Mot So Mo Hinh Trong Co Hoc Da Va Mo Hinh Hoek

7/23/2019 Mot So Mo Hinh Trong Co Hoc Da Va Mo Hinh Hoek

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MT S M HNH TRONG C HC V M HNH HOEK -BROWN

M hnh n hi

Vi khi n hi, cc trng thi ng sut xut hin trong khi cha gy ra cctc ng ha do hay ph hy hoc n gin l xem ng x nh vt liu n hi tun

theo cc nh lut n hi c bn, y l nh lut Hook.

M hnh n hi do

Khi gi tr ng sut t n mt gii hn no , ng x ca vt liu chuyn sang do.

ng x n hi v do c th d dng nhn thy trn biu ng cong quan h ng

sut bin dng khi nn n trc. i vi , trong iu kin ng sut ng hng b,

hu nh ch c bin dng n hi, iu ny th hin thng qua ng cong nn n mu

. Khi th nghim trong iu kin p lc bung ln trong th nghim nn ba trc, mu

xut hin bin dng do.

Hnh 1. T tri sang phi: mu nguyn dng; bin dng 20% di p lc

xung quanh 280 atm.; bin dng 20% di p lc xung quanh 460 atm.

Trong thc t, khi o ng hm su trong khi , do nh hng ca iu kin thi

cng v di tc dng ca ng sut t nhin, xung quanh ng hm xut hin mt

vng t t nhiu b xo trn ti xpv y s xut hin do (vng I, II trong hnh

2). Pha ngoi su trong khi , vn gi trng thi n hi vng III. Trong vng do,


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cc ng sut php tip xc v ng sut php hng bn knh r s gim dn t trng

thi n hi (ng nt ri) sang trng thi ng sut do (ng nt lin) nh minh ha.

Nu khng c chng v t c bn km, vng do s pht trin theo thi

gian v c th dn ti ng hm b ph hoi di dng st nc hm, bc tch lp ti

mt hng hm hoc n (rockbursts) thm ch c th dn ti sp lp hm. Nu chung c trng thi ng sut mi, ng hm s dn n nh (hnh 2b)

Hnh 2. S lc, vng bin dng do v phn b ng sut quanh hm (a)n nh ng hm theo thi gian (b)

M hnh n hi nht

Cc kt qu nhn c cho thy rng trong khi n hi nht, trng ng sut

khng thay i theo thi gian, tng t nh cho mi trng n hi nhng qu trnh bin

dng cng nh dch chuyn va ph thuc vo ta va ph thuc vo thi gian, tuynhin theo thi giancc i lng bin dng v chuyn v t gi tr hu hn. Qu trnh

xy ra thc cht l qu trnh t bin.

Vi cc gi thit khi xung quanh cng trnh ngm c biu hin n hi nht, khi

trong sut thi k s dng s khng c qu trnh ph hy hay ha do xut hin.

Khi n hi nht do

Vi gi thit khi l n hi nht, cc qu trnh bin i c hc cho thy quy lut

bin i theo thi gian. ng nhin do kh nng chu ti ca khi l hu hn, nn

cng c th xut hin hin tng ha do hoc ph hy trong vng xung quanh khong

trng ngm, khi cc tiu chun bn hay ph hy b vi phm. Khi c th chuyn t

trng thi n hi nht sang trng trng thi n hi - nht - do ty theo biu hin hay

bn cht c hcvi nhng din bin phc tp.


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Nhn xt: Nh vy, i vi nhng cng trnh trong , m hnh c chn la s

dng hp l phc v tnh ton nn l m hnh n hi do. L do: c trng c l

phc v tnh ton d dng thu thp trong iu kin th nghim thng thng (khi m cc

thng s v tnh nht hay cc thng s v t bin cha c nghin cu v trin khai

rng ri nc ta). Hn na, m hnh n hi - do s cho php nh gi mc bindng hp l hn khi trng thi ng sut vt qu gii hn n hi m m hnh n hi

khng m phng chnh xc c.

Mt trong nhng m hnh hin i trong C hc hin nay l m hnh Hoek

Brown, c s dng rng ri nh nhng u im ca n.

1. CC PHNG TRNH C BN

gii bi ton t ra trc ht cn xy dng cc phng trnh c bn, bao gm

phng trnh cn bng, phng trnh lin tc ca bin dng v cc iu kin bin. Cc

phng trnh ny ph thuc vo c tnh ca m hnh c chn xy dng cho khi .

Phng trnh cn bng

Do tnh i xng v lin tc v phn b ng sut nn phn t chu tc dng ca cc

thnh phn ng sut nh trn hnh 3.

Hnh 3. Cc thnh phn ng sut v dch chuyn ti phn t th tch dV


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V sau khi o khong trng, khi trong vng xung quanh cng trnh ngm

chuyn sang trng thi cn bng mi, do vy phn t c kho st cng phi trng thi

cn bng tnh. Nh vy tng hp cc lc tc dng ln mt trc bt k phi trit tiu hay

bng 0. C th nu chiu ln trc hng tm i qua trng tm ca phn t, t iu kin

tng cc thnh phn lc tc dng hng tm Pr=0, nhn c:

0;0;

02

..2)(..0

dr

d

rdr

d

dr

dr

ddrddrrdr

dr

ddrP

r

r

rrr

r

r

rrr

(1-1)

y:

- ng sut php theo phng tip tuyn.

r- ng sut php theo phng hng tm.

Cc phng trnh trong (2-1) l cc cch vit khc nhau ca phng trnh cn bng

cho phn t dV. Cc phng trnh cng thng c vit di dng

r

rdr

d

(1-2)

Phng trnh cn bng trn cho thy r quy lut ph thuc gia hai thnh phn ng

sut c bn rv . Thnh phn ng sut th 3 y(dc theo trc y) c xc nh tiu kin l trong qu trnh bin dng mt ct ngang ti y=const lun phng, ngha l bindng ti mi im dc trc y ca mtct ny l hng s hay bng 0 (y=const).

