rendimiento de los soportes en túneles a traves de suelo

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Scanned by CamScanner T u {ì e l e s & , A ¬ A he r a d i a l 1 un ne l s Th ro u g h So il s c h an g e ' " . . . ._ Es i n t hc surroun di n g X s ; ; = d u x : T ine f a v or a b l e d i s t r ib u 1i on ch a r can b e r c ac h co ° ? ' ' h e cuss e d l a t e r i n t hi s sec t i on so m e 1hco r e t i ca l c o n s id e r a t i on s w i u = : : : = : x : XX ; : ffan : X M " X = fi rs t bc p r e sen t e d A mas s o f s o jj w iu ] a 1 1o t i zo n 1 a l s ur f ace i s t o n i ons H ow e ve r i f t hi s i s n o t so t h c m as s o f so il w i l! e v a s su m e d A t d e p t h z t h e v er t i ca l no rma l s t re s s w i l l be 1 z an d ! " lly ac 1 On t h e s u pp o r t s y s t en r an d w i ll cau s e f u r t h e r d i s pl a t h e ho r i zo n t a l s t re ss K . 1 z b e E or e t h c t u nne l i s e xcav a ¢ e d 1f a m en t s i n i t so m e l i n 1e s o ve r . Ve r y l o n g p e r i o d o f r i m e T h us , c i r c u l ar s u pp o n (a 1 u nn c 1 [ i n i n gj i s i m me di a t e l y i ns t a ll e d i ns i d e 1 hc s t r en g t h n n d r i g i di t y o r t h c excava t e d m a1er i a l t h e d cf t h c m ass [ 1 ] t h ç s t re ss s t a l e i n t he m a ss a t t i le t i m e o f i n s t a ll a m a bi li t y o f t h e s u pp or t s y s t em an d t he i n t e r r c B a l ioo b c t ' "i cn t i on d o cs no t d i ff e r í rom \ ha t ex i s t i n g p re v i o u s l y If t h e c i rcu l a r t ï1em a r e o f f un d a men t a l i m p o r t a nc e su pp o H i s n e x ibl e b u t c a p a bl e o f su p p o r t i n g t hc co m p r e s s i ve 1 +f t h e su pp or t w e r e i n fi n i t e l y r i g id 1h c p r es s ur e s t k vc ! o p í n g s t re s s es p r o d u c e d b y t he e ar t h arou n d i t i m me di a t e l y a f l c r i t s i ns t a l l a t i o n w oul d b e t he s am e a s i n t h e A f t e r a l i m e t h e c i rc u l ar ( n ex i bl c ) r i n g c a n on l y b c i n c q u i l i c ase o f t h c nex ibl e s u pp o r t Su b se q u en t l y i t w ou l d n o t d e f o rm b r i u ï ï 1 i f t l 1e r a t l i a l n o r ma l s t r es s es a f f e c t i n g i t are e q ua l i n a l l an d t h e n o n u n i1 o r m p re ss u re d i s 1r i b u t i on w o u l d c on 1i n u e di r e c t i ons I n o r d e r t o f u l f il l t hi s c on d i t i o n t h e ho r i z o n t a l i n d e fi n i t e l y B . N di n g m omcn 1 s w il l d ev e l o p i n t h e Su pp o r t n o r 1n a l s t r es s p r o d u ce d b y t h e ear l 1 1 m u s t i nc r e a se ( i r K ' " 1 ) s y s t em i n acc o r d ance w i t h « r ess s t a t e s t h a t a r c n o l on g e r u w h ere as t h e ve r t i c a l n o r m a l s t r - m u s t d i m i n i s h T hi s s i t ua f or m l y ra d i a l T' i s i s a b as i c t l i s a d .. N l n g c o f r i g id su p p o r t s l i on ca n o n l y b c re a c he d b y m ean s o f d c í o r m a t i on o f t h e w hi c h a p ar t f r o m b e i n g d es i g ne d 1 0 w i t h s t a n d r a d i a l s t ress es , s u p p or t s y s t em b y t he ne c essar y a m oun t a t a ll p o i n t s a n d i n t h e mu s E a l so b e ca p a bl e o f Su pp o , l i n g be n di n g m o m en t s O n c e re q u i re d di r e a i o n T h e c i rc l e b ec o m es s t i g l , l l y e M p 1i c a l A g a i n a n e lli p t i c a l s u pp or t w i 1h i l s sma ll e r ax i s K . T i n 1es t hc I f t h c li n i n g r i n g t o l era t es t h c un if or m , a di a l s t re ss e s 1h a t a r e l ar g er ( v e , t i ca l ) o n c w o u ld un d er g o p rac t ica ll y z e lo be n di n g p ï o d u c e d a sa 1i s f a c t or y c q u i lib r i un l con d i t i on w ill be a c l 1i e v e d m omen t s ev en if i t we r e r i g id T l 1i s ill u s t ra t e s t h e g rea t s o l on g as i l l e a m o un t o t s t r a i n re q u i r e d d oe s no t excee d t o l e ra i n &u e nce o f t h e s ha p e o f l t te c a v i t y a n d t h e i n i t i a l s t ress di st bl c li m i t s o f d e f u[ ma l i on o f t h c r i n g ns w e ll as an y no n b u l i on i n t h e c ase o f ï i g i d su pp o H s y s t ems s t ru c t ura l l i m i t s T he am o u n t o f d e f or m a t i on t i la t t h e r i n g u n d er g o e s b c f a rc i t rea c he s i l s e q u ilib r i u n1 c on d i t i o n d e p e n d s o n t h c c h arac t er i s t i c s o f t he s o il aro un d i l a n d t he i r va r i a t i on w i t h t i m e ¢hc r i n g s l ifl n e ss , t h e di m en . I o n s o f t h e 1 u n nc l nn d 14 7 1 Sm bi li t y a 1 t h e W or k i n g F ace l h c d e p t h a t w h i c h i t i s d [ i v e n 1 f t he li n i n g wer e i n i t i a l l y c ui p t i ca l w i t h i t s s1 na 11 c r ax i s e q u a l Thi s i s i m p o r t an t e s p ec i a ll y i n I . Nnc l s d r i ven i n s o f t g moun d t o K . T i m es t h e l ar g er (ver 1i ca l ) ax i s t hi s s h a p e wou ld b r i n g f or i t I . Nuen ces t he cons 1r uc l i o n m e t h o d s t o b e u s e d n n d t h e a b ou t a ne a r l y u n if o rm di s t r ib u t i o n o f 1hc r a d i a l s t re ss a b ou t un if orm i 1 y a n d ma g n i t u d e o f t he l oa d s On l h c s u pp o r t s 1 1 1 t he t un ne l e ve n if no d e : o r ma t i o n occur s i 1 n n 1e di a 1 e l y a f t e r i ns t a ll a t i on Th c co nc e p t s p r e s e n 1 c d h ere a re sum ma r i ze d i n Fi g ]4 29 1 1 ] I T u nne l s I . Cl a y s Par t a o f t he f i g u r e s how s t i le s t ress d i s t r ib u t i on on a c i rcu l a r t un ne l i m f n e di a t e l y a f t er i n s t a l l a t i o n o f t hc s u p p o r t , nss u n1i . g I n c l a y s t h e s 1a bi l i r y o f t he w or k i n g : a ce d e w n d s on t h e i r t l 1a t t hi s i s i ns t an t an e ous P ar t b s ho w s t h e u l t i m a t e n ea r l y u n d r a i ne d s t ren g t l 1 T h c l on g t erm s t r e n g t h i n t e rm s o t e f f un i[ o rm d i s [ r i b u r i on o f i l ic ra d i a l s t r e s s t h a t i s rc ac l 1e d a f t er t he r i ve s t re sse s t v ilt on l y b e o f i m p or t an c e if t i l e : ac e i s l e [ t e x p o se d t un n e l d c f or m s ns s how n I As t l y Par r c s h o , vs t he i n i t i a ll y a n d u n s u pp o r t e d : or a l o n g p er i o d o f t i me ; c lli p t i ca l cro& s e c t i on re f erre d t o 1n p r i n c i p l e i t i s p o ss ibl e t o ana l y z e t h c s \ t o r t t e rm s t a b ili t y c o n di t i ons o f 1 hc t vo r ki n g f a ce o f a t unn e l i n c l a y A l t h o u g h i n p ra c t i ce ma n y f ac t o r s m a y h a v e a n i n n uen ce w hi c h arc n o t a I b c o f c l a y a bou t a nau ow 1 1o r i zo n t a l c u t m a d e i n a w a l l O1a t s u pp o r t s i t i s ana l y ze d A ss u m i n g a c y l i n d r i c a l s l i p s ur : a c e lik e t h c onc s h o w n i n K o I/ z ( l+ H o ) (r z p r e ss u re f a i l u r e o í t he c \ a y occu r s o f t h e h or i zo n t a l cu t I (w hi c h o b v i o u s l y c d f ace o t a t un ne l ) w °° e x cee d s 6 28 t i me s t h e va l ue o c . . w h i c h i s t h e un d ra i ne d s t ren g t h o t l 1 1c c l a y I f t h e c u t h a s a c i rc u l a r a p c t t u r e , t \" i s r a t i o : DISTRI BUTION , WHE N I AF TER A CERT AIN T I ME c om p ar i son w i t h t he d e p t h a t w h i c h i t w as l o c a t e d t h e c t i t i c a \ wou ld i ncrea s e t o 75 If t l 1e w id t h o f t h e cu t i s a pp rec i a bl p i n : : · : L WWG í s INSTALLED t va l ue o f t h e r a t i o w ill be [ l ] : : ; I E L L I P TIC AL U v F LE XIBL E C IR CU LA R L IN IN G L I N I NG 2 : + r r \ : Fï g 14 29 Di s t r i b u t i on o t r a d i a l s t re ss e s a b ou t n ex i bl e t un ne l r . . li n i n g s o r st r pp o r t s I 1 j , i n nor n ïa ll y co n so l i d a [ c d 1 na t e r i a l 6 z ( 1466 ) s , ,

