## 3 Analysis of Mechanical Properties of Steep Surrounding Rock
### Triaxial Rock Creep Test  
The strength and deformation characteristics of tunnel thin-layer slate with time under in situ stress conditions are studied, and the anisotropy of the time-dependent deformation of surrounding rock caused by different rock strata angles is explored. By using the soft rock true triaxial experimental instrument to simulate the in situ stress environment, the time-dependent creep test of tunnel surrounding rock is carried out by exploring different surrounding rock angles. The test process is shown in Figure 6.  
The triaxial rock creep test of the aging mechanical properties of the deep layered surrounding rock of the tunnel was carried out by laboratory testing, and the strain characteristics of slate with three bedding angles of \(\beta\) = 0\({}^{\circ}\), 30\({}^{\circ}\), 90\({}^{\circ}\) and \(\omega\) = 0\({}^{\circ}\) were obtained, as shown in Figure 7. It can be seen that the strain increment corresponding to each principal stress of the \(\beta\) = 30\({}^{\circ}\) test block is obviously larger than that of \(\beta\) = 0\({}^{\circ}\) and 90\({}^{\circ}\), and the volume strain increment is also larger. In addition, the aging deformation time of the \(\beta\) = 30\({}^{\circ}\) test block is shorter than that of the \(\beta\) = 0\({}^{\circ}\) and 90\({}^{\circ}\) test blocks, indicating that the \(\beta\) = 30\({}^{\circ}\) test block is more prone to damage; the failure of the \(\beta\) = 0\({}^{\circ}\) test block is mainly tensile splitting failure, and the strength is about 110 MPa. The failure of the \(\beta\) = 30\({}^{\circ}\) test block is mainly shear slip failure, and the strength is about 48 MPa. The failure of the \(\beta\) = 90\({}^{\circ}\) test block is mainly splitting failure, and the strength is about 163 MPa. Therefore, it can be concluded that within a certain range, with the increase in the angle of the rock layer, the deformation of the surrounding rock will increase and the failure rate will be faster. However, when the maximum angle of \(\beta\) reaches 90\({}^{\circ}\), the deformation and strength of the surrounding rock will increase, as shown in Figure 8, which presents the variation in the strength of the surrounding rock with the change in the angle of \(\beta\) when \(\omega\) = 0\({}^{\circ}\). \begin{table}
\begin{tabular}{c c c c} \hline
**Serial** & **P** & **Is(50)** & **Rc** \\
**Number** & **Breaking Load (N)** & **Point Load Strength of** & **Uniaxial Compression** \\  & & **Standard Specimens (MPa)** & **Strength of Rock (MPa)** \\ \hline
1 & 272 & 0.10 & 4.0 \\
2 & 178 & 0.03 & 1.60 \\
3 & 192 & 0.05 & 2.25 \\
4 & 130 & 0.05 & 2.49 \\
5 & 246 & 0.08 & 3.26 \\
6 & 162 & 0.084 & 3.57 \\
7 & 0 & 0 & 0 \\
8 & 972 & 0.27  
Figure 6: Triaxial test process diagram. Figure 7: Creep strain–time and stress–strain curves of slate under different loading angles. Considering the loading angle, the strength calculation formula of layered surrounding rock is:  
\[c_{\beta\omega b}=\frac{c_{90}}{1+A[\cos 2\beta_{\min}+\cos 2(\beta-\beta_{\min}) ]^{n}}[1+D\cdot\sqrt[n]{\sin\omega\cos\frac{\pi(\beta-\beta_{\max})}{\pi-2\beta_ {\max}}}\cdot b^{m}] \tag{1}\]  
\[\sin\varphi_{b}=\frac{\sin\varphi_{0}}{\sqrt{1-b+sb^{2}}+t(1-\sqrt{1-b+b^{2}} )\sin\varphi_{0}} \tag{2}\]  
\[b=\frac{\sigma_{2}-\sigma_{3}}{\sigma_{1}-\sigma_{3}} \tag{3}\]  
where \(s=0.98\); \(t=0.88\); \(c_{90}=44.2\) MPa; \(\varphi_{0}=30^{\circ}\); \(\beta_{min}=32.8^{\circ}\); \(\beta_{max}=32.8^{\circ}\); \(A=1.0\); \(n=2.55\); \(D=3\); and \(m=0.5\). Under the most unfavorable angle condition, the layered rock mass is \(C=13\) MPa, \(\varphi=29.65^{\circ}\cdot\varphi_{b}\) is the internal friction angle at different \(b\); \(\varphi_{0}\) is \(b=0\), that is, the internal friction angle in the conventional triaxial compression stress state; \(s\) and \(t\) are material constants, where \(s\) reflects the strength difference of rock at \(b=0\) and \(b=1\), and t controls the influence of intermediate principal stress on the peak strength of rock.