## 4 A New Grouting Evaluation Method
### Calculation of Permeability Coefficient Weights Based on the Equations in This Paper
#### 4.2.1 Analytic Hierarchy Process  
APH model calculations such as Figure 10. In this study, the target layer is how to choose the permeability coefficient value based on the equations in this paper. Suppose the number of grouting inspection holes is \(N_{i}\) and \(N_{1}>N_{2}>\ldots>N_{i},i=1,2,3\ldots\). Combined with the site, we choose five values as follows,  
\[\left\{\begin{array}{c}B_{1}=K_{\min}\\ B_{2}=K_{\max}\\ B_{3}=K_{middle}\\ B_{4}=K_{\max;\min}\\ B_{5}=K_{mean}\end{array}\right.. \tag{35}\]  
Therefore, the criterion layer is,  
\[\left\{\begin{array}{c}A_{1}=Q_{\text{extreme}}-Q_{actual}\\ A_{2}=Q_{\text{median}}-Q_{actual}\\ A_{3}=Q_{mean}-Q_{actual}\end{array}\right.. \tag{36}\]  
Figure 10: Calculation process of AHP.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Different Excavation** & **Water** & **Outflow** & **C1/** & **C2/** & **C3/** & **C4/** & **C5/** & **C5/** & **C6/** & **C7/** & **C8/** \\
**Sections** & **Pressure/MPa** & **Section** & **(L/min-m)** & **(L/min-m)** & **(L/min-m)** & **(L/min-m)** & **(L/min-m)** & **(L/min-m)** & **(L/min-m)** & **(L/min-m)** & **(L/min-m)** \\ \hline \multirow{2}{*}{ZD DK365+333 to +313} & \multirow{2}{*}{1.7} & 18 m & 1.27 & 0.61 & 0.74 & 0.01 & / & / & 1.16 & / & / \\ \cline{3-10}  & & 20 m & 1.42 & 3.78 & 2.72 & 1.47 & / & / & 3.41 & / & / \\ \cline{3-10}  & & 13 m & 1.50 & 1.00 & 0.25 & 0.50 & 0.12 & / & / & / & / \\ \cline{3-10}  & & 15 m & 1.67 & 1.11 & 0.33 & 0.55 & 0.10 & / & / & / & / \\ \cline{3-10}  & & 15 m & 0.89 & 0.29 & / & / & 0.44 & 0.01 & / & / & / \\ \cline{3-10}  & & 18 m & 1.30 & 1.02 & / & / & 1.11 & 0.36 & / & / & / \\ \cline{3-10}  & & 21 m & 1.19 & 0.86 & / & / & 1.66 & 0.79 & / & / & / \\ \cline{3-10}  & & 24 m & 1.11 & 1.94 & / & / & 2.50 & 1.11 & / & / & / \\ \cline{3-10}  & & 27 m & 1.08 & 1.78 & / & / & 2.48 & 1.00 & / & / & / \\ \cline{3-10}  & & 25 m & 1.33 & 1.60 & 1.00 & 0.67 & 0.80 & / & 1.00 & 1.33 & 1.67 \\ \cline{3-10}  & +292.5 circular segment & & 28 m & 1.19 & 2.98 & 2.38 & 8.93 & 2.98 & / & 2.38 & 2.98 & 2.98 \\ \cline{3-10}  & & 25 m & 0.33 & 0.80 & 0.33 & 0.26 & 0.53 & / & / & / & / \\ \cline{3-10}  & & 28 m & 0.40 & 1.00 & 0.40 & 0.30 & 0.55 & / & / & / & / \\ \hline \hline \end{tabular}
\end{table}
Table 10: Actual measurement data of different sections of Qiyue Mountain Tunnel.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**A2 to B** & **B1** & **B2** & **Wi** & **C.R** \\ \hline B\({}_{1}\) & 1 & 7/2 & 0.777778 \\ B\({}_{2}\) & 2/7 & 1 & 0.22222 & 0 \\ \hline \hline \end{tabular}  
We use \(b_{1}=\sum\limits_{j=1}^{n}a_{i}b_{ij}\) to calculate \(B_{1}\), \(B_{2}\), \(B_{3}\), \(B_{4}\), and \(B_{5}\), i.e.,  
\[[B_{1}\ \ B_{2}\ \ B_{3}\ \ B_{4}\ \ B_{5}]=[\ \ \ \ 0.241401\ \ \ \ 0.074277\ \ \ \ 0. 092068\ \ \ 0.026305\ \ \ 0.565948\ ].\]  
Meanwhile, \(C.R.=(\sum\limits_{i=1}^{n}w_{i}C.I._{i})\cdot{(\sum\limits_{i=1}^{n}w_{i}R.I. _{i})}^{-1}=\frac{(w_{1}C.I._{1}+w_{2}C.I._{2}+...+w_{n}C.I._{n})}{(w_{1}R.I._{ 1}+w_{2}R.I._{2}+...+w_{n}R.I._{n})}=0.055083<0.1\) meets accuracy requirements at the same time.