Soil freezing characteristics versus heat extraction rate

(1)

Publisher’s version / Version de l'éditeur:

Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la

première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez

pas à les repérer, communiquez avec nous à PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca.

Questions? Contact the NRC Publications Archive team at

PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the

first page of the publication for their contact information.

https://publications-cnrc.canada.ca/fra/droits

L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site

LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB.

Paper (National Research Council of Canada. Division of Building Research),

1984

READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE.

https://nrc-publications.canada.ca/eng/copyright

NRC Publications Archive Record / Notice des Archives des publications du CNRC :

https://nrc-publications.canada.ca/eng/view/object/?id=a94c8c76-ce21-4938-9d07-57952274fc53

https://publications-cnrc.canada.ca/fra/voir/objet/?id=a94c8c76-ce21-4938-9d07-57952274fc53

NRC Publications Archive

Archives des publications du CNRC

For the publisher’s version, please access the DOI link below./ Pour consulter la version de l’éditeur, utilisez le lien

DOI ci-dessous.

https://doi.org/10.4224/40000431

Access and use of this website and the material on it are subject to the Terms and Conditions set forth at

Soil freezing characteristics versus heat extraction rate

(2)

I&

N21d

National Research

Conseil national

3 .

1257

I

*

Council Canada

de recherches Canada

1 ,

2 m

SOIL FREEZING CHARACTERISTICS VERSUS HEAT EXTRACTION RATE

by

J.-M. Konrad

Presented at

ASME Winter Annual Meeting

New Orleans, LA, December 1984

Heat Transfer Division

Pamphlet Paper No. 84-WAIHT-108,7p.

P I N t C

-

C l O l l

1 GLTJ-G. RFS.

I,

i

S

2

t1.A

R

Y

I

1 I

05-

02-

2

1 I

DBR Paper No. 1257

Division of Building Research

~ ! 3 ! . m 7 " ' l h ~ ~

r ' 3 %

:*-in

\

(3)

Les phgnom8nes a g i s s a n t l o r s du g e l d e s s o l s f i n s non soumis 3

une s u r c h a r g e s o n t d g c r i t s e t r e l i g s a u t a u x d ' e x t r a c t i o n n e t t e

d e c h a l e u r .

Des e x p g r i e n c e s u n i d i m e n s i o n n e l l e s d e soulkvement

dQ a u g e l o n t E t 6 f a i t e s a u Canada s u r un s o l limoneux pour

d i f f s r e n t e s c o n d i t i o n s l i m i t e s d e t e m p g r a t u r e .

11 a 6 t 6 6 t a b l i

q u e l e t a u x d e soulkvement d Q 3 l a f o r m a t i o n d e l e n t i l l e s d e

g l a c e e s t f o r t e m e n t dspendant du t a u x d ' e x t r a c t i o n de

l a

c h a l e u r .

Aucun Ecoulement d ' e a u n ' a Eti5 observ'e

a

d e s t a u x

d ' e x t r a c t i o n s i t u ' e s e n t r e

0,35

e t

0,45

uiW/mm2.

Les t a u x d e

soulkvement s 6 g r G g a t i o n n e l maximums s o n t s u r v e n u s

B

e n v i r o n

0 , l

d / m m 2 .

T o u t e f o i s , pour l e mGme

s o l , d e s v a r i a t i o n s

i m p o r t a n t e s du soulkvement s g g r s g a t i o n n e l o n t 6 t 6 r e l e v ' e e s pour

un t a u x d ' e x t r a c t i o n

de c h a l e u r donnG a u c o u r s d'un g e l

t r a n s i t o i r e .

Les

p r 6 d i c t i o n s du

soul&vement dQ a u g e l

e n r e g i s t r s e s l o r s d ' e s s a i s e f f e c t u s s

2 d e s t a u x d ' e x t r a c t i o n d e

c h a l e u r r e p r 6 s e n t a t i f s d e s c o n d i t i o n s i n s i t u s o n t Ggalement

examin6es.

(4)

THE AM!

J w t r r

ut

mtcnar

17 St., New York, N.Y

hn meeting, d In USA, emens or 00

'

Its Divlslon h e p s o w IS 1 i t l t i o n Full L - - -

.

The S c r e t y shell not ti8 ras~onSlble ror stet inions advanced in papers or in discuss~on a! mee'lngs of the Socrety or 01 _{s or}Sections, or prlrited In tts Publlcat~ons O l ~ c u s ~ ~ n n IS prfnted only if t ~ubltshnd in an ASME Journal

Released tor general publicatlol upon preser redit should be glven !o A S M E

the TRchnlcal Olvls.on, and the au!norfsi. Papers am avairable frorr ASME for vine months

after r

Prtnte

Soil Freezing characteristics Versus Heat Extraction Rate

J.-M.

KONRAD

Division of Building Research, National Research Council of Canada, Ottawa, Ontario, K I A OR6

ABSTRACT

The p r o c e s s e s t h a t a r e o p e r a t i v e d u r i n g

f i n e g r a i n e d s o i l f r e e z i n g w i t h n o a p p l i e d s u r c h a r g e a r e d e s c r i b e d and r e l a t e d t o t h e r a t e of n e t h e a t e x t r a c t i o n . One-dimensional f r o s t h e a v e e x p e r i m e n t s were c a r r i e d o u t on a Canadian s i l t y s o i l under v a r i o u s f r e e z i n g c o n d i t i o n s . It was e s t a b l i s h e d t h a t t h e s e g r e g a t i o n a l h e a v e r a t e i s s t r o n g l y dependent on t h e r a t e of h e a t removal. No w a t e r flow was o b s e r v e d a t h e a t e x t r a c t i o n r a t e s between 0.35 and 0.45 m w / m 2 .

