Attenuating creep of piles in frozen soils

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Attenuating creep of piles in frozen soils

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ATTENUATING CREEP OF PILES I N FROZEN SOILS

by

V.R. Parameswaran

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Reprinted from

Proceedings of a Session, "Foundations

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C e t t e communication a n a l y s e l e s r e s u l t a t s de p l u s i e u r s e s s a i s d e f l u a g e 2 l o n g t e r m e s u r d e s p i e u x dans l e s g e l i s o l s . L ' a u t e u r y c o n s t a t e que c ' e s t l e f l u a g e 2 v i t e s s e d e c r o i s s a n t e

qui prsdomine d a n s l a p l u p a r t d e s c a s . Pour une c o n c e p t i o n r a t i o n n e l l e d e s f o n d a t i o n s s u r p i e u x d a n s l e s zones de p e r g s l i s o l , c e t t e c a r a c t s r i s t i q u e d o i t t t r e p r i s e e n c o n s i d e ' r a t i o n .

Reprinted from Proceedings o f

a Session

Sponsored by TCRR Council,

spri spring

Convention,

Denver, CO, April

29,1985

ATTENUATING CREEP OF PILES I N FROZEN SOILS V.R. Parameswaran*

ABSTRACT

R e s u l t s of s e v e r a l long-term c r e e p t e s t s of p i l e s i n f r o z e n s o i l s a r e analyzed; t h e primary o r a t t e n u a t i n g c r e e p i s predominant i n most c a s e s . For e f f e c t i v e d e s i g n of p i l e f o u n d a t i o n s i n permafrost a r e a s , t h i s a s p e c t should be t a k e n i n t o c o n s i d e r a t i o n .

INTRODUCTION

P i l e f o u n d a t i o n s a r e used e x t e n s i v e l y i n p e r m a f r o s t a r e a s t o i s o l a t e b u i l d i n g s from t h e f r o z e n ground by p r o v i d i n g a n a i r s p a c e between t h e two, t h e r e b y p r e s e r v i n g t h e f r o z e n s t a t e of t h e ground. Timber p i l e s a r e most commonly used, s i n c e t h e y a r e u s u a l l y r e a d i l y a v a i l a b l e and a r e r e l a t i v e l y simple t o i n s t a l l compared t o o t h e r f o u n d a t i o n s . For s p e c i a l p u r p o s e s , s t e e l and c o n c r e t e p i l e s a r e a l s o used i n some i n s t a n c e s .

A p i l e f o u n d a t i o n b e a r s t h e superimposed l o a d s ( s t a t i c due t o t h e weight of t h e s t r u c t u r e , and dynamic due t o moving l o a d s and v i b r a t i n g machinery w i t h i n t h e s t r u c t u r e ) by two mechanisms: a d f r e e z e bond between t h e p i l e and f r o z e n s o i l , and end bearing. I n i c e - r i c h s o i l s , end b e a r i n g i s u s u a l l y n e g l e c t e d and d e s i g n of p i l e f o u n d a t i o n s i s based mainly on t h e s t a t i c a d f r e e z e s t r e n g t h . The e f f e c t of dynamic l o a d s i s a l s o n e g l e c t e d ; i t is probably compensated f o r by t h e f a c t o r of s a f e t y u s u a l l y i n c o r p o r a t e d i n t h e design.

The s o i l a d j a c e n t t o t h e p i l e i n f r o z e n ground i s s u b j e c t e d t o a c o n s t a n t mean s t r e s s and undergoes long-term c r e e p . Design of p i l e f o u n d a t i o n s i s based on an a l l o w a b l e s e t t l e m e n t f o r a s t r u c t u r e d u r i n g i t s l i f e , from which an a v e r a g e a l l o w a b l e s e t t l e m e n t r a t e c a n be c a l c u l a t e d . The o b j e c t i v e of any good d e s i g n i s t o a r r i v e a t a v a l u e of a l l o w a b l e s t r e s s t h a t can be borne by t h e p i l e f o u n d a t i o n , w i t h o u t exceeding t h e t o t a l a l l o w a b l e s e t t l e m e n t d u r i n g t h e l i f e span of t h e s t r u c t u r e . S e v e r a l methods have been used t o c a l c u l a t e s u c h an a l l o w a b l e d e s i g n s t r e s s .

