## 3 Numerical Simulation and Analysis of Support Pressure on Tunnel Face
### Analysis of Calculation Results  
To investigate the effect of overburden thickness on the tunnel-face support pressure under a river, the support ratio \(\lambda\) was taken as 0.5, 0.6, 0.7 0.8, 0.9, 1.0, 1.5, 2.0, 2.5, 3.0, and 3.5. The 11 working conditions are shown in Table 4. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Support Ratio \(\lambda\)** & **0.5** & **0.6** & **0.7** & **0.8** & **0.9** & **1.0** & **1.5** & **2.0** & **2.5** & **3.0** & **3.5** \\ \hline \multirow{3}{*}{Support pressure/kPa} & H\({}_{\text{s}}\) = 3 m & 44.25 & 53.10 & 61.85 & 70.80 & 79.65 & 88.50 & 132.75 & 177.00 & 221.25 & 265.50 & 309.75 \\  & H\({}_{\text{s}}\) = 2 m & 37.15 & 44.58 & 52.01 & 59.44 & 66.87 & 74.30 & 111.45 & 148.6 & 185.75 & 222.9 & 260.05 \\  & H\({}_{\text{s}}\) = 1 m & 30 & 36 & 42 & 48 & 54 & 60 & 90 & 120 & 150 & 180 & 210 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Support pressure values for different support ratios. Figure 6: Distribution of monitoring points in numerical simulation analysis. As shown in Figure 7, when the river overburden is 3 m, the applied pressure obtained from the calculation of the theoretical tunnel-face support pressure decreases, and the normal displacement of the tunnel face gradually increases. When \(\lambda\) = 1.0-0.9, the tunnel face is slightly concave towards the soil. The displacement change is not significant and could be considered to satisfy the equilibrium stabilization requirements. As the support pressure continues to decrease to the active soil pressure (as \(\lambda\) changes from 0.9 to 0.6), the tunnel face displacement shows an approximately linear increasing trend with decreasing support pressure. The tunnel face gradually bulges towards the digging machine, and the surrounding soil slips and fails. When the river channel overburden is 2 m or 1 m, the trend is the same as when the river channel overburden is 3 m. However, as the thickness of the overburden decreases, the displacement of the soil monitoring points caused by the active support pressure continues to increase. When H\({}_{\rm s}\) = 3 m, the maximum normal displacement of the tunnel face is -8 mm; when H\({}_{\rm s}\) = 2 m, it is \(-\)6.5 mm; and when H\({}_{\rm s}\) = 1 m, it is \(-\)5 mm. As shown in Figure 8, when the river overburden is 3 m, the support pressure exerted on the tunnel face increases from static soil pressure to passive soil pressure. The trend is the same when the river channel overburden is 2 m or 1 m. The displacement of the tunnel face increases along the soil direction. However, as the thickness of the overburden decreases, the displacement of the soil monitoring points caused by the passive support pressure continues to decrease. When H\({}_{\rm s}\) = 3 m, the maximum normal displacement of the tunnel face is 56 mm; when H\({}_{\rm s}\) = 2 m, it is 47 mm; and when H\({}_{\rm s}\) = 1 m, it is 38 mm. As illustrated in Figure 9, according to the calculation results, the ultimate support force is 86.63 kPa when the river channel overburden is 3 m (86.63 kPa multiplied by the area of the tunnel surface \(\pi\)D\({}^{2}\)/4 is 881.786 kN), 83.03 kPa when the river channel overburden is 2 m (83.03 kPa multiplied by the area of the tunnel surface \(\pi\)D\({}^{2}\)/4 is 845.142 kN), and 50.81 kPa when the river channel overburden is 1 m (50.81 kPa multiplied by the area of the tunnel  
Figure 8: Plots of passive support pressure and tunnel-face displacement: (a) H\({}_{\rm s}\) = 3 m; (b) H\({}_{\rm s}\) = 2 m; (c) H\({}_{\rm s}\) = 1 m.  
Figure 7: Plots of active support pressure versus tunnel-face displacement: (a) H\({}_{\rm s}\) = 3 m; (b) H\({}_{\rm s}\) = 2 m; (c) H\({}_{\rm s}\) = 1 m.  
surface \(\pi\)D\({}^{2}\)/4 is 517.183 kN). This support force can control the position of the tunnel face to keep it in the best condition. [PERSON] [39] concluded that one factor controlling the settlement deformation of shallow buried jacked pipes was the ground loss rate.