Mechanical properties of ice at Norströmsgrund

Norströmsgrund, Tests 2003

Deliverable No. D-4.3.3

EU FP5 EESD Project – Contract No. EVG1-CT-2000-00024

Revision Control

Rev.- n^o.

Date Prepared Checked Approved Distribution Purpose of release and re- marks

0.1 2003-06-01 LUT LUT STRICE meeting proposal

0.2 2003-10-01 LUT LUT STRICE meeting preliminary report

1.0 2004-01-31 LUT LUT HSVA final report

Main Contact for this document

Lennart Fransson

Luleå University of Technology Tel.: +47 920 49 1000

Division of Structural Engineering, SE-97187 Luleå, Sweden Fax: +47 920 49 1913

http://www.ce.luth.se E-mail: Lennart.Fransson@ce.luth.se

This document has been elaborated and issued by the STRICE Consortium:

Project Co-ordinator: Hamburgische Schiffbau-Versuchsanstalt GmbH (HSVA) Germany

Project partners Cambridge University (CU) United King-

dom Helsinki University of Technology (HUT) - Finland HYDROMOD Scientific Consulting (HYDROMOD) Germany Laboratoire de Glaciologie et Geophysique de l'Environment (LGGE) France

Luleå University of Technology (LUT) Sweden

Norwegian University of Science and Technology (NTNU) Norway Technical Research Centre of Finland (VTT) Finland

This document is sole property of the STRICE Consortium. It must be treated in compliance with its confidentiality classification. Any unauthorised distribution and/or copying without permission by the authors and the STRICE Consortium in terms of the STRICE Consortium Agreement and the relevant project contracts is strictly prohibited and shall be treated as a violation of copyright and whatsoever applicable laws. The responsibility of the content of this document (documents) is fully at the author (authors).

The STRICE project was co-funded by the European Commission under the Energy, Environment and Sustainable Development (EESD) Programme of the 5th Framework Programme under contract number EVG1-CT-2000- 00024.

Mechanical properties of ice at Norströmsgrund, Test 2003

by

Lennart Fransson and Ulf Stenman Luleå University of Technology, Sweden

FINAL

Revision 1.0 – Luleå – January 2004 Restricted

Table of contents

1 Sampling of ice cores... 3

2 Compression test of ice from Norströmsgrund 2003... 3

3 Classification data of tested ice ... 4

4 Compressive strength... 6

4.1 Strain rate control ... 6

4.2 Strength variation ... 6

4.3 Strain rate effect ... 7

4.4 Temperature effect ... 9

5 Crystal Analysis... 10

6 Results from compression tests 2003 ... 14

6.1 Stress-strain curves... 15

6.2 Elastic modulus vs. stress level ... 18

7 Mechanical properties of ice blocks sampled 2003-04-15 ... 22

7.1 Sampling procedure... 22

7.2 Uniaxial ice strength... 23

7.2.1 Horizontal compressive strength... 23

7.2.2 Vertical compressive strength... 24

7.2.3 Tensile strength... 24

8 Proposed ice strength model... 27

8.1 Summary of tests 2001-2003... 28

8.2 Examples ... 29

9 Reference... 29

10 List of figure captions ... 30

1 Sampling of ice cores

In March 20, level ice with a thickness of 59 cm was sampled from an ice floe close to the light- house Norströmsgrund. Large pressure ridges were surrounding the floe, which had a diameter of about 60 meters. A total of 12 large ice cores with a diameter of 200 mm were drilled out along two rows, with an equidistance of two metres in the central part of the floe. The cores were put into plastic bags and were then directly transported with helicopter to the laboratory at Luleå University of Technology. The temperature profile measured at the centre of one core within 5 minutes after taking up the core is shown in Table 1.

