Abstract
This paper presents a study of the interface of geogrid reinforced subballast through a series of large-scale direct shear tests and discrete element modelling. Direct shear tests were carried out for subballast with and without geogrid inclusions under varying normal stresses of \(\sigma _n =6.7\) to \(45\hbox { kPa}\). Numerical modelling with three-dimensional discrete element method (DEM) was used to study the shear behaviour of the interface of subballast reinforced by geogrids. In this study, groups of 25–50 spherical balls are clumped together in appropriate sizes to simulate angular subballast grains, while the geogrid is modelled by bonding small spheres together to form the desired grid geometry and apertures. The calculated results of the shear stress ratio versus shear strain show a good agreement with the experimental data, indicating that the DEM model can capture the interface behaviour of subballast reinforced by geogrids. A micromechanical analysis has also been carried out to examine how the contact force distributions and fabric anisotropy evolve during shearing. This study shows that the shear strength of the interface is governed by the geogrid characteristics (i.e. their geometry and opening apertures). Of the three types of geogrid tested, triaxial geogrid (triangular apertures) exhibits higher interface shear strength than the biaxial geogrids; and this is believed due to multi-directional load distribution of the triaxial geogrid.
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References
Selig, E.T., Waters, J.M.: Track Geotechnology and Substructure Management. Thomas Telford, London (1994)
Indraratna, B., Ngo, N.T., Rujikiatkamjorn, C.: Deformation of coal fouled ballast stabilized with geogrid under cyclic load. J. Geotech. Geoenviron. Eng. 139(8), 1275–1289 (2013)
Suiker, A.S., Selig, E.T., Frenkel, R.: Static and cyclic triaxial testing of ballast and subballast. J. Geotech. Geoenviron. Eng. 131(6), 771–782 (2005)
Trani, L.D., Indraratna, B.: Assessment of subballast filtration under cyclic loading. J. Geotech. Geoenviron. Eng. 136(11), 1519–1528 (2010)
Tutumluer, E., Schmidt, S., Qamhia, I., Basye, C., Li, D., Douglas, S.C.: Ballast properties and degradation trends affecting strength, deformation and in-track performance. In: Proceedings of the AREMA 2015 Annual Conference in Conjunction with the Railway Interchange, Minneapolis, MN, 2015
Ngo, N.T., Indraratna, B., Rujikiatkamjorn, C.: Modelling geogrid-reinforced railway ballast using the discrete element method. Transp. Geotech. 8(2016), 86–102 (2016)
Lekarp, F., Dawson, A.: Modelling permanent deformation behaviour of unbound granular materials. Constr. Build. Mater. 12(1), 9–18 (1998)
Werkmeister, S., Dawson, A., Wellner, F.: Pavement design model for unbound granular materials. J. Transp. Eng. 130(5), 665–674 (2004)
Indraratna, B., Salim, W., Rujikiatkamjorn, C.: Advanced Rail Geotechnology—Ballasted Track. CRC Press, Taylor & Francis Group, London (2011)
Indraratna, B., Ngo, N.T., Rujikiatkamjorn, C.: Behavior of geogrid-reinforced ballast under various levels of fouling. Geotext. Geomembr. 29(3), 313–322 (2011)
Bathurst, R.J., Raymond, G.P.: Geogrid reinforcement of ballasted track. Transp. Res. Rec. 1153, 8–14 (1987)
Fernandes, G., Palmeira, E.M., Gomes, R.C.: Performance of geosynthetic-reinforced alternative sub-ballast material in a railway track. Geosynth. Int. 15(5), 311–321 (2008)
Pokharel, S.K., Han, J., Leshchinsky, D., Parsons, R.L., Halahmi, I.: Investigation of factors influencing behavior of single geocell-reinforced bases under static loading. Geotext. Geomembr. 28(6), 570–578 (2010)
Ngo, N.T., Indraratna, B.: Improved performance of rail track substructure using synthetic inclusions: experimental and numerical investigations. Int. J. Geosynth. Ground Eng. 2(3), 1–16 (2016)
Biabani, M., Indraratna, B., Ngo, N.T.: Modelling of geocell-reinforced subballast subjected to cyclic loading. Geotext. Geomembr. 44(4), 489–503 (2016)
Biabani, M., Indraratna, B.: An evaluation of the interface behaviour of rail subballast stabilised with geogrids and geomembranes. Geotext. Geomembr. 43(3), 240–249 (2015)
Rujikiatkamjorn, C., Indraratna, B., Ngo, N.T., Coop, M.: A laboratory study of railway ballast behaviour under various fouling degree. In: Proceedings of the 5th Asian Regional Conference on Geosynthetics, 2012
Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Géotechnique 29(1), 47–65 (1979)
McDowell, G.R., Harireche, O., Konietzky, H., Brown, S.F., Thom, N.H.: Discrete element modelling of geogrid-reinforced aggregates. Proc. ICE- Geotech. Eng. 159(1), 35–48 (2006)
Tutumluer, E., Huang, H., Bian, X.: Geogrid-aggregate interlock mechanism investigated through aggregate imaging-based discrete element modeling approach. Int. J. Geomech. 12(4), 391–398 (2012)
Ngo, N.T., Indraratna, B., Rujikiatkamjorn, C.: DEM simulation of the behaviour of geogrid stabilised ballast fouled with coal. Comput. Geotech. 55, 224–231 (2014)
Powrie, W., Ni, Q., Harkness, R.M., Zhang, X.: Numerical modelling of plane strain tests on sands using a particulate approach. Géotechnique 55(4), 297–306 (2005)
Powrie, W., Yang, L.A., Clayton, C.I.: Stress changes in the ground below ballasted railway track during train passage. Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit 221, 247–261 (2007)
Harkness, J., Zervos, A., Le Pen, L., Aingaran, S., Powrie, W.: Discrete element simulation of railway ballast: modelling cell pressure effects in triaxial tests. Granul. Matter 18(3), 65 (2016)
Chen, C., McDowell, G.R., Thom, N.H.: Discrete element modelling of cyclic loads of geogrid-reinforced ballast under confined and unconfined conditions. Geotext. Geomembr. 35, 76–86 (2012)
Han, J., Bhandari, A., Wang, F.: DEM analysis of stresses and deformations of geogrid-reinforced embankments over piles. Int. J. Geomech. 12(4), 340–350 (2011)
Sieira, A.C., Gerscovich, D.M., Sayão, A.: Displacement and load transfer mechanisms of geogrids under pullout condition. Geotext. Geomembr. 27, 241–253 (2009)
Aursudkij, B., McDowell, G.R., Collop, A.C.: Cyclic loading of railway ballast under triaxial conditions and in a railway test facility. Granul. Matter 11, 391–401 (2009)
Biabani, M., Ngo, N.T., Indraratna, B.: Performance evaluation of railway subballast stabilised with geocell based on pull-out testing. Geotext. Geomembr. 44(4), 579–591 (2016)
Australian Standard.: Aggregates and rock for engineering purposes; part 7: railway ballast. AS 2758.7. Sydney, Australia (1996)
McDowell, G.R., Harireche, O.: Discrete element modelling of soil particle fracture. Géotechnique 52(2), 131–135 (2002)
Lobo-Guerrero, S., Vallejo, L.E.: Discrete element method analysis of railtrack ballast degradation during cyclic loading. Granul. Matter 8(3–4), 195–204 (2006)
Cui, L., O’Sullivan, C.: Exploring the macro- and micro-scale response of an idealised granular material in the direct shear apparatus. Géotechnique 56(7), 455–468 (2006)
Indraratna, B., Ngo, N.T., Rujikiatkamjorn, C., Vinod, J.: Behavior of fresh and fouled railway ballast subjected to direct shear testing: discrete element simulation. Int. J. Geomech. 14(1), 34–44 (2014)
Indraratna, B., Ngo, N.T., Rujikiatkamjorn, C., Sloan, S.W.: Coupled discrete element-finite difference method for analysing the load-deformation behaviour of a single stone column in soft soil. Comput. Geotech. 63, 267–278 (2015)
Ngo, N.T., Indraratna, B., Rujikiatkamjorn, C.: Micromechanics-based investigation of fouled ballast using large-scale triaxial tests and discrete element modeling. J. Geotech. Geoenviron. Eng, 04016089 (2016). doi:10.1061/(ASCE)GT.1943-5606.0001587
Lu, M., McDowell, G.R.: The importance of modelling ballast particle shape in the discrete elememt method. Granul. Matter 9(1–2), 69–80 (2007)
Hu, M., O’Sullivan, C., Jardine, R.R., Jiang, M.: Stress-induced anisotropy in sand under cyclic loading. Granul. Matter 12, 469–476 (2010)
Itasca: Particle Flow Code in Three Dimensions (PFC3D)—Manual. Itasca Consulting Group, Inc., Minnesota (2014)
Ferellec, J.F., McDowell, G.R.: A method to model realistic particle shape and inertia in DEM. Granul. Matter 12(5), 459–467 (2010)
ASTM D4885-01(2011): Standard Test Method for Determining Performance Strength of Geomembranes by the Wide Strip Tensile Method. ASTM International, West Conshohocken (2011)
Lim, W.L., McDowell, G.R.: Discrete element modelling of railway ballast. Granul. Matter 7(1), 19–29 (2005)
