Numerical modelling of a NATM tunnel construction in London Clay

G.R.DasariIn/(gra/ed Technology Dil.i.sion. Fugro Limi/ed. Hi:mi:1 HL'lnp.s/i:ad. UK,

C.G. RawlingsG(a/t!chnical and 7ilnnt'lling Division. \~ .s:A/kin.s. Epsom. UK

M. D. Bolton(,Ill/bridge Universi/y Engineering Di:par/lnL'n/. UK

AB5TRACf: The finite element program CRItical State Program (CRISP) has bcen used to model the NewAustrian Tunnelling Method (NAT:V1) in London Clay. The non-linear behaviour of the London Clay was

p1odelled by a Strain Dependent ~(odjfied Cam Clay (SDMCq mooel and the tunnel lining was modelledbv col\Stant and time-dependent elastic models. 111e col\Struction process was modelled in two and three

Jimel\Siol\S by removing soil elements in sequence. 111e tunnel lining was either assumed wished.in-placeor introduced after the excavation of each panel. The results obtained from plane strain and three

Jirnel\Sional analyses are compared to assess the importance of arching of soil ahead of tunnel face.

the other hand the finite element method (FEM) ean

model all Ihes~ innuences reasonably, if appropriate

constitutive modl:ls \vith corrl:cl input dat3 are used.

Due to limitations both of sofi\vare and hardw3re thre~

dimensional (30) situations are often analyscd as

though they were t\\.o dimension31 (20). A numbtr of

20 FE simplifications have been developed to modtl

30 tunnels probltms, e.g. axi-symmetric case (Roweand lee, 1992), cross sectional plane strain (~Iair ~I

al., 1981; Rowe and lee, 1989; leca and Clough,

1992; Atzl OInd Mayr, 1994) OInd longitudinal plOlne

strOlin analyses (Romo OInd Diazm, 1980; Guo el al.,

1994).

INTRODUCTION

Thc Nc:w Austri3n Tunnelling Mclhod (NA TM) is aIcchnique in \\'hich ground exposcd by excav31ion islincd with shotcrete to foml a temporary lining, Rapid3nd consistcnt support of frc:shly c;(cava!cd ground,c3sic:r construction of complc;( intc:rsections, andlo,\"cr capilal cost of major equipment are some of thc3d\"ant3g.:s of NA TM. The successful use of Ihemcthod is reli3nt upon high qu31ity working by askillcd work force under continuous engineeringsupc:rvision. Some of the limitations of this method3re that it is slow compared to shield tunnelling inunifoml soils, dealing with water ingress call bedifficult, and it demands skillcd man power. Inparticular, inst3bility at thc tunnel face, unless positivesupPort is provided, can endanger the work force,Kuhnhenn (1995) carefully analyses the typicalcollapses of NA TM tunnels constructed in hard andsoft rocks in Gcml~ny. He highlights the importanceof workmanship and limiting the Icngth of theunsupported section ahead of the shotcrete. AlthoughSA TM was primarily developed for rocks, it is nowbeing used in clayey soils. Therefore, it is importantto understand this method in clayey soils.

There have been many empirical methodsdeveloped to calculate surface settlements due to

tunnelling (Schmidt, 1974; Attewell, 1978; O'Reilly.nd New, 1982; Mair el af., 1993). These methodsh3\'e the limitations of being specific to soil type andun3ble to take account of soil-lining interaction. On

The approximations made to model the 3Dconstruction sequence in each type of 20 analysis toaccount for the 3D redistribution of stresses around theheading broadly may be classified into three

categories:i) percentage unloading methods (Panet and Guenot,1982; Allouani el 01., 1994), where the lining isintroduced after removing a certain percentage of the

initial stresses.ii) volume loss methods (Stallebrass el 01., 1994),where the initial stresses are reduced until a givenvolume loss is achieved, and the rest of the load is leftin place. '

iii) gap parameter methods (Rowe and Lee, 1992),where the defonnation prior to the contact of thelining (hence the surface selliement) is controlled by

'a gap parameter',

491

Gect/!_/1,"al As~~s ,I Unc.-,.-",..nd ConS:,r.,cliOil ~ Sclt G,:;"no. ,Yd,' & Td/'Cf (e.:5)~ /996 8.J.~ema. RClIo!,da,'n ISBN 9O s.: 108:.6 S

