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Investigation of the grain breakage behaviour of 2D granular materials with disordered pore distribution

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Abstract

Granular materials have been widely used in the field of geotechnical engineering. Being one of the intrinsic properties of granular materials, the internal grain porosity greatly affects their mechanical properties, grain crushing in particular. In this article, the single porous grains with different degrees of disordered pore distribution were generated and fully investigated with discrete element method (DEM). The degree of disorder of pore distribution is characterized by parameter Iv. The DEM results demonstrate that both number of pore and the disorder of pore distribution have great effects on crushing strength. A more disordered pore distribution could lead to higher stress concentration and the heterogeneity of stress distribution, which results in a lower crushing strength. The shape of remaining fragments after grain crushing shows that the cracking path becomes more irregular with increasing disorder of pore distribution. For the three studied porosity, the crushing strength complies with an exponential-law diminution with the increase in disorder degree of pore distribution. The grain crushing strength was also statistically analysed by Weibull distribution. Similar to crushing strength, the Weibull modulus, m, of grain crushing strength follows an exponential law, in other words, m decreases with the disorder degree of porous texture. These results deepen our understanding of the effect of pore disorder over crushing behaviour of granular matter.

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References

  1. Ma G, Zhou W, Chang X-L, Chen M-X (2016) A hybrid approach for modeling of breakable granular materials using combined finite-discrete element method. Granul Matter 18:7. https://doi.org/10.1007/s10035-016-0615-3

    Article  Google Scholar 

  2. Zhou X, Ma G, Zhang Y (2018) Grain size and time effect on the deformation of rockfill dams: a case study on the Shuibuya CFRD. Géotechnique. https://doi.org/10.1680/jgeot.17.P.299

    Article  Google Scholar 

  3. Einav I, Guillard F (2018) Tracking time with ricequakes in partially soaked brittle porous media. Sci Adv 4:1–9. https://doi.org/10.1126/sciadv.aat6961

    Article  Google Scholar 

  4. Xiao Y, Liu H, Desai CS, Sun Y, Liu H (2016) Stress–strain–strength response and ductility of gravels improved by polyurethane foam adhesive. J Geotech Eng ASCE 142:06015017. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001433

    Article  Google Scholar 

  5. Zhou W, Ma G, Chang X-L, Duan Y (2015) Discrete modeling of rockfill materials considering the irregular shaped particles and their crushability. Eng Comput 32:1104–1120. https://doi.org/10.1108/EC-04-2014-0086

    Article  Google Scholar 

  6. Wang B, Martin U, Rapp S (2017) Discrete element modeling of the single-particle crushing test for ballast stones. Comput Geotech 88:61–73. https://doi.org/10.1016/j.compgeo.2017.03.007

    Article  Google Scholar 

  7. Ouhbi N, Voivret C, Perrin G, Roux J-N (2017) 3D particle shape modelling and optimization through proper orthogonal decomposition. Granul Matter 19:86. https://doi.org/10.1007/s10035-017-0771-0

    Article  Google Scholar 

  8. Einav I (2007) Breakage mechanics-part I: theory. J Mech Phys Solids 55:1274–1297. https://doi.org/10.1016/j.jmps.2006.11.003

    Article  MathSciNet  MATH  Google Scholar 

  9. Ma G, Zhou W, Chang XL (2014) Modeling the particle breakage of rockfill materials with the cohesive crack model. Comput Geotech 61:1320–1143. https://doi.org/10.1016/j.compgeo.2014.05.006

    Article  Google Scholar 

  10. Xiao Y, Desai CS, Daouadji A, Stuedlein AW, Liu H, Abuel-Naga H (2020) Grain crushing in geoscience materials–key issues on crushing response, measurement and modeling: review and preface. Geosci Front 11:363–374. https://doi.org/10.1016/j.gsf.2019.11.006

    Article  Google Scholar 

  11. Zhou W, Ji X, Ma G, Chen Y (2019) FDEM simulation of rocks with microstructure generated by Voronoi grain-based model with particle growth. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-019-02014-0

    Article  Google Scholar 

  12. Laubie H, Radjai F, Pellenq R, Ulm FJ (2017a) Stress transmission and failure in disordered porous media. Phys Rev Lett 119:1–6. https://doi.org/10.1103/PhysRevLett.119.075501

