Modelling Swelling Rock Behaviour in Tunnelling.pdf - Plaxis

TitleFoto by Christian AmmeringModelling Swelling Rock Behaviour in TunnellingBert Schädlich & Helmut F. Schweiger, Institute for Soil Mechanics and Foundation Engineering, Graz University of Technology, Graz, AustriaThomas Marcher, ILF Consulting Engineers, Innsbruck, AustriaAlthough a great amount of practical experience has been gained in the last decades, tunnel design in swellingrock is still a very challenging task, as the recent examples of the Engelbergtunnel in southern Germany and theChienbergtunnel in Switzerland demonstrate. Reliable prediction of swelling pressures and swelling deformationsespecially in anhydritic rock is extremely difficult due to the heterogeneity of the material and the complexity ofthe involved transport mechanisms. However, modern design codes and engineering practice demand capacitychecks for tunnel linings, which usually can only be provided by numerical analysis with an appropriate constitutivemodel. Such a constitutive swelling model, which adds swelling strains in dependence on the stress level andaccounts for the time dependent evolution of swelling, has been implemented for Plaxis. This article compares theresults of a numerical back analysis with this model to in-situ measurements, using swelling parameters derivedfrom laboratory swelling tests.rocks” are geomaterials which»“Swellingincrease in volume if water is allowedto infiltrate. The most prominent rock typesexhibiting swelling behaviour are certain typesof claystone and anhydrite-bearing rocks, whichcan be commonly found in northern Switzerlandand southern Germany. Tunnelling in suchmaterials is notoriously difficult: If a flexibleinvert lining is installed, large invert heaveevolves after tunnel excavation. In case thesedeformations are prevented by a rigid supportconcept, large swelling pressures may developat the tunnel lining. It is well known that swellingdeformations – at least in claystone – reducewith the logarithm of stress, and that swellingdeformations can be completely suppressed bysufficiently high pressure. The chemical processesin anhydrite swelling, on the other hand, arecompletely different, and the semi-logarithmicrelationship between swelling strains and stresslevel (Grob 1972) is not universally accepted forthese materials. Evolution of swelling with timein both claystone and anhydrite depends onthe availability of water, which is governed bythe permeability of the material, layering of thesubsoil and the amount of water recharge. Assome of these factors relate to characteristics ofthe specific boundary value problem rather thanthe material itself, parameters determining thetime-swell behaviour cannot be transferred fromlaboratory tests to large-scale problems.Constitutive modelThe constitutive model used in this paper hasbeen implemented by T. Benz (NTNU Norway) asa user-defined soil model for PLAXIS. The modelemploys four parameters for strength and stiffnessand three parameters for swelling. f’ and c’ arethe well-known Mohr-Coulomb friction angle andcohesion, E and n are the isotropic elastic Young’smodulus and Poisson’s ratio, respectively. Crossanisotropicelasticity can also be considered but isnot used in this study. The meaning of the swellingparameters is shown in Figure 1 and Figure 2. Themaximum swelling pressure s q0is the axial stressbeyond which no swelling occurs, the swellingpotential k qgives the inclination of the swellingcurve in semi-logarithmic scale and the parameterh qis related to the time until the final swellingstrain has developed (Wittke & Wittke 2005).Cross-anisotropic swelling can be considered inthe model, but again this feature is not used here.(1)If necessary the time-swell behaviour can be relatedto elastic and plastic volumetric strains, e velande vpl, by using parameters A eland A plto define thetime swelling parameter h q:Positive volumetric strains (loosening of thematerial) result in faster approach of the finalswelling strain, while negative volumetric strainsdelay or may even stop the evolution of the swellingstrains. This approach accounts for the dependencyof the swelling rate on the penetration rate of water.Construction of the PfändertunnelThe 6.7 km long first tube of the Pfaendertunnelnear Bregenz (Austria) was constructed in 1976-1980according to the principles of the New AustrianTunnelling method (NATM). While top headingand bench excavation were carried out withoutmajor difficulties, significant invert heave of upto 30 cm was observed after about 75% of thetunnel length was excavated. These observationslead to detailed laboratory investigations of theswelling characteristics of the Pfaenderstockmaterial, an extensive monitoring program and tothe installation of additional anchors in the tunnelinvert.(2)www.plaxis.nl l Spring issue 2013 l Plaxis Bulletin 5

