Skip to main content
SpringerLink
Log in

Influence of grain size and basic element size on rock mechanical characteristics: insights from grain-based numerical analysis

  • Original Paper
  • Published:
Bulletin of Engineering Geology and the Environment Aims and scope Submit manuscript

Abstract

The mechanical properties of rock materials are closely related to their heterogeneous internal structure. It is necessary to reproduce the internal structure of rock materials in more realistic models to learn more about their mechanical properties. In this paper, using the three-dimensional particle flow code (PFC) developed by Itasca, a novel grain-based model (GBM) is proposed to group and fill mineral grains. Then, the GBM is used in numerical simulations of uniaxial compression tests to investigate the influence of grain size and basic element size on the distributions of contacts and microcracks and the mechanical behaviour of numerical samples. The numerical results show that based on the proposed GBM, the heterogeneous structure of granite can be reproduced in a more realistic way by the multilevel division of contacts and microscale cracks. The stress–strain curves of the numerical samples with different grain sizes and basic element sizes can be divided into three stages during loading, including the elastic deformation, nonlinear deformation and post-peak softening stages. As the grain size increases, the number of basic elements contained within a single mineral grain increases. As a result, the number of intragranular contacts increases with increasing bond micro-strength. The external load required to cause macroscopic failure of a sample increases as the number of intragranular cracks increases. As the basic element size increases, the number of basic elements contained within a single mineral grain decreases, and the contact distribution density is significantly smaller. The number of contacts to be fractured decreases when macroscale fracturing of a sample occurs, which leads to a decrease in the value of the external load.

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

  • Aziznejad S, Esmaieli K, Hadjigeorgiou J, Labrie D (2018) Responses of jointed rock masses subjected to impact loading. J Rock Mech Geotech 10:624–634

    Article  Google Scholar 

  • Bahrani N, Kaiser PK (2016) Numerical investigation of the influence of specimen size on the unconfined strength of defected rocks. Comput Geotech 77:56–67

    Article  Google Scholar 

  • Bahrani N, Kaiser PK (2017) Estimation of confined peak strength of crack-damaged rocks. Rock Mech Rock Eng 50:309–326

    Article  Google Scholar 

  • Bauer SJ, Song B, Sanborn B (2019) Dynamic compressive strength of rock salts. Int J Rock Mech Min 113:112–120

    Article  Google Scholar 

  • Chen YQ, Watanabe K, Kusuda H, Kusaka E, Mabuchi M (2011) Crack growth in Westerly granite during a cyclic loading test. Eng Geol 117(3–4):189–197

    Article  Google Scholar 

  • Cheng Y, Jiao YY, Tan F (2019) Numerical and experimental study on the cracking behavior of marble with en-echelon flaws. Rock Mech Rock Eng 52:4319–4338

    Article  Google Scholar 

  • Du HB, Dai F, Xu Y, Liu Y, Xu HN (2018) Numerical investigation on the dynamic strength and failure behavior of rocks under hydrostatic confinement in SHPB testing. Int J Rock Mech Min 108:43–57

    Article  Google Scholar 

  • Dwivedi RD, Goel RK, Prasad VVR, Sinha A (2008) Thermo-mechanical properties of Indian and other granites. Int J Rock Mech Min 45(3):303–315

    Article  Google Scholar 

  • Gao F, Stead D, Elmo D (2016) Numerical simulation of microstructure of brittle rock using a grain-breakable distinct element grain-based model. Comput Geotech 78:203–217

    Article  Google Scholar 

  • Gao F, Walter ED, Kollar M, Wang YL, Szanyi J, Peden CHF (2014) The application of a modified Voronoi logic to brittle fracture modelling at the laboratory and field scale. Int J Rock Mech Min Sci 68:1–14

    Article  Google Scholar 

  • Gong FQ, Zhao GF (2014) Dynamic indirect tensile strength of sandstone under different loading rates. Rock Mech Rock Eng 47(6):2271–2278

    Article  Google Scholar 

  • Ghazvinian E, Diederichs MS, Quey R (2014) 3D random Voronoi grain-based models for simulation of brittle rock damage and fabric-guided micro-fracturing. J Rock Mech Geotech Eng 6(6):506–521

    Article  Google Scholar 

  • Hofmann H, Babadagli T, Zimmermann G (2015) A grain based modeling study of fracture branching during compression tests in granites. Int J Rock Mech Min 77:152–162

