# Early Detection and Stability Assessment of Hazardous Rock Masses in Steep Slopes
## 4 Results and Discussion
### Stability Evaluation Results and Verification  
According to the early identification results, a total of 17 dangerous rock masses were identified, mainly distributed at the cut slope of the slope foot, and the whole risk area was in a band. According to the distribution, they were divided into three dangerous rock belts, and the spatial location and distribution range are shown in Figure 14.  
According to the established system for evaluating the stability of hazardous rock masses, 17 such masses in the study area have been assessed and categorized. The assessment took into account the uneven distribution of rainfall throughout the year, with summer precipitation representing 65% to 67% of the annual total. Consequently, the rainfall index was calculated based on the most unfavorable conditions. The weight and importance of the influence of indicators on the stability of dangerous rock masses are analyzed qualitatively and quantitatively by AHP method. The instability probability P of dangerous rock masses is used to measure the stability of dangerous rock masses. The formula is as follows:  
\[P=\sum_{i=1}^{n}\gamma_{ij}S_{ij} \tag{4}\]  
In the formula, the following apply:  
\(S_{ij}\)--the basic score of the JTH secondary index among the i primary index in the index system;  
\(\gamma_{ij}\)--the weight coefficient of the JTH secondary index in the i primary index in the index system. According to the value range of instability probability \(P\), the stability levels of dangerous rock masses are divided into three levels: unstable, relatively stable, and stable, as shown in Table 12.  
The specific results of this stability evaluation can be found in Table 13. These findings are an important point of reference for implementing appropriate protective and management measures to ensure security and stability within the relevant region. \begin{table}
\begin{tabular}{c c c c} \hline Instability probability \(P\) & \(P\geq 6\) & \(3\leq P<6\) & \(P<3\) \\ \hline Stability classification & Unstable & Relatively stable & Stable \\ \hline \end{tabular}
\end{table} 
Table 12: Stability classification table of dangerous rock masses. Figure 14: Spatial location and distribution. The limit equilibrium theory is used to calculate the stability coefficient of dangerous rock masses and verify the results of the rapid stability evaluation. Figure 15 shows the calculation model of dangerous rock [42,43]. In the figure, the following apply: W--dead weight of dangerous rock mass (kN);  
H--the vertical distance from the top of the posterior edge crack to the unpenetrated segment (m);  
e--master plane deviation distance (m);  
\(\beta\)--main control structural plane inclination (\({}^{\circ}\));  
P--horizontal seismic force (kN). Load combination 1: dead weight + pore water pressure (natural state). \[K_{1}=\frac{0.5W\sin 2\beta\tan\varphi+cH}{W\sin^{2}\beta} \tag{5}\]  
Load combination 3: dead weight + pore water pressure (natural state) + seismic force. \[K_{3}=\frac{(W\cos\beta-P\sin\beta)\tan\varphi+c\frac{H}{\sin\beta}}{W\sin\beta +P\cos\beta} \tag{6}\]