continuum and discontinuum modelling in tunnel engineering

7/28/2019 Continuum and Discontinuum Modelling in Tunnel Engineering

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CONTINUUM AND DISCONTINUU M MODELLINGIN TUNNEL ENGINEERING

Rudarsko-geolaqko-naftni zbornik

Giovanni BARLA, Marco BARLADepf. of'StruclurulundGeotechnical Engineering Politecnico di Torino, Corso Ducu deglr Abruur 24, Tonno, ItalyE-mail: gburlu @polroc.poli~o.t

Vol. 12

Key-words:Tunn el engineering, Continuum and discontinuum mo-delmg, TBM tunnelThc paper discusses continuum and discontinuum modelling intunnel engineering. A bricf rcview of fundamentals is presented inconnection with the use of closed - ormsolutions and computer bascdmethods. A few remarks ar e derived on the choice of eithercontinuum or discontinuum modelling of rock mass behaviour at thedesign analysis stag e. Cons ideration is given to th e validation of dis-continuum mode lling in conne ction with rock mass classification me-thods and cxpected tunnel response to excavation. A w se study of aTBM tunnel (4.75 m diam eter) in qu artzitic micaschists is discussed indetail by paying attention to a comparison of modelling methods -including continuum and discontinuum modeling - pplied at a faultzone.

str. 45-57

1. Introduction

Zagreb, 2000. 1

The prediction of the rock mass response to the excava-tion of a tunnel is a complex engineering problem. Theinterest of the Rock Engineer at the design stage is to assessthe stability conditions of the excavation in the "intrinsicstate" (i.e. when no support/stabilization measures are in-stalled) and following the adoption of suitable methods oftunnel excavation/constructionand support. The key to thesuccess of such a process is the level of understandingachieved in describing the rock mass conditions (in termsof geological, geotechnical, n situ stress, and hydrogeologi-cal parameters) and the ability to account for the funda-mental components of rock mass behaviour, by usingappropriate methods for the analysis of stresses and dis-placements in the rock mass around the tunnel and in thestructural components (pre-supportlpre-stabilizationmeasures; primary and final support, etc.).Anumber of methods are available for the stress analysisof tunnels, from the earliest closed-form solutions to themost recent numerical modelling methods. With the com-putational power today available at a reasonable cost, it ispossible to solve increasingly sophisticated problems. Inparticular, with the advent of numerical methods, we haveassisted to the development of techniques which have beenconceived to model realistically the rock mass behaviour.This is a quite different condition from the early start ofRock Mechanics, when the methods of analysis and thesolutions used were mostly taken from other engineeringdisciplines. This is certainly the case of the 1898 Kirschsolution for the stresses and displacements around a circu-lar hole in a biaxially loaded, homogeneous, isotropic andlinearlv elastic date.Closed-for6 solutions are still of great value for aconceptual understanding of the response of tunnels toexcavation. One could mention in this regard the solu-tlons which are presently available for the analysis of theprogressive development of failure around a circulartunnel in a hydrostatic stress field see for example:Brown e t a l . , 1983; Pa ne t , 14 5), and for theanalysis of the interaction between the rock mass and thesupport. However, the development of modern tech-

* Scientific Sym osium Roc k Mechan ic; and Tunnelling, 30.9 .-2.10. 1999.Zagreb, R d a t i a

Kljufne rijeti: Tunelsko inicnjerstvo, Modelirane kontinuteta idiskontinuitcta, TBM tunelU Elanku je rasp ravljeno mod eliranjc kontin uiteta i diskontinuitetau tunelskom inienjerstvu. Sai eto su opisane osnove zajedno s upora-bom matematizkih rjeienja i raEunalnih numeriEkih metoda. Ra-spravljen je izbor modela k ontinuu rna i diskon tinuum a stjenske maseu odnosu na analizu konstrukcije podgradivanja. U obzir je uzetopohrd ivanje modela diskontinuiteta povezanog s metodama Masifika-cije stjenskih masa i d k i v a n e reakcije tunela pri iskopu.U etaljimaje raspravljen primjer studije TBM tunela (promjera 4,75 m) u kvarci-titnim mikaSistirna, s posebnom pozornosti na usporedivanje metodamodelirania - ukliutuiuCi modeliranie kontinuuma i diskontinuurna- porabfienih u iasjednoj zoni.

niques of tunnel excavation and construction (i.e. thecase of pre-supportlpre-stabilization measures, the fre-quent adoption of pre-treatment ahead of the headingin weak rock masses, the excavation sequences, typicalof large tunnels), ...and even the complexity of rockmassconditions and behaviour, which are better describedtoday than in the past, given the modern investigationtools available, etc. make these solutions of limited valuefor design purposes.If we restrict our attention to modern numerical mod-elling methods and rigorous analysis of tunnelling prob-lems, the decision that the Rock Engineer need to makeat the design analysis stage is the choice between thefollowing two approaches:- Equivalent continuum approach: the rock mass istreated as a continuum with equal in all directionsinput data for the strength and deformability proper-ties, which define a given constitutive relation for themedium: elastic, elasto-plastic, etc.-Discontinuum approach: the rock mass is representedas a discontinuum and most of the attention at thedesign stage is devoted to the characterization of therock elements, the rock joints and discontinuities.Themodelling approach consists in considering the blockynature of the system being analysed. Each block mayinteract with the neighbouring blocks through thejoints. The interest lies in the fact that the fundamen-tal patterns of rock mass behaviour can be considered,as arbitrarily large relative displacements may takeplace at the contacts.

