## 4 Calculation Model of \"Wedge-Prism\"
### Model Checking  
In order to verify the rationality of the modified \"wedge-prism\" calculation model, the results are compared with those from previous centrifuge model tests. Based on the research results of the centrifugal model test of excavation surface stability of Chambon [26], the improved \"wedge-prism\" calculation model is verified. Under certain soil layer parameters, tunnel burial depth and tunnel diameter, the ultimate supporting force of the excavation surface obtained by the centrifugal test results and the calculation model is shown in Table 2. It can be seen from Table 2 that the calculation model results are in good agreement with the centrifugal test results. With the increase in buried depth, the results of the \"wedge-prism\" calculation model are larger  
Figure 8: Variation curve of supporting force of shield excavation face with \(\zeta\). (**a**) Change of buried depth \(C\); (**b**) Change of tunnel diameter \(D\); (**c**) Change of soil cohesive force \(c\); (**d**) Change of the angle of internal friction \(\varphi\); (**e**) Change of unit weight of soil \(\gamma\); (**f**) Change of anisotropy ratio \(k\). than those of centrifugal test, and the difference increases with the increase in buried depth. The main reason might be: with the increase in buried depth, a soil arching effect appears in centrifugal test and gradually plays a role. However, the soil arching effect is not fully considered in the \"wedge-prism\" calculation model, which results in insufficient consideration of the soil force on the sliding block in the calculation model. It can be seen that the modified \"wedge-prism\" model has good accuracy in calculating the ultimate supporting force of the relatively deep buried tunnel. When the burial depth is large (such as \(C/D>3\)), although the calculated ultimate supporting force is relatively conservative, it still has high safety. It should be further noted that for relatively deep buried tunnels (such as \(C/D>1\)), the height \(H\) of the \"prism\" in the \"wedge-prism\" is revised to be 1.9 times the width \(L\) of the \"prism\" (i.e., \(H=1.9\) L). Studies have shown that the range of \(H/L\) in relatively deep tunnels is about 1.5-2.2 (as shown in Table 1). Therefore, it is necessary to objectively evaluate the calculation error of the limit supporting force \(\sigma_{s}\) caused by the value of \(H\) in the modified \"wedge-prism\" model. In the modified \"wedge-prism\" model, two extreme cases of \(H/L=1.5\) and \(H/L=2.2\) are considered, respectively, and the derivative of function (10) with respect to \(H\) is calculated. Since the derivative of \(\sigma_{v}\) with respect to \(H\) is less than 0, \(\sigma_{v}\) decreases with the increase in \(H\). Because the ultimate supporting force \(\sigma_{s}\) increases with the increase in \(\sigma_{v}\) (as shown in Figure 9), \(\sigma_{s}\) decreases with the increase in \(H\). Using \(\sigma_{s}^{H/L=1.5}\), \(\sigma_{s}^{H/L=1.9}\) and \(\sigma_{s}^{H/L=2.2}\) denotes the ultimate supporting force \(\sigma_{s}\) when \(H=1.5\) L, 1.9 L and 2.2 L, respectively. According to the previous analysis, \(\sigma_{s}\) decreases with the increase in \(H\), so \(\sigma_{s}^{H/L=1.5}>\sigma_{s}^{H/L=1.9}>\sigma_{s}^{H/L=2.2}\). According to Table 2, when \(H=1.9\) L, the calculation results are safe and accurate. Therefore, when \(H=1.5\) L, the calculation results tend to be conservative; When \(H=2.2\) L, the safety of calculation results is significantly reduced. In summary, when the burial depth ratio is small, the modified \"wedge-prism\" model can accurately calculate the limit supporting force of excavation face, and the calculation results are safe for practical engineering; When the buried depth ratio is large (e.g., \(C/D>3\)), the calculation results are larger than the centrifugal model test results. At this time, the calculation model results tend to be conservative, but the safety of the calculation results is not affected.