## 3 Example Analyses
### Determination of Weight and Results of Cluster Analysis
#### 3.3.2 Results of Cluster Analysis  
The rock mass quality in the study area was divided into grade I, grade II, grade III\({}_{1}\), grade III\({}_{2}\), grade IV, and grade V. The K-PSO clustering results of rock mass quality in the study area are shown in Table 7. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multicolumn{2}{c}{\(C_{1}\)**/**Saturated**} & \multirow{2}{*}{\(C_{2}\)**/**Spacing**} & \multirow{2}{*}{\(C_{3}\)**/**Wave Velocity \(v\)**} & \multirow{2}{*}{\(C_{4}\)**/**RQD**} & \multirow{2}{*}{\(C_{5}\)**/**Integrity Coefficient**} \\  & & & & & & & \\ \hline Weight & 0.471 & 0.172 & 0.076 & 0.172 & 0.109 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Rock quality evaluation parameter weights based on the weighted least-squares method. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Zone**} & \multirow{2}{*}{\(C_{1}\)} & \multirow{2}{*}{\(C_{2}\)} & \multirow{2}{*}{\(C_{3}\)} & \multirow{2}{*}{\(C_{4}\)} & \multirow{2}{*}{\(C_{5}\)} & \multicolumn{2}{c}{**The New**} & \multirow{2}{*}{**BQ**} & \multicolumn{2}{c}{**Extension**} & \multicolumn{1}{c}{**Field**} \\  & & & & & & & & & & \\ \hline \(P_{1}\) & 0.04 & 0.08 & 0.23 & 0.22 & 0.12 & V & V & V & IV–V \\ \(P_{2}\) & 0.13 & 0.13 & 0.36 & 0.24 & 0.16 & IV & IV & IV & IV–V \\ \(P_{3}\) & 0.26 & 0.21 & 0.43 & 0.50 & 0.28 & IV & IV & IV & IV–V \\ \(P_{4}\) & 0.29 & 0.4 & 0.57 & 0.55 & 0.48 & III\({}_{2}\) & III\({}_{2}\) & III\({}_{2}\) & III\({}_{1}\)–III\({}_{2}\) \\ \(P_{5}\) & 0.42 & 0.35 & 0.49 & 0.46 & 0.36 & III\({}_{2}\) & IV & III\({}_{2}\) & III\({}_{2}\)–IV \\ \(P_{6}\) & 0.67 & 0.45 & 0.7 & 0.66 & 0.53 & III\({}_{1}\) & III\({}_{2}\) & III\({}_{1}\) & III\({}_{1}\)–III\({}_{2}\) \\ \(P_{7}\) & 0.63 & 0.56 & 0.75 & 0.81 & 0.64 & II & II & II & II–III\({}_{1}\) \\ \(P_{8}\) & 0.86 & 0.8 & 0.77 & 0.79 & 0.68 & II & II & II–III\({}_{1}\) \\ \(P_{9}\) & 0.92 & 0.83 & 0.95 & 0.88 & 0.82 & II & I & II & I–II \\ \(P_{10}\) & 0.82 & 0.69 & 0.86 & 0.78 & 0.78 & II & II & II & I–II \\ \(P_{11}\) & 0.97 & 0.97 & 0.84 & 0.90 & 0.75 & II & II & II–III\({}_{1}\) \\ \(P_{12}\) & 1 & 1.1 & 0.9 & 0.93 & 0.79 & I & I & I–II \\ \(P_{13}\) & 1.12 & 0.94 & 0.85 & 0.88 & 0.76 & I & I & I–II \\ \(P_{14}\) & 1.21 & 1.5 & 0.98 & 0.95 & 0.88 & I & I & I–II \\ \(P_{15}\) & 1.19 & 1.43 & 0.93 & 0.94 & 0.80 & I & I & I–II \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Classification comparison table of different methods of 15 sections in PD105. Under the conditions of high stress and a high ground temperature, the rock damage of the RMR system is aggravated, which shows that the rock characteristics change from brittleness to plasticity, and the rheological effect of rock is enhanced. Therefore, the system has poor applicability to deep underground engineering. The Q system can be seen from its system composition. Except for the RQD value, a quantitative index, the other five indexes are qualitatively obtained by field investigation, which has a certain level of experience. At the same time, there are some shortcomings in the application of Q system in high-stress areas. The BQ classification method of rock mass comprehensively refers to the classification basis of rock mass quality at home and abroad, adopts the classification method combining qualitative and quantitative factors, and closely combines the engineering characteristics of rock mass engineering in China, which has strong scientificity and practicability. Therefore, combined with the evaluation parameters of rock mass quality in the study area, this paper chose BQ classification for the comparison of new methods, and further verified the accuracy of the new method when applied to rock mass quality evaluation in combination with field investigation [1; 2; 3; 4; 5; 6]. In this paper, the method was compared with the two methods: the traditional BQ classification method and the nonlinear extension theory commonly used at present.