Table 1. Temperature profile (°C ) through the ice at Norströmsgrund, 2003-03-20, 10:30

air 10 cm 15 20 25 30 35 40 45 50cm water -6.7 -2.1 -1.0 -1.0 -0.5 -0.2 -0.1 -0.1 -0.1 -0.0 -0.0

2 Compression test of ice from Norströmsgrund 2003

Horizontal samples with a diameter of 70 mm were drilled from the large vertical cores at the depths 10, 20, 30, 40, 50 cm. Uniaxial compression tests on these samples were performed with three different nominal strain rates (0.5, 1, 2 x 10 ^–3 s^-1) and three different temperatures (-1, -4, - 10°C). Four ice cores were prepared and tested a few hours after sampling close to the in situ tem- perature (about -1°C) and the original porosity. The rest of the ice was stored at –30 ^oC until the sample preparation, which took place at a room temperature of –10^oC and -4^oC. The compression tests have been given a 3 digit number xyz, where x is the sampling number, y is the core number and z indicates the depth. All test results are given in chapter 6 and the stress-strain curves are shown as multiple graphs in section 6.1.

The methods used for sample preparation and loading tests are also described in the interim report 2001. Test numbers 301-305 was performed with the same method and equipment as before. In fur- ther test series 2003 stiff steel platens were used instead of the compliance platens. Due to practical reasons the cross-head speed was held constant instead of the directly measured ice strain rate.

3 Classification data of tested ice

Grain sizes, density and salinity of the melted ice was measured for all test samples 2003. It was no- ticed that the granular ice with a consistent grain size of 2-3 mm was more saline than the columnar ice with a grain size of 5-6 mm. The average properties of 45 samples used for strength tests (core 1-9) are given in Table 2.

Table 2. Average properties of ice sampled at Norströmsgrund 2003-03-20 Depth

cm

Ice type Grain size mm

Density kg/m³

Salinity ppt

10 G 2 896 1.7

20 G 3 904 1.4

30 K 6 910 0.7

40 K 6 910 0.3

50 K 5 906 0.5

G – granular ice, K – columnar ice

To get a true picture of how the properties varied within the tested ice area (2m x 12 m) and depth all data points are shown in Figure 1. In general the standard deviation is relatively small at each depth and also for the two ice types as a group. Therefore parametric studies of the temperature ef- fect and the strain rate effect on strength were done. It is however important to separate results for the two different brackish ice types Granular ice (2-3 mm) and Columnar ice (5-6 mm).

GrainSize (mm)

0.0 2.0 4.0 6.0 8.0 10.0

0 10 20 30 40 50 60

Depth (cm)

(a)

Density (kg/m3)

880 885 890 895 900 905 910 915 920

0 10 20 30 40 50 60

Depth (cm)

(b)

Salinity (ppt)

0.00 0.50 1.00 1.50 2.00 2.50 3.00

0 10 20 30 40 50 60

Depth (cm)

(c)

Figure 1. Profiles of measured properties for ice sampled at Norströmsgrund 2003-03-20. Grain size (a), den- sity (b) and salinity (c).

4 Compressive strength

4.1 Strain rate control

Compression tests at higher strain rates often resulted in brittle cracks that were catastrophic for the stability of the sample. Therefore it was difficult to control the closed-loop test with the signal from the LVDTs attached to the ice perimeter. Instead the crosshead speed (chosen as the target strain rate multiplied with sample length) was set constant. The actual strain rate (measured with the LVDTs) increased with time even though stiff steel plates were used in contact with the ice sample.

For tests with a nominal strain rate of 0.5e-3 s^-1 strain developed slower in the central part espe- cially during the first 0.1%. The difference was smaller at higher testing speed.

Figure 2. Average strain measured with the built-in stroke gauge (line to the left) and strain measured with the two LVDTs attached on the ice. The three different nominal strain rates correspond to different columns

of diagrams.

4.2 Strength variation

All compressive strength results are plotted in the same diagram, Fig. 3. It can be noticed that the middle ice portion is weaker than the average ice sheet. Otherwise it is no general trend depending on depth. With the used variations of temperatures and strain rates the compressive strength varia- tion was typical 3 to 8 MPa with horizontal loading direction.

Strength (MPa)

0 2 4 6 8 10

0 10 20 30 40 50 60

Depth (cm)

Figure 3. Summary of strength vs. depth for ice sampled at Norströmsgrund 2003-03-20. Temperature varia- tion: -10 to -1 ^oC Strain rate variation: 0.5 to 2 x10^-3

4.3 Strain rate effect

The influence of strain rate is depicted in Figs. 4 – 6. In general maximum strength for columnar ice was found at a nominal strain rate of 10^-3 independent of temperature. Granular ice showed weak dependence on strain rate in the limited interval.

