Compressive Strength of Snow

LULEÅ TEKNISKA UNIVERSITET

Compressive strength of snow

Experimental measurements at ICEHOTEL in April 2012

Nina Lintzén 2012-09-11

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

1. Introduction

Snow is a visco-elastic material which in compression behaves differently depending on the deformation rate. Slow deformation rates will give rise to an elastic-plastic behavior with a continuous deformation process. Fast deformation may cause a discontinuous deformation process or a brittle failure. There is a critical stress or a critical deformation rate at which discontinuity occurs in the deformation.

Moreover, the strength of snow in compression is dependent on several other parameters, for example density, temperature and crystal size of the snow.

Compression tests on snow have been performed at ICEHOTEL in Jukkasjärvi to study the strength and deformation behavior of artificial snow. The strength and deformation behavior of snow from ICEHOTEL have been analyzed in previous studies (Vikström, Bernspång 2001), (Lintzén, Edeskär 2012). The number of previously performed tests have been quite few and performed at different deformation rates. These tests were done in order to get better statistical basic data to determine the strength of artificial snow and to get a better understanding of the parameters which influence the strength and deformation behavior.

As in previous studies snow samples where cut out from different parts of the ICEHOTEL; a wall which had been exposed to sunshine during the season, a wall on the shady side of the building and from the inside of the building.

The tests were performed at a temperature of -4 to-5°C in one of the storage halls in Jukkasjärvi using a constant speed compression tests machine.

The deformation rate during compression of snow is known to have an impact on the test results. The speed was constant during each test but tests were performed at deformation rates between 0.5 mm/s and 5 mm/s which are the possible range of speeds for the machine used.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

2. Snow samples

Snow samples were drilled out from the ICEHOTEL in the middle of April, the days after the hotel was closed for the season. Samples were taken out from one wall which had been exposed to sunshine during the season, from one wall mostly located in the shade and from the inside of the building.

The drill used was a circular drill connected to an electrically driven drilling machine as shown in figure 1. The diameter of the samples was 65 mm and the length was between 14 and 16 cm. Due to some problems with the cutting edge of the drilling tool the samples from the inside of the building had a slightly smaller diameter, about 61 mm.

Figure 1; Drilling out the snow samples

The outside temperature when cutting out the samples was above freezing point making the snow, especially from the outer walls, quite soft and slushy. The samples were placed in sealed plastic boxes in a cold storage room with temperature between -4°C and -5°C, which also was the temperature of the samples at the time for testing.

32 samples were cut out from the wall on the shady side, 20 samples from the wall exposed to sunshine and 28 samples from inside the building.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

3. Test procedure

3.1 Density

The density of all snow samples was calculated by measuring the dimensions and weight of each sample before the compression tests.

3.2 Compression strength

Compression tests were performed at different constant deformation rates using a compression test machine, shown in figure 2. The deformation rate could be varied between 0.5 mm/s up to 5 mm/s. Since the rate of deformation is known to have an impact on the test results, different deformation rates were chosen for the tests. The resisting force as a function of time was recorded for each test using the software EasyView.

Figure 2; Experimental setup for the compression tests

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

The compression strength of each snow samples was calculated by dividing the maximum force by the cross sectional area of the sample according to equation 1.

= (1) 푚푎푥 퐹 휎 퐴 3.3 Young’s modulus

The results from the initial linear part of the curves from the compression tests were used to calculate Young’s modulus. The stress was calculated by dividing the difference in stress over the corresponding difference in axial strain according to equation 2.

Since the true cross sectional area is somewhat larger than the nominal cross sectional area, the true stress is somewhat smaller than the calculated stress. This is assumed to have a minor importance for the overall results. The axial strain was calculated by dividing the grade of compression by the initial length of the tested sample. Hence Young’s modulus, E, has been calculated as:

/ = = (2) ( )/ ∆휎 ∆퐹 퐴 where퐸 ∆ F휖 is the∆ 푡force∗훿 퐿 in Newtons, A is the cross-sectional area of the sample in mm2, t the time in minutes, δ the deformation rate in mm/min and L the initial length of the sample in mm.

3.4 Resisting force after initial yield point

At high deformation rates rupture may occur after the initial yield point. At slow rates the samples will just change in shape and become harder during the deformation. Curves showing the resisting force versus time for tests at different deformation rates are shown in Appendix 1. The slope of the line registering the resisting force after the initial yield point was calculated.

3.5 Time to initial yield point

Depending on the deformation rate the time to reach the initial yield point or time to peak stress will be different. The time was observed for the different deformation rates.

