B u ll .F a c .Ag , . rS a g aU n i v .N o .78:57~65 (1995) BEARINGCAPACITYANDDEFLECTIONOFLATERALLY LOADEDFLEXIBLEPILES V.V.R .N.SASTRY,TatsuyaKOUMOTO,F .J .MANOPPO andJ .E .R.SUMAMPOUW ( L a b o r a t o r yo fC o n s t r u c t i o nE n g i n e e r i n g ) R e c e i ; 廿e dNo世e m b e ; γ18 ,1994 Summary 巴p i l ec a p a c i t y, t h eb e n d i n gmomentv a r i a t i o nw i t hd e p t ha n dt h eh o r i z o n t a ld i s p l a c 巴m e n t s Th 巴l o a dl e v e lo fi n s t r u m e n t e dv e r t i c a ls i n g l ef l e x i b l em o d e lp i l e si nl o o s es a n d,u n d e rl a t e r a l a tt h l o a d sh a v eb e e ni n v e s t i g a t e d . Ther e s u l t so ft h e s el o a dt e s t sa r ecomparedw i t ht h e o r e t i c a l e s t i m a t e sb a s e do nt h ec o n c e p to ft h ee f f e c t i v eemb 日d mentd e p t ho fe q u i v a l e n tr i g i dp i l e sf o r u l t i m a t ea n de l a s t i cc a s e s .R e a s o n a b l巴 a g r e e m e n th a sb e e nf o u n db e t w巴e nt h eo b s e r v e da n dt h e p r e d i c t e db e h a v i o u ro ff l e x i b l ep i l e s . d i n gmoment,d e f l e c t i o n,f l e x i b l ep i l e,i n s t r u m e n t a t i o n,l a t e r a l KeyWo r d s :b e a r i n gc a p a c i t y,加n l o a d,m o d e lt e s t,s a n d INTRODUCTION E x t e n s i v es t u d i e sont h eb e h a v i o u ro fr i g i dp i l e s(Kr >0 . 1 )u n d e rl a t e r a ll o a d shave i n c hHansen1 ,P o u l o sandDavis 9, MeyerhofandS a s t r y5,6). Theses t u d i e s beenr e p o r t e d(Br havel e dt oc l e a rd e s i g nc o n c e p t sa sf a ra sr i g i dp i l e sa r econcemed. However,i np r a c t i c e, mosto ft h ep r o t o t y p ep i l e sa r ef l e x i b l e(Kr<0 . 0 1 )whichbendu n d e rt h ea c t i o no fextemal f o r c e s . Attemptshavebeenmader e c e n t l yt or e l a t et h eb e h a v i o u ro ff l e x i b l ep i l e si nterms o fe q u i v a l e n tr i g i dp i l e sbyi n t r o d u c i n gt h ec o n c e p to fe f f e c t i v ed e p t hf o rb o t hu l t i m a t eand 8 e l a s t i cs t a g e so fl o a d i n g (Meyerhofe ta1 • , S a s t r yandMeyerhof , O l, " Y a l c i nandMeyerh o f 1 3 ). 1 nc o n t i n u a t i o no ft h ep r e v i o u ss t u d i e s, t h ep r e s e n ti n v e s t i g a t i o nc o n s i s t so fi n s t r u m e n t edmodelf l e x i b l ep i l e sb u r i e di nhomogeneousl o o s esandands u b j e c t e dt ol a t e r a ll o a d s . Theb e n d i n gmomentsi nt h ep i l es h a f t,t h et o t a ll o a dandt h el o a dl e v e ld i s p l a c e m e n t s undereachl o a di n c r e m e n twer ・ er e c o r d e d . Theo b s e r v a t i o n swerea n a l y z e dt ov e r i f yt h e a p p l i c a b i l i t yo ft h ee f f e c t i v ed e p t hc o n c e p t st op r e d i c tt h ep i l ec a p a c i t y,maximumb e n d i n g momentandh o r i z o n t a ld e f l e c t i o n so ff l e x i b l ep i l e sunderl a t e r a ll o a d s . B u ll .F a c .A g r .,S a g呂 U n i v .N o .7 8( 19 9 5 ) 5 8 1、a b l e1 P h y s i c a lP r o p e r t i e so fP i l e s R e l a t i v eS t i f f n e s so fPi Ie1 王γ(x1 0 -4) D e p t h A l u m i n i u m A c r y l i c H a r dR u b b e r E s ( M P a ) D(mm) 。