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FRP REINFORCED CONCRETE AND ITS

APPLICATION IN BRIDGE SLAB DESIGN

by

YUNYI ZOU

Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy

Dissertation Adviser: Dr. Arthur Huckelbridge Supported by Saada Family Fellowship

Department of Civil Engineering CASE WESTERN RESERVE UNIVERSITY

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CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES

We hereby approve the dissertation of

______________________________________________________

candidate for the Ph.D. degree *.

(signed)_______________________________________________ (chair of the committee)

________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ (date) _______________________

*We also certify that written approval has been obtained for any proprietary material contained therein.

Yunyi Zou

Clare Rimnac

Dario Gasparini

Robert Mullen

Nov. 11, 2004

Arthur Huckelbridge

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Dedication

To my parents Zou JiShen and Chen XiuFang

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List of Figures

Figure 2.1 Aslan 100 GFRP by Hughes Brothers 38

Figure 2.2 Isorod by Pultrall 39

Figure 2.3 Specimen Section Details and Loading Condition 40

Figure 2.4 Cyclic Load Test Setup 41

Figure 2.5 Sketch of Data Acquisition System 42

Figure 2.6 Specimen C5 x 8.5 H5 44 Figure 2.7 Specimen C3 x 8.5 H5 45 Figure 2.8 Specimen C4 x 8.5 H5 45 Figure 2.9 Specimen C6 x 8.5 H5 46 Figure 2.10 Specimen C3 x 8.5 P5 48 Figure 2.11 Specimen C4 x 8.5 P5 49 Figure 2.12 Specimen C5 x 8.5 P5 50 Figure 2.13 Specimen C5 x 8.5 P5 51

Figure 2.14 Specimen C5 x 8.5 P5OL 51

Figure 2.15 Specimen C5 x 8.5 S5 52

Figure 2.16 Injecting Dye into Cracks 54

Figure 2.17 Typical Crack Profiles 54

Figure 2.18 Definitions of Elastic and Plastic CMOD 56

Figure 2.19 Elastic CMOD under Ramp Load vs Number of Cycles for

Group H Specimens (Pmin=2.2 KN Pmax=15.6 KN) 57

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Group H Specimens (Pmin=2.2 KN Pmax=15.6 KN) 58 Figure 2.21 Elastic CMOD under Ramp Load vs Number of Cycles for

Group P Specimens (Pmin=2.2 KN Pmax=15.6 KN) 58

Figure 2.22 Plastic CMOD under Ramp Load vs Number of Cycles for

Group P Specimens (Pmin=2.2 KN Pmax=15.6 KN) 59

Figure 2.23 Hysteresis of Beam C4x8.5H5 under Cyclic Load 61 Figure 2.24 Hysteresis of Beam C3x8.5H5 under Cyclic Load 62 Figure 2.25 Hysteresis of Beam C5x8.5H5 under Cyclic Load 62 Figure 2.26 Hysteresis of Beam C6x8.5H5 under Cyclic Load 63 Figure 2.27 Hysteresis of Beam C3x8.5P5 under Cyclic Load 63 Figure 2.28 Hysteresis of Beam C4x8.5P5 under Cyclic Load

Static Pre-Cracking 64

Figure 2.29 Hysteresis of Beam C4x8.5P5 under Cyclic Load

Fatigue Pre-Cracking 64

Figure 2.30 Hysteresis of Beam C5x8.5P5 under Cyclic Load 65 Figure 2.31 Hysteresis of Beam C6x8.5P5 under Cyclic Load 65 Figure 2.32 Unit Width Pseudo Energy Loss vs Number of Cycles in Group H 66 Figure 2.33 Unit Width Pseudo Energy Loss vs Number of Cycles in Group P 67 Figure 2.34 Effect of 40% Overload on CMOD Overload Pmax=22.3 KN

Beam C5x8.5H5 68

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Beam C5x8.5P5 69 Figure 2.37 Effect of 40% Overload on CMOD Pmax=22.3 KN

Beam C6x8.5P5 70

Figure 2.38 Elastic and Plastic CMOD under Ramp Load vs Number of Cycles for Specimens C5x8.5H5OL, C5x8.5S5 and

C5x8.5H5M (Pmin=2.2 KN Pmax=15.6 KN) 71

Figure 2.39 Hysteresis of Beam C5x8.5S5 under Cyclic Load 73 Figure 2.40 Effect of 40% Overload on CMOD Overload Pmax=22.3 KN

Beam C5x8.5S5 73

Figure 2.41 Unit Width Pseudo Energy Loss vs Number of Cycles in

Specimen C5x8.5P5OL and C5x8.5S5 74

Figure 2.42 Specimen C5 x 8.5 H5M 75

Figure 3.1 Debonded Length Representation 79

Figure 3.2 A Typical Finite Element Mesh with Debonded Length

Representation of Specimen C4x8.5P4 80

Figure 3.3 Fictitious Material Representation 82

Figure 3.4 A Typical Finite Element Mesh with Fictitious Material

Representation of Specimen C4x8.5P4 82

Figure 3.5 Assumed Stress Distribution at a Cracked Section 84

Figure 3.6 A “Hinge” Model 85

Figure 3.7 Verification of Hinge Model 88

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for Beam C6x8.5H5 (m=3.76) 94 Figure 3.9 Sensitivity Analysis Results on Parameter m

for Beam C5x8.5H5 (C=6.76x10.4) 94

Figure 3.10 Sensitivity Analysis Results on Initial Crack Length a0

for Beam C5x8.5H5 (C=6.76x10.4 m=3.76) 95

Figure 3.11 Sensitivity Analysis Results on Initial Crack Spacing L

for Beam C5x8.5H5 (C=6.76x10.4 m=3.76) 95

Figure 3.12 Sensitivity Analysis Results on Concrete Elastic Modulus

Ec for Beam C5x8.5H5 (C=6.76x10.4 m=3.76) 96

Figure 3.13 Sensitivity Analysis Results on Concrete Elastic Modulus

Ef for Beam C5x8.5H5 (C=6.76x10.4 m=3.76) 96

Figure 3.14 Sensitivity Analysis Results on Specimen Width b

for Beam C5x8.5H5 (C=6.76x10.4 m=3.76) 97

Figure 3.15 Sensitivity Analysis Results on Specimen Height h

for Beam C5x8.5H5 (C=6.76x10.4 m=3.76) 97

Figure 3.16 Crack Length and Crack Opening Increment versus Number

of Cycles, Beam C3x8.5H5, C=6.76x10.4, m=3.48 99

of Cycles, Beam C4x8.5H5, C=6.76x10.4, m=3.57 100

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of Cycles, Beam C4x8.5P5, C=6.76x10.4, m=3.55 101

of Cycles, Beam C5x8.5P5, C=6.76x10.4, m=3.74 102

of Cycles, Beam C6x8.5P5, C=6.76x10.4, m=3.88 102

Figure 3.23 Size Effect of Beam Width on Paris Equation 103

Figure 4.1 Slab Strip Model under One Wheel Load (Girder spacing

1.8m, 16M Bar at 100mm, Slab thickness 215mm) 106

Figure 4.2 Transverse Normal Stress Contours Under One Wheel Load of

Design Truck (Girder spacing 1.8m, 16M Bar at 100mm) 107 Figure 4.3 Slab Strip Model under One Axle Load of Design Truck (Girder

spacing 1.8m, 16M Bar at 100mm, Slab thickness 215mm) 108 Figure 4.4 Transverse Normal Stress Contours Under One Axle Load of

Design Truck (Girder spacing 1.8m, 16M Bar at 100mm) 108 Figure 4.5 Slab Debonded Length Representation under One Axle Load

