Phu'cng phap d e n gian phan tich phi tuyen coc d e n chju tai trong ngang
Simple method in nonlinear analysis of single pile under lateral load
Ngay nhan bai: 20/9/2014 Ngay su^ bai; 13/11/2014 Ngay chap nhan dang: 15/12/2014
Nghiem Manh Hien
T O M T A T :
Bai bao trinh bay phuong phap ddn gian phan tich iing xi^ phi tuyin cua he coc- dat chiu tai trong ngang dat tai dinh coc.
Phuong phap nay dfla t r l n phiiong phap giai tich va phan tii hflu han d6i vdi bcii toan dam tren nen dan hoi vdi phi tuyen cua 16 xo nen dgc tning bc(i diicing cong p-y. PhflcJng phap dilt^c danh gia b a i ^ vi?c so sanh ket qua tinh toan vcfi cac di3 lieu thi nghiem da diidc thilc hien.
TU kh<^a: Cpc ddn, tai trpng ngang, 16 xo phi tuyen, dfldng cong p-y
ABSTRACT
This paper presents a simple method to analyze the nonlinear behavior of piles- soil system under lateral load applied at the pile top. The method based on analytical and finite element methods for beam on elastic foundation with nonlinearity of soil spring characterized by p-y curves. I h e method is evaluated by comparing its results to test data in the literature.
Keywords: Single pile, lateral load, nonlinear spring, p-y curve
TS Ngjiiem Manh Hien Trying Dai hoc Kien triie Ha Noi
1. Gidi thieu
Coe don chju t i i trong ngang cd the phan tfch theo n h i l u phUcmg phap nhflphUcJng p h i p g i i i tich eiia dam tren nen dan hfii v i phUOng p h i p p h i n t f l huU han. Doi vdi bai t o i n phan t f l thanh, d i t n l n dupe m d hlnh hda bang cac Id XO ddc lap cd t h i tuyen tfnh hoac phi tuyen.
Doi vdi nen dat n h i l u Idp, coc thudng duge ehia thanh nhieu doan sao eho moi doan nam trong cung mgt Idp dat. NhUvay, ehuyen vi v i ndi lUe cfla ege dUoc x i c dinh bang viec g i i i he phuong trinh e i n bang n h i l u an so nen trong thyc t l thudng sfl dung cae p h i n mem chuyen d u n g d l tfnh t o i n Phuong p h i p trinh bay trong bai b i o nay eo t h i sfl dung de tinh t o i n ndi lye v i c h u y i n vi cfla coc bang cae bieu thfle don gian [5] CO xet d i n tinh phi tuyen cfla n l n dat dugc dac trUng b^ri dUdng eong p-y.
2. D o cling tUtfng tUcrng duang cua he cpc - dat
Coc ehiu t i l trgng ngang tai dinh epe n h u trong hlnh l a v i d i t nen duge m f i hlnh hda b a n g c a c l d x o n h u t r o n g h i n h lb.Theo p h u o n g phap p h i n t f l hflu han, d i m dudc ehia t h i n h cae p h i n t f l sao cho moi phan t f l v i efi the ed n h i l u phan t f l nam trong cflng mdt Idp dat. Lo xo nen l i d i n hoi tuyen tinh hoae phi t u y i n . Cae bieu thflc dUOc sfl dung de tfnh t o i n theo phuong phap trinh bay sau day dUa tren \-y t h u y l t ciia phan t f l hOU han cho b i i toan dam tr^n nen d i n hfii.
""^ty;
Hinh 1: Sa iJo tinli toan cpc diiu tai trong ngang
Xet phan tCf d i m tren nen d i n hfii nhuhinh l e , theo phflong phap p h i n t f l huU han, ma tran d o eflng cfla d i m bao g o m hai thanh p h i n duoc x i e dinh theo bieu thfle nhU sau [11]:
•[K] = [ K J - f [ K ; _ (1) Trong dd:K l i thanh p h i n ma tran do eiltig : cCia d i m v i K^ la ma tran d d eijfng cfla Id xo nin x i e ^ n h theo b i l u thfle sau:
12 12
13L 156 - 2 2 L
Phuong trinh can bang cfla p h i n t f l dam i tren n l n d i n hoi la:
[K].
