## 3 Numerical Simulation of Tunnel Excavation without Grouting
### Mechanical Response Analysis of I-Type Section Tunnel  
Figure 7a shows the simulated results of surrounding rock deformation on Y = 10 m section with and without grouting in I-type tunnel, where the arrow points to the deformation direction. Without grouting, large deformations are occurred in A and B region in the backfill body. The maximum deformation is 82.56 mm at point C in the A region, which is caused by the poor physical properties of the engineering spoil. The maximum deformation at D in B region is 55.25 mm. The reason is that the B region is connected to the karst cave wall, after the large displacement occurs in A region, the cumulative effect of displacement and the poor mechanical properties of the engineering spoil cause the backfill body produces the landslide phenomenon. Figure 7b shows the deformation of surrounding rock of I-type section with grouting, the displacement of the surrounding rock  
Figure 5: Horizontal convergence (**a**) simulated and (**b**) field monitor results of I-type tunnel. is small and uniform. Although the cumulative effect of displacement causes the landslide in the E region, the maximum displacement is only 31.27 mm. The settlement of tunnel surrounding rock, consist of uniformity and isotropy limestone, is analyzed by [PERSON] et al. and [PERSON] et al. (2019, 2020). The results show that large vertical displacement occurs at the tunnel vault, and small displacement is induced at the invert arch of the tunnel. However, due to the existence of the weak region of engineering spoil backfilled giant karst cave, the maximum displacement is occurred at the contact region of limestone region and backfilled region, which is consistent with the literature result made by [PERSON] et al. (2019). Figure 8a shows the bending moment distribution on the Y = 10 m section before and after grouting in the I-type tunnel, where K and M are the intersections of the karst cave border and the tunnel primary support. The primary support is divided into three regions according to the karst cave boundary. The upper left corner of the karst border is the limestone region, the lower right corner of the karst cave border is the backfilled region, and the contact region is close to K and M. Before grouting, the primary support in the backfill region produces a large bending moment. The maximum moment with a value of 144.03 kN \(\times\) m occurs at the right side of the tunnel bottom, while the primary support in the limestone region produces a small bending moment, and the maximum moment is  
Figure 6: Horizontal convergence of II-type tunnel (**a**) numerical simulation result (**b**) Field monitor result. Figure 7: Displacement of surrounding rock of I-type tunnel (Y = 10 m section) (**a**) without grouting (**b**) with grouting. located at the upper right arch shoulder, only 54.43 kN \(\times\) m. Large bending moment is generated at the primary support in the contact region, and the maximum positive and minimum negative bending moments around K are 88.98 kN \(\times\) m and \(-\)26.20 kN \(\times\) m, respectively, and the maximum positive and minimum negative bending moments around M are 68.44 kN \(\times\) m and \(-\)23.22 kN \(\times\) m, respectively, indicating that large shear force is produced in the contact region. After grouting, the bending moment of the primary support is improved obviously, and a large bending moment of \(-\)34.17 kN \(\times\) m is generated only at the right arch foot, while the primary support within the limestone remains almost unchanged. The maximum positive and minimum negative bending moments occurred around K are 132.29 kN \(\times\) m and \(-\)51.67 kN \(\times\) m, respectively, and the maximum positive and minimum negative bending moments occurred around M are 80.13 kN \(\times\) m and \(-\)50.53 kN \(\times\) m, respectively. The increase of bending moment in the contact region after grouting indicates that a greater shear force is generated in the contact region.