MODELLING OF BOND STRENGTH OF FRP-CONCRETE …jestec.taylors.edu.my/Vol 14 issue 6 December...
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Journal of Engineering Science and Technology Vol. 14, No. 6 (2019) 3309 - 3326 © School of Engineering, Taylor’s University
3309
MODELLING OF BOND STRENGTH OF FRP-CONCRETE INTERFACE ON THE BASIS OF A
COMPREHENSIVE EXPERIMENTAL DATABASE
AHMED M. SAYED
Department of Civil Engineering, Engineering Faculty, Assiut University, Assiut, Egypt
Department of Civil and Environmental Engineering, College of Engineering,
Majmaah University, Al- Majmaah, 11952, Saudi Arabia
E-mail: [email protected]
Abstract
The efficacy of many technologies used to strengthen concrete structures
reinforced by bonded Fiber-Reinforced Polymer (FRP) sheets is mainly
dependent upon the interface that binds concrete substrates to FRP sheets. The
focus of this study is to see how the interface binding FRP to concrete behaves
in different systems of bonding. Clearly, various key variables tend to influence
the load bond strength, FRP thickness, width of FRP composites, the width of
the concrete prism, modulus of elasticity of FRP composites, concrete strength,
and operative bond length of FRP sheets. First, the different models used for
evaluating bond strength under static loading with the entire lengthening of
FRP-concrete interface bond have been revised. A broad database comprising
757 investigational datasets of common joints with FRP concrete bonds has
been designed for calibrating the parameters of the suggested model and
examining the validity thereof. Thereafter, the prediction results from the
recommended model and such models that already exist are compared based
on the collected database. The outcomes show that the mean, the conforming
variant coefficients and the coefficients of correlation given by the suggested
model are 1.00, 18.63% and 0.94, respectively, which indicates the proposed
model of bond strength of the concrete interface composed of FRP under static
load attains greater accuracy as compared to previous models. Through the
examination, it has been comprehended that the width of FRP composites has
no linear impact on ultimate bond strength.
Keywords: Bond strength models, FRP-concrete interface, FRP plates, FRP sheets.
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1. Introduction
Fiber-Reinforced-Polymer (FRP) techniques, used for forming bonds, is considered
to be an effective way of rehabilitating and fortifying reinforced concrete (RC)
structures for the last many years. However, de-bonding FRP from the concrete may
result in fiasco while implementing this technique. Therefore, how the mechanism of
bonding and de-bonding behave in this process need to be understood very keenly.
One of the cardinal factors is the strength of the bond governing the relationship
between bonding and de-bonding. The strength of the bond theoretically fluctuates
for many factors such as, how wide, thick and flexible FRP sheets are, together with
the bond length and the concrete interface performance [1].
For comprehending how the mechanism concerning FRP concrete interface
bonding and de-bonding behave, a few shear methods of testing, e.g., single or
double-lapped shear or bending tests [2, 3] got conducted, as shown in Fig. 1. Such
tests were meant to study the performance of strength of the bond and transfer of
the force in FRP concrete interface.
Fig. 1. Classification of bond tests [2, 3].
Numerous such studies have been previously conducted, that is elaborated in the
sections to follow. Many bond strength models have also been designed in the past,
based on both theoretical investigations and experimental observations. In general,
most of the models that deal with the strength of the bond are categorized in two
ways: The First category, empirical models taken from huge experimental data [4-
10], and second category, theoretical fracture analysis models [11-17]. The first
category includes all models that are based on simple tests, such as bending tests or
double- or single-lapped shear tests, developed for obtaining some parameters.
It is unfortunate that the actual failing of mechanism tends to be far more
complicated than what the shear test is able to show. For applying experimental
models, a number of restrictions of use need to be determined for a particular
case. If not, the anticipated outcomes may result in a substantial deviation from
the actual outcomes.
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Although there are numerous models as mentioned above, limitations and
deficiencies still exist. For all existing models, FRP composites, FRP sheets, and
FRP plates are not considered separately. In addition, all of these models consider
the effect of the FRP width as a linear relationship. However, it may introduce
errors because the failure mode is de-bonding instead of tensile rupture and the
distributing strain of the FRP composites is not constant along the width of FRP
composites [18]. The research community has yet not recognized any of the
suggested models for bond strength because of the limitations in their application.
