Modeling of Confined Circular Concrete Columns Wrapped by Fiber Reinforced Polymer Using Artificial Neural Network

Journal of Soft Computing in Civil Engineering 4-4 (2020) 61-78
How to cite this article: Abbaszadeh MA, Sharbatdar M. Modeling of confined circular concrete columns wrapped by fiber
reinforced polymer using artificial neural network. J Soft Comput Civ Eng 2020;4(4):61–78.
https://doi.org/10.22115/scce.2020.213196.1153.
2588-2872/ © 2020 The Authors. Published by Pouyan Press.
This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Contents lists available at SCCE
Journal of Soft Computing in Civil Engineering
Journal homepage: www.jsoftcivil.com
Modeling of Confined Circular Concrete Columns Wrapped by
Fiber Reinforced Polymer Using Artificial Neural Network
M.A. Abbaszadeh1*
, M.K. Sharbatdar2
1. Department of Civil Engineering, Malard Branch, Islamic Azad University, Malard, Iran
2. Associate Professor, Faculty of Civil Engineering, Semnan University, Semnan, Iran
Corresponding author: mahdi.abbaszadeh@yahoo.com
https://doi.org/10.22115/SCCE.2020.213196.1153
ARTICLE INFO ABSTRACT
Article history:
Received: 25 December 2019
Revised: 05 October 2020
Accepted: 06 October 2020
This study is aimed to explore using an artificial neural
network method to anticipate the confined compressive
strength and its corresponding strain for the circular concrete
columns wrapped with FRP sheets. 58 experimental data of
circular concrete columns tested under concentric loading
were collected from the literature. The experimental data is
used to train and test the neural network. A comparative
study was also carried out between the neural network model
and the other existing models. It was found that the
fundamental behavior of confined concrete columns can
logically be captured by the neural network model. Besides,
the neural network approach provided better results than the
analytical and experimental models. The neural network-
based model with R2
equal to 0.993 and 0.991 for training
and testing the compressive strength, respectively, shows
that the presented model is a practical method to predict the
confinement behavior of concrete columns wrapped with
FRP since it provides instantaneous result once it is
appropriately trained and tested.
Keywords:
Concrete columns;
CFRP;
Confinement;
Artificial neural networks;
Models.

62 M.A. Abbaszadeh, M.K. Sharbatdar/ Journal of Soft Computing in Civil Engineering 4-4 (2020) 61-78
1. Introduction
The need for seismic retrofitting of concrete structures has led to applying a new material which
does not only increase the compressive strength and ductility of concrete members but also
possesses other beneficial advantages like light-weight, high tensile strength and modulus,
easiness to apply, corrosion resistance, and durability. Fiber-reinforced polymer (FRP) is shown
to have these characteristics and has been commonly used for civil infrastructure rehabilitation
applications [1–3]. Confining concrete columns is one of the most remarkable uses of FRP
Fibers. It is an effective method proved by many engineering applications and experiments [1–7].
Significant research concerning the circular columns retrofitted by FRP has been conducted, and
their stress-strain response is predicted by the proposed confinement models having varying
degrees of complexity (sophistication). [3–6,8–14].
Early investigations attempted to use FRP confinement analytical models based on models
previously used for steel sheet [4,9], but it was soon mentioned that this operation yielded
inaccurate and often non-conservative results [15]. Since then, different models particularly
suitable for FRP-confined concrete columns, have been proposed [3,5,6,8,10–15]. Many of these
models are empirical and have been calibrated against their own sets of experimental data, and
some display gross inadequacies when compared to a complete database of experimental results.
The failure stress-strain of FRP-confined concrete [4,16,17] is only provided by the most
available confinement models, whereas the other models estimate the full stress-strain behavior
as bilinear[5,11–14,18]. Most recently, sophisticated rational iterative procedures have been
suggested to derive the complete stress-strain response [6]. Accuracy, however, does not
necessarily follow complexity (sophistication), and with new confinement models being
presented every year, it is far from clear which one(s) should be used in light of the existing test
data [19].
It is challenging to apply the statistical approach to a complex nonlinear system due to the
considerable technique and experience required to choose the right regression equation. In an
attempt to overcome these difficulties, artificial neural networks (ANNs), which provide an
alternative method [20,21], are applied in this study. An ANN is a computational tool by which
the architecture and internal operational features of the human brain and neuron systems are
simulated.
In civil engineering, the methodology of neural networks has been successfully applied to several
areas [22–25]. Governing the quantities being modeled by multivariate interrelationships and the
available “noisy” or incomplete data are the common features of ANNs successful application.
Besides, in developing the neural network model, unlike regression analysis, it is not essential to
presume any functional relationship among the different variables. The relationships are
automatically constructed by ANNs and adjusted based on the used data for training. [24]. Also,
in the future, by adding new results to the training data, it can modify and update its weights
automatically and so be able to predict more accurately.
Recently, several studies have been carried out on the prediction of compressive strength of RC
members using ANN. Naderpour et al. [26] proposed equations to predict the compressive

M.A. Abbaszadeh, M.K. Sharbatdar/ Journal of Soft Computing in Civil Engineering 4-4 (2020) 61-78 63
strength of RC columns strengthened by FRP composites. Cui and Sheikh [27] proposed an
analytical model for circular normal- and high-strength RC columns confined with FRP. Their
constitutive model used an analytical rupture strain of an FRP jacket for predicting the complete
stress-strain curve as well as it accommodated a wide range of concrete strength. Fathi et al. [28]
presented an ANN formulation approach to predict compressive strength for concrete cylinders
confined with CFRP. This approach represented the effect of CFRP confinement on the ultimate
strength of concrete cylinders, which is also provided explicitly in terms of geometrical and
mechanical parameters. The good agreement of the proposed ANN model in comparison to
experimental results was quite satisfactory. Behfarnia and Khademi [29] conducted a
comprehensive study on predicting concrete compressive strength using ANFIS and ANN. They
founded that the ANN model was an effective model for the estimation of concrete compressive
strength. Naderpour and Alavi [30] proposed a model to predict the shear contribution of FRP in
strengthened RC beams using ANFIS. It was concluded that their proposed model provides an
accurate and reliable tool than the guidelines equations. Hosseini [31] developed an ANN model
based on a genetic algorithm to predict the capacity of RC beams retrofitted by FRP. The results
showed that the shear capacity of the considered beams could be predicted by the proposed ANN
model based on a genetic algorithm. Sharifi et al. [32] used the ANN method to investigate the
estimation of the compressive strength of rectangular concrete columns confined by FRP. The
results demonstrated that the proposed model based on ANN gave the best accuracy than the
other models and conducted a sensitivity analysis based on Garson’s algorithm on indicating the
value of used variables. Khan et al. [33] developed a stress-strain model to estimate the strength
and strain enhancement ratio of FRP tube confined concrete cylinders under axial compression
by implementing ANN. The predictions of the developed models had a good agreement with the
experimental investigation results of the compiled database. Naderpour et al. [34] presented an
ANFIS model to predict the ultimate strength of FRP-confined circular RC columns. The
obtained results of the ANFIS model were compared with results from other models. The highest
accuracy to predict the experimental results was observed in the ANFIS model. As can be seen
there is no study about the modeling of confined circular concrete columns wrapped by fiber-
reinforced polymer using an artificial neural network. For this purpose, In this study, the
possibility of using artificial neural networks (ANNs) in predicting the compressive strength of
confined concrete circular columns and corresponding strain by using valid results from past
experiments is explored. Because of the comparatively scarce test data now presented on the
square and rectangular, slender, and eccentrically loaded columns, this paper deals only with
FRP-wrapped circular columns under concentric axial load. Since the ability of the previous
confinement models to predict behavior is somewhat dependent on whether the confinement is
provided by an FRP wrap or tube [35], and so the focus of this study on comparison purposes is
on the wrapped-columns.
2. Fundamental concepts of artificial neural network
An ANN performs as a network by a set of simple processing units called neurons that interact
with each other through weighted connections. As can be seen in figure 1, The function of a
neuron is estimated by a processing element.

Fig. 1. Model of a neuron [36].
The processing units may be arranged logically into two or more layers called input, hidden, and
output layers, shown in Figure 2. The topology or architecture of an ANN is similar to that of the
brain and nervous system; each neuron can have many inputs but only one output. However,
each output branches out to the input of many other processing elements [22]. Receiving input
from its neighboring units, which provides incoming activations, computing, and output, and also
sending the output to its neighbors, are the main duties of processing units. A set of weights can
affect the magnitude of the input being received by the neighboring units and also provide the
strength of the connections among the processing units. The output processing units produce
output compared to the target output data, and the weights are properly modified or adjusted
based on training or learning rule. The output produced by the output processing units is
compared to the target output data, and the weights are appropriately modified or adjusted based
on training or learning rule. Finally, by learning the problem, a stable set of weights adaptively
evolves, which will produce good results.
Fig. 2. The topology of a neural network with one hidden layer [35].

ANN, like structure based on the biological nervous system, represents a surprising number of
characteristics, e.g., learn from experience, and generalize from previous examples to new
problems by inferring solutions through problems beyond those they are exposed to due to
training, process information rapidly [37].
Parker and Werbos independently discovered the Back-propagation learning method. Rumelhart
et al. generalized and developed this method to a workable process.
In back-propagation, learning is accomplished by propagating a set of input training patterns
through a network consisting of an input layer, one or more hidden layers, and an output layer.
Each layer has its corresponding units and weight connections. The calculated outputs at the
output layer are subtracted from the desired (target) output, and the error is obtained by the
squared sum of the output difference. This measurement represents the level at which the
network has learned the input-output data and may be used to determine the gradient of the
learning procedure [22].
Determining the connection weight matrices and the layout of the connections and also the
application of the learning rule by which the neural network obtains the desired relationship
embedded in the training data are primarily involved in the learning process. An error criterion is
usually selected for the network output, and the simulation can be terminated by setting the
maximum number of cycles [24].
The error will approach a minimum value if the network “learns.” After the training phase, the
ANNs can be tested for other input data where the final values of the weights obtained in the
training phase are used. No weight modification is involved in the testing phase. Details of the
BPN algorithm and its variants can be found in the literature [38].
Aiming at empirically validating the performance of an ANN model which has been trained by
presenting it with a set of training patterns, the reliability, and accuracy of the network
performance is evaluated via a selected error matric based on data (referred to as test data),
which was not in training. An ANN prediction model can be evaluated and validated by common
error methods like root mean squared error (RMSE) or the mean absolute error (MAE).
3. Behavior and models of confined circular concrete columns with FRP
A concrete cylinder confined by FRP jacket starts expanding laterally when subjected to axial
compressive stress. The FRP jacket loaded in tension in the hoop direction can limit and decrease
the expansion. The FRP jacket provides confining pressure, which is continuously increased,
whereas the lateral strain of concrete increases due to the linear elastic stress-strain behavior of
FRP, in contrast to steel-confined concrete in which the confining pressure remains constant even
when the steel is in the plastic range [7]. Figure 3 describes the stress-strain behavior of the
confined concrete column. Confinement acts as passive in concrete and only is effective once the
internal cracking increases the volume. Passive confinement enhances the compressive strength
of the concrete and increases its ductility [24].

