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Compressive behavior of concrete cylinders confined by narrow strips of CFRP with spacing
Composites: Part B 39 (2008) 1093–1103
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Composites: Part B journal homepage: www.elsevier.com/locate/compositesb
Compressive behavior of concrete cylinders confined by narrow strips of CFRP with spacing Tae Won Park a, Ung Jin Na a,*, Lan Chung b, Maria Q. Feng a a b
Department of Civil and Environmental Engineering, University of California, Irvine, CA 92697, USA Department of Architectural Engineering, Dankook University, YongIn-gu, Gyeonggi-do 448-701, South Korea
a r t i c l e
i n f o
Article history: Received 11 June 2007 Accepted 16 May 2008 Available online 7 June 2008 Keywords: A. Laminates A. Polymer–matrix composites (PMCs) B. Strength C. Analytical modeling D. Mechanical testing
a b s t r a c t Application of carbon fiber-reinforced polymer (CFRP) is one of the effective strengthening methods for structural members such as reinforced concrete columns and beams. However, air voids and debonds between CFRP and concrete due to poor workmanship may degrade the structural performance otherwise expected by the strengthening. In order to minimize such debonds and ease the installation, the authors propose to wrap compressive concrete members with narrow strips of CFRP laminates with spacing. This paper focuses on an experimental study to investigate the effectiveness of applying the narrow strips of CFRP laminates. In this study, 60 concrete cylinders wrapped with CFRP strips having different spacings and widths are tested under compression load. The effects of several key parameters such as spacing, spliced length, number of layers, and section area of the CFRP laminates are investigated. In addition, stress–strain curves of pre-damaged specimens wrapped with CFRP laminates are also focused. Based on the experimental results, constitutive models of concrete confined by narrow strips of CFRP laminates are proposed. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction A major cause of damage in reinforced concrete (RC) structures such as bridges, building, and wharves is aging and structural deterioration under severe environments. Such deterioration as concrete cracks, corrosion of steel, and deformation of structural members can significantly degrade the structural performance and safety. Therefore, effective and easy-to-use methods are required to repair and strengthen these concrete structures. In addition, it sometimes needs to increase the load capacity of structures for carrying additional loads due to the change of the purpose of structures and the new extension of existing structures. Various methods for strengthening and rehabilitation of RC structures have been developed in the past several decades. Recently, FRP (fiber-reinforced polymer) composite materials have emerged as a cost-effective alternative to conventional materials for repairing, strengthening, and retrofitting deteriorated concrete structures, by externally bonding FRP laminates to concrete structural members. FRP is characterized by high strength fibers embedded in polymer resin. FRP offers such advantages as high strength and stiffness, low density, chemical stability, high durability, and ease of installation. The most common type of FRP in industry is made with carbon, aramid or glass fibers. * Corresponding author. Tel.: +1 949 933 3406; fax: +1 949 824 9389. E-mail addresses: [email protected] (T.W. Park), [email protected] (U.J. Na), [email protected] (L. Chung), [email protected] (M.Q. Feng). 1359-8368/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesb.2008.05.002
Extensive researches have been performed to find various ways to apply FRP for the retrofit of RC members (by externally bonding FRP sheets to concrete members) as well as for constructing new concrete structural members (by filling concrete into FRP tubes) [1–5]. The effectiveness of FRP for seismic retrofit and strengthening of RC structural members has also been evaluated. A widely accepted procedure is to lay up manually several layers of FRP sheets on concrete, layer by layer with overlap, glued with adhesive epoxy. The bonding quality between FRP and concrete, however, is of a concern, as it purely depends on the workmanship. Imperfect bonding condition, particularly the existence of a large area of voids, can degrade the structural integrity and safety that could otherwise be attainable by retrofit/strengthening [6,7]. In order to minimize air voids and ease FRP installation, the authors propose to apply narrow strips of CFRP laminates with spacing, similar to transverse reinforcement steel. This study focuses on the experimental studies related to the compressive behaviors of concrete cylinders. In this experiment, CFRP strips with two different widths (2.5 cm and 5.0 cm) are, respectively, bonded in spiral with spacing on 60 concrete cylinders, as shown in Fig. 1, while the conventional methods usually use several layers of wider sheets, layer by layer with overlap (without spacing). This proposed procedure makes it easier to release all trapped air and to assure CFRP strips fully bonded to concrete. In this study, several key parameters have been considered for the preparation of the test specimens, for example, spacing, spliced length, and section area of the CFRP laminates. The center-to-center
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15cm
a
60cm
H2-I0-O
H
H2-I1-O H2-I1-T H2-I1-TA H2-I1-TB
H2-I2-O
H2-I3-O
H2-I4-O
15cm
b
30cm
N
N2-I1-O N3-I1-O N3-I1-T N3-I1-TA N3-I1-TB
N3-II1-O
N2-II3-O N3-II3-O
Fig. 1. Geometry of CFRP laminates of specimens for (a) Group H and (b) Group N.
spacing of the spiral CFRP strip is taken as one of 2.5 cm, 5.0 cm, 7.5 cm, 10.0 cm, and 12.5 cm. The authors also vary the width of the laminates (2.5 cm and 5.0 cm) and the spliced length (no splice, 24 cm, and 48 cm). In addition, pre-damaged specimens wrapped with CFRP laminates are also tested for the purpose of comparison. Finally, constitutive models of concrete confined by narrow strips of CFRP laminates are proposed based on the experimental results. 2. Experimental study Sixty concrete cylinders with two different dimensions, £15 cm 60 cm (group H in Fig. 1a) and £ 15 cm 30 cm (group N in Fig. 1b), are prepared and then reinforced by a variety of CFRP strips, as illustrated in Fig. 1. These specimens are subjected to compressive loading and their compressive behaviors are observed. The compressive strengths measured from the concrete cylinders, ‘H’ and ‘N’ specimens in Fig. 1, are 26.08 MPa and 20.72 MPa, respectively. In this study, unidirectional CFRP laminates ‘‘Korea Carbon NR-32” are applied with an epoxy adhesive. The CFRP laminates have a nominal tensile strength of 2 GPa and elastic modulus of 155 GPa. The CFRP laminates consist of reinforcement phase of carbon fiber and matrix resin system of polyester. Fiber direction and angle of CFRP strip can be indicated from Fig. 1. The adhesive with 16.2 MPa bond strength is used to bond the CFRP laminates onto the concrete cylinders. 2.1. Specimen and test setup Before retrofitted with the CFRP laminates, the concrete cylinder surface is cleaned with sandpapers. Then a layer of 2 mm epoxy
mortar is applied to cover the concrete surface. Finally, the CFRP laminates are bonded to the surface of each concrete cylinder with the designed spacing, thickness, and splice length of CFRP laminates. To prevent the end fracture at the top and bottom of the concrete cylinders, the top and bottom of the specimens are additionally strengthened with CFRP laminates. The details of CFRP laminates are summarized in Tables 1 and 2. In terms of the notation of each specimen, the first character, H or N, refers to the size of the specimen (H representing cylinders with 15 cm diameter and 60 cm height and N representing cylinders with 15 cm diameter and 30 cm height). The following number, 2 or 3, refers to the thickness of the single layer of the CFRP sheet (2 for 0.2 mm thickness and 3 for 0.3 mm thickness). The next character, I or II, refers to the width of the CFRP laminates (I for 2.5 cm and II for 5.0 cm). The following number represents the center-to-center spacing of
Table 1 Specimen details (group H) Reference
CFRP Thickness (mm)
CFRP Width (mm)
CFRP Spacing (mm)
CFRP Layer (number)
CFRP Spliced length (mm)
H H2–I0–O H2–I1–O H2–I2–O H2–I3–O H2–I4–O H2–I1–T H2–I1–TA H2–I1–TB
– 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
– 25 25 25 25 25 25 25 25
–
– 1 1 1 1 1 2 2 2
– No splice No splice No splice No splice No splice No splice 240 mm 480 mm
25 50 75 100 125 50 50 50
T.W. Park et al. / Composites: Part B 39 (2008) 1093–1103 Table 2 Specimen details (group N) Reference
CFRP Thickness (mm)
CFRP Width (mm)
CFRP Spacing* (mm)
CFRP Layer (number)
CFRP Spliced length (mm)
N N2–I1–O N2–II3–O N3–II1–O N3–II3–O N3–I1–O N3–I1–T N3–I1–TA N3–I1–TB
– 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3
– 25 50 50 50 25 25 25 25
– 50 100 50 100 50 50 50 50
– 1 1 1 1 1 2 2 2
– No splice No splice No splice No splice No splice No splice 240 mm 480 mm
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ment of the specimens, two linear variable differential transformers (LVDT, LT-50 of Tokyo Sokky) are installed on two opposite sides of the cylinder. Fig. 2a illustrates the experiment setup and specimen. Fig. 2b is schematic drawing including specimen, experiment machine and LVDT. 2.2. Test results and discussion
the CFRP laminates (0 for 2.5 cm, 1 for 5.0 cm, 2 for 7.5 cm, 3 for 10.0 cm, and 4 for 12.5 cm). The following character, O or T, refers to the number of CFRP layers applied (O for 1 layer and T for 2 layers). The final notation, A or B, represents the spliced length of the CFRP laminates (A for 24 cm, B for 48 cm, and no A or B for no splice). The specimens marked with only H or N represent concrete cylinders without CFRP strips. For each reference notation, three specimens are, respectively, prepared and average values of experiment results are used. All specimens are subjected to compressive load under displacement control on a Universal Testing Machine (UTM, LT-950 of Forney Inc.) with a maximum load capacity of 2000 kN. The load–displacement data are automatically recorded through a data logger (LC-V and UCAM-58T of Kyowa). For measuring displace-
Tables 3 and 4 summarize maximum loads and damage patterns corresponding to the each reference notation. All specimens wrapped with CFRP laminates show the fracture of CFRP, while specimens without CFRP laminates show typical shear failure in the middle of the specimens. The maximum loads applied to the reinforced specimens are higher than those of the un-reinforced specimens. In Tables 3 and 4, foc is maximum compressive stress (maximum load/section area of the specimens) and f* represents increased portion of maximum compressive stress by confinement. Apparently, the reinforcement by CFRP laminates significantly increases the stress capacity of the specimens. Fig. 3 shows the photos of damaged H (without CFRP) and H2–I2–O (with CFRP) specimens. One can indicate that the H specimen shows shear failure by crack. In case of the H2–I2–O specimen, tensional breakage of CFRP laminates happens after carrying larger strain and stress compared to H specimens. As mentioned before, three specimens with identical CFRP setup are tested for each reference notation. Fig. 4 shows some examples of stress–strain curves obtained from the compression tests of specimens H and N3–II1–O. The end number (1, 2, or 3) following
a
b Spherical Bearing
Load cell Specimen
LVDT Guide
Base
UTM(2000kN) Fig. 2. (a) Details of the experimental setup and (b) schematic drawing.
