Abstract
To quantitatively evaluate the influence of shape on the mechanical behaviors of ballast, a series of 2D direct shear simulations were conducted on particles with different sphericities. The particle contours were obtained from the scanning images of 40 ballast particles, based on which the irregular-shaped particles were precisely reconstructed by clumps in the discrete element models. According to the sphericity, five assemblies were prepared for the direct shear simulation. Higher shear strength, vertical relative displacement and apparent angle of shear resistance were observed in assemblies consisting of low-sphericity particles. To explore the mechanism of macro-mechanical behaviors, an in-depth analysis of the mesoscopic responses was conducted. Two parameters were adopted to evaluate the anisotropy of the contact force distribution observed clearly in all samples and stronger anisotropy was found in samples with low-sphericity particles. The translational and rotational displacements of particles were also analyzed. Larger vertical displacements and less rotations were observed in samples with low-sphericity particles. The results suggest that particles with diverse shapes can produce varying particle interlock states and moving behaviors, hence influence the macro-mechanical behaviors.
Similar content being viewed by others
References
Indraratna, B., Ngo, N.T., Rujikiatkamjorn, C.: Behavior of geogrid-reinforced ballast under various levels of fouling. Geotext. Geomembr. 29(3), 313–322 (2011). https://doi.org/10.1016/j.geotexmem.2011.01.015
Chen, C., Mcdowell, G.R., Thom, N.H.: Investigating geogrid-reinforced ballast: experimental pull-out tests and discrete element modelling. Soils Found. 54(1), 1–11 (2014). https://doi.org/10.1016/j.sandf.2013.12.001
Indraratna, B., Hussaini, S.K.K., Vinod, J.S.: The lateral displacement response of geogrid-reinforced ballast under cyclic loading. Geotext. Geomembr. 39(8), 20–29 (2013). https://doi.org/10.1016/j.geotexmem.2013.07.007
Derakhshani, S.M., Schott, D.L., Lodewijks, G.: Micro-macro properties of quartz sand: experimental investigation and DEM simulation. Powder Technol. 269, 127–138 (2015). https://doi.org/10.1016/j.powtec.2014.08.072
Ovalle, C., Frossard, E., Dano, C., Hu, W., Maiolino, S., Hicher, P.Y.: The effect of size on the strength of coarse rock aggregates and large rockfill samples through experimental data. Acta Mech. 225(8), 2199–2216 (2014). https://doi.org/10.1007/s00707-014-1127-z
Cundall, P., Strack, O.: Discrete numerical model for granular assemblies. Int. J. Rock Mech. Min. Sci. Geomech. Abst. 29(1), 47–65 (1979). https://doi.org/10.1016/0148-9062(79)91211-7
Miao, C.X., Zheng, J.J., Zhang, R.J., Cui, L.: DEM modeling of pullout behavior of geogrid reinforced ballast: the effect of particle shape. Comput. Geotech. 81, 249–261 (2017). https://doi.org/10.1016/j.compgeo.2016.08.028
Ferellec, J.F., Mcdowell, G.R.: A method to model realistic particle shape and inertia in DEM. Granul. Matter 12(5), 459–467 (2010). https://doi.org/10.1007/s10035-010-0205-8
Indraratna, B., Ngo, N.T., Rujikiatkamjorn, C., Vinod, J.S.: Behavior of fresh and fouled railway ballast subjected to direct shear testing: discrete element simulation. Int. J. Geomech. 14(1), 34–44 (2014). https://doi.org/10.1061/(ASCE)GM.1943-5622.0000264
