Abstract
Bonded-particle model (BPM) is widely used to model geomaterials, in which calibration against the results from uniaxial/triaxial compressive tests, Brazilian tensile tests and shear tests have been commonly conducted. However, since different loading rates were used, it is difficult to assess the numerical results of these studies if the effects of the loading rate are ignored. This paper discusses the loading mechanisms associated with different loading rates in the BPM and examines the numerical outputs under these different rates. The results indicate that the time step is an important factor controlling the loading rate of the BPM and should be considered in addition to the velocity of the loading platen. The strain rate, which is usually employed to describe the loading rate in a physical test, cannot be used for the direct comparison of different numerical tests in \(\hbox {PFC}^{\mathrm{2D}}\) due to the time step. A proposed “step strain rate”, which considers the time step, is found to be more appropriate for comparing the loading velocity on specimens of varying sizes. Six different loading rates (0.005, 0.01, 0.02, 0.08, 0.2 and 0.6 m/s) are employed in uniaxial compressive tests and Brazilian tests during this study. After comprehensive examinations, a maximum step strain rate of \(1.1 \times 10^{-8}\, \hbox {step}^{-1}\) is considered to be appropriate for quasi-static uniaxial compressive tests and Brazilian tests using the BPM.
Similar content being viewed by others
References
Cheung LYG, O’Sullivan C, Coop MR (2013) Discrete element method simulations of analogue reservoir sandstones. Int J Rock Mech Min Sci 63:93–103
Cho N, Martin CD, Sego DC (2007) A clumped particle model for rock. Int J Rock Mech Min Sci 44:997–1010
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 45:1335–1346
Cho N, Martin CD, Sego DC, Jeon J (2010) Dilation and spalling in axially compressed beams subjected to bending. Rock Mech Rock Eng 43:123–133
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 discussion. 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 74:129–138
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 40:193–211
Fakhimi A, Lanari M (2014) DEM-SPH simulation of rock blasting. Comput Geotech 55:158–164
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 105:16683–16697
Hazzard JF, Collins DS, Pettitt WS, Young RP (2002) Simulation of unstable fault slip in granite using a bonded-particle model. Pure Appl Geophys 159:221–245
Hsieh YM, Li HH, Huang TH, Jeng FS (2008) Interpretations on how the macroscopic mechanical behavior of sandstone affected by microscopic properties-Revealed by bonded-particle model. Eng Geol 99:1–10
Huang J, Xu S, Hu S (2014) Influence of particle breakage on the dynamic compression responses of brittle granular materials. Mech Mater 68:15–28
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
Jenck O, Dias D, Kastner R (2009) Discrete element modelling of a granular platform supported by piles in soft soil—validation on a small scale model test and comparison to a numerical analysis in a continuum. Comput Geotech 36:917–927
Jeng FS, Li HH, Huang TH (2007) The use of a bonded-particle model for studying the mechanical behavior of weak rock. In: The second half century of rock mechanics 11th congress of the international society for rock mechanics, Lisbon, Portugal
Jeng FS, Wang TT, Li HH, Huang TH (2008) Influences of microscopic factors on macroscopic strength and stiffness of inter-layered rocks—revealed by a bonded particle model. J Mech 24:379–389
Jiang MJ, Yan HB, Zhu HH, Utili S (2011) Modeling shear behavior and strain localization in cemented sands by two-dimensional distinct element method analyses. Comput Geotech 38:14–29
Kim BS, Park SW, Kato S (2012) DEM simulation of collapse behaviours of unsaturated granular materials under general stress states. Comput Geotech 42:52–61
Kwok CY, Bolton MD (2010) DEM simulations of thermally activated creep in soils. Geotechnique 60(6):425–433
Kwok CY, Bolton MD (2011) The role of particle breakage in soil creep. In: 2nd international FLAC/DEM symposium on numerical modeling, Melbourne, Australia
Kwok CY, Bolton MD, Cheng YP (2008) Discrete element simulation of crack growth in a single grain. In: 1st International FLAC/DEM symposium on numerical modeling, Minneapolis, USA
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