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involving larger specimens is needed in order to investigate the size effect.
Table 3 Summary of test results (group H) Reference
Maximum load (kN)
foc (MPa)
f* (MPa)
Damage pattern
H H2–I0–O H2–I1–O H2–I2–O H2–I3–O H2–I4–O H2–I1–T H2–I1–TA H2–I1–TB
456.7 737.5 617.8 504.9 544.2 527.8 724.3 682.1 700.4
26.08 41.69 34.97 30.06 30.80 29.87 41.00 38.61 39.64
– 15.62 8.89 3.98 4.72 3.80 14.92 12.53 13.57
Shear failure by crack Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP
Table 4 Summary of test results (group N) Reference
Maximum load (kN)
foc (MPa)
f* (MPa)
Damage pattern
N N2–I1–O N2–II3–O N3–II1–O N3–II3–O N3–I1–O N3–I1–T N3–I1–TA N3–I1–TB
366.0 487.7 495.8 707.5 457.3 540.0 680.0 586.7 603.3
20.72 27.60 28.06 40.04 29.22 30.56 38.49 33.21 34.05
– 6.89 7.35 19.33 8.50 9.85 17.78 12.49 13.34
Shear failure by crack Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP
the reference notation represents the identification number of each among three specimens. The averaged stress–strain curves are derived for the following analysis. 2.2.1. Effects of specimen size Cylinders with two different heights (60 cm and 30 cm) are tested. To study the effects of the specimen size on the maximum compressive strength of the confined concrete, the ratio of the compressive strengths of confined and unconfined concrete specimens, foc/fc, is observed and compared for two reference cases having different height. The results from specimens H2-I1-O (60 cm height) and N2–I1–O (30 cm height) are compared. These two specimens have identical layout of CFRP strips with same thickness, width, spacing, and the number of layers. These two groups of specimens with different heights show almost the same ratio of compressive strengths. The specimen H2–I1–O (£15 60 cm) exhibits compressive strength ratio (foc/fc) of 1.34, while the specimen N2–I1–O (£15 30 cm) shows 1.33 (Fig. 5). Based on this test, one can indicate that different cylinder heights do not have effects on the effectiveness of the CFRP reinforcement. More study
2.2.2. Effects of spacing of CFRP laminates Stress–strain curves are plotted in Fig. 6 for the specimens with identical width and thickness of CFRP strips except center-to-center spacing. The plot demonstrates the effects of the spacing of CFRP strips on the performance of strengthened concrete specimens. It can be seen that the stress-carrying capacity and the strain capacity of the specimens wrapped with CFRP are improved greatly compared to control specimen H in Fig. 4a. The stress–strain curves of H2–I2–O, H2–I3–O, and H2–I4–O fall after reaching their peak, while the curves of the other specimens continue to increase or hold the stress level after passing turning points. As also observed in Fig. 6, the specimen has smaller spacing shows larger deformation capacity. It can be explained as ductility. Ductility can be defined as the capability of materials to deform while still carry load after passing the turning point. In case of a specimen H2– I4–O with a 12.5 cm center-to-center spacing (10 cm net spacing and 20% ratio of CFRP-bonded area versus total concrete surface area), it shows relatively brittle failure after reaching the peak compressive strength. However, specimens H2–I0–O and H2–I1– O show highly ductile behavior. 2.2.3. Effects of spliced length of CFRP laminates To investigate the effects of the spliced length of CFRP strips, concrete cylinders wrapped with identical CFRP strips but having different spliced lengths (24 cm, 48 cm, or continuous strip without splice) are observed. The stress–strain curves obtained from the compressive tests for three reference notation with identical CFRP layout except spliced lengths are presented in Fig. 7. According to the test results, the specimen wrapped with the continuous CFRP strip (no splice), shows the highest ductility and stress-carrying capacity. But the specimens with 24 cm and 48 cm spliced lengths behave similarly. Even though debonding occurs at the spliced part of the CFRP strip, final breakage of the CFRP strip takes place in other area, not in the spliced part. Thus, it can be indicated that the spliced length, if it is over a certain length, does not have an effect on the confined concrete strength. More experimental study involving specimens with the shorter spliced length of the CFRP strip is needed in order to evaluate minimum spliced length. 2.2.4. Effects of the number of layers and thickness of CFRP laminates In this study, the authors also investigated the effects of the number of layers of CFRP laminates on the compressive strength. Among H and N group specimens, the specimens with the same spacing and the same width of CFRP laminates are focused. The ra-
Fig. 3. Damage patterns of concrete cylinders. (a) H specimen and (b) H2–I2–O specimen.
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50
0 0
0.003
0.006
0.009
0.012
0.015
0.018
Strain (a) Stress-strain curves of H specimens
1.18
1.25
1.15
1.10
1.00 H2-I1-TB
H2-I1-TA
H2-I1-T
0.50
H2-I4-O
0.75 H2-I3-O
H1
10
1.52
1.48 1.34
H2-I2-O
20
1.57
H2-I1-O
H3
1.60
1.50
H2-I0-O
H2
30
1.75
H
Stress (MPa)
40
Ratio of compressive strength of group H
.
2.00
0.25 0.00
SPECIMEN
(a) Ratio of compressive strength of group H 50
2.00
0
0.003
0.006
0.009
0.012
0.015
0.018
Strain (b) Stress-strain curves of N3-II1-O specimens
1.25
0.25 0.00
Fig. 4. Stress–strain curves of H and N3–II1–O.
N3-I1-TB
N3-I1-TA
0.50
N3-I1-T
0.75
N3-I1-O
1.00 N3-II3-O
0
1.65
1.35
N3-II1-O
10
1.33
1.25
N2-II3-O
20
1.60 1.48
1.50
N2-I1-O
N3-II1-O2
1.86
1.75
N
N3-II1-O1
Ratio of compressive strength of group N
Stress (MPa)
40
30
1.93
.
N3-II1-O3
SPECIMEN (b) Ratio of compressive strength of group N
Fig. 5. Ratio of compressive strength of confined and unconfined specimens.
2.2.5. Effects of width of CFRP laminates The specimens with two different widths (2.5 cm and 5 cm) are compared. Fig. 9 compares the stress–strain curves of the specimens wrapped with the CFRP strips having different widths. But,
50
H2-I0-O (spacing : 2.5cm)
40
Stress (MPa)
tio of the maximum compressive strength between the concrete confined by CFRP and the unconfined concrete, foc/fc, is plotted in Fig. 8 for comparison. In case of specimen H2–I1–O (0.2 mm thickness and 1 layer), the ratio foc/fc is 134%, while the ratio of H2–I1–T (0.2 mm thickness and two layers) increases to 157%. In case of N group, the ratios of the maximum compressive strength of N3– I1–O (0.3 mm thickness and one layer) and N3–I1–T (0.3 mm thickness and 2 layers) are 148% and 186%, respectively. The specimens with two layers of CFRP show higher compressive strength but those do not come to double compared with the ratios increased by one layer of CFRP. Therefore, strengthening with one layer of CFRP is more efficient than the case using two layers of CFRP. A similar comparative study is conducted using the concrete specimens with different thickness of CFRP laminates. For the H group specimens with 0.2 mm CFRP thickness, the compressive strength is improved by 51% compared to the unconfined cylinders. The N group specimens with 0.3 mm CFRP thickness shows improved strength by 78%. Comparing these two groups of specimens, the ratio of CFRP thickness is 0.66 (=0.2 mm/0.3 mm) and the ratio of improved compressive strength is approximately 0.65 (=51%/78%). This result shows that the thickness of CFRP do not have effects on the effectiveness of the CFRP reinforcement.
