Experimental study of bond behaviour between concrete and FRP bars using a pull-out test

Composites: Part B 40 (2009) 784–797

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Experimental study of bond behaviour between concrete and FRP bars using a pull-out test Marta Baena, Lluís Torres *, Albert Turon, Cristina Barris Analysis and Advanced Materials for Structural Design (AMADE), Polytechnic School, University of Girona, Campus Montilivi s/n, 17071 Girona, Spain

a r t i c l e

i n f o

Article history: Received 25 February 2008 Received in revised form 29 June 2009 Accepted 18 July 2009 Available online 24 July 2009 Keywords: A. Fibres B. Fibre/matrix bond C. Analytical modelling D. Mechanical testing

a b s t r a c t This paper presents the results of an experimental programme concerning 88 concrete pull-out specimens prepared according to ACI 440.3R-04 and CSA S806-02 standards. Rebars (reinforcing bars) made of carbon-fibre and glass-fibre reinforced polymer (CFRP and GFRP), as well as steel rebars, with a constant embedment length of five times the rebar diameter were used. The influence of the rebar surface, rebar diameter and concrete strength on the bond–slip curves obtained is analysed. In addition, analytical models suggested in the literature are used to describe the ascending branch of the bond–slip curves. To calibrate the analytical models, new equations that account for the dependence on rebar diameter are presented. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction The use of fibre reinforced polymers (FRP) as reinforcement in concrete structures is considered to be a possible alternative to steel in those situations where corrosion is present. However, in contrast to steel, there is yet no standardisation for the surface characteristics of FRP bars. Therefore, determining the bond characteristics of non-standardised commercial rebars is a fundamental requirement for their practical use, as this influences the mechanism of load transfer between reinforcement and concrete. The mechanics of bond stress transfer between FRP reinforcement and concrete has been investigated by many authors [1–5]. The EUROCRETE project [6] studied the influence of rebar type, embedment length and cross-sectional shape, among others; the results were presented in [7,8]. It was concluded that the pullout mechanism of the many existing types of FRP reinforcement differed from that of deformed steel bars and was dependent on even more parameters. This conclusion was also reported in [9,10]. For rebars with a smooth surface, the effect of concrete mechanical properties appeared to be negligible; the bond behaviour was therefore solely dependent on the type of fibres and matrix [11]. However, for rebars with an indented and deformed surface, a strong dependence of bond strength on the confinement pressure was reported in [12]. Among all the results from previous studies, what stands out is the general trend for larger rebar diameters to have lower bond strengths [3,7,8,10,11,13,14]. * Corresponding author. Tel.: +34 972418866; fax: +34 972418098. E-mail address: [email protected] (Ll. Torres). 1359-8368/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesb.2009.07.003

Considerable research efforts have been made to describe the bond behaviour of glass fibre reinforced polymer (GFRP) rebars in plain concrete, as summarised by Cosenza et al. [14]; on the other hand, Belarbi and Wang [15] conducted a study on the pull-out bond–slip response of GFRP and carbon-fibre reinforced polymer (CFRP) rebars embedded in fibre reinforced concrete. Although they found no improvement in the maximum bond strength, the desired ductility was improved for all specimens (in terms of larger slips for maximum bond strength). Moreover, several attempts have been made to formulate analytical models to predict the interfacial bond behaviour of FRP bars. Malvar [12] modelled the overall bond behaviour of FRP bars by introducing two empirical constants whose values depended on the rebar type. Later on, the bond–slip analytical law proposed by Eligehausen et al. [16] for deformed steel rods (BPE model) was applied to FRP rebars by Cosenza et al. [17] and Rosetti et al. [18]. As a result of their study, Cosenza et al. [17,19] proposed an alternative analytical model (called the double branch model) that modified the softening branch of the BPE model with the inclusion of two new parameters. Because most structural problems are dealt with at the serviceability state, a new model for the ascending branch of the bond–slip curve (the CMR model) was also proposed by Cosenza et al. [17]. A complete study of the accuracy of all of these models has been reported by the FIB [20]. All of the reported models depend on several parameters that have to be adjusted to the experimental data. Several attempts have been made to calibrate analytical models, whether by considering the experimental data as a whole or by grouping the results in family types [14,21–23].

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M. Baena et al. / Composites: Part B 40 (2009) 784–797

Fig. 1. Surface deformations and characteristics of rebars (R1–R7).

In this paper, the results of 88 pull-out tests performed according to ACI 440.3R-04 [24] and CSA S806-02 [25] standards are presented with the aim of contributing to the experimental database and to a better understanding of the bond behaviour between concrete and FRP reinforcement. Bond behaviour is analysed for different types of FRP rebars, as well as steel rebars, with the aim of showing the influence of the rebar surface, fibre type, rebar diameter, and concrete strength. Finally, the double branch and the CMR analytical models are calibrated to describe the ascending branch of the bond–slip curves obtained; within the calibration procedure, new equations that show the dependence of the parameters of these analytical models on the rebar diameter are presented. 2. Experimental program 2.1. Materials GFRP, CFRP and steel bars acquired from five different firms were used in this study. The surface treatments and characteristics of the rebars used are shown in Fig. 1 and detailed in Table 1.

Firm A provided CFRP (R1) and GFRP (R2) rebars, both with a sand-coated surface. Firm B provided CFRP rebars with a textured surface (R3) and GFRP rebars with a helical wrapping surface and some sand coating (R4). Firm C supplied GFRP rebars with a grooved surface (R5). Firm D provided rebars (R6) similar to R4: GFRP rebars with a helical wrapping on the surface but no sand coating. Finally, steel rebars (R7) were used for comparison purposes. The nominal diameters of the rebars were 8, 12, 16 and 19 mm, and #3, #4, #5 and #6, where # indicates eighths of an inch. Normalised tests were conducted to determine the cross-sectional areas of the rebars, according to ACI 440.3R4 [24] and CSA S806-02 [25]. The rebar surface treatment, their geometrical and mechanical properties, and the cross-sectional area (measured in the laboratory) are summarised in Table 1. To analyse the influence of concrete strength on the bond behaviour, two different concrete strengths, C1 and C2, were used, with mean compressive strength values of 28.63 MPa (CV = 6.12%) and 52.19 MPa (CV = 6.62%), respectively. The concrete used for the pull-out specimens was prepared in the laboratory and its

Table 1 Geometrical and mechanical properties of the rebars. Firm

Fibre/rebar typea

Resin

Nominal bar diameterb (mm)

Experimental bar diameter (mm)c

Surface treatmentd

Tensile strength (MPa)e

Elastic modulus (GPa)e

(in)

