Principles of Geocryology (Permafrost Studies). Part II, Engineering Geocryology. Chapter III, Basic Mechanics of Freezing, Frozen and Thawing Soils. p. 28-79

Publisher’s version / Version de l'éditeur:

Technical Translation (National Research Council of Canada), 1966

READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE.

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

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.

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/10.4224/20331447

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

Principles of Geocryology (Permafrost Studies). Part II, Engineering

Geocryology. Chapter III, Basic Mechanics of Freezing, Frozen and

Thawing Soils. p. 28-79

Tsytovich, N. A.

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.

NRC Publications Record / Notice d'Archives des publications de CNRC: https://nrc-publications.canada.ca/eng/view/object/?id=1fe129a5-bd1d-4491-a5ca-1cb115e24869 https://publications-cnrc.canada.ca/fra/voir/objet/?id=1fe129a5-bd1d-4491-a5ca-1cb115e24869

This t r a n s l a t i o n i s t h e seventh from t h e Russian permafrost p u b l i c a t i o n " ~ r i n c i p l e s of Geocryology", P a r t I1 ( ~ n g i n e e r i n ~ Q e o c r y o l o q ) . The f i r s t t r a n s l a t i o n i n t h i s group was Chapter I e n t i t l e d P r i n c i p l e Aspects of Engineering Qeocryology (Permafrost s t u d i e s )' by N . I. Saltykov (TT-1215). The second was Chapter V I I

" P a r t i c u l a r Aspects of Mining in Thick ~ e r m a f r o e t " by V.P. Bakakin (TT- 1217 )

.

The t h i r d was C h a p t e r . I1 " ~ e f ormation of S t r u c t u r e s R e s u l t i n g from F r e e z i n g and ha wing" by A . I . Dement'ev (TT-1219). The f o u r t h was Chapter V I I I " ~ e d s f o r Roads and ~ i r f i e l d s " by

G.V. Porkhaev and A.V. S a d o v s k i i (TT-1220). The f i f t h was

Chapter

IX

"underground U t i l i t y ~ i n e s " by G.V. Porkhaev (TT-1221). The s i x t h was Chapter X I " S p e c i f i c F e a t u r e s of t h e Maintenance of S t r u c t u r e s i n Permafrost ~ o n d i t i o n s " by A. I. Dement 'ev (TT-1232 )

.

This t r a n s l a t i o n of Chapter I11 by N.A. Tsytovich e t a l . reviews t h e fundamental a s p e c t s of f r o z e n s o i l mechanics. The mechanics of f r e e z i n g s o i l s a r e d i s c u s s e d with r e s p e c t t o change

In s o i l volume, f r o s t heaving, and r e j e c t i o n of w a t e r from s o i l d u r i n g f r e e z i n g . The p h y s i c a l p r o p e r t i e s of f r e e z i n g s o i l and i c e a r e reviewed. T h i s i s followed by a d i s c u s s i o n of t h e mechanical p r o p e r t i e s of f r o z e n s o i l i n c l u d i n g mechanical bonds, deformation

c h a r a c t e r i s t i c s and compaction under load. The r h e o l o g i c a l pro- c e s s e s I n f r o z e n s o i l s a r e considered i n connection with t h e i r r e l a t i o n t o s h o r t - t e r m and long-term loads. The c h a p t e r concludee w i t h a d i s c u s s i o n of t h e s t r e s s e s and deformation o c c u r r i n g i n thawing s o i l s .

The D i v i s i o n i s g r a t e f u l t o M r . V. Poppe, T r a n s l a t i o n s S e c t i o n , N a t i o n a l Research Council, f o r t r a n s l a t i n g t h i s c h a p t e r and t o

D r . R.J.E. Brown of t h i s D i v i s i o n who checked t h e t r a n s l a t i o n .

Ottawa

May 1966

R.F. Legget D i r e c t o r

NATIONAL RESEARCH COUNCIL OF CANADA

Technical T r a n s l a t i o n 1239

T i t l e t Basic mechanics of freezing, frozen and thawing s o i l s

( ~ s n o v y mekhaniki promerzayuahchikh, merzlykh i protaivayushchikh gruntov)

Author: N.A. Taytovich e t a l .

Reference: P r i n c i p l e a of geocryology (permafrost s t u d i e s ) , P a r t 11, Engineering geocryology, Chapter 111. Academy of Sciences of t h e U.S.S.R. Moscow

1959.

p.28-79

(0snovy g e o k r i o l o g i i (merzlotovedeniya), Chaat' vtoraya, Inzhenernaya geokriologiya, alava 111. Akademiya Nauk SSSR. Moakva 1959. s .28-79 )

BASIC MECHANJCS OF FREEZINC?, FROZEN AND THAWING SOILS

I n t r o d u c t i o n . 1. Mechanics of f r e e z i n g s o i l . 2. P h y s i c a l p r o p e r t i e s of f r o z e n s o i l and i c e . 3 . Mechanical p r o p e r t i e s of frozen s o i l . 4. Rheological processes i n frozen s o i l and i t s s t r e n g t h .

5.

S t r e s s e s i n and deformation of thawing s o i l .

I n t r o d u c t i o n

The mechanics of f r o z e n s o i l s d e a l s w i t h t h e s t u d y of unconsolidated d e p o s i t s cemented t o g e t h e r with i c e and forms p a r t of t h e s c i e n c e of g e n e r a l rock mechanics.

This d i s c i p l i n e was developed i n t h e S o v i e t Union i n response t o

e n q u i r i e s which a r o s e d u r i n g opening up of new r e g i o n s and on I n t r o d u c t i o n o f new c o n s t r u c t i o n methods i n t h e a r e a s of occurrence of f r o z e n s o i l s .

The knowledge of b a s i c mechanics of f r o z e n s o i l s gained i n t h e l a s t t e n y e a r s makes i t p o s s i b l e t o s o l v e t h e problems of c o n s t r u c t i o n by t a k i n g i n t o account changes i n t h e p r o p e r t i e s of f r o z e n s o i l which t a k e p l a c e d u r i n g t h e i n t e r a c t i o n between t h e l a t t e r and t h e s t r u c t u r e .

General aims of mechanics of f r o z e n s o i l s i n c l u d e : e v a l u a t i o n o f p r o p e r t i e s of f r o z e n s o i l i n o r d e r t o t a k e f u l l advantage of i t s p o s i t i v e

c h a r a c t e r i s t i c s , measures t o e l i m i n a t e harmful e f f e c t s of f r e e z i n g and thawing, and d e t e r m i n a t i o n of v a r i o u s f a c t o r s t o be used i n d e s i g n problems i n v o l v i n g f r o z e n s o i l s a s b e a r i n g m a t e r i a l and medium of c o n s t r u c t i o n .

On examining problems of mechanics of f r o z e n s o i l s i t i s n o t enough t o c o n s i d e r homogeneous s o l i d bodies only, o r o n l y t h e mechanics of o r d i n a r y ( u n f r o z e n ) s o i l s , s i n c e e i t h e r approach w i l l n o t account f o r t h e cementation of s o l i d m i n e r a l p a r t i c l e s with i c e . T h i s cementation w i l l vary w i t h tempera- t u r e , because i c e i s a h i g h l y p l a s t i c m a t e r i a l , t h e mechanical p r o p e r t i e s of which depend on t h e n e g a t i v e temperature.

In

developing ways of r a t i o n a l u t i l i z a t i o n of p r o p e r t i e s o f f r e e z i n g , f r o z e n and thawing s o i l s , t h e mechanics of t h e s e t y p e s of s o i l , t o g e t h e r with thermal p h y s i c s , s e r v e s a s a t h e o r e t i c a l b a s i s of e n g i n e e r i n g geocryology ( e n g i n e e r i n g permafrost s t u d i e s )

.

Below we g i v e a n account of b a s i c mechanics of f r e e z i n g , f r o z e n and thawing s o i l s .

1. Mechanics of Freezing S o i l s

1. The Change of Volume of S o i l on Freezinq

The most important process in f r e e z i n g s o i l i s t h e transformation of water contained i n i t i n t o i c e , s i n c e t h i s considerably a l t e r s t h e i n t e r n a l bonds in t h e s o i l and l e a d s t o a r e d i s t r i b u t i o n of moisture and f i n e mineral p a r t i c l e s . The p r o p e r t i e s of i c e i n ~ l ~ s i O n S , e s p e c i a l l y i f i c e forms i n t h i n

f i l m s , d i f f e r from t h e p r o p e r t i e s of water f i l m s . The s t r e n g t h of cemented i c e bonds i s measured in t e n s of kilograms' p e r square centimetre. A l l t h i s g i v e s r i s e t o p r o p e r t i e s of f r o z e n s o i l d i f f e r e n t t o t h o s e of unfrozen s o i l .

