Technical Papers
Apr 1, 2019

Novel 3D Failure Criterion for Rock Materials

Publication: International Journal of Geomechanics
Volume 19, Issue 6

Abstract

The failure criterion of rock material has been used in geotechnical engineering to assess the failure behavior of rocks under complicated stress conditions. In the present study, a new failure criterion is proposed; it takes into consideration the influence of intermediate principal stress for rock materials. The general characteristics of failure surface were analyzed, showing that the failure envelopes are convex and smooth everywhere except at the triaxial compression and triaxial tension conditions. A new shape function is presented to approach the failure criterion in the deviatoric plane, and the smoothness and convexity of the criterion is discussed. The new failure criterion is compared with some classic criteria by cross-sectional failure envelopes in the π plane and meridian failure envelopes in the meridian plane, and the advantages of the new three-dimensional (3D) failure criterion are presented. The results show that the new criterion not only inherits the strength characteristic of the Hoek-Brown failure criterion at the triaxial compression condition, but it also predicts failure stress better than other 3D failure criteria for rocks under complicated stress states.

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Acknowledgments

This research was supported by the State Key Research Development Program of China (2016YFC0600705), the National Natural Science Foundation of China (51574219); the Natural Science Foundation of Jiangsu Province (BK20160252); the National Natural Science Foundation of China (51604263).

