# Research on the Influence of Loading Frequency on the Dynamic Response of Concrete Sleopers
## 2 Selection of Model Parameters and Establishment of the Model
### Validation of Model Parameters  
In this study, the small-sized particles were arranged neatly in a hexagonal manner to construct concrete samples, and the model parameters were verified by compressing the samples and analyzing their mechanical properties after compression. Generally, the smaller the particle size in the model, the more accurate is the model, but the number of particles added in the system will also increase, which increases the calculation time of the computer. The larger the particle size, the fewer particles are added to the sample of the same size, which can reduce the calculation time of the computer and reduce the accuracy of the model. To achieve a balance between accuracy and efficiency, the particle sizes of the test blocks were constructed with particles of 1 mm and 5 mm in size. The initial models of concrete samples established with the two particle sizes are shown in Figure 2. In order to make the figure clearer, Figure 2 uses the position cloud map of the particles to represent the initial model of the sample. \begin{table}
\begin{tabular}{c c} \hline
**Parameter Name** & **Value** \\ \hline Sleeper density/(kg\(\cdot\)m\({}^{-3}\)) & 2500 \\ Normal bond stiffness between the particles inside the sleeper/(N\(\cdot\)m\({}^{-1}\)) & 3.0 \(\times\) 10\({}^{8}\) \\ Tangential bond stiffness between particles in sleepers/(N\(\cdot\)m\({}^{-1}\)) & 3.0 \(\times\) 10\({}^{8}\) \\ Tensile strength of particles inside sleepers/Pa & 3.5 \(\times\) 10\({}^{6}\) \\ Bond strength between particles inside sleeper/(N\(\cdot\)m\({}^{-2}\)) & 1.0 \(\times\) 10\({}^{10}\) \\ Normal contact stiffness between rail and sleeper/(N\(\cdot\)m\({}^{-1}\)) & 3.0 \(\times\) 10\({}^{8}\) \\ Tangential contact stiffness between rail and sleeper/(N\(\cdot\)m\({}^{-1}\)) & 3.0 \(\times\) 10\({}^{8}\) \\ Poisson’s ratio of sleepers & 0.2 \\ Poisson’s ratio of rail & 0.3 \\ Friction coefficient of the sleper & 0.7 \\ Friction coefficient of the rail & 0.5 \\ \hline \end{tabular}
\end{table} 
Table 1: Micromechanical parameters of the discrete element model. In the discrete element model of concrete specimens, walls were added to the top and bottom of the specimen block. The bottom wall was used to constrain the specimen and prevent the specimen from moving downward; the top wall was used for loading purposes. The stress-strain curve of the concrete specimen after vertical compression is shown in Figure 3.  
Figure 3 shows the stress-strain curves of concrete specimens composed of two different particle sizes after compression. From Figure 3, it can be concluded that the compressive strength of the sample composed of 1 mm particle size was 69.588 MPa, and the compressive strength of the sample composed of 5 mm particle size was 69.168 MPa, which meets the requirements of the specification [16], and is consistent with the compressive strength (70 MPa) of concrete in the literature [20]. In the initial stage of strain, the stress in the concrete block increased with increasing strain; when the compressive strength was reached, the stress of the sample decreased sharply with increasing strain until the concrete block was crushed. Therefore, the results demonstrate the feasibility of the parameters of the two-dimensional discrete element model selected in this paper. To further analyze the samples constructed with the two particle sizes, the nephograms of the contact force chain distribution after the compression of the two samples were recorded, and the recorded results are shown in Figure 4.  
Figure 3: Stress–strain curve of concrete specimen. Figure 2: The initial discrete element model of the concrete sample. (**a**) 1 mm particle size. (**b**) 5 mm particle size. Figure 4 shows that the contact force distribution after compression of concrete samples was similar between the two particle sizes; a large contact force was generated near the vertical neutral axis of the sample and vertical cracks appeared in this area.