## 2 Materials and Methods
In Figure 7, the 3D numerical model (complex model) is depicted showing the solid and contact elements and the smeared approach for reinforcing steel. The details of the 3D numerical model are presented in [PERSON] et al. [5]. Figure 6: One-dimensional nonlinear numerical model of a typical tunnel—the Botlek Railway Tunnel (BRT)—based on the Finite Element Method (FEM) using ANSYS [34]: (**a**) top extrude view; (**b**) lateral extrude view; (**c**) isometric view including extrude view. The mechanical properties of each model for BRT, including the experimental model (Exp model), are depicted in Table 3.  
It is possible to observe that the proposed model (1D model with coupling) does not include inelastic mechanical properties in the segments. In order to reduce the computational effort in the 3D model, the compressive damage was ignored because the main damage in the segments was caused by tensile stresses, as reported by [PERSON] et al. [2], [PERSON] et al. [5], [PERSON] et al. [12] and [PERSON] [33]. Figure 7: Three-dimensional nonlinear numerical model of a typical tunnel—the Botlek Railway Tunnel (BRT)—based on FEM using ANSYS [34]: (**a**) isometric view for segments; (**b**) isometric view for joints; (**c**) isometric view for segments and joints; (**d**) top view of the tunnel (reinforcing steel modeled as smeared approach). 40 times smaller than the complex model), and a large degree of insight in the structural behavior is quickly gathered with a minor error of 5% of the structural capacity given by 3D and experimental models. In Figure 8, it is possible to observe that the numerical models of single rings [2] were included (rings without coupling). The structural load capacity of these rings was approximately 80% of the value obtained with the experimental model and the practical model proposed in this study. For this reason, it is important to include the effect of the interaction between rings (coupled rings) due to the TBM effect [5]. Figure 9 shows the deformed configurations of the rings obtained from the experimental and practical numerical models. These are similar in both models, corresponding to Point B (ultimate deformation of the tunnel) of the ovalization load-deformation curves. According to [PERSON] [33], during the experiment, it was not noticed that the deformations of the upper and lower ring were different. However, in the proposed practical model, ring 1 and ring 3 were deformed almost exactly equally, which was logical due to the location of the segment joints of these two rings. The displacements generated in each numerical model for these two points (Point A and Point B) of the ovalization load-deformation curves are depicted in Figure 10. These displacements are very similar between both models. It should be noted that this is due to the longitudinal axial load given in the experiment (1400 kN) producing a \"low\" interaction between rings [5; 11]. In this case, the structural response depends more on the mechanical behavior of the segment and ring joints (moment-rotation and load-deformation behavior for the segment and ring joints, respectively) than the damage in the segments [5]. A practical numerical model that considers the behavior of the segments by means of an elastic material model and the joints using springs will produce a \"good\" estimation of the \"real\" behavior when a \"low\" interaction is produced due to the construction process of the TBM. Figure 9: Deformed configuration obtained from 1D numerical and experimental models. In Figure 11, additional results given by the 3D model are presented. The reinforcing bars of the flexural steel do not yield in Point A. After this point, the segment joints begin to open. In Point B, the reinforcing bars of ring 2 yield in the invert zone, because no joint is present in this location. However, in the other two rings, in the same zone, a yielding of the rebars does not occur due to the location of longitudinal joints. On the other hand, the damage of the reinforced concrete segments in Point A does not occur or is minor.