Study on Bond and Peeling Characteristics between CFRP
Plates and Concrete under Fatigue Loading

March 2014

Wei ZhangStudy on Bond and Peeling Characteristics between CFRP
Plates and Concrete under Fatigue Loading

Graduate School of Systems and Information Engineering

University of Tsukuba
March 2014
Wei Zhang

CONTENTS
LIST OF TABLES ........................................................................................................iii
LIST OF FIGURES ...................................................................................................... iv
DISSERTATION ABSTRACT .................................................................................... vii
1 CHAPTER 1 .......................................................................................................... 1
Introduction
1.1 Research Background ........................................................................................... 1
1.2 Literature Review ................................................................................................. 3
1.2.1 Bond between strengthening materials and concrete.................................. 3
1.2.2 Bond between FRP sheets and concrete ..................................................... 4
1.2.3 Bond between FRP plates and concrete...................................................... 9
1.2.4 Fatigue characteristics of FRP-strengthened concrete elements .............. 10
1.3 Objective and Scope ........................................................................................... 12
1.4 Outline of the Thesis .......................................................................................... 13
2 CHAPTER 2 ........................................................................................................ 15
CFRP Plate Debonding Behavior of Flexurally Strengthened RC Beams
2.1 Introduction ........................................................................................................ 15
2.2 Outline of Experiment ........................................................................................ 19
2.2.1 Test Specimens ......................................................................................... 19
2.2.2 Material Properties .................................................................................. 20
2.2.3 Loading and Measurement ..................................................................... 20
2.3 Experimental Results and Discussion ................................................................ 22
2.3.1 Static Test Results for Specimen RC-S..................................................... 22
2.3.2 Static Test Results for Specimen CS-S ..................................................... 24
2.3.3 Fatigue Test Results for Specimen CS-F .................................................. 27
2.4 Conclusions ...................................................................................................... 31
3 CHAPTER 3 .......................................................................................................... 32
Bond Behavior between CFRP Plates and Concrete under Fatigue Loading
3.1 Introduction ........................................................................................................ 32
3.2 Experimental Program for Static Loading ......................................................... 33
3.2.1 Specimens ............................................................................................... 33
3.2.2 Materials Properties .................................................................................. 34
3.2.3 Loading and Measurement ....................................................................... 34
3.2.4 Experimental Results ................................................................................ 35
3.2.4.1 Failure Progress..................................................................................... 35
3.2.4.2 Load and Displacement Relationships .................................................. 37
3.2.4.3 Bond Strength ....................................................................................... 39
3.2.4.4 Influence of the Confinement Jig .......................................................... 40
3.2.4.5 Strain Distribution of the CFRP Plate ................................................... 41
3.2.4.6 Local Bond Stress and Slip ................................................................... 42
3.3 Experimental Program for Fatigue Loading....................................................... 45
3.3.1 Specimens ................................................................................................. 45i3.3.2 Materials Properties .................................................................................. 45
3.3.3 Loading and Measurement ....................................................................... 46
3.3.4 Experimental Results ................................................................................ 47
3.3.4.1 Failure Progress..................................................................................... 47
3.3.4.2 Load and Displacement Relationships .................................................. 49
3.3.4.3 Strain Distribution ................................................................................. 51
3.3.4.4 Post-Fatigue Monotonic Behavior ........................................................ 56
3.3.4.5 Fatigue Life Prediction of Debonding................................................... 57
3.3.4.6 Local Bond Stress-Slip Relationship .................................................... 58
3.3.5 Proposed Local Bond Stress-Slip Relation under Fatigue Conditions ..... 59
3.3.5.1 Envelope Curve According to Popovics Model .................................... 59
3.3.5.2 Model of Local Bond Stress-Slip Relationship for Fatigue Loading.... 60
3.3.5.3 Adaptability of Proposed Model ........................................................... 63
3.3.5.3.1 Method of Analysis...................................................................... 63
3.3.5.3.2 Comparison of Analytical and Experimental Results .................. 66
3.3.6 Peeling Debonding Behavior under Fatigue Loading .............................. 67
3.3.6.1 Transverse Displacement Relationships................................................ 68
3.4 Conclusions ........................................................................................................ 71
4 CHAPTER 4 ........................................................................................................ 73
Mixed-Mode Debonding Behavior of CFRP Plates and Concrete
4.1 Introduction ........................................................................................................ 73
4.2 Experimental Program........................................................................................ 74
4.2.1 Specimens ............................................................................................... 74
4.2.2 Loading and Measurement ....................................................................... 76
4.3 Experimental Results.......................................................................................... 77
4.3.1 Failure Progress ........................................................................................ 77
4.3.2 Load versus Displacement Relation and Strain Distribution .................... 78
4.4 Evaluation of the Bond Strength ...................................................................... 79
4.5 Conclusions ........................................................................................................ 82
5 CHAPTER 5 Conclusions................................................................................... 83
REFERENCES ............................................................................................................ 86
ACKNOWLEDGMENTS ........................................................................................... 91
PUBLICATIONS ARISING FROM THE THESIS..................................................... 92ii

LIST OF TABLES
Table 2.1: Mechanical properties of concrete .............................................................. 20
Table 2.2: Mechanical properties of reinforcing bar................................................... 20
Table 2.3: Comparisons of the values calculated with standard codes ................. 23
Table 2.4: Comparisons of experimental results with values calculated fromprocedures in standard codes ........................................................................................... 25
Table 3.1: Specimen list.................................................................................................... 33
Table 3.2: CFRP plate properties .................................................................................... 34
Table 3.3: Concrete properties......................................................................................... 34
Table 3.4: Bond strength with calculated values ......................................................... 40
Table 3.5: Comparison of the calculated experimental values ................................. 40
Table 3.6: Specimen list.................................................................................................... 45
Table 3.7: CFRP plate properties .................................................................................... 45
Table 3.8: Concrete properties......................................................................................... 46
Table 3.9: Measurement intervals ................................................................................... 46
Table 3.10: Fatigue test results ........................................................................................ 48
Table 4.1: Specimen list.................................................................................................... 75
Table 4.2: Experimental results .................................................................................... 77
Table 4.3: Comparison of the test results ...................................................................... 82iii

LIST OF FIGURES
Fig.1.1: Single-lap shear bond test .................................................................................... 5
Fig.1.2: Double-lap shear bond test .................................................................................. 5
Fig.1.3: Bending-type shear test ...................................................................................... 6
Fig.1.4: Inserted-type shear bond test ............................................................................... 6
Fig.1.5: Direct tension test .................................................................................................. 7
Fig.1.6: Three-point bending test....................................................................................... 7
Fig.1.7: Wedging splitting test ........................................................................................... 7
Fig.1.8: Dowel test for the FRP sheet-concrete interface ............................................. 8
Fig.1.9: Beam-type (one-directional sheet) dowel force test ....................................... 8
Fig.1.10: Shear-peeling bond test ...................................................................................... 9
Fig.2.1: Possible failure modes for FRP-strengthened RC-beams .......................... 16
Fig.2.2: Major crack-induced debonding ...................................................................... 17
Fig.2.3: Specimen details ................................................................................................. 19
Fig.2.4: Stress-strain relationship of the reinforced steel .......................................... 20
Fig.2.5: Test setup .............................................................................................................. 22
Fig.2.6: Failure mode of specimen RC-S...................................................................... 22
Fig.2.7: Load-versus-deflection relation at the given cycle ...................................... 23
Fig.2.8: Load-versus-stirrup strain relationship........................................................... 23
Fig.2.9 (a): Failure mode of specimen CS-S ................................................................ 24
Fig.2.9 (b): Shear peeling mechanism due to shear crack ......................................... 24
Fig.2.10: Load-versus-deflection relationship at the given position ....................... 25
Fig.2.11: Load-versus-strain relationship ..................................................................... 26
Fig.2.12: CFRP plate strain distribution ........................................................................ 27
Fig.2.13: Photos of the specimen.................................................................................... 27
Fig.2.14: Displacement-versus-fatigue cycle relationships at the given position 28
Fig.2.15: Applied load-versus-displacement relations ............................................. 28
Fig.2.16: Applied load-versus-displacement relations ............................................... 29
Fig.2.17: Transition of displacement D10 and D11 .................................................... 29
Fig.2.18: Strain-versus-fatigue cycle relationships ..................................................... 30
Fig.2.19: CFRP plate strain distributions versus fatigue cycles ............................... 30
Fig.3.1: Specimen details ................................................................................................. 34
Fig.3.2: Data acquisition schematic ............................................................................... 35
Fig.3.3: Confinement jig to prevent concrete splitting............................................... 35
Fig.3.4: Typical failure under static loading ................................................................. 36
Fig.3.5: Load-displacement relationships ..................................................................... 37
Fig.3.6: P-δ curves ............................................................................................................. 41
Fig.3.7: Strain distribution ............................................................................................... 41
Fig.3.8: Position of strain gauges ................................................................................... 43
Fig.3.9: Local bond stress and slip curves .................................................................... 43
Fig.3.10: Popovics model comparisons......................................................................... 44
Fig.3.11: Splitting failure of specimen C36HE-F75 ................................................... 47
Fig.3.12: Specimen C21HE-F75-C with a confinement jig and the failure surfaceiv

............................................................................................................................................... 47

Fig.3.13: Typical failure surface after fatigue loading ............................................... 49
Fig.3.14: Load-crack width curves ................................................................................. 50
Fig.3.15: Strain distribution of specimen C36HS-F70............................................... 51
Fig.3.16: Strain distribution of specimen C36HS-F60............................................... 51
Fig.3.17: Strain distribution of specimen C36HS-F50............................................... 52
Fig.3.18: Strain distribution of specimen C36HE-F75 .............................................. 52
Fig.3.19: Strain distribution of specimen C21HS-F85-T .......................................... 52
Fig.3.20: Strain distribution of specimen C21HS-F80............................................... 53
Fig.3.21: Strain distribution of specimen C21HS-F80-T .......................................... 53
Fig.3.22: Strain distribution of specimen C21HS-F75-T .......................................... 53
Fig.3.23: Strain distribution of specimen C21HS-F70............................................... 54
Fig.3.24: Strain distribution of specimen C21HS-F70-T .......................................... 54
Fig.3.25: Strain distribution of specimen C21HS-F60............................................... 54
Fig.3.26: Strain distribution of specimen C21HE-F75-C .......................................... 55
Fig.3.27: Strain distribution of specimen C13HS-F90............................................... 55
Fig.3.28: Strain distribution of specimen C13HS-F80............................................... 55
Fig.3.29: Strain distribution of specimen C13HS-F70............................................... 56
Fig.3.30: Post-fatigue load-displacement curves ........................................................ 56
Fig.3.31: S-N curve ............................................................................................................ 57
Fig.3.32: Fatigue life prediction method ....................................................................... 58
Fig.3.33: Local bond stress-slip curve of specimen C21HS-F70 ............................ 59
Fig.3.34: Normalized local bond stress-slip relationship for the C21HS-F series 60
Fig.3.35: Unloading branch stiffness ............................................................................. 60
Fig.3.36: Unloading branch stiffness and slip relationship ....................................... 61
Fig.3.37: Unloading branch stiffness and fatigue cycle relationship ...................... 62
Fig.3.38: Infinitesimal element ....................................................................................... 63
Fig.3.39: Comparison of the local bond stress-slip relationships ............................ 64
Fig.3.40: Local bond stress-slip path for analysis ....................................................... 65
Fig.3.41: Strain distribution compared with the C21HS-F70 results ...................... 66
Fig.3.42: Sketch of the transverse displacement measurement ................................ 67
Fig.3.43: Test setup ............................................................................................................ 67
Fig.3.44: Distribution of transverse displacement differences ................................. 68
Fig.3.45: Distribution of transverse displacement differences for specimen
C21HS-F70-T ................................................................................................................... 69
Fig.3.46: Distribution of transverse displacement differences for specimen
C21HS-F75-T ................................................................................................................... 69
Fig.3.47: Distribution of transverse displacement differences for specimen
C21HS-F80-T ................................................................................................................... 70
Fig.3.48: Distribution of transverse displacement differences for specimen
C21HS-F85-T ................................................................................................................... 70
Fig.3.49: Mechanism of peeling off of the CFRP plate ........................................... 71
Fig.4.1: Debonding failure induced by a flexure-shear crack in the concrete beam............................................................................................................................................... 73v

Fig.4.2: Specimen details ................................................................................................. 75
Fig.4.3: Test setup .............................................................................................................. 76
Fig.4.4(a): Typical failure faces of the specimens with small initial angles .......... 77
Fig.4.4(b): Typical failure faces of the specimens with large initial angles ........ 77
Fig.4.5: Load-versus-crack width relationship ............................................................ 78
Fig.4.6: Strain distribution corresponding to marked plots of the load-crack width
relationship .......................................................................................................................... 79
Fig.4.7: Details of the delamination process ................................................................ 80
Fig.4.8: Effect of the peeling angle on the bond strength.......................................... 81
Fig.4.9: Evaluation of the combined fracture bond strength..................................... 82vi

DISSERTATION ABSTRACT
Fiber-reinforced polymer (FRP) systems have emerged as an alternative to traditional
techniques for strengthening concrete, such as steel plate bonding, section
enlargement, and external post-tensioning. FRP strengthening systems use FRP
composite materials as supplemental externally bonded reinforcement. FRP systems
offer several advantages over traditional strengthening techniques, including theirlight weight, ease of installation, and noncorrosive nature.
Strengthening of reinforced concrete (RC) structures using carbon FRP (CFRP) has
emerged as a potential solution to the problems associated with civil infrastructure.
Many researchers have reported significant increases in the strength and stiffness of
CFRP-retrofitted concrete structures. Nevertheless, brittle failures of such retrofitted
systems could prevent the full utilization of CFRP. One possible brittle failure modeis premature debonding of the CFRP, which could occur at load levels significantly
lower than the strength of the CFRP material used in the retrofitted system. Therefore,
the various failure mechanisms possible in CFRP-strengthened concrete structures
must be better understood to achieve a reliable retrofit design. Innovative structuraldetailing is also necessary to utilize CFRP systems more effectively.
When considering the rehabilitation of an RC structure, such as a bridge that has been
subjected to repetitive cyclic loading, the detrimental effects of fatigue over the life of
the structure must be assessed. When such an assessment indicates that the structure
or structural component is approaching its fatigue endurance limit, a strategy isneeded to extend its fatigue life. One potential solution is the bonding of FRP
composites. However, FRP debonding through the concrete substrate has been
identified as an important failure mode because it occurs at lighter load levels and thefailure is very brittle. Indeed, the durability of the FRP-to-concrete bond is recognized
as being critical to the performance of an externally bonded FRP repair system.
Therefore, clearly identifying the degrading effect of fatigue loading on theperformance of externally bonded FRP systems is important.
The technique of bonding steel plates to the external surfaces of RC structures toenhance flexural strength or stiffness has been employed worldwide since the late1960s. Recent increases in bridge design loading requirements worldwide havehighlighted the need for fast, efficient, and durable strengthening methods. Althoughexternal steel plate bonding can provide a satisfactory solution in many cases, it does
have disadvantages, including the need to maneuver heavy plates on site, potential
steel corrosion, and the need for on-going maintenance.
CFRP plates offer several advantages over steel, including their resistance tocorrosion, light weight, and excellent mechanical strength. CFRP is an ideal material
for use in the structural repair and strengthening of concrete structures. The mainvii

attributes of CFRP plates are their high strength, light weight, better resistance tochemicals compared with steel, good fatigue strength, and noncorrosive nature. The
bond behavior between CFRP plates and concrete plays an important role in theeffectiveness of CFRP strengthening. The evaluation of fatigue performance is also
considered an important issue in the strengthening of concrete structures. The work
reported in this thesis considers the development of a comprehensive approach tounderstanding the bond and peeling characteristics of CFRP plate-strengthened
concrete under fatigue loading.
The following is a brief description of the contents of each chapter in the thesis.
Chapter one introduces the research background on structural strengthening andrehabilitation using FRP composites in place of other materials and reviews theliterature on the use of FRP composite materials to strengthen concrete structures. The
research objectives are enumerated, and the research approach is described. Finally,
the aims and outline of this doctoral thesis are introduced.
Chapter two introduces experimental investigations of CFRP plate debonding
behavior using beam specimens flexurally strengthened by CFRP plates and relative
vertical displacement imposed on the two sides of a shear crack in each beam. The
test results confirm the effectiveness of mixed-mode (shear-peeling) debonding in
CFRP plates and local debonding with peeling off as an important factor affecting thefatigue life of concrete structures strengthened by CFRP plates.
Chapter three describes fatigue loading tests of double-faced bond specimens, carriedout to investigate the influence of bond behavior for different concrete strengths,
different types of CFRP plates and different levels of the upper limit fatigue load. The
test results show that the fatigue behavior of the bonding surface between a CFRP
plate and concrete can be characterized by an S-N diagram representing therelationship between the upper limit of the bond stress and the number of load cycles
at debonding. To clarify the fatigue bond damage and predict the fatigue life of thebond, a bond-slip model based on fatigue cycles (N) and the unloading branch
stiffness (ki) in slip was developed. In addition, the transverse displacement in the
CFRP plates and the concrete substrate was measured. The variation in transverse
displacement exhibited an obvious discernible peeling phenomenon with debonding
propagation. The experiment results indicate that the CFRP plate, upon peeling off,
moved from the specimen center to the loading end as the number of fatigue cycles
increased. The peeling off of the CFRP plate is an important failure mode affecting
the debonding progress in the fatigue test.
Chapter four presents the experimental results and the calculation method foranalyzing the bond strength between CFRP plates and concrete interfaces debonded
by both shear and peeling. Twenty-two special double-faced rectangular shear
specimens with CFRP plates bonded on two sides were tested in uniaxial tensileviii

loading. The specimens were designed for various initial angles at the middle toensure that the interface acts in both shear and peeling. Three concrete compressive
strengths were used in this investigation. The results revealed that the bond strength
decreases considerably due to the peeling effect. In addition, the initial attachment
angle plays an important role in the bond strength, combined with the angle effect.
Based on the test results, a calculation method is proposed based on modifying one of
the existing bond strength models for the FRP sheet-to-concrete bonding system. The
proposed modification can accurately predict the bond strength between CFRP plates
and concrete.
Chapter five summarizes the thesis with a retrospective view of the research
objectives and presents the conclusions drawn from the work. Recommendations for
future research are also highlighted in this chapter.

ix

CHAPTER 1
Introduction
1.1

Research BackgroundA substantial amount of society’s resources worldwide are invested in existing
concrete structures, such as bridges, tunnels, and various types of buildings. Each ofthese structures has an expected function and expected life span. However, both thefunction and life span can be influenced by external factors, such as degradation andaltered load situations. Mistakes made in the design or during the construction phase
can also influence the functioning and life span of a structure. Repairing and/or
strengthening these structures can maintain or improve both their functioning and lifespans.
The strengthening or retrofitting of existing concrete structures to resist higher design
loads, correct deterioration-related damage, or increase ductility has traditionally beenaccomplished using conventional materials and construction techniques. Externallybonded steel plates, steel or concrete jackets and external post-tensioning are some of
the many traditional techniques available. In the context of the strengthening problem,
advanced composites have the potential to provide another promising solution.
In recent years, the use of fiber-reinforced polymer (FRP) materials has emerged as analternative to traditional strengthening techniques due to the superior properties ofthese materials, such as their formability, ease of fabrication and bonding, resistanceto corrosion, and light weight. Indeed, FRP reinforcement is one of the mostpromising new developments for concrete structures. FRP reinforcing elements
provide lighter, easier-to-assemble and more durable structures that are free of thedeterioration caused by the corrosion of steel. FRPs consist of synthetic or organic
high-strength fibers, most of which are impregnated with a resin matrix. FRPs areavailable in the form of grids, rods, and ropes for reinforcing and prestressing
concrete members. Various types of FRP reinforcement are currently available inJapan, including rods (round and rectangular), strands, braids, and grids. These types
FRP reinforcement are available with fibers of carbon and aramid (rods), carbon(strands), aramid (braids) and carbon, and aramid and glass (grids). FRP
reinforcement in sheet form (FRP sheets) is typically applied to strengthen or repair
existing structures. Sheets with fiber in one direction are used for strengthening,whereas sheets with fiber in two directions are used for repairs, to improve or restore
durability and to avoid concrete pieces from falling from the structure surface.
In the last decade, the development of strong epoxy glue has led to a technique thathas great potential in the field of upgrading structures. The technique involves gluing
steel or FRP plates to the concrete surface. The plates then act compositely with theconcrete and help to carry the loads. FRP can be more convenient than steel for a1

number of reasons. FRP materials have higher ultimate strength and lower density
than steel. Their installation is easier, and due to their low weight, temporary support
until the adhesive gains sufficient strength is not required. FRP reinforcement can also
be formed on site into complicated shapes and can easily be cut to length on site.
Debonding in FRP-strengthened members occurs in regions with high stressconcentrations, which are often associated with material discontinuities and thepresence of cracks. The propagation path of debonding initiated from stressconcentrations is dependent on the elastic and strength properties of the repair andsubstrate materials, as well as their interfacial fracture properties.
The term “debonding failure” is often associated with a significant decrease inmember capacity due to the initiation or propagation of debonding. Theoretically,
debonding in FRP-strengthened members can occur within or at the interfaces ofmaterials that form the strengthening system, favoring the propagation path that
requires the least amount of energy. Crack propagation in one of the constituent
materials is generally preferred over interface debonding in the design of structural
joints; however, the latter is often encountered, particularly in cases of poor surface
preparation or application. The majority of the debonding failures reported in theliterature have occurred in the concrete substrate. However, other debonding
mechanisms can also be observed, depending on the geometric and material
properties.
Repeated loading alters the fundamental properties of the constituent materials in
reinforced-concrete (RC) structures, which may lead to progressive damage
propagation. The application of FRP to strengthen or retrofit existing structures
should consider the fatigue characteristics of the FRP-concrete bond. Although many
tests have been conducted to investigate the strengthening of RC members with FRP
plates, many aspects of the use of FRP plates remain unclear. To date, little is known
about fatigue damage to FRP plate-concrete bonding systems that experience
mixed-mode fracturing, and in-depth research of the long-term performance of such
systems is necessary before FRP plates gain full acceptance as materials that can beused in civil engineering.
Compared to the fairly extensive experimental and analytical studies on themonotonic behavior of FRP-strengthened RC members, relatively few studies havebeen reported on the fatigue behavior of FRP-strengthened RC beams.
Past research into the fatigue performance of FRP-strengthened RC beams has mainly
focused on demonstrating the overall effectiveness of this strengthening technique. In
most investigations to date, the load or deflection ranges applied to the beams havebeen such that the resulting strain amplitudes in the reinforcing steel have been small.
Under these conditions, the bond performance of the FRP reinforcement is not a
primary concern because the fatigue response is largely governed by the performance2

of the steel reinforcement and concrete. Furthermore, given the brittle characteristicsof the adhesive or concrete in tension, as well as the varying environmental andloading conditions to which a structure can be subjected during its lifetime, thepossibility of other failure modes, such as debonding of the FRP reinforcement,
should be considered. A clear understanding of the behavior at the interface between
the concrete and the bonded FRP reinforcement is thus required.
The bond between concrete and FRP plates plays an important role in thestrengthening of concrete structures. This bond is brittle and therefore exhibits little
ductility at failure. Thus, failure of FRP plate-strengthened concrete structures may
occur suddenly. In other words, adhesively bonded plates are highly prone topremature debonding or peeling. The most common forms of peeling, identified fromtests on simply supported RC beams adhesively bonded with tension face plates, canbe categorized as shear peeling, flexural peeling, combined flexural and shear peeling.
To ensure the properties of the bond between concrete members and externallybonded FRP plates, the bond properties should be better understood.

