Thermally induced water migration in frozen soils

ColdRegionsScienceand Technology,3 (1980) 101--109

101

© Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

THERMALLY INDUCED WATER MIGRATION IN FROZEN SOILS E. Perfect and P.J. Williams Geotechnical Science Laboratories Geography Department, Carleton University Abstract

Introduction

An apparatus has been developed for the

I t is well known that frozen soils contain

d i r e c t measurement of thermally induced water

s i g n i f i c a n t amounts of unfrozen water co-

migration in saturated frozen s o i l s .

e x i s t i n g with the ice phase.

The

frozen soil sample and reservoirs are sand-

This water has

been shown to have a p o t e n t i a l , or equally

wiched between two end plates containing

a Gibbs free energy, r e l a t i v e to pure bulk

P e l t i e r modules.

water which is lower by an amount increasing

These cooling devices are

controlled by a thermoelectric cooling con-

as the temperature decreases.

trol system, which can maintain temperatures

equation (which may be derived from the

constant to within _+ 0.02°C under steady

Clausius-Clapeyron equation, Edlefsen and

state conditions.

Anderson, 1943) relates Gibbs free energy,

The water in the reser-

voirs remains unfrozen because i t contains dissolved lactose.

When a linear temperature

AG, to freezing point depression: ZIG =

(To

gradient is established across the system, water passes from the 'warm' reservoir into the prefrozen sample and out into the second, colder, reservoir.

Observed rates of flow The results

are discussed with regard to current theoretical and applied studies of frozen ground. Unfrozen water in frozen soils has a potent i a l which is lower than pure bulk water by an amount increasing as the temperature decreases. Thus, a temperature gradient in frozen soil implies a flux of water in the direction of decreasing temperature, at a rate dependent on the permeability in the frozen state.

- T)~,

(I)

T where

T = temperature

To - T : freezing point depression r e l a t i v e to the freezing point of pure bulk water

are compatible with permeability values for frozen soils measured e a r l i e r .

A fundamental

= l a t e n t heat of fusion Figure 1 shows the r e l a t i v e Gibbs free energy of the unfrozen water as a function of temperature. The existence of continuous l i q u i d films in frozen soils suggests a permeability; that i s , the p o s s i b i l i t y of water movement. Transport may take place in both the l i q u i d and vapour phases in response to pressure, gravitational, electrical

thermal, matric, osmotic and gradients (Anderson and l,lorgen-

stern, 1973).

When the ice content is high

most water movement takes place in the unfrozen i n t e r f a c i a l

films.

At temperatures

close to zero pore ice i t s e l f

may be perme-

able on account of l i q u i d f i l l e d

crystal

boundaries in i t s structure which act as microscopic channels f o r water flow (Nye and Frank, 1973; Osterkamp, 1975),

Moreover,

102

the hydraulic conductivity of unfrozen saturated s o i l s , but with various modifications to accommodate the presence of a frozen

20.0

sample.

The potential gradient is supplied

by application of hydrostatic pressure to one 10.0

m

reservoir.

Results obtained with the Burt

and Williams permeameter i l l u s t r a t e the dom-

6.0 r-

inant influence of temperature and s o i l type on the permeability in the frozen state.

4

E

Figure 2 shows the apparent hydraulic con-

Z

2.0

d u c t i v i t y values as a function of temperature

Z

for three d i f f e r e n t s o i l s . %

Permeability

generally increases as the temperature rises towards O°C; commonly observed values being 0.6

in the range lO -8 to lO-12 m sec - l .

The ex-

periment appears to produce conditions of flow which can be described by application of

0 o-

Darcy' s Law.

0.2

10.6

0.1 0.0

-0.5

-I,0

Degrees (C) 10,7

Figure 1: Relationship between temperature and potential (or tree energy)/n frozen soft.

SLIMS 10"8

lo`9

detailed experimental and theoretical work by H i l l e r (1970) and M i l l e r , Loch and Bressler (1975) suggests that movement is not r e s t r i c ted to the f l u i d phases.

10.TM z

8

The ice phase may

also be conducive to transport of water by a regelation process.

