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Development of Efficient Prediction Model of FRP-to-Concrete Bond Strength Using Curve Fitting and ANFIS Methods

  • Research Article-Civil Engineering
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Abstract

Externally bonded fiber-reinforced polymer (FRP) plates or sheets have become a common retrofitting approach for sustaining old reinforced concrete structures in the modern era. The capacity of FRP-strengthened structures cannot be accurately estimated because the bond strength between FRP and concrete surface is accurately unpredictable. Various studies are available in the literature to predict the FRP-to-concrete bond strength (FRP-CBS), but they are based on limited experimental data sets and have lesser accuracy. To solve this problem, curve-fitting (CF) and adaptive neuro-fuzzy inference systems (ANFIS) models have been developed to predict the FRP-CBS using 935 datasets. The database was collected from published  literature and the same was used to develop the ML model. Comparison with standard guidelines, including ACI, TR-55 fib, CNR, and JCI, and other analytical models, revealed that the ANFIS model outperformed the CF model and all other analytical models. The ANFIS model achieved a correlation coefficient of 0.9189 and a mean absolute error (MAE) of 2.43 kN, while the CF model achieved a correlation coefficient of 0.7303 and an MAE value of 4.30 kN. Moreover, a parametric study was conducted to identify the influence of each specific parameter on the bond strength. The developed ANFIS-based model can be readily utilized by structural engineers, FRP applicators, and researchers for estimating the FRP-to-concrete bond strength.

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Abbreviations

f at ,f e :

Adhesive tensile strength

A tr :

Area of transverse bar

P u :

Bond strength

L f , L b , l b :

Bonded length of FRP

f ck, f c,f'c, f cu :

Compressive strength of concrete

C :

Concrete cover

f cm :

Concrete cylinder mean compressive strength

d b :

Diameter of FRP

a e :

Distance from FRP to closest concrete block edge

E f :

Elastric modulus of FRP

L :

Embedded length of bar

A f :

FRP cross-section area

p f :

FRP perimeter

\(\varepsilon\) fu :

FRP ultimate strain

d g , h g , D g :

Groove depth

p g :

Groove perimeter

b g ,W g :

Groove width

c :

Intercept of the line coordinate

y min :

Minimum value in the selected data set

L c :

Length of concrete block

y max :

Maximum value in the selected dataset

P u,normalized :

Normalized bond strength

X normalized :

Normalized values

n :

Number of bars being developed along the plane of splitting

m :

Slope of line

s :

Spacing of transverse bars

t f :

Thickness of FRP plie or strip

f f , f fu :

Ultimate tensile strength of FRP

y :

Value to be normalized

b c :

Width of concrete block

b f :

Width of FRP plie

\(\beta\) :

Surface preparation coefficient

\({f}_{ctm}\) :

Mean axial tensile strength of concrete

\(\eta\) :

Calibration factor to consider the effect of the maximum aggregate size

\({G}_{f}\) :

Interfacial fracture energy

\({f}_{ctm}\) :

Mean axial tensile strength

ANFIS-SC:

ANFIS with subtractive clustering

ANFIS:

Adaptive neuro-fuzzy inference system

ACI:

American concrete institute

ANFIS-FCM:

ANFIS with fuzzy c-means clustering

FFA:

ANFIS-firefly algorithm

ACO:

Ant colony optimization

AFRP:

Aramid fiber-reinforced polymer

ABC:

Artificial bee colony

ANN:

Artificial neural networks

BFRP:

Basalt fiber-reinforced polymer

CFRP:

Carbon fiber-reinforced polymer

r :

Cluster center radius

CPs:

Consequent parameters

DEO:

Differential evolution optimization

FRP:

Fiber reinforced polymer

FIS:

Fuzzy inference system

GPR:

Gaussian progress regression

GFRP:

Glass fiber-reinforced polymer

JCI:

Japan concrete institute

M5Tree:

M5 model tree

MAE:

Mean absolute error

RMSE:

Mean absolute percentage error

MF:

Membership function

MLR:

Multiple linear regression

MNLR:

Multiple nonlinear regression

MARS:

Multivariate adaptive regression splines

NS:

Nash-Sutcliffe efficiency index

PSO:

Particle swarm optimization

R :

Correlation Coefficient

PPs:

Premise parameters

RBNN:

Radial basis neural network

MAPE:

Root mean square error

SF:

Squash factor

FRP-CBS:

FRP-to-concrete bond strength

\(\gamma and d\) :

Experimental curve fitting coefficient

\({\beta }_{w}\) :

Width ratio between FRP and concrete

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Authors and Affiliations

  1. AcSIR—Academy of Scientific and Innovative Research, Ghaziabad, 201002, India

    Aman Kumar & Harish Chandra Arora

  2. Structural Engineering Department, CSIR—Central Building Research Institute, Roorkee, 247667, India

    Aman Kumar & Harish Chandra Arora

  3. Department of Hydro and Renewable Energy, Indian Institute of Technology, Roorkee, 247667, India

    Krishna Kumar

  4. School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala, Punjab, 147004, India

    Harish Garg

  5. Department of Civil Engineering, University of Birjand, Birjand, Iran

    Hashem Jahangir

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  1. Aman Kumar
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  2. Harish Chandra Arora
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  3. Krishna Kumar
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  5. Hashem Jahangir
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Corresponding author

Correspondence to Harish Garg.