A

C/R1 C/R1 G/R2 G/R2 G/R2 G/R2

Vynilester Vynilester Vynilester Vynilester Vynilester Vynilester

#3 #4 #3 #4 #5 #6

10.65 13.43 10.22 14.13 16.44 19.55

SC SC SC SC SC SC

1596 1899 778 782 803 612

120 144 45 46 46 42

B

C/R3 C/R3 G/R4 G/R4 G/R4 G/R4

Epoxy Epoxy Vynilester Vynilester Vynilester Vynilester

#3 #4 #3 #4 #5 #6

9.05 12.53 9.28 13.73 16.11 19.14

ST ST HW, HW, HW, HW,

2068 2068 760 690 655 620

124 124 40.8 40.8 40.8 40.8

C

G/R5 G/R5 G/R5

Urethane vynilester Urethane vynilester Urethane vynilester

8 12 16

8.55 13.72 17.25

GR GR GR

1000 1000 1000

60 60 60

D

G/R6 G/R6 G/R6 G/R6

Polyester Polyester Polyester Polyester

8 12 16 19

7.07 12.35 17.36 21.25

HW HW HW HW

689 689 689 689

46 46 46 46

E

S/R7 S/R7 S/R7 S/R7

10 12 16 20

10 12 16 20

– – –

>550 >550 >550 >550

200 200 200 200

a b c d e

G = glass; C = carbon and S = steel. Bar size numbers (in.) are based on the number of eighths of an inch. According to ACI 440.3R-04 (for FRP rebars) and standardised (for steel rebars). SC = sand coating; ST = surface texture; HW = helical wrapping and GR = grooves. From manufacturer specifications.

SC SC SC SC

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Table 2 Composition and characteristics of concrete. Concrete C1 mix

Concrete C2 mix

3

Water (kg/m ) Cement 42.5 (kg/m3) Fine aggregate (kg/m3) Coarse aggregate (kg/m3) Polyfunctional additive Rheobuild 570 (kg/m3)

3

200 325 875 878 2.6

Water (kg/m ) Cement 52.5 (kg/m3) Fine aggregate (kg/m3) Coarse aggregate (kg/m3) Superplasticizer Glenium ACE 325 (kg/m3)

171.5 380 843 943 4.6

Table 3 Experimental results for specimens in C2 concrete. Specimena

fc0 (MPa)

Pmax (kN)

smax (MPa)

smax b (MPa)

sm;le c (mm)

sm;le b (mm)

sm;ue c (mm)

sm;ue b (mm)

smax (MPa0.5)

Failure moded

A-C/R1-#3-1-C2 A-C/R1-#3-2-C2 A-C/R1-#3-3-C2 A-C/R1-#4-1-C2 A-C/R1-#4-2-C2 A-C/R1-#4-3-C2 A-G/R2-#3-1-C2 A-G/R2-#3-2-C2 A-G/R2-#3-3-C2 A-G/R2-#4-1-C2 A-G/R2-#4-2-C2 A-G/R2-#4-3-C2 A-G/R2-#5-1-C2 A-G/R2-#5-2-C2 A-G/R2-#5-3-C2 A-G/R2-#6-1-C2 A-G/R2-#6-2-C2 A-G/R2-#6-3-C2 B-C/R3-#3-1-C2 B-C/R3-#3-2-C2 B-C/R3-#3-3-C2 B-C/R3-#4-1-C2 B-C/R3-#4-2-C2 B-C/R3-#4-3-C2 B-G/R4-#3-1-C2 B-G/R4-#3-2-C2 B-G/R4-#3-3-C2 B-G/R4-#4-1-C2 B-G/R4-#4-2-C2 B-G/R4-#4-3-C2 B-G/R4-#5-1-C2 B-G/R4-#5-2-C2 B-G/R4-#5-3-C2 B-G/R4-#6-1-C2 B-G/R4-#6-2-C2 B-G/R4-#6-3-C2 C-G/R5-8-1-C2 C-G/R5-8-2-C2 C-G/R5-12-1-C2 C-G/R5-12-2-C2 C-G/R5-16-1-C2 C-G/R5-16-2-C2 D-G/R6-8-1-C2 D-G/R6-8-2-C2 D-G/R6-12-1-C2 D-G/R6-12-2-C2 D-G/R6-16-1-C2 D-G/R6-16-2-C2 D-G/R6-19-1-C2 D-G/R6-19-2-C2 E-S/R7-10-1-C2 E-S/R7-10-2-C2 E-S/R7-12-1-C2 E-S/R7-12-2-C2 E-S/R7-16-1-C2 E-S/R7-16-2-C2 E-S/R7-20-1-C2 E-S/R7-20-2-C2

54.93 54.93 54.93 54.93 54.93 54.93 53.54 53.11 53.11 53.11 53.11 53.54 53.11 53.11 53.54 53.11 53.54 53.11 54.93 54.93 54.93 54.93 54.93 54.93 49.55 53.65 53.65 49.55 53.65 49.55 49.55 49.55 49.55 53.65 53.65 53.65 50.50 56.30 50.50 56.30 58.20 56.30 47.89 46.15 47.89 47.89 46.15 47.89 46.15 46.15 49.54 49.99 49.99 49.99 58.20 50.50 49.46 49.54

43.313 53.169 46.599 58.545 55.260 55.558 25.394 28.658 26.290 52.572 48.391 47.196 94.086 91.696 96.176 95.878 90.502 88.411 19.420 17.031 11.954 28.679 28.978 32.263 31.068 29.276 28.082 45.404 51.377 54.065 73.179 68.699 70.491 82.438 83.931 86.619 18.823 20.316 43.015 46.599 72.283 73.179 23.285 20.598 59.106 65.076 92.538 102.389 121.792 113.200 46.897 44.508 65.713 65.414 109.019 102.150 140.378 91.995

24.325 27.860 26.170 20.667 19.508 19.613 15.466 17.454 16.011 16.775 15.441 15.060 22.156 21.594 22.649 15.978 15.082 14.734 13.485 13.021 9.070 11.637 9.940 9.334 22.987 21.661 20.777 15.336 17.353 18.261 17.948 16.850 17.289 14.323 14.582 15.049 16.396 17.697 14.541 15.753 15.468 15.660 29.673 26.250 24.667 27.158 19.553 21.634 17.164 15.953 29.856 28.335 29.052 28.920 27.111 25.403 22.342 14.642

26.118

1.273 1.594 1.509 0.764 0.755 1.197 1.979 1.931 1.883 2.054 1.791 3.111 1.913 2.401 2.045 1.254 1.300 0.646 0.503 0.457 0.715 0.616 0.583 2.398 2.333 2.699 2.261 2.532 2.128 3.888 7.454 7.738 5.087 5.440 4.433 1.613 1.851 1.452 1.391 1.128 1.198 8.266 7.140 9.219 8.617 9.262 6.689 5.497 5.429 5.784 9.510 5.913 8.544 1.633 0.712 0.332

1.459

0.128 0.194 0.216 0.100 0.052 0.079 0.040 0.122 0.059 0.057 0.294 0.242 0.061 0.055 0.123 0.119 0.171 0.083 0.178 0.189 0.230 0.297 0.547 0.522 0.283 4.833 5.709 5.690 3.403 3.733 3.558 0.262 0.206 0.148 0.261 0.261 0.345 3.385 2.738 4.067 2.881 5.577 3.068 2.710 3.539 0.783 0.285 0.803 1.381 1.228 1.189 0.321 0.098

