# Research on an Evaluation Method for the Adaptability of TBM Tunnelling
## 3 Selection of Evaluation Index and Establishment of Fuzzy Function
### Establishment of the Fuzzy Function
#### 3.2.3 Adverse Geology Membership Functions
To sum up, combined with the existing research results and actual engineering conditions, the membership function of large deformations of the surrounding rock is shown in Equation (32):  
\[U_{9}(x)=\left\{ \begin{array}{l}1(x<0.025)\\ \frac{5-x}{5-0.025}(0.025\leq x<0.05)\\ 0(x\geq 0.05)\end{array} \right. \tag{32}\]  
(3) Membership function of water intrushes \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Evaluating** **Indicator**} & \multicolumn{4}{c}{**TBM Operating Conditions**} \\ \cline{2-5}  & **Extremely Strong** & **Strong** & **Medium** & **Weak** \\  & **Deformation** & **Deformation** & **Deformation** & **Conjugation** \\ \hline Deformation & \textgreater{}0.1 & 0.1–0.05 & 0.05–0.025 & \textless{}0.025 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: [PERSON]’s soft rock deformation judgment standard. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Evaluating Indicator**} & \multicolumn{4}{c}{**TBM Operating Conditions**} \\ \cline{2-6}  & **Worse** & **Commonly** & **Secondary** & **Preferably** & **Good** \\ \hline Fracture zone width & \textgreater{}8 & 2–8 & 0.5–2 & 0.1–0.5 & \textless{}0.1 \\ (m) & \textgreater{}8 & 2–8 & 0.5–2 & 0.1–0.5 & \textless{}0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Evaluation criteria for the adaptability of the fracture zone width. Tunnel water intrushes is often encountered in the process of TBM construction. There are many factors affecting water inrush in tunnels. Due to the complexity and variability of tunnel water intrushes, the prediction of water intrushes is not accurate enough. Tunnel water inflow is an important index to evaluate the adaptability of TBM construction to water intrushes. According to the field-measured data, the greater the unit maximum water inflow the higher the risk of water inrush disasters in the tunnel and the worse the adaptability of TBM construction to geology. [PERSON] et al. used the RME evaluation standard for evaluation, while [PERSON] and others used the \"penalty factors\" method to predict the performance of a TBM. The reduction factor of water inflow less than 2 0 L/S is 1, the reduction factor of 20 to 50 L/S is 0.8 and the reduction factor of more than 50 L/S is 0.5. Both the code for the hydrogeological and engineering geological exploration of mining areas (GB12719-1991) and the provisions of water prevention and control in coal mines (2009) require that the aquifers be divided into weak, medium, strong, and extremely strong according to the unit water inflow, \(\Downarrow\), of the borehole. Based on this, the adaptability evaluation criteria of the maximum water inflow are shown in the following Table 11.  
To sum up, combined with the existing research results and actual engineering conditions, the membership function of water inflow is constructed, as shown in Equation (33):  
\[U_{10}(x)=\left\{ \begin{array}{ll}1(x<0.1)\\ \frac{5-x}{5-0.1}(0.1\leq x<5)\\ 0(x\geq 5)\end{array} \right. \tag{33}\]  
(4) Membership function of rock bursts  
The common rock burst criterion includes rock brittleness coefficient, \(\sigma_{\text{c}}/\sigma_{\text{t}}\), the rock stress coefficient, \(\sigma_{\text{0}}/\sigma_{\text{c}}\), the elastic energy index, \(W_{\text{et}}\), the initial stress level, \(\sigma_{1}/\sigma_{\text{c}}\), and the rock brittleness index. Among them, \(\sigma_{\text{0}}\) is the maximum shear stress, \(\sigma_{\text{c}}\) is the uniaxial compressive strength of rocks, \(\sigma_{t}\) is the uniaxial tensile strength of rocks and \(\sigma_{1}\) is the maximum principal stress. See Table 12 for a rock burst evaluation index and intensity classification. For the convenience of parameter acquisition, the initial stress level, \(\sigma_{1}/\sigma_{\text{c}}\), is selected in this paper as the evaluation object of rock bursts [26]. To sum up, combined with the existing research results and actual engineering conditions, the membership function of rock burst is constructed, as shown in Equation (34):  
\[U_{11}(x)=\left\{