## 4 Engineering Case Calculation  
### Engineering Geology Overview  
Figure 12 shows the schematic diagram of the underground rail transit tunnel passing through suburban expressway in Chongqing. It can be seen from satellite terrain map that the left, right and middle lines all obliquely pass through the existing suburban expressway through the underground excavation method. The mileage of the left line is K17+665.000 to K17+739.000, the mileage of right line is K17+659.500 to K17+733.500, and the mileage of middle line is YCK0+600.000 to YCK0+674.000. The length of tunnel passing through the suburban expressway is about 74 m. The schematic diagram of tunnel cross-section shows that the left line and right line tunnels are symmetrically distributed with respect to middle line with a width of 7.06 m, a height of 7.11 m and a buried depth of 16.136 m. The width of middle line tunnel is 7.06 m, the height is 7.56 m, and the buried depth is 7.252 m. The geological survey data show that the buried depth of the three tunnels is less than 2.50 times the height of surrounding rock pressure arch, belonging to the shallow buried tunnel [38]. The length (\(L_{e}\)) of the unsupported section of excavation section is the spacing between arches (0.50 m). The statistical geometric dimensions and excavation parameters are shown in Table 1.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Tunnels** & **Left Line** & **Right Line** & **Middle Line** \\ \hline Buried depth \(H\) (m) & 16.13 & 16.13 & 7.25 \\ Tunnel height \(D\) (m) & 7.11 & 7.11 & 7.56 \\ Tunnel width \(B_{0}\) (m) & 7.06 & 7.06 & 7.06 \\ Upper step height \(D_{0}\) & 3.71 & 3.71 & 3.71 \\ Equivalent width \(l_{0}\) (m) & 5.80 & 5.80 & 5.80 \\ Bottom of core soil \(b_{1}\) (m) & 3.80 & 3.80 & 3.80 \\ Height of core soil \(h\) (m) & 1.80 & 1.80 & 1.80 \\ Length of unsupported & & & \\ section \(L_{e}\) (m) & 0.50 & 0.50 & 0.50 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Geometric dimensions and excavation parameters.  
Figure 11: Variation trend in stability coefficient (\(K\)) with increasing anchor bolt density.  
Table 2 shows the surrounding rock parameters. Above the tunnel vault is mainly artificial fill and silty clay, and the surrounding rock is graded V. The underlying rock is mainly sandstone and sandy mudstone of the Middle Jurassic Shaximiao Formation, and the surrounding rock is graded IV. The exposed strata are Quaternary Holocene artificial fill (Q4 ml), residual slope layer silty clay (Q4 el-4), and sedimentary rock strata of Middle Jurassic Shaxi Temple Formation (J2 s). Since the suburban expressway is a two-way four-lane expressway, the General Specification for Design of Highway Bridges and Culverts states that the standard value of a uniformly distributed load for a Class I lane is 10.50 kN/m [39]. The geological survey data show that the stratum on the left line of tunnel is poor silty clay, which easily leads to the instability of tunnel face during excavation. Therefore, it is necessary to optimize the reinforcement scheme of the tunnel face.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Surrounding Rock** & **Artificial Fill** & **Silty Clay** & **Sandy Mudstone** \\ \hline Thickness (m) & 15.10–22.4 & 0.40–3.50 & 6 \\ Density (kN/m3) & 17 & 18 & 20 \\ Porosity (\%) & 50 & 47 & 20 \\ Cohesion (kPa) & 15 & 30 & 60 \\ Internal friction angle (\({}^{\circ}\)) & 20 & 35 & 40 \\ Lateral pressure coefficient & 0.357 & 0.293 & 0.234 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Surrounding rock parameters.  
Figure 12: Schematic diagram of the underground rail transit tunnel passing through suburban expressway: (**a**) Satellite terrain map of tunnel, (**b**) Schematic diagram of tunnel cross-section.