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Original Articles

Extended finite element method simulation and experimental test on failure behavior of defects under uniaxial compression

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Pages 6966-6981 | Received 24 Jul 2021, Accepted 03 Oct 2021, Published online: 21 Oct 2021

References

  • A. Basu and D. A. Mishra, A method for estimating crack-initiation stress of rock materials by porosity, J. Geol. Soc. India, vol. 84, no. 4, pp. 397–405, 2014. DOI: 10.1007/s12594-014-0145-8.
  • S.-H. Chang, C.-I. Lee, and S. Jeon, Measurement of rock fracture toughness under modes I and II and mixed-mode conditions by using disc-type specimens, Eng. Geol., vol. 66, no. 1–2, pp. 79–97, 2002. DOI: 10.1016/S0013-7952(02)00033-9.
  • E. Hoek and C. D. Martin, Fracture initiation and propagation in intact rock – a review, J. Rock Mech. Geotech. Eng., vol. 6, no. 4, pp. 287–300, 2014. DOI: 10.1016/j.jrmge.2014.06.001.
  • A. Lisjak, P. Kaifosh, L. He, B. S. A. Tatone, O. K. Mahabadi, and G. Grasselli, A 2D, fully coupled, hydro-mechanical, FDEM formulation for modelling fracturing processes in discontinuous, porous rock masses, Comput. Geotech., vol. 81, pp. 1–18, 2017. DOI: 10.1016/j.compgeo.2016.07.009.
  • S. Karimpouli, H. Hassani, A. Malehmir, M. Nabi-Bidhendi, and H. Khoshdel, Understanding the fracture role on hydrocarbon accumulation and distribution using seismic data: a case study on a carbonate reservoir from Iran, J. Appl.Geophys., vol. 96, pp. 98–106, 2013. DOI: 10.1016/j.jappgeo.2013.06.015.
  • A. Bobet and H. H. Einstein, Fracture integrate in rock-type materials under uniaxial and biaxial compression, Int. J. Rock Mech. Min. Sci., vol. 35, no. 7, pp. 863–888, 1998. DOI: 10.1016/S0148-9062(98)00005-9.
  • R. H. C. Wong, K. T. Chau, C. A. Tang, and P. Lin, Analysis of crack integrate in rock-like materials containing three flaws-Part I: experimental approach, Int. J. Rock Mech. Min. Sci., vol. 38, no. 7, pp. 909–924, 2001. DOI: 10.1016/S1365-1609(01)00064-8.
  • M. Sagong and A. Bobet, Integrate of multiple flaws in a rock-model material in uniaxial compression, Int. J. Rock Mech. Min. Sci., vol. 39, no. 2, pp. 229–241, 2002. DOI: 10.1016/S1365-1609(02)00027-8.
  • L. N. Y. Wong and H. H. Einstein, Crack integrate in molded gypsum and Carrara marble: part 1, Rock Mech. Rock Eng., vol. 42, no. 3, pp. 475–511, 2009. DOI: 10.1007/s00603-008-0002-4.
  • L. N. Y. Wong and H. H. Einstein, Crack integrate in molded gypsum and Carrara marble: part 2-microscopic observations and interpretation, Rock Mech. Rock Eng., vol. 42, no. 3, pp. 513–545, 2009. DOI: 10.1007/s00603-008-0003-3.
  • S. Q. Yang, Crack integrate behavior of brittle sandstone samples containing two coplanar fissures in the process of deformation failure, Eng. Fract. Mech., vol. 78, no. 17, pp. 3059–3081, 2011. DOI: 10.1016/j.engfracmech.2011.09.002.
  • S. Q. Yang, Y. Z. Jiang, W. Y. Xu, and X. Q. Chen, Experimental investigation on strength and failure behavior of pre-cracked marble under conventional triaxial compression, Int. J. Solids Struct., vol. 45, no. 17, pp. 4796–4819, 2008. DOI: 10.1016/j.ijsolstr.2008.04.023.
