LIQUID PERMEABILITY OF SNOW

Daisuke KUROIWAInstitute of Low Temperature Science, Hokkaido University, Sapporo, Japan

ABSTRACT

In order to measure the liquid permeability of snow, three types of kerosenepermeamcters were designed for low, medium, and high density snow. The measure-ments were conducted on natural snow cover and artificially compressed snow, andcorrelation between kerosene permeability and porosity was investigated for widerange of porosity of snow.

RÉSUMÉ

Afin de mesurer la perméabilité de la neige aux liquides, trois types de perméamètresau kérosène ont été réalisés pour des neiges à faible, moyenne et haute densité. Lesmesures ont été effectuées sur de la neige naturelle et sur de la neige comprimée artifi-ciellement et la corrélation entre la perméabilité au kérosène et la porosité a étéétudiée pour une large variation de la porosité de la neige.

INTRODUCTION

Fluid permeability of snow is considered to be one of the basic quantities to describethe physical properties of snow. The fluid permeability of snow may depend not onlyon porosity, but also on its structure such as grain size and the space configurationsof air voids or channels. Several types of gases or liquids may be used as the fluid.If we use air as the fluid, the air permeability is obtained, and it has been measuredby various authors such as Bader et al. (1939), Ishida and Shimizu (1955) and Bender(1957). According to Shimizu's experiment, when the air flow velocity was kept lessthan 1 cm/sec, reproducible values of air permeability were obtained, although therelative humidity of the air with respect to ice ranged between 60 and 95% at — 15°C.If the air flow velocity exceeds 1 cm/sec and some temperature gradient exists withinthe snow, its structure may be changed. In principle, therefore, air saturated withrespect to ice at a given temperature should be used in order to avoid any structuralchange due to evaporation and condensation.

If we use water as a fluid, we can obtain the water permeability of snow. From thepractical point of view, the water permeability of snow may be very important tostudy the permeation of melt water through snow strata. Yamada and Nakamura(1967) tried to measure the water permeability of snow in a cold room maintained atnearly 0"C. Since small fluctuations of the room temperature were inevitable, theydesigned their pcrmeametcr carefully in such a way that the temperature of both thesnow sample and the water could be maintained at 0°C through out the experiment.Using this permeameter, they tested whether a reproducible value of the water perme-ability could be obtainable or not. They found the following tendency: when roomtemperature was changed from 0°C to +0.5°C, the waier permeability of snowwas increased gradually with the number of times measurements, but the reverseresults were obtained when the room temperature was lowered from 0°C to — 0.5°C.These experiments suggest that it may be very difficult to measure water permeabilityof snow without interactions occurring between water and snow under the equili-brium condition.

The author attempted to measure the liquid permeability of snow by minimizinginteraction between fluid and snow, and he designed three types of kerosene permea-

380

meters. Kerosene cooled below 0 °C was chosen as the fluid. There may be no substancewhich does not cause absolutely no melting of snow, but the solubility of ice inkerosene can be considered to be negligible below 0°C.

!2cm

-8.5 cm-

KEROSENE

8cm .: SNOW :

. 3.5 cm

-C

KEROSENE

a . for low density

Fig. \a

Figs, la and 16 — Schematic diagrams of kerosene permeameters.

KEROSENE PERMEAMKTERS

Figure 1 shows schematic diagrams of three kerosene permeameters. In thisfigure, a, b, and c are kerosene permeameters used for low, medium and high densitysnow, respectively. The principle of these permeameters are analogous to the ordinaryfalling head method used in soil engineering. In the diagram a, A is a glass measuringcylinder, 12 cm in lengxh, 8.5 cm in diameter, and the bottom of this cylinder is fixedtightly to thick brass plate B with a kerosene-proof resin. C is a sample holder, 8 cmin length and 3.5 cm in diameter, made of thin stainless steel plate. The snow specimencan be prepared readily by inserting C into the desired snow stratum. After sampling

381

the snow, C is screwed to the brass plate B. When A and C are held vertically, thelower end of C is dipped slightly in kerosene in a shallow pan E. If previously cooledkerosene is poured in A, kerosene begins to flow down through the sample and over-flows from E and drains away from F.

