## 3 Finite Element Model of Ballastless Track-Bridge Structural System
### Parameter Selection
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Structural Parts** & \begin{tabular}{c} **Base** \\ **(C30)** \\ \end{tabular} & \
\begin{tabular}{c} **Beam** \\ **(C50)** \\ \end{tabular} &
\begin{tabular}{c} **Slab** \\ **(C55)** \\ \end{tabular} \\ \hline E\({}_{\text{f}}\)/GPa & 25.35 & 28.75 & 29.20 \\ A\({}_{1}\)+ & \(-\)0.0897 & \(-\)0.072 & \(-\)0.0702 \\ A\({}_{2}\)+ & 1 & 1 & 1 \\ x\({}_{1}\) & 1.20102 & 1.2005 & 1.1996 \\ x\({}_{2}\) & 1.9782 & 1.8633 & 1.84728 \\ P\({}_{1}\) & 2.23984 & 2.4988 & 2.54128 \\ P\({}_{2}\) & 0.56608 & 0.6325 & 0.6406 \\ c & 0.53486 & 0.5875 & 0.5938 \\ \(\varepsilon_{\text{k}}\)+/10\({}^{-6}\) & 95.24 & 110.3 & 112.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters related to the uniaxial tensile constitutive model of the concrete material. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Structural Parts** & \begin{tabular}{c} **Base** \\ **(C30)** \\ \end{tabular} & \
\begin{tabular}{c} **Beam** \\ **(C50)** \\ \end{tabular} &
\begin{tabular}{c} **Slab** \\ **(C55)** \\ \end{tabular} \\ \hline E\({}_{\text{f}}\)/GPa & 26.35 & 31.62 & 32.51 \\ A\({}_{1}\)- & 0.00344 & 0.004036 & 0.0027 \\ A\({}_{2}\)- & 1 & 1 & 1 \\ x\({}_{0}\) & 1.06218 & 1.18968 & 1.2152 \\ P\({}_{3}\) & 2.22346 & 2.88136 & 3.0432 \\ \(\varepsilon_{\text{k}}\)-/10\({}^{-6}\) & 1471.8 & 1678.4 & 1727 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters related to the uniaxial compressive constitutive model of concrete material. The connection mode between the beam and the track structure layers has a significant influence on the overall mechanical performance of the structural system. ANSYS Contact elements CONTA173 and TARGE170 with a friction coefficient equal to 0.2 are used to accurately simulate the \"dual textile-one membrane\" geotextile sliding interface between the beam and the base. To connect the slab and the base and coordinate the deformation with each other, shear steel bars are introduced at both ends of the bridge girder joints and the transition section between the side spines and the subgrade. The shear steel bars are simulated by linear spring element Combin14 with longitudinal stiffness of \(3.0\times 10^{5}\) N/mm and vertical tension-compression stiffness of \(2.0\times 10^{6}\) N/mm. The bridge and the base are provided with shear grooves above the fixed supports to transfer longitudinal forces such as train braking force to the piers. The ANSYS linear spring element Combin14 with a stiffness of \(1.0\times 10^{8}\) N/mm is used to simulate the shear grooves since their connection is nearly rigid. Based on the abovementioned material constitutive model and interfacial cohesive zone model, as well as the selection of material parameters, geometric dimensions, element types and connection elements of the different parts of the structure, a three-dimensional finite element model of the CRTS II ballastless slab track-simply supported bridge structural system for the high-speed railway is established, as shown in Figure 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Components** & \(\mathbf{t_{0}}\) & \(\mathbf{\delta_{0}}\) & \(\mathbf{\delta_{c}}\) \\  & **(MPa)** & **(mm)** & **(mm)** \\ \hline Normal direction & 1.792 & 0.0025 & 0.0282 \\ First tangential direction & 0.956 & 0.0152 & 0.0376 \\ Second tangential direction & 0.956 & 0.0152 & 0.0376 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters related to interface cohesive zone model. Figure 4: Finite element model of ballastless track–bridge structure.