## 3 Results and Discussions
### Effect of the Thickness of Soil Interlayer  
(1) Variation in the thickness of the soil interlayer of existing tunnel a  
When the newly excavated tunnel goes through existing tunnel a and crosses existing tunnel b at the same time, comparative experiments are conducted to investigate the effects of the thickness of the soil interlayer between the new and existing tunnels on the surrounding rock mass of the existing tunnels. In this section, the thickness of the soil interlayer is selected as 0.3D, 0.5D, and 0.7D for analysis. Figure 10: Vertical displacement of the rock and soil around the existing tunnels as a function of the excavation footage. (\(h_{1}=0.7D\), \(h_{2}=0.3D\)). Figure 11 shows the deformation characteristics of the rock body around existing tunnel a, by increasing the thickness of the soil interlayer between existing tunnel a and the new tunnel from 0.3\(D\) to 0.7\(D\). The excavation footage of the new tunnel is controlled as a constant. Figure 11: Cont. The maximum deformation of the rock mass around existing tunnel a is analyzed underneath existing tunnel a. When the thickness of the soil interlayer between the new tunnel and existing tunnel a is 0.3\(D\), the settlement that occurs in the rock beneath existing tunnel a is the largest, with a maximum vertical displacement-to-diameter ratio of about 0.0056. As the thickness of the soil interlayer between the tunnels increases, the deformation of the rock beneath existing tunnel a gradually decreases. When the thickness of the soil interlayer is 0.5\(D\), the settlement of the rock directly underneath existing tunnel a becomes smaller, with the maximum vertical displacement-to-diameter ratio being about 0.0048. As the thickness of the soil interlayer continues to increase to 0.7\(D\), the maximum vertical displacement-to-diameter ratio reaches 0.0039 (see Figure 11c). Along the length of the existing tunnel, the maximum deformation of the rock mass around existing tunnel a is located at the center of the tunnel. The deformation decreases from the center to the sides. The deformation pattern conforms to the Gaussian distribution curve. The rules for the other two types of footage are consistent with the above laws and, therefore, will not be repeated. In the case of a new tunnel passing through two existing tunnels at the same time, the fixed excavation footage and the thickness of the soil interlayer of existing tunnel b remain unchanged. As the thickness of the soil interlayer in existing tunnel a increases, the settlement around existing tunnel a decreases. Along with the length of the existing tunnel, the vertical displacement of the tunnel edge decreases from the center of the tunnel axis to the sides of the tunnel. Variation in the thickness of the soil interlayer of existing tunnel bWhen the new tunnel crosses two existing tunnels (a and b) at the same time and the thickness of the soil layer between existing tunnel a and the new tunnel is specified, the vertical displacement of the rock and soil bodies around existing tunnel b is compared with the thickness of the soil layer in the upper crossing of existing tunnel b, which is 0.3\(D\), 0.5\(D\) and 0.7\(D\), respectively. Figure 11: Vertical displacement of existing tunnel a with varying soil layer thicknesses. From Figure 12, it can be seen that the effect of variation in the soil layer thickness of existing tunnel b is itself consistent with the above under the condition that the excavation footage is kept constant. At the end of tunnel excavation (\(L=2.5D\)), when the soil layer thickness decreases from \(0.7D\) to \(0.5D\), the vertical displacement of the rock mass above existing tunnel b increases, with the maximum vertical displacement-to-diameter ratio increasing from \(0.0052\) to \(0.0059\). Subsequently, the soil layer thickness continues to decrease to \(0.3D\), and the maximum displacement-to-diameter ratio of the bulge continues to increase to \(0.0066\) (see Figure 12c).