Skip to main content
SpringerLink
Log in

Fracture evolution of transversely isotropic rocks with a pre-existing flaw under compression tests based on moment tensor analysis

  • Research Paper
  • Published:
Acta Geotechnica Aims and scope Submit manuscript

Abstract

A numerical approach based on the particle discrete element theory is adopted to study the fracture evolution of transversely isotropic rocks with a pre-existing flaw under compression tests. In this approach, the rock matrix is simulated by parallel-bonded contacts and weak planes are represented as bonded contacts, and the acoustic emission characteristics of rock matrix and weak planes are obtained and distinguished using the moment tensor analysis. Firstly, the acoustic emission features of the numerical approach were validated against the test results. Then, parametrical studies were conducted to reveal the combined effect of pre-existing flaw and weak planes on the fracturing morphology of rocks, and six failure patterns were identified. Finally, the fracturing evolution process of each pattern was studied based on the moment tensor analysis.

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
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  1. Ambrose J (2014) Failure of anisotropic shales under triaxial stress conditions. Dissertation, Imperial College London

  2. Bobet A, Einstein HH (1998) Fracture coalescence in rock-type materials under uniaxial and biaxial compression. Int J Rock Mech Min Sci 35:863–889

    Article  Google Scholar 

  3. Chang LF, Konietzky H (2018) Application of the Mohr–Coulomb yield criterion for rocks with multiple joint sets using Fast Lagrangian Analysis of Continua 2D (FLAC2D) software. Energies 11:1–23

    Article  Google Scholar 

  4. Chen YF, Wei K, Liu W, Hu SH, Hu R, Zhou CB (2016) Experimental characterization and micromechanical modelling of anisotropic slates. Rock Mech Rock Eng 49(9):3541–3557

    Article  Google Scholar 

  5. Chong ZH, Li XH, Lu JZ, Chen T, Zhang J, Chen XY (2017) Numerical investigation of acoustic emission events of argillaceous sandstones under confining pressure. Math Probl Eng. ID: 7676417

  6. Cruikshank KM, Zhao G, Johnson AM (1991) Analysis of minor fractures associated with joints and faulted joints. J Struct Geol 13:865–886

    Article  Google Scholar 

  7. Dan DQ, Konietzky H (2014) Numerical simulations and interpretations of Brazilian tensile tests on transversely isotropic rocks. Int J Rock Mech Min Sci 71:53–63

    Article  Google Scholar 

  8. Debecker B (2006) Influence of planar heterogeneities on the fracture behavior of rock. katholieke universiteit leuven, Leuven

    Google Scholar 

  9. Duan K, Kwok CY, Pierce M (2016) Discrete element method modeling of inherently anisotropic rocks under uniaxial compression loading. Int J Numer Anal Methods Geomech 40:1150–1183

    Article  Google Scholar 

  10. Duan K, Wu W, Kwok CY (2018) Discrete element modelling of stress-induced instability of directional drilling boreholes in anisotropic rock. Tunn Undergr Space Technol 81:55–67

    Article  Google Scholar 

  11. Esterhuizen GS, Dolinar DR, Ellenberger JL (2011) Pillar strength in underground stone mines in the United States. Int J Rock Mech Min Sci 48:42–50

    Article  Google Scholar 

  12. Hazzard JF, Young RP (2000) Simulating acoustic emissions in bonded-particle models of rock. Int J Rock Mech Min Sci 37(5):867–872

    Article  Google Scholar 

  13. Hazzard JF, Young RP (2004) Dynamic modelling of induced seismicity. Int J Rock Mech Min Sci 41(41):1365–1376

    Article  Google Scholar 

  14. Itasca consulting group Inc. (2008) Particle flow code in 2 dimensions user’s guide. Itasca consulting group Inc., Minneapolis

    Google Scholar 

  15. Jin J, Cao P, Chen Y, Pu CZ, Mao DW, Fan X (2017) Influence of single flaw on the failure process and energy mechanics of rock-like material. Comput Geotech 86:150–162

    Article  Google Scholar 

  16. Kim H, Cho JW, Song I, Min KB (2012) Anisotropy of elastic moduli, P-wave velocities, and thermal conductivities of Asan gneiss, Boryeong Shale, and Yeoncheon Schist in Korea. Eng Geol 147:68–77

    Article  Google Scholar 

  17. Kim KY, Zhuang L, Yang H, Kim H, Min KB (2016) Strength anisotropy of Berea sandstone: results of X-ray computed tomography, compression tests, and discrete modeling. Rock Mech Rock Eng 49:1201–1210

    Article  Google Scholar 

  18. Kulatilake PHSW, Malama B, Wang JL (2001) Physical and particle flow modeling of jointed rock block behavior under uniaxial loading. Int J Rock Mech Rock Min Sci 38:641–657

