Skip to main content
SpringerLink
Log in

Numerical study on cracking behavior and fracture failure mechanism of fractured rocks under shear loading

  • Published:
Computational Particle Mechanics Aims and scope Submit manuscript

Abstract

Pre-existing fractures in rock engineering significantly affect the entire structural stability. To deepen the understanding of the fracture mechanism of fractured rocks under shear loading, a numerical study based on the distinct element method was conducted to investigate the shear behaviors of rock fractures. A discrete element model with fractures of Barton's ten standard profiles was established, and shear simulations under different normal stresses and joint roughness coefficient (JRC) were carried out. The simulation results show that the shear stress–displacement curve can be divided into three stages: elastic loading stage, inelastic stage and stress drop stage. The shear strength, internal friction angle and cohesion increase with the increase of normal stress and JRC. These macroscopic mechanical characteristics are consistent with the results of previous experimental studies. Most of the microcracks generated during the shearing process are tensile microcracks, which are first formed at the steep position of the fracture profile line, and the proportion of shear microcracks is less than 10%. In addition, the contact force between particles is mainly compressive stress, which is greater in magnitude and density than tensile stress. As the shear proceeds, the displacement of the particles gradually changes from non-uniform distribution to uniform distribution.

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

Similar content being viewed by others

Data availability

Data will be made available on request.

References

  1. Wang SY, Sloan SW, Sheng DC, Yang SQ, Tang CA (2014) Numerical study of failure behaviour of pre-cracked rock specimens under conventional triaxial compression. Int J Solids Struct 51(5):1132–1148. https://doi.org/10.1016/j.ijsolstr.2013.12.012

    Article  Google Scholar 

  2. Zhao YL, Zhang CS, Wang YX, Lin H (2021) Shear-related roughness classification and strength model of natural rock joint based on fuzzy comprehensive evaluation. Int J Rock Mech Min Sci. https://doi.org/10.1016/j.ijrmms.2020.104550

    Article  Google Scholar 

  3. Khosravi A, Serej AD, Mousavi SM, Haeri SM (2016) Effect of hydraulic hysteresis and degree of saturation of infill materials on the behavior of an infilled rock fracture. Int J Rock Mech Min Sci 88:105–114. https://doi.org/10.1016/j.ijrmms.2016.07.001

    Article  Google Scholar 

  4. Jiang M, Liu J, Crosta GB, Li T (2017) DEM analysis of the effect of joint geometry on the shear behavior of rocks. CR Mécanique 345(11):779–796. https://doi.org/10.1016/j.crme.2017.07.004

    Article  Google Scholar 

  5. Wu H, Fan A, Ma D, Spearing AJS, Zheng Z (2023) Fracturing process and initiation mechanism of hard rock tunnels with different shapes: particle flow modeling and analytical study. Comput Part Mech. https://doi.org/10.1007/s40571-023-00594-x

    Article  Google Scholar 

  6. Li Y, Chen L, Wang Y (2005) Experimental research on pre-cracked marble under compression. Int J Solids Struct 42(9):2505–2516. https://doi.org/10.1016/j.ijsolstr.2004.09.033

    Article  Google Scholar 

  7. Hoek E, Martin CD (2014) Fracture initiation and propagation in intact rock—A review. J Rock Mech Geotech 6(4):287–300

    Article  Google Scholar 

  8. Zhang YC, Jiang YJ, Asahina D, Wang Z (2020) Shear behavior and acoustic emission characteristics of en-echelon joints under constant normal stiffness conditions. Theor Appl Fract Mec. https://doi.org/10.1016/j.tafmec.2020.102772

    Article  Google Scholar 

  9. Wang JG, Schweizer D, Liu QB, Su AJ, Hu XL, Blum P (2021) Three-dimensional landslide evolution model at the Yangtze River. Eng Geol. https://doi.org/10.1016/j.enggeo.2021.106275

