## 5 Analysis of Numerical Model Results
### Analysis of Sudden Water Surges in Tunnels with Different Rock Wall Thicknesses  
Figure 11 lists the cloud map of tunnel water gushing at \(t=1800\) ms with rock wall thickness \(d=1.8\) m, 2.4 m, 3.0 m, 3.6 m, and 4.2 m. It can be seen from Figure 11 that, when the thickness of the rock wall is \(d=1.8\) m, the SPH particles of the aquifer are still continuously pouring into the tunnel, and the influx quantity is reduced compared with that when the thickness of the rock wall is \(d=0.6\) m. When the thickness of the rock wall is 2.4 m, the influx of SPH water particles in the tunnel is still obvious; however, the number of SPH water particles is obviously reduced compared with that when the thickness of the rock wall is \(d=1.8\) m. At the same time, it can be observed that the rock wall is affected by the water pressure of the aquifer, resulting in extrusion fold deformation. The cloud map of when the thickness of the rock wall is \(d=3.0\) m shows that there is no influx of SPH particles into the tunnel at \(t=1800\) ms; however, the SPH particles in the aquifer are obviously deformed into the tunnel by the rock wall, creating conditions for a subsequent water influx. However, when the thickness of the rock wall is \(d=3.6\) m, the cloud map shows that, although the SPH particles of the aquifer squeeze the rock wall, the water inflow channel has not been formed, and only the aquifer particles are leaked along the bottom of the aquifer.  
Figure 10: Vibrational velocity curve at measurement point #2.  
The SPH particles of different rock wall thickness models were extracted from adjacent SPH particles and finite element meshes on both sides of the rock wall boundary and at the position of the horizontal line of the blasthole for data analysis. The schematic diagram of measurement point extraction is shown in Figure 12a. It can be seen from Figure 12b that, when the thickness of the rock wall increases from 0.6 m to 4.2 m, the stress of measuring point #1 first decreases, then increases, and then decreases. The stress peaks of measuring point #1 corresponding to each rock wall width are 39.20 MPa, 18.32 MPa, 28.52 MPa, 16.31 MPa, 57.20 MPa, 8.67 MPa, and 9.82 MPa. When the thickness of the rock wall is 3.0 m, it reaches a peak value of 57.20 MPa and then begins to decrease. It can be seen from Figure 12c that the combined vibration velocity of the particles at measurement point #2 also shows a trend of first decreasing, then rising, and then decreasing by 1.26 cm/s, 1.00 cm/s, 2.01 cm/s, 0.48 cm/s, 0.47 cm/s. When the thickness reaches 3.0 m, it reaches a peak value of 1.73 cm/s, and then the peak vibration velocity begins to decrease with an increase in rock wall width. It can be seen from Figure 12d that the variation trend of the displacement map of the SPH particles at measuring point #2 is similar to the combined vibration velocity. For 0.065 m, 0.080 m, 0.029 m, 0.033 m, the peak displacement of 0.08 cm was also reached when the rock wall thickness was 3.0 m, and then the peak displacement began to decrease. From the perspective of stress peak, vibration velocity peak, and displacement peak, the minimum outburst prevention thickness of the rock wall of the karst tunnel under blasting should be greater than the thickness corresponding to the three peaks.  
Figure 12: Model data analysis of different rock wall widths: (**a**) Illustration of measurement points. (**b**) Finite element unit stress diagram for measurement point #1. (**c**) Vibrational velocity diagram of measurement point #2. (**d**) Displacement diagram for measurement point #2.