# Current Practices of Railway Ballastless Track Design Methods in China
## 4 Results and Analysis
### Analysis of Calculation Results of Reinforcement  
Track slabs are usually compressed on one side and tensioned on the other side when subjected to loads. Due to the inferior tensile properties of concrete material, reinforcement on the tension side is necessary to strengthen the track slab. To investigate the discrepancies of the ASM and the LSM in structure design, the reinforcement under the two methods is calculated, and the influence rules of different parameters are analyzed. The new prefabricated track slab is reinforced by HRB400 steel bars with a diameter of 8 mm in the longitudinal direction and 12 mm in the lateral direction. According to the Code for the Design of Concrete Structures (GB 50010-2010) [37], for the prefabricated slab, the height of the relative limit compression zone \(\xi_{b}\) is 0.4992. To ensure that the thickness of the protective layer is not less than 35 mm, the distance from the tensile steel bar to the tensile edge \(a_{s}\) is 39 mm longitudinally and 49 mm laterally. According to the requirement of a minimum reinforcement ratio, the area of the section shall not be less than 579.6 mm\({}^{2}\) longitudinally and 1107.6 mm\({}^{2}\) laterally. In the process of reinforcement design, to ensure that the cracking of the track slab is less than 0.2 mm, the standard combination of the LSM and the main force combination of the ASM play decisive roles. The reinforcement results are shown in Figure 14.  
Figure 13: Moments under combination load of different temperature gradients. The reinforcement ratio of the ASM is greater than that of the LSM in all working conditions. In words, the ASM is more reliable with a greater margin, but the LSM is more efficient and material saving. The LSM can reduce the reinforcement by about 6.5% compared with the ASM. The reinforcement ratios under different working conditions have minor differences, which shows that the influence of the train load is relatively small. However, under the same working conditions, the reinforcement ratios increase obviously with the increase in temperature gradient, which is the main control factor. What is more, the greater the temperature gradient is, the smaller the difference between the two methods is. It is because the temperature gradient load effects of the two methods have similar values. In fact, the determination of the specific partial coefficients of the LSM refers to the design experience of the ASM to some extent, which causes the minor difference between the two methods. Therefore, the LSM can save more materials, but the optimization effect is relatively limited due to the coefficient value determination method of the current LSM specification in China. In particular, in regions with significant temperature fluctuations, the similar temperature load coefficients make the advantage of the LSM even less obvious. To further investigate the optimization effect of the LSM compared to the ASM in track design, the dimensions of the track structure are adjusted under the condition of a fixed amount of reinforcement according to the two methods, and the required thickness is calculated, as shown in Figure 15.  
Figure 14: Reinforcement results under different working conditions. As shown in Figure 15, under a certain quantity of reinforcement, the thickness of the track slab is influenced by temperature, too. With the increase in temperature gradient, the required thickness escalates. When the temperature gradient rises from 65 \({}^{\circ}\)C to 105 \({}^{\circ}\)C, the slab thickness grows by nearly 40%. In addition, the required thickness calculated according to the LSM is consistently less than that calculated according to the ASM. In D1, the maximum disparity in the required thickness between the two methods amounts to 3.4%, while in D2, it is only 0.5%. Similarly, due to the influence of parameter values, the difference in calculation results between the two methods is minor, and the optimization effectiveness of the LSM still requires further enhancement.