Total ice cover

0 2 4 6 8 10

0.0E+00 5.0E-04 1.0E-03 1.5E-03 2.0E-03 2.5E-03 Strain rate (1/s)

Strength (MPa)

-1 -4 -10

Figure 4. Uniaxial compressive strength vs. strain rate at three different test temperatures. Horizontal strength of the total ice cover (average of 5 tests).

Granular ice

0.0 2.0 4.0 6.0 8.0 10.0

0.0E+00 5.0E-04 1.0E-03 1.5E-03 2.0E-03 2.5E-03 Strain rate (1/s)

Strength (MPa)

-1 -4 -10

Figure 5. Uniaxial compressive strength vs. strain rate at three different test temperatures. Horizontal strength of the granular ice (average of 2 tests).

Columnar ice

0.0 2.0 4.0 6.0 8.0 10.0

0.0E+00 5.0E-04 1.0E-03 1.5E-03 2.0E-03 2.5E-03 Strain rate (1/s)

Strength (MPa)

-1 -4 -10

Figure 6. Uniaxial compressive strength vs. strain rate at three different test temperatures. Horizontal strength of the columnar ice. (average of 3 tests).

4.4 Temperature effect

The influence of ambient temperature is depicted in Figs. 7-9. The in situ ice temperature was close to –1 deg., see Table 1. A linear dependence on temperature was found for both granular and co- lumnar ice in this temperature interval.

Total ice cover

0 2 4 6 8 10

-12 -10 -8 -6 -4 -2 0

Temperature (C)

Strength (MPa)

5.00E-04 1.00E-03 2.00E-03

Figure 7. Strength of total ice cover vs. ice temperature.

Granular ice

0.0 2.0 4.0 6.0 8.0 10.0

-12 -10 -8 -6 -4 -2 0

Temperature (C)

Strength (MPa)

5.00E-04 1.00E-03 2.00E-03

Figure 8. Strength of granular ice vs. ice temperature.

Columnar ice

0.0 2.0 4.0 6.0 8.0 10.0

-12 -10 -8 -6 -4 -2 0

Temperature (C)

Strength (MPa)

5.00E-04 1.00E-03 2.00E-03

Figure 9. Strength of columnar ice vs. ice temperature.

5 Crystal Analysis

Vertical and horizontal sections were analysed in cross-polarized light, see Figures 10 and 11. End- cuts from the horizontal cylinders were used to identify the tested ice type and grain size. The aver- age grain size was also calculated as the number of intersections along a 10 cm line on the horizon- tal sections.

The ice consisted of 25 cm granular and crushed grains on top of columnar ice. Ice growth was dis- turbed by growth stagnation at 40 cm depth and by frazil at 48 cm depth. In most end-cuts both granular and columnar ice was observed but the classification was simplified by ignoring thin bands of granular ice in the columnar portion and vice versa. Large vertical melt-channels as shown in Figure 12 were present all the way through down to 45 cm due to a long period of mild tempera- tures and a relatively high salinity at the granular ice layer.

core 1 core 2 core 3 core4

10 cm

20 cm

30 cm

40 cm

50 cm

Figure 10. Endcuts (diam. ~70mm) from test series 1-4. Depth from surface: 10 cm – 50 cm.

50 cm

40 cm

30 cm

20 cm

10 cm

Figure 12. Vertical section of the bottom half of the ice sheet. Notice the large brine channel 15 cm from the bottom and all the way up.

6 Results from compression tests 2003

Table 3. Mechanical properties of ice sampled at Norströmsgrund 2003-03-20.