/ち E p = 6 . 3x1 0 ' M P a E p = 0 . 3x1 0 ' M P a E p = 0 . 0 0 3 X1 0 ' M P a 1 6 0 0 . 0 7 7 1 6,3 4 0 . 0 A 1 * 1 01 .7 P l* R 1 * 1 0 1 4 1 .8 P 2 3 0 . 4 4R 2 3 2 0 0 . 1 5 4 5 1 0 . 6 A 2 * 2 0 6 4 0 0 . 1 9 7 1 8 . 6 A3 1 .2 P 3 * 4 0 N o t e :Ep=Moduluso fe l a s t i c i t yo fp i l e ;B=16mm( P i l ed i a m e t e r ) ; Es=W e i g h t e da v e r a g eh o r i z o n t a ls e c a n tm o d u l u so fs o i li nd e p t hD ; *=P i l en u m b e r 彬 キ 地 MODELTESTS S o i lData DryToyourasandu s e di nt h et e s t swasu n i f o r m l ygradedhavinge f f e c t i v es i z e 0 . 1 2 7 . Theminimumandmaximumv o i dr a t i o so ft h esand m mandu n i f o r m i t yc o e f f i c i e n tニ1.6 e s p e c t i v e l y . Thea n g l eo fi n t e r n a lfrictionφdeterminedfromd i r e c t were0 . 6 1and0 . 9 6,r 3 s h e a rt e s t sperformeda t ap o r o s i t yofη=4 7 % was31 "( Koumoto andKaku). The ,backc a l c u l a t e dfromr i g i dp i l et e s tr e s u l t s, was h o r i z o n t a ls e c a n tmodulusEso ft h esand s e e nt ovaryl i n e a r l yfromz e r oa tgroundl e v e lt o3 6 5kPaa tad e p t ho f3 8 0mm. P i l eData c r y l i candhardr u b b e rp i p e shavingo u t s i d e Themodelp i l e sweremadeo faluminium,a d i a m e t e rBo fabout1 6m mandw a l lt h i c k n e s so f1 4mm. Thep i l e swereb u r i e dt oad e p t h 2 0 m m and 6 4 0 m mi nsand s ot h a t D/B v a l u e s were 1 0,2 0 and 4 0, Do f1 6 0 m m,3 r e s p e c t i v e l y . Ther e l a t i v ep i l es t i f f n e s sKrrangedfrom 10- 1 -10- 5 • Eachp i l ewas i n 守 strumentedwithw i r er e s i s t a n c es t r a i ngagess t a g g e r e da t as p a c i n go f4 0m m ont h e o u t s i d es k i no ft h ep i p e sf o rt h emeasuremento ft h ebendingmoments. Thegageswere p r o t e c t e d by e n c l o s i n gt h ep i l ei np o l y o l e f i nt u b i n g . The d e t a i l so fp i l e st e s t e da r e セe di nTable1 . summar LOOSESAND φ 3 1 0 田 1← 1む STRAIN / ,,1 ' l / 1 1 1 : 1 _ . . d1 GAGESι--- しJ ' → B← F i g .1 E x p e r i m e n t a lS e t u p 1 1 一兆一一 S A S T R Y• K O C l ねT O• l ' v L ¥ N O P P O・ S l l l i ¥ l l P O l : W :BEARlr . :GCAPACITYANDDEFLECTIONOFLATERALLYLOADEDFLEXIBLEP I L E S 5 9 T e s tD e t a i l s Sandwasr a i n e dfromac o n s t a n th e i g h to f5 0 0m mi ns q u a r es t e e lbox4 8 0m mx4 8 0 3 m mi ns e c t i o nand8 0 0m mdeeps ot h a tt h eplacementu n i tw e i g h twas1 3 . 7 2kN/m. 京市en h ep i l ewasp l a c e di np o s i t i o nandt h er a i n i n g t h es o i ls u r f a c er e a c h e dt h er e q u i r e dl e v e l,t c o n t i n u e dt i l lt h et a n kwasf u l. l Theh o r i z o n t a l l o a dwasa p p l i e di n1 0 1 2i n c r e m e n t se a c h e p e n d i n gont h ee s t i m a t e dp i l ec a p a c i t y,a p p l i e da tah e i g h to f2 5 . 