3.6 Viscosity

The viscosity is a parameter of importance for the creep behavior of snow (Yosida, 1956). The viscosity is highly temperature dependent and has a direct influence on the creep strain rate. For plastic deformation of snow the viscosity coefficient, η, can be calculated by the formula:

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

= (3) 푃 whereη 휖 ̇ P is the stress and the axial secondary strain rate i.e. the increasing rate of the strain of snow at the last stage of experiments where snow samples are compressed with a constant load (Kinosita, 1957). 휖̇

4. Results

4.1 Density

The average density of the 32 samples from the wall in the shade was 602 kg/m3. The average density of the 20 samples from the wall exposed to sunshine was 585 kg/m3. The average density of the 28 samples from the inside of the building was 588 kg/m3. The density of all tested samples is shown in figure 3. In general the density is between 550 and 650 kg/m3.

750 Shady side Sunny side Inside 700

] 650 3

Density [kg/m 600

550

500 Figure 3; Density of all tested samples

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

4.2 Compression strength

4.2.1 Compression strength versus density

Compression strength versus density for the samples from the different walls is shown in figures 4-6. The different deformation rates are marked with different symbols so the influence of the different deformation rates also can be noticed.

1.4 Deformation rate = 0.5 mm/s Deformation rate = 1.5 mm/s Deformation rate = 3 mm/s Deformation rate = 5 mm/s

1.2

0.8 Compression strength [MPa]

0.6

0.4

560 580 600 620 640 660 Density [kg/m3] Figure 4; Compression strength vs. density at different deformation rates for the samples from the shady wall.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

1.6

Deformation rate = 1.5 mm/s Deformation rate = 5 mm/s

1.4

1.2

1 Compression strength [MPa]

0.8

0.6

540 560 580 600 620 640 660 Density [kg/m3] Figure 5; Compression strength vs. density at different deformation rates for the samples from the sunny wall.

1.6

Deformation rate = 1.5 mm/s Deformation rate = 5 mm/s

1.4

1.2

1 Compression strength [MPa]

0.8

0.6

540 560 580 600 620 640 660 Density [kg/m3] Figure 6; Compression strength vs. density at different deformation rates for the samples from the wall inside the building.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

Compression strength versus density for samples from different parts of ICEHOTEL and artificial snow not used for constructions tested at a deformation rate of 1.5 mm/min are shown in figure 7.

1.2

New unused snow Snow from inside Snow from sunny side Snow from shady side 1

0.8 Compressive strength [MPa] 0.6

0.4

480 520 560 600 640 680 720 Density [kg/m3] Figure 7; Compressive strength versus density for different types of snow, deformation rate 1.5 mm/min.

4.2.2 Compression strength versus deformation rate

The cylindrical test samples from the shady side of the wall were tested at the deformation rates 0.5 mm/s, 1.5 mm/s, 3 mm/s and 5 mm/s. This corresponds to strain rates of approximately 0.5∙10-3 s-1, 1.6∙10-3 s-1, 3.5∙10-3 s-1 and 5.5∙10-3 s-1. The average compression strength for each deformation rate is shown in figure 8.

Ten samples were tested at 0.5 mm/s, 1.5 mm/s and 5 mm/s respectively and two samples at 3 mm/s using the samples from the shady side. For the samples from the wall exposed to sunshine and the inside of the building, ten samples were tested with each type of snow at 1.5 mm/s and 5 mm/s.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

1.4

Wall - Shade Wall - Sunshine Wall - Inside

1.2

0.8 Average compression strength [MPa]

0.6

0 1 2 3 4 5 Deformation rate [mm/min] Figure 8; Average compression strength vs. deformation rate

The compression strength versus deformation rate for snow samples from a wall inside the building is shown in figure 9. One sample at each deformation rate between 0.5 mm/min and 5 mm/min were tested with intervals 0.5 mm/min.

1.2

1.1

0.9 Compression strength [MPa]

0.8

0.7

1 2 3 4 5 Deformation rate [mm/min] Figure 9; Compression strength vs. deformation rate for samples from a wall inside the building

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

4.2.3 Compression strength versus strain rate

Compression strength versus strain rate for the samples from the shady side of the building is shown in figure 10.

1.4

1.2

1 Compressive strength [MPa] 0.8

0.6

0 0.002 0.004 0.006 Strain rate [s-1]

Figure 10; Compressive strength vs. strain rate for the samples cut out from the shady side of the building.

