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Heaving force of frozen ground. I. Mainly on the results of field
researches
Kinoshita, S.; Ono, T.; National Research Council of Canada. Division of
Building Research
PREFACE
The D i v i s i o n of B u i l d i n g Research i s c u r r e n t l y i n v e s t i g a t i n g t h e behaviour of a v a r i e t y of s m a l l f o o t i n g s i n f r o s t - s u s c e p t i b l e s o i l s with p a r t i c u l a r r e f e r e n c e t o f r o s t - h e a v i n g p r e s s u r e s developed and t h e r e l a t i v e amounts of heaving. It i s hoped t h a t t h i s pro- gramme w i l l provide a b a s i s f o r developing s u i t a b l e s m a l l f o o t i n g d e s i g n s f o r l i g h t s t r u c t u r e s such a s t r a n s f o r m e r s t a t i o n s and
c o t t a g e s . T h i s r e s e a r c h was a l r e a d y in p r o g r e s s when t h i s p a p e r was published. It was found t o p r o v i d e u s e f u l information and r e s u l t s which w i l l a s s i s t i n e v a l u a t i n g t h e DBR/NRC s t u d i e s .
The D i v i s i o n makes a v a i l a b l e E n g l i s h t r a n s l a t i o n s of s t u d i e s i n i t s own f i e l d s , b u t published i n o t h e r languages, with t h e hope t h a t t h i s w i l l be h e l p f u l i n d i s s e m i n a t i n g u s e f u l s c i e n t i f i c
information. The D i v i s i o n is, t h e r e f o r e , indebted t o D r . Makoto k a b a who t r a n s l a t e d t h i s paper and t o Mr. E. Penner of t h i s D i v i s ion, who checked t h e t r a n s l a t io n .
Ottawa R.F. Legget
NATIONAL RESEARCH COUNCIL OF CANADA
Technical Translation 1246
T i t l e : Heaving force o f frozen ground. I. Mainly on the r e s u l t s o f f i e l d researchea
Authors : S e i l t i Klnoshita and Taketoshi Ono
Reference : Low Temperature Science (Teion Kagaku), Ser. A, 21 r 117-139,
1963
I E A V I N G FORCE OF FROZEN GROUND
I. MAINLY ON THE RESULTS OF FELD RESEARCHES*
I. I n t r o d u c t i o n
Ln a g e o g r a p h i c a l a r e a where t h e t e m p e r a t u r e i s low and t h e amount of s n o w f a l l i s s m a l l d u r i n g t h e w i n t e r , t h e ground f r e e z e s . The w a t e r i n t h e u n f r o z e n ground below t h e f r e e z i n g f r o n t i s suclted upwards and f r e e z e s t h e r e .
A s a r e s u l t , t h e f r o z e n ground i n c r e a s e s i t s volume and t h e ground s u r f a c e r i s e s upwards. T h i s phenomenon i s c a l l e d t h e heaving of f r o z e n ground. The heaving of f r o z e n ground, a s might be s u s p e c t e d , i s a complicated phenomenon r e p r e s e n t i n g a combination of v a r i o u s e f f e c t s . The f a c t o r s involved i n t h e heaving o f f r o z e n ground a r e t h e temperature of t h e s o i l , t h e s i z e o f t h e s o i l p a r t i c l e s , t h e i r p h y s i c a l and chemical n a t u r e , t h e amount o f w a t e r i n t h e ground, t h e amount of groundwater, t h e flow v e l o c i t y of t h e w a t e r , e t c . The heaving o f f r o z e n ground h a s been i n v e s t i g a t e d by v a r i o u s workers, b u t t h e r e a r e a number of i m p o r t a n t p o i n t s s t i l l t o be c l a r i f i e d , p a r t i c u l a r l y on t h e f i n e r a s p e c t s o f t h e mechanism of t h e heaving. The p r e s e n t a u t h o r s f e l t t h a t t h e s t r o n g f o r c e t h a t d e s t r o y s v a r i o u s o b j e c t s on t h e ground needs e s p e c i a l l y c a r e f u l and e x t e n s i v e s t u d y . The s t u d y of t h e h e a v i n g f o r c e of f r o z e n ground
i s i m p o r t a n t n o t o n l y f o r e v a l u a t i n g t h e a c t u a l s t a t i s t i c a l d a t a , i n t h e p r a c t i c a l s e n s e , b u t a l s o from an academic s t a n d p o i n t i n e s t a b l i s h i n g a much c l e a r e r mechanism of heaving.
The h e a v i n g f o r c e of f r o z e n ground nay be c o n v e n i e n t l y d i v i d e d i n t o two component f o r c e s . One i s a f o r c e t h a t works a t t h e bottom of an o b j e c t and pushes up t h e o b j e c t ; t h e o t h e r i s a f o r c e which works on t h e f l a n k o f a n o b j e c t , where t h i s f l a n k i s i n c o n t a c t w i t h t h e f r o z e n ground. Oura and K i n o s h i t a have s t u d i e d t h e l a t t e r f o r c e , i . e . t h e heaving f o r c e a g a i n s t t h e s i d e of an o b j e c t , f o r t h e l a s t t h r e e w i n t e r s . They cooperated w i t h t h e
Research S e c t i o n of t h e B u i l d i n g Maintenance Department, E l e c t r i c Communication D i v i s i o n , Hokkaido, and s e t up a f i e l d r e s e a r c h e s t a b l i s h m e n t on a s i d e s t r e e t n e x t t o t h e o f f i c e b u i l d i n g a t Kushiro E l e c t r i c Communication Department.
There t h e y have been c o l l e c t i n g d a t a f o r t h r e e w i n t e r s , 1958-59, 1959-60, and 1960-61. The r e s u l t s have a l r e a d y been p u b l i s h e d (I-)). However, a s t h e f i e l d r e s e a r c h e s t a b l i s h m e n t was r a t h e r c l o s e t o a b u i l d i n g , t h e h e a v i n g of f r o z e n ground was n o t q u i t e a s s t r o n g a s i t had been expected, and t h e y encountered
*
C o n t r i b u t i o n No.635 from Low Temperature S c i e n c e Research I n s t i t u t e , Hokkaido U n i v e r s i t y .v a r i o u s o t h e r Inconveniences. I n t h e f o u r t h w i n t e r , 1961-62, t h e r e f o r e , t h e y s e t up a f i e l d r e s e a r c h e s t a b l i s h m e n t on t h e campus of Kitami J u n i o r T e c h n i c a l College, Kitami-shi, where t h e r e i s more freedom in s e l e c t i o n of a s i t e f o r t h e e x p e r i m e n t a l a p p a r a t u s and more f a c i l i t i e s f o r making, d e t e r m i n a t i o n s .
In
Kitami t h e a u t h o r s b u i l t an a p p a r a t u s which enabled them t o determine t h e h e a v i n g f o r c e b o t h a t t h e bottom of an o b j e c t and on i t s f l a n k . The p r e s e n t p a p e r i s based mainly on t h e d a t a o b t a i n e d i n Kitami.11. The S i g n i f i c a n c e of t h e Heaving Force of Frozen Ground The a u t h o r s d e f i n e t h e h e a v i n g f o r c e of f r o z e n ground a s a f o r c e t o which an o b j e c t on o r i n t h e ground i s s u b j e c t d u r i n g t h e f r e e z i n g o f s o i l , b u t t h i s d e f i n i t i o n does n o t i n c l u d e any q u a n t i t a t i v e a s p e c t of t h e f o r c e
concept. I f we s e e k t o d e f i n e t h e h e a v i n g f o r c e of f r o z e n ground more p r e c i s e l y a s a f o r c e which l i f t s up an o b j e c t on t h e s u r f a c e o f t h e ground, we would r e a c h t o an o b v i o u s l y p a r a d o x i c a l r e s u l t . A s t h e f o r c e which r a i s e s an o b j e c t i s e q u a l t o t h e w e i g h t of t h e o b j e c t , t h e heaving f o r c e would t h e r e - f o r e be p r o p o r t i o n a l t o t h e weight of t h e o b j e c t r a i s e d . I n r e a l i t y , however, t h e amount of heave, 1 . e . t h e h e i g h t of h e a v i n g of an o b j e c t , Is l e s s f o r a h e a v i e r o b j e c t t h a n f o r a l i g h t e r one. For example, it i s w e l l lcnown t h a t i n t h e c a s e of c o n c r e t e - b l o c k b u i l d i n g s one-storey houses o f t e n s u f f e r damage from heavin while two-storey houses, which weigh more, do s o f a r l e s s f r e q u e n t l y ( ' ) . Thus b u i l d e r s a r e encouraged t o p u t up houses of g r e a t e r s t r u c t u r a l weight a s a means of p r o t e c t i n g b u i l d i n g s from t h e h a z a r d s of h e a v i n g on f r o z e n ground.
