## 5 Analysis of Calculation Results  
### Fatigue Life  
Figure 9 illustrates the variation of fatigue life with cyclic strength for cold joint components with casting intervals of 2, 4, and 8 h under initial stress levels of 3.6 kN, 2.4 kN, and 1.8 kN, respectively. From Figure 9, we can see that:  
1. The predicted values of fatigue life from the numerical model for each group of specimens fall between the maximum and minimum measured fatigue life values, and are close to the average fatigue life. This closeness to experimental results validates the reliability of the cohesive fatigue damage elements and the parameters inversely calculated by the BP neural network. The developed cohesive fatigue damage elements and the inversely calculated material parameters can be extended for analyzing the damage of concrete structures with cold joints under aerodynamic fatigue loads of high-speed trains and predicting the crack initiation time of cold joint interfaces.
2. When the initial stress level is low, the cold joint components do not experience fatigue fracture at any cyclic strength, validating the assumption regarding the cohesive fatigue limit made earlier. Below the fatigue limit, the material can undergo an infinite number of cycles without failure. With increasing initial stress level, the components with an 8-h pouring interval are the first to experience fatigue fracture, and their fatigue life gradually decreases with increasing cyclic strength. Next are the components with a 4-h pouring interval, and those with a 2-h pouring interval experience fatigue fracture last. The pouring interval is the primary factor affecting the strength  
\begin{table}
\begin{tabular}{c c c c} \hline
**Interval Time** & \(\sigma_{max,0}\) & \(C_{f}\) & \(\delta_{0}\) \\ \hline
2 h & 0.58 MPa & 0.48 & 0.0007 mm \\
4 h & 0.36 MPa & 0.42 & 0.0004 mm \\
8 h & 0.28 MPa & 0.34 & 0.0002 mm \\ \hline \end{tabular}
\end{table}
Table 1: Fatigue damage parameters corresponding to cold joints at different pouring intervals.  
Figure 8: Neural Network Training Results.  
of the cold joint interface, and the strength of the cold joint interface determines the bearing capacity of the concrete components with cold joints. Therefore, the starting conditions for fatigue damage for cold joints with pouring intervals of 8 h and 4 h are much lower than those for cold joints with a pouring interval of 2 h.
3. As the casting interval increases, the area enclosed by the polygon formed by the maximum and minimum cycle counts gradually decreases, indicating a reduction in the dispersion of component fatigue life with increasing casting interval. Combined with nanoindentation experimental results, when the casting interval is short, the hydration between the first and subsequent castings is very strong. As a result, the interface strength is high and the thickness is large, leading to a high degree of randomness in the crack propagation path under fatigue loading, thus resulting in a large dispersion of fatigue life, as shown in Figure 10a. With increasing casting interval, the hydration at the surface of the first casting gradually diminishes, resulting in weaker and thinner interface regions. Consequently, the randomness of crack propagation paths decreases, leading to a smaller dispersion of fatigue life, as illustrated in Figure 10b [18]. The influence of cold joint interface thickness on fatigue damage and life dispersion was not considered in the numerical simulation. Hence, the fatigue life is a deterministic value. Further research can be conducted in subsequent work to investigate the effect of cold joint interface thickness on cold joint fatigue damage and life dispersion.