Phng trnh lin tc ca bin dng

Hnh 3biu din s dch chuyn ca phn t th tch dV. Di tc dng ca cc thnh

phn ng sut, cnh trong d-c ca phn t dch chuyn i mt on bng u v mt ct

ngoi a-b dch chuyn i mt on bng u+du. Nh vy, lc u chiu di cnh l dr, sau

khi dch chuyn, bin dng c di l dr+du.

T hnh 3c th thit lp c mi quan h gia bin dng tng i theo phng

hng tm v bin dng t i theo phng tip tuyn (vng) ca cnh trong theo cc

phng trnh sau:


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dr

du

dr

drdudrr

r

u

rd

rddur

ds

dsds

)(1

(1-3)

Nh vy, t u = r, c:

dr

dr

dr

rd

dr

dur

)(

Hay

0;

rdr

d

dr

dr r

r

(1-4)

Cc phng trnh trong (2-4)c gi l phng trnh lin tc ca bin dng, cng

cn gi l phng trnh tng thch bin dng.

iu kin bin

Theo s ca bi ton, c iu kin bin sau:

ir

or

PRr

HPr

)(

)(

(1-5)

Trng hp cng trnh ngm khng c kt cu chng, hoc khng chu p lc nc t

pha trong, tng ng vi P i= 0. Nu cng trnh l ging ng (cng trnh thng ng t

mt t), khi cc kt qu nhn c vn ng vi cho mi lt ct ngang qua trc z,

ngay c khi h s p lc ngang khc 1, c th Po=Koz.

Cc phng trnh t (2-1)n (2-5)c coi l cc phng trnh c bn ca bi ton

kho st qu trnh bin i c hc trong khi xung quanh cng trnh ngm (khong

trng ) tit din trn, bn knh bng ri.


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M HNH KHI N HI

nh lut Hooke

Trong h to trc mi quan h gia cc thnh phn ng sut v bin dng ca khi

n hi thun tu c dng (i xng trc):

)(1

)(1

)(1

ryy

yr

yrr

E

E

E

(1-6)

y: E module n hi ca h s poisson

Xt trng hp bin dng phng y=0, nhn c:

)( rz (1-7)

V t c:

r

rr

E

E

1

1

1

1

2

2

(1-8)

Trong trng hp =0,5 phng trnh (1-8) tr thnh:

r

rr

E

E

4

3

4

3

(1-9)

Phng trnh (2-8) gii theo ng sut c dng:


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1)1)(21(

1

1)1)(21(

1

rr

r

E

E

(1-10)

Trong trng hp tng qut, khi l khng ng nht (t nhin, haydo iu kin

cng ngh) cc tham s c hc E v c th m phng dnghm s ca ta, ngha

l :

E=(r,); =(, ) (1-11)

Sau y ch xt trng hp n gin nht vi gi thit khi l ng nht vi cc

gi tr E v khng i.

Li gii ca Kirsch

Kirsch (1898) cho li gii bi ton phn b ng sut theo hai hng quanh ng

hm tit din trn trong mi trng n hi ng cht ng hng (hnh 4). Jaeger &

Cook nu chi tit lp cc biu thc xc nh ng sut ,r, rnh sau:

Cc thnh phn ng sut ti im M(r,):

ng sut php xuyn tm:

2 2 4 21 (1 )(1 ) (1 )(1 4 3 ) os2

r z k k c (1-12)

ng sut php tip xc theo chu vi ng hm tip tuyn:

2 41 (1 )(1 ) (1 )(1 3 ) os22

z k k c (1-13)

ng sut ct:

2 41 (1 )(1 2 3 ) sin 22

r z k (1-14)

Trong :

kh s p lc hng, k= hz


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abn knh ng hm

= a/r

Hnh 4. ng sut trong l trn quanh vt th n hi(Kirsch-1898; Jaeger v Cook -1976)

Cc thnh phn ng sut chnh trong mt phng ct hnh 4ti im M (r,):

ng sut chnh ln nht:

2/1

22

1 )(

4

1)(

2

1

rrr (1-15)

ngsut chnh nh nht:

2/1

22

2 )(

4

1)(

2

1

rrr (1-16)

nghing vi ng thng ng, :

)(

22tan

r

r

(1-17)

T hnh thy rng, ti mt quanh ng hm, r = a, r= = 0 nn:

2cos)1(2)1( ooo

z kk (1-18)


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Ti nh v y hm (= 00v = 1800):

)13( o

o

z k (1-19)

Ti hng v nh hm (= 900v 2700):

)3(o

o

z k (1-20)

Cc quan h c th hin trn hnh

Hnh 5. Bin thin ng sut ti nh, y v hai hng hm trn bin i theo k

(Hoek,1980)

T hnh 5, khi k=0, ng sut ti nh v y hm chu ko, khi k=0,33 th ti

nh v y hm bng 0, khi k>0,33 th trn ton mt hm u l nn. Do vy ng sut

ti hng hm hon ton gim t gi tr ln nht 3zkhi k=0 n 2zkhi k=1.

Kt qu l khi o xong ng hm t chng , ng sut nn ln nht trn mt hm

c th t 2zn 3zv ng sut ko khng vt qu zv tr tuyt i.

ng sut hnh thnh quanh ng hm khng ph thuc hng s n hi (E,) v

kch thc ng hm. Tuy nhin c th lu rng khi ng hm c cng khu lntrong cng khi , trng thi ng sut quanh ng hm ln v nh c th nh nhau

song tnh n nh ca chng khng hn nh nhau v khi cc ng hm c khu cng

ln th xc sut gp cc khuyt tt c hc (t gy, khe nt,) cng nhiu v do vy tnh

n nh km i.