E

Molecules of unfrozen

water freeze on one side of a lens and the

i

1011

\

\

\ \

CASTOR ~ .SLLT.Y. "

\ 10"12

~ONEIDA CLAYEY SI LT

LOAM ( S U P E R C O O L EWATER D IN RESERVOIRS)

l a t e n t heat l i b e r a t e d induces thawing on the opposite side, with a subsequent slow d i s -

10"13

placement of the ice body towards the melting face. Burt and Williams (1976) have developed a permeameter for the d i r e c t measurement of water movement through frozen s o i l s under e s s e n t i a l l y isothermal conditions.

The ap-

paratus is s i m i l a r to that used to measure

.o'.1

~'~

.o°.3

T~M,ERATURE ~C)

.o:4

~'.s

Figure 2: Hydraulic conducttvities o£ frozen soils as a function of temperature. (Experimental determinations).

103

Wherever there is a temperature gradient

commonly observed j u s t below the active layer.

in frozen soil a gradient of free energy is

Pipeline construction in permafrost regions

implied by equation I , i l l u s t r a t e d in Figure

must also take into account the volume changes

I.

associated with slow f r o s t heave of already

Therefore a f l u x of water is to be ex-

pected in the direction of decreasing tem-

frozen ground.

perature, at a rate dependent on the hydrau-

c h i l l e d gas pipeline must be well below O°C.

l i c conductivity of the frozen s o i l .

Consequently, the pipeline w i l l

Assuming transport takes place predominantly

a heat sink, setting up large thermal gradi-

in the unfrozen water films,

ents in the permafrost.

then the f l u x ,

The temperature of a buried, often act as

The resultant poten-

q, can be approximated by Darcy's Law.

tial

gradients can be expected to induce

Because the hydraulic conductivity changes

water migration through the frozen ground

with temperature, r e d i s t r i b u t i o n of moisture

towards the buried pipe.

content w i l l

cumulation may cause s u f f i c i e n t d i f f e r e n t i a l

tend to occur.

As the unfrozen

water accumulates at some point in the frozen s o i l , i t s Gibbs free energy w i l l

As a r e s u l t freezing of the

accumulated water w i l l bility

occur.

heave around the pipe to cause i t

to rupture.

tend to rise

such that the ice and water are no longer in equilibrium.

With time ice ac-

The permea-

of frozen soil decreases with tempera-

Experi mental Method Given a frozen soil sample placed between two bodies of water, application of a temperature gradient across the system should

ture as in Figure 2, while the potential

induce flow within the sample, in the direc-

decreases l i n e a r l y .

tion of decreasing temperature.

lation will

Consequently ice accumu-

be favoured where the permeabil-

i t y is greatest and decreasing rapidly with

Several

important requirements must be met in the development of an experimental apparatus to

temperature; that is, where the temperatures

investigate the flow from a reservoir into

of the frozen ground are r e l a t i v e l y warm.

the sample, and out of the sample into a

Water migration in frozen s o i l s is associ-

second reservoir.

ated with secondary f r o s t heaving of already

I) The j u x t a p o s i t i o n of frozen soil and pure

frozen ground and the development of high

bulk water would cause freezing of the l a t t e r

heaving pressures.

at any temperature below O°C. Therefore,

Mackay et al.

(1979) ob-

served the former e f f e c t in the f i e l d .

The

the potentials (the Gibbs free energy) of the

process has important implications f o r the

water in the reservoirs and the unfrozen soil

long term hydrologic regime of permafrost.

water should be equalized before a temperature

One would expect an upward migration of ice

gradient is established across the system.

and water through the permafrost, on account

2) The heat flow must be uniaxial.