Stahl, M., Konietzky, H.: Discrete element simulation of ballast and gravel under special consideration of grain-shape, grain-size and relative density. Granul. Matter 13(4), 417–428 (2011). https://doi.org/10.1007/s10035-010-0239-y
Lu, M., McDowell, G.R.: The importance of modelling ballast particle shape in the discrete element method. Granul. Matter 9(1), 69 (2006). https://doi.org/10.1007/s10035-006-0021-3
Peña, A.A., García-Rojo, R., Herrmann, H.J.: Influence of particle shape on sheared dense granular media. Granul. Matter 9(3), 279–291 (2007). https://doi.org/10.1007/s10035-007-0038-2
Zhao, S., Zhang, N., Zhou, X., Zhang, L.: Particle shape effects on fabric of granular random packing. Powder Technol. 310, 175–186 (2017). https://doi.org/10.1016/j.powtec.2016.12.094
Alonso-Marroquín, F.: Spheropolygons: a new method to simulate conservative and dissipative interactions between 2D complex-shaped rigid bodies. Europhys. Lett. 83(1), 14001 (2008). https://doi.org/10.1209/0295-5075/83/14001
Alonso-Marroquín, F., Wang, Y.: An efficient algorithm for granular dynamics simulations with complex-shaped objects. Granul. Matter 11(5), 317–329 (2009). https://doi.org/10.1007/s10035-009-0139-1
Ji, S., Sun, S., Yan, Y.: Discrete element modeling of dynamic behaviors of railway ballast under cyclic loading with dilated polyhedra. Int. J. Numer. Anal. Methods Geomech. 41(2), 180–197 (2017). https://doi.org/10.1002/nag.2549
Galindo-Torres, S.A., Pedroso, D.M.: Molecular dynamics simulations of complex-shaped particles using voronoi-based spheropolyhedra. Phys. Rev. E 81(6 Pt 1), 061303 (2010). https://doi.org/10.1103/PhysRevE.81.061303
Džiugys, A., Peters, B.: A new approach to detect the contact of two-dimensional elliptical particles. Int. J. Numer. Anal. Methods Geomech. 25(15), 1487–1500 (2001). https://doi.org/10.1002/nag.180
Baram, R.M., Lind, P.G.: Deposition of general ellipsoidal particles. Phys. Rev. E 85(4 Pt 1), 041301 (2012). https://doi.org/10.1103/PhysRevE.85.041301
Rothenburg, L., Bathurst, R.J.: Numerical simulation of idealized granular assemblies with plane elliptical particles. Comput. Geotech. 11(4), 315–329 (1991). https://doi.org/10.1016/0266-352X(91)90015-8
Ng, T.T.: Shear strength of assemblies of ellipsoidal particles. Géotechnique 54(10), 659–669 (2004). https://doi.org/10.1680/geot.2004.54.10.659
Williams, J.R., Pentland, A.P.: Superquadrics and modal dynamics for discrete elements in interactive design. Eng. Comput. 9(2), 115–127 (1992). https://doi.org/10.1108/eb023852
Morris, G., Neethling, S.J., Cilliers, J.J.: A model for investigating the behaviour of non-spherical particles at interfaces. J. Colloid Interface Sci. 354(1), 380–385 (2011). https://doi.org/10.1016/j.jcis.2010.10.039
Wensrich, C.M., Katterfeld, A., Sugo, D.: Characterisation of the effects of particle shape using a normalised contact eccentricity. Granul. Matter 16(3), 327–337 (2014). https://doi.org/10.1007/s10035-013-0465-1
Wensrich, C.M., Katterfeld, A.: Rolling friction as a technique for modelling particle shape in dem. Powder Technol. 217, 409–417 (2012). https://doi.org/10.1016/j.powtec.2011.10.057
Ai, J., Chen, J.F., Rotter, J.M., Ooi, J.Y.: Assessment of rolling resistance models in discrete element simulations. Powder Technol. 206(3), 269–282 (2011). https://doi.org/10.1016/j.powtec.2010.09.030
