## 3 Research Methods and Parameters
### General Description of the Models  
The tunnel segment model is established based on the airport connecting line (west section) project of the Shanghai metro line, as shown in Figure 4. The study focuses on the stress between the assembled segment and the completed lining, so the model can be simplified as the interactive simulation of the assembled segment and the adjacent ring contact segment. Some minor details are ignored in modellings, such as bolt holes, wedges of segments, grooves, and bolts. Setting springs between the newly assembled segments  
Figure 3: Steps of jack jacking in synchronous propulsion and assembly mode: (**a**) The working condition of the jack when the first segment is assembled; (**b**) The working condition of the jack when the second segment is assembled.  
simulates the role of bolts between segments. In the assembly, the default assembled segments experience no assembly errors, and the assembly of the segments will follow the longitudinal seam bonding principle, that is, default perfect bonding between adjacent segments of the same ring segment. The geometric parameters and mesh properties of the segment are shown in Tables 1 and 2.  
The segments, packers, and gaskets are modeled with first-order hexahedral elements, which can reduce the calculation time of the 3D numerical model and ensure the accuracy of the model calculation. To reflect the inelastic behavior of concrete, the finite element software adopts the isotropic elastic damage and tensile-compression plasticity theory. In order to show the elastic-plastic results of concrete under compression, the isotropic elastic damage and tensile-compression plasticity theory are used in the model. The Mooney-Rivlin strain potential energy model [30; 31] is used for the gasket and packer. The physical parameters of the materials are shown in Table 3.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Input Parameters** & **Value** \\ \hline Tunnel radius (m) & 13.6 \\ Standard segment thickness (mm) & 550 \\ Length of standard segment (m) & 2.03 \\ Angle of standard segment (\({}^{\circ}\)) & 42.35 \\ No. of gasket pairs for each segment (-) & 1 \\ No. of packer pairs for each segment (-) & 1 \\ Gasket depth and thickness (mm) & 70 and 10 \\ Packer depth and thickness (mm) & 300 and 5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Input geometrical parameters for the finite element models.  
Figure 4: Geometry and mesh of finite element models: (**a**) The location of the butyronitrile cork packer and elastic gasket; (**b**) Position of longitudinal loads acting; (**c**) Mesh of standard segments; (**d**) Description of segment orientation.  
When the jack acts on the segment, the segment has been fixed at the assembly position by the robotic arm, and the gasket contacts with the adjacent segment. In the simulation, the default gasket will not have relative displacement, and the gasket is fixed with two adjacent segments by binding. The hard contact relationship is adopted between the assembled segments to minimize the relative positional movement between them. One side of the packer is bound to the new assembly ring. The penalty function is used to simulate the finite sliding of circumferential gasket-segment and segment-segment surface contact. Based on the shear stiffness test of the circular tunnel joint [32], the friction coefficient between fine concrete and liner can be taken as 0.5.