## 3 Analysis of Fatigue Damage Law of Base Plate Structure
### Parametric Analysis  
#### 3.2.1 Influence of the Position of the Load  
The CRTSIII BT system is expected to show varying properties at different loading points. To ascertain this, three typical working conditions were considered in this section. Working condition 1--loaded on the sleeper in the middle of slab span; working condition 2--loaded on the sleeper at a quarter of the slab; working condition 3--loaded on the sleeper at the end of the slab, as shown in Figure 17.  
(2) Working condition 2--load acted on the top of the sleeper at a quarter of the slab  
For working condition 2--loaded on the top of the sleeper at a quarter of the slab. The stress distribution diagram of the base plate when the fatigue is loaded up to 15 million times is shown in Figure 20, and the maximum stress is shown in Table 5.  
As shown in Figure 20, for working condition 2, the maximum longitudinal tension stress of the base plate was located on the lower surface of the base plate below the sleeper at a quarter span. Figure 21a shows the development of the maximum longitudinal tensile stress of the base concrete under the fatigue load of this section. The tensile stress near the bottom of the sleeper was relatively large, and with the increase in fatigue load, the stress on the section continued to increase. When a fatigue load was applied 3 million to 12 million times the longitudinal tensile stress increased rapidly, with maximum longitudinal tensile stress increasing by 0.037 MPa for every 1 million applications of fatigue load. When the load accumulated to 16 million times, the tension near the bottom of the sleeper suddenly changed to zero, indicating that cracking occurred at this time (Figure 21b). (3) Working condition 3: load acted on the top of the sleeper at the end of the slab  
For working condition 3, the load was applied to the top of the sleeper at the end of the slab. The stress distribution diagram of the SCC layer fatigue load applied 12 million times is shown in Figure 22. The stress maximum stress distribution diagram of the base plate under a fatigue load of 12 million applications (working condition 3), is shown in Table 6.  
It can be seen in Figure 22 that for working condition 3, the maximum longitudinal tensile stress of the base plate was located at the slab end sleeper on the lower surface of the base. Under the action of fatigue load, the development of the maximum longitudinal tensile stress of the base plate is shown in Figure 23a. With continued action of the fatigue load, the stress on the section continued to grow. When the fatigue load applied reached 13 million times, the maximum longitudinal tensile stress of the base concrete under the sleeper suddenly changed to zero, indicating that cracking occurred at this time (Figure 23b). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **1 Time of Fatigue** & **6 Million Times of** & **12 Million Times of** \\  & **Load** & **Fatigue Load** & **Fatigue Load** \\ \hline Longitudinal tensile & & & \\ stress (MPa) & 0.76 & 0.92 & 1.12 \\ Lateral tensile stress & & & \\ (MPa) & 0.54 & 0.82 & 1.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Maximum stress of the base under working condition 3. Figure 21: Longitudinal mechanical characteristics of base plate under fatigue load (working condition 2). (**a**) Cross-sectional stress development diagram at the maximum longitudinal tensile stress of the base plate; (**b**) number of cracks at the maximum longitudinal tensile stress of the base plate. (4) Comparative analysis  
By comparing the three working conditions, it can be deduced that when the CRTSIII BT structure system is in working condition 3, the stress of the base plate is relatively large. Under the three working conditions, the lateral and longitudinal tensile stresses of the base concrete increase with the increase of the number of loads. Among them, under working condition 2, the longitudinal tensile stress increased the fastest when an average of 1 million load applications, resulted in stress increase by 0.033 MPa.