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M HNH KHI N HI DO DA TRN TIU CHUN PH HOI

HOEKBROWN

Tiu chun ph hoi Hoek Brown (phin bn nm 2002)

Tiu chun Hoek-Brown ban u (1980) c nh ngha bi cng thc sau, l miquan hgia cc ng sut chnh lc ph hoi:

2/1'

3'

3

'

1

sm

ci

ici

(1-21)

Trong :

' 'l cc ng sut chnh c hiu ln nht v nh nht vo lc ph hoi.

cil cng nn n trc ca vt liu nguyn trng; miv s l cc hng s vtliu, trong s = 1 i vi nguyn trng.

ng sut chnh 3

Hnh 6. Quan h gia cc ng sut chnh ln nht v nh nht cho cc tiuchun Hoek-Brown v Mohr-Coulomb tng ng.

ngsu

tchnh1


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Nhbit,nhiubi ton ak thut,cbit l cc vnnnh mi c, li

c gii quyt thun tin hn nh ng sut ct v ng sutphp. Do , y l mt

trong nhng kh khnny sinh ngay t thigian u.

Ngoi s thay iv cng thc,Hoek, Wood, Shah, Kaiser v Bawden cn a ra

Ch sbn a cht GSI. Chsbn a cht GSI tip tc c m rngcho cc loi yubi Hoek, Marinos v Benissi. Mc ch l thay th cho ch s RMR ca

Bieniawski v RMR khng hon thin trong vic lin h tiu chun ph hoi vi cc

quan trcachttihintrng,cbitl vi ccrt yu. (Gii thiu v GSI xem

ph lc 1)

Di y s tp trung trnh by trnh t tnh ton do Hoek, Carranza-Torres v

Corkum xutp dng tiu chunHoek-Brown tngqut ha cho nt n.

Tiu chun Hoek-Brown tng qut ha

Phng trnh c bn ca tiu chun nycbiudinnh sau:

a

ci

bci sm

'

3'

3

'

1

(1-22)

Trong mb l mtgi trchitgimcahngsvt liumi, v cchobi:

D

GSI

mm ib 1428

100

exp. (1-23)

s v a l cc hngs ca khi v ctnh theo:

D

GSIs

39

100exp (1-24)

3/2015/6

1

2

1 eea GSI (1-25)

D l h s ph thuc vo mc xo trn m khi phi tri qua do h hi n mn

v gii phng ng sut. Gi tr D bin i t 0 i vi khi ti ch khng b xo trn

ti1 i vi khi b xo trn rt mnh. Hng dn la chn D xemph lc 2.

Cngnn n trc nhncbng cch cho = 0 trong cng thc (1-22), ta

c:


12/38

a

cic s. (1-26)

v cngchu ko l:

b

ci

t m

s (1-27)

Cng thc (1-27) nhn c bng cch cho 1 = 3 = t trong cng thc (1-12).

Lu rng gi tr chuyn mch ti GSI = 25 i vi cc h s s v a (Hoek &

Brown, 1997) b b i trong cng thc (1-24) v (1-25) khin cho vic thay i ca

di gi tr GSI tr nn lin tc v trn.

ng sut php v ct c lin h vi cc ng sut chnh bi cc cng thc

ca Balmer:

1/

1/.

22 '3

'

1

'

3

'

1

'

3

'

1

'

3

'

1'

dd

ddn

(1-28)

1/

/).(

'

3

'

1

'

3

'

1'

3

'

1

dd

dd

(1-29)

trong :

1'

3

'

3

'

1 )/(1/ a

cibb smamdd (1-30)

Module bin dng ca khi

Modulebindngca khi c chobi:

40/1010.1002

1)(

GSIci

m

DGPaE

(1-31)

Cng thc (1-31) ng ivici 100 MPa. Vici > 100 MPa, phidng cng

thc (1-32) diy:

40/1010.2

1)(

GSI

m

DGPaE (1-32)


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M hnh khi n hi do da trn tiu chun ph hoi Hoek Brown

Phng php phn tch

phn tch m hnh khi n hi do, cn thit phi c cc phng trnh cn

bng, iu kin bin tng thch, mi quan h gia ng sut v bin dng n hi, vng

do, cc quy lut v tnh lin tc. ng sut v chuyn v trong vng n hi c th cxc nh bng cch quan trc tnh lin tc ca ng sut hng tm v s chuyn v ca

mt tip xc n hi do. Trong vng do th da vo tiu chun v vng do, s lin

tc hay khng lin tc v gc trng n .

Vi iu kin bin dng phng i xng trc, bin dng v chuyn v c biu din

nh sau:

0,0),( zrr

uuruu (1-33)

0,,

zrrr

uru

r

(1-34)

Trong cc i lng r, v z l cc thnh phn hng knh, tip tuyn v dc trc.

Vi cc iu kin tng thch:

0)(

rrhayr

r

r

r

(1-35)

Hoc c biu din di dng phng trnh vi phn:

0

rdr

d tr

tt (1-36)

Vi bin dng v cng b, tng bin dng c phn ra hai thnh phn n hi v

do:

p

ij

e

ijij

(1-37)

Trong cc i lng e v p ch cc thnh phn n hi v do. Ngoi ra, bin dng

n hi cn c chia ra hai thnh phn chuyn v lch v thnh phn th tch

(Timoshenko & Goodier, 1970):

ij

ee

ij

e

ij (1-38)


14/38

Trong eij= thnh phn bin dng lch, e= thnh phn th tch n hi (1/3ekk)

v ij = hng s Kronecker, =1 (i=j), =0 (ij). Trong i, j = 1,2,3 hay ,r,z.

Tng t, thnh phn ng sut ij c chia thnh 2 thnh phn: ng sut lch v

thnh phn th tch:

ijoijij ' (1-39)

Trong ij= thnh phn ng sut lch, o= thnh phn ng sut th tch (1/3kk)

Do cc phng trnh lin quan n cc thnh phn lch v th tch ca ng sut v

bin dng n hi c a ra:

'1ij

e

ijE

(1-40)

o

e

E

21 (1-41)

Trong : E l module n hi v l h s Poisson.

S lin tc ca quy lut dolin h vi s gia tng bin dng do pijv th nng do

Q c a ra:

ij

p

ij

Q

(1-42)

Mi quan h gia ng sut bin dng n hi do v s gia tng ng sut bin dng

c th hin trong cng thc trn thng c dng. S chn la tiu chun ph hoi

(do) v kh nng pht trin vng do c cp n trong phn sau.

