M479 FACTORS AFFECTING UNTER MIGRATION IN FROZE SOILSCU) 14~

COLD REGIONS RESERCH RHO ENGINEERING LAS HAOVER mlX XUi ET AL. JUL 67 CRREL-87-9

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Factors 8ffeCting waterjgaif

in frozen soils

DTICS

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Factors Affecting Water Migration in Frozen Soils

12 PERSONAL AUTHOR(S)Xu Xiaozu, Oliphant, Joseph L. and Tice, Allen R.

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17. COSATI CODES 18. SUBJECT TERMS (Continue on reverse if necessary and identify by block number)FIELD GROUP SUB-GROUP Cold regions Soil-water potential

Frozen soil Water migrationLaboratory tests

19. ABSTRACT (Continue on reverse if necessary and identify by block number)'Soil-water potential was measured on three soils and influencing factors, including water content,

soil texture, dry density and temperature, were investigated. The soil-water potential in unsaturated,unfrozen soils decreases with decreasing soil water content and soil dispersion, and increases with in-creasing temperature and dry density. Unfrozen water contents were determined by pulsed nuclear mag-netic resonance and three factors thought to affect the unfrozen water content at a given temperaturewere investigated. Of these three factors, only increasing the salt concentration caused a large changein the unfrozen water versus temperature curves. Water migration in an unsaturated frozen soil (Morinclay) was determined in horizontally closed soil columns under linear temperature gradients. The fluxof water migration was calculated from the water distribution curves before and after testing. The fluxis directly proportional to the temperature gradient and inversely proportional to the square root of thetest duration, and decreases with decreasing temperature and soil dry density.

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PREFACE

This report was prepared by Xu Xiaozu, a visiting professor from the Lanzhou Institute ofGlaciology and Cryopedology, Peoples Republic of China, Dr. J.L. Oliphant, former Re-search Scientist, and A.R. Tice, Physical Science Technician, of the Research Division, U.S.Army Cold Regions Research and Engineering Laboratory. This paper reports work accom-plished under a cooperative research agreement between CRREL and the Lanzhou Institute.Funding for this research was provided by DA project 4A161102AT24, Research in Snow,Ice and Frozen Ground; Task A, Properties of Cold Regions Materials; Work Unit 002,Properties of Frozen Soils.

Professor Xu expresses his gratitude to the members of the CRREL staff who supportedhim during his visit. In particular, he gives special thanks to Dr. A. Assur, Dr. K. Sterrettand Dr. J. Brown for arranging this intergovernmental research exchange. Dr. M. Kumai, J.Ingersoll and D. Keller are also thanked for assisting in obtaining test data on the soils usedin this investigation. Finally, appreciation is expressed by Professor Xu to E. Chamberlain,Dr. R. Berg, Dr. Y-C. Yen and Dr. S. Colbeck for helpful discussions and suggestions.

The contents of this report are not to be used for advertising or promotional purposes. Ci-tation of brand names does not constitute an official endorsement or approval of the use ofsuch commercial products.

p%

CRREL Report 87-9July 1987

Factors affecting water migrationin frozen soils

Xu Xiaozu, Joseph L. O.iphant and Allen R. Tice

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CONTENTSPage

A bstract ................................................................ iP reface ................................................................. iiN om enclature ............................................................ vIntroduction ............................................................. IPrelim inary studies ....................................................... ,,

Soil-water potential in unfrozen soils ...................................... IUnfrozen water content in frozen soils ..................................... 4

Temperature gradient experiment ........................................... 8Water content profiles after migration .................................. 10Factors affecting the flux ................................................ 10

D iscussion .............................................................. . 15Relationship between the soil-water potential and temperature ................. I5Technical problems with the water migration test ........................... 15

C onclusions ............................................................. 15Literature cited ........................................................... 15

ILLUSTRATIONS

FigureI. Physical properties of soils used in this study ............................ 22. Effect of the water content and soil type on soil-water potential .............. 33. Effect of the dry density on soil-water potential ........................... 34. Effect of the temperature on soil-water potential .......................... 45. Effect of the water content of Morin clay on the unfrozen water content ...... 5 %6. Effect of the dry density of Morin clay on the unfrozen water content ......... 57. Effect of the salt concentration of Morin clay on the NMR signal ............ 6

8. Relationship between molality of Morin clay and the unfrozen water content.. 69. Relationship between molality of Morin clay and initial freezing point ........ 6

10. Comparison of observed and predicted curves ............................ 811. M oisture distribution before testing ..................................... 912. Temperature distribution in horizontal direction .......................... 1013. W ater content profiles at test conclusion ................................. 1114. Water content profile for different test durations .......................... 1215. Influence of testing duration on the flux ................................. 1216. Relationship bet,veen the flux and test duration .......................... 1217. Influence of temperature on the flux ..................................... 1318. End influence of soil column on the flux ................................. 1319. Influence of the dry density on the flux .................................. 1420. Relationship between the flux and temperature gradient .................... 15

%LI

TABLES Page

Table1. Values of the break point coordinates and coefficients A and B .............. 42. Values of the unfrozen water content calculated at different dry densities ...... 63. Values of constants C and D, and other parameters ........................ 74. Values of coefficients A and B, and other parameters ...................... 14

%.'.. *

.,, -.

%~ %

iv S. *Jk

NOMENCLATURE

A coefficient

B coefficient

C constant

D constant

e density of soil water

J flux

A average flux in ith segmentaverage flux in i-I th segment

PW pressure or suction of pore waterQ total fluxT temperature

T freezing point

W volumetric water content of soilW, W total water content at times 71,

T2

WO initial water content

Wu unfrozen water content

Ax length of segment

Yd dry densityAO chemical potential of pore water

soil-water potential S..

4 chemical potential of soil water

P-Wf soil-water potential of break point

Q density of soil water .time

Ik "10.'