(Girder spacing 2.7m, 16M Bar at 100mm, Slab thickness 215mm) 109 Figure 4.6 Transverse Normal Stress Contours Under One Axle Load

of Design Truck(Girder spacing 2.7m, 16M Bar at 100mm) 109 Figure 4.7 Slab Strip Model under One Axle Load of Design Truck(Girder

spacing 3.6m, 16M Bar at 100mm, Slab thickness 215mm) 110 Figure 4.8 Transverse Normal Stress Contours Under One Axle Load of

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Design Truck (Girder spacing 3.6m, 16M Bar at 100mm) 110 Figure 4.9 Transverse Normal Stress Contours Under One Axle Load of

Design Truck (Girder spacing 1.8m, 16M Bar at 150mm) 111 Figure 4.10 Bar Stress Under Design Truck Load with 16M Bars 112 Figure 4.11 Slab Model under Load of Design Truck, Lane Load and

Self-Weight (Girder spacing 1.8m, Slab thickness 215mm,

No Diaphragm) 120

Figure 4.12 Transverse Normal Stress Contours under Loads of Design Truck,

Lane Load and Self-Weight. 120

Figure 4.13 Slab Model under Load of Design Truck Only with Girders Fixed

Vertically (Girder spacing 1.8m, Slab thickness 215mm) 121 Figure 4.14 Transverse Normal Stress Contours Under Design Truck Only

with Girders Fixed Vertically. 121

Figure 4.15 Transverse Normal Stress Contours Under Design Truck Only

with Diaphrams. 122

Figure 4.16 Slab Model under Load of Design Truck, Lane Load and

Self-Weight (Girder spacing 2.7m, Slab thickness 215mm) 122 Figure 4.17 Transverse Normal Stress Contours Under Loads of Design

Truck, Lane Load and Self-Weight. 123

Figure 4.18 Slab Model under Load of Design Load and Self-Weight.

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Figure 4.20 Maximum Crack Opening under Design Load in Model Bridge 124 Figure 4.21 Maximum Crack Opening Under Design Load and Ohio Legal

Load 5C1 in Model Bridge, 1.8 m Girder Spacing 125 Figure 4.22 Slab Model under Load of Ohio Legal Truck Load 5C1 and

Self-Weight (Girder spacing 1.8m, Slab thickness 215mm) 125 Figure 4.23 Transverse Normal Stress Contours Under Loads of Ohio Legal

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List of Tables

Table 2.1 Specimen Descriptions 40

Table 3.1 Calibrated Debonded Length for Group P Specimens 81

Table 3.2 Calibrated Ficticious Material Properties 83

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Acknowledgements

I want to take this opportunity to thank my advisor Dr. Huckelbridge for his guidance. Throughout my research, I have enjoyed our discussions very much. His teaching will benefit me for years to come.

I also feel so fortunate and blessed to have Dr. Saada as my instructor and sponsor. Nothing in this dissertation would be possible without his support. To me, he is a role model for living and working.

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List of Abbreviations

AASHTO American Association of State Highway and Transportation Officials

ACI American Concrete Institute

CMOD Crack Mouth Opening Displacement

FE Finite Element

FRP Fiber-Reinforced Polymers

GFRP Glass FRP

LEFM Linear Elastic Fracture Mechanics

LFD Load Factor Design

LRFD Load and Resistance Factor Design RC Reinforced Concrete

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FRP Reinforced Concrete and its Application in Bridge Slab Design

by

Yunyi Zou

ABSTRACT

For decades, bridge slabs have been troubled by the corrosion of steel reinforcements. The unique corrosion resistance of FRP (Fiber-Reinforced Polymers) bars makes them a promising alternative to steel bars. Because of the relatively low elastic modulus of FRP reinforcement, the post-cracking serviceability often is the controlling factor in the flexural design of FRP reinforced concrete. Since bridge deck slabs are under repeated traffic loads, it is the post-cracking serviceability under cyclic loads that becomes vital in the design and maintenance decision-making process.

Experiments have been conducted to investigate the post-cracking flexural performance of FRP RC (reinforced concrete) under constant amplitude cyclic loading. Each specimen tested was a beam with a single FRP bar at the bottom. Two different types of FRP bars were used. The crack opening was monitored for specimens of different size. Up to 2 million cycles of cyclic loads have been applied at 100% service load levels. It has been found that there are two stages in the crack growth of FRP reinforced concrete. The first stage is early growth, which is characterized by increasing crack mouth opening displacement (CMOD). The second stage is the stabilization of CMOD and crack length. No fatigue failure was encountered in the testing under service loading and moderate overloads. The effects of moderate overload on observed crack

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growth were also investigated. The performances of two different FRP bars were compared. A model was proposed to predict long term crack growth in FRP R/C under cyclic loading, based on the Paris equation.

Two FE (finite element) crack representations were examined. One was a debonded length representation. In this model it was assumed that there was a debonded length around each crack, within which there was no tangential interaction between concrete and reinforcement. Beyond the debonded length, the interface between concrete and reinforcement was tied with no relative movement. The other representation examined was a fictitious material crack representation. A fictitious material was placed in a triangular crack cross section, with a maximum width of 2.5mm (0.1 in). Then, the modulus of elasticity of the fictitious material was calibrated, based on the observed testing results, after crack growth had stabilized. Both representations have been used to analyze bridge slabs. Finally, an empirical slab design was discussed.

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Chapter 1 Background and Introduction of the Problem

The advantages of Fiber-Reinforced Polymers (FRP) include a high ratio of strength to mass, excellent fatigue characteristics, excellent corrosion resistance, electromagnetic neutrality, and a low axial coefficient of thermal expansion. Generally speaking, the disadvantages of FRP reinforcement include its higher cost, lower Young’s modulus (except for Carbon FRP), lower failure strain and lack of ductility. The transverse coefficient of thermal expansion (CTE) is also much larger than the longitudinal CTE. The long-term strength of FRP can be as low as 70% of its short-term strength, and ultra-violet radiation can damage FRP. FRP reinforcement is also not effective for compression reinforcement because of the compression instability of the slender axial fibers. There is a lot of potential to apply FRP in bridge engineering for structural elements in corrosive environments with low ductility demand.

For decades, reinforced concrete slabs have been used as bridge decks both in United States and around the world. The relatively inexpensive concrete and steel reinforcement have served very well in most respects. In recent years, rehabilitation of national highway bridges has been a priority, due to the aging and deteriorating superstructures. One of the major causes of superstructure deficiency is the corrosion of steel reinforcement. In this case, the excellent corrosion resistance and light weight of FRP make it potentially superior in long term performance to conventional reinforcing steel, and, particularly in the case of Glass FRP (GFRP), potentially competitive economically.

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Serviceability covers many different aspects of structural performance related to particular applications. The most commonly encountered serviceability requirements in RC structures are maximum deflection and crack opening control. Cracking is a complex phenomenon, particularly in composite materials. For quasi-brittle materials such as concrete, the tensile stress gradually drops to zero after reaching a peak value. There exists an inelastic zone at the tip of the crack, known as the fracture process zone. Within the fracture process zone, the stress decreases as it approaches the crack tip. Shah (1995) summarized the interaction within the fracture process zone as microcracking, crack deflection, aggregate bridging, crack face friction, crack tip blunting by voids, crack branching, and etc. It has been reported that the measured fracture process zone is almost independent of specimen thickness; the crack length generally is deeper on the sides than in the middle. Consequently, it was pointed out that applicability of linear elastic fracture mechanics (LEFM) is limited for plain concrete to large structures, with a relatively small fracture process zone. In the case of smaller scale structures, the aforementioned complexity in concrete cracks deters the direct application of LEFM.

