## 1 Introduction
In [PERSON] and [PERSON] [28], full-scale tests consisting of segments from the Botlek Railway Tunnel were carried out at the Stevin II Laboratory of the Delft University of Technology. The set-up contained three segmental reinforced concrete rings (lower ring or ring 1, central ring or ring 2 and upper ring or ring 3), with a width of 1.5 m, situated in a vertical position, ignoring the effect of gravity (Figure 2a). Each segmental ring was composed of seven reinforced concrete segments and a keystone (Figure 2a) with a system radius of 4.525 mm and a segment thickness of 400 mm [29]. Longitudinal joints were placed in a stretched bond alignment, resulting in segment joints in the same circumferential location in the upper and lower ring. It should be noted that the three keystones were situated differently in each ring. In the segment joints, no packing material was used (concrete-to-concrete surface contact), while in the ring joints, plywood sheets were used as a packing material. To consider the TBM effect, which produces a coupling effect between rings, 14 jacks were located on top of the segments in the upper ring (Figure 2a), while for representing the water and soil pressures on the segmental rings, 28 jacks per ring were situated on the experimental model (Figure 2b). Three load steps were developed in this experimental test in order to consider the effects during the construction process of the segmental tunnel and due to the soil and water pressures originating in soft soil. In the first load step, we considered a service thrust load given by the TBM (Figure 2a) of 1400 kN  
Figure 2: Experimental tests for the Botlek Railway Tunnel (BRT) carried out at the Stevin Laboratory of Delft University of Technology: (**a**) axial and radial loads created by 14 and 28 jacks per ring, respectively; (**b**) radial jacks applied on the upper ring. (100 kN/jack). It should be noted that, in the experimental model, four steel plates were situated allowing radial translations and restraining the tangential movements of the model, avoiding rigid body rotation. In the second load step, a uniform radial load (Figure 3) of a 225 kN/jack was applied. Finally, in the last load step, an ovalization load was applied (Figure 3), which was increased until the failure (Ultimate State Limit) of the rings, achieving a value of 23.5 kN/jack, according to this equation:  
\[p=q-\Delta q\ Cos(2\varphi) \tag{1}\]  
To represent the structural behavior of this type of structure, there are some simplified models [2; 19] which have been used by engineers in practice to analyze and design segmental tunnels; some of these include beam elements to represent the segments and springs to simulate the nonlinearity of the joints, reducing the computational effort spent in two or three-dimensional models. In general, these simplified models do not consider the coupling effect between rings created by the construction process of the TBM method. This effect modifies the structural response in the lining, increasing its structural capacity as this coupling increases [5]. Thus, there are few research works which include (lab-based) experimental or simplified numerical models that take into account the interaction between rings for the structural analysis of segmental tunnels. This parameter is important to determine the \"real\" structural load capacity of a concrete segmental lining, enhance its structural design and also reduce costs, while a \"rational\" structural design will be able to reduce materials--e.g., concrete volume--by optimizing transversal sections, reducing manufacturing costs and achieving more environmentally friendly designs by reducing CO\({}_{2}\) emissions. This sustainability philosophy has gained increased traction in the construction of segmental tunnels with the incorporation of such new technologies as geopolymers [30; 31] in some projects (geopolymer concrete); e.g., according to [PERSON] et al.