5%

.5 ...p

v

A- A17--,

Factors Affecting Water Migration in Frozen Soils a

XU XIAOZU, J.L. OLIPHANT AND A.R. TICE

INTRODUCTION plicability of the extended Darcy's law to moistureWater migration in frozen soils under a temper- flow in frozen soils.

ature gradient not only changes the structure of The purpose of this report is to describe thefrozen soil and the proportions of ice and unfro- changing characteristics of water migration in fro-zen water, but also results in changes of the physi- zen soils in relation to the temperature, tempera-cal and mechanical properties, and causes ice seg- ture gradient, dry density and time.regation and frost heave. It is of great significance To obtain a deeper understanding of water mi-

both for the explanation of cryogenic phenomena gration in unsaturated frozen soils within a closedin permafrost areas and for engineering design in system and under small temperature gradients, wecold regions. first carried out a series of tests on the soil-water x'-v

To evaluate and predict quantitatively the potential and the unfrozen water content. We be-amount of water migration in frozen soils, much lieve that the gradient of the soil-water potential is ,vresearch work has been done, both theoretically the driving force and that between the solid, liquidand experimentally (Dirksen and Miller 1966, and gas phases, the unfrozen water (liquid phase)Hoekstra 1966, Miller et al. 1975, Anderson et al. is the main path for water migration in frozen1978, Ershov 1979, Williams and Perfect 1979). soils. ..

Most of the previous wcrk has been concentrat- To test this hypothesis, we selected a clayed on the investigation of the relationship between (Morin clay) for our test material and determined .-

water migration and frost heave. The laboratory its flux of water migration. Two sets of tests weremethods most commonly used are as follows, done: one was conducted with different tempera-

A soil column surrounded by insulation is set ture gradients and dry densities, holding the exper-up, either horizontally or vertically, and the tem- imental duration the same, and another with dif- . 4'*

perature is kept below the freezing point at one ferent experimental durations, keeping the tern-

end of the soil column and above at the other. perature gradient and dry density the same.Either a closed system (no external water supply) i.- 1Z

or an open system (having external water supply)is used. Results have shown that, in a partially fro- PRELIMINARY STUDIESzen soil column, the amount of frost heave is 'much greater in the frozen portion than at the fro- Soil-water potential in unfrozen soilszen/thawed boundary.

The most recent research is focused on the cal- Factors affecting the soil-water potentialculation of the amount of water migration in fro- From the point of view of thermodynamics,zen soils, the determination of the hydraulic pa- water migration in a soil-water system is caused byrameters of frozen soils and the explanation of the water not being in equilibrium in the system.driving forces. On the basis of the extended Dar- This results from a combination of many forces,cy's law and the Clausius-Clapeyron equation, including physical, physicochemical, mechanicalmany mathematical models have been proposed and others arising during the water migration pro-using the methods of physicomathematics or ther- cess.modynamics (Xu 1982, O'Neill 1983), and several Except for the gravitational water, the otherapparatus for determining the hydraulic param- types of water, i.e., adsorbed water and chemicallyeters of frozen soils have been set up using meth- bound water, are subjected to an action from sur-ods that look at the stable or quasi-stable state face energy of the mineral particles, or an action(Ershov and Cheverev 1974, Burt and Williams from the capillary forces and adsorption forces.1976, Williams and Wood 1981, Nakano et al. When water in the soil and mineral particles in-1982). A question remains, however, about the ap- teracts in the soil-water system, the decrease in

%.2

free energy of bulk water can be expressed by the soil-water potential is equal to the pressure or suc-soil-water potential, i, which is the work re- tion in the pore water in the equilibrium state, andquired to transfer a unit mass of water under an can be expressed asisothermal condition,

1W PW (2)

where A, is the chemical potential of soil water where Q = density of soil water and P,, = pres-and 0 is the chemical potential of pure water. sure, or suction, in the pore water in the soil-water

Suppose that the density of water in a soil-water system.system is equal to that of the pore water, then the

U.S. Std. Sieve Size U.S. Std. Sieve Size %U.S.~~. -a.Siv'Sz

4 10 40 200 Hydrometer 4 10 40 200 Hydrometertoo 0 10 0,:., .-Io ---€ -I I -4

_ I,600 -

0 110 1 0.1 so -' 20.001

- 40 I 60 o 6 4

i FtM u40-6 0 0- 6

a.. Grvssn.b otws it

Grain ~ .S Stde S(eme GrinSze m

4 I I 0 200 Hydrom600Sand Sit- I a S

e '.0 2- I I

4 10' 4 20 Hydomt

0. ol-0 ' \ -. o

olII I l I hop100 10 .0 . 001 0.001

Grain Size(mm) Grai Sizer(mm

Crs MediwirieFineiSiltFoneClayilt Meiu Cloyr la

Orga ~ ~ ronic Content , Liquid Limit 194 pcfi rvt .5 PorgancCntn0Lui Limit 28.3,,SPeaitic Gravity55 2.66

a. ravs snd.riNorhwetaylt

Fiur .Ph 0ia 40prte 200 sdoilueter tuy

a80 I I20~ "

0 I0

U 80-I

A I 1I 10010 10o 01 001 0.001

Grain Sire (mm)I Sand I Sl rCa

IC'reMediuml Fine SitorCa

Organic Content 0, Liquid Limit 38.3. Plastic Limit 22.8, Plastic Index 15 5%Specific Gravity 2.72. Specific Surface Area 60

c. Morin clay. S

Figure 1. Physical properties of soils used in this study.

2

*~ %'~a 10 %' %, N. Na -a Na~~e e".10,All.-

,WTVWYVVWT

Therefore, the factors afecting the soil-water lanes, in which the soil-water potential decreases 4.

potential, such as the water content, soil type, dry rapidly again.density and temperature, are investigated by the Influence of the soil type on the soil-water po-determination of soil-water characteristic curves. tential. The influence of the soil type implies bothIt has been shown (Williams 1967, Kaliuzhuyi the influences of the mineral composition and the1980) that these curves obtained from the unfro- grain size of soil particles. However, here we onlyzen soils are also applicable to frozen soils, discuss the influence of the grain size distribution.

Three types of soils are used in this study. They With the changing of the soil type from sand toare Graves sand, Northwest silt and Morin clay. clay, the amount of fine-grained particles increas-The physical properties of these soils are shown in es. Consequently, the active specific surface areaFigure 1. increases and the average radius of capillaries de-

Influence of the water content on the soil-water creases. The two changes play a common role, on- .potential. As mentioned above, water in soils is ly to different degrees, in increasing the bondedsubjected to an action from the surface energy of energy of water and decreasing the soil-water po-mineral particles. With the decrease in the degree tential. 'oof saturation, the capillary water is first removed, Again, from Figure 2 it can be seen clearly thatleaving the pellicular water. The forces to which at the same water content the sand has the highestwater is subjected change from capillary forces to value of the soil-water potential, the silt the mid-adsorption forces. As a result, the soil-water po- die value and the clay the lowest.tential always decreases with a decrease in water Influence of the dry density on the soil-watercontent. potential. If the soil type and the water Lontent are

kept the same, the soil-water potential increaseswith the increase in the dry density regardless of

12x05 , I soil type (see Fig. 3). This is ascribable to the

change of the soil structure.The densification process causes a change in

8 roves Sand pore size, especially for large pores, while the ori-'g Y. \"M, o (, 4,3)ginally small pores do not change their size signifi-

\ d. NW Silt cantly. As usual, the pellicular water is in the4 larger pores and the capillary water is in the small-

er pores. Therefore, the change in the pore size re-sults in the transition of water from the pellicular

01 to the capillary, and so increases the soil-water po-010 0.20 030 0.40 0.50

W (cm3/Cm

3 ) tential.