0.179

3.282 4.029 3.531 2.789 2.632 2.646 2.114 2.395 2.197 2.302 2.119 2.058 3.040 2.963 3.095 2.193 2.061 2.022 2.039 1.788 1.255 1.570 1.586 1.766 3.266 2.957 2.837 2.179 2.369 2.594 2.550 2.394 2.456 1.955 1.991 2.055 2.307 2.359 2.046 2.099 2.028 2.087 4.288 3.864 3.564 3.924 2.878 3.126 2.527 2.348 4.242 4.008 4.109 4.090 3.554 3.575 3.177 2.080

P P P P P P P P P P P P P P P P P P PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO S S S S Y Y Y Y PO PO S S

a b c d

19.929

16.310

15.759

22.133

15.265

11.859

10.304

21.808

16.983

17.362

14.651

17.047 15.147 15.564 27.962 25.913 20.594 16.559 29.096 28.986 26.257 18.492

Specimen identification according to Fig. 3. Mean value for similar specimens . -, Not measured (blocked LVDT). PO = pullout; S = splitting; P = peeling off; Y = bar yielding.

0.905

1.955

1.909

2.475

1.533

0.535

0.638

2.477

2.307

6.360

4.987

1.732 1.422 1.163 7.703 8.918 7.976 5.463 7.647 7.229 1.633 0.522

0.076

0.060

0.079

0.268

0.058

0.138

0.150

0.264

0.451

5.411

3.565

0.234 0.205 0.303 3.062 3.474 4.323 3.125 0.534 1.092 1.209 0.210

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composition is given in Table 2. The mean concrete compressive strength of each batch of concrete used in the test specimens was determined through compressive tests on three control samples (300  150 mm cylinders). The mean concrete strength values are presented in Tables 3 and 4.

2.2. Specimens, setup and testing equipment The pull-out tests were performed according to ACI 440.3R-04 [24] and CSA S806-02 [25] standards. A 200 mm cubic mould was used to manufacture the pull-out specimens. The embedment length of the bars (lb = 5db) was properly marked and the bars were placed at the bottom of the concrete cube (see Fig. 2a). The concrete was poured with the FRP rebars in position inside the mould, in the middle of the specimen. After moulding, the specimens were transferred to a curing room for 24 h. Thereafter, the concrete cubes were de-moulded, marked and transferred again to the curing room at a temperature of 20 ± 2 °C and a humidity of about 95%. The pull-out test setup is shown in Fig. 2b. The tests were performed using a servo-hydraulic testing machine with a capacity of 600 kN. Displacement control was selected to capture post-peak behaviour. The load was applied to the reinforcement bar at a rate of 0.02 mm/s and measured with the electronic load cell of the testing machine. The loaded and unloaded end slips were measured with four linear variable differential transformers (LVDTs). An automatic data acquisition system was used to record the data. The experimental programme began with R1, R2, R3 and R4 rebars in C2 concrete. The pull-out specimen identification is defined in Fig. 3. Three nominally identical specimens for each configuration were tested. Since there was only a small discrepancy between the results of the nominally identical specimens, the experimental pro-

Fig. 2. Pull-out test setup.

gramme was continued testing two nominally identical specimens for the rest of tests with C2 concrete and for all the tests with C1 concrete. In total, 88 specimens were tested. 3. Test results The influence of the rebar surface, fibre type, rebar diameter, and concrete strength on the bond behaviour is analysed in this section. In the pull-out test, the stress distribution is not constant along the embedment length. Hence, an average bond stress is defined as:

s¼

P

ð1Þ

pdb lb

where P is the tensile load, db is the rebar diameter, and lb is the embedment length. The relationship between the bond stress

Table 4 Experimental results for specimens in C1 concrete. Specimena

fc0 (MPa)

Pmax (kN)

smax (MPa)

smax b (MPa)

sm;le c (mm)

sm;le b (mm)

sm;ue c (mm)

sm;ue b (mm)

smax (MPa0.5)

Failure moded

A-C/R1-#3-1-C1 A-C/R1-#3-2-C1 A-C/R1-#4-1-C1 A-C/R1-#4-2-C1 A-G/R2-#4-1-C1 A-G/R2-#4-2-C1 A-G/R2-#5-1-C1 A-G/R2-#5-2-C1 B-C/R3-#3-1-C1 B-C/R3-#3-2-C1 B-C/R3-#4-1-C1 B-C/R3-#4-2-C1 B-G/R4-#4-1-C1 B-G/R4-#4-2-C1 B-G/R4-#5-1-C1 B-G/R4-#5-2-C1 C-G/R5-8-1-C1 C-G/R5-8-2-C1 C-G/R5-12-1-C1 C-G/R5-12-2-C1 C-G/R5-16-1-C1 C-G/R5-16-2-C1 D-G/R6-8-1-C1 D-G/R6-8-2-C1 D-G/R6-12-1-C1 D-G/R6-12-2-C1 E-S/R7-12-1-C1 E-S/R7-12-2-C1 E-S/R7-16-1-C1 E-S/R7-16-2-C1

27.80 27.80 29.34 26.50 26.70 26.70 28.30 26.70 26.50 31.30 30.70 31.30 30.00 28.30 30.00 28.30 29.66 29.66 27.16 29.34 26.67 27.16 29.34 29.34 30.00 29.34 26.50 30.70 27.16 29.66

30.471 28.082 36.444 40.028 34.652 35.548 51.676 51.078 11.954 21.810 14.940 20.615 29.276 28.978 42.716 49.884 14.642 14.044 26.887 25.095 54.662 46.001 15.239 11.655 37.937 41.820 28.380 35.249 53.468 68.998

17.113 15.771 12.865 14.131 11.057 11.343 12.169 12.029 9.302 16.972 6.062 8.365 9.888 9.787 10.477 12.235 12.754 12.234 9.089 8.484 11.698 9.844 19.420 14.853 15.832 17.453 12.547 15.584 13.296 17.159

16.442

1.169 1.132 0.699 0.732 1.932 2.051 1.208 1.283 0.518 0.469 0.439 0.372 7.114 5.961 3.608 7.104 1.350 1.337 1.093 1.181 1.284 1.402 5.055 6.146 7.988 1.249 2.620 1.569 1.674

1.151

0.375 0.365 0.145 0.171 0.242 0.260 0.197 0.208 0.053 0.044 0.167 0.157 5.028 4.189 1.907 4.947 0.271 0.352 0.242 0.290 0.327 0.334 3.345 2.631 4.088 0.974 2.085 1.349 1.312

0.370

3.246 2.991 2.375 2.745 2.140 2.195 2.288 2.328 1.807 3.034 1.094 1.495 1.805 1.840 1.913 2.300 2.342 2.246 1.744 1.566 2.265 1.889 3.585 2.742 2.891 3.222 2.437 2.813 2.551 3.151

PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO PO

a b c d

13.498 11.200 12.099 13.137 7.214 9.838 11.356 12.494 8.787 10.771 17.137 16.643 14.066 15.228

Specimen identification according to Fig. 3. Mean value for similar specimens. -, Not measured (blocked LVDT). PO = pullout; S = splitting; P = peeling off; Y = bar yielding.

