• # # # # KHOA HOC - CONG NGHE
NGHIEN CUrU TirOfNG TAG GIUfA CDC DON VA DAT NE^
DAN HOI KHI CHIU TAI TRONG TINH NAM NGANG
THS.NCS NGO QUOC TRiNH Trui'ng Dal hoc Cdng ngh$ GTVT PGS.TS V l i O N G VAN T H A N H , TS. T R A N H U U H A
Truing Dai hoc kiin trOc Hi N0I
Tdm th: Bii bio trinh biy nghiin c(ru twang tic glCra cpc dan vi dit nSn din h6l khi chju til trQng tinh nim ngang b^ng cich dOng h$ so sinh cua phwang phip Nguyen ly cwc trj Gauss. Sw dung phuong phip phSn tw hOu han di giii vi dwa trin kit qui bing s6 nh0n dwpo dc kSt qui chwng minh tinh dung din vi dO tin c$y cua ly thuyit tinh toin.
Abstract: The article presents the Interaction between pile and the elastic ground under horizontal static load by applying comparative system of Gauss extreme value principle method. This solution is solved by the finite element method which proves the reliability of the applied theory
1.0ATVAN0E
T u o n g tdc glOa ooc v d ddt n i n t i i c Id xet t d i siji idm viec dong thdi cua cpc v d moi t r u d n g d l t xung quanh Ody la v i n de du'pc rat n h i i u tdc gia quan tdm nghien c u u tthi xdy di^rng bdi todn mong coc chju tai trong t m h ndm ngang. Cdch xet t u o n g tdc cua cdc p h u o n g phdp trinh bay hien nay chu yeu du'a t r i n phu'ong phdp Ban gian hoa (Simplified procedures) [11] n h u : P h u o n g phdp d u a trdn iy thuyet cdn b I n g gipi han cua nen aal( X.H/I.Kudrln, 1928, Brinch Hansen, 1 9 6 1 ; Brom, 1964a,b); P h u o n g phdp hd s6 nen Winliier (Chang, 1937; Reese vd IVIatloci<, 1956;
K.X Zavriev, 1962; T r I n Binh, 1968); P h u o n g phdp n^n ddn hoi iien tuc (B.N.Gagafov, 1967; Pouios ,1971a,b; L§ B i r c Thdng,1966); P h u o n g phdp d u a n g cong p-y (H/latiock, 1970; Resse etai, 1974;
O'Neiii, 1984; A P i , 1993). Cdc p h u o n g phdp ndy ve p h u o n g di^n xdy d u n g ly t h u y i t vd diSn todn t u o n g a6i d o n gian, tuy nhidn vi#c xdc dinh m o dun phdn iuc nen (he s6 nen ) thi4u ao chinh xdc, m6l tdc gia 6k nghj mpt cdch de xdc djnh v d chu y l u d y a v d p t h u c nghiem d6i v d i tCrng tru'dng h p p eg the hodc, T u o n g tdc d ddy cung d u p e xdt d i n n h u n g c h u a triet de, m d i chi xet d i n t u p n g tdc cua dlit idn cpc ma c h u a xet tu-ong tdc cua cpc idn ik. Mdt l<hdc l(hi giai bdi todn t u o n g tdc thi vi$c d a m bdo d i l u kidn bien id rat kho khan...
Trong bdi bdo nay tdc gia trinh bdy nghien c i i u
t u o n g tdc v d i nghTa chdp c h u y i n vj t u c Id xdt chuyin vj ngang cua coc bdng v d i c h u y i n vj ngang cua d ^ . Cy ddy cpc d u p e x e m n h y d i m chju u l n trdn nin ddn hoi c6 xdt b i l n d a n g t r u p t ngang theo iy thuylt ddm Timoshenkp. P h u o n g phdp xdy d u n g bdi toin id dung hd so sdnh cua p h u o n g phdp Nguydn i y c ^ t n Gauss (PPNLCTG) dd d u p e trinh bdy a [5] vdi hai ldi giai; idl glal d l i v d i h d so sdnh id nOa khdng gian v6 han ddn h i i v d ldi giai d l i v d i h$ so sdnh id khIng gian v6 han ddn h I i .