T h i s would s u g g e s t t h a t t h e amount of h e a v i n g i s less f o r a g r e a t e r
h e a v i n g f o r c e i n t h e f r o z e n ground, s i n c e t h e weight of t h e b u i l d i n g Is l a r g e r . The r e l a t i o n s h i p between t h e h e a v i n g f o r c e and t h e amount of h e a v i n g is shown
In F i g . 1. I n F i g . 1 t h e h e a v i n g f o r c e i s p l o t t e d on t h e o r d i n a t e and t h e amount of heave in t h e a b s c i s s a . P o i n t A i n t h e f i g u r e i n d i c a t e s t h e f o r c e of t h e f r o z e n ground f o r
a
heave o f z e r o , t h a t i s , when t h e s u r f a c e of t h e ground i s s o p r e s s e d down by an o b j e c t s o t h a t t h e r e i s no heave. T h i s f o r c e Is t h e l a r g e s t f o r c e t h a t t h e ground i s c a p a b l e of producing, 1 . e . it i s , under t h e given c o n d i t i o n s , t h e maximum heaving f o r c e . P o i n t B of t h e same f i g u r e shows t h e amount of heave of t h e ground f o r a h e a v i n g f o r c e o f z e r o , 1.e. when t h e r e i s no o b j e c t on t h e s u r f a c e o f t h e ground, o r i n o t h e r words, i t r e p r e s e n t s heave of a f r e e ground s u r f a c e .A s d e s c r i b e d t h u s f a r , t h e heaving f o r c e cannot be d e f i n e d u n c o n d i t i o n - a l l y ; t h e r e f o r e , t h e a u t h o r s w i l l f u r t h e r d e f i n e t h e h e a v i n g f o r c e a s t h e f o r c e shown a t p o i n t A i n F i g . 1, 1.e. t h e maximum h e a v i n g f o r c e . The h e a v i n g
f o r c e determined by us i s t h i s value of t h e maximum f o r c e . A knowledge of t h i s f o r c e may be of some u s e i n s o l v i n g c e r t a i n p r a c t i c a l problems. Even a f t e r c l a r i f y i n g t h e heaving f o r c e by t h e above d e f i n i t i o n t h e r e a r e two
a s p e c t s of i t t o be s t i l l d i s c u s s e d . One i s t h e f o r c e which a c t s a g a i n s t t h e bottom of an o b j e c t i n c o n t a c t w i t h t h e ground s u r f a c e and heaves t h e o b j e c t upwards, 1 . e . t h e v e r t i c a l l i f t i n g f o r c e . The a u t h o r s h e r e a f t e r term t h i s t h e b a s a l heaving f o r c e . The o t h e r a s p e c t i s t h e a d f r e e z i n g f o r c e . An o b j e c t sunk In t h e ground, such a s a hydropole, i s e l e v a t e d by t h e s o i l f r o z e n a l o n g s i d e of t h e o b j e c t . T h i s phenomenon i s c a l l e d " a d f r e e z i n g t ' o r " h o i s t -
f r e e zing"
( 5 ) .
The f o r c e which a c t s a g a i n s t t h e s i d e o f such an o b j e c t i s an a d f r e e z i n g f o r c e . The a d f r e e z i n g f o r c e t h a t t h e a u t h o r s d i s c u s s i n t h i s p a p e r i s a g a i n t h e maximum a d f r e e z i n g f o r c e , 1.e. t h e f o r c e needed t o p r e s s t h e o b j e c t dorm s o t h a t t h e o b j e c t i s n o t e l e v a t e d .A s p r e v i o u s l y d e s c r i b e d , a d f r e e z i n g h a s been s t u d i e d d u r i n g t h e l a s t t h r e e w i n t e r s and t h e r e s u l t s have been r e p o r t e d (
1-3
)111. Methods of Determination
The a u t h o r s s e t up an a p p a r a t u s t o s t u d y t h e b a s a l h e a v i n g f o r c e and a d f r e e z i n g f o r c e on t h e campus o f Kitami J u n i o r College In t h e f a l l o f 1961. Readings of t h e f o r c e s were t a k e n e v e r y day d u r i n g t h e p e r i o d from December
1961 t o A p r i l 1962. The a u t h o r s a l s o measured t h e ground t e m p e r a t u r e on
thermonleters p l a c e d a t s e v e r a l p o i n t s from 0 t o 120 cm from t h e s u r f a c e of t h e ground. They a l s o s t u d i e d t h e amount of heave on p i p e s of v a r i o u s m a t e r i a l s p l a c e d v e r t i c a l l y i n t h e ground. They a l s o o b t a l n e d a s e t of h o u r l y r e a d i n g s f o r t h r e e c o n s e c u t i v e d a y s i n F e b r u a r y when t h e h e a v i n g phenomenon i s a t i t s
peak. F i n a l l y , t h e y made v i s u a l o b s e r v a t i o n s o f t h e f r o z e n ground by d i g g i n g a v e r t i c a l p r o f i l e .
1. Apparatus
Both b a s a l h e a v i n g f o r c e and a d f r e e z i n g f o r c e a r e e q u a l t o t h e f o r c e needed t o p r e s s down on an o b j e c t in a given p o s i t i o n s o t h a t i s i s n o t
heaved. I n o r d e r t o d e t e r m i n e t h e s e f o r c e s , t h e o b j e c t must be f i x e d a t non- moving, s t a n d a r d p o i n t s d u r h g t h e e n t i r e d e t e r m i n a t i o n p e r i o d . To s a t i s f y t h i s c o n d i t i o n , t h e a u t h o r s c o n s t r u c t e d a s t r o n g f o u n d a t i o n a s a s t a n d a r d p o i n t , and b u r i e d i t d e e p l y enough i n t h e ground s o t h a t t h e s u r r o u n d i n g s o i l doe's n o t f r e e z e d u r i n g t h e d e t e r m i n a t i o n p e r i o d . They t h e n s e t up t h e
a p p a r a t u s shown i n F i g . 2 ( a ) . The maximum depth of t h e f r e e z i n g f r o n t i n t h e Kitami a r e a i s g e n e r a l l y assumed t o b e 1 m. The a u t h o r s dug a h o l e i n t h e ground t o 2 m a t which a p p a r e n t l y t h e r e i s no p o s s i b i l i t y of f r e e z i n g , and f i l l e d t h e bottom of t h e h o l e w i t h c o n c r e t e A of 30 cm t h i c k n e s s . The
c o n c r e t e l a y e r was 60 cm wide and
5
m long. I n t o t h i s c o n c r e t e base A, s i x p i e c e s o f i r o n b a r s4
cm i n d i a m e t e r were i n s e r t e d v e r t i c a l l y a t t h e i n t e r v a l sshown i n t h e f i g u r e . Two o f t h e i r o n b a r s were 2.2 m l o n g and f o u r were 2 m
long. A t h r e a d a p p r o x i n ~ a t e l y 10 cm long was c u t a t t h e lower end o f each i r o n b a r . A n u t of 10 cm d i a m e t e r and 5 cm width was f i t t e d t o i t and t h e threaded b a r was i n s e r t e d i n t h e c o n c r e t e b a s e A a t a depth o f 25 cm. The i r o n b a r r e p r e s e n t s t h e s t a n d a r d a g a i n s t which movement was measured. The c o n c r e t e b a s e was prepared s o f i r m l y t h a t even a 10-ton t r a c t i o n f o r c e a p p l i e d t o e a c h one of t h e i r o n b a r s f a i l e d t o move it. The e s s e n t i a l t h i c k n e s s , l e n g t h , and width o f t h e c o n c r e t e b a s e r e q u i r e d f o r t h e purpose were based on c a l c u l a t i o n s by Oura.
A f t e r t h e i r o n b a r s had been b u r i e d I n t h e c o n c r e t e base, t h e e x c a v a t i o n was f i l l e d w i t h s o i l t o t h e o r i g i n a l ground l e v e l - Before t h e completion o f t h e f i l l i n g , f o u r p i p e s o f d i f f e r e n t m a t e r i a l , a l l 1.1 m long, 1, 2, 3 , 4 of F i g . 2 ( a ) , were f i t t e d o v e r t h e f o u r I r o n b a r s of 2 m l e n g t h s o t h a t t h e p i p e s hold t h e i r o n b a r s a t t h e i r c e n t r e and t h e t o p r i m s o f b o t h t u b e s and b a r s a r e a t t h e same l e v e l . The m a t e r i a l , t h i c k n e s s and weight o f t h e p i p e s a r e shown I n Table I.
