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by L.T. Roman

PREDICTION OF CREEP OF FROZEN PEAT BY THE METHOD OF TEMPERATURE-TIMEN LOGY

The main f a c t o r s c o n t r o l l i n g t h e r e s i s t a n c e of f r o z e n p e a t t o l o a d i n ga r e t he h igh amount s of i c e an d u n fr o ze n wa t e r p r e s e n t i n i t and t h e c r e e pof p e a t p a r t i c l e s on t h e o t h e r . Volume f r a c t i o n o f t h e c o n s t i t u e n t s i nf r o z e n p e a t a t t e m p er a tu re s b elow t h a t f o r i n t e n s i v e p h as e t r a n s i t i o n o fmo ist ure (i . e. below -8OC) a r e roug hly as fo l lows: 60-70 i c e , 18-254unf rozen wa te r , 1 -15 pea t pa r t i c l e s , and 2-5 en t r apped a i r . Thus th epr in c i pa l components o f f roze n pea t a r e i c e and unf rozen wa te r.

Uniaxia l compression and rupture t e s t s c a r r i e d o u t by t h e p r e s e n tau thor have shown t h a t t he de fo rmat ion o f spec imens under loads induc ingv i s co u s f lo w , d o es n o t d i s t u r b t h e i r c o n t i n u i ty .The b e a r i ng c a p a c i t y o f f r o z e n p e a t a c t i n g a s a f o o t i n g ca n be

e s t i m a t e d by u s i n g t h e g e n e r a l a p pr oa ch o u t l i n e d by V ya lo v i n h i s d i s c u s s i o no f t h e d e c r e a se o f t h e s t r e n g t h of i c e w i t h t i me [ I ] . A cc or di ng t o t h a ta p pr o ac h t h e n o t i o n of s t r e n g t h i s v a l i d o n l y f o r i c e when s u f f i c i e n t l yl a r g e lo a ds a r e a p p li e d r a p i d l y , l e ad i ng t o b r i t t l e f a i l u r e . A llo wa blelong- te rm load s can be es t ima t ed on ly by knowing th e s t r a i n s and s t r a i nr a t e s . t i s a c o n v e n ti o n t o t a k e t h e l o n g term s t r e n g t h a s e q ua l t o t h es t ress c a us i ng t h e s p e c i f i e d s t r a i n s and s t r a i n r a t e s , which m ust n o t e xc eedth e maximum perm iss ib l e le ve ls . I t i s of p r a c t i c a l i n t e r e s t , how ever, t op r e d i c t f o r f r oz e n p e a t , a s w e l l a s f o r i c e , s e t t l e m e n t s ov er a ny gi v enper iod of t i m e under a sp ec i f i e d load , i n s t ea d of long- te rm s t r eng th .F ur th er mo re , b ec au se o f t h e i r i n c r e a s e d d e f o r m a b i li t y , f r o z e n p e a t s a r e i n ap l a s t i c f r o z e n s t a t e th ro ug ho ut t h e n a t u r a l t e m pe r at u re r a n g e , andc om pu ta ti on s on t h e b a s i s of s t r a i n s a r e a p r e r e q u i s i t e i n c a l c u l a t i o n s o ff o o t i n g s composed of f r o z e n p e a t so i l s . d i f f i c u l t a sp e c t of s e t t l e m e n tp r e d i c t i o n s i s t h e cho ice o f t h e op t imal mathemat ica l mode l capab le ofr e v e a l i n g t h e c h a r a c t e r of d e fo r ma t io n d u r i n g t h e i n i t i a l p e r io d of l o a d in ga nd o f d e sc r i b i n g i t q u a n t i t a t i v e l y f o r a p e ri od t h a t i s s e v e r a l o r d e r sg r e a t e r t h a n t h e d u r a t i o n of t h e t es t .