This lecture is intended to discuss a comparison ofmodelling methods - ncluding continuum and discon-tinuum modelling - applied at a fault zone in a TBMtunnel. Reference is made to a paper recently presentedat the 9'h International Congress on Rock Mechanics inParis(Bar1a & e t a l. , 1999).2. Fundamentals2.1. Continuum versus discontinuum modelling2.1.1. Continuum modelling

The use of continuum modelling in tunnel engineeringmakes it essential to simulate the rock mass response to


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StrengthFs = stress

Rud.-geol.-naft. zb., Vol. 12,Zagreb, 2000.46 Uurfu,G., BurfuM.: ontinuum and discontinuum modellingexcavation by introducing an eq uivalent continuum. Themost comm on way to solve this problem, which seems to INTACTOCKhave gained wide acceptance, is to scale the intact rockproperties down to the rock mass properties by usingempirically define d relationships such as those given byH o e k a nd B r o w n (1997).If use is made of the Hoek-Brown criterion for de-scribing the rock mass behaviour, the starting point ofthe scaling process is the definition of the intact rockmaterial parameters such as oci uniaxial com pressivestrength ) and mi (material con stant which depen ds uponthe propertie s of the rock), which can be obtain ed basedupon the results of u niaxial an d triaxial laboratory test-ing. Then, by using well know n correlations (which de-pend o n the degre e of disturbance to the rock which willvary according to rock type an d excavation meth od) with Ithe m ost frequently ado pted rock mass indices (i.e. trun- Icated Q or RMR alues, or G SI values), the rock mass >parameters such as mb and sb (rock mass cons tants ac-cording to th e H oek-Brown criterion) or c and $ (rock 't, G3mass cohesion and friction angle respectively) can beestimated (Figure 1).Th e next ste in the continuum modelling approach isthe adoption oithe appropriate constitutive relations fo r F i g m I . Hoek-Brown failure criterionr for the ihtacr rock material andthe rock mass. Linear elasticity is commonly used, al- the rock mass. Ifhrtrationof the scalingprocess and dejkittionthounh no nlinea r elasfic constitutive eauatio ns can also of Fuctor of Safetybe adYopted. If the at ten tio n is posed or; the progressivefailure of th e rock m ass, the elasto-plastic models needto be utilized in order to describe the "post-peak" re-sponse.A yield function which is often chosen coincideswith the Hoek -Brown failure criterion: (i) the rock massresponse is elastic, if the state of stress is within thebounds defined by the yield function; (ii) the rock massresponse is plastic, once t he sta te of stress is such as toreach the yield function. A number of "post-peak re-sponses may be postulated depending up on rock massquality; the characteristics show n in Figure 2 are amongthe most frequ ently used for th e solution of tunnellingp ro b le m s( H oe k a n d B r o w n , 1997):(a) Very poo r quality rock mass: the rock mass behaviouris adequa telyrepre sented by assuming that it behavesperfectly plastic, which mea ns th at deformation con-tinues at a constant stress level and that no volumechange is associated with t he ong oing failure.(b) Average quality rock mass: it is reasonable to assume

that a strain-softening behaviour occurs as the rockmass strength is reduced from the in situ to thebroken state; then, once this final, "residual" stat e isreached, deformation will occur at a constant stresslevel.(c) Very good quality hard rock mass: in such a case(hard rock masses, such as massive granites andgneiss) it is assumed that, when the rock massstrength is exceeded, a sudd en strength dro occurs.This is associated with significant dilation o?he rockmass, which is considered to behave as amed ium w ithzero cohesive strength a nd finite friction angle.As summarized by H o e k e t a 1. (1991) - also see

S t a r t f i e l d a n d C u n d a l ( 1 9 8 8 ) - a number ofcomputer-based numerical methods have been devel-oped over the past few decades and these provide themeans for obtaining appro priate solutons to tunnel en-gineering problems in th e framework of the equivalentcontinuum approach. These numerical methods can bedivided into two classes: bou ndary and domain m ethods.Th e boundary me thod s comp rise several types of bound-ary element meth ods (BE M) an d imply the subdivisionof the bou ndary of th e excavation into elements, as the

interior of th e rock mass is represented mathem aticallyas an infinite continuum. T he domain methods, whichinclude the finite element (FEM ) and finite differencemethods (FDM , mply that a physical problem is mod-elled numerical1y by discretizing (i.e. dividing into zonesor elements) the problem region, i.e. the rock mass inwhich the excav ation is to be created.2.1.2.Discontinuurn modellingWith the understanding that rock joints and disconti-nuities in a rock mass play a key role in the response ofa tun nel to excavation, i.e. joints can create loose blocksnear the tunn el p rofile a nd cause local instability; jointsweaken the rock and enlarge the displacement zonecaused by excav ation; joints change the w ater flow sys-tem in the vicinity of th e excavation (see, for example:(Sh en a n d B a r t o n , 1997), theuseofd iscontinuummodelling has been gaining progressive attentio n in tun-nel engineering mainly through the use of the UDECand 3DE C codes, for 2D and 3D discontinuum model-ling respectively. However discontinuum modelling isnot being used as extensively as continuum metho ds andis considered to be a relatively new a nd "not-yet-proven"numerical techniq ue to ap ly for analysis and design inrock engineering projects a r t , 1993).