The l e n g t h o f t h e p a r t o f t h e i r o n b a r s p r o j e c t i n g o u t o f t h e ground i n t o t h e atmosphere was
5
cm i n t h e c a s e of f o u r b a r s o v e r which p i p e s had been f i t t e d , and 25 cm f o r t h e two b a r s w i t h o u t p i p e s .( a ) Determination o f b a s a l f r e e z i n g f o r c e . The a p p a r a t u s t o measure t h e b a s a l f r e e z i n g f o r c e was placed between t h e two i r o n b a r s w i t h o u t p i p e s a s shown a t t h e l e f t s i d e o f F i g . 2 ( a ) . The a p p a r a t u s i s shown i n e n l a r g e d s c a l e i n F i g . 2 ( b ) . The d i s t a n c e between t h e c e n t r e s o f t h e two i r o n b a r s BB i s 40 cm. An i r o n d i s k E 2 cm t h i c k and
15
cm i n d i a m e t e r was placed on t h es u r f a c e of t h e ground, midway between t h e two i r o n b a r s w i t h a load c e l l having a c a p a c i t y of up t o 5 t o n s . A t h r e a d was c u t a t about
15
cm from t h e t o p of t h e i r o n b a r B, and a n u t F 5 cm wide was f i t t e d t o i t . Next, a n i r o n p l a t eG, w i t h two h o l e s c o r r e s p o n d i n g t o b a r s B and a channel, was p l a c e d o v e r n u t s FF on t h e i r o n b a r s . P l a t e G is 1 cm t h i c k , 60 cm l o n g and 12 cm wide; t h e c h a n n e l i s 60 cm long, 12 cm wide and 8 cm deep. The n u t s FF were a d j u s t e d s o t h a t t h e c e n t r e of t h e c h a n n e l was o v e r t h e load c e l l , i n a n e x a c t l y h o r i z o n t a l p o s i t i o n . The n u t s
HH were t i g h t e n e d on t h e i r o n b a r s , and t h e c h a n n e l was
f i x e d i n i t s p o s i t i o n . During t h e p r o c e s s e s , t h e n u t s F and H were screwed r a t h e r t i g h t e r t h a n normally needed s o t h a t the l o a d c e l l was s u b j e c t t o t h e f o r c e o f a p p r o x i m a t e l y some t e n s of kg. T h i s was done f o r f e a r t h e l e a d c e l l might s i n k and disengage from t h e c h a n n e l b e f o r e h e a v i n g s t a r t e d , s i n c e t h e
ground base had n o t c o m p l e t e l y s e t t l e d when t h e a p p a r a t u s was s e t up. The a p p l i e d f o r c e was a p p r o x i m a t e l y z e r o by t h e 1 0 t h o f December, when f r o s t heaving was j u s t s t a r t i n g .
When h e a v i n g o c c u r s , t h e d i s k E placed on t h e ground s u r f a c e i s moved upwards, b u t i t i s l i n k e d t o b a r B and t h e channel 1;hroum t h e load c e l l .
T h e r e f o r e t h e d i s k E cannot move b u t pushes a g a i n s t t h e load c e l l w i t h a f o r c e c o r r e s p o n d i n g t o t h a t shown by t h e load c e l l . The a c t u a l displacement of t h e load c e l l i s very s l i g h t . The i r o n b a r B can s t r e t c h e l a s t i c a l l y , b u t t h e amount; o f t h e e x t e n s i o n 1s n e g l i g i b l e . The f o r c e shown on t h e load c e l l i s t h e b a s a l heaving f o r c e . The s i d e of t h e load c e l l was covered with "homo- s t y r e n e 1 ' + , s o t h a t i t would n o t be s u b j e c t t o sudden change of t e m p e r a t u r e .
A v i n y l c o v e r was placed o v e r t h e channel t o p r o t e c t i t from r a i n .
( b ) Determination of a d f r e e z i n g f o r c e . The a p p a r a t u s f o r t h e determina- t i o n of t h e a d f r e e z i n g f o r c e i s seen a t D i n F i g . 2 ( a ) , and d e t a i l s a r e shown i n F i g . 3. The i r o n b a r B was threaded a t t h e t o p and a ~ n e t a l l i c n u t H of H-shaped c r o s s - s e c t i o n was f i t t e d t o i t a s shown i n F i g .
3 .
One end o f t h e p r e s s u r e gauge A was f i t t e d t o t h e t o p of t h e n u t H, and secured by t h e p i nD. The t o p of t h e p r e s s u r e gauge A was connected t o c y l i n d e r E with a t e r r a c e by p i n F. A metal washer G was placed on t h e d e t e r m i n a t i o n tube and an i r o n c o n n e c t i n g p i p e 20 cm l o n g was p l a c e d o v e r i t . T h r u s t b e a r i n g s and m e t a l washers J, were assembled above p i p e I ( 9 cm i n d i a m e t e r , 4 rnrn t h i c k ) and a n u t was used t o s e c u r e washers J. The p r e s s u r e gauge i s placed wider t r a c t i o n when t h e n u t i s t i g h t e n e d . The t i g h t e n i n g of t h e n u t was d i s c o n t i n u e d a t a t r a c t i o n f o r c e of s e v e r a l t e n s of kg. By t h e 1 0 t h o f December, when t h e f r e e z i n g was about t o occur, t h e t r a c t i o n f o r c e was n e a r l y z e r o .
When t h e ground heaves and t h e measuring p i p e i s r a i s e d , t h e narrow p a r t of p r e s s u r e gauge A i s extended s l i g h t l y . The amount o f t h i s e x t e n s i o n ,
measured by a s t r a i n gauge f i t t e d t o i t , i s a measure of t h e a d f r e e z i n g f o r c e . S i n c e t h e lower p a r t of t h e p r e s s u r e gauge i s secured t o t h e s t a t i o n a r y i r o n b a r , o n l y a t r a c t i o n f o r c e i s a p p l i e d t o t h e pre3sur-e gauge.
h he
maximum e x t e n s i o n of t h e p r e s s u r e gauge i s v e r y s m a l l , b e i n g o n l y 0.02 mm a t a t r a c - t i o n f o r c e o f3
t o n s . )The weight o f t h e measuring p i p e i s approximately
18
kg f o r t h e two c o n c r e t e p i p e s , about 1 0 kg f o r t h e i r o n p i p e and about5
k g f o r t h e v i n y l p i p e , I n c l u d i n g t h e i r o n p i p e I, and washers (3 and J. The a p p a r a t u s was covered w i t h a homo-styrene box, a s shown i n Fig. 2 ( a ) , t o p r o t e c t t h e p r e s - s u r e gauge from sudden changes o f t e m p e r a t u r e .( c ) S o i l . The s o i l a t t h e t e s t s i t e c o n s i s t e d o f c l a y from t h e s u r f a c e t o a d e p t h of 140 cm, and sand below t h a t , a s shovm a t t h e r i & t o f F i g . 2 ( a ) . A f t e r l a y i n g t h e c o n c r e t e base a t a depth of 170 t o 200 cm underground, t h e
s o i l was r e p l a c e d around t h e a p p a r a t u s i n such a way a s t o make t h e ground s t r u c t u r e i d e n t i c a l w i t h t h e o r i g i n a l . The c l a y i n t h e o r i g i n a l s o i l was t h e one which had been e s t i m a t e d t o be most r e a d i l y s u s c e p t i b l e t o heaving i n t h e Kitami a r e a . The c l a y was analysed and t h e d i s t r i b u t i o n o f t h e p a r t i c l e s i z e s
i s shown i n F i g . 4. It c o n s i s t e d of
35%
c l a y ( i n c l u d i n g c o l l o i d ) w i t h p a r t l - c l e d i a m e t e r s s m a l l e r t h a n 0.005 mm, 51$ s i l t w i t h d i a m e t e r s between 0.005 and 0.05, and 14% of sand w i t h d i a m e t e r s between 0.05 and 2 mrn. Thus, a l t h o u g h i t was c l a y , i t may be more p r o p e r l y c a l l e d s i l t c l a y o r loamy s i l t c l a y ( c l a y loam c l o s e r t o s i l t i n i t s n a t u r e ) . In t h e Kitami a r e a , t h e c l a y i s u s u a l l y c a l l e d heavy c l a y .It i s n o t e a s y t o e s t a b l i s h a c r i t e r i o n of s u s c e p t i b i l i t y t o f r o s t heav- i n g , b u t i t i s g e n e r a l l y t h o u g h t t h a t s o i l s c o n t a i n i n g a l a r e r p r o p o r t i o n of f i n e s have a g r e a t e r tendency t o heave on f r e e z i n g . Beskow
('I
s t u d i e d t h e r e l a t i o n s h i p between t h e s i z e o f t h e s o i l p a r t i c l e s and t h e h e a v i n g tendency o f t h e s o i l , and found t h a t h e a v i n g s t a r t e d w i t h s o i l s with p a r t i c l e s i z e s of 0.05 t o 0.1 mm; s o i l s with p a r t i c l e s i z e s of 0.005 t o 0.002 mm were most sub- j e c t t o f r o s t heaving, and t h e s m a l l e r t h e p a r t i c l e s i z e t h e more i n t e n s e t h e heaving w i l l be. The c l a y s t u d i e d by t h e p r e s e n t a u t h o r s , t h e r e f o r e , belongs t o t h e group of s o i l s of g r e a t e r f r o s t heaving tendency.Below 140 cm t h e ground c o n s i s t e d of sand and t h e amount of w a t e r r e t a i n e d i n t h i s l a y e r was v e r y s m a l l . Since t h e heaving is caused by t h e f r e e z i n g of t h e w a t e r c o n t a i n e d i n t h e s o i l , t h e h e a v i n g t h a t t h e a u t h o r s s t u d i e d occurred o n l y i n t h e c l a y l a y e r . Such h e a v i n g i s u s u a l l y c a l l e d 11 c l o s e d system heaving".
