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P r i g ~ r o u s f l e x u r a l a n a l y s i s f : ~ r p a t i a l l y enlbedded

p i l e s s u b j e c t e d t o v e r t i c a l dnd l a t e r a l l a a d s i s p resen ted .

The s o i l r e z c t i ~ n i n t h e embedded p o r b u n 32 t h e p i l e i s

o b t d n e d u s i n g ~ o d u ~ ~ s 3f suugr.s.de r e a c t i a n t ! l c ~ r y . k i l e . . s

~xbedcfed i n bs th c3hes ive and c o h e s i o n l e s s s o i l s have t e e n c ~ n = i d e r e d . The r e s u l t s 3f t h e a n a l y s i s s h ~ w +hat t h e ver-

t i c a l l o a d can i n c r e ~ s e trle l ~ i t e s a l d e f l e c t i : > n t o arl e x t e n t o f about 7 t o 16 p e r c e n t dese f id in~ ; on the degree 3f fixity i f the v e r t i c a i l ~ ~ u i s ~f t r ~ ; ~ ; . t e r 3 f 10 gezcen t 3f the b u c k l i n g load. A c o o ~ p a i s s n 3f t k i € reec; lts ?f t ~ e a~ la lys i s

v.1 th t hose o b t a i n e d using ' i c i ~ i i v ~ l e n t Cant i l e v e r i \ .ethodl

h a s been nlade. i h e con:; 2 r i . 3 2n sl;:k:c;ea t s Lhat t he 'Lc;uiv2.1ent C m t i l e v e r c etii od ' needs mou i l i c ~ ~ t i o n s even v i ! l e n ~ ~ ~ s e d t o

anz lyse a 2 i l e sub2 e c t e d on ly 1:-._teral load . .

';hc l3:-.ds 9n p i l e f . ~ u n ! l . . t i o n s ESJ be ver. tica.1, - - . - I l : : t e r a l , c y c l i c D r d j rnmic Q r 12 2 c?n!bined n. '..ire. kl-?

f o u n c i a t i 2 n s s u p p o r t i r g ~ f f s h I; :: z t ~ : u c ? ~ r e c zr? r e q c i r e d to . t :a.rlsf~r I n t e r 3 1 l : ~ z d ~ i n v i l l i ';;i~n t o s i c l i l lo-..ris. yha

~.!.r-:? ;z foun6zt i :Jn f o r +.ej,e r . t ruc t t s . - s h3ve c>n:ider2blc=

f r e e b t a d i n g i u n s u s j o r t e d ) ltni,".h. 2he ; . resent rl:?*h?d :7f

f l e x u r a l , m z l y s i s z ~ f f r e e stc$lc!inp p i l e s n a be grouped as

f ollotr!~:

c i> :, e t h ~ d ~ ( b r 3 ~ 1 ~ . , 1964, e n , P, 7 2 ) :.;:i-b 'cqnsider ..;.flu.ive,l:..nt lo;-..i.ing zt t9.e g r ~ u n d l e v e l :xld ana1ys.e

"the ernbedaed p o r t i ~ n o f t n e 2 i l e usirig aoc~ulus o f

~ u b g r a d e r e t i c t i ~ n t i l ~ q r y . I n ttqie n e t h ~ d the def le- :q, --.L~

c t i on a t t i le k i l e head i s de termined as the sum of ( 3 - 0 e i l e c t i o n ,IL' g i l o a t the ground l e v e l . (b ) Def- l e c t i 3 n of p i l e head considered as c a n t i l e v e r f ixed

a t tne ground l e v e l ~ n d sub iec ted t o a l a t e r a l load

' 6 ' a t the p i l e head m d ( c ) D e f l e c t i o n of the p i l e , head due ts the s l q e a t the ground l e v e l .

( i i ) I\i.et.i qds (33visson -ad kobinson, 1569, 0 teo , 1S;t 1)

based on f i e p r i n c i p l e o f equ iva len t c a n t i l e v e r wherein i t i s a a s u ~ e d t h a t ~ a r t i a l l y ercbedded p i l e EW be r e p r e ~ e n t e d a:: a c m t i l e v e r with a f i x e d base below t h e grov-na su r face .

( i ) The e f f e c t o f v e r t i c a l l ~ a d on the f l e x u r a l behavi-

cur 3f p i l e s h a s n o t been c o m i d e r e d . Tile l a t e r a l d e f l e c t i 9 n a t t h e he;.c ~ f a f r e e s tanding p i l e can be l a g e and t h i s m~,lll r e s u l t i n the v e r t i c a l load

czusing an sddi t i o n a l c i x e n t ( 2 i g . 1) vktich tends

t o rxagnify the l s t e r a l d e f l e c t i o r . i .lij de,th of fixity of g ec;:iiv,lent cctnt i lever

coniguted b z . s ~ d on bending c r i t e r i a di:Pers fro^ -the

one c g q u t e a based on bu.ckling c r i t e r i a . I t a l s o depends on the f r e e ::t~.ndi~ng l e n g t n s and &he V j ~ e

3f loc,d.~;2i.:: (when bcnding. c r i t e r i 3 n i s used) i . e .

rvhether g i l e i c sub jec ted t o a, l a t e r a l load o r a

c~oxcnt. i h ~ s i n a genera l i sed si t u a t i ~ n m a u ~ n g a

p a r t i c u l a r va lue T o r d e ~ t h o f f i x i t y m g y r e s u l t i n ce r . t i2n a ~ : m n t 3f e r r o r i n t h e computed d e f l e c t i o n .