2. XAY DUNG BAI TOAN THEO PHUDNG PHAP
NGUYEN LY cue TR| GAUSS
Phuong phdp nguydn iy eye trj Gauss cho pliSp diing trang thdi Crng suit cua hd so sdnh dd bilt Jl tinh hd c I n tinh khi hai hd cCjng chju lye tdc dijng gilng nhau [1]
2.1. Lirl giii Oil vdi h^ so sinh li nCra khong gian v6 han din h6i
Xdt cpc hinh trg c6 m l dun ddn hIi Ec, hd s6 poisson pc, nIm trpng bdn khdng gian vp han ddn hIi cd md dun ddn h l i E1, h | s i poisson |j1 chiu tdc dung cua tai trpng tTnh nam ngang P tren b l mil (hinh 1 a). Cpc dyp'c xem id dam chju uln cd xdt din biln dgng trupt ngang, cho ndn viec tinh tcdn cpc dSn v l vide xdc djnh dd vdng (chuyin vj ngang) uc vd ndi lye md men u l n IVl cua tryc dam (tnjc cgc).
Lye P tdc dyng tai dilm dau ciJa trgc cpc cung c4
^ I K i ®
S6 6 n n 20121hk xem n6 tac dgng tryc tiep len nen dat (de x6t td'i :h|ip chuyen vj v^ chuyin vj cua cpc du'a ve chuyen A cua trgc cpc).
Hp so sanh la b^n khdng gian v6 hgn d^n h6i c6 m6 dun dan hoi EO, h$ so poisson pO vS cung chju t^c dgng cua tai trpng tTnh nlm ngang P tr§n b l m$t (hinh lb). Su" dgng loi g\d\ cua Mindlin [10] ta tinh du'pc tr^ng thai ifng sucit vd chuyin vj cua h$ so s^nh(hinh lb). Lucnay, thay cho lye PtScdgng, t^c gia dCing cac trgng thdi irng su4it, biln dgng cua h$
so sanh tdc dgng l§n h$ can tim (hinh la).
Tinh dam c6 x§t din biln dgng tru-pt ngang do lye cat Q gay ra du'pc d l c$p va su* dgng khd phd biln hi^n nay [6], [7], [8]. Tuy nhi§n ly thuylt x6t bien dgng trygl ngang day du Id ly thuylt tfnh hdm dO vdng y(z) vd hdm lye cSt Q(z) dIu Id hdm I n cua bdi todn tinh dim vd t i m [2]; [3]; [4],
Biln dang trupl ngang yc do tgi trgc cpc do lye elt Q gdy ra dup-c xac djnh nhu* sau:
Y,= — Q (1)
GF . . .
a- h§ so xet din sy phan bo irng suat cat khong dIu theo chieu cao dam (coc):
0 = 1.2 doi voi tilt di^n chO nhat a= 1.1 doi vdi tilt dien tron GF- dp ci>ng eat cua d i m
Biln dang y^ lam thay dli gbc xoay cua dyd-ng do vong cua dam (cpc), do do goc xoay do md men uon sinh ra du'p'c xdc djnh nhu' sau:
dy dz
(2) y Id du-o-ng do vong cua dam
X Id biln dgng uln ( dp cong cua du'ong ddn hoi do mo men uln gdy ra)
dcp _ d V ^ i dQ ,3) dz dz' GF • dz
M id md men uln xdc djnh theo cdng thirc sau' d'y a d Q ,
M=EJ.X = E J [ - ^ ^ . - . - l (4) EJ- do cung chong uon cua ddm.
Theo phyong phap nguyen iy eye trj Gauss [1], philm hdm iupng cydng biJc Z cOa bdi todn bao gIm 2 thdnh phln:
Z = Z, + Z , - . min (5) I lyu w t
a) H§ cIn tinh b) H$ so sdnh Hinh 1: M6 hinh bSi toSn khi dCing h$ so s6nh IS ban khfing gian v6 h^n ddn hIi
Zj Id Iupng cuong bLfc xet td'i trgng thdi Crng suit cua he so sdnh tdc dgng l&n h$ cIn tinh.
Z j = J^(CT,-a")e,dV+J^(o,-o;')e^cIV
+ f (a, - o")e,dV + J^ {T,^ -T"^ )y^^dV (6) + f ( T ^ , - T " , ) y ^ , d V + r ( T ^ , - T " j y j , d V - > m i n
Z^ xet lu-ang cu'&ng bO'C cua coc chiu uon c6 xet biln dgng trupt ngang yc trong cpc.