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Rendimiento de los soportes en Túneles a través de Suelo, diferentes tipos de suelo y soportes.

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Page 1: Rendimiento de Los Soportes en Túneles a Traves de Suelo

Scanned by CamScanner

T u { ì e l e s & , A ¬ A he r a d ia l

1 u n n e l s T h r o u gh So i l s

c ha n ge ' " . . . . _ Es in t hc s u r r o u n d i n g X s ; ; = d u x :

T in e fa v o r a b le d is t r i b u 1i o n ch a r c a n be r c a c h c o ° ?' ' h e

c u s s e d la t e r in t hi s s e c t io n s o m e 1hc o r e t ic a l c o n s ide r a t io n s w iu = : : : = : x : XX ; : ffan : XM" X=f i r s t bc p r e s e n t e d A m as s o f s o j j w i u ] a 11o t i z o n 1a l s u r fa c e i s to n io n s H o w e v e r i f t hi s i s n o t so t h c m a ss o f s o i l w i l ! e v

a ss u m e d A t de p t h z the v e r t i c a l n o r m a l s t r e s s w i l l be 1 z a n d ! " l l y a c 1 O n t he s u ppo r t s ys t e n r a n d w il l c a u se f u r t h e r d i sp l a

t he ho r i z o n t a l s t r e ss K.

