Suction and its effects in unfrozen water of frozen soils

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Suction and its effects in unfrozen water of frozen soils

Reprinted from t h e PROCEEDINGS: PERMAFROST INTERNATIONAL CONFERENCE, N A S - N R C , P u b l i c a t i o n 1287

SUCTION AND ITS EFFECTS I N UNFROZEN WATER OF FROZEN SOILS

P. J. WILLIAMS, Norwegian G e o t e c h n i c a l I n s t i t u t e , O s l o

S u b s t a n t i a l q u a n t i t i e s of w a t e r remain unfrozen in s o i l s a t t e m p e r a t u r e s of s e v e r a l d e g r e e s b e l o w ODC [ l , 2 , 3 1 . The proportion of unfrozen w a t e r d e c r e a s e s a s t h e temperature i s l o w e r e d , b u t a s much a s half of the w a t e r may e x i s t unfrozen a t - l ° C . This unfrozen water h a s b e e n a t t r i b u t e d [ 4 ] to the s u c t i o n s or n e g a t i v e pore p r e s s u r e s t h a t d e v e l o p a s a r e s u l t of i c e - l e n s growth in the s o i l . A n e g a t i v e pore p r e s s u r e in a s a t u r a t e d s o i l , in t h e a b s e n c e of e x t e r n a l l o a d i n g , r e s u l t s in a p o s i t i v e e f f e c t i v e s t r e s s ( a s t r e s s a c t i n g a c r o s s the g r a i n - to-grain c o n t a c t s ) e q u a l t o t h e n e g a t i v e pore p r e s s u r e . An i n c r e a s e in e f f e c t i v e s t r e s s c a u s e s c o n s o l i d a t i o n in c o m p r e s s i b l e s o i l s . It i s therefore of i n t e r e s t to i n v e s t i g a t e the c o n s o l i d a t i o n t h a t s h o u l d o c c u r in a frozen s o i l a s a r e s u l t of n e g a t i v e pore p r e s s u r e s in t h e unfrozen part of t h e moisture c o n t e n t . Such c o n s o l i d a t i o n would a l s o confirm thz e x i s t e n c e a n d , to s o m e e x t e n t , t h e magnitude of t h e n e g a t i v e pore p r e s s u r e s - a n d their r e l a t i o n s h i p to t e m p e r a t u r e . FREEZING EXPERIMENTS Direct i n v e s t i g a t i o n of t h e s e e f f e c t s i s d i f f i c u l t b e c a u s e of t h e irregularly d i s t r i b u t e d i c e - l e n s e s in a frozen s o i l w h i c h , on t h e o n e h a n d , g r e a t l y r e d u c e p e r m e a b i l i t y , a n d on the other h a n d , i n c r e a s e t h e o v e r - a l l s o i l volume. It i s n e c e s s a r y to d e v i s e a n experiment in which l e n s formation i s prevented in a part of t h e s o i l l a r g e e n o u g h for s u b s e q u e n t s t u d y of d e g r e e of c o n s o l i d a t i o n a n d w a t e r c o n t e n t . P e r s p e x r i n g s 2.2 cm ID a n d 0 . 4 cm in h e i g h t w e r e m a d e . A ring w a s f i l l e d w i t h a s o i l s a m p l e prepared f l u s h to t h e s u r - f a c e . P i e c e s of a membrane, p r s v i o u s l y s c a k e d in w a t e r , w e r e t h e n placed a c r o s s t h e f a c e s of t h e ring a n d s o i l s a m p l e a n d p r e s s e d tightly a g a i n s t t h e p e r s p e x w i t h a c l a m p a r r a n g e - ment (Fig. 1 ) . A thin s m e a r of petroleum jelly w a s u s u a l l y p l a c e d o n t h e p e r s p e x ring where it c a m e in c o n t a c t w i t h the membrane. Two further p i e c e s of t h e s a m e , or s o m e t i m e s d i f f e r e n t , s o i l were t h e n p r e s s e d a g a i n s t the, e x p o s e d s i d e s of t h e m e m b r a n e s .

This a s s e m b l y w a s s l o w l y c o o l e d to a c h o s e n n e g a t i v e t e m p e r a t u r e . Freezing (with i c e - l e n s formation) o c c u r s in t h e e x p o s e d s o i l , b u t n o t in t h a t b e t w e e n t h e membranes b e c a u s e of t h e a b s e n c e of a n i c e n u c l e u s . S p o n t a n e o u s n u c l e a t i o n d o e s n o t occur-initially b e c a u s e t h e s a l r ~ p l e i s s m a l l a n d s u b s e q u e n t l y for r e a s o n s which w i l l become apparent-and i c e growth c a n n o t o c c u r through t h e membrane. The membrane i s of the water-permeable type u s e d in p r e s s u r e membrane t e s t s

i s ] .

