Investigation of CFRP- and GFRP-confined concrete cylinders under monotonic and cyclic loading

1 Introduction

The strengthening effect of the fiber-reinforced polymer (FRP) lateral confinement has been recognized for more than 10 years. Many mathematical models have been developed since to predict the response of FRP-confined concrete [1–6]. The vast majority of models consider a constant confining pressure exerted by the FRP material on concrete, similar to that provided by materials behaving in a plastic manner, such as conventional transverse reinforcing steel. However, as FRP jackets operate in the elastic range, they generate variable confining pressure. This pressure is dependent on the amount and stiffness of confinement provided. Many models for FRP-confined concrete also assume that the tensile rupture of FRP occurs when the hoop stress in the FRP reaches its uniaxial tensile strength. This is contrary to experimental evidence, which suggests that the FRP hoop rupture strain is sometimes much less than the FRP ultimate material tensile strain; therefore, these models fail to predict the level of confinement with reasonable accuracy. The confinement models must, therefore, be based on an effective rupture strain or strength of FRP obtained in the FRP-confined concrete rather than that obtained from tensile tests. In the absence of reliable models, high factors of safety are required, which make composite materials less economical.

This paper presents details of an experimental work carried out on concrete cylinders wrapped with FRP materials and subjected to both monotonic and cyclic loading. An extensive presentation of this experimental work can be found in [7]. The effect of the type of confinement material, reinforcement ratio based on the jacket stiffness, and type of loading is examined. A model that predicts the behavior of confined concrete, which takes into account the stiffness and effectiveness of different confinement materials, is also briefly introduced.

2 Experimental

2.2 Stress-strain behavior

2.2.1 CFRP confinement

In the case of specimens WC1-1 and WC1-2, the ultimate compressive strength of the confined concrete increased by about 75% of that of the plain (unconfined) concrete, f_co. At failure, the jacket strength was well mobilized in both specimens. The lateral strain in both cases was around 14,000 με. Specimens WC2-1 and WC2-2 appeared to have developed the full capacity of the CFRP jacket, and both of them exhibited an ultimate compressive strength of about 2.7 f_co. Figure 1 shows the normalized axial stress versus the lateral and axial strain for the WC2 specimens. The normalized axial stress is defined as the ratio of f_cl/f_co, where f_cl is the axial compressive strength of the confined concrete. The axial strains have positive values, while the lateral strains have negative values.

Figure 1

Stress-strain curves for WC2 specimens.

Samples WC3-1 and WC3-2 showed an ultimate compressive strength of about 3.5 f_co. At failure, in the cyclic test, the full capacity of the jacket was mobilized, while in the monotonic test, the specimen failed at around 14,500 με, as presented in Figure 2.

Figure 2

Stress-strain curves for WC3 specimens.

2.2.2 GFRP confinement

In the case of specimens WG2-1 and WG2-2, the ultimate compressive strength of confined concrete increased by about 35% with respect to that of the unconfined concrete, f_co. In both cases, the failure took place before the full mobilization of the GFRP jacket, at a lateral strain of about 16,000 με.

The compressive strength of the confined concrete in specimens WG3-1 and WG3-2 increased by about 40% and 50% of f_co, respectively. The failure of WG3-2 took place at a lateral strain of about 15,000 με, while specimen WG3-1 failed prematurely at around 7000 με lateral strain due to the damage of the jacket by the crushing concrete core. Figure 3 shows the normalized stress versus strain for specimens WG3-1 and WG3-2. The dotted line in the WG3-1 curve shows the expected normalized axial stress based on observations made from previous experiments.

Figure 3

Stress-strain curves for WG3 specimens.

In the case of specimens WG4-1 and WG4-2, the ultimate compressive strength of the confined concrete increased by about 90% of f_co. At failure, the GFRP jacket was again not fully mobilized, exhibiting lateral strains of about 16,000 με for both the monotonic loading (WG4-1) and cyclic loading (WG4-2). Figure 4 shows the normalized stress-strain curve for the two specimens.

Figure 4

Stress-strain curves for WG4 specimens.

2.3 Volumetric strain

The normalized axial stress and normalized axial/lateral strain were plotted versus the volumetric strain. The normalized axial strain is expressed as ε_cl/ε_co, and the normalized lateral strain is defined as ε_cr/ε_cor, where ε_cl and ε_cr are the average axial and lateral strains in the confined concrete, and ε_co and ε_cor are the average axial and lateral strains in the unconfined concrete (ε_co=0.002 and ε_cor=0.001). The volumetric strain is defined as (V-V₀)/V₀, where V₀ and V are the initial and final volumes of the concrete, respectively.

2.3.1 CFRP confinement

Figure 5A shows the relationship between the normalized axial stress and the volumetric strain for WC1-1 and WC1-2 specimens. It can be noted that WC1-1 appears to be less damaged than WC1-2, at similar levels of axial load. Both samples show a similar behavior as they developed more or less the same volumetric strain at failure. The maximum contraction of the concrete core for WC1-1 and WC1-2 was reached at about f_co and 0.8 f_co, respectively. The relationship between the axial and lateral strain and the volumetric strain for these two specimens after the initiation of expansion due to cracking is almost linear, as shown in Figure 5B.

