Abstract
Jointed rock masses with different orientations and spacings are widely exposed in rock engineering applications, such as underground caverns, slopes, and tunnels, which significantly influence the rock engineering stability and mechanical behavior of the rock masses. To better evaluate the mechanical response of the jointed rock masses during the engineering excavation period, an equivalent constitutive model for the jointed rock masses was established based on the joint compliance tensor (JCT) and was adopted to analyze the excavation-induced mechanical performance of Jinping II hydropower station underground caverns. First, the calculation method of the joint compliance tensor and equivalent elastic compliance matrix of the rock masses containing multiple joint sets was established considering the deformation characteristics of the joint system comprehensively based on the Oda fracture tensor theory and linear superposition principle. Second, an equivalent constitutive model for the jointed rock masses was established considering the joint spacing and connectivity. Finally, combined with the field investigation and monitoring data, the mechanical mechanism of unloading failure of the jointed rock masses in Jinping II hydropower station underground caverns was analyzed using the proposed model and numerical simulation.
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Acknowledgments
The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (No. U1965205).
References
Adhikary, D., and A. Dyskin. 1998. “A continuum model of layered rock masses with non-associative joint plasticity.” Int. J. Numer. Anal. Methods Geomech. 22: 245–261. https://doi.org//10.1002/(SICI)1096-9853(199804)22:4<245::AIDNAG916>3.0.CO;2-R.
Aladejare, A. E., and Y. Wang. 2018. “Influence of rock property correlation on reliability analysis of rock slope stability: From property characterization to reliability analysis.” Geosci. Front. 9 (6): 1639–1648. https://doi.org/10.1016/j.gsf.2017.10.003.
Amadei, B., and R. E. Goodman. 1981. “A 3D constitutive relation for fractured rock masses.” In Proc., Int. Symp. on the Mechanical Behavior of Structured Media, 249–268. Ottawa, Canada: Carleton University.
Anagnostou, G. 1993. “A model for swelling rock in tunnelling.” Rock Mech. Rock Eng. 26 (4): 307–331. https://doi.org/10.1007/bf01027115.
Aubertin, M., L. Li, and R. Simon. 2000. “A multiaxial stress criterion for short- and long-term strength of isotropic rock media.” Int. J. Rock Mech. Min. Sci. 37 (8): 1169–1193. https://doi.org/10.1016/S1365-1609(00)00047-2.
Barron, N., and B. T. Shen. 2018. “Extension strain and rock strength limits for deep tunnels, cliffs, mountain walls and the highest mountains.” Rock Mech. Rock Eng. 51: 3945–3962. https://doi.org/10.1016/j.jrmge.2016.11.004.
Chang, L., H. Konietzky, and T. Frühwirt. 2019. “Strength anisotropy of rock with crossing joints: Results of physical and numerical modeling with gypsum models.” Rock Mech. Rock Eng. 52: 2293–2317. https://doi.org//10.1007/s00603-018-1714-8.
Chen, L., J. F. Shao, and H. W. Huang. 2010. “Coupled elastoplastic damage modeling of anisotropic rocks.” Comput. Geotech. 37: 187–194. https://doi.org//10.1016/j.compgeo.2009.09.001.
Chen, S. H., and P. Egger. 1999. “Three dimensional elasto-viscoplastic finite element analysis of reinforced rock masses and its application.” Int. J. Numer. Anal. Methods Geomech. 23 (1): 61–78. https://doi.org/10.1002/(SICI)1096-9853(199901)23:1%3C61::AID-NAG958%3E3.0.CO;2-V.
Chen, X., Z. Liao, and X. Peng. 2012. “Deformability characteristics of jointed rock masses under uniaxial compression.” Int. J. Min. Sci. Technol. 22: 213–221. https://doi.org//10.1016/j.ijmst.2011.08.012.
Chen, Y. F., H. K. Zheng, M. Wang, J. M. Hong, and C. B. Zhou. 2015. “Excavation-induced relaxation effects and hydraulic conductivity variations in the surrounding rocks of a large-scale underground powerhouse cavern system.” Tunnelling Underground Space. Technol. 49: 253–267. https://doi.org/10.1016/j.tust.2015.05.007.