Z, = [M^dz + |Qy,dz -^ min (7) trong cdc cong thtec tr§n, V la t h i tich eua khoi dat chLpa cpc can tinh; I Id chilu ddi cpc; cdc u'ng suit a ° , a ; , a j , x%, x^, x^ Id trang thdi irng suat da bilt cua he so sdnh xdc dinh theo lai giai Mindlin (hinh lb); a^, o^, o^, T^, T^, T^^ ; e^, e^, £^, X^, 1.^,1 la cdc Lfng suat, biln dgng eua he can tinh (mnh 'I'a).
Tich phan Z^ thye hien trong niJa khong gian v6 hgn, tich phdn Z^ thye hien tren chilu dai I cua cpc. Hai dai lu'p'ng Z^, Z^ hodn todn dpc lap vd'i nhau ehi>ng ndo chu'a dua dilu ki§n rang bupc: chuyin vj ngang uc cua cpc bing vd'i chuyin vj ngang u cua nin dIt tren suit chilu ddi coc (chgp chuyen vj cua coc va nIn dat):
J,= u (8) Nhu' v^y bdi toan tinh cpc n^m trong mdi tru'dng
dan hoi din v l bai toan tim eye trj cua philm ham (5) v6i rdng bupc (8). Co t h i din bai todn eye trj co rdng buOe v l bdi todn eye trj khong rdng bupc bdng cdch dung thOa s6 Lagrange A(z). Hdm A(z) Id hdm an cIn tinh thay doi theo chieu ddi cgc. Philm hdm Lagrange ma ring F bay gia du'pc vilt nhu- sau:
F=Z,+ Z^+ |?.(z)(u^-u)dz ->min (9) Phu-ong phdp nguyen ly eye tn Gauss xem cac
# # # # # KHOA HOC - CONG NGHE
chuyen vj thyc id cdc chuyin vj do, do dd cdc ilng suat trong nin dlt vd ndi lye trong cpc die Idp dli vdi cdc biln dang, chuyin vi typng irng, cho ndn dilu kidn eye trj cua philm hdm (9) d l i vdi ildn kit hai chieu (tuong tdc glCra cdc phdn t i ) dupe vilt nhu sau;
8F. j,,„,-„';,6(|]dV,J.,„,-,;«(|].V
*i.".'-<.KI*S-*i.""-''KI^^]"
+J^M&,dz +[Q«r.dz+[(u, -u)6X(z)dz
* [ x ( z ) 6 ( . , - . ) d z , 0 5 Id dIu ily biln phdn
2.2. L&i giii aSi v&l h$ so sinh la khdng gian vd han din hdl
Vin xdt bdi todn cpc trong nIn ddn h6l nhu myc 2.1, nhung iuc ndy hd so sdnh Id khdng gian vd han dan hIi cd md dun ddn hIi E,, hd s i poisson p„ vd cung chju tdc dyng cija tai trpng tTnh ncim ngang P trdn be mdt. Su dyng ldi glal cua Keivin [10] ta tinh dupe trang thdi yng suit vd chuyin vj cua he sc sdnh. Luc ndy, thay che iyc P tdc dyng, tdc gia dCing cac trang thdi ung suit, bien dang cua he so sdnh tdc dyng idn hd d n tim.
Oleu klpn dam bao sy Idm vide ding thdi cua cpc khi chju iyc ngang vdi nIn dat id chuyin vj ngang cua coc uc phai bdng chuyin vj ngang ciJa nen dIt'
u,.= u (11) Bdi todn tuong tdc giO'a cpc chju iyc ngang vdi
khil dIt V id bdi todn tinh khIi dIt V khi chju iyc ngang P vd bdi todn tinh cpc bao dam dieu kidn rdng budc (11). Theo PPNLCTG, philm hdm iypng cudng buc Z cIJa bdi todn gIm 2 thdnh phln:
Z = Zj + Z^-.min (12) Z, Id iypng cydng biJc xdt tdi trang thdi ung suit
cua he so sdnh tdc dyng idn hd cIn tinh. Theo [5], ta c6
Zd = Z„ + Z „ - min (13) vdi rdng bupc s^ = 0 trdn mdt thpdng (14)
Zj Id iypng cydng bye d l tinh khIi dlt V
ZV = Ji,K-OsdV^min (15)
Z„,= L ( n , - a ° ) w d n —min
Trpng (15), V Id t h i tich cua khIi dlt cIn tinh; ^ c, id cdc i:i'ng suit, biln dang cOa khIi dlt cua hd cli tinh; S||" id trang thdi ling suit dd bilt ciia hd so sdnl xdc djnh theo idi gidi Keivin
Z „ Id iypng cydng bye xdt tdi dilu kidn mj thodng AB cOa khIl dlt:
(16) vdi Q Id diln tich mdt thodng AB; w id chuyin v khii dlt theo tryc z.