    Article  Google Scholar 

  13. Baud P, Wong TF, Zhu W (2014) Effects of porosity and crack density on the compressive strength of rocks. Int J Rock Mech Min Sci 67:202–211. https://doi.org/10.1016/j.ijrmms.2013.08.031

    Article  Google Scholar 

  14. Wu H, Zhao J, Guo N (2018) Multiscale insights into borehole instabilities in high-porosity sandstones. J Geophys Res Solid Earth 123:3450–3473. https://doi.org/10.1029/2017JB015366

    Article  Google Scholar 

  15. Cnudde V, Cwirzen A, Masschaele B, Jacobs PJS (2009) Porosity and microstructure characterization of building stones and concretes. Eng Geol 103:76–83. https://doi.org/10.1016/j.enggeo.2008.06.014

    Article  Google Scholar 

  16. Zhang W, Sun Q, Zhang Y, Xue L, Kong F (2018) Porosity and wave velocity evolution of granite after high-temperature treatment: a review. Environ Earth Sci 77:1–13. https://doi.org/10.1007/s12665-018-7514-3

    Article  Google Scholar 

  17. Griffiths L, Heap MJ, Xu T, Chen CF, Baud P (2017) The influence of pore geometry and orientation on the strength and stiffness of porous rock. J Struct Geol 96:149–160. https://doi.org/10.1016/j.jsg.2017.02.006

    Article  Google Scholar 

  18. Yang SQ, Huang YH, Tian WL, Zhu JB (2017) An experimental investigation on strength, deformation and crack evolution behavior of sandstone containing two oval flaws under uniaxial compression. Eng Geol 217:35–48. https://doi.org/10.1016/j.enggeo.2016.12.004

    Article  Google Scholar 

  19. Zhang X, Baudet BA, Hu W, Xu Q (2017) Characterisation of the ultimate particle size distribution of uniform and gap-graded soils. Soils Found 57:603–618. https://doi.org/10.1016/j.sandf.2017.04.002

    Article  Google Scholar 

  20. Al-Harthi AA, Al-Amri RM, Shehata WM (1999) The porosity and engineering properties of vesicular basalt in Saudi Arabia. Eng Geol 54:313–320. https://doi.org/10.1016/S0013-7952(99)00050-2

    Article  Google Scholar 

  21. Bai QS, Tu SH, DEM Zhang C (2016) investigation of the fracture mechanism of rock disc containing hole(s) and its influence on tensile strength. Theor Appl Fract Mech 86:197–216. https://doi.org/10.1016/j.tafmec.2016.07.005

    Article  Google Scholar 

  22. Gui YL, Zhao ZY, Zhang C, Ma SQ (2017) Numerical investigation of the opening effect on the mechanical behaviours in rocks under uniaxial loading using hybrid continuum-discrete element method. Comput Geotech 90:55–72. https://doi.org/10.1016/j.compgeo.2017.05.021

    Article  Google Scholar 

  23. Huang YH, Yang SQ, Ranjith PG, Zhao J (2017) Strength failure behavior and crack evolution mechanism of granite containing pre-existing non-coplanar holes: experimental study and particle flow modeling. Comput Geotech 88:182–198. https://doi.org/10.1016/j.compgeo.2017.03.015

    Article  Google Scholar 

  24. Ma G, Chang XL, Zhou W, Ng TT (2014) Mechanical response of rockfills in a simulated true triaxial test: a combined FDEM study. Geomech Eng 7:317–333. https://doi.org/10.12989/gae.2014.7.3.317

    Article  Google Scholar 

  25. van de Steen B, Vervoort A, Napier JAL (2005) Observed and simulated fracture pattern in diametrically loaded discs of rock material. Int J Fract 131:35–52. https://doi.org/10.1007/s10704-004-3177-z

    Article  Google Scholar 

  26. Hu N, Wang B, Tan GW, Yao ZH, Yuan WF (2000) Effective elastic properties of 2-D solids with circular holes: Numerical simulations. Compos Sci Technol 60:1811–1823. https://doi.org/10.1016/S0266-3538(00)00054-3

    Article  Google Scholar 

  27. Zhou W, Xu K, Ma G, Chang X (2019) On the breakage function for constructing the fragment replacement modes. Particuology 44:207–217. https://doi.org/10.1016/j.partic.2018.08.006

