Skip to main content
SpringerLink
Log in

A Numerical Study on the Influence of Coordination Number on the Crushing of Rockfill Materials

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

Crushing of rockfill grains is one of the most important issues in the stability study of rockfill dams/embankments. In engineering applications, crushing characteristics of a rockfill grain depend strongly on its number of contact points with neighboring grains. The present work aims to propose a breakage criterion including the effects of coordination number, which refers to the increase of grain strength with the redistribution of stress towards hydrostatic stress conditions due to the continual crushing of neighboring grains. In order to analyze the influence of coordination number on grain crushing, single-particle crushing tests with different coordination numbers are first simulated by a bonded particle model using the discrete-element method (DEM). The mechanical confinement effects of neighboring grains are investigated by installing rigid walls around crushable agglomerates. One observes that the failure pattern and strength of agglomerates are significantly affected by the coordination number. The grain strength generally increases with increasing coordination number. Based on the results obtained at the grain scale, a new breakage criterion is proposed for rockfill materials. The proposed criterion is then embedded in a population balance model in DEM. The oedometer tests with three different grain sizes are simulated using the proposed criterion. In order to avoid the unrealistic mechanical response and reduce the energy accumulation in the particle spawning, a new numerical procedure is adopted in the simulations. The simulated stress–strain curve, normal compression line, and particle size distribution are in agreement with the experimental results. Comparison between the proposed criterion and some previous criteria illustrates the merits of the new criterion. The micro-responses of the samples, including the evolution of average coordination number and average particle stress, are also discussed. Discrete-element modeling and micromechanical analysis will enhance the understanding of crushing and deformation behaviors of rockfill materials.

Highlights

  • The influence of coordination number on the failure pattern and crushing strength of rockfill grains is investigated at the grain scale.

  • A new breakage criterion is proposed for the crushing of rockfill grains with the consideration of coordination number effects.

  • A new numerical procedure is adopted to avoid the unrealistic mechanical response in the particle spawning.

  • By simulating the oedometer tests with three different grain sizes, the crushing characteristics of rockfill materials are studied at the structure scale.

  • Micro-mechanical analysis and discrete-element modeling will enhance the understanding of the crushing and deformation behaviors of rockfill materials.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

References

  • Alonso EE, Tapias M, Gili J (2012) Scale effects in rockfill behaviour. Géotech Lett 2:155–160

    Article  Google Scholar 

  • Altuhafi FN, Coop MR (2011) Changes to particle characteristics associated with the compression of sands. Géotechnique 61:459–471

    Article  Google Scholar 

  • ASTM I (2017) Standard practice for classification of soils for engineering purposes (unified soil classification system). ASTM D 2487-17e1

  • Åström JA, Herrmann HJ (1998) Fragmentation of grains in a two-dimensional packing. Eur Phys J B 5:551–554

    Article  Google Scholar 

  • Ben-Nun O, Einav I (2008) A refined DEM study of grain size reduction in uniaxial compression. In: Proceedings of the 12th international conference of the international association for computer methods and advances in geomechanics (IACMAG), Goa, India, pp 702–708

  • Ben-Nun O, Einav I (2010) The role of self-organization during confined comminution of granular materials. Philos Trans Roy Soc A 368:231–247

    Article  Google Scholar 

  • Ciantia MO, Arroyo M, Gens A, Calvetti F (2014) Particle failure in DEM models of crushable soil response. In: Hicks MA, Brinkgreve RBJ, Rohe A (eds) Numerical methods in geotechnical engineering, vol 1. CRC Press/Balkema, Leiden, pp 345–350

    Chapter  Google Scholar 

  • Ciantia MO, Arroyo M, Calvetti F, Gens A (2015) An approach to enhance efficiency of DEM modelling of soils with crushable grains. Géotechnique 65:91–110

    Article  Google Scholar 

  • Cil MB, Alshibli KA (2012) 3D assessment of fracture of sand particles using discrete element method. Géotech Lett 2:161–166

    Article  Google Scholar 

  • Cil MB, Alshibli KA (2014) 3D evolution of sand fracture under 1D compression. Géotechnique 64:351–364

    Article  Google Scholar 

  • Cil MB, Sohn C, Buscarnera G (2020) DEM modeling of grain size effect in brittle granular soils. J Eng Mech 146:04019138

