Numerical Back-analysis of In-situ Measurements - Plaxis

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