Research on Stress–Strain Model of FRP-Confined Concrete Based on Compressive Fracture Energy
Abstract
1. Introduction
2. Model Derivation
2.1. Stress–Strain Relationship of Actively Confined Concrete
2.1.1. Compressive Fracture Energy
2.1.2. Stress–Strain Relationship
2.2. Compressive Strength and Strain at Peak Stress of Confined Concrete
- (1)
- For a given lateral confining pressure , assign an axial strain .
- (2)
- Calculate the compressive fracture energy from Equation (1) and the compressive strength and strain at peak stress of confined concrete from Equations (12) and (13), respectively.
- (3)
- Determine according to Equation (11), i.e., if the specimen length satisfies Equation (11), is equal to the specimen length; if the specimen length is smaller than , is taken as ; and if the specimen length is larger than the upper bound of Equation (11), is taken as the upper bound.
- (4)
- Calculate the strain at 50% of peak stress on the descending branch from Equation (9).
- (5)
- Evaluate the stress from Equations (4) and (5).
2.3. Stress–Strain Relationship of FRP-Confined Concrete
2.3.1. Axial–Lateral Strain Correlation
2.3.2. Numerical Method for Stress–Strain Relationship of FRP-Confined Concrete
- (1)
- Input the geometric and material parameters of FRP-confined concrete.
- (2)
- Assign an axial strain .
- (3)
- If the FRP composite and the circular concrete column work in coordination, calculate their lateral strains as equal. Calculate the lateral strain and confining pressure by simultaneously solving Equations (19) and (20).
- (4)
- Check whether exceeds or not. If exceeds , terminate the calculation; otherwise, proceed to the next step.
- (5)
- Calculate from Equation (1) and and from Equations (12) and (13), respectively.
- (6)
- Determine according to Equation (11).
- (7)
- Calculate the strain from Equation (9).
- (8)
- Adhere to the above assumption where, when FRP-confined concrete and actively confined concrete are subjected to the same lateral strain and confining pressure at a specific loading stage, their axial stress–strain relationships are identical at that stage. Evaluate the axial stress from Equations (4) and (5).
3. Model Validation
4. Parametric Analysis and Discussion
5. Conclusions
- (1)
- Empirical formulae for predicting the compressive strength and strain at peak stress of actively confined concrete have been presented by fitting experimental data from the literature.
- (2)
- An assumption correlating the stress–strain relationships of actively confined concrete and FRP-confined concrete has been proposed. Based on this assumption, a numerical method for evaluating the stress–strain relationship of FRP-confined concrete has been developed by combining the stress–strain relationship of actively confined concrete with the axial–lateral strain correlation presented by earlier researchers. Through comparisons with experimental results collected from the literature, the validity of the numerical method has been verified.
- (3)
- The effect of specimen length on the stress–strain relationship of FRP-confined concrete has been evaluated for different confinement conditions and failure strains. The numerical results show that for strong FRP confinement with small failure strains, the specimen length exhibits no influence on the stress–strain relationship of FRP-confined concrete, while for weak FRP confinement with small and large failure strains, the axial stress at an axial strain of 0.006 decreases by 10.12% and 48.79% for an increase in specimen length from 300 mm to 900 mm, respectively. Therefore, it has been concluded that the specimen length effect should be considered when evaluating the stress–strain relationship of weakly confined FRP-confined concrete.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
CFRP | carbon fiber-reinforced polymer |
FRP | fiber-reinforced polymer |
RC | reinforced concrete |
Notation
, , , , , , ,, , | coefficients |
characteristic size of column cross-section, mm | |
elastic modulus of concrete, MPa | |
elastic modulus of FRP or CFRP, GPa | |
compressive strength of unconfined concrete, MPa | |
compressive strength of confined concrete, MPa | |
compressive fracture energy of confined concrete, N mm | |
compressive fracture energy of unconfined concrete, N mm | |
element length, mm | |
fracture process zone length, mm | |
lateral confining pressure, MPa | |
maximum lateral confining pressure provided by FRP to circular concrete column, MPa | |
thickness of FRP or CFRP, mm | |
strain at 50% of peak stress on descending branch of stress–strain curve of confined concrete | |
axial strain | |
strain at peak stress of unconfined concrete | |
strain at peak stress of confined concrete | |
actual tensile rupture strain of FRP | |
direct tensile rupture strain of FRP | |
lateral strain in concrete or FRP | |
axial stress, MPa | |
function in terms of |
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Source | Specimen | Diameter × Length (mm) | (MPa) | FRP Type | (GPa) | (mm) |
---|---|---|---|---|---|---|
Picher et al. [29] | C0 | 150 × 300 | 39.7 | CFRP | 83 | 0.9 |
Mastrapa [30] | B3 | 152 × 305 | 30 | GFRP | 27.63 | 1.75 |
Owen [31] | D12L6 | 298 × 610 | 58.1 | CFRP | 267.37 | 0.66 |
D12L12 | 298 × 610 | 58.1 | CFRP | 267.37 | 1.32 | |
Xiao [32] | LCL1 | 152 × 305 | 33.7 | CFRP | 105 | 0.381 |
LCL2 | 152 × 305 | 33.7 | CFRP | 105 | 0.762 |
Type | Diameter (mm) | Length Range (mm) | (MPa) | (mm) | (GPa) | |
---|---|---|---|---|---|---|
Strong confinement with a small failure strain | 150 | 300–900 | 30 | 0.33 | 240 | 0.01 |
Weak confinement with a small failure strain | 150 | 300–900 | 30 | 0.80 | 10 | 0.01 |
Weak confinement with a large failure strain | 150 | 300–900 | 30 | 0.80 | 10 | 0.03 |
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Wu, M.; Fan, X.; Qian, H. Research on Stress–Strain Model of FRP-Confined Concrete Based on Compressive Fracture Energy. Buildings 2025, 15, 2716. https://doi.org/10.3390/buildings15152716
Wu M, Fan X, Qian H. Research on Stress–Strain Model of FRP-Confined Concrete Based on Compressive Fracture Energy. Buildings. 2025; 15(15):2716. https://doi.org/10.3390/buildings15152716
Chicago/Turabian StyleWu, Min, Xinglang Fan, and Haimin Qian. 2025. "Research on Stress–Strain Model of FRP-Confined Concrete Based on Compressive Fracture Energy" Buildings 15, no. 15: 2716. https://doi.org/10.3390/buildings15152716
APA StyleWu, M., Fan, X., & Qian, H. (2025). Research on Stress–Strain Model of FRP-Confined Concrete Based on Compressive Fracture Energy. Buildings, 15(15), 2716. https://doi.org/10.3390/buildings15152716