## 3 Numerical Modeling Process  
### Dynamic Finite Element Model  
In this study, finite element software (MIDAS/GTS2019 v2.1) was used to establish the dynamic finite element model of a high-speed railway natural foundation and a CFG pile composite foundation spanning the ground fissure zone (Figure 2). The mesh of the numerical model is hexahedron and the element is the entity. The specific modeling process can be found in Appendix A.  
Figure 1: (**a**) China’s high-speed railway network [34]; (**b**) the distribution of faults and ground fissures in the study area (the map was drawn using ArcGIS 10.5 ([[https://www.esri.com/](https://www.esri.com/)]([https://www.esri.com/](https://www.esri.com/)))); (**c**) vertical differential settling due to fissure; (**d**) ground surface cracking due to fissure; (**e**) TY3 ground fissures profile.  
In the numerical model, the intersection angle between the high-speed railway and the ground fissure was set at 90\({}^{\circ}\) (orthogonal), 60\({}^{\circ}\), and 30\({}^{\circ}\) (oblique), respectively. The dip angle of the ground fissure was 80\({}^{\circ}\) and ran through the entire stratum. In order to save on calculation costs, the length of the model was reduced by 50 m in orthogonally passing through the ground fissure, and the other parameters remained unchanged. The stratum within the simulated depth range was simplified into two layers, and its physical and mechanical parameters are shown in Table 1.  
The composite foundation of the numerical model of the cross-ground fissure zone of the Da'xi passenger-dedicated line adopts a pile-raft structure. The piles were CFG piles with a length of 20 m, a diameter of 0.5 m, a spacing of 2 m, and a square layout. A pile-soil contact element was established around the pile element to simulate the slip between the pile and the soil. A C30 reinforced concrete slab with a thickness of 0.8 m and plain concrete cushion of 0.2 m was set above the pile. Both were considered as a unified raft during modeling. The surface layer of the subgrade bed was 0.7 m thick and was filled with graded crushed stone. The bottom layer of the subgrade bed was 2.3 m thick. The slope gradient of the embankment was 1:1.5. To adapt to the active deformation of the ground fissure, the track structure was designed as a ballasted track. The cross-section of the composite foundation in the calculation is shown in Figure 3.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Unit Weight \(\gamma\)** & **Modulus of** & **Poisson Ratio \(\mu\)** & **Cohesion \(\alpha\)/kPa** & **Friction Angle \(\varphi\)/\({}^{\circ}\)** \\  & **/kN\(\cdot\)m\({}^{-3}\)** & **Elasticity E/MPa** & **Poisson Ratio \(\mu\)** & **Cohesion \(\alpha\)/kPa** & **Friction Angle \(\varphi\)/\({}^{\circ}\)** \\ \hline \hline \multirow{2}{*}{1\(\downarrow\) Silt} & 18.0 & 21 & 0.34 & 16.4 & 28.5 \\  & \multirow{2}{*}{2 Interbedding of silty clay and silt} & 19.8 & 30 & 0.32 & 23.75 & 17 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Soil layer parameters [9].  
Figure 2: (a) High-speed railway and ground fissure orthogonal \(\theta=90^{\circ}\); (b) \(\theta=60^{\circ}\); (c) \(\theta=30^{\circ}\).  
Rails, sleepers, CFG piles, and concrete baseplates were considered as isotropic linear elastic materials. The solid elements of the ballast bed and below were subject to the Drucker-Prager (D-P) elastoplastic failure criterion. The fasteners between the rail and sleeper were modeled using the spring-damping elements [36; 37]. The simulation conditions are shown in Table 3.