Ground movements due 10 tunnelling h3veb.:en 3n31ysed in 3D by v3rious rese3rchers (SWObod3er 01., 1989; Lee and Rowe, 1990; Lee and Rowe,1991; Chen and B31d3uf, 1994; Ak.1gi, 1994).S~0b.>d3 tl 01. (1989) an31yscd a NAThI tunnel inrocks using a rheologic31 model in ordcr to undcrsl3ndthc timc.depcndcnt intcr3ction bctWccn shotcrclc andground displ3ccments. Lcc 3nd Ro\vc (1991) an31yscdthc Thunder B3Y tunnel in 3D using the gapparamctcr mcthod. A gap may bc physicallymcaningful for overbreak produced by lunncl boringmachine, or for in~'ard displaccmcnts in NA TM whichoccur prior to sholcreting. But the selcclion of'a valuc'for thc gap paramercr has significant effcct onpredictions. Akagi (1994) analyscd the progressivcadvance of a shield tunnel in soft ground in 3D. Heconcludes that ground displacement and porc pressurepredictions depend much on changes in the inclin:llionof thl: shicld m3chinc. The gcneral lesson for theanalysis of tunnclling is th:lt the actual constructionactivity should b.: modelled as closely as possiblc.

--s...cc -J~r4 . . ("*')

. I"',-

1:0

~a-I,

~~. '~"""" -"""'(119'1.' I"".I ~ " ,. .

~ . ~I, .Y.o~ .. ;...~~

I .. '" II , 1Q1- .~.

I .--"--'f ., -:." 0 --

1(oS x., 1(.. 1£.. IN 1£., 1(.1Ce"'I0~ ,n..

Fig. 1 Shear stiffness-strain variation for

london Clay

2E.7 -T.". ,."""'9"' .-OA -~ I 5E.1.~ 0

OJ

f 1E.';

Ora 5£08.

..

In this papcr the aim was to simulateconstruction or NA TM in two and threc dimcnsionswithout introducing any major arbitrary

approximations.

2. FE PROGRAM, CONSTIT1JllVE MODELS ANDPRODlEM DEFINITION

0(.0 '---=.-=---~0001 OOt Ot 1 10 tOO '.000 to.ooo

T Fig. 2 Assumed Young's modulus-lime relation

for shatcrete

A gcnc:r31 purpose finit.: elc:mcnt progr3m (CRltic31St31C: Programs (CRISP)-dc:vcloped at Cambridge.Drilto 3nd Gunn (1987») which can perfonn 2D and3D gc:ot.:chnical analyses W:lS used. Prc: and postprocc:ssing was carried out using FEMGENIfEMVIEW (Fcms)"s. 1995).

non.lincar cqualion bascd on Ihc data of Fischnallcr

( 1992).

The probl.:m considered here is the analysis ofa NA TM tunnel. The mesh adopted for 20 analysis isshown in Fig. 3. which is a cross section of the 30geometry shown in Fig. 4. In the 20 mesh about 90consolidating lincar strain quadrilaterals werc used. Inthe 30 mesh about 1500 consolidating 20 nOdedlinear strain brick elements were used. Each analysiswas undrained. The tunnel was assumed to be 8m indiameter with a cover of 21m. A 50m wide and 50mdcep scction was chosen for the analysis. This mcshapproximately represents one half of the Heathrowtrial tunnel Type 2 (Deane and Bassett.1995). Theactual tunnel construction technique was notsymmetrical but symmetry was assumed here mainlyto compare 20 and 30 results. Soil properties ~crcassumed to be representative of London Clay. Typicalshotcrete properties were chosen for use in themodelling. The in-situ stress state assumed is givcn inFig. 5, and the water table ~'as assumed to be at

ground level.

Rccent rcscarch (Jardinc et 01., 1986;Simpson, 1992; Bolton et 01., 1993) has shown thatstiffncss-strain variation is important in analysing anyboundary value problem in overconsolidatcd clays.The non-linear stiffness variation of the London Clayhas becn modelled by a Strain Dependent ModifiedCam Clay (SDMCC) which has been ineorporated intoCRISP (Bolton et 01., 199.J). The variation of shearand bulk stiffnesses in the SDMCC model wcreapproximated by po~'er functions (Bolton et 01.,1994). Fig. I gives the shear stiffness-strain variationpredicted by the SDMCC model compared withexperimental data, Jardine et 01. (1984), Jardine et 01.(1991) and Hight and Higgins (1994). The shotcretehas been model'cd as linear elastic and with eitherconstant or time-dependent stiffness (Fig. 2). The timedependency of the shotcrete has been modelled using a

492

'-.-. .