Maximum s e g r e g a t i o n a l h e a v e r a t e s o c c u r r e d a t r a t e s of a b o u t 0.1 m w / m 2 . For t h e same s o i l , however,

s i g n i f i c a n t v a r i a t i o n s i n s e g r e g a t i o n a l h e a v e r a t e s were measured f o r a g i v e n h e a t removal r a t e d u r i n g t r a n s i e n t f r e e z i n g . F r o s t h e a v e p r e d i c t i o n s u s i n g f r e e z i n g t e s t s a t r a t e s of h e a t e x t r a c t i o n r e p r e s e n t a - t i v e of f i e l d c o n d i t i o n s a r e a l s o d i s c u s s e d . INTRODUCTION The p r o p e n s i t y f o r heave of a s o i l u n d e r f r e e z i n g c o n d i t i o n s i s mainly a f f e c t e d by f a c t o r s s u c h a s g r a i n s i z e , p o r e s i z e d i s t r i b u t i o n , a v a i l a b i l i t y of w a t e r , a p p l i e d l o a d s and t h e r a t e of f r e e z i n g . T h i s p a p e r i s concerned w i t h t h e i n f l u e n c e of t h e t h e r m a l boundary c o n d i t i o n s i n a f r o s t h e a v e t e s t . T h e r e f o r e , i t i s r e s t r i c t e d t o a f u l l y s a t u r a t e d s o i l w i t h t h e same g r a i n s i z e d i s t r i b u t i o n a t a g i v e n p o r o s i t y , s u b j e c t e d t o z e r o e x t e r n a l l o a d i n g and f r o z e n w i t h f r e e a c c e s s of w a t e r from a n e x t e r n a l s o u r c e , i . e . , an open s y s t e m f r e e z i n g . Attempts t o e s t a b l i s h a r e l a t i o n s h i p between t h e r a t e s of h e a t e x t r a c t i o n , f r o s t p e n e t r a t i o n and h e a v e h a v e been made by s e v e r a l i n v e s t i g a t o r s . The

c o n c l u s i o n s of t h e s e s t u d i e s a r e c o n t r a d i c t o r y .

Beskow [ l ] d e m o n s t r a t e d , w i t h e x p e r i m e n t s i n which t h e a i r t e m p e r a t u r e above t h e specimen v a r i e d between -2'C and -lO°C, t h a t t h e h e a v i n g r a t e i s n o t a l w a y s i n f l u e n c e d s i g n i f i c a n t l y by t h e r a t e of f r o s t p e n e t r a t i o n . He c o n c l u d e d t h a t , a t c o n s t a n t l o a d on t h e s o i l , t h e r a t e of heave i s independent of t h e r a t e of f r e e z i n g . The U.S. Army Corps of E n g i n e e r s [ 2 ] s t a t e d t h e same c o n c l u s i o n , b u t s p e c i f i e d t h a t i t was

o n l y v a l i d f o r t h e r a n g e of f r e e z i n g r a t e s employed i n i t s i n v e s t i g a t i o n . Loch [ 3 ] found n o dependence between t h e r a t e s of h e a v e a n d h e a t e x t r a c t i o n i n many of t h e s o i l s t e s t e d i n h i s s t u d y . He emphasized t h a t h i s c o n c l u s i o n was o n l y v a l i d f o r t h e r a n g e of h e a t e x t r a c t i o n r a t e s u s e d i n h i s e x p e r i m e n t s .

K a p l a r [ 4 ] , on t h e o t h e r hand, concluded t h a t t h e heave r a t e is dependent o n , o r c o n t r o l l e d by, t h e r a t e of h e a t e x t r a c t i o n . K a p l a r ' s c o n c l u s i o n was s u p p o r t e d by e x p e r i m e n t s performed by Penner [ 5 ] e s t a b l i s h i n g t h a t t h e i c e s e g r e g a t i o n e f f i c i e n c y r a t i o p r o p o s e d by Arakawa [ 6 ] ( t h e s e g r e g a t i o n a l heave r a t e ) was s t r o n g l y dependent on t h e r a t e of h e a t e x t r a c t i o n . Horiguchi [ 7 ] p r e s e n t e d d a t a f o r powder m a t e r i a l s t h a t showed t h a t t h e t o t a l h e a v e r a t e i s s t r o n g l y dependent on t h e r a t e of h e a t removal. F u r t h e r m o r e , d i f f e r e n t forms of t h i s r e l a t i o n s h i p were o b t a i n e d f o r d i f f e r e n t t y p e s of powdered z e o l i t e s depending on t h e p a r t i c l e s i z e . F i n a l l y , Loch

[ a ]

s t u d i e d f i v e

Norwegian s i l t y s o i l s and found t h a t t h e r a t e of h e a v e o b t a i n e d by f r e e z i n g s a t u r a t e d , unloaded s o i l d o e s depend on t h e n e t r a t e of h e a t e x t r a c t i o n . He a l s o e s t a b l i s h e d t h a t a maximum h e a v e r a t e i s o b t a i n e d a t a c e r t a i n v a l u e o r r a n g e of h e a t e x t r a c t i o n r a t e s .

HEAT TRANSFER I N FREEZING SOILS

When a sudden s t e p t e m p e r a t u r e below f r e e z i n g i s

a p p l i e d t o t h e s u r f a c e of a s o i l sample, u n s t e a d y h e a t f l o w i s i n i t i a t e d . The p r o g r e s s a f f r o s t f r o n t i n t o t h e s o i l i s a f u n c t i o n of t h e imbdlance of t h e h e a t s u p p l i e d t o t h e h e a t removed. Heat a s s o c i a t e d w i t h c o o l i n g i s n e g l i g i b l e compared t o t h a t a s s o c i a t e d w i t h t h e l a t e n t h e a t of f r e e z i n g w a t e r . When a wet s o i l i s s u b j e c t e d t o f r e e z i n g , t h e l i q u i d - s o l i d p h a s e change i n v o l v e s two s i m u l t a n e o u s p r o c e s s e s . P o r e w a t e r i n t h e s o i l f r e e z e s i n s i t u a t t h e " i n s i t u " f r e e z i n g t e m p e r a t u r e . Ti, and w a t e r s u p p l i e d from t h e u n f r o z e n s o i l , o r p o s s i b l y a n e x t e r n a l s o u r c e , i s s u c k e d t o t h e f r e e z i n g f r o n t where i t f r e e z e s a t t h e s e g r e g a t i o n f r e e z i n g t e m p e r a t u r e , T The second p r o c e s s u s u a l l y l e a d s t o t h e develqpment o f ' i c e l e n s e s i n s a t u r a t e d s o i l s . For f i n e g r a i n e d s o i l s , depending on t h e i r f r o s t s u s c e p t i b i l i t y , Ts may r a n g e

