Investigation on the Displacement Ductility Coefficient of Reinforced Concrete Columns Strengthened with Textile-Reinforced Concrete

Wang, Boxue; Yin, Shiping; Liu, Ming

doi:https://doi.org/10.1155/2021/3152619

Advances in Civil Engineering

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Abstract Introduction Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2021 | Article ID 3152619 | https://doi.org/10.1155/2021/3152619

Investigation on the Displacement Ductility Coefficient of Reinforced Concrete Columns Strengthened with Textile-Reinforced Concrete

Boxue Wang,¹Shiping Yin,^1,2and Ming Liu²

Academic Editor: Giulio Zani

Received14 Sept 2021

Revised11 Nov 2021

Accepted23 Nov 2021

Published07 Dec 2021

Abstract

To evaluate the seismic performance of reinforced concrete (RC) columns strengthened with textile-reinforced concrete (TRC), based on the ABAQUS numerical analysis results of 15 TRC-strengthened RC columns, the grey correlation theory was used to determine the input variables of the model, and the accuracy of the numerical simulation results is verified by some experiments. Then, according to FEM data, a neural network prediction model was established for the displacement ductility coefficients of TRC-strengthened columns, and a formula was proposed for calculating the displacement ductility coefficient. The results showed that the BP (backpropagation) neural network model had good rationality and accuracy and that the ductility coefficients of the strengthened columns calculated by the model agreed well with the experimental values. Therefore, the model can be applied for predicting the displacement ductility coefficients of TRC-strengthened columns and can be used as a reference for engineering design.

1. Introduction

Ductility is an important index for evaluating the seismic performance of concrete structures, and good ductility could avoid brittle failure of components and provide a certain safety reserve for components under accidental overload [1]. Reinforced concrete (RC) has been widely used in structural engineering applications all over the world [2], and as an important load-bearing component of structures, RC columns should provide sufficient strength, stiffness, and ductility so that the building can withstand earthquakes [3]. Therefore, studying the ductility of RC columns and evaluating their seismic performance are very important topics.

There are still a large number of buildings around the world that are not considered for seismic design and are likely to be affected by earthquakes [4–6]. To reduce the adverse effects of earthquakes on existing structures, several strengthening methods have been proposed and widely applied in practical projects over the past few decades. Because these traditional strengthening methods adopt concrete or steel [6, 7], these methods have shortcomings, such as increasing the structural weight, easily developing rust, and changing the structural appearance. In recent years, with the development of composite materials, fibre-reinforced polymers (FRPs), a new type of reinforcement material, have been used to strengthen and repair existing structures. To evaluate the seismic performance of strengthened structures, many scholars have conducted a series of studies [8–12]. The results in the literature show that FRPs can enhance the ductility and energy dissipation capacity of strengthened columns. Although FRPs have been widely used for effective reinforcement, FRPs are not suitable for use in humid environments because of their poor compatibility with concrete substrates and their lack of vapour permeability due to the use of epoxy resin as an adhesive [13]. More importantly, it is difficult to examine and evaluate the status of the repaired structures, as the structures are obscured by the FRP reinforcement. To this end, Triantafillou et al. [13] introduced the concept of combining textile fibres with inorganic matrix (such as cement mortar). Due to the different matrix strengths and fibre types used by different scholars, this new type of cement-based material also has different names, such as textile-reinforced mortar (TRM) [13, 14], textile-reinforced concrete (TRC) [15], basalt-reinforced mortar (BRM) [16], and fabric-reinforced cementitious matrix (FRCM) [17]. The significant difference between FRP and cement-based matrix composites is the free edge stress concentration of FRP confinement, which will cause premature failure of the reinforcement system [18].