Lim, W.L., McDowell, G.R.: Discrete element modelling of railway ballast. Granul. Matter 7(1), 19–29 (2005). https://doi.org/10.1007/s10035-004-0189-3
Matsushima, T., Katagiri, J., Uesugi, K., Tsuchiyama, A., Nakano, T.: 3D shape characterization and image-based DEM simulation of the lunar soil simulant FJS-1. J. Aerosp. Eng. 22(1), 15–23 (2009). https://doi.org/10.1061/(ASCE)0893-1321(2009)22:1(15)
Ferellec, J.F., McDowell, G.R.: A simple method to create complex particle shapes for DEM. Geomech. Geoeng. 3(3), 211–216 (2008). https://doi.org/10.1080/17486020802253992
Kawamoto, R., Andò, E., Viggiani, G., Andrade, J.E.: Level set discrete element method for three-dimensional computations with triaxial case study. J. Mech. Phys. Solids 91, 1–13 (2016). https://doi.org/10.1016/j.jmps.2016.02.021
Jerves, A.X., Kawamoto, R.Y., Andrade, J.E.: A geometry-based algorithm for cloning real grains. Granul. Matter 19(2), 47 (2017). https://doi.org/10.1007/s10035-017-0716-7
Medina, D.A., Jerves, A.X.: A geometry-based algorithm for cloning real grains 2.0. Granul. Matter 21(47), 1 (2019). https://doi.org/10.1007/s10035-018-0851-9
de Macedo, R.B., Marshall, J.P., Andrade, J.E.: Granular object morphological generation with genetic algorithms for discrete element simulations. Granul. Matter 20(4), 591 (2018). https://doi.org/10.1007/s10035-018-0845-7
Katagiri, J., Matsushima, T., Yamada, Y.: Simple shear simulation of 3D irregularly-shaped particles by image-based DEM. Granul. Matter 12(5), 491–497 (2010). https://doi.org/10.1007/s10035-010-0207-6
Jo, S.A., Kim, E.K., Cho, G.C., Lee, S.W.: Particle shape and crushing effects on direct shear behavior using DEM. Soils Found. 51(4), 701–712 (2011). https://doi.org/10.3208/sandf.51.701
Matsushima, T., Chang, C.S.: Quantitative evaluation of the effect of irregularly shaped particles in sheared granular assemblies. Granul. Matter 13(3), 269–276 (2011). https://doi.org/10.1007/s10035-011-0263-6
Desrues, J., Chambon, R., Mokni, M., Mazerolle, F.: Void ratio evolution inside shear bands in triaxial sand specimens studied by computed tomography. Géotechnique 46(3), 529–546 (1996). https://doi.org/10.1680/geot.1996.46.3.529
Anochie-Boateng, J.K., Komba, J.J., Mvelase, G.M.: Three-dimensional laser scanning technique to quantify aggregate and ballast shape properties. Constr. Build. Mater. 43, 389–398 (2013). https://doi.org/10.1016/j.conbuildmat.2013.02.062
Paixão, A., Resende, R., Fortunato, E.: Photogrammetry for digital reconstruction of railway ballast particles: a cost-efficient method. Constr. Build. Mater. 191, 963–976 (2018). https://doi.org/10.1016/j.conbuildmat.2018.10.048
Wadell, H.: Volume, shape, and roundness of rock particles. J. Geol. 41(3), 310–331 (1932)
Lees, G.: A new method for determining the angularity of particles. Sedimentology 3(1), 2–21 (1964). https://doi.org/10.1111/j.1365-3091.1964.tb00271.x
Schwarcz, H.P., Shane, K.C.: Measurement of particle shape by fourier analysis. Sedimentology 13(3–4), 213–231 (2010). https://doi.org/10.1111/j.1365-3091.1969.tb00170.x
Bowman, E.T., Soga, K., Drummond, W.: Particle shape characterisation using Fourier descriptor analysis. Géotechnique 51(6), 545–554 (2001). https://doi.org/10.1680/geot.2001.51.6.545
Zheng, J., Hryciw, R.D.: Traditional soil particle sphericity, roundness and surface roughness by computational geometry. Géotechnique 65(6), 494–506 (2015). https://doi.org/10.1680/geot.14.P.192