Chen, Y. F., C. B. Zhou, and Y. Q. Sheng. 2007. “Formulation of strain-dependent hydraulic conductivity for a fractured rock mass.” Int. J. Rock Mech. Min. Sci. 44: 981–996. https://doi.org/10.1016/j.ijrmms.2006.12.004.
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.
Cundall, P. A. 1971. “A computer model for simulating progressive large-scale movement in blocky rock systems.” In Vol. 1 of Proc., Int. Symp. on Rock Fracture, 8–11. Nancy, France: School of Engineering Geology.
Cundall, P. A. 1988. “Formulation of a three-dimensional distinct element model—Part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 25 (3): 107–116. https://doi.org/10.1016/0148-9062(88)91214-4.
Das, A. J., P. K. Mandal, P. S. Paul, R. K. Sinha, and S. Tewari. 2019. “Assessment of the strength of inclined coal pillars through numerical modelling based on the ubiquitous joint model.” Rock Mech. Rock Eng. 52: 3691–3717. https://doi.org/10.1007/s00603-019-01826-4.
Do, T. N., and J. H. Wu. 2020. “Simulation of the inclined jointed tock mass behaviors in a mountain tunnel excavation using DDA.” Comput. Geotech. 117: 103249. https://doi.org//10.1016/j.compgeo.2019.103249.
Dyskin, A. V. 1999. “On the role of stress fluctuations in brittle fracture.” Int. J. Fract. 100: 29–53. https://doi.org/10.1023/A:1018664101433.
Feng, X. T., Z. F. Wang, Y. Y. Zhou, C. X. Yang, P. Z. Pan, and R. Kong. 2021. “Modelling three-dimensional stress-dependent failure of hard rocks.” Acta Geotech. 16: 1647–1677. https://doi.org/10.1007/s11440-020-01110-8.
Goodman, R. E., R. L. Taylor, and T. L. Brekke. 1968. “A model for the mechanics of jointed rock.” J. Soil Mech. Found. Div. 94 (3): 637–659. https://doi.org//10.1061/JSFEAQ.000800310.1061/jsfeaq.0001133.
Hart, R., P. A. Cundall, and J. Lemos. 1988. “Formulation of a three-dimensional distinct element model—Part II. Mechanical calculations for motion and interaction of a system composed of many polyhedral blocks.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 25 (3): 117–125. https://doi.org/10.1016/0148-9062(88)91215-6.
Hauseux, P., E. Roubin, D. M. Seyedi, and J. B. Colliat. 2016. “FE modelling with strong discontinuities for 3D tensile and shear fractures: Application to underground excavation.” Comput. Methods Appl. Mech. Eng. 309: 269–287. https://doi.org/10.1016/j.cma.2016.05.014.
Hoek, E., and P. Marinos. 2000. “Predicting tunnel squeezing problems in weak heterogeneous rock mass.” Tunnels Tunnelling Int. 32 (11): 45–51.
Hudson, J. A., J. W. Cosgrove, K. Kemppainen, and E. Johansson. 2011. “Faults in crystalline rock and estimation of their mechanical properties at the Olkiluoto site, western Finland.” Eng. Geol. 117: 246–258. https://doi.org/10.1016/j.enggeo.2010.11.004.
Itasca Consulting Group. 2011. Fast Lagrangian analysis of continua in 3 dimensions, user’s guide. Itasca Flac3D V5.0. Minneapolis: Itasca Consulting Group.
Jiang, Q., X. T. Feng, J. L. Chen, C. S. Zhang, and S. L. Huang. 2008. “Nonlinear inversion of 3D initial geostress field in Jinping II hydropower station region.” Rock Soil Mech. 29 (11): 3003–3010. https://doi/org/10.10.16285/j.rsm.2008.11.015.
Jiang, Q., X. T. Feng, Y. H. Hatzor, X. J. Hao, and S. J. Li. 2014. “Mechanical anisotropy of columnar jointed basalts: An example from the Baihetan hydropower station, China.” Eng. Geol. 175: 35–45. https://doi.org/10.1016/j.enggeo.2014.03.019.
Kaiser, P. K., and M. Cai. 2012. “Design of rock support system under rockburst condition.” J. Rock Mech. Geotech. Eng. 4: 215–227. https://doi.org/10.3724/SP.J.1235.2012.00215.