w, e, w ,
e,
-
F, 1 M, F, M,
T i i t r g n g g i i thiet dfloc dat tai nflt tr^n hay nflt dau cfla phan t f l dam nen p h i n t f l dam dfloc quy dfii tUong dUong v l m o t Id xo cd hai t h i n h phan d p cuing: d p cisng theo phUtJng ngang v i dfi cflng xoay. Phuong trinh can b i n g e u a l o x o n i y l a :
Ma tran d d eflng efla Id xo t f l o n g cTUdng [ K ] e d d a n g :
[«]•
Cac thanh phSn d d cdng trong ma tran (5)
l O Q I ^ ^ I ^ B I T 03.2015
aiMc xic dinh bSng each g i i i phuong trinh c i n bhg (3) ciia p h i n t f l d i m trong cie trUdng hpp:
a)w = l v i e , = 0 , F j = O v a M j = 0 : x i e e n n h jifocF v i M i t i i ^ F i v i i ^ . ^ M , . D i t d l l u kien liien v i nit gpn phflong trinh (3) thanh:
Til phuong trinh (3) v i b i l u thfle (7), Ifle v i ni6rren t^i d i u phan t f l d i m dUdc x i c ^ n h l i :
k„=M,=k,j+k^w, + kj^ej W w, = 1 v i S, = 0, Fj = 0 va M j = 0 : x i c dinh dU(^, v i M , : 1^2 = M, v i k,j = F , . o | t d i l u kien in%6nit gon phuong trinh (3) t h i n h :
11'tUl"]
\ f^ifir phirong trinh (3) v i bieu thflc (10), luc va mfl men t^i d i u p h i n tOl d i m dUoc x i c ^ n h la:
cflng xoay va do cflng ghep efla doan cpc phia dudi doan epe dang xit.
3. Difcfng cong p-y
D u d n g eong p-y m d t i quan he phi t u y i n giua p h i n lUc nen theo phucmg ngang len than cgc v i c h u y i n vj ngang cfla cpc tai d i l m dang x^t. D u d n g eong p-y da dUOe n h i l u t i c g i i n g h i l n cflu n h i ^ 1) Matlock (1970) {4] thye hien thf nghidm cpc fing thep vdi kich thudc that ed d u d n g kfnh 0.3 m trong dat set m I m v i d l x u i t d u d n g cong p-y eho dat set; 2) Reese v i Welch (1975) [9] da thUc h i l n t h i nghi&m t i i trgng ngang eho epe nhfii ed dydng kfnh 0.76 m trong dat set cflng t r l n muc nudc ngam, Oudng eong p-y eho t i i t r g n g tTnh v i t i i trong ddng da dupe phat t r i l n tir thf nghiem nay; 3) Reese cdng sy (1975) [8] da thUc hi^n t h i nghiem t i i trgng ngang cho 2 epe fing thep ed dudng kinh 0.6 m trong dat set efltig dudi mUc nUdc ngam v i xay dUng dfldng cong p-y cho t i i trong tTnh va t i l trpng d d n g ; 4) Reese v i cgng sy (1974) [7] xay d y n g dfldng cong p-y d l md t i fltig xfl cfla d i t c i t dudi t i i trgng tTnh v i t i l trong dgng ngan han; 5) Evans va Duncan (1982) [3] d l x u i t dudng eong p-y doi vdi d i t eat pha hoae s i t pha vdi d i e trflng cfldng do bao gfim e i Iflc dfnh dOn vj v i goc ma s i t trong.
Di dan g i i n trong tinh t o i n theo phuong phap de xuat trong b i i bao niy, dUdng eong p-y ed dang hyperbol sau day dupc sfl dung trong tinh toan [1]:
_ k , g w _
(11)
I Ttr bilu thilc (8) va (11), cac th^nh phSn do olng cua 16 xo lifting duang la:
« - l i k a - 2 k „ k , . k i . + k f , k „ ...
k;.-k„k„
-ak„k,.k,.tk;,k.
kl -k,,k„
(12) + k„
».. = k.
(13)
• k | . 0 ' i . l ' i i - k „ k „ ) + k „ ( k „ k „ - k , k"„ - k „ k „
+ kR,w (15)
trong do: p j ^ phSn lire nen gldi han cOa dat nen; R,!^ he so pha hoai d i / g c x i c ^ n h bSng R,=
p / p ^ v d i p ^ la gia tr] tiem c^n cOa p h i n luc n i n t i l drrdng cong hyperbol.
D o cijmg tiep tuyen cija 16 xo dat nen duoc xac djnh t U v i phan b i l u thiJc (15) co dang nhu sau:
(16)
1 3 ,
^-F[-iiAtk„=.
