A Damage Constitutive Model for a Jointed Rock Mass under Triaxial Compression
Publication: International Journal of Geomechanics
Volume 23, Issue 6
Abstract
Due to the different structural characteristics and in situ environment, jointed rock masses encounter different failure mechanisms. Because of the joints, jointed rock masses show peculiar characteristics such as anisotropy and weakening. To describe the deformation and failure mechanism in jointed rock masses, a novel damage constitutive model of rock mass is proposed here considering the geometric parameters and mechanical properties of joints. A total damage variable is derived on the basis of the strain equivalence hypothesis, which combines the Weibull statistical damage theory for the strength of the rock elements and the fracture mechanics model for joints. This new damage variable reflects the coupled damage inflicted by two damage states, one is initial damage induced by prefabricated joints and the other is joint damage and rock mesoscopic damage under loading. The damage evolution path revealed by the new damage variable corresponds to the evolution of mechanical properties and behaviors induced by changes in the rock mass structure. Afterward, the computational formulation scheme for the model parameters is deduced using the extremum method. The model parameters, m and F0, have a clear physical meaning. The parameter m describes the ductility–brittleness characteristics of jointed rock masses, and F0 reflects the level of strength. This model describes the effect of joints and strain on the evolution of rock mass damage, model parameters, deformation, and failure characteristics. The mechanical behavior of rock mass described by the damage model and the change law of model parameters are consistent with the published experimental results.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors are grateful for financial support from the National Natural Science Foundation of China (Nos. 12172280, 42177144, and 41907259) and the Project Supported by the Natural Science Foundation of Shaanxi Province of China (2020JZ-53).
References
Alejano, L. R., and A. Bobet. 2012. “Drucker–Prager criterion.” Rock Mech. Rock Eng. 45 (6): 995–999. https://doi.org/10.1007/s00603-012-0278-2.
Asadizadeh, M., M. F. Hossaini, M. Moosavi, H. Masoumi, and P. G. Ranjith. 2019. “Mechanical characterisation of jointed rock-like material with non-persistent rough joints subjected to uniaxial compression.” Eng. Geol. 260: 105224. https://doi.org/10.1016/j.enggeo.2019.105224.
Bahaaddini, M., G. Sharrock, and B. K. Hebblewhite. 2013. “Numerical investigation of the effect of joint geometrical parameters on the mechanical properties of a non-persistent jointed rock mass under uniaxial compression.” Comput. Geotech. 49: 206–225. https://doi.org/10.1016/j.compgeo.2012.10.012.
Boon, C. W., G. T. Houlsby, and S. Utili. 2014. “Designing tunnel support in jointed rock masses via the DEM.” Rock Mech. Rock Eng. 48 (2): 603–632. https://doi.org/10.1007/s00603-014-0579-8.
Bustamante, R., and K. R. Rajagopal. 2017. “A nonlinear model for describing the mechanical behaviour of rock.” Acta Mech. 229 (1): 251–272. https://doi.org/10.1007/s00707-017-1968-3.
Cao, W., Z. Fang, and X. Tang. 1998. “Study of statistical constitutive model for soft and damage rocks.” Chin. J. Rock Mech. Eng. 17 (6): 628–633.
Chen, J., S. Fan, Q. Xu, and J. Li. 2011. “Study of anisotropic strength criterion considering joint distribution characteristics of rock mass.” Chin. J. Rock Mech. Eng. 30 (2): 313–319.
Chen, S., and C. S. Qiao. 2018. “Composite damage constitutive model of jointed rock mass considering crack propagation length and joint friction effect.” Arab. J. Geosci. 11 (11): 283. https://doi.org/10.1007/s12517-018-3643-y.
Cherepanov, G. 1979. Mechanics of brittle fracture. New York: McGraw Hill.
Deng, J., and D. Gu. 2011. “On a statistical damage constitutive model for rock materials.” Comput. Geosci. 37 (2): 122–128. https://doi.org/10.1016/j.cageo.2010.05.018.
Ji, H., J. C. Zhang, W. Y. Xu, R. B. Wang, H. L. Wang, L. Yan, and Z. N. Lin. 2017. “Experimental investigation of the anisotropic mechanical properties of a columnar jointed rock mass: Observations from laboratory-based physical modelling.” Rock Mech. Rock Eng. 50 (7): 1919–1931. https://doi.org/10.1007/s00603-017-1192-4.
Lee, H., and S. Jeon. 2011. “An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression.” Int. J. Solids Struct. 48 (6): 979–999. https://doi.org/10.1016/j.ijsolstr.2010.12.001.
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.
