## 4 Numerical Simulation of Interface Damage of Ballastless Track under Temperature Load
### Dynamic Characteristics of the Ballastless Track with Interface Damage  
The effect of existing interface damage on the safety and stability of high-speed railway operation is worth exploring. In this case, the quasi-static damage analysis of the ballastless track under temperature load was performed first to obtain the initial state of the track structure. Then, the train vibration load was applied on the rails to analyze the dynamic response of the ballastless track with three interface contacting conditions of CCBP and ACWL including the perfect bond state, partly damaged but no slippage state (\(\Delta t\)= 5\({}^{\circ}\)C, 15\({}^{\circ}\)C), and the sliding friction contact state. The tensile strain, vertical deformation in ACWL, and dynamic stress in the surface layer of the road bed were selected as the indices.  
In this section, a three-dimensional finite element model of a ballastless track structure containing the rails and fasteners was established. This structure was composed of CHN60 rails, a fastener system, track slab, self-compacting concrete (SCC), CCBP, ACWL, road bed, and soil foundation. The CHN60 rails were modelled by Euler beam element. The fastener system was modelled by spring-damper elements. The vertical and transverse stiffness of the fasteners and pads were 70 KN/m and 30 KN/m, and the vertical and horizontal damping were 60 KN\(\cdot\)s/m and 50 KN\(\cdot\)s/m, respectively. The geometries  
Figure 11: Relationship curves between QUADSCRT/SDEG and \(\pm\Delta t\) in cases 3\(\sim\)6.  
and the material parameters of other components and the model constraints were the same as the former model.  
The train vibration load is regarded as a periodic moving load and simplified to a sine function, as shown in Equation (5).  
\[F(t)=P_{0}+P_{1}\sin\omega_{1}t \tag{5}\]  
where \(F(t)\) is the train vibration load, \(P_{0}\) is the static wheel load, 130 KN, \(P_{1}\) is the vibration load, \(P_{1}=M_{0}a_{i}\omega_{i}{}^{2}\), \(M_{0}\) is the unsprung mass of the train, 750 kg, \(a_{i}\) is the height of geometric irregularity, 0.6 mm, \(\omega_{i}\) is the circular frequency of the vibrating wavelength, \(\omega_{i}=2\pi v/L_{i}\), \(v\) is the train speed, 350 km/h, and \(L_{i}\) is the wavelength of geometric irregularity curve, 2 m.  
The train vibration load was applied on the rails at the joint of the adjacent track slab (case 1) and the center of the base plate (case 2), respectively. The calculation results of dynamic responses are summarized in Table 8.  
As shown in Table 8, the dynamic indices at the adjacent joint and the center of base plate were almost the same. The interface contact state had a great impact on the dynamic response of the whole structure under the train loads. Compared with the perfectly bonded state, for the state where few interface microcracks existed, the transverse tension strain of ACWL was about ten times that of the previous state, while the longitudinal tension strain and the vertical stress in the surface layer of subgrade were about 10 times and 2 times that of the previous state, respectively. When the interface was totally unbonded, the transverse and longitudinal tension strain and vertical displacement of asphalt layer surface were about 134, 50, and 24 times that of the original state. The interface damage had a great influence on the dynamic response of the ballastless track.