The p r e se n t p a p e r c o n s i d e r s t h e p o s s i b i l i t y of p r e d i c t i n g l on g- ti mecre ep of f ro ze n pe at by usin g th e method of temperature- time analogy. s i sw e l l known, t e mp e ra t ur e a f f e c t s r e l a x a t i o n i n f r o z e n s o i l s . T h e i r c r e e pd e f or m a ti o n i n c r e a se s w i t h r i s i n g t e mp e ra t ur e . The two m ai n f a c t o r sa f f e c t i n g t h e d e c r e a s e of c r e ep w i t h d e c re a s e of t e mp e ra t ur e a r e t h ed e c r e a s i n g am ou nts o f u n f r o z e n w a t e r , a nd t h e d e c l i n i n g m o b i l i t y o f t h ec r y s t a l l a t t i c e of i ce o n t h e o ne h an d an d o f s o i l p a r t i c l e m o le c ul e s on t h eo t h e r .

The se f a c t o r s v a r y p r o p o r t i o n a l l y a c c o r d i n g t o te m p e ra t u re v a r i a t i o n s .Moreover, t h e e f f e c t s o f t empera tu re and t i m on t h e s t r a i n are

complementary, which makes i t p o s s i b l e t o e s t a b l i s h a n an al og y b etw een t h ee f f e c t of t e m p e r a t u r e a nd ti m e , o n t h e d e f o r m a bi l i t y . Le t u s assume t h a t a tlower temperatures th e same amount of s t r a i n w i l l o cc ur i n a s o i l und er a

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c e r t a i n l o a d a f t e r a l o n g er p e ri o d of t im e a s t h a t o c c u r r i n g i n t h e sames o i l a t a h i g h e r t e mp er at ur e i n a s h o r t e r d u ra t io n . The r e g u l a r p a t t e r n o ft h e a c c e l e r a t i o n of r e l a x a t i o n makes i t p o s s ib l e t o ap p ly t h e m ethod o fa na lo gy f o r p r e d i c t i n g d e f o r m a b i l it y [ 2 ] . I t depends o n t h e f a c t t h a t t h eex p e r im en ta l d a t a o b t a in ed a t h ig h e r t em p e r a tu r e s c an be us ed t o model c r eepo ve r a l o n ge r ti me i n t e r v a l t h a n t h e d u r a t i o n of t h e t e s t s .

The temperat ure- t ime analogy i s b as ed on t h e r e l a t i o n s h i p of t h ec o n s o l i d a t i o n p r e s s u r e a s a f u n c t i o n o f t im e an d te m p e ra t u re [ 3 ] :

w he re p a nd po a r e d e n s i t i e s a t and I t e m p er a t ur e s, r e s p e c t i v e l y ; q t , 8 )i s t h e f u n c t i o n of t h e c o n s o l i d a t i o n p r e s s u r e ; t i s t ime; t t / a e ; and a.i s t h e t em pe ra tu re -t im e r e d u c t i o n c o e f f i c i e n t . I t i s d i f f i c u l t t o u s ee q u a t i o n 1 ) . I n p r a c t i c e t h e r e d u c t io n c o e f f i c i e n t a e i s determined f romth e depend en ce of t h e co m pl ian ce o n t h e t im e of a c t i o n of t h e l o ad o b t a in edf o r d i f f e r e n t t e mp e ra t ur es . The r a t i o of t h e r e l a t i v e s e t t l e m e n t 6 t os t ress i s assu med t o b e eq u a l t o t h e co mp l ian ce :

A cc ord in g t o t h e c o n d it i o n s of t h e t h e o ry of v i s c o e l a s t i c i t y , t h er e l a t i o n s h i p b etw ee n I t , t h e co m p li ance a t an y s p ec i f i e d t im e and t h e l on g-t r m compliance I-, h as t h e f o r m

where I O s i n s t a n t a n e o u s e l a s t i c c o mp li an ce an d z i s r e l a x a t i o n t im e.Compliance i s d e te r mi n ed e x pr i m e n t a l l y by s u b j e c t i n g s o i l sp ec im en s t o

