Numerical Modeling of Rock Blocks with Nonpersistent Rough Joints Subjected to Uniaxial Compressive and Shear Loadings
Publication: International Journal of Geomechanics
Volume 23, Issue 7
Abstract
Characterizing the mechanical behavior of jointed rocks is important to understand the behavior of structures in rock masses. Jointed rocks can be composed of persistent and nonpersistent joints where the impact of nonpersistent joints requires careful consideration for an accurate rock mass mechanical characterization. Most previous investigations into nonpersistent jointed rocks focused on joints with smooth surfaces, and a few experimental studies focused on nonpersistent rough joints and nothing specific has been reported numerically. Therefore, this study investigated several synthetic jointed rocks with nonpersistent rough joints numerically under uniaxial compressive and shear loadings. The PFC2D-based synthetic rock mass (SRM) approach was adopted to assess the impact of bridge angle (γ) and length (L), joint roughness coefficient (JRC), and normal stress (σn) on the shear strength (τn) and cracking in jointed rocks with nonpersistent rough joints. In addition, the impacts of γ, L, JRC, and joint inclination (θ) on the uniaxial compressive strength (UCS or σcm), elastic modulus (Em), and failure pattern in the jointed blocks were examined numerically. First, several numerical models were developed and verified by the laboratory data, followed by an extensive parametric study to assess the effects of the defined parameters further. The effects of JRC and σn on τn were more pronounced than γ and L due to the formation of interlocking cracks, which could cause significant shear resistance during shear loading. In addition, the numerical results under axial loading revealed that an increase in θ could reduce the deformation modulus and the value of the other parameters, in particular the JRC, could lead to an increase in the strength of jointed samples.
Get full access to this article
View all available purchase options and get full access to this article.
References
Afolagboye, L. O., J. He, and S. Wang. 2017. “Experimental study on cracking behaviour of moulded gypsum containing two non-parallel overlapping flaws under uniaxial compression.” Acta Mech. Sin. 33 (2): 394–405. https://doi.org/10.1007/s10409-016-0624-9.
Amadei, B., and R. E. Goodman. 1981. “A 3D constitutive relation for fractured rock masses.” In Proc., Int. Symp. Mechanical Behaviour of Structured Media, 249–268. Ottawa: Elsevier Scientific.
Asadizadeh, M., M. F. Hossaini, M. Moosavi, H. Masoumi, and P. G. Ranjith. 2019a. “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.
Asadizadeh, M., H. Masoumi, H. Roshan, and A. Hedayat. 2019b. “Coupling Taguchi and response surface methodologies for the efficient characterization of jointed rocks” mechanical properties.” Rock Mech. Rock Eng. 52 (11): 4807–4819. https://doi.org/10.1007/s00603-019-01853-1.
Asadizadeh, M., M. Moosavi, and M. F. Hossaini. 2018a. “Investigation of mechanical behaviour of non-persistent jointed blocks under uniaxial compression.” Geomech. Eng. 14 (1): 29–42.
Asadizadeh, M., M. Moosavi, M. F. Hossaini, and H. Masoumi. 2018b. “Shear strength and cracking process of non-persistent jointed rocks: An extensive experimental investigation.” Rock Mech. Rock Eng. 51 (2): 415–428. https://doi.org/10.1007/s00603-017-1328-6.
Bahaaddini, M. 2017. “Effect of boundary condition on the shear behaviour of rock joints in the direct shear test.” Rock Mech. Rock Eng. 50: 1141–1155. https://doi.org/10.1007/s00603-016-1157-z.
Bahaaddini, M., P. Hagan, R. Mitra, and B. K. Hebblewhite. 2016a. “Numerical study of the mechanical behavior of nonpersistent jointed rock masses.” Int. J. Geomech. 16 (1): 4015035. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000510.
Bahaaddini, M., P. C. Hagan, R. Mitra, and B. K. Hebblewhite. 2014a. “Scale effect on the shear behaviour of rock joints based on a numerical study.” Eng. Geol. 181: 212–223. https://doi.org/10.1016/j.enggeo.2014.07.018.
Bahaaddini, M., P. C. Hagan, R. Mitra, and B. K. Hebblewhite. 2015. “Parametric study of smooth joint parameters on the shear behaviour of rock joints.” Rock Mech. Rock Eng. 48 (3): 923–940. https://doi.org/10.1007/s00603-014-0641-6.
Bahaaddini, M., P. C. Hagan, R. Mitra, and M. H. Khosravi. 2016b. “Experimental and numerical study of asperity degradation in the direct shear test.” Eng. Geol. 204: 41–52. https://doi.org/10.1016/J.ENGGEO.2016.01.018.
