## 5 Conclusions  
This study conducted a comprehensive numerical investigation on the torsional shear deformation characteristics of segment joints, which is induced by the excessive construction torque during TBM tunneling. To achieve this, a refined finite element model of the segment joints was developed using finite element simulation techniques, incorporating factors such as joint construction, mortise and tenon elements, connecting bolts, and reinforcement. The development process of the torsional shear resistance at the segment joints under varying axial forces, for both the structures with and without mortise and tenon, were revealed. In addition, the failure modes of bolts and the damage characteristics of the segment concrete under torsional shear deformation were analyzed. The main conclusions from this study are as follows:  
1. The development of torsional shear deformation of segment circumferential joints consists of three stages: development of the friction at the segment interface (Stage I: 0\({}^{\circ}\) < \(\theta\) < 0.03\({}^{\circ}\)), development of the bolt force (Stage II: 0.03\({}^{\circ}\) < \(\theta\) < 0.09\({}^{\circ}\)), and development of the mortise and tenon force (Stage III: \(\theta\) > 0.09\({}^{\circ}\)). Under low axial force conditions, the contributions of the bolts and the mortise and tenon to improving the torsional shear resistance are more significant, while at high axial forces, their contributions are relatively small. When the axial force is 0 kN, compared to the  
Figure 16: Distribution of compressive damage in segment concrete. (**a**) \(N\) = 1000 kN; (**b**) \(N\) = 2000 kN; (**c**) \(N\) = 3000 kN; (**d**) \(N\) = 4000 kN. friction loading stage (Stage I), the torsional shear resistance of the segmental joint increases by 354.73% in the bolt force stage and 70.22% in the mortise and tenon force stage. When the axial force is 1000 kN, the corresponding increases are 47.87% and 22.17%, respectively. When the axial force is 2000 kN, they are 22.58% and 14.27%, respectively. When the axial force is 3000 kN, they are 13.23% and 8.49%, respectively. When the axial force is 4000 kN, they are 8.12% and 6.12%, respectively. It is noteworthy that axial force is the primary factor in enhancing the torsional shear resistance of the segmental joints. 2. During the development of torsional shear deformation of segment circumferential joints, the bolts come into contact and compress against the walls of the segment bolt holes, leading to the development of shear deformation. When the rotation angle exceeds 0.045\({}^{\circ}\), the bolt stress reaches the yield strength. In the working condition, when the rotation angle increases from 0.04\({}^{\circ}\) to 0.045\({}^{\circ}\), the bolt stress rapidly rises from approximately 850 MPa to 900 MPa. Subsequently, when the rotation angle is further increased, the bolts begin to yield and experience local failure. Therefore, to prevent shear failure of the bolts, it is recommended that the segment's rotation angle be maintained at less than 0.045\({}^{\circ}\) in practical engineering applications. 3. Under the torsional shear deformation, concrete cracking tends to occur around the mortise and tenon and bolt holes. Specifically, cracks in the tenons are primarily distributed near the compression side, while cracks around the bolt holes and in the mortises are mainly located on the non-compressed side, extending toward both the outer and inner arc surfaces of the segment. And concrete crushing is concentrated around the bolt holes and mortise and tenon. Moreover, under significant torsional shear deformation, the tenons are completely crushed, while the mortises experience crushing only on the compressed side. 4. This study investigates the characteristics of large torque generation during TBM construction and explores the torsional shear deformation behavior of circumferential segment joints. The research takes into account the design considerations of segment joints in real-world shield tunnel projects.