1 z be Eo r e th c t u n n e l is e x c a v a ¢e d 1f a m e n t s in i t so m e l in 1e s o v e r . Ve r y lo n g p e r io d o f r i m e T h u s ,

c i r c u la r s u p p o n (a 1u n n c 1 [in in gj is im m e d ia t e ly in s t a l le d i n s id e 1hc s t r e n g t h n n d r i g id i t y o r t hc e x c a v a t e d m a 1e r ia l t h e dc f

t h c m a s s [1] th ç s t r e ss s t a l e in t he m a ss a t t i l e t im e o f in s t a l la m a bi l i t y o f t he s u pp o r t s y s te m a n d t he i n t e r r c Ba l io o bc t ' " i c n

t io n do c s n o t d i f fe r í r o m \ ha t e x is t in g p r e v io u s l y I f t he c i r c u l a r t ï1e m a r e o f f u n da m e n t a l im po r t a n c e

s u ppo H is n e x ib le bu t c a p a b le o f s u ppo r t i n g t hc c o m pr es s iv e 1 +f t h e s u pp o r t w e r e i n f i n i t e ly r ig id 1hc p r e s s u r e s t k v c !o p ín g

s t r e s s es p r o d u c e d by t he e a r th a r o u n d i t im m e d ia te l y a f l c r it s i n s t a l la t io n w ou l d be t he s a m e a s i n th e

A f t e r a l i m e t h e c i r c u la r (n e x ib l c ) r i n g c a n o n ly bc in c qu i l i c a s e o f t h c ne x i ble s u ppo r t Su bse qu e n t ly i t w o u ld n o t d e fo r m

b r i u ï ï 1 i f t l1e r a t l i a l n o r m a l s t r es s es a f fe c t in g i t a r e e qu a l i n a l l a n d t he n o n u n i 1o r m p r e s s u r e d is 1r i b u t io n w o u ld c o n 1i n u e

d i r e c t io n s I n o r d e r t o fu l f i l l t h is c o n d i t io n t he ho r i z o n ta l i n d e f i n i te ly B . N d i n g m o m c n 1s w i l l d e v e lo p i n t he Su p po r t

n o r 1n a l s t r e s s p r o d u c e d by th e e a r l 11 m u s t i n c r e a se ( i r K ' " 1) s ys t e m in a c c o r da n c e w i t h « r es s s t a te s t h a t a r c n o lo n ge r u

w he r e a s t he v e r t ic a l n o r m a l s t r - m u s t d i m i n ish T h is s i t u a fo r m ly r a d ia l T' is is a ba s ic t l i s a d . . N l n gc o f r ig id s u pp o r t s

l i o n c a n o n ly b c r e a c he d by m e a n s o f dc ío r m a t io n o f t he w hi c h a pa r t f r o m b e in g de s ign e d 10 w i t h s t a n d r a d ia l s t r e s s e s ,

s u pp o r t s ys t e m b y t he n e c e s s a r y a m o u n t a t a ll po in ts a n d in the m u s E a lso be c a p a b l e o f Su ppo , l i n g be n d i n g m o m e n t s O n c e

r e qu i r e d d i r e a io n T h e c i r c le b e c o m e s s tig l , l ly e M p 1ic a l Aga in a n e l l ip t ic a l s u pp o r t w i1h i l s s m a l le r a x i s K.

Tin 1e s t hc

I f t h c l i n i n g r i n g t o le r a te s t h c u n i fo r m , a d ia l s t r e sse s 1h a t a r e l a r ge r (v e , t ic a l) o n c w o u ld u n d e r go p r a c t ic a l ly z e l o be n d in g

p ï o d u c e d a s a 1is fa c to r y c qu i l ib r i u n l c o n d i t io n w i l l be a c l1ie v e d m o m e n ts e v e n i f i t w e r e r igid T l1is i ll u s t r a t es th e g r e a t

s o lo n g a s i l l e a m o u n t o t s t r a in r e q u i r e d d o es n o t e x c e e d t o le r ai n &u e n c e o f t he s ha pe o f l tt e c a v i ty a n d th e in i t i a l s t r e ss di st

b lc l im i t s o f d e fu [ m a l io n o f t hc r in g n s w e l l as a n y n o nbu l io n i n t he c a s e o f ï i gid su ppo H s ys t e m s

s t r u c t u r a l l im i t s T he a m o u n t o f d e fo r m a t io n t i l a t t he r in gu n d e r g o e s b c fa r c i t r e a c he s i l s e q u i l ib r i u n 1 c o n d it io n d e pe n d s

o n t h c c h a r a c te r is t ics o f t he s o i l a r o u n d i l a n d t he i r v a r ia t io n

w i t h t im e ¢hc r in g s l i f l n e ss,

the d i m e n . Io n s o f t he 1u n n c l n n d 14 7 1 Sm b i l i t y a 1 t h e W o r k i n g Fa c e

l h c d e p t h a t w h i c h i t is d [ i v e n

1f t he l i n i n g w e r e i n i t ia l l y c u ip t i c a l w i t h i ts s 1n a 11c r a x i s e q u a l T h is is im po r t a n t e s p e c i a l l y in I . N n c l s d r iv e n in s o f t gmo u n d

t o K. Ti m e s th e la r ge r (v e r 1ic a l) a x is t h is s h a pe w o u l d b r in g

fo r i t I . Nu e n c e s t he c o n s 1r u c l io n m e t h o d s t o b e u s e d n n d t h e

a bo u t a n e a r ly u n i fo r m dis t r i bu t io n o f 1hc r a d ia l s t r ess a bo u t u n i f o r m i1y a n d m a g n i t u d e o f t he lo a d s On l h c s u pp o r t s 111

t he t u n n e l e v e n i f n o d e :o r m a t io n o c c u r s i1n n 1e di a 1e ly a f te r

i n s t a l l a t io n

T h c c o n c e p t s p r e s e n 1c d h e r e a r e s u m m a r i z e d i n Fig ] 4 29 11] I T u n n e ls I . C l a y s

Pa r t a o f t he fig u r e s ho w s t i l e s t r e ss d is t r ibu t io n o n a c i r c u la r

t u n n e l i m fn e d ia t e l y a f t e r in s t a l l a t io n o f t hc s u ppo r t, n ss u n 1i . g I n c la ys t he s 1a b i l i ry o f the w o r k in g :a c e de w n d s o n t h e i r

t l1a t t h is is in s t a n t a n e o u s P a r t b s ho w s t h e u l t im a t e n e a r ly u n d r a in e d s t r e n g t l1 T h c lo n g t e r m s t r e n g t h i n t e r m s o t ef f

u n i [o r m d is [ r ibu r io n o f i l i c r a d i a l s t r es s t h a t is r c a c l1e d a f t e r t he r iv e s t r e sse s t v i l t o n ly be o f i m po r t a n c e i f t i l e :a c e is l e [ t e x p o s e d

t u n n e l d c f o r m s n s s ho w n I A s t ly Pa r r c s h o , v s t he i n i t i a l ly a n d u n su p po r t e d :o r a lo n g pe r io d o f t i m e