4m m b e i n g1 1 0N,d . Undere achl o a di n c r e m e n t, t h es t r a i nmeasurements abovegroundl e v e la sshowni nF i g .1 a tt h egagel o c a t i o n swerer e c o r d e dbyu s i n gLoggermateDL1 2 0 0,w h i l et h el o a dl e v e l o a di n c r e m e n tl a s t e dt i l lt h er a t eo ft h e d e f l e c t i o n sweremeasuredbyaLVDT‘ Eachl l yz e r oandt h egageo u t p u t swerec o n s t a n t . h o r i z o n t a ls e t t l e m e n twasp r a c t i c aI 1 0 0 60 (Z) ロ ALUMINIUM( A I,A2 , A 3 ) 番 号 A CRYLlC(pl , P 2 , P 3 ) 繍 R U l l B E R( R l, R 2 ) 相'何回hvd 刊品︿ハ︾白山嗣 KF 脳同開館。 (Z} ぬ︿。、同 40 A 3 口 50 P 3< 1 > A 2 口 。 P l 1 5 0 1 0 0 DEFLECTION (m冊 ) l 申 告 50 co持IPUTEDCAPACITY(N) F i g . 2 T y p i c a lL o a dD e f l e c t i o nC u r v e s F i g .3 C o m p u t e da n dO b s e r v e dC a p a c i t i e so f t h eP i l e s . n N M ω 7 A 守 悶 N 0 出円 M I D G RU M円 EU 2 . 0 0. 1 (自)同国ド弘同信 申. 3 P I L E :A2 D=0 . 3 2田 P I L E :P 2 D = 0 . 3 2m ( a ) O,4l_~一一」ー」ー」ー」ー」ー」 F i g .4 a V a r i a t i o no fB e n d i n gMomentW i t h D e p t ha n dL o a df o rP i l eA2 ( b ) 0 . 4 F i g .4 b V a r i a t i o no fB e n d i n gMomentW i t h D e p t ha n dL o a df o rP i l eP 2 . B u ll .F a c .Ag r . .S a g aU n i v .N o .78 (1995) 6 0 (E.Z)HZ国交)翠白同旬、門戸島国語。ハ} T e s tRe 白u l t s 2 0 Load d e f l e c t i o nc u r v e so ft h ep i l e s ロ ALUM1N1UM(Al,A2,心) I /十 骨 ACRYLlC( P l, P 2, P 3 ) / J t e s t e dweref o u n dt ob es i m i l a rt ot h o s e r e p o r t e de a r l i e r from s i m i l a rt e s t sw i t h l a r g ei n s t r u m e n t e dp i l ei n homogeneous A3 ロ s o i l s( S a s t r yandM e y e r h o f l 0 )w i t hsome 1 0 t y p i c a lr e s u l t sp r e s e n t e di nF i g .2 . The f a i l u r el o a dwasd e t e r m i n e dbye x t e n d i n g t h el i n e a rp o r t i o no ft h el o a dd e f l e c t i o n C T P 3 h e c u r v ea ss u g g e s t e dbyT e r z a g h i12 andt . p i l ec a p a c i t i e sa r ep r e s e n t e di nF i g .3 -OBt 1 0 2 0 T y p i c a l r e s u l t s o f measured bending OBSERVED MOMENT (N.m) momentv a r i a t i o nw i t hd e p t handl o a dl e v e l F i g .5 C o m p u t 巴d a n dO b s e r v 巴d M aximum r ep r e s e n t e di nF i g s .4 f o rp i l e sA2 andP2 a B e n d i n gM o m e n t s ( a )and4 ( b ),r e s p e c t i v e l yw h i l et h eo b s e r v e d maximumb e n d i n gmomentsi nt h ep i l e sa r ep r e s e n t e di nF i g .5 . Themeasuredd e p t h so f t h ep o i n t swheret h emaximumb e n d i n gmomentswereo b s e r v e da r ep r e s e n t e di nF i g .6 T y p i c a lv a l u e so fo b s e r v e dl o a dl e v e lh o r i z o n t a ld e f l e c t i o n sf o rp i l e s P2 and A3 a r e p r e s e n t e di nF i g .7 ( a )and7 ( b ),r e s p e c t i v e l y “ ANALYSISOFRESULTS BearingC a p a c i t y Thee f f e c t i v ed e p t hc o n c e p ta p p l i e dt of l e x i b l ep i l e su n d e ru l t i m a t ea sw e l la