    Article  Google Scholar 

  10. Indraratna B, Oliveira DAF, Brown ET (2010) A shear-displacement criterion for soil-infilled rock discontinuities. Geotechnique 60(8):623–633. https://doi.org/10.1680/geot.8.P.094

    Article  Google Scholar 

  11. Indraratna B, Ranjith PG (2001) Laboratory measurement of two-phase flow parameters in rock joints based on high pressure triaxial testing. J Geotech Geoenviron 127(6):530–542. https://doi.org/10.1061/(asce)1090-0241(2001)127:6(530)

    Article  Google Scholar 

  12. Indraratna B, Oliveira DAF, Brown ET, de Assis AP (2010) Effect of soil–infilled joints on the stability of rock wedges formed in a tunnel roof. Int J Rock Mech Min Sci 47(5):739–751. https://doi.org/10.1016/j.ijrmms.2010.05.006

    Article  Google Scholar 

  13. Ellsworth WL (2013) Injection-induced earthquakes. Science 341(6142):142. https://doi.org/10.1126/science.1225942

    Article  Google Scholar 

  14. Bao XW, Eaton DW (2016) Fault activation by hydraulic fracturing in western Canada. Science 354(6318):1406–1409. https://doi.org/10.1126/science.aag2583

    Article  Google Scholar 

  15. Singh M, Seshagiri RK (2005) Empirical methods to estimate the strength of jointed rock masses. Eng Geol 77(1):127–137. https://doi.org/10.1016/j.enggeo.2004.09.001

    Article  Google Scholar 

  16. Mohammadnejad M, Fukuda D, Liu HY, Dehkhoda S, Chan A (2020) GPGPU-parallelized 3D combined finite–discrete element modelling of rock fracture with adaptive contact activation approach. Comput Part Mech 7(5):849–867. https://doi.org/10.1007/s40571-019-00287-4

    Article  Google Scholar 

  17. Han W, Jiang Y, Luan H, Du Y, Zhu Y, Liu J (2020) Numerical investigation on the shear behavior of rock-like materials containing fissure-holes with FEM-CZM method. Comput Geotech 125:103670. https://doi.org/10.1016/j.compgeo.2020.103670

    Article  Google Scholar 

  18. Zou Z, Hameed M (2018) Combining interface damage and friction in cohesive interface models using an energy based approach. Compos Part A-appl S 112:290–298. https://doi.org/10.1016/j.compositesa.2018.06.017

    Article  Google Scholar 

  19. Zhang JZ, Zhou XP, Zhou LS, Berto F (2019) Progressive failure of brittle rocks with non-isometric flaws: insights from acousto-optic-mechanical (AOM) data. Fatigue Fract Eng M 42(8):1787–1802. https://doi.org/10.1111/ffe.13019

    Article  Google Scholar 

  20. Develi K (2020) Computation of direction dependent joint surface parameters through the algorithm of triangular prism surface area method: a theoretical and experimental study. Int J Solids Struct 202:895–911. https://doi.org/10.1016/j.ijsolstr.2020.06.038

    Article  Google Scholar 

  21. Chen W, Wan W, Zhao Y, Peng W (2020) Experimental study of the crack predominance of rock-like material containing parallel double fissures under uniaxial compression. Sustainability 12(12):5188

    Article  Google Scholar 

  22. Zhao YL, Tang JZ, Chen Y, Zhang LY, Wang WJ, Wan W et al (2017) Hydromechanical coupling tests for mechanical and permeability characteristics of fractured limestone in complete stress-strain process. Environ Earth Sci. https://doi.org/10.1007/s12665-016-6322-x

    Article  Google Scholar 

  23. Agharazi A, Tannant D, Martin CD (2012) Characterizing rock mass deformation mechanisms during plate load tests at the Bakhtiary dam project. Int J Rock Mech Min Sci 49:1–11. https://doi.org/10.1016/j.ijrmms.2011.10.002