    Article  Google Scholar 

  19. Lisjak A, Garitte B, Grasselli G et al (2015) The excavation of a circular tunnel in a bedded argillaceous rock (Opalinus Clay): short-term rock mass response and FDEM numerical analysis. Tunn Undergr Space Technol 45:227–248

    Article  Google Scholar 

  20. Lockner DA, Byerlee JD, Kuksenko V, Ponomarev A, Sidorin A (1991) Quasi-static fault growth and shear fracture energy in granite. Nature 350(6313):39–42

    Article  Google Scholar 

  21. Ma J, Wu SC, Zhang XP, Gan YX (2020) Modeling acoustic emission in the Brazilian test using moment tensor inversion. Comput Geotech 123. ID 103567

  22. Manthei G, Eisenblatter J (2008) Acoustic emission in study of rock stability. In: Grosse C, Ohtsu M (eds) Acoustic emission testing. Springer, Berlin, pp 239–310

    Chapter  Google Scholar 

  23. Morgan SP, Einstein HH (2017) Cracking processes affected by bedding planes in Opalinus shale with flaw pairs. Eng Fract Mech 176:213–234

    Article  Google Scholar 

  24. Nasseri MHB, Rao KS, Ramamurthy T (2003) Anisotropic strength and deformational behavior of Himalayan schist. Int J Rock Mech Min 40(1):3–23

    Article  Google Scholar 

  25. Niandou H, Shao JF, Henry JP, Fourmaintraux D (1997) Laboratory investigation of the mechanical behavior of Tournemire shale. Int J Rock Mech Min 34(1):3–16

    Article  Google Scholar 

  26. Niu LX, Xin YY (2015) Analysis on relationship between macro-parameters and micro-parameters in PFC2D model based on orthogonal design: case of rock uniaxial compression numerical test. Yangtze River 46:53–57

    Google Scholar 

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

    Article  Google Scholar 

  28. Park JW, Song JJ (2009) Numerical simulation of a direct shear test on a rock joint using a bonded-particle model. Int J Rock Mech Rock Min Sci 46:1315–1328

    Article  Google Scholar 

  29. Potyondy DO (2015) The bonded-particle model as a tool for rock mechanics research and application: current trends and future directions. Geosyst Eng 18:1–28

    Article  Google Scholar 

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

    Article  Google Scholar 

  31. Ramamurthy T (1993) Strength and modulus responses of anisotropic rocks. In: Hudson JA (ed) Comprehensive rock engineering, vol. 1. Fundamentals. Pergamon Press, Oxford, pp 313–329

    Google Scholar 

  32. Roya DG, Singh TN, Kodikara J (2017) Influence of joint anisotropy on the fracturing behavior of a sedimentary rock. Eng Geol 228:224–237

    Article  Google Scholar 

  33. Shang J, Duan K, Gui Y, Handley K, Zhao Z (2018) Numerical investigation of the direct tensile behaviour of laminated and transversely isotropic rocks containing incipient bedding planes with different strengths. Comput Geotech 104:373–388

    Article  Google Scholar 

  34. Song YL, Xia CC, Tang ZC, Song YJ (2013) Numerical simulation and test validation for direct shear properties of rough joints under different contact states. Chin J Rock Mech Eng 32:2028–2035 (in Chinese)

    Google Scholar 

  35. Teng JY, Tang JX, Zhang YN, Duan JC, Wang JB (2017) Damage process and characteristics of layered water-bearing shale under uniaxial compression. Rock Soil Mech 38:1629–1638

    Google Scholar 

  36. Tien YM, Kuo MC (2001) A failure criterion for transversely isotropic rocks. Int J Rock Mech Min 38(3):399–412

    Article  Google Scholar 

  37. Wang YL, Tan JX, Dai ZY, Yi T (2018) Experimental study on mechanical properties and failure modes of low-strength rock samples containing different fissures under uniaxial compression. Eng Fract Mech 197:1–20

    Article  Google Scholar 

  38. Wang DJ, Tang HM, Elsworth D, Wang CY (2019) Fracture evolution in artificial bedded rocks containing a structural flaw under uniaxial compression. Eng Geol 250:130–141

    Article  Google Scholar 

  39. Wang Q, Zhang B, Guo SG, Han JG (2019) Effect of anisotropy, angle, and critical tensile stress and confining pressures on evaluation of shale brittleness index—part 1: methodology and laboratory study. Interpretation 7(3):637–646

    Article  Google Scholar 

  40. Wei DM, Dai F, Xu NW, Liu Y, Zhao T (2018) A novel chevron notched short rod bend method for measuring the mode I fracture toughness of rocks. Eng Fract Mech 190:1–15

