Introduction

Extensive studies of the strength properties of snow were made by Butkovich,Reference Butkovich ¹ who investigated the compressive, tensile, shear and torsional strengths of snow as a function of density. A very pronounced dependence of the strength on the density was found which could be expressed in a general formula. The work of disaggregation as a function of density was also reported by Butkovich, who also gives relevant literature references. BenderReference Bender ² has also studied the age hardening of snow by measuring the work of disaggregation. In the present work a beginning has been made of a study of the uniaxial compressive strength of snow cylinders as a function of age and of particle size of snow fractions. Ageing of snow and the effect on the compressive strength of snow of the inclusion of various gases in the atmosphere in which they were kept, were also investigated.

Experimental Details

Materials. Two different snows were used for the experiments. One snow was collected at Wilmette, and stored at −20° C.; experiments were started after about two weeks; the other was collected at Houghton, Michigan, stored at about −15° C. for about four weeks prior to use and subsequently stored at −20° C.

Preparation of Snow Fractions. The snow fractions were prepared on a “Ro-Tap” shaker; the sieves used were of the U.S. standard sieve series. The snow for each of the Houghton snow fractions was obtained after two minutes shaking, whereas the Wilmette snow fractions were obtained after longer periods of shaking, especially for the small size and largest size of particles.

Apparatus and Technique. All strength measurements were carried out at −10°±0.5° C. with a Carver Hydraulic Laboratory Press in conjunction with a Baldwin Load Cell (2000 lb., 900 kg.) and a Leeds and Northrup recorder. A picture of this press is shown in a report by Butkovich on the Ultimate Strength of Ice.Reference Butkovich ³

The snow cylinders were prepared at −20° C. in a Lucite cylinder of 4.38 cm. inside diameter and 25 cm. high. The height was graduated and could easily be read to the nearest mm. About 82.5 gm. of snow were weighed into the tube with an accuracy of 0.1 gm. The snow was then compressed to a height of 10 cm. in the plastic tube with the press to which a suitable piston was attached. Actually only half the compression was carried out at a time, the cylinder was then inverted and the compression completed. Thus large density gradients in the cylinders were avoided. The majority of densities were in the range from 0.548 to 0.552 gm./cm.³. The snow cylinders (diameter 4.38 cm., height 10 cm.) were then removed to a cold room of −10° C. and crushed after a time interval as indicated in the experimental results.

Experimental Results

Ageing of Snow Cylinders. The ageing of snow cylinders was investigated using the un-fractionated, original snow samples, except that the Houghton snow was passed through a 1.19 mm. sieve to remove lumps. Tables I and II and Figs. 1 and 2 show the experimental results for the Wilmette snow. Table III and Fig. 3 show the results for the Houghton snow.

Table I

Compressive Strength as a Function of Ageing of Snow Cylinders at –10° C. Wilmette Snow unfractionated Age of snow: 35–50 days

Table II

Compressive Strength as a Function of Ageing of Snow Cylinders at −10° C. Wilmette snow unfractionated Age of snow: 57 days

Table III

Compressive Strength as a Function of Ageing of Snow Cylinders at −10° c. Houghton snow Age of snow: 30 days

Fig. 1.

Compressive strength of snow cylinders (radius 2.19 cm., height 10 cm., density c. 0.550 gm./cm.³) as a function of the age of the cylinders at −10° C. Each point represents the average of twelve tests. The numbers near the points represent the age in days of the snow from which the cylinder was made. Snow was collected at Wilmette, Illinois. Curve was calculated from equation (1a) with the following constants:

Fig. 2.

Compressive strength of snow cylinders (radius.2.19 cm., height 10 cm., density c. 0.550 gm./cm.³) as a function of the age of the cylinders at −10° C. Each point represents the average of twelve tests. The age of the snow when preparing cylinders was in all cases 57 days. Snow was the same (Wilmette) as that for Fig. 1. Curve was calculated from equation (1a) with the following constants:

Fig. 3.