    Article  Google Scholar 

  24. Sanei M, Faramarzi L, Fahimifar A, Goli S, Mehinrad A, Rahmati A (2015) Shear strength of discontinuities in sedimentary rock masses based on direct shear tests. Int J Rock Mech Min Sci 75:119–131. https://doi.org/10.1016/j.ijrmms.2014.11.009

    Article  Google Scholar 

  25. Han G, Zhang C, Zhou H, Zhang C, Gao Y, Singh HK (2021) A new predictive method for the shear strength of interlayer shear weakness zone at field scales. Eng Geol 295:106449. https://doi.org/10.1016/j.enggeo.2021.106449

    Article  Google Scholar 

  26. Wang YN, Bui HH, Nguyen GD, Ranjith PG (2019) A new SPH-based continuum framework with an embedded fracture process zone for modelling rock fracture. Int J Solids Struct 159:40–57. https://doi.org/10.1016/j.ijsolstr.2018.09.019

    Article  Google Scholar 

  27. Wang J, Li JT, Shi ZM (2022) Crack evolution law and failure mode of red sandstone under fatigue-creep interaction. Fatigue Fract Eng M 45(1):270–284. https://doi.org/10.1111/ffe.13599

    Article  Google Scholar 

  28. Zhou XP, Xia EM, Yang HQ, Qian QH (2012) Different crack sizes analyzed for surrounding rock mass around underground caverns in Jinping I hydropower station. Theor Appl Fract Mec 57(1):19–30. https://doi.org/10.1016/j.tafmec.2011.12.004

    Article  Google Scholar 

  29. Goudie AS (2016) Quantification of rock control in geomorphology. Earth Sci Rev 159:374–387. https://doi.org/10.1016/j.earscirev.2016.06.012

    Article  Google Scholar 

  30. Xie S, Lin H, Duan H (2023) A novel criterion for yield shear displacement of rock discontinuities based on renormalization group theory. Eng Geol. https://doi.org/10.1016/j.enggeo.2023.107008

    Article  Google Scholar 

  31. Xie S, Lin H, Duan H, Chen Y (2023) Modeling description of interface shear deformation: A theoretical study on damage statistical distributions. Constr Build Mater 394:132052. https://doi.org/10.1016/j.conbuildmat.2023.132052

    Article  Google Scholar 

  32. Barla G, Robotti F, Vai L, editors. (2011) Revisiting large size direct shear testing of rock mass foundations. 6th international conference on dam engineering, Lisbon, Portugal. LNEC, Lisbon

  33. Vorobiev O (2008) Generic strength model for dry jointed rock masses. Int J Plast 24(12):2221–2247. https://doi.org/10.1016/j.ijplas.2008.06.009

    Article  Google Scholar 

  34. Xie S, Lin H, Chen Y, Duan H, Liu H, Liu B (2023) Prediction of shear strength of rock fractures using support vector regression and grid search optimization. Mater Today Commun 36:106780. https://doi.org/10.1016/j.mtcomm.2023.106780

    Article  Google Scholar 

  35. Muralha J, Grasselli G, Tatone B, Blümel M, Chryssanthakis P, Yujing J (2014) ISRM suggested method for laboratory determination of the shear strength of rock joints: revised version. Rock Mech Rock Eng 47(1):291–302

    Article  Google Scholar 

  36. Patton FD, editor. Multiple modes of shear failure in rock. 1st ISRM Congress; 1966: OnePetro

  37. Barton N (1973) Review of a new shear-strength criterion for rock joints. Eng Geol 7(4):287–332. https://doi.org/10.1016/0013-7952(73)90013-6

    Article  Google Scholar 

  38. Isrm I (1978) Suggested methods for the quantitative description of discontinuities in rock masses. Int J Rock Mech Min Sci Geomech Abstr 15(6):319–368

    Google Scholar 

  39. Jafari MK, Amini Hosseini K, Pellet F, Boulon M, Buzzi O (2003) Evaluation of shear strength of rock joints subjected to cyclic loading. Soil Dyn Earthq Eng 23(7):619–630. https://doi.org/10.1016/S0267-7261(03)00063-0