    Article  Google Scholar 

  • Hu LH, Liang X, Liang ZZ, Li YC, Zhang ZH, Tang C (2021) Influence of radial stress on strainbursts under true triaxial conditions: insights from a distinct element modelling. Int J Rock Mech Min 138:104577

    Article  Google Scholar 

  • Huang JW, Wang HB, Zhou L, Zhu ZM, Deng Z, Deng A (2022) Analysis of stress intensity factor for a crack emanating from elliptical hole subjected to compressive stress and shear stress. Theor Appl Fract Mech 120:103413

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Itasca Consulting Group Inc (2020) PFC3D (3 dimensional particle flow code), version 6.0. Minneapolis, MN

  • Ju M, Li JC, Li J, Zhao J (2020) Loading rate effects on anisotropy and crack propagation of weak bedding plane-rich rocks. Eng Fract Mech 230:106983

    Article  Google Scholar 

  • Kima KM, Leea S, Cho JY (2019) Effect of maximum coarse aggregate size on dynamic compressive strength of high-strength concrete. Int J Impact Eng 125:107–116

    Article  Google Scholar 

  • Kong L, Ranjith PG, Li QB, Song Y (2022) Rock grain-scale mechanical properties influencing hydraulic fracturing using Hydro-GBM approach. Eng Fract Mech 262:108227

    Article  Google Scholar 

  • Kumari WGP, Ranjitha PG, Perera MSA, Chen BK, Abdulagatov IM (2017) Temperature-dependent mechanical behaviour of Australian Strathbogie granite with different cooling treatments. Eng Geol 229:31–44

    Article  Google Scholar 

  • Lan HX, Martin CD, Hu B (2010) Effect of heterogeneity of brittle rock on micromechanical extensile behavior during compression loading. J Geophy Res 115(B1):414–431

    Google Scholar 

  • Li H, Ma HL, Shi XL, Zhou J, Zhang HN, Daemen JJK (2020a) A 3D grain-based model for simulating the micromechanical behavior of salt rock. Rock Mech Rock Eng 53(6):2819–2837

    Article  Google Scholar 

  • Li XB, Zou Y, Zhou ZL (2014) Numerical simulation of the rock SHPB test with a special shape striker based on the discrete element method. Rock Mech Rock Eng 47(5):1693–1709

    Article  Google Scholar 

  • Li XF, Li HB, Liu LW, Liu YQ, Ju MH, Zhao J (2020b) Investigating the crack initiation and propagation mechanism in brittle rocks using grain-based finite-discrete element method. Int J Rock Mech Min 127:104219

    Article  Google Scholar 

  • Li XF, Li HB, Zhao J (2019) The role of transgranular capability in grain-based modelling of crystalline rocks. Comput Geotech 110:161–183

    Article  Google Scholar 

  • Li XF, Li X, Li HB, Zhang QB, Zhao J (2018a) Dynamic tensile behaviours of heterogeneous rocks: the grain scale fracturing characteristics on strength and fragmentation. Int J Impact Eng 118:98–118

    Article  Google Scholar 

  • Li XF, Zhang QB, Li HB, Zhao J (2018b) Grain-based discrete element method (GB-DEM) modelling of multi-scale fracturing in rocks under dynamic loading. Rock Mech Rock Eng 51(12):3785–3817

    Article  Google Scholar 

  • Lin Y, Zhou KP, Lin YL, Ke B, Gao RG (2020) Weakening laws of mechanical properties of sandstone under the effect of chemical corrosion. Rock Mech Rock Eng 53(4):1857–1877

    Article  Google Scholar 

  • Liu G, Cai M, Huang M (2018) Mechanical properties of brittle rock governed by micro-geometric heterogeneity. Comput Geotech 104:358–372

    Article  Google Scholar 

  • Mahabadi OK, Cottrell BE, Grasselli G (2010) An example of realistic modelling of rock dynamics problems: fem/dem simulation of dynamic Brazilian test on barre granite. Rock Mech Rock Eng 43(6):707–716

    Article  Google Scholar 

  • Mardoukhi A, Mardoukhi Y, Hokka M, Kuokkala VT (2017) Effects of heat shock on the dynamic tensile behavior of granitic rocks. Rock Mech Rock Eng 50(5):1171–1182