H2-I1-O (spacing : 5.0cm)
30
H2-I2-O (spacing : 7.5cm) H2-I3-O (spacing : 10.0cm) H2-I4-O (spacing : 12.5cm)
20
10
0
0
0.003
0.006
0.009
0.012
0.015
0.018
Strain Fig. 6. Stress–strain curves of specimens with different spacing.
these specimens have the same number of layers and the same ratio of bonding area of CFRP (CFRP-bonded area versus total area of the cylinder surface). It is clear that as long as the ratio of bonding area and the number of layers are same, the width of the strip does not have effects on the compressive behavior of the CFRP reinforced cylinders.
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2
10 S.L : SPLICED LENGTH
0.006
0.009
0.012
0.015
Ratio of compressive strength of group H
Stress (MPa)
N3-I1-TB (S.L:48cm)
N3-I1-T
30
20
10
0
0.003
0.006
0.009
0.012
0.015
1.86
1.5
1
0.5
1.6
1.65
1.48
1
0
S.L : SPLICED LENGTH 0
2
N3-I1-O
.
(a) Ratio of compressive strength of group H
50
40
H2-I1-TB
SPECIMEN
Strain (a) Stress-strain curves of group H
N3-I1-TA (S.L:24cm)
H2-I1-TA
0
0.018
N3-I1-TB
0.003
0.5
N3-I1-TA
0
1.52
1
N3-I1-T
0
1
H2-I1-T
20
1.48
1.34
H2-I1-O
Stress (MPa)
H2-I1-TA (S.L : 24cm)
30
1.57
1.5
H
H2-I1-T
N
H2-I1-TB (S.L : 48cm)
40
Ratio of compressive strength of group N
50
0.018
Strain (b) Stress-strain curves of group N
SPECIMEN
(b) Ratio of compressive strength of group N Fig. 8. Effects of the number of CFRP layers.
Fig. 7. Stress–strain curves of specimens with different spliced length.
2.2.6. Comparison between undamaged and pre-damaged specimens Six pre-damaged concrete cylinders are prepared. Each cylinder is divided into three pieces. The damaged cylinder pieces are bonded together with epoxy mortar and then cured. Then, these pre-damaged specimens are strengthened with CFRP laminates. A comparative study is carried out using these pre-damaged concrete cylinders, together with the undamaged cylinders. As shown in Fig. 10, the undamaged and pre-damaged specimens strengthened with the same CFRP laminates exhibit almost identical stress– strain behaviors.
3. Constitutive models for confined concrete A constitutive model for concrete plays an important role in the analysis and design of concrete structures. To predict the peak stress or the stress–strain curves of confined concrete, various constitutive models have been proposed. The most frequently cited model is Mander’s model [8] which has been shown to provide excellent prediction of compressive response of large-scale columns confined by a wide range of transverse reinforcement ratios. Samaan et al. [9] developed a simple FRP-confined concrete model, applicable to circular columns. This model predicts the complete bilinear stress–strain response of FRP-confined concrete in both axial and lateral directions. A very efficient FRP-confined concrete model was recently developed by Hosotani and co-workers [10,11] for circular and rectangular columns. This model is based on comprehensive experimental testing of small-size circu-
lar and rectangular columns confined by carbon fiber sheets. All model parameters were developed from regression analysis conducted on the experimental results. Hoppel et al. [12], Toutanji [13], and Spoelstra and Monti [14] also developed their own models to predict the stress–strain relationship of columns wrapped with FRP composite sheets. Recently, Youssef et al. [2] developed a comprehensive concrete confinement model using experimental data and other reliable data from the literature. 3.1. Stress–strain curves of confined concrete The axial stress–strain relationship for confined concrete is in general shown in Fig. 11. There exist two trends corresponding to the confinement ratio. For concrete with relatively small confinement ratio q, the axial stress of confined concrete increases with strain until it reach the maximum value ft, at which the axial strain is et . At this point, the CFRP is getting fully activated under tensile stresses due to concrete dilation. Thereafter, the axial stress decreases linearly as the axial strain increases. On the other hand, for concrete with relatively large confinement ratio q, the concrete stress fc continues to increase all the way up to failure, but with some deterioration of its axial stiffness as shown in Fig. 11. In this study, the authors focus on the predictions of ft, et , and second slope of stress–strain curve Eg. Referring the constitutive models developed by previous researchers, the axial stress of confined concrete at the boundary point from first to second region, ft is assumed to be the sum of 0 the axial stress of unconfined concrete, fco , and the stress increase due to the confinement, finc
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50
fc f cu
Ascending
N2-II3-O(width : 5.0cm)
30
Axial Stress
Stress (MPa)
40
N2-I1-O(width : 2.5cm)
20
Eg 1
ft
1
Eg
Descending
10 Ec
0
0
0.003
0.006
0.009
0.012
0.015
0.018
εt
Strain (a) Stress-strain curves of group N2
Axial Strain
εc
ε cu
Fig. 11. Stress–strain curves of concrete confined by CFRP laminates.
50
40
30
20
N3-I1-O (width : 2.5cm)
10
0
0
0.003
0.006
0.009
0.012
0.015
0.018
Proposed stress (MPa)
Stress (MPa)
40 N3-II3-O (width : 5.0cm)
30
20
10
Strain
(b) Stress-strain curves of group N3
0 0
10
20
30
40
Experimental stress (MPa)
Fig. 9. Effects of width of CFRP laminates.
Fig. 12. Comparison between experimental and proposed axial stresses ft.
50 Pre-damaged, strengthened
0.004
Undamaged, strengthened
30
Proposed strain
Stress (MPa)
40
20
10
0
0.003
0.002
0.001
0
0.003
0.006
0.009
0.012
0.015
0.018
Strain
0
0
0.001
0.002
0.003
0.004
Experimental strain
Fig. 10. Stress–strain curves of undamaged and pre-damaged specimens.
Fig. 13. Comparison between experimental and proposed axial strains et .
0 0 ft ¼ fco þ finc ¼ fco þ fl0a ;
ð1Þ
where fl0 is the effective lateral confining strength and the constitutive parameter a is the coefficient of the power-law equation which can be obtained from experimental data using regression analysis. The effective lateral confining stress provided by the lateral CFRP laminates fl0 can be represented as follows:
fl0 ¼ 2 ke t n w ECF eCF =ðS DÞ;
ð2Þ
where ke is the confinement effectiveness coefficient and depends on the type of lateral CFRP laminates, t is the thickness of the CFRP laminates, n is the number of layers, ECF is the elastic modulus of the CFRP laminates, eCF is the ultimate strain of the CFRP laminates, D is the diameter of the cylinder, S is the spacing (center to center) of
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the CFRP laminates strip. It can be derived from the equilibrium of the internal forces acting dissected section. fl0 can be rewritten as
fl0 ¼ q ke ECF eCF =2;
ð3Þ
where, q is CFRP confinement ratio given by q = 4 t n w/ (S D) from Eq. (2). Based on the preliminary regression analysis, the authors simply assume ke as
pffiffiffi ke ¼ b= n;
ð4Þ
50
where, constitutive parameter b is a coefficient obtained by regression analysis. According to the experimental results, the effectiveness of the CFRP strengthening does not increase linearly with increase of the number of layers of CFRP laminates, n. This is because the brittle characteristic of epoxy applied in the CFRP laminates becomes more dominant as the number of layers of CFRP laminates increases. To consider such brittle characteristic, Eq. (4) is proposed as the confinement effectiveness coefficient in terms pffiffiffi of n. When the axial stress reaches the compressive stress ft, the corresponding strain of the confined concrete is et . The strain of this
50
N2-I1 series
40
Stress (MPa)
Stress (MPa)
40 30 20 10 0
0
0.003
0.006
0.009
0.012
0.015
50
20
0
0.018
Proposed Experiment
0
0.003
0.006
0.009
0.012
0.015
0.018
Strain (b) Experimental and proposed stress-strain curves of N3-I1 50
N3-II1 series
H2-I2 series
40
40
Stress (MPa)
Stress (MPa)
30
10
Proposed Experimental
Strain (a) Experimental and proposed stress-strain curves of N2-I1
30
20
30 20 10
10
Proposed Experiment
0
0.003
0.006
0.009
0.012
0.015
Proposed Experimental
0
0
0
0.018
0.003
0.006
0.009
0.012
0.015
0.018
Strain
Strain (c) Experimental and proposed stress-strain curves of N3-II1
(d) Experimental and proposed stress-strain curves of H2-I2 50
50
H2-I3 series
H2-I4 series
40
Stress (MPa)
40
Stress (MPa)
N3-I1 series
30 20 10
30 20 10
Proposed
Proposed Experimental
Experimental
0 0
0.003
0.006
0.009
0.012
0.015
0.018
Strain (e) Experimental and proposed stress-strain curves of H2-I3
0 0
0.003
0.006
0.009
0.012
0.015
0.018
Strain (f) Experimental and proposed stress-strain curves of H2-I4
Fig. 14. Comparison between experimental and proposed stress–strain model.