Figure 2. Effect of the water content (W) andsoil type on soil-water potential. 16xo 5 ,TI

Results shown in Figure 2 were obtained by an 12I

extraction method (Ingersoll 1981). They are ingood agreement with the above statement. The -M. ,\process of the soil-water potential changing with (erg/g)8the water content can be divided into three stages: '% Groves Sand Morin Claythe first is the stage of meniscus formation in big \ ,,I.54Ig/cm3 ) (1.413)

capillaries, where the soil-water potential decreas- 4 " (1498)0 636) ,, -,."""

es rapidly and linearly with decreasing water con- . .. -- --

tent. From the first stage to the second, there is anobvious break in the curve, called the break point 010 0.20 0.30 0.40 .50 Uor air entry point. The second is the stage of water W (cm&/rmI)

extraction from the large capillaries, in which thesoil-water potential decreases slowly, and the third Figure 3. Effect of the d-y densi"a, on soil-wateris the stage of water extraction from small capil- potential.

3

% % -%

lo, 5 , soil-water potential and the water content can bewell expressed by a simple power curve

12 = A W- 8 (3)

where p, = absolute value of the soil-water po-Wg/g) 41Graves Sand NW Silt tential

d\yd=1.583 g/cm3 ) 1.5) W = volumetric water content of the soil

\4 0o. 0.5 A and B = coefficients specific to each soil.24D

_- -=--=-.--- , The values of the coordinates of the break point

0.0 0.2 0.0 and coefficients A and B for those soils tested areo.10 0.20 0.30 0.40 0.50o040¢m0.50 ) listed in Table 1.W (CM3/CM3)

By introducing the break point coordinates into

Figure 4. Effect of the temperature on soil- eq 3, we havewater potential. ,,)

lt f w- (4)

Influence of temperature on the soil-water po- I-N

tenial. Figure 4 shows the curves of the soil-water where wf and Wf are the soil-water potential andpotential versus the water content for two kinds of the water content of the break point.soils at the temperatures 0.5°C and 24°C respec- Equation 4 can be rewritten astively. For each kind of soil, the two curves at dif-ferent temperatures are quite parallel. This shows P-w = Pwf WfW -A. (5)that the influence of temperature on the soil-waterpotential has nothing to do with the water content. Combining eq 3 and 5, we haveAlso, the soil-water potential at 24°C is higherthan that at 0.5°C, which is reasonable because A = /f W. (6)the kinetic energy of water molecules is higher athigh temperatures. The higher the kinetic energy Unfrozen water content in frozen soilsof the water molecules, the lower the bonded en- The presence of unfrozen water in frozen soils isergy of water, and the lower the bonded energy of attributable to the soil-water potential mentioned 64,water, the higher the soil-water potential, above. The unfrozen water content in frozen soils

Since the relationship between the soil-water po- not only depends on the composition and proper-tential and the temperature is important for water ties of both the mineral particles and soil solution,migration in frozen soils, we will discuss it in more but also depends on the environment of the soil-detail in the Discussion section of this report. water system-for example, the temperature and

pressure that the system is under. Previous workRelationship between the soil-water potential has established the relationship between the unfro-and the water content zen water content and temperature (Anderson and

If we take the break point on the curve (see Fig. Tice 1973, Banin and Anderson 1974, Konovalov2) as a starting point, the relationship between the 1979, Tice et al. 1982). On the basis of this previ-

,.'.:

Table 1. Values of the break point coordinates and coefficients A and B.

Saturated -V

water Break point coordinate

Soil "Yd content Wf P -f Coefficient in eq 3type (g/rm') (cm'/cm ) (cmI/cm) (erg 1g) A B

Graves sand 1.541 0.431 0.418 -1.2 x 10' -9.7173 x 10' 2.3844Northwest silt 1.465 0.447 0.437 -1.8 X 10' -0.2157 x 10' 7.6171Morin clay 1.413 0.476 0.476 -3.1 x 10' -7.5904 x 10' 4.9973

4

ous work, we investigated the influences of three than 6 1 Iheretore. it i% po' ill i 4 rfactors-the initial water content, dry density and water to pass through Jn i~c ici, rsi Jr, ..,jrsalt concentration -on the unfrozen water content amount of unfrozen water in i~c ier'r rr~.i -

in frozen soils by the nuclear magnetic resonance much less than that in tro/en s,l,

technique reported by Tice et al. (1982). Influence of the dri, (. iiw'. 1! hI, p 1water content f Jigure 6 511(w Iti ..1 'u/cr i .i'.

Factors affecting the unfrozen content at different tenmeatre whet 'ti _iwater content in frozen soils denit change-, from 0 99' to I - 4 li flit dk,: 11

Influence of the initial water content on the un- initial water content remain' di appr'clnd:

frozen water content. Experimental results show 1907 by weight It can he iie i,rti ;f;" "r'tthat the unfrozen water content in frozen Morin water content is relati.clx onstAwr ii. d Jilr x-iTclay decreases with the increase in the initial water perature and A ithin a Awide rangie 4 1 Jr Jrj,r-content at a given temperature and that the differ- For example, there is less than ]o diItcrn,-rence increases with increasing temperature (see the unfrozen water content At tempeIrra! Uri' ~iFig. 5). For the range of the initial water content -1,0.O(

from 4.81016 of dry soil weight to 41.1601 the un- The values of the unfrozen w. Jr w~

frozen water content (Wu) difference changes with those samples with higher drN densiti'c, ll r-

temperature as follows: than those with lower dr densities at emprirw

tures below -2.J~i this is resersed alt erilperaa WU Iftures above -2.0'C and is ascribable to ihe 111IL.