1.2

Literature Review

With FRP composite materials being used increasingly in civil engineering
applications, numerous experimental investigations and analytical studies have been
carried out since the 1990s. This section presents a review of the state of the art andthe related research work conducted to date.

1.2.1 Bond between Strengthening Materials and ConcreteWith the development of technology to upgrade existing concrete structures using
externally bonded FRP composites, a number of issues related to the conventional
structural behaviors of concrete structures after being upgraded have been studied
over the past decade. Among these issues has been a keen interest in clarifying themechanisms of the interface bond between FRP composites and concrete substrates,
because the bonding interface is relatively weak in comparison with the neighboringmaterials in the whole upgraded system. In most strengthening cases, the interface
bond is critical for transferring stresses from the existing concrete structures to theexternally bonded FRP composites. When a structural element is encircled in FRP
composites, the mechanical role of the interface bond becomes less important, but it
retains the function of maintaining the integrity and durability of the composite
FRP-concrete systems. Therefore, strong understanding of the interface bond is aprerequisite for achieving a more reliable but rational design for concrete structures
externally bonded with FRP composites.
Good bond properties are essential to the success of the external reinforcement
technique for repairing or strengthening RC members. Swamy et al. [1.1], Van
Gemert [1.2], and Kobatake et al. [1.3] conducted detailed investigations of the3

properties of the bond between concrete and steel plates. These researchers useddouble-lap shear tests to determine the maximum and average shear stress values, theforce distribution, and the mode of force transfer. Bizindavyi et al. [1.4], Chajes et al.
[1.5], [1.6], and Neubauer and Rostasy [1.7] performed identical pull-out tests oncomposite-to-concrete joints. The aims of these investigations were to study the shear
stress distributions of the bonded interface, to quantify anchorage lengths and toinvestigate the influence of the concrete strength and glue line thickness on the bondstrength. The pull-out test results indicated that there is a measurable bond length
beyond which no further increase in the transferred load can be achieved. This length
has been shown to be a function of the properties and geometry of the specimens andto depend on the surface preparation.

1.2.2 Bond between FRP Sheets and Concrete
It can be said the macro-mechanical behavior of RC members upgraded with FRP
sheets, including their fundamental failure modes and their effects on strength,
capacity, and ductility, have been well established to date, based on a large number ofexperimental and analytical studies over the past decade. However, to achieve arefined design for concrete structures to be upgraded with FRP sheets, further study isneeded into the fundamental issues, such as interfacial bond fracture mechanisms,
selection of bonding or strengthening material, and design detailing. For reliable but
rational and cost-effective use of FRP materials, refined upgrading designs should
follow performance-based design concepts, for which the accuracy of predicting theperformances of FRP-upgraded concrete members relies on accurate material laws, aswell as advanced analytical methods.
The Japan Concrete Institute (JCI) established a technical committee on retrofitting
technology (2001 to 2003), which focused on the interface bond properties between
existing concrete structures and retrofitting materials for both adhesive bonding andoverlaying retrofitting technologies. The objective of the committee was to gain
insight into the micro- and macro-interfacial bonding mechanisms, the selection of the
optimal interface materials and upgrading methods, the improved prediction of theperformances of upgraded concrete structures, and, finally, the improvement of
current upgrading techniques from both a construction and materials point of view. In
general, the research topics on FRP sheet-concrete interfaces can be addressed by thefollowing:
1. Parametric studies on interface bond, including the effects of all interface
components: concrete, bonding layer, and FRP sheets;
2. Test methods for evaluating the interface bond properties;
3. Bond strength and anchorage design;
4. Failure mechanisms of interface bond and bond modeling;
5. Effects of interface bond on the member behavior of concrete structures after
retrofitting;46. Optimized design of interface bond;
7. Durability of interface bond.
For the past few years, external bonding of FRP sheets has emerged as a popularmethod for strengthening RC structures. In this strengthening method, theperformance of the FRP-to-concrete interface in providing effective stress transfer isof crucial importance. Indeed, a number of failure modes in FRP-strengthened RC
members are directly caused by the debonding of the FRP from the concrete.
Therefore, for the safe and economical design of externally bonded FRP systems, asound understanding of the behavior of the FRP-to-concrete interface needs to be
developed.
The various debonding failure modes can be categorized as shear (mode II failure),tension (mode I failure), and a combination of shear and tension (mixed-mode
failure).
① Failure of the FRP sheet-concrete bond under shear (mode II failure)
Various test methods, including the single-lap, double-lap, bending, and inserted shear
bond tests (see Figs. 1.1-1.4), have been developed to characterize local interfacial
shear bond behavior by studying the strain distribution in the FRP sheets or toevaluate the average interfacial bond strength. The interface parameters evaluatedinclude the average shear bond strength, the effective bond length, the maximum
shear bond stress, the interfacial fracture energy, and the local bond stress-slip
relationship.

Fig. 1.1 Single-lap shear bond test

Fig. 1.2 Double-lap shear bond test
5Fig. 1.3 Bending-type shear test

Fig. 1.4 Inserted-type shear bond test
② Failure of the bond between FRP sheets and concrete under tension (mode I
failure)Tensile tests for the interface between FRP sheets and concrete to verify the interface
bond quality are easier to perform than shear bond tests. Three types of tensile test
methods have been reported (Figs 1.5-1.7). Fig. 1.5 illustrates the direct tensile test
method adopted by the “Design and Construction Guidelines for Continuous
Fiber-Reinforced Concrete Structures’’ of the Architectural Institute of Japan (AIJ).
This method is convenient because it evaluates the interface bond qualitatively byobservation. Figs 1.6 and 1.7 illustrate the three-point bending and wedge splitting
tests, respectively [1.8]-[1.10]. These tests can be used to evaluate the Mode I fractureenergy and the tension-softening diagram of FRP sheet-concrete interfaces. The bondproperties of FRP sheet-concrete interfaces under tension can be examinedparametrically and quantitatively using these two methods. Three-point bending tests
have also been used to evaluate the bond degradation of FRP sheet-concrete interfaces
after exposure to severe environmental and fatigue loading [1.11].

6

Fig. 1.5 Direct tension test

Fig. 1.6 Three-point bending test

Fig. 1.7 Wedging splitting test
③ Failure of the bond between FRP sheets and concrete under a combination ofshear and tension (mixed-mode failure)
A more representative interface bond failure for concrete structures retrofitted with
FRP is a combined mode, given that FRP sheet-concrete interfaces are subjected toshear and tension simultaneously. Karbhari and Engineer developed a bond test7

method to evaluate the bond between FRP composites and concrete undermixed-mode loading conditions by producing different interface peeling angles [1.12].
Another widely reported mixed-mode failure of the FRP sheet-concrete interface
occurs in FRP-strengthened RC beams loaded in flexure [1.6 and 1.9]. The interface
debonding may initiate at the tip of a shear-flexural crack, with peeling caused
simultaneously by a crack opening in the longitudinal direction and crack sliding in
the vertical direction.
A new application of FRP strengthening technology in Japan involves bonding FRP
sheets to the bottom surfaces of tunnel linings or elevated bridges to prevent pieces ofdeteriorated concrete from falling. In these strengthening cases, the FRP
sheet-concrete interfaces are subjected mixed-mode loading, as shown in Fig. 1.8.
Two types of test methods have been used to determine the bond properties ofinterfaces under static loading conditions [1.13]-[1.15]. One is a beam-type dowel test
for FRP sheet-concrete interfaces in which a one-directional FRP sheet is bonded tothe bottom of a notched concrete beam (see Fig. 1.9). The other is a slab-type shear
punching test in which a bidirectional rather than a unidirectional FRP sheet isattached to the bottom of a concrete slab. Two fundamental bond characteristics of
FRP sheet-concrete interfaces under the dowel action are obtained from both types oftests: (1) the peeling angle is constant during the interface debonding process, and (2)the vertical force per unit width that an FRP sheet-concrete interface can bear is aconstant value during the interface debonding process.

Fig. 1.8 Dowel test for the FRP sheet-concrete interface

Fig. 1.9 Beam-type (one-directional sheet) dowel force test
Furthermore, a study of the shear-peeling bond strength between FRP sheets andconcrete was performed by Md. Shah Alam et al. [1.16]. The specimens were
designed for different step angles in the middle, to ensure that the interface acted
under both shear and peeling conditions (see Fig. 1.10). Their study presented theexperimental results of bond strength between FRP sheets and concrete interfaces
8

under both shear bond and peeling conditions. The results revealed that the bondstrength decreased considerably due to the peeling effect. In addition, the step angle
and fiber stiffness played important roles in bond strength for a combined effect. The
highest bond strength was observed for the lowest axial stiffness of the laminate.
Based on these test results, a modification was proposed to one of the existing bondstrength models. The proposed modification improved the prediction of the bondstrength between FRP laminate and concrete.

Fig. 1.10 Shear-peeling bond test

1.2.3. Bond between FRP Plates and Concrete
It has been several decades since traditional strengthening techniques, such as steel
plate bonding, were used in renovation engineering to strengthen and retrofit
reinforced concrete members. In recent years, FRP plates have been used as
supplemental externally bonded reinforcement. The development of the carbon
fiber-reinforced polymer (CFRP) plate bonding repair technique has shown to be
applicable to many existing strengthening problems in the building industry, not only
for strengthening but also for cases of rebuilding, as well as when mistakes have been
made during the design or construction phase. This technique can be defined as one inwhich CFRP plates of relatively small thicknesses are bonded with an epoxy adhesive
to, in most cases, a concrete structure, to improve its structural behavior and strength.
The CFRP plates do not require much space, and they contribute to composite action
between the adherents. The adhesive that is used to bond the plate to the concretesurface is a hardy two-component epoxy adhesive. Before FRP plates are bonded tothe surface of the concrete, the surface should first be cleaned or sandblasted down tothe aggregate to ensure a good bond between the concrete and FRP plates. The oldstructure and the new bonded material create a structural relationship that has greater
strength than the original structure.
As they are increasingly used with FRP materials, CFRP plates not only have beenused to strengthen reinforced concrete beams or girders with deficient flexural/shear
9

strength, but they also have been introduced to strengthen deteriorated slabs, masonrywall, bridge girders, and piers. Using FRP wraps around concrete columns, the load
capacity can be improved by lateral confinement [1.17]-[1.18]. For the flexuralstrengthening of concrete beams, FRP plates are bonded to the tension face using
epoxy-based adhesive, which increases both the strength and stiffness of the beams[1.19]-[1.21]. For shear strengthening, FRP plates are bonded to both sides of the RC
beam to provide an additional contribution to its shear capacity [1.22].
Since the 1990s, many experimental studies of RC beams strengthened with FRP
plates have been conducted all over the world [1.23]-[1.29]. These experimental
investigations have focused on the following three aspects, according to their research
objectives:
1. Investigations focusing on the shear strengthening of RC beams;
2. Investigations related to the flexural strengthening of RC beams;
3. Investigations emphasizing the interfacial properties between concrete and FRP
plates.
In all, the bonding of FRP plates on tensile surfaces has been proved to be an effective
method for increasing both the strength and stiffness of concrete members. For a
flexurally strengthened RC beam under external loading, the beam can fail by FRP
debonding from the bottom of a major flexural crack in the span. This failure mode
can also be found in FRP-strengthened, one-way slabs. Debonding failure is inducedby the presence of high shear stress concentrations at the interface around the bottomof the flexural cracks. With an increasing external load, the interfacial crack
propagates toward the plate end until final failure is reached. It is usually observedthat the failure occurs in the concrete, and a thin layer of concrete is attached to thesurface of the debonded FRP plate. Hence, for concrete members strengthened withexternally bonded FRP, the concrete/FRP interfacial behavior should be an importantfocus of investigation.

1.2.4. Fatigue

Characteristics

of

FRP-Strengthened

Concrete

Elements
Recently, many structures, such as bridges, have failed to meet structural andfunctional requirements as a result of corrosion, the expansion of fatigue cracks, andimproper maintenance. In most cases, these types of damage only occur within certain
areas of the structure, and the cost of strengthening the structure is much less than thecost of replacing the whole structure. Traditional retrofitting methods typicallyinvolve welding, bolting, or riveting steel plates to the damaged location. Thesemethods have several drawbacks, such as the weight that the steel adds to thestructure, the fatigue sensitivity of weld defects, stress concentrations, and stressredistribution. FRP possesses notable advantages as a structural material, including
high strength, good corrosion resistance, and better fatigue performance than steel.
10

Therefore, FRP has been widely applied in strengthening and repairing concrete
structures.
Wight and Erki (2001) [1.30] studied the fatigue of prestressed CFRP sheets used tostrengthen concrete slabs. Six one-way, reinforced concrete slabs were constructed
and tested to investigate the effectiveness of using prestressed CFRP sheets forstrengthening concrete slabs subjected to fatigue loading. The test results confirmedthat strengthening reinforced concrete slabs with bonded CFRP sheets, especiallyprestressed CFRP sheets, increased fatigue life. Strains in the steel reinforcement,
plastic creep strains in the concrete, and deflections all decreased. Crack widths weregreatly reduced when the CFRP sheets were prestressed.
Additionally, some key investigations [1.31]-[1.33] have clearly shown that
FRP-strengthened reinforced concrete beams have performed better in terms offatigue than their non-strengthened companions. In most cases, it has been observedthat the failure of FRP-strengthened beams is initiated by successive yielding of thereinforcing steel under tension in one or several locations, culminating in the fatigue
rupture of the bars [1.31]. Whenever debonding of the FRP laminate occurred, it wasconsidered to be a secondary failure mode, resulting from the yielding and rupture of
the reinforcing steel, as well as excessive widening of the cracks. Based on the results
reported by Heffernan (1997) [1.31], it appears that the fatigue life of a concrete beam
depends mainly on the fatigue of the tension steel-reinforcing bars, provided that theserviceability of the beam (cracking in the tension region) is negligible. Barnes andMays (1999) [1.33] suggested that a reasonable criterion for design would be to
expect that, for a plated beam, the fatigue life would be the same as that of acomparable non-strengthened beam, as long as the resulting stress amplitudes in thetension steel reinforcing bars remained identical. However, they cautioned that, as far
as the fatigue performance is concerned, there could be a shift in failure mode fromreinforcing-steel-dominated failure (for under-reinforced members) to bending or
shear-dominated failure modes for over-reinforced members.
To evaluate the effectiveness of epoxy-bonded FRP in prolonging the fatigue lives ofconcrete structures, some researchers have conducted studies on the fatigue behavior
of concrete structures strengthened with FRP and have found that FRP cansignificantly extend the fatigue lives of concrete structures while effectively reducing
the crack growth rate. [1.34]-[1.36]
The fatigue durability of FRP-concrete interfaces is another important issue. Fatigue
failures of reinforced concrete members are usually governed by the fatigue fractureof the reinforcement rather than debonding of the FRP from the concrete substrate.
However, cyclic loading tests on FRP-concrete bonded interface have shown thatinterface debonding propagates progressively as the number of fatigue cycles
increases. [1.37] An FRP-concrete interface with sufficient anchorage length may
retain its interface bonding capacity after the number of cycles expected to cause
11fatigue failure. Nevertheless, progressive local interface delamination adversely
affects the serviceability of FRP-strengthened members and may trigger adeterioration with a combination of failure modes. This possibility underscores thenecessity of studying the fatigue performance of FRP-concrete bonded interface inwhich the concrete substrate has debonded as a result of a combination of fracturemodes.
Studies of the fatigue behaviors of FRP-to-concrete joints were undertaken by
Bizindavyi et al. (2003) [1.36]. In that research, the method used to bond the FRP
laminates to the concrete blocks consisted of in-place bonding and curing of the
GFRP fabric and CFRP sheets directly on the concrete. The concrete surface was first
sandblasted and then cleaned by air blasting. During the preparation of the specimens,a relatively uniform thickness of 1-1.2 mm of adhesive layer was assured usingaluminum guides. The bonded joints were allowed to cure for a minimum of 14 days
before the cyclic bond tests were performed. Bizindavyi et al. presented results froman experimental investigation of a bonded FRP-to-concrete interface under fatigue
loading. The results for the effects of fatigue loading on slip at the FRP-concreteinterface, crack opening, and strain profiles along the bonded FRP joint were
presented and discussed. A power-law expression for the so-called “S-N” curves(cyclic stress ranges versus numbers of cycles to failure) was proposed, and theparameters in this expression were determined from the experimental data. The
influences of various parameters, such as bond length, bond width, and cyclic bondstress levels, on fatigue behavior were discussed.
To date, no appropriate studies have been published that have described mixed-mode
fractures of the FRP plate-concrete interface under fatigue-loading conditions. In
general, mixed-mode fracture failure can be suppressed by limiting the opening ofshear cracks. Therefore, it is important to investigate mixed-mode failure debonding
due to shear crack opening, based on the action of FRP plates in experimental tests of
FRP-reinforced RC beams. Thus, it is important to conduct fatigue tests in which
shear cracking affects the flexural strengthening efficiency of FRP plates.

1.3. Objective and Scope
Although research on the bond behavior of FRP-strengthened concrete elements under
static and fatigue loading has been extensively studied, as described earlier, thesubstantial existing research on the bond behavior of FRP-strengthened concreteelements has not focused much attention on the characteristics of debonding in fatigue.
Therefore, the principal objective and scope of this thesis research are as follows:First, the characteristics of mixed-mode (shear and peeling) debonding due to shear
crack formation in beams flexurally strengthened by CFRP plates and subjected tostatic and fatigue loading were investigated.
12

Next, fatigue testing of double-faced shear bond specimens was carried out toexamine the fatigue bond behavior of CFRP plate-concrete systems. The fatigue
failure of the bond surface between CFRP plates and concrete can be characterized byan S-N diagram representing the relationship between the ratio of the upper limit of
fatigue loading to calculated bond strength and the number of cycles to failure, basedon the results of experiments conducted to investigate the influence of different
concrete strengths and the levels of the upper limit of fatigue loading. The different
debonding modes that occur at the fracture interface were also observed. Furthermore,
the effect of peeling behavior on fatigue damage was examined.
Finally, an experiment was conducted to examine the bond behavior of CFRP plates
and concrete systems in combined fracture mode (peeling and shear) using
initial-angle double-lap shear bond specimens. The specimens were designed for
different initial angles at the middle of the specimen to ensure that the interface acts inboth shear and peeling. A calculation method is proposed for prediction of the bondstrength between a CFRP plate and concrete under combined shear-peeling fracture
conditions.

1.4

Outline of the Thesis

The work reported in this thesis addresses the development of a comprehensive
approach to understanding the bond and peeling behavior of CFRP plate-strengthened
concrete structures under fatigue loading.
The following is a brief description of the contents of each chapter in the thesis:
Chapter one introduces the research background on structural strengthening andrehabilitation using FRP composites in place of other materials and reviews theliterature on the use of FRP composite materials to strengthen concrete structures. The
research objectives are enumerated, and the research approach is described. Finally,
the aims and outline of this doctoral thesis are introduced.
Chapter two introduces experimental investigations of CFRP plate debonding
behavior using beam specimens flexurally strengthened by CFRP plates and relative
vertical displacement imposed on the two sides of a shear crack in each beam. The
test results confirm the effectiveness of mixed-mode (shear-peeling) debonding in
CFRP plates and local debonding with peeling off as an important factor affecting thefatigue life of concrete structures strengthened by CFRP plates.
Chapter three describes fatigue loading tests of double-faced bond specimens, carriedout to investigate the influence of bond behavior for different concrete strengths,
different types of CFRP plates and different levels of the upper limit fatigue load. The
test results show that the fatigue behavior of the bonding surface between a CFRP
plate and concrete can be characterized by an S-N diagram representing the13relationship between the upper limit of the bond stress and the number of load cycles
at debonding. To clarify the fatigue bond damage and predict the fatigue life of thebond, a bond-slip model based on fatigue cycles (N) and the unloading branch
stiffness (ki) in slip was developed. In addition, the transverse displacement in the
CFRP plates and the concrete substrate was measured. The variation in transverse
displacement exhibited an obvious discernible peeling phenomenon with debonding
propagation. The experiment results indicate that the CFRP plate, upon peeling off,
moved from the specimen center to the loading end as the number of fatigue cycles
increased. The peeling off of the CFRP plate is an important failure mode affecting
the debonding progress in the fatigue test.
Chapter four presents the experimental results and the calculation method foranalyzing the bond strength between CFRP plates and concrete interfaces debonded
by both shear and peeling. Twenty-two special double-faced rectangular shear
specimens with CFRP plates bonded on two sides were tested in uniaxial tensileloading. The specimens were designed for various initial angles at the middle toensure that the interface acts in both shear and peeling. Three concrete compressive
strengths were used in this investigation. The results revealed that the bond strength
decreases considerably due to the peeling effect. In addition, the initial attachment
angle plays an important role in the bond strength, combined with the angle effect.
Based on the test results, a calculation method is proposed based on modifying one of
the existing bond strength models for the FRP sheet-to-concrete bonding system. The
proposed modification can accurately predict the bond strength between CFRP plates
and concrete.
Chapter five summarizes the thesis with a retrospective view of the research
objectives and presents the conclusions drawn from the work. Recommendations for
future research are also highlighted in this chapter.