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T.W. Park et al. / Composites: Part B 39 (2008) 1093–1103
intersection point depends on the lateral confining stress provided by the CFRP laminates. A general form for et is assumed as
et ¼
e0co
h finc þk 0 ; fco
3.2. Regression analysis for constitutive modeling The constitutive parameters are obtained by the regression analysis of the experimental data. Based on the regression analysis, parameter a in Eq. (1) is determined as 0.85 and parameter b in Eq. (4) is 2.8. Parameter k and h in Eq. (5) is 0.0033 and 0.7, respectively. In Figs. 12 and 13, the predicted axial stress and strain from proposed constitutive model are presented compared with the actual values observed in the experiments. In these figures, each point stands for a vector representing the accuracy of the prediction. If the points show up nearer around the diagonal, it means the accuracy of the prediction is high. In terms of the ratio of the predicted stress to experimental stress, the mean value of these ratios is 0.974. In case of the axial strain, the mean value of the ratios is 1.062. One can indicate that the proposed constitutive models for the axial stress and strain can yield reasonably good results. For the second slope of the stress–strain curve, Eg, parameters g and l are assumed, respectively, for the ascending and descending curves, depending on the ratio of the CFRP confinement. Based on the experimental results, the slope Eg is positive (ascending) when the ratio of the CFRP bonding area is larger than 50%, while Eg is negative (descending) when the CFRP area ratio is less than 50%.
ð5Þ
where e0co is the strain of the unconfined concrete at the intersection point and finc is the increased compressive strength, fl0a , in Eq. (1). Parameters k and h can be obtained from the regression analysis based on experimental data. As shown in Fig. 11, the stress–strain curve after the intersection point is an ascending or descending curve with a smaller slope than that of the curve before the intersection point. The second slope of stress–strain curve Eg can be obtained from the experi0 mental results. Eg can be assumed as a function of q and fco as below. Various equation forms of Eg are previously reviewed to derive best format in the view of prediction accuracy.
Eg ¼ g
0 fco
q ECF eCF
pffiffiffiffi þ l q ECF ;
ð6Þ
where, constitutive parameters g and l are coefficients obtained by regression analysis.
1.2 Hosotani
Yousse f
Proposed
f't_predict/f't_exp
1 0.8 0.6 0.4 0.2 0 H2- 2
H2- 3
H2- 4
N2- 1-O
N3- 1-O
N3- 1–T
SPECIMEN Fig. 15. Comparison of three constitutive models (ratio of ft).
1.6 1.4
Hosotani
Youssef
Proposed
t_predict/ t_exp
1.2 1 0.8 0.6 0.4 0.2 0 H2- 2-O
H2- 3-O
H2- 4–O
N2- 1-O
N3- 1-O
SPECIMEN Fig. 16. Comparison of three constitutive models (ratio of et ).
N3- 1–T
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T.W. Park et al. / Composites: Part B 39 (2008) 1093–1103
2.5
Hosotani
Youssef
Proposed
2nd E predict/experiment
2
1.5
1
0.5
0
H2-I2
H2-I3
H2-I4
N2-I1-O
N3-II1-O
N3-I1–T
SPECIMEN Fig. 17. Comparison of three constitutive models (ratio of Eg).
Parameters g and l are derived as 1.25 and 0.065 for the ascending curves and 13.5 and 0.29 for the descending curves. Fig. 14 shows the stress–strain curves computed by the proposed constitutive model, in comparison with those experimentally obtained. To plot the stress–strain curves, axial stress and axial strain at the intersection point, ft and et , and second slope Eg are calculated at first. And then using a similar approach used by Hoshikuma et al. [15] and Youssef et al. [2], the stress–strain curve of confined concrete in region before intersection point (e 6 et ) is modeled by the following polynomial function as Eq. (7).
fc ¼ C 1 em þ C 2 e þ C 3 ;
(2)
(3)
ð7Þ
where C1, C2, C3, and m are constant parameters to be determined from the boundary conditions of the stress–strain curves. Good agreement is observed between the experimental and the proposed analytical stress–strain curves, demonstrating the validity of the proposed constitutive model and the parameter values. To show the effectiveness of the proposed constitutive model, the values of ft, et , and Eg calculated from above proposed model are compared with those obtained from other constitutive models proposed by previous researchers. Two existing constitutive models for CFRP-confined concrete (Hosotani et al. [10] and Youssef et al. [2]) are considered in this study. Fig. 15 shows the ratio of ft obtained from the prediction and experiment for each specimen, ðft predict =ft exp Þ. Fig. 16 also represents the ratio of et , et predict =et exp . Both previously suggested models seem to predict ft and et comparatively well. However, in case of Eg in Fig. 17, these previous models do not show similar prediction accuracy. Fig. 17 shows the ratio of Eg for the selected specimens with descending (H2–I2–O, H2– I3–O, and H2–I4–O) or ascending (others) slope. The proposed model seems to predict the behaviors of concrete cylinders confined by narrow strips of CFRP with best accuracy. 4. Conclusions Spiral wrapping of a narrow strip of CFRP laminates is proposed in this study for concrete reinforcement. Based on the compressive tests for sixty concrete cylinder specimens wrapped with CFRP strips having various layouts, the following conclusions can be made: (1) Using CFRP strips to confine concrete is an efficient method to improve strength and ductility of concrete. All concrete specimens strengthened with CFRP laminates show reason-
(4)
(5)
(6)
(7)
able damage patterns with increased strength and ductility, while specimens without CFRP laminates show typical shear failure. In particular, it is found that a narrow strip of CFRP laminates is easy to apply on concrete and the spacing between the strips makes it easy to remove air pockets and ensure bonding quality. The stress and strain capacities of the specimens wrapped with CFRP are improved greatly compared to normal specimen without CFRP retrofit. The spliced length does not have an effect on the confined concrete strength in the range of 24 cm and 48 cm. More experimental study is needed to investigate the minimum spliced length. The effect of confinement on the increase of compressive strength is not linear to the number of CFRP layers. The strength increases only 1.54 times, even though the number of layers doubles. Pre-damaged specimens strengthened with CFRP laminates show the same stress–strain behavior as undamaged specimens strengthened with CFRP laminates. Narrow strips of CFRP laminates can be effectively used for strengthening pre-damaged concrete members. The stress–strain curves of the specimens with a low ratio of confinement (represented by the area ratio) show a descending trend after reaching the maximum stress, while the stress–strain curves of the specimens with a high ratio of confinement show an ascending trend until failure. Constitutive models of a confined concrete are developed based on the compressive test results. Good agreement is observed between the experimental (actual) and analytical (predicted) stress–strain curves, demonstrating the validity of the proposed constitutive model and the parameter values. Such a model is useful for design and analysis of concrete structures strengthened by the proposed narrow strips of CFRP laminates.
More tests involving larger specimens are needed, in order to thoroughly investigate the effects of specimen size on the compressive behavior of concrete confined by spiral narrow strips of CFRP with spacing. In addition, the effects of the other important parameters related to CFRP laminates, for example, fiber direction and the angle of CFRP strips, need to be worked over to deeply understand the compressive behavior of concrete cylinders wrapped with CFRP.
T.W. Park et al. / Composites: Part B 39 (2008) 1093–1103
Acknowledgements The work was partially sponsored by the Korea Institute of Construction and Transportation Technology Evaluation and Planning (Grant No. 05 CTRM D06: High-tech Urban Development Program). The financial support is gratefully acknowledged. References [1] Fam A, Flisak B, Rizkalla S. Experimental and analytical modeling of concretefilled fiber-reinforced polymer tubes subjected to combined bending and axial loads. ACI Struct J 2003;100(4):499–509. [2] Youssef M, Feng MQ, Mossalam A. Stress–strain model for concrete confined by FRP composites. J Compos Part B: Eng 2007;38(5–6):614–28. [3] Seible F, Hegemier GA, Priestley MJN, Innamorato D, Ho F. Carbon fiber jacket retrofit test of rectangular flexural column with lap spliced reinforcement. Advanced composites technology transfer consortium report no. ACTT-95/02, UCSD; 1995. [4] Xiao Y, Wu H. Compressive behavior of concrete cylinders confined by carbon fiber composite jackets. ASCE J Mater Eng 2000;12(2):139–46. [5] Shahawy M, Mirmiran A, Beitelman T. Tests and modeling of carbon-wrapped concrete columns. Compos Part B: Eng 2000;31(6):471–80.
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[6] Au C. Behavior of FRP-confined concrete structures. Thesis, Massachusetts Institute of Technology, Cambridge, MA; 2001. [7] Haroun, MA, Feng MQ, Bhatia H, Baird K, Elsanadedy H. Structural qualification testing of composite-jacketed circular and rectangular bridge column. Technica Report to the California Department of Transportation; 2001. [8] Mander JB, Priestley MJN, Park R. Theoretical stress–strain model for confined concrete. ASCE J Struct Eng 1988;114(8):1804–26. [9] Samaan M, Mirmiran A, Shahawy M. Model of concrete confined by fiber composites. ASCE J Struct Eng 1998;124(9):1025–31. [10] Hosotani M, Kawashima K, Hoshikuma J. A stress–strain model for concrete cylinders confined by carbon fiber sheets (in Japanese). JSCE J Concrete Eng 1998;39(592):37–52. [11] Hosotani M, Kawashima K. A stress–strain model for concrete cylinders confined by bothcarbon fiber sheets and tie reinforcement (in Japanese). JSCE J Concrete Eng 1999;43(620):25–42. [12] Hoppel CR, Bogetti TA, Gillespie JW, Howie I, Karbhari VM. Analysis of a concrete cylinder with a composite hoop wrap. In: Proceedings of ASCE material engineering conference. New York; 1994. p. 191–8. [13] Toutanji H. Stress–strain characteristics of concrete columns externally confined with advanced fiber composite sheets. ACI Mater J 1999;96(3): 397–404. [14] Spoelstra MR, Monti G. FRP-confined concrete model. ASCE J Compos Construct 1999;3(3):143–50. [15] Hoshikuma J, Kawashima K, Nagaya K, Taylor AW. Stress–strain model for confined reinforced concrete in bridge piers. J Struct Eng 1997;123(5):624–33.