u n i a x i a l e x t e n s i o n a nd co m pr es si on t e s t s [ 2 ] . A method has a l s o beend ev el op ed f o r c a l c u l a t i n g c om pl ia nc e f ro m t h e d a t a of c i r c u l a r p l a t e l o a d i n gp e ne t ra t io n t e s t s [ 4 ] However, t h e s e t e s t s a r e l a b o r i o u s , s i n c e s pe ci me nsw i t h i d e n t i c a l p h y s i c a l p r o p e r t i e s must be t e s t e d u nd er a t l e a s t 6-10d i f f e r e n t t em p er at ur e r eg im es w it h r e p r o d u c i b i l i t y a d eq ua te f o r s t a t i s t i c a lp r o ces s in g . The l e a s t l ab o r io u s o f t h e t h r ee m eth od s d e s c r i b ed ab ov e i s t h ec i r c u l a r p l a t e l o a d i n g method. I n c o n t r a s t t o e x t e n s i o n an d c om p re ss io nt e s t s , i t a l l o w s u s t o d i s p e n s e w i t h d e t e r m i n a t i o n s o f u l t i m a t e s h o rt - t er ms t r e n g t h f o r e a c h g i v e n te m pe r at u re r eg im e, a nd t o e l i m i n a t e a d d i t i o n a lt e s t s f o r d e t e r i m i n g t h e m ag ni tu de of t h e s p e c i f i e d s t r e s s . F u rt h er m or e ,c i r c u l a r l o a di n g p l a t e t e s t s a r e w id el y us ed f o r e s t i m a t i ng t h e s t r e n g t h off r o z e n s o i l s [51.

Equa t ions 1 ) and 3 ) have been ob ta ined fo r homogeneous ma te r i a l sw i t h a u n if o rm p h y s i c a l c o n d i t i o n ) a n d d o n o t t a k e i n t o ac c o u nt p h a set r a n s i t i o n s of m oi st u re . T h e re f o re i n t h i s work o u r p ri me o j e c t i v e i s t o

v e r i f y t h e p o s s i b i l i t y o f a p p l y i n g t h e method o f t e m p e ra t ur e -t im e a n al o gyf o r e v a l u a t i n g t h e d e f o r m a b i l i ty of f r o z e n p e a t s , which have a much gr e a t e rt e m p er a t ur e r a n g e o f i n t e n s i v e p h as e t r a n s i t i o n s t h a n m i n e r a l s o i l s . Oure a r l i e r s t u d i e s h av e shown t h a t f o r e ac h d eg r ee d r op i n t e mp e ra t ur e t h ed e c r e a s e i n t h e m o i s t u r e c o n t e n t o n a cc o u n t of u n f ro z e n w a t e r W i s 0.02 i npe a t a t -BC, whereas i n c lay loam t h a t d ecre ase occu rs a t -1 t o -1.5OC.

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Fur thermore , th e valu e of W r em ai ns h i g h i n p e a t e v en a t lower temperatures(90-1202 r e l a t i v e t o t h e w e ig h t o f d r y so i l ) , w hi ch i s p r e c i s e l y t h e r ea s onof i t s i nc reased c r eep de fo rmat ion .