Sample Temp Diam Length Mass Load Depth StrRate Density Strength Salinity GrainSize

20-Mar T (C) D (mm) L (mm) M (g) P (kN) z (cm) (e-3/s) (kg/m3) (MPa) (ppt) (mm)

301 -1 68.7 171.8 572.55 15.567 10 0.5* 899.1 4.20 2.11 2.7 302 -1 68.7 171.8 558.80 9.396 20 0.5* 877.5 2.53 1.11 2.7 303 -1 68.7 171.8 571.86 13.622 30 0.5* 898.0 3.67 0.69 5.0 304 -1 68.7 169.9 555.97 7.699 40 0.5* 882.8 2.08 0.21 5.8 305 -1 68.7 172.3 565.04 12.518 50 0.5* 884.7 3.38 0.59 7.0 311 -1 68.7 172.2 575.49 18.520 10 0.5 901.6 5.00 2.07 2.5 312 -1 68.7 172.1 584.13 16.591 20 0.5 915.6 4.48 0.67 2.9 313 -1 68.7 172.0 582.89 11.845 30 0.5 914.2 3.20 0.52 6.4 314 -1 68.7 172.1 577.09 11.445 40 0.5 904.6 3.09 0.64 7.0 315 -1 68.7 172.2 572.86 11.205 50 0.5 897.5 3.02 0.56 6.4 321 -1 68.7 172.0 577.17 18.616 10 1 905.3 5.02 2.24 2.5 322 -1 68.7 172.2 578.90 14.478 20 1 906.9 3.91 2.39 2.9 323 -1 68.7 172.1 582.99 15.591 30 1 913.9 4.21 0.91 6.4 324 -1 68.7 172.0 583.56 19.089 40 1 915.3 5.15 0.47 5.0 325 -1 68.7 172.1 582.88 14.639 50 1 913.7 3.95 0.56 5.8 331 -1 68.7 172.1 570.03 18.072 10 2 893.5 4.88 1.86 2.5 332 -1 68.7 171.8 573.40 13.158 20 2 900.4 3.55 1.51 2.9 333 -1 68.7 172.0 576.40 12.582 30 2 904.0 3.39 0.65 5.0 334 -1 68.7 172.3 578.30 15.159 40 2 905.5 4.09 0.25 4.7 335 -1 68.7 172.2 570.44 19.273 50 2 893.7 5.20 0.52 6.4 341 -10 68.7 172.5 577.80 26.140 10 0.5 903.6 7.05 1.37 2.5 342 -10 68.7 172.2 580.66 30.261 20 0.5 909.7 8.16 1.19 2.9 343 -10 68.7 172.3 581.92 19.849 30 0.5 911.1 5.35 0.90 7.0 344 -10 68.7 172.3 580.74 23.402 40 0.5 909.3 6.31 0.36 5.8 345 -10 68.7 172.3 579.70 20.673 50 0.5 907.6 5.58 0.68 5.0 351 -10 68.7 172.4 569.43 28.837 10 1 891.0 7.78 1.71 2.5 352 -10 68.7 172.3 580.81 32.382 20 1 909.4 8.74 1.93 2.9 353 -10 68.7 172.4 584.76 23.715 30 1 915.0 6.40 0.96 6.4 354 -10 68.7 172.3 585.86 28.397 40 1 917.3 7.66 0.23 4.6 355 -10 68.7 172.3 584.37 32.070 50 1 915.0 8.65 0.54 3.0 361 -10 68.7 172.3 569.01 32.823 10 2 890.9 8.85 1.36 2.5 362 -10 68.7 172.3 578.00 30.414 20 2 905.0 8.20 1.76 2.9 363 -10 68.7 172.2 582.86 24.251 30 2 913.1 6.54 0.77 4.5 364 -10 68.7 172.2 583.76 18.256 40 2 914.5 4.92 0.23 6.3 365 -10 68.7 164.7 554.87 33.919 50 2 908.9 9.15 0.61 2.8 371 -4 68.8 172.6 570.63 16.439 10 0.5 889.3 4.42 1.15 2.5 372 -4 68.8 172.7 569.15 16.383 20 0.5 886.5 4.41 0.94 2.5 373 -4 68.8 172.5 580.50 14.150 30 0.5 905.2 3.81 0.47 5.0 374 -4 68.8 172.5 584.13 19.209 40 0.5 910.9 5.17 0.20 4.4 375 -4 68.8 172.5 578.08 15.943 50 0.5 901.4 4.29 0.33 5.8