Bournas et al. [19, 20] studied the seismic performance of RC columns strengthened by TRM under earthquake action. Their results showed that TRM can improve the seismic performance and deformation capacity of strengthened columns. Yin et al. [21] explored the influence of different factors on the seismic performance of TRC-strengthened columns, and their results indicated that the ductility coefficient of strengthened columns increased with increasing reinforcement layers and stirrup ratio or decreasing axial compression ratio. Al-Salloum et al. [22] studied the effect of TRM on the shear strength and ductility of beam-column joints with deficient seismic performance. Their results showed that TRM can effectively improve the shear strength and ductility of beam-column joints with defects. In addition, the results in [23, 24] indicate that although the ductility coefficient of TRC-strengthened columns decreases to some extent under environmental erosion, the overall seismic performance of the strengthened columns is good.

Although TRC has received much attention in the field of seismic reinforcement, relatively few studies have focused on the ductility and deformation capacity of specimens after strengthening, and the relationships between various factors and the ductility coefficient have not been quantified. In addition, many problems in strengthening concrete column structures are nonlinear. The factors affecting the ductility of concrete columns are very complex, and there are certain coupling effects between the factors and the ductility of components. However, artificial neural networks have the ability to perform associative reasoning, simulation thinking, and self-adaptive recognition, which can be found in input-output mapping through learning [25, 26]. Therefore, artificial neural networks (ANN) are suitable for nonlinear reasoning and prediction in structural engineering. Backpropagation (BP) neural networks are the most widely used artificial neural networks, as BP neural networks have low requirements and limitations on known data and can make full use of existing data to analyze and study the evolution, development, and movement rules of objects [27, 28]. It has been successfully applied in civil engineering, such as design [29], prediction [30–33], optimization [34], and damage detection and identification [35, 36].

Therefore, based on the team’s previous research results [37, 38], a BP neural network is applied to obtain the mapping relationship between ductility and various influencing factors of TRC-strengthened RC columns. Based on the mapping relationship, a ductility coefficient formula for reinforced columns is deduced, which enables accurate and efficient ductility calculations and provides a scientific basis for the evaluation of seismic performance of components and guidance for engineering design.

2. Grey Correlation Analysis

The grey system theory is based on the sequence operator to realize the law of things in the process of transformation. The original irregular data is generated into regular sequence, and then the differential equation method is used to predict and analyze the development trend of things objectively and scientifically. As the core content of grey system theory, grey correlation analysis is a method to predict the unknown information by using the known information. The grey correlation analysis is used to calculate the grey correlation degree of several factors. The larger the value of the correlation degree is, the greater the influence of the factor on the evaluation index is.

2.1. Significance of Grey Correlation Analysis

In this paper, grey system theory is applied to analyze the factors affecting the displacement ductility coefficient of TRC-strengthened columns, including the strength grade of existing concrete, axial compression ratio, shear span ratio, stirrup space, and number of textile layers. Finite element simulation results of TRC-strengthened columns were adopted as the sample data, and the following grey correlation analysis was carried out to obtain the ranking results of the correlation degree of various factors. The dominant factors affecting the displacement ductility coefficient of TRC-strengthened columns reflect the deformation capacity and seismic performance of TRC-strengthened columns to some extent. Therefore, the results of this study can also provide important references for future theoretical research and design applications of the displacement ductility coefficient of TRC-strengthened columns.

2.2. Correlation Analysis

In this paper, all the relevant correlation coefficients are gathered into one value, and the calculated average value is used to process the information. The correlation coefficient of each factor is calculated (i.e., the average value of all corresponding correlation coefficients), which is a quantitative analysis of the correlation degree between various factors and TRC-strengthened columns. The specific calculations and analyses are described hereafter.

