Abstract
It has been widely accepted that tensile strength plays a dominant role in the failure mechanism of rock or rock-like material. Tensile strength is determined mainly via two methods: the direct tension test and Brazilian test. Due to the strictness of preparing the specimen and difficulty of conducting the direct tension test, Brazilian test has been widely applied to determine the tensile strength of geo-materials. However, there is no exact standard for Brazilian test specimen. Moreover, Brazilian tensile strength (BTS) is affected by many factors, such as loading rate, loading platen width, model size. So far, most parametric studies of geo-materials have involved compression tests, but few studies have systematically focused on Brazilian test. The continuum methods have difficulty reproducing the failure process of Brazilian test, and 2D discrete element methods can not reflect the real mechanical behavior of a 3D cylindrical disk specimen. Moreover, the standard bonded-particle model has intrinsic problems in simulating geo-materials. This paper, using a 3D flat-joint model (FJM3D), investigates the effects of micro-structure and micro-parameters on BTS. The micro-structure consists of model size, model resolution, and degree of heterogeneity. The micro-parameters include the average coordination number, crack density, and bond strength. The effects on BTS are summarized, and this summary will be useful for guiding future Brazilian tests. Finally, FJM3D is used to calibrate Brisbane tuff by Brazilian test and the uniaxial compression test. The simulation results are in good agreement with those measured from experiments, and the failure process of Brazilian test is analyzed in detail at the microscale. Because of the heterogeneity of rock, cracks initiate near the loading platen instead of the center of the specimen. Even so, BTS can be an useful tensile index for geo-materials in a triaxial stress state, which is similar to the physical situations, and Brazilian test is helpful for further understanding the failure mechanism of geo-materials.
Similar content being viewed by others
References
Akazawa T (1943) New test method for evaluating internal stress due to compression of concrete (the splitting tension test)(part 1). J Jpn Soc Civ Eng 29:777–787
Andreev G (1991a) A review of the Brazilian test for rock tensile strength determination. Part I: calculation formula. Min Sci Technol 13:445–456. doi:10.1016/0148-9062(94)90005-1
Andreev G (1991b) A review of the Brazilian test for rock tensile strength determination. Part II: contact conditions. Min Sci Technol 13:457–465. doi:10.1016/0167-9031(91)91035-G
Bahrani N, Valley B, Kaiser P, Pierce M (2011) Evaluation of PFC2D grain-based model for simulation of confinement-dependent rock strength degradation and failure processes. In: Proceedings of 45th US rock mechanics/geomechanics symposium, San Francisco, CA, pp 11–156
Bazant ZP, Kazemi MT, Hasegawa T, Mazars J (1991) Size effect in Brazilian split-cylinder tests: measurements and fracture analysis. ACI Mater J 88:325–332
Birkimer DL (1970) A possible fracture criterion for the dynamic tensile strength of rock. In: The 12th US Symposium on Rock Mechanics (USRMS). American Rock Mechanics Association
Blair S, Cook N (1998) Analysis of compressive fracture in rock using statistical techniques: Part II. Effect of microscale heterogeneity on macroscopic deformation. Int J Rock Mech Min Sci 35:849–861. doi:10.1016/S0148-9062(98)00009-6
Cai M, Kaiser P (2004) Numerical simulation of the Brazilian test and the tensile strength of anisotropic rocks and rocks with pre-existing cracks. Int J Rock Mech Min Sci 41:478–483. doi:10.1016/j.ijrmms.2004.03.086
Carneiro F (1943) A new method to determine the tensile strength of concrete. In: Proceedings of the 5th meeting of the Brazilian Association for Technical Rules, 3d. Section, pp 126–129
Chen WF, Yuan RL (1980) Tensile strength of concrete: double-punch test. J Struct Div 106:1673–1693
Cho S-H, Yang H-S, Katsuhiko K (2003a) Influence of rock inhomogeneity on the dynamic tensile strength of rock. J Korean Soc Rock Mech 13:180–186
