# Analysis of Shield Tunnels Undercrossing an Existing Building and Tunnel Reinforcement Measures
## 4 Model Validation
### Effect of Successive Excavation of Double Shield Tunnels on Displacements of Soil
#### 5.2.2 Internal Forces of Segment  
Figures 15 and 16 show the nephograms of the bending moment and axial force of the segment, respectively. Figure 15 shows that the bending moment of the segment was symmetrically distributed. The top and bottom of the segment were subject to positive bending moments, while the waist of the segments was subject to negative bending moments, which was basically consistent with the conclusion in reference [29]. The maximum positive bending moment of \(85.07\) kN\(\cdot\)m was located at the vault, and the maximum negative bending moment of \(-82.12\) kN\(\cdot\)m was located at the waist. Figure 16 shows that the pressure was everywhere in the segment. The pressure at the front end of the segment was greater than that at the rear end, and the maximum pressure was \(1186.98\) kN.  
For the convenience of describing the bending moment and axial force at different circumferential positions of the segment, as shown in Figure 17, different numbers were used, and the numbers were counterclockwise from the left side of the segment at the arch waist (number 1). Figures 18 and 19, respectively, showed the bending moments and the axial forces at different circumferential positions of segments of left and right tunnels under successive excavation of double shield tunnels, in which the left and right tunnels denoted the left and right excavation tunnels, respectively.  
Figure 16: Axial force nephogram of segment.  
Figure 15: Bending moment nephogram of segment.  
Figure 19: Axial forces at different circumferential positions of segments of left and right tunnels.  
From Figure 18, it can be found that for the sake of the secondary disturbance to the soil caused by the excavation of the right tunnel [30], the magnitudes and locations of the maximum positive and negative bending moments of the segments of the left and right tunnels were different. The maximum positive and negative bending moments of the left tunnel were 87.64 kN\(\cdot\)m and \(-\)88.56 kN\(\cdot\)m, respectively, while the maximum positive and negative bending moments of the right tunnel were 74.01 kN\(\cdot\)m and \(-\)77.68 kN\(\cdot\)m, respectively. Compared to the left tunnel, the maximum positive bending moment of the segment of the right tunnel was reduced by 15.56%, and the maximum negative bending moment was reduced by 12.29%.  
Figure 17: The numbers at different circumferential positions of segment.  
Figure 18: Bending moments at different circumferential positions of segments of left and right tunnels.  
From Figure 19, it can be found that the maximum and minimum axial forces and the positions of the segments of the left and right tunnels were different. The excavation resulted in a secondary release of soil stress so that the maximum axial force of the right tunnel segment was smaller than that of the left tunnel segment. The pressure was everywhere in the segment. The maximum axial forces of the left and right tunnel segments were 1218.7 kN and 1136.9 kN, respectively. The maximum circumferential axial force of the segment of the right tunnel was 6.71% lower than that of the left tunnel.  
During the construction process, the maximum positive bending moment, the maximum negative bending moment, and the maximum circumferential axial force applied to the segment of the left tunnel were larger than those of the right tunnel. Therefore, for the successive excavation, the bending moment and axial force of the segment of the left tunnel should be monitored in real-time.