## 4 Analysis of Engineering Example  
### Engineering Description  
The entrance/exit tunnel MRDK0+457.8-688.2 of Min-Le parking lot belongs to the Shenzhen rail transit line 6 phase II, which is a small radius TBM internal with the curvature radius R = 300 m (as illustrated in Figure 7).  
The reinforced concrete (C50) universal wedge-shaped segments with a ring width of 1.2 m are utilized for the tunnel lining structure. The outer and inner diameters are 6200 mm and 5400 mm, respectively, and the thickness is 400 mm. The rings are connected by ten longitudinal bending  
Figure 6: Sectional schematic diagram of the circular curved beam.  
Figure 7: TBM construction interval with the small radius tunnel.  
bolts (M24). There are a total of 192 rings in the interval. The No. 1 and 2 segments are wrapped by the shield tail brush and sealing materials, the elastic resistance coefficient of foundation at the shield tail \(k_{1}\) = 100 kPa/m; The No. 3 to 5 segments have finished the backfilling of the bottom part by pea gravel, then the elastic resistance coefficient of foundation \(k_{2}\) = 292 MPa/m; The No. 6 to 10 segments have already finished the backfilling of the sidewall by pea gravel, then the elastic resistance coefficient of foundation \(k_{3}\) = 1701 MPa/m; The No. 11 to 96 segments are in the slightly weathered cataclasite formation, then the elastic resistance coefficient of foundation \(k_{4}\) = 1993 MPa/m; The No. 97 to 120 segments are in the slighted weathered granite formation, the elastic resistance coefficient of foundation \(k_{5}\) = 4770 MPa/m; The No. 121 to 192 segments are in the section where the grout is not solidified, the elastic resistance coefficient of foundation \(k_{6}\) is linearly changed, and finally reaching to 10,309 MPa/m. The tangential resistance in the model is provided by the friction between the segments and the surrounding medium. The frictional coefficient between the shield tail brush and the segment is 0.3, and the frictional coefficient between the pea gravel and the segment is 0.5. The action sphere of the tangential resistance can be solved through condition \(N(\varPhi_{ql})=0\).  
The influence range coefficient of the annular gap \(\lambda\) is set as 0.2 in this paper, and the generalized longitudinal equivalent continuous model is utilized to calculate the longitudinal equivalent bending stiffness \((EI)_{eq}\) in the tunnel. The grouting pea gravels haven't formed the ring in the wall back of No. 1 to 1 segments, and the segments haven't undertaken the surrounding rock pressure, then the bending stiffness \((EI)_{eq1}\) = 162.7 GPa-m4; The vertical uniform pressure of No. 11 to 96 segments is 107.7 kPa, the base uniform reaction is 110.8 kPa, the horizontal uniform pressure is 32.3 kPa, and the bending stiffness \((EI)_{eq2}\) = 163.1 GPa-m4; The vertical uniform pressure of No. 97 to 192 segments is 54.9 kPa, the base uniform reaction is 58.0 kPa, the horizontal uniform pressure is 8.2 kPa, and the bending stiffness \((EI)_{eq3}\) = 162.8 GPa-m4.  
The signs of the force and moment are stipulated for the convenience of further study. When the horizontal jack thrust on the outside of the shield curve is larger than that on the inside of the shield curve, the horizontal force couple is positive; when the path of the shield on the outside of the shield curve is larger than that on the inside of the shield curve, the jack thrust deviation angle is positive. When the segment's lateral displacement points to the circle center of the circular curve, this direction is positive, and vice versa. Through the monitoring data, the average of the total auxiliary cylinder jack thrust is 5931.33 kN, the average of the jack thrust on the outside of the shield curve is larger than that on the inside of the shield curve. The average of the force couple caused by the difference of the jack thrust in the horizontal direction is 1708.20 kN-m. The average of the lateral component caused by the path difference of the auxiliary cylinder jack is 40.36 kN.