Cho S-H, Yang H-S, Katsuhiko K (2003b) Influence of rock inhomogeneity on the static tensile strength of rock. J Korean Soc Rock Mech 13:117–124
Cho SH, Ogata Y, Kaneko K (2003c) Strain-rate dependency of the dynamic tensile strength of rock. Int J Rock Mech Min Sci 40:763–777. doi:10.1016/S1365-1609(03)00072-8
Cho N, Martin C, Sego D (2007) A clumped particle model for rock. Int J Rock Mech Min Sci 44:997–1010. doi:10.1016/j.ijrmms.2007.02.002
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, Toronto, pp 113–122
Dan DQ, Konietzky H, Herbst M (2013) Brazilian tensile strength tests on some anisotropic rocks. Int J Rock Mech Min Sci 58:1–7. doi:10.1016/j.ijrmms.08.010
Ding X, Zhang L (2014) A new contact model to improve the simulated ratio of unconfined compressive strength to tensile strength in bonded particle models. Int J Rock Mech Min Sci 69:111–119. doi:10.1016/j.ijrmms.2014.03.008
Ding X, Zhang L, Zhu H, Zhang Q (2014) Effect of model scale and particle size distribution on PFC3D simulation results. Rock Mech Rock Eng 47:2139–2156. doi:10.1007/s00603-013-0533-1
Erarslan N, Williams D (2012a) Investigating the effect of cyclic loading on the indirect tensile strength of rocks. Rock Mech Rock Eng 45:327–340. doi:10.1007/s00603-011-0209-7
Erarslan N, Williams DJ (2012b) Experimental, numerical and analytical studies on tensile strength of rocks. Int J Rock Mech Min Sci 49:21–30. doi:10.1016/j.ijrmms.2011.11.007
Erarslan N, Liang ZZ, Williams DJ (2012) Experimental and numerical studies on determination of indirect tensile strength of rocks. Rock Mech Rock Eng 45:739–751. doi:10.1007/s00603-011-0205-y
Fairhurst C, Cook N (1966) The phenomenon of rock splitting parallel to the direction of maximum compression in the neighborhood of a surface. In: Proceedings of the first congress on the international society of rock mechanics, pp 687–692
Griffith A (1921) The phenomena of flow and rupture in solids. Philos Trans R Soc Lond Ser A 221:163–198
Hajiabdolmajid V, Kaiser P, Martin C (2002) Modelling brittle failure of rock. Int J Rock Mech Min Sci 39:731–741. doi:10.1016/S1365-1609(02)00051-5
Hudson J, Brown E, Rummel F (1972) The controlled failure of rock discs and rings loaded in diametral compression. Int J Rock Mech Min Sci Geomech Abstr (Elseiver) 2:241–248. doi:10.1016/0148-9062(72)90025-3
Inglis CE (1913) Stresses in a plate due to the presence of cracks and sharp corners. Inst Nav Archit 55:219–246
ISRM (1978) Suggested methods for determining tensile strength of rock materials. Int J Rock Mech Min Sci Geomech Abstr 15(3):99–103. doi:10.1016/0148-9062(78)90003-7
Itasca Consulting Group, Inc. (2015) PFC—Particle Flow Code in 2 and 3 Dimensions, Version 5.0, Documentation Set of version 5.00.21. Minneapolis. Itasca
Kemeny J (1991) A model for non-linear rock deformation under compression due to sub-critical crack growth. Int J Rock Mech Min Sci Geomech Abstr (Elseiver) 6:459–467. doi:10.1016/0148-9062(91)91121-7
Kemeny JM, Cook NG (1991) Micromechanics of deformation in rocks. In: Toughening mechanisms in quasi-brittle materials. Springer, pp 155–188. doi:10.1007/978-94-011-3388-3_10
Kittitep F, Sippakorn K (2010) Laboratory determination of direct tensile strength and deformability of intact rocks. doi:10.1520/GTJ103134
Li D, Wong LNY (2013) The Brazilian disc test for rock mechanics applications: review and new insights. Rock Mech Rock Eng 46:269–287. doi:10.1007/s00603-012-0257-7
Martin C, Chandler N (1994) The progressive fracture of Lac du Bonnet granite. Int J Rock Mech Min Sci Geomech Abstr 6:643–659. doi:10.1016/0148-9062(94)90005-1
Mellor M, Hawkes I (1971) Measurement of tensile strength by diametral compression of discs and annuli. Eng Geol 5:173–225. doi:10.1016/0013-7952(71)90001-9
Nakashima S, Taguchi K, Moritoshi A, Shimizu N, Funatsu T (2013) Loading conditions in the Brazilian test simulation by DEM. In: 47th US rock mechanics/geomechanics symposium. American Rock Mechanics Association
Oda M (1977) Co-ordination number and its relation to shear strength of granular material. Soils Foudation Eng 17(2):29–42. doi:10.3208/sandf1972.17.2_29
Perras MA, Diederichs MS (2014) A review of the tensile strength of rock: concepts and testing. Geotech Geol Eng 32:525–546. doi:10.1007/s10706-014-9732-0