Zj Id Iupng cudng bi>c (chuyin ddng) cua cpc ii trinh bdy trong cdng thuc (7) d trdn.
Cd t h i din bdi todn tim eye trj (12) cd rdng buO<
(11) vd (14) v l bdi todn eye trj khdng rdng buOc blng cdch dung thCfa s i Lagrange A nhu sau;
F = Z, * Z, * i>-i(z){". -"I'lz + !,>.,{". > )f ,n - min (17) 0 ddy A,(z), Aj(x,y) id thOa s i Lagrange id iidm I n mdi cua bdi todn.
Nhy vdy, dilu kidn eye trj ciJa F se id:
6F= (,„.-.;,8(|)dV*|,,a,-„>|]dV
+J M8,il2 +JQSi.dzt j(u.-a)8l,(z)dz
+Jx,(z)6(u,-u)dz+j^l,(x.y)S<i,dntJ^o,8J,(«,y)dn=0 6 Id dIu ily biln phdn
3. MOT SO T R U O N G HOP TiNH TOAN Thyc hidn phdp tinh biln phdn d l i vdi (10), (18) se nhdn dypc cdc phuong trinh d l xdc djnh cdc hdm chuyin vj u, v, w cua nIn dlt, hdm chuyin «l ngang uc cua cpc, hdm iyc elt Q, hdm md men M eua cpc vd cdc hdm thua s i Lagrange A. Khd c6 t h i tim dupe idi gidi gidi tich cua bdi tcdn biln phSn trdn, ta tim idi gidi s i cua (10), (18) theo phuong phdp phln ty hcyu han.
Tdc gia dd sy dyng phln mim IVIatiab xdy dyng hai chyang trinh tinh chuyin vj, ndi iyc md men uon cOa cpc theo phuong phdp PTHH theo hai c^ch:
dung hd so sdnh Id bdn khdng gian vd han ddn lioi (chuong trinh IVIstaticPI) vd diing hd so sanh B
m!mi
S6 6 nam 2012KHOA HOC - CONG NGHE ttMti
khdng gian v5 han ddn hIi (chupng trinh KstaticPI).
Phln ty nen dat id phln ty khoi chu nhat 20 nut, mli niit cd 3 chuyin vj u, v, w; phan tO cpc id phln tO' dogn thing mpt chilu. Vi xdt biln dang trupt ngang trpng cpc nen dung hai Ioai phln td: phan tu chuyin vj (hdm bdc 3) vd phln ty Iyc elt (hdm bdc 2)
* Twdng hpp thu nhIt: Kiem tra dd tin cdy cua IJ thuyet tinh todn
Xdc djnh chuyen vj ngang, ndi Iyc md men uln cpc don bing BTCT tilt didn 60x60 cm, cd md dun ddn hoi E^ = 200.000 kG/cm^ chilu ddi I = 5.4m nlm trong nIn dlt dong nhIt cd md dun ddn hii E, = 100 kG/cm^, hd s i Poisson m, = 0.3, chju tdc dyng ciJa iyc nam ngang P = 10.000 kG tdc dgng tai dIu cpc nhy hinh 2.
Hd so sdnh id bdn khdng gian vd ban ddn hIi, cd he s i Poisson m„ = 0.3, ta tInh cho hai trydng hpp md dun ddn hii E,, = 100 kG/cm= vd E, = 200 kG/cm^ SO dyng chuong trinh MstaticPI d l tinh ta dypc kit qua nhu sau:
Nhdn xdt: Kit qua tinh chuyin vi vd md men uln cua cpc trong trydng hpp md dun ddn hIi cua he so sdnh Ej, = lOOkG/cm^ cung bdng chuyin vi vd md men uln ciJa cpc trong trudng hpp md dun dan hil cOa he so sdnh E„ = 200kG/cm^. Bilu dd Chung to Idi giai cua bdi todn dung d i n ve mdt phyong phap iudn va thudt toan sij' dung.
