## 5 Results and Discussion  
### Engineering Application I: Inversion Calculation of Soil-Shield Interaction Force  
The soil layer above the section of Ring 504 is composed of backfill and loess, which is a non-uniform clay stratum. According to the method of this paper and in [27], initial force acting on the shield periphery can be calculated in the non-uniform clay stratum. As shown in Figure 15, the section of Ring 504 is also a non-uniform layer. The loess layer and silty clay each account for about half of the entire excavation surface and can be approximated by 1:1.  
Through the guiding system and data monitoring system of the EPB, when the shield had been advancing at Ring 504, partition cylinder thrust, pitch angle and yawing angle were recorded every 1 min. The time to excavate Ring 504 was about 50 min, but for various reasons, it was interrupted during the tunneling process. Continuous monitoring data were more valuable and informative. The longest continuous boring time of the ring was about 15 min. To avoid the influence of shield start and stop, this study selected continuous monitoring data of 10 min in the middle of this time. The data for a period were selected for analysis and comparison. The measured data of the pitch angle and the yawing angle are shown in Figure 17. The yawing angle varied greatly, while the pitch angle remained basically stable.  
Figure 16: Cutterhead and advance system of shield: (**a**) shield cutterhead; and (**b**) shield cylinder partition.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Shield Type** & **EPB** \\ \hline External diameter (m) & 6.68 \\ The length of shield (m) & 9.0 \\ Shield weight (t) & Approximately 500 \\ Shield eccentricity (m) & Approximately 0.5 \\ Cutter opening ratio (\%) & 35 \\ Maximum total thrust (kN) & 40,860 \\ Number of propulsion cylinders & 22 \\ Maximum advance speed (mm/min) & 80 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of the main specifications for the EPB.  
The pitch angle and the yawing angle had been known through the guiding system. According to the flow chart of the shield attitude calculation (Figure 11), the force of shield-soil interaction during the tunneling process can be inverted. The calculation results are shown in Figure 18. Figure 18 shows the distribution of the total normal earth pressure around the shield periphery. The height of graphs represents the length of shield, the width of graphs represents the shield periphery from 0\({}^{\circ}\) to 360\({}^{\circ}\). Along the line at 180\({}^{\circ}\), it can be found that the normal pressure is gradually decreasing from the bottom to the top of graphs, indicating that the pitch angle of the shield is positive. The gradient of the normal pressure reduction reflects the magnitude of the pitch angle. The stress nephogram on the left or right of the line at 180\({}^{\circ}\) shows the direction of the yawing angle of the shield.  
Figure 17: Pitch angle and yawing angle measured data.  
Figure 18: _Cont._  
The change of the pitch angle of the shield is small, and the fluctuation of the stress nephogram is mainly due to the change of the yawing angle. The stress nephogram can be used to preliminarily determine the degree and the direction of deflection on the horizontal plane of the shield. The greater is the yawing angle, the more severe is the distortion of the stress nephogram. For example, there was a sudden increase of the yawing angle between time = 4 min and time = 5 min, as can be seen from the stress nephogram.