Skip to main content
SpringerLink
Log in

Detailed comparison of nine intact rock failure criteria using polyaxial intact coal strength data obtained through PFC3D simulations

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

Abstract

Study of intact rock failure criteria is an important topic in rock mechanics. In this study, applicability of nine different intact rock failure criteria is investigated for intact coal strength data. PFC3D modeling was used to simulate the laboratory polyaxial tests for cubic intact coal blocks of side dimension 110 mm under different confining stress combinations. A modified grid search procedure is proposed and used to find the best-fitting parameter values and to calculate the coefficient of determination (R 2) values for each criterion. Detailed comparisons of the nine criteria are made using the following aspects: R 2 values, σ 1 − σ 2 plots for different σ 3, shapes on the deviatoric plane, linearity or nonlinearity on the meridian planes. Through the comparisons of R 2 values, σ 1 − σ 2 plots and meridian lines, the modified Wiebols–Cook and modified Lade criteria were found to fit the intact coal strength data best. The nine failure criteria are categorized into three types based on the appearances on the deviatoric plane.

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
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33
Fig. 34

Similar content being viewed by others

Abbreviations

σ 1, σ 2, σ 3 :

Major, intermediate and minor principal stresses at failure, respectively

σ 1′, σ 2′, σ 3′:

Major, intermediate and minor effective principal stresses at failure, respectively

I 1, I 3 :

First and third invariant of stress tensor

I 1′, I 3′:

Modified first and third invariant of stress tensor

J 2 :

Second invariant of deviatoric stress tensor

σ oct :

Octahedral normal stress or mean stress

τ oct :

Octahedral shear stress

σ m,2 :

(σ 1 + σ 3)/2

σ ci :

Uniaxial compressive strength of the intact rock

σ ti :

Uniaxial tensile strength of the intact rock

σ bi :

Strength of the intact rock under triaxial extension stress state for σ 3 = 0

τ :

Shear stress

σ n :

Normal stress

τ 13 :

Major principal shear stress

τ 12 :

Intermediate principal shear stress or minor principal shear stress

τ 23 :

Intermediate principal shear stress or minor principal shear stress

σ 13 :

Normal stresses acting on the τ 13 plane

σ 12 :

Normal stresses acting on the τ 12 plane

σ 23 :

Normal stresses acting on the τ 23 plane

q :

Material constant determined by a certain function of the coefficient of friction in the W–C criterion

c 0 :

Cohesion of the intact rock

φ :

Internal friction angle of the intact rock

m b :

Hoek–Brown constant for the rock mass

m i :

Hoek–Brown constant for the intact rock

s, a :

Constants depending on the rock mass characteristics

D :

Disturbance factor

GSI :

Geological Strength Index

α, k :

Material constants of the D–P criterion

ρ c , ρ t :

Compressive and tensile meridian on the deviatoric planes

κ :

Material constant depending on the density of the soil in Lade–Duncan criterion (1975)

p a :

Atmospheric pressure

m′, η 1 :

Material constants of the modified Lade criterion (1977)

S :

Material constant related to the cohesion and internal friction angle of the rock in the modified Lade criterion (1999)

η :

Material constant representing the internal friction of the rock

A, B, C :

Parameters in the modified W–C criterion

β :

Constant smaller than 1 in Mogi (1967) criterion

C′:

Parameter related to c 0 and φ in the linear unified failure criterion

δ :

Parameter related to φ in the linear unified failure criterion

b :

Intermediate stress parameter in both linear and nonlinear unified failure criteria

ω :

Ratio of σ ci to σ ti for the intact rock in the linear unified failure criterion

θ :

Lode angle

ρ, ξ :

Abscissa and ordinate of the plots on the meridian planes

References

  1. Benz T, Schwab R (2008) A quantitative comparison of six rock failure criteria. Int J Rock Mech Min 45:1176–1186. doi:10.1016/j.ijrmms.2008.01.007

    Article  Google Scholar 

  2. Bieniawski ZT (1976) Engineering classification in rock engineering. In: Proceedings of the symposium on exploration for rock engineering, Johannesburg. pp 97–106

  3. Brown ET (1970) Strength of models of rock with intermittent joints. J Soil Mech Found Div ASCE 96(6):1935–1949

    Google Scholar 

  4. Colmenares LB, Zoback MD (2002) A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks. Int J Rock Mech Min 39:695–729. doi:10.1016/S1365-1609(02)00048-5

    Article  Google Scholar 

  5. Drucker DC (1973) Plasticity theory strength-differential (SD) phenomenon, and volume expansion in metals and plastics. Metall Trans 4(3):667–673. doi:10.1007/BF02643073

    Article  Google Scholar 

  6. Drucker DC, Prager W (1952) Soil mechanics and plastic analysis or limit design. Q Appl Math 10(2):157–165

    Article  MathSciNet  MATH  Google Scholar 

  7. Ewy RT (1999) Wellbore-stability predictions by use of a modified Lade criterion. SPE Drill Complet 14(2):85–91. doi:10.2118/56862-PA

    Article  Google Scholar 

  8. Garvey R, Ozbay U (2011) Computer-aided calibration of PFC3D coal samples using a genetic algorithm. Continuum and distinct element numerical modeling in geomechanics, Itasca Int. Inc., Minneapolis, MN, USA, pp 493–499

  9. 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. doi:10.1029/JZ072i002p00611

    Article  Google Scholar 

  10. He PF, Kulatilake PHSW, Liu DQ, He MC (2016) Development of a new three-dimensional coal mass strength criterion. Int J Geomech. doi:10.1061/(ASCE)GM.1943-5622.0000741

