DAT KHI CO TUNNEL

PIEN BAN KHOA HOC C 6 N G NGHE

XAC D I N H TRANG THAI U'NG SUAT TLT NHIEN TRONG K H 6 | D A T KHI C O TUNNEL

D A O C O N G B i N H - Tliac si - Giao vi6n Bfl mon XD Nh^ va CTCN, Vien Ky ttiult c6ng trinh dac blfit, Hoc vign KTQS.

T R A N V A N L 0 I - Thac si-TrUflng Sy quan Cong binh Binh Difflng.

' M to^n xdc djnh trang thdi \k rk c4n thl^t va c6 y nghia quan trpng trang thi/c t6. Ket qud sg di/flc dung de nghien ciTu dnh hirflng cua Tunnel d^n do lun be mat n^n 6k, nghien cda dnh hi/dng khi co nhiSu Tunnel trong kh6i 6t, nghtSn cAi dnh hi/dng cila Tunnel din khd ndng chju tdi cua nen dat, nghien cijru tinh todn k^ clu ch6ng dd vd kit clu vd cua Tunnel trong thi cflng cung nhi/ trong khai ^dc vd si} dung cong tnnh,... Noi dung bai bdo ^ n h bay cdch xdc dinh tn/dng iTng suit trong kh6i dit do trong liTdng bdn thdn khi cd Tunnel vdi viec diing dng suit lam ^n vd dp dung nguygn ly thi ndng biln dang ci/c tieu ciJa Castigliano

1 . Dat v a n de

0 trang thai ban d4u, trong kh6i dit luon t6n tai mot tru&ng ijffig s u i t t u nhi^n, khi c6 Tunnel, trang thai Crng su4t tir nhi3n cua khdi dSt se bi thay ddi, trong khoi d§t s§ hlnh th^nh m6t trang thAi ung suSt mdl. Di c6 t h i xac dinh dtfcte trang thcii iing suit khi co Tunnel v^ dctm bao cb nghigm 1^ duy n h i t , phuang phap tfnh thudng diing la gi& thi^t t r u ^ cac dieu kien bien xung quanh Tunnel nhu d i l u kidn vd Ung suit hoae chuyen vi [3], [4], [ 5 ] .

Trong npi dung bai b^o, t^c giS trinh bay phUtfng phap x^c djnh s i / thay doi trang thcii i ^ g s u i t t u nhien trong khdi d i t khi co Tunnel mi khdng c i n gia t h i i t trUtSc d i i u ki$n bidn nhu cac phuong ph^p tinh thucffig diing.

2. Xay dirng s o d o t m h

Xet bai toan xac dmh suthay doi nhu hinh laduiSi day.

Xem b&i toan 1^ tuydn tinh, b^i toan xdc djnh (hinh 1 a) se b i n g {hinh 1 b - Bai toan 1) cdng vdi g i ^ tn ciJa phan luc ndy l i y b i n g trpng lupng cua khdl d i t bj l i y di khi thi cdng Tunnel (hinh 1 c - Bai todn 2).

Scf dd bai todn xac c^nh

Nhu vay d l cd k i t qua cua bdi todn (hinh 1a), ta se c i n giai ddng thcri hai bdi todn: Bai todn 1 (so dd tinh toan nhu hlnh 1 b) va Bdi todn 2 (sP dd ti'nh todn nhu hinh l c ) . Bdi todn 1 da dupc trinh bdy trong tai lieu tham khao [2], do dd trong bdi bao nay, tdc gid chi trinh bay phuong phdp gidi bdi toan 2.

3. Ldl giai so va cac cdng thifc ti'nh toan Thay the (ic dung ciia Tunnel bing phiin liic hudng ien Iren k»«>ai«M » « » • » « > HMM'I'^UI'1

Hinh 1: Bieu kidn bien cua khdi dat hdu han

1 1

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Mat tho^g

Tbnnei - B an

1 1

OAy

nl 1 X

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y^"

Thay th^ tac dung cua Tunnel bang phin luc huimg ISti tren

Hlnh 2: Di^u kiin biin cOa khdi dit hdd han Hinh 3: Sd dd chia miSn tinh tain trong Bii toin 2

NGUdi XAY DUNG s 6 THANG 5 & 6 - 2015

XAC DINH TRANG THAI QfNG SUAT TU NHIEN..