0.716 1.992 1.246 0.494 0.406 6.538 5.356 1.344 1.137 1.343 5.055 7.067 1.935 1.622

0.158 0.251 0.203 0.049 0.162 4.609 3.427 0.312 0.266 0.331 3.345 3.360 1.530 1.331

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M. Baena et al. / Composites: Part B 40 (2009) 784–797

Fig. 3. Specimen identification description.

defined by Eq. (1) and the slip between the rebar and the concrete is used to analyse the bond behaviour. The experimental results obtained from the bond tests, as well as the mode of failure, are given in Table 3, for C2 concrete and in Table 4, for C1 concrete. In these tables, fc0 is the concrete compressive strength of the control samples taken from each batch, smax is the bond strength, and sm,le and sm,ue are the slip values at the bond strength for the loaded and the unloaded ends, respectively. The mean values of the bond strength and the corresponding slips of nominally identical specimens are also reported. A normalised bond strength ðsmax Þ, that accounts for the effect of the concrete strength, is defined by

s ffiffiffiffi smax ¼ pmax 0

ð2Þ

fc

3.1. Bond stress–slip relationship The global behaviour of the bond stress–slip relationship is characterised by an initial increase in the bond stress with little

a

slippage, followed by softening once the maximum bond stress is attained. Up to the failure, bond can be attributed to bearing (for deformed or indented bars), adhesion and friction between the rebar and concrete. Once the adhesive bond fails, different behaviours are obtained for different surface treatments. Representative specimen curves for each tested diameter are shown in Figs. 4–10 to illustrate the bond stress–slip relationship obtained for the different specimens. For non-deformed or non-indented bars (R1, R2, and R3), the load transfer is provided by friction and strongly depends on the transverse pressure; later on the friction diminishes as the rebar is pulled further out and the contact surface is damaged. For sand-coated rebars (R1 and R2), Figs. 4 and 5, an initial good bond performance with high bond strength, almost linear behaviour and a relatively small unloaded end slip at the ascending branch of the stress–slip curve is observed. Sanding leads to an increase in the chemical bond, as reported in [9,11]. Once the bond strength is reached, the sand coating surface debonds from the rebar, and an abrupt decay is observed due to the dynamic effects that occur. This phenomenon is observed regardless of the concrete strength; however, for the lower concrete strength (C1) the softening decay is smoother. When using C1 concrete, pull-out of the sand from the resin layer takes place, but for higher concrete strength (C2), a sudden debonding of the whole sand coating layer is observed (see Fig. 11c). The dynamic effects taking place during the test, when the sand-coated layer debonds, explain the unloading and reloading paths observed in Figs. 4 and 5 after the maximum bond stress. CFRP rebars with surface texture (R3) presented a very smooth surface. Consequently, as with R1 and R2 rebars, bond strength is based primarily on chemical adhesion and friction force, and low mechanical bearing forces are expected. However, the behaviour of R3 rebars differs from the behaviour of R1 and R2 rebars. A first peak at a very small unloaded end slip is obtained when the chemical adhesion is lost (see Fig. 6). The debonding of the sand coating observed in R1 and R2 rebars does not take place in R3 rebars and, therefore, after the initial peak, the friction between rebar and concrete increases the maximum bond stress in high strength concrete (C2) and gives a smooth softening decay in the low strength concrete (C1), similar to the behaviour reported in [15]. However, because of its smoother surface, the R3 rebar bond strength is smaller than the R1 rebar bond strength, with the difference being even larger in C2 concrete. Therefore, it can be concluded that for non-deformed/indented rebars (R1, R2, R3), the rebar surface plays a very important role in

A-C/R1

A-C/R1

30

b

#3-3-C1 #4-2-C1 #3-3-C2 #4-2-C2

25

20 Bond Stress (MPa)

Bond Stress (MPa)

#3-3-C1 #4-2-C1 #3-3-C2 #4-2-C2

25

20

15

10

5

0

30

15

10

5

0

5

10 15 Unloaded end slip (mm)

20

25

0

0

5

10 15 Loaded end slip (mm)

Fig. 4. Representative bond–slip curves for R1 rebars for the (a) unloaded and (b) loaded end.

20

25

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M. Baena et al. / Composites: Part B 40 (2009) 784–797

A-G/R2

a 30

b #4-1-C1 #5-2-C1 #3-1-C2 #4-1-C2 #5-2-C2 #6-1-C2

Bond Stress( MPa)

20

15

10

5

0

#4-1-C1 #5-2-C1 #3-1-C2 #4-1-C2 #5-2-C2 #6-1-C2

25

Bond Stress (MPa)

25

A-G/R2

30

20

15

10

5

0

5

10

15

20

0

25

0

5

Unloaded end slip (mm)

10

15

20

25

Loaded end slip (mm)

Fig. 5. Representative bond–slip curves for R2 rebars for the (a) unloaded and (b) loaded end.

a

B-C/R3

B-C/R3

b

30 #3-2-C1 #4-2-C1 #3-1-C2 #4-1-C2

25

#3-2-C1 #4-2-C1 #3-1-C2 #4-1-C2

25

Bond Stress (MPa)

20 Bond Stress (MPa)

30

15

10

5

20

15

10

5

0

0

0

5

10 15 Unloaded end slip (mm)

20

25

0

5

10 15 Loaded end slip (mm)

20

25

Fig. 6. Representative bond–slip curves for R3 rebars for the (a) unloaded and (b) loaded end.

B-G/R4

B-G/R4

30

25

Bond Stress (MPa)

b

#4-2-C1 #5-1-C1 #3-1-C2 #4-3-C2 #5-2-C2 #6-2-C2

20

15

10

5

0

30 #4-2-C1 #5-1-C1 #3-1-C2 #4-3-C2 #5-2-C2 #6-2-C2

25

Bond Stress (MPa)

a

20

15

10

5

0

5

10 15 20 Unloaded end slip (mm)

25

30

0

0

5

10 15 20 Loaded end slip (mm)

Fig. 7. Representative bond–slip curves for R4 rebars for the (a) unloaded and (b) loaded end.