381 -4 68.8 172.3 579.76 24.315 10 1 905.1 6.54 1.35 2.5 382 -4 68.8 172.3 584.50 22.674 20 1 912.5 6.10 1.09 2.5 383 -4 68.8 172.4 585.16 16.904 30 1 913.0 4.55 0.48 4.4 384 -4 68.8 172.6 585.28 21.442 40 1 912.1 5.77 0.39 6.4 385 -4 68.8 121.4 410.50 22.498 50 1 909.6 6.05 0.56 7.8 391 -4 68.8 172.5 566.14 20.729 10 2 882.8 5.58 1.94 2.5 392 -4 68.8 172.6 573.49 19.161 20 2 893.8 5.15 1.40 2.5 393 -4 68.8 172.4 579.62 19.233 30 2 904.4 5.17 0.76 5.0 394 -4 68.8 172.4 577.79 14.350 40 2 901.5 3.86 0.31 5.8 395 -4 68.8 172.3 578.08 20.745 50 2 902.5 5.58 0.51 4.4

*strain rate was controlled with LVDTs attached to the ice

6.1 Stress-strain curves

Data from the compression tests have been stored as ascii-files with the file names No*.txt, where * is the three digit sample number. The five data columns are:

Time (sec), LVDT1 (10^-2 mm), LVDT2 (10^-2 mm), Stroke (mm), Load (kN)

The two LVDTs were attached to the ice at the central part of the ice cylinder (c-c 84 mm). Elapsed time can also be calculated from the sampling frequency, which was 100 Hz. Tests from the same depth are compared in the graphs below. The test temperatures were –1, -10, -4 °C (row 1,2,3) and the strain rates were 0.5, 1, 2e-3 s^-1 (col. 1,2,3). Strain is calculated from the average of the two LVDTs and the stress as the load divided with the cross-sectional area.

6.2 Elastic modulus vs. stress level

Elastic modulus (secant method) has been plotted as a function of stress level in the graphs below.

Tests from the same depth are compared in the graphs below. The test temperatures were –1, -10, -4

°C (row 1,2,3) and the strain rates were 0.5, 1, 2e-3 s^-1 (col. 1,2,3). Strain is calculated from the av- erage of the two LVDTs and the stress as the load divided with the cross-sectional area.

7 Mechanical properties of ice blocks sampled 2003-04-15

7.1 Sampling procedure

Ice blocks with the size of 40 x 100 cm were sampled at the middle of the Holfjarden bay at the coastline about 20 km from the lighthouse Norströmsgrund, see Figure 13. A total of 9 ice blocks were cut with a chainsaw beside each other from the 40 cm level ice. Due to the warm temperature at the day (+ 2) the ice was covered with snow before it was transported to Luleå University of Technology. At the University the ice was cooled slowly down to –25 °C in a coldroom and stored at that temperature covered with a tight plastic foil. Six ice blocks were transported to HSVA in Hamburg for fracture mechanical tests. These test results are given in the STRICE report “Cleavage fracture toughness of warm brackish ice”, authored by Dempsey et al (Delivery D-4.3.4).

In this report uniaxial strength is given based on tests performed on the three remaining ice blocks.

The same test method and sample size (cylinders 70 mm) as described before was used. The stress- strain curves were however not recorded, only the peak values were registered.

Figure 13. Map over the sampling area Holfjärden,20 km from Norströmsgrund.

7.2 Uniaxial ice strength

7.2.1 Horizontal compressive strength

Horizontal strength was measured at a temperature of –10 and 0. The nominal strain rate was set to 10^-3 s^-1. For 8 tested samples at each temperature the average strength was 4.8 MPa at –10 and 3.2 MPa at 0 deg. As expected the central portion was weakest and the fine crystals at the surface were strong. The result is given in Table 4.

Table 4. Horizontal compressive strength of ice from Holfjarden, 2003-04-15.

Sample Temp Diam Length Mass Load Depth Density Strength Salinity

15-Apr T (C) D (mm) L (mm) M (g) P (kN) z (cm) (kg/m3) (MPa) (ppt)