14

CHAPTER 2
CFRP Plate Debonding Behavior in Flexurally
Strengthened RC Beams
2.1

Introduction

The plate bonding technique is now established as a simple and convenient repair
method for enhancing the flexural performance of concrete structures and bridge
beams and slabs in particular. The advantages of this technique are that the work can
be carried out while the structure is still in use and that it is economical compared toother methods. Traditionally, steel plates have been used, but there are problems
associated with using steel plates as external reinforcement for existing concrete
structures, including the need for careful surface preparation of the steel prior tobonding, uncertainty regarding adhesive bond durability and potential corrosion at thesteel-adhesive interface, the awkwardness of maneuvering heavy steel plates, theresulting need for restrictions on plate length and the need for many lapped joints, theneed for anchor bolts, and maintenance painting. FRP plates do not suffer fromcorrosion problems, and most of their mechanical and physical properties are better
than those of steel.
However, in external reinforcement of a reinforced concrete beam, debonding may be
induced by a major flexurally or shear-induced crack in the span. Under suchconditions, there is a relative vertical displacement on the two sides of the major crack.
The FRP plate is then subject to both tensile and peeling forces, resulting in a
combination of shear sliding and opening displacement along the FRP-concreteinterface. In this investigation, the combined effects of tensile and peeling on CFRP
plate debonding are studied.
Bonding of FRP plates to the tensile side has been demonstrated to be an effective
strengthening method for flexurally strengthened RC beams. Different failure modes
for RC beams strengthened with FRP plates have been reported in several
experimental investigations (Ritchie et al. 1991[2.1]; Saadatmanesh and Ehsani
1991[2.2]). The failure modes are summarized as follows and illustrated in Fig. 2.1:
(1) Rupture of the FRP plate at the mid-span,(2) Concrete crushing in the compression zone,(3) Shear failure,(4) Concrete cover separation,(5) Plate end interfacial debonding, and(6) Intermediate crack-induced debonding failure.
FRP rupture and concrete crushing can be considered flexural failures, whereas
concrete cover separation, plate end debonding, and intermediate crack-induced
debonding can be considered local failures.
15

(a) FRP rupture(b) Crushing of compression concrete(c) Shear failure(d) Concrete cover separation(e) Plate end interfacial debonding(f) Crack-induced debonding
Fig. 2.1 Possible failure modes for FRP-strengthened RC beams
16

Early studies in this area focused on analyzing failure modes due to concrete crushingor FRP plate rupturing. When the ultimate failure of the strengthened beam resultsfrom flexural failure (concrete crushing or rupture of the FRP plate), the ultimate
load-carrying capacity can be calculated from conventional section analysis for theconcrete members (Wei et al. 1991 [2.3], Triantafillou and Plevris 1992 [2.4]).
However, the failure mechanisms of local failures are more complicated than those offlexural failures.
Concrete cover separation is often observed in experimental investigations of concretebeams strengthened by externally bonded FRP plates. It is accepted that this failuremode is induced by the formation of a crack at or near the plate end due to the highinterfacial shear and normal stress concentrations caused by the abrupt termination of
the FRP plate. Once a crack occurs in the concrete near the plate end, the crack willpropagate to the level of the tension reinforcement and extend horizontally along thebottom of the tension steel reinforcement. As the external load increases, thehorizontal crack may propagate to cause the concrete cover to “peel off” with the FRP
plate.
In addition, in plate-end debonding failure, FRP debonding initiates from the plate
end and propagates toward the mid-span of a concrete beam. Plate-end debonding
failure is considered to be induced by high interfacial shear and normal stresses at theconcrete-adhesive interface near the plate end. Upon debonding, a thin layer ofconcrete generally remains attached to the FRP plate, indicating that the failure occurs
on the concrete side of the concrete-adhesive interface. This debonding failure isconsidered to be governed mostly by the material properties of concrete.
The plate end is not the only possible location at which debonding failure can beinitiated. Debonding can also occur in the vicinity of flexural or shear cracks inconcrete beams, as shown in Fig. 2.2. When FRP-strengthened RC beams are loadedin flexure, flexural/shear cracks tend to open and induce high interfacial shear stress,
which leads to the initiation of FRP debonding from the concrete substrate. The
propagation of the crack from the bottom to the plate end will lead to the ultimate
failure of the strengthened beam.

Fig. 2.2 Major crack-induced debonding
Many studies have been performed to understand the bond characteristics between
concrete and FRP sheets under different test conditions (for example, the single shear
17

test, the double shear test, the direct tensile test, the modified beam test, and the testwith curvature in beam). However, the laminate-concrete interface is susceptible to
the relative vertical displacement of the shear cracks in the beam. This displacement
can lead to the delamination or peeling of the FRP sheet from the concrete. Someauthors have reported that retrofitted beams could fail due to the failure of theconcrete layer between the FRP sheet and steel or due to the delamination or peelingof the FRP sheet from the concrete. Karbhari et al. [2.5] conducted a pure peeling test
to determine the bond strength between concrete and FRP sheets. Triantafillou andPlevris [2.6] proposed a model for the peeling of debonding mechanisms. However,
CFRP plate-concrete bonding systems subjected to combination of fracture have notbeen studied often.
Furthermore, the fatigue durability of FRP/concrete interfaces is another important
issue. It was reported that the fatigue life of RC members increased after FRP
strengthening. The fatigue failures of strengthened members are usually governed by
the fatigue fracture of steel reinforcement, rather than the overall debonding of FRP
from the concrete substrate. However, cyclic loading tests of the FRP/concrete bonded
interface showed that interface debonding propagates progressively with increases infatigue cycles. An FRP/concrete interface with sufficient anchorage length could keep
its interface bonding capacity after expected fatigue cycles. Nevertheless, progressive
local interface peeling adversely affects the serviceability of FRP-strengthened
members and could trigger brittle failure combined with fracture (shear and peeling).
This observation implies the necessity of studying the fatigue performance of
FRP/concrete bonded interfaces subjected to shear and peeling. Therefore, theobjective of this research was to study the interfacial bond behavior between FRP
plates and concrete for combined shear and peeling conditions under fatigue loading.
As stated previously, local debonding results from the delamination induced by the
opening (Mode I) of a flexural shear crack and the existence of a relative verticaldisplacement between the two sides of the crack. Furthermore, as the number ofloadings increases, the crack will tend to propagate due to crack opening. Therefore,
the load condition is another important factor that affects local delamination under the
combination of flexure and shear.
In chapter 2, the CFRP plate–concrete bonding system has been applied for flexurally
strengthening the RC beam to investigate fatigue local debonding characteristics
based on deflections changing responded to peeling off in CFRP plate between
concrete surface and CFRP plate surface during shear span.

18

2.2

Outline of Experiment2.2.1 Test Specimens
Three RC beams, named RC-S, CS-S, and CS-F, were fabricated in the laboratory.
The RC-S and CS-S beams were tested to confirm shear failure according to the initialdesign and to serve as control beams to evaluate the maximum load level in thefatigue testing of beam CS-F.
The beams were 150 mm wide, 235 mm high and 2,200 mm long. The tension andcompression bars consisted of three 19-mm-diameter and two 10-mm-diameter steel
reinforcing bars. All beams were provided with shear reinforcement consisting of
6-mm-diameter bars spaced 125 mm apart for two shear spans. The stirrup ratio was
0.34%. The dimensions and cross-sectional details of the test beams are shown in Fig.
2.3. The beams were designed for major failure in shear. Two of the beams were
strengthened with CFRP plates at the bottom, and all of the beams were strengthened
with CFRP sheets on the sides of the beams, as shear failure only occurred on the
opposite side. All of the beams were tested in four-point bending. Beams RC-S and
CS-S were tested under static loading, and beam CS-F was tested under fatigue
loading.

Fig. 2.3 Specimen details

192.2.2. Material Properties
The concrete was determined, by testing of 100 × 200 mm cylinder test specimens.
The compressive strength was 22.8 MPa. The mechanical properties of the concrete
are summarized in Table 2.1. The tensile test results for the main bars and the stirrups
are listed in Table 2.2, and the stress-strain relationship is shown in Fig. 2.4. The
CFRP plates had a thickness of 1 mm and a width of 50 mm. The area of the crosssection was 50 mm2. The ultimate strength and elastic modulus of the CFRP plate
were 2,400 MPa and 156 GPa, respectively. The ultimate tensile strain was 1.54%.
The CFRP plate properties are those reported by the manufacturer.
Table 2.1 Mechanical properties of concrete
Concrete Compressive strength Splitting strength 1/3 Secant modulus
σB
σt
Ec
(MPa)
(MPa)
(GPa)
Fc 21
22.8
2.19
22.9
Table 2.2 Mechanical properties of reinforcing bar
Type

Note

Tensilestrength(MPa)

D6(SD295)

Stirrup

517

367*1

176

-*2

D10(SD345)

Compression
bar

553

390

190

22.9

D19(SD345)

Tension bar

588

397

185

22.0

1:

Yield
strength(MPa)

Elastic
modulus(GPa)

Elongation(%)

2* 0.2% offset strength; * rupture outside marks
500

Stress (MPa)

400
300
200

0

1

2

3

4

5

6

7 0

D19-1
D19-2
D19-3

D10-1
D10-2
D10-3

D6-1
D6-2
D6-3

100

1

2

3 4 5
Strain (%)

6

7 0

1

2

3

4

5

6

7

Fig. 2.4 Stress-strain relationship of the reinforced steel

2.2.3 Loading and Measurement
Beams RC-S and CS-S were tested under static loading, and beam CS-F was tested
under fatigue loading. Previous research has clearly demonstrated that
FRP-strengthened structures present better fatigue performance than unstrengthened20

structures. In most cases, it has been observed that the failure of the structure isinitiated by successive yielding of the reinforcing steel in tension, in one or more
locations. When debonding of the FRP laminate occurred, it was considered to be asecondary failure mode resulting from the yielding and failure of steel rebar. The
objective of this research is to investigate the bond and peeling characteristics
between concrete and CFRP plates under fatigue loading. An upper limit fatigue load
greater than those that would be observed in the field was selected to ensure
fatigue-dominated responses. The target upper limit of fatigue load was selected — a“high upper limit fatigue load,” the fatigue life of which should be shorter.
Additionally, the shear crack opening increased obviously due to the high upper limit
fatigue load, and the mixed-mode debonding induced by the shear crack phenomenon
can be observed clearly.
Therefore, in this test, the upper and lower load limits were chosen to correspond to
90% and 6%, respectively, of the experimental maximum load of the static-load
specimen CS-S. The fatigue load was applied as a 1-Hz sine wave of constant
amplitude. This frequency was selected because conventional infrastructure elements
such as bridges typically face loading at varying frequencies between 1 and 5 Hz.
High upper limit fatigue load typically implies that the maximum load exceeds theservice load levels of the beams [2.7]-[2.10] and occasionally exceeds the yield
capacity of the unstrengthened beams [2.11]-[2.13]. The benefit of these high upper
limit fatigue load applications is that relatively rapid fatigue failure of FRP
plate-strengthened beams (i.e., low cycle fatigue) can be observed. Therefore, in our
experimental investigation, high upper limit fatigue load was applied.
Displacements were measured at the mid-span, the loading points, and positions D4 to
D11 to compare the deflection differences of the concrete substrate and the CFRP
plate to confirm debonding. A load cell integrated into the actuator system was used torecord the loads and control the test. A schematic of the instrumentation used is shownin Fig. 2.5. Strains were measured on tensile bars at the mid-span (strain gauges B1,
B2, B3, and B4 in Fig. 2.3) and at the stirrup strains (S1, S2, S3, and S4). Strains werealso measured on the CFRP plate surface, using 2-mm-long strain gauges.
In fatigue testing, full-cycle recordings were obtained for the following cycles: at the
1st cycle and every 20th cycle up to 200 cycles, at every 200th cycle up to 1,000
cycles, at every 1,000th cycle up to 10,000 cycles, at every 10,000th cycle up to
100,000 cycles, and at every 80,000th cycle up to 1,000,000 cycles.

21

Fig. 2.5 Test setup

2.3

Experimental Results and Discussions

2.3.1 Static Test Results for Specimen RC-S
Specimen RC-S failed in shear, as shown in Fig. 2.6. Fig. 2.7 shows theload-deflection relations. The deflection increased from D1 to D2 due to the shear
deformation of the left-side span.
Table 2.3 lists the shear capacities calculated using the procedures given in the AIJ,
JSCE, and ACI codes. [2.14]-[2.16] The JSCE and ACI codes yield conservative
estimates for the shear capacity of the specimen, compared to the AIJ code. The
estimate from the AIJ code agreed well with the test result.

Fig. 2.6 Failure mode of specimen RC-S

22

250
RC-S
Load (kN)

200
150
100
50

D1
D2
D3

0

5

10
15
Deflection (mm)2025Fig. 2.7 Load-versus-deflection relation at the given cycle
Table 2.3 Comparisons of the values calculated with standard codes
Experimental
JSCE code
ACI code
AIJ code
result
Vcal
Vcal
Specimen
Vcal
Vexp
(kN)
(kN)
(kN)
(kN)
157.7
143.0
201.8
237.3
RC-S
*
*
(1.50)(1.66) *(1.18)*

Vexp/Vcal.

Fig. 2.8 presents the load-strain relationship for the stirrups at positions S1 to S4. As
shown in the figure, the stirrup strains at positions S2 and S3 reached the yield strainof 2,085 µ.
250
200

Yield strain

150
100

Load (kN)

50
S1

S2

250
0
200
150
100
50
S4

S3

0

0.5

1

1.5
0
0.5
Stirrups strain (%)

1

1.5

Fig. 2.8 Load-versus-stirrup strain relationship2322.3.2 Static Test Results for Specimen CS-S
Fig. 2.9 presents the failure mode of specimen CS-S. This specimen failed in shear,and peeling off of the CFRP plate from the concrete substrate at the region of theshear crack was observed. In other words, the delamination of the CFRP plate was
induced by the opening up (Mode I) of a shear crack, and a relative verticaldisplacement occurred between the two sides of the crack, thus confirming themixed-mode (peeling and shear) debonding induced by a shear crack.

Fig. 2.9 (a) Failure mode of specimen CS-S
Critical
shear
crack

Fig. 2.9 (b) Shear peeling mechanism due to shear crack
The load-deflection relationship is shown in Fig. 2.10. The deflection increased from
D1 to D2 due to the shear deformation of the left-side span as in the case of specimen
RC-S. Furthermore, it can be seen that the differences in the comparison of D8 andD9 and the comparison of D10 and D11 in response to the peeling off of the CFRP
plate were confirmed.

24

CS-S

200

D4
D5

CS-S
D6
D7

150

Load (kN)

100

250
CS-S

50
0
CS-S

200

D8
D9

200

D10
D11

150

Load (kN)

150

100

100
50
0

CS-S

50

D1
D2
D3

5

10
15
20
Deflection (mm)250

2 4 6 8 10 12 14 16 18 0 2 4 6 8 10 12 14 16 18 20
Deflection (mm)Fig. 2.10 Load-versus-deflection relationship at the given positions
Table 2.4 shows a comparison of the shear capacities calculated from the AIJ code,
JSCE code, and ACI code procedures and the test results. In comparison to theexperimental results for Specimen RC-S, a lower peak load was observed forSpecimen CS-S.
Table 2.4 Comparison of experimental results with values calculated from proceduresin standard codes
Experimental
AIJ code
JSCE code
ACI code
resultSpecimen
Vcal
Vcal
Vcal
Vexp
(kN)
(kN)
(kN)
(kN)
157.7
143.0
201.8
207.9
CS-S
*
*
(1.32)(1.45) *(1.03)*

Vexp/Vcal.

The load-tension bar strain and load-stirrup strain relations are shown in Fig. 2.11. Allof the measured strains increased with increasing load in the tension bars. However,none of the measured tension bar strains reached the yield strain of 2,146 µ at the
maximum load. For the load-stirrup strain relation, the S2 strain reached a yield strainof 2,085 µ.

25

200
150
100

Load (kN)

50

Yield strain
B1

B2

B3

B4

0
200
150
100
50

0

0.05 0.1 0.15 0.2 0.25

00.05 0.1 0.15 0.2 0.25 0.3

Bottom reinforcement strain (%)(a) Bottom reinforcement
200
150

Yield strain

100

Load (kN)

50
S1

S2

0
200
150
100
50
S3
0

0.05 0.1 0.15 0.2 0.25

S4
00.05 0.1 0.15 0.2 0.25 0.3

Stirrups strain (%)(b) Stirrup
Fig. 2.11 Load-versus-strain relationship
The strain distribution of the CFRP plate is shown in Fig. 2.12. As this figure shows,strains increase as the load increases. In addition, within the flexural span (0-200 mm),the same trend of a small decrease in strain along the plate with increasing load isevident. However, within the shear span (200-500 mm), a sudden decrease in strain isobserved with increasing load near the edge of beam, due to peeling of the CFRP
plate.

26

CFRP plate strain (%)

0.25
0.2
0.15
0.1
0.05
0
500
400
300
200
100
0
Strain gauges position from plate center (mm)3.6kN
21.5kN
42.1kN
60.3kN
81.4kN
103.3kN
123.5kN
143.2kN
160.4kN
178.2kN
197.6kN
207.9kN

Fig. 2.12 CFRP plate strain distribution

2.3.3 Fatigue Test Results for Specimen CS-F
Fig. 2.13 shows photos of the specimen at the 1st, 100th, 1,000th, and 2,800th load
cycles. The results of the fatigue test indicate that the specimen failed in shear at
2,800 fatigue cycles. The mixed-mode debonding phenomenon was observed aroundthe position of the shear crack produced at the bottom of the beam.

(a) After 1st cycle(b) After 100 cycles(c) After 1,000 cycles(d) After 2,800 cycles
Fig. 2.13 Photos of the specimen
Fig. 2.14 presents the displacement transitions for positions D1 to D11 at the upper
limit of the fatigue load level versus the number of cycles. The displacements
increased almost linearly with the number of cycles until near failure, when plotted on27

a log scale. The displacements increased rapidly for all measured positions near
failure. The displacement was larger in D9 than D8 because the CFRP plate peeled off
at the shear crack region after 1,000 fatigue cycles. This phenomenon is more evident
close to the shear crack opening with increasing fatigue cycles, as shown in thecomparison of D10 and D11.
20
D6
D7

Pmax=0.9Pult

10

20
D1
D2
D3

15

Pmax=0.9Pult

Displacement (mm)Displacement (mm)Pmax=0.9Pult

D4
D5

15

10
5
0 0
10

101

102
103
Number of cycles

5
0
D8
D9

15

D10
D11

Pmax=0.9Pult

Pmax=0.9Pult

10

104

5
0 0
10

101

102

103

100

101

102

103

104

Number of cycles

Fig. 2.14 Displacement-versus-fatigue cycle relationships at the given positions
The applied load-versus-deflection relationships for all fatigue cycles at the mid-span(D2) and the loading points (D1 and D3) are shown in Fig. 2.15. The deflection
response was D3>D2>D1 at all fatigue cycles, due to the CFRP sheet being confined
opposite the shear span of the test part. Intervening cycles are also shown to provide
an indication of the damage accumulation and the stiffness degradation. In this test,
failure occurred after only 2,800 cycles at the upper-limit load.
250
Fatigue load
Static load

200
150
100
50

D1

0
Fatigue load
Static load

Load (kN)

200
150
100
50

D2

0
Fatigue load
Static load

200
150
100
50
0

D3

2

4

6 8 10 12 14 16 18 20
Deflection (mm)Fig. 2.15 Applied load-versus-deflection relations
28

Fig. 2.16 presents the applied load-versus-displacement relationships for points D4 to
D11. As previously stated, the aim is to investigate CFRP plate debonding in mixed
mode induced by a shear crack. Although the stiffness did not change remarkably, theresidual and maximum displacements seemed to increase as the number of cycles
increased. A sudden increase in the displacement occurred at some points due to shear
crack opening, which is known to lead to increased residual deformations. Fig. 2.17
presents the transitions of displacements at positions D10 and D11 of specimen CS-F.
The difference in displacement between D10 and D11, which was first observed at
838 steps (after 700 cycles) in response to the beginning of the peeling off of the
CFRP plate, was confirmed.
250

250
Fatigue load
Static load

150

150

100

100

50

D4

0
Fatigue load
Static load

200

50

100

100
50

D5

2

4

6 8 10 12 14 16 18 20
Displacement (mm)

250

100

0
Fatigue load
Static load

100

100

6

Fatigue load
Static load

50

D9

4

D10

200
150

2

Fatigue load
Static load

0150

8 10 12 14 16 18 20
Displacement (mm)

D11

0

2

4

6 8 10 12 14 16 18 20
Displacement (mm)Fig. 2.16 Applied load-versus-displacement relations
20
Displacement (mm)0

6 8 10 12 14 16 18 20
Displacement (mm)50

D8Load (kN)

Load (kN)

150

50

4

200

100

200

2

250

150

50

D7

0

Fatigue load
Static load

200

Fatigue load
Static load

200
150

0

D6

0

150

50

Fatigue load
Static load

200

Load (kN)

Load (kN)

200

D10
D11
10

0

200

400

600

800

1000

Measurement step

Fig. 2.17 Transitions of displacements D10 and D1129

Fig. 2.18 presents the strain in the tension bars, stirrups, and CFRP plate as a relationof the number of cycles at the upper limit of the fatigue loading. The strain in thetension bars and stirrups was observed to remain almost constant as the number offatigue cycles increased. The stirrups strain magnitudes were in the order of
S3>S2>S4>S1 due to the path of the shear crack. The plate strains at locations C4, C5,
and C6 indicate slow degradation by peeling of the CFRP plate due to shear cracking
that occurred during the first load cycle. As the number of load cycles increased, theshear crack opening caused the CFRP plate peeling off, resulting in sudden drops at
positions C1, C2, and C3 due to relative vertical displacement through the shear crack
after 700 cycles.

0.1

0
B1
B2
B3
B4

-0.1
-0.2 0
10

1

10

2

3

10
10
Number of cycles

0.2

0
S1
S2
S3
S4

-0.1

4

10

Strain (%)

0.1

Strain (%)

0.2

Strain (%)

0.2-0.2 0
10

1

10

2

3

10
10
Number of cycles

C1
C2
C3
C4
C5
C6

0.1

0
4

10

100

101

102
103
Number of cycles

104(a) Bottom reinforcement(b) Stirrups(c) CFRP plate
Fig. 2.18 Strain-versus-fatigue cycle relationships
The CFRP plate strain distributions at the 1st, 100th, 1,000th, and 2,000th cycles areshown in Fig. 2.19. The CFRP plate strain increased as the applied load increased, as
shown by all gauges along the plate. The longitudinal strain distributions in the CFRP
plate tended to become closer after the shear crack occurred (at 119 kN) with auniform decrease in the strains. In addition, as illustrated in the figure, the peeling offof the CFRP plate moved from the plate end to the specimen center, corresponding to
the shear crack opening, as the number of fatigue cycles increased.

0.1

0
500
400
300
200
100
0
Location of strain gauges from center of plate (mm)0.2

Strain (%)

After 1000 cycles

0.1

0.2

190.6kN
169.5kN
147.0kN
120.5kN
96.6kN
74.9kN
46.4kN
12.1kN

After 100 cycles

Strain (%)

Strain (%)

After 1 cycle

0.1

0
500
400
300
200
100
0
Location of strain gauges from center of plate (mm)0.2

186.5kN
166.3kN
136.1kN
98.7kN
62.3kN
33.3kN
16.7kN

After 2000 cycles

Strain (%)

0.2

0.1

0
500
400
300
200
100
0
Location of strain gauges from center of plate (mm)

0
500
400
300
200
100
0
Location of strain gauges from center of plate (mm)Fig. 2.19 CFRP plate strain distributions versus fatigue cycles

30

185.9kN
172.6kN
135.2kN
109.9kN
85.0kN
61.2kN
32.3kN
15.8kN185.5kN
169.3kN
142.1kN
118.5kN
80.3kN
46.9kN
23.6kN
16.2kN

2.4

Conclusions

All specimens failed in shear. CFRP plate debonding as a result of mixed-mode
fracture induced by a shear crack was verified. In flexurally strengthened concretebeams, when delamination is induced by the opening of a shear crack, a relative
vertical displacement occurs between the two sides of the crack. The failure involves
both interfacial shear and peeling (a combination of Modes I and II), which in turnincreases the probability of premature local collapse. Hence, the bond performance of
this type of structure when strengthened by a CFRP plate depends not only on theshear bond strength of the interface but also on the combined effect of the shear bondand peeling. In evaluating the performance of the externally bonded CFRP plate
strengthening technique, the interfacial bond strength between the CFRP plate and theconcrete under different failure modes is the crucial importance.

