## 2 Materials and Methods  
As mentioned in Section 1, the Botlek Railway Tunnel (BRT) was considered to perform the practical numerical model due to the experimental results gathered in this tunnel by using (lab-based) experimental tests according to [PERSON] and [PERSON] [28] and [PERSON] [33]. These full-scale laboratory tests contributed towards a better understanding of the structural behavior and failure mechanisms of a segmental lining under an Ultimate Limit State (ULS). This tunnel was built in soft soil; according to [PERSON] [17], the height of the saturated soil and height of the unsaturated soil were 22.7 and 2.3 m, respectively. The specific weights of saturated and unsaturated soil were \(18\times 10^{-6}\) and \(16\times 10^{-6}\) N/mm\({}^{3}\), respectively. The elasticity modulus of soil was assumed to be 38.0 MPa. However, to simulate the soil and water pressures on the experimental model tested at the Stevin II Laboratory of the Delft University of Technology, including the effect of the longitudinal axial load created by its construction process, a steel frame with an external diameter of 15.7 m was designed, and this provided the reaction forces of the radial hydraulic jacks. These radial jacks (Figure 2b) were used to simulate the water and soil pressures, installing 28 jacks per ring with a capacity of 850 kN each (84 jacks in total, applying a uniform radial load of 225 kN/jack), considering the load configuration described in Section 1 (Figure 3 and Equation (1)) until the failure of the experimental model (ovalization load of 23.5 kN/jack). This steel frame was designed for stiffness rather than for strength to obtain a similar experimental model and frame displacements [29]. On the other hand, to simulate the longitudinal axial load induced by TBM, 14 jacks with a capacity of 5000 kN each were installed. With this full-scale test, a validation of the numerical results of the proposed practical model was carried out and is presented in Section 3. Furthermore, a comparison with another numerical model, the 3D numerical model, was performed. In Table 1, the geometrical properties are depicted, and in Figure 4, the details of the locations of the segment joints of the three rings and their dimensions are depicted. \begin{table}
\begin{tabular}{c c} \hline \hline
**Geometrical Properties** & **Value** \\ \hline Number of segments & 7 + keystone \\ Internal diameter & 8650 mm \\ Segment thickness & 400 mm \\ Segment width & 1500 mm \\ Segment joint thickness & 170 mm \\ Segment joint width & 1500 mm \\ Relative thickness & 0.43 \\ Slenderness ratio & 21.63 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Geometrical properties of the experimental model of the Botlek Railway Tunnel. The commercial finite element package ANSYS [34] was used to create the proposed numerical model of a typical segmental tunnel: the study case of the BRT tunnel. This model consisted of a one-dimensional model (1D model) composed by beam elements to represent the segments with elastic-linear behavior identified as BEAM188. It should be noted that this beam element is based on Timoshenko beam theory. Consequently, the shear deformation effects were included, while the longitudinal joints were modeled by using inelastic rotational springs, identified as MPC184, by means of the moment-rotation equation proposed by [PERSON] et al. [2]. The circumferential joints were represented by elastic linear springs, identified as COMBIN14. In Figure 5, the modeling strategy used to represent the experimental (lab-based) research performed by [PERSON] and [PERSON] [28] and by [PERSON] [33] is depicted. Figure 4: Botlek Railway Tunnel (BRT): (**a**) longitudinal joint, (**b**) location of longitudinal joints in three rings in the (lab-based) experimental test. When the moment-rotation relations used to represent the mechanical behavior of segment joints consider the axial load at the joint as a constant value, it is necessary to make a series of iterations during the analysis to determine the structural response of the lining.