Numerical Back-analysis of In-situ Measurements - Plaxis

South Toulon Tube: Numerical Back-analysis of In-situ MeasurementsJ.P. Janin, H. Le Bissonnais, A. Guilloux, TERRASOL, Paris, France, D. Dias, University Joseph-Fourier, Grenoble, France, R. Kastner, LGCIE, INSA de Lyon, Lyon, France,F. Emeriault, INP, Grenoble, FranceFull face excavation with ground reinforcement has become a common technique to build large tunnels in soft rock or hardsoil. Nevertheless, at the design phase, it remains difficult to assess the effect of the different construction and reinforcementelements on the control of the ground movements and settlements. In order to improve the understanding of ground responseto this tunnelling method, a monitoring section has been installed during the construction of the south Toulon tunnel (France).An important database was obtained and subsequently used for numerical back-analysis. A 3D FE calculation (PLAXIS 3Dv.2010), modeling the real pre-reinforcements system and workflow steps, permitted to simulate the in situ measurements.»The south Toulon tunnel will connectmotorways A50 and A57 from Nice toMarseille. It is an urban shallow tunnel, 12 m indiameter and 1820 m in length, excavated throughvery difficult heterogeneous soils and with alimited overburden (maximum of about 35 m). Theconstruction method used is full face excavationand ground reinforcement ahead of the tunnelface by pipe umbrellas (long forepoling) andface bolting. The construction sequences andthe amount of reinforcement were continuouslyadapted to the overburden, the soil conditionsand the measured settlements (Janin et al [2011]).In addition to the regular settlement measures, aspecific monitoring zone was set up to improve theunderstanding of ground response and to collectprecise data for validating a 3D numerical model.The complex phenomenon of interaction betweenthe excavation process, the reinforcementsand the ground reaction demand in fact a 3Dapproach. In this paper, the numerical modelis described and the simulation is validated bycomparing it to in situ measurements.2 Presentation on the Analised SectionThe monitoring section is situated in “AlexandreIer” garden on the west side of Toulon at theexcavation progress PM 882. In this zone the coverdepth was about 25 m.extensometer on the tunnel axis and 3 surfacetarget prisms (X, Y, Z) close to the previousinstruments. In addition, 4 radial extensometers,6 vibrating wire strain gauges placed on the steelrib, 5 pressure cells and convergence targets wereinstalled from the tunnel.2.2 GeologyThe geological profile of the section has beendrawn (see Fig. 1) based on the boreholeinvestigations. They showed that the geologicalstratigraphy is generally horizontal and thedegree of alteration of the phyllitic bedrockis considerably high. Despite the variationsof materials characteristics (especially in thebedrock), average ground properties of thedifferent strata were proposed at the detaileddesign phase (see Table 1).2.3 Excavation methodThe south Toulon tunnel was excavated on thebasis of the so-called “ADECO-RS” methoddeveloped by Lunardi [2008]. According to thismethod, pipe umbrellas (6° or 14° of inclination)and horizontal face bolts were installed. Theexcavation process progressed by 1.5 m steps andafter each step one HEB 180 steel rib was installed.In this zone, the tunnel invert (HEB 220 + concrete)was realized with a distance to tunnel face ofabout 39 m.2.1 InstrumentationThe instruments set up in the analyzed sectionare presented in Figure 1. The instrumentationfrom the surface is composed of 2 inclinometerson both sides of the tunnel, one verticalFigure 1: Three-dimensional model10 Plaxis Bulletin l Spring issue 2013 l www.plaxis.nl