When water f r e e z e s in t h e ground, t h e volumetric expansion of i c e g i v e s r i s e t o oonsiderable i n t e r n a l f o r c e s . It i s known t h a t water, which i s pre- vented from volumetric expansion, may on f r e e z i n g develop p r e s s u r e s of up t o 2115 atm. The c o n d i t i o n s i n t h e ground a r e d i f f e r e n t and t h e r e f o r e t h e f o r c e s a r i s i n g on f r e e z i n g of pore moisture a r e much s m a l l e r . However, they a r e l a r g e enough n o t t o be cancelled by t h e weight of s o i l and t h e p r e s s u r e from a s t r u c t u r e . The f o r c e s a r i s i n g on f r e e z i n g of water a r e i n v a r i a b l y l a r g e

enough t o change t h e s o i l s t r u c t u r e , s i n c e f r e e z i n g of pore moisture i s accompanied n o t o n l y by cementation of s o i l p a r t i c l e s with i c e b u t a l s o by t h e i r displacement. The p r o c e s s i s c o n s i d e r a b l y complicated by the f a c t t h a t f r e e z i n g of moist s o i l i s i n v a r i a b l y accompanied by moisture migration.

Formation of i c e i s t h e r e s u l t of moisture migration and l o c a l c o n d i t i o n s , w h k h favour t h e development of l a y e r s , l e n s e s and s i m i l a r f n c l u s i o n s of i c e .

The change i n t h e s o i l volume on f r e e z i n g t a k e s p l a c e due t o t h e i n c r e a s e i n volume of water when i t changes from l i q u i d t o s o l i d s t a t e , a s w e l l a s a r e s u l t of f r e e z i n g of water a r r i v i n g from neighbouring, unfrozen s e c t i o n s of t h e ground. The migration of moisture r e s u l t s

In

_{l a r g e accumulations of} moisture i n t h e form of i c e l a y e r s , e s p e c i a l l y i f c o n d i t i o n s a r e favourable, such a s favourable thermal c o n d i t i o n s and c l o s e proximity of ground water dur-

ing s e a s o n a l f r e e z i n g of t h e ground, o r in t h e c a s e of f r e e z i n g from below ( i f t h e h e a t i s absorbed by t h e underlying f r o z e n l a y e r s ) . The migration of moisture a l s o l e a d s t o i t s r e d i s t r i b u t i o n w i t h i n t h e ground, so t h a t mineral

l a y e r s become somewhat l e s s s a t u r a t e d than was t h e c a s e b e f o r e t h e freeze-up, because of moisture migration t o t h e p l a c e s of formation of i c e l a y e r s .

In

t h e absence of an e x t e r n a l water supply, t h e t o t a l i n c r e a s e i n t h e volume of f r e e z i n g s o i l i s much s m a l l e r than when t h e f r e e z i n g f r o n t l i e s c l o s e t o a water source, 1.e. where t h e groundwater l e v e l i s nearby. Table

I11 c o n t a i n s t h e r e s u l t s of some volume d e t e r m i n a t i o n s of s o i l samples c a r r i e d o u t a t t h e Laboratory of Physics and S o i l Mechanics of t h e I n s t i t u t e of

On t h e b a s i s of given examples a s w e l l a s o t h e r numerous f i e l d observa- t i o n s and l a b o r a t o r y s t u d i e s , we may a r r i v e a t t h e following conclusions.

The f r e e z i n g of s o i l s where t h e r e i s an inflow of water gives r i s e t o t h e l a r g e s t i n c r e a s e i n volume i n s i l t y s o i l s . The slower t h e r a t e of f r e e z i n g , t h e g r e a t e r t h e I n c r e a s e i n volume ( s e e samples

3

and 4 i n Table 111), s i n c e i n t h i s case a l a r g e r amount of water has enough time t o overcome t h e r e e i s t - ance t o i t s movement and a r r i v e s a t t h e f r e e z i n g f r o n t . When t h e r e i s an e x t e r n a l water supply and t h e f r e e z i n g r a t e i s slow, t h e i n c r e a s e i n ground volume may vary between a few and s e v e r a l t e n s of p e r c e n t . The i n c r e a s e In

volume of c l a y t a k e s p l a c e both i n t h e region of c o n s i d e r a b l e changes i n t h e phase composition of water and i n t h e i n t e r m e d i a t e region ( ~ s y t o v i c h , 1955a). Some c l a y s continue t o i n c r e a s e i n volume r i g h t up t o temperatures of -30°C and lower ( e . g . t h e J u r a s s i c c l a y n e a r Moscow). The i n c r e a s e i n volume of sand i s much l e s s , t a k e s p l a c e a t a f a s t r a t e and i s p r a c t i c a l l y over a t temperatures of -0.5 o r -1°C.

2 . F r o s t H e a v i n ~ of S o i l

F r o s t heaving of s o i l i s t h e e x t e r n a l r e s u l t of t h e I n c r e a s e i n i t s volume, which a f f e c t s road s u r f a c e s , s t r u c t u r a l foundations, e t c . A s i s t h e case with t h e I n c r e a s e in ground volume on f r e e z i n g , t h e e x t e n t of f r o s t heaving depends on t h e amount of water p r e s e n t in t h e ground p r i o r t o f r e e z e - up and water drawn t o t h e f r e e z i n g f r o n t d u r i n g migration.

If: hheav i s amount of f r o s t heaving of s o i l ,

w i s moisture c o n t e n t of s o i l I n terms of weight,

ySk i s u n i t weight of s o i l s k e l e t o n , h i s depth of f r e e z i n g of s o i l ,

lo i s r e l a t i v e I c e c o n t e n t of s o i l ,

Q i s volume of water drawn t o t h e f r e e z i n g f r o n t d u r i n g migration and i f t h e s p e c i f i c g r a v i t y of water is e q u a l t o one and i t i s assumed t h a t t h e average i n c r e a s e In t h e volume of water on changing from l i q u i d t o s o l i d s t a t e i s

g$,

then:

hheav =

0.09

wyskhio

+

1.09 Q. (3.1)

The amount of water drawn t o t h e f r e e z i n g f r o n t w i l l be p r o p o r t i o n a l t o the migration r a t e v and t h e time t , i .e

.

we may assume t h a t :

Q =

/

vdt. ( 3 - 2 )

Assuming t h a t t h e Darcy's law l a a p p l i c a b l e i n t h e c a s e of water migra- t i o n , we may w r i t e :

where k i s t h e c o e f f i c i e n t of m i g r a t i o n which is analogous t o t h e c o e f f i c i e n t of f i l t r a t i o n b u t has a d i f f e r e n t numerical value;

I I s t h e h y d r a u l i c g r a d i e n t e q u a l t o t h e r a t i o of t h e l o s s i n p r e s s u r e t o t h e l e n g t h of m l g r a t l o n 1.

The h y d r a u l i c g r a d i e n t i n f r e e z i n g s o i l may b e due t o v a r i o u s c a u s e s . Generally speaking, t h e l e n g t h of m i g r a t i o n 1 w i l l vary and i n 0011 of a given cornposltion w i l l depend on t h e d e p t h of f r e e z i n g h and on t h e d i s t a n c e from t h e p o u n d s u r f a c e t o t h e ground w a t e r l e v e l ho.

We may assume t h a t 1 = h

-

_ho

'

A s i s known, t h e h y d r a u l i c g r a d i e n t i s e q u a l t o :

A t p r e s e n t t h e r e Is no uniform o p i n i o n on how t o determine t h e a c t i n g p r e s s u r e P _{a c t '} 1 . e . t h e p r e s s u r e r e s p o n s i b l e f o r t h e m i g r a t i o n of w a t e r towards t h e f r e e z i n g f r o n t . There i s a s e r i e s of hypotheses, which a g r e e , more o r l e s s , with p r a c t i c a l e x p e r i e n c e . The p r o c e s s of m i g r a t i o n i s t h e outcome of a combination of f o r c e s , which a r e molecular f o r c e s b u t may a p p e a r i n v a r i o u s forms and d i f f e r e n t combinations.

The s i m p l e s t h y p o t h e s i s i s t h e one concerning t h e meniscus ( c a p i l l a r y ) f o r c e s , a c c o r d i n g t o which

'act rn 'capa

It is assumed f u r t h e r t h a t t h e meniscus f o r c e s may be p r e s e n t i n t h e f r e e z i n g s o i l a l s o , s i n c e enclosed a i r bubbles a r e almost i n v a r i a b l y p r e s e n t even i n w a t e r - s a t u r a t e d sand. For example, t h e r e s u l t s of d i r e c t determina- t i o n s show t h a t t h e a i r c o n t e n t i n a r t i f i c i a l l y f r o z e n , w a t e r - s a t u r a t e d sand ( i n t h e p r e s e n c e of a r t i f i c i a l , water Impermeable f r o z e n l a y e r s ) may r e a c h

2

-

7%.

