# 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  
(1) Membership function of a fracture zone  
A fault fracture zone, especially a large-scale fault zone, is a bad geological condition encountered in most tunnelline. The main problem encountered by a TBM entering a weak and broken surrounding rock section is collapse. The rock mass fissures in the fault fracture zone are developed, the groundwater is rich, and the hardness of the rock and soil layers is different, which easily cause cutter head damage as well as water irnush accidents and even endanger the safety of construction personnel and equipment. The wider the fault fracture zone the greater the possibility of collapse during construction. Therefore, the width of a fracture zone is an important evaluation index to characterize the geological adaptability of TBM construction [21]. [PERSON] divided the width of fault fracture zones into five levels. When the width of a fracture zone is less than 0.1 m, it has little impact on tunnel construction. When the width of a fracture zone is in the range of 0.1-0.5 m, the fault fracture zone has a small impact on the TBM. When the width of a fracture zone is in the range of 0.5-2 m, the fault fracture zone has an impact on TBM tunnelling. When the width of a fracture zone is in the range of 2-8 m, it has a great impact on TBM tunnelling. When the width of a fracture zone is greater than 8 m, a TBM jams and is unable to tunnel normally [22; 23]. Therefore, the working conditions of a TBM are divided into five levels according to the width of the fracture zone, as shown in Table 9. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Evaluating** & \multicolumn{5}{c}{**TBM Operating Conditions**} \\ \cline{2-6}
**Indicator** & **Good** & **Preferably** & **Secondary** & **Commonly** & **Worse** \\ \hline CAI (0.1 mm) & \textless{}0.5 & 0.5–1 & 1–4 & 4–5 & \textgreater{}5 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Corresponding relationship between the TBM working conditions and the CAI. To sum up, combined with the existing research results and actual engineering conditions, the membership function of the width of the fracture zone is constructed as shown in Equation (30):  
\[U_{8}(x)=\left\{ \begin{array}{l}1(x<0.1)\\ \frac{8-x}{8-0.1}(0.1\leq x<8)\\ 0(x\geq 8)\end{array} \right. \tag{30}\]  
(2) Membership function of large deformations of the surrounding rock  
Scholars have much in the way of research on the prediction of large deformations of the surrounding rock. Although some results have been achieved, it is still a weak aspect. [PERSON] put forward the concept of a firmness coefficient, which was accepted by Chinese scholars. In China, a similar stress strength ratio is mostly used to characterize the deformation mechanism of the surrounding rock, that is, the ratio between the maximum principal stress, shear stress or vertical principal stress of the surrounding rock and the uniaxial compressive strength. [PERSON] proposed a judgment index of extrusion deformation, shown in Equation (31), based on the above theory, which establishes the relationship between the convergent strain value of the surrounding rock and the ratio of the rock strength to in situ stress. It is commonly used in predicting soft rock deformations [24]:  
\[\xi=\frac{\omega}{D}\times 100\% \tag{31}\]  
where, \(\xi\) is the deformation of the surrounding rock; \(\omega\) is taken as the convergence deformation value of the surrounding rock; and \(D\) is the tunnel diameter. Due to the insufficient amount of data collected in the project, [PERSON]'s method is more convenient to use. Based on this, a judgment standard of soft rock deformations, as shown in Table 10, is obtained. According to [PERSON]'s research on the large deformations of TBMs, it can be concluded that when the large deformations of the surrounding rock reach the strong deformation standard in Table 10 they will have a greater impact on the tunnelling of the TBM [25].