Compressive strength of snow cylinders (radius 2.19 cm., height 10 cm., density c. 0.550 gm./cm.3) as a function of the age of the cylinders at −10° C. Each point represents the average of ten tests. The age of the snow when preparing cylinders was in all cases 28 days. Snow was collected at Houghton, Michigan. Curve was calculated from equation (1a) with the following constants:

The cylinders fractured usually into three pieces in a similar way to that observed by Butkovich (see Fig. 1 of Butkovich’s report Reference Butkovich ¹ ). The number near each of the experimental points in Fig. 1 gives the age of the snow in days from which the twelve cylinders, whose mean strength the points represent, were made. It is seen that the younger the snow, the greater the strength of the cylinders. The cylinders from the Wilmette snow represented in Fig. 2 were all made within 30 hours of each other, as were the cylinders from the Houghton snow represented in Fig. 3.

Compressive Strength as a Function of Particle Size. Table IV gives the compressive strength values as a function of particle size, and Fig. 4 shows the mean strength values as a function of particle size for the Wilmette snow. Most of the Wilmette snow (c. 50 per cent.) was in the size range from 3.5 to 5.0 mm. There is a very appreciable decrease of strength with particle size. Fig. 4 shows again the marked influence of the age of the snow. It was desired at a later date to determine the strength of the snow fraction of large particle size. These later strength values for the older snow were very much lower (see Table IV and Fig. 4, 56 days) than expected from the previous results. In order to check this behavior, tests were repeated on a snow fraction which had been investigated about six weeks earlier. This means that cylinders were prepared of snow six weeks older than that used for the previous fraction. The results (Table IV and Fig. 4, 64 days) show that the strength of the cylinders is very dependent on the age of the snow. This strong dependence is also apparent for the three fractions of small particle size. These measurements were made before the importance of age was realized. For this reason the average strength values for the smaller size fractions are considered to be too small compared with those of the larger size fractions of Table IV.

Table IV

Compressive Strength as a Function of Particle Size at −10° C. Wilmette snow Age of cylinders: 168 hours

Fig. 4.

Compressive strength of snow cylinders as a function of snow particle size (−10° C.). The horizontal lines represent the range of sieve sizes used to obtain the particular fraction. Each point represents the average of twelve tests. The number beside each point gives the age of the snow (Wilmette snow). Each cylinder was aged for 168 hr. at −10° C.

An interesting by-product of this work is given by the densities of the snow fractions before compacting. These densities were obtained by pouring the fractions loosely into the plastic cylinder without compacting. Fig. 5 shows the results. A decrease of density with increasing particle size is observed.

Fig. 5

Density obtained by loosely packing snow fractions (−20° C.). (Wilmette snow)

Because of the strong influence of the age of snow on its strength, a series of experiments were carried out with the Houghton snow on the strength as a function of particle size, all cylinders being prepared within 30 hours of each other.

These results are shown in Table V and Fig. 6. Here again the compressive strength decreases with particle size, however not quite as drastically as for the Wilmette snow. The difference is due to the high age of the lower Wilmette fractions as pointed out previously.

Table V

Compressive Strength as a Function of Particle Size at −10° C. Houghton snow Age of snow: 27 to 28 days Age of cylinders: 168 hours

Fig. 6

Compressive strength of snow cylinders as a function of snow particle size (−10° C.). The horizontal lines represent the range o sieve sizes used. Each point represents the mean of ten tests. Age o snow in all cases was 28 days (Houghton snow). Each cylinder was aged for 168 hr. before breaking

Mixture of Fractions. A number of experiments were also carried out on the strength of mixtures of fractions of the Wilmette Snow. On the whole these results reflect those which were found with single fractions. The results are given in Table VI.

Table VI

Compressive Strength of Mixtures of Fractions at −10° C.Wilmette snow

Influence of Gases on the Compressive Strength of Snow

A number of snow cylinders were prepared which were exposed to gases such as carbon dioxide (CO₂), methane (CH₄) and ammonia (NH₃). Other cylinders were prepared at the same time for comparison and treated in the same way except that they were not exposed to the gases. These are referred to as blanks in Table VII.

