# Deformation Law and Control Limit of CRTSIII Slab Track under Subgrade Frost Heave
## 2 Plastic Damage Analysis Model of Slab Tracks
### Finite Element Model of Slab Track  
#### 2.2.1 Geometric Model  
The beam body finite element theoretical analysis model can accurately reflect the stress and deformation of the slab track structure [44; 45; 46]. Therefore, the finite element software ABAQUS [47] has been used in this study. Based on the plastic damage constitutive relationship of concrete, a nonlinear analysis model of 200 m of CRTSIII slab track on subgrade is established, as shown in Figure 4. The dimensions of the geometric model  
Figure 3: Material parameters of C40 concrete. (**a**) Tensile stress-strain curve; (**b**) compression stress-strain curve; (**c**) tensile stress/damage factor-inelastic strain; (**d**) compressive stress/damage factor-inelastic strain.  
adopt the actual size of the structure. The dimensions of the track slab are 5600 mm \(\times\) 2500 mm \(\times\) 210 mm (length \(\times\) width \(\times\) height). The dimensions of the self-compacting concrete are 5600 mm \(\times\) 2500 mm \(\times\) 100 mm (length \(\times\) width \(\times\) height). The dimensions of the base plate are 5600 mm \(\times\) 2500 mm \(\times\) 210 mm (length \(\times\) width \(\times\) height). The dimensions of the groove are 1000 mm \(\times\) 700 mm \(\times\) 100 mm (length \(\times\) width \(\times\) height). There is also a 20 mm expansion joint between the base plates.  
The model contains 157,652 solid elements and 215,572 nodes. In order to simulate functional characteristics and the interaction relationships of each structural layer of slab track, the reduced integration element C3D8R [47], with eight nodes, is adopted to simulate the slab track main structure. The fasteners are simulated by the spring element with a spacing of 0.63 m, and the pre-stressed reinforcements are arranged on the track slab. The pre-stressed reinforcements layer consists of 12 transverse and 8 longitudinal bars with a diameter of 13 mm, as shown in the black line in Figure 4. The pre-stressed force is simulated by a cooling method (the tension force of single longitudinal and transverse pre-stressed reinforcements is 122 kN and 127 kN, and the corresponding cooling range is 370.9 \({}^{\circ}\)C and 386.1 \({}^{\circ}\)C, respectively). The upper and lower layers of the base plate are equipped with CRB550 cold-rolled ribbed reinforcement mesh, reinforced reinforcements are arranged at the bottom of the groove, and anti-crack reinforcements (diameter: 12 mm; length of a single piece: 700 mm; 16 pieces are arranged around a groove, as shown in the blue lines in Figure 4) are arranged around it. The door-type reinforcement plays the role of connecting the track slab and self-compacting concrete, as shown in Figure 5. Forty groups of portal reinforcements are arranged on the track slab. As shown in Figure 5b, the dotted line is the dividing line, the part above the dotted line is anchored on the track slab, and the part below the dotted line is anchored on the self-compacting concrete. All reinforcements are embedded into the track structure. According to [48], the thickness of the subgrade surface layer is 40 cm.  
The material of the expansion joint of the base plate is easier to damage compared to the reinforced concrete of the base plate itself under an external load. Therefore, this study analyzed the unfavorable conditions that cause the base plate's expansion joint to break.  
Figure 4: Finite element model of CRTSIII slab track on subgrade.