# Reasonable Support Parameters for Loess Tunnel Under Different Water Contents: A Case Study
## 4 Numerical Simulation
### Optimization Analysis of Support Parameters
#### 4.3.2 Optimization Analysis of Support Parameters Under Saturated Water Content  
Through in situ research and a literature review, it was determined that when the water content exceeds 25%, the soil will exhibit soft plasticity characteristics. Therefore, not only was it essential to enhance the support structure, but it was also necessary to bolster the surrounding rock to optimize the support parameters under saturated water content conditions. Usually, methods such as using advanced grouting small conduits (condition 1) or conducting curtain grouting on the surrounding rock (condition 2) were used to reinforce the surrounding rock. Therefore, the advanced grouting small conduit and the conducted curtain grouting adopted the equivalent principle, and the support effect was equivalent to the surrounding rock reinforcement zone (MTPRC, 2018). Figure 17 illustrates the calculation model. The specific optimization conditions and detailed calculation parameter selection are listed in Tables 11 and 12. The surrounding rock deformation after the enhancement of the support strength clearly decreased, and the deformation value still met the deformation demand (MTPRC, 2024). Therefore, the focus of this study was on investigating the stress conditions in the support structure after its parameters were altered. The distributions of the internal forces within the support structure under different working conditions are depicted in Figure 18.  
The internal force distribution diagrams indicate that the stress at the top of the crown exceeds other measuring points of the support structure, and under two different working conditions, the maximum axial force was observed the top of crown. Consequently, the crown of the structure was selected for strength analysis and verification, with the calculated safety factors for each measuring point depicted in Figure 19. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Support** & \multicolumn{2}{c}{**Steel Rib**} & \multicolumn{2}{c}{**Shotcrete**} & \multicolumn{2}{c}{**Equivalent Value**} & \multicolumn{1}{c}{**Poisson’s**} \\ \cline{2-7}
**Parameters** & **Type** & **Spacing/cm** & **Thickness/cm** & **E/kN\(\cdot\)m\({}^{-2}\)** & \(\gamma\)/kN\(\cdot\)m\({}^{-3}\)** & **Ratio \(\mu\)** \\ \hline condition 1 & 122b & 65 & 24 & 29,263,384 & 23.21 & 0.22 \\ condition 2 & 122a & 60 & 26 & 28,671,077 & 23.06 & 0.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Optimizing parameters under saturated water content. Figure 18: The vertical stress cloud diagram and the distribution of the internal force. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Equivalent Reinforcement Zone** & **E/kN\(\cdot\)m\({}^{-2}\)** & \(c\)/kN\(\cdot\)m\({}^{-2}\)** & \(\varphi\)/\({}^{\circ}\) & \(\gamma\)/kN\(\cdot\)m\({}^{-3}\)** & \(\mu\) \\ \hline condition 1 & 800,000 & 50 & 25.3 & 22 & 0.22 \\ condition 2 & 1,000,000 & 230 & 32 & 22 & 0.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Parameters of surrounding rock reinforcement zone. The distribution diagram considering various conditions indicates that safety factors exhibit a symmetrical distribution along the central axis of the tunnel when the water content is saturated, and the minimum safety factor values are all located at the crown top measuring points. As a result, Table 13 shows the findings of the safety evaluation using the top crown measurement point as the key node. As shown in Table 13, the safety coefficients of the compressive resistance of the shotcrete are 2.6 and 3.1, which are greater than the shotcrete safety threshold, and the safety factors for the steel ribs are as follows: the compressive safety factors are 1.8 and 2.1, while the tensile safety factors are 2.9 and 3.4. Notably, the compressive safety factor in condition 1 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 2 satisfied the strength verification requirements.