Contents lists available at ScienceDirect
Composites: Part B journal homepage: www.elsevier.com/locate/compositesb
Compressive behavior of concrete cylinders confined by narrow strips of CFRP with spacing Tae Won Park a, Ung Jin Na a,*, Lan Chung b, Maria Q. Feng a a b
Department of Civil and Environmental Engineering, University of California, Irvine, CA 92697, USA Department of Architectural Engineering, Dankook University, YongIn-gu, Gyeonggi-do 448-701, South Korea
a r t i c l e
i n f o
Article history: Received 11 June 2007 Accepted 16 May 2008 Available online 7 June 2008 Keywords: A. Laminates A. Polymer–matrix composites (PMCs) B. Strength C. Analytical modeling D. Mechanical testing
a b s t r a c t Application of carbon fiber-reinforced polymer (CFRP) is one of the effective strengthening methods for structural members such as reinforced concrete columns and beams. However, air voids and debonds between CFRP and concrete due to poor workmanship may degrade the structural performance otherwise expected by the strengthening. In order to minimize such debonds and ease the installation, the authors propose to wrap compressive concrete members with narrow strips of CFRP laminates with spacing. This paper focuses on an experimental study to investigate the effectiveness of applying the narrow strips of CFRP laminates. In this study, 60 concrete cylinders wrapped with CFRP strips having different spacings and widths are tested under compression load. The effects of several key parameters such as spacing, spliced length, number of layers, and section area of the CFRP laminates are investigated. In addition, stress–strain curves of pre-damaged specimens wrapped with CFRP laminates are also focused. Based on the experimental results, constitutive models of concrete confined by narrow strips of CFRP laminates are proposed. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction A major cause of damage in reinforced concrete (RC) structures such as bridges, building, and wharves is aging and structural deterioration under severe environments. Such deterioration as concrete cracks, corrosion of steel, and deformation of structural members can significantly degrade the structural performance and safety. Therefore, effective and easy-to-use methods are required to repair and strengthen these concrete structures. In addition, it sometimes needs to increase the load capacity of structures for carrying additional loads due to the change of the purpose of structures and the new extension of existing structures. Various methods for strengthening and rehabilitation of RC structures have been developed in the past several decades. Recently, FRP (fiber-reinforced polymer) composite materials have emerged as a cost-effective alternative to conventional materials for repairing, strengthening, and retrofitting deteriorated concrete structures, by externally bonding FRP laminates to concrete structural members. FRP is characterized by high strength fibers embedded in polymer resin. FRP offers such advantages as high strength and stiffness, low density, chemical stability, high durability, and ease of installation. The most common type of FRP in industry is made with carbon, aramid or glass fibers. * Corresponding author. Tel.: +1 949 933 3406; fax: +1 949 824 9389. E-mail addresses: [email protected] (T.W. Park), [email protected] (U.J. Na), [email protected] (L. Chung), [email protected] (M.Q. Feng). 1359-8368/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesb.2008.05.002
Extensive researches have been performed to find various ways to apply FRP for the retrofit of RC members (by externally bonding FRP sheets to concrete members) as well as for constructing new concrete structural members (by filling concrete into FRP tubes) [1–5]. The effectiveness of FRP for seismic retrofit and strengthening of RC structural members has also been evaluated. A widely accepted procedure is to lay up manually several layers of FRP sheets on concrete, layer by layer with overlap, glued with adhesive epoxy. The bonding quality between FRP and concrete, however, is of a concern, as it purely depends on the workmanship. Imperfect bonding condition, particularly the existence of a large area of voids, can degrade the structural integrity and safety that could otherwise be attainable by retrofit/strengthening [6,7]. In order to minimize air voids and ease FRP installation, the authors propose to apply narrow strips of CFRP laminates with spacing, similar to transverse reinforcement steel. This study focuses on the experimental studies related to the compressive behaviors of concrete cylinders. In this experiment, CFRP strips with two different widths (2.5 cm and 5.0 cm) are, respectively, bonded in spiral with spacing on 60 concrete cylinders, as shown in Fig. 1, while the conventional methods usually use several layers of wider sheets, layer by layer with overlap (without spacing). This proposed procedure makes it easier to release all trapped air and to assure CFRP strips fully bonded to concrete. In this study, several key parameters have been considered for the preparation of the test specimens, for example, spacing, spliced length, and section area of the CFRP laminates. The center-to-center
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15cm
a
60cm
H2-I0-O
H
H2-I1-O H2-I1-T H2-I1-TA H2-I1-TB
H2-I2-O
H2-I3-O
H2-I4-O
15cm
b
30cm
N
N2-I1-O N3-I1-O N3-I1-T N3-I1-TA N3-I1-TB
N3-II1-O
N2-II3-O N3-II3-O
Fig. 1. Geometry of CFRP laminates of specimens for (a) Group H and (b) Group N.
spacing of the spiral CFRP strip is taken as one of 2.5 cm, 5.0 cm, 7.5 cm, 10.0 cm, and 12.5 cm. The authors also vary the width of the laminates (2.5 cm and 5.0 cm) and the spliced length (no splice, 24 cm, and 48 cm). In addition, pre-damaged specimens wrapped with CFRP laminates are also tested for the purpose of comparison. Finally, constitutive models of concrete confined by narrow strips of CFRP laminates are proposed based on the experimental results. 2. Experimental study Sixty concrete cylinders with two different dimensions, £15 cm 60 cm (group H in Fig. 1a) and £ 15 cm 30 cm (group N in Fig. 1b), are prepared and then reinforced by a variety of CFRP strips, as illustrated in Fig. 1. These specimens are subjected to compressive loading and their compressive behaviors are observed. The compressive strengths measured from the concrete cylinders, ‘H’ and ‘N’ specimens in Fig. 1, are 26.08 MPa and 20.72 MPa, respectively. In this study, unidirectional CFRP laminates ‘‘Korea Carbon NR-32” are applied with an epoxy adhesive. The CFRP laminates have a nominal tensile strength of 2 GPa and elastic modulus of 155 GPa. The CFRP laminates consist of reinforcement phase of carbon fiber and matrix resin system of polyester. Fiber direction and angle of CFRP strip can be indicated from Fig. 1. The adhesive with 16.2 MPa bond strength is used to bond the CFRP laminates onto the concrete cylinders. 2.1. Specimen and test setup Before retrofitted with the CFRP laminates, the concrete cylinder surface is cleaned with sandpapers. Then a layer of 2 mm epoxy
mortar is applied to cover the concrete surface. Finally, the CFRP laminates are bonded to the surface of each concrete cylinder with the designed spacing, thickness, and splice length of CFRP laminates. To prevent the end fracture at the top and bottom of the concrete cylinders, the top and bottom of the specimens are additionally strengthened with CFRP laminates. The details of CFRP laminates are summarized in Tables 1 and 2. In terms of the notation of each specimen, the first character, H or N, refers to the size of the specimen (H representing cylinders with 15 cm diameter and 60 cm height and N representing cylinders with 15 cm diameter and 30 cm height). The following number, 2 or 3, refers to the thickness of the single layer of the CFRP sheet (2 for 0.2 mm thickness and 3 for 0.3 mm thickness). The next character, I or II, refers to the width of the CFRP laminates (I for 2.5 cm and II for 5.0 cm). The following number represents the center-to-center spacing of
Table 1 Specimen details (group H) Reference
CFRP Thickness (mm)
CFRP Width (mm)
CFRP Spacing (mm)
CFRP Layer (number)
CFRP Spliced length (mm)
H H2–I0–O H2–I1–O H2–I2–O H2–I3–O H2–I4–O H2–I1–T H2–I1–TA H2–I1–TB
– 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
– 25 25 25 25 25 25 25 25
–
– 1 1 1 1 1 2 2 2
– No splice No splice No splice No splice No splice No splice 240 mm 480 mm
25 50 75 100 125 50 50 50
T.W. Park et al. / Composites: Part B 39 (2008) 1093–1103 Table 2 Specimen details (group N) Reference
CFRP Thickness (mm)
CFRP Width (mm)
CFRP Spacing* (mm)
CFRP Layer (number)
CFRP Spliced length (mm)
N N2–I1–O N2–II3–O N3–II1–O N3–II3–O N3–I1–O N3–I1–T N3–I1–TA N3–I1–TB
– 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3
– 25 50 50 50 25 25 25 25
– 50 100 50 100 50 50 50 50
– 1 1 1 1 1 2 2 2
– No splice No splice No splice No splice No splice No splice 240 mm 480 mm
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ment of the specimens, two linear variable differential transformers (LVDT, LT-50 of Tokyo Sokky) are installed on two opposite sides of the cylinder. Fig. 2a illustrates the experiment setup and specimen. Fig. 2b is schematic drawing including specimen, experiment machine and LVDT. 2.2. Test results and discussion
the CFRP laminates (0 for 2.5 cm, 1 for 5.0 cm, 2 for 7.5 cm, 3 for 10.0 cm, and 4 for 12.5 cm). The following character, O or T, refers to the number of CFRP layers applied (O for 1 layer and T for 2 layers). The final notation, A or B, represents the spliced length of the CFRP laminates (A for 24 cm, B for 48 cm, and no A or B for no splice). The specimens marked with only H or N represent concrete cylinders without CFRP strips. For each reference notation, three specimens are, respectively, prepared and average values of experiment results are used. All specimens are subjected to compressive load under displacement control on a Universal Testing Machine (UTM, LT-950 of Forney Inc.) with a maximum load capacity of 2000 kN. The load–displacement data are automatically recorded through a data logger (LC-V and UCAM-58T of Kyowa). For measuring displace-
Tables 3 and 4 summarize maximum loads and damage patterns corresponding to the each reference notation. All specimens wrapped with CFRP laminates show the fracture of CFRP, while specimens without CFRP laminates show typical shear failure in the middle of the specimens. The maximum loads applied to the reinforced specimens are higher than those of the un-reinforced specimens. In Tables 3 and 4, foc is maximum compressive stress (maximum load/section area of the specimens) and f* represents increased portion of maximum compressive stress by confinement. Apparently, the reinforcement by CFRP laminates significantly increases the stress capacity of the specimens. Fig. 3 shows the photos of damaged H (without CFRP) and H2–I2–O (with CFRP) specimens. One can indicate that the H specimen shows shear failure by crack. In case of the H2–I2–O specimen, tensional breakage of CFRP laminates happens after carrying larger strain and stress compared to H specimens. As mentioned before, three specimens with identical CFRP setup are tested for each reference notation. Fig. 4 shows some examples of stress–strain curves obtained from the compression tests of specimens H and N3–II1–O. The end number (1, 2, or 3) following
a
b Spherical Bearing
Load cell Specimen
LVDT Guide
Base
UTM(2000kN) Fig. 2. (a) Details of the experimental setup and (b) schematic drawing.
