# Full-Scale Model Test of Subway Contact Channel under Mechanical Construction +
## 5 Structural Internal Force Analysis  
According to the strain monitoring of each measuring point, it can be considered that the reinforcing bars of the lining structure are in an elastic state. Accordingly, the axial force N and bending moment M of the section can be calculated according to the following formulas [3]:  
\[N=\epsilon_{\mathrm{s}}E_{\mathrm{s}}\cdot A_{\mathrm{s}}+\epsilon_{\mathrm{s} }^{\prime}E_{\mathrm{s}}^{\prime}\cdot A_{\mathrm{s}}^{\prime}+\int_{0}^{h} \sigma[\epsilon(x)]bdx \tag{1}\]  
Figure 16: Variation of the steel bar strain at the waist position of the standard ring.  
Figure 17: Variation of the concrete strain at the waist position of the standard ring.  
\[M=\big{(}\epsilon_{\text{s}}^{\prime}E_{\text{s}}^{\prime}\cdot A_{\text{s}}^{ \prime}-\epsilon_{\text{s}}E_{\text{s}}\cdot A_{\text{s}}\big{)}*(h/2-c)-\int_{0 }^{h}\sigma[\epsilon(x)]b(x-h/2)dx \tag{2}\]  
where \(\epsilon_{\text{s}}\) and \(\epsilon_{\text{s}}{{}^{\prime}}\) are the inner and outer reinforcement strains, respectively; \(A_{\text{s}}\) and \(A_{\text{s}}{{}^{\prime}}\) are the inner and outer reinforcement areas, respectively; \(E_{\text{s}}\) and \(E_{\text{s}}{{}^{\prime}}\) are the inner and outer reinforcement elastic modules, respectively; \(h\), \(b\), and \(c\) are the segment thickness, ring width, and protection layer thickness, respectively; \(\epsilon(x)\) represents the concrete strain at the corresponding position; \(\sigma(x)\) represents the concrete stress determined by the concrete strain at the corresponding position.  
The three-ring segment in the middle of the tunnel structure was selected as the research object. The axial force \(N\) and bending moment \(M\) of each test section under the four conditions were calculated and analyzed, as shown in Figures 18 and 19, respectively.  
Figure 18 shows that the internal force of the segment was redistributed after the end of the test condition and the axial force of each ring segment decreased overall. The axial force of the section near the inversion point of the cutting ring structure decreased first and then increased, and its change fluctuated greatly. The axial force at the upper spandrel position on the cutting side of the half-cutting ring increased significantly, whereas the axial force at the cross-section position near the inflection point of the structure decreased significantly. Considering the deformation and axial force variation (no more than 1000 kN) of the segment, the overall tunnel structure was in a safe state.  
Figure 19: The bending moment variation of the middle three rings under different conditions.  
Figure 18: The axial force variation of the middle three rings under different conditions.  
Figure 19 is a graph of the bending moment change. This figure shows that after the end of the test condition, the bending moments at the same test section position of each ring were basically the same. The tension and compression of the concave surface at the top and waist positions of the segment increased compared with those in the initial condition. At the position of the upper spandrel on the cutting side of the middle three rings, the bending moment decreased significantly with the cutting process. The variation was 200 kN m. The bending moment of the section near the contraflexure point of the structure changed significantly during the dismantling stage (from compression to tension). Comparing the same test sections of the cutting ring and the semi\(-\)cutting ring, the bending moment transmission between the rings was obvious, which was beneficial to the stress of the structure. During the cutting condition, the bending moment of each ring segment decreased and the axial force increased. This was beneficial to the stability of the main tunnel segment structure.