25

30

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M. Baena et al. / Composites: Part B 40 (2009) 784–797

C-G/R5

C-G/R5 8-2-C1 12-2-C1 16-2-C1 8-2-C2 12-1-C2 16-1-C2

25

Bond Stress (MPa)

b

30

20

30 8-2-C1 12-2-C1 16-2-C1 8-2-C2 12-1-C2 16-1-C2

25

Bond Stress (MPa)

a

15

10

5

20

15

10

5

0

0 0

5

10 15 20 Unloaded end slip (mm)

25

30

0

5

10

15 20 Loaded end slip (mm)

25

30

Fig. 8. Representative bond–slip curves for R5 rebars for the (a) unloaded and (b) loaded end.

a

D-G/R6

D-G/R6 8-1-C1 12-2-C1 8-2-C2 12-1-C2 16-2-C2 19-1-C2

25

20

30 8-1-C1 12-2-C1 8-2-C2 12-1-C2 16-2-C2 19-1-C2

25

Bond Stress (MPa)

Bond Stress (MPa)

b

30

15

10

5

20

15

10

5

0

0 0

5

10 15 20 Unloaded end slip (mm)

25

30

0

5

10

15 20 Loaded end slip (mm)

25

30

Fig. 9. Representative bond–slip curves for R6 rebars for the (a) unloaded and (b) loaded end.

the bond strength and this importance increases with the concrete strength. Moreover, it should be noted that the failure mode of the rebars is always located at the interface between the concrete and the rebar or by internal debonding of the rebar itself. For deformed and indented rebars (R4, R5, R6), the crushed concrete sticking to the front of the lugs exerts a wedging action; as a consequence, the surrounding concrete exerts a confinement action on the rebar. Depending on the confinement, pull-out or splitting failures occur. Therefore, the geometry of the rebar is very important for the stress–slip response. The influence of the rebar geometry was analysed by looking at two geometric ratios: as and CLR (see Fig. 12). The first, as, defined as the ratio of the projected rib area normal to the axis to the centre-to-centre rib spacing, is computed for deformed and indented rebars and is presented in Tables 5 and 6. The second, the CLR ratio, is computed for the R5 rebars (see Table 6) because of the difference in surface geometry between R5 rebars and R4 and R6 rebars. The CLR ratio was first presented in [26] to analyse the influence of the lug geometry of indented rebars on bond behaviour and bond strength. It is defined as the ratio between the concrete lug width, wc, and

the sum of the widths of the concrete lug and FRP rebar lug, wc + wf. GFRP rebars with helical wrapping and some sand-coating (R4) presented a surface with a constant rib height but a rib spacing that decreases with the rebar diameter. The shape of the bond stress–slip curves obtained for the higher concrete strength, C2, changes with the rebar diameter, as shown in Fig. 7. For smaller diameters the rib spacing increases, therefore the area to space ratio, as, decreases. For smaller values of as, bearing resistance decreases, producing a more abrupt decay in bond stress after the peak. For larger values of as, larger bearing resistance develops after the point where the chemical adhesion is lost, increasing the bond strength. This explains the difference in the bond stress–slip curve obtained when using smaller diameters (#3 and #4) compared to larger diameters (#5 and #6). For smaller diameters, the unloaded end slip at the maximum bond-stress is significantly smaller than it is for larger diameters. The concrete strength has an important influence on the bearing resistance, which decreases with decreasing concrete strength. Therefore, a smaller influence of rib spacing and as in the bond–slip curve is expected

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M. Baena et al. / Composites: Part B 40 (2009) 784–797

E-S/R7

a 30

b 12-1-C1 16-1-C1 10-1-C2 12-1-C2 16-1-C2 20-1-C2

20

15

10

5

0

12-1-C1 16-1-C1 10-1-C2 12-1-C2 16-1-C2 20-1-C2

25

Bond Stress (MPa)

Bond Stress (MPa)

25

E-S/R7 30

20

15

10

5

0

5

10

15

20

25

Unloaded end slip (mm)

0

0

5

10

15

20

25

Loaded end slip (mm)

Fig. 10. Representative bond–slip curves for R7 rebars for the (a) unloaded and (b) loaded end.

Fig. 11. Examples of failure modes: (a) pull-out with little damage on the rebar surface and some attached concrete; (b) pull-out with damage concentrated on rebar; (c) peel off of the whole resin layer and (d) splitting failure.

Fig. 12. Definition of the ‘‘area to space ratio” (as) and the ‘‘concrete lug ratio” (CLR).

when using C1 concrete, as it can be observed in Fig. 7. The differences observed between the bond–slip curves of #4 and #5 rebars in C2 concrete are not observed in C1 concrete. The experimental results obtained using the specimens with grooved rebars (R5) present an almost linear behaviour until bond strength is reached, with a very small unloaded end slip. Once the bond strength is reached, however, a softening behaviour, followed by an additional undulation of the curve is observed (Fig. 8). This undulation is related to the re-engaged mechanical interlock after the shearing off of the rib or the concrete lug, as the period of oscil-

lations corresponds approximately to the deformation spacing of the rebar (wf + wc in Table 6). A similar undulating behaviour has also been reported for steel bars as indicated in the CEB-FIP Model Code 90 [27]. When using C2 concrete, the shearing off of the ribs is more pronounced and the observed undulations diminish compared to specimens in C1 concrete. A similar undulating behaviour is observed for R4 and R6 rebars. The R5 rebars presented a constant rib height of about 5% of the diameter, which is considered to be sufficient to provide adequate bond behaviour to concrete [7,8,28,29]. Also, the spacing between ribs in R5 rebars is considerably smaller than in R4 and R6 rebars. Therefore, for R5 rebars, the wedging action resulting from the crushed concrete sticking to the front of the ribs is less pronounced than it is for R4 and R6 rebars. This may explain why the bond–slip behaviour of the R5 rebars is more similar to the sand-coated R2 rebars than it is to the R4 and R6 rebars with helical wrapping. Furthermore, the influence of the concrete lug ratio, CLR, has to be considered in order to compare the bond–slip curves obtained for different diameters. R5 rebars presented a constant CLR value of 0.4 for 8 and 12 mm diameter rebars, increasing to 0.47 for a diameter of 16 mm. Due to this increase in the CLR value, the tendency of larger diameter rebars to develop lower bond strengths is not quite followed by R5 rebars (see Tables 3 and 4, and Fig. 8). An increase in the CLR increases the bond strength, as reported by Al-Mahmnoud et al. [26] for rebars

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M. Baena et al. / Composites: Part B 40 (2009) 784–797

Table 5 Geometrical characteristics of R4 and R6 rebars. Firm

Fibre/rebar type

Experimental bar diameter (mm)a

Spacing (mm)

Height (mm)

Area to space ratio, as

B

G/R4 G/R4 G/R4 G/R4

9.28 13.73 16.11 19.14

22.75 21.66 19.60 17.35

0.47 0.47 0.47 0.47

0.633 0.968 1.249 1.669

D

G/R6 G/R6 G/R6 G/R6

7.07 12.35 17.36 21.25

18.39 16.02 16.13 16.42

1.38 1.09 0.84 1.03

1.992 2.873 2.978 4.391

a

Surface characteristics

According to ACI 440.3R-04.

