# Performance of CRTS-II Ballastless Track-Bridge Structural System Rebars under Fatigue Loading Test
## 3 The Result of the Experiment  
### Rebar Strain Amplitude under Dynamic Load  
Currently, the studies of the fatigue performance of pre-stressed concrete beams show that the strain amplitude of the longitudinal steel rebar has a significant influence on the fatigue life of the beams [10]. Fatigue failure of reinforced concrete beams generally starts from fatigue fracture of the steel rebar at the bottom of the beam. Under the fatigue load, fatigue cracks continuously accumulate and expand in the rebar, which results in an increase in the strain amplitude [9; 15]. Therefore, the strain amplitude of the rebar under a fatigue dynamic load is measured by experiment. Before 12 million fatigue cycles, dynamic strain data of the structural system are collected every 50,000 loading cycles; after 12 million fatigue loading cycles, dynamic strain data of the structural system are collected every 100,000 cycles. The dynamic strain amplitude curve is obtained by taking the difference between the maximum and minimum values of each dynamic strain. The evolution of the strain amplitude, according to fatigue loading cycles at L/2 and L/4 sections of X3 rebar, is shown in Figure 4.  
It can be seen from Figure 4 that when the lower limit fatigue load remains unchanged and the upper limit load increases, the strain amplitude of the steel rebar increases proportionally; there is no obvious increasing trend in the steel rebar strain amplitude in loading stage 1, stage 2 and stage 3. When the upper fatigue load is increased to the limit of stage 4, the strain amplitude shows an obvious, increasing trend. The strain amplitude at L/2 section increases by 3.5%, while that at L/4 section increases by 2.1%. During the entire fatigue loading process, the maximum strain amplitude of the steel rebar is 153 \(\upmu\epsilon\), and the corresponding stress value of 30.6 Mpa is less than 1/10 of the yield strength, thus, it is very small and shows the high-cycle fatigue of the steel rebars in the high-speed rail pre-stressed simple-supported box girder. In order to obtain the specific increase ratio of the strain amplitude, the strain amplitude \(\Delta\varepsilon_{N}\) at the end of the fatigue test is divided by the initial strain amplitude \(\Delta\varepsilon_{0}\); the specific values obtained are shown in Table 2. The results show that in stage 1, where the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Program** & **P\({}_{\text{min}}\) (kN)** & **P\({}_{\text{max}}\) (kN)** & **\(\Delta\)P (kN)** & **Frequency** & **Fatigue Cycles** \\ \hline Stage 1 & 300 & 420 & 120 & 3 Hz & 5.0 \(\times\) 10\({}^{6}\) \\ Stage 2 & 300 & 540 & 240 & 3 Hz & 7.0 \(\times\) 10\({}^{6}\) \\ Stage 3 & 300 & 660 & 360 & 3 Hz & 5.0 \(\times\) 10\({}^{6}\) \\ Stage 4 & 300 & 900 & 600 & 3 Hz & 1.0 \(\times\) 10\({}^{6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The loading parameters of the fatigue test. Figure 4: Strain amplitude curve of steel bar: (**a**) L/2 section; (**b**) L/4 section. loading amplitude is the smallest, the strain amplitude decreases; the maximum reduction rate is 2.96%. Many scholars have studied the fatigue performance of reinforced concrete structures and found that the structures only appear in the damage stage (repeated loading leads to the degradation of the mechanical properties of the structure.) [24; 25; 26], but this experiment shows that the steel rebars present no usual fatigue damage in stage 1. There is a sort of \"optimization\" phenomenon. In the following stages 2, 3 and 4, the maximum growth rates of the strain amplitude are 6.43%, 8.61%, and 15.40%, respectively. In the entire fatigue loading process, although stage 4 has the fewest loading cycles, the strain amplitude growth rate is the largest in this stage. It can be seen that the larger the upper fatigue load limit, the faster the strain amplitude growth and the faster the fatigue damage rate.