    Article  Google Scholar 

  • Mei J, Yang L, Sheng XC, Ma XJ, Sui B, Yang WM (2021) An experimental and theoretical investigation of time-dependent cracking and creep behavior of rocks under triaxial hydro-mechanical coupling. Theor Appl Fract Mec 115:103046

    Article  Google Scholar 

  • Meng YY, Jing HW, Liu XW, Yin Q, Wei XC (2021a) Experimental and numerical investigation on the effects of bedding plane properties on the mechanical and acoustic emission characteristics of sandy mudstone. Eng Fract Mech 245(10):107582

    Article  Google Scholar 

  • Meng YY, Jing HW, Liu XW, Yin Q, Zhang L, Liu HX (2021b) Experimental and numerical investigation on the effect of bedding plane properties on fracture behaviour of sandy mudstone(J). Theor Appl Fract Mec 114:102989

    Article  Google Scholar 

  • Nitka M, Tejchman J (2020) Comparative DEM calculations of fracture process in concrete considering real angular and artificial spherical aggregates. Eng Fract Mech 239:107309

    Article  Google Scholar 

  • Peng J, Wong LNY, The CI (2018a) A re-examination of slenderness ratio effect on rock strength: insights from DEM grain-based modelling. Eng Geol 246(28):245–254

    Article  Google Scholar 

  • Peng J, Wong LNY, The CI, Li ZH (2018b) Modeling micro-cracking behavior of bukit timah granite using grain-based model. Rock Mech Rock Eng 51(1):135–154

    Article  Google Scholar 

  • Peng J, Wong LNY, The CI (2021) Influence of grain size on strength of polymineralic crystalline rock: new insights from DEM grain-based modeling. J Rock Mech Geotech 13:755–766

    Article  Google Scholar 

  • Potyondy DO (2010) A grain-based model for rock: approaching the true microstructure proceedings of the rock mechanics in the Nordic countries. Norwegian Group for Rock Mechanics, ISBN, Kongsberg, Norway, pp 225–234

    Google Scholar 

  • Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364

    Article  Google Scholar 

  • Poulsen BA, Adhikary DP (2013) A numerical study of the scale effect in coal strength(J). Int J Rock Mech Min 63:62–71

    Article  Google Scholar 

  • Qi CZ, Wang MY, Qian QH (2009) Strain-rate effects on the strength and fragmentation size of rocks. Int J Impact Eng 36(12):1355–1364

    Article  Google Scholar 

  • Saadat M, Taheri A (2019) Modelling micro-cracking behavior of pre-cracked granite using grain-based distinct element model. Rock Mech Rock Eng 52(11):4669–4692

    Article  Google Scholar 

  • Saadat M, Taheri A (2020) A cohesive grain based model to simulate shear behaviour of rock joints with asperity damage in polycrystalline rock. Comput Geotech 117:103254

    Article  Google Scholar 

  • Saadat M, Taheri A, Kawamura Y (2021) Investigating asperity damage of natural rock joints in polycrystalline rocks under confining pressure using grain-based model. Comput Geotech 135:104144

    Article  Google Scholar 

  • Saksala T, Hokka M, Kuokkala VT, M¨akinen, J., (2013) Numerical modeling and experimentation of dynamic Brazilian disc test on Kuru granite. Int J Rock Mech Min 59:128–138

    Article  Google Scholar 

  • Shao S, Ranjith PG, Wasantha PLP, Chen BK (2015) Experimental and numerical studies on the mechanical behavior of Australian Strathbogie granite at high temperatures: an application to geothermal energy. Geothermics 54:96–108

    Article  Google Scholar 

  • Tian WL, Yang SQ, Elsworth D, Wang JG, Li XZ (2020a) Permeability evolution and crack characteristics in granite under treatment at high temperature. Int J Rock Mech Min 134:104461

    Article  Google Scholar 

  • Tian WL, Yang SQ, Huang YH, Hu B (2020b) Mechanical behavior of granite with different grain sizes after high-temperature treatment by particle flow simulation. Rock Mech Rock Eng 53(4):1791–1807

    Article  Google Scholar 

  • Tian WL, Yang SQ, Wang JG, Zeng W (2020c) Numerical simulation of permeability evolution in granite after thermal treatment. Comput Geotech 126:103705

    Article  Google Scholar 

  • Tizpa P, Jamshidi Chenari R, Farrokhi F (2019a) A note on the compressibility and earth pressure properties of EPS beads-rigid particulates composite. Geotech Geol Eng 37:5231–5243