Further investigation is required in the field for understanding and modelling de-
bonding collapse in the structures of concrete fortified by FRP bond, and
developing guidelines for the relating design and application. Hence, based on
analysing 757 test datasets statistically collected from the existing literature, a
simple, however, more logical and precise, model for bond strength is
recommended in this paper. A comparison of the suggested model has also been
made with the models of bond strength that already exist.
2. Existing Bond Strength Models
A collection of different existing models has been made to evaluate their accuracy
concerning the bond strength of FRP-concrete bonded samples. Eleven models
considering effective bond length from studies by Japan Concrete Institute [4],
Maeda et al. [5], Khalifa et al. [6], Sato et al. [7], Wu et al. [8], Chen and Teng [11],
Teng et al. [12], Lu et al. [13], Neubauer and Rostasy [14], Niedermeier [15] and
Yang et al. [19], four models not regarding effective bond length by Brosens and
Van-Gemert [9], Tanaka [10], Adhikary and Mutsuyoshi [20] and Hiroyuki and
Wu [21] and two models free of bond length by Dai et al. [16] and Taljsten [17]
were reported by Chen and Teng [11], Hamze-Ziabari and Yasavoli [22], Tautanji
et al. [23], Bellini and Mazzotti [24], Tautanji et al. [25], Shrestha et al. [26] and
Vahedian et al. [27]. The categorization of aforementioned models was made either
on experimental models, which are founded straight on the regression of test data
or models that are constructed on fracture mechanics or design schemes usually
grounded on some modest suppositions. Each model has been described briefly
below together with the particulars mentioned in the references citations. Table 1
illustrates the categorization of the enlisted specimen based on the feasible length
of the bond to calculate the anchorage load (Pu).
The facts mentioned above make it evident that a substantial “parametric study”
is essential for developing a model of bond strength that should be advanced as
compared to the previous ones in its design practicability. Such a study having been
carried out can show that an appropriate length of bonding tends to have a huge
effect on the optimal strength of the bond as illustrated in Table 1. The operative
bonding length (Le) is necessary for developing the optimum FRP tensile stress that
could be transferred. Wu et al. [8] offered an operational equation for bonding
length for a fracture model (the linear one) as given below:
09.0'
54.0
395.0
c
ff
e
f
tEL
(1)
The above equation was proposed in accordance with the existing empirical
findings that are statistically analysed for an appropriate length of the bonding. The
proposed effective bonding length equation, Eq. (1) [8], closely agrees with the existing
test outcomes of FRP-to-concrete bonded joints. Moreover, Eq. (1) exhibits improved
3312 A. M. Sayed
Journal of Engineering Science and Technology December 2019, Vol. 14(6)
functionality as compared with already available equations dealing with an appropriate
length of bonding.
Table 1. A brief of bond strength as quantified by
different existing models available in the literature.
Refs. Models Parameters
[4] )93.0(44.0'
cefu fLbP LLtEL effe & 125.057.0
[5] )102.110( 6
ffefu tELbP
mm)& GPa(
; ln58.013.6
ff
tE
e
tE
eL ff
[6] ffcefu tEfLbP3/2'6 42/102.110
[7] )1068.2()2( 52.0' ffcefu EtfLbbP LLtEL effe & 89.1
4.0
[8]
e
e
ffcfw
effcfw
u
LLL
LtEfb
LLtEfb
P if 585.0
if 585.0
1.2
0.541.0'
0.541.0'
bcb
bb
wf
cf
/25.1
/25.2
09.0'
54.0
395.0
c
ff
e
f
tEL
[11] '427.0 cefLwu fLbP
'/1
/2,
c
ff
ebcb
bb
w
f
tEL
f
cf
eL LL when 00.1
eeL LLLL when )2/()(sin
[12] '48.0 cefLwu fLbP
[13]
e
ee
ffff
effff
u
LLL
L
L
LGtEb
LLGtEb