  • S. Q. Yang, D. S. Yang, H. W. Jing, Y. H. Li, and S. Y. Wang, An experimental study of the fracture integrate behaviour of brittle sandstone specimens containing three fissures, Rock Mech. Rock Eng., vol. 45, no. 4, pp. 563–582, 2012. DOI: 10.1007/s00603-011-0206-x.
  • L. N. Y. Wong and H. H. Einstein, Systematic evaluation of cracking behavior in specimens containing single flaws under uniaxial compression, Int. J. Rock Mech. Min. Sci., vol. 46, no. 2, pp. 239–249, 2009. DOI: 10.1016/j.ijrmms.2008.03.006.
  • C. H. Park and A. Bobet, Crack initiation, propagation and integrate from frictional flaws in uniaxial compression, Eng. Fract. Mech., vol. 77, no. 14, pp. 2727–2748, 2010. DOI: 10.1016/j.engfracmech.2010.06.027.
  • C. H. Park and A. Bobet, Crack integrate in specimens with open and closed flaws: a comparison, Int. J. Rock Mech. Min. Sci., vol. 46, no. 5, pp. 819–829, 2009. DOI: 10.1016/j.ijrmms.2009.02.006.
  • R. L. Kranz, Crack-crack and crack-pore interactions in stressed granite, Int. J. Rock Mech. Min. Sci., vol. 16, no. 1, pp. 37–47, 1979. DOI: 10.1016/0148-9062(79)90773-3.
  • H. K. Lee and J. W. Ju, A three-dimensional stress analysis of a penny-shaped crack interacting with a spherical inclusion, Int. J. Damage Mech., vol. 16, no. 3, pp. 331–359, 2007. DOI: 10.1177/1056789506067934.
  • P. Bocca, A. Carpinteri, and S. Valente, Size effects in the mixed mode crack propagation: softening and snap-back analysis, Eng. Fract. Mech., vol. 35, no. 1–3, pp. 159–170, 1990. DOI: 10.1016/0013-7944(90)90193-K.
  • C. Xu and R. J. Fowell, Stress intensity factor evaluation for cracked chevron notched Brazilian disc specimens, Int. J. Rock Mech. Min. Sci., vol. 31, no. 2, pp. 157–162, 1994. DOI: 10.1016/0148-9062(94)92806-1.
  • A. Trädegård, F. Nilsson, and S. Östlund, FEM-remeshing technique applied to crack growth problems, Comput. Methods Appl. Mech. Eng., vol. 160, no. 1–2, pp. 115–131, 1998. DOI: 10.1016/S0045-7825(97)00287-9.
  • O. R. Barani, A. R. Khoei, and M. Mofi, Modeling of cohesive crack growth in partially saturated porous media; a study on the permeability of cohesive fracture, Int. J. Fract., vol. 167, no. 1, pp. 15–31, 2011. DOI: 10.1007/s10704-010-9513-6.
  • X.-H. Tan, J.-Y. Liu, X.-P. Li, L.-H. Zhang, and J. Cai, A simulation method for perme-ability of porous media based on multiple fractal model, Int. J. Eng. Sci., vol. 95, pp. 76–84, 2015. DOI: 10.1016/j.ijengsci.2015.06.007.
  • M. Ţene, M. S. Al Kobaisi, and H. Hajibeygi, Algebraic multiscale method for flow in heterogeneous porous media with embedded discrete fractures (F-AMS), J. Comput. Phys., vol. 321, pp. 819–845, 2016. DOI: 10.1016/j.jcp.2016.06.012.
  • K. Supar and H. Ahmad, XFEM modelling of multi-holes plate with single-row and staggered holes confi gurations, MATEC Web Conf., vol. 103, pp. 02031, 2017. DOI: 10.1051/matecconf/201710302031.
  • B. A. Schrefler and Z. Xiaoyong, A fully coupled model for water flow and air flow in deformable porous media, Water Resour. Res., vol. 29, no. 1, pp. 155–167, 1993. DOI: 10.1029/92WR01737.
