ACI STRUCTUAL JOURNALTECHINICAL PAPER

Title no. 98-S34

Bond Behavior between Fiber-Reinforced Polymer
Laminates and Concreteby Kasumassa Nakaba, Toshiyuki Kanakubo, Tomoki Furuta, and Hiroyuki Yoshizawa

This research examines the bond behavior between fiber-reinforced polymer (FRP) laminates and concrete. To obtain the local bondstress versus slippage relationship, a double-face shear typebond test is conducted. The primary test variables are the types offiber and concrete. The test results show that fiber stiffness influences both the bond strength and shape of stress distribution. The
obtained local bond stress - slip relationships, however, are notinfluenced by the type of fiber. Only the maximum local bond stressinc rea se s as conc rete comp re ssive st rength al so inc rease s.
A new model representing the local bond stress versus slippage
relationship is proposed using Popovics's formula, which has been
adapted to present the concrete compressive stress-strain relationship. A numerical analysis is performed to confirm the model, andexperimental results are presented. The analytical results show agood agreement with the bond strength and strain distribution
found in the experimental results.
Keywords: bond; fiber reinforcement; local behavior; numerical analysis; polymers;
slip; stiffness;

INTRODUCTION
Fiber-reinforced polymers (FRPs) have already been
widely used in the aeronautics and space industries, as wellas in the sport and recreation industries. The resin in thesecase, however, is impregnated between the fine fibers beforehand; after they are shaped in the factory, they are heatedand made into a laminate - type FRP. When such materials areused in civil engineering applications, it is difficult to heatthem at construction sites, so resinless laminates (sheet – typefiber) have been developed which are treated at the work sitewith a resin that hardens at normal ambient temperatures. Fibers used in retrofitting work have fine fibers aligned in asingle direction and are made into thin planes ranging inthickness from 0.1 to 0.4 mm. To improve the bending
strength of columns and beams, these sheets are applied in
the axial direction of the elements, but they are applied perpendicularly to the axial direction when the goal is to increase shear strength and ductility.
The anchorage between concrete and FRP laminates plays
an important role in reinforcing design. As a brittle material, FRP shows a lack of ductility, and the failure mode occurs
suddenly without preceding yielding. Recently, many studies
have been undertaken to understand the bond behavior between concrete and FRP laminates, but current understanding
has not advanced sufficiently to apply FRP laminates, on actual structures. For these reasons, in terms of adhesion, it is necessary to confirm the safety of FRP laminates, or to seek abond length considered to have an adequately safe bondstress, to prevent the appearance and progress of bond rupture. In cases when the bond rupture or anchorage rupture
is unavoidable, it is necessary to obtain the rupture strength
experimentally, based on reliable data that adequately consider safety factors.
ACI Structural Journal/May-June 2001

PREVIOUS RESEARCH
Testing method
Figure 1 shows some specimen types used in the bond test
between FRP laminates and concrete. Experiments using atile or similar methods (Fig.1(a)) to directly obtain the bondstrength have been performed. But in terms of bending andshearing in this method, it is difficult to directly estimate thebond characteristics of the concrete-fiber system. One alternative that has been widely used to solve this problem, andwas adopted in this research, consists of a prism with a notchat the center, reinforced with FRP laminates on both faces(Fig.1(b)). Similarly, another alternative consisting of two
prisms reinforced at the center with FRP laminates (Fig.1(c))
is proposed to estimate the bending. To remove the acting
force's eccentricity in experiments using laminates in both
faces, experiments using laminate in one face (Fig.1(d)) andlaminate inserted in two concrete prisms (designaied Fig.1(e))
have been performed. In this sort of experiment, when the anchorage length is shorter, bond failure with delamination oflaminates usually occurs. When the anchorage length islonger, failure occurs with FRP rupture. Also, it is reported
that when the anchorage length increases, the failure force
tends to be higher, and the apparent average bond stress decreases.
Effective bond length
In a pure tensile experiment, the bond strength at average
stress has the tendency to decrease when the bond area increases.This occurs because the bond stress is not distributed
throughout the full area of the bond length. It has been reported by previous studies that the bond stress is distributed in
the region from the loaded end of the laminate, or from thecrack position, with a length not more than 100mm fromthose points. Previous studies have reported the following
results: 751, 101, 602, 20~903, and 40mm4. Bond stress distribution obtained from these experiments differs form experiment to experiment, and thus must be carefully
considered.
Local bond stress - slip relationship
An important step toward understanding bond behavior
is to have an assumption for local bond stress versus slip
relationship. Tensile strength in the case of bond failure,strain distribution of FRP, and bond stress distributions canbe obtained using bond stress versus slip relationship modelby mathematical or numerical analysis. Experiments on

ACI Structural Journal, V98, No.3,May-June 2001.
MS No.00-131 received May 31,2000, and reviewed under Institute publication
policies. Copyright (c) 2001. American Concrete Institute. All rights reserved. Includeing the making of copies unless permission is obtained from the copyright proprietors.
Pertinent discussion will be published in the March-April 2002 ACI Structural Journal if received by November 1,2001.

