# DEM Analysis of Track Ballast for Track Ballast-Wheel Interaction Simulation
## 3 Strategy and Validation of Numerical Implementation
### Validation  
To validate the numerical strategy, a drop test was conducted. As shown in Figure 8, a \(1000\times 1300\times 700\) mm (width \(\times\) breadth \(\times\) height) steel box was filled with gravel pieces up to a height of 600.0 mm. The sizes of all the gravel pieces were 31.5-50.0 mm, which is suitable for track ballast. The 656-kg weight was freely dropped from heights of 0.5 and 1.0 m. During the drop test, the motion of the weight was measured in the time domain. Furthermore, the depth of penetration into the gravel layer was measured. To prevent a local effect due to deformation of the box, the wall of the box was sufficiently stiffened. The test was conducted twice for each drop height. During the test, the acceleration of the weight was measured via vision-postprocessing in the time domain, and then, the velocity and displacement were evaluated via numerical integration of the measured acceleration.  
Figure 8: \(Cont.\)  
Figure 7: Simulation procedure for ballast–wheel collision.  
Figure 9 shows the numerical model for simulating the drop-test with the same geometric conditions. As shown in the figure, the gravel layer was modeled based on DEM, while the weight was modeled using FEM. In this simulation, the gravel was modeled as simple rigid sphere clumps. Thus, there was a limitation regarding the interlocking effect between the arbitrarily shaped pieces of gravel. This could be one of the sources of the difference between the results from the experiment and the test. Following the procedure shown in Figure 7, explicit dynamic analyses were conducted, and the motion of the dropped weight was obtained. In addition, after the simulation, the penetration depth and the motion of the dropped weight were observed for comparison with the result from the drop test. The DEM-FEM simulation was conducted using ABAQUS V6.17 [19]. The particle packing was performed using a MATLAB-based in-house code, following the procedure shown in Figure 5. After modeling, the explicit dynamic analyses were conducted. The initial time step was set as 1.0 E-5 s, and the total simulation time was 1.5 s. After simulation of the drop test, the vertical motion and final penetration depth of the weight were evaluated and compared with those obtained from the experiment.  
Figure 8: Drop test to simulate the collision between the dropped weight and gravel layer: (**a**) Front view of the drop test; (**b**) gravel layer; (**c**) weight penetration; (**d**) gravel layer after penetration.  
Figure 9: _Cont._  
The displacement curves obtained from the postprocessing of the test, shown in Figure 9c, reveal significant rebounding after full penetration. However, this is not the actual situation; it originated from the cumulative error of the numerical integration. To verify further, the penetration depth after the test was compared with that after the simulation.  
As shown in Table 2, the penetration depths measured from the tests and simulations were very similar. The simulation results clearly show that the penetration depth is affected by the applied friction coefficient between the pieces of gravel. Friction is one of the influencing factors in the interlocking between the pieces of gravel in contact. It can be expected that large friction induces extensive interlocking between the gravels. The physical mechanism is clearly expressed in the simulation results. The test results are not well-matched with each other because tamping was not performed after creating the layer. If tamping had been conducted, the layers would have had very similar properties.  
Figure 10: Comparison between the motions of the dropped weight, obtained from tests and simulations (dropped from 0.5 m height): (**a**) acceleration; (**b**) velocity; (**c**) displacement.  
Figure 11: Comparison between the motions of the dropped weight, obtained from tests and simulations (dropped from 1.0 m height): (**a**) acceleration; (**b**) velocity; (**c**) displacement.