Fig. 3. Applying confinement pressure to the concrete core.
Various analytical and empirical models have been proposed to estimate the compressive
strength, f’cc, and corresponding strain, εcc, of confined concrete columns considering various
parameters [3–6,8–14]. To compare the results obtained from the neural network model, some
remarkable methods are selected and used in this study are outlined in the following. A detailed
discussion was carried out in the literature on the accuracy and comparison of the existing
models [7,19,35]. To ensure uniformity of notation withing the current paper, The notation and
format of the original equations have been modified in most cases. In the following expressions,
Pu represents the ultimate confining pressure applied by an FRP wrap. For a circular concrete
column of diameter D, confined by a circumferential wrap with tensile strength, ffu, and
thickness, nt, this pressure is computed by assuming the failure of concrete when the wrap
reaches its failure stress [14]. Thus, an expression giving the lateral confining pressure at the
ultimate level can be obtained using the equilibrium of forces (Figure 3).
frp
L
L
L E
E
P 
 .
. 
 (1)
D
t
E
E
frp
frp
L
.
2
 (2)
D
t
f
P
frp
frp
u
.
2
 (3)
Where EL is the confinement modulus or lateral modulus.
As for the strength enhancement, almost all models relate f’cc/ f’co to the Pu/ f’co ratio, except for
the Kono model [9], which expresses f’cc/ f’co only as a function of Pu, Samaan et al. [12],
expressed f’cc/ f’co as a function of Pu and f’co, and Xiao and Wu [13], included the ratio f’2
co / EL
as a significant variable. The ductility enhancement, as expressed by the ratio εcc/εco, appears to
be related not just to the strength properties but also to the stiffness of the confining device.
Some of the most important models to predict the compressive strength of confined concrete
used in this study are presented in Table 1.

Table 1
Models of predicting compressive strength of confined concrete.
Author Equation Ref
Fardis and Khalili 1 2.05( )
cc co l co
f f f f
  
  [4]
Saadatmanesh et al.
7.94
1.254 2.254 1 2
l l
cc co
co co
f f
f f
f f
 
      
 
 
 
[9]
Miyauchi et al. 1 2.98( )
cc co l co
f f f f
  
  [5]
Samaan et al. 0.7
1 6( )
cc co l co
f f f f
  
  [12]
Toutanji
0.85
1 2.3( )
cc co l co
f f f f
  
  [11]
Saafi et al.
0.84
1 2.2( )
cc co l co
f f f f
  
  [3]
Karbhari and Gao
0.87
1 2.1( )
cc co l co
f f f f
  
  [14]
Lam and Teng 1 2( )
cc co l co
f f f f
  
  [18]
4. Experimental data
Comprehensive information about the feature of the behavior of the materials should be included
in a good training data set. Therefore, the trained neural network will contain sufficient
information to qualify as a material model. Results of about 187 tests from 18 different
experiments set documented in the published literature were collected.
Although considering the effects of quality parameters in neural networks is possible by
designating numeric variables to them, but in this study, like other existing models, a specific
type of leg was considered Filament wound, wrap, and tube and fiber type (e.g., AFRP, CFRP,
and GFRP) are as variables. The ANN model was trained for CFRP wrapped columns. The
previous researchers just took into account the diameter of the cylinder, D in the prediction
models, and the height of the cylinder, H was not considered, whereas size effect is a relevant
issue that needs specific investigations. Therefore, in this study, to exclude size effect, the
experiment data limited to those which have reported the H/D ratio equal to 2.
Some authors had reported the experimental results with identical properties that are impossible
for a neural network to learn those patterns with the same inputs and different outputs. Therefore,
to prevent falling in this loop, the results of identical specimens were averaged. Eventually, 58
sets out of 180 gathered sets from 9 published literatures [5,10,39–44] were selected, which are
presented in Table 2. These ranges are listed in Table 3 (At first, 187 datasets were collected from
valid references, Then, out of 187 data, 58 homogeneous data were selected, and heterogeneous
data were deleted).