    Google Scholar 

  • Coop MR, Lee I (1992) The behaviour of granular soils at elevated stresses. In: Predictive soil mechanics: proceedings of the Wroth Memorial Symposium held at St Catherine’s College, Oxford, 27-29 July 1992, Thomas Telford Publishing, pp 186–198

  • Coop MR, Sorensen KK, Freitas TB, Georgoutsos G (2004) Particle breakage during shearing of a carbonate sand. Géotechnique 54:157–163

    Article  Google Scholar 

  • Couroyer C, Ning Z, Ghadiri M (2000) Distinct element analysis of bulk crushing: effect of particle properties and loading rate. Powder Technol 109:241–254

    Article  Google Scholar 

  • Daouadji A, Hicher PY (2010) An enhanced constitutive model for crushable granular materials. Int J Numer Anal Methods Geomech 34:555–580

    Article  Google Scholar 

  • Daouadji A, Hicher PY, Rahma A (2001) An elastoplastic model for granular materials taking into account grain breakage. Eur J Mech A-Solid 20:113–137

    Article  Google Scholar 

  • de Bono JP, McDowell GR (2015) An insight into the yielding and normal compression of sand with irregularly-shaped particles using DEM. Powder Technol 271:270–277

    Article  Google Scholar 

  • de Bono JP, McDowell GR (2016a) The fractal micro mechanics of normal compression. Comput Geotech 78:11–24

    Article  Google Scholar 

  • de Bono JP, McDowell GR (2016b) Particle breakage criteria in discrete-element modelling. Géotechnique 66:1014–1027

    Article  Google Scholar 

  • de Bono JP, McDowell GR (2020) On the packing and crushing of granular materials. Int J Solids Struct 187:133–140

    Article  Google Scholar 

  • Devroye L (2006) Chapter 4 nonuniform random variate generation. In: Henderson SG, Nelson BL (eds) Simulation. Volume 13 of Handbooks in operations research and management science. Elsevier, pp 83–121

  • Duriez J, Scholtès L, Donzé FV (2016) Micromechanics of wing crack propagation for different flaw properties. Eng Fract Mech 153:378–398

    Article  Google Scholar 

  • Einav I (2007) Breakage mechanics-part I: theory. J Mech Phys Solids 55:1274–1297

    Article  Google Scholar 

  • Elghezal L, Jamei M, Georgopoulos IO (2013) DEM simulations of stiff and soft materials with crushable particles: an application of expanded perlite as a soft granular material. Granul Matter 15:685–704

    Article  Google Scholar 

  • Eliáš J (2014) Simulation of railway ballast using crushable polyhedral particles. Powder Technol 264:458–465

    Article  Google Scholar 

  • Esnault VPB, Roux JN (2013) 3D numerical simulation study of quasistatic grinding process on a model granular material. Mech Mater 66:88–109

    Article  Google Scholar 

  • Fu R, Hu X, Zhou B (2017) Discrete element modeling of crushable sands considering realistic particle shape effect. Comput Geotech 91:179–191

    Article  Google Scholar 

  • Guida G, Casini F, Viggiani GM, Ando E, Viggiani G (2018) Breakage mechanisms of highly porous particles in 1D compression revealed by X-ray tomography. Géotech Lett 8:155–160

    Article  Google Scholar 

  • Gundepudi M, Sankar B, Mecholsky J Jr, Clupper D (1997) Stress analysis of brittle spheres under multiaxial loading. Powder Technol 94:153–161

    Article  Google Scholar 

  • Hanley KJ, O’Sullivan C, Huang X (2015) Particle-scale mechanics of sand crushing in compression and shearing using DEM. Soils Found 55:1100–1112

    Article  Google Scholar 

  • Huang J, Xu S, Yi H, Hu S (2014) Size effect on the compression breakage strengths of glass particles. Powder Technol 268:86–94

    Article  Google Scholar 

  • Huang Q, Zhou W, Ma G, Ng TT, Xu K (2020) Experimental and numerical investigation of Weibullian behavior of grain crushing strength. Geosci Front 11:401–411

    Article  Google Scholar 

  • Huillca Y, Silva M, Ovalle C, Quezada JC, Carrasco S, Villavicencio GE (2021) Modelling size effect on rock aggregates strength using a DEM bonded-cell model. Acta Geotech 16:699–709

    Article  Google Scholar 

  • Jaeger JC (1967) Failure of rocks under tensile conditions. Int J Rock Mech Min Sci 4:219–227

