# Behavior Characteristics of a Booted Sleeper Track System According to Substructure Deformation
## 3 Results and Discussion
### Possibility of Tension Cracking in the Concrete Bed Due to Substructure Deformation  
In this section, the possibility of tension cracking in the concrete bed due to substructure deformation (i.e., uplift or subsidence) is analyzed by comparing the analysis results with the standard value of concrete flexural strength (i.e., modulus of rupture). Here \(f_{r}=0.63\sqrt{f_{ck}}\) (where \(f_{ck}\) is the standard design compressive strength of concrete), which was calculated according to the 2012 Standard Specifications for Concrete Structures [15; 19]. Figure 10 shows the normal stress induced on the top surface of the concrete bed in the longitudinal (x) direction by substructure deformation. When subjected to 5 mm of substructure uplift, as shown in Figure 10a, at the center of the concrete bed, compressive stress occurred along the rails between the RC sleepers, while tensile stress occurred along the inner and outer faces of the RC blocks. However, at the end of the concrete bed, the inner and outer faces of the RC blocks exhibited greater compressive stresses than did the locations along the rails between the RC sleepers. Figure 10: FE analysis results (normal stress on the top surface of the concrete bed, x direction) for (**a**) 5 mm uplift or (**b**) 5 mm subsidence (positive is tension). Figure 9: FE analysis results (relative displacement between rail and bed, z direction) according to magnitude of (**a**) uplift or (**b**) subsidence. When subjected to 5 mm of substructure subsidence, as shown in Figure 10b, at the center of the concrete bed, tensile stress occurred along the rails between the RC sleepers, while compressive stress occurred along the inner and outer faces of the RC blocks. However, at the end of the concrete bed, the inner and outer faces of the RC blocks were under greater tensile stress than the locations along the rails between the RC sleepers. The results of the concrete bed tensile stress analyses shown in Figure 10 indicated that the locations of the tensile and compressive stresses in the uplift condition were the same as the locations of the compressive and tensile stresses, respectively, in the subsidence condition. The tensile stress results are reported according to substructure displacement conditions in Figure 11 for each location defined in Figure 8a. As can be observed in the tensile stresses reported in Figure 11a, the maximum tensile stress at Section E (i.e., the center of the concrete bed model) exceeded the flexural strength of the concrete bed under uplifts of 10 mm or greater. At Section D, the maximum tensile stress exceeded the flexural strength of the concrete bed under uplifts of 20 mm or greater. On the other hand, at Sections A-C, the maximum tensile stress never exceeded the flexural strength of the concrete bed, even under an uplift of 40 mm; however, at Section C, the maximum tensile stress may exceed the flexural strength under an uplift greater than 40 mm. As shown in Figure 11b, the maximum tensile stress exceeded the flexural strength of the concrete at Sections E and A under subsidences of 35 mm or greater. At Sections B, C, and D, the tensile stress did not exceed the flexural strength of the concrete bed under subsidences up to and likely exceeding 40 mm. Furthermore, the smallest tensile stress occurred at Section C, which was located between the center and the end of the concrete bed. Furthermore, Figure 11b indicates that the tensile stresses at Sections A (end) and E (center) were similar under the substructure subsidence condition. At Section E, this tensile stress occurred at the point of maximum subsidence, and it is considered to be caused by the resulting flexural deformation at this location. At Section A, however, it is proposed that RC sleeper rotation caused compressive stress beneath the sleepers, which induced the observed tensile stress between the sleepers.