isrm-4congress-1979-235_stability analysis of underground cavities in fissured rock masses

8/12/2019 ISRM-4CONGRESS-1979-235_Stability Analysis of Underground Cavities in Fissured Rock Masses

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S TA B I L IT Y A N A LY S IS O F U N DE R GR O UN D C AV IT IE S IN F IS SU R ED R O CK M A S S ES

Analyse de la stabilite des cavltes souterraines dans les rochers solides fissuresDie Stabllltatsanalysa der unterirdischen Hallen in den diskontinualen Felsenmassen

s . Cor i e*

*Facul t y of Mi ni ng and Geol ogy. Beogr ad.

SUMMARY

The paper r ef er s t o t he s t abi l i t y anal ys i s f o r under gr ouna cav i t i es of l ar ge cr os s sec t i on,whi ch ar e t o be const r uct ed e i t her wi t hout or wi t h mi ni mum l i n i ng. Si nce such cavi t i es mayonl y be const r uct ed i n f avor abl e engi neer i ng- geol ogi cal l y condi t i ons , i . e . i n har d r ock masses ,t hei r s t abi l i t y i s i nf l uenced most l y by t he number , conf i gur a t i on and char act er i s t i cs , as wel la s by l a t ent d i scont i nu i t i e s o f f i s su r e s . The p r oposed pr ocedur e makes i t poss i bl e t o i den t i f yt he sa f e t y f uct o r f o r each monol i t h , whi ch i s a f undament a l condi t i on f o r e s t abl i sh i ng o f t henumber , magni t ude and di r ect i on of t he anchor s i n t he under gr ound c~vt y. The pr ocedur e enabl esus t o choose t he bes t l ocat i on. o r i ent a t i on. s i ze and shape o f t he' under gr ound cavi t y.

RESUME

Cet ouvr age se r ef ~r e A l ~anal yse de l a s t abi l i t e des cavi t es sout er r a i nes de gr ande sect i ont r ansver sa l e que l ' on cons t r u i t so i t s ans so i t avec I e r eve t ement mi ni me . Ces cavi t e s ne pouvan tet r e conat r u i t es que dans l es condi t i ons i ng~ni eur s- geol ogi ques f avor abl es , c ' es t - ~- di r e dansl e s r oches en pl ace so l i des , l eur s t abi l i t e e s t l a pl upar t du t emps i n f l uencee pa r I e nombr e ,l a conf i gur a t i on e t l e s ca r ac t e r i s t i ques des f i s su r e s , a i ns i que par l e s di scont i nu i t e s l a t ent e s .Ce p r ocede nous per met de det e r mi ne r I e f ac t eur de s t abi l i t e des monol y t hes ; t out cec i se r t debase pour l a det er mi nat i on du nombr e e t de l a posi t i on des ancr es dans une cavi t e sout er r a i ne.Ce pr ocede r end possi b l e de det er mi ner l a mei l l eur e l ocal i sa t i on. or i ent a t i on. f or me et gr andeurde l a cavi t e sout er r ai ne


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- St r e s ses i n t he r ock mass a r ound t het unne l openi ng o f c i r cul a r c r os s sect i on a r edet er mi ned i n t he same way as f or a homoge-neous, i sot r opi c and e l as t i c medi um

- T he r o ck ma s s i s i n t he pl ane s t r ai nst at e.

The bas i c s t eps i n t he pr oc edur e ar e t hef ol l owi ng:

- T he f i r s t s t e p i s t o de f i ne t he s t a t eof s t r ess ar ound t he under gr ound cavi t y, whatenabl es us t o det er mi ne t he f or ces act i ng onmonol i t hs .

Fi g. 2 St r esses t ' r ,l? e ,'b ,.. at po i nt D.

Knowi ng S,.. G e and '5 , . 8 we can f i nd t hest r ess es ~OJlcl'1i. a t po i n t D f o r an a r bi t r a r ypl ane, maki ng an angl ~wi t h t he r adi ust hr ough D.