I f this

of the geothermal gradient, toward the colder

is not the case then the temperature and

near-surface temperatures (Harlan, 1973).

moisture d i s t r i b u t i o n w i l l

Over long periods of time, the l i m i t i n g

(in cross-section) at any given distance

e f f e c t of low permeability decreases and sig-

along the sample.

n i f i c a n t ice accumulation can occur.

to avoid any radial heat exchange between t h e

Indeed

not be uniform

I t is necessary therefore

this r e d i s t r i b u t i o n may be p a r t l y responsible

sample and the surroundings.

for the segregated ice and massive ice bodies

3) I t is necessary to have the end plate

104

temperatures controlled by a device which is

constant to within ± 0.02°C under steady

able to maintain the required sub-zero tem-

state conditions.

perature with rapid adjustment to fluctua-

f i r m l y in place by two porous brass plates

tions in cooling load.

which are in thermal contact with the thermo-

The design of the experimental apparatus is shown in Figure 3.

In construction i t

is

The soil sample is held

e l e c t r i c cooling plates. To prevent radial heat exchange between

basically similar to that used by Burt and

the frozen sample and a i r at room temperatur~

Williams (1976) to measure the hydraulic

the apparatus is wrapped in a jacket of f i b r e -

conductivity of frozen soil samples under

glass insulation approximately 3.5 cm thick.

isothermal conditions.

The main difference

The entire assembly is then placed in a 'Pre-

is that the hydraulic gradient is created by

cision'

a thermal gradient rather than by a pressure

tains a uniform a i r temperature of between 0

di f f e r e n t i a l .

low temperature incubator which main-

and -I°C.

Continuous monitoring of the tem-

perature p r o f i l e is provided by 5 thermistors Ware I

.__lpr n

Brass Heat Siak

Peltier Module

withcontinucwJ=flowof water t//

located along the sample holder and in the end plates.

)' I

O-ring

]

IJ f Reservoir

O-r~ng

Their estimated l i m i t of accur-

acy is ± O.OI°C.

......

The tips of the thermistors

extend about 0.25 cm into the frozen s o i l .

,=F---

The soil sample is normally saturated under vacuum with deaired, deionized water and then frozen into i t s container.

Co~taqi xigl~l!$erP[//JJ//l~

SoilSample

w

The

method of freezing governs the type and pat-

Thermistors

tern of ice lenses.

To minimize moisture

r e d i s t r i b u t i o n during freezing the sample is frozen rapidly in a r e f r i g e r a t o r and then

AluminiumEndplate

warmed to approximately -0.5°C. co.,.o,T .....

t ~ t ~ t ~ r o i ~ / / / / , / , / / / / l l / I / /// / / f / l

.... T~rmi . . . . . .

On assembly,

the reservoirs are f i l l e d with lactose solution.

The presence of lactose reduces the

potential of the water in the reservoirs to that of the unfrozen soil water.

Ideally, it

appears the concentration of lactose should Fi~u~ 3: Crees-sect/on of the experiment~ apparatus,

be d i f f e r e n t in the two reservoirs (according to t h e i r temperature).

In the tests reported

here, however, a concentration giving a The soil sam~le is contained in a p l e x i -

freezing point depression corresponding to

glass cylinder with a wall thickness of 1.90

the cold end was used in both reservoirs.

cm, and an inside diameter of 5.40 cm.

d i a l y s i s membrane is f i t t e d on each end of

The

cylinder and reservoirs are sandwiched be-

the sample to impede the entry of lactose

tween two aluminum end plates containing

molecules into the soil water.

P e l t i e r modules.

ear temperature gradient is imposed across

These cooling devices are

A

When a l i n -

controlled by a thermoelectric cooling con-

the system, water passes from the warmer re-

trol system which can maintain temperatures

s e r v o i r , into the frozen soil sample, and

105

water moves into the second colder reservoir.

°I

0.1

Inflow and outflow are measured by timing the movement of menisci along capillary tubes. Readings are taken every 30 minutes for a

SLIMS VALLEY SILT SOIL Gradkmt = 0.05 d q l ~ m (C)/~.

period of 6 hours. This procedure may be -0.1.

repeated over several days. Results and Discussion

-0.2,

For most tests, stable and essentially linear temperature gradients were established

-0.3

across the sample, as this appeared to simp l i f y interpretation of the results.

The

time required to establish an approximately

-0.4

/

/

/

•, ,. ~ mM ".~

linear temperature gradient was about 12 hours in all experiments.