Kasumassa Nakaba is a purchasing engineer at Renault do Brazil S/A, Curitiba City ,Parana state, Brazil. He received his civil engineering degree from the Federal University of Paraná, Brazil, and his MS in Engineering form the University of Tsukuba,
Japan.His research interests include the Fiber-reinforced polymer systems for concrete
structures.
ACI member Toshiyuki Kanakubo is Assistant professor at the Institute of Engineering Mechanics and Systems at the University of Tsukuba. He received his PhD inengineering from the University of Tsukuba. His research interests include fiber reinforced concrete, fiber-reinforced polymer for concrete, and bond mechanism of concrete structures.
Tomoki Furuta is a research engineer in Industrial Mechanical Products Division ofBando Chemical Industries, Ltd., Hyougo, Japan. He received his PhD in engineeringfrom the University of Tokyo, Japan. His research interests include hybrid structuresand controlling buildings.
Hiroyuki Yoshizawa is a research engineer at Nippon Steel Composite Co., Ltd.,Tokyo, Japan. He received his PhD in civil engineering from the Ibaraki University,
Japan.

bond that analyze specimens have been carried out, and theproceedures applied to those experiments are divided inthree types, as follows; a) cut off type 3 ; b) bilinear type 4 ;and c) tensile softening type 5 . Figure 2 shows typical models for these three types.
RESEARCH SIGNIFICANCE AND OBJECTIVE
The main objective of this research is to propose a bondstress- versus-slip model that can provide the effective bondlength and the bond strength for externally bonded FRP
laminates to concrete. To reach the objective, double-faceshear type bond test is conducted. The primary test variables are the types of fiber and concrete. A numerical analysis is also performed to compare the proposed model withexperimental results.
Another goal is to address the factors affecting the bondbehavior between FRP laminates and concrete. The factors
are: stiffness (laminate thickness times elastic modulus),
concrete strength, Influence of putty thickness.

EXPERIMENTAL PROGRAM
Specimen
The specimen adopted for this research is shown in Fig. 3.
The specimen consists of a concrete prism (100 x 100 x
600mm) cracked at the center using a hammer on the notch
after the reinforcing with FRP laminates. The two steel bars
also have no connection, which means that the two prisms
are connected only through the FRP laminates. The FRP system used in this research consists of fiber impregnated withepoxy resins, with the primarily preparation of the concrete
substrate using primer and putty. Putty is a thickened epoxy
paste used to fill voids and smooth surface discontinuities.
FRP laminates are bonded at two opposite sides of thespecimen. One of the sides of the specimen was reinforced
with a confinement FRP allowing the occurrence of delamination of the laminate only on the opposite side, where thestrain gages were set. The parameters of the test will be discussed in the following section. Once the tensile force fromthe FRP is transferred into the concrete, there is nearly nobond stress between the unbonded region. This means thatwhen the bonded length exceeds a critical length (equals effective bond length), the fracture load remains constant. This
critical bonded length is smaller than 100mm and the bondlength used for this research was set to 300mm. The laminate width exhibited great influence on the bond behavior
only when it was less than 10mm6. The laminate width chosen for this research was 50mm for all specimens.
The identification of each type of specimen is explained inFig. 4. Three specimens were made for each combination
concrete / mortar - fiber, totaling 36 specimens tested.
Fiber and concrete
Fiber properties are shown in Table 1. The properties ofthe fibers are values obtained from the manufacturer. Because the main objective of this research is to propose a bondstress-versus- slip model for any combinations of concrete /mortar and FRP in general, carbon (standard and high stiffness) and aramid fiber were used. To verify the influence ofthe quality of the substrate, the specimens were made by conLoad

Load

Load

Load

FRP

Concrete
Bond length(a) Direct tensile type(b) Double-face shear type

Load
Depth

Concrete

Load
BondlengthInitial crack
FRP

Width

FRP

Bond Length(c) Bending type

Concrete

Steel
plate

Concrete(d) Single-face shear type(e) Inserted typeFig.1-Bond test specimens.
ACI Structural Journal/May-June 20012

Bond stress

C5(a) Cut off type

Bond stress- SCF Hfiber unit weight
H:high, none:middle, L:low
fiber type
ARF:aramid, SCF:standard carbon,
HCF:high stiffness carbon
fiber installing peculiarity
none:epoxy, P:putty thickspecified compressive strength
5:50MPa, 2:24MPa
concrete type
C:concrete, M:mortar

Slip(b) Bilinear typeFig. 4-Identification of the specimen.

Slip

Bond stressCDP-25(c) Tesile softening type

Strain gauge@15

PI-Gauge

Slip

Fig. 5-Data acquisition sketch.

Fig. 2-Bond stress – slip model.
600
300
150

Table 1−Fiber properties

300

Type of Fiber

Notch

Standard Carbon FiberHigh Stiffness Carbon
Fiber
Aramid100
TOP VIEW
100

Unit
weightρ,g/m2
150/300

Tensilestrength
ft ,MPa
4,200

Elastic
modulus
Ef,MPa261,100

0.165

300

4,400

425,100

0.193

285

2,800

124,500

FRP laminate

Scrapedsurface

Table 2−Concrete and mortar properties

SECTION

50

Type of Base

Confinement FRPThickness
tf ,mm0.167

60

SIDE VIEW

Concrete C5
Mortar M5-1
Mortar M5-2
Concrete C2

Compressive
strengthσB
MPa
57.6
47.1
50.9
23.8

Splittingstrength σt
MPa
3.25
4.65
4.08
1.98

1/3 Secant
modulus Ec
MPa
29,00024,50025,50022,000Fig. 3-Test specimen.
crete and mortar. In addition the influence of concrete
strength (50 and 24MPa) was verified. The actual strengthof the concrete and mortar are shown in Table 2.
Loading and measurements
Each specimen was set in a universal testing machine, andsubmitted to pure tensile force, causing direct shear to beplaced on the laminates. It was not possible, however, toavoid the moment caused by the eccentricity between the top
and bottom grips. It will be discussed in greater detail inan upcoming section. The speed used for load application
was 1mm/min in the heads speed.
Total displacement and crack width at the center were measured using linear variable displacement transducers(LVDTs), as shown in Fig.5. The strain distribution was obtained from 20 strain gages set on the laminate on one face (thegage face) at intervals of 15mm, and one gage on the opposite
sides (the no-gage face), at the center of the specimen.
ACI Structural Journal/May-June 2001

EXPERIMENTAL RESULTS
Failure detail
All the specimens were submitted to tensile force until total
failure of the bond system took place. In the M5 specimens,
the substrate surface on the failure face did not present manypieces of mortar bonded on the laminate. Some pieces ofconcrete on the laminate could be found in the C5 specimens,
and a layer of concrete was bonded on the laminate in the C2
specimens after the failure. Typical failure in specimens C2
is shown in Fig.6. These facts are related to the interface between laminates and concrete, which is the region where theepoxy infiltrates into concrete and mortar, and where it is
supposed to have a concentrated wearing between FRP andconcrete / mortar. The layer of the interface was estimated tohave approximately 1 mm for concrete surface 4 . In thisresearch,the interface was not focused, an aspect that may bestudied in further research.
3

Table 3−Test results

Identification of specimen

C5-SCFH

C5-SCF

C5

C5-SCFL

C5-HCF

C5-ARF

M5-SCFH

M5-SCF

M5

M5-SCFL

M5-HCF

M5-ARF

C2-SCF
C2
C2P-SCF

(1)
(2)
(3)
(1)
(2)
(3)
(1)
(2)
(3)
(1)
(2)
(3)
(1)
(2)
(3)
(1)
(2)
(3)
(1)
(2)
(3)
(1)
(2)
(3)
(1)
(2)
(3)
(1)
(2)
(3)
(1)
(2)
(3)
(1)
(2)
(3)

At max. load
Displacement,
Load, kN
mm
51.26
0.824
50.65
0.847
54.48
0.998
37.81
1.020
33.92
1.174
33.27
1.059
24.39
2.780
23.59
2.782
24.45
2.595
38.98
1.316
38.95
1.428
32.49
1.399
25.52
1.764
25.71
2.597
23.76
1.019
41.28
0.719
44.57
0.684
47.14
0.723
30.70
0.958
33.72
1.318
32.58
1.164
17.51
2.140
17.46
2.038
20.04
2.054
33.12
1.410
32.50
1.040
29.28
0.715
25.71
2.597
24.35
2.256
25.42
1.752
28.18
1.369
27.74
1.343
30.17
1.800
29.08
1.479
30.28
1.569
30.58
1.046