P when 22
when 2
twf fG2
308.0
bcb
bb
wf
cf
/25.1
/25.2
[14]
e
ee
ctffff
ectffff
u
LLL
L
L
LftEbk
LLftEbk
P if 264.0
if 64.0
ctm
ff
f
tE
ec
ct Lf
f2
3/2'
,10
84.1
[15]
e
ee
ffff
effff
u
LLL
L
L
LtEGb
LLtEGb
P when 2278.0
when 278.0
400/1
/2125.1
f
cf
b
bb
fk
ctmffff
tE
e fkcGLctm
ff 2
4,
[18]
ct
ff
f
tE
ctefu fLbP100
08.05.05.0 Le =100 mm
Models not considering effective bond length
[9] ctmfu LfbP 5.0 L in mm
[10] )ln13.6( LLbP fu L in mm
[19] )25.0(3/2'
cfu fLbP L in mm
[20] )88.5( 669.0 LLbP fu L in cm
Models independent of bond length
[16] ffffu GtEbbP 2)2( mm 7.3,524.0236.0'
bfG cf
[17] T
fff GtE
fu bP 1
2
mm 5040 , / refrefcffT ttEtE
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3. Experiments and Database
Currently, an increased sum of experimental research work exits regarding the
bonding of FRP to concrete junctions. Experimentation has been made applying
multiple setups with various kinds of models, involving single shear, double shear,
and bending tests. On the basis of a survey of the literature, a databank having 757
shear tests on FRP-concrete interfaces got collected. Information on the databank of
experimental data is given in Table 2. Single shear, double shear, and bending tests
are incorporated in this databank. The databank that already exists shelters a vast
variety of multiple parameters, as shown in Fig. 2. FRP thickness (tf) from 0.08 to 4.0
mm, width (bf) from 10 to 120 mm, bond length (L) from 20 to 800 mm, and modulus
of elasticity (Ef) fluctuate 22.5 to 425.1 GPa. Cylinder-shaped strength of
compression (f′c) and width of concrete prisms (bc) differ from 16.0 to 76.0 MPa and
100 to 300 mm, in turn. The databank clearly accommodates a vast range for each
parameter with an expectation for providing a trustworthy yardstick to qualify a
variety of models for predicting de-bonding behaviour and the relevant parameters.
Table 2. Review of tested specimens from
experimental studies in existing literature.
Refs. No. of
specimens
Type of FRP sheets Type of FRP plates Type of test
L ≥ Le L < Le L ≥ Le L < Le
[1] 18 16 C 2 C Single
[3] 72 52 C 18 C 2 G Single
[5] 8 6 C 2 C Single
[9] 24 24 C Single
[17] 15 4 G 3 C+6 St 1 C+1 St Single
[19] 7 6 C 1 C Double
[21] 3 3 C Single
[23] 7 7 C Single
[28] 5 5 C Single
[29] 34 15 C 3 C 13 C 3 C Single
[30] 32 11 C 1 C 20 G Single
[31] 19 17 C 2 C Single
[32] 6 3 C 3 C Single
[33] 4 2 C 2 C Single
[34] 26 16C+5G+5A Single
[35] 10 10 C Single
[36] 3 3 C Double
[37] 14 5 C+ 9 B Double
[38] 30 3 C 15C+3A 9 C Double
[39] 3 3 C Double
[40] 18 15C+3A Double
[41] 18 6A+6C+6P Double
[42] 6 3 C 3 C Single
[43] 6 4 C 2 C Double
[44] 36 30C+6A Double
[45] 18 6 C 3 C 6 C 3 C Single
[46] 39 39 C 16 Double+ 23Bending
[47] 30 4C+15G 10C+1G Single
[48] 36 4C+4G+1A 14C+2G+11St Single
[49] 7 7 B Double
[50] 33 27 C 6 C Single
[51] 12 2 C+10 G Double
[52] 22 19 C 3 C 8 Double + 14
Bending
[53] 8 2 C 6 C Single
[54] 5 5 C Single
[55] 123 32 C + 36 G 35C+20G Single
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Fig. 2. Some of the parameters affecting bond strength load.
4. Examining Reliability of Available Models
For examining how reliable and valid the existing models are, a broad verification is
conducted employing a chain of investigational datasets existing in the literature. The
databank taken into consideration consists of 757 experimental tests involving 606
specimens using FRP sheets and 151 specimens using FRP plates. The gathered tests
vary geometrically, FRP thickness (tf), width of FRP composites (bf), modulus of
flexibility of the FRP compounds (Ef), concrete strength (f′c), width of concrete prisms
(bc) and an appropriate bond length of the FRP sheet (L), with a varied range of
geometric and mechanical attributes.
