SpringerLink
Log in

Dual-scale 3DEC-GBM Discrete Element Simulation On Mechanical Behavior and Anisotropic Fracture Evolution Mechanism of Rock Induced by True Three-dimensional Stress

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

Abstract

The excavation of deep underground engineering causes a sophisticated three-dimensional stress redistribution in the surrounding rock, leading to the damage and rupture of the surrounding rock. It is difficult to reveal the fracture mechanism of rocks under complex stress loading path changes through conventional uniaxial or triaxial stress tests. In this study, a marble dual-scale 3DEC-GBM (grain-based modeling) discrete element model was established. The model was according to the practical mineral component of marble and its particle size distribution characteristics. Through laboratory true triaxial tests and numerical simulations, investigations were conducted on the deformation and strength characteristics of marble under true triaxial stress states. The evolution process and characteristics of anisotropic fracture and its microscopic tensile and shear fracture mechanism were also thoroughly investigated. Subsequently, the effects of intermediate principal stress σ2 and minimum principal stress σ3 on the intergranular and transgranular failures of marble as well as cracked anisotropy were analyzed, and the tensile–shear failure mechanism and crack anisotropy evolution law of the marble fracture evolution were determined under different true triaxial stress conditions. Finally, the effects of mineral crystal micromechanical parameters on the mechanical characteristics of marble under true triaxial conditions were examined.

Highlights

  • Macro-meso failure mechanisms of anisotropic deformation and failure of marble induced by true triaxial stresses were revealed through tests and simulations.

  • Pre- and post-peak microcrack anisotropic propagation processes and tensile‒shear mechanisms of marble under true triaxial stresses (σ2, σ3) were investigated.

  • Effects of 3DEC-GBM model meso parameters on mechanical behavior of rock were explored.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30

Similar content being viewed by others

Data Availability

The authors confirm they have included a data availability statement in their main manuscript file. The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

3D:

Three-dimension

3DEC:

Three-dimensional distinct Element

PFC3D:

Three-dimensional particle flow

GBM:

Grain-based model

SEM:

Scanning electron microscopy

σ 1, σ 2 and σ 3 :

Maximum, intermediate and minimum principal stresses, respectively

σ c, σ r :

Peak strength, residual strength, respectively

ε 1, ε 2 and ε 3 :

Maximum, intermediate and minimum principal strains, respectively

ε c :

Peak strain

UCS:

Uniaxial compressive strength

Ρ, E, υ :

Density, Young’s modulus, Poisson’s ratio, respectively

c, φ :

Friction angle, cohesion, respectively

c r, φ r :

Residual friction angle, residual cohesion, respectively

K, G:

Shear modulus, bulk modulus, respectively

∆Z min :

Normal minimum length of deformation element

σ ij, Δσ ij :

Stress of tetrahedral grains, stress increment of tetrahedral grains, respectively

Δε ij, δ ij :

Strain increment of tetrahedral grains, Kroenecker increment, respectively

α 2 :

Material constants related to bulk modulus and shear modulus

F n, F s :

Contact normal force, contact tangential force, respectively

∆ U n, ∆ U s :

Contact normal displacement increment, contact tangential force displacement increment, respectively

T max, F s m ax :

Contact maximum tensile force, contact maximum shear force, respectively

Fs r:

Residual shear strength

A c :

Contact area

τ oct, σ m ,2 :

Octahedral shear stress, octahedral effective intermediate stress, respectively

a, b :

Material parameters

ρ, e, μ :

Density, young’s modulus, poisson’s ratio, respectively

jk n, jk s :

Normal stiffness, shear stiffness, respectively

jf, j c, jt :

Friction angle, cohesion, tensile strength, respectively

jf r, jc r, jt r :

Residual friction angle, residual cohesion, residual tensile strength, respectively

References

  • Al-Ajmi AM, Zimmerman RW (2005) Relation between the Mogi and the Coulomb failure criteria. Int J Rock Mech Min 42(3):431–439

    Google Scholar 

  • Azocar KD (2016) Investigating the mesh dependency and upscaling of 3D grain-based models for the simulation of brittle fracture processes in low-porosity crystalline rock. Dissertation, Queen’s University (Canada)

