Analytical Model for Failure Strength of Brittle Rocks under Triaxial Compression and Triaxial Extension
Publication: International Journal of Geomechanics
Volume 22, Issue 4
Abstract
Rocks exhibit different failure strengths under triaxial compression and extension. The understanding and quantification of their relationship provide theoretical and practical benefits. Conventional Mohr-type criteria cannot distinguish rock failure strengths under triaxial compression and extension. To overcome this limitation, we present an analytical model based on Mohr failure theory to describe the relationship between the rock failure strengths under triaxial compression and extension in a Mohr plane. Our analytical model indicates that rock failure criteria under both triaxial compression and extension can be expressed in power-law forms. The corresponding strength magnitude and Mohr envelope curvature parameters are analytically determined using measured rock properties from uniaxial tension, uniaxial compression, and equibiaxial compression tests. This model is validated using experimental data of five rock types: granite, marble, basalt, dolomite, and sandstone. Compared with four well-known failure criteria, the proposed model demonstrates the ability to predict the failure strengths of rocks under both triaxial compression and extension.
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References
Aldeeky, H., and O. Al Hattamleh. 2018. “Prediction of engineering properties of basalt rock in Jordan using ultrasonic pulse velocity test.” Geotech. Geol. Eng. 36 (6): 3511–3525. https://doi.org/10.1007/s10706-018-0551-6.
Basu, A., D. A. Mishra, and K. Roychowdhury. 2013. “Rock failure modes under uniaxial compression, Brazilian, and point load tests.” Bull. Eng. Geol. Environ. 72 (3–4): 457–475. https://doi.org/10.1007/s10064-013-0505-4.
Böker, R. 1915. “Die mechanik der bleibenden Formanderung in kristallinisch aufgebauten Körpern.” Ver. Deut. Ing. Mitt. Forsch. 175: 1–51.
Cai, M. 2010. “Practical estimates of tensile strength and Hoek–Brown strength parameter mi of brittle rocks.” Rock Mech. Rock Eng. 43 (2): 167–184. https://doi.org/10.1007/s00603-009-0053-1.
Chang, C., and Haimson, B. 2012. “A failure criterion for rocks based on true triaxial testing.” Rock Mech. Rock Eng. 45 (2): 1007–1010. https://doi.org/10.1007/s00603-012-0280-8.
Colmenares, L., and M. 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.
Corfdir, A., and J. Sulem. 2008. “Comparison of extension and compression triaxial tests for dense sand and sandstone.” Acta Geotech. 3 (3): 241–246. https://doi.org/10.1007/s11440-008-0068-x.
Desai, C., and M. Salami. 1987. “Constitutive model for rocks.” J. Geotech. Eng. 113 (5): 407–423. https://doi.org/10.1061/(ASCE)0733-9410(1987)113:5(407).
Drucker, D. C., and W. Prager. 1952. “Soil mechanics and plastic analysis or limit design.” Q. Appl. Math. 10 (2): 157–165. https://10.1090/QAM/48291.
Ewy, R. 1999. “Wellbore-stability predictions by use of a modified Lade criterion.” SPE Drill Complet. 14 (2): 85–91. https://doi.org/10.2118/56862-PA.
Feng, F., S. Chen, Y. Wang, W. Huang, and Z. Han. 2021. “Cracking mechanism and strength criteria evaluation of granite affected by intermediate principal stresses subjected to unloading stress state.” Int. J. Rock Mech. Min. Sci. 143: 104783. https://doi.org/10.1016/j.ijrmms.2021.104783.
Feng, X., R. Kong, C. Yang, X. Zhang, Z. Wang, Q. Han, and G. Wang. 2020a. “A three-dimensional failure criterion for hard rocks under true triaxial compression.” Rock Mech. Rock Eng. 53 (1): 103–111. https://doi.org/10.1007/s00603-019-01903-8.
Feng, F., X. Li, K. Du, D. Li, J. Rostami, and S. Wang. 2020b. “Comprehensive evaluation of strength criteria for granite, marble, and sandstone based on polyaxial experimental tests.” Int. J. Geomech. 20 (2): 04019155. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001544.
Feng, F., X. Li, J. Rostami, D. Peng, D. Li, and K. Du. 2019. “Numerical investigation of hard rock strength and fracturing under polyaxial compression based on Mogi–Coulomb failure criterion.” Int. J. Geomech. 19 (4): 04019005. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001352.
Haimson, B. 2006. “True triaxial stresses and the brittle fracture of rock.” Pure Appl. Geophys. 163 (5–6): 1101–1130. https://doi.org/10.1007/s00024-006-0065-7.
Haimson, B., and A. Bobet. 2012. “Introduction to suggested methods for failure criteria.” Rock Mech. Rock Eng. 45 (6): 973–974. https://doi.org/10.1007/s00603-012-0274-6.
Haimson, B., and C. Chang. 2000. “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 (1–2): 285–296. https://doi.org/10.1016/S1365-1609(99)00106-9.
Handin, J., H. C. Heard, and J. N. Magouirk. 1967. “Effect of the intermediate principal stress on the failure of limestone, dolomite, and glass at different temperature and strain rate.” J. Geophys. Res. 72 (2): 611–640. https://doi.org/10.1029/JZ072i002p00611.
Hoek, E. 1983. “Strength of jointed rock masses.” Géotechnique 33 (3): 187–223. https://doi.org/10.1680/geot.1983.33.3.187.