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involving larger specimens is needed in order to investigate the size effect.
Table 3 Summary of test results (group H) Reference
Maximum load (kN)
foc (MPa)
f* (MPa)
Damage pattern
H H2–I0–O H2–I1–O H2–I2–O H2–I3–O H2–I4–O H2–I1–T H2–I1–TA H2–I1–TB
456.7 737.5 617.8 504.9 544.2 527.8 724.3 682.1 700.4
26.08 41.69 34.97 30.06 30.80 29.87 41.00 38.61 39.64
– 15.62 8.89 3.98 4.72 3.80 14.92 12.53 13.57
Shear failure by crack Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP
Table 4 Summary of test results (group N) Reference
Maximum load (kN)
foc (MPa)
f* (MPa)
Damage pattern
N N2–I1–O N2–II3–O N3–II1–O N3–II3–O N3–I1–O N3–I1–T N3–I1–TA N3–I1–TB
366.0 487.7 495.8 707.5 457.3 540.0 680.0 586.7 603.3
20.72 27.60 28.06 40.04 29.22 30.56 38.49 33.21 34.05
– 6.89 7.35 19.33 8.50 9.85 17.78 12.49 13.34
Shear failure by crack Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP Fracture of CFRP
the reference notation represents the identification number of each among three specimens. The averaged stress–strain curves are derived for the following analysis. 2.2.1. Effects of specimen size Cylinders with two different heights (60 cm and 30 cm) are tested. To study the effects of the specimen size on the maximum compressive strength of the confined concrete, the ratio of the compressive strengths of confined and unconfined concrete specimens, foc/fc, is observed and compared for two reference cases having different height. The results from specimens H2-I1-O (60 cm height) and N2–I1–O (30 cm height) are compared. These two specimens have identical layout of CFRP strips with same thickness, width, spacing, and the number of layers. These two groups of specimens with different heights show almost the same ratio of compressive strengths. The specimen H2–I1–O (£15 60 cm) exhibits compressive strength ratio (foc/fc) of 1.34, while the specimen N2–I1–O (£15 30 cm) shows 1.33 (Fig. 5). Based on this test, one can indicate that different cylinder heights do not have effects on the effectiveness of the CFRP reinforcement. More study
2.2.2. Effects of spacing of CFRP laminates Stress–strain curves are plotted in Fig. 6 for the specimens with identical width and thickness of CFRP strips except center-to-center spacing. The plot demonstrates the effects of the spacing of CFRP strips on the performance of strengthened concrete specimens. It can be seen that the stress-carrying capacity and the strain capacity of the specimens wrapped with CFRP are improved greatly compared to control specimen H in Fig. 4a. The stress–strain curves of H2–I2–O, H2–I3–O, and H2–I4–O fall after reaching their peak, while the curves of the other specimens continue to increase or hold the stress level after passing turning points. As also observed in Fig. 6, the specimen has smaller spacing shows larger deformation capacity. It can be explained as ductility. Ductility can be defined as the capability of materials to deform while still carry load after passing the turning point. In case of a specimen H2– I4–O with a 12.5 cm center-to-center spacing (10 cm net spacing and 20% ratio of CFRP-bonded area versus total concrete surface area), it shows relatively brittle failure after reaching the peak compressive strength. However, specimens H2–I0–O and H2–I1– O show highly ductile behavior. 2.2.3. Effects of spliced length of CFRP laminates To investigate the effects of the spliced length of CFRP strips, concrete cylinders wrapped with identical CFRP strips but having different spliced lengths (24 cm, 48 cm, or continuous strip without splice) are observed. The stress–strain curves obtained from the compressive tests for three reference notation with identical CFRP layout except spliced lengths are presented in Fig. 7. According to the test results, the specimen wrapped with the continuous CFRP strip (no splice), shows the highest ductility and stress-carrying capacity. But the specimens with 24 cm and 48 cm spliced lengths behave similarly. Even though debonding occurs at the spliced part of the CFRP strip, final breakage of the CFRP strip takes place in other area, not in the spliced part. Thus, it can be indicated that the spliced length, if it is over a certain length, does not have an effect on the confined concrete strength. More experimental study involving specimens with the shorter spliced length of the CFRP strip is needed in order to evaluate minimum spliced length. 2.2.4. Effects of the number of layers and thickness of CFRP laminates In this study, the authors also investigated the effects of the number of layers of CFRP laminates on the compressive strength. Among H and N group specimens, the specimens with the same spacing and the same width of CFRP laminates are focused. The ra-
Fig. 3. Damage patterns of concrete cylinders. (a) H specimen and (b) H2–I2–O specimen.
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50
0 0
0.003
0.006
0.009
0.012
0.015
0.018
Strain (a) Stress-strain curves of H specimens
1.18
1.25
1.15
1.10
1.00 H2-I1-TB
H2-I1-TA
H2-I1-T
0.50
H2-I4-O
0.75 H2-I3-O
H1
10
1.52
1.48 1.34
H2-I2-O
20
1.57
H2-I1-O
H3
1.60
1.50
H2-I0-O
H2
30
1.75
H
Stress (MPa)
40
Ratio of compressive strength of group H
.
2.00
0.25 0.00
SPECIMEN
(a) Ratio of compressive strength of group H 50
2.00
0
0.003
0.006
0.009
0.012
0.015
0.018
Strain (b) Stress-strain curves of N3-II1-O specimens
1.25
0.25 0.00
Fig. 4. Stress–strain curves of H and N3–II1–O.
N3-I1-TB
N3-I1-TA
0.50
N3-I1-T
0.75
N3-I1-O
1.00 N3-II3-O
0
1.65
1.35
N3-II1-O
10
1.33
1.25
N2-II3-O
20
1.60 1.48
1.50
N2-I1-O
N3-II1-O2
1.86
1.75
N
N3-II1-O1
Ratio of compressive strength of group N
Stress (MPa)
40
30
1.93
.
N3-II1-O3
SPECIMEN (b) Ratio of compressive strength of group N
Fig. 5. Ratio of compressive strength of confined and unconfined specimens.
2.2.5. Effects of width of CFRP laminates The specimens with two different widths (2.5 cm and 5 cm) are compared. Fig. 9 compares the stress–strain curves of the specimens wrapped with the CFRP strips having different widths. But,
50
H2-I0-O (spacing : 2.5cm)
40
Stress (MPa)
tio of the maximum compressive strength between the concrete confined by CFRP and the unconfined concrete, foc/fc, is plotted in Fig. 8 for comparison. In case of specimen H2–I1–O (0.2 mm thickness and 1 layer), the ratio foc/fc is 134%, while the ratio of H2–I1–T (0.2 mm thickness and two layers) increases to 157%. In case of N group, the ratios of the maximum compressive strength of N3– I1–O (0.3 mm thickness and one layer) and N3–I1–T (0.3 mm thickness and 2 layers) are 148% and 186%, respectively. The specimens with two layers of CFRP show higher compressive strength but those do not come to double compared with the ratios increased by one layer of CFRP. Therefore, strengthening with one layer of CFRP is more efficient than the case using two layers of CFRP. A similar comparative study is conducted using the concrete specimens with different thickness of CFRP laminates. For the H group specimens with 0.2 mm CFRP thickness, the compressive strength is improved by 51% compared to the unconfined cylinders. The N group specimens with 0.3 mm CFRP thickness shows improved strength by 78%. Comparing these two groups of specimens, the ratio of CFRP thickness is 0.66 (=0.2 mm/0.3 mm) and the ratio of improved compressive strength is approximately 0.65 (=51%/78%). This result shows that the thickness of CFRP do not have effects on the effectiveness of the CFRP reinforcement.
