasons can be that these two cores were

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taken one day later than core S3 and the sample for salinity field measurements. For R3-2013 the

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salinity values from laboratory and field tests are in good agreement indicating very little impact of the brine drainage on the results from laboratory testing. No negative effect from sample preparation, such

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as increased brine drainage in horizontal samples (Shafrova and Høyland, 2008 and Moslet, 2007) was

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observed.

The majority of the ice texture within pressure ridges can hardly be compared with that of undeformed

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level ice, so that existing classification systems for level ice (e.g. Michel, 1978 and Cherepanov, 1974)

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are not adequate. Table 3 shows the suggested classification for ice types within first-year pressure ridges, based on the findings from these studies. The ice texture within the consolidated part of

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pressure ridges is essential to study because the structure, shape and size of ice crystals have a great influence on the ice strength (Michel, 1978). Richter-Menge and Cox (1985) suggested a classification scheme for ice from multi-year ridges. Since their observations are close to the ones made here, the same classification table is used with some necessary adjustments. It is not clarified here whether there are major differences in the ice texture, but e.g. recrystallization, mechanical and meteorological impact can further influence the ice texture found within multiyear ridges. Granular and columnar ice types are identic to Richter-Menge and Cox (1985) and are also designated as type I and type II ice (Table 3). Type IIC, which corresponds to columnar freshwater ice (RichterMenge and Cox, 1985) was not found in this study and thus not taken care of.

Journal Pre-proof Richter-Menge and Cox (1985) described type III ice also as a mixture of type I and type II ice, but different characteristics of the ice textures were found here. This category was redefined according to our findings. Samples from rafted ice as a mixture of columnar and granular ice showed a stratified structure (see also Poplin and Wang, 1994) with each layer consisting of granular, randomly oriented columnar and sometimes oriented columnar ice is here classified as Type IIIA. Subcategories IIIA1 to IIIA3 determine the portion of granular and columnar ice respectively within the specimen. Another origin for this ice type can e.g. be the intersection between snow ice and columnar sea ice in the upper

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part of a sea ice cover. Brecciated ice, type IIIB, is assumed to be a product of the immense forces

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exerted during pressure ridge build-up. Broken ice pieces of different sizes were found within a

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refrozen mixture of snow-ice, slush and frazil ice (Richter-Menge and Cox, 1985). From Fig. 7 it can be concluded that the ice within the studied ridges contains mainly of ice types IIIA and IIIB, similar

Compressive strength for ice from first-year ridges

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to ridges presented by e.g. Leppäranta et al. (1995), Kankaanpää (1997) and Høyland (2007).

The results suggest that strength of ice from ridges is higher than from level ice in horizontal loading

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direction, assuming that the level ice texture is mainly granular or columnar. The total average strength

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of granular ice was 4.49 MPa and of columnar ice in horizontal loading direction was 4.07 MPa. Both

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values are lower than the average strength of mixed ice which equaled to 4.93 MPa. A similar conclusion was formulated by Høyland (2007) where σli V <σcl < σli H . Here σli V and σli H are the compressive strengths of level ice in horizontal and vertical direction and σcl denotes the compressive strength for ice from the consolidated layers. For the present study the ratio of vertical to horizontal ice strength for mixed ice types is between 0.95 and 1.12, which indicates isotropy of ice from the consolidated layer. Shafrova and Høyland (2008) studied vertical and horizontal compressive strength of ice from pressure ridges mainly in the field and obtained a strength ratio of 1.1 for the consolidated layer, which is close to the results of the present study. One exception is rafted ice (Type IIIA2 ) that contains high proportions of columnar ice and therefore shows a slight anisotropy in compressive strength with a strength ratio of 1.35. Høyland

Journal Pre-proof (2007) found similar values for ice from the consolidated layer and points out that a part of the samples were taken from rafted ice and thus contain more vertical than random or horizontal crystals. All ice types show a strong correlation of the compressive strength to the total porosity, Fig. 14 and Fig. 15. The average values for total porosity for all different load and ice configurations are given in Tables 4 to 6. It is an important property affecting compressive strength as shown in Timco and Frederking (1990) amongst others. The lowest strength and at the same time the highest total porosity was observed for specimens IIIA1 , Table 4. The total air volume, which was in average 12.3 % for

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Type IIIA1 ice, constitutes 87% of the total porosity. IIIA2 or IIIA3 ice had air volumes of only 4.8 %

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and 7.0 % respectively. Porous zones can be expected within the granular intersections between the

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rafted ice sheets which occur to a highest proportion in type IIIA 1 .Poplin and Wang (1994) also found that rafted ice had partly very low density due to porous zones between the rafted ice layers.

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An equation which relates the vertical and horizontal compressive strengths of columnar sea ice to the

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(1)

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    c  A  1  t  B 

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total porosity was proposed by Moslet (2007), see Eq. 1.

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Both A and B are empirical factors that have to be adjusted for the respective load condition. The

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constant B expresses the maximum total porosity at which ice strength approaches zero, which was 0.7 in Moslet (2007). Timco and Frederking (1990) suggested a maximum total porosity of 0.27 and 0.20 for horizontally and vertically loaded columnar ice. Even though none of the columnar ice samples had higher total porosity than 0.15, in the case of mixed ice the compressive strength was still 0.6 MPa when total porosity was as high as 0.44. Fig. 14 shows that the maximum strength of vertical columnar ice may not be described very well by Moslet’s (2007) approach especially when it comes to total porosities >0.05; but the number of samples here and range of porosity are too low for a strong statement. Since mixed ice shows approximately isotropic behavior, the compressive strength at -10ºC is expressed by choosing constants, which are valid for both load directions. In order to fit Eq. 1 to the present data with help of Matlab, the 5th and 95th percentile of strength was chosen for respective 0.005

Journal Pre-proof - strain interval. The best fit for both percentiles with a coefficient of determination R2 =0.78 was obtained when B is kept at 0.7 and A95% and A5% are equal to 15 and 5.35, respectively (Fig. 16). A fit of Eq. 1 to the average strength values would result in A=9.85. Shafrova and Høyland (2008) also used Eq. 1 for relating compressive strength of ice from ridges to total porosity. A fit to maximum strength values separately for each load direction yields to constant A equal to 9.1 and 7 for vertical and horizontal strength respectively (Fig. 16). The non-isotropic behavior of the ice tested by Shafrova and Høyland (2008) was discussed earlier. Shafrova and Høyland (2008) performed in situ-tests on ice as

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warm as -2°C with an average ice strength in the order of 2 MPa, which explains the lower values for

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A compared to this study because Eq. 1 doesn’t regard the temperature dependency of ice strength.