( i i i ) -e msinua n;onent i n a p i l e s h a f t i s no t equa l t o

t h e f i x e d end rnmien-1; o f the c a n t i l e v e r . The loca-

ti32 2 f the maximun; Eom~nt i n a p i l e x i 11 n o t corre- spond ~3 t h e 2 o s i t i o n of f i x e d en3 o f the c a n t i l e v e r . f'Y I n view of tne DOVE, ;: r i g o r o ~ s a n a l y t i c a l s o l u t i o n

f ~ r ~ , s t l a l l y ecitedcied long r'lexll3.e p i l e sub; e c t e d t o ver- -- Li c 1 IO~U, l d t e r a l l o :J -ylc; n i ~ r i , l L n t, i)d~t:d o:: o , ; d u l u s .;)f ~ u b -

I. ~ i e reac t i3 -n 23prodch is .,esent=d,

A u n i f c r ~ c r a ~ a - s i i c t i 12 p i l e & c r t i 2 l l y :~bedij.ed i n

c s h c s i - v e i c ~ h e s i - ~ n l e s s 2311 rnci s u b j e c t e d t3 lg:,~C.ing ? ~ l d

bou2cltzy con2ii ic?nz 2.2 shown in .Ti$;. 2 csni , iceref i .

: ' i p r e 2 i ?Lj c h 3 v . ~ s f ree-fzee 2ile ( f r e e et 2ile he26 2 r ~ i i

f r t e s t t i p ) :.;ith vertical l g c d 3,' 1 ; : t e r d lozii C, i-nd r l

.n ' r:.311 ~ n t 1,. zt tl:c t~;.. ~ - f l p r e 2 j b j sn3.;,5 f i x e d f r e e \ f i x e d at,

p i l e ?fld y ~ c e at ti&, k i i e ..': ,,.- '-h > A +i b* r ., 2.- ..l l I-,'.! 2 ,. ?.c L C

-,: 1 - 7 l.L~c-2z,l :>,-? - . L - . ,- . ,.),--. . . , , , I . ,. . .z;i~uc.ed t~ be cgna tant

:;i- -;h depth f3r c:1h6sive s!)i 1,c :md i-ncreasin_r -fin. g r l y ;z;ith -.

, ~ K _ J 21 f.3r c31.,esi 2niess s3ils (i l ic: . 3 , .

f r i z t i 3 n -".;y t;e asS.;;rr,ed c o n s t z l t ;.,i't';i ce2t.h ;>rid hence t h e

C , ,

v c ; ~ t _ i c a l l o 2 1 is 2 s s u ~ : ~ d t o decreijse l i n e z l y v i i t n d~;it:b. . . -l in c:;~E. 3 1 ~ ~ ~ ~ e ~ i : 3 i l l e s s S ) L S k l e u : l i i = k i n f r i c t i o n incre3,-

s e s line,tr.iy :;.i.a dep+h m~ hence a e v s r i k c h l l ~ a d x~tri-

. ., -. ' Free-;Yee 1 i l - e i l l < - t ~ t i v ~ J ) ~ . L E ; - (i) >.Lee s t w o i n g ,oc t i c~n . - me governing bendin;. ; ~ s ~ i r i t e ~ u , ~ t i ; n f o r t h e

f l e e s t b r d i r ~ ; ( ~ n ~ u ~ p o r t e d Itn;-t&j 2 3 r t i 3 n oS t h e p i l e is : ' i 7 r 6 . r 1 v :A br; iT?'ig.

J 1) ,-.

( a ) FREE -FREE PILE ( ~ I F I X E D - F R E E PILE

f ig, 1. Beading of a part ial ly embedded p i 1s

Bfg.2. Loadiag and end I

aom%Ltitoru~ considered for &a snalyais

( 1 ) UWHORM ( ii) L INEAR ( 1 ) LINEAR ( i f ) PARABOLIC

P2g.4. Variat ion of v e r t i c a a load

-. ; ;!, ..z i;i j:f ere n t i al cciu I ti .:n ~ , i dl con:.:. t 2 1 . 2 ,",t

coefficicn.t- ,.,;1~ its ~-2;~lc;t;e : - j>lu t i : )n i~ . r i v c r i b;1:

' , - -- . - ' k

: , = a c2s j l : c A, c i n YLz + --- + / . . { 7 , 5 7 1 - t i J

cxaz ST aazc3 m a y s 3 q ( ~ 7 ) PTR cxaz S T

warnom ayz [ T ) - * a l e a ~ ~ f i 3% 10 d g aayl 7~ s u c ~ ~ r ~ m c 3 ayA

*pEaI TesalzT p a q d * cq l ~ n T 3 3 7~ . n a g s a n ( T T )

p m 3uamoT p a g d d s 0; ~ ~ n 5 a a ? $u3incio eyJ (7) - : a n a l ~ f i

a q . j c peaq ay% 3s s u o q y p n c a a q 2 - * s u o r q ~ ~ u c o Xnpunog

; ' o l l ~ w i n g ti] c s -.r:,e ~ r o c e d ~ t r . 3 s.s f ~ r free- i'r.i:e p i l e , "&.e

e:,u a ti 3n 15 c an 1:) e tr ansferre~ 11 'c, ti! 5 YI~J a- ci.~ rr.? t z ~ i o n 2 f 2rn,

in m i ch , hi,-, = I,.?/LB . . .( 21)

'i 'ht c ~ ~ n ~ p l e t ~ s 3 h a c ; n ~f EL. 2G i s given by

'Yhe governirlg u f f e r e ~ t i a l ecju,tian and i t s s o l u t i ~ n f l~r .