    Article  Google Scholar 

  • Tizpa P, Kazempour S, Jamshidi Chenari R, Farrokhi F, Ahmadi H (2019b) Numerical and experimental investigations of the influence of grain size on the compressibility of sand-EPS mixtures. Int J Geosynth Groun 5(4):1–7

    Google Scholar 

  • Tizpa P, Chenari RJ, Farrokhi F (2020) Constraint deformation behavior of sand-EPS beads mixture using discrete element modeling (DEM). Adv Civ Eng Mater 9(1):666–682

    Google Scholar 

  • Vishal V, Pradhan SP, Singh TN (2011) Tensile strength of rock under elevated temperatures. Geotech Geol Eng 29(6):1127–1133

    Article  Google Scholar 

  • Wang Q, Hu X, Zheng W, Li L, Zhou C, Ying C, Xu C (2021a) Mechanical properties and permeability evolution of red sandstone subjected to hydro-mechanical coupling: experiment and discrete element modelling. Rock Mech Rock Eng 54:2405–2423

    Article  Google Scholar 

  • Wang S, Jian Z, Zhang LQ, Han ZH, Zhang FX (2020) Parameter studies on the mineral boundary strength influencing the fracturing of the crystalline rock based on a novel grain-based model. Eng Fract Mech 241:107388

    Article  Google Scholar 

  • Wang ZH, Yang SL, Li LH, Tang YS, Xu GL (2021b) A 3D Voronoi clump based model for simulating failure behavior of brittle rock. Eng Fract Mech 248(2):107720

    Article  Google Scholar 

  • Weng L, Wu ZJ, Liu QS (2019) Numerical analysis of degradation characteristics for heterogeneous rock under coupled thermomechanical conditions. Int J Geomech 19(10):04019111

    Article  Google Scholar 

  • Wong LNY, Zhang YH (2018) An extended grain-based model for characterizing crystalline materials-An example of marble. Adv Theor Simul 1(8):1–14

    Article  Google Scholar 

  • Wu DQ, Jing HY, Xu LY, Zhao L, Han YD (2018) Theoretical and numerical analysis of creep crack initiation combined with primary and secondary stresses. Theor Appl Fract Mec 95:143–154

    Article  Google Scholar 

  • Wu DY, Yu LY, Ju MH, Li SC, Liu RC, Su HJ, Zhou LJ (2022) Study on the mode i fracture properties of granites after heating and water-cooling treatments under different impact loadings. Rock Mech Rock Eng 55(7):4271–4290

    Article  Google Scholar 

  • Wu QH, Weng L, Zhao YL, Guo BH, Luo T (2019) On the tensile mechanical characteristics of fine-grained granite after heating/cooling treatments with different cooling rates. Eng Geol 253:94–110

    Article  Google Scholar 

  • Xu T, Fu TF, Heap MJ, Meredith PG, Mitchell TM, Baud P (2020) Mesoscopic damage and fracturing of heterogeneous brittle rocks based on three-dimensional polycrystalline discrete element method. Rock Mech Rock Eng 53(12):5389–5409

    Article  Google Scholar 

  • Xu Y, Dai F, Xu NW, Zhao T (2016) Numerical investigation of dynamic rock fracture toughness determination using a semi-circular bend specimen in split Hopkinson pressure bar testing. Rock Mech Rock Eng 49(3):731–745

    Article  Google Scholar 

  • Yakaboylu GA, Gupta N, Sabolsky EM, Mishra B (2020) Mineralogical characterization and strain analysis of the marcellus shales. Int J Rock Mech Min 130:104345

    Article  Google Scholar 

  • Yang SQ, Tian WL, Huang YH, Ranjith PG, Ju Y (2016) An experimental and numerical study on cracking behavior of brittle sandstone containing two non-coplanar fissures under uniaxial compression. Rock Mech Rock Eng 49(4):1497–1515

    Article  Google Scholar 

  • Yang SQ, Yin PF, Huang YH (2019) Experiment and discrete element modelling on strength, deformation and failure behavior of shale under brazilian compression. Rock Mech Rock Eng 52:4339–4359

    Article  Google Scholar 

  • Yin Q, Jing HW, Ma GW, Su HJ, Liu RC (2019a) Laboratory investigation of hydraulic properties of deformable rock samples subjected to different loading paths. Hydrogeol J 27:2617–2635