;c l l ip t ic a l c r o & s e c t i o n r e fe r r e d to

1n p r i n c ip le it is po s s i b le t o a n a ly z e th c s \ t o r t t e r m s t a b i l i t y

c o n d i t io n s o f 1hc t v o r k i n g fa c e o f a t u n n e l i n c la y A l t h o u gh i n

p r a c t ic e m a n y fa c t o r s m a y ha v e a n i n n u e n c e w h ic h a r c n o t

aI b c

o f c la y a bo u t a n a u o w 11o r iz o n t a l c u t m a d e i n a w a l l O1a t

su p po r t s i t is a n a ly z e d

A ss u m i n g a c y l i n d r i c a l s l ip su r :a c e l ik e t h c o n c s h o w n in

Ko

I/ z (l+ Ho ) (rz

p r e s s u r e

fa i l u r e o í t he c \ a y o c c u r s

o f th e h o r iz o n t a l c u t

I (w hic h o b v io u s ly c d f a c e o t a t u n n e l)w ° °

e x c e e ds 6 28 t im e s t he v a l u e o 【 c. . w h i c h i s t h e u n d r a i n e d

s t r e n g t h o t l 11c c lay I f t h e c u t ha s a c i r c u l a r a p c t t u r e , t \" is r a t io

:

DIST RI BUTION, WHE N I AFTER A CERTA IN T IM E

c o m pa r iso n w i t h t he de p th a t w h i c h i t w a s lo c a t e d t h e c t it ic a \

w o u ld in c r e a se to 7 5 I f t l1e w id t h o f th e c u t i s a pp r e c ia b lp i n

: : · : L WWG ís INSTAL L ED t

v a l u e o f t he r a t io w i l l be [ l ] :: ; I E L L I P T IC A L

Uv

F L E X IB L E C IR C UL A R L IN IN G L IN IN G 2 : + r r \

: Fïg 14 2 9 D is t r ib u t io n o t r a d i a l st r e ss e s a bo u t n e x ible t u n n e l r. .

l i n in gs o r s t rp po r t s I 1j , in n o r n ï a l ly c o n s o l id a [ c d 1n a t e r ia l 6 z (14 66)

s

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Page 2: Rendimiento de Los Soportes en Túneles a Traves de Suelo

Scanned by CamScanner

2 T u n n e ls 1n F r ic t io n So l isWA L L

. ¥z,

Cu · CONSTE NT STRENGT H Sa n d s Gr a v c l s a n d ru u l l y f r a c t u r e · j r æ i : : i r r m , l i : Jm :

m a t c r i ls o f a f r ic r i t an a l n a t u r e Si la a n d : 1a yc y f l r u h ï * Ji i : a l : :

z 1 (Tho r · Ñ e r l

n a t u r e a n d p ro p o r t io n o f t he i r f in e t r a c 1iu n Bi le c : ìm ks o m e t im e s h a r d to c l a m i ïy ; r11c i r I) c ha v i u r w i ïJ · k f w] m l

'SUR FACE in c lu d c tJ in C A SA O H A N U E s Pta t ic i l y ( Jra r t { r : h a p u r Zj a : e

u s e fu l fo r e s 1a b l i li l 1i n g a r e a s o n a b le c L. : * i l i c a 1j1 m

spj ·.

; o f t il e e x c a v a te d f a c e i n fr ic 1iu n a l w i l s i s [Bn w i u n . r p a t w c

d i1io n A bo v e t hc w a » r t a b l e Jh e ï c mar i al $ v i r e r : d r y la c k

bc a r in E c a pa c i t y w }1e n t he i r s lo pe i s s t ecpr t fm n t bc n a l u r a i

e qu i l ibr i u m s lo pe (C B1a p lc r 6) b u t o n t h c j t h ¬ r h a n d l 7 a r e

v e r y a b l c i r t he fa r c is a l ï, JW U J t o a d , Jp t a n j n c l i n a 1i r m c qu ä j I °

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u n k s s t hc f a c e is o n t h c p o in t o f fa i l u r e [1] C o n s c q u c n l ly n o t i m po s s ib le ) to d r a i n 1i 1c g r a n u la r s o i ls F u n hc r m o r c i t i 5

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l

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t u n n e l l i n g h a s b e c o m e so p o p u l a r Fi n e d a bo v e a n d be l o w by im p e r v io u s c o he s i v e s t r a t a I n 1he s e

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l o n g e n o u g h f o r t h i s t o o c c u r 1hc s t a b i l i t y o f t he f a c e is de t e r Pu t u p i n g l hc pr e ss u r e in t h e s e c o n t i n e d w a t e r be a r i n g l a y e r s

m i n e d b y t he a c t in g e f fe c t i . e s t r e ss e s a n d by t he s he a r s t r c n g t l ï c a n n o t a lw a ys be r e a dily lo w e r e d 1 1 u s l a r ge qu a n t i t ie s o f

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u n d r a i n e d s t r e n g t h T h is c a n bc e i 1he r a fa v o r a ble o r u n fa v o r t o w a r d s t he t u n n e l T t1c se c a s e s r e q u i r e c x r r e m e l y c a r e f u l

a b l e c . N d i t io · ; l h e r e s u l t in c a c l1 s pe c i f i c c a s e de p e n ds o n t he t u n n e l l i n g p r o c e d u r e s w i l h the so i l a l w a y s w e l l s u ppo r t e d b yn a t u r e o t t hc c la y I n a t he r w o r d s t he e v o l u t io n o f t ln s t a b i l i ty c a r e f u l ly c o n t r o l le d s h ie ld s

, o r a i r p r e ssu r e

c o n d i t io n w i t h t im e a b c ys n o l1a r d a n d f a s t r u le s , b u t d e pe n d s O f te n t u n n e l l in g c a u se s a d r o p i n t h e w a ¢e r le v e ls , w i th t h c

o n t h e m a l c r i a l a n d the c i r c u m s t a n c e s i n e a c h c o s e c a v i t y a c 1in g n s a d r a in T h e s e w a t e r le v e ls r e c o v e r a f t e r t h e

