## 3 Finite Element Model of Ballastless Track-Bridge Structural System  
### Parameter Selection  
To simulate the track-bridge structural system, the finite element software ANSYS (ANSYS, Inc., Southpointe, 2600 ANSYS Drive, Canonsburg, PA 15317, USA) was used to establish a nonlinear three-dimensional finite element model of a 3-span (a span of 32 m for each) CRTS II ballastless slab track-simple supported bridge structure (Figure 2). See \"Post-tensioned Prestressed Concrete Simply Supported Box Girder of Prefabricated Ballastless Track for 350 km/h High-Speed Railway\" Standard drawings for the number and shape arrangement of beams. The ANSYS Solid65 element and the Link8 element were used to model the bridge and the prestressing strands, respectively. Figure 3 shows the schematic diagram of the cross-section. The track structure is composed of slab, CA mortar layer and concrete road-bed (base). To model each component of the track system, ANSYS Solid65 element was also used. The mechanical parameters  
Figure 3: Box beam cross-section (mm). Figure 2: Mechanical model of the ballastless track-bridge structure. of each layer of materials are detailed in Table 1. The heavy rail type CHN60 was modelled by 3D Beam189 element. The values of the parameters in the static constitutive model of concrete material are shown in Tables 2 and 3; the values of the parameters in the fatigue constitutive model are as follows; \(A_{3}\)\({}^{+}\) = 0.701, \(A_{4}\)\({}^{+}\) = 1.050, \(A_{5}\)\({}^{+}\) = 8.428, \(A_{3}\)\({}^{-}\)= 0.713, \(A_{4}\)\({}^{-}\) = 1.160, \(A_{5}\)\({}^{-}\) = 5.439, \(A_{\text{M},3}\) = 0.425, \(A_{\text{M},4}\) = 1.1 and \(A_{\text{M},5}\) = 2.7. The static and the dynamic Young's modulus of CA mortar layer material are \(E_{\text{M}0}\) = 5.016 GPa and \(E_{\text{M}0}\) = 11.691 GPa, respectively. The nonlinear spring Combine39 is used to model fasteners, which are of the WJ-8 type with an ultimate displacement of 2 mm, an unloaded longitudinal peak resistance per rail equal to 24 kN/m, and a loaded longitudinal peak resistance per rail equal to 37.2 kN/m [31]. The track structure interlayer interfaces are simulated by the interface cohesive zone model [30]. The mechanical parameters of the interface between the slab layer and the CA mortar layer are shown in Table 4.  
The existing research results show that the shear strength of the interface between C50 concrete and CA mortar layer is lower than the shear strength between C30 concrete and CA mortar layer [32]. Therefore, at the moment of interface damage initiation and interface crack initiation, the displacement at the interface between the base layer and CA mortar layer is taken to be slightly larger than the corresponding displacement at the interface between the CA mortar layer and the slab layer (5 times larger is considered in this paper). Both interfaces are modelled using ANSYS cohesion element Inter205. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Structural Parts** & \begin{tabular}{c} **Density** \\ **(kN/m\({}^{3}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Thickness** \\ **(mm)** \\ \end{tabular} &
\begin{tabular}{c} **Poisson Ratio** \\ **(\mu)** \\ \end{tabular} \\ \hline Base (C30) & 26.00 & 190 & 0.2 \\ CA mortar layer & 18.00 & 30 & 0.2 \\ Slab (C55) & 26.00 & 200 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical parameters of the track structure.