Xem khdi d i t tfnh toan ndm trong ban khdng gian dan hdi t u y l n tinh (hinh 2). Rdi rac hda khdi d i t , si^

dung Cmg s u i t lam in va tim min cua ham muc tidu dupc vidt theo nguydn t h i ndng bidn danp cue t i l u vol cdc rdng budc la hai phuong trinh can bang ufng s u i t vd cdc d i i u kien bien xung quanh khdi d i t nhutrong tai li^u tham khdo[2].

Trdn mat thodng ktidi d i t , tai v| t r i khdng c d tai trpng ngoai tdc dung, o^^^ Id an chua b i i t cua bai todn, o^'"" = 0 v d T'^^ = 0 , tai vj tri cd tdi trpng ngodi tdc dung o^"''' v d ojl'" Id i n chua b i i t cua bai todn, T ' ^ * = 0, tai cdc vj trf khdo d i u c d 3 I n chua

biit Id o^'-^', oJI-^'vdTjIf.

Nhu vdy, bdi todn xac djnh gia tri cua phdn luc nay l i y b i n g trpng luong cQa khdi d i t bj l i y di khi thi cdng Tunnel (hinh l c - Bdi toan 2) Id gidi bai todn tdi uu vol hdm muc tieu dupc vidt theo nguydn ly t h i ndng bidn dang cue t i l u vdi rdng budc Id he phuong trinh can b i n g Ung s u i t vd cdc d i i u kidn bien tren xung quanh khdi d i t tfnh todn.

Tdc gia sCr dgng hdm cd sdn cua p h i n m i m IVIatlab, hdm f m l n c o n , de gidi bai toan vdl ldi giai sd theo phuong phdp sai phan huru han. Cu t h i nhu sau:

Chia midn tfnh todn thdnh 5 midn nhu (hinh 3).

RdJ rac hda k h i i d i t tfnh todn thdnh cac p h i n tiJr chU nhdt, tai mdi d i l m nut cua p h i n tiS nay c d cdc I n Id . Sir dung \ud\ v d 6 ludi sai (tng s u i t o ;

phdn tinh todn c6 kfch thuOc id Ax, Az nhu Bdi todn 1 [2], v i i t ham muc tieu cho cdc diem giii^ vd diem nut cCia p h i n t i r ; v i i t cdc phuong trinh cdn b i n g Ung s u i t cho cdc d i l m giij^ cua p h i n tCr t^i cdc m i i n nhu sau:

Boi vdi mien ngoii Tunnel (miin 1,2, 3, 5):

+ Ham muc tiiu dupc vidt dudi dang sai phin cho diim nim gida d ludi sai phan cd dang nhu sau:

i J' - I Z j

-??i -iz

"+CT;'^'*+cr;^

t<r«> + erf-^ + g ; ' * " + g f i "

(1+1-)

['rr<-rr"trr"tc-"i'

(1)

+ Hai phuvng tiinh cSn bing Ong suit (khdng xit trgng lucmg bin than khoi dit) duoc viet du& dang sei phan cho cAc diSm nim giOa cua canh 6 tu& saipMn CO dang nhUsau:

(2a)

(2b)

+ DiSu kien bien trdn mat thoing nam ngang (bi mat khdi dit):

Tai vj trf khdng c d tai trpng ngodi tdc dung:

o^'-'' = 0 ; T*^' = 0 : aj,'-^' > 0 (3a) Tai vj trf cd tai trpng ngodi tdc dung :

a^'-*' / 0 ; T'^^' = 0 ; a*-^^ ^0 (3b) + Dieu kiin bidn trdn mat trai, mat phai khSl dit -

mat phing (1-m1) va (nl-ml) : Gdi v&i Ung s u i t phdp

^x '• 2 — ( ^ S ' ^ - ^ j J ' ^ ' ) A x A z -^ m i n (4a)

£}6i vdri Ung s u i t t i i p

T^: y —(ri^''*-r;[;-^*) A x A z ^ m i n (4b) i=l,ml G '