By t a k i n g t h e view t h a t f r e e z i n g s o i l i s n o t completely s a t u r a t e d w i t h w a t e r , we can assume t h a t m i g r a t i o n of w a t e r may be due t o t h e d i f f e r e n c e i n vapour p r e s s u r e i n t h e a i r bubbles contained i n t h e ground water, 1 . e . we may a p p l y t h e h y p o t h e s i s of t h e s o - c a l l e d " a i r vacuoles" suggested by M.N.

C)olldshtein I n 1940.

According t o t h i s h y p o t h e s i s , t h e m i g r a t i o n of water t a k e s p l a c e a s a r e s u l t of d i f f e r e n c e s i n vapour p r e s s u r e n e a r t h e f r e e z i n g boundary and i n s t i l l deeper l a y e r s , which i n t u r n depends on t h e t e m p e r a t u r e of t h e ground i n a given a r e a . Then t h e p r e s s u r e w i l l be e q u a l t o ( G o l ' d s h t e i n , 1940):

where q ,

-

q,

i s

t h e d i f f e r e n c e i n vapour p r e s s u r e i n mm of t h e mercury column a t temperatures 3 , and 3,.

By c o n s i d e r i n g e q u a t i o n ( 3 . 4 ) and by s u b e t i t u t i n g P from e q u a t i o n ( 3 . 5 ) i n t o e q u a t i o n ( 3 . 2 ) , we o b t a i n :

R . R u c k l i i followed by H.A. Puzakov adopted a somewhat d i f f e r e n t approach t o t h e d e t e r m i n a t i o n of maximum h e a v i n g o f s o i l by b a s i n g t h e i r arguments on t h e s t u d i e s of A . Ducker and ff. Beskov. In p a r t i c u l a r , b o t h R u c k l i i and

Puzakov assume t h a t t h e s o i l p o s s e s s e s a s p e c i a l " p r o p e r t y of sucking i n " t h e m o i s t u r e on f r e e z i n g , which depends on t h e s o - c a l l e d " s u c t i o n f o r c e " (Puzakov, R u c k l i i and Dficker, 1948; Gol'dshtein, 1948).

On t h e b a s i s of i n v e s t i g a t i o n s by ~ u c k e r and Beskov, R u c k l i i assumes t h a t s u c t i o n f o r c e s v a r y and a r e i n a l i n e a r r e l a t i o n s h i p w i t h d e p t h of f r e e z i n g . Hence he o b t a i n s :

where p i s maximum s u c t i o n f o r c e n e a r t h e ground s u r f a c e , s o

h i s d e p t h o f f r e e z i n g ,

hcr i s d e p t h a t which s u c t i o n f o r c e s a r e e l i m i n a t e d by e x t e r n a l pres- s u r e s , which a r e determined by c o n s i d e r i n g t h e weight of s o i l i t s e l f . By t a k i n g

where y, i s u n i t weight of w a t e r , and by u s i n g e q u a t i o n

( 3 . 3 ,

we o b t a i n :

F u r t h e r s l m p l i f i c a t i o n s were made by N.A. Puzakov by assuming t h a t : ( a ) t h e s u c t i o n f o r c e i s c o n s t a n t , 1 . e . pa = c o n s t ,

( b ) t h e depth of f r e e z i n g i n r e l a t i o n t o time i s determined by t h e e m p i r i c a l formula :

where Ymax i s maximum depth of ground f r e e z i n g i n a given p l a c e ; 'win i s average w i n t e r temperature.

The c a l c u l a t e d v a l u e s of t h e h e i g h t of ground s u c t i o n adopted by

N . A . Puzakov on t h e b a s i s of i n v e s t i g a t i o n s a t t h e Research I n s t i t u t e of Road Construction, and t h e s t u d i e s of Docker and o t h e r s , a r e shown i n Table

IV.

According t o Puzakov, t h e q u a n t i t y of m i g r a t i n g water i s : k P,

Q =

a (ho 2.3 l o g ho

ho

-

J2at

where a i s c l i m a t i c c o e f f i c i e n t e q u a l t o :

It i s , of course, e s s e n t i a l t o regard equation (3.10) a s an approximate formula f o r t h e c a l c u l a t i o n of maximum ground heaving, s i n c e t h e c a l c u l a t e d value of t h e h e i g h t of s o i l s u c t i o n i s n o t p r e c i s e .

3 .

The Squeezing Out of Water i n F r e e z i n g Sand

A s i s known from numerous o b s e r v a t i o n s , t h e i n c r e a s e i n t h e volume of sand on f r e e z i n g amounts t o f r a c t i o n s of a p e r c e n t , even i f t h e r e i s an e x t e r n a l inflow of water. On t h e o t h e r hand, t h e change i n t h e volume of water on f r e e z i n g i n q u a n t i t i e s corresponding t o t h e volume of p o r e s i n t h e sand may reach s e v e r a l p e r c e n t . It f o l l o w s t h a t i n f r e e z i n g sand, water i n t h e excess of pore volume i s squeezed out, away from t h e f r e e z i n g f r o n t . A s

i n d i c a t e d by p r a c t i c a l experience, f o r example d u r i n g r i n g - l i k e f r e e z i n g of sandy s o i l s i n s h a f t s i n k i n g , water i s squeezed o u t i n t o t h e c e n t r a l p a r t of t h e s h a f t and i t s removal r e q u i r e s i n s t a l l a t i o n of p e r f o r a t e d p i p e s . The problem i s , does t h e volume of sand change on f r e e z i n g around f i s s u r e s I n open systems, 1 . e . d u r i n g an u n i n h i b i t e d l a t e r a l outflow of water?

S p e c i a l experimental s t u d i e s of t h i s problem ( ~ s y t o v i c h , 1955b) I n d i c a t e t h a t when u n i n h i b i t e d squeezing o u t of water I n one o r s e v e r a l d i r e c t i o n s i s p o s s i b l e b u t l a t e r a l expansion of t h e m i n e r a l s k e l e t o n of sand i s n o t ,

f r e e z i n g of sand t a k e s p l a c e without any change i n i t s pore volume. On t h e o t h e r hand, i f t h e r e i s

a

p o s s i b i l i t y of l i m i t e d expansion i n one d i r e c t i o n , f r e e z i n g of water-saturated sand r e s u l t s i n a change of i t s pore volume of up t o 1

-

2$, while t h e p o s s i b i l i t y of expansion i n a l l d i r e c t i o n s l e a d s t o changes of up t o 4%.

During t h e u n r e s t r i c t e d f r e e z i n g of a water-saturated sand l a y e r dh i n time d t , t h e volume of water which exceeds t h e pore volume of s o i l due t o expansion B w i l l be pushed o u t sideways on f r e e z i n g . The volume of e x c e s s water Q w i l l be e q u a l t o :

According t o Darcy's law, t h e volume of water f i l t e r e d

i n

time d t i s e q u a l t o : and from t h i s dh where i s r a t e of f r e e z i n g of s o i l , I i s h y d r a u l i c g r a d i e n t , k

i s

c o e f f i c i e n t of f i l t r a t i o n , n i s p o r o s i t y of s o i l .

The r a t e of f r e e z i n g depends on c o n d i t i o n s under which i t i s t a k i n g p l a c e , t h e moisture c o n t e n t and t h e thermophysical p r o p e r t i e s of s o i l , and is t h e r e f o r e n o t a c o n s t a n t f a c t o r , even i n t h e case of t h e same sand d e p o s i t . However, i t i s e a s i l y c a l c u l a t e d i n each case.' The d e t e r m i n a t i o n of t h e h y d r a u l i c g r a d i e n t i s more d i f f i c u l t and r e q u i r e s s p e c i a l t r e a t m e n t in each c a s e .

According t o K h .R. Khakimov ( 1957), we may assume t h a t in t h e case o f sand f r e e z i n g n e a r a f i s s u r e i n a homogeneous d e p o s i t :

I n t h e c a s e of water-bearing sand l o c a t e d between water Impermeable l a y e r s :

where 1 i s l e n g t h of p o s s i b l e f r e e e x i t of water,

P i s p r e s s u r e which i s numerically equal t o t h e d i s t a n c e between ground- water l e v e l and depth of occurrence of t h e given sand horizon.

