## 3 Numerical Simulation of Tunnel Excavation without Grouting
### Mechanical Response Analysis of II-Type Section Tunnel  
Figure 9 shows the displacement simulated result of II-type tunnel on the Y = 10 m section before and after grouting, where the arrow pointing to the direction of displacement. Large displacement is produced in three regions A\({}^{\prime}\), B\({}^{\prime}\) and C\({}^{\prime}\) in the backfill body, where the maximum displacement in A\({}^{\prime}\) region occurs at E\({}^{\prime}\), which is 414.52 mm, and the maximum displacement in B\({}^{\prime}\) region is located at D\({}^{\prime}\), with a value of 581.09 mm. The reason for the large displacement on the side wall of tunnel is the poor mechanical properties of the engineering spoil. Large displacement is produced under the small stress, and the lagging construction of primary support cannot restrain the surrounding rock displacement in time. The maximum displacement of the C\({}^{\prime}\) region at the tunnel bottom occurring at F\({}^{\prime}\), with a value of 66.06 mm. The reason is that after excavation, with the stress release of the surrounding rock, the surrounding rock at the tunnel bottom is squeezed by the surrounding rock on both sides of tunnel, resulting in upward development. After grouting, a large displacement occurred in the G\({}^{\prime}\) region, which is caused by the contact connection between the backfill body and karst cave wall, and a beam effect occurred in the karst cave wall. As a result, the span has a large deflection, and the backfill region has a large displacement due to the contact stress. However, the displacement of surrounding rock is obviously decreased, the maximum displacement in the right and left of the tunnel are located at H\({}^{\prime}\) and J\({}^{\prime}\), which are 29.48 mm and 21.67 mm, respectively. Figure 10 shows the mechanical response of II-type tunnel on Y = 10 m section. K\({}^{\prime}\) and M\({}^{\prime}\) are the intersection between the primary support and the karst cave border on left and right side of the tunnel, respectively. According to the karst cave boundary, the primary support is divided into three regions, one is the limestone region above the boundary, the second is the backfill region below the boundary, and the third is the contact region between the limestone and the backfill region around the K\({}^{\prime}\) and M\({}^{\prime}\). As shown in Figure 10a, in the limestone region, the bending moment gradually increases from the tunnel vault to the K\({}^{\prime}\) and M\({}^{\prime}\), and the maximum bending moment on the left and right sides of the tunnel are 32.03 kN \(\times\) m and 23.32 kN \(\times\) m, respectively. Large bending moment are generated in the contact region, where the maximum positive and minimum negative bending moments around K\({}^{\prime}\) are 63.37 kN \(\times\) m and \(-\)21.55 kN \(\times\) m, respectively, the maximum positive and minimum negative bending moments around M\({}^{\prime}\) are 32.31 kN \(\times\) m and \(-\)24.18 kN \(\times\) m, respectively. These are indicated that large shear forces are generated around the K\({}^{\prime}\) and M\({}^{\prime}\), resulting in bending moment changes. In the backfill region, large bending moments are produced at the tunnel arch foot and the tunnel bottom, and the bending  
Figure 9: Displacement of surrounding rock of II-type tunnel (Y = 10 m section) (**a**) with grouting (**b**) without grouting.