Experimental studies of coupled heat and moisture transfer in soils during freezing

Cold Regfons Science .rid Technology, 3 (1980) 223--232 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

223

EXPERIMENTAL STUDIES OF COUPLED HEAT AND MOISTURE TRANSFER IN SOILS DURING FREEZING

Masami Fukuda Institute of Low Temperature Science, Sapporo, Japan Akin Orhun and James N. Luthin Dept. of Land, Air and Water Resources, University of California,

Davis, CA., U.S.A.

the experiment provide data for a better

ABSTRACT

understanding of coupled heat-water flow in

Moisture and heat flow were measured during the freezing of a column of Tomakomai

freezing soils, and also can be used to

silt soil.

verify the proposed computer simulation

A dual-beam gamma apparatus was

used to measure changes in soil density and moisture content.

models.

The experimental data

showed movement of water through the frozen layer.

EXPERIMENTAL METHODS AND EQUIPMENT The Soil Sample.

The soil used in the

experiment was Tomakomai silt. INTRODUCTION

The soil was

packed in a Plexiglas container measuring

During soil freezing the water in the

i0 x i0 x 20 cm (see Fig. i).

The actual

soil is redistributed and as a result segregated ice lenses are often formed.

i CwlI~ Fkl

This re-

distribution of water in freezing soils causes the frost heave process.

,.....,............, ::::::::::::::::::::

several mechanisms have been proposed to ~i~i~iiiiiiiiiiiiiii

describe coupled flow of moisture and heat.

iiiiiiiiiiii!ii!i!ii

::i::iil]iii?:i~i::i

Computer simulation based upon these models have given reasonable results.

l

il

Recently,

F

iiiiiiiiiii iiiiiii

id Side ~...., ..,, ......

However, very

.:.:.:+:.:+:.:.: •.........,.. ,... ;::;;:::::::::;.:,:.

$0il

:::::::::::::::::::::::::::::::::::_

sm

iii!iiiii!iiii!ii!ii

few experiments have been conducted to test the computer models.

--

iiiiiiiiii ....,............... ..,........,,......, .........,......,... .......,..,,., ,.., ...............,.. ................... .,,......,.......... ....................

A major difficulty in

experimentation is the measurement of the

,,,,,,,,.,.,........

.......,..,.

moisture flow by a nondestructive procedure.

..........,,,,,,.,,.

It is important to be able to measure the transport of water through frozen soils.

The

gamma ray attenuation method for the measure-

5

Ip ©m

to watw sowm

ment of water content in soils has been used by several investigators for the study of soil freezing experiments.

Fig. i.

Experimental apparatus.

height of the soil column inside the container

In our experimental study, we used the

is i0 cm.

A porous plate is attached to the

dual gamma ray attenuation method for the

bottom of the container to which water is

measurement of water flow in freezing soil.

supplied to the soil column.

By using the dual-beam procedure,

soil in the container and the water source,

it was

Between the

possible to measure both the water content

there is a valve which can be used to control

and density simultaneously.

the water supply situation.

The results of

The valve can

224 be a d j u s t e d tion

so t h a t

the experimental

is either an open or closed

The soil container insulation

the surface of the soil column,

circulated

plate.

through

temperature

fluctuation in + 0.3°C.

in a constant

The temperature

The

room was withcondi-

was conducted,

therma-

granulated.

we achieved

days.

performed

due to

Recently,

some experi-

The use of the dual gamma ray method enables

changes

the investigator

in soil moisture

simultaneously.

Nofziger

(1978)

of the application method

uniform soils such as frozen soils of the

tain ice lenses. evaluated moisture

from the cold

In this study,

the gamma ray method

for nonthat con-

the authors

for monitoring

change of the freezing soils.

For a single energy gamma ray system, intensity

to

and soil

of the gamma ray passing

the

through

the soil column is given by

by

temperature

By this procedure,

(1)

I = I 0 exp(-~sPsX-~wP w GX-BcPc XI)

uniform water content and tempera-

ture profiles.