Ultimate
Displacement,
mm
Load kN
51.26
0.824
50.65
0.847
54.48
0.998
37.81
1.020
30.48
1.297
33.14
1.078
23.87
2.981
22.96
2.945
24.45
2.595
37.75
1.476
38.95
1.428
32.49
1.399
25.52
1.813
24.99
3.037
21.77
1.749
41.28
0.719
44.57
0.684
46.39
0.803
30.49
1.529
33.72
1.318
32.58
1.164
17.50
2.140
16.12
2.241
19.98
2.144
33.12
1.410
32.50
1.040
29.28
0.715
25.14
2.665
23.96
2.297
23.40
2.010
27.82
1.644
25.62
1.606
29.89
2.806
28.43
1.512
29.57
1.616
25.24
1.718

Failure mode
Bond failure on gauge face
Bond failure on no gauge face
Bond failure on no gauge face
RuptureBond failure on no gauge face
Bond failure on no gauge face
Bond failure on gauge face
Partial Bond failure with longitudinal rupture on no gage face

Bond failure on gauge face
Rupture on no gauge face
Bond failure on gauge face and rupture on no gage face

Rupture on no gauge face
Bond failure on no gauge face
Bond failure on gauge face
Bond failure on gauge face
Bond failure on gauge face
Bond failure on no gauge face
Bond failure on no gauge face
Bond failure on no gauge face
Bond failure on no gauge face
Bond failure on gauge face
Bond failure on gauge face
Bond failure on no gauge face
Bond failure on gauge face
Bond failure on no gauge face and rupture on gage face

Bond failure on no gauge face
Bond failure on no gauge face
Bond failure on gauge face
Bond failure on no gauge face
Bond failure on no gauge face
Bond failure on no gauge face
Bond failure on gauge face
Bond failure on gauge face
Bond failure on no gauge face
Bond failure on gauge face
Bond failure on no gauge facealso shows the failure mode and the face where the failure took
place. As previously mentioned, gage face herein means theface (side) where the strain gauges were distributed. The opposite, or no-gage, face has only one gage located at the centerof the specimen. The specimens were supposed to be underpure tensile force, but it was not possible to avoid the moment caused by the eccentricity between the top and bottom
grips when the specimens were set on the loading machine.
Due to this, the maximum load was not considered equallydistributed in the two laminates. The maximum load in theface where the failure occurred was calculated as follows
maximum load at failure face = maximum load ×
Fig.6-Typical failure surface
Maximum load
Table 3 shows the maximum load, the ultimate load, and therespective displacements of all specimens tested. This table
ACI Structural Journal/May-June 2001

Strain at failureface(strain at failureface + strain at nofailureface)

4

HCF

40

50
C5-SCF

40
30

SCF
20

ARF
SCFL

5
20

40

60
80
100
Stiffness (t ・Ef) (kN/mm)

Fig. 7-Maximum load versus stiffness relationship
The strain used is obtained from the strain gages at the center of the specimen in both faces. Table 4 includes the average
results of the maximum load at failure face. The specimensthat had rupture or partial rupture were not considered for the
average calculations
Figure.6 shows the maximum load versus stiffness of the
FRP relationship. Each plotted point of the graph consists ofa combination of concrete (C5 and C2) or mortar (M5) with
FRP (carbon and aramid) stiffness. The stiffness is definedas the thickness multiplied by the elastic modulus of the
FRP. It was observed that the maximum load increases as thestiffness of FRP also increases. Specimen C2P-SCF was
made to verify the effect of thickness of putty layer (putty
layer = 1 mm), but the experimental results of C2-SCF and
C2P-SCF did not present a great difference. This means thatthethickness of putty had no significant effect on bond behavior.
Load – displacement relationships
The load-displacement graph was plotted using data obtained from the total displacement and crack width. Total displacement is the average between the data at two opposite
edges, and the crack width is the average of data from two
LVTDs. Examples of these graphs are shown in Fig.8. The
behavior of the specimens during the test can be seen withmore details in these graphs. The load in specimens using aramid (ARF) and low stiffness carbon fiber (SCFL) becomes
constant as it approaches the maximum load, while the displacement continues to grow. On the other hand, SCF, HCF,
and SCFH specimens do not allow an excessive elongation
before the failure, and thus reach higher maximum loads.
Strain distribution
The data obtained from the strain gages on the laminate
was used to create strain versus the distance of the strain
gage from the center of the specimen. Figure.9 shows examples of strain distribution of the C5 series. Each curve isa plot of strain at maximum load. The length of the section,
where the strain distribution has larger slope, becomes longer
as the stiffness of FRP increases. This means that the active bond stress section changes with the stiffness.
LOCAL BOND STRESS - SLIP RELATIONSHIP
Local bond stress
The difference of tensile force is obtained from the strain ofSection i and the relative strain of preceding Section i-1.
The average bond stress of section i,τb,i, has been calculated
ACI Structural Journal/May-June 2001