In the case of FRP RC beams under bending, as soon as cracking occurs, there is a surge of forces in the bars. Cracks tend to grow in fatigue load environments. The tensile forces in the bars and resultant compressive force in concrete increase as depth of intact concrete and fracture process zone decrease. The relatively low Young’s modulus of FRP, which is about one fifth of the Young’s modulus of conventional steel

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reinforcement ratios are similar in magnitude for both cases. Consequently, the aggregate bridging will be less, crack face friction will be smaller, and the zone of microcracking will also be smaller due to suppression by concrete in compression. This is the essential difference between plain concrete, conventional reinforced concrete (RC) and FRP RC, which tends to make LEFM a good approximation for crack modeling for FRP RC.

P. Gergely and L. Lutz (1968) analyzed test results from various investigators on crack openings in conventional reinforced concrete. A multiple regression analysis was performed on crack openings with respect to different variables. It was found that steel stress magnitude was the most important variable. The concrete cover was an important variable but not the only secondary consideration. Bar size was also found not to be a major variable, and crack opening tended to increase with increasing strain gradient. The significant variables identified were effective area of concrete, the number of bars, concrete cover and stress level. The recommended equation for bottom crack in English units was as follows.

c c

s d A

f

w=₀_.₀₇₆β 3 _(1-1)

Where β is the ratio of the distance from the neutral axis to extreme tension fiber to the distance from the neutral axis to the center of the tensile reinforcement; dc is the concrete cover to bar center; fs is the tensile stress in steel bars; Ac is the effective tension area of concrete.

In ACI 440.1R-01, the Gergely-Lutz equation has been modified to estimate the crack opening of FRP RC members by simply replacing the steel strain with FRP strain.

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To account for the difference in bonding between steel and FRP, a corrective coefficient

kb is introduced. The final equation of crack opening in millimeter is as follows.

c c f b f A d f k E w= 2.2β 3 _(1-2)

Where Ef is the Young’s modulus of FRP bar; β is the ratio of the distance from the neutral axis to extreme tension fiber to the distance from the neutral axis to the center of the tensile reinforcement; dc is the concrete cover to bar center; ff is the tensile stress in FRP bars; Ac is the effective tension area of concrete. The coefficient kb is assumed to be one for FRP bars having bond behavior, similar to steel bars. Many researchers have suggested different values for different bar surfaces. ACI 440.1R-01 listed values of kb by Gao et al. to be 0.71, 1.00, 1.83 for three currently popular types of GFRP bars. A value of 1.2 was suggested for deformed FRP bars by the report, in the case of no available experimental data.

Carpinteri et al (1993) used a LEFM to model a simply supported steel RC beam. The total stress intensity factor is the superposition of KI due to the bending moment and to the bar force. An energy concept was used to examine the steel yielding, bar slip and crack growth under different conditions. The total energy was calculated in terms of bending moment and rebar force. The relationship between rebar force and bending moment was derived based on the relationship of energy release rate and stress intensity factors. In the analysis of cyclic loading, three cases were discussed based on comparing the magnitudes of peak moment with plastic flow moment, slippage moment and fracture

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fracture moment. Apparently, this model is more applicable to the case of low cycle fatigue (relatively high rebar stress levels).

In early 1960s, P.C. Paris (1963) applied fracture mechanics to fatigue problems. The proposed equation is as follows.

m K C dN da ) (∆ = (1-3)

Where a is the crack length; N is the number of cycles; ∆K is the stress intensity factor

difference at maximum and minimum loading; C and m are material parameters. Although Paris’s law was developed for steel, researchers have tried to verify if it was also valid for concrete.

Considerable work done has been focused on plain concrete. The report by ACI committee 215 provides general knowledge about fatigue strength of concrete and reinforcement. Fatigue fracture of concrete is characterized by considerably large strains and microcracking. The S-N curve of concrete is approximately linear between 102 and 107 cycles, which indicates that there is no apparent endurance limit for concrete. The fatigue strength for a life of 10 million cycles of load and a probability of failure of 50 percent, regardless of whether the specimen is loaded compression, tension or flexure, is approximately 55 percent of the static ultimate strength.

Perdikaris et al. (1987) conducted experiments on single-edge-notched plain concrete beams under four-point bending. Crack length was also recorded based on the CMOD compliance measurements. It was concluded that the Paris equation results in

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significant errors of 100% although R2’s, which is the fraction of the variance in the data that is explained by a regression, were close to one for different specimens. It was believed that large errors were part of the nature with exponentials.

Baluch et al. (1987) also tried to verify if the Paris equation is valid for concrete. The experiments were three-point bending on single-edge-notched plain concrete beams of 51mm wide x 152mm deep x 1360mm. Similarly, a compliance test was first performed so that crack length could be obtained. For the same beam specimen under different R (=Kmin/Kmax), it was found that Paris equation is applicable in plain concrete. The material parameter m was found to be 3.12, 3.12 and 3.15 at R=0.1, 0.2, 0.3 respectively. It was subsequently concluded that m was independent of R. The material parameter C was reported to be on the order of 10-24 and 10-25; it appeared from the article that the units of C was mm/[Pa m1/2]m , although the units were not stated explicitly. The authors suggested that C might be related to R. Foreman’s equation (1967) which includes the effects of R was also explored by the authors.

) )( 1 ( ) ( max K K R K C dN da c m − − ∆ = (1-4)

where Kc is the fracture toughness of the material of interest at the appropriate thickness. Different material parameters C and m were inferred under different R values for the same type of specimen, however. Therefore, it was concluded that Foreman’s equation was not applicable in plain concrete.

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and notch length. The thickness was constant for all beams. The results of fatigue tests were presented with the plots of log(∆a/∆N) versus log(∆K/∆KIf). Different lines were obtained for different beam size, although they were parallel to each other. The authors combined the Paris law with a size effect law, for fracture under monotonic loading; the revised Paris law is a function of a size adjusted stress intensity function.

Due to the nature of cracks in concrete, a method of compliance calibration is normally used in crack length determination for pure concrete. However, it has been questioned that effects of the fracture process zone will stiffen the crack, and true compliance will be lower than the one obtained from a notched specimen. Therefore, the crack length will presumably always be underestimated by compliance calibration methods.

Swartz et al (1984) investigated the validity of the compliance calibration method, utilizing a three point bending test setup. All specimens had small starter notches at mid-span and they were precracked to a desired crack length using CMOD as a control. It took a couple of cycles for the specimen to achieve the desired crack length according to the compliance calibration curve. Dye would then be applied at the crack section. The test results showed that the compliance method consistently overestimated the actual crack length. The surface cracks revealed by the dye correlated well with the crack depth predicted by a calibrated compliance. For ratios of crack length to beam height greater than 0.26, the difference of average interior crack length and surface crack depth was about 25mm.

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Swartz et al (1981) also compared the effects of fatigue pre-cracking and static pre-cracking. For the same notched plain concrete beams, one group was pre-cracked by fatigue after one million cycles and the other group was statically pre-cracked to the same crack depth. Under three-point and four-point bending, it was reported that failure strength and associated maximum stress intensity factor of the statically pre-cracked beams are slightly higher than those of pre-cracked by fatigue. It was then concluded that static pre-cracking was acceptable, even for fatigue testing.