Appendices

Appendix 1

1.1 CF Model

$$\begin{aligned} {\text{Input}}\;{\text{data }} &= \, \left[ {f_{ck} = \, 0.{2}0{4},b_{c} = \, 0.{133},E_{f} = \, 0.{247}, }\right. \\ & \quad \left.{f_{f} = \, 0.{225},t_{f} = \, 0.0{862}, }\right. \\ & \quad \left.{b_{f} = \, 0.{267},L_{f} = \, 0.{212}} \right] \end{aligned}$$
$$P_{u} = \, 0.{136}f_{ck} + \, 0.{249}b_{c} + \, 0.0{234}E_{f} {-} \, 0.0{379}f_{f} + \, 0.0{982}t_{f} + \, 0.{344}b_{f} + \, 0.{1855}L_{f} - \, 0.0{7575}$$
(37)
$$P_{u,normalized} = 0.{136 } \times 0.{2}0{4} + 0.{249 } \times 0.{133} + 0.0{234 } \times 0.{247}{-}0.0{379 } \times 0.{225} + 0.0{982} \times 0.0{862} + 0.{344} \times 0.{267} + 0.{1855 } \times 0.{212} - 0.0{7575} = 0.{122}$$
(38)
$$P_{u} = \left( {\frac{{P_{u,normalized} }}{0.8} \times 62.4} \right) + 2.4$$
(39)
$$P_{u} = \left( {\frac{0.122}{{0.8}} \times 62.4} \right) + 2.4 = 11.92 kN$$
(40)

The bond strength value obtained by CF model is 11.92 kN, which deviates significantly from the experimental result of Pu = 14.89 kN. Specifically, the bond strength predicted by the CF model is found to be 19.95% lower than the experimental value.

Appendix 2

2.1 ANFIS Model

Input data = [fck = 0.204, bc = 0.133, Ef = 0.247, ff = 0.225, tf = 0.0862, bf = 0.267, Lf = 0.212]

$$W_{1} = \left[ {exp\left( { - \frac{1}{2}\left( {\frac{{f_{ck} - c_{1} }}{{\sigma_{1} }}} \right)^{2} } \right)} \right] \times \left[ {exp\left( { - \frac{1}{2}\left( {\frac{{b_{c} - c_{2} }}{{\sigma_{2} }}} \right)^{2} } \right)} \right] \times \left[ {exp\left( { - \frac{1}{2}\left( {\frac{{E_{f} - c_{3} }}{{\sigma_{3} }}} \right)^{2} } \right)} \right] \times \left[ {exp\left( { - \frac{1}{2}\left( {\frac{{f_{f} - c_{4} }}{{\sigma_{4} }}} \right)^{2} } \right)} \right] \times \left[ {exp\left( { - \frac{1}{2}\left( {\frac{{t_{f} - c_{5} }}{{\sigma_{5} }}} \right)^{2} } \right)} \right] \times \left[ {exp\left( { - \frac{1}{2}\left( {\frac{{b_{f} - c_{6} }}{{\sigma_{6} }}} \right)^{2} } \right)} \right] \times \left[ {exp\left( { - \frac{1}{2}\left( {\frac{{L_{f} - c_{7} }}{{\sigma_{7} }}} \right)^{2} } \right)} \right]$$
(41)
$$Y_{1} = \user2{ }0.09646{ }f_{ck} { } - 1.026{ }b_{c} + { }0.3985{ }E_{f} { } - 6.1{ }f_{f} + { }2.711{ }t_{f} + { }0.2437{ }b_{f} + { }0.7315{ }L_{f} + \user2{ }2.443$$
(42)
$$\frac{{W_{1} Y_{1} + W_{2} Y_{1} + W_{3} Y_{3} + \ldots + W_{28} Y_{28} }}{{W_{1} + W_{2} + W_{3} + \ldots + W_{28} }} = \frac{0.1552}{{1.000}} = 0.1552\user2{ }$$
(43)
$$P_{u} = \left( {\frac{0.155}{{0.8}} \times 62.4} \right) + 2.4 = 14.50 kN$$
(44)

The bond strength value obtained by ANFIS model is 14.50 kN, which is near to the experimental result of Pu = 14.89 kN. Specifically, the bond strength predicted by the ANFIS model is found to be 2.62% lower than the experimental value.

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Kumar, A., Arora, H.C., Kumar, K. et al. Development of Efficient Prediction Model of FRP-to-Concrete Bond Strength Using Curve Fitting and ANFIS Methods. Arab J Sci Eng 49, 5129–5158 (2024). https://doi.org/10.1007/s13369-023-08328-0

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