Tiu chun do

Quy lut chy do xy ra c xem nh tun theo tiu chun ph hoi phi tuyn Hoek

Brown. Trong gii php cho ng x n do ny, tiu chun ph hoi Hoek Brownphin bn mi nht c gii thiu nm 2002 c chn chom hnh ng x ca khi

.

Tiu chun Hoek Brown cho nguyn khi c l mi quan h gia ng sut

chnh ln nht v nh nht (1v 3) ti thi im ph hoi:


15/38

2/1

3

31 1

ci

ici m

(1-43)

Trong :

l cc ng sut chnh ln nht v nh nht vo lc ph hoi.

cil cng nn n trc ca vt liu nguyn trng .

mi l hng s vt liuph thuc vo loi (thng 5 mi 40). Cc gi tr miv

cic th c xc nh t kt qu nn ba trc (Hoek & Brown 1980,Hoek 1995).

Tiu chun ph hoi Hoek Brown sau c m rng xc nh cng

khng ct ca khi . Dng ca m hnh n do c xem nh tiu chun ph hoi

HoekBrown tng qut ha trn quan im bn lc ph hoi (Hoek 1994 v Hoek &

Brown 1997):

a

ci

bci sm

3

31

(1-44)

Cc hng s mb, s v a trong cng thc (2-53)v (2-54)l cc hng s vt liu c

trng cho khi .

Trong thc t, cc thng s ny lin quan n ch tiu nh gi cht lng khi (RMR- Rock Mass Rating) v gn y nht l ch tiu bn a cht (GSI- Geological

Strength Index (Hoek 1994, Hoek & Brown 1997). Bng ch tiu ny (GSI) thay i

trong khong tu 6 n 90 v c th tnh c t th v da trn cu trc ca khi

v cc biu hin trn b mt khi (Hoek & Brown 1997, Hoek, Marinos & Bennisi

1998).

Trong bn cp nht mi nht ca tiu chun ph hoi Hoek Brown, mi quan h

gia cc hng s mb, s v a trong cng thc (2-54)v GSI c a ra nh sau (Hoek

2002):

D

GSImm

ib1428

100exp. (1-45)


16/38

D

GSIs

39

100exp (1-46)

3/2015/6

1

2

1 eea GSI (1-47)

Hnh 7.m t tiu chun ph hoi Hoek & Brown vi cc cht lng khc nhau

(GSI=100, 50 v 5):

Hnh 7. Tiu chun ph hoi Hoek & Brown vi cc cht lng khc nhau

(a). nguyn khi

(b),(c). Khi vi gim ca gi tr GSI

Trong cng thc (1-45)v (1-46), D l mt h s m n ph thuc vo mc

xo trn m khi phi triqua do h hi n mn v gii phng ng sut. N bin

it0 ivikhi ti ch khng b xo trn ti 1 i vi khi b xo trnrt mnh.Tng t, tiu chun ph hoi Hoek & Brown cho cc thng s bn d c

th c nh ngha nh sau:

'

3

31 '

'''

a

ci

bci sm

(1-48)

c tnh nguyn khi:ci=10MPami=15c tnh khi :a)

GSI = 100mb= 15s = 1a = 0,5

b)GSI = 50mb= 2.515s = 3,866x10-3a = 0,506

c) GSI = 5mb= 0,504s = 2,605x10-5a = 0,619


17/38

Cc hng s c bn tin v cc gi tr d (trc khi ph hoi post peak) ca khi .

Hnh 8 th hin cc nh ngha v cc gi tr thi im ph hoi (nh peak) v d

theo cc hng s Hoek & Brown.

Hnh 8. Cc ng bao ti thi im ph hoi v sau khi ph hoi vi tiu chun phhoi Hoek & Brown tng qut ha

Cc ng x sau lc ph hoi(cc thng s d residual parameter) c c trngbi s lin tc (flow rule) lin quan n bin dng do. i vi m hnh vt liu do

hon ton, khng c s suy gim bn bn sau khi ph hoi; do , trng thi do

tip tc xy ra cp ng sut khng i lc ph hoi. Tuy nhin, ng x yu i ca

bin dng thng c quan st c nhng ni cc ng x trc khi ph hoi c s

ph thuc ca bin dng (strain dependent).

M hnh n hi dndo l mt loi ca ng x c m t trn v c c

trng bi s suy gim bn t ngt ti thi im ph hoi (peak) c th hin hnh8. Tiu chun ph hoi Hoek Brown vn c p dng mc d bn trc khi ph

hoi suy gim.

Thc cht vic m rng vng ph hoi ph thuc vo cc gi tr d ca bn

nguyn khi (Hoek& Brown 1980, Brown 1983, Indraratna & Kaiser, 1990a, Carranza-

Torres, 2004). Do , nh hng ca bn nn ca phi c trong cc gi tr d bi v

1)Cc thng s ti thiim nh (ph hoi):ci, mb, s, a

2)Cc thng s sau khiph hoi (d):ci, mb, s, a

Bin dng

ns

ut


18/38

s mt mt cc gi tr ban u bi do s suygim ng sut hoc s gia tng bin dng.

