Skip to main content
Log in

Discrete Element Study on the Effects of Geogrid Characteristics on the Mechanical Response of Reinforced Ballast Under Cyclic Loading

  • Technical Paper
  • Published:
Transportation Infrastructure Geotechnology Aims and scope Submit manuscript


This study presents an investigation into the mechanical behavior of geogrid-reinforced ballast subjected to cyclic loading focusing on the macro- and micromechanical features of the geogrid-ballast interaction mechanism. Key areas of interest include the effects of geogrid placement depth, aperture size, and stiffness on the motion of ballast particles, formation of contact force chains, and energy dissipation. A three-dimensional discrete element model, calibrated with experimental data, simulates ballast box tests performed on 300-mm-thick ballast layers reinforced by geogrids placed at depths ranging from 50 to 250 mm below the tie. The findings reveal that geogrids located within the upper 150 mm of the ballast layer significantly reduce tie settlement by minimizing particle movement, creating well-connected soil structures, and decreasing energy dissipation. Upon identifying 150 mm as the optimal geogrid placement depth, a parametric study evaluates the impact of the geogrid aperture size (A) and stiffness on the behavior of geogrid-reinforced ballast. The geogrid aperture size (A) is varied to give aperture size to ballast diameter (D) ratios ranging from 1.09 to 2.91, while the geogrid’s stiffness ranges from 9.54 to 18.00 kN/m. Results indicate that A/D ratios greater than or equal to 1.45 are required for geogrids to perform satisfactorily, while stiffness appears to wield a negligible influence on the response of geogrid-reinforced ballast.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

Data Availability

The data supporting the findings of this study are available upon reasonable request from the corresponding author.


A :

Contact area between two contacting pieces or geogrid aperture size

\(\overline{A }\) :

Parallel bond cross-sectional area

D 50 :

Mean ballast particle diameter

Δ δ n :

Relative normal displacement increment

Δ δ s :

Adjusted relative shear displacement increment

\({\varvec{\Delta}}{{\varvec{\delta}}}_{{\varvec{s}}}^{{\varvec{k}}}\) :

Shear displacement’s elastic component

\({\varvec{\Delta}}{{\varvec{\delta}}}_{{\varvec{s}}}^{{\varvec{\mu}}}\) :

Shear displacement’s slip component

E m :

Mechanical energy

E mb :

Mechanical body energy

E mc :

Mechanical contact energy

E pot :

Potential energy

E kin :

Kinetic energy

E damp :

Energy dissipated by non-viscous damping

E k :

Strain energy stored in the linear springs

E µ :

Energy dissipated by frictional slip

\(\overline{{E }_{k}}\) :

Strain energy stored in a geogrid’s parallel bond springs

E* :

Linear effective modulus

\(\overline{{E }^{*}}\) :

Parallel bond effective modulus

ε 1 :

Major principal strain

ε 3 :

Minor principal strain

F c :

Contact force between contacting clumps

\({F}_{n}^{l}\) :

Linear normal force

\({{\varvec{F}}}_{{\varvec{s}}}^{{\varvec{l}}}\) :

Linear shear force

\(\overline{{\varvec{F}} }\) :

Parallel-bond force

\(\overline{{F }_{c}}\) :

Mean interparticle contact force

\(\overline{{F }_{n}}\) :

Normal component of the parallel-bond force

\(\overline{{{\varvec{F}} }_{{\varvec{s}}}}\) :

Shear component of the parallel-bond force

g s :

Surface gap

\(\overline{I }\) :

Parallel bond cross section’s moment of inertia

\(\overline{J }\) :

Parallel bond cross section’s polar moment of inertia

k n :

Linear normal stiffness

k s :

Linear shear stiffness

k t :

Geogrid torsional stiffness

\(\overline{{k }_{n}}\) :

Parallel bond normal stiffness

\(\overline{{k }_{s}}\) :

Parallel bond shear stiffness


Linear normal-to-shear stiffness ratio

\(\overline{{\kappa }^{*}}\) :

Parallel bond normal-to-shear stiffness ratio

κ :

Deviatoric strain

L :

Distance between the centroid of two contacting pieces

M t :

Twisting moment

\(\overline{{\varvec{M}} }\) :

Parallel-bond moment

\(\overline{{M }_{t}}\) :

Twisting moment component of the parallel-bond moment

\(\overline{{{\varvec{M}} }_{{\varvec{b}}}}\) :

Bending moment component of the parallel-bond moment

N c :

Number of contacts in a ballast layer

N p :

Number of particles in a ballast layer

n c :

Unit vector defining the contact place

µ :

Friction coefficient

p :

Hydrostatic stress invariant

q :

Deviatoric stress invariant

R :

Radius of a PFC ball

\(\overline{R }\) :

The parallel bond’s radius

σ d :

Deviator stress

σ max :

Maximum normal stress at the parallel-bond periphery

σ 1 :

Major principal stress

σ 3 :

Minor principal stress

τ max :

Maximum shear stress at the parallel-bond periphery

θ t :

aperture rotation


Download references


The first author is grateful for the technical advice provided by Prof. Ge Gao from Shanghai Jiao Tong University.


This research is funded by an NSERC Alliance grant (NSERC ALLRP 5617) in partnership with Titan Environmental Ltd. and by the McGill Engineering Vadasz Doctoral Fellowship sponsored by the Vadasz Family Foundation.

Author information

Authors and Affiliations



RLED: conceptualization, methodology, investigation, formal analysis, visualization, resources, writing—original draft. MAM: funding acquisition, resources, supervision, writing—review and editing. SB: funding acquisition, writing—review and editing.

Corresponding author

Correspondence to Romaric Léo Esteban Desbrousses.

Ethics declarations

Competing Interests

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Desbrousses, R.L.E., Meguid, M.A. & Bhat, S. Discrete Element Study on the Effects of Geogrid Characteristics on the Mechanical Response of Reinforced Ballast Under Cyclic Loading. Transp. Infrastruct. Geotech. (2024).

Download citation

  • Accepted:

  • Published:

  • DOI: