KHOA HQC - C O N G NGHE ik.^
NGHIEN COU TUUNG TAG GlOA KHOI DAT V0I DAT NEN DAN HOI KHI CHIU TAI TRONG TINH NAM NGANG
THS.NCS NGO QUOC TRINH Trudng Dgi hgc Cdng nghp GTVT PGS.TS VUONG VAN T H A N H ; TS. TRAN HCCU H A
Tnid'ng D^i hgc kiin trOc Hk Ndi Tdm tit: Bki bko trinh bky nghidn ciru tuong tkc giO'a khdi dit vdi dit nin dkn hdi khi chju tki trgng tfnh nim ngang bing ckch dung hp so sknh cOa phuong phkp Nguydn 1^ ct/c tti Gauss. Sif dgng phuong phkp phin td- hQu hgn ^ giki vk dg^a trdn kit quk bing s6 nhpn dugc ckc kit quk chdng minh Unh dOng din vk dp tin cpy cOa /j? thuyit ttnh tokn.
Abstract: The article presents the interaction between soil block 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 pmves the reliability of the applied theory.
1. Dat vande
Be nghiSn ci>u tu-ong tkc giOa CQC vk nen dJtt khi chju tai trpng tac d$ng, tnr6e tien Cctn nghien eCru bkl todn tu-ong tac giOa khoi dSt vol d^t nen dkn hoi cdn Igi, dd cung la bai toan rSt eo ban cua ly thuyet 6kn hoi (vi dg xem dong nhlt thu-c SomigIiana)[4].
Trong bai bao nky tkc gia trinh bky phu'ong phap xSy dyng bk\ toan theo phu'ong phdp Nguyen ly CLPC trj Gauss (PPNLCTG) vdi hai idi giai: Id'i giai d6i vdi h$ so sanh ik nCea khdng gian vd han dkn h6i vk loi giai doi vd'i h^ so sanh ik khdng gian vd hgn dkn hoi.
2. Xdy dung bai todn theo phirang phap Nguyen IV ctfc trj Gauss
Phu'ong phdp nguyen ly cgc trj Gauss cho phep diJng trgng thdi irng suat eua hp so sdnh da bilt de tinh h^ din tinh khi hai hp cCing chju lyc tac dgng gi6ng nhau [1]
2.1. Ljn glil dtfi vdl tifi SO sdnh Id nda khfing glan vd han ddn hdi
Gia sir kh6i dat ddn hoi V eSn tinh nlm trong nira khdng gian v6 hgn ddn hdi c6 ede thdng s6 ddn hoi Id E^, p^ (hlnh 1a); hp so sdnh cung Id nOa khdng gian vd hgn dan h6i co cac thdng s6 ddn h6i E^, \i^
(hinh lb). Ca hai hp eung chju tai trpng tTnh nlm ngang gi6ng nhau nhu' hinh v§ 1.
a) H6 cin tinh b) He so s^nh Hinh 1: Md hlnh bdi toan tinh khoi dit khi dung h$ so sdnh Id bdn khong gian vd h^n ddn h6l
Trang thdi i>ng suit cua he so sdnh du'oc xdc djnh theo Id'i giai H/lindlin [4]. Oe tinh he eln tinh (hinh 1a) c6 t h i dDng trang thai u-ng suit cOa h# so sdnh (hinh lb). Theo PPNLCTG, lu'gng eu'd'ng bijc cua bai todn du'oc viet nhu' sau:
Zv= J ; K - < T ; M V * j ; ( a , - a ; ) 8 ^ d V
^ [(.o^-cDe^dy * [ ( i : . , - x ; ) Y ^ d V
-»min (1) Trong (1), V Id the tieh cilia kh6i dit can tinh (hinh
la); £| Id cde biln dgng eua khoi dit; cdc i>ng suit a ° , a \ a \ T V T° . x" 1^ trgng thai li-ng suit da biet eua h^ so sdnh xdc djnh theo Id'i giai Mindlin (hinh lb); cdc ting suit o^, a^, o^, T^, T^, T^ Id trang thdi i>ng suit eua khoi dit cOa hk cin tinh (hlnh 1a).