Table 6 Geometrical characteristics of R5 rebars. Firm

Fibre/rebar type

Bar diameter (mm)a

C

G/R5-8 G/R5-12 G/R5-16

8.55 13.72 17.25

a

Surface characteristics wf (mm)

wc (mm)

5.40 5.32 4.75

3.60 3.68 4.25

CLR

as

0.400 0.409 0.472

1.250 3.260 5.969

According to ACI 440.3R-04.

with a grooved surface. However, it is observed that the CLR does not have any effect on the initial stiffness of the bond–slip curve. GFRP rebars with deeply-marked helical wrapping (R6) presented a surface with a variable rib height and spacing for the different rebar diameters, with as increasing with the rebar diameter. It should be noted that as is much larger in the R6 rebars than it is for the rest of the rebars. The shape of the bond stress–slip curves obtained for R6 rebars (shown in Fig. 9) is significantly different from the others, except for R4 rebars with large diameters (smaller rib spacing). The ascending branch of the curve is clearly non-linear and the slips corresponding to the bond strength are higher than they are for the other rebars. Moreover, for larger diameter R6 rebars (16 and 19 mm), the specimens failed by splitting, indicating that the higher as increases the radial stresses on the specimen. For comparison purposes, pull-out tests with steel rebars were also performed (Fig. 10). For steel rebars, only the unloaded end slip is usually reported in pull-out tests, since not much elongation is expected [30]. In this study, slip data were recorded for both the loaded and unloaded ends. For the tests performed with rebars with nominal diameters of 10 and 12 mm using C2 concrete, the bond capacity was greater than the bar capacity and the steel rebars yielded (see the plateau obtained in curves in Fig. 10b for C2 concrete). For larger diameters, as in the case of R6 rebars, splitting failure occurred. Moreover, the slips corresponding to the maximum strength are small, indicating that an almost linear behaviour is obtained in the ascending branch of the derived bond stress–slip curves. Higher bond strengths are obtained with smaller diameters. 3.1.1. Initial stiffness The influence of the different types of rebar and the rebar diameter on the initial stiffness of the bond–slip curve is analysed in this section. The ascending branches of bond stress versus loaded end slip curves for CFRP and GFRP sand-coated (R1 and R2) and steel (R7) rebars, in C1 and C2 concrete, are analysed. Specimens of similar nominal diameter have been selected in order to eliminate the effects of different rebar diameters. GFRP bars are expected to develop greater slip values than CFRP bars under similar pull-out loads, since their elastic modulus is less than half that of CFRP bars. This is confirmed by the results shown in Fig. 13a. For lower traction forces, the slip of the steel rebars (R7)

is negligible, regardless of the concrete used. However, for FRP rebars, as soon as traction is applied, the slip between the rebar and the concrete can be measured. The ascending branches for the different GFRP rebars used in this experimental study are also plotted in Fig. 13b. Specimens of R5 rebars present the highest initial stiffness because they have the highest Young’s modulus of all the GFRP rebars. However, for the rest of the GFRP rebars, a higher stiffness is obtained when using R2 rebars. R2 and R6 have a similar elastic modulus, while R4 has the smallest elastic modulus, according to manufacturer indications shown in Table 1. However, the experimentally measured Young modulus for R2, R4 and R6 rebars were 46.8, 39.3, and 39.1 MPa, respectively. Therefore, the differences in the initial stiffness, observed in Fig. 13b, are attributed to the differences in the measured rebar stiffness. The influence of the rebar diameter on the initial stiffness is also analysed. As seen in Figs. 4–10, the initial stiffness is not mainly influenced by the rebar diameter. Only the 8 mm diameter R6 rebars presented a different initial stiffness. This may be because of some geometric effect since, in the R6 rebars, the rib spacing and height varies with diameter, although without a defined pattern. However, further investigation is required to analyse this. Finally, it is worth mentioning that no influence of the concrete compressive strength on initial stiffness has been observed when using CFRP and steel rebars; in contrast, when using GFRP with lower Young Modulus values, the higher the concrete compressive strength, the higher the initial stiffness obtained (see Figs. 7b and 13a). This is because of the larger effect that a change in concrete compressive strength (and therefore in the Young Modulus of the concrete) has on the response of a GFRP-reinforced member; i.e, the similar Young Modulus values of the two materials (GFRP and concrete) increase the global response sensitivity to a change in the materials’ properties. When a CFRP-reinforced member is considered, the larger differences in the Young Modulus values of the materials diminish the effect of concrete compressive strength on the global response. 3.1.2. Effect of concrete strength on bond strength The strength of the concrete affects the bond failure mode of the rebar during pull-out (Tables 3 and 4). As indicated in [8,10], for

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M. Baena et al. / Composites: Part B 40 (2009) 784–797

a

A-C/R1-#4-2-C2 A-C/R1-#4-2-C1 A-G/R2-#4-1-C2 A-G/R2-#4-1-C1 E-S/R7-12-2-C2 E-S/R7-12-2-C1

25

20

16 A-G/R2-#4-1-C1 B-G/R4-#4-1-C1 C-G/R5-12-2-C1 D-G/R6-12-1-C1

14 12 Bond Stress (MPa)

Bond Stress (MPa)

b

30

15

10

10 8 6 4

5

2 0

0

0.5

1

1.5 2 2.5 Loaded end slip (mm)

3

3.5

0

4

0

0.5

1

1.5 2 2.5 Loaded end slip (mm)

3

3.5

4

Fig. 13. Influence of type of bar fibres on the initial stiffness. Loaded end curves of (a) R1, R2 and R7 rebars and (b) R2, R4, R5 and R6 GFRP rebars.

concrete with compressive strength approximately greater than 30 MPa, the bond failure occurs at the surface of the FRP rebars. Consequently, the bond strength of FRP rebars does not depend greatly on the value of concrete strength, but rather on the rebar’s properties. However, for lower compressive strength concretes (around 15 MPa), the bond failure mode changes and failure takes place at the concrete matrix interface. This tendency has been confirmed by the tests carried out in this study. Although the concrete strengths were not low enough to produce failure that was caused exclusively by damage in the concrete, less damage in the bars and more in the concrete was detected for lower concrete strengths, and vice versa. When using C1 concrete, all specimens failed in a pull-out mode with failure taking place in the concrete surface. In most cases, the change in concrete compressive strength did not involve a change in failure mode; nevertheless, a change in failure surface did take place, involving more damage on the rebar surfaces (Fig. 11a and b); A change in the failure mode when using C2 concrete was obtained for sand coated rebars (R1 and R2), where debonding of the whole layer of the sand coating from the bar occurred (Fig. 11c). A change in the failure mode when using C2 concrete was also observed for the larger diameters of R6 and R7 rebars. In those cases, concrete splitting, rather than a pull-out failure

a

was observed (Fig. 11d). Furthermore, yielding was observed for the small diameter R7 rebar tested in C2 concrete (see Fig. 10b). The mean bond strengths obtained for the different rebars, as well as the maximum and minimum experimental values obtained, are shown in Fig. 14a. It can be seen that the higher the concrete strength, the higher the bond strength is. Although the increase in strength depends on the type of bar, variations of up to 2.1 are obtained (see Fig. 14b), indicating the effect of the concrete strength on bond strength. 3.1.3. Effect of bar diameter on bond strength Many references in the literature [3,7,8,10,11,13,14] have pointed out that larger bar diameters develop lower bond strengths. During the pull-out test, the peak bond stress moves gradually from the loaded end towards the unloaded end of the bar, while the bond stress value at the loaded end decreases considerably, having a nonlinear distribution of stresses along the bar. It has been suggested by some authors [7,8] that this migration and nonlinear stress distribution would explain the bond strength’s dependence on rebar diameter, since this nonlinear distribution is more evident in the case of the larger embedment lengths needed for larger diameters (lb = 5db), which result in the lower average bond strength values obtained in these tests.

b

30

2.5

C1 C2

25

2

τmax (C2)/τmax (C1)

15

10

1.5

1

0.5

Fig. 14. (a) smax for specimens in C1 and C2 concrete and (b) smax increase ratio due to change in concrete.