According t o e q u a t i o n ( a 3 ) , t h e minimum c o e f f i c i e n t of f i l t r a t i o n which corresponds t o c o n d l t l o n s l e a d i n g t o squeezing o u t of water from f r e e z i n g sand may be determined by:

Pn dh k = - -

I d t '

If t h e a c t u a l c o e f f i c i e n t of f i l t r a t i o n of sand i s g r e a t e r t h a n t h a t c a l c u l a t e d by means of e q u a t i o n ( 3 . 1 1 ) , vrater w i l l be squeezed o u t on f r e e z i n g vlithout d i s turbine; t h e s t r u c t u r e of t h e sand.

It h a s been e s t a b l i s h e d by c a l c u l a t i o n s t h a t t h e minimum c o e f f i c i e n t of f i l t r a t i o n which w i l l o t i l l a f f e c t t h e squeezing o u t of water does n o t exceed 0.1

-

0.2 m/day. Usually, hourever, t h e sand has a l a r g e r c o e f f i c i e n t of f i l - t r a t i o n amounting t o 1

-

20 m/day. Therefore, i n most c a s e s i n v o l v i n g t h e f r e e z i n g of water-bearing sand under c o n d i t i o n s o f an u n r e o t r i c t e d outflow of water, t h e e x c e s s water w i l l be squeezed o u t due t o t h e i n c r e a s e i n i t s volume on c h a n ~ i n g from l i q u i d t o s o l i d s t a t e . Since water p r e s s u r e d i e s o u t i n t h e sand a t a c o n s i d e r a b l e d i s t a n c e , water may continue t o be squeezed o u t even i n t h e case of i t s u n r e s t r i c t e d e x i t b e i n g f a r removed from t h e f r e e z i n g a r e a .

If t h e e x i t of vrater i s u n r e s t r i c t e d i n t h e p r o c e s s of f r e e z i n g and during blockage of t h e sand with i c e , and I f l a t e r a l expansion of t h e water i s n o t p o s s i b l e , a c o n s i d e r a b l e I n c r e a s e i n volume may be observed on f r e e z i n g of water-bearing sand a l s o .

By making use of moisture m i g r a t i o n i n f r e e z i n g f i n e - g r a i n e d s o i l s and by c r e a t i n g a p p r o p r i a t e c o n d i t i o n s f o r t h i s , i t i s p o s s i b l e t o reduce t h e t o t a l moisture and i c e c o n t e n t s of s o i l s , 1 . e . t o d r a i n them t o a c e r t a i n e x t e n t .

A t t h e same time, in f i n e - g r a i n e d water-saturated s o i l s with c o e f f i c i e n t s of f i l t r a t i o n i n t h e o r d e r of hundredths and thousandths of a metre p e r day, t h e squeezing o u t of water on f r e e z i n g

i s

v e r y d i f f i c u l t i f n o t impossible, s i n c e such s o i l s have p r a c t i c a l l y no f r e e vrater, while water p r e s s u r e a r i s i n g i n i n d i v i d u a l , r e l a t i v e l y l a r g e c a v i t i e s d i e s out almost a t once.

I n accordance ~ 1 1 t h t h e physico-chemical t h e o r y of m i g r a t i o n ( ~ y u t y u n o v , 1955), a l l water ( f r e e and bound) i n f r e e z i n g f i n e - g r a i n e d s o i l s i s d i s p l a c e d due t o t h e e f f e c t of t h e m a d l e n t of chemical p o t e n t i a l , b u t Is accumulated i n l a r g e q u a n t i t i e s i f t h e l a t t e r c o i n c i d e s with t h e temperature g r a d i e n t .

Migration of water t a k e s p l a c e n o t o n l y i n t h e course of f r e e z i n g b u t in t h e f r o z e n s t a t e a s w e l l (Tyutyunov, 1 9 5 1 ) ) s i n c e f r o z e n s o i l does c o n t a i n some unfrozen water ( ~ s y t o v i c h , 1947 )

.

The d e s c r i b e d phenomena e q a b l e s T.A. Tyutyunov t o suggest a s p e c i a l type of d r a i n a g e of f r o z e n s o i l s . Drains of s t o n e o r any o t h e r m a t e r i a l which i s a b e t t e r conductor of h e a t than t h e surrounding ground a r e i n s t a l l e d a t a c e r t a i n d e p t h below t h e s u r f a c e , I n t h e l a y e r which thaws i n t h e summer

t h e s u r r o u n d i n g ground. I f auch d r a i n s a r c i n s t a l l e d i n f l n e - g r a i n e d s o i l s s a t u r a t e d w i t h vratcr, t h e n a c c o r d i n g t o I. A. Tyutyunov, t h e groundwater w i l l

m i g r a t e t o t h e dl-nino, f r e e z e and f i l l t h e open s p a c e s 1 ~ 1 t h I c e which v r i l l

remain t h e r e throuphout t h e w i n t e r .

In

t h e surmner tlie i c e accumulated i n t h i s way t u r n s t o f r e e w a t e r which i s n o t r e t a i n e d by t h e s u r f a c e s of s o l i d p a r t i - c l e s and r u n s o f f a l o n g t h e d r a i n s . In t h i s way weakly bound w a t e r t u r n s t o f r e e w a t e r , and may be e a s i l y removed from t h e ground. We should n o t e t h a t a l t h o u g h t h e r e h a s been one s u c c e s s f u l a p p l i c a t i o n of d r a i n a g e of f r o z e n ground, t h i s method i s s t i l l I n t h e e x p e r i m e n t a l s t a g e .

2. P h y s i c a l P r o p e r t i e s o f Frozen S o i l and I c e

1. P h y s i c a l P r o p e r t i e s of Frozen S o i l

As i s lmorm ( ~ s y t o v i c h and Sumgin,

1937),

t h e i n h e r e n t c h a r a c t e r i s t i c o f f r o z e n s o i l , a p a r t from I t s n e g a t l v e t e m p e r a t u r e , is t h e p r e s s u r e o f i c e which forms when t h e p o u n d f r e e z e s and cements t h e m i n e r a l s o i l p a r t i c l e s .

The i c e c o n t e n t i s a s p e c i a l p h y s i c a l p r o p e r t y o f f r o z e n s o i l . D i s t i n c - t i o n s a r e made between r e l a t i v e i c e c o n t e n t lo, which i s t h e r a t i o o f t h e vreight o f i c e and t h e t o t a l weight of w a t e r

In

t h e f r o z e n ground, s a t u r a t i o n w i t h i c e o r i c e c o n t e n t by weight I, which i s t h e r a t i o o f t h e weight o f i c e and t h e t o t a l vreight o f s o i l i n i t s n a t u r a l s t a t e , and i c e c o n t e n t b y volume

-

t h e r a t 1 0 of i c e volume and t h e p o u n d volume.

Frozen s o i l s o u l d be regarded a s a four-component system of p a r t i c l e s . The p h y s i c a l p r o p e r t i e s of t h i s system a r e c o m p l e t e l y d e f i n e d by f o u r f a c t o r s : s p e c i f i c g r a v i t y o f t h e alceleton of f r o z e n s o i l y weight p e r u n i t volume o f

SP

'

u n d i s t u r b e d f r o z e n s o i l Y , t o t a l m o i s t u r e c o n t e n t o f s o i l Wtot ( t h e r a t i o o f t h e weight o f a l l t y p e s of w a t e r and t h e t o t a l weight o f s o i l , 1.e. t h e

m o i s t u r e c o n t e n t determined in a f r e s h sample of s o i l ) , and r e l a t i v e

ice

uon-

t e n t 1,. l n s t e a d of mentioned f a c t o r s ySp, y , Wtot, and lo, u s e i s o f t e n made o f f o u r o t h e r I n d i c a t o r s of p h y s i c a l p r o p e r t i e s o f f r o z e n s o i l : ysp, y, NU,

and Wt, where WU i s t h e amount o f unfrozen w a t e r i n f r o z e n s o i l r e l a t i v e t o t h e weight o f d r y s o i l , and Wt i s t h e t o t a l m o i s t u r e c o n t e n t of f r o z e n s o i l a g a i n i n r e l a t i o n t o t h e weight o f d r y s o i l . The main i n d i c a t o r s o f p h y s i c a l p r o p e r t i e s and formulae f o r t h e d e t e r m i n a t i o n o f i c e c o n t e n t , volume of g a s e s , and o t h e r components o f f r o z e n s o i l a r e shown i n Table V ( ~ s y t o v i c h , 1952).

2. P h y s i c a l P r o p e r t i e s of I c e

S p e c i f i c g r a v i t y of p u r e s o l i d i c e a t oOC and normal atmospheric p r e s s u r e i s 0.9168 p;/cm3.

Apart from a c t u a l i c e (H,o), n a t u r a l i c e a l s o c o n t a i n s s a l t s o l u t i o n s , m i n e r a l and o r g a n i c m a t t e r , a i r p o r e s and u n f r o z e n w a t e r .