I S6 5 nam 2012
mm
Iggg KHOA HOC - CONG NGHE
Theo ly thuyet iin h6i, thay da bi^n d?ng cda khoi dit bling c^c liSn h$: e^ _ 9 v _ _ 9 w
" By ' ' ~ 8z '
8 o " 3 y " ^ 8 x ' ^ « " 8 z * a x ' ^ » ' ° 8 z Sy trong db u, v, w 1^ cSc chuySn vj cOa yi\k\ dkt theo phvfong cSc trgc cua hS toa dO vuftng gbc: xyz, ICic nSy phi4m hSm (1) du'p'C vi4t l^i nhu sau:
Zv- I«'.-:)|^v.i(.,-a;,-dv.
[,, ,Mf^+^ldV-.min (2) PPNLCTG xem cSo chuyin vj thi/c u, v, w trong (2) 1^ dc chuyin vi io, nghTa IS xem cSc biln dang
\i aoc IKp d l i v6i cSo Crng suit thi dilu k\in cyc trj cila (2) dup'c vilt nhu sau;
trong dd S \i dlu iiy biln ph^n.
CMya diy khii dit chi>a ba hdm I n u, v, w, cho n6n ti> (3a) ta nhjn dupc h | 3 phuong trinh:
(,„_,:,a(|].v=o
( V - < . ) < | > v = 0
'Aiv*
(3b)
:v-<.)6(^]av=o
Thyc hi^n ph6p tinh biln phan(tlch phan timg phin) d l i vd'i (3b) ta nhjn dupc ba phuang Irinh
5 a , a t , , a i „ da' , ^ l , dx'^
dn dy dz dx dy dt da a t „ S i „ 9 a ; di' di°^
— L + — 2 - + — 1 1 = — L + — 2 . + — ^ ( 4 ) dy dy dL dy dy dl
3z 9z 3y fe & 9y
v l phai cua (4) thoa mSn phuang trinh can bing khi c6 luc n l m ngang P t i c dgng tai dilm A trong hi so sSnh gay ra (hinh 1 b), chp n§n cic v l trti oiia (4) cDng ia phupng trinh can bing khi c6 lyc nlm ngang P tac dgng tai dilm A cua h | d n tinh (tilnti 1a)gay ra.
Nhu vay bing cich dung h$ so sSnh, ta nlijn dupc ba phuang trinh vi phSn can bing cGa h^dn tinh.
U'u dilm ciJa phuang phdp dung h$ so sdnh ta c6 t h i dupc thiy nhu sau (xem hlnh 2).
Mi^nm6r6ngd^
Khfii dttcSn tinh xft dilu kien bien
w w w w w M m M R l r i t M M M U l
E i , H i
a) Khii dil d n tinh Hinh 2: Cac mS hlnh tinh khii dil
b) M6 hlnh linh bing each dSI c) IM6 hlnh linh dOng h$ so sSnh Ihem cac Id xo
@iKj@ s i s nam 20121
KHOA HOC -CdNG NGHE # # # J
D l xde djnh trgng thdi Ccng suit biln dgng cGa khii dit do lyc ngang P gdy ra, khdng xet trpng tu'O'ng ban thdn cua no (hinh 2a), thong thu-o'ng dOng so d l tinh bing each dgt th§m cdc li§n kit Id xo d hai mdt b6n cua khoi dit (hinh 2b). Tuy nhi§n ede hp s6 d$ cCrng cua Id xo ndy du-oc u'6c djnh dya trdn suy lu^n logic nao do ho$c dya vdo kit qua nghidn c<ru thyc nghi$m. Bdy gid' nlu nhu- ta ddt khii dit cin tInh trong h$ so sdnh (hinh 2c) (miln tinh todn mo r0ng hon khii dit V), thi trdn ede m$t bdn eua nd ed cde O'ng suit phdp cr^vd ede i>ng suit tilp t^,, va T^ tdc dgng, cdn m^t ddy c6 Crng suit phdp o°
vd cdc Crng suit tilp T^^ tdc dgng. Do dd ta khdng cin phai ddt them cdc Ii6n kit Id xo tgi eac bidn, dd chlnh Id U'U diem noi trpi cua phyong phdp so sdnh.
