## 3 Results
### Geometric Analysis of the Tail Brush Compression and the Resulting Pressure
\tag{10}\]  
Pressure Distribution around the Segment Induced by the Tail Brush Due to Vertical Adjustments in the Shield Posture  
Taking vertical posture adjustment as an example, when the shield posture adjusts an arbitrary value \(\Delta d_{p}\), similar to Figure 10, the two-dimensional model representing the relative positions of the shield shell, tail brush, and the segment is drawn in Figure 11.  
From Equation (9), giving the increment of the tail brush compression deformation under arbitrary posture adjustment, and Figure 11, the equation for the tail brush compression deformation increment when the shield posture adjusts in the vertical direction can be obtained as:  
\[\Delta d=\delta_{0}-\left(r_{2}-\sqrt{{x_{1}}^{2}+\left(y_{1}-\Delta d_{p} \right)^{2}}\right. \tag{11}\]  
By setting the shield shell movement to 50 mm, 70 mm, 90 mm, and 100 mm, respectively, the compression deformation of the tail brush at any position around the segment was obtained according to Equation (11) and has been plotted in Figure 12. When the shield moves downward in the vertical direction, the compression deformation of the tail brush at the tunnel arch bottom is the largest while it is the smallest at the crown of the arch; it is worth noting that the distribution of the compression deformation varies approximately linearly in the direction of the tunnel height. Combining Figure 12 and Equation (10), we obtained the distribution of the tail brush pressure around the segment under different vertical posture adjustments (Figure 13). When the shield posture is adjusted downward, the distribution of the pressure induced by the tail brush is extremely uneven along the circumference of the segment, and the pressure at the top of the segment is much larger than that at the bottom due to the distribution of the tail brush compression deformation (shown above). With the increase in the shield posture adjustment, the maximum compression deformation at the top is increased correspondingly, causing the segment to be subjected to increasing pressure; furthermore, the distribution of pressure around the segment circumference becomes more uneven. Figure 11: The relative positions of the shield shell, the tail brush, and the segment under arbitrary vertical posture adjustment. Figure 12: Distribution of the tail brush compression deformation along the tunnel height due to different upward offsets of the shield. As mentioned above, the tail brush has an initial compression deformation of 90 mm. With the adjustment in the shield posture, when the maximum compression deformation is 140 mm at the arch crown, the minimum compression deformation will be 40 mm at the arch bottom; as illustrated in Figure 12, the maximum pressure will be 300.91 kPa at the crown in this case. When the maximum compression deformation is 160 mm at the crown, the minimum compression deformation will be 20 mm at the arch bottom, and the maximum pressure will be 1104.99 kPa at the crown. When the maximum compression deformation is 180 mm at the crown, the minimum compression deformation will be 10 mm at the arch bottom, and the maximum pressure will reach 3263.08 kPa at the crown. When the maximum compression deformation is 190 mm at the crown, the minimum compression deformation will also be 0 mm at the arch bottom and the maximum pressure will further increase to 4629.22 kPa at the crown. Meanwhile, the variation curve in the maximum tail brush pressure together with the maximum compression deformation was plotted in Figure 14. This shows rapid non-linear growth in the maximum pressure with the increase in the maximum compression deformation of the shield tail brush. Therefore, attention should be paid to the control of the shield posture in case the adjustment to the posture is so excessive that the pressure acting on the segment increases rapidly.