S i nc e o ur s t u d i e s a r e e s s e n t i a l l y a pp ro xi ma te , w e c h os e t h e s i m p l e s tmethod ava i l ab le , i .e . c i r c u l a r p l a t e l o a d i n g t e s t s . The s pe ci me ns wereprepared f rom an a i r dr y highmoor c ot to n grass-sphagnum pe at decomposed t o18-20%. To make t h e p e a t homogeneous, we s i f t e d i t t h rough a s c r e en wi th a4 mesh and sa tu ra te d i t w it h d i s t i l l e d water, t h e n p l a c e d i t f o r 4 8 ho u r si n a s i e v e l i ne d w it h f i l t e r pa pe r t o d r a in of f t h e water. The specimenswere i n th e shape of 10 x 10 x 10 cm cubes and were p r e p ar e d w i t h t h e h e l pof met al ca si ng s. The specimens were compacted on a v i b r o p l a t e a n d weref ro ze n a t -4.5OC i n th e underground l abo rat ory of th e Yakut ian Branch of t h eK ra sn oy ar sk P r o m s t r o i n ii p r o e k t I n s t i t u t e . A f t e r t h a t t h e s pe ci me ns w e r es t o re d f o r a t l e a s t t h r ee d ays a t t h e t e m p er a t ur e em ployed i n t h e t e s t sThe des i r ed t empera tu re cond i t ions w e r e c r e a t e d by u s i n g t h e n e g a t i v et e m p er a t ur e of t h e o u t s i d e a i r i n a the rmal ly in su la t e d room, Thee xp er im en ta l d a t a s e l e c t e d f o r t h e a n a l y s i s were o b t a i n e d u n de r c o n d i t i o n sensu r ing t empera tu re va r i a t io ns of f0.3OC o r less o v e r t h e 1 t o -10 r ange ,o r of fO.SC a t lower tem pera ture s. Temperature measurements were t ak en a th o ur ly i n t e r v a l s w i th a mercury thermometer gradu ated i n O.lOc, t ha t wasi n s e r t e d i n t o t h e c o n t r o l s pecimen. The d u r a t i o n of t h e t e s t s was 8 hours.

t t h e "basa l " t empera tu re , which w a s sp ec i f i e d as -13OC, th e dura t ion oft h e t e s t s was 240 h o ur s . The l o a d o n t h e c i r c u l a r p l a t e l o a d i n g wasse le ct ed i n conformi ty wi t h th e sp ec i f ic a t io ns of GOST 21048-75 and var iedf rom 3 t o 15 kg depending on t h e t empera tu re . We s e l e c t e d f o r t h e a n a ly s i s ,r e s u l t s of t h e t es t s i n which t h e s e t t l e m e n t s of t h e c i r c u l a r p l a t e w erec l os e i n magni tude r eg ard les s o f t h e t emp era tu re and amounted t o 0 .09+0.1 c mf i f t e e n mi nu te s a f t e r t h e a p p l i c a t i on o f t h e l oa d.

I n p r e p a r i n g t h e spe ci me ns w e e nd ea vo ur ed t o e n su r e t h a t t h e y w r ehomogeneous and possess ed id en t i ca l phy s ic a l p rop er t i e s . The average va ues

3f t h e i n d i c e s o f t h e s e p r o p e r t i e s ere a s fo l lows: u n i t mass 1 .03 g/cmu n i t mass of t h e sk el e t on 0.17 g/cm de ns i t y 1.5 g/cm mois ture con ten t4 .95; i n i t i a l f r ee zi ng temp erat ure -0.08OC.

The unfrozen water c o n t e n t (as a f r ac t i on ) was dete rminedc a l o r i m e tr i c a l l y f o r a l l t h e t e m p e ra t u r e r e gi m es of t h e t e s t s and amountedt o 2 a t 2.5OC, 1.3 a t -4OC, 0.9 a t -6OC, 0.7 a t -8.5OC, 0.6 a t 9.5OC, 0.5 5a t -13OC, 0.51 a t 25. iC, an d 0.5 a t -28OC.

A cc or di ng t o [ 4 ] t h e c o m pl ia nc e f o r a ny s p e c i f i e d p e r i o d o f t i m e It i sc a l c u l a t e d a c c o rd i n g t o t h e f or mu la

where S i s t h e s e t t l e m e n t of t h e l o a di n g p l a t e ov e r t i m e t r i s t h e r a d i u sof t h e l o ad i n g p l a t e , a nd P i s t h e l o a d on t h e l o a d i n g p l a t e .The compl iance ca lc u l a t ed f rom t h a t fo rmula a s a fun c t i on of t ime i s

shown i n semi log coor d ina tes f o r each t empera tu re r eg ime i n F ig. 1. F u r t h e rp rocess ing o f exper imen ta l da ta wi th th e v iew of de te rmin ing long-t ermc om pl ia nc e re d u c e s t o f i n d i n g t e mp e ra t ur e -t i me r e d u c t i o n c o e f f i c i e n t a e andt o c o n st r u ct i ng a gene ra l i z ed cu rve des c r i b in g th e long-t erm dependence of

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I; on l n t f o r t h e s pe cim en s t e s t e d a t t h e b a sa l t e m p er a t ur e , i . e . a t t h etempera tu re a t which w e wish t o de te rmine th e long- t e rm compl iance o f t h especimens tes ted .