Table 2
Initial Experimental Data as the input of the ANN model.
Reference Code D (mm)
nt
(mm)
Eƒ
(MPa)
fƒu
(MPa)
f'co(MPa)
εco
(%)
f'cce
(MPa)
εcce
(%)
f'ccp
(MPa)
εccp
(%)
Harmon et al.,1992
HA1 51 0.089 235000 3500 41 0.23 86 1.15 84.281 1.191
HA2 51 0.179 235000 3500 41 0.23 120.5 1.57 109.060 1.551
HA3a
51 0.344 235000 3500 41 0.23 158.4 2.5 166.003 2.358
HA4 51 0.689 235000 3500 41 0.23 241 3.6 239.774 3.546
HA5 51 0.179 235000 3500 103 0.4 131 1.1 130.165 1.079
HA6a
51 0.344 235000 3500 103 0.4 193.2 2.05 190.262 1.842
HA7 51 0.689 235000 3500 103 0.4 303.6 3.45 302.877 3.449
Picher et al.,1996 PI1 153 0.36 83000 1266 39.7 0.25 55.98 1.07 59.175 1.016
Watanabe et
al.,1997
WA1 100 0.1675 223400 2728.5 30.2 0.25 46.6 1.511 54.517 1.426
WA2 100 0.5025 223400 2728.5 30.2 0.25 87.2 3.108 90.247 3.193
WA3 100 0.67 223400 2728.5 30.2 0.25 104.6 4.151 100.573 4.047
WA4 100 0.14 611600 1562.7 30.2 0.25 41.7 0.575 40.056 0.576
WA5a
100 0.28 611600 1562.7 30.2 0.25 56 0.876 50.342 0.886
WA6 100 0.42 611600 1562.7 30.2 0.25 63.3 1.298 63.535 1.298
Miyauchi et
al.,1997
MI1 150 0.11 230500 3481 45.2 0.219 59.4 0.945 66.811 0.789
MI2a
150 0.22 230500 3481 45.2 0.219 79.4 1.245 82.268 1.071
MI3 150 0.11 230500 3481 31.2 0.195 52.4 1.213 52.578 1.291
MI4 150 0.22 230500 3481 31.2 0.195 67.4 1.554 60.585 1.584
MI5 150 0.33 230500 3481 31.2 0.195 81.7 2.013 68.754 1.917
MI6 100 0.11 230500 3481 51.9 0.192 75.2 0.956 78.461 0.758
MI7a
100 0.22 230500 3481 51.9 0.192 104.6 1.275 113.373 1.230
MI8 100 0.11 230500 3481 33.7 0.19 69.6 1.406 58.712 1.209
MI9 100 0.22 230500 3481 33.7 0.19 88 1.488 68.772 1.493
Kono et al.,1998
KO1,2 100 0.167 235000 3820 34.3 0.17 61.15 0.9475 58.085 1.009
KO3,4,5 100 0.167 235000 3820 32.3 0.234 59.23 1.07 53.271 1.056
KO6,7,8 100 0.334 235000 3820 32.3 0.234 66.73 1.75 70.693 1.503
KO9,10 100 0.501 235000 3820 32.3 0.234 88.5 1.62 85.391 1.928
KO11,12,13 100 0.167 235000 3820 34.8 0.229 54.7 0.989 59.450 1.001
KO14,15a
100 0.334 235000 3820 34.8 0.229 82.05 2.06 84.221 1.520
KO16,17 100 0.501 235000 3820 34.8 0.229 106.7 2.425 105.693 2.023
Matthys et al., 1999
MA1 150 0.117 220000 2600 34.9 0.21 46.1 0.9 46.101 0.894
MA2a
150 0.235 500000 1100 34.9 0.21 45.8 0.6 32.848 0.400
Shahawy et al.,2000
SH1 153 0.36 82700 2275 19.4 0.2 33.8 1.59 36.723 1.620
SH2 153 0.66 82700 2275 19.4 0.2 46.4 2.21 48.110 2.023
SH3 153 0.9 82700 2275 19.4 0.2 62.6 2.58 62.674 2.594
SH4a
153 1.08 82700 2275 19.4 0.2 75.7 3.56 73.213 3.047
SH5 153 1.25 82700 2275 19.4 0.2 80.2 3.42 80.739 3.359
SH6 153 0.36 82700 2275 49 0.2 59.1 0.62 58.250 0.582
SH7 153 0.66 82700 2275 49 0.2 76.5 0.97 76.804 0.923
SH8 153 0.9 82700 2275 49 0.2 98.8 1.26 94.713 1.339
SH9 153 1.08 82700 2275 49 0.2 112.7 1.9 111.606 1.805
Micelli et al.,2001 MC5,6,7,8a
100 0.16 227000 3790 37 0.19 59.5 1.015 58.357 0.834
Rousakis,2001
RO1,2,3 150 0.169 118340 2024 25.15 0.32 41.48 1.37 39.558 1.335
RO4,5,6 150 0.338 118340 2024 25.15 0.32 59.21 2.017 54.312 1.896
RO7,8,9 150 0.507 118340 2024 25.15 0.32 68.15 2.423 67.774 2.470
RO10,11,12a
150 0.169 118340 2024 47.44 0.31 67.617 0.853 68.977 0.875
RO13,14 150 0.338 118340 2024 47.44 0.31 82.355 1.335 83.805 1.190
RO16,17,18 150 0.507 118340 2024 47.44 0.31 95.755 1.683 94.426 1.452
RO19,20,21 150 0.169 118340 2024 51.84 0.29 78.915 0.67 74.882 0.822
RO22,23,24 150 0.338 118340 2024 51.84 0.29 90.475 1.02 90.038 1.106
RO25,26,27a
150 0.507 118340 2024 51.84 0.29 110.463 1.33 101.137 1.338
RO28,29,30 150 0.845 118340 2024 51.84 0.29 125.76 1.555 117.587 1.772
RO31,32,33 150 0.169 118340 2024 70.48 0.35 84.847 0.707 86.694 0.595
RO34,35,36a
150 0.338 118340 2024 70.48 0.35 99.797 0.9 102.534 0.825
RO37,38,39 150 0.507 118340 2024 70.48 0.35 110.857 1.16 118.436 1.063
RO40,41,42 150 0.169 118340 2024 82.13 0.31 95.837 0.477 86.890 0.484
RO43,44,45 150 0.338 118340 2024 82.13 0.31 98.173 0.44 99.865 0.673
RO46,47,48 150 0.507 118340 2024 82.13 0.31 124.713 0.95 115.013 0.897