411 -10 68.8 163.7 538.9 23.08 5 885 6.21 0.04 412 -10 68.8 170.2 550.4 17.13 15 870 4.61 0.08 413 -10 68.8 170.0 547.0 12.71 25 866 3.42 0.04 414 -10 68.8 169.8 563.6 19.36 35 893 5.21 0.03

average 878.4 4.86 0.05

sdev 12.9 1.17 0.02

421 -10 68.8 169.7 559.3 25.14 5 887 6.76 0.04 422 -10 68.8 170.2 547.7 17.92 15 866 4.82 0.07 423 -10 68.8 165.9 535.0 11.61 25 867 3.12 0.03 424 -10 68.8 169.8 553.2 16.34 35 876 4.40 0.03

average 874.0 4.78 0.04

sdev 9.6 1.51 0.02

431 0 68.8 170.2 560.6 14.82 5 886 3.99 0.03 432 0 68.8 170.3 545.9 11.54 15 862 3.10 0.04 433 0 68.8 170.3 543.4 7.58 25 858 2.04 0.02 434 0 68.8 170.3 567.5 10.13 35 896 2.73 0.02

average 875.7 2.96 0.03

sdev 18.4 0.81 0.01

441 0 68.8 157.4 522.0 14.33 5 892 3.85 0.02 442 0 68.8 170.1 543.4 14.73 15 859 3.96 0.03 443 0 68.8 169.9 538.9 9.70 25 853 2.61 0.02 444 0 68.8 169.8 563.5 11.61 35 893 3.12 0.02

average 874.3 3.39 0.02

sdev 21.0 0.64 0.01

7.2.2 Vertical compressive strength

Vertical cylinders drilled from the central portion of the ice blocks (depth 10 – 30 cm) and tested in compression using the same strain rate (10^-3 s^-1) as for the horizontal samples. The average vertical strength (4.36 MPa) was somewhat higher than the horizontal strength at 25 cm depth (3.27 MPa).

Maximum load in this ice volume was limited by extremely brittle catastrophic axial stability fail- ures. The result is given in Table 5.

Table 5. Vertical compressive strength of ice from Holfjarden, 20 km from Norstromsgrund, 2003-04-15.

Sample Temp Diam Length Mass Load Depth Density Strength

15-Apr T (C) D (mm) L (mm) M (g) P (kN) z (cm) (kg/m3) (MPa)

451-V -10 68.8 153.9 501.6 23.46 20 877 6.31 452-V -10 68.8 153.1 500.5 21.23 20 879 5.71 453-V -10 68.8 152.8 496.6 14.00 20 874 3.77 454-V -10 68.8 153.0 495.8 13.64 20 872 3.67 455-V -10 68.8 153.1 500.3 12.44 20 879 3.35 456-V -10 68.8 153.5 500.4 20.32 20 877 5.47 457-V -10 68.8 153.4 499.3 11.10 20 876 2.99 458-V -10 68.8 153.6 498.5 13.61 20 873 3.66

average 875.8 4.36

sdev 2.8 1.26

7.2.3 Tensile strength

Vertical and horizontal ice cylinders with a diameter of 70 mm were tested in tension at a loading rate of 0.5 kNs^-1. The sample preparation and test methodology is described in the report “Mechani- cal properties of ice from Norströmsgrund, Tests 2001”, STRICE delivery D-4.3.1. The central 20 cm were cut with a chainsaw and the specimens were drilled close to each other. Results from suc- cessful tensile tests are presented in Table 6. The average tensile strength was 1.3 MPa in the verti- cal direction and 1.4 in the horizontal direction. Several tests failed in the horizontal direction be- cause vertical macro cracks or large open brine channels were present. Tensile load from these tests and tests with insufficient bonds to the pulling plate have been omitted in Table 6.

Figure 14. Test set-up before tensile fracturing. Sample V11.

Figure 15. Crystal structure seen on a thin horizontal section. Endcut of sample V13.

Figure 16.Tensile fracture of vertical sample V13.

Table 6. Tensile strength of ice sampled in Holfjarden,2003-04-15

Sample Temp Diam Length Mass Tensile Load Density Tstrength 15-Apr T (C) D (mm) L (mm) M (g) Pt (kN) (kg/m3) (MPa)

