# Ballasted Track

### Objective

The objective of this research is to investigate and understand the mechanical behavior of railroad ballast using Discrete Element Method (DEM) .

### Background

The conventional ballasted tracks have been used widely in many countries around the world. Ballast material is the basic element in ballasted track. It has many functions related to track stability and alignment. A ballasted track consists of two main structures: superstructure and substructure [1] .

Generally, ballast is large, angular, uniformly graded, free of dust and dirt, not prone to cementing action and consequent from crushed hard rock material [2]. Ballast aggregates are laid above the sub ballast layer, between the sleepers (crib), and beyond the sleeper ends (shoulder) as shown in Figure 1.

*Cross section view of the typical ballast track*

The deformation behavior of ballast layer due repetitive loadings is complex and not fully understood yet. Ballast deformation and degradation may cause track realignment and may be the main reason for train derailment. Therefore, periodic ballast maintenance is needed which is a cost and time expensive activity [3, 4].

The substantial role of ballast in railway track as well as the needs of periodic, costly maintenance for ballast to sustain its functions leads to raise the researches and reviews on understanding the mechanical behavior of ballast under repetitive loading for better design and less periodic maintenance.

### Discrete Element Method

#### Main Principles

Discrete Element Method is a numerical method to solve mathematical problems associated to discrete characteristic material like granular material. Each particle has its own properties of displacement, velocity, acceleration and contact forces. Cundall [6,7] introduced the DEM by modelling the progressive failure of rock material in the early 70s.The main principles of DEM mechanism are illustrated in Figure 2.

*Figure 2: Main concept of calculation cycle of DEM.*

Each distinct element in DEM model has six degrees of freedom based on two types of motion; translation and rotation . The main objective of DEM is to calculate those finite rotations and displacements due to interactions of each distinct element during simulation time as shown in Figure 3.

*Figure 3: Particel interactions and resultant forces acting on a particle ‘a’ due to contact with particle ‘b’ and non-contact with particle ‘c’.*

#### Particle shape

There are different particles’ shapes can be used in DEM. Particle shape should be efficient to accurately describe the real shape and at the same it should be simple enough to reduce the computational time. Spherical shape is used widely in DEM models due to its geometrical simplicity and the availability of contact models. However, spheres don’t reflect the real behavior of ballast as they don’t provide the interlocking property of real ballast. Therefore, the multi-spheres approach (clump) is used in this research to model railroad ballast by which number of overlapped or touched spheres are created to form a cluster . Figure 4 shows an example of ballast aggregates modelled as spherical clumps.

*Figure 4:Ballast particles modelled as clumps [8]*

### Software used

In this project, EDEM software by DEM solutions is used because it supports the clumping and clustering of spherical particles and easy in functionality with relative to others. Other software like MATLAB and/or Finite Element Method packages may be used later with coupling to EDEM; to simulate the interaction between track superstructure and ballast layer.

### Refrences

[1] Selig, E.T., and J.M. Waters, Track geotechnology and substructure management: Thomas Telford, 1994.

[2] Indraratna, B., and W. Salim, Mechanics of ballasted rail tracks: a geotechnical perspective: CRC Press, 2005.

[3] Indraratna, B., D. Ionescu, and H.D. Christie," Shear behavior of railway ballast based on large-scale triaxial tests", Journal of Geotechnical and Geoenvironmental Engineering Vol. 124, No. 5, 1998, pp. 439-449.

[4] Sañudo, R., L. Dell'Olio, J.A. Casado, I.A. Carrascal, and S. Diego," Track transitions in railways: A review", Construction and Building Materials Vol. 112, 2016, pp. 140-157.

[5] Chen, C., B. Indraratna, G. McDowell, and C. Rujikiatkamjorn," Discrete element modelling of lateral displacement of a granular assembly under cyclic loading", Computers and Geotechnics Vol. 69, 2015, pp. 474-484.

[6] Cundall, P.A., "A computer model for simulating progressive, large-scale movements in blocky rock system".

[7] Cundall, P.A., and O.D.L. Strack," A discrete numerical model for granular assemblies", geotechnique Vol. 29, No. 1, 1979, pp. 47-65.

[8] Ngo, N.T., B. Indraratna, and C. Rujikiatkamjorn," Micromechanics-based investigation of fouled ballast using large-scale triaxial tests and discrete element modeling", Journal of Geotechnical and Geoenvironmental Engineering Vol. 143, No. 2, 2016, pp. 04016089.