Technical Papers
May 6, 2022

Equivalent Elastic Model and Deformation Characteristics of X-Type Cross-Jointed Rock Mass

Publication: International Journal of Geomechanics
Volume 22, Issue 7

Abstract

The conjugated X-type cross joints are one of the main forms of rock mass in nature. It is a composite geological material with macrodefects like joint fissures, and microdefects like microjoints and microvoids. From the perspective of composite damage, an equivalent elastic model considering macro- and microdefects of rock mass is formulated. First, the micro- and macrodamages caused by cross joint and wing crack propagation are used to build a composite damage model of nonpenetrated cross-jointed rock mass based on the strain equivalence principle. Next, considering the interaction between cross joints and the conditions of wing crack propagation, the stress intensity factor at the tips of cross joints before propagation and that at the tips of wing cracks after propagation are derived, respectively. Third, the macrodamage variables involving the geometric characteristics of cross joints and the friction coefficient of joint surface are derived based on fracture mechanics and strain energy theory. Finally, the proposed model is tested on the samples of similar materials in the cross-jointed rock mass; the interference effect between cross joints is analyzed using digital image correlation technology; the calculated results of the model are compared with the experimental results. The model calculation coincides with the test results, proving the rationality of the model. The model helps understanding the influence law of the interference effect of cross joints on the damage and deformation characteristics of rock mass and has guiding significance for related rock mass engineering practice.

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Acknowledgments

The authors gratefully acknowledge financial support from the National Natural Science Foundation of China (Grant No. 51768025) and the Science and Technology Research Project of the Jiangxi Provincial Department of Education (Grant No. GJJ170562).