The initial water contents

the soil were approximately The dry densities

Measurement Measurements

(1978)

of the gamma ray attenuation

the experiment

cold

content measurement

pointed out the limitation

of 0.05°C.

The soil was conditioned

near O°C for several

Loch and Kay

density

the material was well-

keeping it at a constant

the

ments on soil freezing using dual gamma

determine

every two hours at

Before

did not take place during

in the soil density.

attenuation

were measured by

and water content

the change

sources.

as a function of time and

side of the column.

ice

there may be very large errors

of 8°C.

as a function of the distance

segregation

since

in the moisture

0.003 in.) at 2 cm-

soil were measured

the freezing process

constant

susceptible,

room

reduced heat exchange

were measured

Jame and Norum assumed

that the density of the soil remains throughout

of the soil column.

each point with an accuracy

basis.

of the measurement.

The

along the length of the column.

Temperatures

occurs.

the

temperature

fine copper-constantan

(diameter

conditions when ice segregation

to

If the soil is very frost

temperature

The soil temperatures

that the

from unfrozen

experiment.

of the temperature

the sidewalls

It is well-known

The experiments

temperature

The constant

soil has some

density of the soil must be known in advance

fluids was within + 0.1°C

tions of the experiments

intervals

frozen

The use

When using the single source method,

The fluctuation

the experiments.

having an ambient

couples

fluid.

content of a freezing

limitations.

They

for measuring

density of the soil changes

fluid is

At the bottom

of cooling

constant.

were performed

inserting

moisture

there is a small chamber

of the circulating

through

At

at the bottom of the soil column

is maintained

throughout

of the single source method

the plate and the soil

for the circulation

method.

used CS137 as a gamma ray source.

thermal

there is a

Cooling

from top to bottom.

of the container,

single gamma ray attenuation

system.

is covered with

three cm thick at each side.

brass circulation

freezes

condi-

of

30-35% on a volume

were 1.0 grams/cm 3.

of Soil Moisture

of the soil moisture

Content. content

where

I 0 is the gamma ray intensity

through

air;

Ps is the dry density of the soil,

~s'

~w' and Pc are the mass attenuation

coefficients Plexiglas

for the soil, water,

soil container,

and

and the

respectively;

were made by the dual gamma ray attenuation

0 is the volumetric

method.

Jame and Norum

X 1 are the lengths of the soil column and

moisture

change of freezing

(1976) measured soils by the

the

thickness

water content,

of the column case,

and X and

respectively.

225

If two gamma sources of different energy CO(3.ING F W ~

spectra are used, one will obtain two equations for each case.

In each equation 0 and 0 are

unknown.

Thus, if we apply simultaneous

equations

for these two gamma ray attenuation

situations,

gn(I/Io)Cs

we obtain 8 and 0 as follows:

" YAm " gn(I/Io)Am " UCs + CAm " UCs - Cos " ~sAm

B X • (~wAm " ~sCs " PwCs

p

~n(I/l~cs

" ~vAa " £n(I/Io)~

" Us&,~)

" ~wCs - CCs " ~vAm + CAm " ~wCs

-

XOJsAm " ~JwCs - ~JsCs " ~JwA: )

.... ii? .iiii iii £n(I/lo)Am ~

Ratio of gamma ray intensity-

~n(I/Io)Cs)

column/air

Fig.

2.

Experimental arrangement for d u a l - b e a m gamma r a y m e a s u r e m e n t s .

