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Loading rate effects on cracking behavior of flaw-contained specimens under uniaxial compression

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Abstract

To investigate the loading rate effects on the cracking processes of flaw-contained specimens under compressive loading, rectangular parallelepiped specimens containing centrally located single and double flaw(s) are numerically loaded using the bonded-particle model (BPM). The study reveals that the uniaxial compressive stress (\(\upsigma _\mathrm{c})\) and coalescence stress (\(\upsigma _\mathrm{cc})\) increase significantly, while the first crack initiation stress (\(\upsigma _\mathrm{ci})\) only subtly increases with the increase of loading rate. The trajectories of the first and secondary cracks become shorter while the amount of discrete micro-cracks increases as the loading rate increases. The mode of coalescence cracks changes from tensile-segments-dominant to shear-band-dominant when the loading rate increases. The shape of the stress-strain curves of specimens loaded at different rates also varies. Based on the present study, an upper limit of loading rate of 0.08 m/s deems to be acceptable for cracking processes analysis under static load using the BPM.

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References

  • Aliha M, Ayatollahi M, Pakzad R (2008) Brittle fracture analysis using a ring-shape specimen containing two angled cracks. Int J Fract 153(1):63–68

    Article  Google Scholar 

  • Asadi MS, Rasouli V (2011) PFC2D simulation of directionality in rough fractures shear strength, 2nd International FLAC/DEM Symposium, Ist edn. Itasca Consulting Group, Melbourne, Australia

  • Bazant ZP, Bai SP, Gettu R (1993) Fracture of rock: effect of loading rate. Eng Fract Mech 45(3):393–398

    Article  Google Scholar 

  • Blanton TL (1981) Effect of strain rates from \(10^{-2}\) to \(10\,\text{ sec}^{-1}\) in triaxial compression tests on three rocks. Int J Rock Mech Min Sci Geomech Abstr 18(1):47–62

    Article  Google Scholar 

  • Bobet A, Einstein HH (1998) Numerical modeling of fracture coalescence in a model rock material. Int J Fract 92(3): 221–252

    Google Scholar 

  • Brace WF, Jones AH (1971) Comparison of uniaxial deformation in shock and static loading of three rocks. J Geophys Res 76(20):4913–4921

    Article  Google Scholar 

  • Cho N, Martin CD, Sego DC (2007) A clumped particle model for rock. Int J Rock Mech Min Sci 44(7):997–1010

    Article  Google Scholar 

  • Cho N, Martin CD, Sego DC (2008) Development of a shear zone in brittle rock subjected to direct shear. Int J Rock Mech Min Sci 45(8):1335–1346

    Article  Google Scholar 

  • Clayton JD (2010) Deformation, fracture, and fragmentation in brittle geologic solids. Int J Fract 163:151–172

    Article  Google Scholar 

  • Cundall PA (1971) A computer model for simulating progressive large scale movements in blocky rock systems. In: Proceedings of the symposium of the international society of rock mechanics, Nancy, France

  • Cundall PA, Strack OD (1979) A discrete numerical model for granular assemblies. Geotechnique 29:47–65

    Article  Google Scholar 

  • Fakhimi A (2004) Application of slightly overlapped circular particles assembly in numerical simulation of rocks with high friction angles. Eng Geol 74(1–2):129–138

    Article  Google Scholar 

  • 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): 193–211

    Google Scholar 

  • Fakhimi A, Gharahbagh EA (2011) Discrete element analysis of the effect of pore size and pore distribution on the mechanical behavior of rock. Int J Rock Mech Min Sci 48(1):77–85

    Article  Google Scholar 

  • 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):677–693

    Google Scholar 

  • Hazzard JF, Young RP, Maxwell SC (2000) Micromechanical modeling of cracking and failure in brittle rocks. J Geophys Res Solid Earth 105(B7):16683–16697

    Article  Google Scholar 

  • Hazzard JF, Collins DS, Pettitt WS, Young RP (2002) Simulation of unstable fault slip in granite using a bonded-particle model. Pure Appl Geophys 159(1–3):221–245

    Article  Google Scholar 

  • Hoek E, Bieniawski ZT (1965) Brittle fracture propagation in rock under compression. Int J Fract Mech 1(3):137–155

    CAS  Google Scholar 

  • Itasca (2004) PFC2D (Particle Flow Code in 2 Dimensions) version 3.1, Minneapolis

  • Jackson K, Kingman SW, Whittles DN, Lowndes IS, Reddish DJ (2008) The effect of strain rate on the breakage behaviour of rock. Arch Min Sci 53(1):3–22

    Google Scholar 

  • Kim Y, Chao YJ (2007) Effect of loading rate on dynamic fracture initiation toughness of brittlle materials. Int J Fract 145(3):195–204

    Article  CAS  Google Scholar 

  • Lankford J (1981) The role of tensile microfracture in the strain rate dependence of compressive strenght of fine-grained limestone–analogy with strong ceramics. Int J Rock Mech Min Sci 18(2):173–175