2.2.1. Determination of Correlation Factors

According to the results of existing research, the main factors affecting the displacement ductility coefficient of strengthened RC columns are the strength grade of existing concrete, axial compression ratio, shear span ratio, stirrup space, and strengthening layers. The main content of this paper is to determine the influence of strengthening layers, axial compression ratio, shear span ratio, and other parameters on the ductility coefficient. Therefore, the following correlation factors are selected as the comparison parameter sequence of the system: (1) reinforcement layers x₁ (0, 1, 2, 3, 4), (2) axial compression ratio x₂ (0.2, 0.3, 0.4, 0.5), (3) shear span ratio x₃ (2, 3.8, 5.6), (4) stirrup space x₄ (50 mm, 100 mm, 150 mm), and (5) concrete strength grade x₅ (C30, C40, C50, C60), namely, {x_i(k) | i = 1, 2, 3, 4, 5; k = 1, 2, 3, 4, 5}. The displacement ductility coefficient is obtained from 15 TRC-strengthened columns based on ABAQUS earthquake simulations in [37, 38] used as the generating sequence of the system. The specific geometric dimensions and reinforcing bars of the specimens are shown in Figure 1. And according to [37, 38], the numerical and experimental results match well (shown in Figure 2 [38]), which shows that the established model and the finite element analysis results are rational and accurate. The correlation factors and displacement ductility coefficient involved in the numerical analysis are shown in Table 1.

(a)

(b)

2.2.2. Dimensionless Data

The original data are initialized according to equation (1) [39], and the initialized data are shown in Table 2.

2.2.3. Calculation of Absolute Difference

According to equation (2), the absolute difference between the parent sequence and subsequence in Table 2 (i.e., the absolute difference value results for Δ_i(k)) is shown in Table 3.where is for the parent sequence (dimensionless) and is for the subsequence (dimensionless).

2.2.4. Calculation of the Correlation Coefficient

Equation (3) is used to calculate the correlation coefficient , and the results are shown in Table 4.where is the correlation coefficient; Z is the resolution coefficient, which has a value that is generally between 0 and 1 and is typically taken as 0.5; m is the minimum second-order difference, which is 0 according to ; and M is the maximum second-order difference, which is 3.02 according to .

2.2.5. Calculation of the Correlation Degree

The correlation degree between the subsequence x_i and the parent sequence x₀ is calculated according to equation (4), which is expressed as follows:

The calculated correlation degree is .

2.2.6. Ranking of Correlation Degree

By sorting the correlation degree obtained from the calculation, the results show that the influence degree of each factor on the displacement ductility coefficient of TRC-strengthened columns is shear span ratio > (axial compression ratio, stirrup ratio, concrete strength) > TRC layers. In addition, combined with the value of the correlation degree, these five factors have a great impact on the ductility performance of TRC-strengthened columns. Therefore, based on these five factors, a BP neural network model was established by MATLAB to predict the ductility change trend of the TRC-strengthened columns.

3. Establishment of Neural Network Prediction Model

Based on MATLAB, the BP neural network model is established to predict the displacement ductility coefficient of TRC-strengthened columns. The specific operation steps are as follows.

3.1. BP Neural Network Construction

The structure of BP neural network mainly includes the number of neural network layers and neurons in each layer. Because the three-layer BP neural network has strong nonlinear mapping ability and can approach any nonlinear function, the three-layer BP neural network was used to model in this paper. The numbers of input layers, hidden layers, and output layers are all one. Based on the analysis mentioned above, BP neural network includes five input parameters, i.e., concrete strength grade, axial compression ratio, shear span ratio, stirrup space, and strengthening layers, and the output parameter is displacement ductility coefficient. The number of input layer and output layer neurons in the corresponding model is 5 and 1, respectively. The number of hidden layer neurons is determined by formula (5) [40] and multiple training calculations. The structure of BP neural network model is shown in Figure 3.where D is the number of nodes in the hidden layer, D_i is the number of input nodes, D₀ is the number of output nodes, and a is between 1 and 10.

In addition, the essence of BP learning algorithm is to get the minimum value of error function. Because it uses the steepest descent method in nonlinear programming to modify the weights according to the negative gradient direction of error function, it usually has shortcomings such as low learning efficiency, slow convergence speed, and easy fall into local minimum state. Several optimization techniques are proposed to speed up the convergence of the BP learning algorithm [41, 42]. The results indicate that the Levenberg-Marquardt (L-M) algorithm was very efficient when training networks. The flowchart of L-M algorithm is shown in Figure 4.