An example is

-0.6

shown in Figure 4 (the constant end temperatures represent the temperatures of the thermoelectric cooling plates).

Although the

-0.6

,.oI

2'.0

olo

4'.o

~o

,~o

DISTANCE {era)

temperature profile approaches a steady state situation on a macroscopic scale, there will

Figure 4: Approach to lfneari~ in the ~mperature profile. (experime.t N = I OA).

be continual microscopic perturbations associated with coupled heat and moisture transport.

The fact that a nearly linear tempera-

steady flow of water appears to take place in

ture gradient is achieved suggests that

the direction of decreasing temperature.

radial heat exchange is relatively small com-

Water passes from the 'warm' reservoir into

pared with axial heat flow.

the frozen soil, and there is an outflow

Preceding the establishment of a linear

/

temperature gradient, a steady flux of water is observed entering the reservoirs from both ends of the frozen sample. This is illustrated in Figure 5.

An examination of

2/SO

Figure 4 indicates that i n i t i a l l y both thermoelectric cooling plates are colder than the interior of the frozen soil.

Thus, water

presumably leaves the sample from both ends in accordance with the relationship between temperature and free energy (Equation l ) . Outflow from the 'warm' end of the sample was approximately an order of magnitude greater than from the 'cold' end (see Figure 5). When a linear temperature gradient is established across the system, a f a i r l y

Figure 5: CurnulaMm outflow dur/nf aRo~aeb to//neazity/n the ~m;~ranue j : ~ e . (Zx~dment No. I OA).

106

into the second colder reservoir. ved rates of flow w i l l perature gradient ( i . e .

The obser-

0.1.

be influenced by temthe potential

for

water movement) and the temperatures of the frozen sample ( i . e . ities).

SLIMS VALLEY SILT SOIL

the hydraulic conductiv-

At r e l a t i v e l y warm mean temperatures

-0,1

even a small temperature gradient (~ 0.048°C/ cm) can induce s i g n i f i c a n t rates of flow u~ ~},2

(e.g. 9.85 x 10-5 cm3/min).

At such tempera-

tures the rates of water inflow and outflow

F.

increase markedly with increasing temperature gradients. 7 and 8.

I<

-0.3

Examples are shown in Figures 6, When the mean temperature of the

-0.4 ~-

~

•

Experiment No. 8B [2/00 Mi"]

•

Ex 7 B pi me ~0t2NMini 7o~.

sample is reduced there is a decrease in 'overall'

permeability, and a drop in flow

rates is observed.

,0.5

At a r e l a t i v e l y cold mean

temperature, a gradient of O.Ol6°C/cm produced a flow rate of 3.82 x 10-5 cm3/min,

-0.6 1 0

1!0

2!0

whereas increasing the gradient to 0.048°C/cm at a s l i g h t l y colder mean temperature, pro-

3!0 DISTANCE {cm)

4!0

5!0

" i ' 6.0

Figure 6: Stable temperature ~radLen~ at relativelywarm ~empera P/res.

duced a flow rate of only 1.55 x 10-5 cm3/min (see Figures 9, I0 and I I ) . In all experiments the mean rates of inflow were less than the outflow, by approxi-

observed rates of inflow. Secondly, the concentration of the lactose

mately an order of magnitude, which implies a net loss of water from the frozen s o i l .

In

solution used was such that the potentials of

one respect, a net gain might be expected since permeability decreases with temperature non-linearly as in Figure 2, while the potential

decreases l i n e a r l y .

However, several

3O0

other factors, related to the properties of the experiment i t s e l f ,

could account for the

observed d i s p a r i t y between inflow and outflow rates. F i r s t l y , moisture migration within the

•

'Celd'mdot~qow 3 ~Mm ~ mm~ 1 0 " 6 m fmln ~r pedod~40,-SlN MI.)

frozen soil may r e s u l t in ice lensing at the SO

'cold' end of the sample.

This would give

rise to an increase in the f r o s t heave pressures within the confined sample.