- 3 7 c m -

30

29

26-

24

22

20

18

16

17

12

10

6 -

4-

2-

kerosene

snow

20

18

14

12

109876543I

0.8 cm

b. for mediumdensity C. 1or high

density

Fig. 16.

If we measure the time interval I required for the kerosene head to fall from agiven height Hi to Hz, permeability k is given by

, 2.3 LA' , //,k = " Z T logl° F

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where, L is the length of sample of snow, A and A ' the cross-sectional area of thecylinders A and C, respectively. In this formula, the unit of k is given in cm/sec.The kerosene heads Hi and H» should be measured from the level of the keroseneoverflowing from pan E.

Diagram b is a simple kerosene permeameter made of brass cylinder. The sampleof snow can be readily prepared by inserting the cylinder into snow, and then thecylinder is set vertically in a shallow pan filled with kerosene. Previously cooledkerosene is poured into the top of the cylinder, and the falling kerosene head can beobserved through a slit.

Diagram c shows a permeameter designed for the measurement of kerosenepermeability of high density snow, and it is used mainly in the laboratory. As seenin the figure, the snow specimen is packed into a brass cylinder B, and then B isscrewed to A. A glass burette C, 0.8 cm in diameter and 22 cm in length, is attachedto A. Cooled kerosene is poured into the top of the burette.

EXPERIMENTAL RESULTS

1. Reproducibility of the value of kerosene permeability

In order to investigate the reproducibility of the kerosene permeability, manytests were made with different densities and types of snow. The lime interval / requiredfor the kerosene head to fall from H\ = 13.9 cm to H-> = 8.9 cm was measured repeat-edly for the same specimen of snow. The results are tabulated in table I.

TABLE 1

t: time required fur the kerosene head to fall from H\ = 13.9 cm to Hi = 8.9 cm

No. of test

12345678

Fine-grained snow

/> = 0.227

45.0 sec45.849.249.049.250.049.550.2

p = 0.357

101.2 sec110.1114.0114.5113.6114.51 14.2

Coarse-grained snow

p = 0.395

13.5 sec14.014.014.814.013.814.0

p = 0.492

15.0 sec15.016.015.716.015.315.5

As seen in the table, the value of t for the first and second tests were found to belittle shorter than those for the subsequent tests, but after the third test the / valuesbecame constant. This tendency can be seen more obviously in the second and thirdcolumns than in the fourth and fifth columns of the table- Therefore, in the case oflow density snow, observed values of the permeability for the first and second testsshould be excluded. However, in the case of high density snow, approximately constantvalues were obtained for all repeated tests. In our experiments, all tests were repeated7 or 8 times for the same specimen of snow, and observed values of permeabilitywere averaged, excluding the values of first and second tests.

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Fig. 2 — Horizontal distribution of kerosene permeability.

2. Horizontal distribution of permeability along snow strata

A large block of snow, 92 cm x 100 cm x 50 cm, was cut carefully from thenatural snow cover without causing any disturbance to the original stratification,and stored in the cold room for approximately one month. The upper half of thisblock was composed of fine-grained snow and the lower half of coarse granularsnow that had experienced melting and refreezing before. When a vertically-slice ofthis block was held against light, typical horizontal stratification could be seen in theupper half part, but no layer structure was observed in the lower part, see figure 2.In order to find the horizontal distribution of kerosene permeability k along thesnow strata, 5, 3 and 2 specimens were prepared from layers A, B, and C respectivelyas shown in figure 2. The values of permeability obtained at — 7°C and the snowdensities are tabulated in table 2.

TABLE 2

Horizontal distribution of k along strata

A-layer

B-layer

C-layer

kPkPkP

(cm/sec)(g/cm3)(cm/sec)(g/cm3)(cm/sec)(g/cm»)

0.6920.2271.390.2342.050.395

0.6500.2321.180.2412.110.395

0.6150.2361.170.241

ave. 2.08ave. 0.395

0.5900.236

ave. 1.27ave. 0.238

0.5260.239

ave. 0.615ave. 0.234

384

Fig. 3 — Grain structures of snow layers A, B, and C shown in figure 2.