10

so;

~ ..40m

Fig. 3 Mesh adopted for 20 analysis

construction simul;ltions are shown in Fig. 6. Theactual me;lsuremcnts in thc Hc;lthrow Tri;ll Tunnc!Type 2 (New. and Do\\ers. 199-1) lie ",ithin thcsc twoextremes. Observ;ltions ;Ire closer to thc w'ishcd-in-pl;lce simul;ltion C;lSC (3). although the scqucnti;llconstruction simul;ltion in c;lse (b) migh[ h;lve beenexpec[cd to bc closcr. It is suggestcd [h;l[ [he \vishcd-in-pl;lcc lining is closer to r':;llity bccausc 3D archingin Ihc field is approxim3t.:ly simul;lted in 20 byh;lving Ihc lining alre;ldy in pl;lcc. Thc supportprovided by. a w.ished-in-place lining is obviouslymore [h;ln the 3D arching. [hercrore the predictedsettlcmenls ;Ire sm;lller th;ln [he observ;ltions. A ~Olining pl;lced ;ICIer exc;lv;l[ion gives larger sc[tlemcnlsbeC:lUSC or its in:lbility [0 modcl :lrching ahc:ld or th~tunnel r;lce.

I .. .' ~

~

~Om

Fig. 4 Geometry for 3D analysis

Th~ computed s~nJ~men[s extend much furth~rand gave a flaner trough than [he site measurements.Though [he se[tl~m~nt cu(\"e pr~dicted by non.lin~armodels like the SDMCC is d~~per and narrower thanlinear elastic mod~ls, fi~ld observations are found to

J. TWO DIMENSIONAL MODELLING

~J

~E:,3~.,

A cross section of the NA TM tunnel \\'as analysed in aplane strain modc. The CRJSP analysis started fromthc in-situ strcss state shown in Fig. S. Two typcs ofconstruction techniques were modelled:(a) Ihe lining was assumed to be wished-in-place(b) the lining was constructed sequentially as

i) excavate top halfofpanelii) install lining of top halfiii) excavate bottom half ofpaneliv) install lining of bottom half

The findings from these !\VO idealised cases willbracket the real construction process.

. -- 0 ,. 20 30

c;.tonce to-n a';. oI.ymmeliy,m

Fig. 6 Effect of construction sequence onsurface settlements

.0

3.1 Effect of Construction Sequence

The settlement profiles obtained following the tWo

493

parameters. Ihc samc soil model and Ihc S3mc progrJmas in 20. Thc modc:lling scqucncc "3S similar to thc20 analysis of scqucnli31 construction. andcxca\3lion W3S c3rricd out in thc Z-dircction (Fig. 4)up to 40m (S timcs Ihc diamclcr). Thc lining W3Spl3ccd aftcr the cxcav3tion of tach p3ncl in segmcnts.Thc surface scttlcmcnt profilcs obt3incd in Ihc 3Danalysis at thc scction-( arc givcn in Fig. 8. Thesurfacc scltlcmcnt at this scclion reachcd its ullim3teplanc str3in condition after thc cKc3vaiion h:ldprogrcssed a dist:lncc of 2 tunn~1 diametcrs past thescction. The surfacc scttl~mcrn duc to cxc3vation ofIhc scction-( was about 14 mm and th~ fin31selliemcrn was about 29 mm. This means that 42% ofsurface selllcmcrn was due to cxcav3tion of thatsection and thc remaining 58% of settlement occursafter th~ cxcavalion has passed.

!-< dccpcr and narro"cr still. Thc rCJ~ns for this arc

not fully knO"'l1. but thc follo"ing may be possiblc

c:<planations:i) unccrtaintics associ3tcd with sm311 strain stirTncss

mC3surcmcnl (Fig. I)

ii) crTccI of anisotropy of soil (Ro"c and Lcc, J 989)

iii) cffecI of (cccnt slrcss history (Bolton tl 01.. I 99.J:

StallcbrasStlol., t99.J).