~sCs and ~sAm are mass attenuation coefficients of soil ~wCs and ~wAm are mass attenuation cients of water

coeffi-

Gardner

(1972)

of water content

X is the length of the soil column

pointed out

and d e n s i t y

that

the error

measurements,

due t o t h e r a n d o m n e s s o f gamma r a y e m i s s i o n ,

= ~n(I/10)Am.C~ Ratio of gamma ray inCAm £n(I/10)Cs .-°tensity~'CJ through column CCs case and air

can be e x p r e s s e d as the v a r i a n c e component.

of each'

He noted that the variances of

Am = Americium-241

determination

Cs = Caesium-137

are functions of the thickness of the soil

of water content and density

The 40 mci Caesium-137 and the i00 mci Ameri-

column.

cium-241 were used in this experiment.

equation, we calculated

The two

According

to Gardner's proposed the optimum length

energy peaks from the two different sources

of soil column,

are separated.

errors due to random emission processes of

By a proper setting of the

windows of the pulse-height analyzers,

it was

gamma sources.

taking into account the

The count rates through

possible to adequately discriminate between

the air (106 cpm), water content

these two energy peaks.

a volume basis), density

(i.0 g/cm 3) were

taken into consideration

in the calculation.

sources were accommodated

Both of the gamma in a lead housing

holder and collimated by a slit measuring 23.8 mm x 2.54 mm. scintillation

A sodium iodide crystal

detector is housed in the lead

holder and the opening which faces the gamma ray beam is collimated. is shown in Fig. 2.

The system diagram

Both the lead housing

holder of the gamma ray sources and the scintillation

detector are mounted on a

rigid frame which travels upward and downward, driven by a screw and pinion assembly.

(30-50% on

The variances of water content and density, as a function of the thickness of the soil column, are shown in Figs. 3 and 4.

The i0 cm

length of soil column, which we employed in this study, is adequate for the determination of water content and density by the dual gamma ray attenuation method.

226

de-aired water were placed between the gamma sources and t h e d e t e c t o r .

Water

100

The Changes of

count rate passing through the water were

Content

measured.

A linear regression of the data

gave the attenuation coefficient for water

80

for both Am-241 and Cs-137. 60

as follows:

The values are

~wAm = 0.1181 cm2/gr, with a

regression coefficient of 0.99989.

nwCS

~0

= 0.0849 cm2/gr, with a regression coefficient of 0.99997.

The attenuation coefficient of

20"

Plexiglas was obtained with both Am and Cs. In the case of the determination of the atten0

5

10 LENGTH

Fig. 3.

15

20 cm

uation coefficient for soils,

of $ANPLE

Variance of gamma ray count for moisture content determination as a function of sample length.

the methods

described above are not adequate because of the variations of the densities of dry soils. In order to determine the attenuation coefficient for soils,

Density

12

the dry soil was packed

into Plexiglas boxes having various inside dimensions.

10-

The volumes of the boxes were

carefully measured and the dry soils were weighed.

8-

After determining the density, each

box filled with dry soil was placed in the gamma ray apparatus.

/

&-

ured.

2-

I 10

5 LENGTH

t '~

I 20cm

Of SAMPLE

Variance of gamma ray count as a function of sample length for density determination.

Determination of the Attenuation Coefficient.

the attenuation coefficient of water, soil, and the Plexiglas soil container.

The attenu-

ation coefficients of water and Plexiglas can

For this purpose, Plexiglas plates with different thickness and Plexiglas boxes having different dimensions and filled with distilled,

~

S

/

~o -- 1,5

9

'//~/

rr==o.~a u.lng|

~/

4

be determined with sufficient accuracy because of the uniform densities of the materials.

SOIL

2.5

The accuracy of the dual gamma

ray system depends mainly on the accuracy of

meas-

In Figs. 5 and 6, the values obtained

Am241

Fig. 4.

The intensity of the

gamma ray passing through the box was

Fig. 5 .

6

S

10

12 inl

227

~ER Cs 137-

CONTE~

SOIL

/YY

1,0

ns

/

04

///

i

, - o .oos

T~"*ms

4

O

I

10

12

14cm

Fig. 6. by dividing the count ratio by the measured

Fig. 7.

density are plotted as a function of the length of the dry soil sample.

Effect of shift of attenuation coefficients on calculation of water content.