TIMEI~}

Conse-

quently, some melting of ice may take place towards the warmer end; expulsion of water may then counteract intake and reduce the

Figure 7: Flow ~nduoad by a ~ ~m~a~ ~ t

tem~ram~ ~adient at 'warm' No. 8B).

107

the sample.

40O.

At the end of each experiment a thawed layer, in

for iwJed 2310-Z~10Mhl)

extreme

cases up to 0.8 cm t h i c ~

has been consistently observed at both ends

i.

of the sample.

This is probably due to the

gradual passage of lactose molecules t;~rough the d i a l y s i s membrane into the frozen s o i l . The lactose in the soil water adds an osmotic 1

potential which f u r t h e r lowers the freezing point of the unfrozen water in the soil and causes some melting of ice. !

-

The problem of

o

TIME (mini

diffusion of the lactose into the sample in-

Figure 8: Flow induoed by a large temperature gradient at relatively warm temperatures. (Experiment No. 7B).

creases with time and for this reason experiments were normally terminated a f t e r a period of 3 days. I t has been suggested that the presence of

the water in the 'cold' end reservoir and the

solutes confounds i n t e r p r e t a t i o n of the dyna-

adjacent unfrozen soil water are in e q u i l i -

mics of water transport in frozen soils to

brium.

an unknown degree, and that the use of super-

Since the same concentration of lac-

tose solution was used in the 'warm' reservoir, the resultant

local

cooled water in the reservoirs might simplify

osmotic potential 0.1.

gradient, coupled with the presence of the d i a l y s i s membrane, could be s u f f i c i e n t to p a r t l y counteract the temperature induced potential gradient at the warm end.

A de-

cline in inflow rates may again r e s u l t , on

-0.1

this account.

CASTOR SILTY LOAM SOIL

'

To show that lactose does, in p r i n c i p l e , serve to equalize potentials in the reservoirs and in the unfrozen soil water, an experiment was run using a Slims Valley s i l t soil,

in which there was no temperature gra-

dient.

Both thermoelectric cooling plates

~:

|

~.

-0.2

-0.3,

.0.4

were held at a constant temperature of -0.325°C, while the reservoirs contained lactose solution, the concentration of which was

.0.5

adjusted to give the required freezing point depression.

Once stable temperatures were

achieved, cumulative inflow and outflow were observed to be n e g l i g i b l e ;

there was no ten-

dency for water to be pulled into or out of

-0.6

i!o

,'.o

~o

4'.o

o'.o

olo

DISTANCE (cm|

Figure 9: StebJe temperature gradien~ at relatively oold temperatures,

108

4OO

3B0.

300-

i

250-

_. ZOO.

o

• "Cold'tld ~tflow (Moen flow ~ 3.82~lO'5~3/min)

• 'Cotd'e~d~tttow (MNn ftow fll~l 1.~xlO'§~3/min)

•

•

~Vm~m'mdiBttow (M4tn flow r~t O.27xlO'8~3/mln)

-

% TIME (i'n~]

Figure 10: Flow/nduoed bY a ='na~ temperature ~rad~tmZat re/at/wly co/d temperatures. (Experiment Ilo. 9A).

matters.

Supercooledwater has been used

'm~o

. 't~o

=

d%

-

1~o

T,ME (i,z~q)

.

"A'wm't@,d~ ( M ~ WOW,me 0,00¢m3/min)

. l~'mo

=

.t~e,a

,

•

Figure 11: Flow induoed by a bage tem perap.u~ ~rad~ent at

'co~d'temm,m,mr~. (~xpe~,m~t ~o. tom).

voir into the frozen s o i l , where ice lensing

successfully in the Burt and Williams perme-

would be expected.

ameter, and the results are essentially iden-

atus, a lens was observed at the cold end.

tical to those achieved with lactose solution

A frost-heave pressure is generated by the

(see Figure 2).

lens growth, causing melting of ice at the

An experiment was run with

1£1o

On dismantling the appar-

the present apparatus, using a Castor s i l t y

'warm' end. The subsequent expulsion of

loam soil in which supercooled water was pre-

water into the 'warm' reservoir follows

sent in the end reservoirs, instead of lac-

directly from the rise in porewater pressure.

tose solution.