Adfreeze s t r e n g t h from short-term t e s t s

A few quick t e s t s a r e c a r r i e d out i n t h e l a b o r a t o r y on p i l e s f r o z e n i n t o d i f f e r e n t s o i l s , by l o a d i n g them a t d i f f e r e n t r a t e s , and d e t e r m i n i n g t h e peak a d f r e e z e s t r e n g t h v a l u e s (15). By p l o t t i n g t h e peak a d f r e e z e s t r e n g t h v e r s u s t h e displacement r a t e and e x t r a p o l a t i n g *Research O f f i c e r , D i v i s i o n of B u i l d i n g Research, N a t i o n a l Research

AITENUATING CREEP OF PILES 17

the curves back to the desired (alloyable) settlement rate for a structure, an allowable peak adfreeze strength is obtained. Previously this value was used together with a suitable factor of

safety (9.24). Black and Thomas (3) described prototype pile tests of

72 hours' duration in permafrost soils, and calculated an ultimate bearing strength as that stress at which the test pile attained a displacement of 0.5 mm (0.02 in) in the last third of the test period.

This corresponds to a displacement rate of 3.47 x mmfmin

(8.2 x 10-4 inlhr), which is much larger than the usual allowed

settlement rate of about 25.4 mm (1 in) during the life of a

structure. If the anticipated life of a structure is 25 years, the

allowable settlement rate will be about 2 x mmfmin

(4.72 x inlhr). [For calculations based on such allowable

settlements see (1,14,22)].

The danger in this method,of extrapolation of data from

short-term high-rate tests is that the allowable stress obtained by extrapolation to the desired settlement rate is always much higher than the stress that the pile foundation can withstand under long-term constant load creep conditions. Thus, the allowable stress is

overestimated by this technique and this could lead to premature failure. This was shown by comparing the results from long- and

short-term tests carried out in the laboratory

(17).

However, in

winter when the ground temperature of the active layer is much colder than that of the perennially frozen ground underneath, the piles have a much higher bearing capacity than the allowable design values. Long-term creep tests

A

logical alternative to the previous method is constant load

creep tests carried out in the laboratory or in the field for sufficiently long periods that a rate comparable to the desired settlement rate in the field is obtained. From a plot of stress versus steady-state creep rate, the allowable stress for a desired settlement rate is obtained.

This technique is normally used by designers, but the design is based entirely on the secondary or steady-state creep rate. The instantaneous creep or settlement and the primary stage, where the rate of settlement decreases with time, are neglected. These are assumed to be very small compared to the total creep in the

steady-state regime (11,13), based on the assumption that long-term pile behaviour under static load is analogous to the behaviour of

viscoelastic materials (10). However, the primary creep regime

continues for a considerable period of time, especially under low loads. This has also been observed in field situations (3,12,20,23). Failure time

In the method suggested by Vyalov (25), the difficulties of the two previous methods are somewhat eliminated by considering a "failure time" defined as the time required for the onset of tertiary or accelerating creep at the end of the steady-state regime. For frozen soils at a particular temperature this time (tf) is a function of stress ( 0 ) :

18 FOUNDATIONS

IN

PERMAFROST

w i t h B and 0 c h a r a c t e r i s t i c c o n s t a n t s f o r a m a t e r i a l . Thus, from a p l o t of ILn(tf) vs 110 f o r v a r i o u s t e m p e r a t u r e s , t h e s t r e s s

c o r r e s p o n d i n g t o a d e s i r e d l i f e s p a n can be o b t a i n e d ( s e e a l s o S a y l e s , 21). Vyalov's method t h u s t a k e s i n t o account t h e i n s t a n t a n e o u s d i s p l a c e m e n t , and t h e primary and secondary c r e e p regimes; hence, it could be t h e most s u i t a b l e model t o p r e d i c t t h e d e s i g n l i f e under a p a r t i c u l a r l o a d o r v i c e v e r s a . However, t h e e m p i r i c a l parameters B and 0 have t o be determined from many t e s t s

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

It would be convenient t o have an a n a l y t i c a l model t o p r e d i c t t h e t o t a l c r e e p behaviour of t h e s o i l a t t h e p i l e l s o i l i n t e r f a c e .