It i s of fundamental impor tance t o determine th e thermorheologicalperformance of pe at und er lo ad and t o compare i t t o o t h e r s i m p l e o r com plexm a t e r i a l s .

Compl iance of thermorhe ological ly s im ple substa nces i s determined onlyby t h e r e l a x a t i o n p r o c e s se s r e l a t e d t o t h e m o b i l i t y o f m a c ro mo le cu le s, w h ic hi n c r e a s e s o r a l t e r s w i t h a c ha nge i n te m pe r at u re [ 2 ] . F or t h e se su b s t a n c e st h e r e d u c t i o n c o e f f i c i e n t a u nd er c om pa ra bl e e x p e ri m e n ta l c o n d i t i o n s i n t h er e gi o n of l i n e a r v i s c o e l a s t i t y i s a f u n c t i o n of o ne s i n g l e v a r i a b l e ,i e of temperature . In geometr ic terms i t means th a t wi th a change i nt empera tu re t he compl iance cu rves I = f ( 1 n t ) a r e r i g i d l y d i s p la c e d al o ngt h e t im e a x i s w it ho ut d i s t u r b i n g t h e p a r a l l e l c h a r a c t e r of t h e i rd is pl ac em en t. T h i s g r e a t l y f a c i l i t a t e s t h e d e t e r m i n a t i o n of t h etempera ture -t ime r edu c t io n co ef f i c i en t ae .

I n f r o ze n e a r t h m a te r i al s , p a r t i c u l a r l y i n p e at , a d r o p i n t e m p e r a tu r el e a d s t o a change i n t h e i c e c o nt e n t i n a d d i t i o n t o d e c re a s i ng t h e m o b i li t yof t h e c r y s t a l l a t t i c e of i c e and s o i l p a r t i c l e s . The e f f e c t of t h e s e p ha set r a n s i t i o n s c o m pl i ca t es t h e c ha r a c er of I t - l n t l e a d i n g t o i t s v e r t i c a ld isp lacement . Exper imenta l da ta show t h a t the compliance curves obta ine df o r t h e same s o i l s , b u t a t d i f f e r e n t t empera tu res , ex t r ap o la t ed t o a commonp o l e , w hi ch a l so shows t h a t t h e i r p a r a l l e l c h a r a c t e r becomes d i s t u r b e d andc on se qu en tl y t h a t t h e s o i l s s tu d i e d s ho ul d be r e f e r r e d t ot h e rm o r h eo l o gi c a l ly c omplex so l i d s . The n ee d t o t a k e t h e v e r t i c a ld i sp la c e m e nt i n t o a c c o u nt c om p l i ca t e s t h e c o n s t r u c t i o n of a g e n e r a l i z e dcurve. I t i s t h e r e f o r e of i n t e r e s t t o de t er m in e t h e d e g re e of i t s i n f l u e n c eon th e accuracy o f long- t e rm compl iance de te rmina t i ons . When t h a t e f f e c t i sn o t l a r g e , t h e v e r t i c a l d i spl a c e me n t c a n b e d i s r e g a r d e d an d t h e g e n e r a l i z e dcompl iance cu rve can be cons t ruc ted t h e way i t i s d o n e f o rthe rmorheo log ica l ly s imple bod ies.

