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Frontiers of Earth Science

ISSN 2095-0195

ISSN 2095-0209(Online)

CN 11-5982/P

邮发代号 80-963

2019 Impact Factor: 1.62

Frontiers of Earth Science  2021, Vol. 15 Issue (4): 803-816   https://doi.org/10.1007/s11707-021-0895-8
  本期目录
PFC2D-based investigation on the mechanical behavior of anisotropic shale under Brazilian splitting containing two parallel cracks
Bo HE1,2,3, Jun LIU1,3, Peng ZHAO2,3(), Jingfeng WANG2
1. Key Laboratory of Deep Underground Science and Engineering, Sichuan University, Chengdu 610065, China
2. College of Architecture and Environment, Sichuan University, Chengdu 610065, China
3. Institute of New Energy and Low-Carbon Technology, Sichuan University, Chengdu 610207, China
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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.

Key wordsanisotropy    preexisting cracks    tensile strength    mechanical behavior    PFC2D
收稿日期: 2020-01-04      出版日期: 2022-01-20
Corresponding Author(s): Peng ZHAO   
 引用本文:   
. [J]. Frontiers of Earth Science, 2021, 15(4): 803-816.
Bo HE, Jun LIU, Peng ZHAO, Jingfeng WANG. PFC2D-based investigation on the mechanical behavior of anisotropic shale under Brazilian splitting containing two parallel cracks. Front. Earth Sci., 2021, 15(4): 803-816.
 链接本文:  
https://academic.hep.com.cn/fesci/CN/10.1007/s11707-021-0895-8
https://academic.hep.com.cn/fesci/CN/Y2021/V15/I4/803
Fig.1  
Model types Microparameters Values
SJM Normal stiffness (GPa/m) 10000
Shear stiffness (GPa/m) 2000
Tensile strength (MPa) 4.6
Cohesion strength (MPa) 15
Friction coefficient 0
Friction angle (° ) 70
FJM Young’s modulus of the particle (GPa) 20
Particle radius (mm) 0.15–0.25
Porosity 0.05
Ratio of the normal to shear stiffness 1.66
Tensile strength (MPa) 12
Cohesion (MPa) 45
Friction coefficient 0.5
Tab.1  
Fig.2  
Fig.3  
Fig.4  
Microparameters Values
Normal stiffness/(GPa·m–1) 3000
Shear stiffness/(GPa·m–1) 500
Tensile strength/MPa 0.05
Cohesion strength/MPa 0.05
Friction coefficient 0
Friction angle/(° ) 40
Tab.2  
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  
β = 0° β = 15° β = 30° β = 45° β = 60° β = 75° β = 90°
θ = 0°
θ = 15°
θ = 30°
θ = 45°
θ = 60°
θ = 75°
θ = 90°
  
β = 0° β = 15° β = 30° β = 45° β = 60° β = 75° β = 90°
θ = 0°
θ = 15°
θ = 30°
θ = 45°
θ = 60°
θ = 75°
θ = 90°
  