se l a s t i c s t a g e so fl o a d i n gi ss c h e m a t i c a l l yr e p r e s e n t e di nF i g .8 . Thef l e x i b i l i t yo ft h ep i l ei s 9 measuredbyr e l a t i v es t i f f n e s sf a c t o rKrd e f i n e dbyP o u l o sandDavis [1] Kr=Eplp/EsD4 v e r a g eh o r i z o n t a ls e c a n tmodulus whereE p l p = f l e x u r a lr i g i d i t yo ft h ep i l e,Es=weighteda i nembedmentd e p t hD . Thep i l eb e h a v e sa sar i g i de l e m e n twhenKr> 0 . 1whereasi t behavesa saf l e x i b l ememberwhenKr<0 . 0 1w i t ht r a n s i t i o n a lb e h a v i o u rbetweent h eabove ~ 0 . 8 9 9 0, 1994) o PREVlOUSTESTS 8=73m m(SASTRY& MEYERHOF 1 ~ 0 . 6 ~ • PRESENTTESTS Theory 一一 0. 4 型8(SAND) 0.414(CIAY) @ 0. 4 @ @ @ 忌 臨 LA TlVES TlF FNESSFACTOR (Kr) F i g . 6 R e l a t i o nB e t w 巴e nDm/Da n dK r 1 S A S T R ¥・K O u l l O T O・ l ' v 1 A i :O P P O 'S D I A M P O C W :B E A R I N GC A P A C I T YANDD E F L E C T I O NO FL A T E R A L L YL O A D E DF L E X I B L EP I L E S 6 E Q .[!3J 一 世 - 一ーか- 1 0 一一〈トー 一~ P O U L O S & D A V I S ( 1 9 8 0 ) T E S T S CHANG( 1 9 3 7 ) 5 1 5 。 {E自 ) 戸 z oロハ}同叫民同ぬ 8 工 ー←- T E S T S CHANG( 1 9 3 7 ) 〆 0 /: : f Y ' 臣 I . .A S T ' I C U l . . T l 総" 1 藍 4 。 ( b ) 40 LOAD Q(N) F i g .8 S c h e m a t i cD i a g r a mo fF l e x i b l ea n dE q u i v a l e n tR i g i dP i l e s F i g .7 R e l a t i o nB e t w e e nL o a dL e v e lH o r i z o n t a l D e f l e c t i o nY, a n dL o a dQ,f o r( a )P i l巴 P 2(b)P i l e A3 twol i m i t i n gv a l u e s . Af l e x i b l ep i l eo fd e p t hDcanbec o n s i d e r e da sane q u i v a l e n tr i g i dp i l e e uf o rt h ecomputationo ft h ep i l ec a p a c i t yandt h emaximum o fu l t i m a t ee f f e c t i v ed e p t hD ef o r b e n d i n gmomentwhereasi tcanbet r e a t e da sar i g i dp i l eo fe l a s t i ce f f e c t i v ed e p t hD eu/DandDe/Da r emainly t h ee s t i m a t i o no fd e f l e c t i o n su n d e rworkingl o a d s . Ther a t i o sD a l u ee v e nthought h ev a r i a t i o no fE swithdepthhassomes l i g h te f f e c t c o n t r o l l e dbyt h eKrv ( S a s t r yandMeyerhof" ) .I nt h ea b s e n c eo fs t r u c t u r a lf a i l u r eo ft h ep i l e .t h eu l t i m a t e nhomogeneoussandi so b t a i n e d l a t e r a lc a p a c i t yo faf l e x i b l ep i l eo fembedmentd e p t hDi e us ot h a t byc o n s i d e r i n gt h ee q u i l i b r i u mo fane q u i v a l e n tr i g i dp i l eo fd e p t hD [2] Qh=O.125yBD~u Kb wherey=u n i tw e i g h to ft h es o i l,Kb=e a r t hp r e s s u r ec o e f f i c i e n tf o rt h ep i l e(Meyerhofe t . 