Skip to main content
SpringerLink
Log in

New true-triaxial rock strength criteria considering intrinsic material characteristics

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

A reasonable strength criterion should reflect the hydrostatic pressure effect, minimum principal stress effect, and intermediate principal stress effect. The former two effects can be described by the meridian curves, and the last one mainly depends on the Lode angle dependence function. Among three conventional strength criteria, i.e. Mohr–Coulomb (MC), Hoek–Brown (HB), and Exponent (EP) criteria, the difference between generalized compression and extension strength of EP criterion experience a firstly increase then decrease process, and tends to be zero when hydrostatic pressure is big enough. This is in accordance with intrinsic rock strength characterization. Moreover, the critical hydrostatic pressure \(I_\mathrm{c}\) corresponding to the maximum difference of between generalized compression and extension strength can be easily adjusted by minimum principal stress influence parameter K. So, the exponent function is a more reasonable meridian curves, which well reflects the hydrostatic pressure effect and is employed to describe the generalized compression and extension strength. Meanwhile, three Lode angle dependence functions of \(L_{{\mathrm{MN}}}\), \(L_{{\mathrm{WW}}}\), and \(L_{{\mathrm{YMH}}}\), which unconditionally satisfy the convexity and differential requirements, are employed to represent the intermediate principal stress effect. Realizing the actual strength surface should be located between the generalized compression and extension surface, new true-triaxial criteria are proposed by combining the two states of EP criterion by Lode angle dependence function with a same lode angle. The proposed new true-triaxial criteria have the same strength parameters as EP criterion. Finally, 14 groups of triaxial test data are employed to validate the proposed criteria. The results show that the three new true-triaxial exponent criteria, especially the Exponent Willam-Warnke criterion (EPWW) criterion, give much lower misfits, which illustrates that the EP criterion and \(L_{{\mathrm{WW}}}\) have more reasonable meridian and deviatoric function form, respectively. The proposed new true-triaxial strength criteria can provide theoretical foundation for stability analysis and optimization of support design of rock engineering.

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

Similar content being viewed by others

References

  1. Mohr, O.: Welche Umstände bedingen die Elastizitätsgrenze und den Bruch eines Materials? Zeit. des Ver. Deut. Ing. 44, 1524–1530 (1990)

    Google Scholar 

  2. Griffith, A.A.: The phenomena of rupture and flow in solids. Philos. Trans. R. Soc. A Lond. 221, 163–198 (1920)

    Article  Google Scholar 

  3. Hoek, E., Carranza-Torres, C.T., Corkum, B.: Hoek–Brown failure criterion—2002 edition. In: Proceedings of the 5th North American Rock Mechanics Symposium and 17th Tunnelling Association of Canada Conference, Toronto, Canada, July 7–10 (2002)

  4. You, M.Q.: True-triaxial strength criteria for rock. Int. J. Rock Mech. Min. Sci. 46, 115–127 (2009)

    Article  Google Scholar 

  5. Mogi, K.: Experimental Rock Mechanics. Taylor & Francis, New York (2006)

    Google Scholar 

  6. Michelis, P.: Polyaxial yielding of granular rock. Eng. Mech. 111, 1049–1066 (2011)

    Article  Google Scholar 

  7. Takahashi, M., Koide, H.: Effect of the intermediate principal stress on strength and deformation behavior of sedimentary rocks at the depth shallower than 2000 m. In: Rock at Great Depth, 1. Balkema, Rotterdam, August 30–September 2 (1989)

  8. Chang, C., Hairnson, B.: True triaxial strength and deformability of the German Continental Deep Drilling Program (KTB) deep hole amphibolite. Geophys. Res. 105, 18999–19013 (1987)

    Article  Google Scholar 

  9. Sriapai, T., Walsri, C., Fuenkajorn, K.: True-triaxial compressive strength of Maha Sarakham salt. Int. J. Rock Mech. Min. Sci. 61, 256–265 (2013)

    Google Scholar 

  10. Hosein, R.: New empirical polyaxial criterion for rock strength. Int. J. Rock Mech. Min. Sci. 48, 922–931 (2011)

    Article  Google Scholar 

  11. Lu, D.C., Du, X.L.: Research on nonlinear strength and failure criterion of rock material. Chin. J. Rock Mech. Eng. 32, 2394–2408 (2013)

    Google Scholar 

  12. Zhang, Q., Wang, S.L., Ge, X.R., et al.: A modified Mohr–Coulomb strength criterion considering rock mass intrinsic material strength factorization. Min. Sci. Technol. 20, 701–706 (2010)

    Google Scholar 

  13. Lee, Y.K., Pietruszczak, S., Choi, B.H.: Failure criteria for rocks based on smooth approximations to Mohr–Coulomb and Hoek–Brown failure functions. Int. J. Rock Mech. Min. Sci. 56, 146–160 (2012)

    Google Scholar 

  14. Singh, M., Raj, A., Singh, B.: Modified Mohr–Coulomb criterion for non-linear triaxial and polyaxial strength of intact rocks. Int. J. Rock Mech. Min. Sci. 48, 546–555 (2011)

