Probabilistic Calibration of Compressive Stress–Strain Models for FRP-Confined Concrete in Square Cross Section Members
Publication: Journal of Composites for Construction
Volume 26, Issue 3
Abstract
The confinement effect of concrete by fiber-reinforced polymer (FRP) jackets may significantly enhance the axial compressive performance of concrete, although the results are variable. Therefore, rational calibration of deterministic models for compressive strength and the associated strain and stress–strain (SS) curves is required based on available experimental databases and selected probabilistic models. To improve the accuracy of the probabilistic model, second branch classifications for the stress–strain curve of FRP-confined concrete are identified within a series combination of uncertainties with computerized classification algorithms before probabilistic calibrations. The Bayesian theorem and Markov chain Monte Carlo (MCMC) approaches were used to update a probabilistic model that includes the critical variables that have been established in previous research. Furthermore, eight representative deterministic strength enhancement models, three strain enhancement models, and four stress–strain models were chosen for evaluation using credible intervals (CIs) and confidence levels (CLs) at different strain levels. Different types of FRPs were also analyzed individually to ensure the validity and reliability of the findings. The suggested probabilistic models can predict the properties of ultimate axial stress and related strain, thus offering an effective method for calibrating the confidence level and computational correctness of deterministic models previously published in the literature.
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Data Availability Statement
All data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
Notation
The following symbols are used in this paper:
- B
- width of square concrete specimen (mm);
- Ec
- elastic modulus of concrete;
- Ef
- elastic modulus of fibers;
- Efrp
- elastic modulus of FRP;
- fco
- peak axial compressive stress of unconfined concrete (MPa);
- fcu
- ultimate axial compressive stress of FRP-confined concrete (MPa);
- flu
- nominal confining pressure at ultimate (MPa);
- flu,a
- actual confining pressure at ultimate (MPa);
- fcu/fco
- deterministic strength enhancement of confined concrete;
- (fcu/fco)p
- probabilistic strength enhancement of confined concrete;
- G
- Lag for MCMC;
- ka1, kd1
- probabilistic model parameters of strength enhancement;
- ka2, kd2
- probabilistic model parameters of strain enhancement;
- kɛ,f
- hoop rapture strain reduction factors of fibers;
- kɛ,frp
- hoop rapture strain reduction factors of FRP;
- Kl
- lateral confinement stiffness (MPa);
- Klo
- minimum threshold for comparing with Kl;
- m
- Burn-In for MCMC;
- r
- corner radius of square concrete specimen (mm);
- t
- thickness of FRP material (mm);
- tf
- total thickness of FRP (mm);
- tfrp
- total thickness of fibers (mm);
- W
- K−S test result;
- WN,a
- critical value for K–S test;
- α
- significance level;
- ɛco
- axial strain of unconfined concrete at fco;
- ɛcu
- ultimate axial strain of FRP-confined concrete;
- ɛf
- ultimate tensile strain of the fibers;
- ɛfrp
- ultimate tensile strain of the FRP materials;
- ɛh,rup
- hoop rupture strain of FRP shell;
- ɛcu/ɛco
- deterministic strain enhancement of confined concrete; and
- (ɛcu/ɛco)p
- probabilistic strain enhancement of confined concrete.
References
Abbasnia, R., and H. Ziaadiny. 2015. “Experimental investigation and strength modeling of CFRP-confined concrete rectangular prisms under axial monotonic compression.” Mater. Struct. 48 (1–2): 485–500. https://doi.org/10.1617/s11527-013-0198-y.
ACI (American Concrete Institute). 2011. Building code requirement for structural concrete. ACI 318-11. Farmington Hills, MI: ACI.
Baji, H., H. R. Ronagh, and C. Q. Li. 2016. “Probabilistic design models for ultimate strength and strain of FRP-confined concrete.” J. Compos. Constr. 20 (6): 04016051. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000704.
Chen, L., and T. Ozbakkaloglu. 2016. “Corner strengthening of square and rectangular concrete-filled FRP tubes.” Eng. Struct. 117: 486–495. https://doi.org/10.1016/j.engstruct.2016.03.031.
Chen, Q.-S., B. Yu, and B. Li. 2021. “Probabilistic calibration of strength and strain enhancement models for FRP-confined concrete in circular section.” Constr. Build. Mater. 304: 124673. https://doi.org/10.1016/j.conbuildmat.2021.124673.
de Diego, A., Á Arteaga, and J. Fernández. 2019. “Strengthening of square concrete columns with composite materials. Investigation on the FRP jacket ultimate strain.” Composites, Part B 162: 454–460. https://doi.org/10.1016/j.compositesb.2019.01.017.