    Article  Google Scholar 

  • Kh AB, Mirghasemi AA, Mohammadi S (2011) Numerical simulation of particle breakage of angular particles using combined DEM and FEM. Powder Technol 205:15–29

    Article  Google Scholar 

  • Kozicki J, Donze FV (2008) A new open-source software developed for numerical simulations using discrete modeling methods. Comput Method Appl Mech 197:4429–4443

    Article  Google Scholar 

  • Kozicki J, Donze FV (2009) YADE-OPEN DEM: an open-source software using a discrete element method to simulate granular material. Eng Comput 26:786–805

    Article  Google Scholar 

  • Lade PV, Yamamuro JA, Bopp PA (1996) Significance of particle crushing in granular materials. J Geotech Eng-ASCE 122:309–316

    Article  Google Scholar 

  • Li S, Kasyap SS, Senetakis K (2021) A study on the failure behavior of sand grain contacts with Hertz modeling, image processing, and statistical analysis. Sensors 21:4611

    Article  Google Scholar 

  • Lim WL, McDowell GR (2007) The importance of coordination number in using agglomerates to simulate crushable particles in the discrete element method. Géotechnique 57:701–705

    Article  Google Scholar 

  • Liu X, Wang Y, Zhang Z, Yu Y (2021) DEM investigation on the breakage of spherical aggregate under multi-contact loadings. AIChE J 67:e17294

    Article  Google Scholar 

  • Lobo-Guerrero S, Vallejo LE, Vesga LF (2006) Visualization of crushing evolution in granular materials under compression using DEM. Int J Geomech 6:195–200

    Article  Google Scholar 

  • Luzzani L, Coop MR (2002) On the relationship between particle breakage and the critical state of sands. Soils Found 42:71–82

    Article  Google Scholar 

  • Marketos G, Bolton MD (2009) Compaction bands simulated in discrete element models. J Struct Geol 31:479–490

    Article  Google Scholar 

  • Marsaglia G et al (1972) Choosing a point from the surface of a sphere. Ann Math Stat 43:645–646

    Article  Google Scholar 

  • McDowell GR (2002) On the yielding and plastic compression of sand. Soils Found 42:139–145

    Article  Google Scholar 

  • McDowell GR, Amon A (2000) The application of Weibull statistics to the fracture of soil particles. Soils Found 40:133–141

    Google Scholar 

  • McDowell GR, Bolton MD (1998) On the micromechanics of crushable aggregates. Géotechnique 48:667–679

    Article  Google Scholar 

  • McDowell GR, de Bono JP (2013) On the micro mechanics of one-dimensional normal compression. Géotechnique 63:895–908

    Article  Google Scholar 

  • McDowell GR, Humphreys A (2002) Yielding of granular materials. Granul Matter 4:1–8

    Article  Google Scholar 

  • Nakata AFL, Hyde M, Hyodo H, Murata (1999) A probabilistic approach to sand particle crushing in the triaxial test. Géotechnique 49:567–583

    Article  Google Scholar 

  • Nakata Y, Hyodo M, Hyde AF, Kato Y, Murata H (2001a) Microscopic particle crushing of sand subjected to high pressure one-dimensional compression. Soils Found 41:69–82

    Article  Google Scholar 

  • Nakata Y, Kato Y, Hyodo M, Hyde AF, Murata H (2001b) One-dimensional compression behaviour of uniformly graded sand related to single particle crushing strength. Soils Found 41:39–51

    Article  Google Scholar 

  • Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41:1329–1364

    Article  Google Scholar 

  • Rad MM, Safikhani S, Bauer E (2019) Influence of the loading condition on single grain crushing in DEM simulation. Period Polytech-Civ 63:1152–1158

    Google Scholar 

  • Salami Y, Dano C, Hicher PY, Colombo G, Denain P (2015) The effects of the coordination on the fragmentation of a single grain. In: IOP conference series: earth and environmental science. IOP Publishing, p 012015

  • Salami Y, Dano C, Hicher PY (2019) An experimental study on the influence of the coordination number on grain crushing. Eur J Environ Civ Eng 23:432–448

    Article  Google Scholar 

  • Sandeep CS, Li S, Senetakis K (2021) Scale and surface morphology effects on the micromechanical contact behavior of granular materials. Tribol Int 159:106929

    Article  Google Scholar 

  • Scholtès L, Donzé FV (2013) A DEM model for soft and hard rocks: role of grain interlocking on strength. J Mech Phys Solids 61:352–369

