## 3 Numerical Simulation of Tunnel Excavation without Grouting
### Mechanical Response Analysis of II-Type Section Tunnel
moments at the left and right tunnel arch foot are \(-\)78.34 kN \(\times\) m and \(-\)50.97 kN \(\times\) m, respectively, the maximum bending moment at the tunnel bottom is \(-\)99.14 kN \(\times\) m. After grouting, in the contact region, the maximum positive and minimum negative bending moments around K' are increasing to 65.26 kN \(\times\) m and \(-\)26.25 kN \(\times\) m, respectively, and the maximum positive and minimum negative bending moments around M' are increasing to 40.58 kN \(\times\) m and \(-\)24.35 kN \(\times\) m. These are indicated that the larger shear force is generated in the contact region, because the grouting improves the bearing capacity of surrounding rock in the backfill region, and the shear force increases, but the shear force in the limestone region remains constant. Due to the stress distribution characteristics of the tunnel primary support, the large bending moments occurred at the left and right tunnel arch foot are \(-\)27.29 kN \(\times\) m and \(-\)22.43 kN \(\times\) m.  
Figure 10b shows the torque distribution before and after grouting on the Y = 10 m section in the II-type. Before grouting, the large torque distributed at the left and right tunnel arch foot are 50.46 kN \(\times\) m and \(-\)55.32 kN \(\times\) m, respectively. Due to the symmetry of the strata on the left and right side of tunnel, there is no obvious torque at other location on the tunnel section. However, at the tunnel arch foot, due to the structural characteristics, a large load and complex stress state are occurred, resulting in large torque distribution. Figure 10: Mechanical response of II-type tunnel on Y = 10 m section (**a**) bending moment (**b**) torque (**c**) deformation and (**d**) max principle of support. After grouting, the torque on the tunnel section is 0, indicating that grouting can effectively improve the torque distribution. Figure 10c shows the deformation of the primary support before and after grouting in the Y = 10 m section of II-type tunnel. K' and N' are the first excavation step and second excavation step boundary, respectively. The tunnel vault is in the limestone region, and the deformation of tunnel vault is almost 0 due to the good mechanical property of the surrounding rock. A large deformation occurred at the left step feet of the first and second excavation step, in which the displacement at K' and M' are 30.22 mm and 36.04 mm. The reason is that there is a large area of the karst cave on the left of tunnel. After excavation and before primary support construction, the stress of surrounding rock is fully released, resulting in a large deformation at the feet of the excavation step after the construction of primary support. After grouting, the deformations on the K' and N' are 16.95 mm and 11.78 mm, respectively, the deformation of primary support is effectively improved by grouting. Figure 10 shows the maximum principle distribution before and after grouting on Y = 10 m section of II-type tunnel. Before grouting, a large maximum principle is generated in limestone region, while the maximum principle stress in the backfill region and contact region is small, where the maximum principle stress in the contact region is almost 0. After grouting, the distribution law of the maximum principle stress is almost constant, which is the same as that of I-type tunnel.