3.2. Determine Sample Data

A small number of experiments have been designed to prove the accuracy of the finite element results. After verification, the finite element simulation results are in good agreement with the test results, which proves that the finite element simulation results are accurate. In order to better perform parametric analysis, in this paper, the training sample data (10 groups) and test sample data (5 groups) for the model are determined according to the data obtained from simulation calculations. Moreover, considering the calculation efficiency and error of the model, all the sample data are normalized according to equation (6) before the sample is input into the model. The relevant linear transformation algorithm is expressed as follows:where x is the input vector, min is the minimum value of x, max is the maximum value of x, and y is the output vector.

At the same time, the parameter (weight coefficient) is introduced to obtain the true correlation between the influencing factors and TRC-strengthened columns, and the specific formula is shown in equation (7). The weight coefficient is combined with the data in Table 5 to obtain the input data for the final model. The specific results are shown in Table 6.where is the correlation value between each factor and displacement ductility coefficient calculated in Section 1 and Section 2 of this paper.

In this paper, the five associated values obtained in the previous section are substituted into (7), and the weight coefficients of each factor are obtained as follows: 0.146, 0.210, 0.218, 0.213, and 0.213. Then, the weight coefficients are multiplied by the normalized data to obtain the input data. The detailed results are shown in Table 6.

3.3. Simulation of the Neural Network

The sample data obtained above (shown in Table 6) were input into the established and trained neural network model, and the accuracy of the model was verified by comparing and analyzing the results of the neural network model and the simulated calculation.

3.4. Neural Network Predicted Value

Table 7 and Figure 5 show a comparison between the predicted value of the displacement ductility coefficient calculated by the BP neural network model and the displacement ductility coefficient of the TRC reinforced column obtained by finite element analysis in previous studies.

In addition, data analysis software, Statistical Product and Service Solutions (SPSS) [43], was used to compare the predicted value of displacement ductility coefficient calculated in the above BP neural network model with the experimental value obtained by numerical analysis, and the correlation between the value predicted by the BP neural network and the experimental value was obtained. The specific parameters are shown in Table 8.

Table 8 shows that the R² of the fitting degree between the predicted value of displacement ductility coefficient calculated based on the BP neural network model and the measured value calculated by the above simulation is 0.83. Therefore, the results show that the BP neural network model based on the grey correlation analysis method has a good prediction effect on the displacement ductility coefficient of TRC-strengthened RC columns.

4. Ductility Formula

The displacement ductility coefficient reflects the plastic deformation capacity of the structural member. It is the ratio of the failure displacement of the specimen to the yield displacement, namely,where is the ultimate displacement of the specimen, which is the horizontal displacement when the horizontal load drops to 85% of the peak load; is the yield displacement of the specimen, which is the corresponding horizontal displacement when the specimen reaches the initial yield point.

According to the correlation analysis and grey correlation analysis of the factors influencing the seismic performance of TRC-strengthened RC column mentioned in Section 1 and Section 2, the displacement ductility coefficient of the TRC-strengthened RC column changes with changes in the shear span ratio, axial compression ratio, stirrup space, and concrete strength grade and TRC layers. Therefore, the influences of the shear span ratio, axial compression ratio, stirrup space, and concrete strength grade are considered when deducing the displacement ductility coefficient of the reinforced column.

In this section, the influence of the shear span ratio, axial compression ratio, stirrup ratio, fibre braided mesh layout layers, concrete strength grade, and TRC layers on the displacement ductility coefficient of TRC-strengthened RC columns is considered to establish a function according to [44]. The function form is expressed in the following equation: where μ is the displacement ductility coefficient, λ_s is the characteristic value of the fibre volume, and λ is the shear span ratio. The a, c, d, e, g, i, j are regression coefficients to be determined.

