Rock Mechanics and Rock Engineering

, Volume 45, Issue 5, pp 711–737 | Cite as

Cracking Processes in Rock-Like Material Containing a Single Flaw Under Uniaxial Compression: A Numerical Study Based on Parallel Bonded-Particle Model Approach

  • Xiao-Ping Zhang
  • Louis Ngai Yuen Wong
Original Paper


Cracking processes have been extensively studied in brittle rock and rock-like materials. Due to the experimental limitations and the complexity of rock texture, details of the cracking processes could not always be observed and assessed comprehensively. To contribute to this field of research, a numerical approach based on the particle element model was used in present study. It would give us insights into what is happening to crack initiation, propagation and coalescence. Parallel bond model, a type of bonded-particle model, was used to numerically simulate the cracking process in rock-like material containing a single flaw under uniaxial vertical compression. The single flaw’s inclinations varied from 0° to 75° measured from the horizontal. As the uniaxial compression load was increased, multiple new microcracks initiated in the rock, which later propagated and eventually coalesced into longer macrocracks. The inclination of the pre-existing flaw was found to have a strong influence on the crack initiation and propagation patterns. The simulations replicated most of the phenomena observed in the physical experiments, such as the type, the initiation location and the initiate angle of the first cracks, as well as the development of hair-line cracks, which later evolved to macrocracks. Analyses of the parallel bond forces and displacement fields revealed some important mechanisms of the cracking processes. The first cracks typically initiated from the tensile stress concentration regions, in which the tensile stress was partially released after their initiation. The tensile stress concentration regions subsequently shifted outwards close to the propagating tips of the first cracks. The initiation and propagation of the first cracks would not significantly influence the compressive stress singularity at the flaw tips, which was the driving force of the initiation of secondary cracks. The initiation of microcracking zone consisting almost exclusively of micro-tensile cracks, and that of microcracking zone consisting of micro-tensile cracks and mixed micro-tensile and shear cracks, were found to be correlated with two distinct types of displacement fields, namely type I (DF_I) and type II (DF_II), respectively.


Micro-tensile cracks Micro-shear cracks Bonded-particle model (BPM) Uniaxial compressive loading test 