Because of the large number of specimens and their randomness, the probability of
error exists. Five percent of all specimens are excluded and the full analysis is
performed on the other 95%. Most of the specimens that have been ignored are the same
in each existing model, which indicates the presence of an error in these specimens. The
average value; the coefficients of variation, COVs; the correlation coefficient, r; and the
minimum and maximum ratio of Pu.Exp/Pu.Pred for FRP composite sheets and plates
validation configurations to compare the predictions of the existing models with the
experimental results are illustrated in Table 3.
Table 3. Statistical analysis results regarding the experimental-to-predicted
bond strength proportions of various bond strength models.
Models FRP sheets FRP plates
Refs. Average r COV% Max. Minimum Average r COV
% Maximum Minimum
[4] 1.10 0.86 26.91 2.06 0.60 1.19 0.67 50.06 2.67 0.54
[5] 1.15 0.85 27.47 2.27 0.63 1.32 0.72 46.36 3.01 0.51
[6] 1.23 0.85 27.14 2.53 0.64 1.49 0.64 41.16 2.99 0.42
[7] 1.11 0.26 62.32 3.76 0.29 0.53 0.08 118.16 3.45 0.08
[8] 1.06 0.91 24.06 1.91 0.66 1.16 0.67 36.60 1.98 0.54
[9] 1.10 0.51 51.66 2.95 0.24 1.47 0.10 42.41 2.81 0.17
[10] 1.86 0.62 38.78 4.50 0.67 3.60 0.15 46.81 7.86 0.93
[11] 1.20 0.91 21.21 1.98 0.76 1.28 0.77 38.34 2.56 0.69
[12] 1.09 0.91 22.30 1.92 0.70 1.14 0.77 38.30 2.27 0.62
[13] 1.16 0.91 21.62 1.87 0.70 1.20 0.80 39.24 2.54 0.63
[14] 1.02 0.88 23.24 1.85 0.55 1.11 0.74 38.69 2.19 0.54
[15] 1.05 0.88 24.25 1.95 0.59 1.12 0.76 41.24 2.29 0.61
[16] 0.73 0.87 25.94 1.30 0.37 0.80 0.75 45.57 1.92 0.39
[17] 0.85 0.86 26.10 1.67 0.47 1.00 0.73 48.53 2.35 0.39
[18] 1.05 0.84 27.33 2.12 0.53 1.35 0.74 40.45 2.85 0.41
[19] 0.78 0.60 52.61 2.31 0.24 1.05 0.12 41.92 2.28 0.25
[20] 1.81 0.74 31.44 3.43 0.67 3.28 0.48 34.45 5.47 0.66
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Table 3 makes it evident that the existing models have some accuracy in
predicted bond strength for FRP sheets, however, are inaccurate for FRP plates.
In addition, all of these models take the effect of the FRP width as linear,
however, this is not a true effect because the mode of failure is de-bonding instead
of tensile rupture and the distributing strain of the FRP composite is not constant
along the full width [21]. Additionally, the width of the concrete prism (bc) is
ignored in almost all of the existing models.
Currently, no proposed bond strength model is unanimously accepted by the
research community, because of the inadequate realization and practical application.
Hence, it seems prudent to take these parameters that have been ignored in
existing models for predicted bond strength and incorporate them into a new model
with higher accuracy.
5. Parameters Affecting Anchorage Load and Prediction Bond
Strength Model
A parametric study is conducted for determining as to which, it should be adopted
in the experimental results that will affect the bond strength.
Clearly various key variables tend to influence the load bond strength, FRP
thickness (tf), width of FRP composites (bf), width of concrete prism (bc),
modulus of elasticity of FRP composites (Ef), concrete strength (f ′c) and
operative bond length of FRP sheets (L). In this analysis, all of the parameters
are studied separately.
5.1. FRP thickness effect
The FRP composite thickness is an important element, which has a straight affect
on the strengthening and stiffing of the ultimate load bond strength.
The bond strength, (Pu) is dependent upon the thickening of the plate either as
the functioning of (tf) as described by Maeda et al. [5], Khalifa et al. [6] and Sato
et al. [7], or as the functioning of (tf0.5) as described by Japan Concrete Institute [4],
Wu et al. [8], Chen and Teng [11], Teng et al. [12], Lu et al. [13], Neubauer and
Rostasy [14], Niedermeier [15], Dai et al. [16], Taljsten [17] and Carloni and
Subramaniam [18].