R7-10 R7-12 R7-16 R7-20

R6-8 R6-12 R6-16 R6-19

R5-8 R5-12 R5-16

R4-#3 R4-#4 R4-#5 R4-#6

R3-#3 R3-#4

R2-#3 R2-#4 R2-#5 R2-#6

R1-#3 R1-#4

R7-10 R7-12 R7-16 R7-20

R6-8 R6-12 R6-16 R6-19

0 R5-8 R5-12 R5-16

R3-#3 R3-#4

R2-#3 R2-#4 R2-#5 R2-#6

0

R4-#3 R4-#4 R4-#5 R4-#6

5

R1-#3 R1-#4

τmax (MPa)

20

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M. Baena et al. / Composites: Part B 40 (2009) 784–797

Moreover, the Poisson effect may also have an influence on this phenomenon because of the reduction in the bar diameter when an FRP bar is pulled under tension. This diameter reduction (in absolute value) increases with the bar size, which can lead to a reduction in the frictional and mechanical locking stresses. Further evidence of a relationship between diameter and bond strength can be found using the size effect concept [31]: for geometrically similar specimens, the larger the rebar diameter, the lower the bond strength. This is due to the brittle nature of the failure observed in the pull-out tests and the greater amount of elastic energy available when using larger diameters. The dependence of bond strength on bar diameter can be observed in Fig. 14a. For the specimens in C2 concrete, a general trend of decreasing bond strength with increasing rebar diameters is observed. However, this tendency is not clear with the specimens in C1 concrete. 3.1.4. Effect of surface treatments on bond strength The rebars used in this study (see Table 1 and Fig. 1) are designed to improve the bond in different ways. Due to the importance of the rebar surface on bond behaviour, it is worth comparing the bond strengths obtained for the different rebars. In the case of CFRP rebars (R1 and R3), the higher bond strengths are obtained with the sand coated rebars (R1), irrespective of the concrete strength. In both cases, rebar surface can be considered as non-deformed, with bond strength strongly dependent on the friction resistance provided by the surface treatment. However, three out of four of the GFRP rebars considered in this study belong to the deformed/indented category. Therefore, the analysis of the influence of the surface treatment is carried out with respect to the surface geometry. The highest bond strength is obtained with R6 rebars and can be attributed to their highest as value; for the rest of the GFRP rebars, with either non-deformed surface or deformed surface with low as value, lower bond strengths are obtained because there is little bearing resistance. The smaller rib spacing of R5 rebars results in a smaller wedging action of the crushed concrete in the C2 series, and therefore in bond strength values closer to those of R2 rather than those of the R4 and R6 rebars. The effect of surface treatment can also be analysed with regard to the concrete strength. Damage is expected to be found more in the concrete surface in C1 concrete tests, and more in the rebar surface for the C2 tests. The results show similar bond strength values for C1 concrete, regardless of the surface treatment, while higher differences in bond strength values are found for C2 concrete. Therefore, the surface treatment has a significant influence on bond strength in those cases where failure is not occurring in the concrete.

4. Analytical modelling of bond behaviour A general bond–slip law has not been proposed up to now because of the many factors that exert an influence, including the different behaviours and mechanisms involved in the different types of rebars. The analytical models of bond–slip law available in the literature [12,17–20,23] are aimed at identifying a law and determining its parameters by curve fitting of experimental data. No specific formulations for the different types of rebars have been developed, and dependence on rebar diameter has not been included. Focacci et al. [21] propose a numerical method to calibrate parameters of a given local bond–slip relationship by a computational minimisation of the difference between the experimental and the numerically simulated pull-out test results. In Cosenza et al. [14], the parameters of the double branch and CMR models are calibrated by the least-square error method and curve-fitting. In another work, Pecce et al. [22] establish a numerical procedure that derives the relationship between the tensile stress applied to a reinforcing bar and the slip observed; the method is based on the integration of the differential equation describing the problem of a bar embedded in a concrete block and pulled out by means of a tensile force. Most of the cited works are intended to calibrate laws by considering the data as a whole or grouping them in family types. Subsequently, these laws, which incorporate mean values of parameters, are used to carry out numerical simulations of the experimental tests [21,22]. In some other cases [14,23], each analytical curve is obtained using the coefficients calibrated to its experimental counterpart. In this paper, two theoretical approaches described in the literature [17,19] are used, in which bond stress–slip relationships are calibrated on the basis of the experimental results obtained. The double branch model, proposed in Cosenza et al. [19] as a modification of the BPE model [16], consists of an ascending and a softening branch for the pre- and post-peak bond behaviour, respectively. These two branches are given by the following equations:

s

 ¼

s sm

a ð3Þ

smax s p  ðs  sm Þ ¼1 sm smax

ð4Þ

where a is a curve fitting parameter that must be no larger than 1 to be physically meaningful, sm is the slip at peak bond stress, and p is a parameter based on curve-fitting of experimental data. The experimental results demonstrate that it is worth accounting for the effect of rebar diameter on bond–slip behaviour for high strength concretes. Therefore, to define the double branch model parameters (smax, sm, a) the following equations are used:

Table 7 Identified values of s–s law parameters. Test

smax (MPa)

sm,ue (mm)

Double Branch Model

a

b

sr

B-G/R4-#3-1 B-G/R4-#3-3 B-G/R4-#4-2 B-G/R4-#4-3 B-G/R4-#4-4 B-G/R4-#5-1 B-G/R4-#5-2 B-G/R4-#5-3 B-G/R4-#6-1 B-G/R4-#6-2 B-G/R4-#6-3 Mean value Std. Deviation

22,987 20,777 15,336 17,353 18,261 17,948 16,850 17,289 14,323 14,582 15,049 17,341 2,667

0,230 0,297 0,547 0,522 0,283 4,833 5,709 5,690 3,403 3,733 3,558 2,619 2,277

0,1987 0,1573 0,1838 0,2339 0,2092 0,1746 0,1488 0,2324 0,1396 0,1667 0,1104 0,178 0,039

0,3628 0,2000 0,3691 0,8466 0,3844 0,5105 0,2411 0,7553 0,2208 0,2581 0,1679 0,392 0,226

0,0440 0,0500 0,0668 0,0404 0,0482 0,1585 1,0062 0,5030 0,4347 0,8816 0,5374 0,343 0,356

CMR Model

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M. Baena et al. / Composites: Part B 40 (2009) 784–797

b

25

Bond Stress (MPa)

Bond Stress (MPa)

a

20 15 10

mBEP Model CMR Model Tests #3

5 0

0

0.05

0.1

0.15 0.2 Unloaded Slip (mm)

0.25

10 mBEP Model CMR Model Tests #5

5

0

1

2

3 4 Unloaded Slip (mm)