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Table 5 shows that the mixed samples tested at -10°C had higher strength (in average 30%) compared to samples tested at -3.5°C. Discrepancies to other studies also arise from different test conditions or

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from the highly non-homogenous ice structures that can be found within ridges. A classification

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system for the tested ice samples is thus very useful. It gives valuable information of ice types within ridges and enables a better comparison of results from different studies, but requires a time-consuming

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ice texture characterization of each specimen. Regarding Eq. 1, it can be concluded that the factor A is

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amongst others dependent on ice temperature and load directions. According to this and other above mentioned studies B=0.7 seems to be a good approximation for mixed ice, independent of ice type,

5.3

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loading direction, ice temperature and strain rate (Fig. 17). Stress-strain characteristics and failure behavior

The characteristics for all stress-strain curves (Fig. 9 to Fig. 12) in this study are similar with a prefailure part of non-linear nature of stress-strain behavior. Three different phases in the load history before peak strength are demonstrated in Fig. 3. An initial concave curvature (Phase I) directed upwards is caused by the closing of micro-cracks and pores, but can also be related to imperfections in specimen preparation such as not completely parallel end surfaces. The following inclination of the curve (Phase II) is of linear nature and coherent to elastic behavior. Deformation after reaching the limit of the direct proportional part goes along with elastic and plastic strain (Phase III) until the peak strength is reached. This pre-failure curve is similar for both brittle and ductile failure however the

Journal Pre-proof brittle specimen failed at maximum strength. The post-failure behavior for ductile samples is characterized by a strain-softening branch, accompanied by the coalescence of micro-cracks and geometrical changes. Ductile failure effectuates residual ice strength and thus continuing load action. Høyland et al. (2000) presented similar stress-strain diagrams for ice from first-year ridges in the Baltic Sea. For the investigated ice specimens the failure behaviour was highly influenced by ice temperature, strain rate and ice texture. All specimens tested at -3.5°C showed ductile behaviour. All specimens

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tested at nominal strain rates <10-3 s-1 failed in a ductile manner, whereas those tested at nominal strain

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rates >10-3 s-1 failed in brittle manner. Schulson (1990) showed that there exists a strain rate remarking

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the transition between brittle and ductile behaviour at which compressive strength reaches a maximum. The transition zone here for changing failure behaviour and for maximum compressive strength lies

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around a nominal strain rate of 10-3 s-1 for mixed ice (Fig. 18).

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For ice types that contain columnar ice, the failure behaviour is also affected by load direction (Table 7 and Table 8). 90% of the samples classified as IIA, IIB, IIIA1 and IIIA2 that were loaded in the

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direction of crystal elongation failed in a brittle manner, but only 16% of the horizontally loaded

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specimen. For ice types IIIA3, IIIB1 and IIIB2 no trend concerning load direction was observed, but generally less than 20% of these samples showed brittle failure. Thus ductile failure behavior appeared

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to be dominant for mixed ice types for loading at a nominal strain rate of 10-3 s-1 . Furthermore, the strength for all ice groups with non-oriented ice crystals (Types I, IIIA 3 ,IIIB) was in average higher when ductile failure occurred. This is in contrary to Høyland (2007) and Moslet (2007) who generally found higher brittle than ductile strength. The impact of air and brine volume on the failure behaviour of ice was analysed without finding any noticeable correlations. Høyland (2007) suggested that the brine volume might influence the failure mode. In the present study, both average air volume and average brine volume were equal for specimen with brittle failure and ductile failure with νb =0.02 and νa=0.05. Moslet (2007) suggested the maximum air volume for brittle failure to occur is 0.07. On the contrary a number of samples from present tests showed brittle failure while had significantly higher air volumes with a maximum value

Journal Pre-proof found to be 0.38. The average air volume of all brittle specimen with νa>0.07 was 0.13 with 0.06 standard variation. The residual strength of ductile ice samples at 1.5% strain is approximately 40% to 70% of the peak strength, Table 9, varying with different ice types and load conditions. The residual ice strength after reaching the peak load can become significant for slow ice movements, especially on wide structures. Ice masses can accumulate on structures and increase the load gradually. Here the residual strength is not given for a strain value > 1.5% because the specimens showed high deformations for higher strains

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which excluded assumption of a constant sample area. Further when the samples deform at the contact

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area to the test rig, other stress situations than simple uniaxial compression will emerge, e.g. lateral

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restraint at the end plates will gain higher impact. The residual strength to the peak strength ratio σ1.5 /σP was found for the columnar ice vertically loaded to be 0.38 and for columnar ice loaded

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horizontally to the crystal elongation to be 0.65. Consequently, even though the peak strength is higher

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in vertical direction columnar ice will get stronger in horizontal direction for slow, long-term loading scenarios. The tendency for σ1.5 /σP regarding ice type and loading direction at equal strain rates is

al

σ1.5 /σP (IIH )>σ1.5 /σP (I,III)>σ1.5 /σP (IIV). The ratio σ1.5 /σP was unaffected by ice temperatures and was

rn

increasing for decreasing strain rates, resulting in high residual strength under slow loading. A similar

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trend was observed by Cox et al. (1984).

