Acknowledgement
This paper was financially supported by the National Natural Science Foundation of China (Grant No. 51478395 and Grant No. 51978582). The anonymous referees would likely to be acknowledged by authors for their evaluation of the paper.
References
- ABAQUS Inc. (2014), ABAQUS User's Manual-Version 6.14.
- Alfarah, B., Lopez-Almansa, F. and Oller, S. (2017), "New methodology for calculating damage variables evolution in plastic damage model for RC structures", Eng. Struct., 132(2), 70-86. https://doi.org/10.1016/j.engstruct.2016.11.022.
- Ansari, F. and Li, Q.B. (1998), "High-strength concrete subjected to triaxial compression", ACI Mater. J., 95(6), 747-755. https://doi.org/10.14359/420.
- Balmer, G.G. (1949), "Shearing strength of concrete under high triaxial stress-computation of mohrs envelope as a curve", Structural Research Laboratory Report No. SP-23, US Department of the Interior, Washington, D.C.
- Candappa, D.C., Sanjayan, J.G. and Setunge, S. (2001), "Complete triaxial stress-strain curves of high-strength concrete", J. Mater. Civil Eng., 13(3), 209-215. https://doi.org/10.1061/(ASCE)0899-1561(2001)13:3(209).
- Cervenka, J. and Papanikolaou, V.K. (2008), "Three dimensional combined fracture-plastic material model for concrete", Int. J. Plast., 24(12), 2192-2220. https://doi.org/10.1016/j.ijplas.2008.01.004.
- Chen, Y., Feng, J. and Yin, S. (2012), "Compressive behavior of reinforced concrete columns confined by multi-spiral hoops", Comput. Concrete, 9(5), 341-355. https://doi.org/10.12989/cac.2012.9.5.341.
- Chen, W.F. and Han, D.J. (1988), Plasticity for Structural Engineers, Springer-Verlag, New York, NY, USA.
- Chinn, J. and Zimmerman, R.M. (1965), "Behaviour of plain concrete under various high triaxial compression loading conditions", Technical Report No. WL TR 64-163, Air Force Weapons Laboratory, New Mexico, USA.
- Cicekli, U., Voyiadjis, G.Z. and Al-Rub, R.K.A. (2007), "A plasticity and anisotropic damage model for plain concrete", Int. J. Plast., 23(10), 1874-1900. https://doi.org/10.1016/j.ijplas.2007.03.006.
- Ding, F. and Yu, Z. (2006), "Strength criterion for plain concrete under multiaxial stress based on damage Poisson's ratio", Acta Mech. Solid. Sinica, 19(4), 307-315. https://doi.org/10.1007/s10338-006-0637-1.
- Du, X.L., Lu, D.C., Gong, Q.M. and Zhao, M. (2010), "Nonlinear unified strength criterion for concrete under three-dimensional stress states", J. Eng. Mech., 136(1), 51-59. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000055.
- Ebadi-Jamkhaneh, M., Homaioon-Ebrahimi, A. and Kontoni, D.P.N. (2021), "Numerical finite element study of strengthening of damaged reinforced concrete members with carbon and glass FRP wraps", Comput. Concrete, 28(2), 137-147. https://doi.org/10.12989/cac.2021.28.2.137.
- Etse, G. and Willam, K. (1994), "Fracture energy formulation for inelastic behavior of plain concrete", J. Eng. Mech., 120(9), 1983-2011. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:9(1983).
- Ferrotto, M.F., Cavaleri, L. and Di Trapani, F. (2018), "FE modeling of Partially Steel-Jacketed (PSJ) RC columns using CDP model", Comput. Concrete, 22(2), 143-152. https://doi.org/10.12989/cac.2018.22.2.143.
- Grassl, P. and Jirasek, M. (2006), "Damage-plastic model for concrete failure", Int. J. Solid. Struct., 43(22), 7166-7196. https://doi.org/10.1016/j.ijsolstr.2006.06.032.
- Grassl, P. et al. (2013), "CDPM2: A damage-plasticity approach to modelling the failure of concrete", Int. J. Solid. Struct., 50(24), 3805-3816. https://doi.org/10.1016/j.ijsolstr.2013.07.008.
- Chuanzhi, G.Z.W. (1991), "Investigation of strength and failure criterion of concrete under multi-axial stresses [J]", China Civil Eng. J., 3.
