# Performance of CRTS-II Ballastless Track-Bridge Structural System Rebars under Fatigue Loading Test
## 3 The Result of the Experiment
### Rebar Strain Analysis under Static Load  
During the fatigue loading test of the ballastless track simple-supported box girder structural system, the mechanical properties of materials in the structural system evolve continuously. In order to analyze the evolution of the mechanical properties of the steel rebar after the fatigue loading test, the fatigue press is stopped after a certain number of fatigue loading cycles in the experiment and the static loading test is carried out on the specimen. The variation curve of the rebar strain with the increase in the external load, hereinafter referred to as the load-strain curve of the steel rebar, is obtained as shown in Figure 6.  
The load-strain curve of steel rebar in Figure 6 is dense, the slope change of the curve is relatively small, and the curve keeps an oblique linear shape. It can be seen that the strain of the steel rebars is basically linear with the load increase. Under the first loading stage (3 million loading cycles), the curve inclines in the direction of the strain reduction, while between the 3 and 5 millionl loading cycles, the curve inclines in the direction of the strain increase; the slope of the load-strain curve under the action of the second, third and fourth loading stages is relatively small, the curve is relatively concentrated, and is generally inclined in the direction of the strain increase. From Figure 6, it can be seen that the load-strain curve almost maintains a diagonal straight line throughout the test. The slope of the load-strain curve represents the resistance of steel rebars to deformation in the ballastless track simple-supported box girder structural system, so the change in the slope can be used to characterize the fatigue behavior of the steel rebars. Figure 6: Load–strain curve of ordinary steel bar (**a**) L/2 section; (**b**) L/4 section. Here, the slope \(K_{\rm N}\) of the load-strain curve obtained from each static load test is calculated by the least square method, and the normalized slope \(K_{\rm N}\) is expressed as follows:  
\[K_{\rm N}=\sum_{i=1}^{m}(\varepsilon_{i}-\overline{\varepsilon})\left(P_{i}- \overline{P}\right)/\sum_{j=1}^{m}(\varepsilon_{i}-\overline{\varepsilon})^{2} \tag{2}\]  
where \(i\) represents the i-th loading cycle; \(m\) represents the total number of static load stages; \(P_{i}\) is the \(i\)-th external load; \(\overline{P}\) is the average external load; \(\varepsilon_{i}\) is the \(i\)-th strain increment of steel rebar; \(\overline{\varepsilon}\) is the average v strain increment of steel bar. For the sake of simplicity, the normalized slope of the load-strain curve (Figure 7) is hereinafter referred to as the slope, and the slope of the curve. It can be seen from Figure 7 that in stage 1, the slope of the reinforcement at L/2 and L/4 sections increases first and then decreases, and in stage 2, stage 3, and stage 4, the slope decreases gradually; the increasing rate of the slope is obviously greater than the decreasing rate, and the slope of the steel rebar changes from \"fast\" to \"slow\". At the end of the 18 millionth loading cycle, the slope of the steel rebar is lower than the initial value, showing that there is a continuous degradation of the structure during the whole fatigue loading process [27; 28; 29]. In order to further analyze the specific increased proportion of the slope, the slope ratio \(K_{\rm N}/K_{0}\) under different fatigue times is obtained, as shown in Figure 8, and the specific increase proportion is listed in Table 3.  
It can be seen from Figure 8 and Table 3 that the slope ratio at the L/2 and L/4 sections after 3 million loading cycles gradually increase to the maximum by 5.64% and 6.19%, respectively, and the slope ratio at the end of the test basically decreased by 5.15% and 4.81%, respectively. The change trend of the slope ratio of the rebar at L/2 and L/4 sections is similar. The slope ratio at L/4 section is slightly larger than that at the L/2 section.