Efforts have been made to predict the growth of cracks due to fatigue loading. Balaguru and Shah (1981) proposed a model to simulate the increase of deflection and crack opening for steel RC. The components included in the model were as follows: (a) the cyclic creep of concrete; (b) the reduction of stiffness due to cracking and bond deterioration; (c) reinforcing steel softening. The experimental data was cited from other articles, which was limited to 100,000 or 50,000 cycles. The rebar stress range was between 69 MPa and 276 MPa (10 ksi and 40 ksi). The maximum rebar stress utilized was almost twice the rebar fatigue stress limit. The crack opening was recorded photographically. It appeared that there were only five data points recorded within 100,000 cycles. The general trend of the model was that crack opening always increased with the number of cycles applied. However, the motivation of using a stress range twice the rebar fatigue stress limit may be questioned. A limit of 100,000 cycles is generally

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The finite element method has been widely used in reinforced concrete analysis. There are two different approaches in crack modeling in finite element analysis. One is smeared crack modeling, which is generally better when overall load/deflection behavior is of primary interest. Initially, the concrete is assumed to be isotropic. The reinforced concrete cracks when the stress reaches an assumed failure surface. Instead of literally representing the crack in the concrete FE mesh, the concrete member remains as a continuum. The constitutive equations are then modified to reflect the cracked state.

The other popular method is discrete cracking modeling, utilized when detailed local behavior is investigated, as done early on by Ngo and Scordelis (1967). Based on local stresses in the finite element mesh, some element nodes are separated to model a discrete crack. Since it is costly and tedious, this method is generally only applicable in certain special circumstances.

Darwin (1993) performed a review of finite element analyses on conventional reinforced concrete. The survey results are summarized as follows. (a) Reinforcement. Reinforcements can be modeled in three methods - (1) distributed reinforcement within elements, (2) discrete bar element between element nodes, and (3) uniaxial element embedded in the element. In all cases, reinforcements and concrete are modeled as separate materials. Perfect bonding is always assumed. Fortunately, load-deflection behavior is not sensitive to the bonding unless the failure mode is bond slip, which is not deemed to be a valid design. (b) Concrete under Tension. Tension stiffening and tension softening have improved the numerical stability of simulation. Tension stiffening was

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first used to account for the residual tensile strength of concrete between cracks. Tension softening uses the concept of fracture mechanics to achieve similar effects. (c) Concrete

in Compression. It was found that the overall performance of a model is more related to

the details of crack representation and shear retention after cracking, than the details of different concrete constitutive models in compression. (e) Load Increment. It was advised to take small load increments and assure that convergence is achieved at every step.

Perfect bond models, however, are invalid for the purpose of crack analysis. In the vicinity of a crack, there is inevitable bond-slip between rebar and concrete. Efforts have been made to model bonding. Manufacturers of FRP bars are aware of the necessity to model the bond-slip of their bars. Hughes Brothers, Inc. had sponsored a couple of institutions to investigate the phenomenon. A variety of results were obtained, as different testing methodologies generated different results. This is an indication of the complexity of the issue.

Larralde et al (1993) tested the bonding of FRP bar and concrete. There was a longitudinal helical wrap around bar surface. Since there was little cracking in the concrete after bond failure, it was believed to be an indication of low local bearing stress between the indentations of the FRP bars and the surrounding concrete.

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fatigue loading. C. Shield et al (1997) investigated the thermal and mechanical fatigue effects on the bonding between GFRP bars, steel bars and concrete. The specimens were 300mm x 457mm x 1220mm. At both the top and bottom of a specimen, there was one protruding test bar, with one supplementary bar on each side. The embedment lengths were selected to be about ten diameters or more, in order to ensure sufficient development length. Some specimens were cycled under pullout loads between 18KN and 45 KN for 100,000 cycles. Other specimens were stored in an environmental chamber for three and a half months while temperatures changed between -20oC and 25oC for 20 cycles. Basically, eccentric pull-out tests were conducted. The slips at the loading end and free end were monitored. All of the specimens failed in bond with concrete splitting around the test bars. It was found that GFRP specimens showed no reduction in bond strength after mechanical fatigue, while there was a 13% reduction with steel bars specimens. Thermal fatigue, however, caused more bond degradation in GFRP specimens than in steel bar specimens. In the test setup, the protruding portion of the test bar was loaded, which made it impossible to apply realistic number of cycles, due to the damage to the bar.

C.E. Bakis et al (1998) investigated the effect of cyclic loading on bonding of Glass FRP (GFRP) bars in concrete. The experiment scheme was the RILEM bond beam. The beam section was 100mmx180mm. Some of the bars tested are no longer manufactured. The CP bars in their tests exhibited behavior very similar to the Aslan 100 bars made by Hughes Brothers Inc. The bar diameters were 10.1mm, 12.7mm and 16mm. An embedment length of five diameters was used. The load amplitude was

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selected to achieve 90%, 50% and 75% of the ultimate bond strength. The bar slip at the free ends was recorded. In the case of CP bars, the residual slip after the first cycle was a significant portion of slip at the end of the 100,000 cycles, ranging from 75% to 25%, depending on the load magnitude. It was found that the residual bond stiffness was actually higher than the initial bond stiffness. The actuator displacement verses load observations also supported that conclusion. The authors suggested that slipping of bars might aid the apparent interlocking with concrete. It was also recognized by the authors that bond failure should not occur in properly designed members with working stress of up to 20% of ultimate strength. This work was contradictory to the finding by C. Shield et al. (1997) that cyclic loading did not enhance the bonding stiffness. The experiment setups were similar to each other for the two investigations, but the load levels were very different.

Cosenza et al. (1997) discussed the bonding behavior between concrete and FRP bars, and a survey of bond-slip models was presented. FRP bars were categorized into straight bars and deformed bars. Straight bars were smooth, grain-covered or sandblasted prismatic rods. Deformed bars were ribbed, indented, twisted or braided. It was stated that the bond was controlled by the factors including chemical bond, friction due to FRP surface roughness, mechanical interlock of FRP bars against concrete, normal pressure between FRP bars and concrete. An effect of bar size has been observed, with the average bond resistance decreasing as bar size increased. A top bar effect also exists for

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chemical conditions, however, such as high alkalinity were shown to be detrimental to bonding. Popular bond-slip models are the Malvars model, BPE model, modified BPE model and CMR model. All of these models use exponential functions to model the first branch of increasing bond stress and slip. The softening branch was modeled linearly, for convenience. The authors stated that modified BPM model presented the best agreement with the available experiment results.

A. Katz (2001) tested five different types of FRP bars. Each FRP bar was embedded in a concrete block and 450,000 cycles of cyclic loads were applied. Between each 150,000 cycles, the specimens were immersed in water of 60oC and 20oC to simulate a deterioration process. At the end of the fatigue tests, a pullout test was conducted for each specimen. Three mechanisms of failure observed were abrasion of rod surface, delamination of outer layer of resin, and abrasion of cement particles entrapped between rod and concrete. It was concluded that helical wrapping of FRP bars did not increase bond resistance under cyclic loading. A sand covered bar surface did improve bonding; such bars were able to maintain maximum loading for a relatively long slip.

Flexural response of FRP reinforced concrete were reported by Benmokrane (1996) and other investigators. The general consensus is that at small load, the crack pattern in FRP concrete is similar to that of steel reinforced concrete. As the load increases, however, there are more cracks with larger crack openings in FRP concrete than in traditional steel reinforced concrete, for comparable reinforcement ratios. This

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behavior is expected, since FRP has a much lower modulus of elasticity, compared with traditional steel reinforcement. The moment /curvature diagrams of lightly reinforced FRP beams are clearly bi-linear, with the bend point at the crack initiation moment level.

GFRP reinforced concrete beams were analyzed by Vijay and GangaRao (2001); different modes of failure were compared. The compression controlled failure mode presented not only higher flexural strength, but also a more ductile failure than the tension controlled failure mode. This result was consistent with ACI 440.1R-01 suggested design criteria. A parameter DF was defined as the ratio of energy absorption at ultimate strength to that at a limiting curvature value. To satisfy both the serviceability deflection limit of L/180 and crack opening limit of 0.016 inches, the curvature limit was set to be 0.005/d. The parameter DF then became a unified indicator, covering both serviceability and strength. The tensile strength of concrete is typically assumed to

be '

5 .