Thus, the relationship between Pu and tf needs to be further discussed. It has
been seen that in case more than one layer of fibre sheet is employed to make a
plate, the sum of thickening employed for the purpose of calculating needs to be
produced as a distinct thickening of fibre and all the layers.
A huge discrepancy between the investigational eventual load and projected
strength of the bond was witnessed because the existing models do not
distinguish between sheets and plates with regard to the influence of the
thickness of the FRP composites, and because of their handling of the workable
FRP bond length composites. According to the experimental results, the FRP
composite thickness increases the eventual load bond strength for FRP sheets by
(tf0.57 and tf
0.27) when the effective bond length is less than and more than the total
bond length, respectively; in the case of FRP plates, this increase is instead (tf0.41
and tf0.32) under the same condition as above, as shown in Fig. 3.
3316 A. M. Sayed
Journal of Engineering Science and Technology December 2019, Vol. 14(6)
Fig. 3. Influence of thickness of FRP based on experimental results.
5.2. Effect of elastic modulus of FRP composites
The effect of the elastic modulus of the FRP composites (Ef) renders a key role in
designing guidelines at the time of increasing the contribution of FRP, as
demonstrated in Fig. 4. The bond strength, Pu, is dependent upon the elastic
modulus of the FRP composites as one interaction with the thickening of FRP as
the stiffness of the FRP for all of the existing models.
Thus, there exists a need to separate the influence of the flexible modulus of the
FRP and the thickness of the FRP composites because the mode of failure is de-
bonding instead of tensile rupture. As per the experimental results, the elastic
modulus of the FRP composites causes a growth in the eventual load bond strength
for FRP sheets by Ef0.45 and Ef
0.31 for effective bond lengths less than and more than
the total bond length, respectively; in case of FRP plates, this increase is instead
Ef0.34 and Ef
0.59 for effective bond lengths less than and more than the total bond
length, respectively, as illustrated in Fig. 4.
Fig. 4. Effect of flexible modulus of FRP
composites based on experimental outcomes.
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Journal of Engineering Science and Technology December 2019, Vol. 14(6)
5.3. Effect of FRP composites width
The FRP composites width plays an important role, and every model considers this
influence. The bond strength, Pu, is dependent upon the width of the plate as a
function of (bf)and is linear in all of the existing models. This linearity is true if the
failure mode is a tensile rupture, however, the failure mode considered here is a
bond failure and the contact stress is not uniform along the width of FRP
composites [21]. According to the experimental results, the width of the FRP
composites causes enhancement in the ultimate load bond strength for FRP sheets
and plates by (bf 0.79 and bf
0.32), respectively, as shown in Fig. 5.
Fig. 5. Effect of FRP composites width based on experimental results.
5.4. Effect of concrete strength
The strength of the concrete also is a key element, which has a direct influence on
the strengthening and stiffening of the material that has to be strengthened. The
bond strength, Pu, depends on the concrete strength as a function for all of the
existing models. According to the experimental results, the concrete strength causes
a growth in the ultimate load bond strength for FRP sheets and plates by (f′c0.26 and
f′c0.34), respectively, as illustrated in Fig. 6.
Fig. 6. Influence of concrete strength based on experimental results.
3318 A. M. Sayed
Journal of Engineering Science and Technology December 2019, Vol. 14(6)
5.5. Influence of effective bond length of FRP composites
Various studies by Japan Concrete Institute [4], Maeda et al. [5], Khalifa et al. [6]
Sato et al. [7], Wu et al. [8], Chen and Teng [11], Teng et al. [12] and Carloni and
Subramaniam [18] affirm that an optimal length of bond does exist, and yonder it
is not possible to enhance the fibre bond length further to have an increase in the
load of the anchorage. Most of the aforementioned models are free of Le. These
kinds of models tune out to be erroneous because of the theoretical description of
the situations where the whole tensile strength of the fibre-plate (bonded) is
attained. The database constructed in this research verifies this fact, as the entire
strength of the tensile in respect of the bonded plate is not realized in any dataset
recorded. Hence, the findings of the current study affirm the presence of an optimal
length of the bond. According to the experimental results, the effective bond length
causes a growth in the ultimate load bond strength for FRP sheets and plates by (L
/ Le)0.28 and (L / Le)0.77 for effective bond length more than the total bond length,
respectively, as illustrated in Fig. 7.
