# 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
#### 3.2.2 Geological Condition Membership Functions
To sum up, combined with the existing research results and actual engineering conditions, construct the membership function of the rock mass integrity coefficient, \(K_{\rm v}\), as shown in Equation (26):  
\[U_{\rm S}(x)=\left\{ \begin{array}{l}0(x<0.35)\\ \frac{x-0.35}{0.45-0.35}(0.35\leq x<0.45)\\ 1(0.45\leq x<0.75)\\ 0.85-0.75\\ 0(x\geq 0.85)\end{array} \right. \tag{26}\]  
(3) Membership function of the crustal stress  
In a TBM project of deep buried long tunnels, the problem of large deformations and rock bursts caused by high crustal stress is very prominent. For deep-buried composite bottoms, high ground stress is the leading factor that endangers engineering safety. At present, crustal stress cannot be measured directly [17]. According to the field data and borehole measured data, the in situ stress level can be analyzed by linear regression within different depth ranges. The crustal stress level is generally divided by the strength stress ratio of the surrounding rock, as shown in Equation (27):  
\[T_{\rm s}=\frac{\sigma_{\rm max}}{R_{\rm c}} \tag{27}\]  
\(\sigma_{\rm max}\) is the maximum stress of a tunnel section; \(R_{\rm c}\) is the uniaxial compressive strength of the rock. According to the research at home and abroad, it can be found that a \(T_{\rm S}\) greater than 0.4 will have a great impact on TBM tunnelling, and the impact of \(T_{\rm S}\) on TBM tunnelling can be ignored when the \(T_{\rm S}\) is less than 0.15 [17; 18]. Combined with the engineering experience at home and abroad, the working conditions of a TBM are divided into the following four levels according to the crustal stress level, as shown in Table 7.  
To sum up, combined with the existing research results and actual engineering conditions, construct the membership function of the crustal stress level, as shown in Equation (28):  
\[U_{6}(x)=\left\{ \begin{array}{l}1(x<0.15)\\ \frac{0.4-x}{0.4-0.15}(0.15\leq x<0.4)\\ 0(x\geq 0.4)\end{array} \right. \tag{28}\]  
(4) Membership function of the CAI \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Evaluating Indicator**} & \multicolumn{4}{c}{**TBM Operating Conditions**} \\ \cline{2-5}  & **Good** & **Secondary** & **Commonly** & **Worse** \\ \hline Crustal stress level & \textless 0.15 & 0.15\textless 0.2 & 0.2\textless 0.4 & \(\geq\)0.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Evaluation criteria for the adaptability of the crustal stress level. The CAI is an important evaluation index that reflects the TBM cutter wear and tunnelling efficiency. In general, the higher the wear resistance of the rock the more serious the wear of the TBM cutter, cutter ring and bearing, and the higher the prop loss and construction costs. In serious cases, it even causes an increase in the number of downtime and cutter change, which affects the normal tunnelling of a TBM. Its value is measured by the Cerchar rock machine abrasion test. The Cerchar rock machine abrasion tester consists of an abrasion test device part and a measurement part. According to the calibration conversion of microscope measurements, take 0.1 mm as the basic unit, convert the measured value into the steel needle abrasion value and compare the steel needle abrasion value experience table to judge whether the measurement is reasonable. Calculate the average value of the abrasion values measured at three angles [19] and record it as a single test value. Each sample is tested three times on the surface, and the arithmetic mean of the three test values is the final CAI value of the sample. According to a large number of TBM construction engineering examples at home and abroad, the efficiency of a TBM is the highest when tunnelling in the surrounding rock with low-medium wear resistance, while the tunnelling efficiency in the surrounding rock with strong-extra strong wear resistance is greatly reduced [20].