The volume of pores v a r i e o c o n s i d e r a b l y , from a few i n d i v i d u a l p o r e s , which have p r a c t i c a l l y no e f f e c t on t h e d e n s i t y of i c e , t o

50$

of t h e t o t a l

volume of i c e .

On t h e b a s i s of s i z e , t h e p o r e s i n t h e i c e may be divided i n t o t h r e e t y p e s : (1) macropores which r e a c h up t o 1 mm i n diameter and more and a r e seen by nalced eye; ( 2 ) micropores seen by means of a microscope, and

( 3 )

u l t r a p o r e s which may b e d e t e c t e d o n l y by i n d i r e c t methods, e.g. from a d s o r p t i o n c a p a c i t y of l i g h t and heavy molecules. On formation, u l t r a p o r e s and micropores tend t o assume a more s t a b l e s p h e r i c a l form. The pores become completely f i l l e d , a s t h e main i c e mass becomes more compact. C a p i l l a r i e s (micropores) break up with time and a r e transformed i n t o s p h e r i c a l pores. Development of pores i s connected with formation of t h e s u r f a c e of s e p a r a t i o n

and depends on t h e s u r f a c e energy of marginal phases under c o n d i t i o n s of e q u i l i b r i u m , p r o v i d i n g t h e s u r f a c e formation is i s o t h e m i c and r e v e r s i b l e . The presence of

a

l i q u i d phase i n i c e i s due e i t h e r t o l o c a l overheating, o r t o t h e presence of s a l t s , o r t o an i n c r e a s e i n p r e s s u r e .

C r y s t a l s of which n a t u r a l i c e i s composed a r e d i s t i n c t l y a n i s o t r o p i c i n t h e i r mechanical p r o p e r t i e s . P l a s t i c deformation t a k e s p l a c e i n t h e i c e i n t h e presence of a f o r c e p a r a l l e l t o t h e b a s a l p l a n e of i c e c r y s t a l s . The c r i t i c a l f o r c e n e c e s s a r y f o r t h e d e s t r u c t i o n of molecules in t h e b a s a l p l a n e

i s much l a r g e r than t h e f o r c e , r e s u l t i n g i n s l i d i n g , t h e r e f o r e displacements a l o n g t h e b a s a l plane do n o t lead t o d e s t r u c t i o n . If t h e f o r c e a c t s a l o n g t h e o p t i c a l c r y s t a l a x i s , the e l a s t o - p l a s t i c displacement i s much s m a l l e r than t h e deformation i n t h e b a s a l p l a n e .

Deformation of a c r y s t a l i s a t a minimum, i f t h e f o r c e

i s

a c t l n g a l o n g t h e b a s a l plane b u t t h e displacement plane i s p e r p e n d i c u l a r t o it. In t h i s c a s e p l a s t i c deformation i s s o i n s i g n i f i c a n t t h a t b r i t t l e f a i l u r e s e t s i n beyond the r e g i o n of e l a s t i c deformation ( 0 . l#lyugge, 1899-1900).

The r e g i o n where p u r e l y e l a s t i c p r o p e r t i e s of i c e make themselves f e l t i s

very small and it i s very d i f f i c u l t t o s e p a r a t e t h i s r e g i o n f o r experimental purposes. It Is assumed t h a t t h e e l a s t i c l i m i t of i c e does n o t exceed

0 . 1 k@;/cm2.

According t o t h e most r e c e n t s t u d i e s ( ~ e r d e n n i k o v , 1950), t h e e l a s t i c

l i m i t of i c e E amounts t o 111

.

103 when t h e o p t i c a l c r y s t a l a x i s i s

cm2

'

p e r p e n d i c u l a r t o t h e l e n g t h of t h e sample and t h e temperature

i s

-8OC, while i n t h e case of o p t i c a l axes being p a r a l l e l t o t h e l e n g t h of t h e sample i t i s e q u a l t o

97

.

103 1 . e . i n t h e f i r s t case t h e e l a s t i c l i m i t i s 12$ h i g h e r .

cm2

'

With i n c r e a s e i n p o r o s i t y of i c e , i t s e l a s t i c l i m i t begins t o d e c r e a s e . However, t h e v a r i a t i o n i n p o r o s i t y does n o t exceed 2.5% and i t s e f f e c t on t h e e l a s t i c l i m i t i s n e g l i g i b l e (Save1 lev, 1953 )

.

Previous I n v e s t i g a t o r s (Veinberg, 1940) have e s t a b l i s h e d t h a t w i t h a drop i n temperature, t h e e l a s t i c modulus of i c e 1s i n c r e a s e d .

The presence of s o l i d s a l t s i n t h e i c e h a s no s 1 e ; n i f i c a n t e f f e c t on t h e modulus of e l a s t i c i t y , b u t t h e p r e s e n c e of a l i q u i d phase h a s a marked e f f e c t on i t s e l a s t i c p r o p e r t l e s . According t o experiments c a r r i e d o u t by B.A.

S a v e l f e v (1953), t h e e l a s t i c modulus of s e a i c e may d e c r e a s e by

50$

and more with an i n c r e a s e i n t h e l i q u i d phase. The a n l s o t r o p y i s e s p e c i a l l y n o t i c e a b l e in t h e v i s c o s i t y o f i c e ( ~ h a n i n a and Shul'man, 1949). In t h e p r e s e n c e of a f o r c e a c t i n g a l o n g t h e o p t i c a l a x i s , t h e c o e f f i c i e n t of v i s c o s i t y i s approximately

lo4

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

ax able

vI).

The v i s c o s i t y of s e a i c e i s lower t h a n t h a t of f r e s h - w a t e r i c e . Between temperatures of -1 and -20°C and when t h e s a l t c o n t e n t v a r i e s between 1 and

2@, t h e c o e f f i c i e n t o f v i s c o s i t y f l u c t u a t e s between 0.07 10" and 2.67 10" p o i s e s . For example, I n c a l c u l a t i o n s c o n c e r n i n g i s o t h e r m i c i c e s t r u c t u r e s a t - l ° C , M.M. Krylov u s e s q = 3

.

l o f 4

p o i s e s . 3 . Nechanical P r o p e r t i e s of Frozen S o i l 1. Some General C o n s i d e r a t i o n s

F r e e z i n g and thawing o f s o i l s a r e accompanied by changes in t h e i r mechan- i c a l p r o p e r t i e s r e s u l t i n g from phase t r a n s f o r m a t i o n s o f s o i l m o i s t u r e which have a marked e f f e c t on t h e cementation o f s o l i d m i n e r a l p a r t i c l e s w i t h i c e .

On f r e e z i n g o f w a t e r - s a t u r a t e d sand, p e b b l e s and o t h e r coarse-grained s o i l s i n t h e absence of u n r e s t r i c t e d r u n o f f o f w a t e r , t h e i n c r e a s e i n t h e volume o f water, a s was a l r e a d y a t a t e d , o f t e n changes t h e p o r o s i t y of t h e m i n e r a l s o i l s k e l e t o n by s e v e r a l p e r c e n t r e l a t i v e t o i t s i n i t i a l s t a t e . As

suggested by G.I. Lapkin, t h i s phenomenon i s sometimes c a l l e d " t h e s w e l l i n g " of 8011. The l o o s e n i n g of t h e m i n e r a l s k e l e t o n of f r o z e n s o i l s r e s u l t s from an i n c r e a s e i n t h e volume o f " c o n t a c t 1 ' m o i s t u r e i n t h e p o r e s on f r e e z i n g . It should be noted t h a t t h e s t r e n g t h of i c e cement formed i n t h i s way may be c o n s i d e r a b l e , making f r o z e n ground h i g h l y r e s i s t a n t t o e x t e r n a l f o r c e s . How- e v e r , when cementation d i s a p p e a r s t h e s o i l becomes more compact. The resist- ance of f r o z e n c l a y and c l a y loam t o e x t e r n a l f o r c e s depends on t h e i r

composition and on t h e degree of d i f f e r e n t i a t i o n i n t o compact m i n e r a l i n t e r - l a y e r s and I c e I n c l u s i o n s which appear on f r e e z i n g . For example, t h e s h e a r r e s i s t a n c e of f r o z e n a g g r e g a t e s o i l s under a r a p i d l y i n c r e a s i n g load i s , a s a r u l e , much g r e a t e r t h a n t h e r e s i s t a n c e of t h e same s o i l s b u t n o t i n a n

a g g r e g a t e s t a t e . On thawing, such s o i l s r e t a i n t h e i r i n c r e a s e d p o r o s i t y f o r a c e r t a i n p e r i o d of time which g r e a t l y I n c r e a s e s t h e i r p e r B m e a b i l i t y t o w a t e r and t h e r a t e o f s e t t l e m e n t due t o t h e i r own weight and t h e e x t e r n a l l o a d .

