## 6 Interactions between Segments along the Longitudinal Direction
### Inward Radial Deflection Error  
In the inward radial deflection model, the maximum compression damage factor of the newly assembled segment is almost linearly related to the assembly error. When the first segment is assembled, the maximum damage to the segment will be transferred from both sides of the gasket of the segment to the inner edge of the liner as the deflection angle increases. The inward radial deflection of the segment will aggravate the inward deflection during the natural assembly of the segment, which makes the segment packer more likely to generate contact stress concentration. It is also the main reason for the sudden increase in the maximum compression damage factor. This situation is gradually disintegrated due to the support on both sides during the assembly process of the segment. It can be seen from the maximum damage position of the second and third segments (Table 4) that with the assembly of the segments, the maximum damage position of the segment is transferred to the contact between the adjacent segment and the gasket place. Although there will be extrusion between the segments, the longitudinal contact quality of the segments is better than that of the rear surface, and the rotation that occurs is also smaller. In the synchronous propulsion and assembly mode, the damage possibility and severity of the segment under the inward radial deflection error are evaluated by the compression damage factor. All simulations have reached the damage limit, and the maximum compression damage factor can reach 52%, as shown in Figures 13 and 14. The damage factor of 46% is marked by the dot line, so that the damage angle of the segment can be obtained intuitively. No matter where the initial segment is, the compression damage factor will form a certain mutation after a gentle rise to a certain deflection angle, which is especially obvious in the early stage of segment assembly. On the contrary, when the third segment is assembled, the compression damage factor of the segment will rise slowly and reach a certain limit. Compared with the initial position of the segment at the top and bottom, the effect of inward radial deflection on the lateral segment is smaller, and the damage growth of the segment is slower. When the segment reaches 1\({}^{\circ}\) deflection, the maximum damage to the segment is also smaller. The tensile damage factor of the segment undergoes little change in different positions and during the assembly process, and the peak value is 91.81%. The main tensile damage to the segment occurs at the symmetrical center of the jack, which is mainly caused by the transverse tensile stress caused by the thrust of the jack [39; 40]. Figure 13: Damage to a segment in the presence of inward deflection when the asymmetric error angle is 1\({}^{\circ}\): (**a**) first segment assembly (%); (**b**) second segment assembly (%); (**c**) third segment assembly (%). (Take the segment at the top as an example.) During assembly, the outer joint width of the segment will gradually increase with the maximum inward deflection of the segment. When the initial segment is at the top, the maximum joint of the segment is 10.44 mm, as shown in Figure 15. Similar to the changing trend in the compression damage factor, when the segment damage error changes abruptly, the maximum joint width of the segment increases sharply. The increase of the joint width means that the segment has a higher possibility of damage, which can be referred to as one of the most important sources of evidence when judging the quality of segment assembly in practical engineering. At the same time, the larger joint width will reduce the sealing performance of the gasket [41; 42]. While the joint width of the top segment will undergo a larger increase with greater assembly error, the segments at the other positions will gradually tend to slow down. Obviously, under the action of the larger jack, the joints of the segments will not grow all the time and will gradually stabilize when the error reaches a certain level.