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- 1. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME98NEW MODEL OF CFRP-CONFINED CIRCULAR CONCRETECOLUMNS: ANN APPROACHDr. Salim T. YousifAssistant Prof, Civil Engineering Dept., College of Engineering/University of Mosul, IraqABSTRACTThe application of fiber-reinforced polymer (FRP) composites in civil engineeringworks has increased in recent years, especially in the area of strengthening concrete columns.The objective of this research is to develop new mathematical models for predicting theconfined compressive strength of carbon FRP (CFRP) circular concrete columns usingartificial neural networks (ANNs), which is done using 208 excremental data results collectedfrom the literature. Two mathematical models were developed: one depended on six inputparameters, whereas the other depended only on three important parameters, namely,unconfined compressive strength of concrete, total thickness of the CFRP, and tensilestrength of CFRP along the hoop direction. Comparison of the new two models usingexperimental data showed a good agreement and accuracy of the developed ANN models inpredicting the CFRP-confined compressive strength of circular concrete columns. The newmodels were also used to perform a parametric study to evaluate the effect of the inputparameters on the CFRP-confined compressive strength of circular concrete columns.Key Words: Artificial neural networks, Concrete, Compressive strength, Fiber-reinforcedpolymer confinement, Mathematical modeling1. INTRODUCTIONExternally bonded carbon fiber-reinforced polymer (CFRP) composite sheets andlaminates have been used widely in civil engineering construction to strengthen reinforcedconcrete (RC) components [1] because of their high strength, light weight, ease in use,durability against weather conditions, chemical resistance properties, relative low cost, andease in repair.INTERNATIONAL JOURNAL OF CIVIL ENGINEERING ANDTECHNOLOGY (IJCIET)ISSN 0976 – 6308 (Print)ISSN 0976 – 6316(Online)Volume 4, Issue 3, May - June (2013), pp. 98-110© IAEME: www.iaeme.com/ijciet.aspJournal Impact Factor (2013): 5.3277 (Calculated by GISI)www.jifactor.comIJCIET© IAEME
- 2. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME99These CFRP composites are used for strengthening of columns [2, 3]. Confinement ofthe columns using CFRP jackets is done by wrapping the fibers along the hoop direction ofthe concrete columns.Concrete expands laterally when subjected to axial compression. The FRP jacketprovides a confining pressure to the concrete to resist the expansion caused by the axialcompression. Ultimate failure occurs when the FRP jacket ruptures because of the tensilestress along the hoop direction [3]. Because of the FRP confinement, both the compressivestrength and ultimate strain of the concrete can be improved [1].Artificial neural networks (ANNs) have experienced increased interest over the lastyears and have been successfully applied across a range of engineering problems, includingthe strengthening of columns [4, 5], increasing the capacity of RC beams strengthened withFRP reinforcements [6, 7], prediction of the compressive strength of concrete [8, 9],linearand nonlinear model updating of RC T-beams [10], predicting the bond strength of FRP-to-concrete joints [11], and many other engineering applications.Naderpour et al. [2] employed the ANN to generate a model for predicting thecompressive strength of FRP-confined concrete independently from the network. The modelconsisted of an empirical chart and seven mathematical equations.In the present study, new mathematical models are developed based on ANNs using adatabase built from existing tests on CFRP-confined circular concrete specimens. This newmodel is then compared with the experimental data. Finally, the trained network model isused to perform a parametric study to evaluate the effect of various parameters on the CFRP-confined compressive strength of concrete.2. AVAILABLE EMPIRICAL FRP-CONFINED MODELSThe confining pressure provided by the FRP jacket, as derived from empirical models,is a function of the column’s diameter, stiffness of the FRP jacket, and compressive strengthof the unconfined concrete. A lateral confining stress f1 is produced in the concrete when theconfining jacket and the member is loaded such that the concrete starts to dilate and expandslaterally. The stress is related to the thickness and strength of the FRP by [3]:fଵ ൌଶూౌ୲ୢ(1)where fୖ is the tensile strength of the FRP along the hoop direction, t is the total thicknessof the FRP, and d is the diameter of the confined concrete.Several existing strength models for FRP-confined concrete take the following form[3]:ౙౙౙ′ ൌ 1 kଵభౙ′ (2)wherefୡୡ and fୡ′are the compressive strength of the confined and unconfined concrete,respectively,fଵ is the lateral confining pressure, and kଵis the confinement effectivenesscoefficient.A number of strength models have been proposed specifically for the FRP-confinedconcrete, which employ Eq. 2 with modified expressions for k1. The details of the models canbe seen in [12]
- 3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME1003. ARTIFICIAL NEURAL NETWORKSA neural network is a computer model whose architecture essentially mimics theknowledge acquisition and organizational skills of the human brain [13].The function of artificialneurons is similar to that of real neurons [14]; they are able to communicate via signals sentamong them by a large number of biased and weighted connections. Each neuron has its owntransfer function, which describes how to convert a weighted sum of input to output.The multi-layer perceptron is the most widely used type of ANN [15]. It is both simpleand based on solid mathematical grounds. The input quantities are processed through successivelayers of “neurons.”An input layer (with the number of neurons equal to the number of variablesin the problem) and an output layer always exist. The layers in between are called “hidden”layers. Without a hidden layer, the perceptron can only perform linear tasks. All problems, whichcan be solved by a perceptron, can be solved with only one hidden layer; however, using two ormore hidden layers is sometimes more efficient.3.1 Back-propagation neural networkThe back-propagation (BP) neural network is a multi-layered feed-forward [15, 16]. TheBP neural network adjusts internally the weight values to set the non-linear relationships betweenthe input and the output without giving explicitly the function expression. Further, the BP neuralnetwork can be generalized for the input that is not included in the training patterns.The BP algorithm is used to train the BP neural networks. This algorithm looks for theminimum error function in the weight space using the method of gradient descent. Thecombination of weights that minimizes the error function is considered to be a solution to thelearning problem. The input feed forward can be described by the following steps [15, 17]:Once the input vector ix is introduced into the input layer, it can calculate the input to thehidden layer HJh asiNIijijHJ xwbh ∑=+=1(3)where jb is the bias and jiw is the synaptic weight that connects input neuron i to hidden neuron j.Each neuron of the hidden layer takes its input Hjh , uses it as the argument for a function,and produces an output Hjy given by)( HjHj hfy = (4)The input to the neurons of output layer okh is calculated as∑=+=NHjHjkjkok ywbh1(5)and the network output ky is given by)( okk hfy = (6)where f represents the activation function. Then
- 4. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME101݂ሺ okh ሻ ൌଵଵାషokh. (7)The complete algorithm can be found in [15].3.2 Neural network design and trainingA set of test results were collected from the literature for the axial compressivestrength of the circular confined concrete columns [18–41].The selected database contains208 test results.The data collected from the field were divided randomly into two groups. The firstgroup, which contained 188 results, was used in the training of the neural network, and theother data group, which contained 20 results, was used to test the obtained networks. Themulti-layer feed-forward BP technique was implemented in the current research to developand train the neural network, where the sigmoid transform function was adopted.Different training functions are available in MATLAB [42].The Levenberg–Marquardt (LM) technique have been proven to be an efficient training function and aretherefore used to construct the ANN model. This training function is one of the conjugategradient algorithms that start the training by searching in the steepest descent direction(negative of the gradient) on the first iteration. The LM algorithm is known to be significantlyfaster than the more traditional gradient descent-type algorithms for training ANNs.The input, as well as the output, was scaled in the range of 0.1 to 0.9. The scaling ofthe training data sets was carried out using the following equation:ݕ ൌ.