The characteristic values of stirrup volume and fibre volume can be calculated according to equations (10) and (11), respectively:where is the characteristic value of the stirrup volume; is the compressive strength of the concrete; is the volume matching rate; n is the axial compression ratio; s the sectional area of tensile steel bars; l is the length of the stirrup; A_cor is the concrete core area; is the stirrup space; f_yv is the stirrup design strength; is the cross-sectional area of stirrup; is the perimeter of the stirrups; l₁ and l₂ are the lengths of two sides of the rectangular stirrups; s_g is the stirrup spacing; is the characteristic value of the fibre volume; τ_s and l_s are the section thickness and total perimeter of the carbon fibres, respectively; b and h are the cross-sectional width and height of the column; and f_su is the ultimate tensile strength of the carbon fibres.

Relevant parameters of TRC-strengthened columns that consider the shear span ratio, axial compression ratio, stirrup ratio, TRC layers, and concrete strength grade in Table 9 and the displacement ductility coefficient obtained by numerical calculation are used as the input sample (ten sets of sample data and five sets of test data). Then, the data are substituted into MATLAB software for nonlinear regression to obtain the value of the regression coefficient. Then the regression coefficient is substituted into equation (9) to obtain equation (12). The results of the calculation and analysis are compared as shown in Table 10.

A further comparison between the calculated and experimental displacement ductility coefficient was performed with the data analysis software SPSS, and the predictive value fit of the proposed formula was assessed, as shown in Table 10 and Figure 6. Table 11 shows that the R² is 0.805, the adjusted R² value after considering the number of independent variables is 0.790, and most of the errors between the predicted and simulated values calculated by the formula are within 15%. Therefore, the calculated and experimental results are in good agreement, indicating that the proposed equation can provide a reference for engineering design and seismic performance evaluation.

5. Conclusions

Based on the numerical analysis results, the correlation degree between the TRC layers, axial compression ratio, shear span ratio, stirrup space, concrete strength grade, and ductility of TRC-strengthened columns was analyzed. Furthermore, a BP neural network prediction model based on grey system theory was established in MATLAB, and then a formula was proposed for the displacement ductility coefficient of TRC-strengthened columns. The specific conclusions of this study are as follows:(1)The influence of various factors on the ductility coefficient of reinforced columns is ranked as follows: shear span ratio > (axial compression ratio, stirrup space, and concrete strength grade) > TRC layers. This ranking was obtained by calculating the correlation value between the displacement ductility coefficient and various factors of TRC-strengthened columns. These results indicate that the factors selected in this paper have a substantial impact on the ductility of reinforced columns, and the correlations of these factors are strong.(2)A BP neural network model with three layers was established to predict the displacement ductility coefficient of TRC-strengthened columns. The results show that the model can be used to predict the ductility coefficient of TRC-strengthened columns.(3)Based on the developed BP neural network prediction model, which is based on grey system theory, a formula for calculating the displacement ductility coefficients of TRC-strengthened columns is established by considering the influences of the shear span ratio, axial compression ratio, stirrup space, textile layers, and concrete strength grade on the displacement ductility coefficient. A verification process with relevant data shows that the calculated values are in good agreement with the experimental values, which indicates that the proposed ductility formula has a certain accuracy and rationality and that the formula can be used for predicting displacement ductility coefficients of TRC-strengthened columns and can provide a certain reference for engineering design.

Data Availability

The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

The authors gratefully acknowledge the financial support from the Program of the National Natural Science Foundation of China (Grant no. 51478458). The experimental work described in this paper was conducted at the Jiangsu Key Laboratory of Environmental Impact and Structural Safety in Civil Engineering in the China University of Mining and Technology. The support during the testing from staffs and students at the Laboratory is greatly acknowledged.