In th e distinct elem ent method , the rock mass is rep-resented as an assemblage of discrete blocks which maybe considered either "n ot deformable" or "deformable".Joints and discontinuities are viewed as interfaces be-tween distinct bodies. The important features of thismethod which mak e it appropriate in order to capturethe important mechanisms characterising a discontinu-o u s m e d i u m a r e ( C u n d a l 1 a n d H a r t , 1993): (i) th emethod allows finite displacements detachment; (ii) th emethod recognizes new contacts automatically as thecalculation progresses.In order to apply the distinct element method to thesolution of tunn el problem s, the re a re two crucial issueswhich include the joint geom etry data and the materialproperties assigned to the joints. Th e first issue relatesto the introduction in the m odel of those joints which are


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~ u d . - g e o h a f t . b., ol. 12, Zagreb, 2000.Barfa, G., Barla M.:Continuum and discontinuurn modelling 47

Figure 2. Suggested streass-strainaws for different quulily rock musses, note that the stress scules ure different (Hoek and Brown,1997,modified)

A A

most critical to the response of the rock mass. Thesecond issue is closely connected with the need to assignto the joints in the model the stiffness and strengthproperties of the real joints in situ. Although publisheddata are readily available in the specialised literaturewhich may provide a way to guide into the choice ofappropriate parameters (Bandis, 1993), this aspect ofmodelling still remains difficult. However, it is to beremarked that a significant help in deriving the necessaryinput data for 2D and 3D discontinuum modelling maybe obtained from index testing of joints in drill cores andfrom field mapping (B a r t o n , 1998 and 1999).2.1.3. DiscussionWhen investigating a parficular problem at the designanalysis stage the decision is to choose between contin-uum and discontinuum modelling of rock mass behav-iour. This decision may be based on the analysis of thelikely mechanism (sliding along joints, opening of joints,

/'ELASTICc - 0's o't - o'r

Q - 0.1 0:twI FEMlFDY 1 DEM FEWBEM

W N OFTENIM PERFECTLY R ~ L E

> > >9 a E4

( a J w t y p 0 0 r ~ l W ~ d ~ 0)- -&mass (c) w ty good quality had rod^ mass

Q'I -dr/EUS~K:

Figure 3. Schemulic diu ga m ,sugge.~linghe runge of app lication of dis-continuum modelling in relation to the Q-value (Ba rt on ,1998, modified)block rotation and movement, etc.) which may influencetunnel stability and the joint spacing relative to the sizeof the excavation. Consideration may be given to a sug-gested range of Q-values for which discontinuum mod-elling will be more appropriate than continuum modelling(Q = 0.1-100) as depicted in Figure 3 (Barton,1998).Based upon experience gained so far and a closescrutiny of design analyses which are sometimes used in

*Thc senior auth or dcrivcs thcs c observations through cxpcricncegained in reviewing a nurnbcr of dcsign analyses carricd out in Italyand abroad, in conncction with hydroclcctric, highways and high-spccdrailways projects.

tunnel engineering(*), the following observations can bederived:- Isotropic continuum modelling is being used morefrequently than discontinuum modelling, even incases where the block size is significant, compared tothe size of excavation or the rock mass exhibits astrong anisotropic behaviour.- Numerical modelling is being used too often, even incases where problems are characterised by low levelsof both input data and understanding (it is appropri-

ate to recall the classification of modelling problemsreportedby St ar tf ie ld an d Cu nd al l, 1988,whorecognize this to be the case of most rock mechanicsproblems), or the size of the planned excavation issuch as not to justify this exercise.- It appears that the easy access to computer codes,which make sophisticated methods of analysispromptly available, may result in misuse of thesemethods. Sometimes, the tendency is to be happywithhaving run a model, even if the results obtained are inopen contradiction with empirical design rules andcngineering judgement.2.2. Validation of discontinuum modelling

The use of numerical modelling in engineering prac-ticc, connected with the need to adopt modellingschcmes (continuum versus discontinuum modelling)which are the most appropriate in order to analyse agivcn problem (provided that sufficient data are avail-ahlc), points out that "the modelling of the components,rock, rock joints and discontinuities is far more logicaland relevant than present "black box" continuum mod-els" (B a r to n , 1999). The comparison shown in Figure4 well demonstrates this uoint of view, exueciallv if criti-cal mechanisms of the p6ysical problem Cnder study areto be included in the analysis.There is a relevant question which arises with refer-ence to the use of discontinuum modelling in tunnelengineering and rock engineering, in general. This is inrelation to the complexity of the discontinuum model tobe used in order to be certain that the critical structuralfeatures have not been left out of the analysis ( H a r t ,1993). From one side, the difficulty is in providing suffi-cient geological data; from the other side, the computerhardware requirements may exceed that available.Based on the experience gained so far, a possibleapproach to this problem consists in using discontinuum


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Rud.-geol.-naft. zb.,Vol. 12, Zagrcb, 2000.48 Bark, G., Barla M.: ontinuum and discontinuum modelling

4. Comm ~aon f la) continuum ubiuuitous io dc case and A )di~cdntinuumn'delling esults wheh analysing typical instabii-ity mechanismsaround a TBMexcavated unnel in a weak rockmass

modelIing in connection with rock mass classificationmethods in a framewo rk of crossvalidation of th e ex-pected tunnel response to excavation On ce the specificmodel has been proven to be a w e table in a given rockaass condition, it may be improve and furthervalid atedduring tunnel excavation.A se t of guidelines, given as afunction of Q values, can be used as a form of preliminaryverification of a nume rical model (B a r t o n , 1999).-Support categoriesBased upon analyses of case records, G r i m s ta d an dB a r o n (1993) give the diagram of Figure 5 whichallows one to relate the value of the index Q to thestability and supp ort requirem ents of underground ex-cavation, once the parameter which they called Equiva-lent Dimension is obtained. This parameter is the span,diameter o r wall height of th e sam e excavation dividedby a num erical coefficient which is intended to accountfor its use and the de gree of security which is dem ande dof the support system installed to maintain the stabilityof the excavation.Additional guidelines are available based on the Qsystem which allow one to assess a number of addit ionalparameters dealing with tunnel stability and supportrequirements (B a r t o n et al., 1974): a) the m m m u munsupported span, b) the permanent roof suppo rt pres-sure; c) the bolt length.