5

6

20 Bond Stress (MPa)

Bond Stress (MPa)

15

0

0.3

20 15 10 mBEP Model CMR Model Tests #4

5 0

20

0

0.1

0.2

0.3 0.4 Unloaded Slip (mm)

0.5

15 10

0

0.6

mBEP Model CMR Model Tests #6

5

0

0.5

1

1.5 2 2.5 Unloaded Slip (mm)

3

3.5

4

Fig. 15. Experimental data versus numerical simulations obtained using the mean value of parameters for B-G/R4 tests: (a) B-G/R4-#3 and B-G/R4-#4 specimens, (b) B-G/R4#5 and B-G/R4-#6 specimens.

smax ¼ s0 þ s1 db

ð5Þ

sm ¼ m0 eðm1 db Þ

ð6Þ

a ¼ a0  dab 1

ð7Þ

where s0, s1, m0, m1 and a0, a1 are curve fitting parameters. The other analytical model used in this paper is the CMR model proposed in Cosenza et al. [17]. It is defined as:

 b s ¼ 1  es=sr smax

ð8Þ

where sr and b are parameters based on the curve-fitting of experimental data. The dependence of sr and b on the rebar diameter is proposed to be described by:

b ¼ b0 eðb1 db Þ

ð9Þ

ðr 1 db Þ

ð10Þ

sr ¼ r 0 e

where b0, b1, r0 and r1 are curve fitting parameters.

b

25

Bond Stress (MPa)

Bond Stress (MPa)

a

20 15 10

mBEP Model CMR Model Tests #3

5 0

Usually, the parameters of the analytical models are individually curve fitted by the least-square error method; the results obtained when applying this procedure to all the R4 rebars tests in the C2 series are reported in Table 7. This procedure is not applied to the remaining deformed rebars (R5 and R6) because of the difference in the pattern surface of R5 rebars and the splitting failure that occurred with the R6 rebars. The mean values of the parameters reported at the end of Table 7 are used to carry out numerical simulations of the experimental tests using Eqs. (3) and (8). The results obtained for the different rebar diameters are shown in Fig. 15. It can be seen that these numerical predictions do not correlate well with the experimental data, especially for the lower rebar diameters. However, if the proposed Eqs. (5)–(7), (9), (10) are used to calculate the parameters of the analytical models of the bond–slip curve, the agreement between the numerical predictions and the experimental data is better. This is observed in Fig. 16, where the parameters of Eqs. (5)–(7), (9), (10), fitted for the R4 rebar test re-

0

0.05

0.1

0.15 0.2 Unloaded Slip (mm)

0.25

10 mBEP Model CMR Model Tests #5

5

0

1

2

3 4 Unloaded Slip (mm)

5

6

15 Bond Stress (MPa)

Bond Stress (MPa)

15

0

0.3

20 15 10 mBEP Model CMR Model Tests #4

5 0

20

0

0.1

0.2

0.3 0.4 Unloaded Slip (mm)

0.5

0.6

10 mBEP Model CMR Model Tests #6

5

0

0

0.5

1

1.5 2 2.5 Unloaded Slip (mm)

3

3.5

4

Fig. 16. Experimental data versus numerical simulations obtained using the proposed rebar diameter dependent equations for B-G/R4 tests: (a) B-G/R4-#3 and B-G/R4-#4 specimens, (b) B-G/R4-#5 and B-G/R4-#6 specimens.

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M. Baena et al. / Composites: Part B 40 (2009) 784–797

Table 8 Fitted parameters of smax, sm, a, b and sr. Rebar

Coefficients of smax tendency law

Coefficients of sm tendency law

Coefficients of a tendency law

Coefficients of b tendency law

Coefficients of sr tendency law

so

s1

m0

m1

a0

a1

b0

b1

r0

r1

R4

27.681

0.686

0.0118

0.317

0.4324

0.3399

0.5316

0.0291

0.0019

0.3021

sults which are given in Table 8, are used for the numerical predictions. Hence, it can be seen that there is a dependence of bond parameters on the rebar diameter, which affects not only the bond strength but also the parameters of the available analytical models. Due to good agreement observed in Fig. 16, analogous simulations can be carried out for non-tested rebar diameters with good accuracy if the new proposed equations are used.

acknowledges the support from the University of Girona for Grant BR07/10. Appendix A. Notation list

smax lb db P

sav 5. Conclusions In this paper, the interfacial bond behaviour between different kinds of carbon and glass FRP bars and two different concrete strengths have been analysed. Based on the results of this experimental and analytical study the following conclusions can be drawn: Bond behaviour between FRP bars and concrete depends on many factors including concrete compressive strength, rebar diameter and surface treatment. An increase in bond strength and changes in failure mode and failure surface are observed when changing concrete compressive strength. The analysis of the influence of the surface treatment on bond behaviour confirms the existence of different bond mechanisms for different surface treatments. Furthermore, the influence of rebar surface treatment on bond strength is less important in the low concrete strength C1 series than in the high concrete strength C2 series (in which bond strength influence is more pronounced). For deformed or indented rebars the influence of the surface geometry is analysed using the as and CLR geometric ratios, obtaining higher bond strength for higher values of as. Similarly, an increase in the CLR increases bond strength. The experimental results confirm the tendency of rebars with larger diameters to have lower bond strength, especially in the case of C2 concrete. However, the initial stiffness is not mainly influenced by the rebar diameter. Nevertheless, changes in the initial stiffness due to a change in concrete compressive strength are observed for some specimens of GFRP rebars. The slip values obtained for GFRP are greater than those for CFRP bars. There is also a difference in the first loading branch between the bond–slip law of steel rebars compared to that of FRP rebars, since there is a high level of stiffness with no slip in the steel rebars, whereas the FRP rebars develop slip from the beginning. Finally, the double branch and CMR analytical models suggested in the literature are used to describe the ascending branch of the bond–slip curves. To calibrate the models, new rebar diameterdependent equations are proposed to define the parameters of the ascending branch of the analytical models. The numerical predictions obtained using these new proposed equations present a better agreement with experimental data than those that calibrate the models using the mean values of the parameters. Acknowledgement The authors gratefully acknowledge the support provided by the Spanish Government (Ministerio de Educación y Ciencia), Projects Ref. BIA2004-05253, BIA2007-60222. The first author

fc0 sm,le sm,ue

smax as CLR wc wf

s s sm a, p b, sr s0, s1 m0, m1 a0, a1 b0, b1 r0, r1

average bond strength embedment length rebar diameter tensile load average bond stress concrete compressive strength loaded end slip value at the average bond strength unloaded end slip value at the average bond strength normalised bond strength area to space ratio concrete lug ratio concrete lug width FRP rebar lug width bond stress slip corresponding to s bond stress slip where the average bond strength takes place parameters of the double branch analytical model parameters of the CMR analytical model parameters of the smax tendency equation proposed parameters of the sm tendency equation proposed parameters of the a tendency equation proposed parameters of the b tendency equation proposed parameters of the sr tendency equation proposed

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