(5)

from a b o u t -0.05OC t o -0.50°C. I n some c l a y s , T c a n e v e n t u a l l y b e below -0.5OC. For many s o i l s t h e f n s i t u f r e e z i n g t e m p e r a t u r e i s c l o s e t o O°C and i s p r i m a r i l y a f f e c t e d by p o r e s i z e , a s Ti r e f e r s t o t h e warmest t e m p e r a t u r e a t which i c e can p e n e t r a t e a pore. Both Ts and Ti a r e a l s o dependent on s o l u t e c o n c e n t r a t i o n . S a t i s f y i n g b o t h c o n t i n u i t y of t e m p e r a t u r e a n d h e a t f l u x a t e a c h boundary r e s u l t s i n E q u a t i o n ( 1 ) a t t h e Ti i s o t h e r m and E q u a t i o n ( 2 ) a t t h e Ts i s o t h e r m : where Kf, K f r , K r e p r e s e n t r e s p e c t i v e l y t h e t h e r m a l c o n d u c t l v i t l e s o? t h e f r o z e n l a y e r , t h e f r o z e n f r i n g e between Ts and T. and t h e u n f r o z e n s o i l . w i s t h e i n i t i a l v o l u m e t r i c m o i s t u r e c o n t e n t of t h e s o i l , T i s t h e t e m p e r a t u r e ,

dX

i s t h e f r o s t p e n e t r a t i o n r a t e , z i s d t t h e d e p t h , L i s t h e l a t e n t h e a t of f u s i o n of w a t e r a n d v i s t h e w a t e r i n t a k e r a t e . S i n c e t h e abovementioned f r e e z i n g p r o c e s s e s a r e o p e r a t i v e s i m u l t a n e o u s l y and c o n t i n u o u s l y , and c o n s i d e r i n g c o n t i n u i t y o f h e a t f l u x i n t h e f r o z e n f r i n g e , E q u a t i o n s (1) and ( 2 ) can be combined a s : The l e f t - h a n d t e r m i n E q u a t i o n ( 3 ) i s t h e n e t h e a t e x t r a c t i o n r a t e , and r e p r e s e n t s t h e h e a t f l o w o u t of t h e sample minus t h e h e a t f l o w i n t o t h e sample. FROST HEAVE VERSUS HEAT EXTRACTION RATE

T o t a l h e a v e r a t e ,

ti,

i s t h e sum of t h e s e g r e g a t i o n a l h e a v e r a t e , d s , and t h e h e a v e r e s u l t i n g from t h e volume e x p a n s i o n of p o r e w a t e r by i n s i t u f r e e z i n g . The l a t t e r i s r e l a t e d t o t h e f r o s t p e n e t r a t i o n r a t e . S e g r e g a t i o n a l h e a v e r a t e , h',, i s r e l a t e d t o t h e w a t e r i n t a k e r a t e a s : where Vi and Vw r e p r e s e n t r e s p e c t i v e l y t h e s p e c i f i c volumes of i c e and w a t e r . Combining E q u a t i o n s (3) and ( 4 ) : where

4

i s t h e n e t h e a t e x t r a c t i o n r a t e . T o t a l heave r a t e i s o b t a i n e d a s : When c o n d u c t i n g f r e e z i n g t e s t s i n t h e l a b o r a t o r y , i t i s s t a n d a r d p r o c e d u r e t o measure t e m p e r a t u r e s w i t h i n t h e sample, w a t e r movement t o t h e f r e e z i n g f r o n t and t o t a l h e a v e v e r s u s time. Any f r e e z i n g t e s t c a n t h e r e f o r e be c h a r a c t e r i z e d a d e q u a t e l y a t any t i m e t by t o t a l heave, s e g r e g a t i o n a l h e a v e and p o s i t i o n o f t h e O°C i s o t h e r m . F i g u r e l ( a ) r e p r e s e n t s a t y p i c a l r e s u l t o f a f r e e z i n g t e s t u n d e r c o n s t a n t t h e r m a l boundary c o n d i t i o n s . Unsteady h e a t f l o w p e r s i s t s a s l o n g a s t h e f r o s t f r o n t c o n t i n u e s t o p e n e t r a t e , i . e . , from S t o A". A p e r i o d oE s t a t i o n a r y p o s i t i o n of t h e O°C i s o t h e r m f o l l o w s , d u r i n g which a major i c e l e n s grows u n t i l t e s t i n g i s s t o p p e d a t p o i n t s B, B' and B". For a g i v e n s o i l a n d t e m p e r a t u r e boundary c o n d i t i o n s , i t i s a l s o p o s s i b l e t o c h a r a c t e r i z e t h e e n t i r e f r e e z i n g p r o c e s s by t h e r e l a t i o n s h i p between t h e n e t h e a t e x t r a c t i o n r a t e , t o t a l heave r a t e and s e g r e g a t i o n a l h e a v e r a t e , a s shown by E q u a t i o n s ( 5 )

and ( 6 ) . Using t h e example g i v e n i n Fig. l ( a ) , t h i s p a r t i c u l a r f r e e z i n g t e s t w i l l b e c h a r a c t e r i z e d a t a n y t i m e t by t h e n e t h e a t e x t r a c t i o n r a t e

{

o b t a i n e d from E q u a t i o n (3) and by t h e s l o p e of t h e t a n g e n t a t p o i n t s M and M' of t h e t o t a l and s e g r e g a t i o n a l h e a v e c u r v e s r e s p e c t i v e l y . For f i x e d t h e r m a l boundary c o n d i t i o n s , t h e n e t h e a t e x t r a c t i o n r a t e d e c r e a s e s s t e a d i l y w i t h time. T h e r e f o r e , p o i n t s M and M' i n Fig. l ( b ) move r e s p e c t i v e l y o n two l o c i from t h e r i g h t t o t h e l e f t d u r i n g t r a n s i e n t f r e e z i n g . During t h i s p h a s e t h e r a t e o f w a t e r m i g r a t i o n a f f e c t s t h e t h e r m a l b a l a n c e w i t h i n t h e s o i l a s l a t e n t h e a t i s r e l e a s e d d u r i n g f r e e z i n g . Thermal b a l a n c e a t a n y t i m e t t h e n d e t e r m i n e s t h e r a t e of i n s i t u w a t e r f r e e z i n g . The v e r t i c a l d i s t a n c e between t h e two l o c i may b e viewed a s a measure of t h e f r o s t p e n e t r a t i o n r a t e a t t h e v a r i o u s h e a t e x t r a c t i o n r a t e s .

