## 3 Numerical Modeling  
### Model Construction  
This study adopted the Rhino-Griddle joint modeling method, in order to realistically reflect the complexity and irregularity of the terrain, consider the ground stress in the bias state, and reduce the modeling error. The three-dimensional tunnel model was developed through the tunnel topographic contour, longitudinal cross-section, digital elevation model (DEM), and profile of the portal section. In this study, the satellite image has a pixel size of 35,420 \(\times\) 36,421 and a spatial resolution of 2.3818 m/pixel; the DEM was derived from the PALSAR sensor of ALOS with a resolution of 12.5 m, a pixel size of 4428 \(\times\) 4553, and a spatial resolution of 4.77731 m/pixel. The co-ordinates of both are the WGS-84 co-ordinate system (World Geodetic System 1984 Co-ordinate System). First, the grayscale image was obtained by DEM. The grayscale image is a common form of elevation representation, which  
Figure 1: Geological longitudinal section of the Guanyin Mountain tunnel entrance section.  
uses a linear function to transform the original elevation range into the grayscale color range, dividing the white and black into a number of levels according to the logarithmic relationship between them. The 8-bit grayscale image is represented from 0 to 255; the larger the elevation, the closer to white, and the smaller the elevation, the closer to black. The grayscale image can be used to quickly and completely generate the topography of the tunnel area in line with the realistic terrain. The effects are shown in Figure 2. Subsequently, the area of the tunnel portal section was determined by the latitude and longitude co-ordinates and construction design drawings; the area was divided, and the topographic information such as the geological longitudinal section, portal section profile, and topographic contours were used to adjust the model surface. Then, the zone units were divided according to the rock layers and construction methods, and the complete three-dimensional model was established after stretching and exported to FLAC 3D through the interface software. This model was consistent with the actual topography and realized the refined modeling of the entrance section of the Guanyin Mountain Tunnel. The modeling process is shown in Figure 3.  
Figure 3: Rhino–Griddle joint modeling process.  
Figure 2: (**A**) DEM data; (**B**) grayscale image; and (**C**) Rhino surface model.  
In this study, the area 50 m in the axial direction of the portal section of the Guanyin Mountain Tunnel was simulated and analyzed, and the starting and ending piles of this area are K29+275 to K29+325, respectively. The maximum edge length of the model mesh is 1 m, with the hexahedral elements as the main elements and tetrahedral elements in part, with a total of 465,928 elements. The model width is seven times the hole diameter, and the overlying soil is up to the surface. The lengths of the horizontal (\(X\)-axis), vertical (\(Z\)-axis), and axis (\(Y\)-axis) directions of the tunnel model are 130 m, 55.39-79.70 m, and 50 m, respectively. The inverted arch of the tunnel is 45.80 m from the bottom of the model, and the surface slope along the tunnel orientation is 5.7\({}^{\circ}\). The design burial depth of the left line tunnel is 7.71-12.71 m, and that of the right line tunnel is 18.07-23.07 m. The clearance between the left and right tunnels is 17 m. The tunnel model is shown in Figure 4.