385

As seen in table 2, the value of permeability measured along the A-layer seems todecrese slightly from the left to the right, but the values of density increased graduallyfrom the left to the right. The similar tendency could be seen along the B-layer. Theaverage value of A of A-layer was approximately '/2 of that of B-layer, and ^ of thatof C-layer. Since the bulk density of snow in C-layer was larger than that of A orB-layer, the apparent porosity of C-layer must be smaller than that of A or B-laycr.But the value of A of C-layer was larger than that of A or B-layer. The value of kof B-layer was larger than that of A-layer, in spite of fact that their bulk densitiesare approximately the same. These facts mean that the kerosene permeability of snowmay not be a simple function of the bulk density of snow, and it may depend oninternal structures such as grain size and space configurations of the air voids. Figure 3(A), (B), and (C) show thin sections of the snow layers A, B, and C shown in figure 2.As seen in figure 3, the average grain size of A-layer is smaller than those of B- andC-layers.

3. Relation between horizontal and vertical permeabilities

If we denote horizontal permeability and thickness of individual strata of snowas Ai, A'2, A-3,... and hi, Ao, A.j,. , the resultant vertical and horizontal permeabilitiesKv and Kh are given by:

and

Kh = -(h1kl + h2k2 + h3k3 + ...)

where, H is the total thickness of strata, and H = A1 + A2 + A3 + ••• In order to checkthese relations, several experiments were made. Two typical results, A and B, areshown in figure 4. In this figure, Ai, ko, and A3 and H1,hz, and A3 indicate the horizontalpermeabilities and thicknesses of strata I, 2, and 3, and the total thickness of thelayers H was 15 cm. A4 is the observed vertical permeability of specimen 4 cut verticallythrough three strata, and Kv and Kh arc the resultant vertical and horizontal pcrmea-

h,= 3.5 cm

h2= 8 cm

hj=3.5crn[

J? =0.491

f,= 0^.67

£=0.538

h,- 5.5cm

"ij= 4 cm

b}- 5.5 cm

1 ; 4 if=0.55

o ! ' P n/B.9

k,=Q386.

k,=0586k3=0.336

+= 0.397 k,=0.231 k1=0.236

k,=0.34l Kv-0.285

kj=0.321 Kfc=0.293

f

Fig. 4 — Correlation between horizontal and vertical permeabilities.

386

bilities calculated by the aforementioned relations. The observed value k$ and thecalculated value Kv should be equal, but results showed some disagreement. Thismay arise from the fact that a seemingly homogeneous snow stratum is usually com-posed of many fine strata and it is difficult to measure the thickness and permeabilityof the individual strata. As seen in figure 4, it appears that Kv < Kn- A similar resultwas obtained for many strata of different types of snow.

4. Porosity dependence on kerosene permeability

Bader et ai. (1939) reported that the value of air permeability of snow variedwidely as a function of porosity and types of snow, and lshida and Shimizu (1955)found that air flow resistivity of natural snow depends not only on porosity, but alsoon types of snow. Analogously, it may be predicted that kerosene permeability ofsnow may not be expressed by a simple function of the porosity of snow.

In figure 5, the observed values of kerosene permeability k of natural snow wereplotted against the value of porosity e — 1 - />//>ice- In this figure the types of snoware indicated by different symbols, solid circles represent data from fine-grained snowmeasured in the field, and open circles indicate data from fine-grained snow storedin the cold room for approximately one month. The former data were obtained atair temperatures of — 5 to - 7 °C, while the later data were measured at - 6 °C. As seenin this figure, most k values of fine-grained snow and newly-fallen snow ranged between1.0 and 0.1 cm/sec, while the values of k of coarse granular snow and depth hoarranged between 4.0 and 1.0 cm/sec. In our case, it seems very difficult to find any

1.0.

_ k

• o11

3IDOl

ff.ity

•

cm/sec

A

AA

•. *

t.1 «

A

AA

cP

A

#

•

Ao

*

*

•

largedepth

grainedhoar

tine grainednewly

A

m

* •

•

porosity

fallen

40

0

snow

snowsnow

**

•

e0.5 0.6 0.7 0.8 0.9

Fig. 5 — Porosity dependence on kerosene permeability of various types of snow.