Lan HX, Martin CD, Hu B (2010) Effect of heterogeneity of brittle rock on micromechanical extensile behavior during compression loading. J Geophys Res Solid Earth 115:B01202
Lo CM, Lin ML, Tang CL, Hu JC (2011) A kinematic model of the Hsiaolin landslide calibrated to the morphology of the landslide deposit. Eng Geol 123:22–39
Manouchehrian A, Sharifzadeh M, Marji MF, Gholamnejad J (2014) A bonded particle model for analysis of the flaw orientation effect on crack propagation mechanism in brittle materials under compression. Arch Civil Mech Eng 14(1):40–52
Martin CD, Chandler NA (1994) The progressive fracture of Lac du Bonnet granite. Int J Rock Mech Min Sci Geomech Abstr 31:643–659
Olsson WA (1991) The compressive strength of tuff as strain rate from \(10^{6}\) to \(10^{3}\)/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 N (2006) Discrete element modeling of rock fracture behavior: fracture toughness and time-dependent fracture growth. The University of Texas, Austin
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 46:1315–1328
Potyondy DO (2007) Simulating stress corrosion with a bonded-particle model for rock. Int J Rock Mech Min Sci 44:677–691
Potyondy DO (2010) A grain-based model for rock: approaching the true microstructure. In: Proceedings of rock mechanics in the nordic countries, Kongsberg, Norway
Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41:1329–1364
Shimizu H, Koyama T, Ishida T, Chijimatsu M, Fujita T, Nakama S (2010) Distinct element analysis for Class II behavior of rocks under uniaxial compression. Int J Rock Mech Min Sci 47:323–333
Tang C-L, Hu J-C, Lin M-L, Angelier J, Lu C-Y, Chan Y-C, Chu H-T (2009) The Tsaoling landslide triggered by the Chi-Chi earthquake, Taiwan: insights from a discrete element simulation. Eng Geol 106:1–19
Vesga LF, Vallejo LE, Lobo-Guerrero S (2008) DEM analysis of the crack propagation in brittle clays under uniaxial compression tests. Int J Numer Anal Methods Geomech 32:1405–1415
**a M, Zhao C, Hobbs BE (2014) Particle simulation of thermally-induced rock damage with consideration of temperature-dependent elastic modulus and strength. Comput Geotech 55:461–473
Yan WM (2009) Fabric evolution in a numerical direct shear test. Comput Geotech 36:597–603
Yoon JS (2007) Application of experimental design and optimization to PFC model calibration in uniaxial compression simulation. Int J Rock Mech Min Sci 44:871–889
Yoon JS, Zang A, Stephansson O (2012) Simulating fracture and friction of Aue granite under confined asymmetric compressive test using clumped particle model. Int J Rock Mech Min Sci 49:68–83
Zhang X-P, Wong LNY (2012) 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 X-P, Wong LNY (2013a) Loading rate effects on cracking behavior of flaw-contained specimens under uniaxial compression. Int J Fract 180(1):93–110
Zhang X-P, Wong LNY (2013b) 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):1001–1021
Zhang XP, Wu SC, Zhang B, Pan W (2008a) Particle flow code simulation of specimen mechanical behavior with different geometric parameters of weak seams. J Eng Geol 16:539–545 (in Chinese)
Zhang XP, Wu SC, Zhang ZZ, Hu B (2008b) Numerical simulation and analysis of failure process of soil with weak intercalated layer. Rock Soil Mech 29:1200–1209 (in Chinese)
Zhang X-P, Wong LNY, Wang SJ, Han GY (2011) Engineering properties of quartz mica schist. Eng Geol 121:135–149
Zhao ZH (2013) Gouge particle evolution in a rock fracture undergoing shear: a microscopic DEM study. Rock Mech Rock Eng 46(6):1461–1479
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 69:2302–2329
Acknowledgments
The research was supported by the Academic Research Fund Tier 1 (RG19/10) and the Nanyang Technological University Start Up Grant (M4080115.030). The first author was also supported by the National Natural Science Foundation of China (Grant No. 41302235).
Author information
Authors and Affiliations
Corresponding author
Additional information
**ao-** Zhang was formerly School of Civil and Environmental Engineering, Nanyang Technological University, Block N1, Nanyang Avenue, Singapore 639798, Singapore.
Rights and permissions
About this article
Cite this article
Zhang, XP., Wong, L.N.Y. Choosing a proper loading rate for bonded-particle model of intact rock. Int J Fract 189, 163–179 (2014). https://doi.org/10.1007/s10704-014-9968-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-014-9968-y