    Article  Google Scholar 

  40. Kleepmek M, Khamrat S, Thongprapha T, Fuenkajorn K (2016) Displacement velocity effects on rock fracture shear strengths. J Struct Geol 90:48–60. https://doi.org/10.1016/j.jsg.2016.07.007

    Article  Google Scholar 

  41. Singh HK, Basu A (2018) Evaluation of existing criteria in estimating shear strength of natural rock discontinuities. Eng Geol 232:171–181. https://doi.org/10.1016/j.enggeo.2017.11.023

    Article  Google Scholar 

  42. Barton N, Wang C, Yong R (2023) Advances in joint roughness coefficient (JRC) and its engineering applications. J Rock Mech Geotech. https://doi.org/10.1016/j.jrmge.2023.02.002

    Article  Google Scholar 

  43. Barton N, Choubey V (1977) The shear strength of rock joints in theory and practice. Rock Mech 10(1–2):1–54. https://doi.org/10.1007/BF01261801

    Article  Google Scholar 

  44. Wang G, Wu XL, Zhang XD, Zhang ZS, Zhao ZP, Han W et al (2020) Macro-microscopic study on the shear characteristics of filled joints with different roughnesses. Arab J Sci Eng 45(10):8331–8348. https://doi.org/10.1007/s13369-020-04705-1

    Article  Google Scholar 

  45. Day JJ, Diederichs MS, Hutchinson DJ (2017) New direct shear testing protocols and analyses for fractures and healed intrablock rockmass discontinuities. Eng Geol 229:53–72. https://doi.org/10.1016/j.enggeo.2017.08.027

    Article  Google Scholar 

  46. Xie S, Lin H, Chen Y (2022) New constitutive model based on disturbed state concept for shear deformation of rock joints. Arch Civ Mech Eng 23(1):26. https://doi.org/10.1007/s43452-022-00560-z

    Article  Google Scholar 

  47. Fakhimi A, Norouzi S (2019) Dilation angle in bonded particle simulation of rock. Comput Part Mech 6(2):195–211. https://doi.org/10.1007/s40571-018-0208-5

    Article  Google Scholar 

  48. Gong L, Nemcik J, Ren T (2018) Numerical simulation of the shear behavior of rock joints filled with unsaturated soil. Int J Geomech 18(9):04018112. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001253

    Article  Google Scholar 

  49. Li H, Wong LNY (2012) Influence of flaw inclination angle and loading condition on crack initiation and propagation. Int J Solids Struct 49(18):2482–2499

    Article  Google Scholar 

  50. Zhou X, Chen J (2019) Extended finite element simulation of step-path brittle failure in rock slopes with non-persistent en-echelon joints. Eng Geol 250:65–88. https://doi.org/10.1016/j.enggeo.2019.01.012

    Article  Google Scholar 

  51. Wang Y, Zhou X, Wang Y, Shou Y (2018) A 3-D conjugated bond-pair-based peridynamic formulation for initiation and propagation of cracks in brittle solids. Int J Solids Struct 134:89–115. https://doi.org/10.1016/j.ijsolstr.2017.10.022

    Article  Google Scholar 

  52. Duriez J, Darve F, Donzé FV (2011) A discrete modeling-based constitutive relation for infilled rock joints. Int J Rock Mech Min Sci 48(3):458–468. https://doi.org/10.1016/j.ijrmms.2010.09.008

    Article  Google Scholar 

  53. Lee H, Jeon S (2011) An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression. Int J Solids Struct 48(6):979–999. https://doi.org/10.1016/j.ijsolstr.2010.12.001

    Article  Google Scholar 

  54. Cundall PA, Hart RD (1992) Numerical modelling of discontinua. Eng Computation.

  55. Li Z, Rao QH (2021) Quantitative determination of PFC3D microscopic parameters. J Cent South Univ 28(3):911–925. https://doi.org/10.1007/s11771-021-4653-6