    Article  Google Scholar 

  41. Wei DM, Dai F, Xu NW, Zhao T (2016) Stress intensity factors and fracture process zones of ISRM-suggested chevron notched specimens for mode I fracture toughness testing of rocks. Eng Fract Mech 168:174–189

    Article  Google Scholar 

  42. Wei DM, Dai F, Xu NW, Zhao T, Liu Y (2017) An experimental and theoretical assessment of semi-circular bend specimens with chevron and straight-through notches for mode I fracture toughness testing of rocks. Int J Rock Mech Min Sci 99:28–38

    Article  Google Scholar 

  43. Wigand M, Carey JW, Schütt H, Spangenberg E, Erzinger J (2008) Geochemical effects of CO2 sequestration in sandstones under simulated in situ conditions of deep saline aquifers. Appl Geochem 23:2735–2745

    Article  Google Scholar 

  44. Wong LNY (2008) Crack coalescence in molded gypsum and Carrara marble. Degree thesis, Massachusetts Institute of Technology

  45. Wong LNY, Einstein HH (2009) Systematic evaluation of cracking behavior in specimens containing single flaws under uniaxial compression. Int J Rock Mech Min Sci 46:239–249

    Article  Google Scholar 

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

    Article  Google Scholar 

  47. Yang SQ, Huang YH, Tian WL, Zhu JB (2017) An experimental investigation on strength, deformation and crack evolution behavior of sandstone containing two oval flaws under uniaxial compression. Eng Geol 217:35–48

    Article  Google Scholar 

  48. Yang SQ, Jing HW (2011) Strength failure and crack coalescence behavior of brittle sandstone samples containing a single fissure under uniaxial compression. Int J Fract 168:227–250

    Article  Google Scholar 

  49. Yong S, Kaiser PK, Loew S (2013) Rock mass response ahead of an advancing face in faulted shale. Int J Rock Mech Min Sci 60:301–311

    Article  Google Scholar 

  50. Zhang XM (2010) Experimental study on anisotropic strength properties of sandstone. Electron J Geotech Eng 15:1325–1335

    Google Scholar 

  51. Zhang XP, Wong LNY (2013) Loading rate effects on cracking behavior of flaw-contained specimens under uniaxial compression. Int J Fract 180:93–110

    Article  Google Scholar 

  52. Zhang XP, Zhang Q (2017) Distinction of crack nature in brittle rock-like materials: a numerical study based on moment tensors. Rock Mech Rock Eng 50:2837–2845

    Article  Google Scholar 

  53. Zhang Q, Zhang XP (2019) The crack nature analysis of primary and secondary cracks: a numerical study based on moment tensors. Eng Fract Mech 210:70–82

    Article  Google Scholar 

Download references

Acknowledgements

This research was supported by Regional Joint Fund for Basic and Applied Basic Research Fund of Guangdong Province (2019A1515110836). The opinions expressed in this paper are those of the authors and not of the funding agencies.

Author information

Authors and Affiliations

  1. Key Laboratory of Transportation Tunnel Engineering, Ministry of Education, Southwest Jiaotong University, Chengdu, 610031, Sichuan, China

    Guowen Xu

  2. Department of Civil and Environmental Engineering, Colorado School of Mines, Golden, CO, 80401, USA

    Guowen Xu

  3. Department of Civil and Environmental Engineering, University of California, Los Angeles, USA

    Xiongyu Hu

  4. Sichuan Provincial Transport Department Highway Planning Survey Design and Research Institute, Chengdu, 610041, Sichuan, China

    Rui Tang

  5. Guangzhou Institute of Building Science Co., Ltd., Guangzhou, 510440, China

    Zhenkun Hou

Authors
  1. Guowen Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiongyu Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rui Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhenkun Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiongyu Hu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

See Tables 2, 3, 4, 5 and 6.

Table 2 The relationship between the number of AE events and AE magnitudes for rock with flaw angle of 0°
Full size table
Table 3 The relationship between the number of AE events and AE magnitudes for rock with flaw angle of 30°
Full size table
Table 4 The relationship between the number of AE events and AE magnitudes for rock with flaw angle of 60°
Full size table
Table 5 The relationship between the number of AE events and AE magnitudes for rock with flaw angle of 90°
Full size table
Table 6 The relationship between the number of AE events and AE magnitudes for rock with flaw angle of − 30°
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, G., Hu, X., Tang, R. et al. Fracture evolution of transversely isotropic rocks with a pre-existing flaw under compression tests based on moment tensor analysis. Acta Geotech. 17, 169–203 (2022). https://doi.org/10.1007/s11440-021-01214-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-021-01214-9

Keywords

Search

Navigation