  • M. R. Mohammad Aliha, M. Mousavi, and M. R. Ayatollahi, Mixed mode I/II fracture path simulation in a typical jointed rock slope, 4th International Conference on Crack Paths, Gaeta (Italy), 19–21 September, 2012.
  • N. Sukumar, D. L. Chopp, N. Moës, and T. Belytschko, Modeling holes and inclusions by level sets in the extended finite-element method, Comput. Meth. Appl. Mech. Eng., vol. 190, no. 46–47, pp. 6183–6200, 2001. DOI: 10.1016/S0045-7825(01)00215-8.
  • E. Gordeliy and A. Peirce, Enrichment strategies and convergence properties of the XFEM for hydraulic fracture problems, Comput. Methods Appl. Mech. Eng., vol. 283, pp. 474–502, 2015. DOI: 10.1016/j.cma.2014.09.004.
  • T. Mohammadnejad and A. R. Khoei, An extended fi nite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model, Finite Elem. Anal. Des., vol. 73, pp. 77–95, 2013. DOI: 10.1016/j.finel.2013.05.005.
  • A. R. Khoei, M. Vahab, E. Haghighat, and S. Moallemi, A mesh-independent finite element formulation for modeling crack growth in saturated porous media based on an enriched-FEM technique, Int. J. Fract., vol. 188, no. 1, pp. 79–108, 2014. DOI: 10.1007/s10704-014-9948-2.
  • E. Gordeliy and A. Peirce, Coupling schemes for modeling hydraulic fracture propagation using the XFEM, Comput. Meth. Appl. Mech. Eng., vol. 253, pp. 305–322, 2013. DOI: 10.1016/j.cma.2012.08.017.
  • A. Dahi-Taleghani and J. E. Olson, Numerical modeling of multistranded-hydraulic-fracture propagation: accounting for the interaction between induced and natural fractures, SPE J., vol. 16, no. 03, pp. 575–581, 2011. DOI: 10.2118/124884-PA.
  • M. A. Réthoré, J. Borst, and R. D. Abellan, A two-scale approach for fluid flowin fractured porous media, Int. J. Numer. Meth. Eng., vol. 71, no. 7, pp. 780–800, 2006. DOI: 10.1002/nme.1962.
  • T. P. Cheng and K. W. Fries, Higher-orderXFEM for curved strong and weak dis-continuities, Int. J. Numer. Meth. Eng., vol. 82, pp. 564–590, 2010.
  • S. Mohammadi, XFEM Fracture Analysis of Composites, John Wiley & Sons Incorporated, Chichester, United Kingdom, 2012.
  • S. Natarajan, D. R. Mahapatra, and S. Bordas, Integrating strong and weak dis continuities without integration subcells and example applications in an XFEM/GFEM framework, Int. J. Numer. Meth. Eng., vol. 83, no. 3, pp. 269–294, 2010. DOI: 10.1002/nme.2798.
  • Y. Ju, Y. M. Yang, Z. D. Song, and W. J. Xu, A statistical model for porous structure of rocks, Sci. China Ser. E-Technol. Sci., vol. 51, no. 11, pp. 2040–2058, 2008. DOI: 10.1007/s11431-008-0111-z.
  • L. Hedjazi, C. L. Martin, S. Guessasma, G. D. Valle, and R. Dendievel, Application of the discrete element method to crack propagation and crack branching in a vitreous dense biopolymer material, Int. J. Solids Struct., vol. 49, no. 13, pp. 1893–1899, 2012. DOI: 10.1016/j.ijsolstr.2012.03.030.
  • M. Vahab and N. Khalili, X-FEM modeling of multizone hydraulic fracturing treatments within saturated porous media, Rock Mech. Rock Eng., vol. 51, no. 10, pp. 3219–3239, 2018. DOI: 10.1007/s00603-018-1419-z.