References

Ashby, M. F., and C. G. Sammis. 1990. “The damage mechanics of brittle solids in compression.” Pure Appl. Geophys. 133 (3): 489–521. https://doi.org/10.1007/BF00878002.
Cao, R., P. Cao, H. Lin, and X. Fan. 2017. “Experimental and numerical study of the failure process and energy mechanisms of rock-like materials containing cross un-persistent joints under uniaxial compression.” PLoS One 12 (12): e0188646.
Cao, R. H., P. Cao, H. Lin, G. W. Ma, X. Fan, and X. G. Xiong. 2018. “Mechanical behavior of an opening in a jointed rock-like specimen under uniaxial loading: Experimental studies and particle mechanics approach.” Arch. Civ. Mech. Eng. 18 (1): 198–214. https://doi.org/10.1016/j.acme.2017.06.010.
Cao, R. H., and H. Lin. 2017. “Experimental and numerical study of failure behavior and energy mechanics of rock-like materials containing multiple joints.” Adv. Mater. Sci. Eng. 2017: 6460150.
Chen, X., Z. Z. Liao, and X. Peng. 2012. “Deformability characteristics of jointed rock masses under uniaxial compression.” Int. J. Min. Sci. Technol. 22 (2): 213–221. https://doi.org/10.1016/j.ijmst.2011.08.012.
Chen, X., Z. Z. Liao, and X. Peng. 2013. “Cracking process of rock mass models under uniaxial compression.” J. Cent. South Univ. 20 (6): 1661–1678. https://doi.org/10.1007/s11771-013-1660-2.
Chen, S., and C. S. Qiao. 2018. “Composite damage constitutive model of jointed rock mass considering crack propagation length and joint friction effect.” Arabian J. Geosci. 11 (11): 283. https://doi.org/10.1007/s12517-018-3643-y.
Huang, C., and G. Subhash. 2003. “Influence of lateral confinement on dynamic damage evolution during uniaxial compressive response of brittle solids.” J. Mech. Phys. Solids 51 (6): 1089–1105. https://doi.org/10.1016/S0022-5096(03)00002-4.
Huang, Y. H., and S. Q. Yang. 2015. “Discrete element study on strength and failure behavior of jointed sandstone with two sets of cross-joints.” J. China Coal Soc. 40 (s1): 76–84.
KemenyJ, C. N. W. 1986. “Effective moduli, non-linear deformation and strength of a cracked elastic solid.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 23 (2): 107–118. https://doi.org/10.1016/0148-9062(86)90337-2.
Krajcinovic, D., and G. Silva MA. 1982. “Statistical aspects of the continuous damage theory.” Int. J. Solids Struct. 18 (7): 551–562. https://doi.org/10.1016/0020-7683(82)90039-7.
Kulatilake, P. H. S. W., B. Malama, and J. Wang. 2001. “Physical and particle flow modeling of jointed rock block behavior under uniaxial loading.” Int. J. Rock Mech. Min. Sci. 38 (5): 641–657. https://doi.org/10.1016/S1365-1609(01)00025-9.
Lee, S., and G. Ravichandran. 2003. “Crack initiation in brittle solids under multiaxial compression.” Eng. Fract. Mech. 70 (13): 1645–1658. https://doi.org/10.1016/S0013-7944(02)00203-5.
Lemaitre, J. 1985. “A continuous damage mechanics model for ductile fracture.” Trans. ASME J. Eng. Mater. Technol. 107 (107): 83–89. https://www.sci-hub.ren/10.1115/1.3225775.
Liu, D. Y., K. S. Zhu, and J. W. Fan. 1991. “Strength properties of rock mass joints.” J. Chongqing Inst. Archit. Eng. 13 (4): 40–46.
Liu, F., H. Zhang, and X. Du. 2015a. “Hybrid analytical and MLS based NMM for the determination of generalized stress intensity factors.” Math. Probl. Eng. 2015 (1): 1–9.
Liu, H., and X. Yuan. 2015. “A compressive damage constitutive model for rock mass with a set of nonpersistently closed joints under biaxial conditions.” Math. Probl. Eng. 2015 (PT.5): 1–10.
Liu, H. Y. 2018. “Wing-crack initiation angle: A new maximum tangential stress criterion by considering T-stress.” Eng. Fract. Mech. 199: 380–391. https://doi.org/10.1016/j.engfracmech.2018.06.010.
Liu, H. Y., and S. R. Lv. 2019. “A model for the wing crack initiation and propagation of the inclined crack under uniaxial compression.” Int. J. Rock Mech. Min. Sci. 123: 104121. https://doi.org/10.1016/j.ijrmms.2019.104121.
Liu, H. Y., and F. J. Zhu. 2018. “A damage constitutive model for the intermittent cracked rock mass under the planar complicated stress condition.” Curr. Sci. 115 (3): 559–565. https://doi.org/10.18520/cs/v115/i3/559-565.
Liu, X. W., Q. S. Liu, and Y. Chen. 2015b. “Experimental study of effects of fracture type on strength characteristics and failure modes of fractured rock mass.” Rock Soil Mech. 36 (S2): 208–214.
Tang, S. B. 2015. “The effect of T-stress on the fracture of brittle rock under compression.” Int. J. Rock Mech. Min. Sci. 79 (23): 86–98. https://doi.org/10.1016/j.ijrmms.2015.06.009.
Wang, T. T., and T. H. Huang. 2009. “A constitutive model for the deformation of a rock mass containing sets of ubiquitous joints.” Int. J. Rock Mech. Min. Sci. 46 (3): 521–530. https://doi.org/10.1016/j.ijrmms.2008.09.011.
Wang, Y. T., X. P. Zhou, and Y. D. Shou. 2017. “The modeling of crack propagation and coalescence in rocks under uniaxial compression using the novel conjugated bond-based peridynamics.” Int. J. Mech. Sci. 128-129: 614–643. https://doi.org/10.1016/j.ijmecsci.2017.05.019.
Wang, Z. L., Y. C. Li, and J. G. Wang. 2007. “A damage-softening statistical constitutive model considering rock residual strength.” Comput. Geosci. 33 (1): 1–9. https://doi.org/10.1016/j.cageo.2006.02.011.
Weibull, W. 1951. “A statistical distribution function of wide applicability.” J. Appl. Mech. 18: 293–297. https://doi.org/10.1115/1.4010337.
Yang, S., W. Xu, and L. Wei. 2004. “Statistical constitutive model for rock damage under uniaxial compression and its experimental study.” J. Hohai Univ. 32 (2): 200–203.
Yin, D., S. Chen, X. Liu, and H. Ma. 2018. “Simulation study on strength and failure characteristics for granite with a set of cross-joints of different lengths.” Adv. Civ. Eng. 2018: 2384579.
Zhang, B., S. Li, K. Xia, X. Yang, D. Zhang, S. Wang, and J. Zhu. 2016. “Reinforcement of rock mass with cross-flaws using rock bolt.” Tunnelling Underground Space Technol. 51: 346–353. https://doi.org/10.1016/j.tust.2015.10.007.
Zhang, B., S. Li, X. Yang, X. Kaiwen, L. Jiyang, G. Shuai, and W. Shugang. 2019. “The coalescence and strength of rock-like materials containing two aligned X-type flaws under uniaxial compression.” Geomech. Eng. 17 (1): 47–56.
Zhou, X. P., J. Bi, and Q. H. Qian. 2015. “Numerical simulation of crack growth and coalescence in rock-like materials containing multiple pre-existing flaws.” Rock Mech. Rock Eng. 48 (3): 1097–1114. https://doi.org/10.1007/s00603-014-0627-4.
Zhou, X.-P., Y.-X. Zhang, Q.-L. Ha, and K.-S. Zhu. 2008. “Micromechanical modelling of the complete stress–strain relationship for crack weakened rock subjected to compressive loading.” Rock Mech. Rock Eng. 41 (5): 747–769. https://doi.org/10.1007/s00603-007-0130-2.
Zhang, Z. X. 2002. “An empirical relation between mode I fracture toughness and the tensile strength of rock.” Int. J. Rock Mech. Min. Sci. 39 (3): 401–406. https://doi.org/10.1016/S1365-1609(02)00032-1.
Zhao, D., G. Swoboda, and F. Laabmayr. 2004. “Damage mechanics and its application for the design of an underground theater.” Tunnelling Underground Space Technol. 19: 567–575. https://doi.org/10.1016/j.tust.2004.01.004.

