# Simulation of Track-Soft Soil Interactions Using a Discrete Element Method
## 2 Material and Methods
### Interaction between Soil and Track
#### 2.2.3 Shear Stress-Displacement DEM Simulation and Modification Process  
According to the soil shear stress-displacement test, the virtual soil bin in the DEM simulation was set to 130 mm \(\times\) 120 mm \(\times\) 22 mm containing 400,000 soil particles, considering the computer's capability. The computer's CPU was an Intel 7700 processor with four cores and eight threads, and the simulation time was 42 h.  
The virtual soil bin and the shear simulation process between the soil and track segment with DEM simulation are shown in Figures 8 and 9, respectively. The number of soil particles that produced the bulldozing effect above the track segment was about 165,000, and the soil volume is 85.3 cm\({}^{3}\). The movement speed of soil particles on the track segment was about 0.036 m s\({}^{-1}\), which was less than the movement speed of the track segment 0.05 m s\({}^{-1}\). The difference in the velocity among soil particles led to the bulldozing resistance of the track segment.  
In order to remove the bulldozing resistance caused by soil accumulation, the calculation domain of the particles was adjusted. The soil shear test was performed based on adjusting the particle calculation domain. The virtual soil bin and simulation of the shear process between the clay and track segment with the EDEM software are shown in Figure 10. In the virtual shear simulation, there was no soil accumulation in front of the track segment.  
The image of the motion state of clay particles was derived, as shown in Figure 10. The motion of soil particles near the inner wall of the soil bin was almost static, which indicated that soil particles near the inner wall did not participate in the shear process, and the size of the soil bin was suitable. The motion state of clay particles participating in the shear simulation was about 0.045 m s\({}^{-1}\), which is consistent with the moving speed of the track segment--0.05 m s\({}^{-1}\). According to the motion of the particles in front of the track segment, there were about 23,500 particles, and the effective soil volume involved in the shear process was 24 cm\({}^{3}\). Compared with the soil shear DEM simulation without  
Figure 6: Shear stress–shear displacement test equipment. (**a**) Schematic diagram of soil test equipment. (**b**) PVC track segment (80 mm length, 60 mm width and 12 mm grouser height).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Track Segment** \\ \hline Material & PVC Rigid \\ Length (mm) & 80 \\ Width (mm) & 60 \\ Grouser height (mm) & 12 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameters of track segment structural dimension.  
modification, the volume of accumulated soil causing the error was 60 cm\({}^{3}\). This shows that the error caused by soil accumulation could not be ignored.  
Figure 8: The virtual model of the soil bin and track segment. (**a**) DEM soil bin model with scaled-up particles. (**b**) Virtual track segment model (80 mm length, 60 mm width and 12 mm grouser height).  
Figure 7: Shear stress–displacement test. (**a**) Shear stress–displacement test of clay. (**b**) Shear stress–displacement test of sand. (**c**) Shear stress–displacement test of mixed soil 2\(\#\).  
The mean absolute percentage error (_MAPE_) was applied to evaluate the accuracy of the simulation model. When the _MAPE_ value was close to zero, the DEM simulation model was more consistent with reality.  
\[MAPE=\frac{100\%}{n_{s}}\sum_{i=1}^{n}\left|\frac{\hat{y}_{i}-y_{i}}{y_{i}} \right|, \tag{9}\]  
where \(n_{s}\) is the number of samples, \(y_{i}\) is the test value of samples and \(\hat{y}_{i}\) is the simulation value of samples.