However, simple c r e e p laws a s a p p l i e d t o pure m a t e r i a l s such a s m e t a l s o r i c e cannot be a p p l i e d t o f r o z e n s o i l f o r t h e f o l l o w i n g reasons: ( a ) t h e nonhomogeneous n a t u r e of f r o z e n s o i l and t h e nonuniform d i s t r i b u t i o n of i c e l e n s e s i n t h e m a t e r i a l , and ( b ) v a r i o u s p r o c e s s e s such a s v i s c o e l a s t i c behaviour of i c e , d i s l o c a t i o n p l a s t i c i t y w i t h i n each i c e g r a i n , g r a i n boundary v i s c o u s flow o r r i g i d body r o t a t i o n of g r a i n s , d i f f u s i o n through t h e unfrozen w a t e r i n t h e s o i l , and

i n t e r g r a n u l a r s o i l f r i c t i o n . [For a g e n e r a l review of t h e physico-mechanical p r o c e s s e s o c c u r r i n g i n f r o z e n s o i l s , s e e ( 2 ) l . LABORATORY STUDIES ON THE BEHAVIOUR OF PILES I N FROZEN SOILS

The e x p e r i m e n t a l a p p a r a t u s and procedure used t o measure t h e d i s p l a c e m e n t of p i l e s i n f r o z e n s o i l s i n t h e l a b o r a t o r y under s t a t i c and dynamic l o a d s a r e g i v e n by Parameswaran (16,181.

T y p i c a l c r e e p c u r v e s show t h e displacement of v a r i o u s p i l e s i n d i f f e r e n t f r o z e n s o i l s ( f i g u r e s l ( a ) t o 3 ( a ) ) . I n a l l t h e s e f i g u r e s , t h e primary o r d e c e l e r a t i n g c r e e p regime e x t e n d s over more t h a n h a l f t h e p e r i o d r e q u i r e d f o r t h e o n s e t of t e r t i a r y c r e e p o r f a i l u r e . I n some c a s e s , t h e p i l e s were e n t i r e l y i n t h e primary c r e e p regime w i t h o u t e v e r a t t a i n i n g a s t e a d y - s t a t e regime.

F i g u r e s l ( b ) t o 3(b) show t h e v a r i a t i o n of displacement r a t e s w i t h time, c o r r e s p o n d i n g t o t h e c r e e p c u r v e s i n f i g u r e s l ( a ) t o 3(a). Again, primary c r e e p is dominant f o r v e r y long t i m e s , a s i n d i c a t e d by t h e c o n t i n u o u s d e c r e a s e i n c r e e p r a t e s d u r i n g t h e t e s t period. The a b r u p t peaks s e e n i n some of t h e s e c u r v e s correspond t o an i n c r e a s e i n t h e s t a t i c l o a d on t h e p i l e , hence, a n i n c r e a s e i n t h e s t r e s s a t t h e p i l e l s o i l i n t e r f a c e . These a r e a l s o i n d i c a t e d on t h e c r e e p c u r v e s .

For v a r i o u s p i l e s t e s t e d i n t h e l a b o r a t o r y , t h e t o t a l

d i s p l a c e m e n t ( i n c l u d i n g i n s t a n t a n e o u s ) i n t h e primary c r e e p r e g i o n was much l a r g e r t h a n t h a t i n t h e secondary c r e e p r e g i o n , e s p e c i a l l y f o r wood p i l e s . S i m i l a r behaviour of t h e dominant primary c r e e p regime f o r p i l e s i n f r o z e n s o i l s was observed by p r e v i o u s workers, from p i l e l o a d t e s t s c a r r i e d o u t i n t h e f i e l d (3,12,20,23). _/'

ATTENUATING CREEP OF PILES ₁₉ 25.