7 )a ndD e ui sg i v e nby aJ [3] D e u/D=1.6 5K~・ 12 孟 l Reasonablygoodagreementwass e e nbetweent h ecomputedando b s e r v e dv a l u e so fQh ( F i g .3 ) . Bendingmoments h emagnitudeandl o c a t i o no ft h emaximumb e n d i n gmomenti n I nt h ed e s i g no fp i l e s,t t h ep i l ep l a yav i t a lr o l e .I nt h ep r e s e n tc a s e,t h eb e n d i n gmomenta tgroundl e v e lu n d e r f a i l u r el o a dwasg i v e nbyMO=Qhhwherehi st h ee c c e n t r i c i t yabovet h egroundl e v e lwhere t h el o a dwasa p p l i e d . Theb e n d i n gmomentwass e e nt oi n c r e a s ep a r a b o l i c a l l yupt oad e p t h Dmwheret h emaximumb e n d i n gmomentMmwasr e c o r d e d,andwass e e nt od e c r e a s e r a p i d l yw i t hf u r t h e ri n c r e a s ei nd e p t h( F i g s .4 ( a )and4 ( b ) ) . Thenond i m e n s i o n a ld e p t hr a t i o 6 2 B u ll .F a cAg , . rS a g aU n i v .N o .78 ( l9 9 5 ) 同 Dm/Dwass e e nt obeaf u n c t i o no fKrv a l u eandwasd e c r e a s i n ga sKrwasd e c r e a s i n g . The Mmv a l u ecanbee s t i m a t e do n c ea g a i nbyc o n s i d e r i n gt h ee q u i l i b r i u mo fane q u i v a l e n tr i g i d p i l eo fd e p t hD e us ot h a tf o rh=O, [4J Mm= 0 . 3 6QhD e u R e a s o n a b l eagreementwass e e nbetweent h ecomputedando b s e r v e dv a l u e so fMm ( F i g .5 ) . Thee l a s t i cd i f f e r e n t i a le q u a t i o nf o rt h ei n f i n i t e l yd e e pf l e x i b l ep i l e( K r話 0 . 0 1 )s u b j e c t edt oal a t e r a ll o a da tah e i g h thabovegroundl e v ε Ii sg i v e nby 4 4 [5J Epl d yr /dx ) ェ o abovet h egrounds u f r a c e,andby p( 4 4 2 dY 2 / d x)=p= E s .y belowt h egrounds u r f a c e (Chang)wherepi st h e [6J Epl p( st h ew e i g h t e da v e r a g es e c a n tmodulusi nd e p t hDand n e tp a s s i v ep r e s s u r eont h ep i l e,Esi Y landy 2a r et h el a t e r a ld e f l e c t i o n so ft h ep i l eaboveandbelowt h egroundl e v e la td i s t a n c e x . Theabovee q u a t i o n scanbet r a n s f o r m e da s [7J d4 yr /dx4 =O, and d4 Y 2 / d x4 s4y , i nwhichβ=(Es/4Epl I / 4 . 十4 2=O p) h ed e p t ho f maximum b e n d i n g moment i so b t a i n e d from S o l v i n gt h e s ee q u a t i o n s,t (Koumotoe ta l : ) l i 4 l i 4 t a n -1[ 1 / { 1+1 .4 1 4 ( h /D)Kr } ] . [9J Dm/D=1.414Kr i t hh=O, Dm /D=0. 41 4whichi sa l s oo b t a i n ε dby 1 nt h ec a s eo far i g i dp i l ei nc l a y,w nt h ec a s eo far i g i dp i l ei ns a n dt h ee q u i l i b r i u m c o n s i d e r i n gt h ee q u i l i b r i u mo ft h ep i l e I 49 8 .T h e o r e t i c a lv a l u e so fDm/De s t i m a t e dfrom[ 9 Ja g r e e d c o n s i d e r a t i o n sl e a dt oDm /D=0. r e a s o n a b l yw i t ht h eo b s e r v e dv a l u e s( F i g .6 ) . D i splacem記n t s faf l e x i b l ep i l eo fd e p t h Theh o r i z o n t a lgroundl i n ed i s p l a c e m e n ty oandr o t a t i o n8 0 o Du n d e raworkingl a t e r a ll o a dQ(Q=Qh/3-Qh/2whereQhi st h ep i l ec a p a c i t y )a c t i n gh abovet h egrounds u r f a c ea r ee s t i m a t e dbyr e p l a c i n gt h ef l e x i b l ep i l ew i t hane q u i v a l e n t l1 r i g i dp i l eo fe f f e c t i v ed e p t hDeg i v e nby( S a s t r yandMeyerhof ) [ 1 0 J De /D=2.3K~.2 孟 I y m. [ 1 1 J Y o = { Q / ( E s e D e F y ) } { I Y h十 I ( h /De ) } ) } { I e h十 I 恥 ( h/De ) } [ 1 2 J 仇={Q/(EsemFe hh, I O h,and1 r e whereEse=weighteda v e r a g eh o r i z o n t a ls o i lmodulusi nd e p t hDe, 0m a r ey i e l dd i s p l a c e m e n tandr o t a t i o n e l a s t i ci n f l u e n c ef a c t o r sf o rar i g i dp i l e,FyandFea e s p e c t i v e l yf o raf l e x i b l ep i l e,( P o u l o s& D a v i s9). C o n s i d e r i n ga v e r a g ec o n s t a n t f a c t o r s,r hm=9and1 o m =1 2, y oand8 erec o m p u t e d . Thel o a dl e v e lh o r i z o n t a l v a l u e so f 7 . 5, 0 w p p r o x i m a t e l yo b t a i n e dfrom d i s p l a c e m e n tylwasa a n80 • h [ 1 3 J YI=YO十 t r e T h i se q u i v a l e n tr i g i dp i l emethodi sr e f e r r e dt oa smethod1andt y p i c a lv a l u e so fy1 a p r e s e n t e di nF i g s .7( a )and( b ) .y oand8 a l u e sa r ea l s oe v a l u a t e dbyc o n s i d e r i n g[ 1 1 Jand 0v [ 1 2 J,r e s p e c t i v e l yf o raf l e x i b l ep i l e,i nwhichDei sr e p l a c e dbyDandt h ee l a s t i ci n f l u e n c e a l u e sa r e f a c t o r sa p p r o p r i a t et ot h eKrv a l u ea r ea d o p t e d( P o u l o sandD a v i s9)‘ They1 v t h e no b t a i n e dfrom[ 1 3 Janda r ea l s op r e s e n t e di nF i g s .7 ( a )and(b)‘ T h i sa p p r o a c hw i l lbe r e f e r r e dt oa smethod2 . ‘ S A S T R Y• KOl;'幻1'0・ l ' v I A K O P P O・S U " ! A M P O U W :B E A R I N GC A P A C l TYANDD E F L E C T I O NO FL A T E R A L L Y凶必) E DF L E X I B L EP I L E S 6 3 Ana l t e r n a t emethod(method3 )wasa l s ou s e dt oc a l c u l a t eY lv a l u e sd u et oaworking momentM andl o a dQa c t i n ga tah e i g h thabovegroundl e v e lonaf l e x i b l ep i l eo fd e p t h D embeddedi nas o i lw i t hau n i f o r ms e c a n tmodulusEs (Chang2), [ 1 4 J Yl=[l/F y ][Q{(l 十 ßh)3十 O.5}/(3E p l p • s 3 )十 M(l十 sh ) 2 /(2E β 2 )] pl p. w i t hsymbolsa sb e f o r e . TheseY lv a l u e sa r ea l s oshownf o rcomparisoni nF i g s .7 ( a )and 7 ( b ) . I twass e e nt h a tt h eY lv a l u e se s t i m a t e dfrommethod1d i f f e rbya b o u t土 5%compared t ot h o s ecomputeda c c o r d i n gt omethod2andb o t ht h e s emethodsp r o v i d eaf a i re s t i m a t i o n lv a l u e sandp r o v i d e d o fh o r i z o n t a ld e f l e c t i o n s . Method3wass e e nt ou n d e r e s t i m a t et h eY al o w e rbounds o l u t i o n . CONCLUSIONS A n a l y s i so fmeasurementso ft h eu l t i m a t el o a d s,b e n d i n gmomentsa l o n gt h ep i l es h a f t fs i n g l ei n s t r u m e n t e df l e x i b l emodelp i l e s,b u r i e di nl o o s e andl o a dl e v e ld i s p l a c e m e n t s,o u b j e c t e dt oh o r i z o n t a ll o a d s,havel e dt oab e t t e ru n d e r s t a n d i n go ft h ec o n c e p t sand,ands o fe f f e c t i v ed e p t hf o rt h ed e s i g no ff l e x i b l ep i l e si nhomogeneouss o i l s . Methodshavebeens u g g e s t e df o ro b t a i n i n gt h eu l t i m a t ec a p a c i t yo faf l e x i