A Micromechanics-Based Model of Direct Tensile Fracture in Brittle Rocks under Confining Pressure
Publication: International Journal of Geomechanics
Volume 23, Issue 5
Abstract
A novel micromechanics-based model in brittle rocks is presented during the confined tensile fracture. This model is formulated by using the stress intensity factor of crack under distinct loading modes in the fracture mechanics theory. The confined tensile fracture mechanisms with and without initial crack friction are established. The development process from the confined tensile fracture without initial crack friction to that with initial crack friction is studied. The stress–strain constitutive relationship describing the transformation mechanism from the unloading of axial stress at a compressive state to the loading of axial stress at a tensile state is also studied during the confined tensile fracture. The tension–compression transformation mechanism codetermined by the friction of the initial crack, the angle of initial crack inclination, and the confining pressure is proven. With the decrease of the angle of initial crack inclination or the increase of the confining pressure, the confined tensile fracture constitutive model tends to be dominated by the tensile fracture mechanism with initial crack friction. The confined tensile fracture of brittle rocks tends to happen at the larger angle of initial crack inclination. The reasonableness of the presented model is checked by contrasting the experimental data. Effects of the friction, density, inclination angle and size of the initial crack, and the confining pressure on the tensile relation curve of strain and stress, the tensile relation curve of crack length and stress, the tensile elastic modulus, the tensile stress of crack initiation, and the tensile strength are discussed.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by the Scientific Research Program of Beijing Municipal Education Commission (KM202110016014), the National Natural Science Foundation of China (Grant No. 51708016), and the Pyramid Talent Training Project of Beijing University of Civil Engineering and Architecture (Grant No. JDYC20200307).
References
Aliha, M. R. M., P. Ebneabbasi, H. Karimi, and E. Nikbakht. 2021. “A novel test device for the direct measurement of tensile strength of rock using ring shape sample.” Int. J. Rock Mech. Min. Sci. 139: 104649. https://doi.org/10.1016/j.ijrmms.2021.104649.
Ashby, M. F., and C. G. Sammis. 1990. “The damage mechanics of brittle solids in compression.” Pure Appl. Geophys. PAGEOPH 133 (3): 489–521. https://doi.org/10.1007/BF00878002.
Ban, Y., X. Fu, Q. Xie, and J. Duan. 2020. “Time-sensitivity mechanism of rock stress memory properties under tensile stress.” J. Rock Mech. Geotech. Eng. 12 (3): 528–540. https://doi.org/10.1016/j.jrmge.2019.12.012.
Budiansky, B., and R. J. O’Connel. 1976. “Elastic moduli of a cracked solid.” Int. J. Solids. Struct. 12: 81–97. https://doi.org/10.1016/0020-7683(76)90044-5.
Cai, M., P. K. Kaiser, Y. Tasaka, T. Maejima, H. Morioka, and M. Minami. 2004. “Generalized crack initiation and crack damage stress thresholds of brittle rock masses near underground excavations.” Int. J. Rock Mech. Min. Sci. 41 (5): 833–847. https://doi.org/10.1016/j.ijrmms.2004.02.001.
Carmona, S., and A. Aguado. 2012. “New model for the indirect determination of the tensile stress–strain curve of concrete by means of the Brazilian test.” Mater. Struct. 45 (10): 1473–1485. https://doi.org/10.1617/s11527-012-9851-0.
Chen, Z. H., C. A. Tang, and R. Q. Huang. 1997. “A double rock sample model for rockbursts.” Int. J. Rock Mech. Min. Sci. 34 (6): 991–1000. https://doi.org/10.1016/S1365-1609(97)80008-1.
Gerd, M. 2019. “Application of the cluster analysis and time statistic of acoustic emission events from tensile test of a cylindrical rock salt specimen.” Eng. Fract. Mech. 210: 84–94. https://doi.org/10.1016/j.engfracmech.2018.05.039.
Hawkes, I., M. Mellor, and S. Gariepy. 1973. “Deformation of rocks under uniaxial tension.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 10 (6): 493–507. https://doi.org/10.1016/0148-9062(73)90001-6.
Kaklis, K., S. Maurigiannakis, Z. Agioutantis, and C. Istantso. 2009. “Influence of specimen shape on the indirect tensile strength of transversely isotropic Dionysos marble using the three-point bending test.” Strain. 45 (5): 393–399. https://doi.org/10.1111/j.1475-1305.2008.00560.x.
Li, H., J. Li, B. Liu, S. Li, and X. Xia. 2013. “Direct tension test for rock material under different strain rates at quasi-static loads.” Rock Mech. Rock Eng. 46: 1247–1254. https://doi.org/10.1007/s00603-013-0406-7.