The membrane p o r e s a r e s o s m a l l t h a t i c e growth o n l y o c c u r s within them a t t e m p e r a t u r e s of a t l e a s t s e v e r a l d e g r e e s b e l o w O°C.

A modified d o m e s t i c - t y p e refrigerator w a s u s e d . A mercury c o n t a c t thermometer s w i t c h with a r e l a y s y s t e m maintained a fairly c o n s t a n t t e m p e r a t u r e . To a v o i d d e s i c c a t i o n and to e n s u r e uniform t e m p e r a t u r e , the s a m p l e a s s e m b l i e s w e r e p l a c e d in c l o s e d j a r s together w i t h p i e c e s of i c e t o s t a r t n u c l e a t i o n in the e x p o s e d s o i l . The s p e c i m e n s w e r e g e n e r a l l y maintained a t t h e c h o s e n temperature for three d a y s . T e s t s w i t h thermocouples i n d i c a t e d t h a t t h e s a m p l e a t t a i n e d t h e c h o s e n temperature from 5 to 1 0 h o u r s a f t e r refrigeration.

After r e f r i g e r a t i o n , t h e a s s e m b l y w a s d i s m a n t l e d ; t h e w a t e r c o n t e n t and volume of t h e inner s o i l layer ( l o c a t e d b e t w e e n t h e membranes) were d e t e r m i n e d . A s p e c i a l l y c o n s t r u c t e d g l a s s pycnometer (Fig. 2) c o n t a i n i n g paraffin w a s u s e d to d e t e r m i n e t h e volume. To o b t a i n s u f f i c i e n t a c c u r a c y , c o n - s i d e r a b l e a t t e n t i o n to temperature a n d other e f f e c t s w a s n e c e s s a r y .

M a n y further t e s t s involving determination of w a t e r c o n t e n t o n l y w e r e d o n e o v e r a r a n g e of O0 t o -3.3OC. In a l l c a s e s t h e

Bmss clamping rings,

/

\

/erspex ring ,Soil sample

\

F i g . 1 . Sample a s s e m b l y for f r e e z i n g e x p e r i m e n t s

F i g . 2 . Pycnometer u s e d for dry d e n s i t y d e t e r m i n a t i o n s

w a t e r c o n t e n t of the inner l a y e r w a s s u b s t a n t i a l l y l e s s t h a n t h e i n i t i a l w a t e r c o n t e n t . Preliminary t e s t s showed t h a t t h e w a t e r c o n t e n t of the inner l a y e r s b e c a m e p r a c t i c a l l y c o n s t a n t within t h r e e d a y s . In o n e t e s t s i m i l a r s o i l s a m p l e s p l a c e d in d i f f e r e n t p a r t s of t h e r e f r i g e r a t o r might g i v e r e s u l t s differing b y 1 to 2% of dry w e i g h t . T h i s w a s l a r g e l y d u e to s l i g h t t e m - p e r a t u r e d i f f e r e n c e s . S a m p l e s of t h e s a m e s o i l in o n e b o t t l e c o n s i s t e n t l y s h o w e d s i m i l a r w a t e r c o n t e n t s for t h e inner l a y e r within 0 . 1 t o 0.2% dry w e i g h t . When o n e s a m p l e w a s removed a n d the temperature t h e n lowered for a further p e r i o d , s a m p l e s removed l a t e r s h o w e d lower w a t e r c o n t e n t . In a l l c a s e s moisture c o n t e n t ( i c e a n d water) of t h e o u t e r s o i l l a y e r s (Fig. 1) w a s i n c r e a s e d .

VOLUME MEASUREMENTS

R e s u l t s of i n v e s t i g a t i o n s o n Leda c l a y KNB a r e s h o w n in Fig. 3. From volume d e t e r m i n a t i o n s , dry d e n s i t y ( w e i g h t dry m a t e r i a l p e r u n i t volume of s o i l i n m o i s t c o n d i t i o n in grams per c u b i c c e n t i m e t e r ) w a s c a l c u l a t e d a n d plotted ( F i g . 3 , c r o s s e s ) a s a function of w a t e r c o n t e n t . C o n s o l i d a t i o n of s a m p l e s from t h e inner l a y e r of t h e membrane a s s e m b l y occurred during freezing. T h i s i s c l e a r l y s h o w n b y c o m p a r i s o n with r e s u l t s of o e d o m e t e r t e s t s on s i m i l a r m a t e r i a l (Fig. 3 , c i r c l e s ) . If the m a t e r i a l i s s a t u r a t e d t h e r e i s a unique r e l a t i o n s h i p b e t w e e n d r y d e n s i t y , w a t e r c o n t e n t , a n d e f f e c t i v e s t r e s s , for t h e o b s e r v a t i o n s s h o w n in F i g . 3 . S p e c i f i c w e i g h t of the s o i l ? 2 5