Hany, N. F., E. G. Hantouche, and M. H. Harajli. 2015. “Axial stress–strain model of CFRP-confined concrete under monotonic and cyclic loading.” J. Compos. Constr. 19 (6): 04015004. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000557.
Huang, L., T. Yu, S.-S. Zhang, and Z.-Y. Wang. 2017. “FRP-confined concrete-encased cross-shaped steel columns: Concept and behaviour.” Eng. Struct. 152: 348–358. https://doi.org/10.1016/j.engstruct.2017.09.011.
Jeon, J.-S., S. Mangalathu, J. Song, and R. Desroches. 2019. “Parameterized seismic fragility curves for curved multi-frame concrete box-girder bridges using Bayesian parameter estimation.” J. Earthquake Eng. 23 (6): 954–979. https://doi.org/10.1080/13632469.2017.1342291.
Jiang, T., and J. G. Teng. 2007. “Analysis-oriented stress–strain models for FRP-confined concrete.” Eng. Struct. 29 (11): 2968–2986. https://doi.org/10.1016/j.engstruct.2007.01.010.
Karabinis, A. I., T. C. Rousakis, and G. E. Manolitsi. 2008. “3D finite-element analysis of substandard RC columns strengthened by fiber-reinforced polymer sheets.” J. Compos. Constr. 12 (5): 531–540. https://doi.org/10.1061/(ASCE)1090-0268(2008)12:5(531).
Kent, D. C., and R. Park. 1971. “Flexural members with confined concrete.” J. Struct. Div. 97 (7): 1969–1990. https://doi.org/10.1061/JSDEAG.0002957.
Keshtegar, B., A. Gholampour, T. Ozbakkaloglu, S.-P. Zhu, and N.-T. Trung. 2020. “Reliability analysis of FRP-confined concrete at ultimate using conjugate search direction method.” Polymers 12 (3): 707. https://doi.org/10.3390/polym12030707.
Lam, L., and J. G. Teng. 2003. “Design-oriented stress–strain model for FRP-confined concrete.” Constr. Build. Mater. 17 (6–7): 471–489. https://doi.org/10.1016/S0950-0618(03)00045-X.
Li, B., R. Park, and H. Tanaka. 2001. “Stress–strain behavior of high-strength concrete confined by ultra-high-and normal-strength transverse reinforcements.” ACI Struct. J. 98 (3): 395–406. https://hdl.handle.net/10356/95044.
Li, P., L. Sui, F. Xing, M. Li, Y. Zhou, and Y.-F. Wu. 2019. “Stress–strain relation of FRP-confined predamaged concrete prisms with square sections of different corner radii subjected to monotonic axial compression.” J. Compos. Constr. 23 (2): 04019001. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000921.
Lim, J. C., and T. Ozbakkaloglu. 2014a. “Confinement model for FRP-confined high-strength concrete.” J. Compos. Constr. 18 (4): 04013058. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000376.
Lim, J. C., and T. Ozbakkaloglu. 2014b. “Design model for FRP-confined normal- and high-strength concrete square and rectangular columns.” Mag. Concr. Res. 66 (20): 1020–1035. https://doi.org/10.1680/macr.14.00059.
Lin, S., Y.-G. Zhao, and J. Li. 2019. “An improved wrapping scheme of axially loaded fiber-reinforced polymer confined concrete columns.” Compos. Struct. 226: 111242. https://doi.org/10.1016/j.compstruct.2019.111242.
Mander, J. B., M. J. Priestley, and R. Park. 1988. “Theoretical stress–strain model for confined concrete.” J. Struct. Eng. 114 (8): 1804–1826. https://doi.org/10.1061/(ASCE)0733-9445(1988)114:8(1804).
Nisticò, N., F. Pallini, T. Rousakis, Y.-F. Wu, and A. Karabinis. 2014. “Peak strength and ultimate strain prediction for FRP confined square and circular concrete sections.” Composites, Part B 67: 543–554. https://doi.org/10.1016/j.compositesb.2014.07.026.
Ozbakkaloglu, T., J. C. Lim, and T. Vincent. 2013. “FRP-confined concrete in circular sections: Review and assessment of stress–strain models.” Eng. Struct. 49: 1068–1088. https://doi.org/10.1016/j.engstruct.2012.06.010.