The secant modulus is a measure for the ductility of the material, expressing the strain reached at maximum strength. The secant modulus increased with increasing strain rates for ice types IIIA and IIIB, Table 12. This finding is in line with Poplin and Wang (1994) who showed clear increase for increasing strain rates, Table 14, despite the fact that trend was more distinct than it is for mixed ice and that values for the secant modulus determined by Poplin and Wang (1994) were slightly higher. The former can be explained by the more homogeneous ice as their samples were taken from shore fast and rafted ice. The latter differences can be explained by the difference in testing method, because strain was measured directly on the sample’s midsection, leading to lower strain values because the real sample strain is measured without any impact from machine stiffness or constraint effects. Further analysis of the data showed a decrease of the secant modulus with increasing temperatures and an

Journal Pre-proof impact of the failure mode because higher values were obtained for brittle failures than for ductile failures under the same conditions. Considering that the strain until peak stress consists of elastic and plastic strain, the results for the secant modulus are reasonable. The plastic strain part is enhanced, e.g. the secant modulus decreases, for ductile failure behavior, slower loading rates and increasing ice temperatures. A clear relation between tangent modulus and total porosity is visible in Fig. 13. This relationship is not equally strong for all ice types and load directions because the assigned regions for different

f

tangent moduli values have different inclinations. The tangent modulus was highest for columnar ice

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loaded vertically, which indicates a high rigidity. Mixed ice had higher tangent moduli than granular

pr

ice or columnar ice loaded in horizontal direction. Samples tested at -3.5 °C are situated in the lower part of the region that illustrates the tangent moduli for samples tested at -10 °C, which demonstrates a

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temperature dependency (see also Gold,1958). The average values of tangent moduli regarding

Pr

different ice types and strain rates are summarised in Table 11. The magnitude of these values is in the

5.4

Tensile strength

al

same range as presented by Moslet (2007) and Høyland et al. (2009) for first-year sea ice.

rn

It is unique to present results for direct tensile tests on ice from the consolidated part of first-year

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ridges. The sample shape for the test method presented in section 3 is generally more slender than the cylindrical samples commonly used for tensile tests. Schwarz et al. (1981) suggest that tensile strength on small-scale specimens is not affected by sample size but rather by the ratio of sample size to crystal size. The experimental scatter on ice strength can be reduced when this ratio is above 15 to 20. Since the studied ice is a highly non-homogenous material it is not assured that the requirement on the minimum number of grains is fulfilled for all specimens. Most of the samples contained a lot of finegrained material, Fig. 19, but columnar grains in the range of 0.5 cm to 1 cm are also common. All tested specimens here were classified as type IIIB ice. Compared to other test methods the strain-rate could not be determined and neither values on strain because of the non-linear cross-section. Yet the rounded sample shape was necessary to reduce load concentrations and breakage at the edges of the clamping. Only two out of 35 tests failed because of breakage within the wedge-shaped clamping of

Journal Pre-proof the specimen. All other specimens cracked between the clamping and 15 samples broke in the thinnest part of the specimens. Tensile strength values were between 0.1 MPa and 0.8 MPa (Table 13). The same range of strength values was given in literature for horizontal tensile strength of columnar sea ice (Timco and Weeks, 2010). Cox et al. (1985) tested 36 samples of mixed ice from multi-year pressure ridges in uniaxial tension, see Table 15. Strain rate or temperature variations don’t seem to affect tensile strength. The dependency between brine volume and tensile strength for both data sets is shown in Fig. 20, clearly

f

showing that strength is decreasing with increasing brine volume and that multi-year ice is stronger

oo

than first-year ice samples for same brine volumes.

pr

Dykins (1970) presented relationships between brine volume and vertical and horizontal tensile

 b 

0.311 



 b 

 th  0.821 

0.141 

(3)

rn



(2)

Pr



al



 tv  1.541 

e-

strength (Eq. 2 and Eq. 3) of columnar sea ice.

Strength data versus brine volume (Fig. 20) show a similar correlation than Eq. 3 but the presented

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data points are too few and have a too large scatter for a reasonable data fit. It is obvious that brine volume does affect tensile strength especially for the horizontally ice from the present study. A higher impact of brine volume on the horizontal tensile strength for columnar ice can be explained by the brine pocket distribution, which commonly occurs along the basal planes and thus weakens the ice columns when loaded perpendicular to crystal elongation. Along the columns, brine channel extension and brine migration are not as extensive and thus the strength along columns is less affected by brine (Dykins, 1970). Weissenberger et al. (1992) showed that the brine channels with in granular ice have no prevalent orientation, which is in agreement with isotropic behavior of granular sea ice. When it comes to mixed ice, brine channels are expected to have a similar behavior to that of granular ice. Brine channels should not show any preferred orientation, which makes the influence of brine volume equally relevant for either load direction.

Journal Pre-proof A reason for the strength differences between the multi-year ice samples and the results in this study can be that Cox et al. (1985) loaded the samples vertically. This can lead to higher strength values as they mentioned that their samples contained a big portion of vertically elongated columnar grains. Johnston (2014) reported multi-year ice to be much stronger than first-year ice and less affected by brine volume, which can both be confirmed by the data presented in Fig. 20. The tensile strength vs. total porosity plot (Fig. 21) of all data points does not give any evidence for a correlation. Timco and Weeks (2010) in contrary presented Eq. 4, for horizontal strength of columnar

 th  4.278 t0.6455

oo

f

sea ice, which clearly fits to their evaluated data with a correlation coefficient r 2 of 0.72. (4)

pr

The data presented in Fig. 21 are both underestimated by Eq. 4 and don’t correlate, consequently Eq. 4

e-

does not give any suitable fit to the presented values. This supports the findings from earlier studies

Pr

regarding impact of brine volume on tensile strength, which means that brine channels have a much

Conclusions

rn

6

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higher impact on the tensile strength than only air-filled voids.

Ice properties from the consolidated layer of first-year ice ridges have been studies from ridges

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investigated during the three winters from 2011 to 2013 (Bonath et al. 2018). In total 410 specimen were tested in uniaxial compression and uniaxial tensile tests were conducted on 35 specimen, using a new testing method. A detailed study on the ice texture of the ice cores and specimen resulted in a classification table of ice from first-year ridges. The categorization of the specimen according to the table was a useful tool to interpret the large strength variations within the consolidated layer. 

First-year ice ridges are mainly build up from rafted (26%) and brecciated ice (52%). Those ice classes were described as mixed ice, containing both granular and columnar ice with mainly randomly oriented ice crystals having any size and shape. Pure columnar (18%) was mainly found in the top regions of the ridges and pure granular ice was very rare (4%).