T l suy gim ng sut do c th c xem bng:

cici S .' (1-49)

Trong S i din cho s mt mt bn t bn ca trong trng thi nguynkhi n trng thi d (residual) hoc l o lng cp mt mt bn xy ra tc thi

sau khi t n trng thi ph hoi (peak). Thng s S c trng cho gin (d gy) ca

: do, ha mm v dn.

ci

Hoan toan deo

Bien dang hoa mem

Don

Hnh 9. bn trc lc ph hoi ca cc m hnh khc nhau

Theo , S s thay i trong phm vi 0


19/38

'

''

'''''

a

ci

r

bcir sm

(1-52)

0

''

''

'

r

sm

dr

d

a

ci

r

bcir

(1-53)

ng sut ct (r) ti im bt k theo phng hng tm = 0 cho trng hp bin

dng i xng trc trong iu kin bin dng phng. Khi gng o cha c chng

trong thnh phn trng lng neo = 0 v xt cc iu kin bin r = ri, r= 0, kt qu

ca phng trnh khng tuyn tnh (1-53)c a ra:

ci

b

r

m

s

'

'

'

(1-54)

'1

1

)'1( ln)1'(''a

i

b

a

r

rams

(1-55)

Mt s kt qu nghin cu trc y thng da vo phng php hn ch s hi t,

dng thnh phn p lc bn trong nh l mt thnh phn ca lc chng tc dng lnbin hm. Trong trng hp ny, v ng c tnh, p lc chng phi gim dn

khi s hi t tng ln. Vi trng hp ny, kt qu ca phng trnh khng tuyn tnh (1-

53)c chp nhn vi iu kin bin r = ri, r = Pi:

ci

b

ci

r

m

s

'

'

''

(1-56)

'1

1

)'1()'1(

ln')1'(''''a

i

a

cib

a

ciibr

ramsPm

(1-57)

ng sut trong phm vi n hi

Trong phm vi n hi, s phn b ng sut c a ra bi li gii ca Lame:


20/38

222

1)(

r

r

r

rPhay

r

rPP e

re

e

o

e

reoo

(1-58)

222

1)(

r

r

r

r

Phayr

r

PP

e

re

e

or

e

reoor

(1-59)

Trong rel ng sut php tuyn ti mt n hi do.

S phn b ng sut trong vng n hi tng ng vi gng o c bn knh ln re

c chng bi ng sut bn trong re di cng trng ng sut bn ngoi, re l

khong cch theo phng hng tm m ti l gii hn bin do xung quanh gng

o.

Ti bin gia hai min n hi do (r = re), ng sut bn trong c a ra di dngl thnh phn ca vng do:

ci

b

r

m

s

'

'

'

(1-60)

'1

1

)'1( ln)1'(''a

i

e

b

a

r

rams

(1-61)

T thnh phn ca min n hi ti r = re, cng thc (1-58) v (1-59)c th c sp

xp li nh sau:

)(2reoree

P (1-62)

oree P2 (1-63)

S dng tiu chun v bn ti thi im ph hoi (nh) cho bin do v n hi:a

ci

re

bciree sm

(1-64)

T hai phng trnh (1-62)v (1-64), ta c:


21/38

a

ci

re

bcireo smP

)(2

(1-65)

Li gii chnh xc cho phng trnh trn ch c th thc hin c vi a = 0,5. Tuy

nhin, vi cc phng php s (li gii gn ng), nh phng php Newton Raphson,c th cho cc li gii xp x i vi phng trnh (1-65)(Press, Flannery, Teukolsky, &

Vettering, 1994). V sau, phng trnh (1-65) c gii mt cch c lp khi a = 0,5.

smmPm

Pocicibcibo

cib

re

222 16168

1

8

(1-66)

B thnh phn c du m trong phng trnh trn v rt gn:

ciore MP

(1-67)

842

1 2

12

b

ci

o

b

b m

sP

mm

M

(1-68)

Bn knh ca phm vi vng do

Bn knh ca phm vi vng do rec th c xc nh bng cch cho rng ng sut

theo phng hng tm lin tc ti bin n hi do. Cng gi thit rng cc bin ca

min xt l xa so vi gng o, nh th nh hng ca chng i vi kt qu ca re

l khng ng k:

Cn bng (1-60)v (1-66)(cho reti r = re), bn knh vng do c th c suy ra t

cng thc sau:

X

i

e er

r (1-69)

)1'(

.161688

''

'

'1

21

222

'

'

'

'

'

')1(

am

smmPmmmmP

ss

Xb

a

cicibcibo

ci

b

ci

cibb

ci

boa

(1-70)

Phn tch chuyn v v bin dng

a.

Bin dng trong phm vi n hi


22/38

nh lut Hook c th c p dng xc nh bin dng theo phng hng tm

v tip tuyn trong vng n hi xung quanh phm vi bin dng do (Timoshenko &

Gooder, 1970):

1

1 2

rr E (1-71)

rE

1

1 2 (1-72)

rrG

1 (1-73)

Vi iu kin i xng trc:0,0,0 rzyzxz v 0r (1-74)

0 zyzx

(1-75)

Kt hp vi cc phng trnhtnh ng sut trong phm vi n hi (phng trnh 1-58

v 1-59), thay vo phng trnh (1-71)v (1-72), cho c trng bin dng di iu

kin bin dng phng:

22

22

)21(

2

)(

2

)21(

r

r

G

MP

Gr

r

G

PP

G

eci

o

eore

or

(1-76)

22

22

)21(

2

)(

2

)21(

r

r

G

MP

Gr

r

G

PP

G

eci

o

eore

o

(1-77)

Trong : G m un chng ct.

b.

Bin dng trong phm vi doTng bin dng trong phm vi do c to thnh t cc bin dng trong vng n

hi v vng do c a ra trong phng trnh (1-47). nh lut Hook v s lin tc

c p dng tnh ton bin dng n hi v do. M rng phng trnh (1-37)di

iu kin bin dng phng:


23/38

pet

(1-78)

p

r

e

r

t

r (1-79)

Trong cc bin dng n hi c xem nh l rt nh so vi bin dng do.Xc nh cc bin dng n hi trong phm vi vng do:

Dng nh lut Hook (1-71v 1-72), vi cc ng sut trong phm vi do (cng

thc 1-52v 1-54):

''

'

'

')21(

2

1 aci

ci

b

e

rm

s

G

(1-80)

''

'

' )1(

')21(

2

1 aci

ci

b

e

m

s

G

(1-81)

''2

1 aci

e

r

e

G

(1-82)

Xc nh cc bin dng do trong phm vi do:

Thay cc phng trnh (1-80)v (1-81)vo phng trnh bin dng (cng thc 1-

35), kt hp vi iu kin lin tc (1-42)cho c phng trnh vi phn khng tuyn

tnh sau:

