References
- Abrishambaf, A., Barros, J.A. and Cunha, V.M. (2015), "Tensile stress-crack width law for steel fibre reinforced self-compacting concrete obtained from indirect (splitting) tensile tests", Cement Concrete Compos., 57, 153-165. https://doi.org/10.1016/j.cemconcomp.2014.12.010.
- Akbas, S. (2016), "Analytical solutions for static bending of edge cracked micro beams", Struct. Eng. Mech., Int. J., 59(3), 579-599. https://doi.org/10.12989/sem.2016.59.3.579.
- Alhussainy, F., Hasan, H.A., Rogic, S., Sheikh, M.N. and Hadi, M.N. (2016), "Direct tensile testing of self-compacting concrete", Constr. Build. Mater., 112, 903-906. https://doi.org/10.1016/j.conbuildmat.2016.02.215.
- Aliabadian, Z., Zhao, G.F. and Russell, A.R. (2019), "Failure, crack initiation and the tensile strength of transversely isotropic rock using the Brazilian test", Int. J. Rock Mech. Min. Sci., 122, 104073. https://doi.org/10.1016/j.ijrmms.2019.104073.
- ASTM D2936-08 (2008), Standard Test Method for Direct Tensile Strength of Intact Rock Core Specimens, Annual Book of ASTM Standards, ASTM, West Conshohocken, USA.
- ASTM D2938-86 (1986), Test Method for Unconfined Compressive Resistance of Intact Rock Core Specimens, ASTM Designation, USA.
- ASTM D3967-16 (2008), Standard Test Method for Splitting Tensile Strength of Intact Rock Core Specimens, Annual Book of ASTM Standards, ASTM, West Conshohocken, USA.
- Bi, J., Zhou, X.P. and Qian, Q. (2016), "The 3D numerical simulation for the propagation process of multiple pre-existing flaws in rock-like materials subjected to biaxial compressive loads", Rock Mech. Rock Eng., 49(5), 1611-1627. https://doi.org/10.1007/s00603-015-0867-y.
- Bieniawski, Z.T. and Hawkes, I. (1978), "Suggested method for determining tensile strength of rock materials", Int. J. Rock Mech. Min. Sci. Geomech., 1, 99-103.
- CEB-FIB (2010), The Fib Model Code for Concrete Structures Case Postale 88, CH-1015 Lausanne, Switzerland.
- Chen, W.F. and Trumbauer, B.E. (1972), "Double-punch test and tensile strength of concrete", J. Mater., 7(2) 148-154. https://doi.org/10.1007/BF02403500
- Cundall, P.A. and Strack, O.D.L. (1979), "A discrete numerical model for granular assemblies", Geotechnique, 29(1), 47-65. https://doi.org/10.1680/geot.1979.29.1.47.
- Donze, F.V., Richefeu, V. and Magnier, S.A. (2009), "Advances in discrete element method applied to soil rock and concrete mechanics", Elec. J. Geol. Eng., 8, 1-44.
- Erarslan, N. and Williams, D.J. (2012), "Experimental, numerical and analytical studies on tensile strength of rocks", Int. J. Rock Mech. Min. Sci., 49, 21-30. https://doi.org/10.1016/j.ijrmms.2011.11.007.
- Ghaffar, A., Chaudhry, M.A. and Kamran Ali, M. (2005), "A new approach for measurement of tensile strength of concrete", J. Res. Sci., 16(1), 1-9.
- Hibbitt, H.D., Karlsson, B.I. and Sorensen, E.P. (2012), ABAQUS User's Manual, Dassault Systemes Simulia Corp., USA.
- Hillerborg, A. (1989), The Compression Stress-Strain Curve for Design of Reinforced Concrete Beams, Fracture Mechanics: Application to Concrete, ACI-SP-118, Detroit, USA.
- Hordijk, D.A. (1992), "Tensile and tensile fatigue behaviour of concrete experiments, modelling and analyses", Heron, 37(1), 3-79.
- Itasca Consulting Group Inc. (2003), "PFC2D (particle flow code in 2dimensions) version 3.0", ICGI, 41(8), 1329-1364.
- Khan, M.I. (2012), "Direct tensile strength measurement of concrete", Appl. Mech. Mater., 117, 9-14. https://doi.org/10.4028/www.scientific.net/AMM.117-119.9.
- Kim, J. and Taha, M.R. (2014), "Experimental and numerical evaluation of direct tension test for cylindrical concrete specimens", Adv. Civ. Eng., 2014, 156926. https://doi.org/10.1155/2014/156926.