Kim, J., C. Kim, G. Kim, I. Kim, Q. Abbas, and J. Lee. 2021. “Probabilistic tunnel collapse risk evaluation model using analytical hierarchy process (AHP) and Delphi survey technique.” Tunnelling Underground Space Technol. 120: 104262. https://doi.org/10.1016/j.tust.2021.104262.
Kumar, V., V. Gupta, I. Jamir, and S. L. Chattoraj. 2019. “Evaluation of potential landslide damming: Case study of Urni landslide, Kinnaur, Satluj valley, India.” Geosci. Front. 10 (2): 753–767. https://doi.org/10.1016/j.gsf.2018.05.004.
Lekhnitskii, S. G., P. Fern, and J. J. Brandstatter. 1964. “Theory of elasticity of an anisotropic elastic body.” Phys. Today 17 (1): 84. https://doi.org/10.1063/1.3051394.
Lemos, J. V., R. D. Hart, and P. A. Cundall. 1985. “A generalized distinct element program for modelling jointed rock mass.” In Proc., Symp. International Society of Rock Mechanics, 335–343. Lapland: Swedish Rock Engineering Research Foundation.
Li, S. J., M. Z. Zheng, S. L. Qiu, Z. B. Yao, J. F. Zhou, and P. Z. Pan. 2021. “Analysis of disaster characteristics and long-term in-situ mechanical response of excavation tunnel in Jinping Underground Laboratory of China.” J. Tsin. Univ. (Sci. Technol.) 61 (8): 842–852. https://doi.org//10.16511/j.cnki.qhdxxb.2021.26.015.
Nova, R. 1980. “The failure of transversely isotropic rocks in triaxial compression.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 17: 325–332. https://doi.org//10.1016/0148-9062(80)90515-X.
Oda, M. 1982. “Fabric tensor for discontinuous geological material.” Soils Found. 13 (1): 1–9. https://doi.org/10.3208/sandf1972.22.4_96.
Pariseau, W. G. 2012. “Finite element approach to caving in stratified, jointed rock masses.” Int. J. Rock Mech. Min. Sci. 53: 94–100. https://doi.org/10.1016/j.ijrmms.2012.05.004.
Park, S. H., and T. Adachi. 2002. “Laboratory model tests and FE analyses on tunneling in the unconsolidated ground with inclined layers.” Tunnelling Underground Space. Technol. 17: 181–193. https://doi.org//10.1016/S0886-7798(02)00003-2.
Rehman, H., A. M. Naji, J. J. Kim, and H. K. Yoo. 2019. “Extension of tunneling quality index and rock mass rating systems for tunnel support design through back calculations in highly stressed jointed rock mass: An empirical approach based on tunneling data from Himalaya.” Tunnelling Underground Space Technol. 85: 29–42. https://doi.org/10.1016/j.tust.2018.11.050.
Sainsbury, B. L., and D. P. Sainsbury. 2017. “Practical use of the ubiquitous-joint constitutive model for the simulation of anisotropic rock masses.” Rock Mech. Rock Eng. 50: 1507–1528. https://doi.org//10.1007/s00603-017-1177-3.
Shen, B., J. Shi, M. Rinne, T. Siren, J. Suikkanen, and S. Kwon. 2016. “Two dimensional displacement discontinuity method for transversely isotropic materials.” Int. J. Rock Mech. Min. Sci. 83: 218–230. https://doi.org//10.1016/j.ijrmms.2016.01.012.
Singh, M., K. S. Rao, and T. Ramamurthy. 2002. “Strength and deformational behaviour of a jointed rock mass.” Rock Mech. Rock Eng. 35: 45–64. https://doi.org//10.1007/s006030200008.
Sitharam, T. G., J. Sridevi, and N. Shimizu. 2001. “Practical equivalent continuum characterization of jointed rock masses.” Int. J. Rock Mech. Min. Sci. 38: 437–448. https://doi.org//10.1016/S1365-1609(01)00010-7.
Tien, Y. M., and M. C. Kuo. 2001. “A failure criterion for transversely isotropic rocks.” Int. J. Rock. Mech. Min. Sci. 38: 399–412. https://doi.org//10.1016/S1365-1609(01)00007-7.
Tien, Y. M., M. C. Kuo, and C. H. Juang. 2006. “An experimental investigation of the failure mechanism of simulated transversely isotropic rocks.” Int. J. Rock Mech. Min. Sci. 43: 1163–1181. https://doi.org//10.1016/j.ijrmms.2006.03.011.