- Hany, N.F., Hantouche, E.G. and Harajli, M.H. (2016), "Finite element modeling of FRP-confined concrete using modified concrete damaged plasticity", Eng. Struct., 125(10), 1-14. https://doi.org/10.1016/j.engstruct.2016.06.047.
- He, Z.J. and Song, Y.P. (2008), "Strength regularity and failure criterion of high-strength high-performance concrete under multiaxial compression", J. Southwest Jiaotong Univ., 16(2), 144-149. https://doi.org/cnki:sun:xnjy.0.2008-02-007.
- Hidayat, B.A., Hu, H.T., Hsiao, F.P., Han, A.L., Sosa, L., Chan, L.Y. and Haryanto, Y. (2021), "Seismic behavior and failure modes of non-ductile three-story reinforced concrete structure: A numerical investigation", Comput. Concrete, 27(5), 457-472. https://doi.org/10.12989/cac.2021.27.5.457.
- Hobbs, D.W. (1970), "Strength and deformation properties of plain concrete subjected to combined stress-part 1: Strength results obtained on one concrete", Cement and Concrete Association Technical Report 42, 451, 1-12.
- Hsieh, S.S, Ting, E.C. and Chen, W.F. (1982), "A plasticity-fracture model for concrete", Int. J. Solid. Struct., 18(3), 181-197. https://doi.org/10.1016/0020-7683(82)90001-4.
- Imran, I. and Pantazopoulou, S.J. (1996), "Experimental study of plain concrete under triaxial stress", ACI Mater. J., 93(6), 589-601. https:/doi.org/10.14359/9865.
- Jiang, L., Huang, D. and Xie, N. (1991), "Behaviour of concrete under triaxial compressive-compressive-tensile stresses", ACI Mater. J., 88(2), 181-185. https://doi.org/10.1016/0043-1648(91)90094-B.
- Kim, S.M. and Al-Rub, R.K.A. (2011), "Meso-scale computational modeling of the plastic-damage response of cementitious composites", Cement Concrete Res., 41(3), 339-358. https://doi.org/10.1016/j.cemconres.2010.12.002.
- Kotsovos, M.D. (2015), Finite-Element Modelling of Structural Concrete: Short-Term Static and Dynamic Loading Conditions, CRC Press/Taylor and Francis, Boca Raton, FL, USA.
- Kotsovos, M.D. (1979), "A mathematical description of the strength properties of concrete under generalized stress", Mag. Concrete Res., 31(128), 151-158. https://doi.org/10.1680/macr.1979.31.108.151.
- Kupfer, H., Hilsdorf, H.K. and Rusch, H. (1969), "Behavior of concrete under biaxial stresses", ACI Mater. J., 66(8), 656-666. http://doi.org/10.1061/JMCEA3.0001789.
- Lade, P.V. (1982), "Three-parameter failure criterion for concrete", J. Eng. Mech. ASCE, 108(5), 850-863. https://doi.org/10.1061/JMCEA3.0002874.
- Lade, P.V. (2014), "Estimating parameters from a single test for the three-dimensional failure criterion for frictional materials", J. Geotech. Geoenvir., 140(8), 04014038. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001137.
- Lahlou, K., Aictin, P.C. and Chaallal, O. (1993), "Behaviour of high-strength concrete under confined stresses", Cement Concrete Compos., 14(3), 185-193. https://doi.org/10.1016/0958-9465(92)90012-K.
- Launay, P. and Gachon, H. (1970), "Strain and ultimate strength of concrete under triaxial stresses", ACI Spec., 34(1), 269-282.
- Lee, J. and Fenves, G.L. (1998), "Plastic-damage model for cyclic loading of concrete structures", J. Eng. Mech., 124(8), 892-900. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:8(892).
- Li, Q.B. and Ansari, F. (2000), "High-strength concrete in triaxial compression by different sizes of specimens", ACI Mater. J., 97(6), 684-689.
- Lin, G. and Teng, J.G. (2017), "Three-dimensional finite-element analysis of FRP-confined circular concrete columns under eccentric loading", J. Compos. Constr., 21(4), 04017003. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000772.
- Liu, J. and Foster, S.J. (2000), "3-D finite element model for confined concrete structures", Comput. Struct., 77, 441-451. https://doi.org/10.1016/S0045-7949(00)00007-9.