31

CHAPTER 3
Bond Behavior between CFRP Plates and Concrete
under Fatigue Loading
3.1. Introduction
Debonding failure is often studied in direct shear testing, which involves a CFRP
plate bonded to a concrete prism. By pulling the CFRP plate in the direction of its
length, the bond capacity can be determined. The maximum bond capacity for a given
CFRP plate width and thickness can be determined by performing direct shear testingof members with different CFRP plate bond lengths. Many studies have examined thebond behavior of FRP-concrete systems. The Japan Concrete Institute (JCI)
established a technical committee on retrofitting technology (2001 to 2003) that
focused on the interface bond properties between existing concrete structures andretrofitting materials for both adhesive bonding and overlaying retrofitting
technologies. The “Guide for the Design and Construction of Externally Bonded FRP
Systems for Strengthening Concrete Structures” (ACI 440.2R-2) provides guidanceon the selection, design, and installation of FRP systems for externally strengthening
concrete structures. Information on the material properties, design, installation,
quality control, and maintenance of FRP systems used as external reinforcement ispresented.
The behavior of bonded FRP systems under fatigue loading is, however, expected todegrade relative to their statically loaded counterparts. Thus, designs for
FRP-reinforced concrete structures should account for bond failure associated withdeterioration due to fatigue loads. Fatigue loading is recognized as having adeleterious effect on the performance of externally bonded FRP retrofit systems.
Although many studies have reported on the fatigue behavior of FRP sheet-concrete
systems, few of them have focused on the fatigue behavior of FRP plate-concrete
systems.
The tests described in this chapter are the first in which the bond behavior of CFRP
plates bonded to concrete has been investigated under fatigue loading. Fatigue testingof double-faced bond specimens was carried out. The fatigue behavior of the bondsurface between the CFRP plates and the concrete can be characterized by an S-Ndiagram, which represents the relationship between the bond stress and the number ofcycles at debonding, on a semi-logarithmic scale, based on the experimental results of
the influence of the bond behavior for different concrete strengths, types of CFRP
plates, and upper fatigue loads. The different debonding modes for the various
fracturing modes are also discussed.
In strengthening RC beams by external bonding of FRP plates, the performance of the32

FRP-to-concrete interface in mixed-mode fracture is the crucial importance. Indeed, anumber of debonding failures of FRP-strengthened concrete members have beencaused by shear and peeling of the FRP from the concrete. To clarify the details of
peeling phenomenon, transverse displacements were measured.
Finally, this chapter proposes a new methodology for assessing fatigue bond damage
based on local bond stress-slip relationships for the purpose of studying the interfacial
behavior of CFRP plate-to-concrete interface under fatigue loading, the relationship ofthe bond behavior to the number of fatigue cycles (N), and the effect of the unloading
stiffness ki.

3.2. Experimental Program for Static Loading
3.2.1. Specimens
Specimen details are shown in Fig. 3.1. In this experimental program, prism
specimens with cross-sectional sizes of 150 mm ×150 mm and lengths of 800 mm
were used. The two steel bars had no connection at the center of the specimen. A
crack was introduced at the notch after attaching the CFRP plate. Thus, the two prisms
were connected only through the CFRP plates. The CFRP plates were bonded at the
opposite sides of the specimens. An epoxy adhesive was used to bond the CFRP plates.
One of the sides of each specimen was wrapped by a CFRP sheet, which permitted thedelamination of the CFRP plate on the opposite side only. The CFRP plate bondlength used for this experiment was set to 400 mm. The CFRP plate width was 50 mm.
Nine specimens were tested, as shown in Table 3.1. The test variables were theconcrete compressive strength and the CFRP plate type.
Table 3.1 Specimen list
Concrete strength
Specimens
CFRP plate
Remarks(MPa)
High-strength
C13HS-M
GM510
13.5
C13HE-M
High-stiffness
HM520
C13HE-M-C
With confinement jig
C21HS-M
High-strength
C21HS-M-1
GM510
21
C21HS-M-2
High-stiffness
C21HE-M
HM520
C36HS-M
High-strength
36
GM510
C36HE-M-

33

Fig. 3.1 Specimen details

3.2.2. Material Properties
Table 3.2 presents the properties of the CFRP plates used in this experiment. The
values were obtained from the manufacturer. High-strength and high-stiffness CFRP
plates were used. The concrete strengths are provided in Table 3.3.
Table 3.2 CFRP plate properties
Thickness Elastic modulus Tensile strength
CFRP plate type Name
(mm)
(GPa)
(MPa)
High strength GM510
1.0
156
2,400
High stiffness HM520
2.0
450
1,200
Table 3.3 Concrete properties
Compressive strength 1/3 Secant modulus Splitting strength
Concrete Type
(MPa)
(GPa)
(MPa)
Target 13.5 MPa
21.2
21.4
1.96
25.0
22.3
2.40
Target 21 MPa
25.6
22.8
2.36
Target 36 MPa
39.5
24.9
3.01

3.2.3.

Loading and Measurement

In this experiment, a 1-MN actuator was used to produce static loading. Eachspecimen was set on Teflon sheets to reduce friction with the table. The total
displacement and crack width at the center were measured using linear variabledisplacement transducers (LVDTs), as shown in Fig. 3.2. The strain distribution was
obtained from nine strain gauges set on the CFRP plates on one face (the gauge face)at intervals of 50 mm, one gauge on the opposite side (the no-gauge face) at the centerof the specimen, and two pi gauges set on the notch. To investigate peeling of the
CFRP plate, the transverse displacements were measured. The instrumentation details
are presented in section 3.3.5.
34

Because specimen C36HE-F75 (see Section 3.3.3) failed by concrete splitting andpulling out of the steel bar at an early stage in the loading cycles, a concreteconfinement jig, shown in Fig. 3.3, was used for specimen C13HE-M-C and
C21HE-F75-C to prevent splitting failure. Specimen C13HE-M-C was used toinvestigate the influence of the confinement jig under static loading with specimen
C13HE-M.

Fig. 3.2 Data acquisition schematic

Bolt

Bolt
CFRP
plate
Confinement
jig

Bolt

M24 steel bar

Concrete block

CFRP
plate
Bolt

Section of confinement jig

Fig. 3.3 Confinement jig to prevent concrete splitting

3.2.4. Experimental Results
3.2.4.1.

Failure Progress

All nine specimens were submitted to tensile force until total failure of the bondsystem occurred. The typical specimen failures are presented in Fig. 3.4. The HE
specimen interface layers were thicker than those of the HS specimens. All of thestatic load specimen initial failures were on the concrete face. Specimen C36HS-M
was debonded from the concrete face near the notch, and the left part was debonded
from the adhesive face.

35

Fig. 3.4 Typical failure under static loading36

3.2.4.2.

Load-Displacement Relationships

The load-displacement graph was plotted using the total displacement (δ total) andcrack width (δ cr) data obtained. The total displacement is the average of thedisplacements at two opposite edges, and the crack width is the average of the widths
from the two pi gauges. These graphs are presented in Fig. 3.5, in which the behaviorof the specimens during the test is shown in greater detail. The crack width in the HS
specimen at the maximum load was approximately 0.2 mm greater than in the HE
specimen. However, the maximum load at failure was significantly lower than that of
the HE specimen.
100

100

C13HS-M

P (kN)

P (kN)

C13HS-M

80

80
60
40

60
40
20

20
0

0

0.2

0.4

0.6

0.8

0

1

0

0.2

100

C13HE-M

60
40
20

60
40
20

0

0.2

0.4

0.6

0.8

0

1

0

0.2

0.4

100

80

0.6

0.8

1

δcr (mm)100

C13HE-M-C

80

C13HE-M-C

P (kN)

P (kN)

1

C13HE-Mδtotal (mm)

60
40

60
40
20

20
0

0.8

80
P (kN)

P (kN)

8000.6

δcr (mm)δtotal (mm)
100

0.4

0

0.2

0.4

0.6

0.8

0

1

δtotal (mm)

0

0.2

0.4

0.6

δcr (mm)Fig. 3.5. (a) Load-displacement relationships

37

0.8

1

100

100

C21HS-M

60
40

60
40

20
0

20
0

0.2

0.4

0.6
δtotal (mm)

100

0.8

0

1

P (kN)

P (kN)

20
0

0.2

0.4

0.6
δtotal (mm)

0.8

0.8

1

C21HS-M-1

60
40

0

1

0

0.2

0.4

0.6

0.8

1

δcr (mm)100

C21HS-M-2

80

C21HS-M-2

80
P (kN)

P (kN)

0.6

20

100

60
40
20

60
40
20

0

0.2

0.4

0.6

 total (mm)

100

0.8

0

1

0

0.2

0.4

0.6

 cr (mm)100

C21HE-M

80

0.8

1

C21HE-M

80
P (kN)

P (kN)

0.4

80

40

60
40
20
0

0.2

100

C21HS-M-1

60

0

0

δcr (mm)80

0C21HS-M

80
P (kN)

P (kN)

80

60
40
20

0

0.2

0.4

0.6

0.8

0

1

0

0.2

0.4

0.6

δcr (mm)δtotal (mm)Fig. 3.5 (b) Load-displacement relationships

38

0.8

1

100

100
C36HS-M

60
40
20
0

0

0.2

0.4

0.6
δtotal (mm)

40

0.8

0

1

0

0.2

0.4

0.6

0.8

1

δcr (mm)100

80

C36HE-M

80

C36HE-M
P (kN)

P (kN)

60

20

100

60
40
20
0

C36HS-M

80
P (kN)

P (kN)

80

60
40
20

0

0.2

0.4

0.6
δtotal (mm)

0.8

0

1

0

0.2

0.4

0.6

0.8

1

δcr (mm)Fig. 3.5 (c) Load-displacement relationships

3.2.4.3.

Bond Strength

Many methods for evaluating the bond strength between CFRP sheets and concrete
have been proposed. Some of these methods are based on empirical relations
calibrated with experimental data (Maeda et al. 1997 [3.1]; Tanaka 1996 [3.2]). Other
methods are based on fracture mechanics theories, with numerous parameters
calibrated with experimental data (Yuan and Wu 1999 [3.3]; Kanakubo 2003[3.4]).
The bond strength between a CFRP plate and concrete can be calculated using theprediction formula proposed by Matsunaga (2008) [3.5], shown below (Table 3.4).

 b,max  2.5   B 0.23
le 

2  t f  E f  Se

(3.1)

ke  b,max(3.2)

Pb  ke  b,max  bf  le (lb  le )(3.3)

Pb  k  b,max  bf  lb (lb  le )(3.4)

1  kel1  ke cos( b  ) 
2
le
2

(3.5)

k

where the maximum local bond stress is τb,max, the concrete compressive strength is σB,
the effective bond length is le, the width is bf, the thickness is tf, the elastic modulus of
the CFRP plate is Ef, the local slip of the effective bond area is se (0.234 mm), the39

stress coefficient of the equivalent bond stress block (EBSB) in the case of aneffective bond length is ke (0.428), the bond length is lb, the bond strength is Pb, andthe stress coefficient of the EBSB is k.
Table 3.4 Bond strength with calculated values
Calculated value
Specimenseτb,maxλflekek(mm) (MPa) (mm) (mm)C13HS-M 0.428
0.234 5.06
30,812
184
C13HE-M 0.428 0.440 0.234 5.06 177,763 441
C13HE-M-C 0.428 0.440 0.234 5.06 177,763 441
C21HS-M 0.428
0.234 5.24
29,734180
C21HS-M-1 0.428
0.234 5.27
29,734180
C21HS-M-2 0.428
0.234 5.27
29,600180
C21HE-M 0.428 0.436 0.234 5.24 171,544 433
C36HS-M 0.428
0.234 5.82
26,804
171
C36HE-M 0.428 0.429 0.234 5.82 154,639 411

Pmax
(kN)
39.85
89.06
89.06
40.37
40.60
40.60
91.39
42.60
99.87

The calculated and experimental results are compared in Table 3.5. The ratios of theexperimental to calculated values are close to one, which indicates that theexperimental values are nearly the same as the calculated values.
Table 3.5 Comparison of the calculated and experimental values
Specimen
Calculated value Experimental value
Experimental/Calculated
Pmax (kN)
Pmax (kN)
39.85
C13HS-M
37.90
0.951
89.06
C13HE-M
87.24
0.980
89.06
C13HE-M-C
96.01
1.078
40.37
C21HS-M
42.97
1.064
40.60
C21HS-M-1
41.94
1.033
40.60
C21HS-M-2
39.99
0.985
91.39
C21HE-M
91.92
1.006
42.60
C36HS-M
49.84
1.170
99.87
C36HE-M
104.461.046

3.2.4.4.

Influence of the Confinement Jig

Because specimen C36HE-F75 (see Section 3.3.3) failed due to concrete splitting andpulling out of the steel bar at the early loading cycle, a concrete confinement jig,shown in Fig. 3.3, was installed for specimen C13HE-M-C and C21HE-F75-C toprevent splitting failure. Specimen C13HE-M-C was tested to investigate theinfluence of the confinement jig under static loading with specimen C13HE-M. The
results indicated that the bond strength of C13HE-M-C was 10% higher than that of
C13HE-M. Fig. 3.6 presents the P-δ curves for this specimen.
40

100

100

80

80

80

40

60
40

20

20

0

0

0

0.2

0.4

0.6

0.8

1

δtotal (mm)100

C13HE-M

60
40

0.2

0.4

0.6

0.8

40

0

0

1

60

20

20
0

C13HE-M-C

80
P (kN)

60

C13HE-M-C

P (kN)C13HE-M

P (kN)

P (kN)

100

0

0.2

0.4

0.6

0.8

1

δcr (mm)δtotal (mm)

0

0.2

0.4

0.6

0.8

1

δcr (mm)Fig. 3.6. P-δ curves

3.2.4.5.

Strain Distribution of the CFRP Plate

The data obtained from the strain gauges on the CFRP plate were used to examine
strain distributions. Fig. 3.7 presents the strain distributions of all specimens under
static loading. Certain portions of the strain distributions had larger slopes where theactive bonding stress exists. The local strain of the HS specimen was greater than thatof the HE specimen, and the strain was nearly zero at the load end.
0.6

0.6
C13HE-M

0.3
0.2
0.1
0

0.4
0.3
0.2
0.1

100
200
300
Distance from the notch to load end

0

0.3
0.2

0.3
0.2

0

100
200
300
Distance from the notch to load end

0.6

100
200
300
Distance from the notch to load end

0.6
C36HE-M

0.5

0.4

εCF (%)εCF (%)

0.4

0.1

0.1

0.5

C21HS-M

0.5

εCF (%)εCF (%)

C21HE-M

0.4

0

100
200
300
Distance from the notch to load end

0.6

0.6
0.5

C13HS-M

0.5

0.4

εCF (%)εCF (%)

0.5

0.3
0.2
0.1

C36HS-M

0.4
0.3
0.2
0.1

0
100
200
300
Distance from the notch to load end(mm)

0
100
200
300
Distance from the notch to load end(mm)Fig. 3.7 Strain distribution

41

3.2.4.6.

Local Bond Stress and Slip

The difference in the tensile force was obtained from the strain at section i and therelative strain in the preceding section i-1. The average bond stress at section i, τb,i,
was calculated by dividing the difference in the tensile force by the surface area of theplate, as shown in Equation (3.6).

 b,i ( f , i   f , i 1 )  t f  E f( bi  6  13)

lb

(3.6)

where
 f ,i= strain in the CFRP plate at section itf= thickness of the CFRP plateEf= elastic modulus of the CFRP platelb= interval between gauges (= 50 mm)

The slip of section i, si, is the sum of the differences between the elongation of the
CFRP and that of the equivalent section composed of concrete, an epoxy layer, and asteel bar, measured from the free end of the plate (the loaded end of the specimen) to
section i. The relative displacement between the concrete and the plate at the local endof the plate was assumed to be zero. The slip was calculated using the following
equations:si  si 1  ( f ,i   m,i ) ( b,i  6 13, s1  0)

 f ,i  f ,i   f ,i 12

 lb   f ,i1 lb 
 m,i  m,i 1 m,i  lb   m,i lb
2

P

 m,i  m,i1

 2  b,i  bf lb
Am  Em(  m,1  Pm,1 / Am  Em , Pm,1  Pload )where f ,i= elongation of the CFRP plate at section i

 m,i= elongation of the equivalent section i
42

(3.7)
(3.8)

(3.9)

(3.10)

 m,i= strain of the equivalent section i

Pm , i= force acting on the equivalent section ibf= width of the plate

Pload= tensile load applied by the loading machineAm  E m = stiffness of the equivalent concrete section= Ac  E c  A s  E s  Aad  E ad

A c , A s , A a d =cross-sectional areas of concrete, steel, and adhesive, respectively
E c , E s , E a d =elastic modulus of concrete, steel, and adhesive, respectively

Local bond stresses versus slip (τb vs. s) graphs for each gauge interval were plotted
after calculating all of the data. Fig. 3.8 and Fig. 3.9 show the positions of the strain
gauges and the local bond stress-slip curves, respectively. The CFRP plate strainschanged only slightly at strain gauge positions 10 and 13. Therefore, the curves are
not visible in these position graphs.
Notch
CFRP Plate
7

8

M24

9 10 11 12 13150

6Strain gauge
50 50 50 50 50 50 50 50

Fig. 3.8 Positions of strain gauges
8

8

2
0

0.1
Slip (mm)0.2

C13HE-M-C

6-7
7-8
8-9
9-10
10-11
11-12
12-13

6
4

Localτ(MPa)4Localτ(MPa)

Localτ(MPa)6

8

C13HE-M

6-7
7-8
8-9
9-10
10-11
11-12
12-13

C13HS-M20

0.1
Slip (mm)

0.2

2
0.1
Slip (mm)0.2

8C21HE-M

6
4

Localτ(MPa)

6-7
7-8
8-9
9-10
10-11
11-12
12-13

C21HS-M
Localτ(MPa)

4

0

8

2
0

6-7
7-8
8-9
9-10
10-11
11-12
12-13

6

0.1
Slip (mm)

4
2
0

0.2

Fig. 3.9 (a) Local bond stress and slip curves
43

6-7
7-8
8-9
9-10
10-11
11-12
12-13

6

0.1
Slip (mm)

0.2

8

8

C36HE-M

6-7
7-8
8-9
9-10
10-11
11-12
12-13

6
4

Localτ(MPa)

Localτ(MPa)C36HS-M20

0.1
Slip (mm)

4
2
0

0.2

6-7
7-8
8-9
9-10
10-11
11-12
12-13

6

0.1
Slip (mm)0.2

Fig. 3.9 (b) Local bond stress and slip curves
Fig. 3.10 presents comparisons of the local bond stress-slip relationships obtained forstatic loading. The formula used is the Popovics model, as shown below. [3.6]The experimental result fits the Popovics model closely, confirming that the Popovics
model represents the local bond stress-slip relationship well.
bsn(3.11) b ,m ax

s m ax( n  1)  ( s / s m ax ) n

 b,max =2.5σB0.23(3.12)

smax =0.0429 mm(3.13)

n=3
where τb,max = maximum local bond stress, smax = slip at τb,max, and n = 3.

(3.14)

8
C13HE-M-C

6-7
7-8
8-9
9-10
10-11
11-12
12-13

C13HS-M
6
4

Localτ(MPa)

Localτ(MPa)8Popovics model

2
0

0.1
Slip (mm)40C36HS-M

Popovics model2
0.1
Slip (mm)0.1
Slip (mm)0.2

8Localτ(MPa)

Localτ(MPa)6

Popovics model

2
0

6-7
7-8
8-9
9-10
10-11
11-12
12-13

C21HS-M

4

0.2

8

6-7
7-8
8-9
9-10
10-11
11-12
12-13

6

0.2

6-7
7-8
8-9
9-10
10-11
11-12
12-13

6
4

Popovice model

2
0

0.1
Slip (mm)Fig. 3.10 Popovics model comparisons

44

0.2

3.3. Experimental Program for Fatigue Loading
3.3.1. Specimens
The specimens used for the fatigue load testing were the same size as those used forthe static load testing. A total of 15 specimens were tested. The specimens are listed inTable 3.6. The test variables were the concrete compressive strength, the CFRP plate
type, and the upper limit of the fatigue loading, which had values of 50%, 60%, 70%,
75%, 80%, 85%, and 90%.
Table 3.6 Specimen list
Fatigue load*
Concrete strength
Specimens
CFRP plate(MPa)
Upper limit Lower limit
C13HS-F70
70%
10%High-strength
C13HS-F80
80%
10%
13.5
GM510
C13HS-F90
90%
10%
C21HS-F60
60%
10%
C21HS-F70
70%
10%
C21HS-F70-T
70%
10%High-strength
C21HS-F75-T
75%
10%
GM510
21
C21HS-F80
80%
10%
C21HS-F80-T
80%
10%
C21HS-F85-T
85%
10%High-stiffness
C21HE-F75-C
75%
10%
HM520
C36HS-F50
50%
10%High-strength
C36HS-F60
60%
10%
GM510
C36HS-F70
70%
10%
36
High-stiffness
C36HE-F75
75%
10%
HM520
* Percentage of the bond strength under static load

3.3.2. Material Properties
All of the materials used in the fatigue tests were the same as those used in the static
tests. Table 3.7 and Table 3.8 listed the properties of the CFRP plates and the concrete,respectively.
Table 3.7 CFRP plate properties
Thickness Elastic modulus Tensile strength
CFRP plate type Name
(mm)
(GPa)
(MPa)
High strength GM510
1.0
156
2,400
High stiffness HM520
2.0
450
1,200
45

Table 3.8 Concrete properties
Compressive strength 1/3 Secant modulus Splitting strength
Concrete Type
(MPa)
(GPa)
(MPa)
Target 13.5 MPa
21.2
21.4
1.96
25.0
22.3
2.40
Target 21 MPa
25.6
22.8
2.36
Target 36 MPa
39.5
24.9
3.01

3.3.3. Loading and Measurement
A 1-MN actuator was used for loading in the tests. Each specimen was set on a Teflon
sheet to reduce friction with the table. The total displacement and crack width at thecenter of the specimen were measured using LVDTs, as same in the static tests. The
details of the testing setup were also the same as in the static tests. The strain
distribution was obtained from nine strain gauges with length of 2 mm, placed on the
CFRP plates on one face at intervals of 50 mm. One gauge was placed on the opposite
side at the specimen center. Two pi gauges were set at the position of the notch.
The repetition frequency of the fatigue loading was set to 1 Hz. This frequency waschosen because conventional infrastructure elements, such as bridges, typicallyexperience loading at varying frequencies of 1-5 Hz. Sinusoidal loading was used.
The upper-limit fatigue loadings were set to 50%, 60%, 70%, 75%, 80%, and 90% of
the bond strength under static loading (Pmax), which was among the load-carrying
capacity parameters investigated in the static tests. The lower limit of the fatigue
loading was set to 10% in all experiments. Up to one million fatigue cycles wereapplied if debonding did not occur.
Recordings of full cycles were taken for the following cycles: at the first cycle andevery 20th cycle up to 200 cycles, at every 200th cycle up to 1,000 cycles, at every
1,000th cycle up to 10,000 cycles, at every 10,000th cycle up to 100,000 cycles, andat every 80,000th cycle up to 1,000,000 cycles, as shown in Table 3.9. Static
post-fatigue loading to failure was carried out for those specimens that did not failunder fatigue loading.
Table 3.9 Measurement intervals
CyclesMeasurement interval

1
to 200to 1,000
to 10,000
to 100,000
to 1,000,000

first cycle
per 20 cycles
per 200 cycles
per 1,000 cycles
per 10,000 cycles
per 80,000 cycles

46Because specimen C36HE-F75 failed due to concrete splitting and pulling out of thesteel bar early in the testing process, as shown in Fig. 3.11, the concrete confinement
jig was set for specimen C21HE-F75-C to prevent splitting failure, as shown in Fig.
3.12.