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T hc r e a c t io n c u r v e c a n n o 1 be c a lc u la t e d fo r a g iv e n c a s e , b u 1 a n

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n s s u n 1i n g 1l 1n 1 l hc v n iu c o l K . . c n n be c s l i n t a 1c , I W i l li l ï1c s c m o m g n t c o n s t r u c t io n c o m m e n c e s u n t i l t hc f in a l de s ign s h a pe is

m n l c r i l r l« i l i c u s u u B r is k is i l i c : r u c t u r in = l h c y m 11y s u f lc r u n de r a c h ie v e d ï f a s s o o n a s t he s e c t io n is c x c n v a l e d a ci r c umf c r

l a r Rc a t r e s s e s w 11ic l1 , v c a kc n t he m c n o r n t n 1n ly t ia l s u ppo r t is in s t a l l e d t ha t is c a pa b le o f a v o id i n g a n y s ub

q u e n t d i s p l a c e m e n t i l i e p r e s s u r e c x c r 1c d by 1h c r o o f a n d t h c

14 7 3 R u d in l S1r n in s n n d L o n t l« n n T \ 1n n c l Su p p n > l s

s o n 1c w ha B sm a l le r be c a u se t hc s o i l m o v e s d u r i n g i n s t a l la t i o ï 1w a l ls w i l l n o lo n ge r b e l h i 1l i n d i c a t e d by po i n t A b u t by B . 1 is

i l i c d e a ign o t u t u n n e l su p po n i s d iv i t lc 1l in l a t h r e e w e l l d i l fc rN o r m n l ly ev e n a f l c r in s t a l la t io n o f t h c s u ppo r t a r a d i a l d

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p l a n e s n o r m a l 1o l l1c t u n n e l a x is A n , 1 l a s t l y i l m u s t bc c a p a ble c o n t a c t w j 1h t h c so i l

s t r a i n

w hic l1 c a n bc e s t i 1n a 1e d by c u r v e F c o r r e s po n d in g 10 l hc

T he b a 1 is l o r c s t n h l is h in R i l i c r a d ia l s t r e ss e s 1hc s u p po r t s ho u ld r c a c l i o n o f t he s u p po r t T h is r c p r c sc n 1s t he r e l a t io n s h i p

r e s is 1 is i l l ust m\ cd i n 1 : iR 1 · B3 1 [1] w i1i c h s ho w s th c r a d ia l b c l w e c n rhc r a d ia l lo a d \ l1n l is c a r r ie d b y t i l e s u p p o r t s t r u c t u r e

s t r e ss e s a s n f \ 1n c l in n o f l hc : w c r a gc r a d ia l d is p l a c c m c n 1s a ri d i t s c o r r e s po n d i n g r a d ia l d is p la c c m c n l

t o w a r ds t hc c e n t e r u f 1hc c n v i1y T h c u l t im a t e lo a d O n t he s u pp o r 1 w i l l be 吕 I. E n b y th e i n t

s e c t io n o f t hc tw o r e a c t io n c u r v e s : fo r t l1c s o i l a n d t he s u p p o r t

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p la c e m e n t t ha t c a n b e e x p ' " c dLp

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rc [ (TB + t ' " K o t ] r c l i 1t io n s h ip be t w e e n t he r a d i a l s t r e ss e s a n d t h c r a d ia l s t r a i , 1s

w i l l bc [ l is pla c e d do . N w a r d s t o n d is l a n c c O ii , a b o v e t hc s 1r e ss

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t a k e p l a c e w i t h t im e Se v e r a l d i E【e r e n t so i ls a r c i l lu s » a t e d

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th r o u gh u . .- p fs

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s. .

v e r y d if f e r e n t m a n n e r i n t he d if t e r c n t t y p e s o f s a i l s T his ss e q u e n t t im e d e pe n de n t in c r e m e n t s h o u ld be c o n s id e r e d in

Sc 11in g this e q u a l to E q ( 14 18) w c o b t a in :

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e s t i m a t io n s c a n le a d to a r e a s o n a b l e e v a lu a t io n o f the m e a n

s =

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r a d i a l s t r e s s f o r w i 1ic h a pa r \ ic u la r s u ppo r t s ho u ld be d e s ign e d

c a u se s a n e l e v a t i o n \ n th e s o ì> s r e a ç t io n c u r v e l ik e [ hn t s ho w n

I t thc he ha v io c o t t l \ e s o i t is a pw o x \m a \c \y e la s \ i c i \ s i n t

b y t h c b r o k e n l i n e i n F i g 14 31 I n a l 1n o s t a "y e as c , a r a d ia l a c t io n w i t l ï t he s u ppo r t c o u ld b e d e s c r i b e d a s is s ho w n in F i 吕

n o cm a l s t r e ss s m a l le r t h a n ( T, c a n hc e x p e c t e d

, p o s s i b ly o f t hc 14 33 [11

a r d e r u f t he o n c g iv e n by E q (14 69) O n ly e x pa n s iv e c l a ysm a y e x c e e d t h i s v a l u e

W he n t h e s u p p o r t i s i n c o n ta c t w i t h t hc s o i l a r o u n d i t t hc lo a di t r e c e iv e s a n d d i s p l a c e m e n 1s i t s u f l c r s d e pe n d o n t he i n t e r

ì : b c d e f o r m a t io n i n t l1e s o i l w i l l l o n ly a p a r t ia l r e s t r ic t io n f r o m

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s.

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d i a m e te r t he c o m p r e s s ib i l it y s.

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c o m p u t e d a s : F 1g 14 33 So i l s u ppo r t in t c n 1c t io n c u r v e s (e la s r i c m a t e r ia ls ) [1]

s.

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n (14 7 1) o f t he c i r c u la r s u p po r t t he n i a x in 1u m p r e s s u r e t h a t th is s u pp o r t

s l1o u lt l e x e r t r a d ia l ly o n 1i1c su r r o u n d in g gr o u n d is ( T. . w h ic 11 is

E.