଼ሺ௫ି௫ೌೣሻ௫ೌೣି௫ 0.9.. (8)Any new input data should be scaled before being introduced to the network and thecorresponding predicted values should be unscaled before use.For each model, several architectures of the ANN models were examined by varyingthe number of hidden layers and the training function parameters to establish a suitable andstable network for the project. Each network must be tested and analyzed, and the mostappropriate network must be chosen for a particular project.The parameters used for the input nodes in the ANN modeling were as follows:diameter (d) of the circular concrete specimen (mm), height (L) of the circular concretespecimen (mm), compressive strength (fୡ′) of the unconfined concrete (MPa), total thickness(t) of the CFRP (mm), tensile strength (fୖ) of the CFRP along the hoop direction (MPa),and elastic modulus (EFRP) of the CFRP (MPa).The target node was the compressive strengthof the confined concrete (fୡୡ).The range of the input data used is listed in Table 1. The architecture of the developedANN model is shown in Fig. 1.Table 1: Range of input data used in the ANN modelsInput parameter d (mm) h (mm) fୡ′(MPa) t(mm) fୖ(MPa) EFRP(GPa)MinimumMaximum7020014078818169.70.112.06580440038415
- 5. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME10240 60 80 100 120 140 160406080100120140160Experimental Compressive Strength (MPa)ANNPredictedCompressiveStrength(MPa)R=0.964Test data0 50 100 150 200 250 300050100150200250300Experimental Compressive Strength (MPa)ANNPredictedCompressiveStrength(MPa)Train dataR=0.977A regression analysis was conducted between the network response and thecorresponding targets and a correlation coefficient was found. This option is a measure ofhow well the variation in the output is explained by the targets. If this number is equal to one,then a perfect correlation exists between the target and output predictions.Fig. 2 shows the plot of the experimental compressive strength against thecorresponding ANN predictions for the test data. A linear correlation can be observed, andthe correlation coefficients are 0.977 and 0.964 for the training and the test data, respectively.Therefore, we can conclude that the model successively predicts accurately the compressivestrength of the confined concrete.Fig 1. Architecture of the first ANN modelFig 2. Experimental and corresponding ANN compressive strength for the training and testdata of ANN Modeldhfc’tEFRPfFRPfccInput layer Hidden layer Output layer
- 6. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME1034. IMPORTANCE OF INPUT PARAMETERSBecause the weight of the BP neural network cannot be easily understood in anumerical matrix form, it could be transformed into code values in percentage form bydividing the weights by the sum for all the input parameters, which yields the relativeimportance of each input parameter to the output parameter. The method of partitioningweights, proposed by Garson [17] and adopted by Goh [13], was used in this study todetermine the relative importance of the various input parameters (Fig. 3). The majorimportant parameter that influences the compressive strength of the confined concrete (fୡୡ) isthe tensile strength (fୖ) of the CFRP along the hoop direction with an importance of30.67%, followed by the total thickness (t) of CFRP with an importance of 20.78% and thecompressive strength (fୡ′) of the unconfined concrete with an importance of 19.13%. Thediameter (d) of the circular concrete specimen does not affect the compressive strength of theconfined concrete (fୡୡ) because its importance is only 4.162%. Most mathematical modelsconsider the column diameter as one of the main factors.Fig 3. Importance of input parameters of the first ANN modeld L fc t f (fbr) E (fbr)05101520253035%ImportanceInput Factors4.162%16.00% 19.134%20.783%30.677%9.200%
- 7. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME1045. MODEL DEVELOPMENTS FOR COMPRESSIVE STRENGTH OFCONFINED CONCRETEAnother application of ANNs is in building a mathematical model. The present studycontains six input and one output parameters. A model equation can be established using theweights as the model parameters [43]. The mathematical equation can be written as݂ ൌଵଵାష ሾഇరశ൬ೢళరభశషೣభ൰శ൬ೢఴరభశషೣమ൰శ൬ೢవరభశషೣయ൰ሿ(9)where:1ݔ ൌ ߠଵ ݓଵଵ ൈ d ݓଶଵ ൈ h ݓଷଵ ൈ fୡ′ ݓସଵ ൈ t ݓହଵ ൈ fୖ ݓଵ ൈ Eୖ (10)2ݔ ൌ ߠଶ ݓଵଶ ൈ d ݓଶଶ ൈ h ݓଷଶ ൈ fୡ′ ݓସଶ ൈ t ݓହଶ ൈ fୖ ݓଶ ൈ Eୖ ሺ11)3ݔ ൌ ߠଷ ݓଵଷ ൈ d ݓଶଷ ൈ h ݓଷଷ ൈ fୡ′ ݓସଷ ൈ t ݓହଷ ൈ fୖ ݓଷ ൈ Eୖ (12)The values of weights ݓ and threshold ߠ are shown in Table 2.Table 2: Weights and threshold levels of the ANN