Table 3
Statistic Properties of Training and Testing Sets for the ANN model.
Input and Output Variables
D
(mm)
H
(mm)
nt
(mm)
Ef
(MPa)
ffu
(MPa)
f'co
(MPa)
f'cc
(MPa)
f'cc
(%)
All
Data
Ave. 123.05 245.93 0.39 198917.9 2707.89 44.26 88.23 1.56
Min. 51 102 0.089 82700 1100 19.4 33.8 0.44
Max. 153 305 1.25 611600 3820 103 303.6 4.151
Standard Deviation 35.44 70.72 0.27 123592.9 809.82 20.68 46.29 0.86
Training
Set
Ave. 124.6 249 0.3983 186846 2706 43.48 86.63 1.57
Min. 51 102 0.089 82700 1266 19.4 33.8 0.44
Max. 153 305 1.25 611600 3820 103 303.6 4.151
Standard Deviation 34.78 69.39 0.2804 111888 775.1 20.56 47.34 0.87
Test
Set
Ave. 117.1 234.1 0.35 245193 2715.14 47.26 94.38 1.52
Min. 51 102 0.16 82700 1100 19.4 45.8 0.6
Max. 153 305 1.08 611600 3820 103 193.2 3.56
Standard
Deviation
38.86 77.63 0.25 158095 969.75 21.77 43.43 0.86
5. Application of ANN to FRP confined concrete
Examining the input variables given in the references above can help to select those parameters
for a network model. In general, the following six parameters were concluded in almost all
models for prediction of peak axial stress of FRP confined concrete specimen, f’cc, and
corresponding strain at peak stress, εcc. The six major variables that are used as input nodes in the
ANN model are listed as follows:
D = Diameter of the concrete cylinder
nt = total thickness of the applied FRP
Ef = FRP modulus of the elasticity
ffu = FRP ultimate tensile strength
f’co = peak stress of an unconfined concrete cylinder
εco = strain corresponding to peak stress of an unconfined concrete cylinder
Having the above six input nodes, the two output nodes correspond to maximum axial stress, f’cc,
and strain, εcc, of FRP confined concrete, respectively. The data for 58 columns from the
experiments of Miyauchi et al. [5], Kono et al. [10], Harmon and Slattery [39], Watanabe et al.
[40], Micelli et al. [41], Matthys et al. [42], Shahawy et al. [43], Rousakis [44], were grouped
randomly into training and test data. Forty-six (46) data patterns were used as training data, and
the remaining twelve (12) data patterns were regarded as test data.

In this study, a scientifically available program widely used by researchers during the last decade
was applied for the simulations. The program neural works professional II plus “NW II” [45] is a
multi-paradigm neural network prototyping and development tool which is provided with
powerful diagnostic instruments, such as the root–mean square error (RMSE), network weights,
classification rate, and confusion matrices, for monitoring the network instantly to achieve a
better understanding of the network performance. Once the network is trained and converged, a
test set is presented to the network sequentially to verify the reliability and accuracy of the
network performance. Considering the number of training patterns and aiming at reaching the
desired performance and accuracy of the network, different architecture for the network is
assumed, trained, and then the best will be selected. The best architecture is the one that gives the
nearest predictions to both training and test sets [22].
In this study, the network configuration was obtained once the performance of various
configurations for a fixed number of cycles was monitored. Then, learning parameters were
changed, and learning processes were reported. To yield the best results, two hidden layers with
five neurons in the first hidden layer, and three neurons in the second hidden layer were selected.
Transfer functions were “tangent hyperbolic” and linear for the hidden and output layers,
respectively. Moreover, to avoid over-training, the convergence criteria for stopping the training
network were:
 Root Mean Square Error (RMSE) of 0.01 for normalized data;
 Maximum cycles of 50000
Whereas the error tolerance was not achieved, the simulation stopped when the maximum
number of cycles was reached. In the NW II program, by choosing “Extended Delta-Bar-Delta”
(Ext DBD) as the learning rule, the program sets the following parameters Momentum, Learning
Coefficient Ratio, and f’ offset automatically.
Since tangent hyperbolic transfer function is asymptotic to values -1 and 1, the derivative at or
close to values -1 and 1 will approach zero, producing a minimal signal error, which leads to
slow learning. The input and output data were scaled into the interval [-0.9, 0.9] and the interval
[-0.8, 0.8], respectively, to avoid the slow rate of learning near the endpoints, particularly of the
output range.
When the network is trained, it is presented by the test data to assess the accuracy of the model.
Tables 4 and 5 show the comparison of the performance of the proposed models for RMSE and
R2
, both for training and test data. It can be seen that the BPN model has the best results. To
obtain the maximum strength of confined concrete by the BPN, the values of RMS error are
5.558 MPa for the training set and 6.191 MPa for the testing set; while for the corresponding
strain of confined concrete, the values of RMS error are 0.127 and 0.246 for the training set and
testing set respectively, which are the lowest values among the prediction models. Moreover, the
R2
can be used as an index to indicate how well the considered independent variables (D, nt, ffu
,Ef, f’co, and εco) justify the measured dependent variables (f’cc and εcc) and, subsequently, the
accuracy of the trained network. All values of R2
were found to be greater than 0.983 for the

