# Performance Evaluation of CFRP Reinforced Concrete Members Utilizing Fuzzy Technique

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## Abstract

Aging and structural deterioration under severe environments are major causes of damage in reinforced concrete (RC) structures, such as buildings and bridges. Degradations such as concrete cracks, corrosion of steel, and deformation of structural members can significantly degrade the structural performance and safety. Therefore, effective and easy-to-use methods are desired for repairing and strengthening such concrete structures. Various methods for the strengthening and rehabilitation of RC structures have been developed over the past several decades. Recently, FRP composite materials have emerged as a cost-effective alternative to conventional materials for repairing, strengthening, and retrofitting deteriorating/deficient concrete structures, by externally bonding FRP laminates to concrete structural members. The main purpose of this study is to investigate the effectiveness of the FRP retrofit for circular type concrete columns under the framework of the adaptive neuro-fuzzy inference system (ANFIS). Retrofit ratio, strength of existing concrete, thickness, number of layer, stiffness, ultimate strength of fiber, and size of specimens are used as input parameters to predict strength, strain, and stiffness of the post-yielding modulus. These proposed ANFIS models show reliable increased accuracy in predicting the constitutive properties of concrete retrofitted by FRP, compared to the constitutive models suggested by other researchers.

## Keywords

adaptive neuro-fuzzy inference system FRP retrofitting compressive concrete strength strain 2nd elastic modulus## 1 Introduction

The performance of concrete structures needs to be improved to compensate the deterioraton induced by adverse environment, inadequate maintenance, or spontaneously varied natural conditions. The application of sectional augmentation or steel plate attachment employed to column elements has limitations due to the increase of dead weight to foundations and reduced usability. In contrast, the method employing FRP materials has been broadly propagated, because it enables comparatively simple construction work that could secure the integrity of concrete structures. Due to its advantages of excellent reinforcement effects together with superior durability and corrosion resistance realizable in a rather short construction period, the FRP materials have been broadly employed in recent maintenance and reinforcement works (Al-Nimry and Ghanem 2017).

Richart (1928) et al. conducted a study to improve the strength (of concrete members) through the lateral binding of concrete, whale Mander et al. (1988) demonstrated the effect of lateral binding through their study that mathematically examined the stress–strain relationship of laterally bound concrete; thereafter, researchers have developed the design formulae of laterally bound concrete with the development of diverse kinds of fibers.

Lee et al. (2007) and Cho (2007) also conducted tests to predict the strength and strain of the concrete retrofitted with FRP, and Hosotani and Kawashima (1999) and Youssef et al. (2007) proposed the design formulae of the lateral binding of rectangular and cylindrical columns and then suggested the formulae to predict the ultimate strength and strain of retrofitted structures and the post -yield ductility.

These empirical formulae based on respective experiments were presented independently through previously conducted studies. Thus staff in actual sites may become confused in selecting proper formulae for respective applications; and accordingly, a comprehensive examination of the capability of the performance prediction of each formula is needed. In the meantime, the theory of neural networks which uses the human learning capability beyond the systematic learning of computers has been grafted onto recent engineering applications. The theory does not constitute the causal relationship of variables used for the design through functions, but, it predicts the results by exploiting the neural networks that consist of neurons, which are the basic elements involved in human perception and judgment. The system applied theory has been recently grafted onto the structural engineering applications (Imam et al. 2015, Lee et al. 2017), and rendered excellent predictive effects. For example, Gupta et al. (2006) and Kim et al. (2004) introduced the theory of neural networks that used the mixing ratio to estimate the compressive strength of concrete, and there is a case (Park 2006) that studied the reinforcement effect of concrete beams that employed the carbon fiber sheets for flexural reinforcement. In this study, the theory of neural networks that could imitate the human-decision making capability was applied to the prediction of the stress–strain relationship of concrete retrofitted with FRP.

## 2 Adaptive Neuro-Fuzzy Inference System

The Neural Network (Fukuda 1996) has been known as a representative method that imitates human learning capability, while the Fuzzy Theory is regarded as an alternative way to realize the human decision-making faculty. Recently, neuro-fuzzy techniques that imitate human learning and decision-making capability by combining neural network and fuzzy theories have been developed; and a neuro-fuzzy system like these techniques is introduced in this study. The neuro-fuzzy system is a fuzzy system that introduces the learning capability of neural network; and the combination of fuzzy logic system based on expert knowledge and introduced flexible learning capability is applied to problems that are unable to be solved with conventional concepts.

The fuzzy system (Gil and Park 1995) consists of an input membership function, fuzzy rule, and output membership function (Layer 5). The input membership function indicates Layer 1 that would be enumerated in the input space; and in this study, the reinforcement effect was defined as an influential element. The fuzzy rule is a combination of fuzzy inference concept and back propagation algorithm of neural network; and this also indicates the process of learning (Kim et al. 2004) that reaches the final value of designed neuro-fuzzy network having minimal error and the final objective value that is intended to be attained.