_,

,

I I I - - 3 I I I 111 _C 0 CI 1 I I / , 1 I ' 9 '

0 200 400 600 800 1000 1200 1400 0 200 400 600 800 I000 I200 I400

TIME h TIME. h

F i g u r e I ( a ) Creep curve showing displacement w i t h time f o r a n uncoated B.C. f i r p i l e i n f r o z e n sand ( a v e r a g e g r a i n s i z e : 0.2-0.6 mm (0.008-0.02 i n ) ; m o i s t u r e c o n t e n t : 14% by weight of d r y sand; T = -Z°C (28.4OF). S t r e s s ( T ) a t p i l e / s o i l i n t e r f a c e was 0.238 MPa (34.52 p s i ) , e x c e p t i n r e g i o n A t o B of t h e c u r v e , where T was 0.27 MPa

(39.16 p s i ) . At C and D, t e m p e r a t u r e f l u c t u a t i o n s o c c u r r e d i n t h e c o l d room. ( b ) V a r i a t i o n of d i s p l a c e m e n t r a t e w i t h t i m e f o r c r e e p c u r v e i n F i g u r e 1 ( a ) . 0.12 _I , \ ,

:

0 I I I I I 1 , - 4 = +

z

2

- 6 - m _- m 0 S

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-

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,

,

I 1 I 0 100 200 300 400 500 600 700 800 - 7 - ' 1 1 r 1 1 ~ ~ 0 100 200 300 400 500 600 700 800 900 TIME. h IIME, h F i g u r e 2 ( a ) Creep curve f o r c r e o s o t e d B.C. f i r p i l e i n s i l t y s o i l from Northwest T e r r i t o r i e s ( m o i s t u r e c o n t e n t : 20%; T = -2.5OC (27.5"F); T = 0.1903 MPa (27.60 p s i ) ; t e m p e r a t u r e f l u c t u a t i o n s a t A and B). ( b ) V a r i a t i o n of d i s p l a c e m e n t r a t e w i t h t i m e f o r c r e e p c u r v e i n f i g u r e 2 ( a ) . D i s c u s s i o n Analogous t o t h e t o t a l c r e e p s t r a i n of a m a t e r i a l , t h e t o t a l d i s p l a c e m e n t (A%) of a loaded p i l e i n f r o z e n s o i l c a n be r e p r e s e n t e d by a n e q u a t i o n :

20 FOUNDATIONS IN PERMAFROST

where t h e f o u r terms on t h e r i g h t s i d e r e p r e s e n t t h e i n s t a n t a n e o u s d i s p l a c e m e n t , and t h e d i s p l a c e m e n t s i n t h e primary, secondary and t e r t i a r y c r e e p r e g i o n s , r e s p e c t i v e l y . I n t h i s d i s c u s s i o n o n l y t h e primary o r a t t e n u a t i n g c r e e p behaviour of p i l e s i n f r o z e n s o i l s w i l l be c o n s i d e r e d .

S e v e r a l e q u a t i o n s r e l a t i n g t h e s t r a i n ( E ) and time ( t ) have been used t o d e s c r i b e t h e primary c r e e p behaviour of v i s c o e l a s t i c m a t e r i a l s such a s m e t a l s , r o c k s , c o n c r e t e , and ceramics ( s e e Pomeroy, 15, f o r a review). Some of t h e s e e q u a t i o n s a r e g i v e n below:

Power law: E = Atn ( 3 )

Logarithmic law: E = B1 + B2 L n ( t ) ( 4 )

Hyperbolic law:

E = L

a t

+

b

Exponential law: E = C [ I

-

exp. ( - ~ t ) ]

I n t h e s e e q u a t i o n s t h e c o n s t a n t s A, n , B1, B2, a , b, C and D a r e c h a r a c t e r i s t i c of t h e m a t e r i a l .

The d a t a from t h e p r e s e n t p i l e c r e e p t e s t s i n f r o z e n s o i l s were f i t t e d t o e q u a t i o n s ( 3 ) t o (61, w i t h t h e s t r a i n ( E ) r e p l a c e d by t h e p i l e displacement (AL), u s i n g a s t a n d a r d programme a v a i l a b l e w i t h a desk t o p computer. B e s i d e s t h e s e f o u r e q u a t i o n s , a polynomial of t h e type:

was a l s o f i t t e d t o t h e d a t a .