Ngo, N.T., Indraratna, B., Rujikiatkamjorn, C., Biabani, M.M.: Experimental and discrete element modeling of geocell-stabilized subballast subjected to cyclic loading. J. Geotech. Geoenviron. Eng. 142(4), 04015100 (2016)
Oda, M., Iwashita, K.: Mechanics of Granular Materials: An Introduction. A. A. Balkema, Rotterdam (1999)
D’Addetta, G.A., Ramm, E.: A microstructure-based simulation environment on the basis of an interface enhanced particle model. Granul. Matter 8, 159–174 (2006)
Ouadfel, H., Rothenburg, L.: Stress–force–fabric relationship for assemblies of ellipsoids. Mech. Mater. 33, 201–221 (2001)
Rothenburg, L., Bathurst, R.J.: Analytical study of induced anisotropy in idealized granular materials. Geotechnique 39(4), 601–614 (1989)
Acknowledgements
The Authors would like to acknowledge the Rail Manufacturing CRC, Australasian Centre for Rail Innovation (ACRI) Limited, and Tyre Stewardship Australia Limited (TSA) for providing the financial support needed to undertake this research (Project R2.5.1). The authors are grateful to Professor Glenn McDowell, who has provided valuable discussions and comments with the DEM analysis over the last few years. The Authors are grateful to Mr. Alan Grant, Mr. Cameron Neilson, Mr Duncan Best and Mr. Ritchie McLean for their assistance in the laboratory. Laboratory work conducted by Dr. Biabani is also greatly appreciated.
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Appendix: mathematical framework of DEM modelling
Appendix: mathematical framework of DEM modelling
At a given time, the force vector \(\vec {{\varvec{F}}}\) that represents the interaction between two particles is resolved into normal (\(\vec {F}_N\)) and the shear component (\(\vec {F}_T\)) with respect to the contact plane [39]:
where, \(K_{N}\) and \(K_{T}\) are normal and tangential stiffness at the point of contact; \(U^{n}\) is the normal penetration between two particles (Fig. 13a); \(\delta U^{s}\) is the incremental tangential displacement; and \(\delta \vec {F}_T\) is the incremental tangential force. The new shear contact force is determined by summing the old shear force at the start of the time-step with the increment of elastic shear force.
where, \(\mu \) is the coefficient of friction.
Shear stresses in a given volume V are calculated by the summation of discrete contact forces as:
where \(N_{p}\), \(N_{c}\) are the number of particles and the number of contacts of these particles, respectively; n is the porosity within the given volume; \(x_{i}^{[p]}\) and \(x_{i}^{[c]}\) are the positions of a particle centroid and its contact, respectively; \(n_{i}^{(c,p)}\) is the unit normal vector; and \(f_{j}^{(c)}\) is the force acting at contact (c) arising from a particle.
Contact forces are characterised by the probability density distribution of inter-particle contact orientation \(\bar{E}(\Omega )\) proposed by Ouadfel and Rothernburg [46] as:
where, \(F_{ij}\) is a second order fabric tensor which represents the distribution of contact orientations in the volume of interest, and is determined by:
Note that \(F_{ij}\) is symmetrical (i.e. \(F_{ij}=F_{ji})\) with the three principal values \(F_{11} ,F_{22} ,F_{33} \) where their sum is unity; \(n_{i}^{k}\) is a unit vector representing the orientation of the k contact (Fig. 13b); and the components of a unit vector are (\(\cos \gamma ,\sin \gamma \cos \beta ,\sin \gamma \sin \beta \)). The probability density function of all contacts satisfies:
The principal direction of contact forces, \(\theta _r \) can be described by the following Fourier series approximation introduced by Rothenburg and Bathurst [47], as given below:
where, \(a^{r}\)and \(\theta _r \) are coefficients of anisotropy of contact and the corresponding major principal directions, respectively. By comparing the contact force orientations obtained in DEM simulations with those determined by Eq. 8, the principal direction of contact forces, \(\theta _r \) can then be estimated at a given shear strain during the DEM analysis.
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Ngo, N.T., Indraratna, B. & Rujikiatkamjorn, C. A study of the geogrid–subballast interface via experimental evaluation and discrete element modelling. Granular Matter 19, 54 (2017). https://doi.org/10.1007/s10035-017-0743-4
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DOI: https://doi.org/10.1007/s10035-017-0743-4