    Article  Google Scholar 

  • Lavrov A (2001) Kaiser effect observation in brittle rock cyclically loaded with different loading rates. Mech Mater 33(11):669–677

    Article  Google Scholar 

  • Li XF, Liu GL, Lee KY (2009) Effects of T-stresses on fracture initiation for a closed crack in compression with frictional crack faces. Int J Fract 160(1):19–30

    Article  Google Scholar 

  • Liu C, Knauss WG, Rosakis AJ (1998) Loading rates and the dynamic initiation toughness in brittle solids. Int J Fract 90 (1–2):103–118

    Google Scholar 

  • Logan JM, Handin J (1970) Triaxial compression testing at intermediate strain rates, The 12th U.S. Symposium on Rock Mechanics (USRMS). American Rock Mechanics Association, Rolla, MO

  • Moss WC, Gupta YM (1982) A constitutive model describing dilatancy and cracking in brittle rocks. J Geophys Res 87:2985–2998

    Article  Google Scholar 

  • Olsson WA (1991) The compressive strength of tuff as strain rate from \(10^{6}\) to \(10^{3}/\text{ sec}\). Int J Rock Mech Min Sci Geomech Abstr 28(1):115–118

    Article  Google Scholar 

  • Ozbolt J, Rah KK, Mestrovic D (2006) Influence of loading rate on concrete cone failure. Int J Fract 139(2):239–252

    Article  CAS  Google Scholar 

  • Park JW, Song JJ (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

    Article  Google Scholar 

  • Park CH, Bobet A (2010) Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression. Eng Fract Mech 77(14):2727–2748

    Article  Google Scholar 

  • Perkins RD, Green SJ, Friedman M (1970) Uniaxial stress behavior of porphyritic tonalite at strain rates to \(10^{3}/\text{ second}\). Int J Rock Mech Min Sci 7(5):527–535

    Article  Google Scholar 

  • Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364

    Article  Google Scholar 

  • Potyondy DO (2007) Simulating stress corrosion with a bonded-particle model for rock. Int J Rock Mech Min Sci 44(5): 677–691

    Google Scholar 

  • Shen BT, Stephansson O, Einstein HH, Ghahreman B (1995) Coalescence of fractures under shear stresses in experiments. J Geophy Res Solid Earth 100(B4):5975–5990

    Article  Google Scholar 

  • Tang CA, Kou SQ (1998) Crack propagation and coalescence in brittle materials under compression. Eng Fract Mech 61 (3–4):311–324

    Google Scholar 

  • 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): 925–939

    Google Scholar 

  • Wong LNY, Zhang XP (submitted) Size effects on cracking behavior of flaw-contained specimen under compressive loading. Rock Mech Rock Eng

  • Wong NY (2008) Crack coalescence in molded gypsum and carrara marble, PhD Thesis, Massachusetts Institute of Technology, Cambridge, MA, 876

  • 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):909–924

    Article  Google Scholar 

  • 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):475–511

    Article  Google Scholar 

  • 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):513–545

    Article  Google Scholar 

  • 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):239–249

    Article  Google Scholar 

  • Xia M, Zhou KP (2010) Particle simulation of the failure process of brittle rock under triaxial compression. Int J Miner Metall Mater 17(5):507–513

    Article  CAS  Google Scholar 

  • Yang SQ, Jing HW (2011) Strength failure and crack coalescence behavior of brittle sandstone samples containing a single fissure under uniaxial compression. Int J Fract 168(2): 227–250

    Google Scholar 

  • Zhang ZX (2004) Estimate of loading rate for a TBM machine based on measured cutter forces. Rock Mech Rock Eng 37(3):239–248

    Google Scholar 

  • Zhang XP, Wong LNY (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 45:711–737

  • Zhang XP, 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. doi:10.1007/s00603-012-0323-1

  • Zhang ZX, Kou SQ, Yu J, Yu Y, Jiang LG, Lindqvist PA (1999) Effects of loading rate on rock fracture. Int J Rock Mech Min Sci 36(5):597–611

    Article  Google Scholar 

  • Zhang ZX, Yu J, Kou SQ, Lindqvist PA (2001) Effects of high temperatures on dynamic rock fracture. Int J Rock Mech Min Sci 38(2):211–225

    Article  CAS  Google Scholar 

  • Zhao CB, Hobbs BE, Ord A, Hornby P, Peng SL, Liu LM (2007) Particle simulation of spontaneous crack generation problems in large-scale quasi-static systems. Int J Numer Methods Eng 69(11):2302–2329

    Google Scholar 

  • Zhou XP, Qian QH, Yang HQ (2010) Effect of loading rate on fracture characteristics of rock. J Cent South Univ Technol 17(1):150–155

    Article  Google Scholar 

Download references

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Correspondence to Louis Ngai Yuen Wong.

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Zhang, XP., Wong, L.N.Y. Loading rate effects on cracking behavior of flaw-contained specimens under uniaxial compression. Int J Fract 180, 93–110 (2013). https://doi.org/10.1007/s10704-012-9803-2

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  • DOI: https://doi.org/10.1007/s10704-012-9803-2

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