# Calculation of Reasonable Tension Value for Longitudinal Connecting Reinforcement of CRTSII
## 3 Calculation Model and Experimental Verification
### Finite Element Model and Model Parameters  
In order to study the influence of tension value on the track slab and interface between track slab and CA mortar, a three-dimensional finite element model of a CRTSII slab ballastless track was built according to the actual size of the ballastless track based on the commercial software ABAQUS (Dassault Systemes, Paris, France.), as shown in Figure 6. The track slab, mortar layer, and concrete base were all simulated by solid elements, and the longitudinal reinforcement, constrained by the joint with the track slab concrete, was simulated by a truss element. The cohesive element, described in the above section, was disposed on the bonding layer between the concrete of the track slab and the  
Figure 5: Models of binding-slippage.  
mortar layer, and the debonding of the interface was simulated by the failure of the bonding layer element. Tie constraints were applied between the mortar layer and the concrete base, and all the displacements of the nodes at the bottom of the slab track system were restricted. The model had a total length of 39 m (six track slab), and the parameters are shown in Table 1.  
The load-displacement curve of the interface was obtained by a slab push test on single rail pads carried out by the China Academy of Railway Sciences Corporation Limited (CARS). In order to get the parameters of the interface element, a three-dimensional finite element model was established according to the actual size and constraint mode of the single rail pads push slab test (shown in Figure 7a). \(L=2.55\) m, \(b=0.65\) m, and \(t=0.2\) m. The loading method was simulated by gradually increasing the displacement of the track slab end.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Components** & **Young’s Modulus (Pa)** & **Poisson Ratio** & **Thermal Expansion Coefficient (\({}^{\circ}\)C\({}^{-1}\))** \\ \hline Track slab & \(3.25\times 10^{10}\) & 0.2 & \(1\times 10^{-5}\) \\ CA mortar & \(8\times 10^{9}\) & 0.2 & - \\ Concrete base & \(2.55\times 10^{10}\) & 0.2 & - \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of slab ballastless track model.  
Figure 6: Finite element model.  
Figure 7: Push test on single rail pad and its result. **(a)** Push test on single rail pad. **(b)** Testing and simulated result of push test.  
This paper assumes that the normal stress strength is the same as the shear stress strength, for the reason that the normal stress value is much smaller than the shear stress value in the process of the pushing test, and the normal stress strength is slightly greater than the shear strength based on the interface experiment [20], which resulted in a conservative result.  
Figure 7b shows the simulation results. The simulated load-displacement curve is most consistent with the experimental results with \(\tau_{f}\) = 0.075 MPa, \(\delta_{1}\) = 0.1 mm, \(\delta_{f}\) = 2 mm. It can be seen that the established model agrees well with the experimental results in the ascending phase, while the push force is slightly smaller than the test results in the descending phase. However, overall, there is good consistency for the fitting result, which proves that cohesive parameters are reasonable and credible.