Bahaaddini, M., J. Saymontry, H. Masoumi, and P. Hagan. 2014b. “Experimental study of the shear behavior of rock joints under constant normal load and constant normal stiffness conditions.” In Proc., 48th U.S. Rock Mechanics/Geomechanics Symp., 1650–1656. Alexandria, VA: American Rock Mechanics Association (ARMA).
Bahaaddini, M., G. Sharrock, and B. K. Hebblewhite. 2013a. “Numerical direct shear tests to model the shear behaviour of rock joints.” Comput. Geotech. 51: 101–115. https://doi.org/10.1016/j.compgeo.2013.02.003.
Bahaaddini, M., G. Sharrock, and B. K. Hebblewhite. 2013b. “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.
Bahaaddini, M., G. Sharrock, B. K. Hebblewhite, and R. Mitra. 2012. “Statistical analysis of the effect of joint geometrical parameters on the mechanical properties of non-persistent jointed rock masses.” In Proc., 46th US Rock Mechanics/GeoMechanics Symp., 2778–2786. Alexandria, VA: American Rock Mechanics Association (ARMA).
Bandis, S. C., A. C. Lumsden, and N. R. Barton. 1983. “Fundamentals of rock joint deformation.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 20 (6): 249–268. https://doi.org/10.1016/0148-9062(83)90595-8.
Barton, N. 1976. “The shear strength of rock and rock joints.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 13 (9): 255–279. https://doi.org/10.1016/0148-9062(76)90003-6.
Bieniawski, Z. T., and I. Hawkes. 1978. “Suggested methods for determining tensile strength of rock materials.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 15 (3): 99–103. https://doi.org/10.1016/0148-9062(78)90003-7.
Bobet, A. 2000. “The initiation of secondary cracks in compression.” Eng. Fract. Mech. 66 (2): 187–219. https://doi.org/10.1016/S0013-7944(00)00009-6.
Bobet, A., and H. H. Einstein. 1998. “Fracture coalescence in rock-type materials under uniaxial and biaxial compression.” Int. J. Rock Mech. Min. Sci. 35 (7): 863–888. https://doi.org/10.1016/S0148-9062(98)00005-9.
Brady, B. H. G., and E. T. Brown. 2004. “Rock mechanics for underground mining.” In Rock mechanics: For underground mining, 3rd ed. Dordrecht, Netherlands: Springer.
Brown, E. T., and D. H. Trollope. 1970. “Strength of a model of jointed rock.” J. Soil Mech. Found. Div. 96 (2): 685–704. https://doi.org/10.1061/JSFEAQ.0001411.
Cao, P., T. Liu, C. Pu, and H. Lin. 2015. “Crack propagation and coalescence of brittle rock-like specimens with pre-existing cracks in compression.” Eng. Geol. 187: 113–121. https://doi.org/10.1016/j.enggeo.2014.12.010.
Cao, R.-h., P. Cao, H. Lin, C.-z. Pu, and K. Ou. 2016. “Mechanical behavior of brittle rock-like specimens with pre-existing fissures under uniaxial loading: Experimental studies and particle mechanics approach.” Rock Mech. Rock Eng. 49 (3): 763–783. https://doi.org/10.1007/s00603-015-0779-x.
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: 198214. https://doi.org/10.1016/j.acme.2017.06.010.
Cao, R., R. Yao, J. J. Meng, Q. Lin, H. Lin, and S. Li. 2020. “Failure mechanism of non-persistent jointed rock-like specimens under uniaxial loading: Laboratory testing.” Int. J. Rock Mech. Min. Sci. 132 (April). 104341. https://doi.org/10.1016/j.ijrmms.2020.104341.
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 (7): 2293–2317. https://doi.org/10.1007/s00603-018-1714-8.
Cheng, C., X. Chen, and S. Zhang. 2016a. “Multi-peak deformation behavior of jointed rock mass under uniaxial compression: Insight from particle flow modeling.” Eng. Geol. 213: 25–45. https://doi.org/10.1016/j.enggeo.2016.08.010.
Cheng, H., X. Zhou, J. Zhu, and Q. Qian. 2016b. “The effects of crack openings on crack initiation, propagation and coalescence behavior in rock-like materials under uniaxial compression.” Rock Mech. Rock Eng. 49 (9): 3481–3494. https://doi.org/10.1007/s00603-016-0998-9.
Dershowitz, W. S., and H. H. Einstein. 1988. “Characterizing rock joint geometry with joint system models.” Rock Mech. Rock Eng. 21: 21–51. https://doi.org/10.1007/BF01019674.
