# Numerical Study on Track-Bridge Interaction of Integral Railway Rigid-Frame Bridge
## 3 Project Introduction and Fine Element Model  
The approach bridge of Quanzhou Bay Bridge in the newly-built Fuzhou-Xiamen HSR utilizes multiple 3 \(\times\) 70 m integral rigid-frame bridges. With no bearings throughout the whole bridge, the side piers and middle piers are consolidated with the main girder to form an integral rigid structure. The main girder of the bridge is made of a prestressed concrete box beam with a width of 12.6 m, as shown in Figures 4 and 5. With heights of 44-50 m, the middle piers use solid or hollow rectangle piers, whilst the side piers use thin-wall piers. The side piers, which are located at the junction of two adjacent bridges, share the same foundation. In the calculation, the stiffness of piers is simulated according to the actual stiffness, taking the influence of pile foundations on the stiffness of piers into account. In order to eliminate the influence of boundary conditions on the calculation results, three identical integral rigid-frame integral bridges were built in the more accurate calculation result model, as shown in Figures 6 and 7. The newly-built Fuzhou-Xiamen HSR was designed as a passenger-dedicated line, with a design speed of 350 km/h. China Railway Track System (CRTS) I double-block ballastless tracks were adopted for this HSR line, with spacings of 5.0 m between lines. The line utilizes 60 kg/m rails, WJ-8 fasteners and SK-2 double block sleepers. The sleepers were prefabricated in a factory and laid in-situ, with spacings of 650 mm. The slab bed of the track was cast-in-place with C40 reinforced concrete. With regard to the laying mode of each track layer, the model consists of three layers: 1 rail; 2 track slab plate; 3 base plate and beam body. In order to eliminate the influence of boundary conditions and simplify the modeling work as much as possible, the calculation is based on three integral rigid-frame bridges. The calculation model is shown in the Figures 6 and 7; the main properties of the track and the bridge are listed in Table 1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Structure** & & **Young’s** & **Thermal Expansion** & **Poisson’s** & **Volume** \\
**Layer** & & **Modulus** & **Coefficient** & **Ratio** & **Weight** \\ \hline Rail & U71 & \(2.06\times 10^{5}\) MPa & \(1.18\times 10^{-5}\) & 0.3 & 78.5 kN/m\({}^{3}\) \\ Slab plate & C40 & \(3.40\times 10^{4}\) MPa & \(1.0\times 10^{-5}\) & 0.2 & 25 kN/m\({}^{3}\) \\ Base plate & C40 & \(3.40\times 10^{4}\) MPa & \(1.0\times 10^{-5}\) & 0.2 & 25 kN/m\({}^{3}\) \\ Bridge beam & C50 & \(3.55\times 10^{4}\) MPa & \(1.0\times 10^{-5}\) & 0.2 & 25 kN/m\({}^{3}\) \\ Pier & C50 & \(3.55\times 10^{4}\) MPa & \(1.0\times 10^{-5}\) & 0.2 & 25 kN/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main properties of the track and the bridge. Figure 4: Design rendering of the integral rigid-frame bridge of the Fuzhou–Xiamen high-speed railway (HSR). Figure 5: Cross-section of integral rigid-frame bridge. The key for establishing the analysis model of the CRTS type-I double-block ballastless track and the integral rigid-frame bridge system consists in the accurate simulation of the connections between each layer. The connections between layers are simulated by setting appropriate longitudinal, vertical and lateral linear /nonlinear spring elements. The connection constraint parameters and their corresponding values are specifically provided in the Table 2.  
Several large-scale finite element (FE) software programs, such as ANSYS, ABAQUS and MIDAS, are widely adopted to study the track-bridge interaction of railway bridges ([4; 11; 12; 13; 14; 16; 17; 18; 20; 25; 26; 27; 28; 29]). In [28], an analysis comparing such software with the calculating