1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.8 5

Dry density, g m l c m 3

Fig. 3 . Dry density a s a function o f moisture content

particles was found t o be 2 . 7 8 g per cu c m , and from volu

-

to temperature. This direct procedure, while giving the

metric consideration, dry density and water content relation- approximate magnitude o f the pore pressures, i s not entirely

ship for the saturated state was calculated (Fig. 3 , dashed s a t i s f a c t o r y . Reasons for this are apparent from earlier

l i n e ) . The relationship o f the observed points to this line experimental work [ 4 ] which can be used to obtain a more

shows that the soil was saturated over the range shown. accurate approximation o f the temperature-negative

According t o the e f f e c t i v e stress equation pore-pressure relationship.

6 = 0 - l l

_{INTERPRETATION OF OBSERVED WATER CONTENTS FROM}

where

5

i s e f f e c t i v e s t r e s s , i s total stress (equals CALORIMETRIC STUDIES OF FROZEN SOILS

applied load in oedometer), and p i s pore water pressure,

the load applied in the oedometer i s equal to the e f f e c t i v e In this earlier work, calorimetric methods were used t o deter-

stress (which i s responsible for consolidation) after equilib- mine the quantity o f water remaining unfrozen at various

rium i s reached, because pore water pressure i s then atmos- negative temperatures. Results o f this type can be expressed

pheric ( i . e . , z e r o ) . The relationship b ~ t w e e n dry density a s (and moisture content) and e f f e c t i v e stress i s thus given b y the oedometer t e s t s . The figure for e f f e c t i v e stress shown beside e a c h point in Fig. 3 , obtained from the oedomzter t e s t s , illustrates this relationship.

The magnitude o f e f f e c t i v e s t r e s s e s t o which samples from the membrane experiment have been subjected i s indicated b y those s t r e s s e s that in oedometer t e s t s produced a similar moisture content and dry d e n s i t y . In the absence o f external loading ( a s in the membrane freezing experiment), e f f e c t i v e s t r e s s i s e q u a l , but o f opposite s i g n , to pore water pressure. Positive e f f e c t i v e stress giving rise to consolidation arises from, and i s numerically equal t o , negative pore pressure developed by f r e e z i n g .

RELATIONSHIP OF TEMPERATURE TO NEGATIVE PORE PRESSURE As the temperature i s lowered and more pore water i s trans- ferred to ice m a s s e s , negative pore pressures (and hence the e f f e c t i v e stress) become greater. Negative pore pressure a s a function o f temperature cannot be determined from the f e w observations in Fig. 3 . However, i f water content o f the inner layer from the membrane experiment was known a s a function o f temperature with s u f f i c i e n t accuracy, it would be possible to combine this with information in Fig. 3 to obtain values o f negative pore pressure as a function o f temperature. Water content o f the inner ( i c e - f r e e ) layer, determined in many t e s t s i s shown in Fig. 4 (points and circles) a s a function o f temperature. In general, water content i s l e s s for lower tem- peratures. In addition t o the two soils illustrated, t e s t s were also made on an illitlc clay from Asrum, Norway, and a bentonite from W i n n i p e g , Canada. These t e s t s also showed decreased water content o f the inner layer for lower tempera-

ture. From information in Fig. 3 , it should be possible to find

negative pore pressure (which i s n u m e r i c a l l y equal to the e f f e c t i v e stress causing consolidation) corresponding to the d i f f e r e n t water contents o f the inner layer (Fig. 4) and thus

weight o f watsr remaining unfrozen

dry weight o f soil x 100

and then shown on Fig. 4 . At l e a s t to about - l ° C , water con- tent o f the inner ( i c e - f r e e ) layer in the membrane experiment i s , within limits o f experimental error, equal t o water content o f "normally" frozen soil ( i n which ice i s a l s o present). During the freezing process in the membrane experiment, water i s transferred from the inner layer t o the outer layers (where ice i s formed) because o f a pressure gradient in the water. W h e n water content o f the inner layer becomes constant, the water in both inner and outer layers would be expected t o have the same negative pressure. Thus the situation o f the inner soil l a y e r , isolated by membranes, does not d i f f e r fundamentally from parts o f the normally frozen soil in which i c e - l e n s e s may happen to be a b s e n t . The inner soil layer has the same ( u n f r o z e n ) water content under the same negative pressure.

