# Dynamic Responses of Asphalt Concrete Waterproofing Layer in Ballastless Track
## 6 Result Analysis and Discussion
### Comparison of Dynamic Responses of Track Structure with and without ACWL  
The dynamic responses of track structure with and without ACWL are compared based on the numerical model in this section to discuss the mechanical function of ACWL except waterproofing. The track structure with ACWL means the surface layer of roadbed consists of 80 mm ACWL and 160 mm graded gravel layer in thickness. The thickness of the surface layer of roadbed in the traditional track structure without ACWL is also 240 mm and it is all made of graded gravel. The cement concrete waterproofing layer is used at the shoulders and between two lines in the traditional track structure. The vertical displacement and acceleration at the bottom of each layer in the track structure with and without ACWL when the train speed is 350 km/h are shown in Figure 17. It can be seen from Figure 17 that the introduction of the ACWL reduces the vertical acceleration and displacement of each layer in the track structure compared to the traditional track structure. The average decrease in vertical acceleration and displacement of track structure with the introduction of ACWL is about 13% and 9%, respectively. In terms of the vertical acceleration, ACWL has a greater influence on the adjacent structural layers, base plate and roadbed. It is also seen that ACWL is helpful for improving the settlement of the subgrade, which is a major advantage for the track structure.  
The vertical displacement and stress at the bottom of roadbed in the track structure with and without ACWL are further compared in Figure 18. The peak values of the vertical displacement and stress in Figure 18 decreased by 14.5% and 20.3%, respectively, when the ACWL is included in the roadbed. The reason for the decrease in the dynamic responses at the bottom of roadbed is due to the viscoelastic characteristics of asphalt concrete. The viscous component in the asphalt concrete is capable of hysteresis recovery and energy dissipation. The asphalt concrete can convert part of the kinetic energy transmitted by the superstructure into heat energy and dissipate it in the surrounding environment, which can reduce the vibration of the track structure. To better describe the damping mechanism of ACWL, the time history of the longitudinal stress and strain at the bottom of ACWL is shown in Figure 19a. It is obvious from the Figure 19a that the strain curve lags behind the stress curve due to the viscous components of asphalt concrete. The stress-strain curve is also shown in Figure 19b. The stress-strain curves of elastic materials during the loading and unloading process are straight lines. However, the stress-strain curve at the bottom of ACWL in Figure 19b is a loop, which indicates that energy loss occurs during the loading and unloading process because of the energy dissipation effect of viscous components. Therefore, ACWL is beneficial for improving the stress of the whole track structure and can also reduce the settlement deformation of the subgrade.  
Figure 16: Lateral distribution of dynamic responses of ACWL (**a**) Vertical displacement; (**b**) Vertical stress.  
Figure 17: The dynamic responses of components in the track structure with and without ACWL (**a**) Vertical acceleration; **(b)** Vertical displacement.  
Figure 18: The time history curves of dynamic responses at the bottom of roadbed in the track structure with and without ACWL (**a**) Vertical displacement; **(b)** Vertical stress.