Once a curve f i t was s e l e c t e d , t h e r e g r e s s i o n v a l u e s were c a l c u l a t e d . The q u a l i t y of f i t achieved by r e g r e s s i o n was g i v e n by t h e v a l u e of t h e ' c o e f f i c i e n t of d e t e r m i n a t i o n ' r 2 , given by: where r i s t h e sample c o r r e l a t i o n c o e f f i c i e n t ( f o r d e t a i l s s e e Crow e t a l . , 6 ) . T h e o r e t i c a l l y , t h e c l o s e r t h e v a l u e of r 2 i s t o 1, t h e b e t t e r t h e f i t . Valuea of r2 ( t h e c o e f f i c i e n t of d e t e r m i n a t i o n ) o b t a i n e d by f i t t i n g t h e d a t a from s e v e r a l t e s t s t o t h e f i v e e q u a t i o n s

( 3

t o 7)

showed t h a t , a l t h o u g h t h e polynomial e q u a t i o n gave t h e h i g h e s t value

of r2 f o r most of t h e t e s t s , t h e r e was a tendency f o r t h e polynomial curve t o o s c i l l a t e a b o u t t h e a c t u a l c r e e p curve; hence, it was not

conmidered a good f i t . For most of t h e t e s t s , t h e power law ( e q u a t i o n 3 ) f i t q u i t e w e l l and f o r s o w t e s t s t h e h y p e r b o l i c l a w

ATTENUATING CREEP OF PILES 21

TIME, h

- 7

100 200 300 400

TIME, h

F i g u r e 3 ( a ) Creep c u r v e f o r uncoated B.C. f i r p i l e i n c l a y from Thompson, Manitoba ( m o i s t u r e c o n t e n t : 50% by weight of d r y s o i l ; T = -2.5'C (27.5OF); T = 0.0474 MPa (6.87 p s i ) . A t A t h e d i s p l a c e m e n t r a t e i n c r e a s e d due t o superimposed dynamic l o a d s . ) ( b ) V a r i a t i o n of d i s p l a c e m e n t r a t e w i t h t i m e f o r c r e e p c u r v e i n f i g u r e 3 ( a ) . 0 . 0 7 O.Ob E 0 . 0 5

--

5 _0.04 E

-

0.03 2

:

0.02 - a 0 . 0 1

-

D A T A I 1 100 200 300 400 TIME. h F i g u r e 3 ( c ) Curve f i t t i n g of t h e d a t a of f i g u r e 3 ( a ) u s i n g e q u a t i o n s ( 3 ) t o ( 7 ) . Thick l i n e shows a c t u a l d a t a . o b s e r v a t i o n s r e a s o n a b l y w e l l , t h e maximum d e v i a t i o n s b e i n g l e s s t h a n 25%. The v a l u e s of v a r i o u s c o n s t a n t s u s e d i n e q u a t i o n s ( 3 ) t o ( 6 ) o b t a i n e d from t h e t e s t d a t a a r e g i v e n i n T a b l e I. F i g u r e 3 ( c ) shows t h e r e s u l t of t h e c r e e p t e s t p r e s e n t e d i n f i g u r e 3 ( a ) , and t h e b e s t f i t o f t h e primary c r e e p e q u a t i o n s ( 3 t o 7).

F i g u r e s 4 and 5 ( a ) show two t y p i c a l long-term c r e e p t e s t s w i t h l o a d i n c r e m e n t s a t i n t e r v a l s , and f i g u r e 5 ( b ) shows t h e d i s p l a c e m e n t r a t e s a s a f u n c t i o n of time c o r r e s p o n d i n g t o 5 ( a ) . The p i l e s a r e under primary o r a t t e n u a t i n g c r e e p regime throughout t h e d u r a t i o n of t h e t e s t s . The s p i k e s (A', B ' , C') i n 5 ( b ) c o r r e s p o n d t o t h e l o a d

TABLE I. Values of r 2 and t h e c o n s t a n t s i n e q u a t i o n s ( 3 ) t o ( 6 ) f o r v a r i o u s t e s t s r~ N Mean Value s t r e s s o f r 2 a t p i l e / f o r t h e s o i l power V a l u e s of t h e c o n s t a n t s i n e q u a t i o n s ( 3 ) t o ( 6 ) T e s t i n t e r f a c e law