Figure 5

WC1 specimens: (A) normalized axial stress versus volumetric strain, (B) normalized strain versus volumetric strain.

In the case of the WC2-1 and WC2-2 specimens, the volumetric expansion of the concrete core started when the compressive strength of the unconfined concrete, f_co, was reached, as shown in Figure 6A. Although both specimens showed a ductile behavior, WC2-2 exhibited a larger amount of contraction at the initial stages and a larger amount of expansion in the area of unstable crack propagation. As presented in Figure 6B, the relationship between the axial and lateral strain and the volumetric strain for the monotonic loading is almost quasilinear.

Figure 6

WC2 specimens: (A) normalized axial stress versus volumetric strain, (B) normalized strain versus volumetric strain.

At failure, specimen WC3-1 had an expansion much less than that of specimen WC3-2, as presented in Figure 7A. The contraction point of concrete reached its maximum value at f_co and 0.8 f_co for WC3-2 and WC3-1, respectively. As shown in Figure 7B, although the normalized axial strain values are higher for WC3-2 than WC3-1, the values of the normalized lateral strains seem to be similar for both samples. Unlike the WC2 specimens, the normalized axial strain in WG3-1 throughout loading is lower than the normalized lateral strain in the contraction area. This is not the case with specimen WC3-2, as it was noted in Figure 7B.

Figure 7

WC3 specimens: (A) normalized axial stress versus volumetric strain, (B) normalized strain versus volumetric strain.

2.3.2 GFRP confinement

Figure 8A shows the normalized axial stress versus the volumetric strain for specimens WG2-1 and WG2-2. Both of them responded in a similar way at each level of axial stress. The volumetric expansion of the concrete stated at about 90% of the plain concrete strength, f_co. The relationship between the axial and lateral strain and the volumetric strain for the two specimens is linear or quasilinear after the point of maximum contraction of the confined concrete, as shown in Figure 8B. The maximum contraction of the concrete core for WG3-1 and WG3-2 specimens was reached at about 90% and 65% of the plain concrete strength, f_co, as presented in Figure 9A. The volumetric expansion in WG3-1 reached its maximum value at a very early stage of the loading due to premature failure. Specimen WG3-2 exhibited a higher ductility than WG3-1. Once the expansion of concrete took place, the relationship between the lateral and axial strain and the volumetric strain is linear, as shown in Figure 9B.

Figure 8

WG2 specimens: (A) normalized axial stress versus volumetric strain, (B) normalized strain versus volumetric strain.

Figure 9

WG3 specimens: (A) normalized axial stress versus volumetric strain, (B) normalized strain versus volumetric strain.

Unlike the specimens confined with GFRP jacket presented above, WG4-2 failed at a low volumetric strain, as presented in Figure 10A. Specimen WG4-1 contracted up to 0.9 f_co and expanded linearly. The relationship between the axial and lateral strain and the volumetric strain for the two specimens is linear or quasilinear after the point of maximum contraction of the confined concrete, as shown in Figure 10B.

Figure 10

WG4 specimens: (A) normalized axial stress versus volumetric strain, (B) normalized strain versus volumetric strain.

3 Analytical model [7]

An analytical model that predicts the behavior of the confined concrete, which takes into account the stiffness and effectiveness of the CFRP and GFRP confinement, was proposed by the authors [7]. The model considers the varying pressures of the confinement on the concrete core. The confining strain and stress are determined through an incremental-iterative approach that generates the stress-strain diagram. The ultimate axial strength f_ccl and the ultimate axial strain ε_ccl of the confined concrete are calculated using the following equations:

where α′ω_w is the modified effective confinement index, which is calculated using the expression

The stiffness of the confinement K_j is defined as

The lateral strain in the confining jacket ε_j is calculated through an incremental-iterative approach.

Figures 11 and 12 show the normalized ultimate axial stress f_ccl/f_co and normalize ultimate axial strain ε_ccl/ε_co, respectively, versus the modified effective confinement index α′ω_w. The experimental results are compared with those obtained from the predictive model.

Figure 11

Normalized ultimate axial stress versus the modified effective confinement index α′ω_w.

Figure 12

Normalized ultimate axial strain versus the modified effective confinement index α′ω_w.

From these figures, it can be noted that the model predicts well the behavior of the concrete confined with FRP jacket against the experimental results. The normalized ultimate axial stress for the CFRP-confined specimens computed using the proposed model and other models [8–10] are compared in Figure 13. It can be noted that two models [8, 9] are conservative for all the specimens confined with CFRP jacket, while one model [10] is unconservative for the one and two layers of confinement and conservative for the three-layer confinement.

Figure 13

Normalized ultimate axial stress for CFRP-confined concrete specimens.