1 M Cai (2013). Fracture initiation and propagation in a Brazilian disc with a plane interface: a numerical study. Rock Mech Rock Eng, 46(2): 289–302
https://doi.org/10.1007/s00603-012-0331-1
2 M Cai, P K Kaiser (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
https://doi.org/doi:10.1016/j.ijrmms.2003.12.111
3 C S Chen, E Pan, B Amadei (1998). Determination of deformability and tensile strength of anisotropic rock using Brazilian tests. Int J Rock Mech Min, 35(1): 43–61
https://doi.org/10.1016/S0148-9062(97)00329-X
4 J Claesson, B Bohloli (2002). Brazilian test: stress field and tensile strength of anisotropic rocks using an analytical solution. Int J Rock Mech Min, 39(8): 991–1004
https://doi.org/10.1016/S1365-1609(02)00099-0
5 D O Potyondy, P A Cundall (2004). A bonded-particle model for rock. Int J Rock Mech Min, 41(8): 1329–1364
https://doi.org/doi:10.1016/j.ijrmms.2004.09.011
6 S M Dong (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
https://doi.org/doi:10.1016/j.engfracmech.2007.09.008
7 R J Fowell, C Xu (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
https://doi.org/10.1016/0148-9062(94)90001-9
8 R J Fowell, C Xu, P A Dowd (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
https://doi.org/doi:10.1007/s00024-006-0057-7
9 A Ghazvinian, H R Nejati, V Sarfarazi, M R Hadei (2013). Mixed mode crack propagation in low brittle rock-like materials. Arab J Geosci, 6(11): 4435–4444
https://doi.org/doi:10.1007/s12517-012-0681-8
10 H Guo, H I Aziz, L C Schmidt (1993). Rock fracture-toughness determination by the Brazilian test. Eng Geol, 33(3): 177–188
https://doi.org/10.1016/0013-7952(93)90056-I
11 H Haeri, A Khaloo, M F Marji (2015). Experimental and numerical analysis of Brazilian discs with multiple parallel cracks. Arab J Geosci, 8: 5897–5908
https://doi.org/doi:10.1007/s12517-014-1598-1
12 H Haeri, K Shahriar, M Fatehimarji, P Moarefvand (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
https://doi.org/doi:10.1590/S1679-78252014000800007
13 H Haeri, K Shahriar, M F Marji, P Moarefvand (2014b). Experimental and numerical study of crack propagation and coalescence in pre-cracked rock-like disks. Int J Rock Mech Min, 67: 20–28
https://doi.org/10.1016/j.ijrmms.2014.01.008
14 ISRM (1978). Suggested methods for determining tensile strength of rock materials. Int J Rock Mech Min Sci Geomech Abstr, 15(3): 99–103
https://doi.org/10.1016/0148-9062(78)90003-7
15 D Y Li, Y E Wong (2013). The Brazilian disc test for rock mechanics applications: review and new insights. Rock Mech Rock Eng, 46(2): 269–287
https://doi.org/10.1007/s00603-012-0257-7
16 L C Li, S H Li, C A Tang (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
https://doi.org/10.1007/s11707-014-0427-x
17 J Liu, L Z Xie, B He, Q Gan, P Zhao (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
https://doi.org/10.1016/j.ijggc.2020.103208
18 M Mellor, I Hawkes (1971). Measurement of tensile strength by diametral compression of discs and annuli. Eng Geol, 5(3): 173–225
https://doi.org/10.1016/0013-7952(71)90001-9
19 B Park, K B Min (2015). Bonded-particle discrete element modeling of mechanical behavior of transversely isotropic rock. Int J Rock Mech Min, 76: 243–255
https://doi.org/10.1016/j.ijrmms.2015.03.014
20 B Park, K B Min, N Thompson, P Horsrud (2018). Three-dimensional bonded-particle discrete element modeling of mechanical behavior of transversely isotropic rock. Int J Rock Mech Min, 110: 120–132
https://doi.org/10.1016/j.ijrmms.2018.07.018
21 C Rocco, G V Guinea, J Planas, M Elices (1999). Size effect and boundary conditions in the brazilian test: theoretical analysis. Mater Struct, 32: 437–444
https://doi.org/doi:10.1007/BF02482715
22 T Saksala, M Hokka, V T Kuokkala, J Mäkinen (2013). Numerical modeling and experimentation of dynamic Brazilian disc test on Kuru granite. Int J Rock Mech Min, 59: 128–138
https://doi.org/doi:10.1016/j.ijrmms.2012.12.018
23 V Sarfarazi, H Haeri, M F Marji, Z M Zhu (2017). Fracture mechanism of Brazilian discs with multiple parallel notches using PFC2D. Period Polytech Civ Eng, 61(4): 653–663
https://doi.org/doi:10.3311/PPci.10310
24 Y Suo, Z X Chen, S Rahman (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
25 X Tan, H Konietzky, T Frühwirt, D Q Dan (2015). Brazilian tests on transversely isotropic rocks: laboratory testing and numerical simulations. Rock Mech Rock Eng, 48(4): 1341–1351
https://doi.org/10.1007/s00603-014-0629-2
26 A Tavallali, A Vervoot (2010). Effect of layer orientation on the failure of layered sandstone under Brazilian test conditions. Int J Rock Mech Min, 47(2): 313–322
https://doi.org/doi:10.1016/j.ijrmms.2010.01.001
27 J Wang, L Z Xie, H P Xie, L Ren, B He, C B Li, Z P Yang, C Gao (2016). Effect of layer orientation on acoustic emission characteristics of anisotropic shale in Brazilian tests. J Nat Gas Sci Eng, 36: 1120–1129
https://doi.org/10.1016/j.jngse.2016.03.046
28 Y Wang, C H Li, Y Z Hu, T Q Mao (2017). Brazilian test for tensile failure of anisotropic shale under different strain rates at quasi-static loading. Energies, 10(9): 1324
https://doi.org/doi:10.3390/en10091324
29 Z J Wang, F Jacobs, M Ziegler (2014). Visualization of load transfer behaviour between geogrid and sand using PFC2D. Geotext Geomembr, 42(2): 83–90
https://doi.org/doi:10.1016/j.geotexmem.2014.01.001
30 S C Wu, J Ma, Y Cheng, M F Xu, X Q Huang (2018). Numerical analysis of the flattened Brazilian test: failure process, recommended geometric parameters and loading conditions. Eng Fract Mech, 204: 288–305
https://doi.org/10.1016/j.engfracmech.2018.09.024
31 L Xia, Y W Zeng (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
https://doi.org/10.1016/j.compgeo.2018.01.012
32 B D Yang, Y Jiao, S T Lei (2006). A study on the effects of microparameters on macroproperties for specimens created by bonded particles. Eng Comput, 23(6): 607–631
https://doi.org/10.1108/02644400610680333
33 S Q Yang, Y H Huang (2014). Particle flow study on strength and meso-mechanism of Brazilian splitting test for jointed rock mass. Acta Mech Sinica-prc, 30(4): 547–558
https://doi.org/doi:10.1007/s10409-014-0076-z
34 J Yoon (2007). Application of experimental design and optimization to PFC model calibration in uniaxial compression simulation. Int J Rock Mech Min, 44(6): 871–889
https://doi.org/10.1016/j.ijrmms.2007.01.004
35 R F Yuan, B T Shen (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
https://doi.org/10.1016/j.ijrmms.2017.01.010
36 Y Zhang, T Y Li, L Z Xie, Z P Yang, R Y Li (2017). Shale lamina thickness study based on micro-scale image processing of thin sections. J Nat Gas Sci Eng, 46: 817–829
https://doi.org/10.1016/j.jngse.2017.08.023
37 P Zhao, L Xie, Z Fan, L Deng, J Liu (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
https://doi.org/doi: 10.1007/s12182-020-00510-5
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