Laboratory swelling testsThe Pfaenderstock consists of various layers ofsandstone, conglomerate, claystone and marl,which are summarized as upper freshwatermolasse. The marl (claystone) layers wereidentified as the rock type causing the swellingdue to their high content of Montmorillonite(Weiss et al. 1980). Czurda & Ginther (1983)distinguished between undisturbed molasse marl(series A, Figure 4) and the fault zone material(series B, Figure 5). Series A samples showedhigher swelling potential, but lower maximumswelling pressures than the samples of seriesB. This notable difference was attributed torelaxation and swelling of the series B samplesbefore the samples could be tested.For the back analysis two swelling parametersets are considered, which represent the upperand lower boundary of the test results. The timeswelling parameters A 0, A eland A plare calibratedto match the in situ time-swelling curve.Numerical model and material parametersThe 2D finite element model used in this studyis shown in Figure 6. Tunnel geometry and basicmaterial parameters of the marl layer (E = 2.5 GPa,f’ = 34°, c’ = 1000 kPa) have been taken from Johnet al. (2009). Tunnel overburden is ~200 m abovethe tunnel crown, which is representative of thecross section at km 5+373. Linear elastic plateelements are used for the shotcrete lining, with E =7.5 GPa for the young and E = 15 GPa for the curedshotcrete. The final concrete lining is modelledwith volume elements assuming linear elasticbehaviour and a stiffness of E = 30 GPa. The finallining thickness varies between 50 cm at the invertand 25 cm at the crown.Swelling parameters are listed in Table 1. Sets 1a,1b and 2a only employ A 0for the time dependencyof swelling, while in set 2b evolution of swellingwith time is entirely governed by elastic volumetricstrains.Fig. 1: Semi-logarithmic swelling law (Grob 1972)Figure 2: Influence of h qon evolution of swelling strainsFigure 3: Pfaendertunnel cross section 1st tube (after John & Pilser 2011)Figure 4: Swelling test results, series AFigure 5: Swelling test results, series B6 Plaxis Bulletin l Spring issue 2013 l www.plaxis.nl

Figure 6: Finite element model (dimensions in m)Figure 7: Development of invert heave with timeFigure 8: Profile of vertical displacements, a) numerical analysis at t = 7180 d, b) measurements km5+820 (after John 1982)Figure 9: Development of pressure on the lining (set 1b)Parameter Set 1a Set 1b Set 2a Set 2bSwelling potential k q[%] 3.0 3.0 0.75 0.75Max. swelling stress s q0[kPa] 1000 1500 4000 4000Table 1: Swelling parametersA 05.0e -3 2.5e -3 3.0e -3 0.0A el0.0 0.0 0.0 9.0A pl0.0 0.0 0.0 0.0Calculation phasesAfter top heading / invert excavation (assumingpre-relaxation factors of 75% and 37.5%,respectively), the concrete invert arch is installed.Swelling is confined in the model to an area of 15m x 15 m below the tunnel invert. After a swellingphase of 65 days, the final lining is activated,followed by another swelling phase of 115 days.John (1982) reported that the decision on invertanchoring and pre-stressing was based on theswell heave deformations observed up to thispoint. In the cross section considered here thisresulted in an anchor pattern of 2.2 m spacing.Evolution of invert heave with timeFigure 9 compares the time-swelling curvescalculated with the different parameter setswith the measured invert heave in km 5+373.The measurements plot close to a straightline in logarithmic time scale, which cannot bereproduced exactly by the exponential approachemployed in the model. The match with themeasured invert heave is, however, sufficient froma practical point of view.Set 1a delivers too little invert heave (10mm), andthe development of deformations completelystops after activating the prestressed anchors.Increasing the maximum swelling stress by 50%(set 1b) yields ~50% more deformation and abetter match with the measurements. While such asignificant influence may be expected, it should benoted that experimental results for these two setsplot so close to each other that either of the twoparameter sets appears justified (Figure 4).Surprisingly, sets 2a and 2b – which representmuch smaller free-swell deformations – delivermore invert heave than sets 1a and 1b. This is aresult of the higher maximum swelling stress insets 2a and 2b, which activates swelling in deeperrock layers, yet with a small swelling potential.Swelling deformations are thus more widelydistributed with set 2a and 2b.Modelling the evolution of swelling with timeentirely in dependence on elastic volumetricstrains (set 2b) results in a slightly more prolongedtime-swell-curve than using a constant value of A 0(set 2a). In set 2b the rate of swelling does not onlydecrease due to the convergence with the finalswelling strain, but also due to negative elasticvolumetric strains. The large positive volumetricstrains after tunnel excavation are graduallyreduced in the swelling phases by the increasingswelling pressure.www.plaxis.nl l Spring issue 2013 l Plaxis Bulletin 7

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