## 5 Conclusions
The authors express their gratitude to Ningbo Rail Transit Group Co. Ltd. for the cooperation and support in the research. The authors declare no conflict of interest. The joint specimens used in the bending moment resistance experiments are full-scale and specifically cast for the joint experiments. As shown in Figure 11, the joint specimens are linear, rather than curved segments in order to get precise bending moment values, since according to [PERSON] et al. (2018), the mechanics in the joint of curved and linear lining segments can be considered equal. A specimen is composed of two segments connected by two pairs of cast iron embedded parts (Figure 12). The size of each segment is \(1250\times 1200\times 450\) mm. Four 6.8-M33 short straight bolts connect the cast iron parts. The ends of the segments are put into steel loading supports, and the gaps are filled with steel plates to ensure the segments are tied to the loading supports. A set of horizontal hinged jacks on the right side provide the axial force through pushing on the loading supports. A steel roller constrains the displacement of the left loading support, but the rotational movement is allowed. Two bottom rollers under the loading supports only balance the vertical force and allow the supports to rotate freely. The bending moment is exerted through a vertical jack and a set of distribution beams. The horizontal jacks and vertical jacks provide axial force N and vertical load P. P\({}_{\rm c}\) is the reaction force from the loading support and is equal to the sum of the vertical load P and the dead weight G. The distances between different loads are known, and thus, the bending moment at the joint can be calculated as shown in Figure 10. The axial force N and vertical load P can be adjusted through an electro-hydraulic servo loading system to make the internal forces in the joints equal to target values. A refined nonlinear 3D finite element model is used to obtain the joint's deformation and provide load dependent stiffness values needed in the proposed quasi-rectangular tunnel lining numerical model. An ABAQUS (2018) 3D model of a linear segment including all geometrical details is created. The tested segment is shown in Figure 11. Considering the symmetry of the specimen in the numerical model, only 1/2 of one joint segment is modelled to save calculation time. Half of the concrete segment, a single cast iron embedded part, two bolts, and two bolting pads are constructed as shown in Figure 11. Symmetric displacement constraints are applied to consider the other half of the concrete segment. The other segment is modelled by a symmetry condition represented by a rigid plate and contact conditions allowing for separation as shown in Figure 11. The reinforcement cage is also taken into account in the model. Due to the complexity and irregularity of the embedded parts and geometric details, 280,000 elements are meshed. The fine mesh is targeted at the joint section and the embedded part with the finest size of 7 mm while the coarse mesh is at the far end of the specimen. For the concrete, the concrete damage plasticity model is used, while for the steel a multi-linear elastoplastic model is used. Further information about the FE model and the comparative results can be found in reference [33]. Figure 10: View of specimen and loading device for bending moment resistance experiment. Figure 11: Illustration of bending moment calculation. Appendix B Full-scale shear resistance experiments are carried out to retrieve the joint's shear stiffness under different compressive forces as shown in Figure A4. A tested specimen is composed of 3 segments. The ends of the segments are clamped by steel loading supports, and a set of horizontal jacks on the right side exert compressive forces. Two bottom rollers under the loading supports only sustain the vertical force for balancing the force from the vertical jack. The vertical jacks produce shear forces at the two joints.