References

S. S. Zheng, H. J. Lou, X. F. Wang, and Z. Li, “Study on displacement ductility coefficient of steel reinforced high-strength concrete column,” Advanced Materials Research, vol. 368-373, pp. 1097–1100, 2012.
View at: Google Scholar
B.-T. Huang, Q.-H. Li, S.-L. Xu, and B. Zhou, “Strengthening of reinforced concrete structure using sprayable fiber-reinforced cementitious composites with high ductility,” Composite Structures, vol. 220, pp. 940–952, 2019.
View at: Publisher Site | Google Scholar
H. F. Ghatte, M. Comert, C. Demir, and A. Ilki, “Seismic retrofit of full-scale substandard extended rectangular RC columns through CFRP Jacketing: test results and design recommendations,” Journal of Composites for Construction, vol. 23, no. 1, pp. 04018071∼1–17, 2019.
View at: Publisher Site | Google Scholar
Y. A. Al-Salloum and T. H. Almusallam, “Seismic response of interior RC beam-column joints upgraded with FRP sheets. I: experimental study,” Journal of Composites for Construction, vol. 11, no. 6, pp. 575–589, 2007.
View at: Publisher Site | Google Scholar
M. A. Zanini, L. Hofer, F. Faleschini, P. Zampieri, N. Fabris, and C. Pellegrino, “Preliminary macroseismic survey of the 2016 Amatrice seismic sequence,” Ann. Geophys.-Italy, vol. 59, pp. 1–6, 2016, FastTrack5.
View at: Publisher Site | Google Scholar
F. Faleschini, J. Gonzalez-Libreros, M. A. Zanini, L. Hofer, L. Sneed, and C. Pellegrino, “Repair of severely-damaged RC exterior beam-column joints with FRP and FRCM composites,” Composite Structures, vol. 207, pp. 352–363, 2019.
View at: Publisher Site | Google Scholar
A. Ghobarah and T. El-Amoury, “Seismic rehabilitation of deficient exterior concrete frame joints,” Journal of Composites for Construction, vol. 9, no. 5, pp. 408–416, 2005.
View at: Publisher Site | Google Scholar
C. Yalcin, O. Kaya, and M. Sinangil, “Seismic retrofitting of R/C columns having plain rebars using CFRP sheets for improved strength and ductility,” Construction and Building Materials, vol. 22, no. 3, pp. 295–307, 2008.
View at: Publisher Site | Google Scholar
A. Ilki, C. Demir, I. Bedirhanoglu, and N. Kumbasar, “Seismic retrofit of brittle and low strength RC columns using fiber reinforced polymer and cementitious composites,” Advances in Structural Engineering, vol. 12, no. 3, pp. 325–347, 2009.
View at: Publisher Site | Google Scholar
O. Ozcan, B. Binici, and G. Ozcebe, “Seismic strengthening of rectangular reinforced concrete columns using fiber reinforced polymers,” Engineering Structures, vol. 32, no. 4, pp. 964–973, 2010.
View at: Publisher Site | Google Scholar
C. Jiang, Y.-F. Wu, and G. Wu, “Plastic hinge length of FRP-confined square RC columns,” Journal of Composites for Construction, vol. 18, no. 4, pp. 04014003–4014011∼12, 2014.
View at: Publisher Site | Google Scholar
H. Farrokh Ghatte, M. Comert, C. Demir, and A. Ilki, “Evaluation of FRP confinement models for substandard rectangular RC columns based on full-scale reversed cyclic lateral loading tests in strong and weak directions,” Polymers, vol. 8, no. 9, pp. 323–331∼24, 2016.
View at: Publisher Site | Google Scholar
T. C. Triantafillou, C. G. Papanicolaou, P. Zissimopoulos, and T. Laourdekis, “Concrete confinement with textile-reinforced mortar jackets,” ACI Structural Journal, vol. 103, no. 1, pp. 28–37, 2006.
View at: Google Scholar
L. Koutas, A. Pitytzogia, T. C. Triantafillou, and S. N. Bousias, “Strengthening of infilled reinforced concrete frames with TRM: study on the development and testing of textile-based anchors,” Journal of Composites for Construction, vol. 18, no. 3, pp. 40130155–A4013021∼12, 2014.
View at: Publisher Site | Google Scholar