Fig. 3.11 Splitting failure of specimen C36HE-F75

Fig. 3.12 Specimen C21HE-F75-C with a confinement jig and the failure surface

3.3.4. Experimental Results
3.3.4.1.

Fatigue Progress

The different debonding modes that occurred at different upper limits of fatigue
loading and for different CFRP plate types and concrete strengths were observed. Allof the fatigue specimens’ experimental results are summarized in Table 3.10, andrepresentative photographs are shown in Fig. 3.13. The upper-limit bond stress τup in
Table 3.10 is calculated from Eq. (3.15):

up  Pup / 2bf lb(3.15-1)

low  Plow / 2bf lb(3.15-2)

where Pup = the upper-limit load, Plow = the lower-limit load, bf = the width of the
CFRP plate, and lb= the bond length of the CFRP plate.

47

Table 3.10 Fatigue test results

SpecimenUpper-limit
load Pup(kN)

Lower-limit
load Plow(kN)

Upper-limit
bond stress
τup
(MPa)

C13HS-F70

26.53

3.97

0.663

Lowerlimitbondstressτlow(MPa)0.0993

C13HS-F80

30.32

3.97

0.758

0.0993

256,819

C13HS-F90

34.11

3.97

0.853

0.0993164,012

C21HS-F60

25.78

4.30

0.645

0.1075

C21HS-F70

30.08

4.30

0.752

0.1075No
failure*28,191

C21HS-F70-T

28.68

4.10

0.717

0.102561,313

C21HS-F75-T

30.72

4.10

0.768

0.1025

5,573

C21HS-F80

34.38

4.30

0.860

0.1075

1,779

C21HS-F80-T

32.77

4.10

0.819

0.1025400

C21HS-F85-T
C21HE-F75C

34.82

4.10

0.871

0.1025

68.94

9.19

1.724

0.2298

C36HS-F50

24.92

4.98

0.623

0.1245

C36HS-F60

29.90

4.98

0.748

0.1245600
Nofailure*No
failure*205,175

C36HS-F70

34.89

4.98

0.872

0.1245

4,145

C36HE-F75

78.35

10.45

1.959

0.2613-

Failurecycles127,445

Failure mode

Debonding at
adhesive layer
followed bypeeling off ofthe concrete
Debonding at
the adhesive
layer followedby peeling offof the concrete
Debonding at
the concrete
layer
Debonding at
the adhesive
layerConcrete
splitting* Up to one million cycles
Basically, the bond force-transferring capacity of the CFRP/concrete interface tended
to decrease with the concrete’s compressive strength. In contrast, the failure cycles of
specimen C13HS-F70, C13HS-F80, and C13HS-F90 were 127,445 cycles, 256,819
cycles, and 164,012 cycles, respectively. It was found that the rule that a shorter
fatigue life would result from applying high-level fatigue load to these specimens was
not followed.
As we know, for static failures of CFRP/concrete bonded interface, local interface
debonding is initiated with an increase in the tensile force in CFRP plates. Once thepullout force in CFRP plates reaches a critical value, macro-debonding occurs,
leading to overall failure of the entire interface. However, for the fatigue failures of
CFRP/concrete bonded interfaces, local interface debonding can be caused by agradual increase of the local slip; even the tensile stress in CFRP plates is kept at a
certain value that is smaller than the maximum pullout force. The local interface
debonding can propagate with the increase in fatigue cycles. Once the maximum bondforce that the left bonded length can bear becomes less than the tensile force applied
to the CFRP plates, a fatigue failure of the entire bonded interface will occur.
48

The failure face of specimen C13HS-F90 was divided into two parts. First, debonding
started at the notch at the concrete surface and propagated to the load end. Second, as
the number of fatigue cycles increased, the failure face changed to the adhesive face
until the CFRP plate was completely debonded. The failure face of specimen
C21HS-F80 was entirely on the concrete surface. The failure face mechanism ofspecimen C36HS-F70 was nearly the same as that of specimen C13HS-F90, exceptthat the failure face on the concrete surface was less than that of C13HS-F90.
Specimen C36HS-F50 remained unchanged through one million cycles, after which it
was subject to static loading until failure. Up to the application of one million cycles,
the debonding was mainly from the adhesive face. Thus, after complete debonding,two parts of the failure face were observed.

Failure cycle: 127,445

Failure cycle: 256,819

Failure cycle: 164,012

Post-fatigue failure

Failure cycle: 28,191

Failure cycle: 1,779

Post-fatigue failure

Failure cycle: 205,175

Failure cycle: 4,145

Fig. 3.13 Typical failure surfaces after fatigue loading

3.3.4.2.

Load and Displacement Relationships

Fig. 3.14 presents the load-crack width curves obtained at major measurement
intervals for all specimens. The hysteresis curves of all specimens are similar
throughout the one-million-cycle tests. For any given cycle, the load-crack width
curves exhibit an ascending branch and a descending branch that are close to eachother. The area enclosed by the loops from B (200 cycles) to D (1,000 cycles) does
not change significantly. For the specimens subjected to low-level (≤50%) fatigue
loading and the HE specimens, the slopes of the early loops decrease slightly in theearly cycles and then remain unchanged thereafter, indicating a slight reduction in thebond stiffness at the beginning that does not deteriorate further during subsequent
cycles. However, for the specimens subjected to high-level (>50%) fatigue loading,the slopes of the loops decrease gradually until the end of the tests, indicating acontinuous degradation in the bond stiffness.
49

80

80
C36HS-F50

C36HS-F60
60

Load P (kN)

Load P (kN)

60

40

40
A-1st cycle
B-After 200 cycles
C-After 1000 cycles
D-After 10000 cycles
E-After 100000 cycles
F-After 1000000 cycles

AB C D E F

20
0

0.1

0.2

0.3

0.4

0.5

AB C D E
A-1st cycle
B-After 200 cycles
C-After 1000 cycles
D-After 10000 cycles
E-After 100000 cycles

20
0

0.6

0.1

0.2

0.3

0.4

0.5

0.6

δcr (mm)δcr (mm)
80

80

AB C

C36HS-F70

Load P (kN)

Load P (kN)

40

40

AB C

20
0.1

0.2

0.3

0.4

0.5

A- 1st cycle
B-After 60 cycles
C-After 100 cycles

20

A-1st cycle
B-After 200 cycles
C-After 1000 cycles

0

C36HE-F75

60

60

0

0.6

0.1

0.2

0.3

0.4

0.5

0.6

δcr (mm)δcr (mm)Fig. 3.14 (a) Load-crack width curves

40

A

B

40

C

20

A-1st cycle
B-After 200 cycles
C-After 400 cycles

0.1

0.2

0.3

δcr (mm)

0.4

0.5

A

0

0.6

0.1

0.2

0.3

0.4

0.5

AB C

A-1st cycle
B-After 1000 cycles
C-After 3000 cycles

0.2

0.3

0.4

0.5

60
40

0.6

0

0

A-1st cycle
B-After 200 cycles
C-After 300 cycles

0.1

0.2

0.5

0.6

C21HS-F70

40

A

BC

D

EF

A

B C D

E
A-1st cycle
B-After 200 cycles
C-After 1000 cycles
D-After 10000 cycles
E-After 100000 cycles

20

0.1

0.2

0.3

δcr (mm)

0.4

0.5

0

0.6

0.1

0.2

0.3

0.4

0.5

0.6

δcr (mm)80
AB C D E

C21HE-F75-C

A BCD

E

F

20
0.1

0.2

Load P (kN)

60

40

40

A-1st cycle
B-After 200 cycles
C-After 1000 cycles
D-After 10000 cycles
E-After 100000 cycles
F-After 1000000 cycles

0.3

0.4

0.5

A-1st cycle
B-After 200 cycles
C-After 1000 cycles
D-After 10000 cycles
E-After 100000 cycles

20
0

0.6

0.1

0.2

Load P (kN)

40

A BCD
A-1st cycle
B-After 200 cycles
C-After 1000 cycles
D-After 10000 cycles

0.3

δcr (mm)

0.6

60

60

0.2

0.5

C13HS-F70

C13HS-F80

60

0.1

0.4

80

80
C13HS-F90

0.4

0.5

0.6

A

0

40

BC D E
A-1st cycle
B-After 200 cycles
C-After 1000 cycles
D-After 10000 cycles
E-After 100000 cycles

20
0.1

0.2

Load P (kN)

80

20

0.3

δcr (mm)δcr (mm)

Load P (kN)

0.4

60

60

0

0.3

C21HS-F70-T

C21HS-F60

40

C

80
A-1st cycle
B-After 200 cycles
C-After 1000 cycles
D-After 10000 cycles
E-After 30000 cycles
F-After 60000 cycles

80
Load P (kN)B

δcr (mm)20

δcr (mm)0

A

20

Load P (kN)

60

0.1

40

0.6

80

20

60

δcr (mm)

Load P (kN)

Load P (kN)C

A-1st cycle
B-After 200 cycles
C-After 1000 cycles

C21HS-F75-T

0

B

20

80

40

C21HS-F80-T

60

Load P (kN)60

C21HS-F80
Load P (kN)

Load P (kN)

C21HS-F85-T

0

80

80

80

0.3

0.4

0.5

0.6

A BC D0δcr (mm)Fig. 3.14 (b) Load-crack width curves

50E
A-1st cycle
B-After 200 cycles
C-After 1000 cycles
D-After 10000 cycles
E-After 100000 cycles

20
0.1

0.2

0.3

δcr (mm)

0.4

0.5

0.6

3.3.4.3.

Strain Distribution

Fig. 3.15 to Fig. 3.29 present the strain distributions for particular numbers of fatigue
cycles. The largest strain is observed at 50 mm from the notch in some specimens, due
to a small concrete piece remaining on the CFRP plate. The strain in the HE
specimens is lower than that in the HS specimens. In addition, the active bond stressmoves from the notch to the load end. The strain distribution curves illustrate that as
the number of fatigue cycles increased, the maximum local bond stress moved fromthe notch to the load end. The HS specimens exhibited higher local bond stress thanthe HE specimens.
CFRP plate strain(%)

CFRP plate strain(%)

0.4
After 200 cycles
0.3
0.2
0.1
100
200
300
0
Distance from the notch to the load end(mm)After 1000 cycles
0.3
0.2
0.1
100
200
300
0
Distance from the notch to the load end(mm)0.4
CFRP plate strain(%)

0.4
CFRP plate strain(%)

0.4

After 4000 cycles

After 4145 cycles

0.3

0.3

0.2

0.2

0.1

0.1

100
200
300
0
Distance from the notch to the load end(mm)

100
200
300
0
Distance from the notch to the load end(mm)

0.4

0.4
CFRP plate strain(%)

CFRP plate strain(%)

Fig. 3.15 Strain distribution of Specimen C36HS-F70

After 1000 cycles
0.3
0.2

0.2

0.1

0.1
100
200
300
0
Distance from the notch to the load end(mm)

100
200
300
0
Distance from the notch to the load end(mm)0.4
CFRP plate strain(%)

0.4
CFRP plate strain(%)

After 10000 cycles

0.3

After 100000 cycles

0.3
0.2
0.1

After 200000 cycles
0.3
0.2
0.1
100
200
300
0
Distance from the notch to the load end(mm)

100
200
300
0
Distance from the notch to the load end(mm)Fig. 3.16 Strain distribution of Specimen C36HS-F60

51

0.4
CFRP plate strain(%)

CFRP plate strain(%)

0.4
After 1000 cycles
0.3
0.2
0.1

After 10000 cycles
0.3
0.2
0.1

0.4

0.4
CFRP plate strain(%)

100
200
300
0
Distance from the notch to the load end(mm)

CFRP plate strain(%)

100
200
300
0
Distance from the notch to the load end(mm)After 100000 cycles

After 1000000 cycles

0.3

0.3

0.2

0.2

0.1

0.1

100
200
300
0
Distance from the notch to the load end(mm)

100
200
300
0
Distance from the notch to the load end(mm)Fig. 3.17 Strain distribution of Specimen C36HS-F50
0.4
CFRP plate strain(%)

CFRP plate strain(%)

0.4
After 20 cycles

After 60 cycles

0.3

0.3

0.2

0.2

0.1

0.1

100
200
300
0
Distance from the notch to the load end(mm)

100
200
300
0
Distance from the notch to the load end(mm)

CFRP plate strain(%)

0.4
After 100 cycles

0.3
0.2
0.1
100
200
300
0
Distance from the notch to the load end(mm)Fig. 3.18 Strain distribution of Specimen C36HE-F75
CFRP plate strain (%)

CFRP plate strain (%)

0.4
After 200 cycles

0.3
0.2
0.1

CFRP plate strain (%)

0
100
200
300
Distance from the notch to the load end (mm)0.4After 400 cycles
0.3
0.2
0.1
0
100
200
300
Distance from the notch to the load end (mm)0.4After 600 cycles
0.3
0.2
0.1
0
100
200
300
Distance from the notch to the load end (mm)Fig. 3.19 Strain distribution of Specimen C21HS-F85-T

52

0.4
CFRP plate strain(%)

CFRP plate strain(%)

0.4
After 200 cycles

0.3
0.2
0.1

After 1000 cycles
0.3
0.2
0.1
100
200
300
0
Distance from the notch to the load end(mm)

100
200
300
0
Distance from the notch to the load end(mm)0.4

CFRP plate strain (%)

CFRP plate strain (%)

Fig. 3.20 Strain distribution of Specimen C21HS-F80

After 20 cycles
0.3
0.2
0.1

CFRP plate strain (%)

0
100
200
300
Distance from the notch to the load end (mm)0.4After100 cycles
0.3
0.2
0.1
0
100
200
300
Distance from the notch to the load end (mm)0.4After 300 cycles
0.3
0.2
0.1
0
100
200
300
Distance from the notch to the load end (mm)0.4

CFRP plate strain (%)

CFRP plate strain (%)

Fig. 3.21 Strain distribution of Specimen C21HS-F80-T

After 200 cycles

0.3
0.2
0.1

CFRP plate strain (%)

0
100
200
300
Distance from the notch to the load end (mm)0.4After 1000 cycles
0.3
0.2
0.1
0
100
200
300
Distance from the notch to the load end (mm)0.4After 5000 cycles
0.3
0.2
0.1
0
100
200
300
Distance from the notch to the load end (mm)Fig. 3.22 Strain distribution of Specimen C21HS-F75-T

53

0.4
CFRP plate strain(%)

CFRP plate strain(%)

0.4
After 200 cycles
0.3
0.2
0.1

After 1000 cycles
0.3
0.2
0.1

100
200
300
0
Distance from the notch to the load end(mm)

100
200
300
0
Distance from the notch to the load end(mm)0.4
CFRP plate strain(%)

CFRP plate strain(%)

0.4
After 10000 cycles

After 20000 cycles

0.3

0.3

0.2

0.2

0.1

0.1
100
200
300
0
Distance from the notch to the load end(mm)

100
200
300
0
Distance from the notch to the load end(mm)0.4

CFRP plate strain (%)

CFRP plate strain (%)

Fig. 3.23 Strain distribution of Specimen C21HS-F70

After 1000 cycles
0.3
0.2
0.1

After 10000 cycles
0.3
0.2
0.1
0
100
200
300
Distance from the notch to the load end (mm)

0
100
200
300
Distance from the notch to the load end (mm)

CFRP plate strain (%)

0.4

0.4
After 60000 cycles
0.3
0.2
0.1
0
100
200
300
Distance from the notch to the load end (mm)Fig. 3.24 Strain distribution of Specimen C21HS-F70-T
0.4
CFRP plate strain(%)

CFRP plate strain(%)

0.4
After 1000 cycles

0.2

0.2

0.1

0.1

100
200
300
0
Distance from the notch to the load end(mm)

100
200
300
0
Distance from the notch to the load end(mm)0.40.4
CFRP plate strain(%)

CFRP plate strain(%)

After 10000 cycles

0.3

0.3

After 100000 cycles

0.3

After 1000000 cycles

0.3

0.2

0.2

0.1

0.1

100
200
300
0
Distance from the notch to the load end(mm)

100
200
300
0
Distance from the notch to the load end(mm)Fig. 3.25 Strain distribution of Specimen C21HS-F60

54

0.4
CFRP plate strain(%)

CFRP plate strain(%)

0.4
After 1000 cycles

0.3
0.2

0.2

0.1

0.1

100
200
300
0
Distance from the notch to the load end(mm)

100
200
300
0
Distance from the notch to the load end(mm)

0.4

0.4
CFRP plate strain(%)

CFRP plate strain(%)

After 10000 cycles

0.3

After 100000 cycles

0.3
0.2
0.1

After 1000000 cycles
0.3
0.2
0.1
100
200
300
0
Distance from the notch to the load end(mm)

100
200
300
0
Distance from the notch to the load end(mm)Fig. 3.26 Strain distribution of Specimen C21HE-F75-C
0.4
CFRP plate strain(%)

After 200 cycles
0.3
0.2
0.1

After 1000 cycles
0.3
0.2
0.1
100
200
300
0
Distance from the notch to the load end(mm)

0.4

0.4
CFRP plate strain(%)

100
200
300
0
Distance from the notch to the load end(mm)

CFRP plate strain(%)

CFRP plate strain(%)

0.4

After 10000 cycles

0.3

After 100000 cycles

0.3

0.2

0.2

0.1

0.1
100
200
300
0
Distance from the notch to the load end(mm)

100
200
300
0
Distance from the notch to the load end(mm)Fig. 3.27 Strain distribution of Specimen C13HS-F90
0.4
CFRP plate strain(%)

CFRP plate strain(%)

0.4
After 200 cycles

0.2

0.2

0.1

0.1

100
200
300
0
Distance from the notch to the load end(mm)

100
200
300
0
Distance from the notch to the load end(mm)

0.4

0.4
CFRP plate strain(%)

CFRP plate strain(%)

After 1000 cycles

0.3

0.3

After 10000 cycles

0.3

After 100000 cycles

0.3

0.2

0.2

0.1

0.1

100
200
300
0
Distance from the notch to the load end(mm)

100
200
300
0
Distance from the notch to the load end(mm)Fig. 3.28 Strain distribution of Specimen C13HS-F80

55

0.4
CFRP plate strain(%)

CFRP plate strain(%)

0.4
After 200 cycles

After 1000 cycles

0.3

0.3

0.2

0.2
0.1

0.1

0.4

0.4

CFRP plate strain(%)

100
200
300
0
Distance from the notch to the load end(mm)

CFRP plate strain(%)

100
200
300
0
Distance from the notch to the load end(mm)After 10000 cycles

0.3
0.2
0.1
100
200
300
0
Distance from the notch to the load end(mm)After 100000 cycles
0.3
0.2
0.1
100
200
300
0
Distance from the notch to the load end(mm)Fig. 3.29 Strain distribution of Specimen C13HS-F70

3.3.4.4.

Post-Fatigue Monotonic Behavior

The specimens that endured one million load cycles without failing—C21HS-F60,
C36HS-F50, and C21HE-F75-C—were loaded monotonically to failure. Fig. 3.30
compares the load-crack width and total displacement curves of these specimens withthose of the static specimens.
The post-fatigue bond strengths of specimens C21HS-F60 and C36HS-f50 weresimilar to the strengths under static loading. However, the post-fatigue bond strengthof specimen C21HE-F75-C was higher than that under static loading of specimen
C21HE because the specimen with the confinement jig had a 10% higher bondstrength.
50

50

C21HS

P (kN)

P (kN)

Static load

30
20
10
0

C21HS

40

40

0.4

0.6

0.8

30
20

C21HS-F60 Post-fatigue load

10

C21HS-F60 Post-fatigue load

0.2

Static load

0

1

0.2

40
30
Static load

20

0.8

1

C36HS-F50
Post-fatigue load

10

C36HS

Static load

40

C36HS

P (kN)

P (kN)

0.6

50

50

0

0.4

δcr (mm)δtotal (mm)3020C36HS-F50 Post-fatigue load

10
0.2

0.4

0.6

0.8

1

0

δtotal (mm)

0.2

0.4

0.6

0.8

δcr (mm)Fig. 3.30 (a) Post-fatigue load-displacement curve
56

1

150

150

C21HE

C21HE

50

50

C21HE-F75-C
Post-fatigue load

Static load

0

C21HE-F75-C
Post-fatigue load100

P (kN)

P (kN)

100

0.5

1

Static load0

1.5

δtotal (mm)0.5

δcr (mm)1

1.5

Fig. 3.30 (b) Post-fatigue load-displacement curve

3.3.4.5.

Fatigue Life Prediction for Debonding

A useful way to visualize the time to failure for a specific material is with an S-N curve.
“S-N” indicates the alternating stress versus fatigue cycles to failure, which is plotted as
the alternating bond stress σa on the vertical axis and the logarithm of the number ofcycles to failure on the horizontal axis. The alternating bond stress, σa, is calculated via
Equation (3.16). The S-N curve is shown in Fig. 3.31.

 
 a  up low(3.16)

Alternating bond stress (MPa)2

0.5

C13HS-F70
C13HS-F80
C13HS-F90
C21HS-F60
C21HS-F70
C21HS-F70-T
C21HS-F75-T
C21HS-F80
C21HS-F80-T
C21HS-F85-T
C36HS-F50
C36HS-F60
C36HS-F70

0.4
0.3
0.2
0.1
0 0
10

101

102

103

104

105

106

107

The number of fatigue cycle

Fig. 3.31 S-N curve
To evaluate better the fatigue characteristics of each piece of concrete’s compressive
strength, a regression method was adopted for this study. The fatigue life prediction
method assumes a linear relation between the ratio of the upper-limit fatigue load tothe static load strength and the logarithm of the number of load cycles to failure N, as
expressed in Equation (3.17).
Pup
Pmax

 a  log N  1(3.17)

where Pup = the upper limit fatigue load on the CFRP plate, Pmax = the bond strength
under a static load, N = the number of fatigue cycles, and a = a coefficient for theconcrete compressive strength.