training set and testing set, which represents a significant correlation between the independent
variables and the measured dependent variables.
Table 4
Summary of the Errors of BPN Model for strength.
f'cc Max E. Min E. MAE RMS R2
COV STDV AVG
Training
Set
19.227 0.00125 3.968 5.558 0.993 0.076 0.078 1.021
Testing
Set
12.952 1.142 5.001 6.191 0.991 0.121 0.125 1.036
Table 5
Summary of the Errors of BPN Model for strain.
f'cc Max E. Min E. MAE RMS R2
COV STDV AVG
Training
Set
0.40100 0.00050 0.09500 0.127 0.989 0.105 0.107 1.021
Testing
Set
0.539 0.0089 0.176 0.246 0.983 0.139 0.158 1.138
6. ANN model simulation
A neural network model uses the training examples to learn and construct relationships between
the input and output parameters. Due to the scarce and limited training data, it is expected that
the trained model may not be able to capture the complicated interrelationships among physical
parameters completely. Therefore, it is necessary to validate the performance of the ANN model
in simulating the behavior of physical processes. This can be accomplished through testing the
model with hypothetical data by changing the values of some input parameters. In the parametric
study, two types of columns were used; the M column which has the properties like the Miauchi
[5] specimens used in his experiment (i.e. D=150 mm, nt= 0.11,0.22,0.33 mm, Ef=230500 MPa,
ffu=3481 MPa, f’co=31.2,33.7,51.9 MPa, and εco=0.195%) and S column which is identical to
Shahawy [35] specimens (i.e. D=153 mm, nt= 0.36,0.66,0.9,1.08,1.25 mm, Ef=82700 MPa,
ffu=2275 MPa, f’co=19.4,49 MPa, and εco=0.2%). In the M column, the thickness of the wrapped
FRP, nt, that is one of the most important parameters in confinement, is varied from 0.1 mm to 1
mm for unconfined concrete stresses, f’co, equal to 30, 40, and 50 MPa with keeping constant the
other parameters. Similarly, in the S column, considering constant values for the variables above,
like in the M column, the thickness is varied from 0.35 mm to 1.25 mm for unconfined concrete
stresses equal to 17, 34, and 51 MPa. For the M column, as it was expected and shown in Figure
4 and Figure 5, the network revealed an increasing linear trend in the interval 0.1 to 0.3 for the
thickness, which are the ranges of learning patterns but nonlinear for those patterns out of
training set ranges. In contrast, for the S column, which the range of varying thicknesses is the
same as the range that the model was trained for, the trend of predictions is ever-increasing, and
the model does not need to predict values out of its training ranges. Hence, it is observed that the
ANN model is able to predict the values in its learning patterns regions but poorly in the values
out of it.

Fig. 4. Predictions of the ANN Model for Mcolumn
Fig. 5. Predictions of the ANN Model for S column
7. Discussion and comparison of prediction models
The training and testing data for calculating the predicted maximum strength, f’ccp, and
corresponding strain, εccp, of confined concrete columns are used to compare the neural network
results with other well-known existing models. Since different models may involve different
parameters, the comparison is made by plotting experimental values versus predicted values,
with a 45-degree line corresponding to perfect agreement between predictions and experimental
results (i.e., εcce/εccp =1 and f’cce/ f’ccp=1). As shown in Figure 6 for f’cce versus f’ccp and Figure 7
for εcce versus εccp, points falling in the upper part of the graph show conservative predictions,
while points falling down the line are obtained from theoretical values being higher than the
experimental ones. Figure 6 and Figure 7 clearly show that the least scattered data around the
diagonal line confirms that the neural network-based model is an excellent predictor for the
values of f’cc and εcc, respectively (Because the predictions (points) are closer to the laboratory
values (45-degree line) compared to other models(.

Fig. 6. Comparison of the models in predicting f’cc
Fig. 7. Comparison of the models in predicting εcc.

