# Influence of Uneven Subgrade Frost Heave on Deformation and Damage of CRTSIII Slab Track
## 4 Results and Discussion  
### Superiority of the Damage Plasticity Model Compared with a Linear Elastic Model  
The form of uneven subgrade frost heave was selected to be 20 mm/10 m (wave amplitude/wavelength) and the frost heaving wave peak acted in the middle of the 2# concrete base. In order to compare the difference between the damage plastic model and the linear elastic model, the analytical results of the two models were considered at the same time. Figure 8 shows the vertical deformation of the track structure under frost heaving. Under the action of uneven frost heave, the deformation of the track structure shifted from the bottom to top. The vertical displacement from the subgrade surface to the rail gradually decreased. The vertical deformation of the track structure in the damage-plastic model was significantly larger than that in the linear elastic model. Compared with the linear elastic model, the vertical displacements of the rail, composite slab, and concrete base in the damage plastic model increased by 0.26, 0.67, and 0.93 mm, respectively. This is due to plastic damage to the concrete of the track in this form of frost heaving. The damage of the concrete base appeared when the frost heaving was 2.878 mm, and macroscopic cracks appeared when the frost heaving was 6.598 mm. For the slab, there was slight damage in the beginning due to the existence of prestressed steel bars, and macroscopic cracks were observed when the frost heaving was 8.379 mm, as shown in Figure 9. The damage of concrete material led to a significant increase in its strain, thus, increasing its vertical deformation. When the linear elastic model was used to analyze the concrete, the constitutive relation of the concrete obeyed the generalized [PERSON]'s law, i.e., the stress-strain relationship was linear during loading and unloading, and the concrete would not yield after reaching its tensile strength. However, it could not reflect the softening behavior of concrete material. It was also observed that it could not effectively simulate the plastic strain of the track structure, resulting in low vertical deformation. Figure 7: Comparison between simulation results and theoretical computational results: (**a**) C60 uniaxial tensile; (**b**) C60 uniaxial compression; (**c**) C40 uniaxial tensile; (**d**) C40 uniaxial compression. Figure 10 shows the interlayer seam of the track structure under frost heaving. It was observed that when the frost heaving wave peak acted at the center of the concrete base, due to the unit slab, the seam between the composite slab and the concrete base appeared at the edge of the composite slab, while the seam between the concrete base and the subgrade surface appeared at one-quarter of the base length on both sides of the frost heaving wave peak. The interlayer seam between the base and subgrade surface was significantly higher than that between the self-compacting concrete and base. This was due to the fact that the vertical displacement of the base was greater than that of the composite slab. In addition, the interlayer seam of the track structure in the damage plastic model was smaller than that in the linear elastic model, in which the seam between the self-compacting concrete and base was reduced by 0.11 mm, and the seam between the base and subgrade surface was reduced by 1.84 mm. In the latter, the seam decreased significantly. This is because, as compared with the linear elastic model, the vertical deformation at the central position of the base in the damage plastic model increased significantly, which led to the downward offset of the base on both sides under the action of gravity, resulting in a significant decrease in the seam. Figure 8: Vertical displacement of track structure: (**a**) Linear elastic model; (**b**) damaged plasticity model. Figure 9: Damage cloud of track structure. Figure 11 shows the longitudinal stress on the upper surface of the composite slab and concrete base under frost heaving.