4.3 Elastic modulus

4.3.1 Young’s modulus versus density

Young’s modulus versus density for different snow samples tested at a deformation rate of 1.5 mm/min is shown in figure 11.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

300 ] 2 200

100 E, Young's modulus [N/mm modulus E, Young's

480 520 560 600 640 680 720 Density [kg/m3]

Figure 11; Young’s modulus versus density for different types of snow, deformation rate 1.5 mm/min.

Young’s modulus versus density for samples from different parts of ICEHOTEL tested at 1.5 mm/min and 5 mm/min are shown in figure 12.

240

200 ]

2 160

120

80 E, Young's modulus [N/mm modulus E, Young's

480 520 560 600 640 680 720 Density [kg/m3] Figure 12; Young’s modulus versus density.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

4.3.2 Young’s modulus versus strain rate

Young’s modulus versus strain rate for the samples from the shady side of the building is shown in figure 13.

1000 ] 2 100

10 E, Young's modulus [N/mm modulus E, Young's

0.0001 0.001 0.01 Strain rate [s-1] Figure 13; Young’s modulus versus strain rate for the samples cut out from the shady side of the building.

4.4 Resisting force after the initial yield point

Samples tested at low deformation rates show a linearly increasing resisting force after the initial yield point. Samples tested at higher deformation rates did in general not show the same linear increase of the resisting force after the initial yield point. Those tests were also in general interrupted after the drop in force registered after the initial yield point. If the tests at the higher deformation rates were continued for a longer period of time an increase in force could be registered. Typical curves for the tests at the different deformation rates are shown in Appendix 1.

The slope of the line registering the resisting force versus time after the initial yield point was calculated for the samples tested at 0.5 mm/s and 1.5 mm/s. Figure 14 shows the increase in resisting force in N/s after the initial yield point versus density.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

Shady side 1.5 mm/min Sunny side 1.5 mm/min Inside 1.5 mm/min Shady side 0.5 mm/min

1 Slope of line after yield point [N/s] Slope of line after yield point

0.1

480 520 560 600 640 680 720 Density [kg/m3] Figure 14; Resisting force versus density after the initial yield point.

Figure 15 shows the increase in stress after the initial yield point versus strain rate.

Sunny side 1.5 mm/min Sunny side 5 mm/min Inside 1.5 mm/min Shady side 1.5 mm/min Shady side 0.5 mm/min ] 2

1 Slope of line after yield point [N/mm Slope of line after yield point

0.1

0.0001 0.001 0.01 Strain rate [s-1] Figure 15; Increase in stress after the initial yield point versus strain rate.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

4.5 Time to reach initial yield point

The average time to reach the initial yield point or average time to peak stress for the different strain rates are shown in figure 17.

600

Samples from shady side Samples from sunny side Samples from inside

400

200 Time to initial yield point [sec]

0 1 2 3 4 5 Deformation rate [mm/min] Figure 17; Average time from the start of the test to the initial yield point for the different deformation rates.

Some of the tests were interrupted after reaching the initial yield point and some were continued in order to observe the deformation behavior after the yield point. The average value of the resisting force after 0.5 h for the different strain rates are shown in figure 18. For the tests which were interrupted earlier than after 30 minutes, the line was extrapolated so the value after 30 minutes could be calculated. When the deformation rate is low the rate of increase in resisting force after the yield point is lower than with a higher deformation rate.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

Samples from sunny side Samples from shady side Samples from inside

6 Force after 30 minutes [kN]

0 1 2 3 4 5 Deformation rate [mm/min] Figure 18; Average value of the resisting force 30 minutes from the start of the test for the different deformation rates.

4.6 Viscosity

Calculations of viscosity with test results from compression tests should be based on tests were the stress has been constant and not based on constant speed tests as has been done here. Based on values of stress calculated from the resisting force value after 30 minutes viscosity values were anyway calculated using equation 3. Approximate average viscosity values for some of the samples at different rates of strain are shown in figure 16.

These values are however not considered reliable according to the reason mentioned above. What can be observed from the results though is the dependence on strain rate. In future tests the stress needs to be constant in order for viscosity values to be calculated.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

2.8

2.4 ] -1 2

1.6 Viscosity, η [MPa s

1.2

0.8

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 Strain rate [s-1] Figure 16; Approximate values of the viscosity for different rates of strain.