P i l e and s o i l t y p e No. MPa ( p s i ) (Eq. 3 ) A n B1 B2 a h C D Uncoated BC f i r i n f r o z e n s a n d ( S e e f i g . l a ) S t e e l H - s e c t i o n i n f r o z e n s a n d (-6OC) (21.2"F) C r e o s o t e d BC f i r i n s i l t y s o i l (See f i g . 2 a ) Uncoated BC f i r i n s a n d C o n c r e t e i n nand C o n c r e t e i n s a n d Uncoated s t e e l p i p e

i n

s a n d (-6'C) (21.2"F) Uncoated BC f i r i n Thompson c l a y (See f i g . 3 a ) Dense t r o p i c a l wood i n Thompson c l a y (-2.5'C) (27.5"F)

ATTENUATING CREEP OF PILES 23

TIME. h

F i g u r e 4 R e s u l t of long-term c r e e p t e s t of uncoated B.C. f i r p i l e i n f r o z e n sand a t -2.5OC (27..5"F), w i t h l o a d i n c r e m e n t s a t p o i n t s shown by arrows. S t r e s s e s i n d i f f e r e n t r e g i o n s shown i n T a b l e 11.

increments. E q u a t i o n s (3) t o ( 7 ) were a g a i n f i t t e d t o t h e data along

t h e segments o f t h e c r e e p c u r v e s f o r d i f f e r e n t l o a d s , by e h i f t i n g t h e c o o r d i n a t e a x e s t o t h e p o i n t of t h e l o a d increments. The power law

e q u a t i o n gave the b e a t values of r2. (The polynomial was a g a i n excluded because of o s c i l l a t i o n s about t h e measured creep.) The v a l u e s of the exponent (n) a s w e l l a s t h e s t r e s s corresponding t o e a c h segment of the c r e e p c u r v e s i n f i g u r e s 4 and 5(a) are g i v e n i n

Table 11.

Since t h e power law ( e q u a t i o n 3) f i t t h e primacy creep r e g i o n

well, t h e values of t h e exponent ( a ) o b t a t n e d f o r various t e s t s were

plotted a g a i n s t s t r e s s ( f i m r e 61, t o determine any a t r e s e dependence of this parameter. The ~ c a t t e r in t h e d a t a i e large, e s p e c i a l l y i n

the Lou s t r e s s r e g i o n , and t h e exponent ( n ) does n o t seem t o depend on t h e s h e a r s t r e s s ( T ) a t t h e p i l e / s o i l i n t e r f a c e . An a v e r a g e v a l u e of n wae about 0.46, w i t h a s t a n d a r d d e v i a t i o n of T0.125.

fn the c l a s s i c a l power law c r e e p e q u a t i o n proposed by Andrade, and a p p l i e d t o c r e e p of m e t a l s , r o c k s , e t c . (191, t h e valr-e of the

exponent ( n ) i s 0.33. F o r i c e a l s o , Glen (7) found a v a l u e o f

n = 0.33 t o f i t h i s c r e e p d a t a . S e v e r a l o t h e r workera ( 4 , 5 , 8 ) found, however. t h a t a v a l u e of n

*

0.5 gave a b e t t e r f i t t o t h e prfmary c r e e p f o r g r a n u l a r i c e , columnar g r a i n e d

ice

and f o r s i n g l e c r y s t a l 8 of i c e o r i e n t e d f o r n o n b a s a l g l i d e . The v a l u e of 0.46 observed from

the p r e s e n t c r e e p d a t a on f r o z e n s o i l s is c l o s e t o t h i s l a t t e r v a l u e , which i n d i c a t e s that: the c r e e p of i c e r i c h f r o z e n s o i l a t t e m p e r a t u r e s c l o s e t o t h e m e l t i n g p o i n t of i c e i s governed e s s e n t i a l l y by t h e c r e e p of ice.