In the calorimetric investigations it was a l s o found that the unfrozen water content a s a function o f temperature h a s ,

because o f h y s t e r e s i s , somewhat d i f f e r e n t v a l u e s depending = on whether the soil i s in process o f freezing or thawing

(Fig. 4 ) . In the membrane experiment, similar small d i f f e r - e n c e s in water content are expected depending on whether the measured temperature o f the refrigerator i s reached by cooling or slight warming. Temperature control o f the refrigerator was such that fluctuations o f * 0 . 1°C might occur and t h e s e are largely responsible for the scatter in the points shown. In addition, water content was t o some extent dependent on the degree o f disturbance o f the sample.

This relatively small scatter in the observed points i s s u f f i c i e n t to prevent an accurate calculation o f the relation- ship between temperature and e f f e c t i v e s t r e s s . Fig. 3 shows that small changes in water content are associated with very large changes in e f f e c t i v e s t r e s s , so that it i s necessary t o

know the water content-temperature relationship (Fig. 4) for

G O

5 0

Y

4 0

r:

Gl

.-

;

2'

TI 0 3 Y

;

3 0

Y

c

0 0 h

aJ

+I

P

2 0

10

0

0

-

1

-2

-3

OC

Fig. 4 . Equilibrium water contents o f inner layers (where ice formation did not occur)

I t I

Calorimetric

determinations:

Freezing

- - -

--

-

-

=

=)

limiting values Thawing

---

DETERMINATION.OF TEMPERATURE AND NEGATIVE PORE PRESSURE REUTIONSHIP

Pressure e f f e c t s are generally accepted as mainly responsible for the presence o f unfrozen water in frozen s o i l s . Earlier work [ 4 ] provided a quantitative evaluation o f t h e s e e f f e c t s . Suction-water content relationships [ 6 ] were determined at room temperature for the soils investigated calorimetrically. A hypothesis was proposed that as freezing occurred and water w a s transferred into i c e - l e n s e s , the water remaining in the pores would b e under an increasing suction (negative pore pressure). This suction could b e predicted from suction-water content tests-and i s probably responsible for the presence o f the unfrozen water because o f i t s e f f e c t on the freezing point o f the latter. The suction predicted for each unfrozen water content was found to be related to the temperature b y an equation o f the type b y Schofield [ 7 ] :

where

H = suction expressed a s height o f a column o f water, cm (=g/sq 'cm); L = latent heat o f freezing o f water (3.336 x l o 9 e r g / g ) ; T = temperature, OK; AT = negative

temperature, OC; and gr = gravity.

This relationship could only be determined following a large number o f c a r e f u l l y controlled t e s t s on various soils-

reasoning a s a b o v e . Results are summarized in Fig. 5 , modi- fied from [ 4 ] . Except for a necessary minor correction t o allow for the e f f e c t o f dissolved salts on freezing point, the equation is apparently valid for all s o i l s . The equation gives the freezing-point depression o f water under negative pres- s u r e , which i s in contact with ice under atmospheric pressure

[ a ] .

Although it appears unlikely at f i r s t , t h i s situation probably occurs in soils where the ice phase is in discrete l e n s e s or m a s s e s larger than pore s i z e , while the water l i e s within small pores under the influence o f capillary and other e f f e c t s .

TEMPERATURE AND NEGATIVE PORE PRESSURE CONCLUSIONS Although earlier work [ 4 ] did not show directly the e x i s t e n c e o f negative pore pressures, present experiments clearly dem- onstrate these pressures and a l s o confirm that their magnitude i s similar to that predicted from ( 2 ) . A thermodynamic equa- tion o f the type o f ( 2 ) d o e s , t h e r e f o r e , correctly describe the temperature-pressure relationship for water freezing in s o i l s . On the b a s i s o f the detailed observations made in the earlier work it can then be concluded that ( 2 ) gives the b e s t available approximation o f the relationship between temperature and negative pore pressure (and thus e f f e c t i v e s t r e s s ) in unconfined samples.

APPLICABILITY OF EQUATION ( 2 )

There is an important limitation t o the present experiment in proving the range o f application o f ( 2 ) which remains t o be d i s c u s s e d . This i s illustrated b y Fig. 6 , where water content is shown a s a function o f e f f e c t i v e stress for samples in oedometer and suction t e s t s . So long a s the soil i s saturated, t h e s e t e s t s g i v e , with minor qualification, similar r e s u l t s . At 21% water c o n t e n t , the two s e t s o f r e s u l t s diverge. This i s the shrinkage l i m i t , and desaturation occurs in the suction t e s t s . In Fig. 4 t h i s i s reached in freezing to about - l ° C . O n freezing to lower temperatures the membrane experiments always gave water contents substantially higher than those determined calorimetrically. This i s probably because when desaturation o c c u r s , hydraulic flow is substantially reduced. Transference in the vapor phase may occur, but e v e n a f t e r three w e e k s at the low temperatures, water content remained higher i n the membrane experiment.