Li, N., W. Chen, P. Zhang, and G. Swoboda. 2001. “The mechanical properties and a fatigue-damage model for jointed rock masses subjected to dynamic cyclical loading.” Int. J. Rock Mech. Min. Sci. 38 (7): 1071–1079. https://doi.org/10.1016/S1365-1609(01)00058-2.
Liu, H., L. Li, S. Zhao, and S. Hu. 2019. “Complete stress–strain constitutive model considering crack model of brittle rock.” Environ. Earth Sci. 78 (21): 629. https://doi.org/10.1007/s12665-019-8643-z.
Liu, H., C. Xing, and L. Zhang. 2016. “A biaxial compression damage constitutive model for rock mass with non-persistent joints.” Rock Soil Mech. 37 (9): 2610–2616.
Liu, H. Y., S. R. Lv, L. M. Zhang, and X. P. Yuan. 2015. “A dynamic damage constitutive model for a rock mass with persistent joints.” Int. J. Rock Mech. Min. Sci. 75: 132–139. https://doi.org/10.1016/j.ijrmms.2015.01.013.
Liu, Y., and F. Dai. 2018. “A damage constitutive model for intermittent jointed rocks under cyclic uniaxial compression.” Int. J. Rock Mech. Min. Sci. 103: 289–301. https://doi.org/10.1016/j.ijrmms.2018.01.046.
Lu, W. B., Z. D. Zhu, Y. X. He, and X. C. Que. 2021. “Strength characteristics and failure mechanism of a columnar jointed rock mass under uniaxial, triaxial, and true triaxial confinement.” Rock Mech. Rock Eng. 54 (5): 2425–2439. https://doi.org/10.1007/s00603-021-02400-7.
Meng, Q. X., H. L. Wang, W. Y. Xu, and Y. L. Chen. 2019. “Numerical homogenization study on the effects of columnar jointed structure on the mechanical properties of rock mass.” Int. J. Rock Mech. Min. Sci. 124: 104127. https://doi.org/10.1016/j.ijrmms.2019.104127.
Phuor, T., I. S. H. Harahap, and C. Y. Ng. 2022a. “Bearing capacity factors for rough conical footing by viscoplasticity finite-element analysis.” Int. J. Geomech. 22 (1): 04021266. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002256.
Phuor, T., I. S. H. Harahap, and C.-Y. Ng. 2022b. “Bearing capacity factors of flat base footing by finite elements.” Int. J. Geomech. 148 (8): 04022062. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002835.
Phuor, T., I. S. H. Harahap, C. Y. Ng, and M. A. M. Al-Bared. 2021. “Development of the skew boundary condition for soil–structure interaction in three-dimensional finite element analysis.” Comput. Geotech. 137: 104264. https://doi.org/10.1016/j.compgeo.2021.104264.
Prudencio, M., and M. Van Sint Jan. 2007. “Strength and failure modes of rock mass models with nonpersistent joints.” Int. J. Rock Mech. Min. Sci. 44 (6): 890–902. https://doi.org/10.1016/j.ijrmms.2007.01.005.
Ranjith, P. G., M. Fourar, S. F. Pong, W. Chian, and A. Haque. 2004. “Characterisation of fractured rocks under uniaxial loading states.” Int. J. Rock Mech. Min. Sci. 41 (3): 43–48. https://doi.org/10.1016/j.ijrmms.2004.03.017.
Ren, J. X., M. C. Yun, X. T. Cao, K. Zhang, Y. Liang, and X. Chen. 2022. “Study on the mechanical properties of saturated red sandstone under freeze–thaw conditions.” Environ. Earth Sci. 81 (14): 376. https://doi.org/10.1007/s12665-022-10503-9.
Saeidi, O., V. Rasouli, R. G. Vaneghi, R. Gholami, and S. R. Torabi. 2014. “A modified failure criterion for transversely isotropic rocks.” Geosci. Front. 5 (2): 215–225. https://doi.org/10.1016/j.gsf.2013.05.005.
Sakurai, S. 2010. “Modeling strategy for jointed rock masses reinforced by rock bolts in tunneling practice.” Acta Geotech. 5 (2): 121–126. https://doi.org/10.1007/s11440-010-0117-0.
Saroglou, H., and G. Tsiambaos. 2008. “A modified Hoek–Brown failure criterion for anisotropic intact rock.” Int. J. Rock Mech. Min. Sci. 45 (2): 223–234. https://doi.org/10.1016/j.ijrmms.2007.05.004.
Shen, Y., G. Yang, T. Rong, H. Jia, M. Wang, and H. Liu. 2017. “Localized damage effects of quasi-sandstone with single fracture and fracture behaviors of joint end under cyclic freezing and thawing.” Chin. J. Rock Mech. Eng. 36 (3): 562–570. https://doi.org/10.13722/j.cnki.jrme.2016.0122.