7 f_c , with an assumed elastic modulus of '

57000 f_c (using U.S. units with stress

units in psi). The tensile strain at cracking is thus assumed to

be ε_cr =7.5 f_c' 57000 f_c' =0.0013 . The curvature at first cracking ψ_cr is approximately 2ε_cr/h=0.0026/h, for a symmetric section. Vijay and GangaRao thus have used twice the curvature at first cracking as the limiting curvature in their design criterion.

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element analysis, utilizing a smeared crack representation. A cracking stress of 0.1fc’ was used for plain concrete, with Kupfer's (1969) criterion. Cracks were only deemed possible in the directions parallel to the transverse and longitudinal reinforcement, i.e., the model failed to simulate nonorthogonal cracks. New material parameters were assigned for each round of analysis. The element utilized was an eight node isoparametric solid element, of the same size for the entire model, with edges parallel to the edges of model. Comparing analytical results with available experimental data, the study indicated that load-deflection was accurately simulated in the analysis, while the predicted stresses in the reinforcements were very different from those observed experimentally. The work was limited to the ultimate strength studies of RC slabs, and the serviceability of these slabs was not investigated.

Many researchers including Graddy et al.(1995) and others have noticed the effect of arching action in traditional steel reinforced concrete. Before a concrete slab cracks, the dominant resistance is flexure. After the concrete cracks, a “dome” architecture exists underneath the concentrated loads, if the cracked concrete is excluded. In-plane, or membrane stress, then becomes more significant. The results of theoretical analysis and experiments have shown that the arching action contributes to the slab strength. Arching action for multiple wheel loads is uncertain, however, especially in the case of FRP reinforced concrete slabs. Arching effect at service load levels for FRP slab has not been investigated.

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Canadian investigators have been active in the research of fiber reinforced concrete and steel-free bridge deck system. The transverse reinforcements are mainly external steel straps or FRP bars. B. Bakht et al (2000) reviewed different types of straps. They included fully studded straps, partially studded straps, cruciform straps, FRP bars and diaphragms. Three models of steel free slabs with different straps were tested to failure under monotonic loading. The mode of failure was mostly punching shear failure as expected, but at a much larger load. An additional specimen was tested under 1000 cycles of pulsating load between 0 and 88 KN (20 Kips) prior to the static testing. The results of the latter static testing indicated that the forces in straps increased, due to shakedown in the slab. The authors concluded that actual failure loads of the steel-free deck slabs are more than 10 times larger than the theoretical failure load attributable to bending alone.

Similar research was conducted by Salem et al (2002). A finite element model was developed for a steel free concrete deck. The lateral reinforcement was a cruciform strap. The concrete was fiber reinforced concrete, so as to control cracking due to creep and shrinkage. The results showed that the load at slab failure was only increased by 11% for a two girder model and 15% for a three girder model, when the inertia of girders was increased by 150%. The position and location of the lateral straps were also analyzed. The ultimate load of the slab was insensitive to the strap position. For practical purposes, it was recommended to weld the straps to the top flange of girders.

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Yost (2002) tested the performance of concrete slabs reinforced by FRP grids. The product is commercially known as NEFMAC, and is composed of continuous high strength reinforcing fibers, impregnated within a vinyl ester resin. A two dimensional grid sheet was formed with redundant “overlaying”. The test was conducted under monotonic loading with AASHTO HS25 truck load. The ultimate load was five times as much as the HS25 criterion. The field testing of a bridge slab had shown that the strains and deflections were well within the design limits.

The effects of pulsating and moving loads on traditionally reinforced concrete slabs were studied by Perdikaris et al (1988, 1989). The research covered both the AASHTO orthotropic reinforced slabs and the Ontario isotropic reinforced slab. In the prototype, the three beams were space at 2.13m (7 ft). The orthotropic reinforcement pattern consisted of a top and bottom layer of transverse and longitudinal steel reinforcing bars 19M (#6) spaced at 188mm and 376mm respectively. In the isotropic reinforcement pattern, the spacing in both directions was 437mm. In either case, the spacing was fairly large. The restricting boundary conditions were considered in the research. Models of 1/6.6 and 1/3 scale were tested. The maximum fatigue load was 60% of the static ultimate strength, which was fairly high. The results showed that fatigue life of slabs with isotropic reinforcement is twenty times that with orthotropic reinforcement. The factors of safety at static ultimate failure are 14 and 23, however, for those of isotropic and orthotropic reinforcements, respectively.

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Bridge slabs are constantly under traffic load. Due to serviceability requirements, such as crack opening and lateral load distribution, ultimate strength is usually not crucial in the slab design. However, the AASHTO design methodology is still presented from the perspective of strength design. The design moment in the load factor design (LFD) methodology was assumed to be (S+2)P/32 per foot of slab width, where S is the effective span length of slab in feet and P is the design wheel load. The formula is in U.S. units. In the AASHTO load and resistance factor design (LRFD), an equivalent width of bridge slab was defined for strength design in AASHTO Table 4.6.2.1.3-1. In the case of a concrete slab over multiple girders, the width is taken as 660+0.55S for positive moment and 1220+0.25S for negative moment, where the girder spacing is S. The methodology is believed to simplify the bridge deck design process.

The Ontario Highway Bridge Design Code has recognized the in-plane or membrane forces in typical bridge slabs. The slab design was reduced to a prescription of isotropic reinforcement. The reinforcement pattern is orthogonal in the slab. A minimum reinforcement ratio of 0.003 is required in both directions, top and bottom. The restrictions of the empirical design are as follows. a.) The span length of a slab is less than 3.6m (12 ft). b.) The ratio of span to thickness does not exceed 15. c.) The slab thickness is 225mm minimum and the spacing of the bars is 300mm maximum. d.) Intermediate diaphragms will not be spaced at more than 8m. The crack control requirements are then assumed to be met automatically.

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A similar empirical design methodology is available in AASHTO (2000). Reinforcement is required at both directions of each face. The minimum amount of reinforcement is 0.570 mm2/mm of steel for each bottom layer and 0.380 mm2/mm of steel for each top layer. The maximum spacing of reinforcement is 450 mm.

The most common type of bridge is a concrete deck, supported on multiple girders. Except in the case of large horizontal curvature, girders are usually analyzed and designed individually. In other words, 1-D finite element analysis is common practice in the bridge design consulting industry. Therefore, the AASHTO design codes have traditionally provided lateral distribution factors which account for the maximum possible portion of wheel load (half of axial load) acting on one girder. In the AASHTO LFD design codes, simple formulas of load distribution factors are listed. For girder spacing S less than 3.6m (12 feet), the distribution factor (DF) is S/5.5. In the current LRFD codes, the formulas for DF are as follows.

1 . 0 3 3 . 0 4 . 0 ) 12 ( ) ( ) 14 ( 06 . 0 s g Lt K L S S

DF = + (one design lane loaded) (1-5)

1 . 0 3 2 . 0 6 . 0 ) 12 ( ) ( ) 5 . 9 ( 075 . 0 s g Lt K L S S

DF = + (two or more design lane loaded) (1-6)

where S is the girder spacing; L is the bridge span, Kg is longitudinal stiffness parameter and ts is slab thickness. Many researchers have been involved in the evaluation of distribution factors. The majority of the work has been finite element analysis of bridge structures of steel reinforced concrete slabs on multiple girders. Mabsout el al (1997) reviewed finite element analysis of bridges and analyzed a bridge with a span of 17m (56 ft). Concrete slabs may be modeled with shell elements or isoparametric continuum

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elements. Girders may be modeled as 3-D beam elements with rigid links to the slab. Sometimes, the web may be modeled with shell elements and flanges may be modeled with beam elements, or the entire girder may be modeled with shell elements. It was found that different models produced distribution factors similar to NCHRP 12-26 (1987), but all were less than AASHTO (1996). The analysis results showed that the distribution factor decreased, as the bridge span became larger.

