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.
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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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