  • M. Haddad and K. Sepehrnoori, XFEM-based CZM for the simulation of 3D multiple-cluster hydraulic fracturing in quasi-brittle shale formations, Rock Mech. Rock Eng., vol. 49, no. 12, pp. 4731–4748, 2016. DOI: 10.1007/s00603-016-1057-2.
  • S. Natarajan, Enriched finite element methods: advances & applications, PhD. Thesis, Institute of Mechanics and Advanced Materials, Theoretical and Computational Mechanics, Cardiff university, Cardiff, Wales, U.K., 2011.
  • N. Rodriguez-Florez, A. Carriero, and S. J. Shefelbine, The use of XFEM to assess the influence of intra-cortical porosity on crack propagation, Comput. Methods Biomech. Biomed. Eng., vol. 20, no. 4, pp. 385–392, 2017. DOI: 10.1080/10255842.2016.1235158.
  • N. R. Florez, Mechanics of Cortical Bone: Exploring the Micro- and Nano-Scale, PhD. Thesis, Department of Bioengineering, Imperial College London, London, UK, 2015. DOI: 10.25560/26602.
  • P. O. Bouchard, F. Bay, and Y. Chastel, Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria, Comput. Methods Appl. Mech. Eng., vol. 192, no. 35–36, pp. 3887–3908, 2003. DOI: 10.1016/S0045-7825(03)00391-8.
  • H. Li and L. N. Y. Wong, Influence of flaw inclination angle and loading condition on crack initiation and propagation, Int. J. Solids Struct., vol. 49, no. 18, pp. 2482–2499, 2012. DOI: 10.1016/j.ijsolstr.2012.05.012.
  • A. Bobet and H. H. Einstein, Numerical modeling of fracture integrate in a model rock material, Int. J. Fract., vol. 92, no. 3, pp. 221–252, 1998. DOI: 10.1023/A:1007460316400.
  • P. Hosseini-Tehrani, A. R. Hosseini-Godarzi, and M. Tavangar, Boundary element analysis of stress intensity factor KI in some two-dimensional dynamic thermoelastic problems, Eng. Anal. Bound. Elem., vol. 29, no. 3, pp. 232–240, 2005. DOI: 10.1016/j.enganabound.2004.12.009.
  • X. Lu and W. L. Wu, A subregion DRBEM formulation for the dynamic analysis of two-dimensional cracks, Math. Comput. Model., vol. 43, no. 1–2, pp. 76–88, 2006. DOI: 10.1016/j.mcm.2005.03.009.
  • X. P. Zhang and L. N. Y. Wong, Crack initiation, propagation and integrate in rock-like material containing two flaws: a numerical study based on bonded-particle model approach, Rock Mech. Rock Eng., vol. 46, no. 5, pp. 1001–1021, 2013. DOI: 10.1007/s00603-012-0323-1.
  • A. Ghazvinian, V. Sarfarazi, W. Schubert, and M. Blumel, A study of the failure mechanism of planar non-persistent open joints using PFC2D, Rock Mech. Rock Eng., vol. 45, pp. 677–693, 2012.
  • V. Sarfarazi, A. Ghazvinian, W. Schubert, M. Blumel, and H. R. Nejati, Numerical simulation of the process of fracture of echelon rock joints, Rock Mech. Rock Eng., vol. 47, no. 4, pp. 1355–1371, 2014. DOI: 10.1007/s00603-013-0450-3.
  • J. W. Park and J. J. Song, Numerical simulation of a direct shear test on a rock joint using a bonded-particle model, Int. J. Rock Mech. Min. Sci., vol. 46, no. 8, pp. 1315–1328, 2009. DOI: 10.1016/j.ijrmms.2009.03.007.
  • Z. Wu and L. N. Y. Wong, Frictional crack initiation and propagation analysis using the numerical manifold method, Comput. Geotech., vol. 39, pp. 38–53, 2012. DOI: 10.1016/j.compgeo.2011.08.011.