0ln)1'(''2

')1(

1

)1('')21(ln)1'(''.2

'

'1

'

)'1(

'1

'

)'1(

a

a

b

acip

b

a

a

ib

aci

p

ri

rams

GN

r

mar

r

amsrGdr

d

(1-83)

iu kin bin c dng gii phng trnh (2-93):


24/38

G

M cip

2

ti r = re (1-84)

Phng trnh phi tuyn (1-83)c th c gii bng cc phng php s. Kt qu

cho phng trnh (1-83)vi iu kin bin c m t trn:

re

r

a

a

i

b

aN

b

ci

N

eci

N

p

drr

ramsrma

G

rG

M

r '1'

''11''

1

1

ln)'1(')'2)(1(2

21

(1-85)

C th thy t cng thc (1-85), hm s tch phn c trong kt qu ca phng

trnh vi phn. Li gii hon chnh c thc chp nhn vi phn tch phn trong

cng thc (1-85)c gii bng phng php s (phng php gn ng).

c. Trng chuyn v hng tm

Trng chuyn v c th nhn c thng qua mi quan h gia chuyn v -bin

dng tha mn cc iu kin sau:

u

rr

ur .

1 (1-86)

rur

r

(1-87)

Cc iu kin ca bin dng phng vi cc bin dng i xng ( r) cho thy tng

bin dng c lp vi cc thnh phn bin dng theo phng tip tuyn. Do ,

trng chuyn v theo phng hng tm c th c biu din nh sau:

tr

r

u

hay dru trr (1-88)

Trng chuyn v c a ra di dng:


25/38

re

r

aN

bciN

N

eN

cia

ci

ci

r

drrmar

rr

M

bm

s

Gr

u

'1''

)1(

1

1

'

.)'2)(1(1

')1(

'

'

')21(

2

1

(1-89)

Trong c th c rt ra t cng thc (1-45):

'1

1

)'1( ln)1'(''a

i

b

a

r

rams

(2-65)

245tan

sin1sin1 2

N , : gc trng n. (1-90)

V sau, s hi t ca b mt n hi do ca hm c th c xc nh bng cch

thay r = ritrong cng thc trn:

re

ri

aN

bciN

i

N

eN

i

cia

ci

i

r

drrmar

rr

Ms

Gr

u

'1''

)1(

1

1

'

.)'2)(1(1

'')1(

2

1

(1-91)

B qua bin dng n hi do n rt nh so vi bin dng do, cng thc trn c

th c n gin thnh:

re

r

aN

bciNi

N

eN

i

ci

i

r

drrmar

rr

M

Gr

u

'1''

)1(

1

1

.)'2)(1(

12

1

(1-92)

NHN XT

M hnh n hi do da trn tiu chun ph hoi Hoek Brown cn c trn c s

kt qu th nghim hng lot cc mu v thit lp c ng bao c dng phi tuyn.


26/38

Trn c s ny, cc phng trnh m t trng thi ng sut bin dng ra i cho php

nh gi, m phng cc bi ton xy dng thc t trong ph hp hn.

Cc c trng c l ca (ci, mb, s, a) trong tiu chun ph hoi Hoek Brown c

th thu thp c da trn kt qu th nghim mu (ci) v kt qu kho st hin

trng (mb, s, a) thng qua gi tr GSI t c th m phng tnh ton chnh xc vph hp hn.


27/38

TRNG THI NG SUT BIN DNG TRONG MI TRNG

XUNG QUANH NG HM

Bng 1. Kt qu tnh ton ch tiu khi nn theo tiu chunph hy Hoek-Brown

Loi Cc thng s tnh ton IA2 IB IIA IIB

graniteKhng nn mu , MPa 20 65 87 100

Ch s cng a cht, GSI 30 40 60 70

Hng s Hoek-Brown, mi 29 29 29 29

H s ph hy, D 0.5 0.5 0.5 0.5

Gc ma st trong khi , o 35 48 57 61

Lc dnh khi , C MPa 0,4 0,7 1,2 1,8

Khng nn khi , MPa 2,8 10,7 24,2 36,3

Moun bin dng khi , MPa 485 2124 10000 18590

bincht

gneiss

Khng nn mu , MPa 20 70 90 100



H s ph hy, D 0,5 0,5 0,5 0,5

Gc ma st trong khi , o 36 48 56 58

Lc dnh khi , C MPa 0,45 0,7 1,1 1,3

Khng nn khi , MPa 2,8 11,3 21,7 27,4

Moun bin dng khi , MPa 600 2825 9556 14270

Vic tnh ton c thc hin nh s tr gip ca phn mn Phase2 (Rocscience

Canada) trn c s m hnh theo tiu chun ph hoi Hoek Brown. Do b tr ng

hm su 100m nn chu p lc a tng do ct t vi gi tr xp x 27kN/m 3 x100m

= 2,7MN/m2. S m phng c m t nh trong hnh vvi cc s liu a cht u

vo c tnh ton trong on ng hm gn ca nhn nc nm trong granite .


28/38

Hnh. M hnh tnh ton cng trnh ngm ak Mi 3 trong giai on thi cng


29/38

Bng 2. S liu tnh ton theo tiu chun Hoek Brown cho nguyn khi

Loi Cc thng s tnh ton IA2 IB IIA IIB

Granite

Khng nn mu , ci(MPa) 20 65 87 100


Hng s Hoek-Brown, mi 29 29 29 29H s ph hy, D 0,5 0,5 0,5 0,5

M un n hi, Mpa 1000 15000 25000 30000

mb 1,035 1,666 4,317 6,95

s 0,0001 0,0003 0,0048 0.0183

a 0,522 0,511 0,503 0,501

Do cng trnh khng c th nghim o hm ngang nn s liu tnh ton cho vng

b ph hy (bin dng do) c tnh ton da vo ch tiu cng a cht GSI csuy ra t nguyn khi theo cng thc sau:GSIr= GSI.e

-0.0134GSI . y, GSIr l ch

tiu cng a cht trong vng b ph hy (bin dng do). S liu cho trong bng

3.3.