Rodriguez, J., Johansson, J., Edeskär, T.: Particle shape determination by two-dimensional image analysis in geotechnical engineering, pp. 207–218. Danish Geotechnical Society (2012)
Mitchell, J.K., Soga, K.: Fundamentals of Soil Behavior, 3rd edn. Wiley, London (2005)
Sevi, A.F.: Physical modeling of railroad ballast using the parallel gradation scaling technique within the cyclical triaxial framework. Ph.D. Missouri University of Science and Technology, United States - Missouri (2008)
Gao, R., Du, X., Zeng, Y., Li, Y., Yan, J.: A new method to simulate irregular particles by discrete element method. J. Rock Mech. Geotech. Eng. 4(3), 276–281 (2012). https://doi.org/10.3724/SP.J.1235.2012.00276
Garcia, X., Latham, J.P., Xiang, J., Harrison, J.P.: A clustered overlapping sphere algorithm to represent real particles in discrete element modelling. Geotechnique 59(9), 779–784 (2009). https://doi.org/10.1680/geot.8.T.037
Taghavi, R.: Automatic clump generation based on mid-surface. In: Continuum and Distinct Element Numerical Modeling in Geomechanics (2011)
Itasca: PFC (Particle Flow Code in 2 and 3 Dimensions), Version 5.0 [User’s Manual]. Itasca Consulting Group, Minneapolis (2014)
Indraratna, B.: Mechanics of Ballasted Rail Tracks: A Geotechnical Perspective. Taylor & Francis, London (2005)
Indraratna, B., Wijewardena, L., Balasubramaniam, A.: Large-scale triaxial testing of greywacke rockfill. Geotechnique 43(1), 37–51 (1993). https://doi.org/10.1680/geot.1993.43.1.37
Masson, S., Martinez, J.: Micromechanical analysis of the shear behavior of a granular material. J. Eng. Mech. 127(10), 1007–1016 (2001). https://doi.org/10.1061/(ASCE)0733-9399(2001)127:10(1007)
Rothenburg, L., Bathurst, R.J.: Analytical study of induced anisotropy in idealized granular materials. Geotechnique 39(4), 601–614 (1989). https://doi.org/10.1680/geot.1989.39.4.601
Cui, L., O’Sullivan, C.: Exploring the macro- and micro-scale response of an idealised granular material in the direct shear apparatus. Geotechnique 56(7), 455–468 (2006). https://doi.org/10.1680/geot.56.7.455
Kozicki, J., Niedostatkiewicz, M., Tejchman, J., Muhlhaus, H.B.: Discrete modelling results of a direct shear test for granular materials versus FE results. Granul. Matter 15(5), 607–627 (2013). https://doi.org/10.1007/s10035-013-0423-y
Tian, J., Liu, E., Jiang, L., Jiang, X., Sun, Y., Xu, R.: Influence of particle shape on the microstructure evolution and the mechanical properties of granular materials. C.R. Mec. 346(6), 460–476 (2018). https://doi.org/10.1016/j.crme.2018.03.006
Zhang, L., Thornton, C.: A numerical examination of the direct shear test. Geotechnique 57(4), 343–354 (2007). https://doi.org/10.1680/geot.2007.57.4.343
Acknowledgements
This work was financially supported by National Natural Science Foundation of China (NSFC) (Grant Nos. 51878521, 51178358). The support is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors Yangzepeng Liu, Rui Gao and Jing Chen all declare no conflicts of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Liu, Y., Gao, R. & Chen, J. Exploring the influence of sphericity on the mechanical behaviors of ballast particles subjected to direct shear. Granular Matter 21, 94 (2019). https://doi.org/10.1007/s10035-019-0943-1
Received:
Published:
DOI: https://doi.org/10.1007/s10035-019-0943-1