* Tru'dng hpp thu hai: Sp sdnh kit qua cua hai Idi giai theo hai chypng trinh tinh MstaticPI vd KstaticPI khi iyc ngang ddt tai dIu cpc.
Vin bdi todn nhy trudng hpp thy nhat, tuy nhldn trong trydng hpp ndy ta tinh theo hai cdch: dCing h$
so sdnh id bdn khdng gian v6 han ddn hIi (chuong trinh IVIstaticPI) vd h# so sdnh Id khdng gian vd han ddn hIi (chypng trinh KstaticPI), md dun ddn hii oija hd so sdnh id E„ = 100 kG/cm'. Lye ngang P=10.000 kG dat tai mat dlt( dau coc) ta dypc kit qua nhu sau:
Nhdn xdt:
- Tren hinh 5, 6 cho thIy chuyin vi, md men khi tinh theo chyong trinh IVIstaticPI (Uc-MI; Mc-MI) xap xT bang chuyin vj, md men cua cpc tinh theo
Kh6i ddi V Mien ma rOng clfi \i.\. difiu ki^n hiSn
Hinh 2. So' d l tinh cpc (J$t trong ntra khSng gian ve hgn a^n h6i.
Hinh 3.
Bilu ad chuyin vj cua cpc tinh theo hai tryfirg hp'p E„=100;
Ej, = 200kG/
facBE-os ISBE-OS
§ «aiE->05
; ; ; • •
' o » . J . « '
Hinh 4.
Bilu dfi ma men u l n cOa CQC tinh theo hai tru'b'ng hep Eg = 100;E;,=
200kG/cm^
Hinh 5.
Bieu 6h chuyen vi cua cpc tinh theo chifo'ng trinh Mstatld vd Kstatid khi Iyc ngang d$t tr6n m$t ait.
...u:a^....Si...._
- / . - ; -i • r . . . . \ . . . . : Hinh 6.
Bilu d l ma men u l n cua cpc tinh theo chu'cng trinh Mstatid vd Kstatid khi Iyc ngang a$t trfen m§t a l t .
# # # # # KHOA HOC - CONG NGHE
chuong trinh KstaticPI(Uc-KI, Mc-KI). Sai s i Idn nhIt khoang 5%. Sd dT cd dd sai Idch nhy vdy Id do anh hudng cua dilu kidn mdt thodng (bl rdng mdt thodng khoi dat chya cpc Id hOu han dem so sdnh vdi mdt thodng vd hgn ciJa khdng gian vd hgn ddn hIi).
" Trudng hpp thi> ba: So sdnh kit qud cua hai Idl gidi theo hai chypng trinh tinh MstaticPI vd KstaticPI khi Iyc ngang d$t tai chdn cpc.
Vdn bdi todn nhy trydng hpp thu hai, nhung che Iyc ngang P=10.000 kG ddt tgi chdn cpc, ta dupe kit qud nhu sau:
Nh|n xdt:
- Trdn hinh 7, 8 cho thIy chuyin vj, md men khi tinh theo chuong trinh MstaticPI (Uc-M2; Mc-M2) gin nhu trung kbit vdi chuyin vi, md men cua cpc tinh theo chuong trinh KstaticPI (Uc-K2, Mc-K2). Sd dT cd dp sai Idch rIt nhd nhu vdy Id do Iyc ddt dydi sau so vdi mdt thodng, vi vdy khdng b| dnh hudng bdi dilu kidn mdt thodng.
* Trudng hpp thy ty; So sdnh kit qua cua bai todn vdi kit qua nghien cuu thyc nghidm cua Youngho Kim, Sangseom Jeong, Jinoh Won [9].