Here, the \({\text{O}}_{\text{i}}^{1}\) represents the membership function corresponding to each node at ‘Level 1’; and x denotes the input value of each ‘Node’. The \(c_{i}\) and \(a_{i}\) represent the membership function designed by the central value and value of standard deviation of the i-th input value at the first Layer 1. The parameter(s) of membership function is (are) determined at Layer 1 through the Eq. (1).

In the figure above, the node implies the number of rules; and by calculating the fuzzy product using Eq. (2), the output of each node is represented as a strength of active function(s) of the rule(s).

Where, {pi, qi, ri} means the parameter set of final rule(s).

Values input into the output layer will generate resulting output values if they are converged within the predetermined error rate; otherwise, they will be re-input into Layer 2 for reiterative calculation.

## 3 Prediction of Retrofitting Effects through the Neuro-Fuzzy System

### 3.1 Gaining of the Training Data

Prediction design for confined concrete using ANFIS.

CASE | Training set | Test set | |
---|---|---|---|

1 | Number of strength (F | 284 | 16 |

2 | Number of strain (ε | 96 | 16 |

3 | Number of Secondary elastic modules (E | 87 | 16 |

The 284 data (Case-1) represented the compressive strength (F_{t}), the 96 test specimens (Case-2) gave the information of strain (ε_{t}), and the 87 test specimens (Case-3) provided the information of Post Yielding Modulus(Eg) that were used to predict the effects of reinforcement; and the accuracy of prediction and applicability of the neuro-fuzzy system to the actual field were examined.

### 3.2 The Learning of Data

Samples for training data set in this study (part in 284 samples)

Data unit | f’ | t | Layer ply | Kind – | E | f | ρ (%) | D cm | h cm | F |
---|---|---|---|---|---|---|---|---|---|---|

1 | 38.6 | 0.031 | 1 | G | 73.3 | 755 | 0.816 | 15 | 31 | 45.5 |

2 | 30.2 | 0.017 | 1 | A | 224.6 | 2716 | 0.68 | 10 | 20 | 46.6 |

3 | 26.2 | 0.1 | 1 | G | 19.1 | 330 | 2.632 | 15 | 61 | 33.5 |

4 | 39.4 | 0.142 | 1 | G | 19.9 | 363 | 5.569 | 10 | 20 | 63.1 |

5 | 41.0 | 0.009 | 2 | C | 235 | 3500 | 0.706 | 5 | 10 | 117.0 |

6 | 45.2 | 0.011 | 2 | C | 230.5 | 3481 | 0.293 | 15 | 30 | 52.4 |

7 | 33.7 | 0.011 | 3 | C | 230.5 | 3481 | 0.440 | 10 | 20 | 109.9 |

8 | 35.0 | 0.08 | 3 | G | 36 | 560 | 2.105 | 15 | 44 | 83.0 |

9 | 43.7 | 0.0193 | 2 | A | 210 | 2173 | 0.772 | 10 | 20 | 88.0 |

10 | 33.28 | 0.0167 | 4 | C | 235 | 3550 | 0.668 | 10 | 20 | 111.1 |

11 | 20.79 | 0.0193 | 2 | A | 210 | 2173 | 0.772 | 10 | 20 | 72.8 |

### 3.3 Distribution of the Data used for the Learning

### 3.4 Results of the Learning of Data

#### 3.4.1 Results of the Learning

Figure 5b illustrates the results with prediction error of 3.0% obtained from the neuro-fuzzy system applied to the prediction of axial strain of test specimens being broken, while Fig. 5c represents the results with prediction error of 8.1% rendered by the neuro-fuzzy system applied to the prediction of secondary post-yield elastic moduli of 87 cylindrical test specimens laterally bound with the reinforcement fiber.

#### 3.4.2 Statistical Examination

Each model renders the shape of normal distribution; and that of Case-2 represents the highest probability distribution function. The values of the standard deviation were 0.075 (Case-1), 0.051 (Case-2), and 0.107 (Case-3); and the results show the lowest accuracy of the learning conducted to predict the secondary elastic moduli.

#### 3.4.3 Analysis of Errors

The range of error was examined to assess the accuracy of learning of the neuro-fuzzy system. Equation (6) representing the percentage of error, the Root Mean Square Error (RMSE) representing the degree of error of predicted values, and the error of R2 (Absolute fraction of variation) representing the deviation of predictions from the test results were used to analyze the accuracy of learning of neuro-fuzzy system.

^{2}representing the degree of deviation were 0.9957, 0.9982, and 0.9831 respectively showing the favorable level of learning.

Results of the Statistical analysis.

Case-1 (F | Case-2 (ε | Case-3 (E | |
---|---|---|---|

RMSE | 4.79 | 0.00097 | 428.7 |

R | 0.99889 | 0.99979 | 1.009 |

E.R | 5.4 | 4.1 | 8.1 |

#### 3.4.4 Comparison of the Results of Learning with the Results Obtained from the Existing Formulae

f’c: the compressive strength of concrete; fcu: the ultimate compressive strength of the test specimen retrofitted with FRP; flu: the effective strength of reinforcement at the ultimate compressive strength.