    Article  Google Scholar 

  • Shi D, Cao D, Deng Y, Xue J (2021) DEM investigations of the effects of intermediate principal stress ratio and particle breakage on the critical state behaviors of granular soils. Powder Technol 379:547–559

    Article  Google Scholar 

  • Sukumaran B, Einav I, Dyskin A (2006) Qualitative assessment of the influence of coordination number on crushing strength using DEM. In: Proc. of the fifth world congress on particle technology, 23–27 April, Orlando, Florida, USA

  • Tapias M, Alonso EE, Gili JA (2015) A particle model for rockfill behaviour. Géotechnique 65:975–994

    Article  Google Scholar 

  • Tarantino A, Hyde AF (2005) An experimental investigation of work dissipation in crushable materials. Géotechnique 55:575–584

    Article  Google Scholar 

  • Todisco MC, Coop MR, Guo Q, Senetakis K (2015) The effect of the coordination number on particle crushing. In: International symposium on geomechanics from micro to macro, IS-Cambridge 2014. Taylor and Francis-Balkema, pp 1063–1068

  • Todisco M, Wang W, Coop M, Senetakis K (2017) Multiple contact compression tests on sand particles. Soils Found 57:126–140

    Article  Google Scholar 

  • Tong CX, Zhang KF, Zhang S, Sheng D (2019) A stochastic particle breakage model for granular soils subjected to one-dimensional compression with emphasis on the evolution of coordination number. Comput Geotech 112:72–80

    Article  Google Scholar 

  • Tsoungui O, Vallet D, Charmet JC (1999) Numerical model of crushing of grains inside two-dimensional granular materials. Powder Technol 105:190–198

    Article  Google Scholar 

  • Turcotte DL (1986) Fractals and fragmentation. J Geophys Res-Sol Earth 91:1921–1926

    Article  Google Scholar 

  • Tyler SW, Wheatcraft SW (1989) Application of fractal mathematics to soil water retention estimation. Soil Sci Soc Am J 53:987–996

    Article  Google Scholar 

  • Varadarajan A, Sharma KG, Venkatachalam K, Gupta AK (2003) Testing and modeling two rockfill materials. J Geotech Geoenviron 129:206–218

    Article  Google Scholar 

  • Wang P, Arson C (2016) Discrete element modeling of shielding and size effects during single particle crushing. Comput Geotech 78:227–236

    Article  Google Scholar 

  • Wang W, Coop M (2016) An investigation of breakage behaviour of single sand particles using a high-speed microscope camera. Géotechnique 66:984–998

    Article  Google Scholar 

  • Wang J, Yan H (2013) On the role of particle breakage in the shear failure behavior of granular soils by DEM. Int J Numer Anal Methods Geomech 37:832–854

    Article  Google Scholar 

  • Wang P, Karatza Z, Arson C (2019) DEM modelling of sequential fragmentation of zeolite granules under oedometric compression based on XCT observations. Powder Technol 347:66–75

    Article  Google Scholar 

  • Wang ZY, Fang YF, Feng WQ, Tian XJ, Lin JF (2022) Comparative study on particle size effect of crushable granular soils through DEM simulations. Lithosphere 2021:1608454

    Article  Google Scholar 

  • Weerasekara NS, Powell MS, Cleary PW, Tavares LM, Evertsson M, Morrison RD, Quist J, Carvalho RM (2013) The contribution of DEM to the science of comminution. Powder Technol 248:3–24

    Article  Google Scholar 

  • Xiao Y, Liu H, Chen Y, Jiang J, Zhang W (2014) Testing and modeling of the state-dependent behaviors of rockfill material. Comput Geotech 61:153–165

    Article  Google Scholar 

  • Xiao Y, Liu H, Ding X, Chen Y, Jiang J, Zhang W (2016) Influence of particle breakage on critical state line of rockfill material. Int J Geomech 16:04015031

    Article  Google Scholar 

  • Xiao Y, Meng M, Daouadji A, Chen Q, Wu Z, Jiang X (2020) Effects of particle size on crushing and deformation behaviors of rockfill materials. Geosci Front 11:375–388

    Article  Google Scholar 

  • Xu M, Hong J, Song E (2017) DEM study on the effect of particle breakage on the macro-and micro-behavior of rockfill sheared along different stress paths. Comput Geotech 89:113–127