57

The change of the slope in Eq. 3.17 might indicate a change in the fatigue resistancebased on concrete compressive strength; in other words, the reduced slope of Eq. 3.17
indicates that the current FRP plate-concrete bonding system might lose its fatigue
resistance at a fast rate. A summary of the concrete compressive strength constants isgiven as follows. These constants indicate that, as with all similar applications, thebond, and thus the capacity, is controlled by the concrete compressive strength. Above
all, coefficients with relationships with concrete compressive strength were generated
by linear regression.
a = -0.038 (in case of C13HS specimens)a = -0.065 (in case of C21HS specimens)a = -0.080 (in case of C36HS specimens)
Fig. 3.32 (a) presents the normalized maximum applied load in the upper-limit load
(Pup/Pmax) versus the number of cycles to failure (N). A linear regression analysis of
the results for specimens C13HS, C21HS, and C36HS yielded the relation between
the coefficient and compressive strength shown in Fig. 3.32 (b). The following best-fit
curve was obtained:
Pup
Pmax

 0.0021 B  log N  1 (σB in MPa)

(3.18)For a given type of CFRP plate, a higher concrete compressive strength corresponds
to a shorter fatigue life.
1
C21(-0.065)

Coefficient ( )Pup/Pmax

0.8

0C13(-0.038)

0.6
C36(-0.080)

0.4
0.2
0

C13HS
C21HS
C36HS

1

2

3
4
Log(N)

5

6

-0.02

-0.06
-0.08
-0.1
0

7

21.2MPa-0.04
25.6MPa

=-0.0021B

39.5MPa

1020
30
Concrete compressive strength (MPa)

40

(a)
(b)
Fig. 3.32 Fatigue life prediction method
In the present research, as shown in Fig. 3.32(a), little difference was observed in theslopes of the regression lines for the three types of concrete compressive strength,
suggesting that the same mechanism of failure might be operating in all three concrete
strengths. In other words, the concrete strength was treated as the dominant factor in
fatigue performance. In all of the above, the coefficient could be linked to changes in
concrete strength, based on linear regression.

3.3.4.6.

Local Bond Stress-Slip RelationshipThe method for calculating the local bond stress and slip for specimens subjected to58

0-50 m m

C21HS-F70
2

1 cycle200 cycles

11000 cycles

0

0.02

0.04
0.06
Slippage (mm)

0.08

0.1

3

3
50-100 m m

C21HS-F70
2

10000 cycles

200 cycles

C21HS-F7021000 cycles
1 cycle20000 cycles

1

1

0

Local bong stress (MPa)3Local bong stress (MPa)

Local bong stress (MPa)fatigue loading is the same as the method used for specimens subjected to static
loading. The local bond stress-versus-slip (τ vs. s) graphs for the 0-50-, 50-100-, and100-150-mm gauge intervals for the C21HS-F70 specimen are plotted in Fig. 3.33,
which illustrates that the local bond stress-slip relationship of the selected specimens
under fatigue loading is nearly elastic. However, the stiffnesses of the curves decreaseas the number of fatigue loading cycles increases. The maximum bond stress also
decreases for the 0-50- and 50-100-mm intervals.

0.02

0.04
0.06
Slippage (mm)

0.08

0.1

100-150 m m

20000 cycles

10000 cycles
1000 cycles
200 cycles
1 cycle

0

0.02

0.04
0.06
Slippage (mm)

0.08

0.1

Fig. 3.33 Local bond stress-slip curve of specimen C21HS-F70

3.3.5 Proposed Local Bond Stress-Slip Relation under Fatigue
Load Conditions
3.3.5.1 Envelope Curve According to the Popovics Model
The objective of this section is to propose a model that can represent the local bondstress-slip relationship under fatigue load conditions. First, the Popovics model ischosen to express the envelope curve. This model, which was originally proposed todescribe the stress-strain curve for concrete compressive behavior, is shown below.

where

i
s
n
 i 
 max smax (n 1)  (si / smax )n(3.19)

max  2.5B0.23(3.20)

 i = local bond stresss i = slip (mm) m a x = maximum local bond stresss max = slip at  max (= 0.0429 mm)

n= constant (= 3) B = concrete compressive strength

The adaptability of the Popovics model to local bond stress-slip curves was previously
investigated for FRP sheet-to-concrete bonding systems [3.6]. This model has also59been adapted to the development of local bond stress-slip curves for CFRP
plate-to-concrete bonding systems for the case of monotonic loading [3.5], and thevalues of τmax, smax, and n used were those obtained in that study.
Fig. 3.34 provides examples of the envelope curve from the Popovics model for the
C21HS-F series and their experimental curves. The local bond stress and slip arenormalized by Eq. (3.20) and smax, respectively. The experimental curves correspondto the fatigue load condition just inside the envelope curves.
1e/max

0.8

C21HS-F60
0-50mm50-100mm
100-150mm
Envelope curvemax=5.2M Pa
smax=0.0429mm
n=3

0.6
0.4

C21HS-F80
0-50mm50-100mm
100-150mm

C21HS-F70
0-50mm50-100mm
100-150mm

Envelope curvemax=5.2M Pa
smax=0.0429mm
n=3

Envelope curvemax=5.2M Pa
smax=0.0429mm
n=3

0.2
0

0.5 1 1.5 2 2.5 3 3.5 0 0.5 1 1.5 2 2.5 3 3.5 0 0.5 1 1.5 2 2.5 3 3.5 4
se/smax

Fig. 3.34 Normalized local bond stress-slip relations for the C21HS-F series

3.3.5.2 Model of the Local Bond Stress-slip Relationship for
Fatigue Loading
As described in the previous section, the local bond stress-slip relations in fatigue
loading are nearly linear. The stiffness of the curve gradually decreases as the numberof fatigue cycles increases. If this part of the curve is included in the unloading andreloading branches of the curves, the local bond stress-slip relation under fatigue
loading can be characterized by a certain point on the envelope curve and by thestiffness, as shown in Fig. 3.35. The stiffness of the local bond stress-slip relation
under fatigue loading can be evaluated using the unloading branch of the experimental
curve, and thus, the unloading branches based on the experimental values have alinear relation for all fatigue cycles. Therefore, the stiffness of the unloading branch(ki) at all fatigue cycles can be obtained. This model uses a linear approximation of
the unloading-reloading path for simplicity.
1
Loading branch
Unloading branch
Fitting line

0.8

e/max

Envelope curve
0.6
0.4
0.2

0

(se/smax , e/max)
Hysteresis
loop ofExp.values

Fitting for
unloading branchextending to envelope) ki Unloading stiffness

1

2
se/smax

3

4

Fig. 3.35 Unloading branch stiffness60

Fig. 3.36 illustrates the relationship between the stiffness of the unloading branch ki
and se/smax for specimen C21HS-F70 at the gauge intervals of 0-50, 50-100, and100-150 mm. se is defined as the slip at the cross point on the envelope curve and theextended line from the experimental unloading branch, as shown in Fig. 3.35. The
solid line indicates the values estimated from the least-squares regression equation
shown as Eq. (3.21).
3

C21HS-F70

Exp. values at 0-50 mm
Exp. values at 50-100 mm
Exp. values at 100-150 mm

2.5
2

ki

1.5
1
-0.83(Se/Smax)

ki=2.21e

0.5

0

1

2

3

se/smax

4

5

6

Fig. 3.36 Unloading branch stiffness and slip relationshipki  2.21  e

0.83(se)
smax(3.21)

where
ki= stiffness of the local bond stress-slip relation in fatigue
se= slip on the envelope curve
The decrement of the stiffness is evaluated by the decrement ratio, which is defined as
the stiffness at any arbitrary loading cycle divided by the stiffness of the unloading
branch at the first loading cycle, ki/k1.
As we know, modeling of fatigue damage has two major aspects: establishing afatigue failure criterion; and a damage accumulation rule. In the traditional approach
to fatigue, the failure criterion relates to fatigue failure (i.e., fatigue life) regarding thenumber of applied loading cycles to cause that failure (usually having fixed orconstant amplitude). An analytical expression of the fatigue failure criterion is the S-N
curve, which plots the stress level, S, of the constant-amplitude cycles against thecharacteristic number of cycles to failure, N, at this stress level. In modeling fatigue
damage with an S-N curve, the shape of the curve is usually fixed by an empiricalparametric expression; these parameters are used to match the shape to a particular setof experimental data. Because of the large scatter of experimental fatigue lives,
particularly at lower stress levels, practical measurement of these shape parameters
requires statistical methods, such as linear and nonlinear regression analysis.
Likely a more sound approach, from a physical point of view, is to treat damage
accumulation as the process of evolution of a damage parameter under the loading
history. This evolution is most naturally specified in terms of a differential equation
with regard to the loading cycles, although other mathematical expressions might also61

prove appropriate. Examples for the damage parameter include residual stiffness andresidual strength.
In association with such an approach, the failure criterion is postulated in terms of a
critical (failure) value for the chosen damage parameter. Integration of theevolutionary damage equation can be undertaken for either constant orvariable-amplitude loadings. For the constant amplitude case, analytical integration isoften possible, which also allows for a relationship between the critical damage
parameter and the fatigue life, N, to be established. From this relationship, an S-N
curve model can also be derived, which places the S-N curve approach on a soundbasis.
Fig. 3.37 illustrates the relationship between the stiffness decrement ratio ki/k1 and thenumber of fatigue loading cycles N on a logarithmic scale. Regression analysis
yielded Eq. (3.22):
Exp. values at 0-50mm
Exp. values at50-100mm
Exp. values at100-150mm

1.2 C21HS-F70

ki/k1

1
0.8
0.6
0.4
0.2 0
10

ki/k1=-0.117log(N)+1
101

102

Cycles

103

104

105

Fig. 3.37 Unloading branch stiffness and fatigue cycle relationshipki
 1  0.117  log( N )k1(3.22)

where
ki= stiffness of the local bond stress-slip relation in the fatigue cycle
k1= unloading stiffness at the first cycle
N= number of fatigue cycles
Fig. 3.37 shows the relationship between fatigue life (number of loading cycles until
failure) and the stiffness decrement ratio ki/k1. It can be seen that the S-N curve can beapproximately described as linear if N is expressed on a logarithmic scale, and thefatigue life decreases with increases in the stiffness decrement ratio.
In science and engineering, a semi-log graph or semi-log plot is a method ofvisualizing data that are related according to an exponential relationship. One axis isplotted on a logarithmic scale. This type of plot is useful when one of the variables
being plotted covers a large range of values, and the other has only a restricted range— the advantage being that it can bring out features in the data that would not easily62be seen if both variables had been plotted linearly.
Many researchers have developed fracture models to predict the theoretical load
response for the debonding failure mode of FRP attached to concrete for static loading
conditions (Taljsten 1996[3.7]; Yuan et al. 2001[3.8]; Wu and Niu 2000[3.9]). In thepresent research, linear regression analysis of the fatigue test results was conducted todevelop a relation for the ratio of the unloading branch stiffness (ki) to the unloading
stiffness at the first cycle as a function of the number of fatigue cycles (N). According
to this model, the bond shear stress increases linearly with the interfacial slip until itreaches the stress (τe) at the Popovics envelope, representing the hysteresis path at any
arbitrary number of fatigue cycles. Therefore, as the number of fatigue cycles
increases, the bond stiffness decreases along the envelope of the Popovics curve
because interfacial softening is assumed. In summary, the failure mode under fatigue
loading, based on the proposed model, should be identical to that for a specimen of
the same concrete compressive strength under static loading.
Furthermore, it is indicated that the S-N relationships for all of the CFRP
plate/concrete bonded interfaces can become unique if the stiffness ki is expressed by
the stiffness decrement ratio. In other words, the fatigue life is independent of thestiffness decrement by local position changing for the CFRP plate/concrete interface if
the same stiffness decrement ratio is maintained.

3.3.5.3

Adaptability of the Proposed Model

3.3.5.3.1 Method of Analysis
An analysis was performed to confirm the proposed local bond stress-slip relationshipfor fatigue loading. This analysis was performed by calculating the equilibrium withthe acting force and the compatibility of deformation of an infinitesimal element, asshown in Fig. 3.38. This analytical method can be summarized in the following steps:

Fig. 3.38 Infinitesimal element
1. The values of k1 at the intervals 0-50, 50-100, and 100-150 mm are obtained bystatic analysis at the upper limit of fatigue loading. Furthermore, se/smax on theenvelope curve at the first cycle can be obtained.
63

2. The value of ki at any arbitrary number of cycles can be determined from Eq. (3.22)
using the value of k1.
3. According to Eq. (3.21), se/smax on the envelope at any arbitrary number of cycles
can be obtained via ki. Additionally, τe/τmax can be calculated from the envelope curve
based on the Popovics model.
4. Using the values of ki, se, and τe, the straight line presenting the local bondstress-slip relation under fatigue loading is fixed according to Eq. (3.23).

 i   e  ki  max  (se  si )(3.23)

smax

Fig. 3.39 presents a comparison of the proposed local bond stress-slip models and theexperimental results for the C21HS-F series. The proposed models display good
agreement with the experimental results, except for those at the 100-150-mm interval,
due to the limited amount of effective test data.
1A
M odel at 50-100mm
B NA at 1 cycle
N at 100 cycle
C NBC at 1000 cycle
D ND at 10000 cycle

M odel at 0-50mm
cycle
NA at 1
NB at 100 cycle
NC at 1000 cycle
ND at 10000 cycle
A Exp.values C21HS-F60

0.8
0.6

C

Exp.values C21HS-F60

B
C
D

0.4

M odel at 100-150mm
cycle
NA at 1
NB at 100 cycle
NC at 1000 cycle
ND at 10000 cycle
Exp.values C21HS-F60

D

B

0.2
A

0
1
0.8
e/max

A M odel at 50-100mm
B NA at 1 cycle
NB at 100 cycle
C N
at 1000 cycle
D NCD at 10000 cycle

M odel at 0-50mm
cycle
NA at 1
NB at 100 cycle
NC at 1000 cycle
cycle
A ND at10000
Exp.values C21HS-F70

0.6

B

0.4

C

M odel at 100-150mm
cycle
NA at 1
NB at 100 cycle
NC at 1000 cycle
ND at 10000 cycle
Exp.values C21HS-F70

D
C

Exp.values C21HS-F70

B

D

0.2
A

0
1

A
M odel at 50-100mmcycle
A at 1
B N
N at 100 cycle
C NBC at 1000 cycle
10000 cycle
D ND atExp.values
C21HS-F80

M odel at 0-50mm
cycle
NA at 1
NB at 100 cycle
NC at 1000 cycle
ND at 10000 cycle
A
Exp.values C21HS-F80

0.8
0.6

B

0.4

M odel at 100-150mm
NA at 1cycle
NB at 100 cycle
NC at 1000 cycle
ND at 10000 cycle
Exp.values C21HS-F80

D
C

C
D

B

0.2
0

1

2

3

4

5

6

0

1

2

3
4
se/s max

5

6

0

A
1

2

3

4

5

6

7

Fig. 3.39 Comparison of the local bond stress-slip relationships
Next, the following infinitesimal element analysis was conducted for an arbitrary
number of cycles.
Assuming that the internal bond stress of the element is constant, the slip is obtained
from the difference in elongation between the CFRP plate and the equivalent concretepart (concrete, adhesive, and steel). The bond stress is estimated from the proposed64bond stress-slip model for fatigue loading:
A. The slip at the load end s1 is determined.
B. The bond stress of infinitesimal element i (τi) is calculated using Eq. (3.23).
C. The increment of force is ΔPf,i; the elongation of the CFRP plate is δf,i, and theelongation of the equivalent concrete part is δm,i. The infinitesimal element i is
calculated using the following formulas: Pf , i   i  b f   x(3.24)

 f ,i 

i 1
 Pf , ix(   Pf , k )
2t f  b f  E f k 1

(3.25)

 m ,i n Pf , ix(   Pm , k )
2Am  E f k  i 1

(3.26)

D. The slip si, tensile load Pf,i, and CFRP plate strain εf,i are calculated using thefollowing formulas:si  si 1  ( f ,i   m ,i )(3.27)

Pf , i  Pf , i   P f , i(3.28)

 f ,i 

Pf , i(3.29)

t f bf  E f

If the value of si exceeds the value of se, it is assumed that the bond stress-slip relation
moves to the envelope curve, as shown in Fig. 3.40.
Popovics envelope curve
n=3

Local bond stress ()Cross point coordinate(se,e)Path for analysis

(si)=e-ki(max/smax)(s e-si)
if si<se(si)=(max/smax)(3s i)/(2+(s i/smax)3) if si>se) ki .(max/smax)
Slip (s)Fig. 3.40 Local bond stress-slip path for analysis

65

3.3.5.3.2 Comparison of the Analytical and Experimental Results
Fig. 3.41 compares the analytical and experimental results for the strain distributionsof the CFRP plate for specimen C21HS-F70 after 100, 1,000, and 10,000 loading
cycles. The results from the strain distribution analyses based on the proposed model
correspond well to the test results, although the unloading-reloading straight-line
paths obtained from the numerical analysis do not correspond well with theexperimental results for the 100-150-mm interval (Fig. 3.39).
In the present research, linear regression analysis of the fatigue test results was
conducted to develop the relationship for the ratio of the unloading branch stiffness(ki) with the unloading stiffness at the first cycle as a function of the number of fatigue
cycles (N). The strain distributions in the CFRP plate could be numerically calculated
from the bond-slip model. The comparison of strain distributions between tests andpredictions for specimen C21HS-F70 is shown in Fig. 3.41. Comparisons areundertaken for the given cycle for the same effective stress transfer length during thestage of debonding propagation. It was found that the proposed model was in close
agreement with the test results. In other words, strain distributions could be evaluatedby the proposed model.
0.2
k1=0.380.1

N=1000-50mmk1=0.38

N=10000-50mmk1=0.38

C21HS-F70
Analysis
Experimental(30.0kN)

C21HS-F70
Analysis
Experimental(30.1kN)

N=10000
0-50mmC21HS-F70
Analysis
Experimental(29.9kN)0
N=10050-100 mm

Strain(%)

k1=0.820.1

N=100050-100 mm

k1=0.82

C21HS-F70
Analysis
Experimental(30.1kN)

N=10000
50-100 mm

k1=0.82

C21HS-F70
Analysis
Experimental(30.0kN)

C21HS-F70
Analysis
Experimental(29.9kN)0
N=100100-150 mm

k1=2.19

0.1

0C21HS-F70
Analysis
Experimental(30.1kN)
100

200

N=1000100-150 mm

k1=2.19

N=10000
100-150 mm

k1=2.19

C21HS-F70
Analysis
Experimental(30.0kN)

300
0
100
200
300
0
100
Location of strain gauges from specimen center (mm)C21HS-F70
Analysis
Experimental(29.9kN)
200

300

Fig. 3.41 Strain distributions compared with the C21HS-F70 results

66

400

3.3.6 Peeling Debonding Behavior under Fatigue Loading
The transverse displacements of the CFRP plate and concrete surface were measured
for specimens C21HS-M1, C21HS-M2, C21HS-F70-T, C21HS-F75-T, C21HS-F80-T,
and C21HS-F85-T to study the debonding phenomenon. The measurement details of
the transverse displacement are shown in Fig. 3.42, and the test setup is shown in Fig.
3.43.

Fig. 3.42 Sketch of the transverse displacement measurement

Fig. 3.43 Test setup67

3.3.6.1 Transverse Displacement Relationships

D3-D4
0.2

D5-D6

D7-D8

D9-D10C21HS-M-1

0.1
0

-0.1
0
80
160
240
Position of CDP from specimen center (mm)Distribution of displacement (mm)Distribution of displacement (mm)Fig. 3.44 to Fig. 3.48 present the distributions of the transverse displacement
differences between the concrete substrate and the CFRP plate at the same sectional
position. This difference in the transverse displacement is considered to correspond to“floating” of CFRP plate with respect to the concrete substrate. The transverse
displacement difference exhibits some sudden increases representing peeling off ofthe CFRP plate. Some results clearly illustrate that the location of peeling off of the
CFRP plate moved from the specimen center to the load end as the number of fatigue
cycles increases.

0kN
3.7kN
7.3kN
9.7kN
13.8kN
16.1kN
18.5kN
21.5kN
23.3kN
26.3kN
29.4kN
31.8kN
34.0kN
35.4kN
37.4kN40.0kN
41.9kN

D12-D110.2

D14-D13

D16-D15

D18-D17

C21HS-M-1

0.1
0
-0.1
0
80
160
240
Position of CDP from specimen center (mm)

0kN
3.7kN
7.3kN
9.7kN
13.8kN
16.1kN
18.5kN
21.5kN
23.3kN
26.3kN
29.4kN
31.8kN
34.0kN
35.4kN
37.4kN40.0kN
41.9kN

D3-D4
1.5

D5-D6

D7-D8

D9-D10C21HS-M-2
1
0.5
0
0
80
160
240
Position of CDP from specimen center (mm)

0.0kN
1.9kN
6.6kN
8.2kN
9.2kN
9.6kN
13.2kN
15.3kN
18.8kN
21.3kN
24.4kN
27.3kN
28.6kN30.8kN
34.5kN
37.2kN40.0kN

Distribution of displacement (mm)Distribution of displacement (mm)(a) Specimen C21HS-M-1
D12-D11
1.5

D14-D13

D16-D15

C21HS-M-2
1
0.5
0
0
80
160
240
Position of CDP from specimen center (mm)(b) Specimen C21HS-M-2
Fig. 3.44 Distribution of transverse displacement differences

68

D18-D17
0.0kN
1.9kN
6.6kN
8.2kN
9.2kN
9.6kN
13.2kN
15.3kN
18.8kN
21.3kN
24.4kN
27.3kN
28.6kN30.8kN
34.5kN
37.2kN40.0kNDistribution of displacement (mm)

D3-D4
0.8

D5-D6

D7-D8

4.2kN
5.1kN
8.2kN
12.1kN
15.7kN
19.4kN
25.9kN
29.4kN

C21HS-F70-T
At 1000-cycle

0.6

D3-D4

0.4

D5-D6

D7-D8

D3-D4

D5-D6

D7-D8

4.5kN
7.8kN
10.7kN
14.1kN
19.7kN
24.9kN
27.9kN
29.7kN

C21HS-F70-T
At 10000-cycle

4.1kN
7.1kN
10.7kN
13.7kN
18.1kN
23.3kN
27.1kN
29.1kN

0.2
C21HS-F70-T
At-60000-cycle

0
0

80

Distribution of displacement (mm)D12-D11160

D14-D13

D16-D15 D12-D11

C21HS-F70-T
At 1000-cycle

0.2

0
80
160
0
Position of CDP from specimen center (mm)

4.2kN
5.1kN
8.2kN
12.1kN
15.7kN
19.4kN
25.9kN
29.4kN

0.1

D14-D13

D16-D15

D12-D11

4.5kN
7.8kN
10.7kN
14.1kN
19.7kN
24.9kN
27.9kN
29.7kN

C21HS-F70-T
At 10000-cycle

80

160

0

80

160

80

160

D14-D13240

D16-D15 D18-D17
C21HS-F70-T
At 60000-cycle

4.1kN
7.1kN
10.7kN
13.7kN
18.1kN
23.3kN
27.1kN
29.1kN0-0.1
0

D9-D10

0

80

160

240

Position of CDP from specimen center (mm)Distribution of displacement (mm)Fig. 3.45 Distribution of transverse displacement differences for specimen
C21HS-F70-T
D3-D4
0.1

D5-D6

D7-D8

D3-D4
4.6kN
6.3kN
8.8kN
12.2kN
20.0kN
23.7kN
27.9kN30.4kN

C21HS-F75-T
At 200-cycle

0.05

D5-D6

D7-D8

D3-D4

D5-D6

D7-D8

4.7kN
6.7kN
9.4kN
15.1kN
18.9kN
22.6kN
27.7kN30.2kN

C21HS-F75-T
At 1000-cycle

D9-D104.2kN
5.9kN
10.0kN
13.0kN
17.1kN
22.9kN
24.3kN30.4kN

0

C21HS-F75-T
At 5000-cycle

0

80

160

0

80

160

0

80

160

240

Distribution of displacement (mm)Position of CDP from specimen center (mm)D12-D11 D14-D13 D16-D15
0.3