Li, X., X. Che, H. Yan, and C. Qi. 2022. “A micro–macro method for evaluating progressive and direct tensile fractures in brittle rocks.” Geomech. Geophys. Geo. 8: 133. https://doi.org/10.1007/s40948-022-00450-x.
Li, X., C. Ma, C. Qi, and Z. Shao. 2020. “Crack velocity- and strain rate-dependent dynamic compressive responses in brittle solids.” Theor. Appl. Fract. Mech. 105: 102420. https://doi.org/10.1016/j.tafmec.2019.102420.
Li, X., C. Qi, Z. Shao, and C. Ma. 2018. “Evaluation of strength and failure of brittle rock containing initial cracks under lithospheric conditions.” Acta. Geophys. 66 (2): 141–152. https://doi.org/10.1007/s11600-018-0123-4.
Li, X., and Z. Shao. 2016. “Investigation of macroscopic brittle creep failure caused by microcrack growth under step loading and unloading in rocks.” Rock Mech. Rock Eng. 49 (7): 2581–2593. https://doi.org/10.1007/s00603-016-0953-9.
Liao, Z. Y., J. B. Zhu, and C. A. Tang. 2019. “Numerical investigation of rock tensile strength determined by direct tension, Brazilian and three-point bending tests.” Int. J. Rock Mech. Min. Sci. 115: 21–32. https://doi.org/10.1016/j.ijrmms.2019.01.007.
Liu, Z., H. Zhou, W. Zhang, S. Xie, and J. Shao. 2019. “A new experimental method for tensile property study of quartz sandstone under confining pressure.” Int. J. Rock Mech. Min. Sci. 123: 104091. https://doi.org/10.1016/j.ijrmms.2019.104091.
Okubo, S., and K. Fukui. 1996. “Complete stress–strain curves for various rock types in uniaxial tension.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 33 (6): 549–556. https://doi.org/10.1016/0148-9062(96)00024-1.
Saadat, M., and A. Taheri. 2020. “Modelling micro-cracking behaviour of granite during direct tensile test using cohesive GBM approach.” Eng. Fract. Mech. 239: 107297. https://doi.org/10.1016/j.engfracmech.2020.107297.
Su, F., and P. Pan. 2018. “Experimental study on confining pressure effect of hard rock indirect tensile test and mechanical mechanism.” IOP Conf. Ser. Mater. Sci. Eng. 423: 012018. https://doi.org/10.1088/1757-899X/423/1/012018.
Tada, H., P. C. Paris, and G. R. Irwin. 1985. The stress analysis of cracks handbook. St. Louis: Del Res.
Tao, R., M. Sharifzadeh, Y. Zhang, and X.-T. Feng. 2020. “Analysis of mafic rocks microstructure damage and failure process under compression test using quantitative scanning electron microscopy and digital images processing.” Eng. Fract. Mech. 231: 107019. https://doi.org/10.1016/j.engfracmech.2020.107019.
Thomas, R. N., A. Paluszny, and R. W. Zimmerman. 2020. “Growth of three-dimensional fractures, arrays, and networks in brittle rocks under tension and compression.” Comput. Geotech. 121: 103447. https://doi.org/10.1016/j.compgeo.2020.103447.
Yang, L., Y. Jiang, S. Li, and B. Li. 2013. “Experimental and numerical research on 3D crack growth in rocklike material subjected to uniaxial tension.” J. Geotech. Geoenviron. Eng. 139 (10): 1781–1788. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000917.
Zhang, Y., H. Deng, J. Deng, C. Liu, and B. Ke. 2019. “Peridynamics simulation of crack propagation of ring-shaped specimen like rock under dynamic loading.” Int. J. Rock Mech. Min. Sci. 123: 104093. https://doi.org/10.1016/j.ijrmms.2019.104093.
Zhang, Y., Q.-Y. Zhang, X.-Y. Zhou, and W. Xiang. 2021. “Direct tensile tests of red sandstone under different loading rates with the self-developed centering device.” Geotech. Geol. Eng. 39: 709–718. https://doi.org/10.1007/s10706-020-01515-y.
Zhou, X.-p. 2004. “Analysis of the localization of deformation and the complete stress–strain relation for mesoscopic heterogeneous brittle rock under dynamic uniaxial tensile loading.” Int. J. Solids. Struct. 41 (5–6): 1725–1738. https://doi.org/10.1016/j.ijsolstr.2003.07.007.
Zhou, X., Z. Jia, and F. Berto. 2019. “Simulation of cracking behaviours in interlayered rocks with flaws subjected to tension using a phase-field method.” Fatigue. Fract. Eng. Mater. Struct. 42 (8): 1679–1698. https://doi.org/10.1111/ffe.13009.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 23 • Issue 5 • May 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Apr 17, 2022
Accepted: Nov 30, 2022
Published online: Feb 28, 2023
Published in print: May 1, 2023
Discussion open until: Jul 28, 2023
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.