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Rock Mechanics and Rock Engineering

, Volume 52, Issue 11, pp 4319–4338 | Cite as

Numerical and Experimental Study on the Cracking Behavior of Marble with En-Echelon Flaws

  • Yi Cheng
  • Yu-Yong JiaoEmail author
  • Fei Tan
Original Paper
  • 237 Downloads

Abstract

En-echelon fractures have been commonly observed in nature. To understand the interaction of en-echelon flaws, numerical simulation with flat-jointed model and laboratory experiment has been conducted on specimens containing en-echelon flaws of various configurations. With reliable micro-parameters of the flat-joint contact through a comprehensive calibration, numerical results reveal a strong interaction in flaw configurations of extensional bridges but a mild interaction in flaw configurations of contractional bridges. The patterns of linking cracks are found to be dependent on the flaw configurations. Furthermore, two typical linking cracks, tensile and shear cracks, are identified in terms of contact force evolution, crack development, micro-components and damage zone width. Experimental results not only verify the above conclusions given by simulation, but also provide more distinctions between tensile and shear cracks in grain scale. Based on these findings, an empirical correlation is suggested between debonding behavior in PFC models and microcracking behavior in laboratory experiments. Finally, the tendency of crack initiation stress and peak stress in simulation and experiment is compared and explained with respect to the flaw-array angle. A good agreement between simulation and experiment indicates the capability of the flat-jointed model of PFC2D in handling complex crack coalescence problems in rocks.

Keywords

En-echelon flaws Flat-jointed model Tensile crack Shear crack Microcrack Carrara marble 

Notes

Acknowledgements

The authors appreciate suggestions from anonymous reviewers very much to improve the quality of this paper. This study was supported by the China National Natural Science Foundation (No.: 41702314, No.: 11672360, No.: 51479191 and No.: 11402280) and Hubei Provincial Natural Science Foundation of China (No.: 2016CFA023).

