## 3 Numerical Model  
### Establishment of Numerical Model  
FLAC\({}^{\text{3D}}\) was used to establish the numerical model of the double-arch tunnel. To avoid the influence of boundary condition setting on the simulation results, the boundary of the model was expanded to a certain range based on the study area. In tunnel modeling, it is generally considered that the scope of the affected area was defined between three times and five times of tunnel diameter. Therefore, the length of the model was set as 120.00 m (the maximum single tunnel diameter in this project was 14.6 m). The width of the model was set as 140.00 m according to the excavation length along the longitudinal axis of the tunnel in the actual construction. The surface of the model was established according to the actual terrain and the distance from the highest point to the bottom of the model was 69.46 m. In the model, the fault fracture zone was generalized as an area with a width of 20.00 m in the excavation direction and a dip angle of 60\({}^{\circ}\). As the thickness and distribution range of silty clay were small in practice, silty clay was not considered in the model. The soil layer in the model was divided into four parts, and their types and thicknesses were as follows: miscellaneous fill soil, 2-13.46 m thick; fully weathered granite, 22 m thick; strongly weathered diabase, 34 m thick; The width of the fault fracture zone was 20 m. The rock and soil in the model were established by solid elements. The Xinghu Road on the upper part of the tunnel was an urban expressway, and the road load was simplified to a uniformly distributed load of 21.5 kN/m\({}^{2}\), which was applied according to the position of the road in the scene, as shown in Figure 2a. In the model, the underground pipelines were simulated by shell structural units, and were arranged in the form of the longitudinal section of the tunnel, with a total of eight locations with a spacing of 10 m, as shown in Figure 2b. The lining of the three pilot tunnels was simulated by shell structural elements, as shown in Figure 2c. The lining and partition wall of the main tunnel was established by solid units, and their thickness and shape were established according to the actual situation, as shown in Figure 2d. The anchor bolts and advanced small conduits of the pilot tunnel were simplified as anchor cable units. The length of the anchor bolt was 2.5 m, the circumferential spacing was 0.6 m, and the longitudinal spacing was 1 m. The length of the advanced small conduit was 3.5 m, the circumferential spacing was 0.4 m, the longitudinal spacing was 3 m, and the extrapolation angle was 15\({}^{\circ}\) with the tunnel axis, as shown in Figure 2e. The long pipe shed at the portal of the main tunnel and the long pipe shed ahead of the tunnel body were also simulated by the anchor cable element. The external diameter of the long pipe shed was 159 mm and the circumferential spacing was 35 cm. The length of the long pipe shed at the entrance of the main tunnel was 40 m, with  
Figure 1: Longitudinal profile of the double-arch tunnel. an elevation of 1\({}^{\circ}\). The length of the long pipe shed ahead of the tunnel body was 20 m, with an elevation of 30\({}^{\circ}\), as shown in Figure 2f. Figure 3 shows the cross-section of the numerical calculation tunnel model. The side pilot tunnel was a straight wall semi-circular arch section, and the middle pilot tunnel was a small radius horseshoe-shaped section. The cross-sectional area of the pilot tunnel was 49.8 m\({}^{2}\), and the cross-sectional area of the side pilot tunnel was 26.7 m\({}^{2}\), and the two adjacent pilot tunnels were approximately 15 m apart in the horizontal direction. The three-bench reserved core soil method was adopted for the main tunnel, and the excavation section of the single tunnel was 119.3 m\({}^{2}\). The calculation steps in the numerical simulation were based on the on-site construction method and construction process.