D12-D11 D14-D13 D16-D15

4.6kN
6.3kN
8.8kN
12.2kN
20.0kN
23.7kN
27.9kN30.4kN

C21HS-F75-T
At 200-cycle

0.2
0.1

C21HS-F75-T
At 1000-cycle

D12-D11 D14-D13 D16-D15 D18-17

4.7kN
6.7kN
9.4kN
15.1kN
18.9kN
22.6kN
27.7kN30.2kN

4.2kN
5.9kN
10.0kN
13.0kN
17.1kN
22.9kN
24.3kN30.4kN

C21HS-F75-T
At 5000-cycle

0
0

80

160

0

80

160

0

80

160

240

Position of CDP from specimen center (mm)Fig. 3.46 Distribution of transverse displacement differences for specimen
C21HS-F75-T

69

Distribution of displacement (mm)

D3-D4
D5-D6
0.1
0.08 C21HS-F80-T
At 20-cycle
0.06
0.04
0.02
0
-0.02
-0.04
0
80

D7-D8

D3-D4
4.3kN
5.6kN
9.8kN
13.6kN
17.8kN
22.1kN
26.1kN
29.5kN
32.0kN
33.5kN

D5-D6

D7-D8

D3-D4

D5-D6

D7-D8

4.4kN
8.0kN
13.3kN
19.7kN
25.8kN30.5kN
33.3kN

C21HS-F80-T
At 100-cycle

D9-D10
4.4kN
7.4kN
10.7kN
16.8kN
23.1kN
26.9kN
31.2kN
33.0kN

C21HS-F80-T
At 300-cycle

160

0

80

160

0

80

160

240

D14-D13

D16-D15

D18-D17

Distribution of displacement (mm)Position of CDP from specimen center (mm)D12-D11 D14-D13
0.8

D16-D15 D12-D11
4.3kN
5.6kN
9.8kN
13.6kN
17.8kN
22.1kN
26.1kN
29.5kN
32.0kN
33.5kN

C21HS-F80-T

0.6 At 20-cycle
0.4
0.2

D14-D13 D16-D15

D12-D114.4kN
8.0kN
13.3kN
19.7kN
25.8kN30.5kN
33.3kN

C21HS-F80-T
At 100-cycle

4.4kN
7.4kN
10.7kN
16.8kN
23.1kN
26.9kN
31.2kN
33.0kN

C21HS-F80-T
At 300-cycle

0
0

80

160

0

80

160

0

80

160

240

Position of CDP from specimen center (mm)Distribution of displacement (mm)Fig. 3.47 Distribution of transverse displacement differences for specimen
C21HS-F80-T
D3-D4
0.4

D7-D8

0.2
0.1
0

C21HS-F85-T
At 200-cycle

D12-D11
1
0.8

D3-D4

D5-D6

D3-D4

80

160

D14-D13

D16-D15 D12-D11

0.4

D7-D8

D14-D1380

D16-D15 D12-D11 D14-D13

160

4.7kN
5.2kN
7.3kN
11.3kN
16.1kN
20.7kN
25.3kN
29.5kN
32.5kN
34.3kN

C21HS-F85-T
At 600-cycle

160

0
80
160
0
Position of CDP from specimen center (mm)

80

240

D16-D15 D18-D17

4.5kN
5.4kN
7.2kN
10.5kN
14.7kN
19.4kN
24.0kN
28.3kN
32.3kN
34.8kN

C21HS-F85-T
At 400-cycle

0.2
80

D9-D10
4.7kN
5.2kN
7.3kN
11.3kN
16.1kN
20.7kN
25.3kN
29.5kN
32.5kN
34.3kN

080
160
0Position of CDP from specimen center (mm)

4.7kN
7.9kN
11.3kN
15.3kN
22.1kN
26.3kN
31.5kN
34.8kN

C21HS-F85-T
At 200-cycle

D5-D6

C21HS-F85-T
At 600-cycle

C21HS-F85-T
At 400-cycle

0.6

0
0

D7-D8

4.5kN
5.4kN
7.2kN
10.5kN
14.7kN
19.4kN
24.0kN
28.3kN
32.3kN
34.8kN

4.7kN
7.9kN
11.3kN
15.3kN
22.1kN
26.3kN
31.5kN
34.8kN

0.3

-0.1
0

Distribution of displacement (mm)

D5-D6

160

240

Fig. 3.48 Distribution of transverse displacement differences for specimen
C21HS-F85-T
Around the “floating” position of the CFRP plate, the CFRP plate is pulled from thesubstrate at a certain angle (the “peeling angle”) due to the peeling force, as shown in
Fig. 3.49. The interface is subjected to shear and tensile stresses; hence, debonding
occurs due to mixed-mode fracture. The reason for the decrease in stiffness and thedebonding of the plate under fatigue loading is considered to be an influence of thepeeling.
70

Fig. 3.49 Mechanism of peeling off of the CFRP plate

3.4 Conclusions
The main purpose of this chapter was to investigate the fatigue behavior of the bondbehavior between the CFRP plate and concrete.
The double-faced bond specimens were divided into two groups according to theloading method (static or fatigue loading). The following conclusions can be drawn.
Nine specimens were tested under static loading. The type of debonding failure
observed was similar to that observed in previous research. The failure face wasnearly debonded from the concrete surface. The bond strength increased withincreasing stiffness of the CFRP plate and increasing concrete strength. The
experimental bond strength values agree well with the calculated values proposed
previously. Furthermore, the peeling phenomenon in the CFRP plate was observed in
the transverse displacement measurements.
Fifteen specimens were tested under fatigue loading. The primary fatigue failuremodes were identified in these studies and are described as follows:
1. Fatigue failure occurs at the initiation of debonding from the notch position.
2. Fatigue debonding of the faces consists of two components. The first component isdebonding from the concrete face near the notch, and the second component isdebonding from the adhesive face to the load end.
3. S-N curves for the fatigue failure of the bond were proposed. The fatigue-limit bondstress after one million cycles was considered for specimens with concrete strengthsof 13, 21, and 36 MPa.
4. The monotonic post-fatigue tests indicate that the peak load is not influenced by thefatigue cycles.
5. The stiffness of the local bond stress-slip curve decreases as the number of fatigue
loading cycles increases. The reduction coefficient for stiffness is determined from thenumber of cycles.
71

6. A local bond stress-slip model was proposed based on the experimental results, anda numerical analysis was performed to confirm the proposed model. The local bondstress-slip model for fatigue loading is based on an evaluation of the stiffness andenvelope curves produced by the Popovics model.
In addition, the transverse displacements of the CFRP plates and concrete substrate
were measured. The variation in transverse displacement exhibited an obvious
discernible peeling phenomenon with debonding propagation. The experiment results
indicate that the CFRP plate, upon peeling off, moves from the specimen center
toward the load end as the number of fatigue cycles increases. The peeling off of the
CFRP plate is an important failure mode affecting the progression of debonding in thefatigue test.

72

CHAPTER 4
Mixed-Mode Debonding Behavior of CFRP Plates
and Concrete
4.1. Introduction
For FRP plate-strengthened concrete members, failure often occurs by FRP plate
debonding from the concrete substrate, which can be initiated from either the end of
the FRP plate or the mouth of a flexural or shear-flexural crack. Premature failure
initiated from the plate end is attributed to the presence of high shear and normal
stress concentrations, which have been widely studied (Roberts, 1989[4.1], Malek etal, 1998[4.2], Rabinovich et al, 2000[4.3], EI-Mihilmy et al, 2001[4.4]).
Another possible location for interfacial cracks is the mouth of a flexural-shear crack
in a concrete beam. When debonding of an FRP plate occurs as a result of a major
flexural crack, there is no relative vertical displacement between the two sides of thecrack. In this situation, the debonding of the FRP plate from the substrate of theconcrete beam can be considered interfacial debonding in mode II. However, when
the debonding failure of the FRP plate is initiated by a major flexural-shear crack,both vertical and horizontal displacements between the two sides of the flexural-shear
cracks can be observed. Both shear and peeling in the vicinity of the crack are shownin Fig. 4.1. This debonding failure can be regarded as FRP plate debonding as a resultof both interfacial shear and peeling effects (a combination of modes I and II), called
mixed-mode failure. In this case, a reduction in the bond strength occurs, which
increases the probability of premature local collapse. Hence, the bond performance of
this type of structure, strengthened by an FRP plate, depends not only on the shear
bond strength of the interface but also on the combined effect of shear bond andpeeling. In evaluating the performance of the externally bonded FRP plate
strengthening technique, the interfacial bond strength between the FRP plate andconcrete for different failure modes is the crucial importance.

Fig. 4.1 Debonding failure induced by a flexure-shear crack in the concrete beam73

As discussed in the previous chapter, the double-faced shear fatigue test experimentresults indicate that the CFRP plate, upon peeling off, moves from the specimen
center toward the load end as the number of fatigue cycles increases. The peeling offof the CFRP plate is an important failure mode affecting the progression of debonding
in the fatigue test. Indeed, the peeling angle is the most important factor to respond to
the peeling progress. Therefore, the mixed-mode debonding behavior is investigatedby focusing on the peeling angle.
The main objective of this chapter is to investigate the effect of the mixed-mode
debonding behavior between the CFRP plate and the concrete. To achieve thisobjective, special double-faced bond specimens, in which the plates are attached at
specific initial angles, were employed to introduce combined shear and peeling effects
on bonded CFRP plates. The strain distributions along the CFRP plates during theloading process for cases with different initial angles demonstrate the peelingbehavior of the CFRP plates. The failure process was characterized according to thestrain distribution at different stages. The effects of the concrete strength and theinitial angle on the ultimate responses were studied based on the experimental results.
Finally, a method for predicting the mixed-mode fracture bond strength is proposed.

4.2. Experimental Program
4.2.1. Specimens
Uniaxial tensile loading tests were carried out on specimens with CFRP plates bonded
on two sides. A total of 12 specimens were prepared, with curved surfaces to connect
two different cross sections for each specimen, to allow for the attachment of an
initial angle. The specimen details are shown in Fig. 4.2. The level difference between
two different cross sections of a specimen is called the step height. The M24 steel bars
had no connection at the middle of the specimen, and a pre-crack was introduced
before loading, meaning that the two concrete blocks were only connected with CFRP
plates. Cylinders were tested at the same time as the specimens to determine thematerial properties.
The specimen list is shown in Table 4.1. All of the specimens were designed with a“pre-unbond” region setting near the center to clarify the combination of componentsof the fracture failure at the bonding part. Small initial angles of 2° and 4° and large
initial angles of 10° and 20° and target concrete compressive strengths of 13.5 and 21
MPa were considered. The concrete properties are also listed in Table 4.1.
High-strength CFRP plate of 1 mm in thickness (GM510) were utilized.
Other important evaluated FRP-concrete interface characteristic parameters include
the properties of the adhesive layers. It has been found that adhesive layers with lower
elastic moduli but good ductility can have higher interface bond strengths. The
mechanical properties of adhesive layers can be adjusted by changing the elastic
74

modulus of either the resin or putty. However, the effective bond length increases
when the elastic modulus of the adhesive layers decreases. In other words, it ispossible to obtain different experimental results when different adhesives are used.

Fig. 4.2 Specimen details
Table 4.1 Specimen list
Concretecompressive
Specimenstrength
S13-2-1
S13-2-2
S13-4-1
S13-4-2
S13-10
S13-20
S21-2-1
S21-2-2
S21-4-1
S21-4-2
S21-10
S21-20Concrete
splittingstrength

MPa

MPa

18.4

1.97

Concrete
Designed
Pre-unbond Step
1/3
initiallengthheightsecantangle θstrengthGPadegree
mm
mm
2

16.9

1.89

20.3

8.8
250

19.6

4

17.5

10
20

35.0
72.5

200

2
31.0

2.87

25.4

8.8
250

4
30.8

2.46

CFRP
plate

10
20

23.0

75

17.5
200

35.0
72.5

High
strengthwith 1mm
thickness

4.2.2. Loading and Measurement
All specimens were subjected to tensile force to cause shear and peeling debonding at
the interface of the specimen. Fig. 4.3 presents the test setup for loading with anactuator for the large-initial-angle specimens and loading with a universal testingmachine for the small-initial-angle specimens. For each combination of test variables,
one specimen was instrumented with eight strain gauges on the CFRP plate surface on
one side. These gauges were spaced at intervals of 50 mm from the center of the
CFRP plate to the load end. On the opposite side, one gauge was used at the center ofthe plate. In addition, the total displacements and crack widths at the specimen center
were measured using LVDTs and Pi gauges, respectively.

(a) For specimens with large initial angles(b) For specimens with small initial angles
Fig. 4.3 Test setup
76

4.3

Experimental Results

4.3.1 Failure Progress
The experimental results are provided in Table 4.2. The calculated bond strength was
determined using the previously proposed calculation method (Matsunaga et al.
2008[4.5]) for the shear bond strength of the CFRP plate. All specimens were
subjected to tensile force until debonding failure occurred on either side. Typicalfailure surfaces from the experimental results are shown in Fig. 4.4. The post-failure
photographs indicate that the failure surfaces of the specimens with initial angles of
10° and 20° were between the CFRP plate and the adhesive, whereas the specimens
with initial angles of 2° and 4° were debonded at the concrete surface. The specimens
with large initial angles exhibited clear peeling of the plate, whereas the debonding
progress in the specimens with small initial angles was largely controlled by shear
debonding. Nevertheless, all debonding was considered to be due to the combinationof two fracture modes (peeling and shear).
Table 4.2 Experimental results
Maximum load P Calculated bond strength Pcal
P/PcalSpecimenkN
kN
S13-2-1
20.8
0.54
S13-2-2
20.3
0.53
S13-4-1
15.5
0.40
38.7
S13-4-2
16.0
0.41
S13-105.1
0.13
S13-205.5
0.14
S21-2-1
23.4
0.61
S21-2-2
24.3
0.63
S21-4-1
20.8
0.54
41.4
S21-4-2
17.0
0.44
S21-107.3
0.19
S21-206.1
0.16

Failure face
Concrete layer
Adhesive layer
Concrete layer
Adhesive layer

Fig. 4.4 (a) Typical failure faces of the specimens with small initial angles

Fig. 4.4 (b) Typical failure faces of the specimens with large initial angles

774.3.2. Load-versus-Displacement Relation and Strain Distribution
The load-crack width curves are presented in Fig. 4.5. In the small-initial-angle
specimens, the CFRP plate peeled off toward the load end of the specimen as thetensile load increased. However, in the large-initial-angle specimens, the 10° and 20°
specimens exhibited different behaviors as the CFRP plate delaminated. In one
specimen, there was an abrupt decrease up to the maximum tensile load and a gradualincrease to failure. In the other specimens, the maximum tensile load up to the peakload was reached and then gradually decreased until failure. The sudden decreases inload evident in the curves represent the propagation of the CFRP plate delamination.

S13-2-1
S13-2-2

10

10

0.2

0.4
0.6
Crack width (mm)

0.8

20

1

0

Load P (kN)

0.4
0.6
Crack width (mm)

0.2

0.4
0.6
Crack width (mm)0.8

1

S21-4-1
S21-4-2

0

0.2

0.4
0.6
Crack width (mm)6Load (kN)

Load (kN)1

S13-20

6
4
2
0.2

0.4
0.6
Crack width (mm)

0.8

1

4
2
0

8

0.2

0.4
0.6
Crack width (mm)

0.8

1

8
S21-20

S21-106
Load (kN)

6
Load (kN)

0.8

8
S13-10

4
2
0

1

10

8

0

0.8

20

S21-2-1
S21-2-2

10

0

0.2

Load P (kN)0

S13-4-1
S13-4-2

20
Load P (kN)

Load P (kN)

20

0.2

0.4
0.6
Crack width (mm)

0.8

4
2
0

1

0.2

0.4
0.6
Crack width (mm)Fig. 4.5 Load-versus-crack width relationship
78

0.8

1

Fig. 4.6 presents the strain distributions observed, with tensile load-versus-crack
width diagrams for some selected specimens. The strain distributions correspond tothe marked plots on the tensile load-versus-crack width diagrams. As expected, some
negative strains were observed due to bending of the CFRP plate during progressive
debonding in the large-initial-angle specimens, as in the case of the FRP sheet (Alamet al. 2012[4.6]). As the debonding progressed, the negative strain moved toward theload end. In contrast, there was no negative strain in the debonding progress of thesmall-initial-angle specimens. The curve trends for the small-initial-angle specimens
are similar to those for the shear bond behavior, which is consistent with thedifferences in the debonding failure faces discussed in the previous photographs.

10

10

0kN
8.1kN
15.0kN
19.3kN
20.1kN

0.2

0.4
0.6
Crack width (mm)

0.8

0

1

0.2

0.4
0.6
Crack width (mm)S13-2-20.8

1

010.4kN
15.5kN
20.0kN
23.4kN
22.7kN

0.15
Strain(%)

0.15

0.2

S21-2-10kN
8.1kN
15.0kN
19.3kN
20.1kN

0.1

S21-4-1

0kN
10.1kN
17.3kN
19.8kN
15.9kN
19.4kN
20.2kN10

10.4kN
15.5kN
20.0kN
23.4kN
22.7kN

0.2

0.2

Strain (%)

20

0.2

0.4
0.6
0.8
Crack width (mm)S21-4-1

0kN
10.1kN
17.3kN

0.15
Strain(%)

0

S21-2-1

Load P (kN)

20

Load P (kN)S13-2-2

Load P (kN)

20

0.1

1

19.8kN
15.9kN
19.4kN
20.2kN

0.1

0.05

0.05

0.05

0
50
100 150 200 250 300 350
Location of strain gauges from specimen center (mm)050
100 150 200 250 300 350
Location of strain gauges from specimen center (mm)050
100 150 200 250 300 350
Location of strain gauges from specimen center (mm)

8

8

8

S13-100.2

0.2
S13-10

0.1

0.4
0.6
Crack width (mm)

0.8

1

0kN
3.5kN
3.4kN
2.6kN
2.8kN
2.5kN

0

4

0kN
2.93kN
2.6kN
2.47kN

2
0

0.2

0.4
0.6
Crack width (mm)

0.8

1

4

0kN
4.4kN
3.5kN
2.7kN
3.1kN
3.0kN

2
0

0.2

0.4
0.6
0.8
Crack width (mm)

1

0.2

0.2
0kN
2.93kN
2.6kN
2.47kNS13-200.1
0S21-10Strain (%)

20Strain (%)

Load (kN)

0kN
3.5kN
3.4kN
2.6kN
2.8kN
2.5kN

Strain (%)

Load (kN)

4

6
Load (kN)6

6

S21-10

S13-20

0.1

0kN
4.4kN
3.5kN
3.0kN
4.2kN
2.7kN

0

-0.1

-0.1

-0.1

0
50 100 150 200 250 300 350
Location of strain gauges from specimen center (mm)050 100 150 200 250 300 350
Location of strain gauges from specimen center (mm)050 100 150 200 250 300 350
Location of strain gauges from specimen center (mm)Fig. 4.6 Strain distributions corresponding to marked plots of the load-crack width
relationship4.4. Evaluation of the Bond Strength
The effect of the combination of fracture modes on the bond strength was evaluatedusing the same method as that for the FRP sheet (Alam et al. 2012[4.6]); thus, therelationship between the tensile load ratio (P/Pcal) and the peeling angle (tan θp) wasused to evaluate the combination of fracture bond strengths. A detailed delamination79

process is illustrated in Fig. 4.7. As the load increased, the plate delaminated due tothe peeling effect, and the bond length and peeling angle (tan θp) between the CFRP
plate and the concrete face decreased. The delaminated region is defined as the
distance from where the pre-unbond region starts on the test part of the specimen to
the strain gauges, where the minimum (negative) strain was observed in the cases ofthe large-initial-angle specimens. The residual of the CFRP plate bonded length is theeffective bonded region, which gradually decreases until failure. The peeling angle
was obtained as the angle between the axial direction and a tangential line from thespecimen surface to the position of minimum strain appearing in the CFRP plate. The
load P corresponding to this minimum strain was recorded from the data to fit therelation of the tensile load ratio and peeling angles. In the case of thesmall-initial-angle specimens, the values after the sudden decrease of the tensile load
were selected because no negative strains were recorded. For example, in specimen
S13-2-2, the values which for load P at the first sudden drop occurred until before thenext sudden drop load value occurred, which was selected according to the debonding
region of the starting point of step height to the strain gauge at 100 mm from thespecimen center. Subsequently, the values continued to be selected step by step,corresponding to the debonding region and extending to the strain gauge at 150 mm.
The same method for selecting values was applied to the debonding region extending
to the strain gauge at 200 mm, 250 mm, 300 mm, and 350 mm from the specimen
center.
The ratio of the tensile load P to the calculated bond strength Pcal, according to Eqs.
(4.1) to (4.5) (Matsunaga et al. 2008[4.5]) was plotted against the peeling angle (tanθp), as shown in Fig. 4.8. The tensile load decreases as the peeling angle increases.
The relationship between the tensile load ratio and peeling angle can be obtained asshown in the figure.

Fig. 4.7 Details of the delamination process

80

0.8

P/P cal

0.6
0.4
-1.46

y=0.003x

0.2
0

0.05

0.1
tan θp

S13-2-2
S21-2-1
S13-4-2
S21-4-1
S13-10
S21-10
S13-20
S21-200.15

0.2

Fig. 4.8 Effect of the peeling angle on the bond strength

 b,max  2.5   B 0.23
le 

2  t f  E f  sek e   b ,max

(4.1)
(4.2)

Pb  ke  b,max  bf  le (lb  le )(4.3)

Pb  k  b,max  bf  lb (lb  le )(4.4)

1  kel1  ke cos( b  ) 
2
le
2

(4.5)

k

where the maximum local bond stress is τb,max, the concrete compressive strength in
MPa is σB, the effective bond length is le, the width of the CFRP plate is bf; thethickness is tf; the elastic modulus is Ef; the local slip of the effective bond area is se(0.234 mm); the stress coefficient of the EBSB in the case of effective bond length iske (0.428); the bond length is lb; the bond strength is Pb; and the stress coefficient of
the EBSB is k (Kanakubo et al. 2003) [4.7].
Plots of the calculated shear bond strength with respect to the peeling angle and theevaluated tensile load ratio are shown in Fig. 4.9. The bond strength calculated using
Eqs. (4.1) to (4.5) was obtained as the difference between the bond length (lb) and theeffective bond length (le). In this experiment, the tensile load was considered to havereached the shear bond strength when the entire plate was delaminated. In other words,
the bond length decreased as the plate delaminated. Thus, the bond length is shorter
than the effective bond length. The trends in the shear bond strength curves calculated
according to the method described above are shown in the figure. The intersection
points represent the bond strength for the combined fracture mode. Therefore, thecorresponding values of P/Pcal can be calculated using the values of tan θp at theseintersections. The values of P/Pcal, tan θp, and the calculated bond length for eachspecimen are provided in Table 4.3. The predictions agree well with the test results.