References

Al-Ajmi, A. M., and R. W. Zimmerman. 2005. “Relation between the Mogi and the Coulomb failure criteria.” Int. J. Rock Mech. Min. Sci. 42 (3): 431–439. https://doi.org/10.1016/j.ijrmms.2004.11.004.
Argyris, C., and D. Schön. 1974. Theory in practice: Increasing professional effectiveness. San Francisco: Jossey Bass.
Benz, T., and R. Schwab. 2008. “A quantitative comparison of six rock failure criteria.” Int. J. Rock Mech. Min. Sci. 45 (7): 1176–1186. https://doi.org/10.1016/j.ijrmms.2008.01.007.
Cai, M. 2008. “Influence of intermediate principal stress on rock fracturing and strength near excavation boundaries—insight from numerical modeling.” Int. J. Rock Mech. Min. Sci. 45 (5): 763–772. https://doi.org/10.1016/j.ijrmms.2007.07.026.
Chang, C. D., and B. Haimson. 2000. “True triaxial strength and deformability of the German Continental Deep Drilling Program (KTB) deep hole amphibolite.” J. Geophys. Res. B: Solid Earth 105 (B8): 8999–9013. https://doi.org/10.1029/2000JB900184.
Colmenares, L. B., and M. D. Zoback. 2002. “A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks.” Int. J. Rock Mech. Min. Sci. 39 (6): 695–729. https://doi.org/10.1016/S1365-1609(02)00048-5.
Gudehus, G. 1973. “Elasto-plastische stoffgleichungen fur trockenen sand.” [In German.] Ingenieur-Archiv. 42 (3): 151–169. https://doi.org/10.1007/BF00533041.
Hoek, E., and E. T. Brown. 1980. “Empirical strength criterion for rock masses.” J. Geotech. Eng. Div. 106 (GT9): 1013–1035.
Hoek, E., C. Carranza-Torres, and B. Corkum, 2002. “Hoek-Brown failure criterion—2002 edition.” In: Proc., 5th North American Rock Mechanics Symp. and 17th Tunnelling Association of Canada Conf.: NARMS-TAC 2002, edited by R. Hammah, 267–271. Toronto: University of Toronto Press.
Hoek, E., P. Marinos, and M. Benissi. 1998. “Applicability of the geological strength index (GSI) classification for very weak and sheared rock masses. The case of the Athens Schist Formation.” Bull. Eng. Geol. Environ. 57 (2): 151–160. https://doi.org/10.1007/s100640050031.
Jiang, H. 2017. “Three-dimensional failure criteria for rocks based on the Hoek-Brown criterion and a general Lode dependence.” Int. J. Geomech. 17 (8): 04017023-1-12. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000900.
Jiang, J., and S. Pietruszczak. 1988. “Convexity of yield loci for pressure sensitive materials.” Comput. Geotech. 5 (1): 51–63. https://doi.org/10.1016/0266-352X(88)90016-X.
Kim, M. K., and P. V. Lade. 1984. “Modelling rock strength in three dimensions.” Int. J. Rock Mech. Min. Sci. 21 (1): 21–33. https://doi.org/10.1016/0148-9062(84)90006-8.
Lade, P., and J. Duncan. 1975. “Elasto-plastic stress–strain theory for cohesionless soil.” J. Geotech. Eng. Div. 101 (10): 1037–1053.
Lee, Y. K., S. Pietruszczak, and B. H. Choi. 2012. “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.
Lin, F. B., and Z. P. Bažant. 1986. “Convexity of smooth yield surface of frictional material.” J. Eng. Mech. 112 (11): 1259–1262. https://doi.org/10.1061/(ASCE)0733-9399(1986)112:11(1259).
Liu, M. D., and B. N. Indraratna. 2011. “General strength criterion for geomaterials including anisotropic effect.” Int. J. Geomech. 11 (3): 251–262. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000082.
Melkoumian, N., S. D. Priest, and S. P. Hunt. 2009. “Further development of the three-dimensional Hoek–Brown yield criterion.” Rock Mech. Rock Eng. 42 (6): 835–847. https://doi.org/10.1007/s00603-008-0022-0.
Mortara, G. 2008. “A new yield and failure criterion for geomaterials.” Géotechnique 58 (2): 125–132. https://doi.org/10.1680/geot.2008.58.2.125.
Pan, X. D., and J. A. Hudson. 1988. “A simplified three dimensional Hoek-Brown yield criterion.” In Proc., Symp. on Rock Mechanics and Power Plants, 95–103. Lisbon, Portugal: International Society for Rock Mechanics and Rock Engineering.
Piccolroaz, A., and D. Bigoni. 2009. “Yield criteria for quasibrittle and frictional materials: A generalization to surfaces with corners.” Int. J. Solids Struct. 46 (20): 3587–3596. https://doi.org/10.1016/j.ijsolstr.2009.06.006.
Priest, S. D. 2012. “Three-dimensional failure criteria based on the Hoek–Brown criterion.” Rock Mech. Rock Eng. 45 (6): 989–993. https://doi.org/10.1007/s00603-012-0277-3.
Singh, B., R. K. Goel, V. K. Mehrotra, S. K. Garg, and M. R. Allu. 1998. “Effect of intermediate principal stress on strength of anisotropic rock Mass.” Tunnelling Underground Space Technol. 13 (1): 71–79. https://doi.org/10.1016/S0886-7798(98)00023-6.
Su, D., Z. L. Wang, and F. Xing. 2009. “A two-parameter expression for failure surfaces.” Comput. Geotech. 36 (3): 517–524. https://doi.org/10.1016/j.compgeo.2008.09.001.
Willam, K. J., and E. P. Warnke. 1975. “Constitutive model for the triaxial behavior of concrete.” In Concrete structures subjected to triaxial stresses 19, III-1. Zurich, Switzerland: International Association of Bridge and Structural Engineers.
Zhang, L. Y., and H. H. Zhu. 2007. “Three-dimensional Hoek-Brown strength criterion for rocks.” J. Geotech. Geoenviron. Eng. 133 (9): 1128–1135. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:9(1128).
Zhou, X. P., Y. D. Shou, Q. H. Qian, and M. H. Yu. 2014. “Three-dimensional nonlinear strength criterion for rock-like materials based on the micromechanical method.” Int. J. Rock Mech. Min. Sci. 72 (Dec): 54–60. https://doi.org/10.1016/j.ijrmms.2014.08.013.
Zienkiewicz, O. C., and G. N. Pande. 1977. “Some useful forms of isotropic yield surfaces for soil and rock mechanics.” In Finite elements in geomechanics, edited by G. Gudehus, 179–190. New York: John Wiley and Sons.

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 19Issue 6June 2019

History

Received: Apr 5, 2018
Accepted: Nov 29, 2018
Published online: Apr 1, 2019
Published in print: Jun 1, 2019
Discussion open until: Sep 1, 2019

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Authors

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Professor, State Key Laboratory for Geomechanics and Deep Underground Engineering, China Univ. of Mining and Technology, Xuzhou, Jiangsu 221008, China. Email: [email protected]
Doctor, State Key Laboratory for Geomechanics and Deep Underground Engineering, China Univ. of Mining and Technology, Xuzhou, Jiangsu 221008, China (corresponding author). Email: [email protected]
Hongmei Cheng [email protected]
Doctor, School of Mechanics and Civil Engineering, China Univ. of Mining and Technology, Xuzhou, Jiangsu 221008, China. Email: [email protected]
Chengzheng Cai [email protected]
Doctor, State Key Laboratory for Geomechanics and Deep Underground Engineering, China Univ. of Mining and Technology, Xuzhou, Jiangsu 221008, China. Email: [email protected]

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