The p l a c e on t h e campus of Kitami J u n i o r C o l l e g e where t h e a p p a r a t u s was s e t up, was f i r s t p r e p a r e d by smoothing o u t h i l l o c k s w i t h t h e aforementioned ground s t r u c t u r e (and upper c l a y l a y e r and a lower sand l a y e r ) s o a s t o make i t uniformly f l a t . A s a r e s u l t , t h e h e a v i n g occurred where t h e s u r f a c e con- s i s t e d of c l a y , w h i l e t h e p a r t where t h e sand l a y e r r i s e s t o t h e s u r f a c e d i d n o t show any heaving.
2. Determination of t h e Heaving Force
The load c e l l used t o determine t h e b a s a l h e a v i n g f o r c e i s a p r e s s u r e gauge combined w i t h a s t r a i n gauge and h a v i n g a maximum c a p a c i t y of
5
t o n s .A c a b l e extended t o t h e i n s i d e of a b u i l d i n g n e a r t h e a p p a r a t u s , and was connected t o a s t a t i c d i s t o r t i o n i n d i c a t o r . The f o r c e could be c a l c u l a t e d from t h e r e a d i n g s o f t h i s gauge.
The p r e s s u r e gauge used f o r d e t e r m i n i n g t h e a d f r e e z i n g f o r c e i s shown a t t h e r i g h t of F i g . 3 . The m a t e r i a l is s t a i n l e s s s t e e l and t h e p i e r c e d b l o c k s a t b o t h ends measure 3 x
3
x 3 cm. The h o l e s a r e 1 . 2 cm i n d i a m e t e r anda r e s e t a t r i g h t a n g l e s t o each o t h e r . The c r o s u - s e c t i o n of t h e t h i n n e r p a r t of t h e c e n t r e i s 1 x
3
cm w i t h a l e n g t h of5
cm. On each of t h e wider s i d e s( 3
x 5 cm), two s t r a i n gauge elements were mounted. One of t h e two e l e m e n t s on e a c h s i d e i s mounted i n t h e d i r e c t i o n o f t h e e x t e n s i o n of t h e p r e s s u r e gauge (T i n t h e f i g u r e ) , while t h e o t h e r i s p l a c e d a t right a n g l e s ( C i n t h e f i g u r e ) t o i t . When a t r a c t i o n f o r c e a c t s on t h e p r e s s u r e gauge, t h e element a t T i s s t r e t c h e d while t h e one a t C c o n t r a c t s . The f o u r s t r a l n - g a u g eelements a r e connected t o a b r i d g e c i r c u i t i n t h e o r d e r TCTC. A c a b l e l e a d i n g t o t h e l a b o r a t o r y i s connected t o a s t a t i c d i s t o r t i o n i n d i c a t o r . When a
t r a c t i o n f o r c e a c t s on t h e p r e s s u r e gauge, t h e e l e c t r i c r e s i s t a n c e of t h e f o u r e l e m e n t s TCTC changes and a c o r r e s p o n d i n g i n d i c a t i o n i s given on t h e s t a t i c d i s t o r t i o n i n d i c a t o r . Plhen we know t h e r e l a t i o n s h i p between t h e f o r c e a c t i n g on t h e p r e s s u r e gauge and t h e r e a d i n g on t h e i n d i c a t o r , we can c a l c u l a t e t h e heaving f o r c e from t h e r e a d i n g . The r e a d i n g v a r i e d on t h e f o u r p r e s s u r e
gauges, b u t a f o r c e of 1 t o n showed t h e r e a d i n g s approximately between 445 and 460. A s f o r a s t a t i c d i s t o r t i o n I n d i c a t o r , t h e a u t h o r s used one w i t h a
c a r r i e r wave a t 165 c y c l e s , and t h e r e a d i n g s were t a k e n once o r t w i c e a day.
I n t h e middle of February, r e a d i n g s were t a k e n e v e r y hour f o r t h r e e c o n s e c u t i v e days.
3 .
Other D e t e r m i n a t i o n s( a ) The amount of heaving. B e s i d e s t h e p i p e s f o r a d f r e e z i n g determina- t i o n , f i v e p i p e s of d i f f e r e n t m a t e r i a l were b u r i e d a t t h e s i t e . These
m a t e r i a l s were wood, wood coated w i t h v i n y l a c e t a t e p a i n t , i r o n , i r o n coated with v i n y l a c e t a t e p a i n t , and hard v i n y l . These were n o t p r e s s e d down b u t were allowed t o r i s e w i t h t h e heaving, and t h e e x t e n t o f t h e i r r i s i n g was determined. Although t h e y were f r e e t o r i s e , t h e h e a v i n g f o r c e , n e c e s s a r y t o move t h e p i p e i s i d e n t i c a l w i t h t h e weight of t h e p i p e , a s t h e a u t h o r s have
shown i n S e c t i o n 11, S i g n i f i c a n c e o f t h e Heaving Force of Frozen Ground. T h e r e f o r e , t h e e x t e n t of heaving determined by t h i s procedure i s f o r a
c o n s t a n t heaving f o r c e . A l l t h e p i p e s (and b a r s * ) were 1 m long, and t h e y were b u r i e d v e r t i c a l l y i n t h e ground s o t h a t t h e t o p of t h e p i p e was f l u s h w i t h t h e s u r f a c e . T h e l r d i a m e t e r s , t h i c k n e s s e s and weights a r e shown i n Table 11.
The d e t e r m i n a t i o n s were c a r r i e d o u t a s f o l l o w s : t h e t o p end of t h e i r o n b a r a t t a c h e d t o t h e c o n c r e t e base i n t h e ground was t a k e n as t h e s t a n d a r d f o r no movement, and t h e h e i g h t of t h e t i p s o f e a c h p i p e was measured w i t h a
s u r v e y o r ' s l e v e l a t t h e b e g i n n i n g of t h e w i n t e r . Subsequently, t h e
d e t e r m i n a t i o n was taken d u r i n g t h e season of heaving, and t h e d i f f e r e n c e between t h e two l e v e l s i s t h e e x t e n t of heaving o f each p i p e .
The e x t e n t of heaving of t h e p o u n d s u r f a c e was a l s o determined by p l a c i n g a s m a l l I r o n p l a t e on t h e ground and d e t e r m i n i n g t h e h e i g h t of t h e p l a t e . The q u a n t i t y i s t h e h e a v i n g f o r z e r o heaving f o r c e and corresponds t o p o i n t B i n F i g . 1.
( b ) Temperature a t t h e ground s u r f a c e and below. The t e m p e r a t u r e was taken w i t h s i x Carlson t h e r n ~ o m e t e r s xihich were p l a c e d h o r i z o n t a l l y on t h e ground and underground a t d e p t h s of 12 cm, 22 cm, 50 cm, 82 cm and 120 cm. The r e a d i n g s from e a c h thermometer were o b t a i n e d w i t h t h e C a r l s o n i n d i c a t o r
s p e c i f l e d f o r t h e thermometer.
( c ) Depth of f r e e z i n g f r o n t . Deternilnation of t h e t e m p e r a t u r e g i v e s a s e t of t e m p e r a t u r e d i s t r i b u t i o n c u r v e s a t v a r i o u s d e p t h s underground. The c u r v e s enabled t h e a u t h o r s t o e s t i m a t e t h e d e p t h a t which t h e temperature i s
o°CJ and t h u s t h e d e p t h of t h e f r e e z i n g f r o n t .
( d ) A i r t e m p e r a t u r e . The t e m p e r a t u r e which a f f e c t s t h e heaving d i r e c t l y
i s t h e ground t e m p e r a t u r e , b u t t h e d a i l y maximum and minimum atmospheric t e m p e r a t u r e s , a s w e l l a s t h e mean d a i l y t e m p e r a t u r e of t h e a i r , a l s o had t o be t a k e n i n t o a c c o u n t . The d a t a were s u p p l i e d by t h e Kitami Weather S t a t i o n , which was l o c a t e d n e a r t h e e x p e r i m e n t a l s i t e .
