continuum and discontinuum modelling in tunnel engineering

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Rud.-geol.-naft. zb., Vol. 12, Zagreb, 2000.54 Burla, G., Burlu M.: Continuum and discontinuurn modellingtigated by adopting discontinuous models, with the 2Ddistinct element code, UDEC (I t a s c a, 1996). The rockmass surrounding the tunnel' was represented by twodiscontinuous models as follows.Figure 19. Computed ykldedwnes around the tunnel and dejormed meshusing* elustic-brittle-phstic coastitutive model3.6.1. Deterministic modelThe rock mass was considered to be intercepted bythree sets of joints, and foliation. Different spacing,degree of persistence and shear strength properties wereintroduced in the model so as to simulate the 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 whichfollows Mohr-Coulomb criterion. The properties of rockblocks and joints are listed below:MaterialProperties(*)Zone (Figure 8 and 10)Em .tGPa]The analyses were carried out with the same assumptionsgiven above for the material and joint properties vm [-Iand the in situ state of stress. The results obtained aregiven in Figure 20 by showing the plot of the yielded c [MPalzones around the tunnel and the deformed mesh.4 r7(*> c = cohesion: &I = friction angle: E, = rock mass\ I ? 0 " , .adeformation modulus; v, = Poisson's ratio.JointProperties(*)1K,, [GPa/ml 40Ks [GPa/ml 4c [MPa] 0.1+ r"l 33JointZone (Figure 8 and 10) (Figure 8and 10)(*) K,,, K, = normal and shear stiffness; c = jointcohesion; $ = joint friction angle.Figure 20. Compufedyieldedzone.s uround the tunnel and deformed meshusing the elastic-hriftle-plasli con.$titutive model for two po,~siblegeologicul condilionv along the tunnel aris3.6. Discontinuum modellingWith the understanding that discontinuities (majordiscontinuities and jointing) play a key role in the developmentof tunnel instability, the problem was also inves-3.6.2. Discrete Feature Nefwork (DFN) modelA Discrete Feature Network model was also createdby using the procedures implemented in the FracMancode (Dershowitz et al.. 1995). The results ofgeologic mapping on the right wall of ihe tunnel formedthe basis for defining; the input data in terms of orientation,size and degree-of fracturing for the ioint sets J1.52and ~3 a, b. The& were superim~osed wiih foliation anddiscrete features represented by the two sub-paralleldiscontinuities described above. The 3D volume realizedin this way is shown in Figure 22, where also shown is theplot of the joint sets given with the FracMan code.The UDEC model was obtained by taking a crosssection orthogonal to the tunnel axis through the 3DD m volume of Figure 22. This network of 2D fracturesis not directly amenable to UDEC analysis as the fratturesneed to be well connected and no isolated fracturescan be handled by the code. At the same time, it wasnecessary to cross-validate the model against the rockmass conditions around the tunnel. This was carried outby increasing the block size in the original 2D networkmodel both at the crown and on the left wall, to account
~"d.-geol.-naft. zb., Vol. 12, Zagreb, 2000.Barla, G., Barla M.: Continuum and discontinuum modelling 55Figure 21. Detail of UDEC &termhistic model showing regi~n,~ withdifferent material and joint properiiesfor the generally better rock mass conditions in thesezones.A random process which cancels the fracture tracesexceeding a given limit-length fixed was used in conjunctionwith the Set edge command which is available withthe UDEC code. A typical model finally developed isshown in Figure 23. As for the deterministic modeldescribed above, the joints were assumed to behave asMohr-Coulomb joints and the blocks were treated as anelasto-plastic material. The input data are the same aslisted above and shown in Figure 21.TUNNEL FACEFigure 22.30 Dkcrete Feature Network model created by the Frac-Mancode with plot ofjoint sets. This is typical for rock conditions onfhe rigk wall3.6.3. ResultsFor both the deterministic and DFN models the samestress conditions as assumed for 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 the discontinuum approach, thecalculations were carried to simulate tunnel excavation asfor the finite element models by using stress boundaryconditions. Also, no account was taken for the water pressuredistributed around the tunnel. The main interest wasposed on the yield zones, as shown by blocks which arefailing, and on shear displacements induced along joints(Figure 24). Attention was also paid to the pattern of blockmovements at the right wall (Figure 25).The results obtained show that both the deterministicand DFN models capture well the overstressing conditionsand block movements of right wall. As for theelastic-brittle-plastic model which accounts for the presenceof the two sub- arallel discontinuities, the deepeningof breakout on t l!e right wall is well reproduced withthe discontinuum approach (compare Figure 19 withFigure 24). However, in the latter case (Figure 24) nosignificant instability is seen to develop at the left wall,unlike the continuum approach (Figure 19). The similarityis evident with the actual conditions in the tunnel,where the TBM jammed because of instability and blockmovement at the right wall (Figures 14 and 15).The continuum ap roach appears to capture some ofthe adverse factors w E ich were significant in the instabilityconditions that developed during TBM excavation:- the elastic-plastic-brittle behaviour of rock material,- the highly anisotropic stress regime with a very lowstress ratio,- the presence of unfavourable dominant discontinuitiesat the right wall.In comparison, the discontinuum approach shows in aremarkable manner the block movement developing onthe right wall, whereas the tunnel remains stable alongthe periphery away from the fault zone at the crown andright wall.4. ConclusionsModern numerical modelling methods by the use ofeither the equivalent continuum or discontinuum approachhave been discussed by underlying some of the fundamentalconcepts and guidelines, when investigating tunnelproblems at the design analysis stage. With reference tomodelling in engineering practice, the interest has been
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continuum and discontinuum modelling in tunnel engineering

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