The s c a t t e r of t h e r e s u l t s shown i n f i g u r e 6 and t h e wide v a r i a b i l i t y of t h e v a l u e s of o t h e r c o n s t a n t s shown i n T a b l e s 1 and 11

24 FOUNDATIONS IN PERMAFROST

TABLE 11. Values of s t r e s s and t h e power law exponent ( n ) f o r v a r i o u s segments of c r e e p c u r v e s i n f i g u r e s 4 and 5 ( a ) Segment of c u r v e 4(A) 4(B) 4(C) 4(D) 4(E) 4 ( F ) S t r e s s (T) a t p i l e l s o i l i n t e r f a c e 0.523 0.604 0.644 0.682 0.722 0.762 MPa ( p s i ) (75.86) (87.60) (93.41) (98.92) (104.72) (110.52) Segment of c u r v e S t r e s s (T) a t p i l e / s o i l i n t e r f a c e 0.802 0.121 0.152 U.181 0.243 MPa ( p s i ) (116.32) (17.55) (22.05) (26.25) (35.24)

A'ITENUATING CREEP OF PILES

TIME. h

Figure 5(a)

Long-term creep curve for uncoated B.C. fir pile in

Thompson clay at -2.5OC (27.5OF).

Arrows indicate load

increments. Stresses in regions

A to D shown in

Table

11.

. b l I I 1 l l l I I I I 0 ZOO 400 600 800 1000 1200 1400 1600 LBO0 2000

TIME, h

Figure 5(b)

Variation of displacement rate with time for creep curve

in figure 5(a).

point out the variability of parameters in nonhomogeneous frozen

soils. It appears that a general creep equation cannot be obtained

that will predict with accuracy the behaviour of pile foundations in

frozen soils. Each test gives its own characteristic values; thus

large safety factors become imperative in designing foundations in

frozen ground. In spite of the scatter and variability in the values

of the creep parameters, the results presented here show that primary

or attenuating creep is the dominant regime to be considered in the

design of pile foundations in frozen ground for the long-term support

of structures.

26 FOUNDATIONS IN PERMAFROST

F i g u r e 6 V a r i a t i o n of power law exponent (n) w i t h s t r e s s .

(0.

0 , 0 ) d a t a from t h r e e d i f f e r e n t t e s t s w i t h s t e p l o a d i n g

( e )

i n d i v i d u a l c o n s t a n t l o a d c r e e p t e s t s Conclusions Long-term c r e e p t e s t s c a r r i e d o u t i n t h e l a b o r a t o r y u s i n g d i f f e r e n t p i l e s embedded i n v a r i o u s f r o z e n s o i l s showed t h a t , f o r s t r e s s e s i n t h e range 0-1 MPa a t t h e p i l e f s o i l i n t e r f a c e , t h e dominant regime i a primary o r a t t e n u a t i n g c r e e p , where t h e d i s p l a c e m e n t r a t e d e c r e a s e s c o n t i n u o u s l y w i t h time. D i f f e r e n t primary c r e e p e q u a t i o n s proposed t o d e s c r i b e t h e a t t e n u a t i n g c r e e p of v i s c o e l a s t i c m a t e r i a l s , such a s power law, l o g a r i t h m i c , h y p e r b o l i c , e x p o n e n t i a l , and

polynomial e q u a t i o n s , were f i t t e d t o t h e d a t a from t h e p r e s e n t p i l e c r e e p t e s t e . Although no unique parameters could be d e r i v e d by c u r v e f i t t i n g , t h e power law e q u a t i o n c l o s e l y f i t most of t h e o b s e r v a t i o n s . The average v a l u e of t h e power law exponent ( n ) o b t a i n e d was 0.46.

For proper d e s i g n of p i l e f o u n d a t i o n s i n permafrost a r e a s , t h e primary c r e e p regime h a s t o be c o n s i d e r e d i n d e t a i l , and n o t t h e s t e a d y - s t a t e regime only.

Acknowledgements

The a u t h o r wishes t o e x p r e s s h i s s i n c e r e thanks t o C o l i n Hubbs f o r c o n d u c t i n g t h e e x p e r i m e n t s , and t o Douglas B r i g h t f o r computation and p l o t t i n g . T h i s paper is a c o n t r i b u t i o n from t h e D i v i s i o n of B u i l d i n g Research, N a t i o n a l Research Council of Canada, and i s

p u b l i s h e d with t h e a p p r o v a l of t h e D i r e c t o r of t h e D i v i s i o n . References

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ATTENUATING CREEP OF PILES 27

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