H2-I1-O (spacing : 5.0cm)
30
H2-I2-O (spacing : 7.5cm) H2-I3-O (spacing : 10.0cm) H2-I4-O (spacing : 12.5cm)
20
10
0
0
0.003
0.006
0.009
0.012
0.015
0.018
Strain Fig. 6. Stress–strain curves of specimens with different spacing.
these specimens have the same number of layers and the same ratio of bonding area of CFRP (CFRP-bonded area versus total area of the cylinder surface). It is clear that as long as the ratio of bonding area and the number of layers are same, the width of the strip does not have effects on the compressive behavior of the CFRP reinforced cylinders.
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2
10 S.L : SPLICED LENGTH
0.006
0.009
0.012
0.015
Ratio of compressive strength of group H
Stress (MPa)
N3-I1-TB (S.L:48cm)
N3-I1-T
30
20
10
0
0.003
0.006
0.009
0.012
0.015
1.86
1.5
1
0.5
1.6
1.65
1.48
1
0
S.L : SPLICED LENGTH 0
2
N3-I1-O
.
(a) Ratio of compressive strength of group H
50
40
H2-I1-TB
SPECIMEN
Strain (a) Stress-strain curves of group H
N3-I1-TA (S.L:24cm)
H2-I1-TA
0
0.018
N3-I1-TB
0.003
0.5
N3-I1-TA
0
1.52
1
N3-I1-T
0
1
H2-I1-T
20
1.48
1.34
H2-I1-O
Stress (MPa)
H2-I1-TA (S.L : 24cm)
30
1.57
1.5
H
H2-I1-T
N
H2-I1-TB (S.L : 48cm)
40
Ratio of compressive strength of group N
50
0.018
Strain (b) Stress-strain curves of group N
SPECIMEN
(b) Ratio of compressive strength of group N Fig. 8. Effects of the number of CFRP layers.
Fig. 7. Stress–strain curves of specimens with different spliced length.
2.2.6. Comparison between undamaged and pre-damaged specimens Six pre-damaged concrete cylinders are prepared. Each cylinder is divided into three pieces. The damaged cylinder pieces are bonded together with epoxy mortar and then cured. Then, these pre-damaged specimens are strengthened with CFRP laminates. A comparative study is carried out using these pre-damaged concrete cylinders, together with the undamaged cylinders. As shown in Fig. 10, the undamaged and pre-damaged specimens strengthened with the same CFRP laminates exhibit almost identical stress– strain behaviors.
3. Constitutive models for confined concrete A constitutive model for concrete plays an important role in the analysis and design of concrete structures. To predict the peak stress or the stress–strain curves of confined concrete, various constitutive models have been proposed. The most frequently cited model is Mander’s model [8] which has been shown to provide excellent prediction of compressive response of large-scale columns confined by a wide range of transverse reinforcement ratios. Samaan et al. [9] developed a simple FRP-confined concrete model, applicable to circular columns. This model predicts the complete bilinear stress–strain response of FRP-confined concrete in both axial and lateral directions. A very efficient FRP-confined concrete model was recently developed by Hosotani and co-workers [10,11] for circular and rectangular columns. This model is based on comprehensive experimental testing of small-size circu-
lar and rectangular columns confined by carbon fiber sheets. All model parameters were developed from regression analysis conducted on the experimental results. Hoppel et al. [12], Toutanji [13], and Spoelstra and Monti [14] also developed their own models to predict the stress–strain relationship of columns wrapped with FRP composite sheets. Recently, Youssef et al. [2] developed a comprehensive concrete confinement model using experimental data and other reliable data from the literature. 3.1. Stress–strain curves of confined concrete The axial stress–strain relationship for confined concrete is in general shown in Fig. 11. There exist two trends corresponding to the confinement ratio. For concrete with relatively small confinement ratio q, the axial stress of confined concrete increases with strain until it reach the maximum value ft, at which the axial strain is et . At this point, the CFRP is getting fully activated under tensile stresses due to concrete dilation. Thereafter, the axial stress decreases linearly as the axial strain increases. On the other hand, for concrete with relatively large confinement ratio q, the concrete stress fc continues to increase all the way up to failure, but with some deterioration of its axial stiffness as shown in Fig. 11. In this study, the authors focus on the predictions of ft, et , and second slope of stress–strain curve Eg. Referring the constitutive models developed by previous researchers, the axial stress of confined concrete at the boundary point from first to second region, ft is assumed to be the sum of 0 the axial stress of unconfined concrete, fco , and the stress increase due to the confinement, finc
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50
fc f cu
Ascending
N2-II3-O(width : 5.0cm)
30
Axial Stress
Stress (MPa)
40
N2-I1-O(width : 2.5cm)
20
Eg 1
ft
1
Eg
Descending
10 Ec
0
0
0.003
0.006
0.009
0.012
0.015
0.018
εt
Strain (a) Stress-strain curves of group N2
Axial Strain
εc
ε cu
Fig. 11. Stress–strain curves of concrete confined by CFRP laminates.
50
40
30
20
N3-I1-O (width : 2.5cm)
10
0
0
0.003
0.006
0.009
0.012
0.015
0.018
Proposed stress (MPa)
Stress (MPa)
40 N3-II3-O (width : 5.0cm)
30
20
10
Strain
(b) Stress-strain curves of group N3
0 0
10
20
30
40
Experimental stress (MPa)
Fig. 9. Effects of width of CFRP laminates.
Fig. 12. Comparison between experimental and proposed axial stresses ft.
50 Pre-damaged, strengthened
0.004
Undamaged, strengthened
30
Proposed strain
Stress (MPa)
40
20
10
0
0.003
0.002
0.001
0
0.003
0.006
0.009
0.012
0.015
0.018
Strain
0
0
0.001
0.002
0.003
0.004
Experimental strain
Fig. 10. Stress–strain curves of undamaged and pre-damaged specimens.
Fig. 13. Comparison between experimental and proposed axial strains et .
0 0 ft ¼ fco þ finc ¼ fco þ fl0a ;
ð1Þ
where fl0 is the effective lateral confining strength and the constitutive parameter a is the coefficient of the power-law equation which can be obtained from experimental data using regression analysis. The effective lateral confining stress provided by the lateral CFRP laminates fl0 can be represented as follows:
fl0 ¼ 2 ke t n w ECF eCF =ðS DÞ;
ð2Þ
where ke is the confinement effectiveness coefficient and depends on the type of lateral CFRP laminates, t is the thickness of the CFRP laminates, n is the number of layers, ECF is the elastic modulus of the CFRP laminates, eCF is the ultimate strain of the CFRP laminates, D is the diameter of the cylinder, S is the spacing (center to center) of
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the CFRP laminates strip. It can be derived from the equilibrium of the internal forces acting dissected section. fl0 can be rewritten as
fl0 ¼ q ke ECF eCF =2;
ð3Þ
where, q is CFRP confinement ratio given by q = 4 t n w/ (S D) from Eq. (2). Based on the preliminary regression analysis, the authors simply assume ke as
pffiffiffi ke ¼ b= n;
ð4Þ
50
where, constitutive parameter b is a coefficient obtained by regression analysis. According to the experimental results, the effectiveness of the CFRP strengthening does not increase linearly with increase of the number of layers of CFRP laminates, n. This is because the brittle characteristic of epoxy applied in the CFRP laminates becomes more dominant as the number of layers of CFRP laminates increases. To consider such brittle characteristic, Eq. (4) is proposed as the confinement effectiveness coefficient in terms pffiffiffi of n. When the axial stress reaches the compressive stress ft, the corresponding strain of the confined concrete is et . The strain of this
50
N2-I1 series
40
Stress (MPa)
Stress (MPa)
40 30 20 10 0
0
0.003
0.006
0.009
0.012
0.015
50
20
0
0.018
Proposed Experiment
0
0.003
0.006
0.009
0.012
0.015
0.018
Strain (b) Experimental and proposed stress-strain curves of N3-I1 50
N3-II1 series
H2-I2 series
40
40
Stress (MPa)
Stress (MPa)
30
10
Proposed Experimental
Strain (a) Experimental and proposed stress-strain curves of N2-I1
30
20
30 20 10
10
Proposed Experiment
0
0.003
0.006
0.009
0.012
0.015
Proposed Experimental
0
0
0
0.018
0.003
0.006
0.009
0.012
0.015
0.018
Strain
Strain (c) Experimental and proposed stress-strain curves of N3-II1
(d) Experimental and proposed stress-strain curves of H2-I2 50
50
H2-I3 series
H2-I4 series
40
Stress (MPa)
40
Stress (MPa)
N3-I1 series
30 20 10
30 20 10
Proposed
Proposed Experimental
Experimental
0 0
0.003
0.006
0.009
0.012
0.015
0.018
Strain (e) Experimental and proposed stress-strain curves of H2-I3
0 0
0.003
0.006
0.009
0.012
0.015
0.018
Strain (f) Experimental and proposed stress-strain curves of H2-I4
Fig. 14. Comparison between experimental and proposed stress–strain model.