(07) (CC) ence of pore size (see Table 2) Ao teer ru't'

below -2.0'C, the unfrozen water contei irrla1.0 < -10 es with the increase in the dn. densits, helau 'tit

2.0 <- 1.0 soil-water potential is higher at high dir% der'u'3.0 <- 0.2 At temperatures above -2 1~ , the film wate' .r

large pores is not frozen because its trielW .i

All the curves shown in Figure 5 are quite paral- is lower than that of the capillarN water 1%, ticlel for the change in the initial water content. dry density increases, the transition of water !oll

When the initial water content reaches or ex- the film to the capillar% will result in dIe~ivaxoliceeds the value of saturation in frozen soils, ice the unfrozen water contentlenses are formed. The bottom curve shown in Influence of the salt c-oncentration Arl the- is'"

Figure 5 is obtained from pure ice made from dis- Zen water content. To change the salt 'n.r:tilled water. It shows that the pure ice still has un- tion of the solution in the soil-water ".sten. Av

frozen water in it when the temperature is higher used solutions of sodium chlortde with three .1,

20 20,W=481'-4116% 'C 99 7 '4

316 Jr16

12 1l2

0 0

4 -- -4 1 2 2 ~ -C

Temperature (*C) T

Figure S. Effect of the water content of Morin Figure 6. Effect ol/the (1r, pi-. t~.' ,Iclay on the unfrozen water content, clay on the unfriz'~

Table 2. Values of the unfrozen water content (W.) calculated from eq 7 at different drydensities.

W'Id by weight by volume W, at various temperatures (%)

(g/cm') (%) (cm'/cm') -0.5°C -I.O°C -2.0*C -5°C -l0C -15*C -20°C

0.997 19.47 0.194 18.64 11.68 7.33 3.95 2.48 1.89 1.561.079 19.58 0.211 18.90 12.01 7.64 4.19 2.67 2.05 1.691.263 19.39 0.245 17.61 11.44 7.44 4.20 2.73 2.12 1.781.331 19.36 0.258 17.37 11.33 7.39 4.20 2.74 2.13 1.791.432 19.26 0.276 17.95 11.57 7.46 4.18 2.70 2.09 1.741.581 19.23 0.304 16.66 11.09 7.38 4.31 2.87 2.26 1.911.643 19.34 0.318 17.37 11.45 7.55 4.35 2.87 2.25 1.891.714 19.06 0.327 16.06 10.78 7.24 4.28 2.87 2.27 1.93

',V,%t

ferent concentrations of 0.1, 0.5 and 1.0 mol, re- where W, = unfrozen water content (% byspectively, and mixed these with the oven-dried weight)Morin clay. The initial water content was kept at T = temperature below freezing (0C)approximately 24%. C and D = constants characteristic of each soil.

The results show that the unfrozen water con-tent increases greatly with the increase in the salt Equation 7 can be expressed as a straight line onconcentration, and that there is a good linear rela- log-log paper. On this straight line there is a start-tionship between them (Fig. 7 and 8) because thefreezing point decreases linearly with the increase 20in the molality (Fig. 9). .-

Prediction of the unfrozen water content 6by two-point or one-point methods

Anderson and Tice (1972) presented the follow- 12 t. mot NoCIing equation describing the relationship betweenthe unfrozen water content and the negative tern- -perature 08 - 0.5 %

-,WU C - 0.1

(7) Z 04 2Natural

0000 -5 -10 - -20 25

Temperature (C)

800 Figure 8. Relationship between molality of '.

,, .Morin clay and the unfrozen water content.

IMolality (mol)

S*0 0.2 0.4 0.6 0.8 1.0

• . o "o • 1.0Omol NoCI -

0,400 Noo --

I - I0 , I mol 'o-

0 010 2

-20 -t0 0 10 20 , 4%,"lTemperature (*C) - _5[ __ 1___ __ I___ I___ ,,

Figure 7. Effect of the salt concentration of Figure 9. Relationship between molality ofMorin clay on the NMR signal. Morin clay and initial freezing point. 'V

6

I,0

7 .%'K, r 5 ,3 3K~s.'f r'-3 ,3' " ,~v.', S ,'v'- (.". ' ' .. .".,.',' . ?,, ,':,', ,, '" ':.,', ;',i":.,'_,'".',:,: .2"."-"-, ¢... J .

U pj.jIrFnpParunSIS~lrf nfl s- .uwra

Table 3. Values of constants C and D In eq 7, and other parameters.

W. d concntration Tf Constant ASoil type (M) (X/cm') (moO (C) C D

Morin clay 4.81 1.401 - -7.09 14.4099 -0.56029.26 1.545 - -2.04 13.8692 -0.5673

14.38 1.602 - -0.79 12.6011 -0.551219.44 1.671 - -0.41 11.8345 -0.555225.77 1.532 - -0.24 11.7509 -0.554130.90 1.545 - -0.19 11.8075 -0.574136.07 1.416 - -0.11 10.4109 -0.556441.16 1.343 - -0.09 10.6700 -0.5675

19.47 0.997 - -0.47 11.678 -0.6733 .19.58 1.079 - -0.47 12.0125 -0.653819.39 1.263 - -0.43 11.4438 -0.622119.36 1.331 - -0.42 11.3301 -0.616619.26 1.432 - -0.45 11.5740 -0.632819.23 1.581 - -0.39 11.0903 -0.586719.34 1.643 - -0.42 11.4507 -0.601319.06 1.714 - -0.37 10.7822 -0.5746

19.27 1.473 0.1 NaCI -0.72 15.8527 -0.595819.05 1.472 0.5 NaCI -2.25 34.4404 -0.732219.06 1.544 1.0 NaCG -3.80 50.7306 -0.732719.13 1.812 1.99 SW -6.79 85.868 -0.784024.71 1.614 0.1 NaCI -0.47 15.3221 -0.6246 5

24.12 1.715 0.5 NaCI -1.94 40.7384 -0.790923.69 1.648 1.0 NaCI -3.79 69.8565 -0.8109

Northwest silt 16.67 1.523 - -0.13 5.2752 -0.5675 P 'Fairbanks silt 40.46 -- -0.02 6.8988 -0.4735-- P

Graves sand 18.08 1.543 - -0.02 1.6945 -0.6104p -,"i w-

ing point with the coordinates of the initial water mine is the slope of the straight line, D, if the ini-content (Wo) and the freezing point (Tf). Then, the tial water content and the freezing point of a soil r "., .slope of the line is are given.