-Ae e~bec i aea le::;,tri 35 tne silt? sr'e s x e as given by ;.;~s.

4 hi12 13

bounazry c o n a i t i 3 n s - i t i = 3 , i t he s 1 0 ~ c is zero i . e .

dkv/dz = 0 ana ( i i ) 'Lhe c!3meilt i s equal t~ t h e fixed. end J

'I -, ronient, i. e. d ' b /de2 = -bbp 3'

The c o n d i t i ~ n s zt b e ti2 s.nci tle c o n t i n u i t y c3nr i i t ior ls a t

gra7ilnd l e v e l are same as g iven ~y h q s . 13 t o It?. /s i

( c ) 2ree-Free P i l e i n C o h e s i ~ n l e s s b3ils.- Yhe governing d i f f e r e n t i a l - equat i3n i n nan-dimensional form may be g i v e n

f o r 0 \( Z 4 Z2

2 i n which @' = v/(z,) ; and %he r e l a t i v e s t i f f n e s s f a c t o r

C

R 51 B I / n , . The c o ~ p l e t e so l u t i o n of Eqs. 23 and 24 a r e

g iven by, r e s p e c t i v e l y

Batcl Z $ = A1 cos V U s + A2 s i n VUz + --- U

.&To +i

( d ) 2ixed-Free P i l e i n Cohesionless Soi l . - m e governing (1 d i f f e r e n t i a l equat ion and i t s s o l u t i 3 n f o r tne fkee stand-

ing (unsupported) p o r t i o n o f t h e p i l e a re same as given by Eqns. 20 and 22. S i m i l a r l y the governing d i f f e r e n t i a l equa- t i m and i t s s o l u t i o n for the ercbedded length o f t h e p i l e are same as g iven by Eqns. 24 and 26.

R U u LTS BND DISCUSSIONS

m e a n a l y s i s has been p rogramed and t h e r e s u l t s a re

obta ined u s i n g DEC-20 systeni. The r e s u l t s a re presented

f o r p a r t i a l l y enbedded long f l e x i b l e p i l e s i n cohesive and

cohes ion less s o i l s . Z f f e c t ~f a i a l load on d e f l e c t i o n and beyLd.dir?g EoEent 3f t he p i l e s i s discussed. C h a t s are prese- n t e d f o r top d e f l e c t i o n c o e f f i c i e n t , $t and maximum morrent

c o e f f i c i e n t , AIYm which a r e g e n e r a l l y r e q u i r e d f o r design. A comparison sf the l L q u i v d e i ~ t Cant i lever Lethod1 and t h e

proposed r i g o r o u s a n a l y s i s is n;ade. f-4

I t h a s been repor ted by various i nves t iga to r s (Reese -

U E

MB

ED

DE

D

LE

NG

TH

, Z2

k,

P .

(39

0

U

0, h

0

P.

Y p

l 4 nF

J

m a

w

hm

O

YH

,

P- e F

J P

O@

J

0 - d P

C*

P

O

D

i t i s observed t l&t ifi t h e case of p a r t i d l y e ~ b e d d e d p i l e s ,

t h e v e r t i c a l load i n c r e a s e c the top d e f l e c ~ o n and m s i m m 43 , 4 -J

moment s i g n i f i c a n t l y . ? o r e x w p l e , f o r a p i l e having a un- -. supported length = 2 t9y d e f l e c t i o n c o e f f i c i e n t

?Yt . i n c r e a s e s f r o & 13.7'3 t3 1 2 .CJL ( i n c r e a s e i s a b m t 15.68 per- cent) and .rr.simIc rr.orrAsnt c a e f f i c i e n t , Ah., i n c r e a s e s from

2.17 t o 2.55 ( i n c r e a s e i s a b X t 17.5 percent ) when v e r t i c a l *

load i n c r e a s e s f r o n 6 = Q.3 1;2 L = 3.03. T h i s i s due t o +Ae \

f a c t t i1: i t thc l : . teral d e f l e c t i a n a t t n s 2 i l e head i s l a r g e

cind the addi t i ~ n a l n:Drrent, cziused due t o t h e e c c e n t r i c i t y ~f v e r t i c a l Igad a4i the d e f l e c t e d p o s i t i o n (Fig . lj i s sig-

nificant.

Pigures 7 a d t sh3-iv r e s p e c t i v e l y , t y p i c a l d e f l e c t c

i o n and ~ o m e n t curves f o r g i l e s ' h a v i n g f i x e d f r e e end condi-

t i ~ n s . The r e s u l t s a r e p r e s e ~ ~ t e d f g r U = 0.0 and U = 0.06. U = 3.06 corresiJonds t o n e a i 2 10 p a c e n t of buckl ing load

f o r a f i x e d f r e e p i l e having L1 = 2.0. 1-t can be seen from -

Zig. 7 a d t, t h a t though the ve rLdca l load i n c r e a s e s the 9 top d e f l e c t i o n a?d n-mimum r, o l ~ e n t s i g n i f i c z n t l y the i n c r e a s e

i s no t as ruch as gbserved i-1 the case of p i l e $ having free- f r e e end condi t ions . F3r exa lq ie f o r a p i l e having an unsu-

pported length Z1 = 2.0 tne ~ o p d e f l e c t i o n c3efrJ icient '4Jt increase^ from 3.51 t o 4.97 ( i n c r e a s e i s abou t 6.62 percent )

and niixinun, o.on.ent c o e f f i c i e n t , q , , from -.1.71 t o - l . t 2

( i n c r e a s e i s abaur 6.26 percent ) when v e r t i c a l lohd i s inc-

c r e ~ s e d from b = 0.0 t o u = 13.06.