The slopes

of the fitted regression line indicate the

used his method, which consisted of packing

attenuation coefficient.

a dry soil into a soil column container

The dashed line

shows the 90% confidence zone of regression.

consisting of three sections held together by

Goit et al. (1978) indicate that errors, due

masking tape.

to the variations of the attenuation coeffi-

the column, it was shaken for three hours.

cient of soils, cause wide variations in the

The top section was carefully removed;

measurement of the water content.

middle section was also removed and the soil

They

After packing the soil into

the

assumed that only one value of the attenua-

was scraped off with a straight edge.

tion coefficient, due to the use of Am and Cs,

ends were covered with Plexiglas plates.

varied.

Actually,

in the case of using the

Both

Then counts were taken through the middle

dual gamma ray system, both values may vary

section.

After counting,

at the same time.

weighed.

We repeated the process six times.

The effect of a shift of

the soil was

the two attenuation coefficients on the cal-

By this method, we obtained the attenuation

culation of water content were calculated for

coefficients of soils as follows:

one pair of water content and soil density values and given on Fig. 7.

The shift in

U s Am = 0.2778 ~ 0.002 cm2/gr

water content is due to the deviation of the values of the attenuation coefficient.

In

U s Cs = 0.0752 + 0.002 cm2/gr

the fig. 7, the percentage numbers on the lines imply the shifts from the actual water content.

If an accuracy of 1% or less of

water content is desired,

The attenuation coefficient of a mixture of ice and water were also measured.

the attenuation

The

mass attenuation coefficient for water should

coefficients for Am-241 and Cs-137 must be

be equal for both the solid and liquid phases.

determined within a deviation of less than

During the melting process of ice, the inten-

0.5%.

Gardner

(i972) suggested a way for

determining the coefficient of dry soil.

sity of gamma ray passing ice water mixtures We

228 were measured.

The equation for ice water

RESULTS AND DISCUSSION

system is:

A number of experiments were conducted using several different temperature gradients

~n (I/l0) = ~w

"

and at various initial moisture contents,

Ow X

which resulted in different rates of freezing where Ln (I/I0) is the count ratio, ~w is the

front advance.

attenuation coefficient and is constant for

periments,

both ice and water, p

From the results of the ex-

it is observed that moisture

changes of freezing soil in a closed system

is the density of ice w or water, X is the length of the gamma path

occur in both the frozen and unfrozen zones.

through the ice water.

Moisture flow through the frozen layer was

Dividing %n (I/I 0) ice

by ~n (I/I0) water, we obtained the following

measured in our experiments.

ratios:

in Fig. 9, at the i cm depth in front of the

For example,

o

NAm = 0.914256 + 0.00305 NCs = 0.911389 + 0.00478

o

0

10

% 60

~

50

~--.

2~

70

~0

These ratios are almost equal to ratio of

o

30'

density of ice to water.

According to Dorsey (1940), the d e n s i t y

~ 20' 10'

of ice at 0°C is 0.9168 g/cm 3 and water at 0°C is 0.9921 g/cm 3.

Thus, the ratio of

densities of ice to water is 0.924.

, I

In

, 2

, 3

~

, 5

~

, 7

~

, 9

, 10 cm

DEPTH

Fig. 8, the i n c r e a s e of ~n ( I / I 0) i n d i c a t e s Fig. 9. ice

CS

•

Wa~

Am

.-- .....

Cs

Water content fluctuations as a function of depth at various times after the initiation of freezing.

"c

-B o.~ -

.175

~ o~.

o%

- 1~

i C

¢m

-I i

Elape~

Fig. 8.

,

T~e

-2

Effect of phase change ice ÷ water on count r a t e .

-3

that the change of water-ice to water during the m e l t i n g p r o c e s s agreed w i t h D o r s e y ' s d a t a . Regardless of the water or ice phase,

the

measured water content means the equivalent unfrozen water content.

Fig. i0.