3.2 Stiffness ofShotcrcte

There are recent developments in sholcrete technologyto get higher stiffness/strength. But the usefulness orth.:se high strength concretes ror tunnel lining isuncertain. A rew analyses "'ere conducted !O find outthe efr.:et or d.:pend.:ney or settlements on shotcretcstiffness. The sho!cre[e is mod.:lled as linear elasticwith a Young's modulus of 5 x 10s kPa, 50 timesstiff.:r, and 50 times softcr. Another analysis wascarried out ,,'ith [he time dcpendcnt stiffness sho"'n inFig. 2. It is assum.:d that shotcretc is "ished-in-place,as this case is thc most affecled by stiffness orshotcrcte. Th.: results in Fig. 7 show that ther.: is asignificant reduction or ground mo,ements due to aninitial increase in stiffness, after "hich there seems tobe little effect. Thererore. thcre is an optimum valueor the Young's modulus or lining ror a given soil.Time dependence or stiffness do.:s not have muchinnuence as it erosses the oplilnum value 5x10~ kPavalue in a short time. Figs. 6 & 7 suggest that it is theearly placing and harJ.:ning or the shotcrct.: whichrcduces surracc settlements rather than the Ions-termstiffncss.

The surface scttlemcnts obtained at Section-2, 8m (I tunn.:1 diamcter) inside the mcsh are shown inFig. 9. From the r.:sults it can be observcd that againthe plane slrain condition at this scction \vas rcachedafter Ihc excavation had progresscd 2 tunncl diametersfrom this seclion. The ultimate displacement which

0 ---.. - -..5- . .:: : :~~.~. ' ~ """-.;'J--:--"I. .. ~.~ -~:-.:"-"" ..10 - ,..~... .--'if .. ";""-' , '

e . -..;,", _I '" e..~ ".,". Ii."- ..=..,/", ~."" "."':.. ," " ~..)""' ,

~ . ...,., .,:' ~',II' co ~ .70' ; . "p ...(1...,." .:. . ,,:;;.J. .~_I !

.75 - .,' 01 ..-.,'. ~"..,..,.;' ,..fl , )OTmO ,

.]G- .~_' 50..cC .

"""""""""",-,.)5 ' -,

0 '0 20 30 40O nco Oom ..,. Or """"Y. m

Fig. 8 The surface settlement profiles at thecross section-1

4. nlREE DIMENSIONAL MODELLfNG

A 3D analysis was carried out \\1th the same material

~

" w""' PO"" !"mtZ-"'onl :, , !

'" 30,,",E :" """'~ SO"iCCModol i1"-"21 L__"."",,"'j

-2'

-'0 0 10 20 30Ololonoo t..n ax;, of 'YnvftO1rt. m

Fig. 9 The surface settlement profiles atSection-2

.0

494

If an unlined clastic tunnel is :In:llysed :IS 2Dplane strain :lnd progressi~'e construction in 3D. thenthe ultimate settlcmcnts reached in both cases are Ihcsamc. Ho"ever, if :I lined tunncl is an:llysed in 2Dand 3D using a non-linear soil model. as in the presentstudy, the rcsulrs will diffcr. becausc of theinteraction bct\o;ecn the soil and the tunnel lining. Theintroduction of lining elemcnlS at :I section restrictsfurther dcfonnation in a 3D analysis. This is importantbecause it is wrongly thought that ultimate conditionsdue to tunnclling can bc ob!:lined with a 20 analysis

(Allouaniela/..1994).

o.:curred 3t the section-! is mor: than the section-2.(his is duc to Ihe support of lining on one side and3rching orlhe soil on (he olhcr side.

The ullimalc surfacc settlements obt.1ined in20 and 3D anal)sis are eompared in Fig. 10. Thesurracc settlemcnts obtained in 2D planc s!rainanal)'sis of scquential construction are about 3 lime!grealCr !han !he corrcsponding 3D analysis.

The present study dr:monslr:ltes that theultimate r:onditions re3ched in both C3ses differ by 3f3ctor of thrr:e in terms of sr:ttlemenls (Fig. 10) fortypical propertir:s of London CI3Y. This explains thcrr:asons for rr:duction of only 34% of nod31 forces toobtain observed seulcmcnls in an approximate 20planr: strain anal>.sis e.g. Stallebrass el 01. (1994).

./0

..0

~

lOr...,...

.I~ 0- ,. 20 30 --;.~t3IQ.~ d_'Y-"

Fig. 10 Ultimate surface settlement obtained in20 and 3D analyses together with field

observations.