This hypothesis appears to account for the

I n i t i a l l y , the results from

this experiment appear surprising, since

observed reversal in flow.

water moved into the frozen s o i l , at the

apparent decline in flow rates over the dura-

'cold' end, and outflow took place from the

tion of the experiment (4 days).

'warm' end.

In other words, water appeared

There was no

Although analysis of the results is made

to be moving in the opposite direction to the

di f f i cult by the complex thermodynamic si tu-

hydraulic gradient implied by the temperature

ation and the number of variables involved,

profile.

the experiments as a whole demonstrate the

Inflow and outflow rates were es-

sentially equal, and ranged from 1.08 x lO-4

movement of unfrozen water within soils at

to 8.22 x lO-4 cm3/min.

below O°C, in response to temperature gra-

Further consideration suggests that this

dients.

Interpretation of the results ob-

phenomenon should not be surprising since

tained is in the preliminary stage, and thus

the supercooled water is not in thermodynamic

any hypotheses developed must be tentative.

equilibrium with the unfrozen soil water; i t

However, the results do appear to coincide

is to be expected that i t will be pulled into

with much of our current theoretical under-

the frozen soil.

standing of frozen soils.

The greatest difference in

The apparatus

potentials exists across the cold end of the

should not be viewed s t r i c t l y as a permea-

sample; thus water moves from the cold reset-

meter, rather the frozen soil is acting in

109

general, as a kind of pump. Calculation of ' o v e r a l l ' hydraulic conductivity values is possible, but the apparatus i s , perhaps, best regarded as providing a novel approach to the well-known frost cell experiment.

Modifi-

cation should include monitoring of the frost heave pressure generated in the sample.

The

application of counter-pressures on the outflow reservoir, s u f f i c i e n t to stop flow, would permit a measure in mechanical terms, of the temperature-induced driving forces. Acknowledgements Discussions with Dr. J.K. Torrance, Dr. M.W. Smith, and D. Patterson are g r a t e f u l l y acknowledged as well as the technical assistance of L. Boyle and A. Pendlington.

Burr, T.P. and P.J. Williams, 1976. "Hydraulic conductivity in frozen s o i l s " , Earth Surface Processes, Vol. I , No. 4, pp. 349-360. Edlefsen, N.E. and A.B.C. Anderson, 1943. "Thermodynamics of soil moisture", Hilgardia, 15, pp. 31-298. Harlan, R.L., 1973. "Analysis of coupled h e a t - f l u i d transport in p a r t i a l l y frozen s o i l " , Water Resour. Res., 9, pp. 1314-1322. Mackay, J.R.; J. Ostrick; C.P. Lewis; and D. K. Mackay, 1979. "Frost heave at ground temperatures below O°C, Inuvik, Northwest T e r r i t o r i e s " , Sci. Tech. Notes in Current Res. Part A, Geol. Surv. Can., Paper 79-IA, pp. 403-405. M i l l e r , R.D., 1970. "Ice sandwich: functional semi permeable membrane", Science, 169, pp. 584-585.

The work was

carried out in the Geotechnical Science Laboratories, under contract with the Earth Physics Branch, Department of Energy Mines

M i l l e r , R.D.; J.P.C. Loch; and E. Bresler, 1975. "Transport of water and heat in a frozen permeameter", Soil. Sci. Soc. Am. J., Vol. 39, pp. 1029-1036.

and Resources, Canada. References Anderson, D.M. and N.R. Morgenstern, 1973. "Physics, chemistry and mechanics of frozen ground: a review", Permafrost: 2nd Int. Conf., North American Contributions. Nat. Acad. Sci., Washington, D.C., pp. 257288.

Nye, J.F. and F.C. Frank, 1973. "Hydrology of the intergranular veins in a temperate glacier", Publication No. 95, Int. Assoc. Sci. Hydrology. Osterkamp, T.E., 1975. "Structure and properties of ice lenses in frozen ground", Proc. Conf. SoilWater Problems in Cold Regions, Calgary, pp. 89-111.