20

C5-SCF(1)C5-SCF(2)C5-SCF(3)

10

C5
M5
C2
C2P

10

0

C5-SCF

30

20
15

50

Load (kN)

25

Load (kN)SCFH

C5-SCF(1)C5-SCF(2)C5-SCF(3)10Total disp0

1

Crack width2
Displ (mm)012Displ (mm)Fig.8- Examples of load - displacement relationship
1.6

Strain (%)

Pmax (kN)30

1.4
C5-ARF
C5-HCF
C5-SCF
C5-SCFH
C5-SCFL

1.2
1
0.8
0.6
0.4
0.2
0

50

100

150

200

250

300

Position from center (mm)Strain gauge@15

CenterLoadedend

Fig.9-Strain distribution on the laminate in C5 series
dividing the difference of tensile force by the surface area ofthe laminate, as shown in Eq. (1).

τ b, i =(ε f , i − ε f , i −1 ) ⋅ t f ⋅ E f (i = 2 – 20)
∆l b

(1)

where,

εf , i
tf
Ef
∆lb

=
=
=
=

strain of FRP of section i;
thickness of FRP;
elastic modulus of FRP; andinterval between gages (= 15mm).

Slip
The slip of Section i, si, is the sum of the difference between the elongation of FRP and the elongation of the equivalent section compounded of concrete, epoxy layer and steel
bar, from the free end of the laminate (or the loaded end of thespecimen) to Section i. It is assumed that the relative displacement between concrete and laminate at the free end of
the laminate is zero. The slip is calculated using the following equations.
si = si −1 + (δ f , i − δ m, i )δ f ,i =δ m, i =(i＝ 2 - 20，s1＝ 0)

ε f , i − ε f , i −12

ε m, i −1 − ε m, i2(2)

⋅ ∆lb + ε f , i −1 ⋅ ∆lb(3)⋅ ∆lb + ε m, i ⋅ ∆lb(4)

5

Table 4 Maximum load at failure face and fitting results
Maximum
experimentalload ,kN
11.79
21.60
16.35
25.63
11.48
12.43
16.37
15.70
22.29
9.35
15.71
14.68

Maximumbond stressaverage,MPa

Total average

7.173
9.129
7.494
6.790
7.328
6.497
7.710
6.253
6.834
7.438
6.989
5.602

MPa

7.583

6.946

6.295

Slip at maximum
bond stress average

mm
0.063
0.060
0.072
0.060
0.072
0.066
0.046
0.067
0.063
0.059
0.052
0.087

8
6
4

Total average,
mmn average Total average
3.3
3.3
0.065
3.2
2.5
3.7
3.1
3.2
3.4
0.060
3.0
2.9
2.5
3.3
3.2
0.070
2.9
2.7

Analytical load ,
kN
12.56
20.81
16.68
22.99
11.99
12.35
20.41
16.37
22.51
11.78
15.24
15.24

y=3.5x0.19

C510

C5-ARF
C5-HCF
C5-SCF
C5-SCFH
C5-SCFLτmax (MPa)τ(MPa)

Specimen
C5-ARF
C5-HCF
C5-SCF
C5-SCFH
C5-SCFL
M5-ARF
M5-HCF
M5-SCF
M5-SCFH
M5-SCFL
C2-SCF
C2P-SCF

Stiffness tｆ⋅Ef
kN/mm
24.04
70.14
43.60
87.19
21.80
24.04
70.14
43.60
87.19
21.80
43.60
43.60

2

8
6
M5

C2
4

0

0.05

0.1

0.15

0.2
slip (mm)2ln y=a + b ln xa=1.24b=0.187

Pf

Pf -ΔPf

τ(MPa)

Fig. 10- Measured bond stress vs. slip of C5 series
9n=3.1

gauge interval
19-18
18-17
17-16

0

C5-ARF(3)

n=3.4

0.1

0.15

40

50

60

were plotted. Figure 10 shows examples of C5 series.
These curves have a tendency to become a parabolic in form.
The approximation and fitting of a model will be discussed
in the following section.

