# Reasonable Support Parameters for Loess Tunnel Under Different Water Contents: A Case Study
## 4 Numerical Simulation
### Optimization Analysis of Support Parameters  
#### 4.3.1 Optimization Analysis of Support Parameters Under Natural Water Content  
In response to the high support strength in the original design parameters, it was previously common to adopt measures such as changing the type of steel rib, increasing the longitudinal spacing between steel ribs, using shotcrete of a lower strength grade, or reducing the thickness of the shotcrete. By statistically analyzing the support parameters of similar projects of the same type, the recommended values of support parameters applicable to natural water-bearing formations were obtained, as shown in Table 9. The stress distribution of the support structure under different working conditions was obtained through numerical simulation, and the internal force distribution maps were obtained through conversion, as shown in Figure 15. It should be noted that based on the construction experience of similar projects, the deformation of the surrounding rock of the loess tunnel using the support parameters in the table is much smaller than the reserved deformation of 150 mm. Therefore, the deformation of the surrounding rock will not be studied here. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Water Content**} & **Shotcrete** & **Steel Rib** & & **Safety Factor** & \\ \cline{2-6}  & **Axial** & **Axial** & **Bending** & & **Steel Rib** & **Steel Rib** \\  & **Force/KN** & **Force/KN** & **Moment/KN-m** & & **Tensile** & **Compressive** \\ \hline
16.1\% & 1381.4 & 152.7 & 42.8 & 3.4 & 2.7 & 4.3 \\
21.5\% & 1642.1 & 181.5 & 50.4 & 2.8 & 2.3 & 3.7 \\
26.9\% & 1912.2 & 211.3 & 80.1 & 2.2 & 2.3 & 1.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Calculation results under different water contents. The internal force distribution diagrams show that the stress at the top of the crown is greater than at other sites, and under two different working conditions, the maximum axial force is observed at the top of the crown. The crown of the structure was selected for strength analysis and verification, with the calculated safety factors for each measuring point plotted as shown in Figure 16. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Support Parameters**} & \multicolumn{2}{c}{**Steel Rib**} & \multirow{2}{*}{**Shotcrete**} & \multicolumn{2}{c}{**Equivalent Value**} & \multirow{2}{*}{**Poisson’s**} \\ \cline{2-2} \cline{5-6}  & **Type** & **Spacing/cm** & **Thickness/cm** & & \(E\)/kN\(\cdot\)m\({}^{-2}\) & \(\gamma\)/kN\(\cdot\)m\({}^{-3}\) & **Ratio \(\mu\)** \\ \hline condition 1 & I18 & 60 & 24 & 27,485,250 & 22.7 & 0.22 \\ condition 2 & I18 & 70 & 26 & 26,548,769 & 22.5 & 0.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Optimizing parameters under natural water content. Figure 16: Distribution diagram of safety factors. Figure 15: The vertical stress cloud diagram and the distribution of the internal force. The distribution diagram considering various conditions indicates that the safety factors exhibit a symmetrical distribution along the central axis of the tunnel when the water content is natural, and the minimum safety factor values are all located at the crown top measuring points. As a result, Table 10 shows the findings of the safety evaluation using the top crown measurement point as the key node. As shown in Table 10, the safety coefficients of the compressive resistance of the shotcrete are 2.8 and 2.4, and the safety factors of condition 1 and 2 are not less than the threshold value, 2.4, of the shotcrete. The safety factors of the steel ribs are as follows: the compressive safety factors are 2.3 and 1.9, while the tensile safety factors are 4.6 and 3.2. Notably, the compressive safety factor in condition 2 is below the standard requirement of 2.0 for compressive strength in steel structures, failing to meet the optimization requirements. In summary, the optimization parameters of working condition 1 satisfied the strength verification requirements.