The most c h a r a c t e r i s t i c p r o p e r t y of a l l t y p e s o f f r o z e n s o i l s , e s p e c i a l l y a t a t e m p e r a t u r e c l o s e t o O°C (between -0.1 and - l O c ) , i s t h e e a s e of flow under a l o a d , r e s u l t i n g from t h e p l a s t i c p r o p e r t i e s of i c e and t h e p r e s e n c e o f t e n of c o n s i d e r a b l e amounts of water, a s f o r example i n c l a y , which d e t e r - mines t h e v i s c o s i t y of t h i s t y p e of f r o z e n s o i l . Due t o t h e i r marked flow, which depends a l s o on t h e t e m p e r a t u r e , t h e load r e s i s t a n c e of f r o z e n s o i l s i s g r e a t l y a f f e c t e d by t h e d u r a t i o n of t h e l o a d . If t h e l o a d is i n c r e a s e d r a p i d - l y b u t does n o t l a s t long, t h e r e s i s t a n c e of f r o z e n ground i s h i g h ( s i m i l a r t o t h a t of s t r u c t u r a l c o n c r e t e ) , b u t i n t h e p r e s e n c e o f a long-term load t h e

i n t e r n a l bonds between p a r t i c l e s of f r o z e n s o i l a r e weakened ( r e l a x e d ) and t h e r e s i s t a n c e i s g r e a t l y reduced. T h e r e f o r e , when c a l c u l a t i n g t h e r e s i s t a n c e o f f o u n d a t i o n s o i l s , i t i s e s s e n t i a l t o c o n s i d e r n o t t h e temporary r e s i s t a n c e o f f r o z e n s o i l t o e x t e r n a l load by l n t r o d u c l n g an a p p r o p r i a t e c o e f f i c i e n t o f s a f e t y , b u t i t s long-term s t r e n g t h determined by c o n s i d e r i n g t h e r e l a x a t i o n o f l o a d s w i t h t i m e . On thawing, t h e s t r e n g t h o f f r o z e n s o i l s i s reduced in a n i r r e g u l a r f a s h i o n accompanied by t e x t u r a l and s t r u c t u r a l changes. The l a t t e r r e s u l t in

ground s e t t l e m e n t due t o compression when t h e load i s below a t h r e s h o l d v a l u e , c a u s i n g t h e s o i l t o b e p r e s s e d o u t from below t h e a r e a under l o a d , and i n a slump when t h e load i s g r e a t e r t h a n t h i s t h r e s h o l d v a l u e . Slumps a r e observed mainly on thawing of c l a y e y s o i l , c l a y loam and s i l t c o n t a i n i n g l a r g e q u a n t i -

t i e s of i c e . Deformation r e s u l t i n g from a change i n i c e volume on m e l t i n g o c c u r s a l s o i n sand and g r a v e l , which can s e t t l e t o a c o n s i d e r a b l e e x t e n t on thawing b u t soon become s t a b i l l z e d a g a i n .

2 . I n t e r n a l Mechanical Bonds and D e f o r m a b i l i t y o f Frozen S o i l

The load r e s i s t a n c e o f f r o z e n ground i s determined by t h e s t r e n g t h o f i n t e r n a l bonds between i n d i v i d u a l p a r t i c l e s , which form a g g r e g a t e s o f f r o z e n s o i l s , and t h e s t r e n g t h of bonds between t h e s e a g g r e g a t e s . It i s v e r y d i f - f i c u l t t o s t u d y t h e n a t u r e of i n t e r n a l bonds because of complex i n t e r a c t i o n s o f v a r i o u s components of f r o z e n s o i l s . These bonds a r e u s u a l l y termed

cohesion.

Cohesion o f f r o z e n s o i l s i s t h e i r b a s i c mechanical c h a r a c t e r i s t i c s i n c e a l l a s p e c t s o f t h e i r l o a d r e s i s t a n c e a r e d i r e c t l y r e l a t e d t o i t .

In

p a r t i c u - l a r , t h e b e a r i n g c a p a c i t y and t h e s t a b i l i t y o f f r o z e n f o u n d a t i o n s o i l s depend mainly on t h e c o h e s i v e f o r c e s . T h e r e f o r e t h e s t u d y o f i n t e r n a l bonds which determine t h e v a l u e s of c o h e s i v e f o r c e s i s one o f t h e most i m p o r t a n t t a s k s of

Cohesion of f r o z e n s o i l s may be r e g a r d e d an c o n s i s t i n g of t h r e e components.

T h e moot i m p o r t a n t form 1s c o h e s l o n by ccrilentation, r e o u l t i n g from bonds betwccn i c e c r y s t a l s and m i n e r a l p a r t i c l e s . It depends f i r s t of a l l on t h e i c e c o n t e n t and t e m p e r a t u r e of t h e f r o z e n s o i l , a s w e l l a s on i t s rncchanical and m i n e r a l o ~ i c a 1 c o n ~ p o s i t i o n . Under n a t u r a l c o n d i t l o n a i t h a s no c o n s t a n t v a l u e e v e n i n t h e same t y p e of s o i l and may v a r y vrith t i m e , depending on s e a s o n a l v a r i a t i o n s i n t h e t e ~ r i p e ~ a t u r e of f r o z e n s o i l . On thawing, c o h e s i o n b y cementation i s e l i m i n a t e d .

Piolecular cohesion r e s u l t s from f o r c e s of m o l e c u l a r a t t r a c t i o n between m i n e r a l s o i l p a r t i c l e s and depends on t h e a r e a of c o n t a c t s u r f a c e s o f t h e s e p a r t i c l e s and t h e d i s t a n c e s between them. A s the ground becomes more compact,

t h i s t y p e of c o h e s i o n i s increased, 1.e. It l a a f u n c t i o n of p r e s s u r e . F i n a l l y , s t r u c t u r a l c o h e s i o n r e f l e c t s t h e e f f e c t of d i v e r s e p h y s i c a l , physico-chemical, mechanical and o t h e r p r o c e s s e s t a k i n g p l a c e w i t h i n t h e r o c k i n t h e c o u r s e of i t s g e o l o g i c a l f o r m a t i o n and c a u s i n g an i n c r e a s e i n c o h e s i o n r e l a t i v e t o what i t was a t f l r s t . lh f r o z e n s o i l s t h i s form of c o h e s i o n a l s o r e f l e c t s t h e changes i n t h e i r s t r u c t u r e ~ h i c h o c c u r r e d on t h e f r e e z i n g of groundwater. The s u b d l v l s l o n o f c o h e s i o n i n t o components and t h e terms

a p p l i e d t o them a r e a r b i t r a r y , s i n c e a l l forms of c o h e s i o n depend on m o l e c u l a r a t t r a c t i o n . However, i t e n a b l e s u s t o form a f a i r l y c l e a r p i c t u r e o f deforma- t i o n p r o c e s s e s I n f r o z e n s o i l s , t h e n a t u r e o f which i s d e s c r i b e d below

(Vyalov, 1954 )

.

It i s known ( ~ s y t o v i c h and Sungin, 1937) t h a t t h e load a p p l i e d t o f r o z e n ground c a u s e s a concentration o f s t r e s s e s a t t h e c o n t a c t s between m i n e r a l p a r t i c l e s and i c e c r y s t a l s . P l a s t i c f l o w of i c e talces p l a c e . - c r e a s e I n p r e s s u r e l e a d s t o a d e c r e a s e i n t h e m e l t i n g t e m p e r a t u r e of i c e and d i s t u r b s t h e e q u i l i b r i u m between f i l m w a t e r and I c e which i s I n c o n t a c t w i t h It. A s a

r e s u l t , i c e melts i n p l a c e s o f I n c r e a s e d p r e s s u r e and forms more f i l m w a t e r , which under t h e i n f l u e n c e o f t h e p r e s s u r e g r a d i e n t i s d i s p l a c e d from t h e h i g h p r e s s u r e r e g i o n t o t h e zone where t h e p r e s s u r e i s lower. There It f r e e z e s a g a i n a f t e r a t t a i n i n g a s t a t e of e q u i l i b r i u m w i t h t e m p e r a t u r e and p r e s s u r e b u t some of i t may be p r e s s e d o u t o n t o t h e f r e e s u r f a c e . The f a c t t h a t i c e m e l t s and w a t e r i s d i s p l a c e d h a s been confirmed by experiments (Vyalov, 1 9 5 4 ) .