Compl iance a t a temperature of -13OC was se le ct ed a s th e r ef er en cecurve. It was t a ken nea r t he lower l i m i t of t h e te m p e ra t u re c o n d i t i o n s ,u n de r w hi ch t h e t e s t s w er e c a r r i e d o u t ( F ig . l ) , s i n c e t h e u pp er c u r v e s w ereu s e d f o r c o n s t r u c t i o n of a g e n e r a l i z e d cu r ve an d f o r i t s e x t r a p o l a t io n i n t ot h e r e g i o n of a l o n g e r t i m e i t e r v a l t h a n t h e d u r a t i o n of t h e t e s t s . Thea n a l y s i s i n c l u d e d :1. C o n s t r u c t i o n of a g e n e r a l i z e d cu r v e o n t h e as sum p ti o n t h a t t h e p e a tt e s t e d i s a t h e r m o r h e o l o g i a l l y simple m a t e r i a l .

To d et e rm i ne t h e r e d uc t i on c o e f f i c i e n t t h e d i s t a n c e on t h e h o r i z o n t a lb etw ee n e a c h p a i r o r n e i g hb o u ri n g c u r v e s A h a e i s m ea su re d a t s e v e r a l v a l u e sof l n t w i t h i n t h e t e s t i n g p er io d. Assuming t h a t t h e c u rv e s a r e p a r a l l e l , weaverage the r es u t l s of th e Aha e measuremen ts and ob t a in t he fo l lowingv a l ue s f o r e a c h p a i r of e x p e ri m e n ta l cu r ve s : e5 e4 2.76; e4-03 1.78 ;e3 e2 0.78; 02-G1 1.05; and Q1-Q0 1.6. The r e su l t s of t h emeasurements ar e used t o co ns t r uc t a graph of Alnae as a f u n c t i o n o ftemp erat ure (8-e0) (Fig. 2 a) . A f t e r t h a t we f i n d t h e a n a l y t i c a l e x p r es s i o nof lnae = f ( 8 ) , w hi ch f o r o u r d a t a h a s t h e f o l l o w i n g fo rm :

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D ur in g t h e c o n s t r u c t i o n of t h e g en e r a l i z ed cu r ve t h e ex p e r i m en t a l f u n c t i o n sI t f ( 1 n t ) become r i g i d l y d i s p l a c e d t o t h e r i g h t by t h e c o rr e sp o nd i ng I n agvalue. The new t ime tran sfor med f o r them w l l be

The g en e r a l i z ed cu r v e t h u s o b t a i n ed on t h e a s su m pt i on t h a t t h e p e a tspec imens t e s t ed were thermorheo log ica l ly s imple s o l i ds i s shown by th ed o t t e d l i n e i n F ig . 1.2. Cons t ruc t ion of a genera l i zed curve on th e assumption th a t t he f roze np ea t t e s t e d i n a t h e r m o r h eo l o g ica l l y com plex m a t e r i a l . F orthermorheo log ica lly complex ma te r i a l s th e t empera tu re- t ime co ef f i c i en t i s af u n c t i o n n o t o n l y of t em p e ra t u re , b u t a l s o o f d e f o r m a ti o n time a s a r e s u l to f w hich t h e com pl iance cu r v es u nd er go a v e r t i c a l , a s w e l l a s a h o r i zo n t a ld i sp l acem en t . T ak in g i n t o co n s i d e r a t i o n t h a t di sp lacem ent , t h e r ed u c t i o nc o e f f i c i e n t w i l l be de te rmined [2 ] as

l n a9 , t l n a e ( O , t o > [ l + f ( T > l ,where t o i s t h e "basa l " r eadou t t ime and ln t - ln tO.

The f i r s t component of equa t ion (7) i s found from 8-e0 a s a fun ct io n oflnag a t a f ixed "basa l " t ime . Th i s func t ion depends on one s i g l e a rgument ,i . e . on t empera tu re . I n th e cas e examined i t s v a l ue p ro ve d t o be c l o s e t oequa t ion (6 ) :

To d e te r mi n e f ( T ) we f i n d p a r t i a l d e r i v a t i v e s u l n a e ( 8 , t ) / u t , w hic h a r et r ansfo rmed t o a f or m t h a t i s i n v a ri a n t r e l a t i v e t o t h e change i nt em p er a t ur e , w i t h t h e h e l p of t h e f u n c t i o n of s i m i l i t u d e ( F i g . 2 b) .