Elf 210 /I 105 J " El ' 'rong dd K^, Kj^, and K^, | i ad cflng, dfi
'' \ p , + k , R , w J
P h i n lyc nen tdi han cho d i t set dflOc x i e i^ii) I , . dinh theo cdng thfle sau:
+ ' * " t ' ' " p , = 2 e d + Tdz + 2.83cz (17) Trong d d : c l i Iflc dinh t h o i t nfldc; d l i d u d n g kinh cgc; z l i do s i u tfnh t o i n ; Y la t r g n g Iflpng neng cfla d a t G i i trj p h i n Iflc nen tdi han khdng Idn hon gia t n sau:
p , = l l c d (18) Murehison v i O'Neill (1984) [6] d l x u i t
dudng cong p-y dong thdi vdi p h i n lUe n l n tdi han t r o n g d i t c i t vdi g i i tri nhd hdn trong hai g i i tri sau:
p, = Yz[d(Kp - K , ) + z K p t a n < p t a n p ] ^ g j p, = ydzrKp+2K[,Kptan(p-tan(p-K,J j j o ) Trong do: tp l i gdc ma s i t t r o n g ; p = 45 + <p /2; K„. K, va K^ tUOng flng l i he so ap lue dat tinh.
ap lyc dat ehii ddng v i i p lyc dat bj ddng.
4. Quy trinh tinh toan
Dd cflng tuong duong cfla mgt doan cpc dugc x i e dinh theo c i c cdng thfle (12), (13) v i (14). D l x i c djnh dfi cflng t o i n bd cgc; t h i n eoc duoc p h i n chia t h i n h n h i l u doan sao cho mfii doan d i e trung v i t l i l u , t i l t dien v i d i e trUng d i t nen l i giong nhau, d d cflng efla moi mOt doan cpc bao gom hai t h i n h phan: t h i n va mui.
Q u i trinh tfnh t o i n duge t i l n h i n h t f l doan cgc phia dflfii iin tren. Dfi cihig tflOng dUcmg ciia doan dudi ehinh l i dfi eflng mfli cfla do^n trin.
Chuyin vj cfla dinh efla phan doan ege b i t ky dugc tinh toan b i n g c i c h g i i i hi phuong trinh hai an so nhu sau:
k,, K\
Dot vdi p h i n doan epe thijT n h i t
M, M
(21)
[22}
Trong dd F v i M l i lye ngang v i mo men ngoai Iflc t i c dung tai dinh cgc Chuyin vi tai dinh cfla p h i n doan_cgc l i :
'F,k^-k,;M, ] -F,k,; + k,|M, I
(241 (23)
Chuyen vi d day moi p h i n doan cpc duge x i c dmh tUOng t u t f l phuong trinh (3)'
[k» k«Jl8ji-(k,.», + k..6,)j
Trong dd cie thanh phan do eflng dfloc tfnh nhUsau:
[I; m. a^l; li -
Giii phuong trinh (24) d l x i c ^ n h c h u y i n VI tai day moi phan doan cgc:
F,k^ - k j . M j
-ki+k3,k«
Q u i trinh tinh t o i n t f l dudi len khi tinh dd cflng tflong dUcmg efla he eoc-nln v i t f l ttin xuong khi tinh chuyen v\ va ndi Iflc cfla cpc,
Khi p h i n tfch phi t u y i n , t i i trgng t i c dung dflge chia t h i n h c i c budc nhd, c i c bude tfnh toan dupe thflc hien theo t i m g bUdc Chuyin vi cfla ege tai mfii bUde dUge tich luy t f l c i c bflde t r u d c Dd cflng cfla 16 xo tai mfii bUde dUOC l l y theo dfi eflng t i l p t u y i n theo bieu thflc (16).
S . V i d u t f n h t o a n
L^ t h u y l t trinh b i y d tren dupe i p dyng d l tinh t o i n mdt v l dy cho cpc don chiu t i i trgng ngang. Cgc duoc tfnh toan l i cpc ong t h i p [10]
ed dfldng kinh n g o i i l i 324 m m , c h i l u d i y t h i n h ong l i 9 m m duoc bjt d i u trudc khi ddng
^ dudi mat d i t V i t lieu l i m d u n g dUdng cong p-y l i dUdng hyperbol trong d i n dd s i u 11.9
coc l i t h ^ p ASTM A252 Grade 3 ed cudng dp l i 404.6 M N / m ' . Mfi men quan tfnh cfla tilt dien epe l i 1.16x10" mm*. Hai thanh t h ^ p gdc duoe g i n v i o t h i n eoc d l b i o ve cac d i u d o l i m gia t i n g m d men q u i n tfnh than epe v i ed gia t n l i 1.43x10" mm*. Cae d i e trUng cfla dSt n l n trinh b i y trong hinh 2. He so nen da dUpc * l u chinh d l k i t q u i tfnh t o i n c h u y i n vi dinh eoc phu hgp vdi k i t q u i d o e h u y i n vf khi t i i trpng va c h u y i n vj nhd.