  • Chen X, Liao Z, Peng X (2012) Deformability characteristics of jointed rock masses under uniaxial compression. Int J Min Sci Techno 22(2):213–221

    Google Scholar 

  • Chen W, Konietzky H, Tan X, Frühwirt T (2016) Pre-failure damage analysis for brittle rocks under triaxial compression. Comput Geotech 74:45–55

    Google Scholar 

  • Chen S, Li H, Zhou H, Chen X, Liu T (2021) Route selection of deep-lying and hard rock tunnel in the Sichuan-Tibet Railway based on rock burst risk assessment. Q J Eng Geol Hydroge 48(5):81–90

    Google Scholar 

  • Cundall PA (1988) Formulation of a three-dimensional distinct element model. Int J Rock Mech Min Sci & Geomech 25(3):107–116

  • Fabjan T, Ivars DM, Vukadin V (2015) Numerical simulation of intact rock behaviour via the continuum and Voronoi tesselletion models: A sensitivity analysis. Acta Geotech Slov 12(2):5–23

    Google Scholar 

  • Fairhurst CE, Hudson JA (1999) Draft ISRM suggested method for the complete stress-strain curve for intact rock in uniaxial compression. Int J Rock Mech Min 36(3):279–289

    Google Scholar 

  • Farahmand K, Vazaios I, Diederichs MS, Vlachopoulos N (2018) Investigating the scale-dependency of the geometrical and mechanical properties of a moderately jointed rock using a synthetic rock mass (SRM) approach. Comput Geotech 95:162–179

    Google Scholar 

  • Farahmand K, Diederichs MS (2015) A calibrated Synthetic Rock Mass (SRM) model for simulating crack growth in granitic rock considering grain scale heterogeneity of polycrystalline rock, In 49th US Rock Mechanics/Geomechanics Symposium

  • Feng XT, Guo HS, Yang CX, Li SJ (2018) In situ observation and evaluation of zonal disintegration affected by existing fractures in deep hard rock tunneling. Eng Geol 242(14):1–11

    Google Scholar 

  • Feng XT, Haimson B, Li XC, Chang CD, Ma XD, Zhang XW, Suzuki K (2019) ISRM suggested method: determining deformation and failure characteristics of rocks subjected to true triaxial compression. Rock Mech Rock Eng 52:2011–2020

    Google Scholar 

  • Fu TF, Xu T, Zhu WC, Wang XW (2020) Damage Characteristics of Sandstone Under Triaxial Compression Based on Polycrystalline Discrete Element Method. J Northeast Univ (nat Sci) 41(7):968

    Google Scholar 

  • Gao FQ, Stead D (2014) The application of a modified Voronoi logic to brittle fracture modelling at the laboratory and field scale. Int J Rock Mech Min 68:1–14

    Google Scholar 

  • Gao FQ, 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

    Google Scholar 

  • Ge X, Ren J, Pu Y, Ma W, Zhu Y (2001) Real-in time CT test of the rock meso-damage propagation law. Sci China Ser E 44:328–336

    Google Scholar 

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

    Google Scholar 

  • Haimson B, Rudnicki JW (2010) The effect of the intermediate principal stress on fault formation and fault angle in siltstone. J Struct Geol 32(11):1701–1711

    Google Scholar 

  • Handin J, Heard HC, Magouirk JN (1967) Effects of the intermediate principal stress on the failure of limestone, dolomite, and glass at different temperatures and strain rates. J Geophys Res 72(2):611–640

    Google Scholar 

  • He MC, Miao JL, Feng JL (2010) Rock burst process of limestone and its acoustic emission characteristics under true-triaxial unloading conditions. Int J Rock Mech Min 47(2):286–298

    Google Scholar 

  • He BG, Wang L, Feng XT, Zhen RL (2023) Failure Modes of Jointed Granite Subjected to Weak Dynamic Disturbance Under True-Triaxial Compression. Rock Mech Rock Eng 56:7939–7956