From Table 3 we can see that the value of DIn Wo - In Wu changes with the soil type and salt concentration,

D = In T - In Tf (8) and does not change very much for a given soil,

From eq 8 we have the following expression, even though the initial water content and the dry .. 2,density vary over a wide range. Therefore, by thewhuation:is exactly the same as Konovalov's (1979) measurements of two freezing points at two differ-ent initial water contents, we can calculate the

Wo ITD constant D by eq 8, and then predict the unfrozen-w "j-,. (9) water content by eq 10. This is called the two-

point method.

qnuation 9can berewritten Again, from eq 10, we haveEuto9caberewritten as,/%

SWoTT - . (10)u T (12)

Comparing eq 7 and 10, we have if T - 1 °C. Then, ,

C=Wo . (Il) W r= -= W.Tn

To predict the unfrozen water content in frozen D = InTf (I3) _____

soils by eq 10, the only constant we need to deter- .55' .,

7

%~ %

It. I I ' 1

o Observeda One-point Method Predicted

12 -o Two-point Method]

- and iSalt Added

Wwu

\ Sand

0 -4 -8 -12 -16 -20

Temperature ('C)

a. Dartmouth sand with salt added and no salt added. St

o Observed (NMR method)24- a One-point Method Predicted\\ Clay * Two-point MethodP

SS

20: y \ Sol t Added -_o

W,_

1u

Temperature (*C) I

b. Morin clay.

Figure 10. Comparison of observed and predicted curves.

The unfrozen water content in frozen soils only TEMPERATURE GRADIENTneeds to be determined once at -IC. Then, we EXPERIMENTcan calculate D by eq 13. This is called the one-point method. The apparatus used in this test was described in

Comparisons of both the observed and the pre- detail in a separate paper (Oliphant et al. 1983);dicted results fom the sand and clay are shown in however, to give readers a clear picture of it, weFigure 10. Errors of predicting the unfrozen water will describe it briefly.content are I to 301o on the average for the two- The apparatus consists of two aluminum blockspoint method and 1 % or so for the one-point of the same size-30.5 cm long, 11.2 cm wide andmethod. 2.54 cm thick. Each block has five semicircular

p8%89

IL =4.i 15.€ St *"a ',,.S.-' ". .% %" _" ".'S ".'=." '. -. ** " i. ... .... ..... - -%"" " p -. -/ -$ "" " "" -" ;". " - -'',"-

20 - Weight I 2.5

.......... ..... ...... ...16 ~ 0 o 0 2. E0o

- " 00 0 0 n.-,00 0 0 . 000 0,00 0 1

-2 0 0 0 0 0 0 10 Dry Density08 -- , ."

4--0.500

I I I I 0 .

0 10 20 30

Distance Along Tube (cm)

Figure 11. Moisture distribution before testing. a,.,

grooves that are spaced 1 cm apart along one of its water content of 20% is about -0.4 0C (see Tablefaces. When the two blocks are bolted together, 3). The temperature selected for the cold end of

five holes, 0.95 cm in diameter, are formed, into the soil column depended on the required temper-which the plastic soil columns are placed. At each ature gradient.end of the two blocks there is a reservoir connect- To start the test, we put five blank soil columnsed to a circulating refrigerated bath to keep tem- into the blocks until the expected linear tempera-

perature constant, with an accuracy of ±0.02°C. ture gradient was established. After that, we ex-The two reservoirs are also made up of aluminum, changed the blank ones for the five clay-filled col-

and are 11.2 cm long, 5.08 cm wide and 5.08 cm umns. Several days later, these soil columns were

thick. quickly removed to the coldroom and each was 10"

The whole apparatus is surrounded by foam in- sectioned into 44 segments. The total water con- Z

sulation and set up horizontally in a constant- tent of each segment was determined gravimetric- V.temperature room with the ambient temperature ally.maintained close to 0°C. Thermocouples are in- The average moisture flux was calculated by theserted into the two blocks along the middle following expression:groove, 2.54 cm apart, to monitor the temperaturedistribution both horizontally and vertically. (WL W')&x "Vd (14

As mentioned earlier, we used oven-dried Morin A = Ji-I + _ -, (14)

clay for these experiments. The clay was mixedwith distilled water to obtain an initial water con- where Ji-I and Ji = average flux of the i- .h andtent of approximately 2047o, and then placed in a ith segments, respectively (g/ 4 .

sealed bottle for 2 or 3 days to allow moisture cm, s)equilibration. Then, it was packed carefully into Wi' and W! = total water content at times r,the plastic tubes, which have 0.95-cm o.d., 0.792- and r, respectively, in weightcm i.d. and are 27.8 cm long. Two rubber stoppers fractionapproximately 0.5 cm long were inserted into both Ax = length of the segment (cm)ends of each tube to prevent moisture loss. The "Yd = dry density of the soil (g/cm ). ,'.packed soil columns were then put aside for I or 2 By using the apparatus and following the exper-days at room temperature to allow moisture equil- imental procedure mentioned above, we foundibration in the tubes. Afterwards, they were re- that the moisture distribution in the soil columnmoved to the coldroom to be frozen. was sometimes not uniform before testing (Fig.

We define frozen soil as a soil in which ice and 11). The temperature gradient in the horizontal di- "unfrozen water coexist. To keep the soil specimen rection is quite linear (Fig. 12) and stable during ,

always in the frozen state during testing, we fixed testing, but there is still a temperature differencethe temperature at the warm end of the soil col- occurring in the vertical direction within 0.1 0 toumn at about or lower than -0.6 0 C. This is be- approximately 0.4°C, which depends on the tern- ,cause the freezing point of Morin clay at the initial perature gradient.