81

1.2
Calculated bond strength1
0.8
P/Pcal

S13-4
S21-4

0.6

S13-10
S21-10

S13-20
S21-200.4
0.2 S13-2
S21-2
0

P/Pcal=0.003tanθ-1.46

0.02 0.04 0.06 0.08 0.1 0.12 0.14
tan θpFig. 4.9 Evaluation of the combined fracture bond strength
Table 4.3 Comparison of the test results
Specimen
S13-2-1
S13-2-2
S13-4-1
S13-4-2
S13-10
S13-20
S21-2-1
S21-2-2
S21-4-1
S21-4-2
S21-10
S21-20Calculatedbond length
(mm)
61.5
39.5
13.9
7.9
61.5
39.5
13.9
7.9

Experimental
values
P/PcalTan θp(crosspoint)

Calculated
values
P/Pcal

0.54
0.53
0.40
0.41
0.13
0.14
0.61
0.63
0.54
0.44
0.19
0.16

0.026
0.026
0.038
0.038
0.060
0.092
0.026
0.026
0.038
0.038
0.060
0.092

0.62
0.62
0.36
0.36
0.18
0.10
0.62
0.62
0.36
0.36
0.18
0.10

Experimental/
calculated
values
0.87
0.86
1.13
1.15
0.71
1.43
0.99
1.02
1.52
1.24
1.04
1.64

4.5. Conclusions
The bond behavior under the combined fracture mode was observed using special
specimens that had a step height at the surface. The results confirm that the tensile
load decreases as the peeling angle increases. The failure surfaces of the specimens
with large initial angles were between the CFRP plate and the adhesive, whereas the
specimens with small initial angles were debonded at the concrete surface. The
peeling angle affected the failure surface and caused the transition of the failure mode,i.e., from Mode II to Mode I, in which the bond strength was less than the shear bondstrength. The relationship between the peeling angle and the tensile load wasdetermined to evaluate the bond strength under the combined fracture mode. A
calculation method for the combined fracture mode was proposed based on the test
results. The proposed method accurately predicts the bond strength between the CFRP
plate and concrete under combined shear and peeling fracture conditions.

82

CHAPTER 5
Conclusions
In this thesis, several problems related to bond and peeling debonding failure in CFRP
plate-strengthened concrete under fatigue loading were investigated. The main
conclusions of this research are summarized below.
When debonding of the CFRP plate is induced by a shear crack in the strengthened
beam, both horizontal and vertical displacements occur between the two sides of thecrack. A series of static and fatigue loading tests was carried out to investigate theeffect of the vertical displacement on the CFRP debonding behavior under fatigue
loading. For specimens with bonded CFRP plates, final failure was associated withthe debonding of the CFRP plate from the substrate of the concrete block, from theshear crack to the supporting point. In the vertical displacement measurements in thefatigue test, clear differences were observed in the deflection-versus-fatigue cycle
relationship near the position of the shear crack. The peeling effect caused by thevertical displacement at a shear crack, due to crack propagation with fatigue cycles,
was recognized.
The effect of parameter configuration on the fatigue failure mode was investigatedthrough double-faced shear fatigue tests. The following were identified in these tests:
1. Fatigue failures occur at the initiation of debonding from the notch position.
2. The fatigue debonding at the faces consists of two components. The firstcomponent is debonding from the concrete face near the notch, and the second
component is debonding from the resin face to the load end.
3. S-N curves for the fatigue failure of the bond were proposed. The fatigue-limit bondstress up to one million cycles was considered for specimens with concrete strengthsof 13, 21, and 36 MPa.
4. The results of monotonic post-fatigue tests indicated that the peak load is not
influenced by fatigue cycles.
5. The stiffness of the local bond stress-slip curves decreases as the number of fatigue
loading cycles increases. The stiffness reduction coefficient was determined from thenumber of cycles.
6. A local bond stress-slip model was proposed based on the experimental results, anda numerical analysis was performed to validate the proposed model. (1) The tensileload-versus-deformation (crack width) curves exhibited nearly linear behavior withrespect to the number of fatigue loading cycles, and the stiffnesses of the curves
83gradually decreased as the number of loading cycles increased. (2) The local bondstress-slip relationship under fatigue loading exhibited nearly elastic behavior. The
stiffnesses of the curves decreased as the number of loading cycles increased. (3) A
local bond stress-slip model for fatigue loading was developed by evaluating thestiffness and envelope curves given by the Popovics model. (4) The proposed local
bond stress-slip model and strain distribution obtained from the numerical analysis
using the proposed model agreed well with the experimental results.
In addition, the transverse displacements measurements in double-faced shear tests
indicate a clear peeling phenomenon as the debonding progressed. The experimentresults indicate that when peeling off, the CFRP plate moved from the specimen
center toward the load end as the number of loading cycles increased. These results
show that the peeling off of the CFRP plate is an important failure mode that affects
the progress of debonding in fatigue testing.
Furthermore, the bond behavior under the combined fracture mode was examinedusing special specimens that had a surface step height. The tensile load was found to
decrease as the peeling angle increased. The relationship between the peeling angle
and the tensile load was determined to evaluate the bond strength under the combined
fracture mode. A calculation method for the combined fracture mode was proposed
based on the test results. The proposed method accurately predicts the bond strength
between the CFRP plate and concrete under combined shear and peeling fracture
conditions.
The purposes of the present research were to investigate the characteristics ofdebonding in FRP-strengthened concrete in mixed-mode failure under fatigue loading
and to develop and experimentally validate a calculation method for predicting thebond strength between a CFRP plate and concrete under combined shear-peeling
failure conditions.
Fatigue loading resulting in shear-peeling fracture of the CFRP plate at the major
shear crack in CFRP-plated RC beams in chapter 2 was confirmed. To understand ingreater depth the fatigue bond behavior between concrete and CFRP plates,
double-face shear bond tests were performed in chapter 3. The results indicated that
local delamination due to shear-peeling in CFRP plates subjected to fatigue loading
was the most important factor affecting the debonding progress of FRP-strengthened
concrete structures. Therefore, to evaluate the bond strength of combinations, fracturemode was considered. In chapter 4, a simple calculation method for the bond strengthof combination fracture mode, based on peeling angle derived from the shear-peelingphenomenon, was devised.
Based on the current research, some recommendations for design procedure can be
made.
84

In CFRP-plated beams with relatively long shear spans or in which the end peel mode
has been effectively mitigated, debonding initiates at flexural/shear cracks near theregion of maximum moment. Under loading, these cracks open and induce highinterfacial shear stress, causing delamination, which propagates across the shear spanin the direction of decreasing moment. This mode of debonding is properly termed“intermediate flexural-shear crack-induced debonding.” Available guidance for thedesign of external FRP plate-bonding systems should take the approach of limiting thestress (or strain) in the FRP plate to mitigate debonding. Indeed, the fatigue bondbehavior of FRP plate-bonding systems is expected to limit the stress (or strain) that isrecommended to mitigate bond failure associated with deterioration due to fatigue
loading.
Moreover, fatigue-induced local delamination due to shear-peeling in FRP plates is an
important factor that affects the service life of FRP-strengthened concrete structures.
Hence, the bond strength with mixed-mode fractures should be considered in theinitial design.
Furthermore, although mixed-mode failure could be quantified in the present researchin terms of the loss of strength of the interface due to peeling angle variation, otherparameters, such as type of adhesive and temperature, could possibly have affected
the experimental results. Additionally, the rate of progression of interfacialdegradation under fatigue loading is not currently predictable; hence, the following
recommendations for future research are made to address limitations in the current
knowledge.
1.

Progressive damage propagation at the interface between concrete and CFRP
plates should be further investigated. The failure sequence or governing factors
must be investigated based on changing parameters. Detailed
debonding/delamination failure mechanisms should be fully disclosed.
2. Detailed design guidelines should be developed for the fatigue limit state of RC
beams externally strengthened with FRPs, particularly for the relationship of
mixed-mode bond strength and fatigue life. Design guidelines should be
improved to include detailed information, such as the level of environmental
conditions, applied loading ranges, and expected fatigue lives.
3. Further experimental investigations over a variety of load ranges and frequencies,
including more realistic peak overload and variable amplitude load, should be
conducted.

85

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1.15. Dai J. G., Ueda T., Sato Y., and Jaqin H. “Dowel resistances of bond interfaces
between FRP sheets and concrete”, CICE 2004, Australia
1.16. Md. Shah Alam, Toshiyuki Kanakubo, Akira Yasojima. “Shear-Peeling Bond
Strength between Continuous Fiber Sheet and Concrete”, ACI Structural Journal,
Vol. 109, No. 1, January-February 2012. pp. 75-82.
1.17. Priestley, M.; Seible, F., and Calvi, G. “Seismic Design and Retrofit of Bridges”,
John Wiley and Sons, New York, NY, 1996.
1.18. Saadatmanesh H., and Ehsani M.R. “RC beams strengthened with GFRP plates.
I: experimental study”, Journal of Structural Engineering, vol. 117, No. 11, 1991.
pp.3417-343.
1.19. Ritchie P.A” Thomas D.A” Lu L.W., and Connelly G.M., “External
strengthening of concrete beams using fibre reinforced plastic”, ACI Structural
Journal, vol. 88, 1991. pp. 490-500.
1.20. Saadatmanesh H., and Malek A.M. “Design guidelines for strengthening of RC
beam with FRP plates”, Journal of Composites for Construction, vol. 2, No. 4,
1998. pp. 158-164.
1.21. Meier U. “Strengthening of structures using carbon fibre/epoxy composites”,
Constr Building Material; 1995, 9(6): pp.341-351.
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123, No. 7, 1997. pp. 903-911.
1.23. Swamy R.N., Jones R., and Charif A. “The effect of external plate
reinforcement on the strengthening of structurally damaged RC beams”, The
Structural Engineer, vol. 67, 1989. pp. 45-56.
1.24. Wei, A., Saadatmanesh, H. and Ehsani, M. R. “RC beams strengthened with
FRP plates. II: Analysis and parametric study”, J. Struct Rngrg., ASCE, 117(11),1991. pp. 3434-3435.
1.25. Triantafillou, T. C., and Plevris, N. “Strengthening of R/C beams withepoxy-bonded fiber-composite materials”, Mater. Struct. 25, 1992. pp. 201-211.
1.26. Sharif A., Alsulaimani G.J., and Ghaleb B.N., “Strengthening of initially loaded
reinforced concrete beams using FRP plates”, ACI Structural Journal, vol. 91,
No. 2, 1994. pp. 160-168.
1.27. Ziraba Y.N., Baluch M.H., Basunbul I.A., Azad A.K., and Al-Sulaimani G.J.,
and Sharif AM. “Combined experimental-numerical approach tocharacterization of steel-glue-concrete interface”, Materials and Structures, vol.
28, 1995. pp. 518-525.
1.28. Pham H., and Al-Mahaidi R., “Experimental investigation into flexural
retrofitting of Reinforced Concrete Bridge beams using FRP
composites” ,Composite Structures, vol. 66, 2004. pp. 617-625.
1.29. Brena S.F., and Macri B.M., “Effect of Carbon-Fiber-Reinforced Polymer
87

laminate configuration on the behavior of strengthened reinforced concretebeams”, Journal of Composite for Construction, vol. 8, No. 3,2004.pp. 229-240.
1.30. Wight G. and Erki M.A., “Pre-stressed CFRP for strengthening concrete slabs infatigue”, International Conference on FRP Composites in Civil Engineering
CICE 2001 Ed .J.G.Teng. Hong Kong, 2001. ISBN: 0-08-043945-4.
1.31. Heffernan, P. J., and Erki, M. A. “Fatigue behavior of reinforced concrete beams
strengthened with carbon fiber reinforced plastic laminates” ,J. Compos. Constr.,82, 2001. pp.132-140.
1.32. Schlafli, M., and Bruhwiler, E. “Fatigue of existing reinforced concrete bridge
deck slabs”, Eng. Struct., 1998. pp.991-998.
1.33. Barnes, R. A., and Mays, G. C. “Fatigue performance of concrete beams
strengthened with CFRP plates”, J. Compos. Constr., 1999. pp.63-72.
1.34. Swamy R. N. “Debonding of Carbon Fiber Reinforced Polymer Plate fromConcrete Beams”, Proceeding. Ins. Civ. Engrs Structs & Bldgs, 134, 1999.
pp.301-317.
1.35. Rahimi H., and Hutchinson A. “Concrete Beams Strengthened with Externally
Bonded FRP Plates, Journal of Composites for Construction”, ASCE, Vol. 5, No.
1, 2001. pp.44-56.
1.36. Bizindavyi, L., Neale, K. W., and Erki, M. A. “Experimental investigation ofbonded fiber reinforced polymer-concrete joints under cyclic loading”, J.
Compos. Constr., 72, 2003. pp.127-134.
1.37. Dai, J.G., Sato, Y., Ueda, T. and Sato, Y. “Static and fatigue bond characteristics
of interfaces between CFRP sheets and frost damage experienced concrete”,
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Farmington Hills, MI , 2005. pp.1515-1530.
CHAPTER 2
2.1. Ritchie P.A., Thomas D.A., Lu L.W., and Connelly G.M., “External
strengthening of concrete beams using fiber reinforced plastic”, ACI Structural
Journal, vol. 88, 1991.pp. 490-500.
2.2. Saadatmanesh H., Ehsani M.R., “RC beams strengthened with GFRP plates I:
experimental study”, Journal of Structural Engineering, vol. 117, No. 11, 1991.
pp.3417-343.
2.3. Wei, A., Saadatmanesh, H., and Ehsani, M. R. “RC beams strengthened with
FRP plates. II: Analysis and parametric study”, J. Struct Rngrg., ASCE, 117(11),1991. pp.3434-3435.
2.4. Triantafillou,T. C.,and Plevris, N. “Strengthening of R/C beams withepoxy-bonded fiber-composite materials”, Materials and Structures,2(5),1992.
pp.201-211.
2.5. Karbhari, V. M.; Engineer, M.; and Eckel II, D. A., “On the Durability ofComposite Rehabilitation Schemes for Concrete: Use of a Peel Test,” Journal of
Materials Science, V. 32, No. 1, 1997. pp. 147-156.
2.6. Triantafillou, T. C., and Plevris, N., “Strengthening of RC Beams with88

Epoxy-Bonded Fiber-Composites Materials,” Materials and Structures, V. 25,
1992. pp. 201-211.
2.7. Masoud, S., Soudki, K., and Topper, T. “CFRP-strengthened and corroded RC
beams under monotonic and fatigue loads.” J. Compos. Constr., 5(4), 2001.
pp.228-236.
2.8. Masoud, S., Soudki, K., and Topper, T. “Post repair fatigue performance of
FRP-repaired corroded RC beams: Experimental and analytical investigation.” J.
Compos. Constr., 9(5), 2005. pp.441-449.
2.9. Heffernan, P. J., and Erki, M. A. “Fatigue behavior of reinforced concrete beams
strengthened with carbon fiber reinforced plastic laminates.” J. Compos. Constr.,8(2), 2004. pp.132-140.
2.10. Toutanji, H., Zhao, L., Deng, Y., Zhang, Y., and Balaguru, P. “Cyclic behavior of
RC beams strengthened with carbon fiber sheets bonded by inorganic matrix.” J.
Mater. Civ. Eng., 1(81), 2006. pp.28-35.
2.11. Papakonstantinou, C. G., Petrou, M. F., and Harries, K. A. “Fatigue behavior of
RC beams strengthened with GFRP sheets.” J. Compos. Constr., 5(4), 2001.
pp.246-253.
2.12. El-Hacha, R., Wight, R. G., Heffernan, P. J., and Erki, M. A. “Prestressed CFRP
sheets for strengthening reinforced concrete structures in fatigue.” Proc., 6th Int.
Symp. on Fiber-Reinforced Polymer (FRP) Reinforcement for Concrete
Structures (FRPRCS-6), Vol. 1, Singapore, 2003. pp.895-904.
2.13. Brena, S. F., Benouaich, M. A., Kreger, M. E., and Wood, S. “Fatigue tests ofreinforced concrete beams strengthened using carbon fiber-reinforced polymer
composites.” ACI Struct. J., 102(2), 2005. pp.305-313.
2.14. Architectural Institute of Japan. “Design Guideline for Earthquake ResistantReinforced Concrete Buildings Based on Ultimate Strength Concept”, 1988.
2.15. Japan Society of Civil Engineers. “Standard Specifications for Concrete
structure-2002”, Structural Performance Verification, March, 2002.
2.16. ACI-ASCE Committee 426. “The Shear Strength of Reinforced Concrete
Members”, ASCE St.Div.vol.99, ST6, June 1973.
CHAPTER 3
3.1. Maeda, Toshiya, Asano, Yasuyuki, Sato, Yasuhiko, Ueda, Tamon and Kakuta,
Yoshio. “A Study on Bond Mechanism of Carbon Fiber Sheet”, Proceedings of
the Third International Symposium on Non-Metallic (FRP) Reinforcement forConcrete Structures, Vol. 1, Japan Concrete Institute, Japan, 1997. pp. 279-286.
3.2. Tanaka, T. “Shear Resisting Mechanism of Reinforced Concrete Beams with
CFS as Shear Reinforcement. Graduation Thesis”, 1996. Hokkaido University.
3.3. Yuan, H. Wu, Z.S. and Yoshizawa, H. “Theoretical solutions on interfacial stresstransfer of externally bonded steel/composite laminates”, Journal of Structural
Mechanics and Earthquake Engineering, JSCE, No. 675/1-55, 2001. pp.27-39.
3.4. Kanakubo T., Furuta T., and Fukuyama H., “Bond Strength between
Fiber-Reinforced Polymer Laminates and Concrete”, Proceedings of 6thInternational Symposium on Fiber-Reinforced Polymer (FRP) Reinforcement89

for Concrete Structures, Vol.1, 2003. pp.133-142.
3.5. Matsunaga K., Kanakubo T., et al., “Study on Bond between CFRP Plate andConcrete”, Summaries of Technical Papers of Annual Meeting of Architectural
Institute of Japan, C-2, 2008. pp.307-310. (In Japanese).
3.6. Nakaba K., Kanakubo T., Furuba T., and Yoshizawa H., “Bond Behavior
between Fiber-Reinforced Polymer Laminates and Concrete”, ACI Structure J.,
98(3), 2001. pp.359-367.
3.7. Chajes M.J., Finch W.W. jr, Januska T.F. and Thomson T.A. jr. “Bond and force
transfer of composite material plates bonded to concrete”, ACI Structural J. Vol.
93, 1996. pp.208-217.
3.8. Yuan, H. Wu, Z.S. and Yoshizawa, H. “Theoretical solutions on interfacial stresstransfer of externally bonded steel/composite laminates”, Journal of Structural
Mechanics and Earthquake Engineering, JSCE, No. 675/1-55, 2001. pp.27-39.
3.9. Wu, Z., Yuan, H. and Niu, H. “Stress transfer and fracture propagation indifferent kinds of adhesive joints”, ASCE Journal of Engineering Mechanics,
Vol. 128, No. 5, 2002, pp.562-573.
CHAPTER 4
4.1. Roberts T.M., “Approximate analysis of shear and normal stress concentrationsin the adhesive layer of plated RC beams”, The Structural Engineer, vol. 67，No.
12, 1989. pp. 229-23.
4.2. Malek, A. M., Saadatmanesh, H., and Ehsani, M. R. “Prediction of failure loadof R/C beams strengthened with FRP plate due to stress concentration at theplate”, ACI Struct. J, 95(2), 1998. pp.142-152.
4.3. Rabinovitch H., and Frostig Y., “Closed-form high order analysis of RC beams
strengthened with FRP strips”, Journal of Composites for Construction, vol. 4,
No. 2, 2000. pp. 65-74.
4.4. El-Mihilmy M.T., and Tedesco J.W., “Prediction of anchorage failure forreinforced concrete beams strengthened with fiber-reinforced polymer plates”,
ACI Structural Journal, vol. 98, No. 3, 2001. pp. 301-314.
4.5. Matsunaga K., Kanakubo T., et al., “Study on Bond between CFRP Plate andConcrete”, Summaries of Technical papers of Annual Meeting of Architectural
Institute of Japan, C-2, 2008. pp.307-310. (in Japanese).
4.6. Alam M.S., Kanakubo T., and Yasojima A., “Shear-Peeling Bond Strength
between Continuous Fiber Sheet and Concrete”, ACI Structure Journal, V.109.
No.1, 2012. pp.75-80.
4.7. Kanakubo.T., Furuta.T., and Fukuyama.H. “Bond Strength between
Fiber-Reinforced Polymer Laminates and Concrete”, Proceedings of 6thInternational Symposium on Fiber-Reinforced Polymer (FRP) Reinforcement
for Concrete Structures, Vol.1, 2003. pp.133-142.

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ACKNOWLEDGEMENTS
I would like to express my deepest appreciation to my thesis supervisor, Associate
Professor Toshiyuki Kanakubo, for his valuable guidance and constructive
supervision, invaluable feedback, and friendly communication during this research
project over the years. Without his support and encouragement, this thesis could nothave been completed. His broad research experience and keen insight have impressedme deeply throughout this research program and will certainly encourage me for the
rest of my life.
I would also like to thank my thesis committee members, Prof. Yuki Sakai, Prof.
Yasuo Yamada, Associate Prof. Gaku Shoji, and Assistant Prof. Akira Yasojima, fortheir valuable suggestions and constructive comments on my research.
I would like to acknowledge a technical staff member, Mr. Kojima, from the
Kanakubo Laboratory for his extremely important assistance in the experimental
work.
I also thank all of my friends for their help in the research，especially Mr. Kohei
ASANO, Mr. Jianhua YU, Mr. Taichi KIMURA, Mr. Takayuki SANO, Mr. Kenji
SUZUKI, Mr. Xiangwei GUAN, Mr. Daiki IGARASHI, Mr. Shimei MAN, and Mr.
Ryoichi TSUKIZAKI.
Special thanks are also expressed to my family for their endless love and continuous
support throughout this research study.

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PUBLICATIONS ARISING FROM THE THESIS
1. Wei Zhang, Toshiyuki Kanakubo:“Bond Behavior between Concrete and CFRP Plate under Fatigue Loading”,
Proceedings of the 4th Asian Concrete Federation International Conference,
Tue-S4.3-01, 2010.11.
2. Wei Zhang, Toshiyuki Kanakubo:“Experimental Study on Bond Behavior between CFRP Plate and Concrete under
Combination of Fracture Mode (Ⅰ)”, the 14th JSCE International Summer
Symposium in 2012,Section V-197, 2012.9.
3. Wei Guanxiang, Wei Zhang, Toshiyuki Kanakubo:“Experimental Study on Bond Behavior between CFRP Plate and Concrete under
Combination of Fracture Mode (Ⅱ)”, JSCE Annual Meeting in 2013, Section V-023,
2013.9. (In Japanese)
4. Wei Zhang, Toshiyuki Kanakubo:“Local Bond Stress-Slip Relationship between CFRP Plate and Concrete under
Fatigue Loading”, Accepted for publishing in ACI Structural Journal, 2013.
5. Wei Zhang, Toshiyuki Kanakubo:“Experimental Study on Bond Behavior between CFRP Plates and Concrete under
Combination of Fracture Mode (Ⅱ)”, Proceedings of the 4th Asia Pacific Conferenceon FRP Composites in Structures, Section B-4, 2013.12.

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