Be i n g t hc n 1o d u l u s o t c Ja s [ ic i t y o f t h e s u p po r t n l a t c r ia l O r The 1o t a l v e r 1ic a l p r e s s t 1r e e x e r t e d b y t h c s o i l (E qu a 1io n

fo r a r e la t iv e ly t h ic k s u p p o r t : (14 69) m a d e i t p o ss ib l e t o c a lc u l a t e t he m e a n r a d ia l s t r e s s t h a t

m u s t bc ba l i ï n c c d w i l h z e r o d i sp Ba c e 1n c n t,

b u t in F i g 14 2 9 i t

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r c a n be s e e n t h a t a m a x im u n '" e q u a l t o cr . M a y o c c u r ) O n t h c

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p e n n i t l e d b e f o r e t l1c s o i l c e a s e d t o m o v e o f i t s o w n a c c o r d A n

( 14 72) o t hc r ha n i l i r t h c d e v e lo p m e n t o f a u p o s s ib l e s t r a i n s w e r e

T h e r i g id i t y o f l h c s o i l is ha r de r Bo e v a lu n t c , a n d i n n 1a t c r i a ls u l t i1n a l e r a d ia l d i s p la c e m e n t w o u ld o c c u r w h ic h w i l t b e c a l le d

t h a t a r e n o t pe r fe c t ly e l a s t ic i t de p e n d s o n t h e d is p la c e m e n t u r w h ic h c o u ld b e c a lc u la t e d u n de r e l a s t ic h y p o t l1e s e s u s i n g

i t u n d e r go e s A n u p p e r l i m i t c o u ld be o b ra i n e d f r o m a n e la s t ic fo r m u la s a l r e a d y d is c u s s e d in [ 11e c o r r e s p o n d in g s e c t io n s A s is

a n a lys is I f s. Re fe r s to 1hc r ig id i t y o f t he m ar t c r i a l a r1d E

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t o t i l e m o d u l u s o f e l a s t ic i t y o f t h a t m a t e r i a l Ta k in g E q (14 17 ) c u r v e (s e e & g 14 3 1) i f i i b e h a v e s c ïa s t i c a l l y T h is a 1r v e ha s a

in t o a c c o u n t Fo r t he t u n n e l w a l l t he fo l lo w in g e q u a t io n w i l 1 be s lo p e s. .

I n d e e d u r c a n be c a lc u l a t e d u s i n g E q UL4 17 ) s o t h a t :

t r u e :

; : i + : : w h e r e p r e fe r s t o t he p r e s su r e a r o u n d t hc e n t i r e p e r i m e t e r o f s po n d in g o r d i n a t e ha s i 1 v a l u e o í ü

. s o t h a t t hc s lo pe o í th e

( h c s u p pu r l : T he r i g i d i ty o t thc s o i l h a s be e n de fi n e d St r a igl1l c u r v e w i l l bc E. / ( 1 + p ) w h ic h is t h e v a lu e o f s

. .

a c c o r d in g ly a s : a c c o r d i n g to E q ( 14 74)

T l1c SUppo r t w i l l be c o n s 1r u c t e d a f t e r a c e r t a i n d i s p la c e m e n t u i ,

s.

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. . . w h ic h t a k e s p la c e a s s o o n a s t he s e c t io n o f t u n n e l is e x c a v a t e d1 + ( 14 74 ) i r d is p la c e m e n t s c o n t i n u e t o o c c \ n ,

lo i 1ds w i l l b e t r a n s m i \ l c d 10

: l

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t 11o s u l 1l ro r 1 í , 1l l . ' " i n » i l m r e w t iu n c l i r v o o f rh1t t li l l p lh M w i t h a 1) M u k c n r e n s u 1m b lc c x 1i m n l c u f 1hc lo a ds o r c o 1n i i r c r \ iv c c i r :

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. ( I : i* 14 1J ) W hc 1c t hc l w , 1 sl ml Hhl r c n c t io n c u r v e s c u 1n l c r c n t i11l p r e s s u r e s t l1n t w i l l de v c in p o n i l i c su ppo r t

c ic n 1 10 m n i n 1n 1n t l1c \l l pln=c1ncr11 o l 1ho ßr u u n \ l n t n v a lu e n o lc x c e c t l i n l. u l 1 u . u n t l 1h c \ l l p i n 11 l w i l l hn v c t l c f1l 11n c t l h y ï B.

Hy t i l e s 1r l1p o 1t

T l1is n \ c \ ho d n l o v n l 11n l iu n i \ o l l l 1n i 1c , I p 1 n c l i> n l l i s e , fo r s o i l \

J ) c . N s it le r t i i e po ss ib i l i 1y l l1a l b t 1c k l i n g m a y u c c u r i n s o l n c

n r c i 1o l c ln s l lc n l 1h c IE V c I \ n f s l 1 i 1i n l i c e \ w 1i n R in tu n i t c ls T hc Br u r l s u f l l1= s 11p p n r 1

CU 1Y CS n f 1i1e so i l n n t l l h c n 1p 1w11 l ix n e c c s s i \ 1y Th Gc c l 1r v c s

ru n c e in 1hc c a se u n r l c r c o m i t lc r u 1iu n

d e pc 111l o n i l i c p m p e r l ic s n f l h c s n i l n n t l c o n s 1r u c ¢iu n pn t c e

T hc c o n 1p r c « iu n s t r e s s e s o n l lï c s u ppo r t a r c r c l a 1c d l o t he

d u r e s c m p l u yc d n n cl n 1u h f l1c p lu 11c t l u n i l i e B, n s is u f i n l n 1m a

m e n n r i 1t l iu ï p r e ss u r e i n 1h c fo l lo w i n g c x p r c ss in n :

l iem . H1a i r c \ l In 1m 1n s t r u n 1c n t a l in n p r o w 1u n » a , pa

(14 76)

14 7 4 D ls l o r 1l o n u f r n n u e 1 Su p p o r t s m e a n r a din l p r e ss u r e s u f l c r c d b y 1hc s u ppo r t ; n is i h c e x t e r n a l

w B1c r c : u . Is 1hc c u rn p r e s s io n s t r e ss o n t hc s U pp o r t ; p is the