Figure 14 shows the relationship between the normalized ultimate lateral strain ε_ccr/ε_cor, derived using the analytical model, and lateral jacket stiffness K_j (ε_ccr is the ultimate lateral strain in the jacket and ε_cor is the lateral strain of 0.001). The predicted results are compared with the experimental results considered in the paper. It can be noted that the model predicts well the behavior of all the CFRP-confined specimens, while the model is unconservative for the specimens confined with four layers of GFRP.

Figure 14

Normalized ultimate lateral strain versus lateral jacket stiffness.

The effectiveness of the FRP confinement estimated using the proposed model versus the lateral jacket stiffness K_j is presented in Figure 15. The results are compared with those obtained from the experimental testing and those determined using the fib-Bulletin 14 [8].

Figure 15

Confinement effectiveness versus lateral jacket stiffness.

Again, the analytical model predicts well the effectiveness of the CFRP confinement (with the exception of four layers of GFRP). The effectiveness of the confinement estimated according to the fib-Bulletin 14 [8] is lower than that corresponding to the experimental results and that predicted by the proposed model.

The experiments on confined concrete show that if more lateral strain is allowed at the same confinement stress, the axial strain increases. However, this increase in axial strain takes place after concrete starts crushing (or dilating) and, hence, may not be that beneficial, especially if cyclic loading is expected. Therefore, it is worth examining the critical stress f_cr at which dilation in concrete takes place. The following equation is proposed for determining the critical stress:

where E_co is the tangent modulus of elasticity of concrete [1]. Equation (5) is very useful particularly when the strengthening is required to enhance the column axial capacity. It is essential that the service stresses are maintained below f_cr, otherwise, progressive damage will deteriorate the concrete. Figure 16 shows the variation of the normalized critical stress f_cr/f_co for different amounts of lateral jacket stiffness K_j . For low confinement stiffnesses, there is a small increase in the normalized critical stress, while for large confinement stiffnesses, there is a significant increase in the normalized critical stress.

Figure 16

Normalized critical stress versus lateral jacket stiffness.

Further work needs to be carried out in order to compare the results predicted by this model with those predicted by other models and/or obtained from experimental testing carried out by other authors.

4 Results and discussion

The results of the experimental work are summarized in Figure 17A and B. In these figures, the normalized ultimate axial stress f_ccl/f_co and normalized ultimate axial strain ε_ccl/ε_co are plotted versus the effective confinement index αω_w. The confinement coefficient α=1 for circular sections and the volumetric ratio ω_w=2f_l/f_co, where f_l is the confinement pressure exerted by the confinement material on the concrete core.

Figure 17

FRP-confined specimens: (A) normalized ultimate axial stress versus effective confinement index, (B) normalized ultimate axial strain versus effective confinement index (m, monotonic; c, cyclic).

For all the confinement materials, an enhancement of concrete strength is noted for both the monotonic and cyclic loading. The smallest increase in strength was achieved by the concrete confined with the GFRP jackets, while the largest increase was achieved by the CFRP-confined concrete. The stress-strain response of all specimens under cyclic loading is nonlinear, with a parabolic shape, up to failure.

The energy dissipation during the unloading and reloading cycles is considerable for all the FRP-confined concrete specimens, especially in the case of those confined with carbon fibers. Significant plastic strains after unloading are also noticeable. No stiffness degradation upon reloading was observed. For all the confinement materials, the stress-strain relationship for the monotonic loading may serve as an envelope for cyclic loading.

As shown in Figure 17B, the normalized ultimate axial strains follow the same pattern as the normalized ultimate axial stresses presented in Figure 17A. The smallest ultimate normalized axial strain was experienced by the concrete confined with GFRP jacket, followed by the concrete confined with CFRP jacket. The relationship between the normalized axial strain and the volumetric strain for all the specimens during the expansion phase is linear or quasilinear. The normalized axial and lateral strain increases with the increase in the number of FRP layers. The analytical model predicts well the axial stress and strain of the FRP-confined specimens. The model also predicts well the lateral strain of the concrete confined with CFRP and gives reasonable results for the specimens confined with GFRP. In addition to that, the model clearly shows that the effectiveness of the confinement depends on the stiffness of the lateral jacket; in particular, the effectiveness of the FRP jacket increases with the increase in its stiffness. The model has also been used by the authors to predict successfully the behavior of concrete pretensioned with FRP jackets.

5 Conclusions

Cylinders confined with CFRP and GFRP jackets. The study shows that concrete confined with FRP material has increased strength and deformability. Under monotonic loading, the FRP materials exhibit a more or less bilinear relationship between strain and stress, while under cyclic loading, this relationship becomes more nonlinear, but with a similar envelope for monotonic loading. Depending on the stiffness and strength of the confining material, both the ductility and the concrete strength could increase under cyclic loading. This has important safety implications, especially in regions with seismic activity.

An analytical model that predicts the behavior of the confined concrete, which takes into account the stiffness and effectiveness of the CFRP and GFRP jacket is presented. The model predicts well the behavior of both CFRP- and GFRP-confined concrete specimens. The model shows that the effectiveness of confinement increases with an increase in the lateral jacket stiffness. Further work needs to be done in order to compare the results predicted by this model with the ones predicted by other models and/or obtained from experimental testing carried out by other authors.