## 4 Verification of the Outputs of the Neuro-Fuzzy System

### 4.1 Design of Experiment and Preparation of Test Specimens

Summary of retrofitting specimen property.

Mix properties of concrete.

Design | Slump | W/C (%) | Mixture (kg/m | |||||
---|---|---|---|---|---|---|---|---|

C | W | S | G | Air | Admix | |||

21 MPa | 12 cm | 54.7 | 328 | 180 | 865 | 950 | 4.5 ±1.5% | 1.5 |

### 4.2 Reinforcement of Test Specimens

Properties of FRP.

Tensile strength (MPa) | Modulus of elasticity (GPa) |
---|---|

1991 | 158.2 |

### 4.3 The Test and Measurements

A Universal Testing Machine (UTM) of the capacity of 2000 kN was employed in the test. Test specimens were placed on the center of the loader by using auxiliary fittings made of iron that were fitted on the center of the loading frame, and the load cell was installed on each test specimen.

### 4.4 Results of the Test

Summary of the testing data.

Specimen | F | ε | E |
---|---|---|---|

H* | 26.61 | 0.0023 | − 25,974** |

H2-I 0 | 32.63 | 0.003 | 12,810.59 |

H2-I 1 | 31.28 | 0.0033 | 2527.83 |

H2-I 2 | 30.67 | 0.0028 | − 13,138.2** |

H2-I 3 | 31.43 | 0.0027 | − 24,890.9** |

H2-I 4 | 30.48 | 0.0027 | − 34,703.1** |

H2-I 1-T | 34.86 | 0.0032 | 11,652.96 |

H2-I 1-A | 35.33 | 0.0037 | 5081.056 |

H2-I 1-B | 37.02 | 0.0036 | 22,674.68 |

N* | 21.13 | 0.0018 | − 19,276.4** |

N2-I0 | 25.70 | 0.0031 | 3156.05 |

N2-II3 | 26.66 | 0.0031 | 2852.00 |

N3-II1 | 26.83 | 0.0039 | 9814.00 |

N3-II3 | 25.87 | 0.0035 | 4602.43 |

N3-I1 | 26.57 | 0.0034 | 6210.99 |

N3-I1-T | 29.07 | 0.0036 | 8967.37 |

N3-I0-A | 28.59 | 0.00378 | 5697.24 |

N3-I1-B | 29.81 | 0.0037 | 7984.13 |

### 4.5 Results of the Verification of the Neuro-Fuzzy System

In this study, 16 data as represented in Table 1 were used to verify the performance of the neuro-fuzzy system designed in the study. The data set used for the verification of the performance of the neuro-fuzzy system comprises the compressive strength of concrete to be retrofitted, the thickness of reinforcement, the number of layers of fiber reinforcement, the elastic modulus and rupture strength of the reinforcement, the volumetric ratio of the reinforcement to concrete, and the dimensions of members to be retrofitted, which were set as data for an input layer as the data set used for the learning of the neuro-fuzzy system, through which the compressive strength, strain, and post- yielding modulus of the output layer were estimated.

## 5 Conclusions

- (1)
The compressive strength of concrete members to be retrofitted, thickness of reinforcement, number of reinforcing layers of reinforcement, elastic modulus of reinforcement, rupture strength of reinforcement, volumetric ratio of reinforcement to concrete members to be retrofitted, and dimensions of the concrete member to be retrofitted can be used as variables of the input layer of the learning of the neuro-fuzzy system to estimate the compressive strength, strain, and secondary modulus of elasticity of the retrofitted members of the output layer.

- (2)
The 284 data obtained from tests conducted in previous studies were employed as the data set for the learning of the adaptive neuro-fuzzy inference system (ANFIS) developed for this study, together with 16 test specimens retrofitted with fiber reinforcement to predict the effects of reinforcement. The results of the prediction of the effects of reinforcement showed errors of 11.5% for the predicted breaking strength, 7.5% for the predicted strain, and 16.7% for the predicted secondary elastic modulus.

- (3)
An adaptive neuro-fuzzy inference system (ANFIS) was designed in this study to learn the data obtained from experiments using the test specimens prepared by dimensional ratios of the diameter and length of each test specimen of 1:2 and 1:4; and the performance of learning of the neuro-fuzzy system was verified through tests that rendered excellent predictions of the effects of fiber reinforcement. Thus it was estimated that the build-up of databases of actual members, such as columns or beams, would be desirable for further applications of this system.

## Notes

### Authors’ Contributions

LC has designed this paper as a whole. He also applied a fuzzy algorithm to concrete specimens. TP performed the experimental study and wrote the paper. MH performed the analysis study. All authors read and approved the final manuscript.

### Acknowledgements

The present research was conducted by the research fund of Dankook University in 2016.

### Competing Interests

The authors declare that they have no competing interests.

### Availability of Data and Materials

Not applicable.

### Funding

Dankook University.

### Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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