# Reasonable Support Parameters for Loess Tunnel Under Different Water Contents: A Case Study
## 2 Introduction of Engineering Project
### Compressive Modulus \(E_{\mathrm{s}}\) and Deformation Modulus \(E_{0}\)  
The natural water content compressive modulus \(E_{\mathrm{s}}\) was measured to be 29.5 MPa using the WG-type single-lever consolidation instrument. Based on the research results for soil mechanics [40; 41], the deformation modulus \(E_{0}\) and compression modulus \(E_{\mathrm{s}}\) follow the following functional relationship:  
\[E_{0}=\beta\cdot E_{\mathrm{s}}=(1-2\mu K_{0})\cdot E_{\mathrm{s}} \tag{3}\]  
where \(\beta\) represents the soil parameters, \(\beta=1-2\mu K_{0}\), \(0\leq\beta\leq 1\), \(\mu\) represents the Poisson's ratio, \(\mu=K_{0}/(1+K_{0})\), and \(K_{0}\) represents the static side pressure coefficient.  
According to the specifications, it can be shown that \(\beta\) for clayey loess takes values in the range of 1.6 to 2.8 [40], and the deformation modulus \(E_{0}\) of the surrounding rock under natural water content can be obtained as 24.7 MPa by substitution. According to the regularity test of compression modulus \(E_{\mathrm{s}}\) and water content \(w\), the compression modulus \(E_{\mathrm{s}}\) under median water content was 20.2 MPa, and the compression modulus \(E_{\mathrm{s}}\) under  
Figure 4: Test results of loess strength parameters.  
saturated water content was 13.4 MPa. Substituted into Equation (3), the deformation modulus \(E_{0}\) under median water content was 16.9 MPa, and the deformation modulus \(E_{0}\) under saturated water content was 11.2 MPa.  
According to the technical specifications for the classification of loess water content [41], the water content of loess can be divided into low water content (\(w<10\%\)), general water content (\(10\%\leq w<17\%\)), high water content (\(17\%\leq w<25\%\)), and extremely high water content (\(w>25\%\)). This research indicates that the correlation between the shear strength and the water content of loess is such that within the 10-17% water content range, variations in water content have a minimal effect on the strength of loess. Nonetheless, once the water content surpasses this threshold, the shear strength of loess becomes significantly affected by changes in water content. In particular, when the water content surpasses 25%, it is difficult for the loess tunnel face to self-stabilize, and additional measures need to be taken to pre-reinforce the surrounding rock.  
Therefore, taking into account the test outcomes for the surrounding rock at Fengshouling Tunnel, three different rock strength parameters with natural water content of 16.1%, median water content of 21.5%, and saturated water content of 26.9% are selected to represent rock strength parameters under general water content, high water content and extremely high water content, respectively.  
By adjusting the water content \(w\) and combining it with relevant specifications [31], the deformation modulus \(E_{0}\), cohesion \(c\), internal friction angle \(\varphi\), soil density \(\gamma\) and other surrounding rock parameters under different water contents are obtained, as shown in Table 4.