# 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  
(1) Membership function of the rock uniaxial compressive strength  
The uniaxial compressive strength of rock is an important index for predicting the TBM evaluation model. The lower the \(R_{\rm c}\) the higher the TBM's penetration rate, and the faster the tunnelling. The higher the \(R_{\rm c}\) the lower the TBM's penetration rate, and the slower the tunnelling. With the increase in the uniaxial compressive strength of the rock, the TBM's penetration rate efficiency gradually declines. However, when the \(R_{\rm c}\) is too low, the self-stabilizing time of the surrounding rock after TBM tunnelling is extremely short, or even cannot be stabilized. When the \(R_{\rm c}\) value is within a certain range, the tunnelling of the TBM can not only maintain a certain speed but also keep the surrounding rock of the tunnel self-stabilizing for a certain period of time. It is generally believed that when the rock uniaxial compressive strength, \(R_{\rm c}\), is between 40 and 75 MPa, the TBM has strong adaptability; however, when the rock uniaxial compressive strength, \(R_{\rm c}\), exceeds 180 MPa or is lower than 15 MPa, it is not conducive to TBM construction [16]. To sum up, combined with the existing research results and actual engineering conditions, construct the membership function of the rock uniaxial compressive strength, \(R_{\rm c}\), as shown in Equation (25):  
\[U_{4}(x)=\left\{ \begin{array}{l}0(x<15)\\ \frac{x-15}{40-15}(15\leq x<40)\\ 1(40\leq x<75)\\ \frac{180-x}{180-75}(75\leq x<180)\\ 0(x\geq 180)\end{array} \right. \tag{25}\]  
(2) Membership function of the rock mass integrity coefficient  
The rock mass integrity coefficient, \(K_{\rm v}\), is an index reflecting the integrity of the rock mass. The integrity coefficient of the rock mass is the square of the ratio of the longitudinal wave velocity between the rock mass and the rock. The integrity coefficient can be measured by the dynamic method. According to the integrity coefficient of the rock mass, the integrity degree of the rock mass can be classified into five categories: complete, relatively complete, relatively broken, broken, and extremely broken. The development degree of the structural planes (joints, bedding, schistosity, and faults) in the rock mass (i.e., rock mass integrity) is an important geological factor affecting the TBM tunnelling efficiency. Generally, when the rock mass is very complete, if the strength of the surrounding rock is high, it is not conducive to TBM tunnelling, and when the integrity of the rock mass is low, the TBM penetration rate is fast and its efficiency is high; however, when the structural plane is particularly developed and the rock mass integrity is very poor, the rock mass has been broken or loose, and the overall strength is very low. As the surrounding rock of the project, it has no self-stability. At this time, the TBM tunnelling speed is very slow and the efficiency is very low. Therefore, when the rock mass structural plane is especially developed or undeveloped, it is not conducive to TBM tunnelling. Judging from the tunnelling situation of the TBM construction tunnel, when \(K_{\rm v}\geq 0.85\) the rock mass is very intact; if the rock compressive strength of the corresponding rock mass \(R_{\rm c}>150\) MPa, the TBM tunnelling efficiency is very low. When \(0.45\leq K_{\rm v}\leq 0.75\), the rock mass is relatively complete; if the corresponding \(R_{\rm c}=30\)-\(60\) MPa, the TBM tunnelling efficiency is the highest. When \(K_{\rm v}<0.35\), the rock mass is very broken and mostly located in the fault influence zone, the engineering geological conditions are very poor and the surrounding rock of the tunnel is prone to collapse and instability, which seriously affects the normal tunnelling of the TBM, and the tunnelling efficiency is very low [16].