Tigures 5 t o t a l s o silow that as Zl i n c r e a s e s , -the

13 in t o f zero d e f l e c t i o n and tile p o i n t of aurimnl m n e n t

s h i f t u p r a r d s . ?or e x a q l e I i ~ e ;orit i . .n o f n#imrn noment rrovee fronl z2 = 1.0& t3 0 .jG a s Z1 i s - i n c r e a s e d from O t o 2

f ~ r f r ee - f ree s i l e v , i t h U = 0 . 0 .

F i x i t y a t the h e ~d 3 '. t h ~ f l c n . : . n l ' lerbsr s t r q n ~ l y influences b 3 t h c ief lec t ion :::d xonent . Yhc dec r t e of f i x i t y

B, zt the k i l e h b ~ d c m be d t 2 i n e d a s t h e r a t i o s f We (1 -

V) Z z W

DEFLECTION COEFFICIENT, A~

F O R Um0.06 FOR U-0.0 y = 1.0

BMQ-0.0

f r e e

k = CONSTANT FOR U*0-0 6

B M a= 0.0

Fig *&

MOMENT COEFFICIENT 8 - AM,

T y p i c a l moment curve f o r f ixed m free p i l e in eoheaive soil 5 4~

Eorrent a t -the p i l e head t3 t n2L t sf t h e rcm,ent a t tine ;Fie head 3f a f i x e d h e s d e d 2ile ( n o i ~ t ~ . t l , n a t t h e & i l e head; . k c c o r b n g l y t h e zer3 p e r c e n t f i x i t j - co= . r e s i ;~nds ta t h e ca se 2 : f r ~ c headed ~ i l e a i lOO ;er.'ccnt fixit;;: cr)y7:ezxqnd, t,3

the C ~ E E of f i x e d heaaed p i l e . g ~ v i s s o n (1573) s c g g e s t s t h a t -tine ciegree of f i x i t y *-st can u s u a l l y b e d e v e l 3 p e d between

+he p i l e head a d tine g i l e eas i s 31 t n e orde r ~f 50 yer- c e n t . A c o m p a i s o n of r e s ~ l t s f )l: 'ii = 0.0 ar,d iT = i) .03 shoq~vs

that f o r a 2 i l e having an u n s u ~ ~ o r t e d length Z - 2.0 and a 1 -

degree of f i x i t y , ? 3f 30 ijercenQ6-1 the sile head, t h e top

c o e f f i c i e n t & ~ n , 4 . E 2 5 w -Ci.kLO \ i n c r e ; i ~ e i s about 2.5 - .

e n ) md a i x i ~ u r , ; i s ~ i l.i-zt. rr.onlen t c x f f i c i c n t fron 1.375. t o 1.575 ( i n c r e z s e i s a b w t 1G.6 gercen t ) when v e r t i c a l load

i n 5 p r s c t i z a l si- tuati Jn, tt .c e f f e c t 3f vertical 13.12 rray ,

r L f l ~ f ~ c t + L , t t h e ;fcrl;ical l ~ s 6 sl ; ' ruf icc~ntly h f f e c t s

tLie f l k x u r a l iri;r?c~vi3ur 32 pc . r t id . ly e~~.-ced[-ied p i l e s hiis two

i m p l i f i c a t i 3 n viith I c g d d ~ ts tile p e s e a t day p r a c t i c e i n a n a l y s i s mu des ign ~f 2ilt~.

(i) ,file ' L q u i v d e n t Czn t i l eve r a -e t i l~d ' v,hich is used i n tile a ~ a l y s i s 3f y ~ ~ t i - , . l l ~ a:-Gedded p i l e s do n g t t & e i n t o

5ccJunt t h e e f f e c t ~f s c i a l load , Therefs re the use of

' Ec_uivaifnt C m t i l e v e r i. et~;:>u' f a r m a l y s i s of v e i t i c a l l y

~ n i l i , t e r a l l y loaded p xtidl) eabeaaed 3ile.s w i l l r e s u l t

i n under e s t i l ~ a t i o n o f t o p d e f l e c t i o n aad Piaximrn monents.

( i i j i t s h ~ z i l d b e enslcrc-d t h z t t h e l L ~ t e r . s i d e f l e c t i x l

under the con;bined v e r t i c a l and l a t e r a l loads does n o t exceed the perr r i ~ s i b l e lird ts.

(b) Sohes ionleYs 6oi.l.- k e s ~ l z s f p r tk ie c a s e :)f 2 i l e s i~

cohes ionleas s ~ i l a r e alss g b t d n e d and faund t o be sf the

s s e n;;ture 2s 3f tLe p i l e i n c2hesive s a i l s . The g e n e r a l

conc lus ians a r r ived aith r e g a d s t o the e f 3 c t of v e r t i c a l l3ad a r e v a U d f o r p i l e s i n cohes i3niess s ~ i l s d s 3 .