0.2
s (mm)

Fig. 11-Fitting results by Popovics equation

ε m, i =30

Fig.12-Relationship between maximum bond stress and concrete
compressive strength

n=5.5

3

0.05

20

Concrete compressive strength (MPa)

6

0

10

Pm , i −1 − 2 ⋅ τ b , i ⋅ b ⋅ ∆l b
Am ⋅ E m(5)( ε m ,1 = Pm ,1 / Am ⋅ E m , Pm ,1 = Pload )PROPOSAL OF LOCAL BOND STRESS - SLIPRELATION
Fitting for Popovic's equation
The objective of this research is to present a model that canrepresent the local bond stress versus slip (τb versus s) relationship. The formula chosen to calculate the bond stress wasPopovics's equation7, shown as follows

τbwhere,
δ f ,i=elongation of FRP in Section i;δ m, i=elongation of equivalent Section i;

ε m, i=strain of equivalent Section i;

Pm, i

=

force acting on equivalent Section i;= width of laminate;= tensile load obtained by loading machine; and= stiffness of equivalent section.
Am ⋅ E m
After calculating all the data, local bond stress versus slip
(τb versus s) graphs for each gage interval for all specimens

b
Pload

ACI Structural Journal/May-June 2001

=

s

⋅

n

τ b, max smax (n −1) + (s / smax)n(6)

where,
τ b, max
s max= maximum local bond stress;= slip at τ b, max ; andn=constant.

τb,max and smax are obtained directly from the experimental τb versus s relationship. The value of n is calculated by theleast square method using normalizedτb versus s relationship. Figure 11 shows graphically some results of Specimen
6

si

Si-1

Pf − ∆Pfτb,ipf
Epoxy layer

Table 5-Effective bond length for eachcombination concrete/mortar – FRPFRP
Pm +ΔPm

Pm

Concretedxδm,iExperimental results (kN)

Fig. 13-Infinitesimal element.

30

Stiffness (tf ・Ef) ,kN/mm

65.9
95.7
63.5
133.5
120.3
70.3
96.6
67.0
134.1
121.2
99.1

24.04
43.60
21.80
87.19
70.14
24.04
43.60
21.80
87.19
70.14
43.60

= constant = 3; and= concrete compressive strength , MPa.
When adapting this model, concrete compressive strength
should be kept between 24 and 58 MPa.

C2-SCF
C2P-SCF
C5-HCF
M5-HCF
C5-SCFH
M5-SCFH

101020Analytical result (kN)30

C5-ARF(3).Table 4 includes the fitting results of the average of three specimen's combination of concrete and mortarFRP. Maximum local bond stress, τb,max , ranges from 5.6 to
9.1MPa and slip atτb,max ranges from 0.052 to 0.087mm.
The constant n is almost 3. Though these values have noclear relationship to FRP type, τb,max shows a tendency to increase when the concrete compressive strength increases.
The relationship between the maximum bond stress averageand the respective concrete/mortar strength was analyzed.
The approximation follows equation lny = a + b lnx, witha = 1.24 and b = 0.187. The result isτb,max = 3.5 σB0.19 , andis shown in Fig.12. The adopted values of smax and n are theaverage of the all specimens, shown in Table 4. The final results for Popovics's model are
τb
s
n
(7)
=
⋅
τ b , max s max (n − 1) + ( s / s max ) n

τ b , max = 3.5σ B

0.19

where,

τb= local bond stress , MPa;s=

= slip at τ b, max = 0.065mm;

n
σB

C5-SCFL
M5-SCFL
C5-ARF
M5-ARF
C5-SCF
M5-SCF

Fig.14-Relationship between experimental maximum load
and analytical maximum load.

τ b, max

Effective bond length mm

C5-ARF
C5-SCF
C5-SCFL
C5-SCFH
C5-HCF
M5-ARF
M5-SCF
M5-SCFL
M5-SCFH
M5-HCF
C2-SCF

s max

20

0

Specimen

slip ,mm:= maximum local bond stress, MPa;

ACI Structural Journal/May-June 2001

(8)

ADAPTATION OF PROPOSED MODEL
Method of analysis
To confirm the proposed bond stress-slip relationship, ananalytical program was performed. This was done by analyzing the equilibrium of the acting force and the compatibilityof deformation at an infinitesimal element, shown in Fig.13.
Assuming that the internal bond stress of the element is constant, the slip is obtained from the difference of deformation
between laminate and the equivalent section (concrete,epoxy and steel). The bond stress is calculated using the slip,
and was obtained by the following sequence:(i = 2 to n : n is the number of the infinitesimal element)
1.Denominating the slip at free end as s1;
2.The bond stress of the infinitesimal element i ( τ b,i) is
calculated using the slip at section i-1 (si-1) on the model;
3.The increment of forceΔPf,i, the elongation of the laminateδf,i, and the elongation of the equivalent section,δm,i oftheinfinitesimal element i are calculated using the following
equations∆Pf , i = τ b, i ⋅ b ⋅ ∆x