    Article  Google Scholar 

  • Yin Q, Liu RC, Jing HW, Su HJ, Yu LY, He LX (2019b) Experimental study of nonlinear flow behaviors through fractured rock samples after high-temperature exposure. Rock Mech Rock Eng 52:2963–2983

    Article  Google Scholar 

  • Yu D, Liu EL, Sun P, Xiang B, Zheng QS (2020a) Mechanical properties and binary-medium constitutive model for semi-through jointed mudstone samples. Int J Rock Mech Min 132:104376

    Article  Google Scholar 

  • Yu LY, Fu AQ, Yin Q, Jing, H.w., Zhang, T., Qin, H., (2020b) Dynamic fracturing properties of marble after being subjected to multiple impact loadings. Eng Fract Mech 230:106988

    Article  Google Scholar 

  • Yu LY, Zhang T, Wu DY, Wu BB, Ma LJ, Wei JB (2020c) Numerical investigation of the effect of grain size to particle size ratio on the dynamic fracture toughness of granite by using PFC3D GBM. Geomech Geophys Geoenerg Georesour 8:72

    Article  Google Scholar 

  • Yu QL, Ranjith PG, Liu HY, Yang TH, Tang SB, Tang CA, Yang SQ (2015) A mesostructure-based damage model for thermal cracking analysis and application in granite at elevated temperatures. Rock Mech Rock Eng 48(6):2263–2282

    Article  Google Scholar 

  • Zhang H, Lu CP, Liu B, Liu Y, Zhang N, Wang HY (2020a) Numerical investigation on crack development and energy evolution of stressed coal-rock combination. Int J Rock Mech Min 133:104417

    Article  Google Scholar 

  • Zhang T, Yu LY, Li J, Ma LJ, Su HJ, Zhang MW, Xu XL, Peng YX (2022a) Numerical investigation of the effects of the micro-parameters of the transgranular contact on the mechanical response of granite. Theor Appl Fract Mec 118:103259

    Article  Google Scholar 

  • Zhang T, Yu LY, Su HJ, Zhang Q, Chai SB (2022b) Experimental and numerical investigations on the tensile mechanical behavior of marbles containing dynamic damage. Int J Min Sci Techno 32:89–102

    Article  Google Scholar 

  • Zhang XP, Wong LNY (2013) Crack initiation, propagation and coalescence in rock-like material containing two flaws: a numerical study based on bonded-particle model approach. Rock Mech Rock Eng 46:1001–1021

    Article  Google Scholar 

  • Zhang XP, Jia PQ, Peng J, Wu SC, Zhang Q (2020b) A grain-based model considering pre-existing cracks for modelling mechanical properties of crystalline rock. Comput Geotech 127:103776

    Article  Google Scholar 

  • Zhang YH, Wong LNY (2019) An extended grain-based model accounting for microstructures in rock deformation. J Geophys Res Sol Ea 124(1):125–148

    Article  Google Scholar 

  • Zhou L, Zhu ZM, Wang M, Ying P, Dong Y (2018) Dynamic propagation behavior of cracks emanating from tunnel edges under impact loads. Soil Dyn Earthq Eng 105:119–126

    Article  Google Scholar 

Download references

Funding

The research presented in this paper was carried out under the financial support of the National Natural Science Foundation of China (Grant Nos. 52179118, 52104101, 52174092), funded by the Graduate Innovation Program of China University of Mining and Technology (2022WLKXJ032) and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX22_2581).

Author information

Authors and Affiliations

  1. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, China

    Tao Zhang, Liyuan Yu, Yuxuan Peng, Minghe Ju, Qian Yin & Shiping Jia

  2. College of Geology and Environment, Xi’an University of Science and Technology, Xian, Shaanxi, 710054, China

    Jiangbo Wei

Authors
  1. Tao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liyuan Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuxuan Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Minghe Ju
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Qian Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jiangbo Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Shiping Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liyuan Yu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest. All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. This article does not contain any studies with animals performed by any of the authors. Informed consent was obtained from all individual participants included in the study.

Rights and permissions

Springer Nature or its licensor 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

Zhang, T., Yu, L., Peng, Y. et al. Influence of grain size and basic element size on rock mechanical characteristics: insights from grain-based numerical analysis. Bull Eng Geol Environ 81, 347 (2022). https://doi.org/10.1007/s10064-022-02856-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10064-022-02856-z

Keywords

Search

Navigation