- Li, S., Wang, H., Li, Y., Li, Q., Zhang, B. and Zhu, H. (2016), "A new mini-grating absolute displacement measuring system for static and dynamic geomechanical model tests", Measurement, 82, 421-431. https://doi.org/10.1016/j.measurement.2017.04.002.
- Liao, Z.Y., Zhu, J.B. and Tang, C.A. (2019), "Numerical investigation of rock tensile strength determined by direct tension, Brazilian and three-point bending tests", Int. J. Rock Mech. Min. Sci., 115, 21-32. https://doi.org/10.1016/j.ijrmms.2019.01.007.
- Liu, Y., Dai, F., Xu, N., Zhao, T. and Feng, P. (2018), "Experimental and numerical investigation on the tensile fatigue properties of rocks using the cyclic flattened Brazilian disc method", Soil Dyn. Earthq. Eng., 105, 68-82. https://doi.org/10.1016/j.soildyn.2017.11.025.
- Martin, C.D. (2014), "The direct and Brazilian tensile strength of rock in the light of size effect and bimodularity", Proceedings of the American Rock Mechanics Association: 48th U.S. Rock Mechanics/Geomechanics Symposium, Minneapolis, M.N., USA.
- Mier, V.J. (1986), "Multiaxial strain-softening of concrete", Mater. Struct., 19(111), 179-200. https://doi.org/10.1007/BF02472035.
- Mohammad, A. (2016), "Statistical flexural toughness modeling of ultra-high-performance concrete using response surface method", Comput. Concrete, Int. J., 17(4), 477-488. https://doi.org/10.12989/cac.2016.17.4.477.
- Omar, H., Ahmad, J., Nahazanan, H., Mohammed, T.A. and Yusoff, Z.M. (2018), "Measurement and simulation of diametrical and axial indirect tensile tests for weak rocks", Measurement, 127, 299-307. https://doi.org/10.1016/j.measurement.2018.05.067.
- Pan, B., Gao, Y. and Zhong, Y. (2014), "Theoretical analysis of overlay resisting crack propagation in old cement concrete pavement", Struct. Eng. Mech., Int. J., 52(4), 167-181. https://doi.org/10.12989/sem.2014.52.4.829.
- Potyondy, D.O. and Cundall, P.A. (2004), "A bonded-particle model for rock", Int. J. Rock Mech. Min. Sci., 41(8), 1329-1364. https://doi.org/10.1016/j.ijrmms.2004.09.011.
- Ramadoss, P. (2014), "Combined effect of silica fume and steel fibers on the splitting tensile strength of high-strength concrete", Int. J. Civ. Eng., 12(1), 99-103.
- Ramadoss, P. and Nagamani, K. (2006), "Investigations on the tensile strength of high-performance fiber reinforced concrete using statistical methods", Comput. Concrete, Int. J., 3(6), 389-400. https://doi.org/10.12989/cac.2006.3.6.389.
- Ramadoss, P. and Nagamani, K. (2008), "Tensile strength and durability characteristics of high-performance fiber reinforced concrete", Arab. J. Sci. Eng., 33(2), 307-319.
- Ramadoss, P. and Nagamani, K. (2013), "Stress-strain behavior and toughness of high-performance steel fiber reinforced concrete in compression", Comput. Concrete., Int. J., 11(2), 149-167. https://doi.org/10.12989/cac.2013.11.2.149.
- Sardemir, M. (2016), "Empirical modeling of flexural and splitting tensile strengths of concrete containing fly ash by GEP", Comput. Concrete, Int. J., 17(4), 489-498. https://doi.org/10.12989/cac.2016.17.4.489.
- Sarfarazi, V., Ghazvinian, A., Schubert, W., Nejati, H. and Hadei, R. (2016), "A new approach for measurement of tensile strength of concrete", Periodica Polytech. Civ. Eng., 60(2), 199-203. https://doi.org/10.3311/PPci.8328.
- Sarfarazi, V., Haeri, H. and Bagher Shemirani, A. (2017), "Direct and indirect methods for determination of mode I fracture toughness using PFC2D", Comput. Concrete, Int. J., 20(1), 39-47. https://doi.org/10.12989/cac.2017.20.1.039.
- Shang, J., Duan, K., Gui, Y., Handley, K. and Zhao, Z. (2018), "Numerical investigation of the direct tensile behaviour of laminated and transversely isotropic rocks containing incipient bedding planes with different strengths", Comput. Geotech., 104, 373-388. https://doi.org/10.1016/j.compgeo.2017.11.007.
- Shaowei, H., Aiqing, X., Xin, H. and Yangyang, Y. (2016), "Study on fracture characteristics of reinforced concrete wedge splitting tests", Comput. Concrete, Int. J., 18(3), 337-354. https://doi.org/10.12989/cac.2016.18.3.337.