A t p o i n t A, t h e r m a l b a l a n c e i s s u c h t h a t n o f u r t h e r i n s i t u w a t e r f r e e z i n g i s r e q u i r e d . I n Fig. l ( b ) , t h e two c u r v e s r e p r e s e n t i n g t o t a l and s e g r e g a t i o n a l h e a v e r a t e s merge, and dX/dt i s t h e n e q u a l t o z e r o . F o r

dX

= 0 , E q u a t i o n s ( 5 ) and ( 6 ) d t STATIONARY

t

I

-,-

FROST FRONT a ) C O N V E N T I O N A L G R A P H

-

T I M E -ICE LENS FORMATION WlTH

"IN-SITU" FREEZ l NG SEGREGATIONAL- HEAVE RATE 0 (IA

6

N E T H E A T E X T R A C T I O N RATE b l H E A V E RATE V S N E T H E A T E X T R A C T I O N R A T E F I G U R E 1 C H A R A C T E R I Z A T I O N OF A F R E E Z I N G T E S T W l T H R E S P E C T TO THE N E T H E A T E X T R A C T I O N R A T E

(6)

i n d i c a t e t h a t t h e t o t a l h e a v e r a t e and s e g r e g a t i o n a l heave r a t e a r e e q u a l and t h a t t h e y a r e l i n e a r l y r e l a t e d t o t h e n e t h e a t e x t r a c t i o n r a t e . The s l o p e o f t h i s p a r t i c u l a r l i n e i s (V /V ) ( 1 / ~ ) . A t p o i n t A t h e f r o s t

₁

w f r o n t r e a c h e s i t s maximm p e n e t r a t i o n i n t h e s o i l . If t h e r a t e of h e a t e x t r a c t i o n o b t a i n e d a t t h i s p o i n t i s m a i n t a i n e d c o n s t a n t , by c h a n g i n g t h e c o l d s t e p t e m p e r a t u r e f o r example, t h e r a t e of h e a v e w i l l a l s o remain c o n s t a n t . F u r t h e r m o r e , t h e f r o s t f r o n t w i l l remain s t a b l e . The r e p r e s e n t a t i v e p o i n t of t h i s f r e e z i n g c o n d i t i o n , t h e n , i s s t i l l p o i n t A. On t h e o t h e r hand, i f t h e t e m p e r a t u r e boundary c o n d i t i o n s a r e m a i n t a i n e d c o n s t a n t w i t h t i m e , w a t e r m i g r a t i o n and growth of t h e f i n a l i c e l e n s c o n t r i b u t e t o c h a n g e s i n h e i g h t of t h e specimen. The t e m p e r a t u r e g r a d i e n t s d e c r e a s e s l o w l y b u t s t e a d i l y w i t h a c o n c o m i t a n t d e c r e a s e i n n e t h e a t e x t r a c t i o n r a t e . The r e p r e s e n t a t i v e p o i n t of s u c h f r e e z i n g w i l l move a l o n g t h e s t r a i g h t l i n e t o w a r d s t h e o r i g i n . For t h e t e s t r e p r e s e n t e d by F i g . l ( a ) , t h e f r e e z i n g i s s t o p p e d a t p o i n t B. It i s n o t e w o r t h y t o s t r e s s t h a t a l l r e p r e s e n t a t i v e p o i n t s l o c a t e d on t h i s l i n e c o r r e s p o n d t o t h e growth of a s i n g l e i c e l e n s , i t s f o r m a t i o n r a t e b e i n g d i c t a t e d by t h e r a t e of h e a t removal. Another i c e l e n s w i l l o n l y b e g e n e r a t e d a s a r e s u l t of a change i n n e t h e a t e x t r a c t i o n l a r g e r t h a n {(A) t h a t would o n l y be p o s s i b l e w i t h a change i n t h e r m a l boundary c o n d i t i o n s . I f s u f f i c i e n t f r e e z i n g t i m e i s a v a i l a b l e , t h e r e p r e s e n t a t i v e p o i n t of t h e f r e e z i n g c o n d i t i o n ( f i x e d t e m p e r a t u r e boundary c o n d i t i o n s ) may u l t i m a t e l y r e a c h t h e o r i g i n where b o t h t h e n e t h e a t e x t r a c t i o n r a t e a n d t h e h e a v e r a t e s a r e z e r o . In t h e c a s e of a s o l u t e f r e e , s a t u r a t e d , unloaded s o i l , t h e above c o n d i t i o n means t h a t t h e t e m p e r a t u r e a t t h e b a s e of t h e i c e l e n s i s O°C and t h e p r e s s u r e i n t h e l i q u i d - l i k e w a t e r f i l m a d j a c e n t t o i t i s a t m o s p h e r i c , i . e . , n o more d r i v i n g p o t e n t i a l f o r mass t r a n s f e r , and t h e sample r e a c h e s t r u e t h e r m a l s t e a d y s t a t e . It must b e emphasized t h a t i n c r e a s i n g s o l u t e c o n c e n t r a t i o n s b e n e a t h t h e i c e l e n s by s o l u t e r e j e c t i o n c o u l d p r o d u c e a c o n d i t i o n of n o w a t e r f l o w t o t h e c u r r e n t i c e l e n s a t a p o s i t i v e n e t h e a t removal r a t e . T h i s , i n t u r n , may r e s u l t i n s l i g h t t e m p e r a t u r e a d j u s t m e n t s w i t h o u t f r e e z i n g i n o r d e r t o a t t a i n t r u e t h e r m a l s t e a d y s t a t e . TESTING PROCEDURE The f r e e z i n g c e l l u s e d d u r i n g t h i s i n v e s t i g a t i o n h a s been d e s c r i b e d by Konrad [9]. T h e r m i s t o r s were p l a c e d i n t h e s i d e of t h e w a l l of t h e c y l i n d r i c a l c e l l t o measure t h e t e m p e r a t u r e d i s t r i b u t i o n i n t h e s o i l sample. The c e l l was h e a v i l y i n s u l a t e d and p l a c e d i n a c o l d room a t +0.5OC. T e s t i n g was c a r r i e d o u t u s i n g Devon s i l t , which i s h i g h l y f r o s t - s u s c e p t i b l e . The p r o p e r t i e s of Devon s i l t a r e a s f o l l o w s : l i q u i d l i m i t = 46%; p l a s t i c l i m i t = 2%; s p e c i f i c g r a v i t y = 2.70; p e r c e n t a g e p a s s i n g a200 = 95%; and p e r c e n t a g e c l a y s i z e (t0.402 mm) = 28%. The samples w e r e p r e p a r e d by c o n s o l i d a t i n g a s l u r r y t o a p r e s s u r e of 210 kPa. A f t e r p r i m a r y c o n s o l i d a t i o n was c o m p l e t e , e a c h sample was p l a c e d i n t h e f r e e z i n g c e l l where i t rebounded u n d e r z e r o l o a d . The s a t u r a t e d s a m p l e s were f r o z e n i n t h e a x i a l d i r e c t i o n e i t h e r from t h e t o p down o r from t h e bottom up. Water was s u p p l i e d f r e e l y a t t h e warm end. When a sample f r o z e downwards, t h e t o p p l a t e was m a i n t a i n e d a t a c o n s t a n t t e m p e r a t u r e below O°C and t h e b o t t o m p l a t e was h e l d a t a p a r t i c u l a r t e m p e r a t u r e above O°C. F r e e z i n g p r o g r e s s e d i n e a c h c a s e t o s t e a d y s t a t e c o n d i t i o n , i.e., a s t a t i o n a r y f r o s t f r o n t . Thus a p e r i o d of d e c e l e r a t i n g f r o s t p e n e t r a t i o n was o b t a i n e d