Mgt khdc vdi cdch Idm dd, khdng nhu-ng dam bdo dilu ki$n trdn bidn, trdn m$t thodng cua khii dit md c6n dam bao (Seu ki$n bidn d vd cung, boi vi Id'i gidi cOa Mindlin vd Kelvin cQng dd thda mdn cdc dilu kien k l trdn.
2.2. Ldi giiii flol v6l H so sdnh IJi hhdng glan va han din hfii
Hp so sdnh du'oc diing Id khdng gian vd hgn ddn hii vdi ldi giai Kelvin du'oc trinh bdy trong [4].
X6t tru'dng hop lye P tde dgng nam ngang tren khii dit V (hinh 3a). Mgt AB Id m$t thodng.
Cho lyc ngang P tdc dgng Idn khdng gian ddn hii (hinh 3b), dijng loi giai Kelvin tinh du'oc trang thai ijng suit <Tjj trong nd. Vi hp eln tfnh Id nira khong gian (hinh 4a) cho ndn chi cd t h i dOng nO'a dudi cua khdng gian v6 han (hinh 3b) Idm hp so sanh.
Tuy nhien lOc nay trgng thdi <rng suit G° chi lu'ong p
difong vdi lyc—, cho nen ta phdi d$t 2 lyc P di tinh trgng thdi i>ng suit CT^ theo ldi giai Kelvin. Tru'd'ng hop lyc nlm ngang P ddt 6 dd sdu c so vdi mgt
thodng thi dCing hai lyc P d§t doi xu-ng qua m|t AB (hinh 3c). Trong ea hai so d l tinh tren thi trdn m^t AB cdn cd cdc Crng suit a° tdc dgng
Id'i giai Mindlin dli vdi nO'a khdng gian ddn hoi khi chju lye nlm ngang P xult phdt tCr Idi gidi Kelvin vdi so d l tinh nhu- hinh 3c vd tim cdch bao dam
o° = 0 trdn m$t thodng AB [4]
Hoc t$p cdch Idm trdn, khi tinh khii dit V ehju lye nlm ngang P, tdc gia su" dgng Idi gidi Kelvin vdi so d l tinh hinh 3e d l xdc djnh trgng thdi Crng suit aJ.
Trong tru-dng hop ndy trdn mdt thodng AB cua khoi dit V edn ed cdc irng suit a" tdc dyng, cho ndn theo PPNLCTG ta viet dilu ki0n tren mgt thodng nhu' sau:
^ A B = J L ^ j K - ^ " ) w ] d " A B - m i n (5a) Vd dilu kipn eye trj cOa nd Id:
SZ^ = J[^[K-(^!)5w]dn^B =0 {5b) vdi O^ Id dipn tich m0t thodng AB
Do cd lyc thing dCrng tdc dgng d bd mdt cho nen xdt thdm dilu kidn s^ = 0 trdn mat thoang AB. Nhu' vpy bdi todn tinh khii dit V nlm trong nO'a khong gian dan hoi vdi viee dung ldi giai Kelvin du'oc vilt nhu' sau:
Z = Zy + Z ^ - • min (6) Vdi rang bupe s^ = 0 trdn mgt AB.
Z^= [ ( a , - o ^ K d V + [ ( a , -a;)8^dV +
^ ( a , - o ^ K d V + | ( x , , - < ) r x , d V .
min (7)
Khdi dait V cSn linh A, , \ , ,B A.
a) b) c) Hlnh 3: M6 hlnh bai toan linh khll dil khi dCing h$ so sdnh la khdng gian vd hgn dan h6i
I Si 5 nam 2012
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' # # # # KHOA HOC - C O N G N G H E
Trong (7), V Id t h i tich cOa khii d i t e l n tinh (hlnh 3a); Cy Id cdc biln dgng cOa k h i i d i t ; cdc O'ng s u i t
^ x . <^°y. <^l. T^xy, •^l^. -^Iz Id trgng thdi O'ng s u i t dd biet cOa h$ so sdnh xdc djnh theo ldi gidi Kelvin vdi hai lyc P(h]nh 3c); cdc O'ng s u i t o , a a^, x^, x^, x Id trgng thdi Crng suit cOa khii d i t cua h$ c i n tinn (hinh 3a).