The p r o m s 3 of i c e m c l t i n ~ and w a t e r d i s p l a c e m e n t i n a p a r t i c u l a r s e c t i o n of t h e ground 13 accomparlied by a d e c r e a s e i n s t r u c t u r a l c o h e s i o n and c o h e s i o n

by c e n c n t a t i o n and t h i s r e s u l t s i n I r r e v e r s i b l e d e f o r m a t i o n . T h i s d e f o r m a t i o n may o c c u r o n l y a t a p r e s s u r e h i g h e r t h a n t h e f o r c e s o f i n t e r n a l i n t e r a c t i o n d e t e r m i n i n g t h e s t a t e of e q u i l i b r i u m i n t h e system: u n f r o z e n w a t e r

-

I c e

-

m i n e r a l p a r t i c l e s . Of major importance i n t h i s c o n n e c t i o n i s t h e v a l u e of t h e

i n i t i a l p r e s s u r e g r a d i e n t and ~ r l i c t t ~ r o r n o t u n f r o z e n w a t e r i s firm]-y h e l d , which d e t e r m i n e s t h e g o o o i b i l l t y of dlsplaceinent of f i l m w a t e r ( ~ i o z a , 1950). S i n c e t h e dlsplaccnlcnt of f i l n l w a t e r i n t h e p r o c e s s of ~ t r u c t u r a l d e f o r m a t i o n t a l t e s p l a c e g r c d u n l l y , t h i s deforn:ntion t a k e s p l a c e ~ ; r - a d u a l l y a l o o , 1 . e . t h e phenomenon of c r e e p i s obscrvcd.

The p l a c e which becolnes v a c a n t a s a r c s u l t of displacement of m o i s t u r e and a i r i s f i l l e d w i t h s o l i d p a r t i c l e s ; t h c o e a r e c l o s e l y packed under t h e i n f l u e n c e o f p r e s s u r e , and t h i s g i v e s r i s e t o m o l e c u l a r c o h e s i o n . Thus two m u t u a l l y opposed phenomena o c c u r i n t h e ground under t h e i n f l u c n c e of p r e s s u r e : on t h e one hand, t h e r e i s a weakenin6 ( r e l a x a t i o n ) of s t r u c t u r a l c o h e s i o n and c o h e s i o n by c e m e n t a t i o n , and on t h e o t h e r an l n c r e a a s e i n m o l e c u l a r c o h e s i o n , 1.e. s t r e n g t h e n i n g of t h e s o i l . If t h e load 1 3 such t h a t a l t h o u * i t l e a d s t o

s t r u c t u r a l d e f o r m a t i o n , i t does n o t excced a c e r t a i n t h r e s h o l d v a l u e , weaken- i n g w i l l be compensated b y s t r e n z t h e n i n g and a s t a t e o f e q u i l i b r i u m w i l l be r e e s t a b l i s h e d i n t h e ground w i t h t i m e , 1 . e . d e f o r m a t i o n v r i l l become s t a b i l i z e d . T h i s p r o c e s s may be regarded a s a t t e n u a t i n g c r e e p accompanied by changes i n

volume (compaction). I-Iov;ever, I f t h e load does exceed a c e r t a i n t h r e s h o l d v a l u e , t h e n d e s t r u c t i o n of I n t e r n a l bonds i s no l o n g e r compensated by

s t r e n g t h e n i n g and p l a s t i c - v i s c o u s f l o ~ v , o r s o - c a l l e d u n a t t e n u a t i n g d e f o r m a t i o n due t o c r e e p , o c c u r s i n t h e ground. I n time t h i s deforniatlon r e a c h e s t h e s t a g e of p r o g r e s s i n g f I-OIV, vrhich l e a d s t o t o t a l d e s t r u c t i o n of i n t e r n a l bonds, 1 . e . t o s o i l f a i l u r e .

A long-term f o r c e which if exceeded r e s u l t s i n u n a t t e n u a t i n g d e f o r m a t i o n

i s known a s t h e u l t i m a t e long-term s t r e n g t h ( o r t h e u l t i m a t e long-term

r e s i s t a n c e ) o f f r o z e n ground. In o t h e r urords, t h e u l t i m a t e long-term s t r e n g t h c o r r e s p o n d s t o such a s t r e s s , p r i o r t o which u n a t t e n u a t l n g d e f o r m a t i o n does n o t s e t i n i r r e s p e c t i v e of t h e d u r a t i o n of l o a d , b u t i f i t i s exceeded t h e n f a i l u r e v r i l l o c c u r w i t h t i m e . On t h e b a s i s of vihat h a s been s a i d t h u s f a r and by c o n s i d e r i n g t h e s t u d i e s of d e f o r m a t i o n of f i n e - g r a i n e d u n f r o z e n and f r o z e n s o i l s , vre may d i s t i n g u i s l i f o u r t y p e s of d e f o r m a t i o n of f r o z e n ground ( ~ e n i s o v , 1951; Vyalov,

1954;

T a y t o v i c h , 1954) :

( 1 ) E l a s t i c d e f o r m a t i o n r e s u l t i n g from c l a o t i c changes i n m i n e r a l and i c e l a t t i c e s , a s w e l l a s from e l a s t i c compression of m o i s t u r e and a i r c o n t a i n - ed I n f r o z e n ground.

( 2 ) R e v e r s i b l e a d s o r p t i o n d e f o r m a t i o n r e s u l t i n g from changes i n t h e t h i c k n e s s of w a t e r f I l 1 : ~ ~ and i n volume of w a t e r a t t h e c o n t a c t s between s o l i d p a r t i c l e s , which o c c u r due t o e x t e r n a l p r e s s u r e s and phase t r a n s f o r m a t i o n s of w a t e r and changes I n t h e c o n t a c t s u r f a c e s of i c e .

( 3 ) S t r u c t u r a l d e f o r ~ r l n t i o n due t o conlpaction r e s u l t i n g from i r r e v e r s i b l e phase transformation of I c e and m i g r a t i o n of m o i s t u r e formed i n t h i s way, and of a c e r t a i n anount of u n f r o z e n w a t e r , an w e l l a s a i r , whIcli l e a d s t o

s t r u c t u r a l changes ( r c n ~ ' r a n ~ c l t i c n t of ncr;regates ) acconlpanied by compaction of t h e s o i l ,

1 . e .

by reduction i n p o ~ o s i t y of i t s m i n e r a l s l t e l e t o n .

( 4 ) P l a s t i c - v i s c o u a deformation vrliich o c c u r s v ~ i t h o u t any changes I n s o l l v o l w ~ ~ e and r e s u l t s from i s r c v e r s l b l c diaplaccnicnt o f particles and i c e flow.

The f i l , s t two t y p e s of d e f o r m a t i o n w e r e v e l > n i b l e , t h e l a s t two a r e i r r e v e r s i b l e . A s f a r 3s f r o z e n ground i s conccrncd, t h e l a s t tvro t y p e s of d e f o r r ~ l a t i o n a r e t h e most inlportant, 1 . e . deformation due t o s t r u c t u r a l conipac- t i o n and deformation due t o p l a s t i c flow.

R e l a t i o n Setwecn S t r e s s e s and Deformation of Frozen S o i l

In a g e n e r a l c a s e , t h e r e l a t i o n between t h e s t r e s s a and t h e r e l a t l v e d e f o r m a t i o n h, which i s e s t a b l i s h e d rihen a load i s a c t l n g on f r o z e n ground,

i s n o n - l i n e a r , i . e . s t r - l c t l y spealcing, f r o z e n s o l l does n o t obey Hooke l o law. Due t o r h e o l o g i c a l p r o p e r t i e s of f r o z e n s o i l s , t h e r e l a t i o n of a t o h changes w l t h time. On t h e b a s i s of l n v e s t l g a t i o n s c a r r i e d o u t by t h e I g a r k a Perma- f r o s t S t a t l o n t o g e t h e r w l t h t h e n o r t h e r n e x p e d l t l o n under t h e a u s p i c e s of t h e A r k t i k p r o e k t (Vyalov, 1953-1956), i t h a s been e s t a b l i s h e d t h a t when t h e r a t e of l o a d i n g Is r a p l d and t h e r e i s no time f o r development of p l a s t i c deforma- t i o n , t h e c u r v e h = f ( a ) (FIE.

6 )

i s v e r y s t e e p and i s c l o s e t o a s t r a l g h t l i n e . With an i n c r e a s e i n tlie d u r a t i o i ? of t h e load o r a r e d u c t i o n i n t h e r a t e of l o a d i n g , t h e c u r v e s h = f ( o ) g r ~ a d u n l l y become more g e n t l e and t h e magnitude of d e s t r u c t i v e f o r c e I s reduced. \,hen t h e d u r a t i o n of load Is l n f l n l t e l y long, t h e r e l a t i o n between s t r e s s and d e f o r m a t i o n i s e x p r e s s e d by a l i m i t i n g curve

which

c o r r e s p o n d s t o t h c lorecst value of d e s t r u c t i v e f o r c e knovn a s t h e u l t i m a t e long-term s t r e n g t h .