N 9 n - D i ~ ~ n s i ~ n a l D e f l e c t i ~ n C 2 e f f i c i e n t at t h e Y i l e Head

Il'hk ; t ~ x i , s i k l e 1 ~ t e r ~ l load is g e n e r a l l y based 3rr o e 2 ~ y r L ~ s i b l e l a t € l c ~ l clc;icc-L;~~n Qt t h e d i l e head. The

der" lec t l3n st LTe k i l e he,d i s d e p n d e n t 3n a p s t f r~7~1 t h e

n ~ ~ n i t u a e 3 2 1 , terz l l ~ n d , xhe u n ~ u p p o r t e d length , the

dc,ree 3f flxiTJr 2.t t h e p i l e ht-ad , ~ n d the n ~ ~ ~ g n i t u d e of l o d d . ' /nerer 'art : tde r e s l t s f o r d e f l e c t i o n at t h e

r l l ~ he,td a e 21 e s e n - ~ e d in tiie ; , Y E 3f c h a t s f ~ r - J ~ , ~ ~ ~

v d u e s ~f u n ~ u p p o r t e c l Len; ti: U1, " (?ecrce o f f i x i t j ; , 3 dr,d

~ l ; z l -. l ~ ~ d f a c tsr, b . dll;u;.e CJ t h e t~~ d e f l e c t 8 a n

c o e z f i c i e n t ;3-t f o r p i l t i z l $ ~:.;sBded y i l r s i n c ~ k i ~ i v e s o i l . The r e s u i t s a r e pressn--c b -' f3r ir = 0.0 arid U = 0.3; 2nd

de:~rec o f fixity, E = v .O1 u;?d 1.0. a i r i . 1 ~ r e s a l t c f o r

FREE STANDING LENGTH 821 Fig.5 .Uef lec t ion at the pile

head for p i l e in c3hesive s o i l

-FOR U-0.03 FOR U-0.0 y = 1.0

FREE STANDING LENGTH $21

Pig, ,y .Def lec t i2n at t h e p i 1 head for p i l e s in c* hes i3n less soi 1

I t cm be a o v m t h a t t h e l t i t e r a . l de r ' l c c2Lm v ~ x i e s

l i n e a r l y v , i t . h degree 0 5 fixit;:. 3 ihere fore fro:!. t,",~: r e s u l t s rr .ecente6 d e f i ~ ~ t i 3 n v ~ ~ l u e ~ c;ll 't\e 3 k ~ t c i c e d f ~ r an3; o t h e r

Ciegree o f f i x i t y bj- i irle;lr in ' ier201L+L m. it is ;;so T x n d J . - 1 .

. t ,?1 .ti3nU:~,,, :,etv,hen i _lm.cJ '"; ' t i s a > g r n x i ~ x t c l y l l n c ; ~

';kt:, 3 3 o i l t 13 p e r c e n t s7f -the b~ci(1i.w load. i h e r ~ f 3 1 . e ~ ~ i n g -- .

the c n 3 z t s yreae-n-ted i:- i i g . 5 .31d 13 f a r .L = 0.0 mil L&.u;~

i h - A v a l u e s f3r 0th:~ ~ i i l i l e 31' L u2- t~) 13 2ercen-t 32 buck- Y b

-I. a n g 1 ~ ~ 2 can b e obta i f i e6 usin:; l i n e a x inter ;oiazidn ( o r

Non-diniendsnal Laxinun: i:.or.ent C o e f f i c i e n t

F o r t he structural design sf y i l - e s i t i s necebsary

t3 .ltn.on. the -lr!: juin?~;u) mar-cat i n the p i l e s h a f t . ca,se of

frc-t-free p i l e a , i c e mzxinrdn siorjent ( pos i t i v e nomen t ) occurs

st SoLie dep th 5~jlox7 t n e ground leve, i . l n t i e c m e of f i x e d

f r e e ~ i l e s tne m r : e n t 2% tfie p i l e head i s n :a : inum (negat ive

monent) . 3'31. s i l e s h i u i n g in termedia te f i x i t j i c snh i t i3ns a t tine p i l e head, t h e ~ . J i n ? c m~r ren t occurs e i ~ e r . at t h e p i l e Gejd j nagati-ue rn3centj. 3r at s3i1ie depth be low t h e

gr-,und l e v e l ( y o r i t i v e n3r.entj depenbcg upDn ~e hearee of fixi t y .

Figure i1 a d 12 z i v e r e s y e c t i v e l y -!he max ix run i 33si-

t i v e i~~scient i+ and EiOi i lCn t 5% t h e gi l e head, -&. . fsr p a r t i - AWL 3 *L1

1 5ri:bedded & l e s i n co!le;ive s o i l . l h e results a e p:,asen- t e d f o r LI = 0.0 ;fnd :! = 2 . 5 3 a d ciegree 3f f i x i t y , F = 0,0.5 3~ 1.0. Sil idlTz r e s u l t L fs;. ~ i i r ; s in c o h e s i s n l e u ~ s o i l a r e

=reden ted in 2i.c. 13 :>-i12- 14.