Bng 3. S liu tnh ton theo tiu chun Hoek Brown cho ph hy

(bin dng do)

Loi IA2 IB IIA IIB

Granite

Khng nn mu , ci(MPa) 20 65 87 100Ch s cng a cht, GSI 20 23 27 27


H s ph hy, D 0 0 0 0

mb 1,666 1,854 2,139 2,139

s 0,0001 0,0002 0,0003 0,0003

a 0,544 0,536 0,527 0,527

Kt qu tnh ton m phng bng chng trnh on cng v na cng th

hin cc hnh.


30/38

Hnh 4. Gi tr ng sut chnh 1 v3 trong cng IIA.

Hnh 5. Vng do xung quanh bin cng trnh

Chuyn v max = 0.0003944m

Hnh 6. Gi tr chuyn v xung quanh cng trnh


31/38

Hnh 7. Gi tr ng sut chnh 1trong IA2 na cng.

Hnh 8. Gi tr ng sut chnh 3trong IA2 na cng.

Chuyn v max = 0.025429m

Hnh 9. Gi tr chuyn v xung quanh cng trnh.


32/38

Hnh 10. Vng do xung quanh bin cng trnh.

NHN XT

Phn b ng sut chnh nh nht xung quanh cng trnh ngm trong cng v na

cng l nh nhau: gi tr ng sut chnh nh nht tngdn n gi tr ng sut ca ct n phm vi nh hng cch vch hm 2,5 ln ng knh (15m).

Trong mi trng cng, khi trng thi ng sut cha vt bin do, ng x cami trng trong phm vi n hi, iu kin n nh v bin dng c m b o. Do bin php gia c cng trnh c th khng cn thit hoc c gim thiu ng k.

Trong mi trng na cng, vng do xut hin trong phm vi 3m k t vch cngtrnh: ng sut chnh ln nht c khuynh hng b st gim trong khi ng sut chnhnh nht nh trong mi trng n hi. Do s xut hin vng do xung quanh cngtrnh trong na cng, chuyn v ca xung quanh v hm c gi tr ng k vlm yu khi . Trong trng hp ny, cc bin php gia c nh neo trong hockt cu b tng chu lc phi c b sung m bo iu kin lm vic n nh cacng trnh.

Chuyn v ca tnh ton theo m hnh n hi do ph hp vi ng x thc t vc gi tr ln hn ng k so vi trng hp xem l mi trng n hi nn c thgy nt n bin chu vi cng trnh.

M hnh n hi do da trn c s tiu chun ph hoi Hoek Brown (phin bn

nm 2002) cho php nh gi cc thnh phn ng sut v bin dng hp l khi trng

thi ng sut ca mi trng vt qu phm vi n hi v khc bit ng k so vitrng hp xem l mi trng n hi.


33/38

PHLC 1: GII THIU V H THNG PHN LOI THEO CH

TIU BN A CHT GSI (GEOLOGICAL STRENGTH INDEX)

Hoek v Brown nhn ra rng tiu chun ph hoi ca khi s khng c gi tr thc tin no nu nh n khng lin quan n cc quan st, nh gi a cht ti hin trng,

cng vic m c th c thc hin d dng bi cc k s a cht ti cng trng. H

xem xt s pht trin mt h thng phn loi trong qu trnh pht trin tiu chun vo

nhng nm cui ca thp nin 70 nhng h t b nh v trong thi gian ny c

h thng phn loi khi RMR ca Bieniawski a ra t nm 1974 v c cng

nhn trong gii c hc . H thng RMR (v c h thng phn loi Q) c pht trin

nh gi cht lng khi trong qu trnh thi cng v gia c chng cng trnh

ngm, v trong n bao gm mt s cc thng s khng cn thit cho vic nh gi ctnh v cht lng khi . Nc ngm v cc thng s v hng cu trc trong RMR;

nc ngm v cc thng s v ng sut trong Q c gii quyt tt hn bng phng

php s v cc thng s ny khng lin quan trong vic nh gi cht lng khi . Do

, thng ch bn thng s u trong h thng RMR ( bn khi , nh gi RQD,

chiu rng vt ct, v cc tnh cht ca vt ct) l c dng cho vic nh gi cht

lng khi .

Trong thi gian u th h thng phn loi RMR c s dng rt hiu qu bi v hu

ht cc vn u c p dng vi khi c cht lng tng i t t (30


34/38

ng dng n trong tiu chun ph hoi Hoek Brown c tip tc pht trin bi Hoek

(1994), Hoek et al. (1995) v Hoek & Brown (1997) nhng i vi cng th n vn

tng ng vi h thng phn loi RMR. K t nm 1998, trong qu trnh gii quyt

cc kh khn gp phi khi thi cng ng hm Hy Lp, Evert Hoek v Paul Marinos

pht trin h thng GSI nh ngy nay trong c c vic nh gi cht lng khi

yu (Hnh PL1-1) (Hoek et al. 1998; Marinos v Hoek 2000, 2001). Bn cnh h cng

m rng p dng cho khi khng ng nht (hnh PL1-2) (Marinos v Hoek 2001).


35/38

Hnh PL1- 1. Bng c tnh gi tr GSI chung cho cc quan st, nh gi a cht

PH N PHI N M NG/B C T -Khng c s kt dnh do cc phin

mng hay nhiu mt phng ct.

PH H Y- C u trc lin k t y u, kh i to thnh bi s pha trn gia cckhi tam gic v trn

PH N KH I/KH NG NGUY NTRNG/ NT- Un np vi cc phnkhi tam gic c to thnh bi rtnhiu cc vt nt giao ct nhau. Lu dnto thnh phn lp hay phin

C U TR C PH N KH I MNHPhn khi , khi khng nguyn trngto thnh bi cc phn khi tam gicgiao ct nhau do bi 4 hay nhiu vt ct

CH TIU BN A CHT CHO KHI

NG NHT

(Hoek v Marinos, 2000)

T cc iu kin thch hc, cu trc v b mt

khi v tnh lin tc, c tnh gi tr GSI trung

bnh. ng qu c gng chnh xc. Chng hn

nh nm trong khong 33 n 37 th hp l hn l

chn vi GSI =35. Ghi ch rng bng ny khng

p dng cho cu trc kim sot s ph hoi.