Table VII

Effect of Gases on the Compressive Strength of Snow

The experimental procedure was as follows. The cylinders were made in the usual way at −20° C. They were then placed in a wide-necked bottle and exposed to a small amount of gas. The amounts were measured approximately by counting bubbles passed through a washbottle (160 bubbles for each experiment, or very approximately 100 to 150 ml. at N.T.P.). The samples treated with carbon dioxide and methane did not show any difference from the untreated samples, whereas the samples treated with ammonia had a distinctly wet appearance. The untreated and treated samples were then evacuated under a bell jar until the ammonia smell could not be detected any more; the samples treated with the other two gases were evacuated for the same length of time. The cylinders were then stored for 168 hours at −10° C. and broken. The results are given in Table VII. It is seen that the strength of the cylinders treated with ammonia has decreased considerably compared with untreated samples, whereas carbon dioxide and methane apparently do not influence the strength.

Discussion

The ageing curves for the snow cylinders made from the Wilmette and Houghton snows can be fitted very satisfactorily by an equation as follows:

or

where S _o is the initial and S _f the final compressive strength and k a rate constant. The curves in Figs. 1, 2 and 3 were calculated with the following constants:

It should be noted that equation (1a) and (1b) is the same as that for a first-order chemical reaction where one compound B is formed from a compound A: A → B. Differentiation of (1a) gives:

and at t = o, S _t = S _o.

Some experiments performed by BenderReference Bender ² on the work of disaggregation are shown in Fig. 7. These results can also be expressed by equation (1a), although not quite as closely as the previous ones. It would be of interest to study the ageing of snow as a function of temperature. The rate constant k can probably be expressed by an exponential law, k = A exp(−E/RT), where A and E are constants, R the gas constant, and T the absolute temperature. An energy of activation E could then be derived, which might throw some light on the ageing process. This ageing process has something to do with recrystallization, diffusion and sublimation in the contact areas between snow particles.

Fig. 7.

Ratio of work of disaggregation al time t to work al t=0 as a function of time. Curves (1) and (2) are averaged experimental curves for −5° C. and −20° C. respectively. Curves (3) and (4) are calculated from equation (1a).

The great effect of the age of the snow from which they are made on the compressive strength of the cylinders of equal age is quite remarkable. This must be due to the metamorphism Reference Bader ⁴ snow undergoes as it ages. New snow particles have numerous ramifications and protuberances, which are in an unstable state. Recrystallization, sublimation and surface migration take place rounding the particles. Thus the whole system tends to become more stable with age. Consequently, less bonding will take place on compression with old than with new snow. The strength of snow specimens as a function of the age of snow merits further study.

The decrease of compressive strength with decrease in particle size seems surprising at first. Microscopic examination shows that the snow passes from a more spherical shape to a more elongated one as the particle size decreases. It seems also to be the case that the smaller particles have less ramifications than the larger ones. One factor which might be of decisive importance in this connexion is the following. It was shown in Fig. 6 that the smaller the particle size, the higher the density obtained by just pouring the sample into the plastic cylinder. Probably less work of compaction is required to compress the finer particles to the same density than the larger ones. Therefore the larger particles will be under much more strain and stress than the smaller ones. In order to relieve this unstable condition, rearrangement has to take place, which leads to finer bonding. It would be of interest to carry out studies on fractions of differently shaped snow particles, such as spheres, needles, etc. A beginning has been made by Fuchs.Reference Fuchs ⁵ It would also be of interest to study snow cylinders by the replica technique developed by Fuchs.Reference Fuchs ⁶ This would give an insight as to the number of bridges between snow particles as a function of specimen density, temperature, work of compression, etc.

The effect of gases, such as ammonia (NH₃) is not surprising. An exothermic reaction takes place forming NH₄OH. A concentrated solution is produced on the surface of the particles which serves as a lubricant for further compression. However, it does not seem possible to remove subsequently all of the NH₄OH and (NH₄)₂CO₃ which is formed by absorption of CO₂ from the air. Thus a film will be center between the snow particles weakening the whole structure. Experiments also show that for the same work of compression, the untreated snow still has a higher strength.

It is the author’s pleasure to thank Mr. E. M. Schwarz for competent performance of the tests.

MS. received 24 July 1958