continuum and discontinuum modelling in tunnel engineering

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Rud.-geol.-naft. zb., Vol. 12, Zagrcb, 2000.48 Bark, G., Barla M.: Continuum and discontinuum modellingFigwe 5. Estimated supporf cuiegork~ hed yon the tunnelling qutalhtyindex Q (Grimstad and 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 are given in consistent units (i.e.MPa); SPAN and HE1 b HT (the width and height of thetunnel) are given in mm.4. Comm~aon of la) continuum ubiuuitous iodc case and A)di~cdntinuum ;n'delling results wheh analysing typical instabiiitymechanisms around a TBMexcavated lunnel in a weak rockmassmodelIing in connection with rock mass classificationmethods in a framework of crossvalidation of the expectedtunnel response to excavation Once the specificmodel has been proven to be awe table in a given rockmass condition, it may be improve a and furthervalidatedduring tunnel excavation. A set of guidelines, given as afunction of Q values, can be used as a form of preliminaryverification of a numerical model (B art o n , 1999).-Support categoriesBased upon analyses of case records, Grim st a d andBar ton (1993) give the diagram of Figure 5 whichallows one to relate the value of the index Q to thestability and support requirements of underground excavation,once the parameter which they called EquivalentDimension is obtained. This parameter is the span,diameter or wall height of the same excavation dividedby a numerical coefficient which is intended to accountfor its use and the degree of security which is demandedof 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 additionalparameters dealing with tunnel stability and supportrequirements (Bart o n et al., 1974): a) the mmmumunsupported span, b) the permanent roof support pressure;c) the bolt length.2.2.1. Case ExamplesWith the case history in mind, which is to be discussedin the following, a 4.75 m diameter tunnel was taken asa typical problem to be used for validation of the discon-Figure 6. Four UDEC d e b wirh difierent Qvalucr: model 1-Q=8.5;made1 2 - Q=4.l; madel 3 - Q=1.9; model 4 - Q=0.67
~~d.-pol.-naft. zb., Vol. 12, Zagreb, WOO.Barla, G., Bark M.: Continuum and discontinuurn modellingtinuurn modelling by the 2D Distinct Element codeUDEC (I t a s c a, 1996). The intent has been to investigatethe 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 discontinuities(S, = schistosity, J1, J2 joints) have beenintroduced with the parameters assigned so as to obtaina range of Q values from 8.5 for model 1 to 0.67for model4. For all the models the initial state of stress is assumedto be given by: ov (vertical stress) =16.2 MPa, oh (horizontalstress) = 4 MPa, which represent a gravity inducedstress state at a depth of about 600 m, with anassumed stress ratio (ado,) of 0.25. The joint spacing foreach system shown in Figure 6 is as follows:ModelSchistosityJOINT SPACING (m)For all the models the rock blocks are deformableblocks with the assumption that the intact rock (gneiss)is considered as an elasto-plastic material which followsthe Mohr-Coulomb yield criterion. The properties areassigned as follows:Young's modulus E =60 GPaPoisson's ratio v=0.25Cohesionc= 30 MPaFriction angle $=33"The discontinuities are assumed to be Mohr-Coulombjoints, i.e. elasto-perfectly plastic joints, with normal K,,and shear K, stiffness given as follows: K,, = 40 GPaIm,K, = 4 GPa/m. The cohesion is always considered to bezero, with the friction angle $ taken as 58", 38", 22' and11' respectively for models 1, 2, 3 and 4, for both theschistosity and joints.- Unsupported tunnelA first series of analyses was carried out in intrinsicconditions, i.e. the tunnel is always left unsupported,with the disturbed zone defined as follows (S he n a n dBarton, 1997):- failure zone, where loose rock blocks are falling intothe tunnel;- open zone, where joints open up;- shear zone, where joints experience a certain sheardisplacement (3 mm).The 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 is stable, whereas models 2 to4 exhibit progressively critical conditions; (2) the openand shear zones appear to grow as the rock mass qualitydecreases from model 1 to 4, in line with the behaviourin terms of failure zones, (3) the results obtained seemto agree with the estimated support categories shown inFigure 5, where only the tunnel simulated with model 1would require no support, and models 2 to 4 would needdifferent and progressively more severe support measures.Figure 8. Oprm zones around the tunnel fbr models I to 4Figure 9. Shear zones around the lunnel for model9 I to 4Figure 7. Yielded and loose blocks around fhe tunnel fw modelv 1 lo 4- Supported tunnelAs a direct consequence of the analyses describedabove and based upon the guidelines of Figure 5 in termsof support requirements, the following stabilizationmeasures were introduced in models 2 to 4.
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continuum and discontinuum modelling in tunnel engineering

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