Skip to main content
Log in

PFC2D-based investigation on the mechanical behavior of anisotropic shale under Brazilian splitting containing two parallel cracks

  • Research Article
  • Published:
Frontiers of Earth Science Aims and scope Submit manuscript

Abstract

A validated particle flow code (PFC2D)-based model was developed to investigate the indirect tensile mechanical behavior of shale containing two central parallel cracks under Brazilian splitting test conditions. The results show that preexisting cracks have a significant and insignificant influence on the tensile strength of shale under LPL and LVL conditions, respectively. When L ⩾ 10 mm, changing the L and H values has little effect on the tensile strength of shale. However, the inclusion of preexisting cracks have a positive effect on reducing the anisotropy of the shale specimens, and in the case of an L/D ratio of 0.3, the shale anisotropy is the lowest. Four failure modes were formed at different β and θ values under LPL conditions. In the case of β⩾60°, the failure mode is mainly affected by β, and when β⩽45°, the failure mode is more complicated than in the case of β⩾ 60°. Only three major failure modes were observed under LVL conditions; in the case of 45°⩽β⩽75° and θ⩽30°, the most complex failure mode occurred.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Cai M (2013). Fracture initiation and propagation in a Brazilian disc with a plane interface: a numerical study. Rock Mech Rock Eng, 46(2): 289–302

    Article  Google Scholar 

  • Cai M, Kaiser P K (2004). Numerical simulation of the Brazilian test and the tensile strength of anisotropic rocks and rocks with pre-existing cracks. Int J Rock Mech Min, 41(3): 450–451

    Article  Google Scholar 

  • Chen C S, Pan E, Amadei B (1998). Determination of deformability and tensile strength of anisotropic rock using Brazilian tests. Int J Rock Mech Min, 35(1): 43–61

    Article  Google Scholar 

  • Claesson J, Bohloli B (2002). Brazilian test: stress field and tensile strength of anisotropic rocks using an analytical solution. Int J Rock Mech Min, 39(8): 991–1004

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Dong S M (2008). Theoretical analysis of the effects of relative crack length and loading angle on the experimental results for cracked Brazilian disk testing. Eng Fract Mech, 75(8): 2575–2581

    Article  Google Scholar 

  • Fowell R J, Xu C (1994). The use of the cracked Brazilian disc geometry for rock fracture investigations. Int J Rock Mech Min Sci Geomech Abstr, 31(6): 571–579

    Article  Google Scholar 

  • Fowell R J, Xu C, Dowd P A (2006). An update on the fracture toughness testing methods related to the cracked chevron-notched brazilian disk (CCNBD) specimen. Pure Appl Geophys, 163(5–6): 1047–1057

    Article  Google Scholar 

  • Ghazvinian A, Nejati H R, Sarfarazi V, Hadei M R (2013). Mixed mode crack propagation in low brittle rock-like materials. Arab J Geosci, 6(11): 4435–4444

    Article  Google Scholar 

  • Guo H, Aziz H I, Schmidt L C (1993). Rock fracture-toughness determination by the Brazilian test. Eng Geol, 33(3): 177–188

    Article  Google Scholar 

  • Haeri H, Khaloo A, Marji M F (2015). Experimental and numerical analysis of Brazilian discs with multiple parallel cracks. Arab J Geosci, 8: 5897–5908

    Article  Google Scholar 

  • Haeri H, Shahriar K, Fatehimarji M, Moarefvand P (2014a). On the crack propagation analysis of rock like Brazilian disc specimens containing cracks under compressive line loading. Lat AM J Solids Stru, 11(8): 1400–1416

    Article  Google Scholar 

  • Haeri H, Shahriar K, Marji M F, Moarefvand P (2014b). Experimental and numerical study of crack propagation and coalescence in precracked rock-like disks. Int J Rock Mech Min, 67: 20–28

    Article  Google Scholar 

  • ISRM (1978). Suggested methods for determining tensile strength of rock materials. Int J Rock Mech Min Sci Geomech Abstr, 15(3): 99–103

    Article  Google Scholar 

  • Li D Y, Wong Y E (2013). The Brazilian disc test for rock mechanics applications: review and new insights. Rock Mech Rock Eng, 46(2): 269–287

    Article  Google Scholar 

  • Li L C, Li S H, Tang C A (2014). Fracture spacing behavior in layered rocks subjected to different driving forces: a numerical study based on fracture infilling process. Front Earth Sci, 8(4): 472–489

    Article  Google Scholar 

  • Liu J, Xie L Z, He B, Gan Q, Zhao P (2021). Influence of anisotropic and heterogeneous permeability coupled with in-situ stress on CO2 sequestration with simultaneous enhanced gas recovery in shale: quantitative modeling and case study. Int J Greenh Gas Control, 104: 103208

    Article  Google Scholar 

  • Mellor M, Hawkes I (1971). Measurement of tensile strength by diametral compression of discs and annuli. Eng Geol, 5(3): 173–225