Figwe 5. Estimated supporfcuiegork~ e d yon the tunnellingqutalhtyindex Q (Grimstadand Barton, 199 )- Tunnel deformation (B a r t o n , 1998)

Vertical:Horizontal: Ah =

where: %and ah (the vertical and horizontal in situ stresscomponents), crc [the uniaxial compressive strength ofthe intact rock material ar e given in consistent units (i.e.MPa); SPANand HE1bHT (the width and height of th etunne l) ar e given inmm.2.2.1.Case ExamplesWith the case history in mind, which is to be discussedin the following, a 4.75 m d iameter tu nnel was taken asa typical problem to be used fo r validation of the discon-

Figure 6. Four UDEC d e b irh difierent Qvalucr: model 1-Q=8.5;made1 2 - Q=4 .l; madel 3 - Q=1.9; model 4 -Q=0.67


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~ ~ d . - p o l . - n a f t .b., Vol. 12, Zagreb, WOO.Barla, G., Bark M.: Contin uum and discontinuurn modellingtinuurn modelling by the 2D Distinct Element codeUDEC (I t a s c a , 1996). The intent has been to investi-gate the influence of rock mass conditions by the Qindex, on the disturbed zone around the tunnel.

Four models have been used as shown in Figure 6.With dimensions 20x20 m, three sets of persistent dis-continuities (S, = schistosity, J1, J2 joints) have beenintroduced with the parameters assigned so as to obtaina range of Q values from 8.5 for mod el 1 o 0.67for model4. For all the mod els the initial state of stress is assumedto be given by: ov vertical stress) =16.2 M Pa, oh hori-zontal stress) = 4 MPa, which represent a gravity in-duced stress state at a depth of about 600 m, with anassumed stress ratio (ado,)of 0.25. The oint spacing foreach system shown in Figure 6 is as follows:JOINTSPACING (m )

Model Schistosity

For all the models the rock blocks are deformableblocks with the assum ption that the intact rock (gneiss)is conside red as an elasto-plastic material which followsthe M ohr-Coulomb yield criterion. Th e properties a reassigned as follows:Young's modulus E =60 GPaPoisson's ratio v=0.25Cohesion c= 30 MP aFriction angle $=33"The discontinuities are assumed to be Mohr-Coulombjoints, i.e. elasto-perfectlyplastic joints, with normal K,,and shear K, stiffness given as follows: K,, = 40 GPaIm,K, = 4 GPa/m. T he cohesion is always considered to bezero, with the friction angle $ taken as 58", 38", 22' and11 respectively fo r models 1, 2, 3 and 4, for both theschistosity and joints.

Figure 7.Yielded and loose blocks around fhe tunnel f w modelv 1 lo 4

- Unsupported tunnelA first series of analyses was carried out in intrinsicconditions, i.e. the tunnel is always left unsupported,with the disturbed zone d efined as follows (S h e n a n dB ar t o n , 1 9 9 7 ) :- ailure zone, where loose rock blocks are falling intothe tunnel;- open zone, where joints open u p;- shear zone, where joints experience a certain sheardisplacement (3 mm).Th e results obtained for the 4 models, are illustratedin Figures 7 to 9, where the failure, open and shear zonesaround the tunnel are depicted. The following remarksare made: (1) the failure zones computed around thetunnel show that model 1 s stable, whereas models 2 to4 exhibit progressively critical conditions; (2) the openand sh ear zones ap pear to grow as the rock mass qualitydecreases from m odel 1 o 4, in line with the behaviourin terms of failure zones, (3) the results obtained seemto ag ree with the estimated supp ort categories shown inFigure 5, where only the tunnel simulated with model 1would req uire no support, and m odels 2 to 4would needdifferent and progressively more severe support mea-sures.

Figure 8. Oprm zones around the tunnel fbr models I to 4

Figure 9. Shear zones around the lunnel for mod el9 I to 4

- Supported tunnelAs a direct consequence of the analyses describedabove and based upon the gu idelines of F igure5 in termsof support requirements, the following stabilizationmeasures were introduced in models 2 to 4.


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Rud.-geol.-naft. zb.,Vol. 12,Zagreb, 2000.50 Burlu, G., Burlu M.: Continuum and discontinuum modelling

E l

Figure 10.Pont Ventoux-Clarea F2 tunnelModel Bolts n. Bolt lenght Bolt spacing(') Schortcretethickness

(' )~ ol ts re supposed to be installed according to a square patternTh e bolts were simulated by using the CA BLE optio navailable within the U D EC code, which allows one toconsider a bolt fully bond ed to th e rock mass. The sho t-Crete was introduced in the model by the STRUCToption which consists in simulating it as a series of beamsconnected to th e rock mass.As a first estimate of the predictive capability of theUD EC discontinuum modelling of the suppo rted tunnelthe attention is posed on comparing the verfical andhorizo ntal displacem ents Av and Ah given by the em piri-cal Q based formulae reported above and the results ofUD EC computations:

Model23

Av [mm] Ah [mm]estimated-computed estimated-computed4.5- 5.0 2.6- 2.69.2-10.2 4.7- 5.3

3. Case study3.1. Background information

The case study considers the problems occurred o n 11Septemb er 1997, at ch 2360 m, when crossing a fault zonewhich caused the TBM to become temporarily stuckduring excavation of the F2 tunnel, one of the majorelement of the Pont V entou x- Susa Hydropower Projectin the Susa Valley, near Torino. This tunnel (4.75 mdiameter) is being excavated by an open TB M configu-ration through uartzitic micaschists unde r a coverwhich is to reach B00 m maximum (Figure 10).Following the first 1800 m approximately where therock mass conditions wh ere generally good, with RMRvalues ranging from 65 to 75 (Figure ll ) , TBM tunnel-ling in th e F2 tunne l became progressively more severewith the approaching of the fault zone. At present, thetunnel is experiencing very severe dificultieswith consid-