The information in Fig. 3 cannot be extrapolated to apply beyond the shrinkage limit (which i n the case o f Leda clay

S u c t i o n k g l c m 2 Fig. 5 . T h e o r e t i c a l a n d e x p e r i m e n t a l r e l a t i o n s h i p b e t w e e n temperature a n d s u c t i o n

40

*

+

observations

with ocdomctcr

o

observations in

suction tests

LEDA CLAY

KNB

PRESSURES O N THE ICE PHASE

0

F i g . 6 . Comparison of o b s e r v a t i o n s from s u c t i o n - w a t e r c o n t e n t t e s t s and from oedometer t e s t s

0 . 1

1

10

Agreement of e x p e r i m e n t a l o b s e r v a t i o n s w i t h (2) i m p l i e s t h a t the p r e s s u r e o n t h e i c e ( a t l e a s t where i t i s in c o n t a c t w i t h t h e water) i s a l w a y s a t m o s p h e r i c . M o s t of t h e i c e i s in b o d i e s c o n s i d e r a b l y larger t h a n pore s i z e , a n d might b e s u p - p o s e d to c a r r y the e f f e c t i v e s t r e s s , e s p e c i a l l y a t p o i n t s of c o n t a c t w i t h s o i l g r a i n s ( i c e and g r a i n s may b e s e p a r a t e d b y a bound film of w a t e r ) . The e x i s t e n c e in t h e i c e of a p o s i t i v e p r e s s u r e g r e a t e r t h a n a t m o s p h e r i c i s in c o n f l i c t with e v i d e n c e in F i g . 5 , e v e n w h e n a l l o w a n c e i s made for e x p e r i m e n t a l e r r o r s . C u r v a t u r e of very s m a l l r a d i i w i l l c a u s e i n c r e m e n t s o r d e c - r e m e n t s of p r e s s u r e l o c a l l y w i t h i n t h e i c e [ 9 , l o ] . I t i s s u g g e s t e d t h a t t h e i c e s u r f a c e w i l l b e c o n c a v e over g r a i n s a n d c o n v e x into p o r e s , with r a d i i s u c h t h a t l o c a l s t r e s s e s a r e r e l i e v e d a n d t h e i c e s u r f a c e in c o n t a c t with w a t e r i s uniformly a t a t m o s p h e r i c p r e s s u r e . Work now b e i n g c a r r i e d out i n v o l v e s f r e e z i n g t e s t s on simples under v a r i o u s e x t e r n a l l y a p p l i e d t o t a l - s t r e s s c o n d l ~ i o n s a n d may g i v e further information o n t h i s p o i n t .

CONCLUSIONS

Effective stress

6,

kg/cm2

Experiments involving f r e e z i n g of s o i l s a m p l e s , with r e s t r i c t e d i c e - l e n s development s h o w t h a t water w h i c h r e m a i n s unfrozen w i t h i n a f r e e z i n g s o i l h a s a n e g a t i v e p r e s s u r e . T h i s n e g a t i v e pore p r e s s u r e g i v e s r i s e t o a n e f f e c t i v e s t r e s s w h i c h c a u s e s c o n s o l i d a t i o n . T h i s volume d e c r e a s e w i l l u s u a l l y b e o b s c u r e d by i c e - l e n s g r o w t h .

N e g a t i v e pore p r e s s u r e i s g r e a t e r a t lower t e m p e r a t u r e s . Unfrozen w a t e r in s a t u r a t e d s o i l moves f r e e l y a l o n g pore p r e s - s u r e g r a d i e n t s . The e x p e r i m e n t s confirm !hat, for tempera- t u r e s down t o t h e l e v e l a t which the s h r i n k a g e limit i s r e a c h e d , a n e q u a t i o n of t h e t y p e proposed b y Schofield g i v e s a p p r o x i m a t e l y the s u c t i o n ( n e g a t i v e pore p r e s s u r e ) , in unconfined s a m p l e s , a s a f u n c t i o n of t e m p e r a t u r e .

The e f f e c t i v e s t r e s s d e v e l o p e d , e v e n a t t e m p e r a t u r e s of -0

.a0

t o -1. O°C, c a u s e s c o n s i d e r a b l e c o n s o l i d a t i o n in com- p r e s s i b l e s o i l s . T h i s , together w i t h d i s c o n t i n u i t i e s l e f t by i c e - l e n s e s , r e s u l t s in a s p e c i a l s t r u c t u r e in s o i l s s u b j e c t e d t o a f r e e z e - t h a w c y c l e .