V11 -10 68.8 152.4 489.4 6.32 864 1.70

V12 -10 68.8 158.9 513.4 6.98 869 1.88

V13 -10 68.8 170.5 544.3 3.84 859 1.03

V14 -10 68.8 160.4 512.3 6.76 859 1.82

V15 -10 68.8 169.5 539.2 856

V16 -10 68.8 170.3 538.3 2.59 850 0.70

V17 -10 68.8 169.8 540.7 3.98 856 1.07

V18 -10 68.8 169.9 539.7 3.69 854 0.99

average 858 1.31

sdev 6 0.47

H11 -10 68.8 152.8 492.5 2.20 867 0.59

H12 -10 68.8 150.1 479.9 860

H13 -10 68.8 154.5 501.3 873

H14 -10 68.8 153.4 493.8 8.28 866 2.23

H15 -10 68.8 153.2 493.6 867

H16 -10 68.8 150.9 487.8 2.83 870 0.76

H17 -10 68.8 152.6 487.4 859

H18 -10 68.8 147.3 473.9 6.97 865 1.87

average 866 1.36

sdev 5 0.81

8 Proposed ice strength model

For ice load design purpose it is necessary to adjust the stress potential or the effective ice pressure to ice temperature, compressive strength, ice type and velocity of moving ice. In this study ice ve- locity is assumed to be in the ductile to brittle transition range where maximum compressive strength is obtained for small horizontally loaded samples, usually equal to a strain rate of 10^-3 s^-1. The temperature then becomes the single most important variable for each well-defined ice type. Ice temperature is a function of air temperature but also solar radiation and wind speed affect the rela- tionship. In general this is a delicate problem to solve or predict from weather station data espe- cially because the ice surface may also be covered with insulating snow or even worse, by slush.

Without further discussion ice surface temperature θ_i(0) is considered much higher than the mini- mum air temperature θ_a in a 50-year return period, see Timco & Frederking (1990) where the sur- face temperature in Canadian cold sea ice was well described by

4 6 . 0 ) 0

( = _a −

i θ

θ … (1)

Ice thickness hfor land fast ice can be estimated with the well-known formula dt

k

h^{2 = 1}

∫

^−θ_a^{− … (2)}

and the decay of ice strength σ₀ is proposed to be calculated in a similar way as dt

k

∫

_a⁺

′ +

=σ θ

σ_{0 0 2} … (3)

where θ_a⁻and θ_a⁺ are negative respectively positive degrees after ice formation date and σ₀′ is the ice strength first time approaching the melting point. The temperature integral is taken as the sum of daily min. plus daily max. temperature divided by 2. Today’s temperature sampling are often more frequently and thus the summation can be done hour-by-hour.

From hundreds of uniaxial compression tests on ice from the Gulf of Bothnia during the STRICE project it was found that the lowest strength decreases over the season at the melting point, see Ta- ble 1. The mechanism for such strength decay is unclear but it is assumed that internal melting and melt channel formation is the main cause. It has also been observed that this decay effect is almost forgotten when the sample is refrozen back to cold temperatures (-10) as long as the brine channels are small. The test results also suggest a model where linear temperature dependence can be as- sumed in the interval –10 to 0 degrees Celsius. If compressive strength σ_c is denoted positive we will then get

i

c σ σ σ θ

σ 10

0 10

0 −

+ −

= ⁻ … (4)

, where σ₀and σ₋₁₀ is the compressive strength at zero and –10 and θ_i is the ice temperature.

Based on other experimental data each well-defined ice type can be thermally and mechanically modelled by the two material constants k and k . In most design situations temperature effects on

the ice strength should be considered using experimental data on both σ₀and σ₋₁₀ even though the variance of average ice temperatures can be small from one location to another. The temperature ef- fect is not always as important as one might think simply because the ice bottom is constantly at the melting point. The average compressive strength σ_c assuming linear ice temperature distribution is

) 0 20 (

0 10

0 i

c σ σ σ θ

σ −

+ −

= ⁻ … (5)

8.1 Summary of tests 2001-2003

Table 7. Summary of test results on ice from Norströmsgrund 2001-2003. The numbers have been obtained from linear regression at different ice depths.

