Comprehensive Evaluation of Strength Criteria for Granite, Marble, and Sandstone Based on Polyaxial Experimental Tests
Publication: International Journal of Geomechanics
Volume 20, Issue 2
Abstract
Cubic specimens of three rocks—granite, marble, and sandstone, representing very strong rock, moderately strong rock, and weak rock, respectively—were tested under polyaxial stress. The objective was to determine the optimal strength criteria for these rocks by using the polyaxial test data. Experimental results indicated that the failure strength considerably depended on and for all the rocks. Seven well-known rock-strength criteria were employed to examine the true-triaxial data with regard to the predictability in practical applications, comparison between the best-fitting functions (experimental data) and theoretical (predicted) solutions, stress trajectories on the deviatoric plane, and stress trajectories on the meridian plane and space. A detailed analysis and comparison of these criteria showed that the Mogi–Coulomb criterion, modified Wiebols–Cook criterion, and modified Lade criterion provided a better prediction of the polyaxial strength for the three rocks in most cases, which is attributed to the high dependence and sensitivity of the selected rocks. The Mogi 1971 and 1967 criteria could not be correlated to the strength parameters (cohesion and frictional angle) and failed to predict the real strength values of an in situ rock mass without complex polyaxial compression tests. Furthermore, the stress trajectories on the deviatoric plane illustrated their disadvantages in theoretical interpretation and numerical implementation. The inferiority of the Mohr–Coulomb criterion and Drucker–Prager (DP) criterion in describing the rock strength under polyaxial stress was verified by the higher deviation between the theoretical (predicted) strength values and experimental strength values. The nonconformity between the stress trajectories and experimental data for the Mohr–Coulomb criterion and DP criterion on the meridian plane and in the space validates the preceding viewpoint.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors acknowledge the financial support of the State Key Research Development Program of China (2016 YFC0600706), the Key projects of National Natural Science Foundation (Grant No. 41630642), and the National Natural Science Foundation of China (Grants Nos. 51474250 and 51774326). Kun Du was supported by the Natural Science Foundation of Hunan Province, China (Grant No. 2017JJ3390), the China Postdoctoral Science Foundation (Grant No. 2016M602432), and the Key Laboratory of Deep Coal Mine Excavation Response and Disaster Prevention and Control at Anhui University of Science and Technology (Grant No. KLDCMERDPC15104).
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.
Al-Ajmi, A. M., and R. W. Zimmerman. 2006. “Stability analysis of vertical boreholes using the Mogi–Coulomb failure criterion.” Int. J. Rock Mech. Min. Sci. 43 (8): 1200–1211. https://doi.org/10.1016/j.ijrmms.2006.04.001.
Alexeev, A., V. Revva, L. Bachurin, and I. Prokhorov. 2008. “The effect of stress state factor on fracture of sandstones under true triaxial loading.” Int. J. Fract. 149 (1): 1–10. https://doi.org/10.1007/s10704-008-9214-6.
Bresler, B., and K. S. Pister. 1957. “Failure of plain concrete under combined stresses.” Trans. Am. Soc. Civ. Eng. 122: 1049–1068.
Brown, E. T., and E. Hoek. 1978. “Trends in relationships between measured in-situ, stresses and depth.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 15 (4): 211–215. https://doi.org/10.1016/0148-9062(78)91227-5.
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., and B. C. Haimson. 2000. “True triaxial strength and deformability of the German Continental Deep Drilling Program (KTB) deep hole amphibolite.” J. Geophys. Res. Solid Earth 105 (88): 18999–19013. https://doi.org/10.1029/2000JB900184.
Chang, C., and B. C. Haimson. 2012. “A failure criterion for rocks based on true triaxial testing.” Rock Mech. Rock Eng. 45 (6): 1007–1010. https://doi.org/10.1007/s00603-012-0280-8.
Chen, Z. H., L. G. Tham, M. R. Yueng, and P. K. K. Lee. 2003. “Numerical simulation on damage and failure of brittle rocks under different confining pressures.” Int. J. Geomech. 3 (2): 266–273. https://doi.org/10.1061/(ASCE)1532-3641(2003)3:2(266).
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.
Cui, J., H. Hao, Y. C. Shi, X. B. Li, and K. Du. 2017. “Experimental study of concrete damage under high hydrostatic pressure.” Cem. Concr. Res. 100 (Oct): 140–152. https://doi.org/10.1016/j.cemconres.2017.06.005.