B i n g cdch vilt p h i l m hdm m d r^ng Lagrange, du-a bdi todn cyc trj cd rdng buOc v l bdi todn cyc trj khdng rdng b u | c nhy sau:
F = Z^ + Z ^ + A 6 , - * m i n (8) A = l(x,y) Id thCra s l Lagrange Id hdm I n mdi cOa
bdi todn.
D i l u ki$n cyc trj cOa F sd Id:
5F = 5Zy + 6 Z ^ + 6Ae^ = 0 (9)
3. Mot SO UUAng hap tinh todn
Xet khii d i t V n l m trong nO'a khdng gian vd hgn ddn h i i cd cdc thdng s l ddn h i i Id E^, p^; phgm vi d i t m d rpng xung quanh c6 cdc thdng s l ddn h i i E,, M^. (hinh ve 4). Khii d i t chju tdc dgng cua lyc n l m ngang P d$t tgi m$t d i t .
Tdc gia dd dung p h i n mem Matlab xdy dyng hai ehu'ong trinh tinh chuyin vj cua khii dat V theo phuong phdp PTHH vdi phan td khii chu' nhdt 20 nut, mdi nut c6 3 I n chuyin vj u, v, w [2],[3] theo hai each: dung hp so sdnh Id bdn khdng gian vd hgn ddn h i i (chuong trinh Mstatici) vd diing hp so sdnh Id khdng gian vd hgn ddn h i i (chu-ong trinh Kstatid).
* Trudng hop 1: Cho tinh c h i t khii d i t V e l n tinh gilng tinh c h i t mdi trudng d i t m d rdng xung quanh (eua h | so sdnh), E,, = E, = 100 kG/em^; h$
s l poisson Mo = Ml = 0.3; lyc ngang P = 10000 kG tdc dgng tgi d l u cpc.
Ta nhan du'oc b i l u do quan he giij'a chuyen vj ngang tgi v| tri true giu'a cua khoi dat vdi chieu sSu theo hai chu'ong trinh tinh ( M s t a t i c i , K s t a t i d ) nhif
- Tr6n hmh 5a, nhan thay ket qua chuyen vi cua k h l i d i t can tim (tinh theo p h u o n g phap PTHH- chu'ong tnnh M s l a t i c l ) (Uc_M1) hoan toan trung khit v o l ket qua chuyen vi cua moi t r u d n g dat it he so sanh (tmh theo lai giai giai tich cua Mindlin) {U(:0_M1)
- I r o n hinh 5b, nhan thay k6t qua c h u y i n vt cua khoi dat khi tinh theo chu'ong t n n h K s t a t i d (Uc^KI), xap xi b^ng k i t qua chuyen vi cua khoi dSt khi tinh t h e o c h u ' o n g i n n h M s t a t i c i (Uc_M1) S d d l c o d p s a i Ipch nho n h u vay la do be rpng mdt thoang cua khoi
Kh6i dfft V c ^ tmh Mien md rOng d^
xet di^u kifin bi£n
Hinh 4. M6 hinh tinh khii dit d^t trong ni>a khdng gian vd hgn ddn hii
SIB
a) Tmh theo chuong trmh Mstatici
b) Tmh theo chu'cng trmh Mstatici va Kstatid
Hinh 5. Bieu 6b chuyen vi khoi dat theo chieu sau khi cho mo dun dan hoi cua khoi dat can tinh bang md dun dan hoi cua he so sanh
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56 5 nam 2012 iKHOA HOC - CONG NGHE Ui
dit Id hOu hgn so sanh vdi mgt thodng vd hgn cua nO'a khdng gian vd hgn ddn hoi (Idi glai khii dit can tinh cd be rdng mdt thodng rat nh6, so sdnh vdi mdt thodng vd hgn cOa khdng gian vd hgn ddn hit; m|it khdc phai chia lyc tdc dgng t^p trung thdnh nhilu lye thdnh phin do tinh chit vd hgn cOa chuyin vj vd dng suit tai dilm ddt lyc dd (dilm kjr dj).