    Google Scholar 

  • Hoek E, Marinos PG, Marinos VP (2005) Characterisation and engineering properties of tectonically undisturbed but lithologically varied sedimentary rock masses. Int J Rock Mech Min Sci 42(2):277–285

    Google Scholar 

  • Jia L, Chen M, Zhang W, Xu T, Zhou Y, Hou B, ** Y (2013) Experimental study and numerical modeling of brittle fracture of carbonate rock under uniaxial compression. Mech Res Commun 50:58–62

    Google Scholar 

  • Jiang Q, Song LB (2018) Application and prospect of 3D printing technology to physical modeling in rock mechanics. Chin J Rock Mech Eng 37(1):23–37

    Google Scholar 

  • Jiang Q, Feng XT, **ang TB, Su GS (2010) Rockburst characteristics and numerical simulation based on a new energy index: a case study of a tunnel at 2500 m depth. Bull Eng Geol Environ 69:381–388

    CAS  Google Scholar 

  • Jiang Q, Zhong S, Cui J, Feng XT, Song L (2016) Statistical characterization of the mechanical parameters of intact rock under triaxial compression an experimental proof of the ** marble. Rock Mech Rock Eng 49:4631–4646

    Google Scholar 

  • Kaiser PK, Kim B, Bewick RP, Valley, (2011) Rock mass strength at depth and implications for pillar design. Min Technol 120:170–179

    Google Scholar 

  • Kazerani T, Zhao J (2010) Micromechanical parameters in bonded particle method for modelling of brittle material failure. Int J Numer Anal Met 34(18):1877–1895

    Google Scholar 

  • Knauth M, Minkley W (2014) Modeling of the mechanical and hydraulic behavior of salt rocks on a discontinuum-mechanical basis, In 48th US Rock Mechanics/Geomechanics Symposium

  • Li C, Prikryl R, Nordlund E (1998) The stress-strain behaviour of rock material related to fracture under compression. Eng Geol 49(3–4):293–302

    Google Scholar 

  • Li XF, Li HB, Zhao J (2017) 3D polycrystalline discrete element method (3PDEM) for simulation of crack initiation and propagation in granular rock. Comput Geotech 90:96–112

    Google Scholar 

  • Li X, Feng F, Li D, Du K, Ranjith PG, Rostami J (2018a) Failure characteristics of granite influenced by sample height-to-width ratios and intermediate principal stress under true-triaxial unloading conditions. Rock Mech Rock Eng 51:1321–1345

    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 51:3785–3817

    Google Scholar 

  • Liang K, **e L, He B, Zhao P, Zhang Y, Hu W (2021) Effects of grain size distributions on the macro-mechanical behavior of rock salt using micro-based multiscale methods. Int J Rock Mech Min 138:104592

    Google Scholar 

  • Ma T, Lin D, Tang L, Li L, Tang CA, Yadav KP, ** W (2022) Characteristics of rockburst and early warning of microseismic monitoring at qinling water tunnel. Geomat Nat Haz Risk 13(1):1366–1394

    Google Scholar 

  • Mair K, Abe S (2009) Effects of gouge fragment shape on fault friction: New 3D modeling results. Geophys Res Lett 36(23):557–620

    Google Scholar 

  • Mayer JM, Stead D (2017) Exploration into the causes of uncertainty in UDEC Grain Boundary Models. Comput Geotech 82:110–123

    Google Scholar 

  • Mcbeck J, Mair K, Renard F (2019) How porosity controls macroscopic failure via propagating fractures and percolating force chains in porous granular rocks. J Geophys Res-Sol Ea 124(9):9920–9939

    Google Scholar 

  • Mogi K (1967) Effect of the intermediate principal stress on rock failure. J Geophys Res 72(20):5117–5131

    Google Scholar 

  • Mogi K (1971) Effect of the triaxial stress system on the failure of dolomite and limestone. Tectonophysics 11(2):111–127

    Google Scholar 

  • Müller C, Frühwirt T, Haase D, Schlegel R, Konietzky H (2018) Modeling deformation and damage of rock salt using the discrete element method. Int J Rock Mech Min 103:230–241