In summary, the advantages of FRP make it a potentially better choice in applications such as bridge deck slabs. The performance of FRP RC under monotonic loading has been understood fairly well. ACI 440.1R-01 proposes to design for a strength failure mode of concrete crushing, to achieve better ductility. Some other criteria which are serviceability oriented have been reported.

The serviceability of FRP RC, particularly in fatigue environments, deserves to be further investigated before engineers can be expected to be confident with this fairly new material. The predicted maximum crack opening of FRP RC has been converted from conventional RC, although the bond properties are different for steel and FRP. The Paris law appears to be applicable in concrete, with a size effect being detected. FRP itself possesses excellent fatigue properties; the bond durability under cyclic loads, however, has not been thoroughly investigated. There have been varying results, mostly based on pullout tests, on residual bond strength following limited cyclic loads.

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Verification with a different experimental methodology is needed. The current bridge design code is conservative in terms of load distribution. Although the current design methodology is strength oriented, serviceability is often the critical factor in bridge deck slab design. The finite element method has been successfully used for a long time in bridge structural analysis; analysis results are typically based on uncracked concrete slab properties, which is generally reasonable for steel RC.

Crack growth in FRP reinforced concrete is yet fully understood, particularly in fatigue environments. Investigation of FRP RC fatigue performance is crucial in applications such as bridge slabs. In this study, experimental results on fatigue testing of FRP RC will be presented. Subsequently, the crack opening displacement and crack growth will be modeled utilizing the finite element method and fatigue/fracture theory, respectively. A finite element model will be developed to simulation the crack opening of the test specimens. A fatigue model will be created to simulate the observed crack growth under cyclic loading. An empirical equation for final crack opening will be proposed. A sensitivity analysis on the crack growth model will also be conducted to evaluate the effects, the uncertainty and the randomness of different parameters. The finite element model will then be extended to the analysis and crack opening estimation of realistic FRP reinforced concrete bridge deck slabs under actual AASHTO wheel loads. Finally, the overall performance of an FRP RC slab on a single span bridge of multiple girders will be analyzed. Under the condition of a cracked slab, the lateral load distribution factor will be discussed. Other implications on the serviceability provisions in ACI 440.1R-01 will be discussed.

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Chapter 2 Experimental Analysis of FRP Reinforced Concrete under Fatigue Load

Motivation for the Testing Program

Due to its high corrosion resistance, FRP is set to be a promising alternative to steel reinforcement in bridge decks. Typically a major concern in an FRP bridge slab is its serviceability, rather than its strength. Crack opening is one of the important indicators of serviceability. Crack opening and its growth in FRP RC are related to the fatigue characteristics of FRP bar, concrete, and their interface. The bond-slip and crack growth mechanisms at different rebar spacing have not yet been fully investigated.

The behavior of FRP reinforced concrete under fatigue loading has been investigated thus far by simple pullout tests, or by RILEM beam bond tests, following an interval of cyclic loading. There are two shortcomings with these approaches. One is that the testing condition is not the actual working condition of rebar in an environment such as a bridge deck. A small bond length is normally used in a RILEM beam or a concrete pull-out block. Conclusions drawn under such conditions may not always be applicable to typical in service conditions. The second issue is that such tests are sensitive to specimen imperfections. With portions of bar exposed, the bar is susceptible to local damage due to unintentional stress concentrations and eccentricities which may not be representative of in-service conditions; such variations can be especially critical in fatigue testing.

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The proposed experiment focused on fatigue-induced crack growth in FRP RC under service-level cyclic loading, in specimens more representative of in-service applications. Specimens were actual beams reinforced with FRP bars. Beams of different widths were used to simulate bridge slabs of different bar spacing/reinforcement ratios. Traditionally, the minimum thickness of a bridge slab is 215 mm (8.5 inches). Concrete bridge slabs are typically designed with sufficient depth such that no shear reinforcement is needed, and so that the expected load distribution among bridge girders is achieved. Therefore, the performance of FRP reinforced concrete in the flexural response modes is of primary interest to bridge deck designers.

Description of the Testing Program

FRP beams of identical depths and spans, but with four different widths were fabricated. The concrete was composed of type III cement, water, fine aggregate and coarse aggregates with weight proportions of 1.0/ 0.5/ 2.0/ 2.83. The nominal compressive strength target was 34.5MPa (5000 psi). The compressive strength from a cylinder test was 27.9 MPa (4045 psi). The tensile strength from a split-cylinder test was 4.9 MPa (715 psi).

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Figure 2.1 Aslan 100 GFRP by Hughes Brothers

The first set of FRP bars tested, which are reported herein, were Aslan 100 GFRP made by Hughes Brothers, Inc. (see Figure 2.1). As shown above, the bars are sand coated with a helical wrap along the length. The reported tensile strength is 655 MPa (95 ksi) for No. 16 (#5) bars. The reported modulus of elasticity is 40.8 GPa (5.92E6 psi). To simulate a typical bridge slab section, beams were all 1830 mm (6 feet) long and 215mm (8.5 inches) thick. The beam widths were 76 mm, 102 mm, 127 mm and 152 mm (3, 4, 5 and 6 inches) which represent typical bar spacing in bridge decks. For identification purposes, they are categorized as group H and they are labeled as C3x8.5H5, C4x8.5H5, C5x8.5H5, C6x8.5H5, respectively. The first letter C stands for the constant amplitude; the beam size in U.S. units follows; H shows the manufacture of the bars as Hughes Brothers, Inc.; the last number is the size, #5, of the FRP bar. Within each beam, there was one No. 16 FRP bar (#5 diameter 5/8 inches) at the bottom of each beam (tensile region) with 25 mm (1 inch) cover to the bar surface.

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Figure 2.2 Isorod by Pultrall

The second set of FRP bars tested were Isorod GFRP made by Pultrall, ADS Composites Group (see Figure 2.2). The bars are also sand coated, without a helical wrap along the length. The tensile strength is 674 MPa (98.9 ksi) for #5 bars. The modulus of elasticity is 42 GPa (6.1x106 psi). Similarly, test specimens were all 1830 mm (6 feet) long and 215mm (8.5 inches) thick. The beam widths were 76 mm, 102 mm, 127 mm and 152 mm (3, 4, 5 and 6 inches) which represent typical bar spacing in bridge decks. For identification purposes, they are categorized as group P and they are labeled as C3x8.5P5, C4x8.5P5, C5x8.5P5, C6x8.5P5, respectively.

One extra specimen, C5x8.5P5OL, of section 127mmx215mm with bars of Isorod was made to investigate the effect of overload pre-cracking. One more specimen, C5x8.5H5M, of section 127mmx215mm with bars of Aslan 100 was singled out with cracks adjacent to each other, to investigate the effect of multiple cracks. One specimen, C5x8.5S5, of section 127mmx215mm was made of 16M (#5) steel rebar, for comparison purposes.

