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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.
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.