    Article  Google Scholar 

  • Ye Y, Zeng Y, Sun H, Liu Y, Chen X, Ma W (2021) An experimental study on the influence of multiple contacts and size on contact behavior of marble sphere. Granul Matter 23:1–13

    Article  Google Scholar 

  • Zhang, C., Zhao, Y. & Bai, Q. 3D DEM method for compaction and breakage characteristics simulation of broken rock mass in goaf. Acta Geotech. 17, 2765–2781 (2022). https://doi-org.ressources-electroniques.univ-lille.fr/10.1007/s11440-021-01379-3

  • Zhao X (2021) Experimental study and numerical modeling of crushing and mechanical behavior of rockfill materials: influence of particle size. Ph.D. thesis, University of Lille, France

  • Zhao B, Wang J, Coop MR, Viggiani G, Jiang M (2015) An investigation of single sand particle fracture using X-ray micro-tomography. Géotechnique 65:625–641

    Article  Google Scholar 

  • Zhao CF, Pinzón G, Wiebicke M, Andò E, Kruyt NP, Viggiani G (2021) Evolution of fabric anisotropy of granular soils: X-ray tomography measurements and theoretical modelling. Comput Geotech 133:104046

    Article  Google Scholar 

  • Zheng W, Tannant DD (2018) Grain breakage criteria for discrete element models of sand crushing under one-dimensional compression. Comput Geotech 95:231–239

    Article  Google Scholar 

  • Zhou W, Yang L, Ma G, Chang X, Cheng Y, Li D (2015) Macro-micro responses of crushable granular materials in simulated true triaxial tests. Granul Matter 17:497–509

    Article  Google Scholar 

  • Zhou W, Yang L, Ma G, Chang X, Lai Z, Xu K (2016) DEM analysis of the size effects on the behavior of crushable granular materials. Granul Matter 18:1–11

    Article  Google Scholar 

  • Zhou W, Wang D, Ma G, Cao X, Hu C, Wu W (2020) Discrete element modeling of particle breakage considering different fragment replacement modes. Powder Technol 360:312–323

    Article  Google Scholar 

  • Zhu F, Zhao J (2019) A peridynamic investigation on crushing of sand particles. Géotechnique 69:526–540

    Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the financial support from the State Key Program of National Natural Science Foundation of China (No. U2040221), the Open Sharing Fund for the Large-scale Instruments of Hohai University (Nos. GX202205B; GX202204B), and the 111 Project (No. B13024). The first author gratefully acknowledges the financial support from China Scholarship Council (No. 201806710020). The oedometer test simulations in this paper have been done on the HPC Computing Mésocentre of University of Lille. The authors gratefully thank the anonymous reviewers for their constructive comments as well.

Author information

Authors and Affiliations

  1. College of Civil and Transportation Engineering, Hohai University, Nanjing, 210098, China

    Xiaolong Zhao & Jungao Zhu

  2. Key Laboratory of Geomechanics and Embankment Engineering of Ministry of Education, Hohai University, Nanjing, 210098, China

    Xiaolong Zhao & Jungao Zhu

  3. Univ. Lille, CNRS, Centrale Lille, UMR 9013-LaMcube-Laboratoire de Mécanique, Multiphysique, Multi-échelle, 59000, Lille, France

    Xiaolong Zhao, Yunlong Wu, Yun Jia & Jean-Baptiste Colliat

  4. Univ. Lille, ULR 4515-LGCgE-Laboratory of Civil Engineering and Geo-Environment, 59000, Lille, France

    Hanbing Bian

Authors
  1. Xiaolong Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jungao Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yunlong Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yun Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jean-Baptiste Colliat
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Hanbing Bian
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

XZ: conceptualization, methodology, software, writing—original draft, and funding acquisition. JZ: writing—review and editing, and funding acquisition. YW: writing—review and editing, and methodology. YJ: conceptualization, supervision, writing—review and editing, and methodology. J-BC: supervision, writing—review and editing, and methodology. HB: writing—review and editing, and methodology.

Corresponding author

Correspondence to Yun Jia.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, X., Zhu, J., Wu, Y. et al. A Numerical Study on the Influence of Coordination Number on the Crushing of Rockfill Materials. Rock Mech Rock Eng 55, 6279–6300 (2022). https://doi.org/10.1007/s00603-022-02985-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-022-02985-7

Keywords

Search

Navigation