    Google Scholar 

  • Nicksiar M, Martin CD (2014) Factors Affecting Crack Initiation in Low Porosity Crystalline Rocks. Rock Mech Rock Eng 47(4):1165–1181

    Google Scholar 

  • Park CH, Bobet A (2010) Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression. Eng Fract Mech 77(14):2727–2748

    Google Scholar 

  • Peng J, Wong LNY, Teh CI (2017) Influence of grain size heterogeneity on strength and microcracking behavior of crystalline rocks. J Geophys Res-Sol Ea 122(2):1054–1073

    Google Scholar 

  • Peng J, Wong LNY, Teh CI (2021) Influence of grain size on strength of polymineralic crystalline rock: New insights from DEM grain-based modeling. J Rock Mech Geotech 13(4):755–766

    Google Scholar 

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

    Google Scholar 

  • Potyondy DO (2010) A grain-based model for rock: approaching the true microstructure, Proceedings of rock mechanics in the Nordic Countries 9–12

  • Sinha S, Walton G (2021) Importance of block damage in confined laboratory-scale Bonded Block Model simulations, In 55th US Rock Mechanics/Geomechanics Symposium

  • Sinha S, Walton G (2020) A study on Bonded Block Model (BBM) complexity for simulation of laboratory-scale stress-strain behavior in granitic rocks. Comput Geotech 118:103363

    Google Scholar 

  • Takahashi M, Koide H (1989) Effect of the intermediate principal stress on strength and deformation behavior of sedimentary rocks at the depth shallower than 2000 m, In ISRM international symposium

  • Wang X, Cai M (2018) Modeling of brittle rock failure considering inter- and intra-grain contact failures. Comput Geotech 101:224–244

    Google Scholar 

  • Wang X, Cai M (2019) A comprehensive parametric study of grain-based models for rock failure process simulation. Int J Rock Mech Min 115:60–76

    Google Scholar 

  • Wang B, Chen Y, Wong TF (2008) A discrete element model for the development of compaction localization in granular rock. J Geophys Res Sol 113:B3

    Google Scholar 

  • Wang Z, Wang T, Wu S, Hao Y (2021) Investigation of microcracking behaviors in brittle rock using polygonal grain-based distinct method. Int J Numer Anal Met 45(13):1871–1899

    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 53:5389–5409

    Google Scholar 

  • Yang YM, Ju Y, Chen JL, Gao F (2014) Cracks development features and energy mechanism of dense sandstone subjected to triaxial stress. Chin J Rock Mech Eng 33(4):691–698

    CAS  Google Scholar 

  • Yao C, Jiang QH, Shao JF (2015) Numerical simulation of damage and failure in brittle rocks using a modified rigid block spring method. Comput Geotech 64:48–60

    Google Scholar 

  • Zhao XG, Wang J, Cai M, Cheng C, Ma LK, Su R, Li DJ (2014) Influence of unloading rate on the strainburst characteristics of Beishan granite under true-triaxial unloading conditions. Rock Mech Rock Eng 47:467–483

    Google Scholar 

  • Zheng Z, Feng XT, Zhang X, Zhao J, Yang CX (2019) Residual strength characteristics of CJPL marble under true triaxial compression. Rock Mech Rock Eng 52:1247–1256

    Google Scholar 

  • Zheng Z, Feng XT, Yang CX, Zhang XW, Li SJ, Qiu SL (2020) Post-peak deformation and failure behaviour of **** marble under true triaxial stresses. Eng Geol 265:105444

    Google Scholar 

  • Zheng Z, Su GS, Jiang Q, Pan PZ, Huang XH, Jiang JQ (2022) Mechanical behavior and failure mechanisms of cylindrical and prismatic rock specimens under various confining stresses. Int J Damage Mech 31(6):864–881

    Google Scholar 

  • Zheng Z, Su H, Mei GS, Wang W, Liu H, Zhang Q, Wang YJ (2023a) A thermodynamic damage model for 3D stress-induced mechanical characteristics and brittle–ductile transition of rock. Int J Damage Mech 32(4):623–648