Drucker, D. C., and W. Prager. 1952. “Soil mechanics and plastic analysis or limit design.” Q. Appl. Math. 10 (2): 157–165. https://doi.org/10.1090/qam/48291.
Du, K., R. Su, M. Tao, C. Yang, A. Momeni, and S. Wang. 2019. “Specimen shape and cross-section effects on the mechanical properties of rocks under uniaxial compressive stress.” Bull. Eng. Geol. Environ. https://doi.org/10.1007/s10064-019-01518-x.
Du, K., M. Tao, X. B. Li, and J. Zhou. 2016. “Experimental study of slabbing and rockburst induced by true-triaxial unloading and local dynamic disturbance.” Rock Mech. Rock Eng. 49 (9): 3437–3453. https://doi.org/10.1007/s00603-016-0990-4.
Duan, K., C. Y. Kwok, and X. D. Ma. 2017. “DEM simulations of sandstone under true triaxial compressive tests.” Acta Geotech. 12 (3): 495–510. https://doi.org/10.1007/s11440-016-0480-6.
Ewy, R. T. 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. J. Chen, D. Y. Li, S. T. Hu, W. P. Huang, and B. Li. 2019a. “Analysis of fractures of a hard rock via unloading of central hole with different sectional shapes.” Energy Sci. Eng. https://doi.org/10.1002/ese3.432.
Feng, F., X. B. Li, R. Jamal, D. X. Peng, D. Y. Li, and K. Du. 2019b. “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.
Feng, F., X. B. Li, and D. Y. Li. 2017. “Modeling of failure characteristics of rectangular hard rock influenced by sample height-to-width ratios: A finite/discrete element approach.” C.R. Mec. 345 (5): 317–328. https://doi.org/10.1016/j.crme.2017.03.001.
Haimson, B. C., 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.
Hajiabdolmajid, V., P. K. Kaiser, and C. D. Martin. 2002. “Modelling brittle failure of rock.” Int. J. Rock Mech. Min. Sci. 39 (6): 731–741. https://doi.org/10.1016/S1365-1609(02)00051-5.
He, P. F., P. H. S. W. Kulitilake, X. X. Yang, D. Q. Liu, and M. C. He. 2018. “Detailed comparison of nine intact rock failure criteria using polyaxial intact coal strength data obtained through PFC3D simulations.” Acta Geotech. 13 (2): 419–445.
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.
Jiang, H. 2018. “Simple three-dimensional Mohr-Coulomb criteria for intact rocks.” Int. J. Rock Mech. Min. Sci. 105 (May): 145–159. https://doi.org/10.1016/j.ijrmms.2018.01.036.
Lade, P. V. 1977. “Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces.” Int. J. Solids Struct. 13 (11): 1019–1035. https://doi.org/10.1016/0020-7683(77)90073-7.
Li, L., P. K. K. Lee, Y. Tsui, L. G. Tham, and C. A. Tang. 2003. “Failure process of granite.” Int. J. Geomech. 3 (1): 84–98. https://doi.org/10.1061/(ASCE)1532-3641(2003)3:1(84).
Li, X. B., K. Du, and D. Y. Li. 2015. “True triaxial strength and failure modes of cubic rock specimens with unloading the minor principal stress.” Rock Mech. Rock Eng. 48 (6): 2185–2196. https://doi.org/10.1007/s00603-014-0701-y.
Li, X. B., F. Feng, and D. Y. Li. 2017. “Numerical simulation of rock failure under static and dynamic loading by splitting test of circular ring.” Eng. Fract. Mech. 53 (11): 184–201. https://doi.org/10.3901/JME.2017.11.184.
Li, X. B., F. Feng, D. Y. Li, K. Du, P. G. Ranjith, and R. Jamal. 2018. “Failure characteristics of granite influenced by sample height-to-width ratios and intermediate principal stress under true-triaxial unloading conditions.” Rock Mech. Rock Eng. 51 (5): 1321–1345.
Liu, X. W., Q. S. Liu, L. Wei, and X. Huang. 2017. “Improved strength criterion and numerical manifold method for fracture initiation and propagation.” Int. J. Geomech. 17 (5): E4016007. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000676.
Ma, X. D., and B. C. 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.
Ma, X. D., J. W. Rudnicki, and B. C. Haimson. 2017a. “The application of a Matsuoka-Nakai-Lade-Duncan failure criterion to two porous sandstones.” Int. J. Rock Mech. Min. Sci. 92 (Feb): 9–18. https://doi.org/10.1016/j.ijrmms.2016.12.004.