'Trudng hop 2: Ta cho tinh chat kh6i dat can tinh khac tinh chit moi tru'dng dat md rpng xung quanh (cua he so sanh), tire la giu' nguyen mo dun dan hoi cua khii dit can tinh nhu' trong trud'ng hop 1, EQ = 100 kG/cm-, thay mo dun dan h6i ciia he so sanh E, = 200 kG/cm^; p,, = p, = 0 3
Ta nhan du'oc bilu do quan he giO'a chuyin vi ngang tai v| tri true giua cua khii ddt vdi chilu sau theo hai chu'ong trinh tinh (Mstatici; Kstatid) nhu- hinh 6 sau;
Nhdn xdt:
- Hinh 6a eho thiy kit qua ehuyin vj eua khii dit eln tim (tinh theo chuong trinh Mstatici) trong trudng hpp ndy (Uc_M2) eOng bang chuyen vj cua khii dit ein tim (tinh theo chuong trinh Mstatid) trudng hyp 1 (Uc_M1)
- Hinh 6b cQng cho thiy kit qud chuyin vj cOa khii dit khi tinh theo chuong trinh Kstatid (Uc_K2), xip XI bing kit qua chuyin vj eua khii dit khi tinh theo chuong trinh Mstatid (Uc_M2).
Td trudng hop tinh todn 1 va 2 ed the nh§n thay ring, cho dCi hp so sdnh ed thay doi ho^c khdng thay doi md dun ddn hii so vdi hp eln tinh thi ehuyin vi eua khii dit eln tim Id khdng thay dli.
* Trudng hyp 3: Ta cung eho tinh chat khoi dit cin tinh khdc tinh chit mdi trudng dit md rdng xung
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nh theo chi^ang trinh Mstatici va Kstatid
Hinh 6. Bieu d6 chuyen vj cua khoi dat theo dd sSu khi thay (Joi mo dun dan hoi cua he so sanh
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h theo chu'ong trinh lyistatici va Kstatid
Hinh 7. Bieu do chuyen vi cua khoi dat khi thay d l i md dun dan hoi khoi dat c^n tinh
I So 5 nam 2012
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quanh (cua hp so sdnh), nhung Iln ndy ta gid nguydn md dun ddn hii cOa hp so sdnh E, = 100 kG/
cm^ cdn md dun ddn h i i cOa khii dit cin tinh tdng glp ddi so vdi trudng hyp 1, EQ= 200 kG/cm^ MQ
= Ml =0.3
Ta nh$n duyc bilu d l quan h$ gida chuyin vj ngang tgi vj tri trgc gida cOa khii dit vdi ehilu sdu theo hai chuong trinh tinh (Mstatici; Kstatid) nhu hlnh 7 sau:
Nh$n x6t:
- Hinh 7a cho thiy kit qud chuyin vj cua khii dit (tinh theo chuong trinh Mstatid) trong trudng hyp ndy (Ue_M3) nhd hon chuyin vj cOa khii dit (tinh theo chuong trinh Mstatici) trong trudng hyp 1 (Uc_M1). Nhu vPy khi dp edng cOa khii dit cin tinh tdng thi chuyin vj giam vdi cOng dilu kidn chju lyc, dilu ndy hodn todn phu hyp vdi thyc t l .
- Tren hinh 7b, cOng cho thay
kit qud chuyin vj cOa khii dit khi tinh theo chuong trinh Kstatid (Uc_K3), x i p xf bing kit qud chuyin vj ciJa khii d i t khi tinh theo chuong trinh Mstatici (Uc_
M3).
k. K^t ludn
- Thdng qua cdc trudng hp-p tinh todn trdn dk chung td tfnh dOng d i n vd 6p tin e$y cOa bdi todn 19 thuylt xdy dyng theo phuong phdp dung h$ so sdnh cOa PPNLCTG.
- Phuong phdp dOng hd so sdnh cho ta nh$n duye Idi gidi eOa h i cin tim dya trdn h$ dd bilt khi cho hai hp ciing chju lyc gilng nhau.