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Specimen Width (mm) Height (mm) Reinforcement Test Sequence C3x8.5H5 76 215 16M (Aslan 100) 2 C4x8.5H5 102 215 16M (Aslan 100) 3 C5x8.5H5 127 215 16M (Aslan 100) 1 C6x8.5H5 152 215 16M (Aslan 100) 4 C5x8.5H5M 127 215 16M (Aslan 100) 5 C3x8.5P5 76 215 16M (Isorod) 6 C4x8.5P5 102 215 16M (Isorod) 7 C5x8.5P5 127 215 16M (Isorod) 10 C6x8.5P5 152 215 16M (Isorod) 9 C5x8.5P5OL 75 215 16M (Isorod) 8 C5x8.5S5 127 215 Steel 11

Table 2.1 Specimen Descriptions

Figure 2.3 Specimen Section Details and Loading Condition 25mm

215mm

610mm 610mm 610mm

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Figure 2.4 Cyclic Load Test Setup

The specimens were all under four point bending (see Figure 2.3 and 2.4). The beam was loaded symmetrically with two loads at the third points. The cracks within the pure bending region were monitored. The maximum cyclic service load was determined based on the creep rupture stress limit of 0.20ffu for FRP bars, in accordance with ACI 440.1R-01, resulting in a cyclic rebar stress level of 645 MPa (~20 ksi). The minimum and maximum loads were 2225 N (500 lb) and 15600 N (3500 lb) respectively. The resulting moments are greater than the theoretical cracking moments. Based on nominal

kb value of 1.2, the predicted crack openings are 0.68 mm, 0.75 mm, 0.80 mm and 0.84 mm for beam widths of 76 mm, 102 mm, 127 mm and 152 mm, respectively.

According to ACI 440.1R-01, the performance of FRP is dependent on the testing frequency. Endurance limit was found to be inversely proportional to loading frequency

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in carbon FRP. Higher cyclic loading frequencies in the 0.5 to 8 Hz range corresponded to higher bar temperatures due to sliding friction. For a bridge slab under traffic load, the stress of a rebar reaches maximum when a truck axle load is applied on the top of the slab at the same location. For a truck with axle spacing of 3.6m (12 feet) at 65 miles per hour, the frequency of passing axles may be as high as 7.94. However, for a bridge of 10,000 ADTT (average daily truck traffic), the truck load is applied at a frequency of 0.23 Hz. So, the overall frequency is 1.8 Hz, which is the product of 7.94 and 0.23. Therefore, the frequency at which load was cycled was at 2 Hz in the tests. The percentage of overload was decided based on traditional AASHTO load factor design. The overload was defined to have the value of γ factor at 1 instead of 1.3 in the factored load. Therefore, for

specimen C5x8.5H5 and C6x8.5H5, the effect of a modest (30% to 40%) overload was also investigated.

Figure 2.5 Sketch of Data Acquisition System MTS System Crack Opening Displacement Gage Specimen

Knife Edge Grouted to Specimen

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Static pre-cracking was used. The loading was stopped as soon as cracks became visible for all specimens, except in the case of the overload pre-cracking investigation. MTS clip-on crack opening displacement gages 632.02B-20 and 632.02C-20 were then installed on the cracks which had been initiated as shown above. The maximum arm displacements of the instruments are +2.540 mm to -1.270 mm (+0.1000 in to -0.050 in) and +3 mm to -1 mm (+0.118 in to -0.039 in)), respectively. Two DCDTs were also fastened on each side of the specimen in the mid-span to measure the relative beam deflection, within the pure bending region, for average curvature estimation. All eleven specimens were tested under the same initial cyclic load amplitude. The crack mouth opening displacement (CMOD) was recorded under a ramp load and the first 20 cycles of cyclic load at the beginning of each test interval, in order to track the evolution of crack development with increasing load cycle counts.

Experimental Results

(1) Group H - Aslan 100 GFRP Rebar by Hughes Brothers, Inc.

The first specimen tested was C5x8.5H5. Two cracks appeared within the pure bending region after static pre-cracking and two more cracks were observed immediately after the test started. The approximate crack spacing was 190mm (7.5”). After the first test interval of 5,000 cycles, the crack lengths became visually constant. After more cycles were applied, there was no sign of distress with the specimen, and all cracks were stable. All crack tips stopped at approximately 38mm (1.5 inches) below the top of beam, which was near the theoretical neutral axis. The specimen did not appear to have

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any distress at the end of testing of one million cycles. The crack length was virtually the same. There was no concrete spalling near the rebar at the bottom of specimen. It was also found that there was no scaling in the specimen – concrete surfaces were sound with no loss of surface mortar and aggregates. To investigate the effect of overload, Pmax was increased to 22,300 N (5.0 kips), corresponding to a rebar stress level of 25 ksi. After 10,000 cycles of this overload, the specimen was still in good condition.

Figure 2.6 Specimen C5 x 8.5 H5

The second specimen tested was C3x8.5H5. Three cracks appeared at static pre-cracking and three more were observed at 20,000 cycles. The crack spacing was between 130mm (4.5 inches) to 165mm (6.5 inches). The tips of the cracks stopped at approximately 50mm (2 inches) below the top of beam. Due to the larger bearing stress at both supports, the concrete at the bearing locations started crumbling near the end of 2 million cycles of testing. There was no sign of concrete distress elsewhere in the specimen. No overload was applied due to the degraded condition of the concrete in the

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Figure 2.7 Specimen C3 x 8.5 H5

The behavior of specimen C4x8.5H5 was similar. Three initial cracks were generated at static pre-cracking. Two more cracks appeared at 6000 cycles. The average crack spacing was between 130mm ( 4.5 inches) and 180mm ( 7 inches). The tips of the cracks stopped at approximately 45mm ( 1.75 inches) below the top of beam, up to 1.8 million cycles. To investigate the effect of overload, Pmax was again increased to 22,300 N (5.0 kips) for 15,000 cycles. No addition distress was found in the specimen.

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The behavior of specimen C6x8.5H5 was somewhat different. Only one crack was generated at static pre-cracking. Extra load was added after the appearance of the first crack but no additional cracks appeared. During the subsequent fatigue testing, no new cracks appeared up to 140,000 cycles, at which point the CMOD gage debonded. (The single crack had ceased to grow in length, however, prior to 10,000 cycles.)

The Pmax was raised at that point to 20000 N (4.5 kips) to explore the effect of overload. A new crack appeared 700 cycles later. The newly formed crack was instrumented, and Pmax was again lowered to its initial value of 15,600 N ( 3.5 kips). After an additional 35,000 cycles of fatigue load at Pmax of 15,600 N, the primary crack did not show any sign of further growth induced by the 700 cycles of overload. Therefore, Pmax was raised back to 20,000 N and 40,000 additional cycles were applied, with both the primary crack and secondary crack remaining stable.

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To further investigate the overload effect, Pmax was finally increased to 22,300 N (5.0 kips). A third crack was found around 400 cycles; a total of 40,000 cycles were applied at this load level, with the second and third cracks monitored. All cracks became stable and no addition signs of distress were noted.

(2) Group P - Isorod GFRP made by Pultrall, ADS Composites Group

The first specimen tested was C3x8.5P5. Three cracks appeared at static pre-cracking within the pure bending region and one outside the pure bending region. The average spacing was 150mm (6 inches). After the first run of 3,000 cycles, the crack lengths became visually constant. After more cycles were applied, there was no sign of distress such as spalling and scaling with the specimen, and all cracks were stable. No new cracks were found in the specimen. The controlling system crashed at a load cycle count of 30,000. All crack tips stopped at approximately 45mm (1.75 inches) below the top of beam. The specimen did not appear to have any distress at the end of 270,000 testing cycles. To investigate the effect of overload, Pmax of 20,000 N (4.5 kips) was applied. After 10,000 cycles of overload, the specimen was still in good condition.