Temperature distribution for Fig. 9.

229 freezing content

front,

decreased.

advanced

beyond

increased.

the estimated

perature

position

at about

front

the water

an elapsed

of the freezing

front

The tem-

at the same

and was b e l o w

At the freezing drop in water

content

time of 42 hrs,

4 cm depth.

at 1 cm depth,

-1.8°C

the water

As the freezing

this point,

After

was located

was

or 0°C isotherm,

front,

content

there was a sharp

in the unfrozen

layer.

This d i s c o n t i n u i t y

profile

means

of water

that the drying

just behind

front.

in Fig.

tempera-

No.!2

point

1 hours

o

? ~

water

content

depression,

at this point.

the temperature

had dropped

After

II*,t,5 23/.0

the

then some water

must be frozen

o

. . . .

at this point

was 0.46 cm3/cm 3 and if one considers freezing

the freezing

ii at a 1 cm

time,

the freezing

ture of the water. The measured

content

zone in the

u~nfrozen side exists For example,

soil

102 hours,

to -3.0°C.

40.

§30.

During 2O

this

time period

moisture point

content

increased

in question

front.

occurred

results

(1969)

indicates

through

the

though

the

10 ¸

the freezing

the frozen

2

a

through

at 1 cm depth,

with a thickness

was calculated.

The results

z.

5

'~

"I

,0

¢m

DEPTH

soil.

with Hockstra's

In the case of Fig.

the flux of water

1

that moisture

are in agreement

findings.

(test #6),

even

was behind

This clearly

migration These

(42 to 102 hours),

Fig.

ii.

Water after

9

content for various times the initiation of freezing.

the plane

of 2.4 mm, "¢

are as follows:

For T mean = -2.13°C Q = 2.956

x 10 -7 g/s

• cm 2

For T mean = -2.62°C Q = 2.069 x 10 -7 g/s

• cm 2

For T mean = -2.98°C Q = 2.045

The calculation

x 10 -7 g/s

was performed

• cm 2

as follows

for

iI

¢m

T mean = -2.13°C: Fig. at 42 hours

the water

content

= 46.94%

at 70 hours

the water

content

= 49.92%

depth,

12.

Temperature d i s t r i b u t i o n for experimental data in Fig. ii.

the water

from the initial The increase

in water

per unit volume

content

of soil is 0.0298

the time interval

is 28 hours,

unit area 2.98 x 10-2/28 2 g/s

•

cm

.

is 2.98% or yr.

Since

the flux per

x 60 x 60 = 2.95 x 10-7

11.85%

during

temperature

freezing

decreased

content

the time p e r i o d

The temperature

span dropped

content water

profile

sharply

of 32% to of 0 to 7 hrs.

indicated

that the

at 1 cm depth at the same to -1.64°C.

point

depression

time

However,

if the

of water

is

230 considered,

it may be assumed

1 cm is not frozen.

that water at

Using Tomakomai silt,

pressure is about 1.6 x 10 -8 cm/sec. the

the transport of water mass

Thus,

to the freezing

unfrozen water contents at various degrees

front through the layer between 1 and 2 cm

below 0°C were measured.

depth may be calculated as 3.31 x 10 -4

The following

empirical equation was obtained.

gr/sec.cm 2.

At the 2 cm depth, by a similar

calculation,

the flux to the freezing front

W=

may be estimated as 2.10 x 10 -4 gr/sec.cm 2.

a . Tb

The speed of the advancing freezing front controls

where W = volumetric

unfrozen water content

(cm3/cm 3)

the water content increments

frozen layer.

in the

If we compare Fig. 15 to Fig. 17,

a = constant = 0.19778

it is obvious

b = constant = -0.3046

of test #4 is faster than #5.

that the freezing front speed Also,

if

T = absolute value of freezing point depression.

compared,

If we substitute

and Fig. 16 show that the water contents are

the equation,

the value of T as 1.64 into

the unfrozen water content is

0.17 cm3/cm 3.