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 22Issue 7July 2022

History

Received: Jul 24, 2020
Accepted: Feb 6, 2022
Published online: May 6, 2022
Published in print: Jul 1, 2022
Discussion open until: Oct 6, 2022

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Zhengding Deng [email protected]
Ph.D. Lecturer, School of Architectural and Surveying Engineering, Jiangxi Univ. of Science and Technology, Ganzhou 341000, China. Email: [email protected]
Tongfa Deng [email protected]
Associate Professor, School of Architectural and Surveying Engineering, Jiangxi Univ. of Science and Technology, Ganzhou 341000, China (corresponding author). Email: [email protected]
Professor, School of Architectural and Surveying Engineering, Jiangxi Univ. of Science and Technology, Ganzhou 341000, China. Email: [email protected]
M.D. Student, School of Architectural and Surveying Engineering, Jiangxi Univ. of Science and Technology, Ganzhou 341000, China. Email: [email protected]
Xingxin Zhan [email protected]
M.D. Student, School of Architectural and Surveying Engineering, Jiangxi Univ. of Science and Technology, Ganzhou 341000, China. Email: [email protected]
Associate Professor, School of Architectural and Surveying Engineering, Jiangxi Univ. of Science and Technology, Ganzhou 341000, China. Email: [email protected]

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  • Damage constitutive model and mechanical properties of jointed rock mass under hydro-mechanical coupling, Theoretical and Applied Fracture Mechanics, 10.1016/j.tafmec.2022.103735, 123, (103735), (2023).

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