R. Ortlepp and S. Ortlepp, “Textile reinforced concrete for strengthening of RC columns: a contribution to resource conservation through the preservation of structures,” Construction and Building Materials, vol. 132, pp. 150–160, 2017.
View at: Publisher Site | Google Scholar
M. Di Ludovico, A. Prota, and G. Manfredi, “Structural upgrade using basalt fibers for concrete confinement,” Journal of Composites for Construction, vol. 14, no. 5, pp. 541–552, 2010.
View at: Publisher Site | Google Scholar
L. Ombres and S. Verre, “Structural behaviour of fabric reinforced cementitious matrix (FRCM) strengthened concrete columns under eccentric loading,” Composites Part B: Engineering, vol. 75, pp. 235–249, 2015.
View at: Publisher Site | Google Scholar
A. Zinno, G. P. Lignola, A. Prota, G. Manfredi, and E. Cosenza, “Influence of free edge stress concentration on effectiveness of FRP confinement,” Composites Part B: Engineering, vol. 41, pp. 523–532, 2010.
View at: Publisher Site | Google Scholar
D. A. Bournas, T. C. Triantafillou, K. Zygouris, and F. Stavropoulos, “Textile-reinforced mortar versus FRP jacketing in seismic retrofitting of RC columns with continuous or lap-spliced deformed bars,” Journal of Composites for Construction, vol. 13, no. 5, pp. 360–371, 2009.
View at: Publisher Site | Google Scholar
D. A. Bournas and T. C. Triantafillou, “Bar buckling in RC columns confined with composite materials,” Journal of Composites for Construction, vol. 15, no. 3, pp. 393–403, 2011.
View at: Publisher Site | Google Scholar
S. P. Yin, Y. Li, Y. Yang, and T. Ye, “Influencing factors of seismic performance of RC columns strengthened with textile reinforced concrete,” Journal of Zhejiang University (Engineering Science), vol. 51, no. 5, pp. 904–913, 2017, in Chinese.
View at: Google Scholar
Y. A. Al-Salloum, N. A. Siddiqui, H. M. Elsanadedy, A. A. Abadel, and M. A. Aqel, “Textile-reinforced mortar versus FRP as strengthening material for seismically deficient RC beam-column joints,” Journal of Composites for Construction, vol. 15, no. 6, pp. 920–933, 2011.
View at: Publisher Site | Google Scholar
S. P. Yin, Y. Yang, T. Ye, and Y. Li, “Experimental research on seismic behavior of reinforced concrete columns strengthened with TRC under corrosion environment,” Journal of Structural Engineering, vol. 143, no. 5, pp. 04016231–1∼11, 2017.
View at: Publisher Site | Google Scholar
Y. Li, S. P. Yin, and W. J. Chen, “Seismic behavior of corrosion-damaged RC columns strengthened with TRC under a chloride environment,” Construction and Building Materials, vol. 201, pp. 736–745, 2019.
View at: Google Scholar
Q. H. Feng and W. C. Yuan, “Comparative study on BP neural network and RBF neural network in performance evaluation of seismic resistance for pier columns,” Structural Engineers, vol. 23, no. 5, pp. 41–47+69, 2007, in Chinese.
View at: Google Scholar
H. X. Fu and H. Zhao, MATLAB Neural Network Application Design, China Mechine Press, Beijing, China, 2010.
K. B. Kim, K. B. Sim, and S. H. Ahn, “Recognition of concrete surface cracks using the ART1-based RBF network,” Lecture Notes in Computer Science, no. 3972, pp. 669–6751, 2006.
View at: Publisher Site | Google Scholar
Q. H. Feng and W. C. Yuan, “A method based on RBFNN to predict the shear strength of steel reinforced high-strength concrete columns,” Structural Engineers, vol. 24, no. 3, pp. 60–65, 2008, in Chinese.
View at: Google Scholar
S. Wang, G. Sun, W. Chen, and Y. Zhong, “Database self-expansion based on artificial neural network: an approach in aircraft design,” Aerospace Science and Technology, vol. 72, pp. 77–83, 2018.
View at: Publisher Site | Google Scholar