Thus,

the measured water con-

tent by gamma ray attenuation that value.

is far less than

In the same time period,

7 hrs,

the water content profile in Fig. 14

close to each other.

However,

content in the frozen layer of the #5 test are much greater than that of the #4 test. The discontinuity

of water content profile

the water content at the 2 cm depth is 30.69%.

(the #5 test after freezing)

In a previous experiment,

than the #4 case.

we obtained

the

the water

is more distinct

The difference of the test

relationship between water content and pore

conditions between #4 and #5 is only the

water pressure.

freezing front advance speed.

The characteristic

curve

(Fig. 13) which relates water content

to pore

The slower

freezing front speed results in greater increase in water content in the frozen soil.

% % 50

Tomakamat

~ O h o ~ ......

60-

Slit

.

50 ~40

40

12

""''

....

30

8

( J 3O

lO 2O

DEPTH 20

Z5

Pore Woter

Fig. 13. water pressure,

3,0

15

~

Pre~,fe

Fig. 14.

Characteristic curve for Tomakomai silt. shows

dient of water between

that the potential

gra-

the 1 cm depth and 2 cm

depth reaches 35875 cm/cm.

The estimated

hydraulic conductivity at this pore water

Moisture content distribution at various times after the initiation of freezing for soil column initially at about 40% moisture.

231

CONCLUSION ~__!

The water content and temperature profiles

.5

in the freezing,

unsaturated

soil were ob-

tained by the gamma ray attenuation method. .3

Water migration

.2

to both unfrozen and frozen

soil layers were monitored with adequate

W tl

accuracy.

0

Ocm

-1

The flux rate of water through

the frozen layer was obtained by direct measurement.

-2

The moisture

flow rate depends

upon the speed with which the freezing front

-3

advances.

The boundary between the frozen

-4

and unfrozen soil determined -5

the temperature

.

profile.

The water content profiles do not

coincide because of the presence of unfrozen Fig. 15.

Temperature distribution for experiment shown in Fig. 14.

water in an extremely dry soil moisture condition.

% 80"

~ .

70• ~a,

The water content and temperature

0 how

.

profiles provide data for the application

14

a

23

.

3~8

of computer models.

60

These considerations

will be discussed in a forthcoming paper. ',', \

5°J ACKNOWLEDGMENT This work was supported by a grant from the National Science Foundation.

°I i0

0

LITERATURE CITED i

i

1

2

Fig. 16.

~

s

s

7

8

~

~0¢m

~ Water content in sample frozen at slow rate compared to Fig. 14 & i~

.5

"3

.1

-2

Gardner, W., G. S. Campbell and C. Calisendorff. 1972. Systematic and random errors in dual gamma soil bulk density and water content measurement. Soil Sci. Soc. Am. Proc. 36:393-398. Goit, J. B., P. H. Groenevalt, B. D. Kay and J. G. P. Loch. 1978. The applicability of dual gamma scanning to freezing soils and the problem of stratification. Soil Sci. Soc. Am. Jour. 42:858-862.

.2

~

Dorsey, N. E. 1940. Properties of ordinary water substances. Reinhold Publishing Company, N. Y. 466 pp.

2 6

8

10 cm DEPTH

-3 4

Jame, Y. and D. Norum. 1976. Heat and mass transfer in freezing unsaturated soil in a closed system. Edmonton Conference on Soil Water Problems in Cold Regions. Am. Geo. Union. p. 46-62.

-5

Fig. 17.

Temperature distribution for experiment shown in Fig. 16.

Loch, J. P. G. and B. D. Kay. 1978. Water redistribution in partially frozen, saturated silt under several temperature gradients and overburden loads. Soil Sci. Soc. Am. J. 42:400-406.

232 Nofziger, D. L. 1978. Errors in gamma-ray measurements of water content and bulk density in non-uniform soils. Soil Sci. Soc. Am. Jour. 42:845-850.