Figure 1 I . A view of the F2 tunnel in the section where the gneiss rockmuss was generally gooderable delays with respect to t he expected adv ance rate.Figure 12 shows two ph otog raphs taken following chain-age 2360 m, where the fault of interest in this papercrossed the tunnel, affecting progress significantly.3.2. Description of the overstre ss problem a t ch 2360 m

Th e sketch shown in F igure 13 gives a simplified illus-tration of the conditions at the tunnel face where theTB M became temporarily stuck as a consequence ofoverstressing and a 25 cm block movement of the rightsidewall (Figure 14). Th e quartzitic micaschist is c h a r a ~terized by th e presence of th ree to four joint systemsincluding foliation. Based on geologic mapping, whichwas carried ou t by the contractor's geologist (Pont Ven-toux, 1997) once the TBM could drill a few meters aheadof th e section whe re it jamm ed (Figure 15),at least twosub-parallel discontinuities could be evidenced, the sec-ond of which (a fault with st nk e N66E and d ip 83 to theS, which inte rcepts th e tunne l axis) has a clay filling andgouge with ape rtur e ranging from a few centimeters tomore than a decimeter.The rock mass conditions were estimated on a 7 rntunnel length, from ch 2349 to ch 2356 m, with RM Rindex equal to 31. According to a more co mplete Q -log-ging estimate du e to B a r t o n (1997), from ch 2350 to ch


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Rud.-Seol.-naft.b., Vol. 12,Zagreb, 2000.G.,Barlu M.: Continuum and discontinuum modelling 51-

ure 12.A view offlu 2 tunnel: (a) ef! (b)right walls, where stability cond itions became very di fi ul l so us to require continuos placement of liner" plaler

Figure 13. Skelch of the rock corulitwns a1 rltr Jitce

Figure 14. Phologruph showing the heau OJ TBM jammed wilh rockoverstressing and block movem ent o f the right .stdewaII2360 m, an extreme range of Q-values of about 0.007("exceptionallypoor" - ocally) to 0.3 ("poor") showed aweighted mean of all recordings of ab out 0.05. Water isflowing through the joints at a temperature of 20. Noquantitative data have bee n rec orde d of the water pres-sure, which seems unlikely to be exceeding, with an

Figure 15.Rock mass conditions on the tunnel (a) eft (b) ig& walls. Thepholograph was taken when the TBM was moved aheadoverburden of 650m, a maximum of 6 to 7 MPa (outsidethe tunnel drainag e area).3.3. Rock mass strength

The rock mass strength in the section of interest islargely controlled by the g enerally "poor" conditions andthe limited sh ear streng th along discontinuities. Typicalstrength pro perties derived from triaxial testing of rocksampIes are as follows:


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Rud.-gco1.-naft.zb., Vol. 12,Zagreb, 2000.52 Rarlu, G.,Barla M.: Continuum an d discontinuum modellingm. , r[-I6.1

where o ~ , ~nd a o,, a re the uniaxial compressivestrength values (peak an d residual) and mipp nd mi,, arethe corresponding Hoek-Brown empirical constants.For very good quality rock masses, which is the casefo r a significant tunnel length (Figure l l ) , typical rockmass properties can be defined on th e basis of th e Geo-logical Strength Index (GSI) as follows:Intact rock strength oCi 144 MPaHoek-Brown constant m, =7.0Geological Strength Index GSI=70Hoek-Brown constant mb =2.4Hoek-Brown constant s =0.02Rock mass compressivestrength o,,= 27.2 MPaDeformation modulus E, =35 GPa

3.4. In situ stress conditionsIn view of the high overburden an d closer valley side,associated with evidence of deformation and thin slab-bing in isolated sections along th e tunnel length, it wasrecommended that stressmeasurements by means of flat-jack tests an d hydraulic minifracture tests be carriedout. At present only the flat-jack test data are available Gas follows, derived from measurements around th e sec- - r=02 /tion of th e tunnel a t ch 950 m, where th e overburden isapproximately 400 m: Figure 16. (a ) M m u m rincrpul .!tre.r\ contours. (6 ) Computed andmeusured tangential strrsse.s Fht-jack slot tests, wtth overbur-

Angle with respect to Jack presyure den of 400m approximatelyFlat-jack slot horizontal axisPI [MPal values of oCind s = 1. The stability of th e tunnel wasM I 0 34.8 assessed by computation of th e strength factor contoursM2 +50 3.3 as shown in Figure 17. T he implication is that th e rockmass inside the unit strength factor contour (SF(m,ol = 1)M 3 -45 23.5 will be unstable, unless well retained.

Based on a stress concentration study in linearly elas- the above simplifiedtic conditions around th e tunnel using th e finite element linearly elastic costitutive model, no influence of hy-method and the phase2 code cur a n d c k u *, drostatic head considered, etc.) th e tunnel experi-1997), as shown in ~i~~~~1 , he initial stresses in th e ences localized failure at th e sidewalls which deepensbplane perpendicular to th e tunnel axis were evaluated to inside the rock mass as the micaschist intact rockbe as follows: uniaxial compressive strength decreases from 100MPa to 75 MPa. This would signify that in the highlyol = maximum principal stress =13 MPa anisotropic stress regime of the tunnel, as evidencedo3= minimum principal stress = 2.6 MPa with a I?, value equal to 0.2, localized slabbing insta-

O1 = angle of olwith respect to the vertical axis =15O bility cannot be ruled out, if the rock strength is in therange 100-75 MPa.3.5. Continuum modelling3.5.1. The m = 0 approach