5. Discussion

Most of the values of the density for the tested samples were between 550 kg/m3 and 650 kg/m3, which is the same as for previously tested samples from the ICEHOTEL. Since the weather was above zero when the samples were cut out, all samples where quite soft and wet, but the inner parts and the inside walls of the building were more compact and harder than the outer layer. However the density is in the same range for all samples.

The density has been shown to have larger influence on the ultimate strength than the temperature and crystal size (Gold, 1956). A factor of importance is the bonding between snow grains which changes with time and which also is dependent on thermodynamic forces. The internal structure of the snow and the network connections of the ice grains constitute the base for the mechanical properties (Kinosita, 1967).

Higher content of ice in the snow gives higher density. Some of the samples which appeared to have a high content of ice cracked during loading as shown in figure 18, or broke as a brittle failure while the samples which were soft and homogeneous became plastically deformed. The slow deformation rates allow the snow samples to deform and become distorted. The samples which were allowed to deform under a quite long period of time were very deformed when the test was interrupted, figure 19.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

Figure 18; Cracked snow sample Figure 19; Deformed snow sample

The compression strength increased with increasing density. This is in agreement with previous studies (Vikström, 2001, Lintzén, Edeskär, 2012). The compression strength also increased with increasing deformation rate, which also has been observed in other tests were snow has been compressed at constant deformation rates (Kinosita, 1957, 1958, 1967). The average compression strength was higher from the samples cut out from the inside. Those samples appeared to be harder. They were also less affected by weather changes and not as soft as those from the outside were when they were cut out.

Many of the previously carried out tests on samples from ICEHOTEL were done at a higher deformation rate (6 mm/min) which presumably is the reason that some of the values obtained in those tests are higher than in the current tests. Nevertheless the values are in the same range as those from earlier experiments with snow from ICEHOTEL. The values are however somewhat lower than values presented by Bader (1962) on natural snow. However it is not clear what the deformation rate was for those tests. The values are similar to results presented by Mellor (1975) but it is difficult to make any exact comparisons since test temperatures, deformation rates and type of snow which is tested are different.

The deformation of snow is strongly influenced by the speed of deformation (Kinosita, 1967). At slow speeds the samples deform plastically, which was seen in the performed tests. At higher speeds the deformation mode is brittle. The reason why slow deformation speeds give rise to plastic deformation while high deformation speeds produce brittle fracture are changes of internal texture of snow during the deformation (Kinosita, 1967). Plastic behavior is associated with dislocations within the ice grains which form the crystal network. Brittleness is associated with disjoinment of the connections in the network. There is a critical deformation rate between the plastic and brittle behavior. The maximum speed of deformation for the machine used for the tests did not seem to be fast enough for brittle failure though.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

When the samples were loaded at speeds 1.5mm/min the resisting force, F, continued to rise at first rapidly and then slowly, without any discontinuous depression. The samples became more and more deformed as shown≤ in figure 20, but no definite value of the force F seemed to be possible to reach. For the higher deformation rates a drop could be observed after reaching the peak value after which a slow increase of the resisting force again was recorded (figure 6, appendix 1).

Tests done with natural snow to find the boundary velocity at which the deformation behavior turns from plastic to destructive show that the critical velocity is dependent on the density for the snow and on the test temperature (Kinosita, 1957). The equations showing the dependence are based on test results and written as:

= 11 + 0.4 / (4) ∗ and 푣 푇 푚푚 푚푖푛

= 30 / (5) ∗ where T is the푣 temperature∗ 휌 푚푚 in °C푚푖푛 and ρ the density in gram/cm3 (Kinosita, 1958).

Using these equations the critical speeds for the samples tested would be about 9 mm/min based on equation 4 and between approximately 15 mm/min and 18 mm/min based on equation 5. As observed in the tests, 5 mm/min, which was the maximum speed for the machine used, was not fast enough for a brittle fracture. The plastic contraction of the snow will not damage the snow but make it stronger. For future experiments it would be interesting to test samples at higher speeds to observe the critical boundary velocity for the artificial snow from ICEHOTEL.

Young’s modulus, E, increased with increasing density and increasing strain rate. The values are lower than compared to results presented by Mellor (1975).

The behavior of snow under an applied load is determined primarily by the nature of the bonds between grains (Gold, 1956). If the strength of the bonds is exceeded the snow structure will collapse resulting in a sudden increase in the density. As the snow settles the snow approaches a maximum value. In this state the strength properties of the grains and the boundary conditions associated with the loading play a significant role in determining the behavior of the snow.