Journal Pre-proof 

The random ice structure in the consolidated layer is decisive for the approximate isotropic strength behavior of mixed ice. The highest strength anisotropy of mixed ice in compression has type IIIA2 with a vertical to horizontal strength ratio equal to 1.3. The average strength ratio of all other mixed ice samples is 1.0. The mean strength of mixed ice is higher than of granular ice or columnar ice in horizontal direction, but lower than columnar ice in vertical direction. The mean ice strength for mixed ice tested at -3.5°C is 30% lower than at -10°C (3.6 MPa and 4.9 MPa, respectively). A non-linear pre-failure part of all stress-strain diagrams for mixed ice run through three

f



oo

phases; the curves started with an initial concave upwards curve, followed by a steep linear

pr

part and flattened out rapidly towards peak strength. At peak strength the ice either breaks brittle or is accompanied by post-failure strain softening. 25% of all samples tested at a

e-

nominal strain rate of 10-3 s-1 failed in a brittle manner. The average strength for most of the

Pr

mixed ice types is higher for ductile specimens than for brittle ones, except for type IIIA2 containing vertically elongated columnar ice. Ductile failure occurred for all specimens tested

al

at strain rate lower than 10-3 s-1 and all specimens tested at ice temperature -3.5°C. Strain rates



rn

higher than 10-3 s-1 provoked brittle failure. The residual strength to the peak strength ratio, σ1.5 /σP , depends on strain rate, ice texture and

Jo u

for anisotropic ice also on load direction. For ductile ice specimen the residual strength at 1.5% strain and at strain rate -10-4 s-1 was 73% of the peak strength and only 53% at strain rate 10-3 s-1 . Thus the ratio σ1.5 /σP is increasing for decreasing strain rates and σ1.5 / σP (IIH )> σ1.5 / σP (I och III)> σ1.5 / σP (IIV). 

The tensile strength of ice from the consolidated layer was measured by a novel method resulting in values between 0.14 MPa and 0.79 MPa. The mean value was 0.42 MPa at 1.0 mm/s loading rate and 0.45 MPa at 0.1 mm/s. Strength differences are not caused by different loading rates, but due to differences in brine volume, which was in a range of 0 to 40 ppt in the present study, as tensile strength shows a strong relationship to brine volume.

Journal Pre-proof For defining ice strength of mixed ice and finding a reliable material model for mixed ice, tests for a wider range of test parameters would be of advance. The tensile strength and tensile behavior of mixed ice requires a lot more attention.

Acknowledgements This work was supported by the Research Council of Norway project number 195153. The Coldtech group attending the field work, the Crew on KV Svalbard and Assoc. Prof. Lars Bernspång at Luleå

oo

f

University of Technology are thanked for their support. Two anonymous reviewers are thanked for

Jo u

rn

al

Pr

e-

pr

their help to improve the manuscript.

Journal Pre-proof

List of Symbols Description/Definition

A

Parameter

B

Parameter

Esec

Secant modulus

Eini

Initial secant modulus

Etan

Tangent modulus

S

Salinity

T

Temperature



Strain

𝜀̇

Strain rate

𝜀̇𝑛𝑜𝑚

Nominal strain rate

 P (95%)

Failure strain at 95th percentile for peak strength values

νa

Air volume

νb

Brine volume

νt

Total porosity

νt,h

Total porosity of horizontally loaded samples

νt,v

Total porosity of vertically loaded samples

ρi

Ice density

σc

Compressive strength

σcl

Compressive strength of the consolidated layer

σch

Horizontal compressive strength

σcv

Vertical compressive strength

σli H

Horizontal compressive strength of level ice

σli V

Vertical compressive strength of level ice

σP ,

Peak compressive strength

Jo u

rn

al

Pr

e-

pr

oo

f

Symbol

Journal Pre-proof 95th percentile of peak strength values

σt,

Tensile strength

σth,

Tensile strength in horizontal load direction

σt,min

Minimum tensile strength

σt,max

Maximum tensile strength

σtv,

Tensile strength in vertical load direction

σ1.5

Compressive strength at 1.5% of strain

σ1.5(95%)

95th percentile of residual strength values at 1.5% of strain

#

Number of samples

#h

Number of samples loaded in horizontal direction

#h+v

Number of samples loaded in horizontal and number of samples loaded in vertical direction

#v

Number of samples loaded in vertical direction

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rn

al

Pr

e-

pr

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f

σP (95%)

Journal Pre-proof

References [1]

Bjerkås, M. ( 2006). Ice actions on offshore structures. Doctoral thesis. Norwegian University of Science and Technology, NTNU, Trondheim, Norway, 139-158.

[2]

Bonath, V., Petrich, C., Sand, B., Fransson, L., & Cwirzen, A. (2018). Morphology, internal structure and formation of ice ridges in the sea around Svalbard. Cold Regions Science and Technology, 155, 263-279.

[3]

Cherepanov, N.V. (1974). Classification of ice of natural water bodies. Oceans '74, IEEE

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f

International Conference on Engineering in the Ocean Environment. Halifax, N.S., Canada. Vol. 1, 97–101.

Cox, G., & Weeks, W. F. (1983). Equations for determining the gas and brine volumes in seaice samples. J.Glaciol, 29(102), 306-303.

Cox, G., & Richter-Menge, J. (1985). Tensile strength of multi-year pressure ridge sea ice

e-

[5]

pr

[4]

[6]

Pr

samples. Journal of Energy Resources Technology, 107(3), 375-380. Cox, G. F. N., Richter-Menge, J. A., Weeks, W. F., Mellor, M., Bosworth, H. W., Durell, G.,

al

and Perron, N. (1985). Mechanical Properties of Multi-Year Sea Ice. Phase II: Test Results.

Cox, G. F., Richter-Menge, J. A., Weeks, W. F., Mellor, M., & Bosworth, H. (1984).

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[7]

rn

U.S. Army Cold Regions Research and Engineering Laboratory. CRREL Report 85-16.

Mechanical Properties of Multi-Year Sea Ice. Phase I. U.S. Army Cold Regions Research and Engineering Laboratory. CRREL Report 84-9. [8]

Dykins, J. E. (1970). Ice Engineering-Tensile Properties of Sea Ice Grown in a Confined System. Naval Civil Engineering Lab., Port Hueneme, CA. No. NCEL-TR-689.