In order to determine to what extent the adoption ofa continuum modelling approach can provide a reason-able interpretation of tunnel instability,numerical analy-ses were first carried out to assess th e stability conditionsby using a constant deviatoric stress criterion as pro-posed by (M a r t i n et a 1. (1997).T he initial stresses o, and 0 3 at the cross section ofinterest (ch 2360 m) were assumed to be proportionallyhigher in relation to th e higher overburden of 650 m.Also, th e stress ratio (q,)f th e minimum stress tomaximum stress (03/01) n th e plane of th e tunnel crosssection was considered equal to 0.2, as in th e section ofthe flat-jack measurements.The m = 0 analyses were performed by using thephases2code and th e Hoek-Brown criterion for different

3.5.2. The elastic-brittle-plasticmodelThe analyses above considered overstressing of th erockmass around the tunnel periphery,without account-ing for th e presence of discontinuities.Therefore, it wasdecided to analyse th e same instability problem by intro-ducing these features in th e numerical model.As shown in Figure 18, the model comprises two

parallel discontinuities near the right sidewall, dippingtoward th e tunnel. In order to account fo r the rock massdisturbance due to jointing in th e proximity of the dis-continuities and th e apparently more massive rock onth e left sidewall,where relatively little slabbing and over-stressing was present, it was decided to introduce threedifferent regions in th e model with the following mate-rial properties, according to the Hoek-Brown failurecriterion:


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Em [GPalvm [-Ioci [MPalm, 1-1

~ u d . - g e o h a f t .b., Vol. 12, Zagreb, 2000.Barla, G.,Barla M.: ontinuum and discontinuurn modelling 53Material properties Region (Fibwrc 18) Joint propcrtics Joint (Figurc 19)

2 17.5 12500.35 125

150 0.080.74 0

1.00 for: K,, K,= normal and shear stiffness; h = joint0.001 aperture; c = joint cohesion;+ = joint friction angle.for:Gci = intact rock strength; mb ,mbr, sb, Sr = Hoek-Brown constants;Em rock mass cleformation modulus;V m = Poisson's ratio.

The rock mass surrounding the tunnel was specifiedas plastic and the elastic-brittle-plastic option of phase2was activated b specifying the constants for peakstrength (mb ,S$ different than residual strength (mb,sr) only for t i e more massive rock mass conditions. Thevalues were chosen on the basis of personal judgementwith the purpose to account for the better rock massconditions on the sidewall. The discontinuities were in-troduced in the model by using the joint option of phase2,with the following joint properties:

Figure 18.Defuil ofthe FEM model near fhefunnelshowing regions wifhdifferent material propetties a d oidv (refer to vulues in pre-vious fables)

o,,= 75 MPa

Figure 17.Strength factor conlou rs determined with them = 0 upproachfor the funn el at ch 2360 m (on.=IOO, 75MPu).

Figure 19shows the deepening of the failure zones inthe right and left walls as predicted by the elastic-brittle-plasticmodel. The results of such an analysisis the moresignificant deepening of breakout on the right wall inagreement with observations in the tunnel where stressfailure and block movement actually occurred duringface advance, resulting in jamming of the TBM.It is conduded that the structural discontinuitiesnearthe tunnel govern to a significant extent the stabilityconditions.This is a very relevant aspect combined withthe high overburdenand highlyanisotropicstressregimein the resent situation, and eftect of water, which wasnot inc7 ded in the numerical analysis.3.5.3.Lessons learnedThe future geological and hydrogeological conditionsalong the tunnel alignment anticipate the presence of clayfilled discontinuities with unfavorable orientation as expe-rienced in the actual situation, with high hydrostatic head.Then, the lessons learned so far need to be taken intoaccount in order to carefully assess the interactive behav-iour between the rock surround and TBM. In fact, thetunnelling conditions could become more problematic,as they involve already highly stressed rock masses, withthe overburden expected to rise up to 800m maximum.With this in mind, also considering that the TBM isdriven along a curved axis, i t is of interest to use thepredictive capability of the elastic-brittle-plastic modelto analyse two possible scenarios:1) the discontinuities run parallel to the tunnel axis, atthe crown;2) the discontinuities are at the left wall.


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tigated by adopting discontinuous models, with the 2Ddistinct element code, UD EC (I t a s c a , 1996). The rock

Figure 19. Computed ykl ded wn es around thetunnel and dejormed meshusing* elustic-brittle-phsticcoastitutive model

mass surrounding t he tun nel ' was represented by twodiscontinuous models a s follows.3.6.1.Deterministic model

The rock mass was considered to be intercepted bythree sets of joints, and foliation. Different spacing,degree of persistence and shear strength propertieswereintroduced in the model so as to simulate th e rock massconditions away from the fault zone as illustrated inFigure 21. The joints were again assumed to be Mohr-Coulomb joints, i.e. elasto-perfectly plastic joints. Theblocks were treated as an elasto-plastic material whichfollowsMohr-Coulomb criterion. T he properties of rockblocks and joints are listed below:MaterialProperties(*)

The analyses were carried out with the same assump- Em .tGPa]tions given above for th e material an d joint properties vm [-Iand th e in situ state of stress. T he results obtained aregiven in Figure 20 by showing the plot of th e yielded c [MPalzones around the tunnel and th e deformed mesh. 4 r7

Zon e (Figure 8 and 10)

(*>c = cohesion: & = friction angle: E, = rock mass\ I ? 0 " , .adeformation modulus; v, = Poisson's ratio.JointProperties(*)

JointZone (Figure8 and 10) (Figure 8and 10)

1K,, [GPa/ml 40Ks [GPa/ml 4c [MPa] 0.1+ r"l 33(*) K,,, , = normal and shear stiffness; c = jointcohesion; $ = joint friction angle.