S. Tohidi and Y. Sharifi, “Neural networks for inelastic distortional buckling capacity assessment of steel I-beams,” Thin-Walled Structures, vol. 94, pp. 359–371, 2015.
View at: Publisher Site | Google Scholar
I. M. Nikbin, S. Rahimi, and H. Allahyari, “A new empirical formula for prediction of fracture energy of concrete based on the artificial neural network,” Engineering Fracture Mechanics, vol. 186, pp. 466–482, 2017.
View at: Publisher Site | Google Scholar
Ł. Sadowski, M. Piechówka-Mielnik, T. Widziszowski, A. Gardynik, and S. Mackiewicz, “Hybrid ultrasonic-neural prediction of the compressive strength of environmentally friendly concrete screeds with high volume of waste quartz mineral dust,” Journal of Cleaner Production, vol. 212, pp. 727–740, 2019.
View at: Publisher Site | Google Scholar
V. L. Tran, D. K. Thai, and S. E. Kim, “Application of ANN in predicting ACC of SCFST column,” Composite Structures, vol. 228, Article ID 111332, 2019.
View at: Publisher Site | Google Scholar
T. Y. Liu, P. Zhang, Y. F. Wang, and Y. F. Ling, “Compressive strength prediction of PVA fiber-reinforced cementitious composites containing Nano-SiO2 using BP neural network,” Materials, vol. 13, p. 521, 2020.
View at: Publisher Site | Google Scholar
C. S. N. Pathirage, J. Li, L. Li, H. Hao, W. Q. Liu, and P. H. Ni, “Structural damage identification based on autoencoder neural networks and deep learning,” Engineering Structures, vol. 172, pp. 13–28, 2018.
View at: Publisher Site | Google Scholar
Z. Tan, D. Thambiratnam, T. Chan, T. H. T. Chan, and H. A. Razak, “Detecting damage in steel beams using modal strain energy based damage index and artificial neural network,” Engineering Failure Analysis, vol. 79, pp. 253–262, 2017.
View at: Publisher Site | Google Scholar
M. Liu, S. P. Yin, and W. J. Chen, “Seismic behaviour of TRC-strengthened RC columns under different constraint conditions,” Science and Engineering of Composite Materials, vol. 26, no. 1, pp. 360–378, 2019.
View at: Google Scholar
Y. Li, S. P. Yin, J. Y. Dai, and M. Liu, “Numerical investigation on the influences of different factors on the seismic performance of TRC - strengthened RC columns,” Journal of Building Engineering, vol. 30, pp. 101245–101251∼11, 2020.
View at: Publisher Site | Google Scholar
W. L. Pan, Application of Grey System Theory in Security Engineering and Research on Aided Software, Dalian Jiaotong University, Dalian, China, 2018.
G. Mirchandani and W. Cao, “On hidden nodes for neural nets,” IEEE Transactions on Circuits and Systems, vol. 36, no. 5, pp. 661–664, 2002.
View at: Publisher Site | Google Scholar
I. N. Daliakopoulos, P. Coulibaly, and I. K. Tsanis, “Groundwater level forecasting using artificial neural networks,” Journal of Hydrology, vol. 309, pp. 229–240, 2005.
View at: Publisher Site | Google Scholar
H. Naderpour, O. Poursaeidi, and M. Ahmadi, “Shear resistance prediction of concrete beams reinforced by FRP bars using artificial neural networks,” Measurement, vol. 126, pp. 299–308, 2018.
View at: Publisher Site | Google Scholar
J. L. Lu, X. M. Wang, H. Wang, Z. M. Hong, and Y. Y. Shan, “Applying of SPSS software in the teaching of mathematical statistics,” in Proceedings of the International Conference on Future Computer Supported Education (ICFCSE 2011), pp. 584–587, PEOPLES R CHINA, Chongqing, China, September 2011.
View at: Google Scholar
W. H. Yu, Study on Ductility Performance of Reinforced High concrete Columns Confined by CFRP, Dalian University of Technology, Dalian, China, 2010, in Chinese.

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Copyright © 2021 Boxue Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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