d u r i n g e a c h t e s t , f o l l o w e d by a p e r i o d of s t a t i o n a r y f r o s t f r o n t , d u r i n g which a major i c e l e n s c o u l d grow. The t e m p e r a t u r e p r o f i l e , w a t e r movement i n t o t h e sample, and t o t a l h e a v e v e r s u s t i m e were m o n i t o r e d w i t h a d a t a a c q u i s i t i o n system. RESULTS F r e e z i n g T e s t s w i t h C o n s t a n t Thermal Boundary C o n d i t i o n s T a b l e 1 summarizes t h e t h e r m a l and g e o m e t r i c a l c o n d i t i o n s of d i f f e r e n t f r e e z i n g t e s t s w i t h no e x t e r n a l l y a p p l i e d l o a d . F i g u r e s 2 t o 5 i l l u s t r a t e t y p i c a l r e s u l t s o b t a i n e d from t h i s t e s t s e r i e s . As shown i n F i g s . 3 and 5, t h e measured t e m p e r a t u r e s were l i n e a r t h r o u g h t h e samples f o r t h e s t e a d y s t a t e c o n d i t i o n , c o n f i r m i n g o n e d i m e n s i o n a l h e a t f l o w . Owing t o t h e s m a l l h e i g h t of t h e samples, t h e t e m p e r a t u r e d i s t r i b u t i o n d u r i n g t r a n s i e n t h e a t f l o w was a l s o l i n e a r i n b o t h f r o z e n and u n f r o z e n s o i l l a y e r s a s shown i n Fig. 3. Net h e a t e x t r a c t i o n r a t e s w e r e r e a d i l y o b t a i n e d from t h e t h e r m a l c o n d u c t i v i t i e s of t h e u n f r o z e n and f r o z e n s i l t , which were r e s p e c t i v e l y 1.47 mW/(mm°C) and 1.76 mW/(mm°C).

E L A P S E D T I M E , h

F I G U R E

2 E X P E R I M E N T A L R E S U L T S F R O M T E S T E 4

I 1 I I 1 f

T O T A L H E A V E

\f N/

-

,fi-

'

I

-

y

m

G R O W T H

O F F I N A L

-

I C E L E N S

-

H E A V E

-

I I t I I I I I I I I

-

i

O B S E R V E D

-

-2

-

---

----

-

I I I I I I

(7)

Table 1. Sunrmary of F r e e z i n g T e s t Conditions TEMPERATURE. O C T e s t Height (cm) I n i t i a l NS- 1 + 1.1

-

3.4 10.4 NS-4 + 1.1

-

2.5 7.6 NS-5

+

1.1

-

6.2 10.0 NS-7

+

1.1

-

3.5 12.0 NS-9

+

1.0

-

6.0 28.0 E2 + 3.5

-

3.6 13.5 E4 + 3.0

-

5.5 7.8 E6 + 0.4

-

3.5 7.1 E7 + 2.0

-

3.5 7.0

-

4 1 1 6 1 ~ 1

Ty-:

~ ~

,

1 ,

INITIAL T E M P E R A T U R E . 'C

MOISTURE CONTENT A!TR TEMPERATURE PROFILE AT THE END OF FREEZING. % OF DRY WEIGHT

TRANS lENT FREEZ lNG

hours

M O I S T U R E C O N T E N T A F T E R T E M P E R A T U R E P R O F I L E _{D U R I N G} F R E E Z I N G . % O F D R Y W E I G H T

F I G U R E 3

R E S U L T S F R O M T E S T E 4

FINAL ICE LENS

-

W n

0

10 20 30 40 50 60 ELAPSED TIME, h FIGURE 4

EXPERIMENTAL RESULTS FROM TEST N S - 1

FIGURE 5

RESULTS FROM TEST N S - 1

Figure 6 summarizes t h e curves of n e t h e a t e x t r a c t i o n r a t e v e r s u s w a t e r i n t a k e f l u x and Fig. 7 p r e s e n t s t o t a l heave r a t e v e r s u s n e t h e a t e x t r a c t i o n r a t e .