    Article  Google Scholar 

  • Park B, Min K B (2015). Bonded-particle discrete element modeling of mechanical behavior of transversely isotropic rock. Int J Rock Mech Min, 76: 243–255

    Article  Google Scholar 

  • Park B, Min K B, Thompson N, Horsrud P (2018). Three-dimensional bonded-particle discrete element modeling of mechanical behavior of transversely isotropic rock. Int J Rock Mech Min, 110: 120–132

    Article  Google Scholar 

  • Rocco C, Guinea G V, Planas J, Elices M (1999). Size effect and boundary conditions in the brazilian test: theoretical analysis. Mater Struct, 32: 437–444

    Article  Google Scholar 

  • Saksala T, Hokka M, Kuokkala V T, Mäkinen 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 

  • Sarfarazi V, Haeri H, Marji M F, Zhu Z M (2017). Fracture mechanism of Brazilian discs with multiple parallel notches using PFC2D. Period Polytech Civ Eng, 61(4): 653–663

    Google Scholar 

  • Suo Y, Chen Z X, Rahman S (2018). Experimental and numerical investigation of fracture toughness of anisotropic shale rocks. In: Proceedings of the 6th Unconventional Resources Technology Conference (URTeC), Houston, TX, USA

  • Tan X, Konietzky H, Frühwirt T, Dan D Q (2015). Brazilian tests on transversely isotropic rocks: laboratory testing and numerical simulations. Rock Mech Rock Eng, 48(4): 1341–1351

    Article  Google Scholar 

  • Tavallali A, Vervoot A (2010). Effect of layer orientation on the failure of layered sandstone under Brazilian test conditions. Int J Rock Mech Min, 47(2): 313–322

    Article  Google Scholar 

  • Wang J, Xie L Z, Xie H P, Ren L, He B, Li C B, Yang Z P, Gao C (2016). Effect of layer orientation on acoustic emission characteristics of anisotropic shale in Brazilian tests. J Nat Gas Sci Eng, 36: 1120–1129

    Article  Google Scholar 

  • Wang Y, Li C H, Hu Y Z, Mao T Q (2017). Brazilian test for tensile failure of anisotropic shale under different strain rates at quasi-static loading. Energies, 10(9): 1324

    Article  Google Scholar 

  • Wang Z J, Jacobs F, Ziegler M (2014). Visualization of load transfer behaviour between geogrid and sand using PFC2D. Geotext Geomembr, 42(2): 83–90

    Article  Google Scholar 

  • Wu S C, Ma J, Cheng Y, Xu M F, Huang X Q (2018). Numerical analysis of the flattened Brazilian test: failure process, recommended geometric parameters and loading conditions. Eng Fract Mech, 204: 288–305

    Article  Google Scholar 

  • Xia L, Zeng Y W (2018). Parametric study of smooth joint parameters on the mechanical behavior of transversely isotropic rocks and research on calibration method. Comput Geotech, 98(JUN): 1–7

    Article  Google Scholar 

  • Yang B D, Jiao Y, Lei S T (2006). A study on the effects of microparameters on macroproperties for specimens created by bonded particles. Eng Comput, 23(6): 607–631

    Article  Google Scholar 

  • Yang S Q, Huang Y H (2014). Particle flow study on strength and mesomechanism of Brazilian splitting test for jointed rock mass. Acta Mech Sinica-prc, 30(4): 547–558

    Article  Google Scholar 

  • Yoon J (2007). Application of experimental design and optimization to PFC model calibration in uniaxial compression simulation. Int J Rock Mech Min, 44(6): 871–889

    Article  Google Scholar 

  • Yuan R F, Shen B T (2017). Numerical modelling of the contact condition of a Brazilian disk test and its influence on the tensile strength of rock. Int J Rock Mech Min, 93: 54–65

    Article  Google Scholar 

  • Zhang Y, Li T Y, Xie L Z, Yang Z P, Li R Y (2017). Shale lamina thickness study based on micro-scale image processing of thin sections. J Nat Gas Sci Eng, 46: 817–829

    Article  Google Scholar 

  • Zhao P, Xie L, Fan Z, Deng L, Liu J (2021). Mutual interference of layer plane and natural fracture in the failure behavior of shale and the mechanism investigation. Petrol Sci, 18(2): 618–640

    Article  Google Scholar 

Download references

Acknowledgements

We acknowledge the financial support from the Science and Technology Department of Sichuan Province (Nos. 2021YFH0048 and 2021YFH0118) and a project funded by the China Postdoctoral Science Foundation (No. 2020M683253).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Peng Zhao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

He, B., Liu, J., Zhao, P. et al. PFC2D-based investigation on the mechanical behavior of anisotropic shale under Brazilian splitting containing two parallel cracks. Front. Earth Sci. 15, 803–816 (2021). https://doi.org/10.1007/s11707-021-0895-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11707-021-0895-8

Keywords

Navigation