SamplingDate Ice type Depth σ⁰

(

σ₋₁₀ −σ₀

)

/−10 σ₋₁₀

dd/mm yyyy G, K, M cm MPa MPa/deg MPa 20/3 2001 K 8 4.172 -0.189 6.062 20/3 2001 K 18 5.897 -0.194 7.837 5/4 2001 K 5 3.257 -0.310 6.361 5/4 2001 K 15 4.417 -0.396 8.381 5/4 2001 K 25 4.871 -0.391 8.776 5/4 2001 K 35 4.783 -0.322 7.999 2/3 2002 K 5 3.194 -0.222 5.409 2/3 2002 G 15 2.504 -0.361 6.109 2/3 2002 K 25 3.924 -0.174 5.659 21/3 2002 K 5 2.566 -0.388 6.446 21/3 2002 K 15 3.024 -0.402 7.044 21/3 2002 K 25 3.105 -0.416 7.265 20/3 2003 G 10 4.987 -0.292 7.908 20/3 2003 G 20 3.633 -0.523 8.861 20/3 2003 K 30 3.786 -0.253 6.314 20/3 2003 K 40 4.772 -0.284 7.614 20/3 2003 K 50 3.669 -0.510 8.766 15/4 2003 G 5 3.921 -0.257 6.486 15/4 2003 K 15 3.533 -0.118 4.714 15/4 2003 K 25 2.324 -0.095 3.270 15/4 2003 K 35 2.924 -0.188 4.801 G-Granular ice K-Columnar ice

8.2 Examples

Example 1:

Calculate the average compressive strength of an ice cover where the ice surface temperature is a) –9 ^oC and b) 0 ^oC. The air temperature has never been above the melting point, σ₀′ = 4 MPa and

−10

σ = 8 MPa.

Solution:

a) c i

( )

9 5.8

[

^MPa

]

20 4 4 8

) 0 20 (

0 10

0 − =

− + −

− = + −

=σ σ⁻ σ θ σ

b) σ_c =4

[

MPa

]

Example 2:

How is the average compressive strength affected by air temperature when the ice is in a state of melting?

Solution:

Eq. (3) is rewritten as ^σ_c ^{=σ0′ +}k²

∫

^θ_a⁺dt, which implies that the strength is decreasing propor- tional to the sum of the positive air temperature once the ice has reached the melting point. This process depends on solar radiation, salinity and thickness of the brackish ice. One first guess is that it needs to average temperatures above the freezing point for a certain time before the strength starts to decrease. After that, n positive degree-days are needed to melt the ice crystal bonds completely.

The assumption yields k₂ =−σ₀′ n

[

MPa/deg,day

]

9 Reference

Timco, G.W. and Frederking, R.M.W., 1990. Compressive strength of sea ice sheets. Cold Regions Science and Technology, 17 (1990) 227-240.

10 List of figure captions

Figure 1. Profiles of measured properties for ice sampled at Norströmsgrund 2003-03-20. Grain size (a), density (b) and

salinity (c). ... 5

Figure 2. Average strain measured with the built-in stroke gauge (line to the left) and strain measured with the two LVDTs attached on the ice. The three different nominal strain rates correspond to different columns of diagrams.6 Figure 3. Summary of strength vs. depth for ice sampled at Norströmsgrund 2003-03-20. Temperature variation: -10 to -1 ^oC Strain rate variation: 0.5 to 2 x10^-3... 7

Figure 4. Uniaxial compressive strength vs. strain rate at three different test temperatures. Horizontal strength of the total ice cover (average of 5 tests)... 7

Figure 5. Uniaxial compressive strength vs. strain rate at three different test temperatures. Horizontal strength of the granular ice (average of 2 tests). ... 8

Figure 6. Uniaxial compressive strength vs. strain rate at three different test temperatures. Horizontal strength of the columnar ice. (average of 3 tests)... 8

Figure 7. Strength of total ice cover vs. ice temperature. ... 9

Figure 8. Strength of granular ice vs. ice temperature. ... 9

Figure 9. Strength of columnar ice vs. ice temperature. ... 10

Figure 10. Endcuts (diam. ~70mm) from test series 1-4. Depth from surface: 10 cm – 50 cm. ... 11

Figure 12. Vertical section of the bottom half of the ice sheet. Notice the large brine channel 15 cm from the bottom and all the way up. ... 13

Figure 13. Map over the sampling area Holfjärden,20 km from Norströmsgrund. ... 22

Figure 14. Test set-up before tensile fracturing. Sample V11. ... 25

Figure 15. Crystal structure seen on a thin horizontal section. Endcut of sample V13... 25

Figure 16.Tensile fracture of vertical sample V13. ... 26