References

  1. Atkinson B (1979) Fracture toughness of Tennessee sandstone and Carrara marble using the double torsion testing method. In: International journal of rock mechanics and mining sciences & geomechanics abstracts, vol 16. Pergamon, 49–53Google Scholar
  2. Atkinson BK (1987) Fracture mechanics of rock. Academic, LondonGoogle Scholar
  3. Aydin A (1978) Small faults formed as deformation bands in sandstone. Pure Appl Geophys 116(4):913–930Google Scholar
  4. Bahaaddini M, Sharrock G, Hebblewhite B (2013) Numerical direct shear tests to model the shear behaviour of rock joints. Comput Geotech 51:101–115Google Scholar
  5. Bobet A, Einstein H (1998) Numerical modeling of fracture coalescence in a model rock material. Int J Fract 92(3):221–252Google Scholar
  6. Bouchard PO, Bay F, Chastel Y (2003) Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria. Comput Methods Appl Mech Eng 192(35–36):3887–3908Google Scholar
  7. Cheng Y, Wong LNY, Zou CJ (2015) Experimental study on the formation of faults from en-echelon fractures in Carrara Marble. Eng Geol 195:312–326Google Scholar
  8. Cho N, Martin CD, Sego DC (2007) A clumped particle model for rock. Int J Rock Mech Min Sci 44(7):997–1010Google Scholar
  9. Cloos E (1955) Experimental analysis of fracture patterns. Geol Soc Am Bull 66(3):241–256Google Scholar
  10. Coli M, Livi E, Berry P, Bandini A, Jia XN (2010) Studies for rockburst prediction in the Carrara Marble (Italy), pp 367–373. Rock Stress and Earthquakes, Taylor & Francis Group, London, WOS: 000290973700059Google Scholar
  11. Cundall P, Potyondy D, Lee C (1996) Micromechanics-based models for fracture and breakout around the mine-by tunnel. In: Martino JB, Martin CD (eds) Proceedings, international conference on deep geological disposal of radioactive waste, Winnipeg. Canadian Nuclear Society, TorontoGoogle Scholar
  12. Einstein HH, Veneziano D, Baecher GB, O’Reilly KJ (1983) The effect of discontinuity persistence on rock slope stability. Int J Rock Mech Min Sci Geomech Abstr 20(5):227–236Google Scholar
  13. Eoin R (1988) En échelon vein array development in extension and shear. J Struct Geol 10(1):63–71Google Scholar
  14. Fakhimi A (2004) Application of slightly overlapped circular particles assembly in numerical simulation of rocks with high friction angles. Eng Geol 74(1):129–138Google Scholar
  15. Fakhimi A, Villegas T (2007) Application of dimensional analysis in calibration of a discrete element model for rock deformation and fracture. Rock Mech Rock Eng 40(2):193–211Google Scholar
  16. Franklin JA, Hoek E (1970) Developments in triaxial testing technique. Rock Mech Rock Eng 2(4):223–228Google Scholar
  17. Gamond JF (1983) Displacement features associated with fault zones: a comparison between observed examples and experimental models. J Struct Geol 5(1):33–45Google Scholar
  18. Gehle C, Kutter HK (2003) Breakage and shear behaviour of intermittent rock joints. Int J Rock Mech Min Sci 40(5):687–700Google Scholar
  19. Ghazvinian A, Sarfarazi V, Schubert W, Blumel M (2012) A study of the failure mechanism of planar non-persistent open joints using PFC2D. Rock Mech Rock Eng 45(5):677–693Google Scholar
  20. Hazzard JF, Young RP, Maxwell S (2000) Micromechanical modeling of cracking and failure in brittle rocks. J Geophys Res Solid Earth (1978–2012) 105(B7):16683–16697Google Scholar
  21. Horii H, Nemat-Nasser S (1985) Compression-induced microcrack growth in brittle solids: axial splitting and shear failure. J Geophys Res 90(B4):3105–3125Google Scholar
  22. Itasca (2008) PFC2D Version 4.0. Theory and background. Itasca Consulting Group Inc, MinneapolisGoogle Scholar
  23. Kim Y-S, Peacock DCP, Sanderson DJ (2003) Mesoscale strike-slip faults and damage zones. J Struct Geol 25:793–812Google Scholar
  24. Knauss W (1970) An observation of crack propagation in anti-plane shear. Int J Fract 6(2):183–187Google Scholar
  25. Lajtai E, Carter B, Duncan E (1994) En echelon crack-arrays in potash salt rock. Rock Mech Rock Eng 27(2):89–111Google Scholar
  26. Lee H, Jeon S (2011) An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression. Int J Solids Struct 48(6):979–999Google Scholar