Singh, J., T. Ramamurthy, and G. Rao. 1989. “Strength anisotropies in rocks.” Indian Geotech. J. 19 (2): 147–166.
Sun, X., J. Li, L. Wang, J. Bai, and Z. Jiang. 2014. “Experimental research on anisotropic mechanical characteristic of samples with single prefabricated joint.” Rock Soil Mech. 35 (Suppl. 1): 29–34+41.
Swoboda, G., X. P. Shen, and L. Rosas. 1998. “Damage model for jointed rock mass and its application to tunnelling.” Comput. Geotech. 22 (3): 183–203. https://doi.org/10.1016/S0266-352X(98)00009-3.
Tiwari, R. P., and K. S. Rao. 2006. “Post failure behaviour of a rock mass under the influence of triaxial and true triaxial confinement.” Eng. Geol. 84 (3–4): 112–129. https://doi.org/10.1016/j.enggeo.2006.01.001.
Wang, J., W. D. Song, and J. X. Fu. 2018. “A damage constitutive model and strength criterion of rock mass considering the dip angle of joints.” Chin. J. Rock Mech. Eng. 37 (10): 2253–2263. https://doi.org/10.13722/j.cnki.jrme.2018.0496.
Wang, T. T., and T. H. Huang. 2013. “Anisotropic deformation of a circular tunnel excavated in a rock mass containing sets of ubiquitous joints: Theory analysis and numerical modeling.” Rock Mech. Rock Eng. 47 (2): 643–657. https://doi.org/10.1007/s00603-013-0405-8.
Wang, Z., Y. 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.
Xie, H., Y. Ju, and L. Li. 2005. “Criteria for strength and structural failure of rocks based on energy dissipation and energy release principles.” Chin. J. Rock Mech. Eng. 24 (17): 3003–3010.
Xu, C. S., and P. Dowd. 2010. “A new computer code for discrete fracture network modelling.” Comput. Geosci. 36 (3): 292–301. https://doi.org/10.1016/j.cageo.2009.05.012.
Yang, Q., X. Chen, and W. Zhou. 2005. “Anisotropic yield criterion for jointed rock masses based on a two-order damage tensor.” Chin. J. Rock Mech. Eng. 24 (8): 1275–1282.
Yang, S., and Y. Huang. 2017. “An experimental study on deformation and failure mechanical behavior of granite containing a single fissure under different confining pressures.” Environ. Earth Sci. 76 (10): 2–22. https://doi.org/10.1007/s12665-017-6696-4.
Yuan, X., H. Liu, and J. Liu. 2015. “Constitutive model of rock mass with non-persistent joints based on coupling macroscopic and mesoscopic damages.” Rock Soil Mech. 36 (10): 2804–2814. https://doi.org/10.16285/j.rsm.2015.10.009.
Zhang, H., L. Lei, and G. Yang. 2015. “Characteristic and representative model of rock damage process under constant confining stress.” J. China Univ. Min. Technol. 44 (1): 59–63. https://doi.org/10.1007/s11802-015-2374-x.
Zhang, H., and G. Yang. 2010. “Research on damage model of rock under coupling action of freeze–thaw and load.” Chin. J. Rock Mech. Eng. 29 (3): 471–476.
Zhang, H. M., C. Yuan, G. S. Yang, L. Y. Wu, C. Peng, W. J. Ye, Y. J. Shen, and H. Moayedi. 2019. “A novel constitutive modelling approach measured under simulated freeze–thaw cycles for the rock failure.” Eng. Comput. 37 (1): 779–792. https://doi.org/10.1007/s00366-019-00856-4.
Zhao, H., X. Li, Y. Luo, Q. Dong, and J. Huang. 2017. “Characteristics of elastic wave propagation in jointed rock mass and development of constitutive model by coupling macroscopic and mesoscopic damage.” Rock Soil Mech. 38 (10): 2939–2948. https://doi.org/10.16285/j.rsm.2017.10.022.
Zhao, Y., H. Liu, S. Lu, C. Xing, and L. Zhang. 2015. “3-dimensional compression damage constitutive model of jointed rock mass based on deformation components.” J. Cent. South Univ. (Sci. Technol.) 46 (3): 991–996. https://doi.org/10.11817/j.issn.1672-7207.2015.03.029.
Information & Authors
Information
Published In
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Mar 21, 2022
Accepted: Dec 19, 2022
Published online: Mar 22, 2023
Published in print: Jun 1, 2023
Discussion open until: Aug 22, 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.