Hav ing ca lcu la t ed ln a accord ing t o fo rmula (6 ) , we co ns t ru c t ag en e r a l i z ed cu r v e r i g i d l y i kp laci ng ex p e r i m en t a l v a l u e s o f t f ( l n t ) byth e magni tude lnae ca l cu la t ed accord ing t o fo rmula (7 ) . The curveo b t a i n ed i s shown i n F ig . 1 by t h e so l i d l i n e . It may thu s be see n t h a t iti s p o s s ib l e t o c o n s t r u ct a more accu r a t e g en e r a l i z ed cu r v e by t a k i n g i n t oacco u nt t h e v e r t i c a l d i sp l acem en t . T h i s i s conf irmed by exper imental d at aof long-term compliance de ter mi na tio ns a t t h e " b a sal " t em p er a t u re : t h ee x pe r im e nt a l p o i n t s f a l l on t h e g e n e r a l i z e d cu r v e c o n s t r u c t e d as i s done fo rr eh o l o g i ca l l y s i m p l e m a t e r i a l s .

t sh ou l d b e n o t ed t h a t t h e p ro ce s s i n g of ex p e ri m en ta l d a t a i s g r e a t l yc om pl ic at ed i f t h e v e r t i c a l d i s pl a ce m en t i s acco u nt ed f o r by t h e s t an d a r dmethods. S ince th e displace ment occurs mainly as a r e s u l t of p h aset r a n s i t i o n s , we ha ve a t t e m pt e d t o e s t i m a t e t h e i r e f f e c t on c om pl ia nc ei n d i r e c t l y w i th t h e vie w of s i m p l i f y i n g t h e p ro c ed u re s i n vo l ve d i nco n s t r u c t i o n o f a g en e r a l i z e d cu rv e .

The volume of s o i l occupie d by water and ga se s, i .e . by t h e componentsp r i m a r i l y r e s p o n s i b l e f o r t h e pr e se n ce of t h e v e r t i c a l d i s pl a ce m e nt f a c t o r ,

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and the volume occup ied by i c e and pea t p a r t i c l e s can be de te rmined a t eachtemperature . The r e l a t i v e c o n t e n t o f i c e an d p e a t ( k ) c a n r e a d i l y beexpressed through t h e i r volume i n un i t volume of th e so i l :

where yck i s u n i t mass of t h e s o i l sk e l e t o n , g/cm y r i s densi ty , g /cm Wci s t h e t o t a l mo is tu re c o t e n t ; W i s t h e u nf r o ze n w a t e r c o n t e n t , a nd y x i sSt h e dens i ty of i ce , g/cm

The e f f e c t o f the gas con ten t and of th e unf rozen wa te r , on t h ec om pl ia nc e c a n be c a l c u l a t e d by r e f e r r i n g t h e s t r e s s e s t o t h e a r e a o cc up ie dby i c e a nd p e a t p a r t i c l e s r a t h e r t ha n t o t h e t o t a l a r e a of specim en. T ha ta r ea can be c a l cu la t e d on ly approximately by assuming th a t i t i sp r o p o r t i on a l t o t h e r e l a t i v e c o nt e n t of s o i l p a r t i c l e s an d i c e ( k ). The newvalu e of compl iance ; w i l l t h e n be e q u a l t o I t k .

The v a l u e s of k c a l c u l a t e d f o r t h e p e a t s a mp le s t e s t e d a c c o r d i n g t of o r m l a ( 9 ) , f o r e a ch t em p er a tu re r eg im e a r e a s f o l lo w s:

The g r a p hs I t k f ( 1 n t ) and t h e g e n e r a l i z e d c u r ve c o n s t r u c t e d f o r t h e sef u n c t i o n s , a s i s d on e f o r t h e r m o rh e o l o g i c a l l y s i m p le so l i d s , a r e shown i nFig . 3. t i s e v i d e n t fro m t h e g r ap h t h a t i n t r o d u c t i o n of t h e c o e f f i c i e n t kmakes i t p o s s i b l e t o b r i n g t h e g e n e r al i z ed c u r v e c l o s e r t o t h e e x pe r im e nt a ld a t a .