    Google Scholar 

  • Zheng Z, Cai ZY, Su GS, Huang SL, Wang W, Zhang Q, Wang YJ (2023b) A new fractional-order model for time-dependent damage of rock under true triaxial stresses. Int J Damage Mech 32(1):50–72

    Google Scholar 

  • Zheng Z, Deng B, Li SJ, Zheng H (2023c) Disturbance mechanical behaviors and anisotropic fracturing mechanisms of rock under novel three‑stage true triaxial static‑dynamic coupling loading. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-023-03696-3

  • Zheng Z, Tang H, Zhang Q, Pan PZ, Zhang XW, Mei GX, Wang W (2023d) True triaxial test and PFC3D-GBM simulation study on mechanical properties and fracture evolution mechanisms of rock under high stresses. Comput Geotech 154:105136

    Google Scholar 

  • Zheng Z, Li RH, Zhang Q (2023e) A novel anisotropic deterioration mechanical model for rock ductile–brittle failure under 3D high-stress and its application. Comput Geotech 162:105665

    Google Scholar 

  • Zheng Z, Xu HY, Zhang K, Feng GL, Zhang Q, Zhao YF (2024a) Intermittent disturbance mechanical behavior and fractional deterioration mechanical model of rock under complex true triaxial stress paths. IJMST 34(1):17–136

  • Zheng Z, Deng B, Liu H, Wang H, Huang SL, Li SJ (2024b). Microdynamic mechanical properties and fracture evolution mechanism of monzogabbro with a true triaxial multilevel disturbance method. IJMST. https://doi.org/10.1016/j.ijmst.2024.01.0012095-26

  • Zheng Z, Li RH, Zhang Q, Huang XH, Wang W, Huang SL (2024c) Mechanical parameter evolutions and deterioration constitutive model for ductile-brittle failure of surrounding rock in high-stress underground engineering. Underground Space 15:131–152

    Google Scholar 

  • Zhu DF, Tu SH, Ma HS, Zhang XW (2017) A 3D Voronoi and subdivision model for calibration of rock properties. Model Simul Mater Sc 25(8):085005

    Google Scholar 

Download references

Acknowledgements

The authors acknowledge the financial support received from the National Natural Science Foundation of China (Grant No. 52109119), the Guangxi Natural Science Foundation (Grant No. 2021GXNSFBA075030), and the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin (China Institute of Water Resources and Hydropower Research) (Grant No.IWHR-SKL-202202), the Guangxi Science and Technology Project (Grant No. GuikeAD20325002), and the China Postdoctoral Science Foundation Project (Grant No. 2022M723408). The authors sincerely thank Professor **a-Ting Feng and his teams for their help in the experiment.

Author information

Authors and Affiliations

  1. State Key Laboratory of Featured Metal Materials and Life-Cycle Safety for Composite Structures, Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, College of Civil Engineering and Architecture, Guangxi University, Guangxi, Nanning, 530004, China

    Zhi Zheng, Shouxin Li & Zhengyun Qin

  2. Key Laboratory of Ministry of Education On Safe Mining of Deep Metal Mines, Northeastern University, Shenyang, 110819, China

    Zhi Zheng

  3. State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, Institute of Water Resources and Hydropower Research, Bei**g, 100048, China

    Qiang Zhang

Authors
  1. Zhi Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shouxin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhengyun Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qiang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

ZZ: conceptualization, experiment, methodology, writing, software; SL: data analysis, writing—editing and review; ZQ: investigation, writing-original draft, visualization; QZ: data analysis, software, writing—editing and review, supervision.

Corresponding authors

Correspondence to Zhi Zheng or Qiang Zhang.

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

Springer Nature or its licensor (e.g. a society or other partner) 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

Zheng, Z., Li, S., Qin, Z. et al. Dual-scale 3DEC-GBM Discrete Element Simulation On Mechanical Behavior and Anisotropic Fracture Evolution Mechanism of Rock Induced by True Three-dimensional Stress. Rock Mech Rock Eng 57, 3885–3915 (2024). https://doi.org/10.1007/s00603-023-03754-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-023-03754-w

Keywords

Search

Navigation