Lly thdng so dIu vdo cua bdi todn trong [9] d l tinh todn: Coc thep cd dudng kinh ngodi 1.02m;
chieu day thdnh ing 0.016m; chieu ddi 26m, md dun ddnhdiE^= 1,0.10« kG/cm=, dp cung E^J^= 6,3.10"
kG cm^ dat trong nIn dlt gIm 4 Idp Idp 1 ddy 5,2m la Idp sdt bien trdn cd E,, = 70kG/cm=; p,, = 0,35; Idp 2 ddy 10,4m Id Idp set biln dudi cd cd E^^ = lOOkG/
cm^; Ua = 0,3; Idp 3 ddy 5,2m Id Idp bdn cd E „ - 250kG/cm'; p „ = 0,3; Idp dudi cung ddy 5,2 m Id Idp dd cd E „ = 25000 kG/cm', hd s i Poisson m „ = 0.25.
chiu tdc dung cua lye nlm ngang lln lypt Id P = 200;
400; 600; 800 kN tdc dyng Idn dly cpc. Tdc gid xdy dung chuong trinh tinh MstaticPLs, dypc kit qua chuyin vj vd md men uln cOa cpc nhy sau:
- Nhdn xdt: kit qua chuyin vj, m i men uln ciJa bai todn tinh theo phuong phdp dCing h$ so sdnh eua PPNLCTG typng dii phCi hpp vdi kit qua nghiSn eyu eua [9] ca v l hinh dgng, tri s i vd vj tri dgt gid tri s i Idn nhIt, nhe nhIt, diem uln...
Hinh 7.
Bilu d l chuyin vj cua cpc tinh theo chuong trinh Mstatld vd Kstatid khi Iyc ngang ddt tai chdn cpc.
*.o«,o,
—
1 ^ ^^^
/t"'""-r- \
^-. . —_- : \ .
Hinh 8.
Bilu a l md men u l n cOa cpc tinh theo chuxrng trinh Mstatid vd Kstatid khi Igc ngang a$t t^l chdn CQC.
. 1
Hinh 9.
Bilu d l chuyin vi cua cpc tinh theo chutmg trinh MstaticPLs.
mm
S6 6 nam 201214. KET LUAN
- Thdng qua c^c tru'dng hyp tinh todn trSn chirng to tinh dung d i n va dO tin e|y cua bai todn ly thuylt xay dyng theo phu-ang phap dCing h0 so sdnh eua PPNLCTG. K i t qua cua bdi todn ti^m c$n g i n vd'i kit qua eua mOt s i nghi§n CLFU thyc nghigm tr§n t h i gib'i.
- Cdch tinh Iu'O'ng tdc cua tdc gid e6 the ducyc xem Id each tinh tu'ong tdc d l y du khi eh$p chuyin vj cua cgc vd chuyin vi cua dlt va x6t du'p'c cd trgng thdi U'ng suit 6" ca mdi tru'b'ng dlt, epe.
- Khi tinh cpc thi tinh nhu- d i m chju uln e6 x6t tai biln dgng tru-pt ngang vd'i vi$c dung hai hdm dp vong y vd hdm Iyc elt Q Id hai hdm I n , Id ly thuylt day du ve dim.
- U'u dilm cua phu'ong phdp dung h$ so sdnh Id khong eIn ddt them cdc lien kit phg a biSn khIi dlt chCra cpc vd vd'i each Idm ndy khdng nhOng dam bao dieu kien tren bien, tren m^t thodng cua khoi dat chija cpc md cdn dam bao dilu ki^n bien 6 vd cung, bai vi lai giai eiJa Mindlin hodc Kelvin cung da thoa mdn cdc dieu ki^n k l tr§nB
Lateral displacement (mm)
Hinh 11.
Bilu a l chuyin vi cua cpc tinh theo [9] khi chju Iyc ngang tdc dyng: 200, 400, 600, 800 kN.
Bending Moment (KN m) 1200 1600 2000
- 5 -
£ S.,5-
- 2 0 -
- 2 5 -
'
n' h)J^
^y ')
„ ™
Matlock
Hinh 12.
Bilu d l m6 men uon cua cpc tinh theo [9] khi chju Iyc ngang t^c dyng: 200, 400, 600, 800 kN
TAI LIEU THAM KHAO
[1] Ha Huy Cirang. Phu-ang phap nguyen ly ct^c tn Gauss. Tap chi Khoa hpc va ky thu§t, IV/2005 Tr112+118
[2] Vu Thanh Thuy. Nghien ctju nOi li^c va chuyen vi cua he thanh chju u6n khi xet td'i anh huang cua bi^n dangtru-Ql Lugn ^n ti4n sTth^ng 12/2010.
[3] Doan Van Duan. Nghien CCPU on (^nh a^n hoi cua ket cau h$ thanh c6 x6t aen bi6n dang tru-pl. Lugn Sn ti^n sT, th^ng 8/2011
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