Depth (m) Soils g(kN/m 3 )E ref 50 = Eref oed(MPa)E ref ur = 3. E ref 50(MPa)c’ (kPa) j’ (°) y (°) v urK 00 to 3.5 Fill 19 1.6 4.8 2 20 0 0.2 0.53.5 to 5.9 Colluviums 20.8 40 120 10 30 0 0.2 0.5Below 5.9 Bedrock 24.2 240 720 40 25 0 0.2 1Table 1: Main geotechnical parametersSupport type Support description E (GPa) Thickness (m)Walls’ tunnel HEB 180 (spacing 1.5 m) + 25 cm shotcrete 13.5 0.25Tunnel invert HEB 220 (spacing 1.5 m) + 30 cm shotcrete 14 0.3Tunnel face 15 cm shotcrete 10 0.325 m. A three-dimensional non uniform mesh withsmaller elements around the excavation is used.Finally, the model contains 158000 tetrahedralelements and 247000 nodes. All movements arefixed at the bottom of the model and horizontaldisplacements are blocked in model’s lateralfaces.Table 2: Mechanical parameters of tunnel supportFigure 2: Geological section and instruments3 Three-dimentional Back-analisysA three-dimensional model was realized tosimulate the tunnel excavation process of thearea where the monitoring zone had been placed.The analysis was carried out by means of thethree-dimensional finite element code PLAXIS 3D(version 2010).3.1 GeometryConsidering the geometry symmetry, only halfof the entire domain is taken into account in theanalysis as shown in Fig. 2. The real shape ofToulon tunnel with a cross section area of 120 m 2 isimported from CAD. The tunnel is then modeledby extruding the surface in X direction. The tunneltemporary support and the pre-reinforcementare modeled and the process is explained in thefollowing paragraph.In order to avoid boundary effects, the extensionof the mesh is equal to 150 m in X and Y directionsand 70 m in Z direction. The cover depth is about3.2 Mechanical parameters and simulation of theexcavation processThe ground is represented by the non linearelasto-plastic HS model (Hardening Soil Model)implemented in the PLAXIS code. Hejazi [2008]showed, in a tunnel excavation study, that thismodel might produce ground deformationsthat better fit with in situ measurements thanusing the linear elastic/Mohr-Coulomb model.The geotechnical parameters considered in thesimulation are listed in Table 1. The initial stressfield is considered as isotropic (in conformity withthe studies previously realized on Toulon soils byConstantin [1988] and Dias [1999]).In the numerical model, the shotcrete at tunnelface, the excavation support and the tunnel invertare modeled by “plate” elements with a linearelastic behavior. The mechanical parameters aredefined in Table 2. The parameters of support andtunnel invert are determined by homogenizationbased on steel and shotcrete characteristicsand rib’s spacing. A rigid interface is consideredbetween the support and the ground.www.plaxis.nl l Spring issue 2013 l Plaxis Bulletin 11

South Toulon Tube: Numerical Back-analysis of In-situ MeasurementsThe calculation is carried out in drainedconditions. The tunnel excavation is simulated ina first stage by 10 steps, 3 meters long, followedby 60 steps with an excavation length of 1.5 m asdone in situ. In each phase, the tunnel lining isinstalled 1.5 m behind the tunnel face, on whichthe shotcrete application is simulated as well. Thetunnel invert is activated 39 m behind the tunnelface progress.The pre-reinforcements, i.e. the pipes constitutingthe long forepoling and the face bolts, aresimulated using “embedded pile” structures (seeFig. 3). Thanks to in situ pullout tests, a realisticlimit skin resistance could be introduced betweenthe piles and the soil. The maximum frictionresistance measured along the soil/bolt interfaceis equal to 135 kN/m.Figure 4 shows the main characteristics of the pre-reinforcement system considered in the numericalsimulation, based on works realized in the studiedzone.As far as the umbrella pre-support is concerned,13 autodrilling pipes (51/33 mm) were takeninto account and renewed every 9 m. The sameinclination of 6° has been kept all along the modelin order to simplify the meshing.As for the face bolts, a constant length of 18 mis considered. Besides, Dias and Kastner [2005]proved that the bolting system is characterizedby the global stiffness (E•S). Therefore, the samenumber of bolts (20) is kept all along the modelin order to simplify the meshing. The real boltingdensity, installed in situ, is simulated varyingproportionally the bolts’ modulus and the frictionresistance based on the material characteristicslisted in Table 3.4 Comparisons Between Numerical Simulationand MeasurementsFigure 5a shows the settlements of differentsurface points, placed directly above the tunnelaxis in the analyzed zone, against their distancefrom the tunnel face. The excavation started toinfluence settlements more or less 30 m aheadof the tunnel face. Afterwards, settlementsaccelerated and finally reach a threshold 50m behind the tunnel face with a settlement ofaround 20 mm. The progression of settlementsobtained with the numerical calculation fits withthe measurements evolution. Similarly, threedimensionalmodeling seems to well represent theshape of the transverse settlement trough both interms of maximum settlement and trough width(see Fig. 5b).The final measurements of inclinometermovements in the monitoring section planeSteel boltsFibreglass boltsModulus E (GPa) 210 40Cross section A (m 2 ) 0.488 10 -3 0.8 10 -3Moment of inertia I (m 4 ) 0.0327 10 -6 ~ 0Table 3: Face bolts characteristicsFigure 3: Umbrella forepoling and face bolts modeledwith embedded pilesFigure 4: Simulation of pre-reinforcements in the numerical modelFigure 5: Comparison between in situ measurements and 3D simulation - Settlement evolution against tunnel face advance (a) and transverse settlement trough (b)12 Plaxis Bulletin l Spring issue 2013 l www.plaxis.nl