F i g u r e 6 shows t h a t each sample experienced a wide range of h e a t e x t r a c t i o n r a t e s during each f r e e z i n g t e s t . Furthermore, i t i s s t r i k i n g t h a t a l i m i t i n g r a t e of h e a t removal e x i s t s a t which no water flow t o t h e f r e e z i n g f r o n t i s p o s s i b l e , For Devon s i l t , t h i s l i m i t i n g r a t e of h e a t e x t r a c t i o n i s approximately between 0.35 and 0.45 mw/mmZ. Within t h e range of h e a t e x t r a c t i o n r a t e s of 0.5 t o 0.1 m ~ / n r m ~ , t h e r a t e of

NO IN-SITU FREEZING

FIGURE 6

SEGREGATIONAL HEAVE RATE VERSUS NET HEAT EXTRACTION RATE FOR OEVON S I L T

(8)

N E T H E A T E X T R A C T I O N R A T E , rnWlrnm 2 F I G U R E 7 T O T A L H E A V E R A T E V E R S U S N E T H E A T E X T R A C T I O N R A T E F O R D E V O N S I L T m o i s t u r e f l o w i n t o t h e sample i n c r e a s e d a s t h e r a t e of h e a t removal d e c r e a s e d . I n a l l f r e e z i n g t e s t s , a maximum w a t e r m i g r a t i o n r a t e was o b t a i n e d f o r a r a t e o f h e a t removal of a b o u t 0.1 mw/mm2. For r a t e s of h e a t e x t r a c t i o n between 0 and 0.1 mw/mm2, t h e r a t e of m o i s t u r e m i g r a t i o n d e c r e a s e d w i t h d e c r e a s i n g r a t e s o f h e a t removal. A s no f u r t h e r f r o s t advance o c c u r s , a l l t h e c u r v e s c h a r a c t e r i z i n g e a c h f r e e z i n g t e s t i n t e r s e c t t h e s t r a i g h t l i n e c o r r e s p o n d i n g t o t h e f i n a l i c e l e n s f o r m a t i o n c o n d i t i o n . A s d i s c u s s e d e a r l i e r , t h e r e p r e s e n t a t i v e p o i n t of t h e f r e e z i n g s o i l i s t h e n moving on t h i s l i n e toward 0 i f t h e n e t h e a t e x t r a c t i o n r a t e s t i l l c o n t i n u e s t o d e c r e a s e . It i s s t r i k i n g t h a t f o r t h e same s o i l , d i f f e r e n t s e g r e g a t i o n a l h e a v e r a t e s were o b t a i n e d f o r t h e same r a t e of h e a t removal d u r i n g

t h e whole p h a s e of t r a n s i e n t f r e e z i n g . F u r t h e r m o r e , t h e d i f f e r e n t f r e e z i n g c o n d i t i o n s of t h e p r e s e n t s e r i e s r e s u l t e d i n d i f f e r e n t p o s i t i o n s of t h e r e p r e s e n t a t i v e p o i n t when t h e f r o s t f r o n t became s t a t i o n a r y . The g e n e r a l s h a p e of t h e s e c u r v e s , however, i s t h e same f o r a l l t e s t s . Another i m p o r t a n t f e a t u r e i s t h e d i f f e r e n c e i n s h a p e of t h e c u r v e s c h a r a c t e r i z i n g t h e dependence o n h e a t e x t r a c t i o n r a t e of t h e t o t a l h e a v e r a t e and t h e w a t e r i n t a k e f l u x . T h i s a r i s e s from t h e f a c t t h a t t h e s h a p e of t h e t o t a l h e a v e r a t e c u r v e s depend on t h e r a t e of f r o s t advance and t h e amount of h e a t r e l e a s e d by t h e m i g r a t o r y w a t e r a s i t f r e e z e s a t t h e s e g r e g a t i o n f r e e z i n g l e v e l . P a r t i c u l a r l y , a t t h e b e g i n n i n g of f r e e z i n g when t h e w a t e r i n t a k e f l u x i s r e l a t i v e l y

small, t o t a l h e a v e rates a r e t h e n mainly d i c t a t e d by t h e r a t e of f r o s t p e n e t r a t i o n . T h e r e f o r e , v a r i o u s s h a p e s of t o t a l h e a v e r a t e s v e r s u s n e t h e a t e x t r a c t i o n c u r v e s w i l l b e o b t a i n e d , depending on t h e f r e e z i n g c o n d i t i o n s . I n some t e s t s t h e t o t a l h e a v e r a t e d e c r e a s e d s t e a d i l y w i t h d e c r e a s i n g h e a t e x t r a c t i o n r a t e s . I n o t h e r s , an i n i t i a l d e c r e a s i n g r a t e was f o l l o w e d by a r e l a t i v e l y c o n s t a n t v a l u e f o r h e a t

removal r a t e between 0 . 1 5 and 0.30 mw/mmZ. The h e a v e

r a t e t h e n d e c r e a s e d u n t i l t h e c u r v e i n t e r s e c t e d t h e

l i n e c o r r e s p o n d i n g t o i c e l e n s f o r m a t i o n w i t h o u t f u r t h e r f r o s t advance. T e s t s which induced h i g h m o i s t u r e f l o w r a t e s combined w i t h a r e l a t i v e l y s m a l l f r o s t p e n e t r a t i o n r a t e were c h a r a c t e r i z e d by a n i n c r e a s i n g h e a v e r a t e t o a maxinum, f o l l o w e d by a d e c r e a s i n g r a t e f o r t h e r e m a i n i n g phase of t r a n s i e n t f r e e z i n g . The v a r i o u s s h a p e s o b t a i n e d f o r Devon s i l t compare q u i t e w e l l w i t h t h o s e o b t a i n e d by Horiguchi (1978) f o r v a r i o u s t y p e s of z e o l i t e s . The above r e s u l t s show a s t r o n g dependence of t h e r e l a t i v e amounts of s e g r e g a t i o n a l heave and i n s i t u h e a v e o n t h e way e a c h specimen was f r o z e n . Seeking a r e l a t i o n s h i p between t o t a l h e a v e r a t e and h e a t e x t r a c t i o n r a t e , a s i s done by most of t h e r e s e a r c h e r s , w i l l i n e v i t a b l y l e a d t o a p p a r e n t l y c o n t r a d i c t o r y r e s u l t s . F r e e z i n g T e s t w i t h C o n s t a n t N e t Heat E x t r a c t i o n R a t e One s o i l s a m p l e was f r o z e n u n d e r f i x e d t e m p e r a t u r e boundary c o n d i t i o n s f o r a b o u t 24 h o u r s . By t h a k t i m e , t h e f r o s t f r o n t was s t a t i o n a r y f o r a b o u t 10 h o u r s and t h e f i n a l i c e l e n s was a few m i l l i m e t e r s t h i c k . J h r i n g t h e f o l l o w i n g 24 h o u r s , t h e t e m p e r a t u r e g r a d i e n t i n t h e f r o z e n zone was m a i n t a i n e d c o n s t a n t by manually

