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
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
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
Bobet A, Einstein HH (1998) Numerical modeling of fracture coalescence in a model rock material. Int J Fract 92(3): 221–252
Brace WF, Jones AH (1971) Comparison of uniaxial deformation in shock and static loading of three rocks. J Geophys Res 76(20):4913–4921
Cho N, Martin CD, Sego DC (2007) A clumped particle model for rock. Int J Rock Mech Min Sci 44(7):997–1010
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
Clayton JD (2010) Deformation, fracture, and fragmentation in brittle geologic solids. Int J Fract 163:151–172
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
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
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
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
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
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
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
Hoek E, Bieniawski ZT (1965) Brittle fracture propagation in rock under compression. Int J Fract Mech 1(3):137–155
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
Kim Y, Chao YJ (2007) Effect of loading rate on dynamic fracture initiation toughness of brittlle materials. Int J Fract 145(3):195–204
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
Lavrov A (2001) Kaiser effect observation in brittle rock cyclically loaded with different loading rates. Mech Mater 33(11):669–677
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
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
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
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
Ozbolt J, Rah KK, Mestrovic D (2006) Influence of loading rate on concrete cone failure. Int J Fract 139(2):239–252
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
Park CH, Bobet A (2010) Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression. Eng Fract Mech 77(14):2727–2748
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
Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364
Potyondy DO (2007) Simulating stress corrosion with a bonded-particle model for rock. Int J Rock Mech Min Sci 44(5): 677–691
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
Tang CA, Kou SQ (1998) Crack propagation and coalescence in brittle materials under compression. Eng Fract Mech 61 (3–4):311–324
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
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
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
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
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
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
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
Zhang ZX (2004) Estimate of loading rate for a TBM machine based on measured cutter forces. Rock Mech Rock Eng 37(3):239–248
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
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
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
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
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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