    Article  Google Scholar 

  56. Zhou XP, Zhang JZ, Yang SQ, Berto F (2021) Compression-induced crack initiation and growth in flawed rocks: a review. Fatigue Fract Eng M 44(7):1681–1707. https://doi.org/10.1111/ffe.13477

    Article  Google Scholar 

  57. Cundall PA (2000) Numerical experiments on rough joints in shear using a bonded particle model. In: Lehner FK, Urai JL, editors. Aspects of Tectonic Faulting: In Honour of Georg Mandl. Berlin, Heidelberg: Springer Berlin Heidelberg p. 1–9

  58. Park J-W, Song J-J (2009) Numerical simulation of a direct shear test on a rock joint using a bonded-particle model. Int J Rock Mech Min Sci 46(8):1315–1328. https://doi.org/10.1016/j.ijrmms.2009.03.007

    Article  Google Scholar 

  59. Bahaaddini M, Sharrock G, Hebblewhite BK (2013) Numerical direct shear tests to model the shear behaviour of rock joints. Comput Geotech 51:101–115. https://doi.org/10.1016/j.compgeo.2013.02.003

    Article  Google Scholar 

  60. Shi C, Xu W (2015) Techniques and practice for numerical simulation of particle flow. China Building Construction Industry Press, Beijing, China

    Google Scholar 

  61. Xie S, Lin H, Cheng C, Chen Y, Wang Y, Zhao Y et al (2022) Shear strength model of joints based on Gaussian smoothing method and macro-micro roughness. Comput Geotech 143:104605. https://doi.org/10.1016/j.compgeo.2021.104605

    Article  Google Scholar 

  62. Cundall PA, Strack OD (1979) A discrete numerical model for granular assemblies. Geotechnique 29(1):47–65

    Article  Google Scholar 

  63. Tarokh A, Fakhimi A (2014) Discrete element simulation of the effect of particle size on the size of fracture process zone in quasi-brittle materials. Comput Geotech 62:51–60. https://doi.org/10.1016/j.compgeo.2014.07.002

    Article  Google Scholar 

  64. Yue Z, Meng F, Zhou X, Wang X, Zhang L, Wang Z (2022) Influence of non-persistent joint aperture and inclination angle on the shear behavior and fracture mode of solid rock and concrete material. Constr Build Mater 316:125892. https://doi.org/10.1016/j.conbuildmat.2021.125892

    Article  Google Scholar 

  65. Poulsen BA, Adhikary D, Guo H (2018) Simulating mining-induced strata permeability changes. Eng Geol 237:208–216. https://doi.org/10.1016/j.enggeo.2018.03.001

    Article  Google Scholar 

  66. Li K, Han D, Fan X, Yang Y, Wang F (2022) Shear rupture behaviors of intact and granulated Wombeyan marble with the flat-jointed model. Arch Civ Mech Eng 22(1):51. https://doi.org/10.1007/s43452-022-00377-w

    Article  Google Scholar 

  67. Itasca Consulting Group I (2014) PFC—Particle Flow Code, Ver. 5.0. Itasca Minneapolis

  68. Coetzee CJ (2017) Calibration of the discrete element method. Powder Technol 310:104–142. https://doi.org/10.1016/j.powtec.2017.01.015

    Article  Google Scholar 

  69. Sharrock B, Akram M, Mitra R (2009) Application of synthetic rock mass modeling to estimate the strength of jointed sandstone. 43rd US Rock Mechanics Symposium and 4th US-Canada Rock Mechanics Symposium

  70. Ding X, Zhang L, Zhu H, Zhang Q (2014) Effect of model scale and particle size distribution on PFC3D simulation results. Rock Mech Rock Eng 47(6):2139–2156. https://doi.org/10.1007/s00603-013-0533-1