The time to reach the initial yield point decreased with about 80% when the deformation rate increased from 0.5 mm/min to 1.5 mm/min. A further decrease with 67% was observed when the deformation rate increased from 1.5 mm/min to 5 mm/min. The grade of contraction for the 0.5 mm/min deformation rate at the initial yield point was 39%. Corresponding values at the initial yield point for the deformation rate 1.5 mm/s and 5 mm/s were about 23%.

The measured value of the resisting force after 30 minutes of loading is linearly increasing with increasing deformation rate. This shows that the snow become harder as it is deformed and compressed if it does not break.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

Regarding the viscosity, constant deformation tests should not be used for calculation of values as was done here. For future experiments also constant load tests should be performed in order for values of axial viscosity to be calculated. Axial viscosity, or unconfined viscosity, for snow can be calculated by creep tests under uniaxial compressive stress (Mellor, 1977). A cylinder of snow can be subjected to a constant axial dead load and allowed to deform until the plot of displacement against time appears to be linear. At that time the final strain rate should be recorded against initial stress and initial density, values which then are used for calculating the viscosity. Calculations and interpretations of the viscosity seem to be difficult though and it may be easier and give more correct data values to compare by instead directly studying stress-strain rate data.

A source to possible errors from the tests could be when the samples became plastically deformed during loading and the plates against which the sample of snow was attached became declined. This resulted in distorted snow samples as can be seen in figure 20 which may give incorrect values of the resisting force.

Figure 20; Compressed snow samples.

For future tests higher deformation rates should be used in order to find the critical speed of deformation at which the behavior changes from elastic-plastic to brittle.

If constitutive equations and failure criteria are properly formulated, the constants which express material properties ought to be the same for any type of loading conditions, and they should therefore be measurable from a variety of tests (Mellor, Cole, 1981).

Since the internal structure of the snow, the network connections of the ice grains and size and shape of snow crystals constitute the base for the mechanical properties it is of importance to find a good method to be able to also study these things in future tests.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

6. Conclusion

The density for artificial snow used for ICEHOTEL is higher than for natural snow. The compression strength and Young’s modulus of snow increase with increasing density.

The deformation speed or strain rate has a large influence on the mechanical behavior. The compression strength and Young’s modulus increase with increasing deformation rate or strain rate.

The deformation mode is also dependent on the deformation rate. Elastic-plastic behavior was observed for all performed tests. The maximum deformation rate used was not high enough for brittle behavior.

7. References Bader. H, 1962, The Physics and Mechanics of Snow as a Material, Cold Regions Science and Engineering, Part II, Section B, July 1962.

Gold, L.W. (1956) The strength of snow in compression, Journal of Glaciology, Vol.2, No.20, October 1956, pp. 719-725.

Haynes, D. (1978) Effect of temperature on the strength of snow-ice, CRREL Report 78-27, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire.

Kinosita, S. (1957) The Relation between the Deformation Velocity of Snow and Two Types of its Deformation (Plastic and Destructive), Low temperature science, Series A, Physical sciences 16, pp.139-166. Hokkaido University.

Kinosita, S. (1958) The Relation between the Deformation Velocity of Snow and Two Types of its Deformation II, Low temperature science , Series A, Physical sciences 17, pp.11-30. Hokkaido University.

Kinosita, S. (1967) Compression of snow at constant speed, Physics of Snow and Ice: proceedings, 1967. Hokkaido University.

Lintzén, N, Edeskär, T. (2012) Study on basic material properties of artificial snow, NGM Copenhagen.

Mellor. M, 1975, A review of basic snow mechanics, IAHS Publication, Vol.114, 1975, pp.251-291.

Vikström, L, Bernspång, L. (2002) Strength and deformation behavior of snow and snow structures, Research Report 2002:13, ISSN:1402-1528, Luleå University of Technology.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

APPENDIX 1

Figure 2; Sample from the shady side of the building, deformation rate 0.5 mm/min.

Figure 2; Sample from inside the building, deformation rate 1 mm/min.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

APPENDIX 1

Figure 3; Sample from the side exposed to sunshine, deformation rate 1.5 mm/min.

Figure 4; Sample from inside the building, deformation rate 2 mm/min.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

APPENDIX 1

Figure 5; Sample from the shady side of the building, deformation rate 3 mm/min.

Figure 6; Sample from inside the building, deformation rate 4 mm/min.

Compression strength of snow – Experimental measurements at ICEHOTEL in April 2012 DRAFT 1

APPENDIX 1

Figure 7; Sample from the shady side of the building, deformation rate 5 mm/min.