Potyondy D (2011) Parallel-bond refinements to match macroproperties of hard rock. In: Proceedings of the second international FLAC/DEM symposium, Melbourne: Minneapolis. Itasca, pp 459–465
Potyondy DO (2012) A flat-jointed bonded-particle material for hard rock. In: Proceedings of 46th U.S. rock mechanics/geomechanics symposium, Chicago, USA, June 24–27
Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41:1329–1364. doi:10.1016/j.ijrmms.2004.09.011
Rocco C, Guinea G, Planas J, Elices M (1999a) Size effect and boundary conditions in the Brazilian test: theoretical analysis. Mater Struct 32:437–444. doi:10.1007/BF02482715
Rocco C, Guinea GV, Planas J, Elices M (1999b) Size effect and boundary conditions in the Brazilian test: experimental verification. Mater Struct 32:210–217. doi:10.1007/BF02481517
Scholtès L, Donzé F-V (2013) A DEM model for soft and hard rocks: role of grain interlocking on strength. J Mech Phys Solids 61:352–369. doi:10.1016/j.jmps.10.005
Schöpfer MP, Abe S, Childs C, Walsh JJ (2009) The impact of porosity and crack density on the elasticity, strength and friction of cohesive granular materials: insights from DEM modelling. Int J Rock Mech Min Sci 46:250–261. doi:10.1016/j.ijrmms.2008.03.009
Swab JJ, Yu J, Gamble R, Kilczewski S (2011) Analysis of the diametral compression method for determining the tensile strength of transparent magnesium aluminate spinel. Int J Fract 172:187–192. doi:10.1007/s10704-011-9655-1
Tomac I, Gutierrez M (2012) Evaluation of the Brazilian test size effect using discrete element modeling. In: 46th US rock mechanics/geomechanics symposium. American Rock Mechanics Association
Ulusay R (2015) The ISRM suggested methods for rock characterization, testing and monitoring: 2007–2014. Springer International Publishing, Berlin
Van de Steen B (2001) Effect of heterogeneities and defects on the fracture pattern in brittle rock status: published
Wang Y, Tonon F (2009) Modeling Lac du Bonnet granite using a discrete element model. Int J Rock Mech Min Sci 46:1124–1135. doi:10.1016/j.ijrmms.05.008
Wang Q-Z, Xing L (1999) Determination of fracture toughness K IC by using the flattened Brazilian disk specimen for rocks. Eng Fract Mech 64:193–201. doi:10.1016/S0013-7944(99)00065-X
Wang Q, Jia X, Kou S, Zhang Z, Lindqvist P-A (2004) The flattened Brazilian disc specimen used for testing elastic modulus, tensile strength and fracture toughness of brittle rocks: analytical and numerical results. Int J Rock Mech Min Sci 41:245–253. doi:10.1016/S1365-1609(03)00093-5
Wu S, Xu X (2015) A study of three intrinsic problems of the classic discrete element method using flat-joint model. Rock Mech Rock Eng. doi:10.1007/s00603-015-0890-z
Yang B, Jiao Y, Lei S (2006) A study on the effects of microparameters on macroproperties for specimens created by bonded particles. Eng Comput 23:607–631. doi:10.1108/02644400610680333
Zhang Y, Stead D (2014) Modelling 3D crack propagation in hard rock pillars using a synthetic rock mass approach. Int J Rock Mech Min Sci 72:199–213
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. doi:10.1007/s00603-011-0176-z
Zhang Z, Kou S, Yu J, Yu Y, Jiang L, Lindqvist P-A (1999) Effects of loading rate on rock fracture: fracture characteristic and energy partitioning. Int J Rock Mech Min Sci 36:597–611. doi:10.1016/S1365-1609(00)00008-3
Zhao J, Li H (2000) Experimental determination of dynamic tensile properties of a granite. Int J Rock Mech Min Sci 37:861–866
Acknowledgments
The research was supported by the Key Program of Natural Science Foundation of China (51074014, 51174014) and Beijing Training Project for the Leading Talent in S & T (Z151100000315014). The authors would also like to thank Dr. David Potyondy, the Chief Scientist at Itasca Consulting Group, for his valuable comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xu, X., Wu, S., Gao, Y. et al. Effects of Micro-structure and Micro-parameters on Brazilian Tensile Strength Using Flat-Joint Model. Rock Mech Rock Eng 49, 3575–3595 (2016). https://doi.org/10.1007/s00603-016-1021-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00603-016-1021-1