[9]

Gold, L. W. (1958). Some observations on the dependence of strain on stress for ice. Canadian Journal of Physics, 36(10), 1265-1275.

[10] Høyland, K. (2007). Morphology and small-scale strength of ridges in the north-western Barents sea. Cold Regions Science and Technology, 48(3), 169-187.

Journal Pre-proof [11] Høyland, K. V., Kjestveit, G., Heinonen, J., Määttänen, M. (2000). LOLEIF ridge experiments at Marjanimi; The size and strength of the consolidated layer. In: Proc. of the 15th Int. Symp. on Ice (IAHR), Gdansk, Poland. 1: pp. 45-52. [12] Kankaanpää, P. (1997). Distribution, morphology and structure of sea ice pressure ridges in the Baltic Sea. Fennia - International Journal of Geography 175(2), 139-240. [13] Kuehn, G., Lee, F. W., Nixon, W., & Schulson, E. (1990). The structure and tensile behavior of first-year sea ice and laboratory-grown saline. Journal of Offshore Mechanics and Arctic

f

Engineering, 112, 357.

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[14] Leppäranta, M., Lensu, M., Kosloff, P., & Veitch, B. (1995). The life story of a first-year sea

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ice ridge. Cold Regions Science and Technology, 23(3), 279-290. [15] Michel, B., 1978. Ice mechanics. Laval University Press.

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[16] Moslet, P. O. (2007). Field testing of uniaxial compression strength of columnar sea ice. Cold

Pr

Regions Science and Technology, 48(1), 1-14.

[17] Poplin, J., & Wang, A. (1994). Mechanical properties of rafted annual sea ice. Cold Regions

al

Science and Technology, 23(1), 41-67.

rn

[18] Richter-Menge, J., & Cox, G. (1985). A preliminary examination of the effect of structure on the compressive strength of ice samples from multi-year pressure ridges. Journal of Energy

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Resources Technology, 107(1), 99-102. [19] Richter-Menge, J., & Jones, K. (1993). The tensile strength of first-year sea ice. Journal of Glaciology, 39(133), 609-618. [20] Sammonds, P., Murrell, S., & Rist, M. (1998). Fracture of multiyear sea ice. Journal of Geophysical Research, 103(C10), 21795-21,815. [21] Schulson, E. M. (1990). The brittle compressive fracture of ice. Acta Metallurgica Et Materialia, 38(10), 1963-1976. [22] Schwarz, J., Frederking, R., Gavrillo, V., Petrov, I., Hirayama, K., Mellor, M., et al. (1981). Standardized testing methods for measuring mechanical properties of ice. Cold Regions Science and Technology, 4(3), 245-253.

Journal Pre-proof [23] Shafrova, S., & Høyland, K. V. (2008). Morphology and 2D spatial strength distribution in two arctic first-year sea ice ridges. Cold Regions Science and Technology, 51(1), 38-55. [24] Sinha, N. K. (1978). Short-term rheology of polycrystalline ice. Journal of Glaciology, 21(85), 457-474. [25] Strub-Klein, L., & Sudom, D. (2012). A comprehensive analysis of the morphology of firstyear sea ice ridges. Cold Regions Science and Technology, 82(0), 94-109. [26] Timco, G., & Burden, R. (1997). An analysis of the shapes of sea ice ridges. Cold Regions

f

Science and Technology, 25(1), 65-77.

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[27] Timco, G., & Frederking, R. (1990). Compressive strength of sea ice sheets. Cold Regions

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Science and Technology, 17(3), 227-240.

[28] Timco, G., & Weeks, W. (2010). A review of the engineering properties of sea ice. Cold

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Regions Science and Technology, 60(2), 107-129.

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[29] Weissenberger, J., Dieckmann, G., Gradinger, R., & Spindler, M. (1992). Sea ice: A cast technique to examine and analyze brine pockets and channel structure. Limnology and

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rn

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Oceanography, 37(1), 179-183.

Journal Pre-proof

Tables 𝜀̇(s -1 ) -2

10 10-3 5·10-4 10-4

T=-3.5°C #v 9 -

T=-10°C

#h 32 -

#v 16 102 16

#h 16 230 15 15

oo

f

Table 1. Testing scheme f or compression tests.

Loading rate

Pr

Table 2. Testing scheme f or tensile tests.

pr

0.1(mm/s) 25

e-

#h

1 (mm/s) 10

Designation

Characterization

Granular

I

Isometric, regular crystals (e.g. freezing of water saturated snow)

Columnar

II

Elongated ice crystals with a vertical crystal growth

IIA

c-axis normal to growth d irection, ice crystals are elongated with pris matic habit

Mixed

rn

c-axis randomly oriented (e.g. transition zone), ice crystals are elongated with pyramidal habit

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IIB

al

Ice type

III

Mixture of types I and II, refrozen

IIIA

Horizontal stratification of granular and columnar ice layers (e.g. rafted ice)

IIIA 1 IIIA 2 IIIA 3 IIIB

a) mainly granular ice b) mainly columnar ice c) granular/columnar 60/40 to 40/60 Angular or rounded ice frag ments of d ifferent sizes are refro zen within a granular ice mass

IIIB1 IIIB2

Refrozen ice mass containing small ice fragments (< 1cm) Refrozen ice mass containing larger broken ice pieces (> 1cm)

Table 3 Structural classification of ice f rom f irst-year pressure ridges.