9

.S It ,

".?w

* rw * :W'W - ' V V ." .',.,..".", ".', " .'.,. './Z"'

0 -- T sidered as an external force that causes a soil-_ Grad T z0 0236*C/cmGrad ...... water potential gradient for water migration in the

frozen soil column. The soil-water potential at the-2 --- ,01024 place with higher temperature is greater than that

u- - at the place with lower temperatures. Unfrozen0' 693 water in frozen soil migrates in the direction of de-

creasing temperature under the soil-water poten-E tial gradient; thus, the thermodynamic equilibri-

-6' um between ice and unfrozen water at the placewith higher temperature is upset by the unfrozen

t -3o46, water decreasing. The potential of unfrozen water-036 is lower than that of ice. A new potential gradient

S._ occurs in the direction from ice to unfrozen watero 20 3C and causes a transition from ice to unfrozen

Ostonce (cm water, so the total water content at the place with

Figure 12. Temperature distribution in horizontal di- higher temperature is decreasing. On the otherrection. hand, the thermodynamic equilibrium between ice

and unfrozen water at the cold end is destroyed bythe increasing unfrozen water, resulting in the

Water content profiles phase transition of unfrozen water to ice. Thisafter migration process passes through the test from the very

Figure 13 illustrates the distribution curves of beginning to the end and along the whole length ofthe total water content in frozen Morin clay under the soil columns. In the closed system, i.e., underdifferent temperature gradients for 5 days. From the case without an external water supply, waterthese figures, it can be seen that unfrozen water in migration will be stopped when the stored water inthe frozen soil columns migrates from the warm the dry part of the soil column is exhausted.end (segment 1) to the cold (segment 44), and taateach soil column can be divided into two sections Factors affecting the fluxaccording to the relationship between the total The flux of water migration can be calculatedwater contents before and after migration. The by eq 14 according to the total water contentsection adjacent to the warm side is called the measurements. In this case, we only used one soil"drying part," in which the final total water con- type, Morin clay, so that the flux can be consid-tent is less than its initial water content, and the re- ered as a function of the following four factors:maining section of the soil column is called the"wetting part," in which the final total water con- J = f(@, T, 'Yd, gradT) (15)tent is higher than the initial.

The length of the drying part becomes shorter where r = time, or test durationand shorter, and the degree of drying becomes lid = the dry density of the soil (g/cm)higher and higher as the temperature gradient goes T = temperature (°C)up. gradT = temperature gradient (0C/cm).

There are two peaks in the wetting part: one oc-curring at the front of this part and the other at Influence of timethe end. The front peak gradually becomes sharp- To investigate the relationship between the fluxer and sharper as the temperature gradient goes and time, four tests with different durations of 2,up. 5, 10 and 16 days, respectively, were conducted

Figure 14 illustrates the total water content pro- under a given set of conditions: gradT = 0.1693files of the soil columns under the temperature °C/cm, "Yd = 1.45 to 1.47 g/cm', and T = - 0.9'gradient equal to 0.1693 °C/cm for 2, 5 and 10 to approximately 5.2°C.days respectively. It shows that the front peak of Figure 15 shows that the flux decays with timethe wetting part moves towards the cold end of the and that there is a good relationship between themsoil column as the test duration increases. (see Fig. 16), i.e., the flux is inversely proportional

Water migration in the liquid phase in the fro- to the square root of timezen soil can be explained as follows. In these ex-periments, the temperature gradient can be con- J = (A T- + B)T,gradTd (16)

10

20 Gad TOO236°C/cm, 7r5doys

w -(%) 8 8.

16- 0 4 r

T("C)o 8

20-

16

12-

10 20 30 40 ".0

No of Segments

a. gradT = 0.0236 C/cm.

18 2 Grd TGO 0551 C/Cm

w ,- T5 days

(%) '"_P

46 I 1 I I ." . '

-04 ..

- 08

(C) -12-16-20 O

16

wu12

8 40I 10 20 30 40

No of Segments

b. gradT 0.055) 0 C/cm.

20- Grad T-0. 1024 *C/cm, T5 daysA 5!3 gi

w AJ.-f %J

(%I 18

0-

'd

20

1 10 20 30 40 J

oof Sgment

c. gradT = 0. 1024 0 C/cm. a

Figure 13. Water content profiles at test conclusion. 5

IF.

V. %.

20" Crod T-0.3465 C/cm, T-5 days

(%)

16 * I J _ _

T -4'(*CI -6 -l

-to-g0o i I I

20

Wu

'0o I , I ::%10 20 30 40

No of Segments

d. gradT = 0.3465 °C/cm.

Figure 13 (cont'd). Water content profiles at test conclu-sion. "m,

30 ,

:W-17 92%, d- 460 g/cm3 ,

T -2 days %,',

18. 81 5 4- 5 ',W 1859 1452 torL€

1 I0 20 30 40 50 ",

'p

Figure 14. Water c'ontent profile for different test dur- :'ations.r"

v .

..

I 0 20 3 40 50 r T + ],'

T- 09- -52 0 C-14-47g/mI %

Groi ThO 1693°C/cm

4ro2days

,o5 E 2 5*Ca,0 ' -30

104

".. ...... - -a ;

0 10 20 30 -1Distance Along Tube (c m) ,,

Figure 15. Influence of testing duration on the Figure 16. Relationship between the flux and"4

flux. test duration.

12

-40o

Q = (A 7' + B)Tgrad.)d (17) 3O.i, 8 T_ T-- T _T__ - -- T -T-G r a d T ( C / c m ) ld ( / m 1) !

where Q = the total flux; A and B are empirical 00236 1 572 1coefficients. 2 00394 49 3

• 00 39 4 4 9 3

Figure 16 also shows that the slope of the 2 001 460No

0 1024 543 ,- .%

straight line changes with temperature. The higher 0 1693 1460the temperature, the steeper the slope. 0 3465 469 0.

It should be noted that there is a contradiction o,in eq 16 and 17. Theoretically, when r = 0, J or Qshould be zero, too. But experimentally, there isstill a coefficient B.

0 -2 -4 -6 -8 -10 ''.

Influence of temperature Temperature ('C)

Figure 17 shows the flux versus temperaturecurves for different dry densities and temperature Figure 17. Influence of temperature on thegradients, but within the same test duration of 5 flux.days. From Figure 17, it can be seen clearly thatthe flux decreases with decreasing temperature, %but the curve shapes change with temperature gra- of the soil columns was complete and the other .4

dient. At lower temperature gradients, for in- was cut into halves. Results (Fig. 18) show that thestance less than 0.1 *C/cm, the curves are in the flux in the first half column is fairly close to thatconvex shape and then, with the increase in tem- of the front part in the complete one, but quiteperature gradient, the curve shapes become gradu- different from that of the end part; the flux in theally linear and concave, secondary half column is just the extension of that

There are two possible explanations of the phe- of the front part of the complete column. There-nomena mentioned above. One is that the lower fore, it can be concluded that the flux at the end oftemperature gradient causes the lower soil-water each soil column is reduced by end effects. Omit- Je

potential gradient. As a result, the first peak of the ting the flux at the end part, we obtain a good rela-wetting part in the soil column occurs slowly; in tionship between the flux and temperature asother words, !he length of the drying part is great-er. Another reason could be the "end influence," J = (A T-9)gradT,-d, t. (IR1,which means that the flux must be zero at the endof each soil column, no matter how great the flux The values of coefficients A and B in eq 10is close to the end. tained for different temperature gradients,

To investigate the end influence, a second, par- densities and test durations, are listed in Tab),allel test was conducted. Two soil columns, havingapproximately the same dry density and initial Influence of the dry densitywater content, were tested under the same temper- From Figure 19 it can be seen that the flux atature gradient and for the same test duration. One first increases with the increase of the dry density.