Cpc duoe chia t h i n h 20 doan trong d d mfii do^n coe d i l l n i m trong eung mdt ldp 3it So bflde t i i trong l i 11 bflde vdi mfii bUde cd g i i tri l i 20 kN. Thfle hi#n q u i trinh tfnh t o i n flng vdi m i l budc t i l trgng, duSng cong quan hi lUc v i c h u y i n vj dinh coe nhutr&n hinh 3. Oudng cong lyc v i chuyen vj t f l k i t q u i tfnh t o i n cd s f l x i p xl k h i tfit vdi dudng cong lyc v i c h u y i n vj t f l k i t q u i t h i nghiem. D i l u n i y eho t h i y sy phfl hop efla d f l li^u tinh t o i n va phUcmg p h i p tinh t o i n .
phan tfeh cgc d o n chju t i i trgng ngang.
s i : t i . H-" —•—•
tfl ami i T i " ' " "
ih 2: Coc vh cac ldp d i t nen [10]
• / "
KInti 3. Quan he life va chuyen vi dau coc 6. K i t l u | n
PhUcmg p h i p don g i i n tfnh t o i n coc dOn chiu t i l trpng ngang dua tren phflong p h i p p h i n t f l hCai han eho dam tren n l n d i n hoi. l i u d i l m cua phucmg p h i p l i ehi can tfnh t o i n theo c i c b i l u thfle dai so van cd t h i x i c djnh dUde c h u y i n vi v i nfii Iflc cfla cgc d d n dfldi t i e dung eua t i i trong ngang dat tai dinh ege ed x^t d i n tinh phi t u y i n cfla nen d a t Tfl so s i n h k i t q u i tfnh t o i n v i k i t q u i t h i nghiem c h u y i n vi dinh cgc phuong p h i p nay ed the tin c i y dUoc khi sfl
TAI Lilu THAM KHAO
1. Nghiem Manh H i l n (2009), Phiflmg phap fltfn giSn t i n h toan coc diJn chiu t i i trong dilTig va ngang Be tin nghien ciiu khoa hoc cap truimg, Tnifmg fiai hoc K i l n tnic Ha Noi.
2. Cook, R. D., Malkus, D. S. and Plesha, M. L , (2002), Concepts and Applications of Finite Element Analysis. ThinJ Edition. John Wfiley and Sons, Inc
3. Evans, L I and Duncan, J. M. (1982), Simplified Analysis of Lateral Loaded PAtS Report No. UCB/GI/82-04, Geotedinical Bigineering, Department of Qvil Engineenng. University (rf California, Berkeley.
4. M a t l o d t H. (1970), ConelatiDns for Design of Laterally Loaded Piles in Soft Qay. Proc Offshore Tedinology a n f . , Houston, Taxes, Vol. 1, Paper No. 1204, pp, 577-594.
5 Nghiem, K. M. (2009), Soil-Pile-Structiire Interaction EffectsofHigh-nse Building underSeismic Shaking. Dissertation, University of Colorado Denver.
6. Murdiiswi, J.M. and O'Heill, M.W. (1984), Evaluation of p-y relationships in cohesionless sols. In andysis and design of pile foundations. ASCE, NewYork, pp. 1 7 4 - 1 9 1 .
7 Reese, L C , Cox, W. R. and Koop, F. D. (1974), Analysis of laterally Loaded Pile in Sand. Proc OfFshore Technology Conf, Houston, Taxes, 1970,VoL II, Paper No 2080, pp 473-484.
8 Reese.l C.Cox.W R.andKoop,F.O.(1975),FieldtesBng and analysis of laterally loaded piles in stifF day. Proc o f t h e VII Annual OffchoreTechnology Conf., Houston, Taxes, 2(0CT 2312) 672-690.
9. Reese, L C and Weldi, R. C (197S), Lateral Loading of Deep Foundation in Stiff aay. J. Geotedi. Eng. Div., ASCE, V o l 1 0 1 , N ( i . 6 T 7 , p p , 6 J 3 - « 9 .
10 Rollins, K. M., IL G. Olsen, D. H. Jensen, B. H. Garrett, R.
I. Olsen, and J, J Egbert (2006), Pile ^ d n g Effects on lateral Pile Group Behavior. Analysis. Journal of Geotedinical and Geoenviranmental Engineenng, ASCL vol.l32(10), pp 1272- 1283.
11 Smith, I M.. Gnffiths, D. V (2004). Programming the finite element method John Wiley fi Sons, F o i i d i Edition.