;i cfoc.p.zison !I.:-' ike r e s u l t s o b t a n e d sing the gz, ;2dvalen t c',~J--~-; l eve r 1, e:.. od* ( T C ' ! 1 '. ~i t h those ob t d n e d

s s i n g t h e yr.~i;;sed rigsi 'ove ;i1cJ;h3d i s ~.. : ide i n 9r.iler t o b r i n g

'32 t t!': F :z$ ,$ ~ ~ i r i ! a t i :3n i :.?-u:> lved ~ f i d L. mi ta.t l dnz of ti1 e ' LqLki-

embedded y i l e s .

. . 1 . 5 1 e V L ~ . ., i,9 3 f ,A ;? t , ined g s i n g ' 5 ~ : ~ i v ~ i e n t Cant i -

J L l e v e r Ze-&xi' as g r 9 2 ~ s e d Sjr 3av i s san and 2,fobinson (1565)

t n , t fJr :i r^r~t--r 'r€e 2 i l c , t h e dnf l e c a ~ n vskdes o b t d n e d by 1. t,?th t i l e r e t h ~ d s a c . ~ $ y r 3 X i ~ , ~ . t e l y t h e s a l e vjhen "

dl is gre3.- t e ~ . ti-1s.n 2 . 371 viil~*es ~f L7 l e s s UL-a 2.0, ~ A e u ~ e af

L

" i ~ ~ ~ i v r i l e n t Carrt-~lever. i e t i ioLi > ; i t h averGze va,lues 3f d e p ~ & ... o f f i x i t y (1.4 i. f o r c3hes ive s o i l s and l.bY ffor c3hesion-

FOR UxO.03

, FREE

k :CONSTANT

. FOR U = 0.0 = 1.0

F I X E D H EAD

FREE STANDING LENGTH 3 21 F R E E STANDING LENGTH,Z1

i?ig. 11 .h.i.axiRun; p s s i t i v e molilent r ' ig. 12.b.3nent at t he p i l e f ~ r p i l e s i n cohes ive hedd P a r d i l e s i n cohe. s o i 1

0

FOR Uo0.03 ----- FOR U.O.0

F R E E - HEAD

I I I

F R E E HEAD

0 1 2 3 L 1

o 1 I I I J 0 1 2 3 L

FREE STANDING LENGTH, Z1

2ig. 13 .b~aximum p o s i t i v e rnD- nent f ~ r p i l e s i n c o h e s i a n l e s s s o i l

k : ? h ' X

FOR U=O.O

y - 1.0

FIXED

/HEAD

0

F R E E

* I I I

0 1 2 3 L FREE STANDING LENGTH 3 Z1

Fig .14 .h~ment a t the pile ' head f3r p i l e s i n

c o h e s i ~ n l e s s s o i l

, l o s s s o i l s ) u ~ l i l result i n s i g n i f i c a n t e r r o r . T o r z1 use of sxac t v a l u e s o f de2th C I ~ f i x i t y g iven by i lavisson and Sobsnson ( 15 69 hhowever re;- It;, in r e ~ s q n a b l e qreernent bet-

l oad , t h e use ~f 'Gquivalerlt ' C antilever BLetnodl h w e v e r , w i l l r e s u l t i n 'under. esJdr:.;.;tion ~f d e f l e c t i g n 5s the meth~d does

n ~ t t a k e i n t o , zcc~u i~- t the e i ' l e c t of vertical load .

t i a-L, 1 1 - C3n.pzrison gf d e f c c t i g n s obt-nrd u ~ i n g ILqciv* l e n t S~~ , .n t i l ever l:.stl,qd' (LCL) 2nd ",.:e p g ~ o s ~ d s a l y s i s

u = 0.3 b~~.< = 0.0 -- - -- - Unsup-INhon-~1~-ensional d e f l e c t i o n c o e f f i c i a t a t t h e p i l e 3:tod hfi.d: iiyt length/-,

I rogosed ana g s i s Yercentage m- zl u s:rlg, ~ L ~ ~ ~ e y e --- oheslve voneslan ~ 3 n ~ ; s l v e oneslon o l e s lve o e s l o G

l e s s l e s s l e s s s o i l s o i l s o i 1 -- s o i 1 s o i l s o i 1 - -

0 0 -3 15 1.944 1.432 2.441 36.1 29 . 3 (1.365j ( 2 . 3 5 6 ) (4.62) ( l .63j

1 4.KIt 7.317 5.151 7 0765 11.2 5 e b C 4.943) (7.7161 (3.61) j 0.66)

2 13.1 l b .251 l j .791 lL .593 5 .O 1 .6 i 13.27) ( l~ .5%j (3.74) ( 0.15)

4 5 2 05 65.04 53.214 64.762 1.5 -0 04 10 453.E; 547.7 497 01 543.6 0 * 7 -G .& -- -----

( ~ h e ~ ~ d u e $ g i v e n i n b racke t s e thoLe obta ined using exac t de2th of f i x i t y )

( i i ) Fixed-Tree pi le . - The v a i u e s of %t, obtained us ing 'E$uiv;lent Ca++'i i lever hletho?' m e g iven i n 'I'zble 2 f o r U=i)

a l o n s x i t h til3ee s k t a i s e d u s i ~ ~ . the p r e r e n t ana ly s i s f o r

c o ~ , p a r i s ~ n . it is o ~ s e l v e d ̂&at i n the case sf f i x e d f r e e