  27. Li H, Wong LNY (2012) Influence of flaw inclination angle and loading condition on crack initiation and propagation. Int J Solids Struct 49(18):2482–2499Google Scholar
  28. Lin P, Logan JM (1991) The interaction of two closely spaced cracks: a rock model study. J Geophys Res 96(B13):21667–21675Google Scholar
  29. Ma GW, An XM, Zhang HH, Li LX (2009) Modeling complex crack problems using the numerical manifold method. Int J Fract 156(1):21–35Google Scholar
  30. Martel SJ, Boger WA (1998) Geometry and mechanics of secondary fracturing around small three-dimensional faults in granitic rock. J Geophys Res 103(B9):21299–21314Google Scholar
  31. McGrath AG, Davison I (1995) Damage zone geometry around fault tips. J Struct Geol 17(7):1011–1024Google Scholar
  32. Myers R, Aydin A (2004) The evolution of faults formed by shearing across joint zones in sandstone. J Struct Geol 26(5):947–966Google Scholar
  33. Nicholson R, Pollard DD (1985) Dilation and linkage of echelon cracks. J Struct Geol 7(5):583–590Google Scholar
  34. Ning Y, Yang J, An X, Ma G (2011) Modelling rock fracturing and blast-induced rock mass failure via advanced discretisation within the discontinuous deformation analysis framework. Comput Geotech 38(1):40–49Google Scholar
  35. Peng S, Johnson AM (1972) Crack growth and faulting in cylindrical specimens of chelmsford granite. Int J Rock Mech Min Sci Geomech Abstr 9(1):37–86Google Scholar
  36. Peng J, Wong LNY, Teh CI, Li Z (2017) Modeling micro-cracking behavior of Bukit Timah granite using grain-based model. In: Rock mechanics and rock engineering, vol 51, pp 135–154Google Scholar
  37. Petit J-P, Barquins M (1988) Can natural faults propagate under mode II conditions? Tectonics 7(6):1243–1256Google Scholar
  38. Pollard DD, Segall P, Delaney PT (1982) Formation and interpretation of dilatant echelon cracks. Geol Soc Am Bull 93:1291–1303Google Scholar
  39. Potyondy DO (2012a) PFC2D flat-joint contact model. PFC Development Files, I. C. G. Inc., Minneapolis, MNGoogle Scholar
  40. Potyondy DO (2012b) A flat-jointed bonded-particle material for hard rock. U.S. Rock Mechanics/Geomechanics Symposium, ChicagoGoogle Scholar
  41. Potyondy DO (2013) PFC2D flat-jointed material creation and testing. PFC Development Files, I. C. G. Inc., Minneapolis, MNGoogle Scholar
  42. Potyondy D, Cundall P (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364Google Scholar
  43. Sagong M, Bobet A (2002) Coalescence of multiple flaws in a rock-model material in uniaxial compression. Int J Rock Mech Min Sci 39:229–241Google Scholar
  44. Sarfarazi V, Ghazvinian A, Schubert W, Blumel M, Nejati H (2014) Numerical simulation of the process of fracture of echelon rock joints. Rock Mech Rock Eng 47(4):1355–1371Google Scholar
  45. Shengli M, Zhihui D, Wentao Ma (1995) experimental study on evolution of physical field during deformation of en-echelon faults. Seismol Geol 17(4):327–335Google Scholar
  46. Siad L, Megueddem M (1998) Stability analysis of jointed rock slope. Mech Res Commun 25(6):661–670Google Scholar
  47. Strouboulis T, Babuška I, Copps K (2000) The design and analysis of the generalized finite element method. Comput Methods Appl Mech Eng 181(1):43–69Google Scholar
  48. Tchalenko J, Ambraseys NN (1970) Structural analysis of the Dasht-e Bayaz (Iran) earthquake fractures. Geol Soc Am Bull 81(1):41–60Google Scholar
  49. Trädegård A, Nilsson F, Östlund S (1998) FEM-remeshing technique applied to crack growth problems. Comput Methods Appl Mech Eng 160(1):115–131Google Scholar
  50. Vallejos JA, Salinas JM, Delonca A, Ivars DM (2017) Calibration and verification of two bonded-particle models for simulation of intact rock behavior. Int J Geomech 17(4):06016030Google Scholar
  51. Wang Y, Tonon F (2009) Modeling Lac du Bonnet granite using a discrete element model. Int J Rock Mech Min Sci 46(7):1124–1135Google Scholar
  52. Wang B, Martin U, Rapp S (2017) Discrete element modeling of the single-particle crushing test for ballast stones. Comput Geotech 88:61–73Google Scholar