  1. Bieniawski ZT (1967) Mechanism of brittle fracture of rock: part II—experimental studies. Int J Rock Mech Min Sci 4(4):407–423Google Scholar
  2. Bobet A (2000) The initiation of secondary cracks in compression. Eng Fract Mech 66(2):187–219CrossRefGoogle Scholar
  3. Bobet A, Einstein HH (1998a) Fracture coalescence in rock-type materials under uniaxial and biaxial compression. Int J Rock Mech Min Sci 35(7):863–888CrossRefGoogle Scholar
  4. Bobet A, Einstein HH (1998b) Numerical modeling of fracture coalescence in a model rock material. Int J Fract 92(3):221–252CrossRefGoogle Scholar
  5. Bocca P, Carpinteri A, Valente S (1990) Size effects in the mixed-mode crack-propagation-softening and snap-back analysis. Eng Fract Mech 35(1–3):159–170CrossRefGoogle Scholar
  6. Bombolakis EG (1963) Photoelastic stress analysis of crack propagation within a compressive stress field. PhD thesis, Massachusetts Institute of Technology, CambridgeGoogle Scholar
  7. Brace WF, Bombolakis EG (1963) A note on brittle crack growth in compression. J Geophys Res 68(12):3709–3713CrossRefGoogle Scholar
  8. Brace WF, Paulding BW, Scholz C (1966) Dilatancy in fracture of crystalline rocks. J Geophys Res 71(16):3939–3953CrossRefGoogle Scholar
  9. Chaker C, Barquins M (1996) Sliding effect on branch crack. Phys Chem Earth 21(4):319–323CrossRefGoogle Scholar
  10. Chan HCM, Li V, Einstein HH (1990) A hybridized displacement discontinuity and indirect boundary element method to model fracture propagation. Int J Fract 45(4):263–282CrossRefGoogle Scholar
  11. Chang SH, Lee CI (2004) Estimation of cracking and damage mechanisms in rock under triaxial compression by moment tensor analysis of acoustic emission. Int J Rock Mech Min Sci 41(7):1069–1086CrossRefGoogle Scholar
  12. Chen G, Kemeny JM, Harpalani S (1995) Fracture propagation and coalescence in marble plates with pre-cut notches under compression. In: Symposium on fractured jointed rock masses, LakeTahoe, CAGoogle Scholar
  13. Chinnery MA (1966) Secondary faulting. Can J Earth Sci 3:163–174CrossRefGoogle Scholar
  14. Cho N, Martin CD, Sego DC (2007) A clumped particle model for rock. Int J Rock Mech Min Sci 44(7):997–1010CrossRefGoogle Scholar
  15. Cox SJD, Meredith PG (1993) Microcrack formation and material softening in rock measured by monitoring acoustic emissions. Int J Rock Mech Min Sci Geomech Abstr 30(1):11–24CrossRefGoogle Scholar
  16. Damjanac B, Board M, Lin M, Kicker D, Leem J (2007) Mechanical degradation of emplacement drifts at Yucca Mountain—a modeling case study part II: lithophysal rock. Int J Rock Mech Min Sci 44(3):368–399CrossRefGoogle Scholar
  17. Diederichs MS (2000) Instability of hard rock masses: the role of tensile damage and relaxation. University of Waterloo, WaterlooGoogle Scholar
  18. Dresen G, Stanchits S, Rybacki E (2010) Borehole breakout evolution through acoustic emission location analysis. Int J Rock Mech Min Sci 47(3):426–435CrossRefGoogle Scholar
  19. Feng XT, Chen SL, Zhou H (2004) Real-time computerized tomography (CT) experiments on sandstone damage evolution during triaxial compression with chemical corrosion. Int J Rock Mech Min Sci 41(2):181–192CrossRefGoogle Scholar
  20. Grgic D, Amitrano D (2009) Creep of a porous rock and associated acoustic emission under different hydrous conditions. J Geophys Res 114:B10201. doi: 10.1029/2006JB004881
  21. He MC, Miao JL, Feng JL (2010) Rock burst process of limestone and its acoustic emission characteristics under true-triaxial unloading conditions. Int J Rock Mech Min Sci 47(2):286–298CrossRefGoogle Scholar
  22. Healy D, Jones RR, Holdsworth RE (2006) Three-dimensional brittle shear fracturing by tensile crack interaction. Nature 439(7072):64–67CrossRefGoogle Scholar
  23. Hoek E, Bieniawski ZT (1965) Brittle fracture propagation in rock under compression. Int J Fract Mech 1(3):137–155Google Scholar
  24. Holcomb DJ, Costin LS (1987) Damage in brittle materials: experimental methods. In: Lamb JP (ed) Proceedings of the 10th US national congress of applied mechanicsGoogle Scholar
  25. Horii H, Nematnasser S (1985) Compression-induced microcrack growth in brittle solids: axial splitting and shear failure. J Geophys Res Solid Earth Planets 90(NB4):3105–3125CrossRefGoogle Scholar
  26. Hosseini-Tehrani P, Hosseini-Godarzi AR, Tavangar M (2005) Boundary element analysis of stress intensity factor K-I in some two-dimensional dynamic thermoelastic problems. Eng Anal Bound Elem 29(3):232–240CrossRefGoogle Scholar
  27. Huang JF, Chen GG, Zhao YH, Wang R (1990) An experimental study of the strain field development prior to failure of a marble plate under compression. Tectonophysics 175(1–3):269–284Google Scholar
  28. Ingraffea AR, Heuze FE (1980) Finite-element models for rock fracture-mechanics. Int J Numer Anal Methods Geomech 4(1):25–43CrossRefGoogle Scholar
