modelling of bond strength of frp-concrete …jestec.taylors.edu.my/vol 14 issue 6 december...

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.

3310 A. M. Sayed

Journal of Engineering Science and Technology December 2019, Vol. 14(6)

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.

Modelling of Bond Strength of FRP-Concrete Interface on the . . . . 3311


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


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



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

3314 A. M. Sayed


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



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


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.



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


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.



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


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.



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


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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