Ma, X. D., J. W. Rudnicki, and B. C. Haimson. 2017b. “Failure characteristics of two porous sandstones subjected to true triaxial stresses: Applied through a novel loading path.” J. Geophys. Res. Solid Earth 122 (4): 2525–2540. https://doi.org/10.1002/2016JB013637.
Manouchehrian, A., and M. Cai. 2015. “Simulation of unstable rock failure under unloading conditions.” Can. Geotech. J. 53 (1): 22–34.
Michelis, P. 1985. “Polyaxial yielding of granular rock.” J. Eng. Mech. 111 (8): 1049–1066. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:8(1049).
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. 1971. “Fracture and flow of rocks under high triaxial compression.” J. Geophys. Res. 76 (5): 1255–1269. https://doi.org/10.1029/JB076i005p01255.
Mogi, K. 2007. Experimental rock mechanics. London: CRC Press.
Nadai, A., and P. G. Hodge. 1950. Vol. 1 of Theory of flow and fracture of solids. New York: McGraw-Hill.
Pakzad, R., S. Wang, and S. Scott. 2018. “Numerical study of the failure response and fracture propagation for rock specimens with preexisting flaws under compression.” Int. J. Geomech. 18 (7): 04018070. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001172.
Takahashi, M., and H. Koide. 1989. “Effect of the intermediate principal stress on strength and deformation behavior of sedimentary rocks at the depth shallower than 2000m.” In Rock at great depth, edited by V. Maury and D. Fourmaintraux, 19–26. Rotterdam, Netherlands: A.A. Balkema.
Vachaparampil, A., and A. Ghassemi. 2017. “Failure characteristics of three shales under true-triaxial compression.” Int. J. Rock Mech. Min. Sci. 100 (Dec): 151–159. https://doi.org/10.1016/j.ijrmms.2017.10.018.
Wang, F., B. Y. Jiang, S. J. Chen, and M. Z. Ren. 2019a. “Surface collapse control under thick unconsolidated layers by backfilling strip mining in coal mines.” Int. J. Rock Mech. Min. Sci. 113 (Jan): 268–277. https://doi.org/10.1016/j.ijrmms.2018.11.006.
Wang, F., J. L. Xu, and J. L. Xie. 2019b. “Effects of arch structure in unconsolidated layers on fracture and failure of overlying strata.” Int. J. Rock Mech. Min. Sci. 114 (Feb): 141–152. https://doi.org/10.1016/j.ijrmms.2018.12.016.
Weng, L., X. B. Li, X. Y. Shang, and X. F. Xie. 2018. “Fracturing behavior and failure in hollowed granite rock with static compression and coupled static–dynamic loads.” Int. J. Geomech. 18 (6): 04018045. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001132.
Wiebols, G. A., and N. G. W. Cook. 1968. “An energy criterion for the strength of rock in polyaxial compression.” Int. J. Rock. Mech. Min. 5 (6): 529–549. https://doi.org/10.1016/0148-9062(68)90040-5.
You, M. Q. 2009. “True-triaxial strength criteria for rock.” Int. J. Rock Mech. Min. Sci. 46 (1): 115–127. https://doi.org/10.1016/j.ijrmms.2008.05.008.
Yu, M. H. 2002. “A unified failure criterion for rock material.” Int. J. Rock Mech. Min. 39 (8): 975–989. https://doi.org/10.1016/S1365-1609(02)00097-7.
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).
Zhang, X. W., X. T. Feng, X. C. Li, B. Haimson, and K. Suzuki. 2017. “ISRM suggested method for determining stress–strain curves for rocks under true triaxial compression.” Rock Mech. Rock Eng. 50 (10): 2847. https://doi.org/10.1007/s00603-017-1282-3.
Zhao, J. H., N. Jiang, L. M. Yin, and L. Y. Bai. 2019. “The effects of mining subsidence and drainage improvements on a waterlogged area.” B. Eng. Geol. Environ. 78 (5): 3815–3831. https://doi.org/10.1007/s10064-018-1356-9.
Zhou, S. H. 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.
Zuo, Y. J., T. Xu, Y. B. Zhang, and Y. P. Zhang. 2012. “Numerical study of zonal disintegration within a rock mass around a deep excavated tunnel.” Int. J. Geomech. 12 (4): 471–483. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000155.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 20 • Issue 2 • February 2020
Copyright
©2019 American Society of Civil Engineers.
History
Received: Jun 20, 2018
Accepted: May 30, 2019
Published online: Nov 30, 2019
Published in print: Feb 1, 2020
Discussion open until: Apr 30, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.