- Shuraim, A.B., Aslam, F., Hussain, R. and Alhozaimy, A. (2016), "Analysis of punching shear in high strength RC panelsexperiments, comparison with codes and FEM results", Comput. Concrete, Int. J., 17(6), 739-760. https://doi.org/10.12989/cac.2016.17.6.739.
- Silva, R.V., De Brito, J. and Dhir, R.K. (2015), "Tensile strength behaviour of recycled aggregate concrete", Constr. Build. Mater., 83, 108-118. https://doi.org/10.1016/j.conbuildmat.2015.03.034.
- Swaddiwudhipong, S., Lu, H.R. and Wee, T.H. (2003), "Direct tension test and tensile strain capacity of concrete at early age", Cem. Concrete Res., 33, 2077-2084. https://doi.org/10.1016/S0008-8846(03)00231-X.
- Tran, K.Q., Satomi, T. and Takahashi, H. (2019), "Tensile behaviors of natural fiber and cement reinforced soil subjected to direct tensile test", J. Build. Eng., 24, 100748. https://doi.org/10.1016/j.jobe.2019.100748.
- Van Mier, J.G.M. (1992), "Assesment of strain softening curves for concrete", TU Delft, Mekelweg, Netherlands.
- Vonk, R.A. (1993), "A micromechanical investigation of softening of concrete loaded in compression", Heron, 38(3), 3-94.
- Wang, Q., Jias, X., Kou, S., Zang, Z. and 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. https://doi.org/10.1016/S1365-1609(03)00093-5.
- Wei, X.X. and Chau, K.T. (2013), "Three dimensional analytical solution for finite circular cylinders subjected to indirect tensile test", Int. J. Solids Struct., 50, 2395-2406. https://doi.org/10.1016/j.ijsolstr.2013.03.026.
- Xie, N.X. and Liu, W.Y. (1989), "Determining tensile properties of mass concrete by direct tensile test", ACI Mater. J., 86(3) 214-219.
- Yaylac, M. (2016), "The investigation crack problem through numerical analysis", Struct. Eng. Mech., Int. J., 57(6), 1143-1156. https://doi.org/10.12989/sem.2016.57.6.1143.
- Zain, M.F.M., Mahmud, H.B., Ilham, A. and Faizal, M. (2002), "Splitting tensile strength of high-performance concrete", Cem. Concrete. Res., 32, 1251-1257. https://doi.org/10.1016/S0008-8846(02)00768-8
- Zhang, Z.X. (2002), "An empirical relation between mode I fracture toughness and the tensile strength of rock", Int. J. Rock Mech. Min. Sci. Geomech., 93, 401-406. https://doi.org/10.1016/S1365-1609(02)00032-1
- Zhang, D., Hou, S., Bian, J. and He, L. (2016), "Investigation of the micro-cracking behavior of asphalt mixtures in the indirect tensile test", Eng. Fract. Mech., 163, 416-425. https://doi.org/10.1016/j.engfracmech.2016.05.020.
- Zheng, W., Kwan, A.K.H. and Lee, P.K.K. (2001), "Direct tension test of concrete", ACI Mater. J., 98(1) 63-71.
- Zhou, F.P. (1988), "Some aspects of tensile fracture behaviour and structural response of cementitious materials", Report TVBM-1008, Lund Institute of Technology, Lund, Sweden.
- Zhou, X.P. and Yang, H.Q. (2012), "Multiscale numerical modeling of propagation and coalescence of multiple cracks in rock masses", Int. J. Rock Mech. Min. Sci., 55, 15-27. https://doi.org/10.1016/j.ijrmms.2012.06.001.
- Zhou, X.P. and Wang, Y. (2016), "Numerical simulation of crack propagation and coalescence in pre-cracked rock-like Brazilian disks using the non-ordinary state-based peridynamics", Int. J. Rock Mech. Min. Sci., 89, 235-249. https://doi.org/10.1016/j.ijrmms.2016.09.010.
- Zhou, X.P., Zhang, Y.X., Ha, Q.L. and Zhu, K.S. (2008), "Micromechanical modelling of the complete stress-strain relationship for crack weakened rock subjected to compressive loading", Rock Mech. Rock Eng., 41(5), 747-769. https://doi.org/10.1007/s00603-007-0130-2.
- Zhou, X.P., Bi, J. and Qian, Q. (2015), "Numerical simulation of crack growth and coalescence in rock-like materials containing multiple pre-existing flaws", Rock Mech. Rock Eng., 48(3), 1097-1114. https://doi.org/10.1007/s00603-014-0627-4.