Einstein, H. H., and R. C. Hirschfeld. 1973. “Model studies on mechanics of jointed rock.” J. Soil Mech. Found. Div. 99 (3): 229–248. https://doi.org/10.1061/JSFEAQ.0001859.
Einstein, H. H., R. C. Hirschfeld, R. A. Nelson, and R. W. Bruhn. 1969. “Model studies of jointed-rock behavior.” In Proc., 11th US Symp. Rock Mech. New York: American Institute of Mining, Metallurgical, and Petroleum Engineers Inc.
Fereshtenejad, S., J. Kim, and J.-J. Song. 2021a. “Experimental study on shear mechanism of rock-like material containing a single non-persistent rough joint.” Energies 14 (4): 987. https://doi.org/10.3390/en14040987.
Fereshtenejad, S., J. Kim, and J.-J. Song. 2021b. “Empirical model for shear strength of artificial rock containing a single nonpersistent joint.” Int. J. Geomech. 21 (8): 04021123. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002099.
Gehle, C., and H. K. Kutter. 2003. “Breakage and shear behaviour of intermittent rock joints.” Int. J. Rock Mech. Min. Sci. 40 (5): 687–700. https://doi.org/10.1016/S1365-1609(03)00060-1.
Ghazvinian, A., V. Sarfarazi, W. Schubert, and M. Blumel. 2012. “A study of the failure mechanism of planar non-persistent open joints using PFC2D.” Rock Mech. Rock Eng. 45 (5): 677–693.
Goldstein, M., B. Goosev, N. Pvrogovsky, R. Tulinov, and A. Turovskaya. 1966. “Investigation of mechanical properties of cracked rock.” In Proc., 1st Congress Int. Society for Rock Mechanics. Lisbon, Portugal: National Laboratory of Civil Engineering.
Grasselli, G. 2006. “Manuel Rocha medal recipient shear strength of rock joints based on quantified surface description.” Rock Mech. Rock Eng. 39 (4): 295–314. https://doi.org/10.1007/s00603-006-0100-0.
Guo, J., P. Liu, S. Huang, Y. Qian, and G. Liu. 2020. “Cracking processes and failure modes of rock-like specimens with a set of non-persistent joints.” Geotech. Geol. Eng. 3 (39): 1237–1257.
Huang, C., W. Yang, K. Duan, L. Fang, L. Wang, and C. Bo. 2019. “Mechanical behaviors of the brittle rock-like specimens with multi-non-persistent joints under uniaxial compression.” Constr. Build. Mater. 220: 426–443. https://doi.org/10.1016/j.conbuildmat.2019.05.159.
Huang, Y.-H., S.-Q. Yang, W.-L. Tian, W. Zeng, and L.-Y. Yu. 2016. “An experimental study on fracture mechanical behavior of rock-like materials containing two unparallel fissures under uniaxial compression.” Acta Mech. Sin. 32 (3): 442–455. https://doi.org/10.1007/s10409-015-0489-3.
Itasca Consulting Group. 2022. PFC2D manual. Minneapolis: Itasca.
Ivars, D. M., et al. 2011. “The synthetic rock mass approach for jointed rock mass modelling.” Int. J. Rock Mech. Min. Sci. 48 (2): 219–244. https://doi.org/10.1016/j.ijrmms.2010.11.014.
Jade, S., and T. G. Sitharam. 2003. “Characterization of strength and deformation of jointed rock mass based on statistical analysis.” Int. J. Geomech. 3 (1): 43–54. https://doi.org/10.1061/(ASCE)1532-3641(2003)3:1(43).
Korinets, A., and H. Alehossein. 2002. “Technical note On the initial Non-linearity of compressive stress-strain curves for intact rock.” Rock Mech. Rock Eng. 35 (4): 319–328. https://doi.org/10.1007/s00603-002-0030-4.
Kovari, K., A. Tisa, H. H. Einstein, and J. A. Franklin. 1983. “Suggested methods for determining the strength of rock materials in triaxial compression: Revised version.” Int. J. Rock Mech. Min. Sci. 20 (6): 283–290.
Lajtai, E. Z. 1969. “Shear strength of weakness planes in rock.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 6 (5): 499–515. https://doi.org/10.1016/0148-9062(69)90016-3.
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.
Ma, C., W. Yao, Y. Yao, and J. Li. 2018. “Simulating strength parameters and size effect of stochastic jointed rock mass using DEM method.” KSCE J. Civ. Eng. 22 (12): 4872–4881. https://doi.org/10.1007/s12205-017-1581-y.
