# Reasonable Support Parameters for Loess Tunnel Under Different Water Contents: A Case Study
## 2 Introduction of Engineering Project
### Surrounding Rock Strength  
Direct Shear Test  
Surrounding rock parameters of Fengshouling Tunnel were obtained through indoor experiments, and the relationship between strength parameters of loess and water content was studied. Figure 3 displays the experimental setup and the prepared samples, while the outcomes of the direct shear tests are presented in Table 2.  
Research results are based on water content and loess strength parameters [22; 37; 38; 39], exponential and linear functions are used to fit the relationship, and the fitting equations are presented in Table 3, with the corresponding fitting relationships depicted in Figure 4.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Type of Lining**} & \multicolumn{2}{c}{**Steel Rib**} & \multicolumn{2}{c}{**C25 Shotcrete**} & \multirow{2}{*}{**Bolt at the Sidewall**} & \multirow{2}{*}{**Secondary Lining**} \\ \cline{2-2} \cline{5-5}  & **Type** & **Spacing** & **Thickness** & \\ \hline Va & I20a & 60 cm & 26 cm & \(\Phi\)22 system anchors & C30 concrete with a \\ Vb & I18 & 60 cm & 24 cm & with a length of 3.5 m & thickness of 50 cm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Support parameters of Fengshouling Tunnel.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multirow{2}{*}{**Water Content _w/\%_**} & \multirow{2}{*}{**Natural Density \(\gamma\)/kg\(\cdot\)m\({}^{-3}\)**} & \multicolumn{2}{c}{**Shear Strength Index**} \\ \cline{3-4}  & & & **Cohesion _c/kPa_** & **Internal Friction Angle \(\varphi^{c}\)** \\ \hline
1 & 15.66 & 18.6 & 15.3 & 22.1 \\
2 & 14.83 & 13.1 & 16.6 & 22.3 \\
3 & 15.45 & 16.6 & 14.6 & 22.1 \\
4 & 16.51 & 16.8 & 13.5 & 21.9 \\
5 & 17.72 & 15.8 & 12.1 & 21.8 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Direct shear test results.  
Figure 3: Direct shear test.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Shear Strength Index**} & \multicolumn{2}{c}{**Fitting Formula**} & \multicolumn{1}{c}{**Correlation Coefficient**} \\ \hline cohesion \(c\) & \(c\) = 77.463 \(\times\) 10\({}^{-0.105w}\) & 0.94 \\ internal friction angle \(\varphi\) & \(\varphi\) = \(-0.1684w\) + 24.74 & 0.93 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Function of strength parameters and water content.  
Table 3 shows that the correlation coefficients for both the exponential and the linear functions are identical, each measuring 0.93, indicating that the equations in Table 3 can effectively represent the functional relationship between the strength characteristics of loess and its water content.  
According to the in situ soil geological survey data,  
\[G_{\mathrm{s}}=\frac{eS_{\mathrm{r}}}{w}=\frac{0.726\times 0.597}{0.161}=2.692 \tag{1}\]  
\[w_{\mathrm{sr}}=\frac{m_{\mathrm{wsr}}}{m_{\mathrm{s}}}=\frac{e}{G_{\mathrm{s} }}=\frac{0.726}{2.692}=26.9\% \tag{2}\]  
where \(G_{\mathrm{s}}\) is the specific gravity of soil particles, \(e\) is the pore ratio, \(w\) denotes the average natural water content. \(S_{\mathrm{r}}\) is the degree of saturation, \(w_{\mathrm{sr}}\) is the saturated water content expressed as a percentage, \(m_{\mathrm{sr}}\) is the mass of water in saturated soil in grams; and \(m_{\mathrm{s}}\) is the mass of soil particles in grams.  
Based on the calculated saturated water content \(w_{\mathrm{sr}}\) and the relationships between water content and the strength parameters of the surrounding rock, we determined the following values for the saturated state: cohesion \(c\) is 4.6 kPa, and the internal friction angle \(\varphi\) is 20.2\({}^{\circ}\). To find the median water content, we calculated the median value between the saturated water content and the natural water content, resulting in a median water content of 21.5%. At this median water content, the cohesion \(c\) is 8.1 kPa, and the internal friction angle \(\varphi\) is 21.1\({}^{\circ}\).