# Track-Bridge Interaction of CWR on Chinese Large-Span Bridge of High-Speed Railway
## 2 Research Model of Track-Bridge Interaction
### Research Model Proposed by Scholars
The rail additional force of the Hongshuiihe cable-stayed bridge is calculated, and the representative actual freight train braking force spectrum is obtained by establishing the longitudinal dynamic model of locomotive and vehicle. A large-scale, dynamic, nonlinear finite element program, DZXL, is compiled, which can be used for the static and dynamic calculation of the coupling effects of brake, flexure, andbrake flexure [14]. Taking Wuhu Yangtze River Bridge (180 + 312 + 180 m), a three-span, continuous steel truss girder, fan-shaped double-cable plane cable-stayed bridge, as an example, the time history curve of train braking force is applied to the bridge, and the response envelope diagram of rail longitudinal force on the bridge span and the shear response time history of the pier bottom are obtained [15; 16]. In 2001, [PERSON] used the nonlinear beam element to simulate track-bridge contact and the rigid arm to simulate the beam span height. Based on algor nonlinear structural finite element analysis software, the mechanical model of the interaction between the plane bar track structure and the bridge was established. The calculation results of the model were similar to the measured results [17]. [PERSON] established a mechanical model for calculating the additional force of CWR on a ballasted track fastener bridge with small resistance, which can comprehensively consider the interaction of the rail, sleeper, and beam. The model can consider the longitudinal relative displacement of the sleeper and the rail [18; 19; 20]. In his doctoral dissertation, a three-dimensional finite element model is used to study the parameters of the track-bridge interaction in the super-large bridge crossing Xingyan highway of Qinhuangdao Shenyang passenger-dedicated line as an example, and the working conditions of double track loading and opposite loading of trains are compared [21]. VBA of AutoCAD combined with general finite element ANSYS is used for secondary development. The 3D solid model of the beam body is automatically generated according to the two-dimensional cross-section of bridge to calculate the interaction between the beam and the rail [22]. In 2007-2009, [PERSON] deduced the exact stiffness formulations considering the loading history of \"temperature change\", \"sudden change of ballast stiffness when the train reaches the bridge\", \"bending of the supporting structure\", and \"braking\" [23; 24]. In 2012, [PERSON], [PERSON], and [PERSON] proposed the unequal length rail-bridge coupling element based on the significant difference of bending stiffness between the track and the bridge. The dynamic response models of the train track-bridge interaction system with two bridge structures were established by using unequal length and equal length rail-bridge coupling elements [25]. In 2014, [PERSON] and [PERSON] deduced the expression of longitudinal resistance considering loading history, established the differential equation of relative displacement of beam and rail, and solved the longitudinal force of rail and the horizontal force of pier and abutment, iteratively. The calculation results were closer to the actual situation [26]. In 2015, [PERSON] proposed a new calculation model based on the original CWR calculation model on a continuous rigid-frame bridge, the stress characteristics of the rigid-frame bridge, and the principle of the track-bridge interaction, mainly simplifying the piers. The simplified model can be used for calculation under telescopic, broken rail, and braking conditions, but the error is large under flexure conditions [27]. Through a series of indoor tests, [PERSON], [PERSON], and [PERSON] have carried out accurate resistance performance tests on fasteners commonly used in elevated urban rail transit in China. A new nonlinear analysis model of the track-bridge interaction is proposed, which considers the load history effect and the change of longitudinal resistance of the track fasteners under different load conditions [28].