# Early Detection and Stability Assessment of Hazardous Rock Masses in Steep Slopes
## 4 Results and Discussion
### Stability Evaluation Results and Verification
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Number of Dangerous**} & \multicolumn{8}{c}{**Evaluation Index Value**} & \multicolumn{3}{c}{**Instability**} & \multicolumn{1}{c}{**Stability**} \\ \cline{2-13}  & \(X_{\textbf{11}}\) & \(X_{\textbf{12}}\) & \(X_{\textbf{13}}\) & \(X_{\textbf{14}}\) & \(X_{\textbf{21}}\) & \(X_{\textbf{22}}\) & \(X_{\textbf{31}}\) & \(X_{\textbf{32}}\) & \(X_{\textbf{33}}\) & **Probability (P)** & **Classification** \\ \hline W1 & 1 & 1 & 7 & 4 & 7 & 10 & 4 & 7 & 7 & 5.56 & Relatively stable \\ W2 & 7 & 1 & 4 & 4 & 4 & 10 & 4 & 7 & 7 & 4.91 & Relatively stable \\ W3 & 10 & 4 & 1 & 4 & 7 & 7 & 4 & 7 & 7 & 4.78 & Relatively stable \\ W4 & 10 & 10 & 4 & 4 & 7 & 10 & 4 & 7 & 7 & 7.35 & Unstable \\ W5 & 3 & 1 & 10 & 4 & 4 & 10 & 4 & 7 & 7 & 5.76 & Relatively stable \\ W6 & 10 & 4 & 4 & 4 & 10 & 10 & 4 & 7 & 7 & 6.10 & Unstable \\ W7 & 10 & 0 & 7 & 4 & 10 & 10 & 4 & 7 & 7 & 5.54 & Relatively stable \\ W8 & 10 & 4 & 1 & 4 & 4 & 10 & 4 & 7 & 7 & 5.22 & Relatively stable \\ W9 & 10 & 1 & 4 & 4 & 10 & 10 & 4 & 7 & 7 & 5.36 & Relatively stable \\ W10 & 1 & 1 & 4 & 4 & 10 & 10 & 4 & 7 & 7 & 6.22 & Unstable \\ W11 & 10 & 1 & 4 & 4 & 10 & 10 & 4 & 7 & 7 & 5.36 & Relatively stable \\ W12 & 10 & 1 & 1 & 4 & 4 & 10 & 4 & 7 & 7 & 4.48 & Relatively stable \\ W13 & 7 & 1 & 4 & 4 & 4 & 1 & 4 & 7 & 7 & 2.90 & Stable \\ W14 & 4 & 1 & 7 & 4 & 4 & 1 & 4 & 7 & 7 & 3.33 & Unstable \\ W15 & 4 & 1 & 4 & 4 & 4 & 1 & 4 & 7 & 7 & 2.90 & Stable \\ W16 & 10 & 1 & 4 & 4 & 4 & 1 & 4 & 7 & 7 & 2.90 & Stable \\ W17 & 10 & 1 & 4 & 4 & 4 & 4 & 4 & 7 & 7 & 3.57 & Relatively stable \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Evaluation results of dangerous rock stability in the study area. Figure 15: Calculation model. In the formula, \(c\)--Adhesive force (kPa);  
\(\varphi\)--Internal friction Angle (\({}^{\circ}\)). Among them, the calculation method of the shear strength parameters of the critical rock main control structural plane is as follows:  
\[c=k_{c}\overline{C}[R_{c}] \tag{7}\]  
\[\varphi=k_{\varphi}\overline{\varphi}[\varphi_{0}] \tag{8}\]  
\[\overline{C}=-0.0016R^{2}+0.09398R+5.2815 \tag{9}\]  
\[\overline{\varphi}=-0.0001R^{2}+0.0073R+0.8996 \tag{10}\]  
In the formula, \(R\)--Penetration rate (\(\%\));  
\(\overline{C}\)--equivalent bond force;  
\(\overline{\varphi}\)--equivalent internal friction angle;  
\([R_{c}]\)--standard value of uniaxial compressive strength of intact rock (kPa);  
\([\varphi_{0}]\)--internal friction angle of intact rock of dangerous rock;  
\(k_{c}\), \(k_{\varphi}\)--the strength correction coefficient can be determined according to the safety level of the prevention and control project. Referring to the evaluation criteria for the stability of dangerous rock [43] (Table 14), according to the measured results, it can be seen that the height of dangerous rock W14 is 4.5 m, the inclination is 86.7\({}^{\circ}\), the fracture depth is 1.0156 m, and the volume is 103 m\({}^{3}\). According to the engineering geological data of the study area, the density of the dangerous rock mass is 2.85 g/cm\({}^{3}\), the seismic intensity is level VII, and the seismic impact coefficient is 0.5. According to the data, the stability coefficient of dangerous rock mass W14 is 0.69 under the working condition 1 and 0.68 under the working condition 3. According to the evaluation criteria of the stability of dangerous rock, the dangerous rock mass W14 is assessed as unstable, which is consistent with the evaluation results, which proves that the stability evaluation method of dangerous rock masses is reliable.