l o w e r i n g t h e c o l d - s i d e t e m p e r a t u r e a c c o r d i n g t o t h e

amount of measured heave. The warm-end t e m p e r a t u r e was

m a i n t a i n e d c o n s t a n t d u r i n g t h e e n t i r e p r o c e s s . Equation 2 shows t h a t t h e w a t e r i n t a k e r a t e , and c o n s e q u e n t l y t h e h e a v e r a t e , a r e c o n s t a n t i f t h e n e t h e a t e x t r a c t i o n r a t e i s c o n s t a n t . F i g u r e 8 shows t h a t t h e measured h e a v e r a t e d u r i n g t h a t second p h a s e , i n which t h e h e a t f l u x o u t of t h e sample was a p p r o x i m a t e l y c o n s t a n t s i n c e t h e t e m p e r a t u r e g r a d i e n t n e a r t h e c o l d s i d e was m a i n t a i n e d c o n s t a n t , i s c o n s t a n t . Moreover, a s s o o n a s t h e t e m p e r a t u r e boundary c o n d i t i o n s a r e

1 1

i G H l C E L E N S /

PHASE 1 PHASE 2 PHASE 3

0 2 5 5 0 7 5 1 0 0 1 2 5 1 5 0 T I M E , h F I G U R E 8 E F F E C T O F N E T H E A T E X T R A C T I O N R A T E D U R I N G I C E L E N S F O R M A T I O N W I T H N O I N - S I T U F R E E Z I N G

(9)

a g a i n c o n s t a n t w i t h t i m e , t h e r e p r e s e n t a t i v e p o i n t moves s l o w l y towards z e r o and t h e r a t e of h e a v i n g d e c r e a s e s s l o w l y w i t h time. DISCUSSION The r e s u l t s p r e s e n t e d i n F i g u r e s 6 t o 8 d e m o n s t r a t e c l e a r l y t h a t t h e r a t e of f r o s t h e a v e o f s a t u r a t e d , unloaded s o i l depends on t h e n e t r a t e of h e a t e x t r a c t i o n f r o m t h e s o i l . However, n e t h e a t e x t r a c t i o n r a t e does n o t a p p e a r t o b e t h e o n l y v a r i a b l e i n f l u e n c i n g t h e h e a v e r a t e s i n c e s e v e r a l v a l u e s of h e a v e r a t e s have been o b t a i n e d f o r t h e same s o i l and a t a g i v e n r a t e of h e a t removal. Konrad a n d Morgenstern

[ l o , 11,121 e s t a b l i s h e d t h a t f r o s t heave d u r i n g t r a n s i e n t f r e e z i n g f o r u n l o a d e d s o i l s was a l s o dependent upon t h e s u c t i o n a t t h e f r o s t f r o n t and t h e o v e r a l l t e m p e r a t u r e g r a d i e n t i n t h e f r o z e n zone n e a r t h e f r e e z i n g f r o n t . Loch

[8],

c o n s i d e r i n g t h a t t h e r a t e o f h e a t e x t r a c t i o n i s t h e i n d e p e n d e n t v a r i a b l e i n t h e f r o s t h e a v e p r o c e s s , p r o p o s e d t o perform f r e e z i n g tests a t a s t a n d a r d r a t e of h e a t e x t r a c t i o n r a t h e r t h a n a t a s t a n d a r d r a t e of f r o s t p e n e t r a t i o n . Because t h e r a t e of h e a t e x t r a c t i o n i s dependent on t h e t h e r m a l c o n d i t i o n s and t h e t h i c k n e s s of t h e f r o z e n and u n f r o z e n l a y e r s , i t c a n n o t be an i n d e p e n d e n t v a r i a b l e i n t h e f r o s t h e a v e p r o c e s s . T h e r e f o r e , c o n d u c t i n g f r e e z i n g t e s t s a t a r a t e of h e a t removal c o n s i s t e n t w i t h f i e l d d a t a , w i t h o u t c o n s i d e r i n g t h e abovementioned v a r i a b l e s , may n o t r e s u l t i n a p r o p e r f r o s t h e a v e s i m l a t i o n . Konrad and Morgenstern [10,11,12] r e l a t e t h e d e g r e e of t h e r m a l imbalance d u r i n g t r a n s i e n t f r e e z i n g t o t h e r a t e of c o o l i n g of t h e f r o z e n l a y e r n e a r t h e O°C isotherm. The r a t e of c o o l i n g i s d e f i n e d a s t h e change of COLD PLATE TEMPERATURE TOP OF SAMPLE AT T l M E

(t + A t )

D U R I N G TOP OF SAMPLE A T T I M E

t

A t

--

FROST ADVANCE A T ' O o c y ~ ~ x D U R I N G

At

TEMPERATURE A T T l M E

t

TEMPERATURE AT T l M E ( t

+ A t )

W A R M PLATE TEMPERATURE F I G U R E 9 R A T E O F C O O L I N G N E A R T H E C U R R E N T F R O S T L I N E t e m p e r a t u r e p e r u n i t t i m e a t t h e f r o s t f r o n t a s i l l u s t r a t e d i n Fig. 9. It c a n b e c a l c u l a t e d a s : dT/dt (O°C) = g r a d T dX/dt, (7 T h i s v a r i a b l e h a s t h e a d v a n t a g e of combining b o t h t h e g e o m e t r i c a l and t h e r m a l c o n d i t i o n s of t h e f r e e z i n g system.