Ulusay, R., M. Ekmekci, E. Tuncay, and N. Hasancebi. 2014. “Improvement of slope stability based on integrated geotechnical evaluations and hydrogeological conceptualisation at a lignite open pit.” Eng. Geol. 181: 261–280. https://doi.org/10.1016/j.enggeo.2014.08.005.
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: 521–530. https://doi.org//10.1016/j.ijrmms.2008.09.011.
Wang, T. T., and T. H. Huang. 2014. “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: 643–657. https://doi.org//10.1007/s00603-013-0405-8.
Wei, J. B., J. H. Deng, D. K. Wang, D. W. Cai, and J. Z. Hu. 2010. “Characterization of deformation and fracture for rock mass in underground powerhouse of Jinping I hydropower station.” Chin. J. Rock Mech. Eng. 29 (6): 1198–1205.
Xu, D. P., X. T. Feng, D. F. Chen, C. Q. Zhang, and Q. X. Fan. 2017. “Constitutive representation and damage degree index for the layered rock mass excavation response in underground caverns.” Tunnelling Underground Space Technol. 64: 133–145. https://doi.org/10.1016/j.tust.2017.01.016.
Xu, D. P., X. Huang, S. J. Li, H. S. Xu, S. L. Qiu, H. Zheng, and Q. Jiang. 2021. “Predicting the excavation damaged zone within brittle surrounding rock masses of deep underground caverns using a comprehensive approach integrating in situ measurements and numerical analysis.” Geosci. Front. 13 (2): 101273. https://doi.org/10.1016/j.gsf.2021.101273.
Yang, W., Q. Zhang, P. G. Ranjith, R. Yu, G. Luo, and C. Huang. 2019. “A damage mechanical model applied to analysis of mechanical properties of jointed rock masses.” Tunnelling Underground Space Technol. 84: 113–128. https://doi.org//10.1016/j.tust.2018.11.004.
Yoshida, H., and H. Horii. 2004. “Micromechanics-based continuum model for a jointed rock mass and excavation analyses of a large-scale cavern.” Int. J. Rock Mech. Min. Sci. 41 (1): 119–145. https://doi.org//10.1016/s1365-1609(03)00080-7.
Zhao, J. S., X. T. Feng, Q. Jiang, and Y. Y. Zhou. 2018. “Microseismicity monitoring and failure mechanism analysis of rock masses with weak interlayer zone in underground intersecting chambers: A case study from the Baihetan hydropower station, China.” Eng. Geol. 245: 44–60. https://doi.org/10.1016/j.enggeo.2018.08.006.
Zhou, W. Y., Y. G. Liu, and J. D. Zhao. 2003. “Multi-potential based discontinuous bifurcation model for jointed rock masses and its application.” Comput. Methods Appl. Mech. Eng. 192: 3569–3584. https://doi.org/10.1016/S0045-7825(03)00356-6.
Zhou, Y. Y., X. T. Feng, D. P. Xu, and Q. X. Fan. 2017. “An enhanced equivalent continuum model for layered rock mass incorporating bedding structure and stress dependence.” Int. J. Rock Mech. Min. Sci. 97: 75–98. https://doi.org//10.1016/j.ijrmms.2017.06.006.
Zhou, Y. Y., D. P. Xu, K. Liu, and D. F. Chen. 2021. “Understanding the failure mechanism of a large underground cavern in steeply dipping layered rock mass using an enhanced ubiquitous-joint model.” Bull. Eng. Geol. Environ. 80: 4621–4638. https://doi.org//10.1007/s10064-021-02213-6.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 23 • Issue 1 • January 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jan 21, 2022
Accepted: Aug 8, 2022
Published online: Nov 4, 2022
Published in print: Jan 1, 2023
Discussion open until: Apr 4, 2023
ASCE Technical Topics:
- Constitutive relations
- Construction engineering
- Construction methods
- Engineering fundamentals
- Excavation
- Geomechanics
- Geotechnical engineering
- Joints
- Mathematics
- Methodology (by type)
- Models (by type)
- Numerical models
- Rock masses
- Rock mechanics
- Spacing
- Structural engineering
- Structural members
- Structural systems
- Structures (by type)
- Underground structures
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