IV. R e s u l t s of t h e Determinations 1. O u t l i n e
F i g u r e
5
shows a l l t h e ground and a i r t e m p e r a t u r e v a l u e s o b t a i n e d ( b o t h i n t h e upper g r a p h ) , t h e f r e e z i n g f r o n t , 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 ground ( i n t h e middle g r a p h ) , and t h e h e a v i n g f o r c e s ( l o w e r g r a p h ) . Readings were t a k e n once o r twice a day from t h e b e g i n n i n g of December t o about t h e 1 0 t h of A p r i l . The t e m p e r a t u r e s a t d e p t h s of 50 cm, 82 cm, and 120 cm v a r i e d a l m o s t r e c t i l i n e a r l y from t h e b e g i n n i n g of t h e w i n t e r u n t i l e a r l y i n t h e s p r i n g , b u t a t 22 cm i t shows c o n s i d e r a b l e d i s c o n t i n u i t y . A t 1 2 cm d e p t h t h e degree of t h e d i s c o n t i n u i t y i s even more marked and a t t h e s u r f a c e (broken l i n e ) i t i s s t i l l more s o . The f l u c t u a t i o n s a r e more o r l e s s p a r a l l e l t o t h e mean d a i l y a i r t e m p e r a t u r e (broken and d o t t e d l i n e ) .The broken l i n e i n t h e middle graph shows how t h e f r e e z i n g f r o n t advances i n t o t h e ground. The ground s u r f a c e f r o z e on Dec.
16,
a f t e r which t h e f r o s t p e n e t r a t e d p r o g r e s s i v e l y d e e p e r i n t o t h e ground u n t i l t h e f a r t h e s t advance of t h e f r e e z i n g f r o n t was reached on March 10, when i t was 57 cm. During t h i s p e r i o d t h e r e was some v a r i a t i o n i n t h e r a t e of advance of t h e f r e e z i n g f r o n t . N e v e r t h e l e s s , t h e f r e e z i n g f r o n t d i d go c o n t i n u o u s l y d e e p e r i n t h e ground.A f t e r March 10, t h e i c e began m e l t i n g from t h e bottom up, and a f t e r A p r i l 2, i t s t a r t e d t o m e l t from t h e ground s u r f a c e a l s o . When t h e equipment was recovered on A p r i l 30, t h e r e was o n l y a s m a l l f r o z e n l a y e r o f approximately
1 cm t h i c k n e s s a t 52 cm d e p t h . The s o l i d l i n e and t h e broken and d o t t e d l i n e of t h e middle graph show t h e t e m p e r a t u r e g r a d i e n t s o f t h e f r o z e n s o i l and of unfrozen s o i l s , r e s p e c t i v e l y , n e a r t h e f r e e z i n ~ f r o n t . The v a l u e s were o b t a i n e d from t h e v e r t i c a l d i s t r i b u t i o n of t h e underground t e m p e r a t u r e . A s
seen i n t h e f i g u r e , t h e t e m p e r a t u r e g r a d i e n t d e c r e a s e s r e c t i l i n e a r l y f o r t h e lower l a y e r o f unfrozen ground, and t h e r e i s f a i r l y l a r g e f l u c t u a t i o n i n t h e upper l a y e r o f f r o z e n ground.
The lower graph o f F i g . 5 shows t h e v a r i o u s h e a v i n g f o r c e s . The c u r v e s
1
of t h e h e a v i n g f o r c e s a r e remarkably i r r e g u l a r and a r e i n s t r i k i n g c o n t r a s t t o t h e curve o f t h e f r e e z i n g f r o n t , which i s very smooth. The v a l u e s o f t h e peaks a r e s e v e r a l t i m e s g r e a t e r t h a n t h o s e i n t h e t r o u g h s . There a r e f i v e such peaks ( ~ e c . 22 t o 25, Jan.
19,
Jan. 29, Feb. 10, March 1) and f o u r t r o u g h sa an.
1, Jan. 22, Feb. 3, Feb. 1 4 ) i n t h i s curve. I n f r o n t o f e a c h t r o u g h t h e r e i s a maximum o r minimum* i n t h e t e m p e r a t u r e curve of t h e upper graph, two o r t h r e e days p r i o r t o t h e d a t e o f t h e t r o u g h i n t h e lower graph. The same tendency can be s e e n i n t h e curve o f b a s a l f r e e z i n g f o r c e and t h e f o u r a d f r e e z i n g f o r c e s . The r e a s o n f o r t h i s f l u c t u a t i o n and p a r a l l e l i s m w i l l be d i s c u s s e d i n a l a t e r s e c t i o n .Throughout t h e e n t i r e t e s t p e r i o d t h e l a r g e s t f r e e z i n g f o r c e s o b t a i n e d were t h e b a s a l f r e e z i n g f o r c e s f o r t h e i r o n , v i n y l , c o n c r e t e and c o a t e d c o n c r e t e t u b e s , i n t h a t o r d e r . These were determined from t h e a d f r e e z i n g f o r c e s . S i n c e t h e t u b e s were of d i f f e r e n t t h i c k n e s s t h e a u t h o r s cannot com- p a r e t h e dependence of t h e a d f r e e z i n g f o r c e s on t h e m a t e r i a l s of t h e t u b e ; t h e v a l u e s i n t h e f i w r e a r e a c t u a l observed v a l u e s . However, t h e v a l u e s o b t a i n e d f o r t h e two c o n c r e t e t u b e s were v e r y d i f f e r e n t , and t h e f o r c e shown f o r t h e coated t u b e was f a r s m a l l e r t h a n t h e one shown f o r uncoated t u b e . The former was 70 t o 5C$ o f t h e l a t t e r .
The l a r g e s t v a l u e s o f h e a v i n g a r e shown i n T a b l e 111.
The u n i t a d f r e e z i n g f o r c e , 1.e. t h e f o r c e p e r u n i t a r e a , was o b t a i n e d by d i v i d i n g t h e h e a v i n g f o r c e b t h e s i d e a r e a o f t h e t u b e t h a t s t a y s in t h e f r o z e n ground. The v a l u e s ( 3 f o f a d f r e e z i n g f o r c e f o r t h e c o n c r e t e tube, t h e i r o n t u b e , and t h e v i n y l t u b e o b t a i n e d i n Kushiro ( a l l
90
mrn t h i c k ) showed a c o n s t a n t s t r e n g t h r a t i o o f 1 0 : 6 :3
throughout t h e w i n t e r . The maximumv a l u e s were 1970 kg o r 2 . 1 k@;/cm2 f o r t h e c o n c r e t e tube, 1280 kg o r 1.37 k@;/cm2
f o r t h e i r o n t u b e , and 600 kg o r 0.64 ke;/cm2 f o r t h e v i n y l t u b e . On t h e o t h e r hand, t h e a u t h o r s 1 p r e s e n t d e t e r m i n a t i o n s gave l a r g e r v a l u e s f o r i r o n and
v i n y l t u b e s t h a n t h a t f o r t h e c o n c r e t e t u b e s . The r e a s o n s f o r t h i s d i s -
crepancy may be found i n t h e f a c t t h a t t h e c o n c r e t e t u b e had a f a i r l y smooth s i d e s u r f a c e , t h a t t h e c o n t a c t between t h e s o i l and t h e t u b e s were n o t q u i t e e q u a l i n each c a s e and s u f f i c i e n t time was n o t allowed between t h e s e t t i n g up of t h e t u b e i n t h e ground and t h e s t a r t of measurements. These a r e , however, t e n t a t i v e e x p l a n a t i o n s , and t h e a u t h o r s p l a n t o conduct more d e t e r m i n a t i o n s i n t h e n e x t and f o l l o w i n g w i n t e r s when t h e s o i l w i l l have s e t t l e d s t e a d i l y .