- Lubliner, J., Oliver, J., Oller, S. and Onate, E. (1989), "A plastic-damage model for concrete", Int. J. Solid. Struct., 25(3), 299-326. https://doi.org/10.1016/0020-7683(89)90050-4.
- Menetrey, P. and Willam, K.J. (1995), "Triaxial failure criterion for concrete and its generalization", ACI Struct. J., 92(3), 311-318. https://doi.org/10.14359/1132.
- Mills, L.L. and Zimmerman, R.M. (1970), "Compressive strength of plain concrete under multiaxial loading conditions", ACI J. Proc., 67(10), 802-807. https://doi.org/10.14359/7310.
- Mohammadi, M. and Wu, Y.F. (2019), "Modified plastic-damage model for passively confined concrete based on triaxial tests", Compos. Part B Eng., 159(2), 211-223. https://doi.org/10.1016/j.compositesb.2018.09.074.
- Muthukumar, G. and Kumar, M. (2014), "Failure criteria of concrete-A review", Comput. Concrete, 14(5), 503-526. https://doi.org/10.12989/cac.2014.14.5.503.
- Newman, K. and Newman, J.B. (1971), "Failure theories and design criteria for plain concrete", Struct. Solid. Mech. Eng. Des., 963-995.
- Oller, S., Onate, E., Oliver, J. and Lubliner, J. (1990), "Finite element non-linear analysis of concrete structures using a "plastic-damage model"", Eng. Fract. Mech., 35(1-3), 219-231. https://doi.org/10.1016/0013-7944(90)90200-Z.
- Ottosen, N.S. (1977), "A failure criterion for concrete", J. Eng. Mech., 103(4), 527-535. https://doi.org/10.1061/JMCEA3.0002248.
- Ozbakkaloglu, T., Gholampour, A. and Lim, J.C. (2016), "Damage-plasticity model for FRP-confined normal-strength and high-strength concrete", J. Compos. Constr., 20(6), 04016053. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000712.
- Papanikolaou, V.K. and Kappos, A.J. (2007), "Confinement-sensitive plasticity constitutive model for concrete in triaxial compression", Int. J. Solid. Struct., 44(21), 7021-7048. https://doi.org/10.1016/j.ijsolstr.2007.03.022.
- Pisano, A.A., Fuschi, P. and De Domenico, D. (2013), "A kinematic approach for peak load evaluation of concrete elements", Comput. Struct., 119(4), 125-139. https://doi.org/10.1016/j.compstruc.2012.12.030.
- Piscesa, B., Attard, M.M. and Samani, A.K. (2018), "3D Finite element modeling of circular reinforced concrete columns confined with FRP using plasticity based formulation", Compos. Struct., 194(6), 478-493. https://doi.org/10.1016/j.compstruct.2018.04.039.
- Podgorski, J. (1985), "General failure criterion for isotropic media", J. Eng. Mech., 111(2), 188-201. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:2(188).
- Raza, A. and Ahmad, A. (2020), "Reliability analysis of proposed capacity equation for predicting the behavior of steel-tube concrete columns confined with CFRP sheets", Comput. Concrete, 25(5), 383-400. https://doi.org/10.12989/cac.2020.25.5.383.
- Richard, B., Ragueneau, F., Cremona, C. and Adelaide, L. (2010), "Isotropic continuum damage mechanics for concrete under cyclic loading: Stiffness recovery, inelastic strains and frictional sliding", Eng. Fract. Mech., 77(8), 1203-1223. https://doi.org/10.1016/j. engfracmech.2010.02.010.
- Richart, F.E., Brandtaeg, A. and Brown, R.L. (1928), A Study of the Failure of Concrete under Combined Compressive Stresses, University of Illinois, Engineering Experiment Station, Urbana, USA.
- Sarikaya, A. and Erkmen, R.E. (2019), "A plastic-damage model for concrete under compression", Int. J. Mech. Sci., 150(1), 584-593. https://doi.org/10.1016/j.ijmecsci.2018.10.042.
- Saritas, A. and Filippou, F.C. (2009), "Numerical integration of a class of 3d plastic-damage concrete models and condensation of 3d stress-strain relations for use in beam finite elements", Eng. Struct., 31(10), 2327-2336. https://doi.org/10.1016/j.engstruct.2009.05.005.
