## 4 Results and Discussion
### The Calculation Process of the Improved VFS Method  
(1) Determining attracting interval, extended interval, and M point  
Before calculating the parameters of the VFS model, it should be pointed out that Equations (11)-(13) are available for fixed intervals, while levels I and IV in rockburst prediction criteria are semi-interval forms such as \([-\infty,L_{max}]\) and \([L_{min},+\infty]\). Here, a pseudo-boundary is obtained using the polynomial regression analysis method, assuming that the trend of increasing or decreasing of boundary eigenvalues is consistent with level L and can be recognized (Figure 9). Based on rockburst classification criteria and the polynomial regression technique, all quantitative boundaries of the levels for all indicators can be obtained and the VFS model parameters \(\left[a_{ij},b_{ij}\right]\), \(\left[c_{ij},d_{ij}\right]\), and \(M_{ij}\) for all level can be determined as follows:  
\[\left[a_{ij},b_{ij}\right]=\left[ \begin{array}{cccc}[0.1,\ 0.3]&[0.3,\ 0.5]&[0.5,\ 0.7]&[0.7,\ 0.9]\\ [52.57,\ 40]&[40,\ 26.7]&[26.7,\ 14.5]&[14.5,\ 1.57]\\ [0.5,\ 2]&[2,\ 3.5]&[3.5,\ 5]&[5,\ 6.5]\end{array} \right] \tag{38}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Levels**} & \multicolumn{4}{c}{**Rockburst Indicators**} \\ \cline{2-5}  & \(\sigma_{\theta}\)/\(\sigma_{e}\) & \(\sigma_{d}\)/\(\sigma_{t}\) & \(w_{et}\) \\ \hline None (I) & \(<\)0.3 & \(>\)40.0 & \(<\)2.0 \\ Light (II) & 0.3–0.5 & 26.7–40.0 & 2.0–4.0 \\ Moderate (III) & 0.5–0.7 & 14.5–26.7 & 4.0–6.0 \\ Strong (IV) & \(>\)0.7 & \(<\)14.5 & \(>\)6.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The classification criteria of rockburst intensity. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Project Name**} & \multicolumn{2}{c}{**Main Prediction Indicators**} & \multirow{2}{*}{**Actual Situation**} \\ \cline{3-4}  & & \(\sigma_{\theta}\)/\(\sigma_{e}\) & \(\sigma_{d}\)/\(\sigma_{t}\) & \(w_{et}\) \\ \hline
1 & Diversion tunnel of Tianshengqiao II hydropower station & 0.34 & 23.97 & 6.60 & Moderate \\
2 & Underground cavern of Longyangugia hydropower station & 0.11 & 31.23 & 7.40 & None \\
3 & Diversion tunnel of Yuziki hydropower station & 0.53 & 15.04 & 9.00 & Moderate-strong \\
4 & Diversion tunnel of Lijiazio hydropower station & 0.10 & 23.00 & 5.70 & None \\
5 & Diversion tunnel of Jinping II Hydropower Station & 0.82 & 18.46 & 3.80 & Light-moderate \\
6 & Underground powerhouse of Sima hydropower station, Norway & 0.27 & 21.69 & 5.00 & Moderate \\
7 & Sewage tunnel, Norway & 0.42 & 21.69 & 5.00 & Moderate \\
8 & Diversion tunnel of Vietus hydropower station, Sweden & 0.44 & 26.87 & 5.50 & Light \\
9 & Guanyue Tunnel, Japan & 0.38 & 28.43 & 5.00 & Moderate-strong \\
10 & No.2 branch cave of Fatra hydropower station & 0.41 & 29.73 & 7.30 & Light \\
11 & Underground tunnel of Liubuge hydropower station & 0.23 & 27.78 & 7.80 & None \\
12 & Diversion tunnel of Taiplinyi hydropower station & 0.38 & 17.55 & 9.00 & Moderate \\
13 & Underground cavern of Puugugou hydropower station & 0.35 & 20.50 & 5.00 & Moderate \\
14 & Underground powerhouse of Laxiwa hydropower station & 0.32 & 24.11 & 9.30 & Moderate \\
15 & Heggura Tunnel, Norway & 0.36 & 24.14 & 5.00 & Moderate \\
16 & Cooling water tunnel of Forsmax nuclear power station, Sweden & 0.39 & 21.67 & 5.00 & Moderate \\
17 & Mine tunnel of Rasum chor, USSR & 0.32 & 21.69 & 5.00 & Moderate \\
18 & Mine tunnel of Raibl, Italy & 0.77 & 17.50 & 5.50 & Moderate \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Basic data of 18 typical rockburst cases around the world. where the first row is the attracting interval of \(\sigma_{\theta}/\sigma_{c}\) to four levels and the remaining rows represent \(\sigma_{c}/\sigma_{t}\) and \(w_{et}\). \[\left[M_{ij}\right]=\left[ \begin{array}{cccc}0.1&0.4&0.6&0.9\\ 52.57&33.35&20.6&1.57\\ 0.5&2.75&4.25&6.5\end{array}