ACKNOWLEDGMENTS

I am i n d e b t e d to my c o l l e a g u e s a t the Norwegian G c o t e c h n i c a l I n s t i t u t e , J

.

Moum a n d 0 . Ihlen S o p p , and t o t h e D i r e c t o r , L. Bjerrum, for a s s i s t a n c e and s t i m u l a t i n g d i s c u s s i o n .

REFERENCES

[ l ] 2 . A. N e r s e s s o v a , N . A. T s y t o v i c h . " M c r z l y e g r u n t y kok s l o z h n y e mnogofaznye s i s t e m y , " M a t . po laboratornym i s s l c d . merzlykh q r u n t o v , Akad. Nauk SSSR, I n s t . M c r z l o t . S b . 2 ,

1 9 5 7 , p p . 10-22.

[ 2 ] C . W . Lovell. "Temperature Effects on P h a s e C o m p o s i - tion and Strength of Partially-Frozen S o i l , " Hiqhway

Res.

Bd. Bull. N o . 1 6 8 , 1 9 5 7 , p p . 74-95.

[ 3 ] P . J . W i l l i a m s . " S p e c i f i c H e a t and Unfrozcn W a t e r C o n - tent of Frozen S o i l s , " P r o c . 1 s t C a n a d i a n C o n f . Permafrost, 1 9 6 3 , pp. 109-126.

[ 4 ] P. J . ' W i l l i a m s . "Unfrozen W a t e r C o n t e n t of Frozen S o i l s and S o i l Moisture S u c t i o n , " G e o t e c h n i q u e , S e p t . 1964. [ 5 ] L. A. R i c h a r d s . " P r e s s u r e Membrane A p p a r a t u s , C o n - s t r u c t i o n and U s e , " Aqr. E n q r . , Vol. 2 8 , 1 9 4 7 , p p . 451-460. [ 6 ] D . C r o n e y , J . D . C o l e m a n , P . M . Bridge. "Suction of M o i s t u r e Held in S o i l a n d Other Porous M a t e r i a l s , " Road R e s . T e c h . Paper 2 4 , 1952 (D.S . I . R . , R.R.L., Harmondsworth, M i d d l e s e x . )

.

[ 7 ] R. K . S c h o f i e l d . "The pF of the W a t e r in t h e S o i l , "

3rd

I n t l , C o n g . S o i l S c i . T r a n s . , Vol. 2 , 1 9 3 5 , p p . 37-48. [ 8 ] N. E. E d l e f s e n , A. B. C

.

Anderson. "Thermodynamics of S o i l M o i s t u r e , " Hi!gardia, Vol. 1 5 , 1943, No. 2, p p . 119-120. [ 9 ] D. H . Everett. "The Thermodynamics of F r o s t Damage t o Porous S o l i d s , " T r a n s . F a r a d a y S o c . , Vol. 5 7 , 1 9 6 1 , P t . 9 , p p . 1541-1551.

[ l o ] L. W . G o l d . "A P o s s i b l e Forcc M e c h a n i s m A s s o c i a t e d w i t h the Freezing of W a t e r in Porous M a t e r i a l s , " S i g h w a y R e s . Bd. Bull. No. 1 6 8 , 1 9 5 7 , p p . 65-73.

A. D i s c u s s i o n

R. 3. MILLER, C o r n e l l University-This i s a very i n t e r e s t i n g a n d s i g n i f i c a n t c o n t r i b u t i o n . W i l l i a m s adroitly a v o i d s t h e problems i n h e r e n t in the u s e of h i s s e c o n d e q u a t i o n , or s e e m s to ( c f . comments on paper by Lange and McKim)

,

b y k e e p i n g the i c e p h a s e o u t s i d e the s a m p l e . This m a n e u v e r , w h i c h a l l o w s the i c e - l e n s e s t o grow a t a t m o s p h e r i c p r e s s u r e , o s t e n - s i b l y f i x e s t h e p r e s s u r e o n the i c e p h a s e and e x c l u d e s i c e from the p o r e s where the p r e s s u r e in t h e i c e i s unknown when the w a t e r p r e s s u r e i s unknown. T h i s i s o n e of the f e w e x a m p l e s of u s e of the e q u a t i o n in a manner t h a t r e d u c e s the u n c e r t a i n t i e s of the boundary c o n d i t i o n s .

