# Reasonable Support Parameters for Loess Tunnel Under Different Water Contents: A Case Study
## 4 Numerical Simulation
### Simulation Analysis of Original Design Support Parameters
#### 4.2.3 Safety Analysis of Supporting Structures  
In this paper, the comprehensive safety factor method in the Specifications for Design of Highway Tunnels (JTG/TD70\(-\)2018) was used to check and evaluate the primary support of Fengshouling Tunnel [35]. Its strength should conform to Equations (10)-(12). The equations are as follows:  
\[K_{\text{hy}}N_{\text{h}}\leq\alpha R_{\text{hy}}A_{\text{h}} \tag{10}\]  
\[K_{\text{g}}(\frac{N_{g}}{A_{g}}+\frac{M_{g}}{W_{g}})\leq R_{\text{gy}} \tag{11}\]  
\[K_{\text{g}}(\frac{N_{g}}{A_{g}}-\frac{M_{g}}{W_{g}})\leq R_{\text{gl}} \tag{12}\]  
where \(K_{\text{hy}}\) is the compressive safety factor of the compressive strength of the shotcrete (kPa); \(\alpha\) is the eccentric influence coefficient; \(R_{\text{hy}}\) is the compressive ultimate strength of the shotcrete (kPa); \(K_{\text{g}}\) is the compressive safety factor of the compressive and tensile strength of the steel rib (kPa); \(W_{\text{g}}\) is the steel rib checking calculation of the cross-section bending strength (m\({}^{3}\)); \(R_{\text{gy}}\) is the compressive ultimate strength of the steel rib (kPa); and \(R_{\text{gl}}\) is the ultimate tensile strength of steel rib (kPa).  
Considering the characteristics of the internal force distribution, the axial force and bending moment of the crown structure are much greater than those of the side walls and invert when choosing the measuring points in the crown for assessing the safety factor. According to the calculation method's specifications, the axial force is supported by both the steel ribs and the shotcrete, whereas the bending moment is supported solely by the steel ribs. The calculated safety factors for each measuring point are shown in Figure 14.  
The distribution diagram of the safety factors at different water contents shows that the axial force and bending moment are symmetrically distributed along the tunnel's central axis, which corresponds to the distribution of the internal forces, and the minimum safety factor values are all located at the crown top measuring points. As a result, Table 8  
Figure 14: Distribution diagram of safety factors.  
shows the findings of the safety evaluation using the top crown measurement point as the key node.  
As shown in Table 8, when the water content increased from 16.1% to 21.5%, the bending moment of the steel rib increased by 17.7%, the axial force of the shotcrete increased by 18.8%, the compression safety factor of the shotcrete decreased by 17.6%, the compression safety factor of the steel rib decreased by 14.8%, and the tensile safety factor of the steel rib decreased by 13.9%; when the water content rose from 21.5% to 26.9%, there was a corresponding 58.9% increase in the steel rib bending moment, the axial force of the shotcrete increased by 16.5%, the compression safety factor of the steel rib did not change, and the tensile safety factor of the steel rib changed significantly, reducing 56.7%. The compressive safety coefficient values of the shotcrete under three different water contents indicate that the shotcrete meets the safety requirements [32]. However, the tensile safety factor of the steel rib with a water content of 26.9% is less than 2.0, which does not satisfy the structural load-bearing requirements.  
In summary, the support under natural water content has a high safety reserve, and optimization of the support parameters is achievable through the reduction in the support strength. The primary support under the median water content satisfied the structural safety requirements and did not require the optimization of support parameters. However, the steel rib compressive safety factor under saturated water content did not satisfy the safety requirements, and it was imperative to enhance the design parameters in order to ensure structural safety and stability.