- Seow Puay Eng, C. (2006), "A unified failure criterion for normal, high-strength and steel fibre-reinforced concrete", Ph.D. Dissertation of Philosophy, National University of Singapore, Singapore.
- Sfer, D., Carol, I. and Gettu, R. (2002), "Study of the behavior of concrete under triaxial compression", J. Eng. Mech., 128(2), 156-163. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:2(156).
- Shahbeyk, S., Moghaddam, M.Z. and Safarnejad, M. (2017), "A physically consistent stress-strain model for actively confined concrete", Comput. Concrete, 20(1), 85-97. https://doi.org/10.12989/cac.2017.20.1.085.
- Sirijaroonchai, K. (2009), "A macro-scale plasticity model for high performance fiber reinforced cement composites", Ph.D. Dissertation of Philosophy, University of Michigan, Ann Arbor, USA.
- Szwed, A. and Inez, K. (2020), "Yield condition for concrete under moderate hydrostatic pressure", J. Theor. Appl. Mech., 58(2), 325-338. https://doi.org/10.15632/jtam-pl/116578.
- Taliercio, A.L.F. and Gobbi, E. (1997), "Effect of elevated triaxial cyclic and constant loads on the mechanical properties of plain concrete", Mag. Concrete Res., 49(181), 353-365. https://doi.org/10.1680/macr.1997.49.181.353.
- Tasuji, M.E. and Nilson, A.H. (1978), "Stress-strain response and fracture of concrete in biaxial loading", ACI J., 75(7), 306-312. https:/doi.org/10.14359/10944.
- Voyiadjis, G.Z., Taqieddin, Z.N. and Kattan, P.I. (2008), "Anisotropic damage-plasticity model for concrete", Int. J. Plast., 24(10), 1946-1965. https://doi.org/10.1016/j.ijplas.2008.04.002.
- Wang, C.Z., Guo, Z.H. and Zhang, X.Q. (1987), "An experimental investigation of biaxial and triaxial compressive concrete strength", ACI Mat. J., 84(2), 92-100. https://doi.org/10.1186/1532-429X-11-S1-O73.
- Willam, K.J. and Warnke, E.P. (1975), "Constitutive model for the triaxial behavior of concrete", IABSE Proceedings International association of bridge and structural engineers, Bergamo, Italy, May.
- Wu, J.Y., Li, J. and Faria, R. (2006), "An energy release rate-based plastic-damage model for concrete", Int. J. Solid. Struct., 43(3-4), 583-612. https://doi.org/10.1016/j.ijsolstr.2005.05.038.
- Wu, J.Y. (2004), "The elastoplastic damage constitutive model of concrete based on the damage energy release rate and the application in structural non-linear analysis", Ph.D. Dissertation of Philosophy, Tongji University, Shanghai, China.
- Wu, S., Zhang, S., Guo, C. and Xiong, L. (2017), "A generalized non-linear failure criterion for frictional materials", Acta Geotech., 12(6), 1353-1371. https://doi.org/10.1007/s11440-017-0532-6.
- Xie, J., Elwi, A.E. and MacGregor, J.G. (1995), "Mechanical properties of three high-strength concretes containing silica fume", ACI Mater. J., 92(2), 135-145. https://doi.org/10.14359/9764.
- Yu, M.H. and Li, J.C. (2012), Computational Plasticity: With Emphasis on the Application of The Unified Strength Theory, Springer Science and Business Media.
- Yu, T., Teng, J.G., Wong, Y.L. and Dong, S.L. (2010), "Finite element modeling of confined concrete-II: Plastic-damage model", Steel Constr., 32(3), 680-691. https://doi.org/10.1016/j.engstruct.2009.11.013.
- Zhang, J. and Li, J. (2012), "Investigation into Lubliner yield criterion of concrete for 3D simulation", Eng. Struct., 44(11), 122-127. https://doi.org/10.1016/j.engstruct.2012.05.031.
- Zhang, J. and Li, J. (2014), "Construction of homogeneous loading functions for elastoplastic damage models for concrete", Sci. China, 57(3), 490-500. https://doi.org/10.1007/s11433-013-5188-0.
- Zheng, F., Wu, Z., Gu, C., Bao, T. and Hu, J. (2012), "A plastic damage model for concrete structure cracks with two damage variables", Sci. China Tech. Sci., 55(11), 2971-2980. https://doi.org/10.1007/s11431-012-4983-6.