Journal Pre-proof Ice type I IIA IIB

Number of specimen #h #v #h+v 15 15 33 24 57 11 11

#p(%) 4.0 15.2 2.9

Avg. compressive strength and avg. total porosity σch (MPa) νt,h (%) σcv (MPa) νt,v (%) 4.49 7.1 4.22 5.0 8.90 2.5 3.62 7.1 -

σcv / σch (-) 2.11 -

IIIA 1 IIIA 2 IIIA 3

19 12 13

3 26 24

22 38 37

5.9 10.2 9.9

3.31 4.63 4.30

13.6 6.9 8.7

3.49 6.22 4.08

16.0 7.1 9.8

1.05 1.35 0.95

IIIB1 IIIB2

75 53

24 18

99 71

30.2 21.7

4.96 4.91

7.7 6.2

5.20 5.50

7.2 5.4

1.05 1.12

pr

Vertical load  cv  stdev (MPa) 8.90±3.31 5.35±2.00 4.00±1.13

Pr

e-

#h (-) 15 41 167 21

#h (-)

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Temperature: -10°C Horizontal load Ice type  ch  stdev t (MPa) (%) I 4.49±1.99 7.1±3.3 II 4.16±1.17 5.2±2.0 III 4.71±1.56 7.6±6.3 unknown 4.60±1.01 7.3±3.4 Temperature: -3.5°C Horizontal load Ice type  ch  stdev t (MPa) (%) II 2.83±0.12 8.9±1.1 III 3.51±0.63 7.9±1.6

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f

Table 4 Overview on number of horizontal and vertical samples (#h, #v, #h+v ), the percentage of the total number of specimen (#p), average compressive strength (σ cv , σ ch ), average total porosity (νt ,h , νt ,v ) for respective loading direction and the ratio between vertical and horizontal compressive strength (σ c v /σ c h ) f or different ice types.

3 29

Vertical load  cv  stdev (MPa) 3.74±0.39

Ratio  cv  ch  

t (%) 2.5±1.1 7.6±4.1 8.9±4.8

#v (-) 24 86 15

t

#v (-)

Ratio  cv  ch  

9

1.06

(%) 9.2±1.4

2.14 1.14 0.87

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Table 5 Compressive strength (σ c v, σc h ), total porosity (νt ) and number of specimen for vertical and horizontal load direction and the ratio between vertical and horizontal compressive strength (σ cv /σ ch ) for different ice types and testing temperatures of -10°C and 3.5°C.

Journal Pre-proof

#h (-) 16

#h (-) 15 44 154 17

#v (-)

Ratio  cv  ch  

3 13

1.11

Vertical load  cv  stdev (MPa) 9.44±2.77 5.44±2.02 4.00±1.13

t (%) 4.4±1.1 8.5±4.0 8.9±4.8

#v (-)

Ratio  cv  ch  

18 69 15

2.32 1.16 0.84

Vertical load  cv  stdev (MPa) -

t (%) -

#v (-)

Ratio  cv  ch  

-

-

t (%) 5.7±0.8 6.7±4.3

#v (-)

Ratio  cv  ch  

3 13

1.13

pr

11 4

Vertical load  cv  stdev (MPa) 7.05±2.29 3.83±1.23

e-

#h (-)

t (%) 5.3±1.3 6.7±4.5

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#h (-)

Vertical load  cv  stdev (MPa) 7.51±6.70 4.80±1.74

f

Nominal strain rate: 10 -2 (1/s) Horizontal load Ice type  ch  stdev t (MPa) (%) II III 4.34±1.53 6.3±3.0 Nominal strain rate: 10 -3 (1/s) Horizontal load Ice type  ch  stdev t (MPa) (%) I 4.49±2.00 7.1±3.3 II 4.07±1.18 5.5±2.2 III 4.68±1.57 8.0±6.4 unknown 4.77±0.97 7.0±3.3 Nominal strain rate: 5·10 -4 (1/s) Horizontal load Ice type  ch  stdev t (MPa) (%) III 4.30±1.11 6.2±3.4 unknown 3.82±0.86 8.9±3.8 Strain rate: 10 -4 (1/s) Horizontal load Ice type  ch  stdev t (MPa) (%) II III 3.40±0.64 6.3±1.8

15

Ice type

#h

#v

σc

rn

#h+v

al

Pr

Table 6 Compressive strength (σ c v, σc h ), total porosity (νt ) and number of specimen for vertical and horizontal load direction and the ratio between vertical and horizontal compressive strength (σ c v /σ c h ) f or different ice types and nominal strain rates

stdev

S

ρi

νt 3

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(-) (-) (-) (MPa) (MPa) (psu) (kg/(m )) (%) I 2 2 0 2.41 1.2 4.74 849 10.5 IIA 17 3 14 7.69 3.3 4.24 901 4.7 IIB 7 3 4 7.87 5.3 4.15 887 6.2 IIIA1 3 1 2 3.66 0.6 5.84 896 6.3 IIIA2 19 1 18 6.46 1.8 4.51 873 7.9 IIIA3 4 1 3 4.38 3.1 2.70 826 11.7 IIIB1 11 10 1 3.68 1.7 2.28 881 5.5 IIIB2 9 4 5 4.10 1.3 4.28 874 7.5 unknown 12 0 12 4.17 1.0 3.31 872 7.0 Table 7. The number of horizontal and vertical specimen and average values for compressive strength (σ c) with standard deviation (stdev), salinity (S), density (ρ) and total porosity(νt ) for ice samples with brittle failure behavior , tested at -10°C and a strain rate of 10 - 3 ·s - 1 .

Journal Pre-proof #h+v

#h

#v

σc

stdev

ρi (kg/(m3 ))

S

Ice type

νt,

T=-10°C 𝜖𝑛𝑜𝑚 =10-3 s-1

 P (95%) (MPa)

 P (95%) (%)

 1.5(95%) (MPa)

 P (95%) (MPa)

I II IIIA

9.60(V) 5.64 4.09 (*5.64)

0.65(V) 0.49 0.53 (*0.44)

3.64(V) 3.20

 P (95%) (%)

 1.5(95%) (MPa)

7.54 5.64(H) 6.49

0.58 0.60(H) 0.37

3.65 3.67(H) 3.29

2.92(H) 5.50

0.37(H) 0.48

1.83(H) 2.16

6.22

0.54

3.32

4.13

0.42

2.20

Pr

2.99 (*3.08)

 1.5(95%)  P (95%) (MPa) (MPa)

al

IIIB

T=-3.5°C 𝜖𝑛𝑜𝑚 =10-3 s-1

 P (95%) (%)

e-

Type

pr

T=-10°C 𝜖𝑛𝑜𝑚 =10-4 s-1 (*5·10-4 s-1 )

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f

(-) (-) (-) (MPa) (MPa) (psu) (%) I 13 13 0 4.81 1.9 4.46 884 6.6 IIA 29 29 0 4.41 1.0 4.22 900 4.8 IIB 6 6 0 4.45 1.1 4.11 893 5.5 IIIA1 4 3 1 2.46 2.0 2.06 664 28.6 IIIA2 14 11 3 5.46 2.0 4.55 884 6.7 IIIA3 13 6 6 4.93 1.0 3.99 857 9.2 IIIB1 67 53 14 5.59 1.6 3.84 873 7.4 IIIB2 40 33 7 5.34 1.3 3.43 879 6.5 unknown 20 17 3 4.44 1.2 4.11 866 8.3 Table 8. The number of horizontal and vertical specimen and average values for compressive strength (σ c ) with standard deviation (stdev), salinity (S), density (ρ i ) and total porosity(νt ) for ice samples with ductile failure behavior, tested at -10°C and a strain rate of 10 - 3 ·s- 1 .

