# Risk Assessment of Drilling and Blasting Method Based on Nonlinear FAHP and Combination Weighting
## 4 Case Study
### Membership Calculation  
Based on the construction site conditions at the Daliangshan No. 1 Tunnel construction section on the Leshan-Xichang Expressway, the expert evaluation method is used to assess the secondary indicators for the risk assessment of the drilling and blasting construction of the Daliangshan No. 1 Tunnel. The membership degrees of each risk assessment indicator are obtained, as shown in Table 8.  
Based on the secondary indicators, single-factor evaluation matrices are constructed and further transformed into nonlinear fuzzy comprehensive evaluation matrices. The nonlinear fuzzy comprehensive evaluation matrices are as follows:  
The nonlinear fuzzy evaluation matrix for geological risk is  
\[\mathbf{Q}_{1}=\begin{bmatrix}0&0&3&6&1\\ 0&0&8&2&1\\ 0&0&2&7&1\\ 6&3&1&0&0\end{bmatrix} \tag{26}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Indicator Layer** & **Indicator Weight** & **Factor Layer** & **Subjective Weight** & **Objective Weight** \\ \hline \multirow{4}{*}{Geological risk T\({}_{1}\)} & \multirow{4}{*}{0.0569} & \multicolumn{2}{c}{Tunnel collapse t\({}_{11}\)} & 0.0474 & 0.2322 & 0.1115 \\ \cline{3-4}  & & Water and sand inrush t\({}_{12}\) & 0.2201 & 0.1843 & 0.2077 \\ \cline{3-4}  & & Rock burst t\({}_{13}\) & 0.0666 & 0.3359 & 0.1600 \\ \cline{3-4}  & & Borenoble collapse t\({}_{14}\) & 0.6658 & 0.2476 & 0.5208 \\ \hline \multirow{4}{*}{On-site risk T\({}_{2}\)} & \multirow{4}{*}{0.1852} & \multicolumn{2}{c}{Underground pipeline failure t\({}_{21}\)} & 0.7085 & 0.1071 & 0.5000 \\ \cline{3-4}  & & Existing buildings deformation t\({}_{22}\) & 0.0603 & 0.4552 & 0.1973 \\ \cline{3-4}  & & Surface subsidence t\({}_{23}\) & 0.2311 & 0.4376 & 0.3027 \\ \hline \multirow{4}{*}{Equipment risk T\({}_{3}\)} & \multirow{4}{*}{0.5016} & \multicolumn{2}{c}{Supporting structure deformation t\({}_{31}\)} & 0.0282 & 0.2730 & 0.1131 \\ \cline{3-4}  & & Poor ventilation t\({}_{32}\) & 0.2610 & 0.0476 & 0.1870 \\ \cline{3-4}  & & Water accumulation t\({}_{33}\) & 0.0829 & 0.2494 & 0.1407 \\ \cline{3-4}  & & Lining leakage t\({}_{34}\) & 0.1046 & 0.1710 & 0.1276 \\ \cline{3-4}  & & Blasting network failure t\({}_{35}\) & 0.5233 & 0.2590 & 0.4317 \\ \hline \multirow{4}{*}{Blasting risk T\({}_{4}\)} & \multirow{4}{*}{0.2562} & \multicolumn{2}{c}{Borenoble spacing t\({}_{11}\)} & 0.2240 & 0.1712 & 0.2057 \\ \cline{3-4}  & & & Borenoble depth t\({}_{22}\) & 0.1549 & 0.1384 & 0.1491 \\ \cline{3-4}  & & Number or type of borehole t\({}_{33}\) & 0.0935 & 0.0446 & 0.0766 \\ \cline{3-4}  & & Drilling equipment t\({}_{44}\) & 0.0953 & 0.0817 & 0.0906 \\ \cline{3-4}  & & Blasting charge structure t\({}_{45}\) & 0.0280 & 0.1422 & 0.0676 \\ \cline{3-4}  & & Discontinuous slag discharge t\({}_{46}\) & 0.0248 & 0.0824 & 0.0448 \\ \cline{3-4}  & & Blast jet lag t\({}_{7}\) & 0.0659 & 0.0678 & 0.0666 \\ \cline{3-4}  & & Misfire or residual blasting t\({}_{48}\) & 0.0175 & 0.1984 & 0.0802 \\ \cline{3-4}  & & Poor blasting effect t\({}_{9}\) & 0.2960 & 0.0733 & 0.2188 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Index weights for risk assessment of deep excavation construction.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c} \hline \hline
**Risk Level** & **t\({}_{12}\)** & **t\({}_{13}\)** & **t\({}_{14}\)** & **t\({}_{21}\)** & **t\({}_{22}\)** & **t\({}_{23}\)** & **t\({}_{31}\)** & **t\({}_{32}\)** & **t\({}_{33}\)** & **t\({}_{34}\)** &The nonlinear fuzzy evaluation matrix for site risk is  
\[\textbf{Q}_{2}=\begin{bmatrix}0&0&7&2&1\\ 0&0&3&6&1\\ 0&3&6&1&0\end{bmatrix} \tag{27}\]  
The nonlinear fuzzy evaluation matrix for equipment risk is  
\[\textbf{Q}_{3}=\begin{bmatrix}0&2&6&1&0\\ 1&6&3&0&0\\ 1&6&3&0&0\\ 0&2&6&2&0\\ 0&3&5&2&0\end{bmatrix} \tag{28}\]  
The nonlinear fuzzy evaluation matrix for blasting risk is  
\[\textbf{Q}_{4}=\begin{bmatrix}2&6&2&0&0\\ 0&2&4&4&0\\ 2&5&3&0&0\\ 4&3&1&0&0\\ 0&0&1&6&3\\ 0&0&2&5&3\\ 0&0&3&6&2\\ 0&0&3&4&3\\ 1&7&2&0&0\end{bmatrix} \tag{29}\]