Nhng ni mcc mt t gyc hng bt li

khi o s lm nh hng ti ng x ca . Sc

chng ct ca b mt s gim khi c nc. Khi

nh gi khi trong vng trung bnh n rt

yu th vi iu kin m t nn dch chuyn qua

bn phi. p lc nc ngm s c gii quyt

bng vic phn tch ng sut c hiu.TRNGTHIBMT

KHI

NGUY N KH I HAY C CH C -Cc mu nguyn khi hay c chc hin trng cng vi mt vi vt ct

C U TR C PH N KH I- C c u trcphn khi cht ch hnh lp phng tobi b 3 vt ct

CU TRC

CHIUGIMC

AS

LINKTGIACCKHI

R

TT

T

Rtcng,

bmtkhngbphongh

a

T

T

Cng,

bphonghat,

bmtcm

unust

TRUNGBNH-Bngphng,pho

nghatrungbnhvb

mtbthayi

YU

-Bmtbphonghamnhviccmnhvnbao

phhaylpnht

R

TY

U

-Bm

tbphongh

amnhvicclpst

mmbaophhaylpnht

CHI U GI M CH T LNG B MT


36/38

Hnh PL1- 2. Bng c tnh gi tr GSI cho khi khng ng nht, phn lp.

R T Y U - B mt b phong hamnh vi cc lp st mm bao phhay lp nht

YU - B mt b phong ha mnhvi cc mnh vn bao ph hay lpnht

TRUNG BNH - Bng phng, phongha trung bnh v b mt b thay i

T TCng, b phong ha t, b mt c munu st

RT TTRt cng, b mt khng b phong ha

B.

Ctkt

xenlncc

lpbtkt

mng.

C.

Ct

kt

xen

ln

bt

kt.

D.

Phin

btktxen

lncclp

ctkt.

E.

Ph

in

bt

ktyuhayc

cha

stxen

lncclpct

kt.

C,D,

EvG

n

uton

pnhiu

hay

thnmtnhngkhngthay

i

cng.

Bindngkinto,

t

gyhay

mts

lin

tcth

chu

nxu

nF

vH

F.

Bin

dng

kin

to,un

np

mnh/tgy,ccphnbtkthay

cchastxenlnviccl

pct

ktbindng,

khnglint

cto

thnhcutrchnn.

H.

Ccphinbtkthaycchast

tothnhcutrchnn.c

cha

nhiutist.Cclpctkt

mng

binithnhccm

unh.

G.

Ccphinbtkt

haycchastkhong

b

xen

k

c

hay

khngcvirttcc

lc

tkt.

A.

Phnlpdy,ctktphnkhim

nh.

nhhngcalplpnhtgiaccmtphn

lplkhngngk.

Trongcc

nghmnnghaymidc,ccmtphnlpn

yc

thlmm

tnnh.

THNHPHNVCUTRC

CHTIUBNACHTCHOKHIKHNGNGNHT

,PHNTNG

(HoekvMarinos,2001)

Tcciukinthchhc,cutrcvbmt

khiv

tnhlintc,ctnhgitrGSI

trungbnh.

ngqucg

ngchnhxc.

Chnghnnhn

mtrongkhong33n37th

hplhnlchnviGSI=35.

Ghichrng

tiuchu

nphhoiHoek-Brownkhngp

dngchocutrckimsotsphhoi.

Nhngnimccmttgychngbtli

slmnhhngtingxca.bncamtskhisgimkhicncng

m.

Khinhgikhitrongvngtrungbnh

nrty

uthviiukin

mtnndch

chuy

nquabnphi.

plcncng

m

khn

glmthayigitrGSIvscgii

utbn

vic

hntchns

utchiu.

NH GI B MT KH I V

KHNG LIN TC (mt phn lp)

Bindngsauqutrnhkinto


37/38

V ngoi ca khi M t khi Gi tr D

khuyn ngh

N mn c kim sot cht

lng rt tt, hoc o bng c

gii bi my khoan hm TBM

s gy nn xo trn rt nh cho

khi b nn p ba chiu xung

quanh hang hm.

D = 0

o c gii hoc bng th cng

trong cht lng km

(khng n mn) gy ra xo trn

rt nh cho khi bao quanh.

Nu iu kin nn p

(squeezing) gy ra bng nn

ln, th xo trn c th lnghim trng, tr phi c thi

cng mt vm nga tm thi

(nh trong nh).

D = 0

D = 0,5

Khng lmvm nga

Vic n mn cht lng rt ti

trong mt hm cng s sinh

ra ph hoi cc b nghim

trng, phm vi c th su n

2m hay 3m vo khi xung

quanh.

D = 0,8


38/38

V ngoi ca khi M t khi Gi tr D

khuyn ngh

N mn quy m nh ti cc mi

dc cng trnh dn dng gy ra

h hi khi trung bnh, cbit l nu c s dng k thut

n mn c iu khin nh th

hin trn phn bn tri ca bc

nh. Tuy nhin, vic gii phng

ng sut s gy ra mt s xo

trn nht nh.

D = 0,7

N mn tt

D = 1,0

N mn ti

Cc mi dc m khai thc l

thin rt ln s phi chu s xo

trn kh ln don mn i tr

khi lng ln v cng do s

gii phng ng sut t vic o

b lp t ph bn trn.

Trong mt s loi mm, cth tin hnh o bng cch

bc x v san i nh mc

h hi n cc mi dc s gim

i.

D = 1,0

N mn i tr

D = 0,7

o bng c

gii

Bng 1: Hng dn xc nh h s xo trn D

Mot So Mo Hinh Trong Co Hoc Da Va Mo Hinh Hoek

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