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Figure 2.10 Specimen C3 x 8.5 P5

The second specimen was C4x8.5P5. Within the pure bending region, only one crack appeared at static pre-cracking and one more was observed at 400 cycles. A clip gage was immediately installed for the new crack. An additional crack appeared at load cycle 1000. The average spacing was 200mm (8.5 inches). The tips of the initial cracks stopped at approximately 38mm (1.5 inches) below the top of beam after the application of 900,000 load cycles. Excessive overload was tested at Pmax of 29,000 N (6.5k), which resulted in 276 MPa (40 ksi) of rebar stress. This stress level was equivalent to the data cited by Balaguru and Shah (1981) in their model to simulate the increase of deflection and crack opening for steel RC. The general trend of their model was that crack opening always increased with the number of cycles applied. After 200 cycles of overload, existing cracks started branching and a new crack appeared. After 3000 cycles of overload, the concrete cover started falling off, as debonding became more pronounced; it

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Specimen C5x8.5P5 behaved somewhat differently. One initial crack of 130mm long was generated at static pre-cracking. One new crack appeared at 110 cycles. At around 900 cycles, two new cracks appeared, with one crack of initial surface length 120mm (4.75 in), between the first two cracks at the midspan region. The average crack spacing was 115mm (4.5 inches) within the pure bending region. The tip of the newer crack at midspan was dormant for about 100,000 cycles, and then began growing. (Unfortunately, no more gages were available to acquire the crack opening evolution of this crack.) The tips of all cracks stopped at approximately 50mm (2 inches) below the top of the beam at 1.25 million cycles. To investigate the effect of overload, Pmax of 22,300 N (5.0 kips) was applied for 10,000 cycles. By the end of the test, the concrete at the left bearing started crumbling.

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The specimen C6x8.5P5 behaved similarly. Only one crack was generated at static pre-cracking, as expected. No extra load was initially added, to avoid any plastic hardening of the concrete-rebar interface bonding. During the subsequent fatigue testing, no new cracks appeared up to 1,300,000 cycles. The Pmax of the cyclic load was then raised to 22300 N (5.0 kips) to explore the effect of overload. One new crack appeared within 400 cycles of overload. After 50,000 cycles of overload, however, there was no indication of severe distress. Subsequently, Pmax was raised to 29,000 N (6.5 kips). The two existing cracks then started branching. After 155,000 cycles of this overload were applied, the specimen was still in good shape. All cracks became stable and no addition signs of distress were found.

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(3) Overload Pre-cracking

In all tests to this point, cracks had been generated with minimum possible static loading, which is equivalent to fatigue pre-cracking. Experiments were also conducted to investigate the case of overload pre-cracking. Additional static overload was applied after cracks had appeared, followed by cyclic load at service level. For specimen C5x8.5P5OL, there was no further growth of crack length during the course of fatigue testing. For specimen C6x8.5H5, crack lengths did continue developing during fatigue testing..

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(4) Conventional steel RC

A similar test was conducted for a specimen made with conventional steel reinforcing. Static pre-cracking was used, and five cracks appeared, with two very close to each other. The initial crack length was between 100mm (4 inches) and 120mm (4.75 inches). The crack spacing was ranging between 140mm (5.5 inches) to 180mm (7 inches). As cyclic load testing started, there was no visible growth of the cracks. No new crack was generated during the test. At the end of 1,000,000 cycles, there was no sign of distress within the specimen.

To further investigate the overload effect, Pmax was first increased to 22,300 N (5.0 kips). The specimen was still in good shape after 150,000 cycles. Then, Pmax was then increased to 29,000 N ( 6.5 kips) which represented 200% of working stress; the specimen appeared to be intact after 30,000 cycles of this load level.

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For all specimens, the attempts to monitor average curvature through the measurement of relative displacements within the test section, failed to produce consistently usable results, particularly for large cycle counts. First, the magnitude of deflection at the mid-span, relative to the line of the two 1/3 span loading points, was very small in magnitude (only on the order of a few thousandths of an inch), resulting in a low resolution for the measured DCDT data to begin with. It was also inevitable for specimens to shift positions over time under the dynamic load, even though a minimum non-zero load was maintained, and to exhibit some secondary torsional movement, due primarily to minor imperfections in the specimen and supports, all of which contributed to measurement difficulties. It was decided finally to utilize only the more reliable crack gauge data in the subsequent analyses.

(5) Crack Profile Characterization

The crack profile may be investigated in the methods of laser holographic interferometry, acoustic emission and dye penetration. For some specimens in group P, the crack length profile was investigated using dye penetration. A notch was made at the top of a crack for a specimen. The specimen was then loaded in the three point bending mode, so as to open the crack. As the cracks opened up, rubber sheets were clamped to each side of the specimen around the crack (see Figure 2.14). Black ink was injected into the notch, penetrating the crack until reaching the tip the crack. After about two hours, the reinforcement was cut off and the crack examined; the images of cross sections of C4x8.5P5, C5x8.5P5 and C6x8.5P5 are illustrated in Figure 2.15.

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Figure 2.16 Injectiing Dye into Cracks

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Quantitative Discussion

The balanced reinforcement ratio is 0.0048, for an FRP tensile strength of 655MPa (95 ksi) and a concrete strength of 27.6 MPa (4000 psi). The reinforcement ratios tested were 0.013, 0.010, 0.008 and 0.007 for specimens C3x8.5H5, C4x8.5H5, C5x8.5H5 and C6x8.5H5, respectively. Specimen C6x8.5H5, which displayed a somewhat different behavior than the other specimens, had the lowest reinforcement ratio, although it was still slightly over-reinforced. As mentioned earlier, the predicted service load crack openings, based on ACI 440.1R-01 criteria, were between 0.68 mm and 0.84 mm for all four specimens, at the suggested nominal kb value of 1.2. The experimental results show that the service load crack openings, measured immediately after static pre-cracking, were 0.15 mm, 0.16 mm and 0.17 mm for group H specimens C3x8.5H5, C4x8.5H5 and C5x8.5H5, respectively. These experimental observations were only about 25% of the predicted value. The opening of the single crack in specimen C6x8.5H5 was 0.26mm, which was still less than 30% of the predicted value. In group P, the service load crack openings, measured immediately after static pre-cracking, were 0.16 mm, 0.17 mm, 0.19 and 0.22 mm for group P specimens C3x8.5P5, C4x8.5P5, C5x8.5P5 and C6x8.5P5, respectively. Based on these limited tests, it appears that the modified Gergely-Lutz equation may be overly conservative in predicting actual static service load crack openings, at least for the bars tested in this investigation. According to the limited test results, a kb value of 0.4 may be more realistic for initial static crack opening prediction. Another finding was that there was hardly any difference between group H and group P. The reason is that initial static CMOD at working stress level is

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more related to the modulus of elasticity of FRP bars than the surface bonding. The elastic properties of two groups of FRP bars were approximately the same.

The growth of crack opening versus number of cycles may be represented by a sum of an elastic CMOD and a plastic CMOD. The elastic CMOD is calculated as the difference of CMOD at maximum and minimum load, which disappears after unloading. The residual CMOD at minimum load is the plastic CMOD, which does not disappear after the removal of loading (see Figure 2.18), and tends to show a greater increase with the number of applied load cycles than elastic CMOD does.

Figure 2.18: Definitions of Elastic and Plastic CMOD Plastic CMOD Elastic CMOD CMOD ∆Load

abaqus

FRP REINFORCED CONCRETE AND ITS

APPLICATION IN BRIDGE SLAB DESIGN

by

YUNYI ZOU

Yunyi Zou

Clare Rimnac

Dario Gasparini

Robert Mullen

Nov. 11, 2004

Arthur Huckelbridge

Dedication

To my parents Zou JiShen and Chen XiuFang

Table of Contents

List of Figures

List of Tables

Acknowledgements

List of Abbreviations

FRP Reinforced Concrete and its Application in Bridge Slab Design