20xl0 e

- o Grad T-O35431Ckm,y-I 591 g/cm3 .W-1930%16 \ 03543 1578 1919

12-

4-

-2 -4 -6 -8 -O

Temperature (1C)

Figure 18. End influence of soil column on the flux.

13

Table 4. Values of coefficients A and B In eq 18, and other parameters.

W "Yd gradT T J = A T-B(M) (g/cm') ('C/cm) (day) ('C Point A x 10 ' B Residual

18.37 1.572 0.0236 5 -0.91 - -1.02 8 5.7400 1.8491 0.134518.54 1.383 0.0276 5 -0.64 - -0.92 18 4.2541 1.5233 0.277518.43 1.473 0.0276 5 -0.64 - -0.99 22 6.6387 0.8500 3.379818.38 1.493 0.0394 5 -0.89 - -1.30 17 6.8936 0.9197 0.739718.10 1.581 0.0394 10 -0.89 - -1.25 16 8.8158 1.1342 0.3764

18.06 1.591 0.0394 21 -0.72 - -1.25 23 3.8801 0.7988 0.302716.19 1.261 0.0551 5 -0.81 - -1.41 19 5.2688 1.1816 1.514616.08 1.557 0.0551 5 -0.91 - -1.61 22 11.6524 0.7273 4.876519.66 1.538 0.0630 t0 -0.58 - -1.35 21 9.7729 0.4977 3.849319.82 1.550 0.0630 15 -0.74 - -1,54 22 7.7385 1.5038 1.5146

18.52 1.147 0.1024 5 -0.64 - -2.07 24 9.9279 0.3134 19.527718.61 1.314 0.1024 5 -0.64 - -2.07 24 11.4902 0.5021 8.117118.34 1.543 0.1024 5 -0.64 - -2.07 23 14.9033 1.1085 17.727817.92 1.460 0.1693 2 -2.46 - -3,80 14 31.9381 0.8646 1.385718.82 1.450 0.1693 5 -1.02 - -3.80 28 15.4163 0.6824 10.5542

18.59 1.452 0.1693 10 -1.13 - -3.90 28 11.6791 0.8285 1.4293 ,.^18.04 1.453 0.1693 16 -1.23 - -3.50 23 10.5257 1.2731 1.3293 %17.64 1.465 0.1693 16 -1.33 - -4.01 27 10.1175 1.1028 0.695817.71 1.475 0.1693 16 -1.33 - -3.91 27 10.0092 1.2272 1.074713.90 1.514 0.1732 10 -1.76 - -4.29 25 16.7113 1.2006 3.0150

14.80 1.446 0.1732 10 -1.76 - -3.76 20 8.6353 0.6279 0.374318.63 1.469 0.3465 5 -1.65 - -5.66 20 32.4343 1.1140 6.812417.45 1.640 0.1693 5 -1.03 - -4.74 37 10,8448 0.8957 15.802417.57 1.638 0.1693 5 -0.92 - -4.10 31 11.1044 0.9668 10.575316.77 1.292 0. 1693 5 -1.02 - -4.84 38 9.6400 0.6866 2.8564

When the dry density reaches a certain value, how- 24,1 68

ever, the flux reaches a maximum, and after that, V Mon cloythe flux decreases with the increase in the dry den- 20- Grad T-0 1693 'C/cm

sity. 1 _T=5 daysThe change of the dry density does not have N- EI 'C

much influence on the unfrozen water content as 12we have demonstrated in Figure 6, but it does in- P2fluence the soil microstructure. When the dry den-sity is low, there are many large pores in the soilcolumn, so that the continuity of the unfrozenwater film among soil particles is poor. In this 212 4 i6 i8

case, increasing the dry density may offer more -yopportunities for unfrozen water passing through d

these paths because of the increasing continuity of Figure 19. Influence of the drythe unfrozen water films. Therefore, there is an density on the flux.optimal density for water migration in frozensoils. After that, if the dry density keeps increas- water migration in frozen soils. Figure 20 showsing, soil particles are in contact with each other that the flux is directly proportional to the temper-more and more, they cut off the path for water mi-graton nd aus a ecrese n te fux.ature gradient if the temperature, the dry densitygration and cause a decrease in the flux, and the test duration are all kept the same. Then,

we haveInfluence of temperature gradient

The temperature gradient causes the driving J (A + BgradT)T.d, (19)force-the soil-water potential gradient-for

14

%,'%

-- ------- There are two technical prublems in our tests.3210iOne is a temperature difference in the vertical di-

28- -' rection and another is a density difference along[-424- the soil column. Both of them affect the results of

1-15 -4 tests to different degrees and sometimes lead to

20 failure.

16k- To solve the first problem, we suggest that the

2 reservoirs be enlarged and the insulation material" , -, be thickened. To solve the second problem, a way

SMorin Clay to pack the soil columns more evenly along theirl =d 0 C length is required.

4[ r=5days -

0 o 020 030 040

Grad T ( C/cm) CONCLUSIONS

Figure 20. Relationship between theflux and 1. Relationships between the soil-water poten-temperature gradient. tial and the water content, between the unfrozen

water content and temperature, and between thesoil-water potential and temperature, can be rep-

So far, we have proved experimentally that the resented by a power law equation.

extended Darcy's law is still applicable for water 2. The unfrozen water content in frozen Morin

migration in frozen soils, even if the temperature clay changes with the initial water content and the Ngradient goes down to as low as 0.0236 0C/cm. dry density only within a range of 3% of dry soil

weight, and increases linearly with the increase in

the molality because of the linear freezing point

DISCUSSION depression.3. The curves of the unfrozen water content ver-

Relationship between the soil-water potential sus temperature are quite parallel with the changeand temperature in the initial water content and rotate a little bit

We have described the relationship between the counterclockwise with the change in the dry densi-

soil-water potential and the water content in eq 3 ty.

to 6 and the relationship between the unfrozen 4. The flux of water migration in unsaturated,

water content and the temperature in eq 7 to II. frozen Morin clay is directly proportional to the

Combining those equations mentioned above, we temperature gradient, inversely proportional to

can obtain the equations describing the relation- the square root of the test duration, decreases with

ship between the soil-water potential and tempera- the decrease of temperature in the power law

ture as follows: form, and changes with the dry density. ' "5. The behavior of water migration in unsatu- .'