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intersection point depends on the lateral confining stress provided by the CFRP laminates. A general form for et is assumed as
et ¼
e0co
h finc þk 0 ; fco
3.2. Regression analysis for constitutive modeling The constitutive parameters are obtained by the regression analysis of the experimental data. Based on the regression analysis, parameter a in Eq. (1) is determined as 0.85 and parameter b in Eq. (4) is 2.8. Parameter k and h in Eq. (5) is 0.0033 and 0.7, respectively. In Figs. 12 and 13, the predicted axial stress and strain from proposed constitutive model are presented compared with the actual values observed in the experiments. In these figures, each point stands for a vector representing the accuracy of the prediction. If the points show up nearer around the diagonal, it means the accuracy of the prediction is high. In terms of the ratio of the predicted stress to experimental stress, the mean value of these ratios is 0.974. In case of the axial strain, the mean value of the ratios is 1.062. One can indicate that the proposed constitutive models for the axial stress and strain can yield reasonably good results. For the second slope of the stress–strain curve, Eg, parameters g and l are assumed, respectively, for the ascending and descending curves, depending on the ratio of the CFRP confinement. Based on the experimental results, the slope Eg is positive (ascending) when the ratio of the CFRP bonding area is larger than 50%, while Eg is negative (descending) when the CFRP area ratio is less than 50%.
ð5Þ
where e0co is the strain of the unconfined concrete at the intersection point and finc is the increased compressive strength, fl0a , in Eq. (1). Parameters k and h can be obtained from the regression analysis based on experimental data. As shown in Fig. 11, the stress–strain curve after the intersection point is an ascending or descending curve with a smaller slope than that of the curve before the intersection point. The second slope of stress–strain curve Eg can be obtained from the experi0 mental results. Eg can be assumed as a function of q and fco as below. Various equation forms of Eg are previously reviewed to derive best format in the view of prediction accuracy.
Eg ¼ g
0 fco
q ECF eCF
pffiffiffiffi þ l q ECF ;
ð6Þ
where, constitutive parameters g and l are coefficients obtained by regression analysis.
1.2 Hosotani
Yousse f
Proposed
f't_predict/f't_exp
1 0.8 0.6 0.4 0.2 0 H2- 2
H2- 3
H2- 4
N2- 1-O
N3- 1-O
N3- 1–T
SPECIMEN Fig. 15. Comparison of three constitutive models (ratio of ft).
1.6 1.4
Hosotani
Youssef
Proposed
t_predict/ t_exp
1.2 1 0.8 0.6 0.4 0.2 0 H2- 2-O
H2- 3-O
H2- 4–O
N2- 1-O
N3- 1-O
SPECIMEN Fig. 16. Comparison of three constitutive models (ratio of et ).
N3- 1–T
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2.5
Hosotani
Youssef
Proposed
2nd E predict/experiment
2
1.5
1
0.5
0
H2-I2
H2-I3
H2-I4
N2-I1-O
N3-II1-O
N3-I1–T
SPECIMEN Fig. 17. Comparison of three constitutive models (ratio of Eg).
Parameters g and l are derived as 1.25 and 0.065 for the ascending curves and 13.5 and 0.29 for the descending curves. Fig. 14 shows the stress–strain curves computed by the proposed constitutive model, in comparison with those experimentally obtained. To plot the stress–strain curves, axial stress and axial strain at the intersection point, ft and et , and second slope Eg are calculated at first. And then using a similar approach used by Hoshikuma et al. [15] and Youssef et al. [2], the stress–strain curve of confined concrete in region before intersection point (e 6 et ) is modeled by the following polynomial function as Eq. (7).
fc ¼ C 1 em þ C 2 e þ C 3 ;
(2)
(3)
ð7Þ
where C1, C2, C3, and m are constant parameters to be determined from the boundary conditions of the stress–strain curves. Good agreement is observed between the experimental and the proposed analytical stress–strain curves, demonstrating the validity of the proposed constitutive model and the parameter values. To show the effectiveness of the proposed constitutive model, the values of ft, et , and Eg calculated from above proposed model are compared with those obtained from other constitutive models proposed by previous researchers. Two existing constitutive models for CFRP-confined concrete (Hosotani et al. [10] and Youssef et al. [2]) are considered in this study. Fig. 15 shows the ratio of ft obtained from the prediction and experiment for each specimen, ðft predict =ft exp Þ. Fig. 16 also represents the ratio of et , et predict =et exp . Both previously suggested models seem to predict ft and et comparatively well. However, in case of Eg in Fig. 17, these previous models do not show similar prediction accuracy. Fig. 17 shows the ratio of Eg for the selected specimens with descending (H2–I2–O, H2– I3–O, and H2–I4–O) or ascending (others) slope. The proposed model seems to predict the behaviors of concrete cylinders confined by narrow strips of CFRP with best accuracy. 4. Conclusions Spiral wrapping of a narrow strip of CFRP laminates is proposed in this study for concrete reinforcement. Based on the compressive tests for sixty concrete cylinder specimens wrapped with CFRP strips having various layouts, the following conclusions can be made: (1) Using CFRP strips to confine concrete is an efficient method to improve strength and ductility of concrete. All concrete specimens strengthened with CFRP laminates show reason-
(4)
(5)
(6)
(7)
able damage patterns with increased strength and ductility, while specimens without CFRP laminates show typical shear failure. In particular, it is found that a narrow strip of CFRP laminates is easy to apply on concrete and the spacing between the strips makes it easy to remove air pockets and ensure bonding quality. The stress and strain capacities of the specimens wrapped with CFRP are improved greatly compared to normal specimen without CFRP retrofit. The spliced length does not have an effect on the confined concrete strength in the range of 24 cm and 48 cm. More experimental study is needed to investigate the minimum spliced length. The effect of confinement on the increase of compressive strength is not linear to the number of CFRP layers. The strength increases only 1.54 times, even though the number of layers doubles. Pre-damaged specimens strengthened with CFRP laminates show the same stress–strain behavior as undamaged specimens strengthened with CFRP laminates. Narrow strips of CFRP laminates can be effectively used for strengthening pre-damaged concrete members. The stress–strain curves of the specimens with a low ratio of confinement (represented by the area ratio) show a descending trend after reaching the maximum stress, while the stress–strain curves of the specimens with a high ratio of confinement show an ascending trend until failure. Constitutive models of a confined concrete are developed based on the compressive test results. Good agreement is observed between the experimental (actual) and analytical (predicted) stress–strain curves, demonstrating the validity of the proposed constitutive model and the parameter values. Such a model is useful for design and analysis of concrete structures strengthened by the proposed narrow strips of CFRP laminates.
More tests involving larger specimens are needed, in order to thoroughly investigate the effects of specimen size on the compressive behavior of concrete confined by spiral narrow strips of CFRP with spacing. In addition, the effects of the other important parameters related to CFRP laminates, for example, fiber direction and the angle of CFRP strips, need to be worked over to deeply understand the compressive behavior of concrete cylinders wrapped with CFRP.
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Acknowledgements The work was partially sponsored by the Korea Institute of Construction and Transportation Technology Evaluation and Planning (Grant No. 05 CTRM D06: High-tech Urban Development Program). The financial support is gratefully acknowledged. References [1] Fam A, Flisak B, Rizkalla S. Experimental and analytical modeling of concretefilled fiber-reinforced polymer tubes subjected to combined bending and axial loads. ACI Struct J 2003;100(4):499–509. [2] Youssef M, Feng MQ, Mossalam A. Stress–strain model for concrete confined by FRP composites. J Compos Part B: Eng 2007;38(5–6):614–28. [3] Seible F, Hegemier GA, Priestley MJN, Innamorato D, Ho F. Carbon fiber jacket retrofit test of rectangular flexural column with lap spliced reinforcement. Advanced composites technology transfer consortium report no. ACTT-95/02, UCSD; 1995. [4] Xiao Y, Wu H. Compressive behavior of concrete cylinders confined by carbon fiber composite jackets. ASCE J Mater Eng 2000;12(2):139–46. [5] Shahawy M, Mirmiran A, Beitelman T. Tests and modeling of carbon-wrapped concrete columns. Compos Part B: Eng 2000;31(6):471–80.
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[6] Au C. Behavior of FRP-confined concrete structures. Thesis, Massachusetts Institute of Technology, Cambridge, MA; 2001. [7] Haroun, MA, Feng MQ, Bhatia H, Baird K, Elsanadedy H. Structural qualification testing of composite-jacketed circular and rectangular bridge column. Technica Report to the California Department of Transportation; 2001. [8] Mander JB, Priestley MJN, Park R. Theoretical stress–strain model for confined concrete. ASCE J Struct Eng 1988;114(8):1804–26. [9] Samaan M, Mirmiran A, Shahawy M. Model of concrete confined by fiber composites. ASCE J Struct Eng 1998;124(9):1025–31. [10] Hosotani M, Kawashima K, Hoshikuma J. A stress–strain model for concrete cylinders confined by carbon fiber sheets (in Japanese). JSCE J Concrete Eng 1998;39(592):37–52. [11] Hosotani M, Kawashima K. A stress–strain model for concrete cylinders confined by bothcarbon fiber sheets and tie reinforcement (in Japanese). JSCE J Concrete Eng 1999;43(620):25–42. [12] Hoppel CR, Bogetti TA, Gillespie JW, Howie I, Karbhari VM. Analysis of a concrete cylinder with a composite hoop wrap. In: Proceedings of ASCE material engineering conference. New York; 1994. p. 191–8. [13] Toutanji H. Stress–strain characteristics of concrete columns externally confined with advanced fiber composite sheets. ACI Mater J 1999;96(3): 397–404. [14] Spoelstra MR, Monti G. FRP-confined concrete model. ASCE J Compos Construct 1999;3(3):143–50. [15] Hoshikuma J, Kawashima K, Nagaya K, Taylor AW. Stress–strain model for confined reinforced concrete in bridge piers. J Struct Eng 1997;123(5):624–33.