Ozbakkaloglu, T., and T. Xie. 2016. “Geopolymer concrete-filled FRP tubes: Behavior of circular and square columns under axial compression.” Composites, Part B 96: 215–230. https://doi.org/10.1016/j.compositesb.2016.04.013.
Pan, Y., R. Guo, H. Li, H. Tang, and J. Huang. 2017. “Analysis-oriented stress–strain model for FRP-confined concrete with preload.” Compos. Struct. 166: 57–67. https://doi.org/10.1016/j.compstruct.2017.01.007.
Razali, N. M., and Y. B. Wah. 2011. “Power comparisons of Shapiro–Wilk, Kolmogorov–Smirnov, Lilliefors and Anderson–Darling tests.” J. Stat. Model. Anal. 2 (1): 21–33.
Richart, F. E., A. Brandtzæg, and R. L. Brown. 1928. A study of the failure of concrete under combined compressive stresses. Bulletin No. 185. Urbana, IL: Univ. of Illinois at Urbana Champaign, College of Engineering. Engineering Experiment Station.
Sheikh, S. A., and S. M. Uzumeri. 1982. “Analytical model for concrete confinement in tied columns.” J. Struct. Div. 108 (12): 2703–2722. https://doi.org/10.1061/(ASCE)0733-9445(1983)109:12(2952).
Tasdemir, M. A., C. Tasdemir, S. Akyüz, A. D. Jefferson, F. D. Lydon, and B. I. G. Barr. 1998. “Evaluation of strains at peak stresses in concrete: A three-phase composite model approach.” Cem. Concr. Compos. 20 (4): 301–318. https://doi.org/10.1016/S0958-9465(98)00012-2.
Triantafyllou, G. G., T. C. Rousakis, and A. I. Karabinis. 2015. “Axially loaded reinforced concrete columns with a square section partially confined by light GFRP straps.” J. Compos. Constr. 19 (1): 04014035. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000496.
Wang, D. Y., Z. Y. Wang, S. T. Smith, and T. Yu. 2016. “Size effect on axial stress–strain behavior of CFRP-confined square concrete columns.” Constr. Build. Mater. 118: 116–126. https://doi.org/10.1016/j.conbuildmat.2016.04.158.
Wei, Y.-Y., and Y.-F. Wu. 2012. “Unified stress–strain model of concrete for FRP-confined columns.” Constr. Build. Mater. 26 (1): 381–392. https://doi.org/10.1016/j.conbuildmat.2011.06.037.
Wu, G., Z. S. Wu, and Z. T. Lü. 2007. “Design-oriented stress–strain model for concrete prisms confined with FRP composites.” Constr. Build. Mater. 21 (5): 1107–1121. https://doi.org/10.1016/j.conbuildmat.2005.12.014.
Youssef, M. N., M. Q. Feng, and A. S. Mosallam. 2007. “Stress–strain model for concrete confined by FRP composites.” Composites, Part B 38 (5–6): 614–628. https://doi.org/10.1016/j.compositesb.2006.07.020.
Yu, B., S. Liu, and B. Li. 2019a. “Probabilistic calibration for shear strength models of reinforced concrete columns.” J. Struct. Eng. 145 (5): 04019026. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002307.
Yu, B., R. Tang, and B. Li. 2019b. “Probabilistic calibration for development length models of deformed reinforcing bar.” Eng. Struct. 182: 279–289. https://doi.org/10.1016/j.engstruct.2018.12.047.
Zeng, J.-J., Y.-C. Guo, W.-Y. Gao, J.-Z. Li, and J.-H. Xie. 2017. “Behavior of partially and fully FRP-confined circularized square columns under axial compression.” Constr. Build. Mater. 152: 319–332. https://doi.org/10.1016/j.conbuildmat.2017.06.152.
Zhu, J. Y., G. Lin, J.-G. Teng, T.-M. Chan, J.-J. Zeng, and L.-J. Li. 2020. “FRP-confined square concrete columns with section curvilinearization under axial compression.” J. Compos. Constr. 24 (2): 04020004. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000999.
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Journal of Composites for Construction
Volume 26 • Issue 3 • June 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: May 27, 2021
Accepted: Dec 20, 2021
Published online: Feb 23, 2022
Published in print: Jun 1, 2022
Discussion open until: Jul 23, 2022
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