## 5 Numerical Analysis according to Tunnel Size
### Numerical Analysis Results by Tunnel Size  
Figure 17 shows the vibration reduction effect according to the size of the pilot tunnel for each cross-sectional area of the back expansion blasting. The cross-sectional diameters of the NATM expansion blasting were classified into 10.0 m, 15.0 m, and 20.0 m, and at this time, the vibration velocity was measured for the pilot tunnel diameters of 3.0 m and 5.0 m for each cross-sectional diameter. Figure 17a,b shows the results of vibration velocity measurement at the rear of the TBM and at the excavation surface of the TBM when the expansion blasting cross section is 10.0 m and the pilot tunnel size is 3.0 m and 5.0 m. As the size of the pilot tunnel increased from 3.0 m to 5.0 m, the vibration velocity measured at the rear of the TBM and the excavated surface of the TBM decreased by 22.17% and 15.55%, respectively. These results prove that as the diameter of the pilot tunnel is equal to the size of the NATM extension blasting, the vibration velocity decreased due to the  
Figure 16: Measurement point.  
Figure 15: Cases of analytical modelling according to size of NATM tunnel and TBM pre-excavation tunnel.  
securing of a free surface. In other words, as the diameter of the blasting surface and the diameter of the TBM excavation became equal, a larger free surface was secured, which decreased the vibration velocity. Figure 17c-f show the results when only the expansion blasting cross-sectional diameter increased to 15.0 m and 20.0 m, respectively, under the same conditions. Compared to the previous expansion blasting cross-sectional diameter of 10.0 m, the vibration velocity increased significantly as the NATM expansion blasting cross-sectional area increased. This may be attributed to the fact that the blasting area simulated by the outer shell hole blasting experiences an increase in the number of blasting holes as the NATM expansion blasting cross-sectional area increases. However, as the pilot tunnel diameter increased from 3.0 m to 5.0 m, the vibration velocity decreased by 33.90% and 25.70% (when the expansion blasting cross-sectional diameter was 15.0 m), and 73.02% and 69.34% (when the expansion blasting cross-sectional diameter was 20.0 m) at the rear and the excavation surface of the TBM, respectively. From these results, it can be inferred that the larger the expansion blasting cross-sectional diameter, the greater the vibration velocity reduction effect due to the securing of a free surface. In summary, the vibration velocity decreases as the expansion blasting cross-sectional diameter and the cross-sectional diameter of the pilot tunnel due to the TBM pre-excavation become equal. Thus, it can be concluded that selecting the TBM pre-excavation pilot tunnel size considering this factor is important for the stability of the TBM and the ground.  
Figure 17: Cases of analytical modelling according to size of NATM tunnel and TBM pre-excavation tunnel. (**a**) The rear of the TBM (NATM = 10); (**b**) The TBM excavation surface (NATM = 10); (**c**) The rear of the TBM (NATM = 15); (**d**) The TBM excavation surface (NATM = 15); (**e**) The rear of the TBM (NATM = 20); (**f**) The TBM excavation surface (NATM = 20).