387

simple correlation between k and £. However, if we assume that the empirical formulafound by Bader et al- (1939) is applicable to the kerosene permeability of snow, therelationship between k and e may be expressed by

k = aeNN-e'

where, a and N are considered to be characteristic constants for snow structure suchas grain size and space configuration of air voids or channels. The numerical valuesof these constants can be determined graphically by plotting k/e against k.

Ö 02" ÖA 06 Öl To Î2 K

Fig. 6 — Relation between k/e and k for fine-grained snow.

388

In figures 6 and 7, values of k/e for various types of snow are plotted against A:.The relations between k and e are represented by straight lines. In figure 6, the dataof fine-grained snow in the field are distributed along the straight line 1, while thedata of fine-grained snow stored in the cold room are distributed along a differentstraight line 2. The calculated values of the characteristic constants a and N aregiven in each figure.

k=QEN

Q-0.6

N-0.65

permeability cm/Sec

Fig. 7 — Relation between k/e and k for coarse-grained snow.

The density of natural snow in Japan ranges between 0.1 and 0.5 g/cm3. In otherwords, the porosity of natural snow ranges between 0.45 and 0.9 as shown in figure 5.In order to find the kerosene permeability of highly densified snow, the followingexperiments were conducted in the cold room kept at — 5 °C. Two blocks of fine-grainedsnow were rubbed against each other to make powdered snow. The pulverized snowwas packed in the brass cylinder B of the c-typc permeameter shown in figure lb. Thecylinder was placed under a motor-driven compression apparatus. The snow inthe cylinder was compressed by a piston at a velocity of I mm/hr until the desired

389

density was obtained. The apparent density of the compressed snow was estimatedfrom the volume change during compression. The porosity could be reduced from0.4 to 0.05. Immediately after compression, cylinder B was screwed to A of c-type

1Ö1'

10

10"

10

cm/sec

fD-\3

cr

0.1 0.2 0.3 0A 0.5porosity £

Pig. 8 — Porosity dependence on kerosene permeability for artificially compressedsnow.

390

permeameter and the permeability was measured. In figure 8, the observed values ofk of the artificially-compressed snow are plotted scmi-logarithmically against porosity.As seen in this figure, k seems to decrease exponentially with decreasing porosity.

CONCLUDING REMARKS

Three types of kerosene permeameters were designed for low, medium and highdensity snow. The principle of these permeameters is analogous to the ordinaryfalling-head method used in soil engineering. The reproducibility of the kerosenepermeability k was carefully investigated by repeating many tests on the same sample ofsnow. In the case of low density snow, less than 0.36 g/cm3, a slight difference wasfound between the k values for the first and second tests and those of subsequent tests.After the third test, a reproducible value of k was obtained. The value of k for thefirst or second test was found to be approximately 10 to 15% larger than those obtainedin subsequent tests. This difference is presumably caused by the fact that the lowdensity snow specimen may be slightly compressed by the kerosene pressure. Forhigh density snow, however, the difference was not observed.

Horizontal and vertical permeabilities of snow strata were observed in the fieldand laboratory. The value of the resultant horizontal permeability was found to belarger than that of the vertical permeability. The relation between kerosene permeabilityk and porosity of snow K showed a wide scatter in the range of porosity 0.45 to 9.0.The values of k for fine-grained snow varied between 10-1 and 1.0 cm/sec, whilek values for coarse-grained snow varied between 1.0 and 4.0 cm/sec.

In order to find the kerosene permeability of highly densified snow, many measure-ments were made on artificially compressed snow. The porosity of snow was reducedfrom 0.4 to 0.05. The value of k decreased logarithmically from I0"1 to 10~4 cm/sec.

The author is indebted to Dr. Nakamura, Institute of Snow and Ice Studies,Nagaoka, and Messrs. Suzuki, Sato, Kitahara for assistance of this research.

REFERENCES

BADER, H. el a]., (1939): Der Schnee und seine Metamorphose. Beitrage zur Geologieder Schweiz, Geolechnische Serie, Hydrologie, Lieferung 3, Bern.

BENDER, J.A., (1957): Air permeability of snow, S1PRE Research Report 37, p. 19.ISHIDA, T. and SHIMIZU, H., (1955): Determination of air flow resistance through

snow layers (in Japanese). Teion Kagaku, Ser. A, vol. 14, pp. 33-42.

391