Also, the Figs. 6 and 7 shows that Xiao and wu model has the highest deviation in predicting
compressive strength among other models while in term of strain this model and Samaan model
has the highest deviation. These figures also show that the models are more accurate in
predicting compressive strength compared to strain.
While the correlation between the values of experimental and predicted from previous models is
more scattered. The values of RMSE (Root Mean Square Error) and R2
(Absolute Fraction of
Variance) of the training and testing results for the prediction models are also listed in Table 6
based on the following equations for comparison purposes.
 
 
2
cc(exp ) cc( )
1
2
cc(exp ) cc(exp )
1
2
1
N
erimental predict
i
N
erimental erimental
i
f f
f f
R 

 

 
 



(4)
2
cc(predict) cc(exp )
1
1
( )
N
erimental
i
RMSE f f
n 
 
 
 (5)
It can be observed that the smallest RMSE and the largest R2
(closest to 1) for both the training
and testing sets are derived by the BPN model. The large deviation for the analytical models
shows that the analytical models performed well for their test data but poorly on other data.
Moreover, the prediction models have been compared using the average value (AVG), standard
deviation (STD), and coefficient of variation (COV) of the ratio of f’cce/ f’ccp and εcce/εccp. Table 6
indicates that for the ratios of f’cce/ f’ccp, the neural network model possesses the least COV value
of 7.6% (with AVG= 1.021 and STD= 0.098) and 12.1% (with AVG= 1.036 and STD= 0.125) for
the training and testing sets, respectively. Similarly, for the ratios of εcce/εccp, the ANN model
possesses the least COV value of 10.4% (with AVG= 1.021 and STD= 0.107) for the training set
and 13.9% (with AVG= 1.138 and STD= 0.158) for testing set. It is seen that the predictions of
the ANN model, even for test data, are relatively better than the results of analytical models. The
performance of the ANN model is improved by an increase in the number and distribution of the
training database.
The maximum error is related to the Kono model and equal to 356.6 for training data, while the
minimum error is related to BPN, Miayuchi, and Kono models and equal to 0 for training data.
The lowest 2
R is for Karbahari & Gao model and related to strain prediction.
8. Conclusions
This study showed the application of the neural network method for predicting the complex
nonlinear behavior of concrete columns confined with FRP wraps. It is not possible to propose
an ANN model that is used for columns with a broad range of values as input parameters due to
the data limitation.

Table 6
Statistic results for the prediction models.
Statistic
Maximum
Error
Minimum
Error
Mean
Absolute
Error
Root Mean
Square
Error
(RMSE)
2
R
Coefficient
of
Variance
Standard
Deviation
Average
Train
Set
Test
Set
Train
Set
Test
Set
Train
Set
Test
Set
Train
Set
Test
Set
Train
Set
Test
Set
Train
Set
Test
Set
Train
Set
Test
Set
Train
Set
Test
Set
Fardis
f'cc(Richart) 187.7 103.4 0.249 1.481 35.38 31.93 54.29 47.1 0.934 0.925 0.239 0.22 0.185 0.177 0.773 0.806
f'cc (Newman) 153.5 104.7 1.026 2.371 32.34 30.18 44.1 42.06 0.952 0.948 0.196 0.171 0.15 0.135 0.761 0.79
εcc 3.851 3.33 0.127 0.368 1.301 1.247 1.522 1.499 0.162 -0.042 0.524 0.642 3.145 3.74 6.001 5.831
Saadatmanesh
f'cc 85.65 83.29 0.033 0.235 19.98 18.86 26.5 28.36 0.904 0.935 0.182 0.138 0.152 0.118 0.838 0.86
εcc 1.749 1.719 0.018 0.136 0.58 0.593 0.698 0.727 0.851 0.83 0.285 0.243 0.214 0.181 0.752 0.742
Miayuchi
f'cc 81.82 50.52 0.118 0.275 18.45 16.19 26.78 22.58 0.95 0.944 0.201 0.175 0.183 0.165 0.91 0.944
εcc 1.865 1.269 0 0.034 0.567 0.452 0.693 0.559 0.861 0.873 0.252 0.287 0.19 0.227 0.757 0.793
Kono
f'cc 356.6 188 0.56 3.172 22.61 23.75 56.11 55.17 0.919 0.9 0.225 0.203 0.239 0.213 1.064 1.05
εcc 7.542 3.639 0 0.014 0.722 0.647 1.323 1.181 0.629 0.564 0.447 0.344 0.548 0.381 1.227 1.108
Samaan
f'cc 55.66 28.27 0.117 1.067 12.23 9.149 16.46 12.35 0.947 0.96 0.162 0.129 0.158 0.131 0.975 1.015
εcc 3.066 2.053 0.21 0.096 1.456 1.065 1.57 1.257 0.168 0.697 0.638 0.421 0.386 0.265 0.605 0.628
Tutanji
f'cc 134.7 95.58 2.261 0.152 28.76 26.53 39.19 37.59 0.954 0.951 0.189 0.162 0.148 0.131 0.781 0.81
εcc 9.523 7.892 0.028 0.124 2.029 1.842 2.878 2.82 0.825 0.981 0.425 0.431 0.229 0.26 0.539 0.603
Saafi
f'cc 39.99 27.49 0.096 0.091 10.79 10.15 13.12 12.85 0.961 0.96 0.156 0.118 0.154 0.12 0.988 1.017
εcc 10.02 8.346 0.012 0.14 2.137 1.941 3.016 2.97 0.818 0.98 0.434 0.462 0.228 0.276 0.525 0.596
Xiao & Wu
f'cc 173.1 69.98 0.987 4.724 32.77 28.7 45.73 36 0.824 0.766 0.599 0.397 0.668 0.422 1.116 1.062
εcc 8.413 6.885 0.002 0.058 1.903 1.724 2.717 2.608 0.829 0.971 0.367 0.324 0.203 0.19 0.551 0.585
Karbahari
& Gao
f'cc 34.16 24.46 0.047 1.112 10.28 10.55 12.66 12.7 0.962 0.96 0.156 0.119 0.16 0.125 1.02 1.051
εcc 3.889 3.343 0.129 0.389 1.313 1.261 1.536 1.511 0.041 -0.047 0.556 0.65 3.53 4.018 6.351 6.179
Lam
&Teng
f'cc 26.67 29.21 0.504 3.483 11.34 11.93 13.36 13.77 0.961 0.958 0.171 0.136 0.181 0.149 1.054 1.088
εcc(CFRP) 4.818 1.933 0.005 0.041 0.817 0.709 1.209 0.966 0.885 0.969 0.326 0.223 0.246 0.167 0.756 0.746
Lam &Teng
(Design
Model)
f'cc 30.36 31.26 0.74 1.76 11.39 11.87 13.5 14.76 0.962 0.959 0.167 0.13 0.181 0.146 1.087 1.12
εcc(CFRP) 2.108 0.551 0.002 0.013 0.384 0.209 0.526 0.28 0.883 0.965 0.311 0.211 0.321 0.214 1.032 1.015
BPN
Network
f'cc 19.23 12.95 0.001 1.142 3.968 5.001 5.558 6.191 0.993 0.991 0.076 0.121 0.078 0.126 1.021 1.036
εcc 0.401 0.539 0 0.009 0.095 0.176 0.128 0.246 0.989 0.984 0.105 0.139 0.107 0.158 1.021 1.138
The ANN model seemed to be admissible in simulating the behavior of FRP-confined circular
concrete columns, although limited in applicability. Reasonable predictions of the ANN model
were derived for values inside the training region. The ability and advantage of using ANNs to
model physical operations are presented in this study. Unlike theoretical models, which rely on
the assessment of a mathematical equation or solution, the ANN solution process is not
formulated clearly. Instead, the relationships are automatically constructed and adapted