Oura ( 7 ) and K i n o s h i t a conducted a s e t o f experiments t o determine t h e s t r e n g t h of f r e e z i q g by p u l l i n g a b a r , which had been b u r i e d v e r t i c a l l y and f r o z e n i n moistened s o i l , o u t of t h e f r o z e n ground. The determined s t r e n g t h o f f r e e z i n g v a r i e d more o r l e s s depending on t h e n a t u r e o f t h e s o i l , t h e t e m p e r a t u r e and t h e v e l o c i t y o f e x t e n s i o n o f t h e b a r . The s t r e n g t h was
a p p r o x i m a t e l y 9 kg/cm2 a t -2OC f o r an i r o n b a r . T h i s s t r e n g t h of f r e e z i n g i 8
v e r y much g r e a t e r t h a n t h e maximum f o r c e s shown i n Table 11. T h i s f a c t
s u g g e s t s t h a t t h e heaving f o r c e determined a t t h e s i t e of t h e f i e l d experiment does n o t i n c l u d e t h e f o r c e t h a t i s needed t o break t h e s u r f a c e o f f r e e z i n g . 2. Continuous D e t e r m i n a t i o n s
There i s a f a i r l y l a r g e f l u c t u a t i o n a t a few p o i n t s a l o n g t h e curve o f t h e h e a v i n g f o r c e . Each o f t h e peaks and t r o u g h s i s d i v i d e d i n t u r n w i t h s m a l l e r f l u c t u a t i o n s . The s m a l l e r f l u c t u a t i o n s a r e m o s t l y due t o t h e d i f f e r - e n t r e a d i n g s t a k e n a t two d i f f e r e n t t i m e s o f day, 9:00 AM and 5:00 PM. F o r example, t h e h e a v i n g f o r c e c u r v e of t h e i r o n b a r shows small i n c r e a s e and
d e c r e a s e of t h e f o r c e , such a s 2460 k g a t 9 AM, Feb. 25; 230 k g a t 5 PM on t h e same day; 2400 kg a t 9 AM, Feb. 28; 2350 k g a t 5 PM of t h e same day. In o r d e r t o determine t h e amplitude o f t h e v a r i a t i o n of t h e f o r c e f o r a one-day p e r i o d , t h e a u t h o r s took r e a d i n g s e v e r y h o u r f o r about t h r e e days from 6 PM, Feb. 15 t o 12 AM, Feb. 18. The r e s u l t s a r e shown i n F i g . 6. A s i t was l e a r n e d
s u b s e q u e n t l y , t h e h e a v i n g f o r c e was a t t h a t time e x p e r i e n c i n g a r a p i d l n c r e a a e t o a peak; t h e r e f o r e t h e f l u c t u a t i o n s i n a s i n g l e day were n o t v e r y g r e a t .
The b a s a l h e a v i n g f o r c e d u r i n g t h i s p e r i o d was doubled from 1450 kg t o 2900 kg. The a d f r e e z i n g f o r c e a l s o i n c r e a s e d , from 1320 kg t o 2200 k g on t h e i r o n t u b e , from 980 kg t o 1600 k g on t h e v i n y l p i p e , from 635 k g t o 1080 kg on t h e c o n c r e t e p i p e , and from 440 k g t o 670 k g on t h e c o a t e d c o n c r e t e p i p e . No s e v e r e f l u c t u a t i o n was observed of t h e s e d e t e r m i n a t i o n v a l u e s , d u r i n g t h e t e s t p e r i o d f o r e i t h e r t h e b a s a l h e a v i n g f o r c e o r t h e a d f r e e z i n g f o r c e s , e x c e p t f o r t h e sudden i n c r e a s e s of t h e b a s a l h e a v i n g f o r c e a t 1 PM, Feb. 1 6 and a t 12 AM, Feb. 17, which were o t h e r w i s e f a i r l y c o n s t a n t b e f o r e . A l l
f o u r a d f r e e z i n g f o r c e s decreased s l i g h t l y d u r i n g t h e p e r i o d between 12 AM and
5
PM on Feb.17.
The t e m p e r a t u r e a t t h e ground s u r f a c e v a r i e d s i n u s o i d a l l y . Correspond- i n g l y t h e t e m p e r a t u r e s a t 12 cm and 22 cm underground d e p t h v a r i e d more o r l e s s s i n u s o i d a l l y . However, t h e peak and t r o u g h v a l u e s showed a l a g in
r e l a t i o n t o t h e maximum and minimum ground s u r f a c e t e m p e r a t u r e s , and a l s o t h e amplitude of t h e d a i l y v a r i a t i o n of t h e underground t e m p e r a t u r e s was s m a l l e r t h a n t h a t of t h e ground s u r f a c e t e m p e r a t u r e . There was p r a c t i c a l l y no change of t e m p e r a t u r e a t d e p t h s of 50 cm and 120 cm
a able
IV).According t o t h e h e a t conduction t h e o r y , when t h e ground s u r f a c e 27L
t e m p e r a t u r e uo changes a c c o r d i n g t o uo = A s i n
-
t , t h e t e m p e r a t u r e u a t Tunderground d e p t h x changes a c c o r d i n g t o t h e e x p r e s s i o n
Here, T i s t h e amplitude and x i s t h e t e m p e r a t u r e d i f f u s i o n r a t e of t h e s o i l . The v a l u e of x was c a l c u l a t e d from t h e d a t a of Table 111 and was found t o be 0.035 t o 0.06 ( c . G . S . u n i t s ) . T h i s v a l u e i s s m a l l e r t h a n t h e x v a l u e of 0.07 of common s o i l .
3.
Observation of V e r t i c a l S e c t i o nA photograph was t a k e n on Feb. 16 of a v e r t i c a l s e c t i o n a l o n g a h o l e dug n e a r t h e s i t e of t h e e s t a b l i s h m e n t . The photograph i s shown i n F i g .
7.
There a r e innumerable t h i n l o n g Ace l a y e r s l y i n g s i d e by s i d e h o r i z o n t a l l y , g i v i n g t h e Impression of f r o s t columns. G e n e r a l l y whenever t h e c l a y l a y e r heaves, t h e same frost-column f r e e z i n g i s observed i n t h e ground(8). The i c e l a y e r s a r e g e n e r a l l y t h i c k e r a t t h e t o p , some of them b e i n g a s t h i c k a s 1 0 mm. A tt h e bottom, t h i n i c e l a y e r s of 1 mm t h i c k n e s s and 1
-
4 cm l e n g t h a r e a l i g n e d s i d e by s i d e . The r e l a t i o n between t h e advance of t h e f r o s t f r o n t and t h e f o r m a t i o n of i c e l a y e r s was i n v e s t i g a t e d , b u t t h e a u t h o r s were unable t o o b t a i n a d e f i n a t e c o r r e l a t i o n between them.The f r o z e n ground was e x t r e m e l y h a r d , and i t had a n impact compression s t r e n g t h of a b o u t 200
-
300 kg/cm2; t h e r e f o r e , i t was n o t e a s y t o c u t t h ev e r t i c a l s e c t i o n . However, a few c a v i t i e s were found i n s i d e t h e f r o z e n ground, and o c c a s i o n a l l y a clod of f r o z e n s o i l of t h e s i z e of a f i s t chipped o f f
e a s i l y . It i s known t h a t some c a v i t i e s a r e formed i n f r o z e n ground(8), b u t t h e c a v i t i e s found In t h i s t e s t p l o t might have been formed when t h e s o i l f i l l i n g t h e empty s p a c e d r i e d o u t b e f o r e f r e e z i n g i n w i n t e r . The u n u s u a l l y small h e a t d i f f u s i o n c o e f f i c i e n t v a l u e may be due t o t h e s e c a v i t i e s .
4. The Amount of Heaving
The v a l u e o f t h e h e a v i n g of t h e t u b e s used f o r t h i s d e t e r m i n a t i o n s t a r t i n g Nov. 23, i s shown i n F i g . 8. The d e t e r m i n a t i o n had t o be d i s c o n - t i n u e d from J a n . 24 t o A p r i l 30 because of t h e f a i l u r e of a l e v e l . The amount of h e a v i n g of t h e ground s u r f a c e ( N O .
6
o f t h e f i g u r e ) i s based o n l y on two d e t e r m i n a t i o n s , b u t t h e amount was e s s e n t i a l l y t h e same a s t h a t observed i n o t h e r t u b e s f o r t h e same p e r i o d . The amount of h e a v i n g was g r e a t e s t f o r t h e wooden b a r ( c o a t e d ) , followed by t h e v i n y l p i p e , wooden b a r and i r o n t u b e s( b o t h c o a t e d and uncoated p i p e s show n e a r l y i d e n t i c a l v a l u e s ) i n t h a t o r d e r . The h e a v i n g f o r c e s under t h e s e c o n d i t i o n s a r e i d e n t i c a l w i t h t h e weight of t h e p i p e s . T h e r e f o r e , t h e h e a v i n g f o r c e i s g r e a t e s t on t h e i r o n p i p e s and de-
c r e a s e s i n t h e o r d e r of wood b a r s and v i n y l p i p e s a s shown i n T a b l e 11.
Except f o r t h e c o a t e d wooden b a r , t h e t u b e s t h a t showed g r e a t e s t h e a v i n g f o r c e showed t h e l e a s t heaving. T h i s r e l a t i o n s h i p c o r r e s p o n d s w e l l w i t h t h e r e s u l t s i n F i g . 1. The a u t h o r s p l a n t o s t u d y t h e r e l a t i o n s h i p more c a r e f u l l y , u s i n g p i p e s made of t h e same m a t e r i a l b u t h a v i n g d i f f e r e n t w e i g h t s .
S i n c e t h e a u t h o r s d i d n o t o b t a i n s u f f i c i e n t t e s t v a l u e s f o r h e a v i n g under a c o n s t a n t h e a v i n g f o r c e , t h e y were u n a b l e t o i n v e s t i g a t e t h e s m a l l f l u c t u a t i o n s o f t h e (maximum) h e a v i n g f o r c e due t o t h e amount o f h e a v i n g when i t was z e r o , a s d e s c r i b e d i n t h e p r e v i o u s s e c t i o n . However, a l t h o u g h t h e (maximum) h e a v i n g f o r c e d e c r e a s e d ( l o w e r c u r v e of F i g . 5 ) i n t h e p e r i o d o f Jan.
