Modelling Swelling Rock Behaviour in Tunnelling.pdf - Plaxis

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Modelling Swelling Rock Behaviour in TunnellingFigure 10: Variation of maximum swelling stressFigure 11: Variation of time swelling parameters (set 1b)Figure 12: Variation of rock stiffness (set 1b)Figure 13: Variation of stress pre-relaxationDistribution of swelling strains over depthThe proportion of the rock mass which is affectedby swelling depends primarily on the maximumswelling stress. For set 1b (s q0= 1500 kPa) theswelling zone is confined to about 2 m below thetunnel invert, which matches well with the slidingmicrometer measurements in the neighbouringcross section km 5+820 (Figure 8). The swellingzone with set 2a (s q0= 4000 kPa) is much deeperdue to the higher maximum swelling pressure,even though similar invert heave is obtained withboth parameter sets. These results indicate thatthe maximum in situ swelling pressure is ratherin the range of 1000-2000 kPa than close to thein-situ stresses.Swelling pressureFigure 9 shows the distribution of swellingpressure on the tunnel invert lining for differentstages in time for parameter set 1b. Thecircumferential distance L is measured from thetunnel invert, such that L = 0 m is directly at theinvert and L = 5 m is the end of the swelling area.No pressure measurements are available.Due to the stiffer support provided to the tunnellining at the sides of the tunnel, the maximumswelling pressure does not occur at the tunnelinvert but at a distance of ~3.8 m.Anchor prestressing increases the normal stresson the lining by about 90 kPa. The difference tothe distributed prestressing force of (0.8*640kN / 2.2 m / 2.2. m) = 106 kN/m 2 is a result of thealready closed final lining, which distributes partof the applied load in circumferential direction.Comparing the increase in pressure to the swellingline of set 1b at 200-300 kPa (Figure 4) explains thelimited influence of prestressing in the numericalcalculations. Even though anchor prestressingincreases the pressure by ~45%, reduction of finalswelling strain is only about 18% due to the semilogarithmicswelling law. Additionally, the effectof prestressing diminishes rapidly with increasingdistance to the tunnel, and the deeper rock layersremain virtually unaffected.Variation of maximum swelling pressureThe calculated invert heave is notably sensitiveto the maximum swelling pressure s q0assumedin the numerical analysis. As the variation of thisparameter in the laboratory swelling tests israther large– albeit concealed by the logarithmicstress scale – s q0has been varied from 500 kPato 2000 kPa (A 0= 2.5e -3 ). Results indicate a linearincrease of invert heave with s q0(Figure 10). Thisis primarily the result of the increasing depth ofthe swelling zone below the tunnel invert (Figure8), and not so much due to higher swelling strainsdirectly underneath the tunnel invert.Influence of other material parametersThe influence of other material parameters onswelling deformations is limited. As expected, thetime swelling parameter A 0has a notable influenceon the evolution of swelling deformations, butnot on final deformations (Figure 11). Varying theelastic rock stiffness had virtually no effect onswelling deformations after tunnel excavation(Figure 12), but naturally changed deformationsduring tunnel excavation. Variation of the 2Dpre-relaxation factors – which in most practicalcases are an educated guess rather than athoroughly derived parameter – also had nonotably influence on swelling deformation (Figure13). As no temporary invert lining was installedafter top heading excavation, stresses in the rockmass at the tunnel invert drop to ~0 during tunnelexcavation, independent of the pre-relaxationfactors applied in the excavation phases.8 Plaxis Bulletin l Spring issue 2013 l www.plaxis.nl
Concluding remarksThis article presented the results of a backanalysis of measured swelling deformations in thePfaendertunnel (Austria). A constitutive modelbased on Grob’s swelling law and exponentialconvergence with final swelling strains over timewas used for the numerical calculations. Inputswelling parameters were derived from laboratoryswelling tests. Due to the large variation oflaboratory test results, the sensitivity of modelpredictions on the input swelling parameters wasinvestigated.Different sets of swelling potential k qandmaximum swelling stress s q0delivered verysimilar swelling deformations at the tunnellining, as increasing s q0is roughly equivalentto increasing k q. However, good match withthe measured displacement profile below thetunnel invert was only obtained with s q0= 1500kPa, which represents the upper edge of theexperimental results on undisturbed molassemarl. Using higher values of s q0(and lower valuesof k q) delivers too large swelling zones. The invertheave measurements plot close to a straight linein logarithmic time scale, which cannot be exactlyreproduced by the exponential approach of theconstitutive model. The match with the measuredevolution of swelling, however, is sufficient from apractical point of view.References• Czurda, K. A., and Ginther, G. (1983) “Quellverhaltender Molassemergel im Pfänderstock beiBregenz, Österreich“, Mitt. österr. geolog. Ges.,76, pp. 141-160.• Grob, H. (1972) “Schwelldruck im Belchentunnel“,Proc. Int. Symp. für Untertagebau, Luzern,pp. 99-119.• John, M. (1982) “Anwendung der neuen österreichischenTunnelbauweise bei quellendemGebirge im Pfändertunnel“ Proc. of the 31stGeomechanik Kolloquium, Salzburg, Austria.• John, M., Marcher, T., Pilser, G., and Alber, O.(2009) “Considerations of swelling for the 2ndbore of the Pfändertunnel”, Proc. of the WorldTunnel Congress 2009, Budapest, Hungary, pp.50-61.• John, M., and Pilser, G. (2011) “Criteria forselecting a tunnelling method using the firstand the second tube of the Pfänder tunnel asexample”, Geomechanics and Tunnelling, 4(11),pp. 527-533.• Weiss, E. H., Müller, H. M., Riedmüller, G.,and Schwaighofer, B. (1980) “Zum Problemquellfähiger Gesteine im Tunnelbau“, Geolog.Paläont. Mitt. Innsbruck, 10(5), pp. 207-210.• Wittke, W., and Wittke, M. (2005) “Design, constructionand supervision of tunnels in swellingrock”, Proc. 31st ITA World Tunnelling Congress2005, pp. 1173-1178.www.plaxis.nl l Spring issue 2013 l Plaxis Bulletin 9
Page 1 and 2: TitleFoto by Christian AmmeringMode
Page 3: Figure 6: Finite element model (dim

Modelling Swelling Rock Behaviour in Tunnelling.pdf - Plaxis

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