    Article  Google Scholar 

  28. Fakhimi A, Alavi Gharahbagh E (2011) Discrete element analysis of the effect of pore size and pore distribution on the mechanical behavior of rock. Int J Rock Mech Min Sci 48:77–85. https://doi.org/10.1016/j.ijrmms.2010.08.007

    Article  Google Scholar 

  29. Nguyen TT, Bui HH, Ngo TD, Nguyen GD, Kreher MU, Darve F (2019) A micromechanical investigation for the effects of pore size and its distribution on geopolymer foam concrete under uniaxial compression. Eng Fract Mech 209:228–244. https://doi.org/10.1016/j.engfracmech.2019.01.033

    Article  Google Scholar 

  30. Cui Z, Huang Y, Liu H (2017) Predicting the mechanical properties of brittle porous materials with various porosity and pore sizes. J Mech Behav Biomed Mater 71:10–22. https://doi.org/10.1016/j.jmbbm.2017.02.014

    Article  Google Scholar 

  31. Itasca PFC3D Manual (Version 5.0). Itasca Consult. Gr. Inc.minneap (2014) www.itascacg.com/

  32. 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. https://doi.org/10.1016/j.gsf.2019.07.007

    Article  Google Scholar 

  33. Christoffersen J, Mehrabadi MM, Nemat-Nasser S (1981) A micromechanical description of granular material behavior. J Appl Mech 48:339–344. https://doi.org/10.1115/1.3157619

    Article  MATH  Google Scholar 

  34. McDowell GR, Bolton MD (1998) On the micromechanics of crushable aggregates. Géotechnique 48:667–679. https://doi.org/10.1680/geot.2000.50.3.315

    Article  Google Scholar 

  35. Nguyen DH, Azéma E, Sornay P, Radjai F (2015) Bonded-cell model for particle fracture. Phys Rev E Stat Nonlinear Soft Matter Phys 91:1–9. https://doi.org/10.1103/PhysRevE.91.022203

    Article  MathSciNet  Google Scholar 

  36. McDowell GR, Amon A (2000) The application of Weibull statistics to the fracture of soil particles. Soils Found 40:133–141. https://doi.org/10.3208/sandf.40.5_133

    Article  Google Scholar 

  37. Ma G, Zhou W, Regueiro RA, Wang Q, Chang X (2017) Modeling the fragmentation of rock grains using computed tomography and combined FDEM. Powder Technol 308:388–397. https://doi.org/10.1016/j.powtec.2016.11.046

    Article  Google Scholar 

  38. Cheng YP, Nakata Y, Bolton MD (2003) Discrete element simulation of crushable soil. Géotechnique 53:633–641. https://doi.org/10.1680/geot.2003.53.7.633

    Article  Google Scholar 

  39. Cavarretta I, O’Sullivan C, Coop MR (2017) The relevance of roundness to the crushing strength of granular materials. Géotechnique 67:301–312. https://doi.org/10.1680/jgeot.15.P.226

    Article  Google Scholar 

  40. Huang J, Xu S, Yi H, Hu S (2014) Size effect on the compression breakage strengths of glass particles. Powder Technol 268:86–94. https://doi.org/10.1016/j.powtec.2014.08.037

    Article  Google Scholar 

  41. 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. https://doi.org/10.1016/j.gsf.2018.10.010

    Article  Google Scholar 

  42. Lim WL, McDowell GR, Collop AC (2004) The application of Weibull statistics to the strength of railway ballast. Granul Matter 6:229–237. https://doi.org/10.1007/s10035-004-0180-z

    Article  Google Scholar 

  43. Hai-juan Z, Gang M, Weir Y, Wei Z, Xiao-lin C (2017) Size effect on the crushing strengths of rock particles. Rock Soil Mech 38:2425–2433. https://doi.org/10.16285/j.rsm.2017.08.032

    Article  Google Scholar 

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Funding

This study was funded by the National Key R&D Program of China (No. 2017YFC0404806), China Scholarship Council (Joint PhD program, No. 201906270118) and Open Research Fund of Key Laboratory of Failure Mechanism and Safety Control Techniques of Earth-Rock Dam of the Ministry of Water Resources (YK319007).

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Correspondence to Wei Zhou.

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Huang, Q., Zhou, W., Ma, G. et al. Investigation of the grain breakage behaviour of 2D granular materials with disordered pore distribution. Comp. Part. Mech. 8, 1033–1045 (2021). https://doi.org/10.1007/s40571-020-00379-6

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