  • Y. C. Cai, H. H. Zhu, and X. Y. Zhuang, A continuous/discontinuous deformation analysis (CDDA) method based on deformable blocks for fracture modeling, Front. Struct. Civ. Eng., vol. 7, no. 4, pp. 369–378, 2013. DOI: 10.1007/s11709-013-0222-x.
  • X. Y. Zhuang and C. Augarde, Aspects of the use of orthogonal basis functions in the element-free Galerkin method, Int. J. Numer. Meth. Eng., vol. 81, pp. 366–380, 2010.
  • H. Zhu, X. Zhuang, Y. Cai, and G. Ma, High rock slope stability analysis using the enriched meshless shepard and least squares method, Int. J. Comput. Methods, vol. 08, no. 02, pp. 209–228, 2011. DOI: 10.1142/S0219876211002551.
  • Itasca, PFC2D (Particle Flow Code in 2 Dimensions) Version 3.1, Itasca Consulting Group, Minneapolis, Minn, USA, 1999.
  • D. O. Potyondy and P. A. Cundall, A bonded-particle model for rock, Int. J. Rock Mech. Min. Sci., vol. 41, no. 8, pp. 1329–1364, 2004. DOI: 10.1016/j.ijrmms.2004.09.011.
  • X. P. Zhang and L. N. Y. Wong, Cracking processes in rock-like material containing a single flaw under uniaxial compression: a numerical study based on parallel bonded-particle model approach, Rock Mech. Rock Eng., vol. 45, pp. 711–737, 2012.
  • H. Lee and S. Jeon, An experimental and numerical study of fracture integrate in pre cracked specimens under uniaxial compression, Int. J. Solids Struct., vol. 48, no. 6, pp. 979–999, 2011. DOI: 10.1016/j.ijsolstr.2010.12.001.
  • T. P. Fries and T. Belytschko, The extended/generalized finite element methods: an overview of the method and its applications, Int. J. Numer. Met. Eng., vol. 84, no. 3, pp. 1–6, 2000.
  • M. Xie, Finite element modelling of discrete crack propagation, PhD Thesis, University of New Mexico, USA, 1995.
  • Z. Yang, An energy-based crack growth criterion for modeling elastic–plastic ductile fracture, Mech. Res. Commun., vol. 32, no. 5, pp. 514–524, 2005. DOI: 10.1016/j.mechrescom.2004.10.001.
  • F. Erdogan and G. C. Shih, On the crack propagation in plates under plane loading and transverse shear, J. Basic Eng., vol. 85, no. 4, pp. 519–527, 1963. DOI: 10.1115/1.3656897.
  • M. Hussain, S. Pu, and J. Underwood, Strain Energy Release Rate for a Crack Under Combined Mode I and Mode II, In Irwin G. (Ed.), Fracture Analysis: Proceedings of the 1973 National Symposium on Fracture Mechanics, Part II, (West Conshohocken, PA: ASTM International, 1974), pp. 2–28. DOI: 10.1520/STP33130S.
  • G. C. Sih, Strain-energy-density factor applied to mixed mode crack problems, Int. J. Fract., vol. 10, no. 3, pp. 305–321, 1974. DOI: 10.1007/BF00035493.
  • G. N. Wells and L. J. Sluys, A new method for modelling cohesive cracks using finite elements, Int. J. Numer. Meth. Eng., vol. 50, no. 12, pp. 2667–2682, 2001. DOI: 10.1002/nme.143.
  • J. Oliver and A. E. Huespe, Continuum approach to material failure in strong discontinuity settings, Comp. Meth. Appl. Mech. Eng., vol. 193, no. 30–32, pp. 3195–3220, 2004. DOI: 10.1016/j.cma.2003.07.013.
  • H. Haeri and V. Sarfaraz, Shear behavior on non-persistent joints in concrete and gypsum specimens using combined experimental and numerical approach, Struct. Eng. Mech., vol. 69, no. 2, pp. 221–230, 2019.

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