    Article  Google Scholar 

  71. Bahaaddini M, Hagan PC, Mitra R, Khosravi MH (2016) Experimental and numerical study of asperity degradation in the direct shear test. Eng Geol 204:41–52. https://doi.org/10.1016/j.enggeo.2016.01.018

    Article  Google Scholar 

  72. Xie SJ, Lin H, Chen YF, Yong R, Xiong W, Du SG (2020) A damage constitutive model for shear behavior of joints based on determination of the yield point. Int J Rock Mech Min Sci. https://doi.org/10.1016/j.ijrmms.2020.104269

    Article  Google Scholar 

  73. Meng F, Wong LNY, Guo T (2022) Frictional behavior and micro-damage characteristics of rough granite fractures. Tectonophysics 842:229589. https://doi.org/10.1016/j.tecto.2022.229589

    Article  Google Scholar 

  74. Nasir O, Fall M (2008) Shear behaviour of cemented pastefill-rock interfaces. Eng Geol 101(3):146–153. https://doi.org/10.1016/j.enggeo.2008.04.010

    Article  Google Scholar 

  75. Xu W, Lin H, Cao R (2018) Simulation and macro-mesoscopic parameter analysis for direct shear of filled rough joints. J Southwest Jiaotong Univ 53(3):548–557

    Google Scholar 

  76. Gu Xue F, Seidel Julian P, Haberfield CM (2003) Direct shear test of sandstone-concrete joints. Int J Geomech 3(1):21–33. https://doi.org/10.1061/(ASCE)1532-3641(2003)3:1(21)

    Article  Google Scholar 

  77. Jiang YJ, Wang YH, Yan P, Luan HJ, Chen YQ (2019) Experimental investigation on the shear properties of heterogeneous discontinuities. Geotech Geol Eng 37(6):4959–4968. https://doi.org/10.1007/s10706-019-00955-5

    Article  Google Scholar 

  78. Yin T-B, Zhuang D-D, Li M-J, Li X-B (2022) Numerical simulation study on the thermal stress evolution and thermal cracking law of granite under heat conduction. Comput Geotech 148:104813. https://doi.org/10.1016/j.compgeo.2022.104813

    Article  Google Scholar 

  79. Dang Y, Yang Z, Liu X, Lu C (2023) Numerical study on failure mechanism and acoustic emission characteristics of granite after thermal treatment. Comput Part Mech 10(5):1245–1266. https://doi.org/10.1007/s40571-023-00556-3

    Article  Google Scholar 

  80. Eftekhari M, Baghbanan A, Hashemolhosseini H, Amrollahi H (2015) Mechanism of fracture in macro- and micro-scales in hollow centre cracked disc specimen. J Cent South Univ 22(11):4426–4433. https://doi.org/10.1007/s11771-015-2990-z

    Article  Google Scholar 

Download references

Acknowledgements

This paper gets its funding from Projects (42277175) supported by National Natural Science Foundation of China and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX23_0276).

Author information

Authors and Affiliations

  1. School of Civil Engineering, Southeast University, Nanjing, 210096, Jiangsu, China

    Shijie Xie

  2. School of Resources and Safety Engineering, Central South University, Changsha, 410083, Hunan, China

    Hang Lin, Hongwei Liu & Baohua Liu

  3. Department of Sustainable Development, Environmental Science and Engineering, Royal Institute of Technology, 10044, Stockholm, Sweden

    Hongyu Duan

Authors
  1. Shijie Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hang Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongyu Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hongwei Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Baohua Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

SX: Methodology, Data curation, Writing—original draft. Hang Lin: Investigation, Supervision, Funding acquisition. HD: Conceptualization, Writing—original draft. HL: Investigation. BL: Writing—review & editing. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Shijie Xie.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

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

Xie, S., Lin, H., Duan, H. et al. Numerical study on cracking behavior and fracture failure mechanism of fractured rocks under shear loading. Comp. Part. Mech. 11, 903–920 (2024). https://doi.org/10.1007/s40571-023-00660-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40571-023-00660-4

Keywords

Search

Navigation