(9)

δ f ,i =∆P f , i  i −1∆x Σ ∆Pf , k +2 
t f ⋅ b ⋅ E f  k =1

(10)

δ m, i =∆P f , i ∆x  n Σ ∆Pm , k +
2 Am ⋅ E m  k =i +1(11)

4.Calculation of slip si, tensile load Pf,i, and FRP strain εf,iusing the next equationss i = s i −1 + (δ f , i − δ m , i )(12)Pf , i = Pf , i −1 + ∆Pf , i

(13)

7

Table 6−Parameters of Kamiharako et al. experimentConcrete

34.9
36.3
36.3
36.3
34.9
34.9
38.8
36.3
41.5
41.5
38.8
36.5
42.4
36.5
35.1
53.4
75.5
42.4

27500
28000
28000
28000
27500
27500
29000
28000
30000
30000
29000
28100
30300
28100
27600
34000
40400
30300

Fiber type

Carbon0.111

270

Aramid0.169

80

CarbonAramidCarbon

0.111
0.169
0.222

270
80
270

Carbon0.111

270Table7- Analytical results using Kamiharako et al.
parameters

Specimen
S1-1
S1-2
S1-3
S1-4
S1-5
S1-6
S1-7
S1-8
S1-9
S1-10

Maximum load
average fromexperiment ,kN
6.25
5.78
9.84
8.78
12.89
14.71
12.83
22.52
29.84
29.38

ε f ,i =FRPElastic
Thickness, mm modulus ,GPa Width ,mm Length ,mm

Maximum loadfrom analysis ,kN
5.31
5.45
10.57
10.67
15.17
15.75
16.12
26.11
35.84
45.21

Comparison
exp/ana
1.18
1.06
0.93
0.82
0.85
0.93
0.80
0.86
0.83
0.65

Pf , itf ⋅b⋅ Ef(14)

5. The bond stress calculation is repeated from the infinitesimal slip of the free end to the step where the bond stressbecomes extremely small.
The tensile load acting on the laminate is Pf,n, and the Δx
adopted is 0.1mm.
Comparison between analytical results andexperimentalExperimental results
The proposed model was adapted and verified using thenext graph Fig.14. Fig.14 shows the comparison between
experimental and analytical results of the maximum load. It canbe seen that the analytical results represent very well theexperimental results.
Effective bond length
The bond stress is distributed in a limited area of the laminate, and the load is sustained in the vicinity of the loading
point. When the delamination of the laminate occurs due to
ACI Structural Journal/May-June 2001

Bond Stress (MPa)Elastic
modulus, MPa

10
10
20
20
30
30
30
50
70
90
30
30
30
30
30
30
30
30

145
250
145
175
100
175
250
250
175
175
175
200
175
200
175
175
175
175

Failure mode
Fiber rupture
Fiber rupture
Fiber rupture
Bond failure
Bond failure
Fiber rupture
Bond failure
Fiber rupture
Bond failure
Bond failure
Bond failure
Bond failure
Fiber rupture
Bond failure
Bond failure
Fiber rupture
Bond failure
Bond failure

8C5-SCFH

7
6 τmax = 7.56MPa
54
3 τmax/10 = 0.756MPa

first pointsecond point2
1

effective bond length

0

150
200
250
300
Distance from center (mm)Fig.15-Example of effective bond length.

Effective bond length (mm)Specimen
S1-1
S1-2
S1-3
S1-4
S1-5
S1-6
S1-7
S1-8
S1-9
S1-10
S2-1
S2-2
S3-1
S3-2
S4-1
S5-1
S5-2
S6-1

Compressive
strength ,MPa

50

100

150
HCF

120
90
60

SCF
ARF
SCFL

C5
M5
C2

30
0

SCFH

20

40

60
80
100
Stiffness (t ・Ef) (kN/mm)
Fig.16-Effective bond strength versus stiffness.

the fracture of concrete, the active bonding area shifts to a
new area, and it continues until the delamination propagatescompletely.It is assumed that when the bond stress reaches
a maximum level,it keeps the form and moves to the free endof the laminate.
8Experimental results (kN)

50
40

1.The maximum load increases as the stiffness of FRP
also increases;
2.Putty thickness is shown to have no affect, and the incremental increase of its layer did not imply an increase inmaximum load; and3.Maximum local bond stress is not influenced by the typeof FRP, but increases as concrete compressive strength increases.