,= M 7" (20) rated, frozen soils is something like that in the un-saturated, unfrozen soils. Darcy's law is still ap- %

M = Lf WBW-BTfBD (21) plicable to frozen soil, even though the tempera-

ture gradient goes down to as low as 0.0236

N = BD (22) OC/cm.

Equation 20 shows that the soil-water potentialdecreases with the decreasing temperature in fro- LITERATURE CITEDzen soils.

Anderson, D.M. and A.R. Tice (1973) The unfro-

Technical problems with the zen interfacial phase in frozen soil water systems,water migration test physical aspects of soil water and salt in ecosys-

Water migration in frozen soils is not only de- tems. In Ecological Studies. Berlin: Springer-Ver-

pendent on the properties of frozen soils and the lag, vol. 4, pp. 107-124.

soil-water potential gradient, but is also largely Anderson, D.M., R. Pusch and E. Penner (1978)

controlled by the microstructure. Physical and thermal properties of frozen ground.

15

. ... . . .. .- , -- - .. -:,A

I a.- -. -:= : 1= V- u -N = w% r ,, U = L w Ul K- PKK: r a . r. Er,. f N.PJj , ,,, P,'.p - w . . . ,-u

In Geotechical Engineering for Cold Regions ameter. Soil Science Society of America, Proceed-(O.B. Andersland and D.M. Anderson, Ed.). New ings, 39(6): 1029-1035.

York: McGraw-Hill, pp. 37-102. Nakano, V., A.R. Tice, J.L. Oliphant and T.F.Banin, A. and D.M. Anderson (1974) Effects of Jenkins (1982) Transport of water in frozen soil. 1:salt concentration changes during freezing on the Experimental determination of soil-water diffus-unfrozen water content of porous materials, ivity under isothermal conditions. Advances inWater Resources Research, 10(1): 124-128. Water Resources, 5: 221-226.Burt, T.P. and P.J. Williams (1976) Hydraulic Oliphant, J.L., A.R. Tice and Y. Nakano (1983)conductivity in frozen soils. Earth Surface Proc- Measurement of water migration due to a temper-esses, 1: 349-360. ature gradient in frozen soil. In Permafrost:Dirksen, C. and R.D. Miller (1966) Closed-system Fourth International Conference. Washington,freezing of unsaturated soil. Soil Science Society D.C.: National Academy Press, pp. 951-956.of America, Proceedings, 30: 168-173. O'Neil, K. (1983) The physics of mathematicalErshov, E.D. (1979) Moisture Transfer and Cryo- frost heave models: A review. Cold Regions Sci-genic Structures of Dispersed Rocks. Moscow ence and Technology, 6: 275-291.University, p. 212. Tice, A.R., J.L. Oliphant, Y. Nakano and T.F.Ershov, E.D. and V.G. Cheverev (1974) Methodi- Jenkins (1982) Relationship between the ice andcal Instructions for Field and Laboratory Deter- unfrozen water phases in frozen soil as determinedmination of Moisture Transfer Parameters for by pulsed nuclear magnetic resonance and physi-Fine-Grained Ground. Moscow University. cal desorption data. USA Cold Regions ResearchHoekstra, P. (1966) Moisture movement in soils and Engineering Laboratory, CRREL Reportunder temperature gradients with the cold-side 82-15.temperature below freezin,. Water Resources Re- Williams, P.J. (1967) Properties and behavior ofsearch, 2(2): 241-250. freezing soils. Norwegian Geotechnical Institute,Ingersoll, J. (1981) Method for coincidentally de- Publication No. 72.termining soil hydraulic conductivity and moisture Williams, P.J. and E. Perfect (1979) Investigationretention characteristics. USA Cold Regions Re- of rates of water movement through frozen soils.search and Engineering Laboratory, Special Re- Final Report for Department of Energy, Minesport 81-2. and Resources, Ottawa, DSS File No. SU-KL 229-Kalluzhuyi, I.L., N.S. Morozova and K.K. Pay- 7-1562.lova (1980) Determining Soil-Water Potentials of Williams, P.J. and J.A. Wood (1981) Investiga-Low-Moisture Frozen Soils. Vol. 264. Leningrad tion of pressure changes in frozen soils duringGosudarstvenny gidrologicheskii Institute. thermally induced moisture migration. Final Re-Konovalov, A.A. (1979) Quantitative Analysis of port to the Department of Energy, Mines and Re-the Relation Between the Main Thermophsical sources, Ottawa.Characteristics of Frozen Soils. Osnovaniya, Xu Xiaozu (1982) Research in the question ofFundamenty i Mekhanika Gruntov, No. I, pp. 14- water migration in frozen soils abroad. Journal of16. Glaciology and Cryopedology, 4(3): 1 03-108.Miller, R.D., J.P.G. Loch and E. Bresler (1975)Transport of water and heat in a frozen perme-

pp.

16

L '--- .' ' " 'd X ,, .. ....... ..- .- .......

Pr %

A facsimile catalog card in Library of Congress MARC format is repro- -..

duced below. ".

Xu Xiaozu "..

Factors affecting water migration in frozen soils /Xu Xiaozu, Joseph L.,".

Oliphant and Allen R. Tice. Hanover, N.H.: U.S. Army Cold Regions Re-,-.'

search and Engineering Laboratory; Springfield, Va.: available from Na- -

tional Technical Information Service, 1987. •.,

v, 25 p., illus.; 28 cm. (CRREL Report 87-9.) -.-

Bibliography: p. 15. "'

1. Cold regions 2. Frozen soil. 3. Laboratory tests. 4. Soil-water potential. .-,

5. Water migration. . Oliphant, Joseph. L. I. Tice, Allen R. Il. United..-

States. Army. Corps of Engineers. IV. Cold Regions Research and Engi---..

neering Laboratory, Hanover, N.H. V. Series: CRREL Report 87-9.

%1

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