Fig. 7. Impact of the optimal length of bond comprising
FRP composites based on experimental outcomes.
5.6. Impact of width of concrete prism
Concrete prism width has an influence on the effective strain of FRP composites.
The breadth proportion concerning the sheet that is bonded to the member of
concrete (bf/bc) register a substantial impact on the eventual strength of the bond.
In case the width of the bonded sheet turns out to be less in relation to the concrete
member, the transferred strength from the sheet to the concrete results in a
distribution of hat is not identical throughout the width of the concrete member.
Some of the existing models consider this effect as a coefficient βw, as shown
in Table 1. The present study introduces the element of breadth in the new model
as a separate parameter. When the width of the concrete prism increases, the
effective strain also increases; this leads to slower de-bonding failure [56]. While
analyzing the regression of this investigational database, it was observed that the
average enhancement in the ultimate bond strength was (bc0.21) for all of the cases
of FRP composite sheets and plates.
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Journal of Engineering Science and Technology December 2019, Vol. 14(6)
5.7. Prediction of the bond strength model
The element considered in the present study, show the geometrical and
configurational characteristics needed to fix the strength of the bond concerning the
FRP-concrete interface by analysing the regression of this experimental database
as demonstrated in Figs. 3 to 7.
On the basis of the regression analysis of this empirical database of 757
specimens, earlier a clarification was given that the bond strength of the FRP-concrete
interface fluctuated with the fluctuations in tf, bf, Ef, f′c, bc, and L/ Le; it can be noticed
that all the parameters have a nonlinear influence on the bond strength of the FRP-
concrete interface. Therefore, the relation between the bond strength of the FRP-concrete
interface and those nonlinear affecting limitations is articulated in two equations based
upon the type of FRP composites (sheet or plate), as shown in Eqs. (2) and (3).
For FRP sheets:
e
0.280.2131.027.079.026.0,
2
0.2145.057.079.026.0,
1
LLfor )(
eLLfor
ecfffcs
cfffcs
u
L/LbEtbfC
bEtbfC
P (2)
For FRP plates:
e
0.77
e
0.2159.032.032.034.0,
2
e
0.2134.041.032.034.0,
1
LLfor )(L/L
LLfor
cfffcp
cfffcp
u
bEtbfC
bEtbfC
P (3)
where the constants Cs1, Cs2, Cp1, and Cp2 are slopes of the association between the
rise in the ultimate load bond strength gathered from the experimental outcomes
and the integrated limitations, as displayed in Fig. 8. For FRP sheets with effective
bond lengths less than and more than the total bond length, the corresponding Cs1,
and Cs2 are 0.879 and 2.620, respectively. For FRP plates with effective bond
lengths less than and more than the total bond length, the corresponding Cp1, and
Cp2 are 12.380 and 0.865, respectively.
Fig. 8. Relation between ultimate load bond strength gained
from empirical results and integrated corresponding parameters.
3320 A. M. Sayed
Journal of Engineering Science and Technology December 2019, Vol. 14(6)
6. Comparison of the New Model with Experimental Results
For examining as to how reliable and valid the newly suggested model is, a
thorough confirmation is rendered utilizing empirical data existing in the previous
studies. The database taken into consideration is made of 757 investigational tests,
that include 495 specimens using FRP sheets with effective length of the bond
lesser than the total bond length, 111 specimens using FRP sheets with effective
bond length more than the total bond length, 94 specimens using FRP plates with
effective bond length less than the total bond length and 57 samples using FRP
plates with effective bond length more than the total bond length. The empirical
data considered are presented in Table 2.
A graphic representation of the empirical and statistical value is compared in
Fig. 9. The recommended model brings the diverse variants of FRP composites into
contemplation the figure. As for the FRP composite sheets and plates, the mean
value of Pu.Exp/Pu.Pred is 1.00 and the coefficient of correlation, r, is 0.94, whereas
the conforming coefficients of variation, COVs, are 17.14% and 18.18% and the
range between minimum and maximum ratios Pu.Exp/Pu.Pred is 0.66 to 1.54 and 0.66
to 1.48, correspondingly. The preceding values display that, from a numerical
viewpoint, the recommended model is likewise trustworthy for all the ultimate load
bond strengths considered in the analysis. In addition, the two lines in the figure
confined to a ±20% deviance from the fresh model expectation and from the
investigational values are also conveyed. Approximately, all of the outcomes
pour inside these bounds and the average value of the new model prophecies are
discovered to be higher near the finding of the experiment.