Thus t h e r e l a t l o n between d e f o r m a t l o n and s t r e s s of f r o z e n ground i s

e x p r e s s e d by a f a m i l y of c u r v e s ( s e e P i g . 6 ) , t h e p a r a m e t e r s o f which a r e t h e These c u r v e s may be d u r a t i o n o f t h e load and t h e r a t e of l o a d i n g v =

x.

d e f i n e d by e q u a t l o n

where a(t) Is a non-dimensional c o e f f l c l e n t of s t r e n e t h e n i n e which d e f i n e s t h e c u r v a t u r e of l i n e s ; and A i s t h e nlodulus of d e f o r m a t i o n (kl/cm2), which

d e f i n e s t h e s l o p e o f l i n e s . F a c t o r t i n d l c a t e s t h a t t h e s e p a r a m e t e r s v a r y w i t h d u r a t i o n of t h e l o a d . \.hen t = 0, a = a l and A = Ai; when t 4 ~ , a = _{a e}

and A = A,, where t h e s u b z c r l p t s "1" and "e" r e f e r t o " l n i t l a l " and "end" v a l u e s of p a r a m e t e r s A and u . In some canes a may approach u n i t y and c o e f - f i c i e n t A w i l l t h e n bc c q u a l t o t h e n~odulus of l i n e a r d e f o r m a t i o n E, w h i l e e q u a t i o n ( 3 . 1 2 ) ~111 acsurne t h e fol>m of t h e e q u a t l o n f o r a l i n e a r l y deformed v l a c o u s body:

where E v a r i e s between Ei and E e .

Equation ( 3 . 1 3 ) may be regarded a s a v a r i a t i o n of e q u a t i o n ( 3 . 1 2 ) f o r u s e I n approximate c a l c u l a t i o n s , which makes i t p o a s i b l e t o a p p l y t h e w e l l -

developed mathematical t h e o r y of e l a s t i c i t y .

However e q u a t i o n (3.13) remains t r u e o n l y u n t i l t h e load g i v e s r i s e t o such a s t r e s s i n t h e ground, t h e e x c e s s of which ( a t t h e g i v e n r a t e o f l o a d - i n g ) l i i l l r e s u l t i n u n a t t e n u a t i n g p l a s t i c f l o w . Beyond t h i s t h r e s h o l d t h e

p r o c e s s o f d e f o r m a t i o n can no l o n g e r be e x p r e s s e d by t h e above e q u a t i o n , s i n c e t h e c u r v e s h = f ( a ) w i l l have i n f l e x i o n s , which a r e e s p e c i a l l y s h a r p on

l o g a r i t h n ~ i c c u r v e s .

The p l a s t i c l i m i t o r , i n o t h e r words, t h e y i e l d p o i n t i s a v a r i a b l e

f a c t o r which depends on t h e d u r a t i o n o f t h e load and t h e r a t e o f l o a d i n g . The l o n g e r t h e d u r a t i o n , t h e lower t h e load r e s u l t i n g i n s o 1 1 flow. \ h e n t - r m ,

of becomes e q u a l t o t h e long term s t r e n g t h al. Thus t h e p l a s t i c l i m i t Is n o t c o n s t a n t and depends on t h e time f a c t o r . On t h e o t h e r hand, t h e long-term s t r e n g t h a ₁ i s c o n s t a n t and may be r e g a r d e d a s t h e minimum v a l u e of t h e p l a s t i c l i m i t when t h e d u r a t i o n of t h e load i s i n f i n i t e l y long.

T o t a l d e f o r m a t i o n o f f r o z e n s o i l c o n s i s t s of e l a s t i c d e f o r m a t i o n hel, which i s c o m p l e t e l y r e c o v e r a b l e , and r e s l d u a l p l a s t i c d e f o r m a t i o n Ares. The

s e p a r a t i o n o f t h e two forms may be achieved o n l y by t e s t s i n v o l v i n g removal of t h e load a f t e r e a c h experFmenta1 s t e p . Both Ares and A e l depend on t h e time f a c t o r ( h e l d e p e n d s o n i t because o f e l a s t i c a f t e r - e f f e c t s ) , as i n d i c a t e d by F i g . 6.

Thus i n a g e n e r a l c a s e t h e r e l a t i o n between h a n d 0 1 s

as

f o l l o w s :

However, a s may be s e e n from F i g . 6, t h e e l a s t i c p a r t of d e f o r m a t i o n h a s a r e l a t i v e l y s m a l l e f f e c t on t h e o u t l i n e o f t h e curve d e n o t i n g t o t a l deforma- t i o n . T h e r e f o r e t h e r e l a t i o n between t o t a l d e f o r m a t i o n and l o a d may be

e x p r e s s e d by t h e second h a l f o f e q u a t i o n ( 3 . 1 4 ) :

Obviously, t h e c o e f f i c i e n t s A and a i n e q u a t i o n ( 3 . 1 2 ) w i l l d i f f e r some- what from t h e p u r e l y p l a s t i c c o e f f i c i e n t s A1 and a' i n e q u a t i o n ( 3 . 1 4 ) , s l n c e e l a s t i c d e f o r m a t i o n o c c u r s i r r e s p e c t i v e of t h e load and t h e d u r a t i o n of i t s

In

t h e absence of a well-defined r e l a t i o n between s t r e s s and deformation, t h e mechanim of deformation of f r o z e n 3011 under a load exceeding t h e u l t i -

mate long-term s t r e n g t h depends on t h e r a t e of p l a s t i c flow, which i n t u r n depends on t h e value of the c o n s t a n t l y p r e s e n t l o a d . I n g e n e r a l , t h e r e l a t i o n between t h e r a t e of p l a s t i c - v i s c o u s flow and a c t i n g s t r e s s ( t h e excess s t r e s s over long-term r e s i s t a n c e ) i s d e s c r i b e d (Vyalov, 1953) by t h e e x p o n e n t i a l e q u a t i o n : where

E T

i s s t e a d y r a t e of r e l a t i v e deformation, q i s c a l c u l a t e d c o e f f i c i e n t of v i s c o s i t y , B i s non-dimensional parameter, o 1s a c t i n g p r e s s u r e , Oel i s u l t i m a t e long-term s t r e n g t h . I n t h e m a j o r i t y of c a s e s t h e value of B i s c l o s e t o u n i t y , t h e r e f o r e t h e curve C = f ( 0 ) can be o f t e n apgi-oximately r e p r e s e n t e d by a s t r a i g h t l i n e

(Fig.

7 ) .

In t h i s c a s e e q u a t i o n (3.15) w i l l assume t h e form of t h e well-

known Bingam-Shvedov e q u a t i o n d e s c r i b i n g t h e s t e a d y flow of a p l a s t i c - v i s c o u s body :

where -q i s t h e t r u e c o e f f i c i e n t of v i s c o s i t y .

4. E f f e c t of Composition of Frozen S o i l s on T h e i r S t r e n g t h

\hen e v a l u a t i n g t h e e f f e c t of t h e composition of f r o z e n s o i l s on t h e i r s t r e n g t h , t h e g r a i n s i z e (mechanical) and m i n e r a l o g i c a l composition of p a r t l - c l e s must be considered, a s w e l l a s t h e phase composition of groundwater. The

e f f e c t of t h e phase composition of w a t e r and of mineral p a r t i c l e s on t h e s t r e n g t h of f r o z e n s o i l s has n o t been thoroughly i n v e s t i g a t e d by anyone.

Data a v a i l a b l e i n the l i t e r a t u r e have been obtained f o r a s t a n d a r d r a t e of I n c r e a s e I n t h e load

(15

-

20 k d c m 2 p e r minute) and t h e r e f o r e r e f l e c t t h e momentary r a t h e r t h a n t h e long-term s t r e n g t h of f r o z e n s o i l s .

Frozen sand, t h e p o r e s of which a r e completely f i l l e d with i c e and water,

i s many times more r e o i s t a n t t o e x t e r n a l f o r c e s t h a n f r o z e n c l a y s o i l . For example, t h e compression s t r e n g t h of specimens of f r o z e n q u a r t z sand

( l o &

of p a r t i c l e s r a n g l n g from 1

-

0.05 mm, moisture c o n t e n t Wtot = 5 temperature -l°C ) amounts t o about 60 ke/cm2, while t h e compression s t r e n g t h of f r o z e n c l a y a t t h e same temperature ( c o n t e n t of f r a c t i o n l e s s t h a n 0.005 mm 50$, m o i s t u r e conten Wtot =

3 5 $ )

i s o n l y 11 kg/cm2. Again a t -lo°C, t h e u l t i m a t e