八 s w n s s e c 11 n l t l 1e b c * l n n ln H u l r l1is s e c l ln n w he n n \ u ppn 1 1 I

r a t l iu s n f 1hc s u p pn r l ; a n t l f is i hc 1h ic k n e s s o f 1B1c s u p p o r t

n c x i b lc i l a lw n ys t 1n d c r g u c s s o m e u i s l u r l iu n bw 1w c c n t hc in i t ia l 1n c la ys p t lc pc n d s o n cr . A n t i o n t he s 11r c hn r gc fa c t o r a l r c a d :

n n d n n a l in s i n l l n t in n s i n ge s T l1is t l i \ 1u r 1in n is 1i1c r e s \ 1l l n í l ï1c

t l is c u s s c t l I n . N l t o r n 1c d iu n l c la ys t hc s t 1r c h n r g c l a c 1u r

c ha n ge s t ï1i ï 1 t u k e 11ln c = in l hc 1u , r i1 ' " \ a l a n t i v c r l ic n l t l i a n l . I e r s

M n y h e v e r y l1igh m d l hc v u lu c o l p n 1n y r c 1n a in c lo se t o

I t w a s i \ ts o w c n ho w in 1h c w c i1se s l hc bc n di n g n l o lin c n l s l hnt h ( 1 + K' " 1

d i : \ n l c t c r s h c k w [ w i l hl i n h v '" r a h ïc l i11l i l s w 1l ic l1 de pe n d s o n l hc

as a . I n s l i f l p r e c o n w ll ida tM c h1ys , K' " a y bc h ighe r l hn n o n o

h 1n c t i u n o f t 11c t u n n e l i l i c n n l u r c n f 111e s o i l a n d t i i e d e # r e e i n

\ , u t 1l1c s u r c ha r ge fa c to r t e n ds l o h c In r s m a l le r 111c 1w o c f fe c l s

w h ic h t hc s lw p c u f t hc 1u n n c l c o r r c x p ' " 1" " I" qui l i br i um x : H X . T s o 1l1n t , ° . N g . In r e p r e s c n 1s a n

c o r r e s po n d i n g t o 1hc i n i l i n l s t r e s q s l a t e 1n : r i c 1i n n n l c o n t i n u o u s 1n n lc r ia ls , ï hc r c is u s u a l ly 1i u lc lu n d

A l l s u p po r t s l1u v c n c e r t a i n n n 1o u n t u f r ig id i t y ; a n , 1 w he n ï 1s a i n c r e n t e , \ 1 w i t h l i m e N n d t he de s ign ïn c ss u r c c i 1n b c I n r s m a l lu rr e s u l t o f \ l1is i l i c c h u 1r ge s i n t l ia n \ c 1c r s n l c s m a l le r l l1n n t lm s c 1l1n n a .

T hc r a cl iu l p r e s s u r e c n n bc c s 1in 1a t c d o n 1hc b a s is o fc o n e s po 1n l i n g t o n n id c n l l y n c x lb1c Su p p o r t o f 1i1e s n 1n c s lu ï pc 111c i t lc a s c x p r e s s c t l i n $ 14 7 3 A d a n ge r i n 1hi s CI 1SC is l ha lbe n d i n g m o n 1e n l s [ lc v c l , : p in 1i1c \ u p lH ) r B T he s e m a y bc c a v i t ie s o r v n jd s 1n n y bc le t t bc 1w c e n 1h c so i l i r n t l m 1p po r 1

r e d u c e d i f p a r l n f t hc so l l d c fo r 1n a t io n is a l lu w c t l l o l a k e pl ac ca u s i 11g la r ge i n c r e a ses in \ hc p r e ss t 1r c o n t he s 11p po r t w he n

b c :o r c in s t n i i n t io n n f t i l e . 11p l» ) H O n 1h c o 1hc r h u n d The t l r c y s u bs c , 1u c n 1l y c u mu l " A , c l1i n = is 1hc 1n a in r e a s o n w h ys u ppo r t w i l l d e v c in p n o be n d i n g m n m c n 1s i r i t c a n Uc fo r n 1 b y i l i c p r e ss u r e s a p p l ie d by th e s e so i ls n r c r c l m iv c l y In w 1n w e a k

i l i c a 1n o u n t c ' " cspondi nR t o l hc c 11a n =c s i n t ï in 1n c l c r 1ha t so i ls t h e r c a c 1io n c u r v e s fo r l hc s o i l n 11d t he s n p p u r 1 u s u a l lyw o u ld bc s u l fc r c d b y n n id e a l l y n c x ib lc s u p pn r 1 w i 1ho u 1 10 0 in 1. Rc e p 1 o n c a n o t he r a t a bo u t t f

.

m u c h e f lo r t ï n ï : ig 14 29 i \ = n 1\ l re s e c u ho w 1hc c o n sc r v iB1i v c

in c r c n s c in 1h c h o r iz o n l n l d i n n \ c l c r (c i r c u la r \ u n r 1c l)! Co n 11n e n l s A bo u t 1) i f re r e n 1 Su p po r t Sy s l n ïm

T hc r ig i d i t y o f l h c s u ppo r t d o c s n o t g r c m ly in f lu e n c e t l1c A g a i n r e fe r r i n g t o I I I s o n i c c o m n \ c n l s w i l l n o w ln n m dc a b o u t

n m o u 11t o f di or t i on 1l1a 1 1n k c s p la c e ! . Su f i c la ys , t y p ic a l l hc in f1u e n e c o f c e r t a i n c ha r u c [c r is t ic s o f the d i f fe r e n t s u p po r t

v a lu e s ío r d is to r t io n r n n gc f r o m 0 3 l a (1 7 % (de f i n e d a s t he sy ' " 1 n s

pc r c c n r n gc u f s l1u r 1c n l n g o r le n g t h e n i n g o f l hc r a d iu s i n r c l i t 1io n 1? l e J lb1Nly o f m ¢ : ru pp o N $ : B o rh l h c u r y a n d c x pc r ic n c c i n d ic i 1t e

