# DEM Analysis of Track Ballast for Track Ballast-Wheel Interaction Simulation
## 1 Introduction  
Dereailment of a rapidly moving train may lead to fatal consequences, thus such accidents should be prevented through effective means, such as derailment-prevention devices and structures. In Europe and in Japan, Korea, and several other countries, effective derailment-prevention methodologies have been studied and developed, such as derailment-containment walls [1; 2; 3; 4]. In addition to the fundamental prevention concepts, these studies have suggested design methods and provisions for the walls. Recently, a new type of structural system for derailment-containment prevention (DCP), which is constructed between the rails, has been developed in Korea [4], as shown in Figure 1. The concrete structural member is located between rails to restrict the horizontal movement of derailed train. To design the structural member and to validate its performance as a DCP system, the structural responses of the member under contact, and the impact forces induced by a derailed train, should be investigated by rational procedures. Through simulations and experiments, the performance of the newly proposed system has been verified, and an appropriate design procedure for this system has been suggested [1; 4]. However, the prevention performance has been investigated only for concrete track ballast, even though in several cases, the track ballast can be constructed as a gravel track bed. This indicates that, apart from concrete ballast, the DCP systems should be additionally examined for train derailment over a gravel ballast. As mentioned before, in several cases, the track ballast comprises pieces of gravel of irregular shapes, which form the track bed, as shown in Figure 2. When a train is derailed, the wheel of the derailed train will contact the ballast, and the interaction between the gravel pieces and the contacted wheel will affect the subsequent behavior of the derailed train. Therefore, for designing, verifying, and optimizing rational DCP systems with gravel ballast systems, this interaction should be analyzed to investigate the behavior of the derailed train after it contacts the ballast. For the modeling and simulation of the track ballast, the finite-element method (FEM) has been widely used because of its reliability and convenience. By using the conventional FEM approach, the ballast is modeled as shell or solid elements, with material properties equivalent to those of gravel layers in the two-or three-dimensional domain, respectively. Even when appropriate material models are applied, there is a limitation regarding the interaction between the gravel pieces in contact. The gravel pieces can be in contact or separate from each other. However, if the gravel layer is  
Figure 1: Overview of the derailment-containment prevention (DCP) wall developed in Korea [1]. Figure 2: Conventional track ballast (ballast for rapid trains in Korea): (**a**) track ballast; (**b**) pieces of gravel for the ballast. modeled using the conventional FEM, the interaction characteristics cannot be effectively considered because this approach does not allow the separation of elements that share nodes and exhibit a very large deformation. To rationally design the DCP, the post-behavior of the derailed train should be analyzed first to evaluate the required physical quantities, including the impact load on the DCP structural members due to the derailed train. When the train is derailed over gravel ballast, it can be assumed that the interaction between the ballast and train, which is induced by the contact between the gravel and the wheel of the bogie, directly affects the subsequent behavior of the derailed train. Therefore, rational numerical modeling and simulation methods for the ballast should be studied to perform the post-behavioral analysis of a train derailed over gravel ballast. As mentioned earlier, the track ballast has been modeled based on FEM approaches. [PERSON] (1998) studied the long-term settlement characteristics and the effect of the tamping process on the dynamic behavior of the ballast, using FEM approaches.