## 2 Indoor Experiment and Establishment of Finite Element Model
### Finite Element Model
#### 2.2.2 Criteria for Fatigue Failure of Slab Ballastless Track Structure  
When analyzing the fatigue load of the track slab, it is necessary to simplify the fatigue shape according to the fatigue characteristics of the steel and concrete materials (Figure 8) to obtain the fatigue analysis of unequal step length in the numerical simulation, where D represents structural damage, \(N\) represents the number of load actions, and \(N\)/ represents the number of ultimate fatigue loads [41]. 1. The initial stage of fatigue. In the process of initial fatigue, track damage caused by fatigue gradually begins to occur. Therefore, a smaller fatigue step should be used in the simulation at this stage, and the fatigue step lengths adjacent to this stage can be different. 2. The development stage of fatigue. This process is the main stage of fatigue damage to the track slab, accounting for about 80% of the total fatigue time [41]. At this stage, the damage of the slab presents a stable development trend. Therefore, in the numerical simulation, the simulation can be carried out with an equal step length. The step length can also be longer than the initial stage of fatigue, and the fatigue load can be applied in the form of a cyclic jump. 3. The failure stage of fatigue. At this stage, micro-cracks have been generated inside the track slab due to long-lasting fatigue, so the fatigue damage develops rapidly and maintains an unstable trend. Therefore, in the numerical simulation at this stage, the fatigue step length should also be relatively small. According to the description of the three stages of fatigue failure of the track slab, the three stages in the entire fatigue process can each account for 10, 80, and 10%, respectively of fatigue failure. Therefore, using an interpolation method, the fatigue characteristics of the track slab under the action of adjacent load steps can be related to each other. Thus, a whole process analysis model of the track slab under the cumulative action of fatigue load can be established, which greatly simplifies the fatigue numerical simulation of the track slab. [29]. 1. Criteria for failure judgment of track slab concrete Through the continuous action of the fatigue load, the internal damage of the track slab concrete structure continues to spread. Therefore, after a large number of cycles of  
Figure 8: Three-stage simplified diagram of track slab under fatigue load. \begin{table}
\begin{tabular}{c c} \hline
**Structure Part** & **Model the Selected Element** \\ \hline Concrete & Solid65 element \\ Rail & Beam188 element \\ Fasteners/foundation & Combin14 element \\ The base plate is in contact with the self-compacting concrete layer & Contact174, target170 element \\ Track slab in contact with self-compacting concrete & Contact174, target170 element \\ \hline \end{tabular}
\end{table} 
Table 3: Finite element for each structure. fatigue load, the mechanical properties of its structure are destroyed because the maximum stress necessary to cause cracking of the track slab concrete has not been reached [44]. According to the long-term study on the fatigue performance of track slab concrete, it can be deduced that the internal fatigue residual strain \(\Delta\varepsilon_{r}\) of the track slab concrete structure under the same amplitude of long-term load is 40% of the ultimate strain \(\varepsilon_{0}\). At this threshold value, the concrete structure of the track slab has already suffered serious internal damage and cannot continue its service as designed. Thus, the concrete structure of the track slab is said to have failed. The damage criteria are expressed in Equation (1) below:  
\[\Delta\varepsilon_{r}\geq 0.4\varepsilon_{0}=0.4f_{c}/E_{0} \tag{1}\]  
(2) Criteria for failure judgment of rail slab reinforcement  
Because the rail slab is equipped with a steel structure, the steel undergoes brittle fracture under repeated fatigue loads. Consequently, the fatigue failure criterion can be indicated by the critical value of brittle failure.