Fig. 9. Predicted ultimate load bond strengths by new model.
7. Comparison of New Model with Existing Models
The anticipated results of the recommended model for the studies that tend to
validate have been put in comparison with the expected results deducted from the
formulated equations précised in the studies conducted earlier. Figure 10 illustrates
the average value, the minimum and maximum values of the ratio Pu.Exp/Pu.Pred for
FRP composite sheets and plates validation configurations to present the contrast
of the expected results of the suggested existing models and a new model with the
experimental outcomes.
Modelling of Bond Strength of FRP-Concrete Interface on the . . . . 3321
Journal of Engineering Science and Technology December 2019, Vol. 14(6)
The newly suggested model hold the excellent average in respect of Pu.Exp/ Pu.Pred,
the conforming coefficient of fluctuation tends to be less as compared to other models
and the coefficient of correlation is greater when compared to other modelled designs
for predicted bond strength.
In order to confirm how reliable, the anticipated outcomes are, the selected
outcomes from the existing models with relatively high accuracy are compared,
including the models by Wu et al. [8], Teng et al. [12] and Neubauer and Rostasy [14] and the proposed new model. The relationship between the number of specimens and
the ratio of Pu.Exp/Pu.Pred, are shown in Fig. 11. The results indicate that the projected
model can make accurate predictions for the FRP-concrete bond strength. Especially
for the bond strength of FRP plates to concrete, the anticipated results achieved much
higher accuracy than the results from other models.
Fig. 10. Statistical analysis results for average, minimum and
maximum values of the ratio Pu.Exp/Pu.Pred for FRP composites.
(a) FRP sheets. (b) FRP plates.
Fig. 11. Probabilistic distribution of experimental to-anticipated bond
strength proportions of new and different bond strength models.
3322 A. M. Sayed
Journal of Engineering Science and Technology December 2019, Vol. 14(6)
8. Conclusions
This article dwells upon gathering a database pertaining to usual shear tests dealing with
FRP-concrete interfaces. Based on the regression examination of this database, a novel
design of bond-strength for extrinsically bonded fibre-reinforced concrete interfaces is
suggested. An evaluation and a comparison for the working of the newly proposed bond
strength model have been made to the models that already exist. Hence, it can be
concluded, as mentioned below, based on what has been performed in this paper:
The accumulated database of 757 test datasets, covering wide-ranging interrelated
elements, is anticipated to offer a trustworthy standard for the qualification of
various models of envisaging de-bonding behaviour and correlated limitations.
Through the examination, it has been comprehended that the width of FRP
composites has no linear impact on ultimate bond strength.
The new bond strength model offers nearer agreement with the investigational
outcomes than existing models. The mean value of Pu.Exp/ Pu.Pred is 1.00; the
coefficient of correlation is 0.94; and the conforming coefficients of variants are
17.14% and 18.18% for FRP composite sheets and plates, respectively. Hence, the
suggested model is expected to provide more logical and concrete anticipated
results about the bond strength of FRP-concrete interfaces.
The outcomes demonstrate that the newly suggested model bears the capability
for assessing the bond strength of FRP-concrete interfaces in an amply accurate
and reliable manner. Therefore, it can be used as a successful instrument for
evolving design-procedures having the capability to ensure the security of the bond
strength of FRP-concrete interfaces.
Acknowledgement
Deanship of Scientific Research, Majmaah University, deserves special thanks
for his generous support for the accomplishment of this task under Project
Number No. 1439-46.
Nomenclatures
A Aramid
B Basalt
bc Concrete number’s width
bf FRP plate or sheet width
C Carbon
Ef Modulus of elasticity of FRP sheet
EC Modulus of elasticity of concrete
f′C Cylinder concrete compressive strength.
fct Tensile concrete strength
G Glass
Gf Interfacial fracture energy
L Bonding length
Le Effective bonding length
Pu Ultimate bond strength
r Coefficients of correlation
R2 Coefficient of determination
tf FRP total thickness
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Journal of Engineering Science and Technology December 2019, Vol. 14(6)
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