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Table 9 The 95 percentile values for peak stress (σP ), failure strain (εP ) and residual stress (σ 1 .5 ) at 1.5 % strain for ductile ice samples. The indices (H) and (V)mean that the value contains either only horizontally or only vertically loaded samples.

T=-10°C 𝜖𝑛𝑜𝑚 =10-3 s -1

Type

 P (95%) (MPa)

IIH IIV IIIA IIIB

3.54 13.72 8.63 8.22

 P (95%) (%)

T=-10°C 𝜖𝑛𝑜𝑚 =10-2 s -1

 P (95%)

 P (95%) (%)

(MPa)

0.46 0.80 0.52 0.64

15.26 5.22 8.08

0.80 0.40 0.60

Table 10 The 95 percentile values for peak stress (σ P ) and failure strain (εP ) for brittle ice samples.

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Type I IIV IIH IIIA IIIB

𝜖𝑛𝑜𝑚 =10-4 s -1 T=-10°C Etan (GPa) stdv (GPa) 4.87 2.87 3.03

𝜖𝑛𝑜𝑚 =10-3 s -1 T=-10°C Etan (GPa) stdv (GPa)

0.60 0.54 0.62

3.19 5.43 2.64 3.09 2.13

𝜖𝑛𝑜𝑚 =10-3 s -1 T=-3.5°C Etan (GPa) stdv (GPa)

1.32 1.09 0.69 1.06 0.77

2.43 2.51 2.16

𝜖𝑛𝑜𝑚 =10-2 s -1 T=-10°C Etan (GPa) stdv (GPa)

1.13 0.65

3.34 3.49 4.32

0.54

3.68 1.09 1.21

Table 11 Average tangent moduli (Et an ) with standard deviation in GPa for different ice types, different nominal strain rates (𝜖𝑛𝑜𝑚 ) and ice temperatures (T) .

0.10 0.29 0.20

1.46 3.24 1.16 1.89 1.31

f

𝜖𝑛𝑜𝑚 =10-2 s -1 T=-10°C Esec stdv (GPa) (GPa)

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1.83 1.11 1.02

𝜖𝑛𝑜𝑚 =10-3 s -1 T=-3.5°C Esec (GPa) stdv (GPa)

0.58 0.89 0.45 1.00 0.36

0.91 1.34 1.06

0.08 0.26 0.24

2.23 2.02 2.31

2.20 -

0.60 0.58

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I IIV IIH IIIA IIIB

𝜖𝑛𝑜𝑚 =10-3 s -1 T=-10°C Esec (GPa) stdv (GPa)

pr

Type

𝜖𝑛𝑜𝑚 =10-4 s -1 T=-10°C Esec (GPa) stdv (GPa)

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Table 12 Average secant moduli (Es e c) with standard deviation in GPa for different ice types, different nominal strain rates (𝜖𝑛𝑜𝑚 ) and ice temperatures (T) .

 i  stdev

 t , min

 t , max

885±17

νb (%) 1.3

νa (%) 2.8

νt (%) 4.1

0.45±0.15

4.9±0.9

890±12

2.6

3.7

6.3

0.42±0.15

0.14

0.67

3.2±2.0

886±16

1.7

3.2

4.8

0.44±0.15

0.14

0.79

Loading rate:

# (-)

S±stdev (psu)

(kg/m )

0.1 mm/s

23

2.5±1.9

1.0 mm/s

10

All

33

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al

3

 t  stdev

(MPa)

(MPa) (MPa) 0.16 0.79

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Table 13 . Average values for salinity (S), ice density ( ρi ), brine volume (νb ), air volume (νa ), total porosity (ν t ) and tensile strength (σ t ) and the minimum and maximum tensile strength (σ t ,m i n ,σ t,m ax ) of ice samples f rom f irst-year ice ridges.

T

(°C) Landfast ice Horizontal Vertical Rafted Ice Horizontal Vertical

𝜀̇=10-3 s -1 Esec Eini (GPa) (GPa)

(°C)

𝜀̇=10-4 s -1 Esec (GPa)

Eini (GPa)

T

(°C)

𝜀̇=10-5 s -1 Esec (GPa)

Eini (GPa)

T

-3.4 -3.5

2.17 5.34

5.78 8.42

-3.6 -2.6

0.84 3.42

3.07 6.96

-3.5 -3.2

0.23 1.92

2.51 5.9

-2.7

2.15

5.90

-3.1 -2.86

0.81 1.61

3.39 4.58

-2.9

0.21

2.58

Table 14. Average values for ice temperature (T), secant (Esec) and initial (Eini ) secant modulus (GPa) for different strain rates (  ) from Poplin and Wang (1994).

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T: -5°C /   10 5 s -1 T: -5°C /   10 3 s -1 T: -20°C /   10 5 s -1 T: -20°C /   10 3 s -1

9 9 9 9

νt (‰) 78 108 82 77

 t  stdev (MPa)

 t , min (MPa)

 t , max (MPa)

0.82±0.17 0.61±0.16 0.71±0.16 0.75±0.16

0.57 0.41 0.49

1.03 0.83 0.92

0.48

0.92

For all samples: Average salinity = 0.787 psu ± 0.885 psu; Average density at -20°C = 846 kg/m 3 ± 37 kg/m3

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Pr

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Table 15. Uniaxial tensile strength of ice from multi-year ice ridges from Cox and RichterM enge (1985).