3.6 .2. Discrete Feature Nefwork (DFN) modelA Discrete Feature Network model was also createdby using the procedures implemented in the FracMancode (D e rs h o w i t z e t a l . . 1995). The re su lts ofgeologic mapping on the right wall of ih e tunnel form edthe basis for defining; th e in put data in terms of orien ta-tion, size and degree-of fractur ing for th e ioint sets J1.52and ~3 a, b. The& were sup eri m ~o sed iih foliation anddiscrete features represented by the two sub-paralleldiscontinuities described above. Th e 3D volume realizedin this way is shown in F igure 22, where also shown is theplot of the joint se ts given with th e FracM an code.The UDEC model was obtained by taking a crosssection orthogonal to the tunnel axis through the 3DFigure 20. Compu fedyieldedzone.s round the tunnel and deformed mesh D m olume of Figure 22. This network of 2D fracturesusing the e lastic-h riftle-pla slic on.$titutivemodel for two po,~si- is not directly amenable to UDEC analysis as th e frat-ble geologicul condilionv along the tunnel aris tures need to be well connected and no isolated fractures

3.6. Discontinuum modelling can be handled by the code. At the same time, it wasnecessary to cross-validate the model against the rockWith the understanding that discontinuities (major mass conditions around the tunnel. This was carried ou tdiscontinuities and jointing) play a key role in the devel- by increasing the block size in t he original 2D networkopmen t of tu nnel instability, the problem was also inves- mod el both at th e crown and o n the left wall, to account


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~"d.-geol.-naft .zb.,Vol. 12,Zagreb, 2000.Barla,G., Barla M.: ontinuu m and d iscontinuum modelling 55

Figure 21. Detail of UDEC &termh istic model showing regi~n,~ithdifferent material a nd joint properiiesfor the generally better rock mass conditions in thesezones.A random process which cancels th e fracture tracesexceeding a given limit-length fixed was used in conjunc-tion with the Set edge command which is available withthe UDEC code. A typical model finally developed isshown in Figure 23. As fo r th e deterministic modeldescribed above, th e joints were assumed to behave asMohr-Coulomb joints and the blocks were treated as anelasto-plastic material. The input data are th e same aslisted above and shown in Figure 21.

TUNNEL FACE

Figure 2 2 . 3 0 Dkcrete Feature Network model created by the Frac-Mancode w ith plot ofjo int sets. Thisis ypicalfor rock conditions onfhe igk wall3.6.3.Results

For both the deterministic and DFN models the samestress conditions as assumed fo r the continuum modelsWere applied.

Figure 23. Detail of UDEC-DFN model showing regions with differentmaterid properlies and jointsIn order to investigate whether the continuum approachcan yield similar results to th e discontinuum approach , thecalculations were carried to sim ulate tunnel excavation asfor the finite element models by using stress boundaryconditions. Also, no account was taken for the water pres-sure distributed around th e tunnel. The main in terest wasposed on the yield zones, as shown by blocks which arefailing, and on shear displacements induced along joints

(Figure 24). Atten tion was also paid to the pattern of blockmovements at the right wall (Figure 25).Th e results obtained show that both the deterministicand D FN models capture well the overstressing condi-tions and block movements of right wall. As for theelastic-brittle-plasticmodel which accounts for the pres-ence of the two sub- arallel discontinuities, the deep en-ing of breakout o n tle righ t wall is well reproduced withthe discontinuum approach (com pare Figure 19 withFigure 24). However, in the latte r case (Figure 24) nosignificant instability is seen to develop at the left wall,unlike the continuum approach (Figure 19). Th e similar-ity is evident with the actual conditions in the tunnel,where the TBM jamm ed because of instability and blockmovem ent at the right wall (Figures 14and 15).Th e continuum ap roach appears to capture some ofthe adverse factors wEich were significan t in the instab i-lity conditions that developed during TBM excavation:- he elastic -plastic-brittle behaviour of rock material,- the highly anisotropic stress regime with a very lowstress ratio,- he presence of unfavourable dominant discontinui-ties at t he right wall.In com parison, the discontinuum approach shows in aremarkable ma nner th e block movem ent developing onthe right wall, whereas the tunnel remains stable alongthe periphery away from the fault zone at the crown andright wall.4. Conclusions

Modern numerical modelling methods by the use ofeither the equivalent continuum o r discontinuum approachhave been discussed by underlying some of the fundamen-tal concepts and guidelines, when investigating tunnelproblems at the design analysis stage. With reference tomodelling in engineering practice, the interest has been


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Rud.-geol.-naft. zb., Vol. 12, Zagreb, 2000.56 Barla, G., Barla M.: Continuum and discontinuum modelling

%I (a) i

Figure 24.YeIdedblocks undsheardi.splacementsalong the join& aroundthe tunnel; (a) determm isficmodel, (b) DFN modelplaced on the adoption of discontinuum models whichgive a far more realistic and representative picture ofrock mass behaviour than equivalent continuum models.Modelling of rock mass around a 4.75 m diametertunnel excavated by a n ope nTBM configuration throughquartzitic michaschists has been described, with atten -tion paid to the instability conditions that developedwhen crossing through a fault zone. The calculationswere performed by using the finite element method andthe distinct elem ent method, according to a two dimen-sional modelling format, three-dimensional repre-sentation being too lim ited and not justifiable in respectof the uncertainties of the input data.With the finite element method an equivalent contin-uum approach was applied, including the influence oftwo major discontinuities on the right wall. With thedistinct element m ethod a fully dicontinuum approachwas used by either a deterministic or discrete featurenetwork model. Th e discontinuum representation of th erock mass captures in a rem arkable m anner t he instabil-ity conditions that developed at the TBM head duringexcavation. In comparison, the continuum repre-senta tion gives a mo re idea lised illustration of the insta-bility. It is concluded that for stability analysis peculiargeologic conditions such as fault zones around the tunnelrequire specific models, which reflect the given condi-tions in the m ost rea listic way possible.