  29. Kao CS, Carvalho FCS, Labuz JF (2011) Micromechanisms of fracture from acoustic emission. Int J Rock Mech Min Sci 48(4):666–673CrossRefGoogle Scholar
  30. Kawakata H, Cho A, Kiyama T, Yanagidani T, Kusunose K, Shimada M (1999) Three-dimensional observations of faulting process in Westerly granite under uniaxial and triaxial conditions by X-ray CT scan. Tectonophysics 313(3):293–305CrossRefGoogle Scholar
  31. Ko TY, Einstein HH, Kemeny J (2006) Crack coalescence in brittle material under cyclic loading. In: Golden rocks 2006, proceedings of the 41st US symposium on rock mechanics (USRMS): “50 years of rock mechanics-landmarks and future challenges”, Golden, Colorado, 17–21 June, ARMA/USRMS 06-930Google Scholar
  32. Lajtai EZ (1970) A theoretical and experimental evaluation of the Griffith theory of brittle fracture. Tectonophysics 11(2):129–156CrossRefGoogle Scholar
  33. Lajtai EZ (1974) Brittle fracture in compression. Int J Fract 10(4):525–536CrossRefGoogle Scholar
  34. Lan H, Martin CD, Hu B (2010) Effect of heterogeneity of brittle rock on micromechanical extensile behavior during compression loading. J Geophys Res 115:B01202. doi: 10.1029/2009JB006496
  35. Li YP, Chen LZ, Wang YH (2005) Experimental research on pre-cracked marble under compression. Int J Solids Struct 42(9–10):2505–2516CrossRefGoogle Scholar
  36. Li YH, Liu JP, Zhao XD, Yang YJ (2010) Experimental studies of the change of spatial correlation length of acoustic emission events during rock fracture process. Int J Rock Mech Min Sci 47(8):1254–1262CrossRefGoogle Scholar
  37. Lockner DA (1995) Rock failure, in rock physics & phase relations: a handbook of physical constants. American Geophysical Union, Washington, DC, pp 127–147Google Scholar
  38. Lockner DA, Byerlee JD, Kuksenko V, Ponomarev A, Sidorin A (1991) Quasi-static fault growth and shear fracture energy in granite. Nature 350(6313):39–42CrossRefGoogle Scholar
  39. Lockner DA, Byerlee JD, Kuksenko V, Ponomarev A, Sidorin A (1992) Observation of quasi-static fault growth from acoustic emissions. In: Evans B, Wong T-F (eds) Fault mechanics and transport properties of rocks. Academic press, New York, pp 3–31CrossRefGoogle Scholar
  40. Lu XP, Wu WL (2006) A subregion DRBEM formulation for the dynamic analysis of two-dimensional cracks. Math Comput Model 43(1–2):76–88CrossRefGoogle Scholar
  41. Martin CD (1993) The strength of massive Lac du Bonnet Granite around underground openings. Ph.D. Thesis, University of ManitobaGoogle Scholar
  42. Martin CD, Chandler NA (1994) The progressive fracture of Lac du Bonnet granite. Int J Rock Mech Min Sci Geomech Abstr 31(6):643–659CrossRefGoogle Scholar
  43. Martinez AR (1999) Fracture coalescence in natural rock. MSc Thesis, Massachusetts Institute of Technology, CambridgeGoogle Scholar
  44. Moradian ZA, Ballivy G, Rivard P, Gravel C, Rousseau B (2010) Evaluating damage during shear tests of rock joints using acoustic emissions. Int J Rock Mech Min Sci 47(4):590–598CrossRefGoogle Scholar
  45. Mughieda O, Alzo’ubi AK (2004) Fracture mechanisms of offset rock joints—a laboratory investigation. Geotech Geol Eng 22:545–606CrossRefGoogle Scholar
  46. Nematnasser S, Horii H (1982) Compression-induced nonplanar crack extension with application to splitting, exfoliation, and rockburst. J Geophys Res 87(NB8):6805–6821CrossRefGoogle Scholar
  47. Nesetova V, Lajtai EZ (1973) Fracture from compressive stress concentrations around elastic flaws. Int J Rock Mech Min Sci 10(4):265–284CrossRefGoogle Scholar
  48. Nie W, He MC, Zhao ZY (2010) Acoustic emission signature of different oriented sandstone specimens. In: Xie F (ed) Rock stress and earthquakes, pp 189–194Google Scholar
  49. Park CH, Bobet A (2009) Crack coalescence in specimens with open and closed flaws: a comparison. Int J Rock Mech Min Sci 46(5):819–829CrossRefGoogle Scholar
  50. Park CH, Bobet A (2010) Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression. Eng Fract Mech 77(14):2727–2748CrossRefGoogle Scholar
  51. Peng S, Johnson AM (1972) Crack growth and faulting in cylindrical specimens of chelmsford granite. Int J Rock Mech Min Sci 9(1):37–86CrossRefGoogle Scholar
  52. Petit JP, Barquins M (1988) Can natural faults propagate under modeII conditions? Tectonics 7(6):1243–1256CrossRefGoogle Scholar
  53. PFC2D (Particle Flow Code in 2 Dimensions) Version 3.1. 2004. Itasca Cons Group, MinneapolisGoogle Scholar
  54. Potyondy DO, Cundall PA (1998) Modeling notch-formation mechanisms in the URL mine-by test tunnel using bonded assemblies of circular particles. Int J Rock Mech Miner Sci Geomech Abstr 35:510–511CrossRefGoogle Scholar
  55. Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364CrossRefGoogle Scholar
  56. Potyondy DO, Cundall PA, Lee CA (1996) Modelling rock using bonded assemblies of circular particles. In: Aubertin M, Hassani F, Mitri H (eds) Rock mechanics tools and techniques, vols 1 and 2, pp 1937–1944Google Scholar
