## 5 Interactions between Segments along the Circumference
### The Segment at the Top  
When the initial segment is assembled on top of the tunnel, the segment will rotate inward. The main reason for the rotation of the segments concerns the packer and gaskets between the segments. The jack thrust in the synchronous propulsion and assembly mode will make the segment fit as close to the ring segment as possible, but the unevenness between segments makes the segment and segment contact form a deep beam. It is worth noting that, at this time, the deformation of the inner and outer sides of the packer and the gasket is different, and the inner side is deformed more seriously than the outer side. When the first segment is assembled, the maximum rotation of the front of the segment is 9 mm, and the front surface rotates greatly as a whole under the action of the jack. At this time, the segment rotates around the two sides of the packer. When the segment is at the top, gravity further increases the inward rotation. When the second segment is assembled, since the support of the segment has been assembled, the rotation of the connecting part of the segment is significantly reduced. There is a certain extrusion between adjacent segments, mainly at the contact of the front of the segment, so the rotation of the free side of the push end of the first segment increases slightly, as shown in Figure 8. The longitudinal seam of the segment presents a small upper seam and a large lower seam. When the third segment is assembled, the rotation of the segment is significantly reduced due to the clamping of the segments on both sides, and the main rotation area is the unconstrained area. It is worth noting that, due to the continuous assembly of the segments, the direction of gravity is not the same. During the assembly process of the second and third segments, the direction of their gravity no longer contributes to the inward deflection of the segments. Compared with the assembly of the first segment, the degree of freedom of the rotation axis of the segment as a whole is constantly changing, so the degree of deflection of the segment is gradually reduced. Taking the free side edge of the assembled segment as the starting point, according to the angle, it can be seen that the stress of the front, the rear, and the centreline of the segment at different assembly stages presents different stress distributions (Figure 9a). When the first segment is assembled, the stress of the segment is mainly concentrated at  
Figure 8: The interaction between segments when the segments are at the top: (**a**) first segment assembly; (**b**) second segment assembly; (**c**) third segment assembly. the front and the rear of the segment and the maximum stress is 13 N/mm\({}^{2}\). When the segment is at the top, the segment has an obvious tendency to rotate inward, so the stress on the rear of the segment is relatively large. In particular, the stress on both sides of the rear increases rapidly. The main reason is that when the segment rotates, the rotation axis of the segment will autonomously choose to rotate along the edges on both sides of the segment. When the second segment is assembled, one side of the segment is supported by the assembled segment, so the stress at the rear of the segment is significantly reduced. At this time, the transmission of the stress of the segment is affected, and the stress at the front increases slightly. When the third segment is assembled, at least one side of all segments is supported, the stress distribution of segments is relatively uniform, and the overall stress is distributed within 3.5-10.5 N/mm\({}^{2}\). The inward rotation of segments is improved. When the third segment is assembled, the middle segment will be squeezed a little, so the stress will surge to a certain extent at the rear and centreline of the segment. It can be seen from Figure 10a that the direction and size of the bending moment of the segment are constantly changing due to the assembly of segments.