modela. Weights from node i in the input layer to node j in the hidden layernodesݓi=1 i=2 i=3 i=4 i=5 i=6 Hidden threshold ߠJ=1J=2J=30.28-0.10-2.07-7.901.003.828.93-5.712.713.36-7.006.1510.19-17.30-2.851.537.58-0.60-5.7317.600.68b. Weights from node i in the hidden layer to node j in the output layernodeWiji=7 i=8 i=9 output threshold θjJ=4 1.53 -16.41 2.51 12.53Equation (9) is long and complex because it contains six independent variables. Onthe other hand, it can predict accurately the compressive strength (fୡୡ) of the confinedconcrete (Fig.2) with a correlation coefficient equal to 0.964.The equation length depends on the number of nodes in the input and hidden layers.To simplify the equation, the most importance input parameters, which are the compressivestrength (fୡ′), of the unconfined concrete the total thickness(t) of CFRP, and the tensilestrength(fୖ) of the CFRP along the hoop direction, were used in training the second ANNmodel with two nodes in the hidden layer. The result was the development of an ANN modelwith a regression of 0.9259 (Fig. 4).The small number of connection weights of the neuralnetwork enables the ANN model to be translated into a relatively simple formula in which thecompressive strength of the confined concrete (fୡୡ) can be expressed as follows:
- 8. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME105fୡୡ ൌଵଵାష మఴభ.రఱశభయళ.ళఱభశషೣభ శమఴఴ.ఴలభశషೣమ(13)where:1ݔ ൌ െ2.50 0.40fୡ′ െ 0.64t 1.90fୖ (14)2ݔ ൌ 2.90 െ 0.36fୡ′ 0.34t െ 1.42fୖ. (15)Before using Eqs. 10–12, 14, and 15, all input variables must be scaled between 0.1and 0.9 using Eq. 8 for the data ranges shown in Table 1. The predicted values obtained fromEqs. 9 and 13 are scaled between 0.1 and 0.9. To obtain the actual values, these had to beunscaled using Eq. 8.In contrast to all previous models, the second ANN model depends on thecompressive strength (fୡ′) of the unconfined concrete, the total thickness (t) of CFRP, and thetensile strength(fୖ) of the CFRP in the hoop direction, whereas the geometry of the columnis not considered in this ANN model.Fig. 4. Experimental and corresponding ANN compressive strength of the test data of secondModelGaussian distributions are perhaps the most important model for studying thequantitative phenomena in the natural and behavioral sciences, such as the problemsencountered in structural analysis and design. To determine the suitability of the developedCFRP-confined model, all 208 experimental and predicted confined compressive strengthvalues were taken, and the results of the confined compressive strength ratio40 60 80 100 120 140 160 180 200406080100120140160Experimental Compressive Strength (MPa)ANNPredictedCompressiveStrength(MPa)Test dataR=0.9259
- 9. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME106(predicted/experimental) were statistically analyzed with a 0.5% level of significance usingthe SPSS software V.16.The average and variance of all values were found to be 92% and 0.02, respectively.Fig.5 shows the frequency histogram of the confined compressive strength ratio(fcc)pred./(fcc)Exp population curve. The (fcc)pred./(fcc)Exp values are distributed around their meanvalues. The magnitude of the frequency becomes smaller when the value moves away fromthe mean central value. The probability of obtaining a ratio between 90% and 95% is 85%.Fig. 5. Histogram and normal distribution curve for the second mathematical model6. PARAMETRIC STUDYOne of the advantages of the ANN models is that parametric studies can be easilyconducted by simply varying one input parameter while all other input parameters are set toconstant values. Parametric studies can verify the performance of the model in simulating thephysical behavior of the CFRP-confined concrete due to the variation in certain parametervalues.The second ANN model and Eq. 13 were used to complete this parametric study.Figs. 6 and 7 show the relationship between the compressive strength (fୡ′ሻof theunconfined concrete and that of the CFRP-confined concrete (fୡୡ) under different values oftensile strength (fୖ) of the CFRP and total thickness(t) of the CFRP, respectively. Ingeneral and regardless of the other parameters, the compressive strength (fୡୡ) increases withthe increasing compressive strength (fୡ′ሻof the unconfined concrete.Fig. 6 shows the effect of the tensile strength (fୖ) of the CFRP on the compressivestrength of the CFRP-confined concrete (fୡୡ) under different values of compressivestrength(fୡ′) of the unconfined concrete with a constant total thickness (t) equal to 0.22mm.
