# DEM Analysis of Track Ballast for Track Ballast-Wheel Interaction Simulation
## 5 Conclusions  
In this study, a rational modeling method and an analysis for gravel-filled track ballast were investigated to simulate track-derailed train interaction. Because of the characteristics of the track ballast, a DEM-based modeling and analysis strategy was used for modeling the ballast. Once the track ballast was modeled with numerous rigid particles, the interaction between the track ballast and objects of any shape could be simulated.  
* Based on the DEM approach, each piece of gravel is modeled as a rigid body to ensure an efficient simulation. To consider the elasticity of the gravel and the friction effects between the gravel pieces in contact, an appropriate contact model should be applied. In this study, the Hertz-Mindlin contact model was applied to consider the normal and tangential contact forces and the friction force. The nonlinear normal and tangential stiffnesses were estimated using the equation of the contact model considering the size, elastic modulus, and Poisson's ratio of the gravel. Apart from the contact between the pieces of gravel, a contact model between the gravel and contacted objects was also used along with the Hertz-Mindlin model.
* To validate the simulation method, a drop test was conducted, and the experiment was reproduced via a DEM-based simulation. The comparison results, including vertical acceleration, velocity, displacement, and the penetration depth of the freely dropped weights, exhibit very good agreement. Therefore, the feasibility and rationality of the simulation method was verified.
* The effects of the applied friction coefficient on the interaction between the gravel layer and the clashing object were studied. According to the results, the friction coefficient between the contacted gravel pieces significantly affects the geotechnical properties of the layer filled with gravel. The coefficient governs the interlocking effect in the gravel layer and, thus, this coefficient also affects the rigidity of the layer.
* The friction coefficient between the gravel and the object does not significantly affect the interaction between the layer and the clashing object. According to the simulation, the results converge when a coefficient over 0.5 is applied. In addition, based on both the experiment and simulation, a coefficient of 0.5 for the track ballast-steel wheel contact is appropriate.  
Although the simulation results agree well with the test results, limitations still exist to be improved for simulation of derailed train-track ballast interaction as below:  
Figure 15: Comparison of friction-energy dissipation for different friction coefficients between the gravel and the weight.  
* The effect of the shapes of different pieces of gravel could not be considered because simple rigid sphere clumps were used.
* To simulate derailed train-track ballast interaction, the collision cases which induce the shearing motion of the gravel of track as well as vertical motion should be further validated.
* For real track ballasts tamping effect should be taken into account.
* Further study is needed to find the rational range of friction coefficients between irregular gravels for real ballast track.  
Conceptualization, S.K., N.-H.L. and K.-J.K.; methodology, S.K. and H.-U.B.; software, S.K.; validation, S.K. and H.-U.B.; formal analysis, S.K. and H.-U.B.; investigation, S.K. and H.-U.B.; resources, N.-H.L.; data curation, K-J.K. and H.U.B.; writing--original draft preparation, S.K. and N.-H.L.; writing--review and editing, S.K. and N.-H.L.; visualization, H.-U.B.; supervision, S.K.; project administration, N.-H.L.; funding acquisition, N.-H.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Railway Technology Research Program, funded by the Ministry of Land, Infrastructure, and Transport of the Korean government, grant number 17 RTRP-B122273-02.  
The authors declare no conflict of interest.