    Google Scholar 

  11. Hoek E (1968) Brittle failure of rock. In: Stagg KG, Zienkiewicz OC (eds) Rock mechanics in engineering practice. Wiley, New York, pp 99–124

    Google Scholar 

  12. Hoek E, Brown ET (1980) Empirical failure criterion for rock masses. J Geotechn Eng Div ASCE 106(GT9):1013–1035

    Google Scholar 

  13. Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Min 34(8):1165–1186. doi:10.1016/S1365-1609(97)80069-X

    Article  Google Scholar 

  14. Hoek E, Wood D, Shah S (1992) A modified Hoek–Brown criterion for jointed rock masses. In: Hudson JA (ed) Eurock 1992: rock characterization: ISRM symposium, Chester, U.K. Thomas Telford, London, pp 209–213

  15. Hoek E, Kaiser PK, Bawden WF (1995) Support of underground excavations in hard rock. A.A. Balkema, Rotterdam

    Google Scholar 

  16. Hoek E, Carranza-Torres C, Corkum B (2002) Hoek–Brown failure criterion-2002 edition. In: Proceedings of NARMS-Tac conference, Toronto, vol 1, pp 267–273

  17. Itasca (2003) PFC3D user’s manual, version 4.0. Itasca Consulting Group Inc., Minneapolis

    Google Scholar 

  18. Itasca (2008) 3DEC user’s guide. Itasca Consulting Group Inc., Minneapolis

    Google Scholar 

  19. Kulatilake PHSW, Park J, Malama B (2006) A new rock mass failure criterion for biaxial loading conditions. Geotech Geol Eng 24(4):871–888. doi:10.1007/s10706-005-7465-9

    Article  Google Scholar 

  20. Lade PV (1977) Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces. Int J Solids Struct 13(11):1019–1035. doi:10.1016/0020-7683(77)90073-7

    Article  MATH  Google Scholar 

  21. Lade PV, Duncan JM (1975) Elasto-plastic stress-strain theory for cohesionless soil. J Geotech Eng Div ASCE 101(10):1037–1053

    Google Scholar 

  22. Ma X, Rudnicki JW, Haimson BC (2014) True triaxial tests in two porous sandstones: experimental failure characteristics and theoretical prediction. In: Proceedings of 48th US rock mechanics/geomechanics symposium, American Rock Mechanics Association, Minneapolis, MN

  23. Mogi K (1967) Effect of the intermediate principal stress on rock failure. J Geophys Res 72(20):5117–5131. doi:10.1029/JZ072i020p05117

    Article  Google Scholar 

  24. Mogi K (1971) Fracture and flow of rocks under high triaxial compression. J Geophys Res 76(5):1255–1269. doi:10.1029/JB076i005p01255

    Article  Google Scholar 

  25. Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364. doi:10.1016/j.ijrmms.2004.09.011

    Article  Google Scholar 

  26. Singh B, Goel RK, Mehrotra VK, Garg SK, Allu MR (1998) Effect of intermediate principal stress on strength of anisotropic rock mass. Tunn Undergr Space Technol 13(1):71–79

    Article  Google Scholar 

  27. Wang RR, Kemeny JM (1995) A new empirical failure criterion for rock under polyaxial compressive stresses. In: Proceedings of 35th U.S. rock mechanics symposium, American Rock Mechanics Association, Reno, Nevada, pp 453–458

  28. Wiebols GA, Cook NGW (1968) An energy criterion for the strength of rock in polyaxial compression. Int J Rock Mech Min 5(6):529–549. doi:10.1016/0148-9062(68)90040-5

    Article  Google Scholar 

  29. Yu MH (2002) Advances in strength theories for materials under complex stress state in the 20th century. Appl Mech Rev 55(3):169–218. doi:10.1115/1.1472455

    Article  Google Scholar 

  30. Yu MH (2002) A unified failure criterion for rock material. Int J Rock Mech Min 39(8):975–989. doi:10.1016/S1365-1609(02)00097-7

    Article  Google Scholar 

  31. Zhou SH (1994) A program to model the initial shape and extent of borehole breakout. Comput Geosci 20(7/8):1143–1160. doi:10.1016/0098-3004(94)90068-X

    Article  Google Scholar 

Download references

Acknowledgements

The research was funded by the National Institute for Occupational Safety and Health (NIOSH) of the Centers for Disease Control and Prevention (Contract No. 200-2011-39886) and the State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining & Technology, Beijing (Contract No. SKLGDUEK1416).

Author information

Authors and Affiliations

  1. Rock Mass Modeling and Computational Rock Mechanics Laboratories, University of Arizona, Tucson, AZ, 85721, USA

    Peng-fei He, Pinnaduwa H. S. W. Kulatilake & Xu-xu Yang

  2. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology (Beijing), Beijing, 100083, China

    Peng-fei He, Dong-qiao Liu & Man-chao He

  3. Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China

    Peng-fei He

  4. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, China

    Xu-xu Yang

Authors
  1. Peng-fei He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pinnaduwa H. S. W. Kulatilake
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xu-xu Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dong-qiao Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Man-chao He
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pinnaduwa H. S. W. Kulatilake.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

He, Pf., Kulatilake, P.H.S.W., Yang, Xx. et al. Detailed comparison of nine intact rock failure criteria using polyaxial intact coal strength data obtained through PFC3D simulations. Acta Geotech. 13, 419–445 (2018). https://doi.org/10.1007/s11440-017-0566-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-017-0566-9

Keywords

Search

Navigation