Mehrdad, I., H. R. Nejati, K. Goshtasbi, and A. Nazerigivi. 2022. “Effect of brittleness on the micromechanical damage and failure pattern of rock specimens.” Smart Struct. Syst. 29 (4): 535–547. https://doi.org/10.12989/SSS.2022.29.4.535.
Muralha, J., G. Grasselli, B. Tatone, M. Blümel, P. Chryssanthakis, and J. Yujing. 2014. “ISRM suggested method for laboratory determination of the shear strength of rock joints: Revised version.” Rock Mech. Rock Eng. 47 (1): 291–302. https://doi.org/10.1007/s00603-013-0519-z.
Park, C. H., and A. Bobet. 2009. “Crack coalescence in specimens with open and closed flaws: A comparison.” Int. J. Rock Mech. Min. Sci. 46 (5): 819–829. https://doi.org/10.1016/j.ijrmms.2009.02.006.
Park, C. H., and A. Bobet. 2010. “Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression.” Eng. Fract. Mech. 77 (14): 2727–2748. https://doi.org/10.1016/j.engfracmech.2010.06.027.
Park, J.-W., and J.-J. Song. 2009. “Numerical simulation of a direct shear test on a rock joint using a bonded-particle model.” Int. J. Rock Mech. Min. Sci. 46 (8): 1315–1328. https://doi.org/10.1016/j.ijrmms.2009.03.007.
Patton, F. D. 1966. “Multiple modes of shear failure in rock.” In Proc., 1st Congress Int. Society for Rock Mechanics, 509–513. Lisbon, Portugal: International Society for Rock Mechanics and Rock Engineering.
Pierce, M., P. Cundall, D. Potyondy, and D. Mas Ivars. 2007. “A synthetic rock mass model for jointed rock.” In Proc., 1st CA–US Rock Mech. Symp., 341–349. Alexandria, VA: American Rock Mechanics Association (ARMA).
Potyondy, D. O. 2012. “A flat-jointed bonded-particle material for hard rock.” In Proc., 46th US Rock Mech. Symp. Alexandria, VA: American Rock Mechanics Association (ARMA).
Potyondy, D. O., and P. A. Cundall. 2004. “A bonded-particle model for rock.” Int. J. Rock Mech. Min. Sci. 41 (8): 1329–1364. https://doi.org/10.1016/j.ijrmms.2004.09.011.
Prudencio, M., and M. Van Sint Jan. 2007. “Strength and failure modes of rock mass models with non-persistent joints.” Int. J. Rock Mech. Min. Sci. 44 (6): 890–902. https://doi.org/10.1016/j.ijrmms.2007.01.005.
Saeb, S., and B. Amadei. 1992. “Modelling rock joints under shear and normal loading.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 29: 267–278. https://doi.org/10.1016/0148-9062(92)93660-C.
Sagong, M., and A. Bobet. 2002. “Coalescence of multiple flaws in a rock-model material in uniaxial compression.” Int. J. Rock Mech. Min. Sci. 39 (2): 229–241. https://doi.org/10.1016/S1365-1609(02)00027-8.
Sarfarazi, V., A. Ghazvinian, W. Schubert, M. Blumel, and H. R. Nejati. 2014. “Numerical simulation of the process of fracture of echelon rock joints.” Rock Mech. Rock Eng. 47 (4): 1355–1371. https://doi.org/10.1007/s00603-013-0450-3.
Sarfarazi, V., H. Haeri, A. B. Shemirani, and Z. Zhu. 2017. “Shear behavior of non-persistent joint under high normal load.” Strength Mater. 49 (2): 320–334. https://doi.org/10.1007/s11223-017-9872-6.
Shaunik, D., and M. Singh. 2019. “Strength behaviour of a model rock intersected by non-persistent joint.” J. Rock Mech. Geotech. Eng. 11 (6): 1243–1255. https://doi.org/10.1016/j.jrmge.2019.01.004.
Singh, M., K. S. Rao, and T. Ramamurthy. 2002. “Strength and deformational behaviour of a jointed rock mass.” Rock Mech. Rock Eng. 35 (1): 45–64. https://doi.org/10.1007/s006030200008.
Singh, M., and B. Singh. 2008. “High lateral strain ratio in jointed rock masses.” Eng. Geol. 98 (3–4): 75–85. https://doi.org/10.1016/j.enggeo.2007.11.004.
Tang, C. A., P. Lin, R. H. C. Wong, and K. T. Chau. 2001. “Analysis of crack coalescence in rock-like materials containing three flaws—part II: Numerical approach.” Int. J. Rock Mech. Min. Sci. 38 (7): 925–939. https://doi.org/10.1016/S1365-1609(01)00065-X.