Received: 2000-05-24Accepted: 2000-09-21

Figure 25. Block movemertls around the funnel , (a ) deterministic model,(6 ) DFN d l

REFERENCESB a r l a , G . , M . B a r l a , L . R e p e t t o (1999): Continuug anddiscontinuum modelling for design analysis of tunnels. 9 . nt.Coner. on Rock Mech. Paris. France.B a n d i s ,"s . (1993): ~n ~ i n ee r i n eroperties and characterization ofrock discontinuities. Com~ rehenslve ock E n e in e e ~ e . olume

1. Fundamenta ls ~ u d s o i.A , editor). pp. 153-183. Perg amo nPr e~ s, xford (UIi.B a r t o n , N ., R . ' ~ i.n , J . L u n d e (1974): Engineering classifi-cation of jointed rock maqses for the design of tunnel supportRock Mechanics. Vol. 6, pp.189-236.B a r t o n , N . (1997): Pont Ventoux H ydropower Project. Tunne lF2-Poet Ventoux.Assessment of geological condilwns andsuppofiforch 2350-dWO Rep ort to Nocon. 25 October ;%gdB a r t o n , N . (1998): Quantitative description of rock m awes for thedesign of NMT reinforcement Sp ec~ al ecture 1). Int. Conf. onHydro Power Developm ent Inh malayas. Shimla, Ind iaB a r t o n , N . 61999): General report concerning some 2Dthcenturylessons an 21S'centurychallenges in ap lied rock mechanics.9thInternational Congress on Rock ~ e c ia n ic s. ugust 25 -28.1999, Paris.B r o w n , E.T., J . W . B r a y , B . L a d a n y i , E. Hoek 1983):Character istic ine calculations fur rock tunnels.J. Geotec .Eng.Div. Am. Soc. Civ. E n p .109. pp.15-39.

I,C u n d a l l , P . A., R . D . H a r t (1993): Numerical modelling ofdiscontinua. Comprehensive Rock Engineering. Volume 2.Analysis and Design Methods (Hudson J.A., editor). pp. 231-261. Pergamon Press, Oxford (UK).C u r r a n , J . H . a nd C or ku n, B. T . (1997): phase2. 2D finiteelcm ent program for calculating stresses and estimating su portaround underground excavations. Reference Manual and fu to -rial Manual. Rock Engineering Gro up. University of Toro nto.D e r s h o w i t z , W . , G . L c c , J . G e i e r , P . L a P o i n t c ,(1995):FracMan Interactivc Discrcte Feature Data Analysis,


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Geometric Modelling and Exploration Simulation. User docu- di derivuione nel tratto Pont Ventoux - F2 (Dott. Geol. G.men tation. Vers ion 2.50. Seattle . Gold er A.s.wciates Inc. Ven turini).G r i m s t ad , E . N . B r t o n (1993): Updating the Q-system for S h e n , B . N . B a r t o n (1997): The disturbed zone around tunnelsNMT. Proc. of Int. Symp. on Sprayed Concrete. Modern use of in jointed rock masses. lnf.J . Rock Mech. Min.Sci. Vol. 34 , pp.wet mix sprayed concrete for underground sup orf. Fagernes 117-125.

me om pan, 0pS.m and erg, editors). ~o nv cg ian nC retc Asso- S t a r t i e 1d , A . M . C u n d a l 1 P . A . (1 988): Towards a meth-ciation. Oslo. odology for rock mechanics modelling. Inf. J. Rock Mech. Min.art , R .D . ( l F 3 ) : +n introduction to distinct etement modelling Sci. Vol.25, pp. 99- 106.for rock engmeenn g. C omprehensive Rock Engineering. Vol-ume 2. Analysis and Design Method s Hudson J.A., editor). pp. 6. Acknowledgements245-263. Perg amo n Press, Oxford (Uk .Hock, E . , M . W ., G r a b i n s k y , M . S . D i c d c r i c h s (1991): The work described in this paper was carried out withNumerical modelling for und ergrou nd excavation design: Trurw. the financial support of the [talian Ministry for Univer-Imt. Min. hfeb l. VollOO.January-April1991, PP. A22-A30. sity and Technological Research (M.U.R.S.T.) as part ofH o e k , E , E . , T . B r ow n (1997): Practical estima tes of rock mass the R~~~~~~. programme tn n n e ~ i n gn difficultcondi-strength. Inl. . Rock Mech.Mn Sci. Vol.34, pp.1156- 1186.It a sc a Consulting Gro u (1996): UDE C (Universal Distinct Ele- tions" 40%). The authors would like to acknowledge theMinnesota, &A.ment ~ e ) ,ersion 5.0. olum e 1: user's manual. volum e 11: help o G. Giampieri and L. Repetto, former students atVerification roblem s and example applications. Minn eapo lis, the Politecnico di Torino.

M a r t i n , C . D . , D. . M c C r e a t h , M. to ch m al (1997): The permission of AEM (Azienda Energetica Metro-Btim atingsu port dema nd-load caused by stress-induced failure politana) Torino, Owner the Pant VentOux-SusaH ~ -around tunncfh. Int. Symp. on Roc k Support, Lillehammer, June dropower Project, to publish this paper on the F2 tunnel1997. is gratefully acknowledged. The authors would also likep a n e , M . (1995): Le calcul des tunne ls par la mCthod conv ergen ce- to thank the following companies involved in the projectcontinement. Presses de 1'Ecole Nationale des Ponts et described in the paper: ~ ~ ~ ~ l d i.~.A.,~~~l~nd N ~ ~C h a u . ~ ~ .p on V e n t o u x (1997): Nota relativa al sopralluogo effettuato indata 8/10/1997 In corrispon denza del fro nte di scavo della galleria

continuum and discontinuum modelling in tunnel engineering

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