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6e.dAcosc

1)er.dAcoscC

'lJred A sincC

br.dA.sin.:

Fi g. 4 El ement ar y i nt er nal f or ces

The val ues of unknown s t r es ses bn and 'bn ar ef ound f r om t he equat i ons of equi l i br i um f ort he el ement ar y pr i sm ( Fi g. ( )

Sn.dF-GrdFsin~+ U'redF sin.ccos.c-

-~e.dFcos~ + 'G'redFcosc.sinc{'::: abndF+ (5f'dFsinCcosc:C.+15'redFsin2c:.-

-GedFcoscCsinC- '5er dFcos2ol = a

(4)

(5)

. Nor mal f or ces ana t angent i al f or ces act i ngon monol i t hs ar e t he r esul t ant s of t he cor -r espondi ng st r esses E)n I '6n and S c/ equa t i ns ( 1) . . . . ( 11) / .

Knowi ng nor mal f or ces and t angent i alf or ces. we exami ne t he st abi l i t y of monol i t hsal ongsi de t he sur f aces of di scont i nui t i es. Thi s pr oc edur e wi l l be shown on a monol i t hM (Fig. 5).

Fi g. 5. A posi t i on o f mono l i t h M i nt h k


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The sur f ac es of di s cont i nui t i es we wi l l s i gn

as Ai wher e i ndex " i " co r r e sponds t o i ndex" i " at t he f or c es Ni and Si .

The shear s t r engt h at t he s l i di ngs ur f a ce Al i s

N , tg'f, + c,A, (12)wi t h par t i a l saf e t y f ac t or

K '- N,tg'f1+c,A, (13)1- S,

The shea r s t r enght at t he s l i di ng sur f ac e A2 i s

N 2tg ~ +

~A2wi t h pa~t i al saf et y f act or

K~= N2tg'l~; c2A2 (15) The s hea r s t r engt h at t he s ur f ac es of

di s con t i nui t i e s A) and A4 we wi l l s i gn l : : .

l : : . = N 3tg'f 3 + C3A3+ Ndg 'P4 +c4A4 (16)As t he r es ul t of t he s hear s t r e ngt h of

s ur f ac es A) and A4, i t comes t o t he i nc r eas i ngof t he pa r t i a l s a f e t y f act o r s , i . e . we a r eget t i ng t he g l obal saf e t y f ac t or s .

We obt a i n t he condi t i on t hat t he g l obalsaf e t y f ac t or s f or s l i d i ng of monol i t h M,a l ongs i de t he s l i di ng sur f aces Al and A2 ar eequa l one t o ano t her , i . e .

(14)

K = K2 = K (17)

and i n t he c as e when i t i s

(25)

t hen t he g l obal saf e t y f ac t or of monol i t h M*i s

(26)

(27)

The s t abi l i t y of al l ot her mono l i t hs ar o -und t he t unnel i s , anal yzed i n t he same way.

I n t he par a t i cul ar case, when t he s l i d i ngsur f aces ar e par a l l e l one t o anot her ( Fi g . 1) ,


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Fi g . 8 . For ces act i ng on monol i t h M; w i st he wei ght of t he monol i t h

ar e t he st r engt hy par amet er s f or t he cor r es-pondi ng sur f aces of di scont i nui t i es. Thi s pr oc edur e may be t he bas i s f or t he

anal ys i ng t he s t abi l i t y of monol i t hs when in

t he r ock mass t her e i s t he t hr ee di menai onals t a t e and i n t he case when t he under gr oundcav i t y hss no t onl y t he c i r cul a r c r oss sect i on,but has di f f er ent c r os s s ec t i ons . I n t hat c as e

t he most di f f i cul t pr obl em i s t o det er mi ne t he


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Hors-texte Tunnel sous-marin du Pas-de-ealais

Fig. 150. - Machine Beaumont, pour Ie creusement des tunnels dans les roches tendres.

isrm-4congress-1979-235_stability analysis of underground cavities in fissured rock masses

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