b l ep i l eo f d e p t hD i ns a n dands u b j e c t e dt ol a t e r a ll o a dby r e p l a c i n gt h ef l e x i b l ep i l ew i t h an h er a t i oDeu/Db e i n gaf u n c t i o no ft h er e l a t i v e e q u i v a l e n tr i g i dp i l eo fe f f e c t i v ed e p t hD e u,t p i l es t i f f n e s sK r . Theb e n d i n gmomentv a r i a t i o nw i t hd e p t hcana l s ober e a s o n a b l ye s t i m a t e dfromt h e c o n c e p to fe q u i v a l e n tr i g i dp i l es u b j e c t e dt ot h e o r e t i c a ls o i lp r e s s u r ed i s t r i b u t i o nont h ep i l e s h a f t . Themagnitudeandp o s i t i o no fmaximumb e n d i n gmomentwerer e a s o n a b l ye s t i matedfromt h ec o n c e p to fe q u i v a l e n tr i g i dp i l e . Theh o r i z o n t a ld i s p l a c e m e n to ft h ep i l e headu n d e rworkingl a t e r a ll o a dwasr e a s o n a b l ye s i m a t e dbyr e p l a c i n gi tw i t har i g i dp i l e o fe l a s t i ce f f e c t i v ed e p t hDe,t h er a t i oDe/Db e i n go n c ea g a i nd e p e n d e n tonKr,andu s i n g t h ee x p r e s s i o n ss u g g e s t e de a r l i e rf o rar i g i dp i l e . Although,t h ep r e s e n tl i m i t e dmodelp i l et e s t sonl a t e r a l l yl o a d e di n s t r u m e n t e dp i l e s ti sf e l tt h a tc o n s i d e r a b l ef u r t h e rt e s t i n go fmodelp i l e so f s u p p o r tt h ep r o p o s e dc o n c e p t s,i o g e t h e rw i t hf u l ls c a l ei n s t r u m e n t e dp i l et e s t s w i d e rr a n g eo fr e l a t i v es t i f f n e s so ft h ep i l e,t u n d e rl a t e r a ll o a d si sv e r ymuchn e e d e dt ov e r i f yt h ep r o p o s e dc o n c e p t s . LEDGEMENTS ACKNO羽T Ther e s e a r c ha tt h eSagaU n i v e r s i t ywasc o n d u c t e dp a r t l yw i t ht h ef u n d sp r o v i d e dby Ja panS c i e n c eand t h eNa t u r a lS c i e n c eandE n g i n e e r i n gR e s e a r c hC o u n c i lo fCanada ( TechnologyFund),andS a i n tMaryU n i v e r s i t y,H a l i f a x,C a n a d a . 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CanadianG ε o t e c h n i c a lJ o u r n a 司 SASTRY• KOUMOTO・ MANOPPO・ SUMAMPOUW:B E A R I N GC A P A C I T YANDD E F L E C T I O NO FL A T E R A L L YL O A D E DF L E X lB L EP I L E S 6 5 横方向蒋重下におけるたわみ性杭の 支持カおよび変形 パンカマミディ V.R.N.サストリ@甲本達也@ ファピアン1.マノッポ・ヨゼフ E .R.スマンボー (生産環境工学講座) 王 子 成 8年 1 1月1 8日 受理 摘 要 傾斜荷重を受けるたわみ性杭の設計に際しては,杭の横方向支持力および水平変位特性を知 r (= EpI EsD4,ただし, ることが重要である.たわみ性杭の鉛直支持力は,杭の相対離性 K p/ p:杭のたわみ闘性, D 杭の根入れ深さ, Es:深さ Dにおげる土の王子均水平方向弾性係数) E p l の大きさには無関係であるが,横方向支持力は K rが減少するにつれて小さくなる. r三 五0 . 1の場合杭は剛性杭とみなされ,水平荷重下ではこの杭は杭中央部のある点を 一般に, K 中心に回転する.これに対してヲ K r三 五0 . 0 1の場合杭はたわみ性杭とみなされ,水平荷重下では rが上述の両限界値の中間にある場合は,杭は水平荷重下 この杭は杭中央部で曲げ変形する.K において両杭の中間の挙動を示す. これまで,杭の弾性変形状態および極限支持力状態における杭の有効根入れ深さの概念を導 入してヲたわみ性および翻性雨杭の間の関係を求める試みを行っており,かなりの成果を得て いる. 本論文は,ゆるい砂地盤に設置したたわみ性モデル杭の水平荷重下における支持力および変 形特性を実験的に明らかにするとともに,提案した概念の適用性を検討したものである.
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