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Figure Captions Fig. 1 Test set-up for uniaxial compression tests. Fig. 2 System deformation for different load levels. Fig. 3 Typical stress-strain curve for mixed ice under uniaxial compression. Fig. 4 Specimen dimensions and example for a specimen tested in uniaxial tension. Fig. 5 In-situ salinity profiles from level ice (left). Salinity profiles from the ridges in 2012 and 2013

f

from field and laboratory measurements are compared (middle, right).

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Fig. 6 Examples of horizontal and vertical thin sections for ice samples from first-year pressure ridges

pr

for defining different ice types.

Fig. 7 Ridge profiles and ice types within the ridges measured in 2012 and 2013. Ice type

e-

classification is described in Table 3. Black lines surround the ridge cross-section, grey lines mark the

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snow cover and the grayed out areas show the consolidated layer. Fig. 8 Frequency distribution of compressive strength values of all tested specimen.

al

Fig. 9 P95 stress-strain diagram for mixed ice at strain rate 10-3 s-1 and temperature -10°C. Histograms

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show the distribution of failure strength, failure strain and residual strength.

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Fig. 10 P95 stress strain diagrams at nominal strain rate 10-3 s-1 and temperature -3.5°C. Fig. 11 P95 stress strain diagrams at nominal strain rate 10-3 s-1 and temperature -10°C. Fig. 12 P95 stress strain diagrams at nominal strain rates 10-4 s-1 (5·10-4 s-1 ) and temperature -10°C. Fig. 13. Identified regions that cover tangent moduli values for different ice types are plotted vs. total porosity. Fig. 14 Compressive strength vs. total porosity for granular and columnar ice types. The dashed line and the dot and dashed line show the data fit for the strength of columnar ice in vertical and horizontal load direction suggested by Moslet (2007). Fig. 15 Compressive strength vs. total porosity for mixed ice types.

Journal Pre-proof Fig. 16. Compressive strength vs. total porosity for mixed ice from pressure ridges. The continuous line is a fit to the average compressive strength, the dot and dashed lines are fit to the strength represented by 95% and 5% of all specimen loaded vertically and horizontally. The dashed lines show the data fit for the strength of ice from ridges suggested by Shafrova and Høyland (2008). Fig. 17 Compressive strength vs. total porosity for mixed ice at loaded at different nominal rates and ice temperatures. Fig. 18 Compressive strength and strength variation are shown in boxplots for respective strain rate

oo

f

and loading direction. Typical stress-strain curves above the boxplots illustrate material behavior at certain strain rate.

pr

Fig. 19 Four examples for thin sections across the middle part of the tested specimens.

e-

Fig. 20 Tensile strength vs. brine volume for all strength data (present study and Cox et al., 1985) and

Pr

Eq. 3.

Fig. 21 Tensile strength vs. total porosity for all strength data (present study and Cox et al., 1985) and

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Eq. 4.

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Pr

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Fig. 1 Test set-up f or uniaxial compression tests.

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f

Figures

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Fig. 2 System deformation f or different load levels.

Fig. 3 Typical stress -strain curve f or mixed ice under uniaxial compression.

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al

Pr

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f

Fig. 4 Specimen dimensions and example for a specimen tested in uniaxial tension.

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Fig. 5 In -situ salinity profiles f rom level ice (left). Salinity prof iles from the ridges in 2012 and 2013 f rom f ield and laboratory measurements are compared (middle, right).

Fig. 6 Examples of horizontal and vertical thin sections for ice samples from first-year pressure ridges f or defining different ice types.

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rn

al

Pr

e-

pr

oo

f

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Fig. 7 Ridge profiles and ice types within the ridges measured in 2012 and 2013. Ice type classif ication is described in Table 3. Black lines surround the ridge cross -section, grey lines mark the snow cover and the grayed out areas show the consolidated layer.

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f

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Pr

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Fig. 8 Frequency distribution of compressive strength values of all tested specimen.

Fig . 9 P95 stress-strain diagram for mixed ice at strain rate 10 -3 s -1 and temperature -10°C. Histograms show the distribution of f ailure strength, f ailure strain and residual strength.

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f

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Fig. 10 P95 stress strain diagrams at nominal strain rate 10 - 3 s - 1 and temperature -3.5°C.

Fig. 11 P95 stress strain diagrams at nominal strain rate 10 - 3 s - 1 and temperature -10°C.

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Fig. 12 P95 stress strain diagrams at nominal strain rates 10 -4 s -1 (5·10 - 4 s -1 ) and temperature -10°C.

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Pr

e-

pr

Fig . 13. Identified regions that cover tangent moduli values for different ice types are plotted vs. total porosity.

Fig. 14 Compressive strength vs. total porosity for granular and columnar ice types. The dashed line and the dot and dashed line show the data fit for the strength of columnar ice in vertical and horizontal load direction suggested by M oslet (2007).

Fig. 15 Compressive strength vs. total porosity f or mixed ice types.

pr

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f

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Pr

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Fig . 16. Compressive strength vs. total porosity for mixed ice f rom pressure ridges. The continuous line is a f it to the average compressive strength, the dot and dashed lines are fit to the strength represented by 95% and 5% of all specimen loaded vertically and horizonta lly. The dashed lines show the data f it for the strength of ice from ridges suggested by Shafrova and H ø yland (2008).

Fig. 17 Compressive strength vs. total porosity for mixed ice at loaded at different nominal rates and ice temperatures.

f

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al

Pr

e-

pr

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Fig . 18 Compressive strength and strength variation are shown in boxplots for respective strain rate and loading direction. Typical stress -strain curves above the boxplots illustrate material behavior at certain strain rate.

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Fig. 19 Four examples f or thin sections across the middle part of the tested specimens.

Fig. 20 Tensile strength vs. brine volume for all strength data (present study and Cox et al., 1985) and Eq. 3 .

f

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al

Pr

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pr

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Fig. 21 Tensile strength vs. total porosity for all strength data (present study and Cox et al., 1985) and Eq. 4.

Journal Pre-proof Highlights:

f oo pr ePr al rn

  

Uniaxial tensile and compressive strength of the consolidated layer from first-year ridges are presented 78% of all tested specimen from the ridge are from rafted or brecciated ice. The ice strength of the consolidated layer is isotropic. A new method for testing uniaxial tensile strength of ice is presented.

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