## 4 Torsional Shear Deformation Characteristics of Segment Joints
### Load-Bearing Performance of the Segment Joints  
Figure 11 presents the distribution of the rotational angle at the segmental joint (C10), where \(\theta\) represents the rotational angle about the center of the segment. A counterclockwise rotation is considered positive. The boundary conditions and loading methods established in this study are designed to simulate the torsional-shear deformation of the segmental joint, thereby enabling an analysis of its torsional-shear bearing capacity. As shown in Figure 11, the rotational deformation of the segmental joint is predominantly concentrated in the movable segment, which undergoes uniform rotation. In contrast, the fixed segment exhibits no rotational deformation. The anchoring section of the bolts, however, experiences rotational deformation in unison with the movable segment. Upon significant rotational deformation of the bolt, the contact region between the bolt and the bolt hole is activated. This contact is constrained by the fixed segment, inducing torsional shear deformation in the bolt. As the rotation of the movable segment increases, the mortise and tenon joint also comes into contact, leading to torsional shear deformation of the tenon. Figure 12 illustrates the load-displacement relationships for the segment joints. As shown in the figure, the force transmission process during torsional shear deformation of the segment circumferential joints occurs in three distinct stages: development of the segment interface friction (Stage I), development of the bolt force (Stage II), and development of the mortise and tenon force (Stage III). Notably, during the segment interface friction and bolt force stages, the load-bearing performance is similar for joints with and without the \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{
\begin{tabular}{c} **Joint** \\ **Configuration** \\ \end{tabular} } & \multicolumn{2}{c}{**Pretightening**} & \multirow{2}{*}{**Axial Force (kN)**} \\ \cline{1-1}  & & & 0 \\  & C2 & & 1000 \\  & C3 & Non-mortise and & & 1000 \\  & C4 & tenon (NMT) & 95.96 & 2000 \\  & C5 & & & 4000 \\ \hline  & C6 & & & 0 \\  & C7 & Mortise and tenon & & 1000 \\  & C8 & (MT) & 95.96 & 2000 \\  & C9 & & & 3000 \\  & C10 & & & 4000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Computational cases. Figure 11: Rotational angle distribution of the segment joint. mortise and tenon. However, in the final stage, the presence of the mortise and tenon significantly enhances shear resistance. The first stage (Stage I) corresponds to the segment interface friction force stage (\(0^{\circ}<\theta<0.03^{\circ}\)). During this stage, neither the bolts nor the mortise and tenon participate in force transmission due to gaps between the bolts and their holes, as well as gaps within the mortise and tenon. Therefore, the primary source of torsional shear resistance is the friction at the segment interface. An increase in the applied axial force during this stage enhances the segments' resistance to torsional shear. For instance, in the absence of axial force, the maximum tangential force is 20.58 kN. In comparison, axial forces of 1000 kN, 2000 kN, 3000 kN, and 4000 kN result in an increase in the tangential force by 487.85%, 962.88%, 1416.38%, and 1940.62%, respectively. This highlights the crucial role of axial force in improving the initial frictional resistance. The second stage is the bolt force stage (\(0.03^{\circ}<\theta<0.09^{\circ}\)). Once the rotational angle exceeds \(0.03^{\circ}\), contact is established between the bolts and the bolt holes, enabling the bolts to begin resisting shear forces. The effectiveness of the bolts in resisting shear is more pronounced under lower axial forces. As the axial force increases, the relative contribution of the bolts diminishes. Specifically, under axial forces of 0 kN, 1000 kN, 2000 kN, 3000 kN, and 4000 kN, the maximum tangential forces increase by 354.73%, 47.87%, 22.58%, 13.23%, and 8.12%, respectively.