- 10. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME107The compressive strength of the confined concrete (fୡୡ) strongly affects the tensile strength(fୖ) of the CFRP, especially under high unconfined compressive strength and high tensilestrength of the CFRP. For the unconfined compressive strength of 25 MPa, changing thetensile strength of the CFRP from 2,500 MPa to 4,000 MPa led to an increase in the confinedcompressive strength from 55.18 MPa to 56.6 MPa (increasing by 2.57%), whereas for theunconfined compressive strength of 65 MPa, the same change in the tensile strength (fୖ) ofthe CFRP led to an increase in the confined compressive strength (fୡୡ) from 75.64 MPa to87.27 MPa (increasing by 15.37%).Fig 6. Effect of the tensile strength of the CFRP on the compressive strength of the FRP-confined concreteFig. 7 shows the effect of the total thickness(t) of the CFRP on the compressivestrength of the CFRP-confined concrete (fୡୡ) for different values of compressive strength(fୡ′)of the unconfined concrete with a constant tensile strength (fୖ) equal to 3,000 MPa. Fordifferent thicknesses(t) of CFRP, the curves are parallel, that is, a low or high unconfinedcompressive strength wields the same effect on the compressive strength of the CFRP-confined concrete with different thicknesses.7. CONCLUSIONSTwo mathematical models for predicting the confined compressive strength of anCFRP circular concrete column have been developed using the ANN approach. Theimportance study showed that the diameter and height of the specimen and the elasticmodulus of CFRP had little effect on predicting the confined compressive strength of theCFRP circular concrete column; hence, they were excluded from building the second ANNmodel, leaving only three input parameters. Both parametric and importance studies showedthat the tensile strength of CFRP had an effect on predicting the confined compressivestrength of the CFRP circular concrete column. Finally, the ANN approach was proven to begood and efficient in developing the mathematical models.20 25 30 35 40 45 50 55 60 65 70 7530405060708090100ConfinedCompressiveStrength(MPa)Compressive Strength (MPa)f=1000MPaf=2500MPaf=4000MPat=0.22 mm
- 11. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 3, May - June (2013), © IAEME108Fig 7. Effect of the total thickness of the CFRP on the compressive strength of the CFRP-confined concreteREFERENCES[1] J.G. Teng, L. Lam., Behavior and modeling of fiber reinforced polymer-confinedconcrete, J. Struct. Eng. 130 (11) (2004) 1713-1723.[2] A.H. Naderpour, G. Kheyroddin, A. Ghodrati. Prediction of FRP-confined compressivestrength of concrete using artificial neural networks, Compos.Struct. 92 (12) (2010) 2817–2829.[3] L. Lam, J.G. Teng, Strength models for fiber-reinforced plastic-confined concrete, J.Struct. Eng. 128 (5) (2002) 612-623.[4] H.M. Elsanadedy, Y.A. Al-Salloum, S.H. Abbas H,Alsayed, Prediction of strengthparameters of FRP-confined concrete, Compos.:Part B. 43(2) (2012) 228–239.[5] A.K. Mehmet, C. Murat, H.A. Musa, I. Alper, Estimation of flexural capacity ofquadrilateral FRP-confined RC columns using combined artificial neural network, J. Struct.Eng. 42 (2012) 23–32.[6] H.M. Tanarslan,M. Secer, A. Kumanlioglu, An approach for estimating the capacity ofRC beams strengthened in shear with FRP reinforcements using artificial neural networks,Const. Build. Mat. 30 (2012) 556–568.[7] S.T. Yousif, A.T. Majed, Modeling of ultimate load for R.C. beams strengthened withCarbon FRP using artificial neural networks, AL-Rafidain Eng. J.18(6) (2010) 28-41.[8] T.A. Adriana, B.L. Monica, J.N. Koji, Prediction of compressive strength of concretecontaining construction and demolition waste using artificial neural networks, Const. Build.Mat. 38 (2013) 717–722.[9] Z.H. Duan, S.C. Kou , C.S. Poon , Prediction of compressive strength of recycledaggregate concrete using artificial neural networks, Const. Build. Mat. 40 (2013) 1200–1206.20 25 30 35 40 45 50 55 60 65 70 75405060708090100110ConfinedCompressiveStrength(MPa)Compressive Strength (MPa)t=0.22 mmt=0.33 mmt=0.44 mmf=3000MPa
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