## 3 Middle Rock Pillar Classification Method
### Numerical Model Establishment
Numerical Model Validation  
The vault settlement of main line tunnel was used to verify the numerical model. The excavation footage in the numerical model was 5 m. The footage in site excavation was 4-4.6 m/d. Therefore, each excavation footage of the numerical model corresponded to one day of excavation footage on site. The ZK2+665 mileage section of the main tunnel was selected as the monitoring section. The simulated vault settlements were verified with the observation (Figure 5). The maximum difference between the simulated value and the observed one was 1-2 mm, the results of which were relatively close. The observed value and the simulated value of vault settlement were both in the rapid deformation stage. The numerical simulation values were smaller than the measured ones due to the large mechanical disturbance, blasting, and the change in rock mass properties caused by groundwater, etc. Numerical Simulation Analysis  
To describe the stability in the middle region of the full-length middle rock pillar, a target section was selected every 5 m along the tunnel excavation direction, with 23 target sections numbered 1-23. Additionally, a monitoring point was set at the middle position of the middle rock pillar on each target section, as shown in Figure 1.  
Figure 6 shows the percentage of displacement of the measuring points on different target planes (different width-span ratios) compared with that of the measuring points on target Section No. 1 (tunnel entrance). The left coordinate axis in the figure is the percentage of displacement of measuring points on different target sections and the displacement of measuring points on target Section No. 1; the four curves correspond to different excavation schemes. The right coordinate axis is the specific value of the width-span ratio, corresponding to the column of each section. Figure 6a shows that when the vertical displacement of the central area of the middle rock pillar was before target Section No. 3 and the width-span ratio was within 0.11-0.20, the slope of the displacement curve was obviously large, indicating that the range of the width-span ratio had a significant impact on the vertical displacement. Figure 6b shows that the horizontal displacement of  
Figure 5: Comparison between the measured value and simulated value of the vault settlement. the central area of the middle rock pillar increased when the corresponding width span ratio was between 0.11 and 0.27 before target Section No. 4, which was not conducive to the stability of the middle rock pillar, and the width-span ratio was not conducive to the horizontal displacement. Figure 6: Relationship between the displacement and the width–span ratio of the central area of the middle rock pillar: (**a**) vertical displacement; (**b**) horizontal displacement. Figure 7 shows the percentage of the stress of the measuring points on different target sections compared with that of the measuring points on target Section No. 1. Before target Section No. 18, when the corresponding width-span ratio was within 0.11-1.00, the slope of the stress curve in the central area gradually decreased, and the influence of the clear distance on the stress value gradually decreased. When the width-span ratio was 1.00, the slope tended to be zero. Figure 8 shows the percentage of the maximum equivalent plastic strain of the measuring points on different target sections compared to the maximum equivalent plastic strain of the measuring point on target Section No. 1. The maximum equivalent plastic strain appears near target Section No. 5, and the corresponding width-span ratio ranges from 0.11 to 0.32. The maximum curve of the equivalent plastic strain rapidly flattened from a rapidly falling state, and the range of the plastic zone distributed in the central region of the middle rock pillar was significantly reduced or even disappeared.