ACKNOWLEDGEMENTS

This \vork \vas carried out in close association wilhstaff from Ih~ Geotcchnical and Tunnelling Divisionof W.S.Atkins. The help rcndcred by thc computingstaff of Cambridge Univcrsity EngineeringDepar1ment to run the 3 dimensional analysis isgratefully ackno\vlcdgcd. The first author \vishes tothank the Cambridge Common Wealth Trust for ils

financial SUPP°r1.

5 DISCUSSION AND CONCLUSIONS

A review of existing methods of analysis of lunnels inthe light of NA TM has been carried out. The analysis,,( NA TM is a complex problem 10 anal)'se by anysingle mcthod and predictions dr-pend to a largee~lenl on the assumptions made in modelling. Becauseor Ihese complcxities FEM may not br- used for thedirect design ofNATM tunnels, However, the FEM is3n extremely po\\Oerful analysis tool, and its ability toprr-dicl true engineering perfonnance is dependcntupon the quality of the calibration exercisest:::J.:rtaken against trial tunnels or high quality casertcords (AGS, 1994).

REFERENCESI. AGS (199-1). Validation and use of geotechnical

software. Vcrsion 1.0.2. Akagi, H. (1994). Computational simulation of

shield IUnnclling in soft ground. From memoirs ofschool of science and enginecring, WasedaUniversity, No.58, 85-119.

3. . Allouani, M., Bahar, R., Cambou, B. and Rezgui,

B. (1994). Evaluation of displacements duringtunnelling in soft soil. 8th IACMAG, WestVirginia, Siriwardane and Zaman (cds), 2535-2540.

4. Attewell, P.B. (1978). Ground movements causedby tunnelling in soil. Proc. of Large groundmovements and structures, Cardiff, edilcd byGeddes, Pcntcch Prcss, London, 812-948.

5. Atzl, G.V. arid Mayr, J.K. (1994). ' FEM-Analysis

of Heathrow NATM trial tunncl', Proc. ofNumcrical mcthods in gcotcchnical Enginccring,Smith (cd.), Balkcma, Rottcrdam, 195-201.

NATM has been ana lysed under 20 and 30contJjtions. It W3S shown that the constructionscqucnce has a significant effect on the predictedground movements. Analyses carried out to study thecrr~ct of varying the stiffness of shotcrete indicate thatth~r' is an upper limit to the useful stiffness (or liningthickness) for a given soil. In order to reducemovements it is the early placement of the shotcrete..hich is more important than the eventual stiffness.

495

20.~lair, R.J., Gunn, M.J. and O'Rcil')., :.of.P. (I'Ground mo\cmcnts :around sh:allow tunncls inclay. Proc. of I Oth ICS~IFE, Stockholm, 323-3

21.M:air, R.J., Taylor, R.N. and Cracegirdlc(1993). Subsurface sculem~nt promcs :atunnels in cl:ays. G.:otechnique, Vol.43, No.2.

320.22.Ne\v, C.M. and no~.ers.K.H. (1994). Grt

movement mod~1 validation at the tl.:atlexpr.:ss trial tunnel. Tunnelling .94. IMM, Lon

302-329.23.0'Reilly, M.P. and New, B.~f. (1982). Seul.:rr

nbove tunnels in the UK-lhcir m:agnitud~

prediction. Tunn.:lling '82, IMM, London,181.

24.Panet, M. and Gu.:not, A. (1982). An:afysieonvergenee b.:hind the fnce of a tunnel. Proc.Symp. Tunn.:lling '82, 197-20".

25.Romo, M.P. and Diazm, C. (1980). Face sIal:nnd ground seulcment in shield tunnelling. Pro-10th Intemation:a1 Conf.:rcnc~ on Soil McchJnnd Found:ation Engin~ering, Stockholnl, V

357-360.26.Rowe, R.K. nnd Lee, K.M. (1989). Deforn1:at

c:aused by surf:aec loading :and tunnelling: th.:of cl:.stic nnisolropy. Gcotcchnique, Vol.39, :-

125-140.27.Row.:, R.K. nnd Lee, K.M. (1992). An evnlu3

of simplified techniques for estim:ating tl-dimension:.1 undrained ground movemcnts dl:tllnn.:lling in soft soils, C:.n:ldi:.n G.:otcch., Vo

39-52.28.SchnJidl, B. (1974). Prediction of s.:ul.:ments

to tunnelling in soil: Ihre~ e:ase histori~s. Pro.:2nd R:.pid Excnvntion nnd Tunnelling Conf~r.:Snn Francisco, Vol.2, 1179-1199.