+ Dieu kiin bidn tren mat diy khdi dit (khdng xil trong luang ban than khoi dit) - mit phang (m 1 -m 1):

0 d i vdi ung s u i t phdp

• m i n (5a) Bfli vdl ilr\Q suat tiep

(=l.nl '-'

A x A z -^ m i n (5b)

+ Oieu kidn dng suit phip duong:

TU d i i u kidn ung s u i t phap duong dupc viit disH dang sai phdn cho cdc d i l m nut ciJa d ludi sal phdn

cd dang nhu sau: o'^"^' 2:0 (6) N G U d i X A Y D U N G S O T H A N G 5 & 6 - 2 0 1 5

XAC DINH TRANG THAI UfNG S U A T TU NHIEN..

06\ vd\ mien trong Tunnel (mien 4):

+ Him muc tiiu dupc vidt dudi dang sai phan eho diSm nam giQa d ludi sai phin cd dang nhUsau:

--m^

-W7,<T + l + f r;

: pn

' S i l -SZi

+ 1 1 - ^ ftr"+o

(1)

(!+»')

f'r^^' + r;^-'-»+r^^"+T^^'''-'y

+ Hai phuong tnnh cin bing Ong suat (xet phan luc cd gii trj bang nhung ngupc chiiu vdi trgng lupng ban thin khdi dit) dupc viSt dudi dang sai phin cho eic diem nam gida cua canh d ludi sai phan cd dang nhu sau:

(<'

j-i)+oOj*» o'.'*'-"+o»-"

2 2

<

Ax

(2a)

fc

>.

••*''+<

2

0+1)

Ax

C +

2

T < ; "

(2c)

+ Dieu kiin biin tren mat thoing nim ngang (bS mat khdi dit):

Tai vj trf khdng cd tdi trpng ngodi tdc dung :

g^.j) ^ Q . ^(.j) 3 0 ; o^"^* 2 0 (3a) Tai vj trf cd tai trpng ngoai tdc dyng :

o"'^' * 0 ; T^' = 0 ; o'^'J^ 5 0 (3b)

+ £?/iu kien bien tren mat trii, mat phai khoi dit - mat phing (1-m1) va (nl-ml) :

€}6i vdi ijmg suit phdp

cr^: ^ —(oS''*-aS;-^')^AxAz -^ min (4a)

€)di vdi Ung suit tiip

r ^ : y - ( r l ; ' " - r

AxAz -> min (4b) + Didu kien bien tren mat day khdi dat (khdng xet trgng lupng bin than khoi dit) - mat phing (ml-ml):

Bdi vert Ung suit phap

^^' S —(c^r-''-o-f "'•'')'AxAz ^ min (sa)

B6\ vdi Ung suit tiip

'.•• Z ^ ( ^ r - " - r*'-'»f AxAz^min (jt)

+ Didu kien dng suit phip ducmg:

Tis diiu ki$n Ung suit phdp duong dupc viit dudi dang sai phdn cho cdc dilm nut ciia d lucri sal phan

cd dang nhu sau: o^'''' s 0 (6) 4. Khao sat sd

TU phuong phap xay dung bdi toan nhu da trinh bdy cr trdn. Trong mdi tru&ng Matlab, tac gia da xdy dung chuong trinh tfnh de gldi ddng thdi Bdi todn 1 va Bai todn 2 nhdm xdc dinh su thay dll trang thai Ung suat tu nhien trong khdi dat do trpng lutmg bdn thdn khi cd Tunnel. Trong pham vi bai bdo chi trinh bdy khao sdt sd tren md hlnh nin dit Id dan hdi tuyin tfnh.

Khao sat khii dit cd kich thutic (12x12)m dupc rdi rac thdnh 144 phin tCr hinh chu" nhat cd kfch thudc mdi phdn tCf Id Im. Khdi dit cd md dun dan hdi E = 10 MPa, he sd Poisson v = 0.3, trong luong rieng y = 20 kN/m^ Trong khdi dit cd Tunnel tiit dien (4x4)m dupc trinh bdy nhu (hinh 4).