I t i s i n t e r e s t i n g t o n o t e t h a t unfrozen water c o n t e n t v e r s u s temperature r e l a t i o n s h i p s o b s e r v e d under two e x p e r i m e n t a l c o n d i t i o n s d i v e r g e a t t h e s h r i n k a g e l i m i t , b u t a g r e e down t o t h a t p o i n t . T h i s s u g g e s t s t h a t w h e r e i t w a s p r e s e n t , the membrane prevented i c e e n t r y into t h e pore s y s t e m of t h e s a m p l e under c o n d i t i o n s where e n t r y o c c u r r e d in the a b s e n c e of the membrane. C o n s e q u e n t l y , s o m e w a t e r in t h e s a m p l e w i t h the membrane f a i l e d t o f r e e z e simply b e c a u s e n u c l e a t i o n of f r e e z i n g w a s b l o c k e d by t h e membrane and t h e unfrozen w a t e r c o n t e n t o b s e r v e d w a s g r e a t e r than t h a t o b s e r v e d w h e n t h e membrane w a s a b s e n t . T h i s e x p l a n a t i o n o b v i a t e s t h e n e e d for t h e e x p l a n a t i o n offered b y W i l l i a m s , b u t a t the s a m e time d o e s n o t i n v a l i d a t e h i s s u g g e s t i o n . For t h e a b o v e e x p l a n a t i o n t o b e v a l i d , i t i s n e c e s s a r y t o a s s u m e t h a t e i t h e r t h e membrane a l s o b l o c k e d a i r e n t r y or t h a t t h e s u r f a c e e n e r g y of t h e a i r - w a t e r i n t e r f a c e e x c e c d s t h a t of the i c e - w a t e r i n t e r - f a c e . O t h e r w i s e t h e w a t e r in q u e s t i o n would h a v e b e e n d i s - p l a c e d b y a i r i n s t e a d of i c e , where the l a t t e r w a s e x c l u d e d b y t h e membrane. Either or b o t h a r e p r o b a b l e .

B. CLOSURE-I am indebted t o Miller for drawing my a t t e n t i o n t o a n important p o i n t .

I s i t to b e e x p e c t e d t h a t the w a t e r c o n t e n t of t h e layer b e t w e e n t h e membranes w i l l b e e q u a l t o t h e (unfrozen) water

c o n t e n t of "normally f r o z e n " s o i l s ? The problem i s most e a s i l y u n d e r s t o o d b y c o n s i d e r i n g t h e e x t e n t t o w h i c h i c e in "normally frozen" s o i l i s l o c a l i z e d into a f e w r e l a t i v e l y large b o d i e s o r i s d i s p e r s e d through the p o r e s . As temperature i s

lowered i c e w i l l tend t o e n t e r s m a l l e r and s m a l l e r p o r e s . The s i z e of the p o r e s of the membrane i s s o s m a l l t h a t it i s q u i t e c e r t a i n t h a t i c e c a n n o t grow through them e x c e p t a t t e m p e r a - t u r e s far lower t h a n t h o s e of i n t e r e s t in t h e p r e s e n t c a s e . At some much h i g h e r temperature there w i l l b e a s i g n i f i c a n t number of p o r e s in t h e s o i l l a y e r b e t w e e n t h e membranes w h i c h would h a v e c o n t a i n e d i c e h a d the membranes n o t p r e v e n t e d t h i s . If t h e s e p a r t i c u l a r p o r e s a r e water-filled a t t h a t

t e m p e r a t u r e , then t h e w a t e r c o n t e n t of the l a y e r w i l l b e h i g h e r . Following Everett [ l ] the s i z e of pore's e n t e r e d by i c e a t a s u c t i o n , u i s g i v e n b y

w h e r e ,y. i s t h e i n t e r f a c i a l e n e r g y i c e / w a t e r . If u i s t h e s u c t i o n e ' 3 a b l i s h e d a t a g i v e n temperature ( i n a g r e e m e n t w i t h (2)) then p o r e s of larger r a d i u s than r , a r e i c e f i l l e d a t t h a t t e m p e r a t u r e . From t h e s u c t i o n - m o i s t u r e c o n t e n t curve (Fig. 6). it a p p e a r s t h a t a l a r g e number of p o r e s of Leda c l a y KNB a r e e m p t i e d a t a s u c t i o n of a b o u t 1 1 kg/ s q c m . The s i z e of p o r e s d r a i n e d a t a g i v e n s u c t i o n i s g i v e n b y a s i m i l a r e q u a t i o n

w h e r e (I,, i s t h e i n t e r f a c i a l e n e r g y a i r / w a t e r . Both ,yiw

and ,y a r e now q u i t e a c c u r a t e l y known [ Z ] . H e r e w e n e e d o n l y c g c s i d e r the r a t i o b e t w e e n them, t h a t i s , a p p r o x i m a t e l y 2 to 5 to s e e t h a t p o r e s e n t e r e d b y a i r a t a s u c t i o n o f 1 1 kg/sq cm might b e e n t e r e d b y i c e a t a l i t t l e over 4 kg/sq c m . From ( 2 ) , t h e l a t t e r s u c t i o n o c c u r s a t a b o u t -0.4'C. In the c a s e of the l a y e r b e t w e e n t h e membranes s u c h p o r e s w i l l b e w a t e r f i l l e d a t l e a s t u n t i l a s u c t i o n of

