# Analysis of the Interaction Effects of Shield Structure Oblique Passing under an Existing Tunnel
## 5 Deformation Characteristics of Existing Tunnels
### Transverse Internal Force  
The bending moments and axial forces in the five profiles of the existing tunnel after the excavation of the shield tunnel LT and RT are shown in Figure 12. This paper stipulates that if the lining external edge bending moment for the tensile state and the internal edge of the compression state for the positive bending moment show an otherwise negative bending moment, the axial force tension is positive and pressure is negative.  
After the RT excavation, the axial forces and bending moments corresponding to each cross-section changed due to the transverse deformation produced. The positive bending moment values generated at the left and right arch foot of section 2-2 were larger, the maximum variation value at the right arch foot was 5.4209 kN.m/m, and the negative bending moment values generated at the edge of the inverted arches of section 2-2 and section 4-4 were larger. It is noteworthy that only the negative bending moment at the edge of the inverted arch of section 2-2 was significantly reduced (maximum change value was 5.5903 kN.m/m). At the same time, the axial forces increase in a certain area of each section; for example, the axial forces increase in section 1-1 at the bottom of the arch, at the left arch foot, and at the right side of the arch top; in section 2-2, the axial forces increase only at the top of the arch and at the left and right sides of the arch top. In section 3-3, the axial forces increase at the left side of the arch and at the top of the arch. In sections 4-4 and 5-5, the axial forces increase in all the parts except the bottom of the arch. As can be seen in Figure 12, the inconsistency of the stress variation pattern between section 1-1 and section 3-3 is due to the asymmetry of the existing tunnel stress release due to the oblique underpass of the shield tunnel. After the completion of the RT underpass, the axial pressure increases significantly at the top of the arch (that in section 2-2 increases up to 8.23%), and the axial pressure decreases significantly at the bottom of the arch (that in section 2-2 decreases up to 85.37%). Since sections 4-4 and 5-5 are outside the shield tunneling influence zone, their axial forces change slightly after the completion of the shield left line underpass.  
After LT excavation was completed, sections 3-3 and 5-5 also showed the same inconsistent characteristics in their internal force change patterns. The lining internal force change laws of cross sections 3-3, 4-4, and 5-5 were similar to those of cross sections 1-1, 2-2, and 3-3 after RT excavation, respectively. However, because of the larger volume loss caused by the LT excavation, the lining internal force change values of sections 3-3, 4-4, and 5-5 were larger than those of sections 1-1, 2-2, and 3-3 before the LT excavation in the case of double-line penetration.  
The internal forces in the five sections of the existing tunnel during the shield tunnel underpass are shown in Figure 13 (all internal forces in all sections are taken as absolute values), from which it is obvious that the internal forces in each section are located within the broken ring envelope (maximum axial force is 0.95 MN/m, maximum bending moment is 0.028 MN.m/m), which indicates that although the shield tunnel allows the existing tunnel to generate large bending moments and axial forces during the construction process, the existing tunnel lining does not break the ring (i.e., the tunnel lining cracks), meaning that the existing tunnel lining structure is in a safe state.  
Figure 12: _Cont._  
Figure 12: Axial forces and bending moment diagram of the existing tunnel section.