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Hinh 4: Rdi rac hda vi chia mibn khdi dit cd Tunnel Kit qua phan bd Ung suit CT^ va a„ dupc trinh bay tren hinh 5 vd hinh 6 ducrt day :

Tru'dng hap 2 :

GiC nguyen cac thdng s6 khao sdt bdi todn nhu NGUdi XAY DUNG SO THANG 5 & 6 • 2015

XAC DINH TRANG THAI QfNG SUAT T\J NHIEN..

x(m) x(m)«

Oz ( M P a )

Hlnh 5: BdUng ddng mdc dng suat a ^ (MPa)

a^(MPa)

Hlnh 7: Bddng ddng mdc dng suit a ^ f/WftJ trudng hpp 1 nhung m d rdng pham vi khdi ddt tfnh todn theo c h i i u sdu (tang them 2 p h i n tCr theo c h i i u sdu khdi d i t ) . Ta nhdn dupc k i t qua phan bd Ung s u i t dj vd a^ dupc trinh bdy tren hinh 7 vd hinh 8 dudi day:

5. Ket luan

- SCr dyng md hinh tfnh nhu tac gid d i x u i t cd the gidi dupc mdt idp cdc bdi todn xdc dinh trang thai iJmg s u i t trong khdi ddt cd Tunnel k l d i n trpng lucng ban thdn k h i i d i t , khi xem n i n d i t la mdi tnjdng khde vdi ddn hdi t u y i n tfnh;

- Phuong phdp tfnh todn tren cho phep khdng nhijng xdc ^ n h dupc dUng ddn didu kien tren bien ciJa Tunnel md cdn xdc (^nh dupc s u phdn bd Ung s u i t xung quanh Tunnel Idm cP s d cho viec nghien curu, tfnh todn k i t c i u chdng d d hay k i t cdu chju luc chfnh trong Tunnel.

- Khi m 6 rdng khdi d i t khao sat, ta se nhan dupc thdm gid tn Ung s u i t az, ax tai phdn md rdng ciia khdi d i t tfnh todn trong khi cac gia trj ung s u i t tai p h i n khdi d i t truti"c khi dupc m d rpng Id khong thay doi. Ndu giCr nguydn kfch thudc, vj trf cua Tunnel thi s u phdn bd Ung sudt xung quanh Tunnel cung khong thay doi. Cac quy lu§t phdn b i Ung s u i t trong khdi ddt gidng nhu khi chua md rOng pham vi tinh toan cua khdl d i t . D i i u

I a^ (MPa)

Hinh 8: Dddng ddng mdc dng suit a , (MPa) ndy chUng td rdng, mac du chi gidi h^n xdt k h i i dit tinh todn Id hiJu han nhung hodn todn cd t h i md r$ng khdi d i t tfnh todn d i n vd han md k i t qud tfnh todn vin dUng d i n va cho dd chfnh xdc cao hay ndi cdch khde la d i i u kidn k h i i d i t n i m trong mdi trudng vd han cung se dupc thda man.

- Bai toan xdc dinh s u thay doi trang thdi Ung su^t ban d i u trong khdi d i t do trpng lupng bdn thdn khi ct>

Tunnel la bai todn r i t quan trpng trong qud trinh thi cdng Tunnel trong thyc td.Q

Tdi lieu Iham ktiSo

1. Oao Cdng Binh, ^ dung ptidOng phip nguyin ly cut; tti Gauss dong cd hoc. Tap chi X&y di/ng, Bo Xay di/ng, s6 thdng 01/2014;

2. Qio Cflng Binh, X^y ddng md hinh bii toin phing xie 0t trang thii dng suit ban diu trong ndn dit do trgng Idgng bin tl^- Tap chi Xay difng, Bg Xay difng, s6 thdng 11/2014;

3. Mindlin R.D., Sdess distnbution around a tunnel. Trans. ASCE, p.1117-1153.1940.

4 . Muir Wood A.M, The circular tunnel in elastic growii Geotechnique25,No.1,115-127.

5. Verruijt A.. A complex variable solution lor a delorming arcu- iar tunnel in an elastic half-plane, Int. J. Numer. Anal. Methods Geomech. 2 1 , p . 7 7 - 8 9 , 1 9 9 7

N G U d i X A Y D U N G s 6 T H A N G 5 & 6 • 2 0 1 5