~ i l e t h e r e i b a s i g n i f i c a n t c i i l e r e n c e i r ; the top d e f l e c t i 3 n

v n l u e s up to Z1 < 1.0. Keiuo:?i:cle agrsen.ent i s obt;;i.ned only f 3 ~ . z1 2 4. h ' ~ r example i n t h e czse of cohesive s o i l s , the

percentage d i f f e r e n c e betiyeen the L$-t v a l u c s i n as h i g h as

& .39 pe rcen t -;,hen Z1 = O .i) s d 14 p e r c e n t a t Z1 = 3. yhe

corresponding v a l c e c for cohes iunle-s s o i l s a re 4t .27 per- m-'

--

. -. c b . ? . ; l t l ~ c : r e r ' i ~ be f r e e ,;;iljr,

-- --- - ---- L nsi.ii-\ 1 ~ ~ : ~ . - a i 3 . ~ r ~ ; i ~ n a i deZ2.c:c2~i 331 c3 ei'ficit-R.? a t t h e , i l e iL.tea i h e z u .

leaiti:j- 7. , , -- i j s i n ~ ; ;-Ch ~ 1 . 3 ~ 9 ~ € . a jl?-aljisi s' ; k l b c € n t g e Z1 i f e r e s e 5 ----- -

--

I n or8uer t o avoid this e r r x in c o r r ~ g u t a t i ~ n of def-

l e c t i ~ n v a l u e s , ~ ~ ~ u f i e d v a l u e s o f depth. o f r ' i x i t y f ~ r f i x e d

headed p z t i a l l y ercbeddec! &11k I n cohes ive aria cohesi3nlecs

sails f ~ r v a i 3 u s u n s u y g o 2 t e ~ l c r g t h s a 8 2; esen ted in Pig.

13 ' a e s e v a l ~ ~ s =e ~ ; ~ ; i c , * b l e oniy when the re is no v';rAd- c.d load. %hen t i l e re i s v e r x i c d load, i t . s h ~ u l d be r e a l i s e d

t h a t use of ' t q u i v a l e a t C a t i l e v e r I L e t h ~ d t v i i l l r e s u l t

i n m d e r estig.a+don or' d e f l e c t i o n s .

ti) 3ree-free ~ i l e .- W e t L ! _ u i v c e n t C a x T j l e v e r i,.eti;9ut

~ k v i ~ u s l y sucges t s tcac i c e u .o~ . sn t t h e f i x e d end sf w e

er;ui . t ra lent c ~ n t i l e v e r is design rn3sel;t;. 3ov;cvzr, i t i s

f~und m;.-..t in ct2-se of f r a e iic;;aed p i l e t:Ie i i x e d cnd r..orr,ent 3 f the ' e ; u iva l en t ~ ~ " n t i l e - r e l . ' i s n i g h e r tilacl t i e 3c-t;~~l

I

:( e

n ~ i m l ~ noo!ent o b t j n e d u;i^.; t n e 2r.o:s-sd t l iemy i n t h e

\ -- J. p i l e s h h f t . $.trice i n o r l $ e ~ * r.; ;et t h ~ liirt? i.;-Xi~liIL 0011.5.k'lt

f ron; the ' bc ;u iva len t C a n t i l e v e r 3. ~ t i i o d ' . r educ t ion factors;

based on the r e s u l t s o f the p r e s e n t a n d y s i s a e suggested

and - . the sane we preseri ted in Eig. 16. 2.3 I-

----- ------------

i I I I , i k m CONSTANT

1-3 0 ' 2 L 6 8

10

i!e,,z

F R E E STANDING LENGTH , 21

2.1

Big. 12 .Biodified depth 9f fixity f o r f ixed f r e e p l h . I F

\ AFTER DIVlSSON AND

\ ROEINSON ( 19651

\ - \ ---- - PROPOSED THEORY

FREE-FREE PILE - k r CONSTANT

\ \ SR ST

Z r n a x u 4

1.9 1 ------- o w - - - - - -

\

F R E E STANDING LENGTH. 21

pig. 1 6 S e d u c t i a n f a c t o r f o r maximam p o s i tipa, '

moment f o r a free headed pile

. - i l i j 2 i x e d - 3 e t y l i a . - ;z is + . L i ~ L ~ t h h t in Ck9e fi:,:Ed

h a i d e d .iis ivhen t h e r e is no ver.';ic.;l 13aiJ cfie Kocent sbt;hir.ed f ror . the ' iquivalen ' , C=it . i lever l i ~ t f i a d t 1 .$B -. . -

~ : s tllf rlYBTi:ES ~e$ t ! ! 3: f i x i t y f . j l coilesivf s o i l arlu l . C y '

i n case of cohesisnlesi ; s o i l j found t o b e in 9 3 ~ 8 w r E ~ - .>

r e n t 1,vitn ale a c t u z l nofieri-t. vorl.ent v;>ues ,s coziPuted

using t h e ~ r o 2 s s e d o,il t i i l ied i jepal of f i x i t y (Big. lt;) a e id ;?:)oli agreement only f-r u n s u p y o ~ t f d l e r l ~ t i : ~ ec;ilzi t o a d

51.eater ' c h a 2 . l h e r e l ' j r e , v,il-.n u c i ~ k ule r[.sdij'ir;d ec;u-ivl:- - l e n t l eng th , a c o z r e c t i 3 n f d ~ t 3 2 . 8s g iven i n 2 ig . 17

1-0 -

C/o- - k =CONSANT -- ---k *hi,"

