## 3 Results
### Surrounding Rock Excavatability Classification Based on Rock-Breaking Data
#### 3.1.3 Establishment of TOPSIS-Based Surrounding Rock Excavatability Classification Criteria  
The \(BQ\) values of the two projects with different surrounding rock conditions were calculated. The \(SER\) and \(PR\) values in the corresponding stable phases were analyzed. Finally, \(BQ\) was fitted with \(SER\) and \(PR\) (Figures 19 and 20), with R\({}^{2}\) = 0.8209 and 0.8001, respectively, indicating good correlations. The optimal fitting equations are expressed as Equations (16) and (17). Analysis of variance shows that the significance values of Equations (16) and (17) were 0.000 (<0.01). This indicates that the fitting performance was excellent, and the models were accurate and reliable. \[SER= 13.5779e^{-(BQ/184.7545)}+0.0098 \tag{16}\]  
\[PR= -0.0073 BQ+6.0691 \tag{17}\]  
With \(BQ\) values as the independent variable, six classification intervals of \(SER\) and \(PR\) were calculated using Equations (16) and (17). Thus, an \(SER\) evaluation and classification system was established for the TBM construction section, incorporating geological and tunneling parameters (Table 5). When \(SER\) is at Grade L-1, the rock is mostly soft, exhibiting fractures and low strength; TBMs have small rolling disc cutter wear losses and high rock-breaking efficiency; the surrounding rock shows good overall excavatability. As the \(SER\) grade increases from L-1 to L-6, rock strength and integrity gradually increase; the TBM rock-breaking efficiency decreases; SRE decreases. \begin{table}
\begin{tabular}{c c} \hline \hline \(BQ\)-Based Excavatability Classification & \(BQ\) \\ \hline
1 & \(<\)200 \\
2 & 325–200 \\
3 & 397–325 \\
4 & 507–397 \\
5 & 657–507 \\
6 & \(>\)657 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Surrounding rock excavatability grade classification based on the \(BQ\) value. Figure 19: Correlation between \(SER\) and \(BQ\). Actual TBM excavation was used to further verify the rationality of the proposed system. However, in practice, the system in Table 5 may encounter a problem in that _SER_ and _PR_ indicate different grades at the same moment of excavation. This problem can cause ambiguity when determining the grade. Therefore, a method that fuses these two indicators for evaluation is needed before example validation. In this study, TOPSIS was used to avoid this problem. According to the principle of TOPSIS, the classification boundaries of individual grades in Table 5 were used as samples. By calculating the SRE closeness of each grade, the final TOPSIS-based classification is shown in Figure 21. To better illustrate the TOPSIS-based SRE classification criteria, sample closeness and classification closeness were compared using some excavation data. For example, the closeness values of the 23 rd and 36 th samples were calculated as 0.3625 and 0.5203, lying within the range of 0.2985-0.4079 and 0.4079-0.6194, respectively. Thus, the SRE grades were determined as L-3 and L-2, respectively. In addition, the SRE evaluation indexes selected in this study were all positive indexes; i.e., SRE increases as _SER_ and _PR_ increase. From Figure 21, the classification intervals of Grades L-1, L-2, and L-6 were larger than those of L-3-L-5. This is because of the following. (1) For L-1 and L-6, some limits of their _BQ_ ranges are uncertain. This results in wider _BQ_ ranges and thus larger classification intervals for L-1 and L-6 (particularly more significant for L-1). (2) The actual surrounding rocks involved in Grades L-1 and L-2 have a relatively soft texture and low integrity. Table 5 shows that the penetration distribution was broader for the surrounding rocks with the above characteristics (Classes IV and V). Therefore, L-1 and L-2 exhibited a wider penetration distribution compared with L-3-L-5, further leading to a relatively larger classification interval for these grades. Figure 20: Correlation between _PR_ and _BQ_.