Wang, P., F. Ren, S. Miao, M. Cai, and T. Yang. 2017. “Evaluation of the anisotropy and directionality of a jointed rock mass under numerical direct shear tests.” Eng. Geol. 225: 29–41. https://doi.org/10.1016/j.enggeo.2017.03.004.
Wang L.-y., W. z. Chen, X. y. Tan, X.-j. Tan, J.-q. Yuan and Q. Liu. 2019. “Evaluation of mountain slope stability considering the impact of geological interfaces using discrete fractures model.” J. Mt. Sci. 16: 21842202. https://doi.org/10.1007/s11629-019-5527-3.
Wittke, W. 2014. Rock mechanics based on an anisotropic jointed rock model. Berlin: Wilhelm Ernst & Sohn.
Wong, L. N. Y., and H. H. Einstein. 2009. “Crack coalescence in molded gypsum and Carrara marble: Part 1. Macroscopic observations and interpretation.” Rock Mech. Rock Eng. 42 (3): 475–511. https://doi.org/10.1007/s00603-008-0002-4.
Wong, R. H. C., and K. T. Chau. 1998. “Crack coalescence in a rock-like material containing two cracks.” Int. J. Rock Mech. Min. Sci. 35 (2): 147–164. https://doi.org/10.1016/S0148-9062(97)00303-3.
Xiong, L., H. Chen, X. Geng, and Z. Xu. 2020a. “Influence of joint location and connectivity on the shear properties of artificial rock samples with non-persistent planar joints.” Arabian J. Geosci. 13 (13): 565. https://doi.org/10.1007/s12517-020-05589-z.
Xiong, L., H. Chen, and Y. Zhang. 2020b. “Direct shear tests of artificial jointed rock specimens with parallel joints.” Arabian J. Geosci. 13 (10): 373. https://doi.org/10.1007/s12517-020-05424-5.
Yang, S.-Q., M. Chen, Y.-H. Huang, H.-W. Jing, and P. G. Ranjith. 2020. “An experimental study on fracture evolution mechanism of a non-persistent jointed rock mass with various anchorage effects by DSCM, AE and X-ray CT observations.” Int. J. Rock Mech. Min. Sci. 134 (September): 104469. https://doi.org/10.1016/j.ijrmms.2020.104469.
Yang, X.-X., and W.-G. Qiao. 2018. “Numerical investigation of the shear behavior of granite materials containing discontinuous joints by utilizing the flat-joint model.” Comput. Geotech. 104 (August): 69–80. https://doi.org/10.1016/j.compgeo.2018.08.014.
Zare, S., S. Karimi-Nasab, and H. Jalalifar. 2021. “Analysis and determination of the behavioral mechanism of rock bridges using experimental and numerical modeling of non-persistent rock joints.” Int. J. Rock Mech. Min. Sci. 141 (September 2020): 104714. https://doi.org/10.1016/j.ijrmms.2021.104714.
Zhang, X.-P., and L. N. Y. Wong. 2013. “Crack initiation, propagation and coalescence in rock-like material containing two flaws: A numerical study based on bonded-particle model approach.” Rock Mech. Rock Eng. 46 (5): 1001–1021. https://doi.org/10.1007/s00603-012-0323-1.
Zhang, Z.-l., and T. Wang. 2020. “Numerical analysis of loess and weak intercalated layer failure behavior under direct shearing and cyclic loading.” J. Mountain Sci. 17 (11): 2796–2815. https://doi.org/10.1007/s11629-020-6178-0.
Zhao, Y., S. Liu, Y. Jiang, K. Wang, and Y. Huang. 2016. “Dynamic tensile strength of coal under dry and saturated conditions.” Rock Mech. Rock Eng. 49 (5): 1709–1720. https://doi.org/10.1007/s00603-015-0849-0.
Zhou X., and J. Chen. 2019. “Extended finite element simulation of step-path brittle failure in rock slopes with non-persistent en-echelon joints.” Eng. Geol. 250: 6588. https://doi.org/10.1016/j.enggeo.2019.01.012.
Zhou, X. P., H. Cheng, and Y. F. Feng. 2014. “An experimental study of crack coalescence behavior in rock-like materials containing multiple flaws under uniaxial compression.” Rock Mech. Rock Eng. 47 (6): 1961–1986. https://doi.org/10.1007/s00603-013-0511-7.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 23 • Issue 7 • July 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Mar 24, 2022
Accepted: Feb 17, 2023
Published online: May 12, 2023
Published in print: Jul 1, 2023
Discussion open until: Oct 12, 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.