29.Sin1pson, o. (1992). Thirty-second RnnLeeture: Relaining structures: displ:acemcntdesign, Geot~chnique, Vol.42, No..~, 541-576.

30.Stallebrass, S.E., Joviciv, V. and Ta)-Ior, !(1994). The influence of recent stress histor:ground movements around tunnels. Pre-fa:Deformation of Geomaterials, Sapporo, J3Shibuya, Mitachi & Miura (eds.), Balke

Rouerdam, 615-620.31.Swoboda, G., M~rtz, W. and Schmid, A. (IS

Three dimensional numerical models to simLtunnel excavation. NUMOG 1[1., Ed. PietruszcS. and Pande, G,N., Elsevier Science Publi~Ltd., London, 536-548.

6. Bolton, M.D.. Sun. H.W. and Britto, ,\.M. (1993).Finitc: clcmcnl an.1lyscs or bridge abutmcnls onfirm clay. Computcrs and Gc:olc:chnics, Vol.15,

:-.'0.4,221-245.7. Bollon, M.D., Das.1ri, G.R. and Brilto, A.M.

(1994). Putting small str3in non-linearity into~Iodilicd Cam Clay modc:I, 8th IACMAG, WCSIVirginia, Siri"'ard3nc and Zam"n (cds), 537-542.

8. Britlo, A.M. & Gunn, M.J. (1987). Crilical statesoil mc:ch3nics via linit~ cl~mcnls. Chich~stcr: EllisHorwood Limilcd.

9. Chen, W. and Baldaur, S. (1994). Prcdiclion orground dcrormalions due to excavation-Applicationto tunncllining dc:sign in \\'cak rock, 8th IACM.-\G,West Virginia, Siriward"nc and Zaman (cds), 2565-2570.

10.Deanc, A.P. and Bassett, R.H. (1995). Thc:H~alhro\v Exprcss tri311unncl. Proc. or Insln. Civ.Engrs., Geot~.:hnical Enginc:cring, Vol. 113, July,144-156..

II.Femsys (1995). Users Guidc: 10FEMGEN,'FE~IV(EW. Fcmsys lid., Lcichesler,UK.

12.Fischnaller, G. (1992). Diplomarbcit, F"kult:!l furbauingcni~uf\\'c:scn und Archileklur, Univcrsit:ilInnsbruck.

13.Guo, C., Nguycn-minh, D. and Br3h:lm, S. (1994).Stc:ady linitc clemcnl mclhod ror an31ysis oradvancing tunncls undc:r non-unirorm loading.Proc. or Numc:ric31 methods in Gc:olechnic31Enginecring, Smith (cd.), Dalkenla, Roltcrdam,209-213..

14.J3rdinc:, R.J., Potts, D.M., Fouric, A.B. andBurland, J.B. (1986). Studies or the innuencc ornon-linc3r stress-strain char3cteristics in soil-structure interaction, Gcotcchniquc, Vol.36, No.3,377-396.

15.Jardine, R.J., Symcs, M.J. & Bur13nd, J.B. (1984).Thc mcasurcmcnt or soil stirrncss in thc triaxialapparatus. Gcbtcchniquc, Vol.34, No.3, 323-340.

16.J"rdinc, R.J., Potts, D.M., St.John, H.D. and Hight,D.W. (1991). Some practical applications ofa non-lincar ground model, Xth ECSMFE, Florcnec,Volume 1,223-228.

17.Kuhnhcnn, K (1995). Accuracy of NATMdemonstrations through typical failure casts. Proc.of Rapid Excavation and Tunncl Construction,Sandicgo, USA, 667-679.

IS.Lec, K.M. and Rowc, R.K. (1991). An analysis ofthrcc-dimcnsional ground movements: the ThundcrBay tunnel. Canadian Gcotceh. JI., Vol.28, 25-41.

19.Lcca, E. and Clough, G.W. (1992). Preliminarydesign for NA TM tunnel support in soil. JI. ofGcotcch. Engg., ASCE, Vol.118. No.4. 55S-575.

496