0.8 - PROPOSED DEPTH

Zmax OF FIXITY

0.6 I I 0 0.5 1 SO 1.5

, I J

2.0

F R E E STANDING LENGTH , 21

?ig .l7 . h e d u c t i ~ n f a c t o r f o r p i l e head m~ment for a f ixed headed p i l e

1. v e r t i c a l 1323 i ; icre&ses 1 k t e r . d c e f l e c t i ~ n a d r;i;-ai-

i l ~ n ! ~0n;en t sigrii. fi c ~ ~ L J ? . 2h 3 i:-, crekse in s i l e helid d e f l e c t -

i s n and riisinurfi Koc.en-!! G U E t~ :, v e r t i c a l l o a d 3f 10 2 e r c e n t

3f t lcckl ing l o a d can bc sf z b a u t 7 p e r c e n t t~ 1 6 percent ;

cle;endir<; on t h e degre;: o f f i x i t y of t h e p i l e h e ~ ~ d .

F J ~ f i x e d headed g i l e s , the t tse 3f values of fixity sugges- m . .

ted by i j a v i s e ~ n r;nd I i o b i n s ~ n (1965) w i l l r e s u l t i n s i g n i f i - ../I

c s n t e r r o r , p ; ; i r t i c i l l s l y r"~r p i l e s having snialler unsupg3r-

t ed l e n g t h s hherei l i . t h e e r r o r i n com;?uted d e f l e c t i o n could

be ~ f the wCer ol' 2 0 percen t . Therefore , va lues of d e p t h of

f i x i t y for f i x e d headed p i l e s we suggested based on t h e

r e s u l t s o f the 2 r z s e n t analysis.

3 . 'khe f i x e d e ~ i d r;~n.ent as obta ined fror!: the 'Equivalen t C a n t i l s v e r L e th3dq i s nuch l u r g e r t h a n t h e naximo! moment o b t d a e d using t h e rL csen t r i g o r o u s a n a l y s i s , Therefore, tile

suggested correctl .- .n f a c t o r s s h ~ u l d be used t o o b t d n the

d e s i g n :~ .ment f r 3 ~ tilo c o q ~ t ' e d valLles o f f i x z d .:r_d 7-3!3- ,2t

3 f t h e er-1;.iviileiit c ~ n t i l e v e r .

k5 $.UiS\iC&j

1 , , . < , 1 , . - r / 9 ' L a t e r a l 3-csist;nce of p i l e s in C.2hc- :jive a ~ i i s ' , 2 o~ i . . nz~ l nf ' +he L. o i l i: .echmics ma Povadatiom Z i v i z i s n, L C $ , ~Tol.>t),lTo *jI.i:2, P r o c , ~ a g e r 3E25 ,pp -27-63.

F q

2. Dn.-vi~on,6.. i.( 1560; , 'Beh3v i .mr 3f F l e x i b l e V e r t i c a l iji l r ; ? ~ Subjec ted t:, l : . o~?~cn t ,Shc . s and d i a l Jioaa' ,Ph.T).thesie subnitteci t o Ur,ivcr si-'i;;. 3f 1 LlAnoir., i : rbsna , llinais, ' i . ;d

3 . D,.7~isson,l. .:i. ; a d k9bin;~n,K.L,( lcJ6>) , 'Bending and 3i3ucl.;- l i n g .;f kar . . t ia i ly E ~ : ~ e d d e d E i l e s ( , kroc.'VI ICLBJ?E '491.2, ~2.233-246,

4 , Leyden,!Y.V.( 1971) , ' i l a s t i c k l a s t i c Analysis ~f L a t e r a l l y L3aded t 'ree S t ~ q d i n g i'i l e s ' , DL INGLNIE;;~~E/J~G L ~ / N B 2 ' j / 11 J U N I 1371.

5, a c k , and L~ese,L.C.,(lC,~),~Generalized S o l u t i c ~ n s f o r L a t e r a l l y io?. ted 2 i l e z 1 , d m r n d o f the S o i l L.ech+ n i c s and Y o u n d ~ t i r ~ n s a i v i s i o n , k C E , V o l .E6, ND.SB:~, 3a3er ij3.262;) ~ J S ,63-5 1.

6. Oteo,C.b.(l '>&,lj , I i , ;Sic$lified i;na.l;rsis ~f ;t'.iles qri,& L a t e r a l b a d & ' , li ICLI-TE, S t ~ c k h ~ 1 . m .

C - r . xaaszruy, G. j 1'; 74.1, F l e x u r a l Zehaviour r>f A x i a l l y a d

L a t e r z l l y Lo a ~ e C I n d i v i uuzl ~ . i l e s sad G r o u p s of P i l e s t , rh.3. t l ;ct is s ~ . ; i i i t t t~ i ; i?dixL ln;jtiL-iut& or" :, c i ~ n z e , 3 3ngi-ii~re, l i l d i - .

6. hed3.y, .k.L . sad ? . l i ~ m , ~ k : _ ~ , ,;.S . j l i r / G ) , ' i;i;ckling of &11gr ,?nd ; Z . . i . ~ ; , l ) - -1;. e ~ c i e d L ' i l e ~ ' , J ' ~ u z ; ~ L ; ~ 3f ~ & e : o i l iQLech- . . . ,:nits and 'I':zunitaJ<iclr,s 3iv.~s;.;:n, ~ ' J L , ~ ~ o . z 1 ~ . 6 . m.