    Article  Google Scholar 

  15. Yu, M.H.: Twin Shear Theory and Its Application. Science Press, Beijing (1998)

    Google Scholar 

  16. Zhang, L.Y., Zhu, H.H.: Three-dimensional Hoek–Brown strength criterion for rocks. J. Geotech. Geoenviron. Eng. ASCE 133, 1128–1135 (2007)

    Article  Google Scholar 

  17. Zhang, Q., Zhu, H.H., Zhang, L.Y.: Modification of a generalized three-dimensional Hoek–Brown strength criterion. Int. J. Rock Mech. Min. Sci. 59, 80–96 (2013)

    Google Scholar 

  18. Jiang, H., Wang, X.W., Xie, Y.L.: New strength criteria for rocks under polyaxial compression. Can. Geotech. J. 48, 1233–1245 (2011)

  19. Benz, T., Schwab, R., Kauther, R.A., et al.: A Hoek–Brown criterion with intrinsic material strength factorization. Int. J. Rock Mech. Min. Sci. 45, 210–222 (2008)

    Article  Google Scholar 

  20. Benz, T., Schwab, R.: A quantitative comparison of six rock failure criteria. Int. J. Rock Mech. Min. Sci. 45, 1176–1186 (2008)

    Article  Google Scholar 

  21. Liolios, P., Exadaktylos, G.: Comparison of a hyperbolic failure criterion with established failure criteria for cohesive-frictional materials. Int. J. Rock Mech. Min. Sci. 63, 12–26 (2013)

    Google Scholar 

  22. Colmenares, L.B., Zoback, M.D.: A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks. Int. J. Rock Mech. Min. Sci. 39, 695–729 (2002)

    Article  Google Scholar 

  23. Al-Ajmi, A.M., Zimmerman, R.W.: Relation between the Mogi and the Coulomb failure criteria. Int. J. Rock Mech. Min. Sci. 42, 431–439 (2005)

    Article  Google Scholar 

  24. Desai, C.S., Somasundaram, S., Frantziskonis, G.: A hierarchical approach for constitutive modelling of geologic materials. Int. J. Numer. Anal. Met. 10, 225–257 (1986)

    Article  MATH  Google Scholar 

  25. Argyris, J.H., Faust, G., Szimmat, J., et al.: Recent development in the finite element analysis of pressure container reactor vessel. Nucl. Eng. Des. 28, 42–75 (1974)

    Article  Google Scholar 

  26. Bardet, J.P.: Lode dependences for isotropic pressure sensitive elastoplastic materials. J. Appl. Mech. 57, 498–506 (1990)

    Article  Google Scholar 

  27. Jiang, J., Pietruszczak, S.: Convexity of smooth yield surface of friction materials. Comput. Geotech. 5, 51–63 (1988)

    Article  Google Scholar 

  28. Lade, P.V., Duncan, J.M.: Elastoplastic stress–strain theory for cohesionless soil. J. Geotech. Eng. Div. 101, 1037–1053 (1975)

    Google Scholar 

  29. Matsuoka, H., Nakai, T.: Stress-deformation and strength characteristics of soil under three different principal stress. Proc. Jpn. Soc. Civ. Eng. 232, 59–70 (1974)

    Article  Google Scholar 

  30. Willam, K.J., Warnke, E.P.: Constitutive model for the triaxial behavior of concrete. In: International Association for Bridge and Structural Engineering, Seminar on Concrete Structure Subjected to Triaxial Stresses, Bergamo, Italy, May 17–19 (1974)

  31. Haimson, B., Chang, C.: A new true triaxial cell for testing mechanical properties of rock, and its use to determine rock strength and deformability of Westerly granite. Int. J. Rock Mech. Min. Sci. 37, 285–296 (2000)

    Article  Google Scholar 

  32. Wang, R.R., Kemen, J.M.R.: A New Empirical Failure Criterion for Rock Under Polyaxial Compressive Stresses. In: The 35th U.S. Symposium on Rock Mechanics, Reno, Nevada, June 5–7 (1995)

Download references

Acknowledgements

This project was supported by the National Natural Science Foundation of China (Grants 51204168, 51579239), the China Postdoctoral Science Foundation funded project (Grants 2013M531424, 2015M580493), the National Basic Research 973 Program of China (Grants 2013CB036003, 2014CB046306), and the Fundamental Research Funds for the Central Universities (Grant 2012QNB23).

Author information

Authors and Affiliations

  1. State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, 221116, China

    Qiang Zhang, Cheng Li, Xiaowei Quan, Yanning Wang, Liyuan Yu & Binsong Jiang

Authors
  1. Qiang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cheng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaowei Quan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yanning Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Liyuan Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Binsong Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Binsong Jiang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Q., Li, C., Quan, X. et al. New true-triaxial rock strength criteria considering intrinsic material characteristics. Acta Mech. Sin. 34, 130–142 (2018). https://doi.org/10.1007/s10409-017-0723-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-017-0723-2

Keywords

Search

Navigation