10 1lw o r ig i n a l r a d iu s ) I n s 1i f f c la ys d i n u n io n u s u a l ly r a n ge s l ha l n c x i b i l i \ y is " qu a l i \ y 1h n t sh o u ld h c s o u gh t r a t he r t h a n

f r o m 0 m 0 3% R e fc r c n c c 111 i n c lu d e s d a t a a bo 111 d is t n r 1io ir1 a v o id e d A l 1ho u gh i t is t r u e t ha t H r ig i t l s u p po r t r e s is t s d i s t

o bs e r v e d In s c v c r n l 1u n n c l s w i1ic h m a y se r v e a s a n o r m l u r l ia n i l I a ls o t r u c 1ha t \ hc r c d u c 1io n in d i« n r t in n t h a i is

c s \ n b l is h in g l hc d is t o r t io n t i l i , 1 c a n bc c x & c 1c d i n s i rn i l a r a c h ie v e d is t 1o l v e r y i \ p p r e c ia b l c e v e n t h u u g h t h c r c t p i r e d

t u n n e ls s t r e n g t h is g r c a 1ly i n c r e a s e d T Il e r ig id s u p po : t h a s t o to \c + a t c

l a r he a v ie r lo a ds a n d o í t e n r igi t h t y wwk s a ga i n s t s ta bi l i t y

14 7 5 C e n e r n 1 D c s l* n Re c o n n n e n d n l 1o ï u n o n u n i fo r m p r e s s u r e s I l ha s a l r e a d y b e e n s t a t e t l h o , v r ea s

C u r r e n t c x pc r ic n c c n l a kc s i l t w i t e c le a r 1h a 1 a l l \hc d e s ig n

u n i :o r rn a n d p r e v e n t s b e n d i n g m o m e n ts Th is l e a d s to fa r

m e t ho d s w h ic h a s s u 1n e th n 1 1u n n e l s u ppo r t s a r c a : fe c 1c [ l by l i gh t e r a n d m o r e e c o n o m i c a l s e c t io n s bc u c r a b le t o w i t hs t a n d

p r e s s u r e s c o r r e s & m d i n g 10 a c t iv e o r pa s s iv e g l o s o r e v e n

p r e s s u r e s w i1l1o u t ta i l in g 1361o n e s c o r r e s po n d i n g 1o e a r l l1 p r c w u r c a i r e s l a r c r a r e ly v a l id

F u r 111c n n o r c d e s ig n m e t h o d s w hic h i1ss u m e i ll a t a Su ppa r t is l n a c c o r d a n c e w i t h i hc [o r e go i p g c o n s idc r a 1i o n s c r i t e r i a c

s u b je c t e d l o t 11c e r: c c t o f n f ix c t ] lo t 1d in g s y s t e m r e ga r dle s s o f c o r n in g t hc ty pe s o l 1n a t c r in ls t h a t w i l l be s u i t a b l e fo r su p po r t

c o n s 1r u c 1io n p r o c e d u r e s o r o f w h a t 1n n y h a ppe n i n 1i1e s o i l c o n s l m c t io n c a n bc c sl a b l ishc d F o r t h o s e in s 1a l la t i o n s w h e r e

s hu u ïd b c r c j c c l c d C o n s ide r a t io n s s u c h a s w hc 1l1e r a t c m d is t o r t io n s a r c a c c c p l a b lc o n a cc o u n t o f th c n a t u r e o f th e s o i l

po r a r y p l u s a pc r 1n a n c n r s u pp o r r s ys t e m o r j u s t n pc r m a ï 1c n t s u p pu r l s m u s t ha v e a h igh c o m p r e ss iv c s t r e n g th, s o a s t o hc

o n e w i l l b c e m p lo y e d i \ r e l u n da n t e n i a l T hc ío l l o w in g d c s ig 1r c a pa b le o f r e s is t i n g t i l e e q u a l r a d ia l s t r e s s e s a n d i n c lu d i n g t he

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H = W c a* i k l : : +PW T = ·

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ha n d a pe r f ec t ly p e r v io u s tu n n e l w i l l

l 11c e x c a v a t io n sys t e m 111 c ffe c 1i v c s o i l p r e s s u r e , a l th o u gh t il e n o w

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: : = x ; s a . . M u a y

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e x p a n s i v e m a t e r ia i s t he r a p id c o n s t r u c t io n o f a t e m p o r a r ys u p po r t e l i m i n a t e s m a n y o f l hc r is ks d e r i v i n g f r o m t he d e v e lo p · z o n e s a r o u n d t hc 1u n n c l w h i c h s e r v e s t he d u a l : u r p e

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m a n e n t s u pp o r t s y s 1c m po te n t ia l ly u n s a b le z o n e s

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c a n bc v e r y r e a s o n a b ly e s 1i m a l e d u s i n g t he c r i te r ia g i v e n i n t h is c x t e n l A n d m i n im u m p r e c a u t io n s s l 1o u l d b e t a k e n w i t h r e s p e e l

s a m e s e c 1io n ba se d o n t hc i sp l a c e m e n s o b c r v c d n t e l e m : : =" " t 11e s lo w s e e pa ge o f w a t e r i n t o t h e t u n n e l a n d

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a c c o m p l is h e d in v ie w o r I l i c u s u a l u r ge n c y o f c ' " t r uct i o ·

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s ys t e m F u r the r m o r e s in c e t h is r e s 1o r a l io n o f p r e s su r e u s u a l ly

t h e bc l t a v i . r o f t he s e s u p p o r ts T 11e s c c h a n g e s m a y b e c a u s e d

d o e s n o t r e p r e s e n t a s e r io u s p r o b le m e v e n in t he pe r m a n e n t

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s u p po r t s y s t e m

c r o s s i n gs u t l1c s o i l o r r o c k b e h a v e s e la s t ic a l l y Ti l e e f f e c t s o f

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o f s u pe r po s i t io n o f s t r e s se s a n d s t r a i n s 1n e l a s t o p l a s t i cn e ighbo u r i n g t u n n e ls ca n b e j u d ge d by i t pp l y i n g t h c p r i n c ip l e

1o l ; ge r in s t a l la t io n is po s t po n e d l hc m o r e e c o n o m ic a l s t i l l i l b e

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