  53. Weiss J, Schulson EM (2009) Coulombic faulting from the grain scale to the geophysical scale: lessons from ice. J Phys D Appl Phys 42(21):214017Google Scholar
  54. Willemse EJM, Peacock DCP, Aydin A (1997) Nucleation and growth of strike-slip faults in limestones from Somerset, U.K. J Struct Geol 19(12):1461–1477Google Scholar
  55. Wong LNY, Einstein HH (2009a) Crack coalescence in molded Gypsum and Carrara marble: part 1. Macroscopic observations and interpretation. Rock Mech Rock Eng 42(3):475–511Google Scholar
  56. Wong LNY, Einstein HH (2009b) Crack coalescence in molded Gypsum and Carrara Marble: Part 2. Microscopic observations and interpretation. Rock Mech Rock Eng 42(3):513–545Google Scholar
  57. Wong LNY, Zhang X-P (2014) Size effects on cracking behavior of flaw-containing specimens under compressive loading. Rock Mech Rock Eng 47(5):1921–19310Google Scholar
  58. Wong RHC, Leung WL, Wang SW (2001) Shear strength studies on rock-like models containing arrayed open joints. In: Proceedings of the 38th U.S. rock mechanics symposium, Washington D.CGoogle Scholar
  59. Wu Z, Fan L (2014) The numerical manifold method for elastic wave propagation in rock with time-dependent absorbing boundary conditions. Eng Anal Bound Elem 46:41–50Google Scholar
  60. Wu Z, Wong LNY (2012a) Elastic–plastic cracking analysis for brittle–ductile rocks using manifold method. Int J Fract 180(1):71–91Google Scholar
  61. Wu Z, Wong LNY (2012b) Frictional crack initiation and propagation analysis using the numerical manifold method. Comput Geotech 39:38–53Google Scholar
  62. Wu Z, Wong LNY (2013) Modeling cracking behavior of rock mass containing inclusions using the enriched numerical manifold method. Eng Geol 162:1–13Google Scholar
  63. Wu S, Xu X (2016) A study of three intrinsic problems of the classic discrete element method using flat-joint model. Rock Mech Rock Eng 49(5):1813–1830Google Scholar
  64. Wu Z, Liang X, Liu Q (2015) Numerical investigation of rock heterogeneity effect on rock dynamic strength and failure process using cohesive fracture model. Eng Geol 197:198–210Google Scholar
  65. Xu X, Wu S, Gao Y, Xu M (2016) Effects of micro-structure and micro-parameters on Brazilian tensile strength using flat-joint model. Rock Mech Rock Eng 49(9):3575–3595Google Scholar
  66. Yan C, Zheng H (2017) FDEM-flow3D: a 3D hydro-mechanical coupled model considering the pore seepage of rock matrix for simulating three-dimensional hydraulic fracturing. Comput Geotech 81:212–228Google Scholar
  67. Yan C, Zheng H, Sun G, Ge X (2016) Combined finite-discrete element method for simulation of hydraulic fracturing. Rock Mech Rock Eng 49(4):1389–1410Google Scholar
  68. Yang SQ, Dai YH, Han LJ, Jin ZQ (2009) Experimental study on mechanical behavior of brittle marble samples containing different flaws under uniaxial compression. Eng Fract Mech 76(12):1833–1845Google Scholar
  69. Yoon J (2007) Application of experimental design and optimization to PFC model calibration in uniaxial compression simulation. Int J Rock Mech Min Sci 44(6):871–889Google Scholar
  70. Zhang X-P, Wong L (2012a) 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 45(5):711–737Google Scholar
  71. Zhang X-P, Wong LNY (2012b) 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):1001–1021Google Scholar
  72. Zhang X-P, Wong LNY (2013) Loading rate effects on cracking behavior of flaw-contained specimens under uniaxial compression. Int J Fract 180(1):93–110Google Scholar
  73. Zhang X-P, Wong LNY (2014) Choosing a proper loading rate for bonded-particle model of intact rock. Int J Fract 189(2):163–179Google Scholar
  74. Zhang XP, Zhang Q (2017) Distinction of crack nature in brittle rock-like materials: a numerical study based on moment tensors. Rock Mech Rock Eng 50(10):2837–2845Google Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of EngineeringChina University of GeosciencesWuhanChina
  2. 2.School of Civil and Environmental EngineeringNanyang Technological UniversitySingaporeSingapore
  3. 3.State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil MechanicsChinese Academy of SciencesWuhanChina

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