By us ing the compliance va lues de termined accord ing t o th e t h r eem ethods d i s c u s se d e a r l i e r , and by employing th e te chn iqu e developed byVyalov f o r e s t i m a t i n g t h e l on g- te rm s t r e n g t h of f r o z e n so i l s [6 and 71, wc a l c u l a t e d t h e e q ui v a le n t c oh es io n of t h e p e a t us ed i n t h e t e s t s a t a

ba sa l tem pe rat ure of -13OC ov er t h e t i m i n t e r v a l l n t 12.9. The r e s u l t sobta ined were a s fo l lows: 0.367 MPa according t o th e ge ner al i ze d compliancecurve f o r a thermorh eological ly s imp le so l i d ; 0.45 MPa acc ordin g t o th e samecurve , bu t wi th k c oe f f i c i e n t accoun ted fo r ; 0.497 MPa accord in g t o thegene ra l i z ed cu rve of compl iance f o r a the rmorheo l og ica l ly complex so l i d ; and0.52 MPa ac co rd in g t o t h e method prop ose d by Vyalov. t i s ev iden t f romt h e s e r e su l t s t h a t p e a t h a s a n i n c r e a se d d e f o r m a b i l it y . Even a t lowtempera tu res (-13OC) i t s long- term equ iva len t cohesion i s l ow er t h a n t h a tca l cu la t ed accord ing t o th e long-t erm s t r e ng th equa t io n ob ta ined by Vya lovf o r f roze n minera l so i l s . The method of t empera tu re- time ana logy i sg e n e r a l l y a c c e p t a bl e f o r p r e d i c t i n g s e t t l e m e n t s of f r o z e n p e a t s o i l s , w h ic hmust then be r egarded as the rmorheo log ica l ly complex s o l id s , i n wh ich th ephase t r a ns i t io ns o f moi s tu re cause a v e r t i c a l d i sp lacemen t o f compl iancecurves .

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BIBLIOGRAPHY1 Vyalov S.S., Dokuchaev V.V., Sheinkman D.R. Podzemnye l dy i

sil nol idstye grunty kak osnovaniya sooruzhenii (Ground Ice andIce-rich Soils as Footings for Superstructures). Leningrad, Stroiizdat,19/6, 165 p

2. Urzhumtsev Yu.S., Maksimov R.D. Prognostika deformativnosti polimernykhmaterialov (Prediction of Deformability of Polymers). Riga, Zinantne,1975, 416 p

3. ~erri zh. Vyazko-uprugie svoistva polimerov (Viscoelastic Propertiesof Polymers). Moscow, Izd-vo inostr. lit., 1953, 535 p.

5. Tsytovich N A Mekhanika merzlykh gruntov (Mechanics of Frozen Soils).Moscow, Vyssh. shkola, 1973, 445 p.

6. Vyalov S.S. Reologicheskie svoistva i nesushchaya sposobnost merzlykhBruntov (Rheological Properties and Bearing Capacity of Frozen Soils).Moscow, Izd-vo AN SSSR, 1959, 185 p

7. Vyalov S.S. Ulitel noe razrushenie merzlogo grunta kaktermoaktivirovannyi protsess (Long-time failure of frozen soils as athermally activated process). -In: I1 Mezhdunar. konf. pomerzlotovedeniyu (The I1 International Permafrost Conference). Dokladyi soobshcheniya (Papers and Communications). Yakutsk, Kn izd-vo, 1973,issue 4, pp. 16-26.

Figure 1. Compliance of the frozen cotton grass-sphagnum peat tested withcircular plate loading, at different temperatures, as a functionof the time of action of the load. 1-Generalized compliancecurve constructed as is done for a thermorheologically simplematerial; 2-Generalized compliance curve constructed as is donefor a thermorheologically complex material; 9.5OC;Q2 -8.5OC; Q3= 6.0C; 8 -4.0C; Q5 -2.5OC.

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