19
and 24, t h e amount o f h e a v i n g c o n t i n u o u s l y i n c r e a s e d , a s i t had i n t h e p r e v i o u s p e r i o d (shown i n F i g .8 ) .
When t h e a p p a r a t u s was r e c o v e r e d on A p r i l 30, t h e c o a t e d wooden b a r
showed t h e most h e a v i n g w i t h 14 cm. The v i n y l p i p e , i r o n p i p e and c o a t e d i r o n p i p e showed 9.6 cm,
5.8
cm and 4.9 cm, r e s p e c t i v e l y . A l l t h e s e p i p e s hadt h e i r top-end f a c e s o r i g i n a l l y b u r i e d l e v e l w i t h ground s u r f a c e , b u t a l l t h r e e top-ends were above t h e ground s u r f a c e when t h e y were r e c o v e r e d . There were c a v i t i e s between t h e bottoms o f t h e p i p e s and t h e s o i l b e n e a t h t h e p i p e and o n l y a s l i g h t p r e s s u r e a t t h e t o p of t h e p i p e was r e q u i r e d t o cause i t t o drop t h r o u g h t h e empty s p a c e between t h e p i p e and t h e s o i l .
V. R e l i e f of t h e Heaving Force
A s p r e v i o u s l y d e s c r i b e d , f r e e z i n g o f t h e ground p r o c e e d s downwards b u t t h e h e a v i n g f o r c e i n c r e a s e s and d e c r e a s e s c o n t i n u o u s l y . F i g u r e
5
shows t h a t b o t h a i r t e m p e r a t u r e and ground t e m p e r a t u r e a r e h i g h e r when t h e curve o f h e a v i n g f o r c e i s i n i t s t r o u g h . During t h i s p e r i o d , t h e downward movement o ff r e e z i n g s t o p s o r p r o c e e d s e x t r e m e l y s l o w l y . On t h e o t h e r hand, i t i s a l s o known from e x p e r i m e n t s i n a low t e m p e r a t u r e l a b o r a t o r y , t h a t t h e f r e e z i n g
f o r c e i s r e l i e v e d d u r i n g t h e p e r i o d when heaving s t o p s . T h e r e f o r e t h e
a u t h o r s concluded t h a t t h e d e c r e a s e of heaving f o r c e i s due t o t h e phenomenon of r e l i e f .
1. Low Temperature Laboratory Experiment
The a u t h o r s conducted model experiments on b a s a l heaving f o r c e and a d f r e e z i n g f o r c e .
Wet s o i l i n a wooden box of 10 cm x 10 cm x 5 cm s i z e was brought i n t o a
low t e m p e r a t u r e l a b o r a t o r y cooled t o a c e r t a i n teniperatur~e, and f r o z e n . A
s m a l l i r o n p i p e of 1 . 6 cm d i a m e t e r was i n s e r t e d a t t h e c e n t r e o f t h e s u r f a c e o f t h e f r o z e n s o i l and was p r e s s e d downwards a t t h e t o p a t a c o n s t a n t
v e l o c i t y . The f o r c e g e n e r a t e d was r e c o r d e d , through a load c e l l and s t r a i n gauge, w i t h an e l e c t r o n t u b e a u t o m a t i c r e c o r d e r . In t h i s experiment t h e p i p e
i s b u r i e d i n t h e s o i l s o t h a t t h e s o i l n o t coming i n t o c o n t a c t w i t h t h e p i p e does n o t move. However, i n t h e f i e l d experiment t o determine t h e b a s a l heav- i n g f o r c e , t h e i r o n p l a t e on t h e s u r f a c e o f t h e ground remained i n p l a c e and t h e s o i l , on e i t h e r s i d e of t h e p l a t e , moved upwards due t o heaving. In t h e experiment t h e p i p e was p r e s s e d downwards a t a speed of 1.3 mm/mln. The compression curve i s shown i n F i g . 9 . The curve moves upwards almost r e c t i - l i n e a r l y from t h e p o i n t A, where t h e compression s t a r t e d . I f t h e p r e s s u r e i s d i s c o n t i n u e d a t p o i n t B, t h e f o r c e d r o p s a c c o r d i n g t o a n e x p o n e n t i a l f u n c t i o n a s t h e s o i l c o n t i n u e s t o be compressed w i t h t h e compression s t r a i n a t t h e
p o i n t B. A f t e r 26 h o u r s , t h e f o r c e d e c r e a s e d t o 40 kg from t h e i n i t i a l 140 kg.
T h i s phenomenon o f t h e f o r c e , d e c r e a s i n g while t h e compression s t r a i n remains c o n s t a n t , i s t h e phenomenon o f r e l i e f . It i s known t h a t t h e h i g h e r t h e
t e m p e r a t u r e t h e f a s t e r t h e r e l i e f . The r e s u l t s o b t a i n e d by model e x p e r i m e n t s on t h e r e l i e f of t h e b a s a l f r e e z i n g f o r c e a r e shown a s c u r v e s B, D, F i n t h e l o g a r i t h m i c graph, F i g . 10. The f o r c e t h a t was shown a t t h e beginning o f r e l i e f i s t a k e n a s
lo&.
The example o f F i g . 9 , i s r e p e a t e d a s t h e curve Fof F i g . 10.
A box of t h e same s i z e a s t h e one used f o r t h e above experiments was f i l l e d w i t h wet s o i l b u t w i t h a h o l e o f 2 cm d i a m e t e r i n t h e middle o f t h e bottom o f t h e box. Through t h e c e n t r e h o l e , an i r o n rod o f 1 . 6 cm d i a m e t e r , was passed. The s o i l was f r o z e n i n t h e same way and p r e s s u r e was a p p l i e d t o t h e t o p of t h e b a r s o a s t o move i t downwards a t a c o n s t a n t v e l o c i t y . In t h i s c a s e , t h e b a r moves downwards and t h e f r o z e n s o i l a d h e r i n g t o i t py f r e e z i n g a l s o moves downwards with t h e b a r , b u t t h e s o i l n o t i n c o n t a c t with t h e b a r does n o t move. In t h e f i e l d experiment, i t w i l l be r e c a l l e d t h a t t h e b a r remained s t a t i o n a r y w h i l e t h e s o i l t h a t was f a r enough away from i t moved
upwards. The r e l i e f curve o b t a i n e d by t h i s model experiment o f a d f r e e z i n g f o r c e d e t e r m i n a t i o n i s shown by t h e d o t t e d c u r v e s A , C , E of t h e l o g a r i t h m i c graph, F i g . 10.
The s o i l used i n t h i s s e t of experiments i s clay-loam from Hakuro- N i s h i k i o k a and comprises 23% c l a y ( i n c l u d i n g c o l l o i d s ) , 33% s i l t , 44% sand. The m o i s t u r e c o n t e n t was a d j u s t e d t o 17$.
Curves A, B, C, D, E, F a r e almost r e c t i l i n e a r . The s l o p e is s h a r p e r f o r t h e h i g h e r t e m p e r a t u r e , 1 . e . r e l i e f i s f a s t e r . The p o i n t s E 1 and B' a t t h e lower r i g h t of F i g . 10 a r e t h e c o n t i n u a t i o n o f t h e E and B, b u t a r e q u i t e f a r away from t h e r e c t i l i n e a r e x t e n s i o n s o f E and B. T h i s i s because t h e tempera- t u r e was r a i s e d r a p i d l y a f t e r t h e f i n a l d e t e r m i n a t i o n s o f E and B. The temper- a t u r e was r a i s e d from -4OC t o -1°C f o r E 1 and from -23°C t o - 3 O C f o r B f . It
i s a l s o shown in t h e f i g u r e t h a t t h e b a s a l heaving f o r c e i s r e l i e v e d more slowly t h a n t h e a d f r e e z i n g f o r c e .
According t o Wakahama ( l o ) , r e l i e f of s t r e s s i n p o l y c r y s t a l l i n e i c e i s much f a s t e r t h a n i n f r o z e n s o i l . For i c e a t
-8"C,
t h e f o r c e 10 minutes a f t e r t h e t e r m i n a t i o n o f compression i s o n l y 6* o f t h a t 1 minute a f t e r t h e termina- t i o n , and 30$ of t h a t a f t e r 5 minutes. I f we assume t h a t t h e s i d e of a b a r and t h e f r o z e n s o i l a r e joined o n l y by i c e , t h e r a t e of r e l i e f should be i d e n t i c a l w i t h t h a t of i c e . The curve D o f t h e r e l i e f a t -8OC i n F i g . 10,however, shows t h a t t h e r e l i e f of t h e f r o z e n so11 1s v e r y much s l o w e r t h a n t h a t o f i c e . T h e r e f o r e t h e f r e e z i n g which i n v o l v e s t h e f r o z e n s o i l does n o t seem t o depend o n l y on t h e amount of i c e i n t h e s o i l .