Kamiharako

30

ACKNOWLEDGEMENTS

20

CarbonAramidno bondfailure100

10 20 30 40 50
Analytical result (kN)

Fig. 17-Results from Kamiharako et al.
It is also determined herein that the effective bond length isthe distance between two points that correspond to 10% of the
maximum bond stress. Fig.15 shows graphically the effecttive bond length. The effective bond length for each combination concrete / mortar - FRP are shown in Table5. It can beseen that the effective bond length is related to the stiffness of
FRP. Table 5 is graphically represented in Fig.16.

Comparison with previous study
To verify the validity of this model, the maximum load
was calculated by the model proposed in this research using
data from Kamiharako’s previous study6, and was comparedwith the experimental results. The experiment had used thesame specimen with a cross section of 100 x 100mm. The
parameters are: concrete strength, type of fiber (carbon andaramid), width and length of laminate, layer of laminates,and elastic modulus of resin. The parameters are shown in
Table 6 and the results are shown in Table7. The results are
represented graphically in Fig.17. Analytical strengths show
good correspondence with the experimental strengths formost specimens. The ratio of experimental values to analysis becomes smaller, when the width of laminates becomeslarger. It is supposed that failure other than bond delamination took place when the width of the laminates was almost
same as the width of specimen.

CONCLUSIONSIn this research, a local bond stress – slip model was proposed based on Popovics's equation, which represents withgood accuracy the experimental results. The model was also
verified by comparing the test results from a previous study
with the analytical results obtained with the present model.
Additionally, the effective bond length for each combinationof FRP – concrete / mortar was presented. The following conclusions can be made from this experiment:

ACI Structural Journal/May-June 2001

The financial assistance provided by University of Tsukuba Project is
gratefully acknowledged.

Am ⋅ E mb
Efn
Pf , i
Pload
Pm, i
s
s max
tf
∆lb

∆Pf ,i∆Pm,i∆xδ f ,iδ m, iε f ,iε m, iσBτbτ b, max

=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=

NOTATIONS
stiffness of equivalent section
width of laminate
elastic modulus of FRP
constant for Popovics's equation
force acting on FRP Section i
tensile load obtained by loading machine
force acting on equivalent Section i
slip
slip at τ b , max
thickness of FRP
interval between gages
increment of acting force of FRP in Section iincrement of acting force of equivalent Section ilength of infinitesimal element
elongation of FRP in Section ielongation of equivalent Section istrain of FRP of Section istrain of equivalent Section i
concrete compressive strength
local bond stressmaximum local bond stress
REFERENCES

1.Horiguchi, T. and Saeki, N., “Effect Test Method and Quality of Concrete on Bond Strength of CFRP Sheet,”Proceedings of Third International Symposium of Non-Metallic (FRP) Reinforcement for Concrete
Structures, Vol. 1, 1997, pp. 265-270.
2.Okano, M.; Ohuchi, H.; Moriyama, T.; Matsumoto, N.; and Wakui,
H., “Carbon Fiber Retrofit of Railway Viaducts Columns, ” Proceedings ofThird International Symposium of Non-Metallic (FRP) Reinforcement forConcrete Structures, Vol. 1, 1997, pp. 403-410.
3.Maeda, T.; Asano, Y.; Sato, Y.; Ueda, T.; and Kakuta, Y., “A Study on
Bond Mechanism of Carbon Fiber Sheet, ” Proceedings of Third International Symposium of Non-Metallic (FRP) Reinforcement for Concrete
Structures, Vol. 1, 1997, pp. 279-286.
4.Sato, Y.; Kimura, K. and Kobatake, Y., “Bond Behavior between
CFRP Sheet and Concrete (Part 1), ” Journal of Structural and Construction Engineering, Architectural Institute of Japan, Vol. 500, 1997, pp. 75-82(in Japanese).
5.Brosens K. and Van Gemert D. “Anchorage Design for Externally
Bonded Carbon Fiber Reinforced Polymer Laminates”, Fiber Reinforced
Polymer Reinforcement for Concrete Structures, American ConCrete Institute, Frmington Hills, Mich., 1999, pp. 635-645.
6.Kamiharako, A., Shimomura, T., Maruyama, K. and Nishida, H.,“Analysis of Bond and Debonding Behavior of Continuous Fiber Sheet
Bonded on Concrete”, Journal of Materials, Concrete Structures and Pavements, Japan Society of Civil Engineers, Vol. 634, 1999, pp. 197-208. (inJapanese)
7.Popovics,S.“A Numerical Approach to Complete Stress-StrainCurveof Concrete”, Cement and Concrete Research, Vol. 3, 1973, pp. 583-559.

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