Bdng phuong phdp s l - PPPTHH, tdc gid ed t h i l$p Igi Idi glai eOa Mindlin tu Idl giai cOa Kelvin, tdc Id din td Idi gidi khdng gian vd hgn ddn hii (Idi gidi Kelvin) ve Idi giai bdn khdng glan vd hgn ddn hii (Idi gidi Mindlin).
- Tdc gid dk xky dyng dugi bki todn tuong tdc gida khli d l ddn hii vdi nln d i t ddn hii cdn.|
md khdng d n ddt thdm cdc liM kit phg, ddm bdo duyc dilu ki^n trdn bidn, m$t thodng cOa khli dil vd d vd cungB
TAI LIEU THAM K H A O [1] Hd Huy Cu'ang. Phu'ang phdp
nguySn ly cyc tri Gauss. T^p chi Khoa hQC vk k^ thujit, IV/2005Tr.112+118.
[2] O.CZienkiewicz. CBE, FRS vi R.L Taylor. The Finite element method Voiuni2, Fourtf) edition Mc Graw-Hill Bocrit company. 1991
[3] Klaus-Jurgen Bathe. Finite element Procedures. Part one.
Prentice- Hall International, Inc.
1996.
[4} K.BpeG6Mfl, >K.Tennec, JI.Bpoyeen (1987), Mercvibi rpaHMHHux sneueHTOB, DepeBCvi c flHrnHHCKoro.
MocKsa (MMP)
TIM HIEU VE QUY BAO TRI DUfiiNG BO
(Xem tidp trang 6) si} dgng di/frng bO. Hal losi phi ndy khdc nhau d vk mgc Wiu thu, a6i tucmg thu... eg t h i nhy sau:
Vk mgc tifig; Ph( si> dgng du'd'ng bd thu d l t?o nggln quan ly bao tri du'dng bO d6l vdl du'dng do Nhd nu'dc d^u tu: thu d l qudn ly bdo tri vd hodn v l n dlu tu' d l i vdl du'dng d l u tu' d l thu hil v l n (du'dng BOT, PPP...); Phi h?n che phu'ong ti#n giao thang cd nhdn dudng bO nhlm h?n c h i sg"
gla tdng s l lu-png phu-ong ti^n cd nhdn, gdp phin gidm thilu tai nan glao thong vd un t i c glao thdng;
thu d l tao nguon chi dlu tu ndng cao ndng Igc ciJa hi thing kit
c l u ha ting glao thdng dudng bd vd d l u tu cho cdc cdng trinh ddm bdo an todn glao thdng.
V l dli tu'O'ng: Phi sir dung du'dng bd thu vdl tit cd phucng tl$n glao thdng co' gidi du'dng bO, bao gIm: xe d td; mdy k*o; ro mode, so ml ro mode du'p'C k6o bdi d td, mdy kdo vd xe md td hai bdnh, xe md td ba bdnh, xe g i n mdy. Trong khi dd Phi ban c h i phuong tldn glao thong cd nhdn dudng bd chi thu m$t phin nhd trong s l dd; eg t h i Id xe ehd ngudl tif 9 ChS ngoi trd xulng, xe md td, khdng thu phi doi vdl xe cdng (xe ciJa eo quan hdnh ehinh, don vj
sg nghilp cdng l$p; xe qudn dfii;
xe cdng an; xe cua ca quan, t6 chdc ngo^i glao nude ngodi).
V l tinh phdp ly: Phi si> dgng dudng bO Id loai phi dd cd trong danh mgc phi, 1$ phi vd dang thu'c hl$n; trong khi dd, phi h^n c h i phuong tl$n glao thdng ca nhan dudng b$ Id mOt loai pM mdi, dd duoc QuIc hOi cho cliij truong d l Chlnh phu trinh iiy ban Thudng vg QuIc hOI ban hinh (Nghj Quylt s l 21/2011/QH13 ngdy 26/11/2011 cfla ky hppth(|, 2, QuIc hOi khda XIII v i chit vk vd trd Idl chit vln)B
Ngudn: Bd GTVT