1 1 kg/sq cm i s r e a c h e d . The w a t e r c o n t e n t for t h i s layer might therefore b e e x p e c t e d t o d i v e r g e from c a l o r i m e t r i c a l l y d e t e r m i n e d w a t e r c o n t e n t s a t t h i s t e m p e r a t u r e . The r e l a t i v e l y i m p r e c i s e o b s e r v a t i o n s d o n o t r e v e a l t h i s ; i t i s a l s o o p e n to q u e s t i o n w h e t h e r t h e s e s i m p l e c o n s i d e r a t i o n s may b e a p p l i e d t o p o r e s of the s i z e found in c l a y s where much of t h e w a t e r i s bound t o the p a r t i c l e s and probably not s u s c e p t i b l e t o f r e e z i n g in t h e u s u a l s e n s e . In a n y c a s e , the p r e s s u r e in the w a t e r in t h e s o i l b e t w e e n t h e membranes a n d t h a t o u t s i d e them c a n b e a s s u m e d e q u a l a t t h e termination of e a c h t e s t . M e a s u r e m e n t s of w a t e r c o n t e n t of t h e inner l a y e r a l l o w determination of e f f e c t i v e s t r e s s d e v e l o p e d , a n d t h u s of s u c t i o n , a t l e a s t u n t i l the s h r i n k a g e limit i s r e a c h e d . The c o n s i d e r a t i o n s g i v e n a b o v e a r e r e l e v a n t t o e a r l i e r [ 3 ] e x p e r i m e n t a l e v i d e n c e ( F i g . 5 ) , t h a t (2) d e s c r i b e s t h e r e l a - t i o n s h i p b e t w e e n temperature and s u c t i o n in t h e w a t e r p h a s e of frozen s o i l s . T h e y s u g g e s t a n e x p l a n a t i o n for t h e t e n d e n c y of e x p e r i m e n t a l p o i n t s ( o b t a i n e d u s i n g c o n v e n t i o n a l s u c t i o n - m o i s t u r e c o n t e n t t e s t s ) t o l i e under t h e t h e o r e t i c a l c u r v e . The s i z e of t h e c o r r e c t i o n t h a t might b e made t o s u c h p o i n t s , o n a c c o u n t of t h e d i f f e r e n c e in i n t e r f a c i a l e n e r g i e s ,yiw and

-..

,yaw i s l a r g e l y beyond the s c o p e of the p r e s e n t d i s c u s s i o n . I t a p p e a r s t o b e s m a l l for t e m p e r a t u r e s a t which t h e r e i s l i t t l e e n t r y of i c e i n t o the p o r e s b u t might t h e o r e t i c a l l y involve a , , r e d u c t i o n b y t h r e e - f i f t h s of t h e s u c t i o n shown for c a s e s w h e r e i c e i s w i d e l y d i s p e r s e d through t h e p o r e s . I t i s m o s t r e l e v a n t w h e r e s o i l p o r e s a r e l a r g e , a n d where c o n s e q u e n t l y i c e e n t r y o c c u r s a t r e l a t i v e l y h i g h t e m p e r a t u r e s . Another p a p e r in t h i s v o l u m e , by M i l l e r , d i s c u s s e s t h e matter in further d e t a i l . REFERENCES

[ 1 1 D . H . E v e r e t t . "The Thermodynamics of F r o s t Damage t o Porous S o l i d s , " T r a n s . F a r a d . S o c . , Vol. 5 7 , 1 9 6 1 , Pt. 9 , pp. 1541-1551.

[ 2 1 E . H e s s t v e d t . The I n t e r f a c i a l Energy I c e / W a t e r , Norwe- g i a n G e o t e c h . I n s t . , P u b . No. 5 6 , 1 9 6 4 .

[ 3 ] P . J . W i l l i a m s . "Unfrozen W a t e r C o n t e n t of Frozen S o i l s a n d S o i l M o i s t u r e S u c t i o n , " GBotechnique, S e p t . 1 9 6 4 .