  57. Prikryl R, Lokajicek T, Li C, Rudajev V (2003) Acoustic emission characteristics and failure of uniaxially stressed granitic rocks: The effect of rock fabric. Rock Mech Rock Eng 36(4):255–270CrossRefGoogle Scholar
  58. Read RS, Martin CD (1996) Technical summary of AECL’s mine-by experiment. Phase 1 excavation response. AECL‐11311, COG-95-171, Atomic Energy of Canada Limited, BangaloreGoogle Scholar
  59. Reches Z, Lockner DA (1994) Nucleation and growth of faults in brittle rocks. J Geophys Res Solid Earth 99(B9):18159–18173CrossRefGoogle Scholar
  60. Reyes O, Einstein HH (1991) Failure mechanism of fractured rock—a fracture coalescence model. In: Proceedings of the seventh international congress on rock mechanics. Aachen, Germany, pp 333–340Google Scholar
  61. Roering C (1968) The geometrical significance of natural en-echelon crack-arrays. Tectonophysics 5(2):107–123CrossRefGoogle Scholar
  62. Sagong M, Bobet A (2002) Coalescence of multiple flaws in a rock-model material in uniaxial compression. Int J Rock Mech Min Sci 39(2):229–241CrossRefGoogle Scholar
  63. Shen B, Stephansson O (1994) Modification of the G-criterion for crack propagation subjected to compression. Eng Fract Mech 47(2):177–189CrossRefGoogle Scholar
  64. Shen BT, Stephansson O, Einstein HH, Ghahreman B (1995) Coalescence of fractures under shear stresses in experiments. J Geophys Res Solid Earth 100(B4):5975–5990CrossRefGoogle Scholar
  65. Tang CA, Kou SQ (1998) Crack propagation and coalescence in brittle materials under compression. Eng Fract Mech 61(3–4):311–324CrossRefGoogle Scholar
  66. Tang CA, Lin P, Wong RHC, Chau KT (2001) Analysis of crack coalescence in rock-like materials containing three flaws—Part II: numerical approach. Int J Rock Mech Min Sci 38(7):925–939CrossRefGoogle Scholar
  67. Tham LG, Liu H, Tang CA, Lee PKK, Tsui Y (2005) On tension failure of 2-D rock specimens and associated acoustic emission. Rock Mech Rock Eng 38(1):1–19CrossRefGoogle Scholar
  68. Thompson BD, Young RP, Lockner DA (2009) Premonitory acoustic emissions and stick-slip in natural and smooth-faulted Westerly granite. J Geophys Res 114:B02205. doi: 10.1029/2008JB005753
  69. Wong LNY (2008) Crack coalescence in molded gypsum and Carrara marble. Massachusetts Institute of Technology, CambridgeGoogle Scholar
  70. Wong RHC, Chau KT (1998) Crack coalescence in a rock-like material containing two cracks. Int J Rock Mech Min Sci 35(2):147–164CrossRefGoogle Scholar
  71. Wong LNY, Einstein HH (2006) Fracturing behavior of prismatic specimens containing single flaws. In: Proceedings of the 41st US symposium on rock mechanics, Golden, CO (paperARMA/USRMS06-899)Google Scholar
  72. Wong LNY, Einstein HH (2007) Coalescence behavior in Carrara marble and molded gypsum containing artificial flaw pairs under uniaxial compression. In: Proceedings of the first Can-US rock mechanics symposium, Vancouver, pp 581–589Google Scholar
  73. 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):475–511CrossRefGoogle Scholar
  74. 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):513–545CrossRefGoogle Scholar
  75. Wong LNY, Einstein HH (2009c) Systematic evaluation of cracking behavior in specimens containing single flaws under uniaxial compression. Int J Rock Mech Min Sci 46(2):239–249CrossRefGoogle Scholar
  76. Wong LNY, Einstein HH (2009d) Using high speed video imaging in the study of cracking processes in rock. Geotech Test J 32(2):164–180Google Scholar
  77. Wong RHC, Chau KT, Tang CA, Lin P (2001) Analysis of crack coalescence in rock-like materials containing three flaws—part I: experimental approach. Int J Rock Mech Min Sci 38(7):909–924CrossRefGoogle Scholar
  78. Wong RHC, Guo YSH, Li LY, Chau KT, Zhu WS, Li SC (2006) Anti-wing crack growth from surface flaw in real rock under uniaxial compression. In: 16th Eur conf fracture (EFC16), Alexandroupolis, Greece, pp 825–826Google Scholar
  79. Xu C, Fowell RJ (1994) Stress intensity factor evaluation for cracked chevron notched Brazilian disc specimens. Int J Rock Mech Min Sci Geomech Abstr 31(2):157–162CrossRefGoogle Scholar
  80. 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):871–889CrossRefGoogle Scholar
  81. Zhang X-P, Wong LNY, Wang S-J, Han G-Y (2011) Engineering properties of quartz mica schist. Eng Geol 121(3–4):135–149CrossRefGoogle Scholar
  82. Zhou XP, Zhang YX, Ha QL (2008) Real-time computerized tomography (CT) experiments on limestone damage evolution during unloading. Theor Appl Fract Mech 50(1):49–56CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.School of Civil and Environmental EngineeringNanyang Technological UniversitySingaporeSingapore
  2. 2.Key Laboratory of Engineering Geomechanics, Institute of Geology and GeophysicsChinese Academy of SciencesBeijingChina

Personalised recommendations