# DEM Analysis of Track Ballast for Track Ballast-Wheel Interaction Simulation
## 1 Introduction
In that study, the ballast was modeled as shell elements, and the equivalent material properties, such as internal friction angle, dilation angle, and cohesion, which had been evaluated through a simple experiment, were applied using the Mohr-Coulomb plastic model. Although this approach could be applied in ballast modeling for relatively small-deformation problems, it still has limitations with respect to directly considering the interactions between the pieces of gravel in contact, especially the interlocking effect between these pieces. [PERSON] et al. [PERSON] et al. (2018) studied methodologies for analyzing the ultimate lateral pressure of penetrated pile in undrained clay based on FEM. Although the approach can be applied for relatively large deformable soil layers, separation of the gravels cannot be simulated by the approach. [PERSON] and [PERSON] [PERSON] and [PERSON] (1998, 2000) suggested the vibration analysis method of a rigid circular disk embedded in a transversely isotropic solid. [PERSON] et al. [PERSON] (1998) studied the closed-form solution for lateral translation of an inextensible circular membrane embedded in a transversely isotropic half-space. However, there are still limitations for considering the time-varying change of the geotechnical properties of the ballast due to the applied forces. To overcome these limitations, other approaches have been studied based on the discrete-element method (DEM). Using DEM, each piece of gravel can be modeled as an individual object with efficient calculation; therefore, the interaction between the gravel elements in the ballast, including slip, separation, and re-attachment, can be analyzed. [PERSON] et al. [PERSON] et al. (2018) performed a DEM-based analytical study to simulate the effect of the tamping process on the compactness of track ballast. [PERSON] et al. [PERSON] et al. (2018) studied a simulation method for the permanent settlement of track ballast due to cyclic loading, based on the DEM approach. [PERSON] et al. [PERSON] et al. (2018) investigated the influencing factors in ballast settlement using a DEM simulation. Furthermore, [PERSON] et al. [PERSON] et al. (2018) studied the relation between the geogrid rib size and the particle size distribution of ballast materials using a DEM simulation. When DEM approaches are used, the modeling method used for the gravel, including the shape and initial positions of the gravel pieces, is important. [PERSON] et al. [PERSON] et al. (2018) studied a modeling method for arbitrarily shaped gravel pieces using a clump of circles in 2D for DEM simulation. [PERSON] and [PERSON] and [PERSON] and [PERSON] (2018) studied the generation and particle-packing method of sand in a DEM simulation. They suggested a method to determine the number and initial positions of the particles to satisfy the pre-defined size distribution, shape, and density of the sand layer. [PERSON] and [PERSON] and [PERSON] (2018) also studied a method to rapidly generate a particle layer using the DEM approach. In recent studies, the individual particles have been modeled as sphere-type rigid bodies or clumps consisting of spheres, to ensure efficient calculation. [PERSON] et al. [PERSON] et al. (2018) adopted a DEM simulation approach using specifically shaped objects with fast tracking for contact between the objects, using their in-house simulation code, DBLOCK3D. As alternatives to the conventional FEM, DEM approaches are being used to model and simulate ballast. If a rational modeling and simulation method for track ballast is used, the simulation method for analyzing the behavior of the derailed train can be investigated considering the interaction between the ballast and the derailed bogie. For the simulation, DEM approaches can be effectively used. This study aims to propose a method for modeling track ballast filled with gravel pieces and simulating a ballast-wheel collision.