For m a t e r i a l s i n which i h e compression f o r c e i s r e l i e v e d while a c o n s t a n t compression s t r a i n remains c o n s t a n t , t h e e l a s t i c compression f o r c e , which i s p r o p o r t i o n a l t o t h e s t r a i n , i s n o t t h e o n l y f o r c e a c t i n g on t h e m a t e r i a l d u r i n g t h e p e r i o d o f i n c r e a s i n g compressive s t r a i n . The f o r c e which i s c o n t i n u o u s l y r e l i e v e d i n t h e course o f compression must a l s o be c o n s i d e r e d p a r t of t h e a c t i n g f o r c e s . Such m a t e r i a l s a r e termed v i s c o u s e l a s t i c . The s t r a i n F of a v i s c o u s e l a s t i c body a t a compressive s t r a i n h can be shown a s
Here, C i s a p r o p o r t i o n a l c o n s t a n t and f a c o n s t a n t f u n c t i o n . The f i r s t term on t h e r i g h t r e p r e s e n t s t h e e l a s t i c p a r t of t h e f o r c e and t h e second term t h e r e l i e f . The curve ~ ( t ) when t h e s t r a i n h ( t ) t a k e s a c o n s t a n t v a l u e H i n formula ( 1 ) i s t h e curve o f t h e r e l i e v i n g f o r c e .
The f o r c e ~ ( t ) d e c r e a s e s a l o n g t h e c u r v e s i n Fig. 10, i n v a r i o u s c a s e s o f r e l i e f of heaving f o r c e s . The r e l i e v i n g f o r c e curve i s almost r e c t i l i n e a r
a f t e r 0.1 min, on a l o g a r i t h m i c graph. In t h i s case, within t h e l i m i t of t > E ( E x 0 ) , s e t t i n g upper l i m i t of i n t e g r a t i o n of t h e formula ( 1 ) a s t
-
E ,and t h e f u n c t i o n f ( z ) a s f ( z ) = ( a i s a c o n s t a n t ) , t h e formula conforms t o t h e a c t u a l f a c t s . That i s t o say formula ( 1 ) becomes
When h ( t ) = constant), t h e f o r c e d e c r e a s e s according t o t h e formula
The r e l i e v i n g f o r c e curve of Fig. 10 i s expressed by
( 3 ) .
The c o n s t a n t a of formula ( 3 ) shows t h e s l o p e of t h e curve of Fig. 10, and when a i s l a r g e r t h e-
s l o p e i s s t e e p e r , which s i g n i f i e s f a s t e r r e l i e f o r t h e r e l i e f a t a h i g h e r temperature.If t h e heaving occurs a t a c o n s t a n t v e l o c i t y , 1 . e . h ( t ) = b t ( b i s a c o n s t a n t ), formula ( 2 ) becomes
t
~ ( t ) = C b t
+
aCb(t-
E )-
aCbt loge ( 4 )and
Since t h e value of t h e expression w i t h i n t h e b r a c k e t o f ( 3 ) i s between 1 and 0,
Therefore, equation
( 5 )
givea Cb >-
> 0. That l a t o say, although Fd t
i n c r e a s e s , t h e r a t e of i n c r e a s e i s always s m a l l e r than t h e r a t e Cb of t h e i n c r e a s e due t o t h e e l a s t i c f o r c e only, and t h i s r a t e of i n c r e a s e of F
becomes s m a l l e r and s m a l l e r i n t h e course of time.
Although t h e s t r e s s d e c r e a s e s while t h e s t r a i n remains c o n s t a n t , t h e s t r a i n i t s e l f I s a c t u a l l y reduced I n s i d e of t h e m a t e r i a l . Even a f t e r t h e movement of t h e i r o n p i p e t h a t p r e s s e s a g a i n s t t h e s o i l c e a s e s , t h e movement of t h e s o i l p a r t i c l e s c o n t i n u e s and t h e s t r a i n i s reduced s o . t h a t t h e f o r c e decreases, and I n t h e f r e e z i n g experiments t h e f r e e z i n g of t h e s o i l t o t h e b a r g r a d u a l l y d e c r e a s e s and t h e f o r c e d e c r e a s e s . Thus r e l i e f of t h e s t r e s s is due t o f r e e z i n g and s t r a i n deformation.
The f u r t h e r t h e r e l i e f of s t r e s s , t h e l a r g e r t h e value of t h e c o n s t a n t a , and, a t t h e same time, i f heaving t a k e s p l a c e a t a c o n s t a n t r a t e , t h e I n c r e a s e of heaving f o r c e i s l a r g e r , a s shown by formulae ( 4 ) and
( 5 ) .
Inon t h e d i f f e r e n c e s of m a t e r i a l . The d i f f e r e n c e s a r e due t o t h e d i f f e r e n c e s i n t h e value of a . I n o t h e r words, a s m a l l e r heaving f o r c e r e s u l t s i n a f a s t e r r e l i e f of t h e s t r e s s and hence a f a s t e r r a t e of strain-deformation r e l i e f . The s m a l l e r heaving f o r c e of t h e coated concrete pipe compared with t h e uncoated one can be explained by t h e f a c t t h a t t h e r e l i e f of s t r a i n defornlation a t t h e frozen s u r f a c e i s f a s t e r f o r a coated s u r f a c e causing f a s t e r s l i d i n g of t h e p a r t i c l e s around t h e f r o z e n s u r f a c e .
In t h e low- t e n ~ p e r a t u r e la b o r a t o r y experiment, t h e a u t h o r s used s o i l which was d i f f e r e n t from t h a t of t h e f i e l d experiment. The i n c r e a s e of t h e heaving f o r c e , shown i n t h e case where 1 rnm of t h e f r e e s u r f a c e i s heaved upwards a t t h e f i e l d experimental s i t e , was estimated a s u s i n g t h e value of t h e compression f o r c e which was used t o depress t h e s u r f a c e 1 mm i n t h e low-
temperature l a b o r a t o r y experiment. The estimated values a r e shown i n Table V.
Although t h e estimated values a r e n o t n e c e s s a r i l y c o r r e c t , e s p e c i a l l y s i n c e t h e r a t e s a r e d i f f e r e n t , and t h e two phenomena a r e n o t t h e same f o r t h e f i e l d experiment and f o r low-temperature l a b o r a t o r y experiment, i t i s c l e a r l y shown t h a t t h e r e i s a l a r g e i n c r e a s e of t h e heaving f o r c e by heaving of t h e f r e e s u r f a c e by o n l y a s much a s 1 mm upwards. However, i f heaving s t o p s , t h e heaving f o r c e d e c r e a s e s t o l e s s than h a l f a f t e r one day, i f t h e temperature i s high. A c t u a l l y t h e ground temperature a t t h e a i t e of t h e f i e l d experiment was h i g h e r than - 5 O C , except f o r t h e p a r t of t h e ground n e a r t h e s u r f a c e .
2 . Discussion of t h e R e s u l t s of t h e Determination
It was found t h a t t h e (maximum) heaving f o r c e decreases when t h e heaving
of t h e f r e e ground s u r f a c e s t o p s . Unfortunately t h e a u t h o r s a r e unable t o i n v e s t i g a t e t h e r e l a t i o n s h i p between t h e amount of heaving h and t h e (maximum)
heaving f o r c e a t t h i s moment, a s they d i d n o t conduct continuous determinations
of t h e amount of heaving h of t h e f r e e ground s u r f a c e . However, i t i s known t h a t t h e amount of heaving h i s not p r o p o r t i o n a l t o t h e f r e e z i n g f r o n t depth
.
It i s a l s o lmown t h a t t h e amount of i c e i n t h e l a y e r a t t h e f r e e z i n g f r o n t i n c r e a s e s when t h e depth of t h e f r e e z i n g f r o n tC
remains c o n s t a n t ( 1 1 ) .However, t h e g e n e r a l tendency i s t h a t t h e g r e a t e r t h e depth of f r e e z i n g t h e g r e a t e r t h e amount of heaving. Therefore, i t i s important t o s t u d y t h e r a t e
of i n c r e a s e of t h e depth of t h e f r e e z i n g f r o n t E . d t
Figure 11 shows a t y p i c a l example of temperature d i s t r i b u t i o n i n t h e ground. The temperature g r a d i e n t n e a r t h e f r e e z i n g f r o n t i s s t e e p e r above t h e f r o n t ( f r o z e n l a y e r ) than below i t (unfrozen l a y e r ) , and t h e f r e e z i n g f r o n t i t s e l f i s t h e p o i n t of d i s c o n t i n u a t i o n . This i s due t o r e l e a s e of l a t e n t h e a t of water in t h e ground f r e e z i n g a t t h e f r e e z i n g f r o n t . The r a t e of i n c r e a s e