Konrad and Morgenstern [13] a l s o e s t a b l i s h e d t h a t a s t a n d a r d f r e e z i n g t e s t may b e c a r r i e d o u t w i t h f i x e d t e m p e r a t u r e boundary c o n d i t i o n s i n which t h e f r o s t heave r a t e o b t a i n e d a t t h e o n s e t of a s t a t i o n a r y f r o s t f r o n t i s measured. Because t h e t e m p e r a t u r e g r a d i e n t s i n t h e f i e l d a r e s i g n i f i c a n t l y s m a l l e r t h a n t h o s e u s e d i n most l a b o r a t o r y t e s t s , t h e r a t e of c o o l i n g i n t h e f i e l d d u r i n g t r a n s i e n t f r e e z i n g ( E q u a t i o n 7 ) i s v e r y c l o s e t o t h a t o b t a i n e d i n a l a b o r a t o r y t e s t n e a r s t e a d y s t a t e . Konrad and Morgenstern [13] showed t h e n t h a t t h e r a t i o of s e g r e g a t i o n a l h e a v e r a t e and t e m p e r a t u r e g r a d i e n t i n t h e f r o z e n s o i l n e a r O°C was t h e same i n b o t h c a s e s .

CONCLUSION

During t r a n s i e n t f r e e z i n g , i.e., advancing f r o s t f r o n t , t h e r a t e of h e a v e i n a n u n l o a d e d s o i l i s a f u n c t i o n of t h e n e t r a t e of h e a t e x t r a c t i o n . For Devon

s i l t and c o n s t a n t t e m p e r a t u r e boundary t e s t s , maximum s e g r e g a t i o n a l h e a v e r a t e s (heave r e s u l t i n g from f r e e z i n g of i n t a k e w a t e r ) o c c u r r e d a t n e t h e a t e x t r a c t i o n r a t e s of a b o u t 0.1 mw/mm2 i n d e p e n d e n t l y of t h e i n i t i a l t h e r m a l c o n d i t i o n s . A c r i t i c a l r a t e o f n e t h e a t e x t r a c t i o n r a t e a t which no w a t e r f l o w o c c u r r e d i n t o t h e sample was o b t a i n e d f o r h e a t removal r a t e s between 0.35 and 0.45 mw/mm2 f o r a l l t h e f r e e z i n g t e s t s . F o r t h e same s o i l , however, d i f f e r e n t v a l u e s of t h e s e g r e g a t i o n a l h e a v e r a t e was measured f o r a g i v e n n e t h e a t e x t r a c t i o n r a t e i n d i c a t i n g a dependency of t h e f r o s t heave v a r i a b l e s on t h e way t h e s o i l

i s

f r o z e n . It may n o t b e p o s s i b l e , t h e r e f o r e , t o o b t a i n c o n s i s t e n t r e l a t i o n s h i p s between t o t a l h e a v e r a t e and n e t h e a t e x t r a c t i o n r a t e f o r a g i v e n s o i l . I t c a n a l s o be concluded from t h e r e s u l t s of t h e l a b o r a t o r y s t u d y t h a t when t h e f r o s t l i n e i s s t a t i o n a r y , t h e h e a v e r a t e i s e s s e n t i a l l y p r o p o r t i o n a l t o t h e n e t h e a t e x t r a c t i o n r a t e . ACKNOWLEDGEMENT T h i s work h a s been s u p p o r t e d i n p a r t by f u n d s f r o m t h e N a t i o n a l R e s e a r c h C o u n c i l of Canada. The

Experimental work h a s been conducted a t t h e U n i v e r s i t y of A l b e r t a .

REFERENCES

1. Beskow, G., " S o i l f r e e z i n g and f r o s t h e a v i n g w i t h s p e c i a l a p p l i c a t i o n t o r o a d s and r a i l r o a d s , " Swedish Geol. Soc., S e r i e s C , No. 375, 1935. 2. Cold Room S t u d i e s

-

T h i r d I n t e r i m R e p o r t U.S.

Army, Corps of E n g i n e e r s , Tech. Rep. 43, 1958. 3. Loch, J.P.G., F r o s t h e a v e mechanism and t h e r o l e

of t h e t h e r m a l regime i n heave e x p e r i m e n t s on Norwegian s i l t y s o i l s , Norwegian Road Re s e a r c h L a b o r a t o r y , 1977, Meddelelse nr.50.

4. K a p l a r , C.W., Phenomenon and mechanism o f f r o s t h e a v i n g , Highway Research Record 304, 1970, pp. 1-13.

5. Penner, E., I n f l u e n c e o f f r e e z i n g r a t e o n f r o s t h e a v i n g , Highway Research Record 393, 1972, pp. 56-64.

(10)

Arakawa, K., " T h e o r e t i c a l s t u d i e s of i c e s e g r e g a t i o n i n s o i l , " J o u r . G l a c i o l o g y , Vol. 6 , No. 44, 1966, pp. 255-260. Horiguchi, K., " E f f e c t s of t h e r a t e of h e a t removal on t h e r a t e of f r o s t heaving," P r o c e e d i n g s of t h e I n t e r n a t i o n a l Symposium on Ground F r e e z i n g , Ruhr-University, Bochum W. Germany, 1978,

pp. 25-30.

Loch, J.P.G., " I n f l u e n c e of t h e h e a t e x t r a c t i o n r a t e on t h e i c e s e g r e g a t i o n r a t e of s o i l s , " F r o s t i J o r d , 20, 1979, pp. 19-30.

Konrad, J.-M., " F r o s t heave mechanics

,"

Ph.D. t h e s i s , The U n i v e r s i t y of A l b e r t a , Edmonton, A l t a . , 1980. Konrad, J.-M., a n d Morgenstern, N.R.," A m e c h a n i s t i c t h e o r y of i c e l e n s f o r m a t i o n i n f i n e g r a i n e d s o i l s

,"

Canadian G e o t e c h n i c a l J o u r n a l , 17, 1980, pp. 473-486.

Konrad, J-M., and Morgenstern, N.R., "The s e g r e g a t i o n p o t e n t i a l of a f r e e z i n g s o i l , " Canadian G e o t e c h n i c a l J o u r n a l . v. 18. 1981. pp. 482-491.

Konrad, J.-M. and Morgenstern, N.R., " P r e d i c t i o n of f r o s t heave i n t h e l a b o r a t o r y d u r i n g t r a n s i e n t f r e e z i n g , " Canadian G e o t e c h n i c a l J o u r n a l , v. 19, 1982, pp. 250-259. Konrad, J.-M. a n d Morgenstern, N.R., " F r o s t s u s c e p t i b i l i t y of s o i l s i n terms of t h e i r s e g r e g a t i o n p o t e n t i a l , " Proc. F o u r t h I n t . Conf. on P e r m a f r o s t , F a i r b a n k s , Alaska, 1983, pp. 660-665.