Hoek, E., and E. Brown. 1997. “Practical estimates of rock mass strength.” Int. J. Rock Mech. Min. Sci. 34 (8): 1165–1186. https://doi.org/10.1016/S1365-1609(97)80069-X.
Hoek, E., C. Carranza-Torres, and B. Corkum. 2002. “Hoek–Brown failure criterion—2002 edition.” In Vol. 1 of The Proc., of NARMS-Tac, 267–273. Toronto: University of Toronto Press.
Jaeger, J. C., N. G. W. Cook, and R. Zimmerman. 2007. Fundamentals of rock mechanics. 4th ed. Oxford, UK: Blackwell.
Lee, H., and B. Haimson. 2011. “True triaxial strength, deformability, and brittle failure of granodiorite from the San Andreas Fault Observatory at depth.” Int. J. Rock Mech. Min. Sci. 48 (7): 1199–1207. https://doi.org/10.1016/j.ijrmms.2011.08.003.
Ma, X., and B. Haimson. 2016. “Failure characteristics of two porous sandstones subjected to true triaxial stresses.” J. Geophys. Res. Solid Earth 121 (9): 6477–6498. https://doi.org/10.1002/2016JB012979.
Mehranpour, M., and P. Kulatilake. 2016. “Comparison of six major intact rock failure criteria using a particle flow approach under true-triaxial stress condition.” Geomech. Geophys. Geo-Energy Geo-Resour. 2 (4): 203–229. https://doi.org/10.1007/s40948-016-0030-6.
Mogi, K. 1967. “Effect of the intermediate principal stress on rock failure.” J. Geophys. Res. 72 (20): 5117–5131. https://doi.org/10.1029/JZ072i020p05117.
Mogi, K. 2007. Experimental rock mechanics. London: Taylor & Francis Group.
Paterson, M. S., and T. F. Wong. 2005. Experimental rock deformation—The brittle field. 2nd ed. Heidelberg, Germany: Springer.
Ramana, Y., and L. Sarma. 1987. “Split-collar tensile test grips for short rock cores.” Eng. Geol. 23 (3–4): 255–261. https://doi.org/10.1016/0013-7952(87)90092-5.
Ramsey, J., and F. Chester. 2004. “Hybrid fracture and the transition from extension fracture to shear fracture.” Nature 428 (6978): 63–66. https://doi.org/10.1038/nature02333.
Sharpe, J. 2017. “Failure of rock at low mean stress.” Master’s thesis, Dept. of Civil, Environmental, and Geo-Engineering, Univ. of Minnesota.
Shen, J., R. Jimenez, M. Karakus, and C. Xu. 2014. “A simplified failure criterion for intact rocks based on rock type and uniaxial compressive strength.” Rock Mech. Rock Eng. 47 (2): 357–369. https://doi.org/10.1007/s00603-013-0408-5.
von Kármán, T. 1911. “Festigkeitsversuche unter allseitigem druck.” Zeit. Ver. Deut. Ing. 55 (42): 1749–1759.
Wu, W., and D. Kolymbas. 1991. “On some issues in triaxial extension tests.” Geotech. Test. J. 14 (3): 276–287. https://doi.org/10.1520/GTJ10572J.
You, M. 2010. “Mechanical characteristics of the exponential strength criterion under conventional triaxial stresses.” Int. J. Rock Mech. Sci. 47 (2): 195–204. https://10.1016/j.ijrmms.2009.12.006.
Yu, H., K. Ng, D. Grana, V. Alvarado, J. Kaszuba, and E. Campbell. 2020. “A generalized power-law criterion for rocks based on Mohr failure theory.” Int. J. Rock Mech. Min. Sci. 128: 104274. https://doi.org/10.1016/j.ijrmms.2020.104274.
Zeng, B., D. Huang, S. Ye, F. Chen, T. Zhu, and Y. Tu. 2019. “Triaxial extension tests on sandstone using a simple auxiliary apparatus.” Int. J. Rock Mech. Min. Sci. 120: 29–40. https://doi.org/10.1016/j.ijrmms.2019.06.006.
Zeng, F., Y. Li, and J. F. Labuz. 2018. “Paul–Mohr–Coulomb failure criterion for geomaterials.” J. Geotech. Geoenviron. Eng. 144 (2): 06017018. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001829.
Zhou, S. 1994. “A program to model the initial shape and extent of borehole breakout.” Comput. Geosci. 20 (7–8): 1143–1160. https://doi.org/10.1016/0098-3004(94)90068-X.
Zhu, W., L. G. J. Montesi, and T. F. Wong. 1997. “Shear-enhanced compaction and permeability reduction: Triaxial extension tests on porous sandstone.” Mech. Mater. 25 (3): 199–214. https://doi.org/10.1016/S0167-6636(97)00011-2.
Zoback, M. D. 2007. Reservoir geomechanics. Cambridge, UK: Cambridge University Press.
Zoback, M. D., and J. D. Byerlee. 1976. “Effect of high-pressure deformation on permeability of Ottawa sand.” AAPG Bull. 60 (9): 1531–1542.
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Published In
International Journal of Geomechanics
Volume 22 • Issue 4 • April 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jul 22, 2021
Accepted: Nov 30, 2021
Published online: Feb 2, 2022
Published in print: Apr 1, 2022
Discussion open until: Jul 2, 2022
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