according to the presented training data. By comparing the outputs of the models to experimental
results, it was concluded that the presented ANN model had the best performance in term of
predicting the experimental results due to the closest value of R2
to 1, equal to 0.993 and 0.991
for training and testing of compressive strength and 0.989 and 0.984 for training and testing of
strain, respectively. In light of neural techniques to other areas of structural engineering can open
new directions for further research.
References
[1] Mirmiran A. Concrete composite construction for durability and strength. Proc Symp Extending
Life Span Struct, 1995, p. 1155–60.
[2] Mirmiran A, Shahawy M. Behavior of concrete columns confined by fiber composites. J Struct Eng
1997;123:583–90.
[3] Saafi M, Toutanji H, Li Z. Behavior of concrete columns confined with fiber reinforced polymer
tubes. Mater J 1999;96:500–9.
[4] Fardis MN, Khalili H. Concrete encased in fiberglass-reinforced plastic. J Proc, vol. 78, 1981, p.
440–6.
[5] Miyauchi K, Nishibayashi S, Inoue S. Estimation of Strengthening Effects wi th Carbon Fiber
Sheet for Concrete Columm. Proc Third Internatio nal Symp Non-Metallic FRP Concr Struct
Japan, vol. 224, 1997.
[6] Spoelstra MR, Monti G. FRP-confined concrete model. J Compos Constr 1999;3:143–50.
[7] Teng JG, Lam L. Behavior and Modeling of Fiber Reinforced Polymer-Confined Concrete. J Struct
Eng 2004;130:1713–23. doi:10.1061/(ASCE)0733-9445(2004)130:11(1713).
[8] Teng JG, Chen J-F, Smith ST, Lam L. FRP: strengthened RC structures. Front Phys 2002:266.
[9] Saadatmanesh H, Ehsani MR, Li MW. Strength and Ductility of Concrete Columns Externally
Reinforced With Fiber Composite Straps. ACI Struct J 1994;91:434–47. doi:10.14359/4151.
[10] Kono S, Inazumi M, Kaku T. Evaluation of confining effects of CFRP sheets on reinforced
concrete members. Second Int Conf Compos InfrastructureNational Sci Found, vol. 1, 1998.
[11] Toutanji H. Stress-strain characteristics of concrete columns externally confined with advanced
fiber composite sheets. Mater J 1999;96:397–404.
[12] Samaan M, Mirmiran A, Shahawy M. Model of Concrete Confined by Fiber Composites. J Struct
Eng 1998;124:1025–31. doi:10.1061/(ASCE)0733-9445(1998)124:9(1025).
[13] Xiao Y, Wu H. Compressive behavior of concrete confined by carbon fiber composite jackets. J
Mater Civ Eng 2000;12:139–46.
[14] Karbhari VM, Gao Y. Composite jacketed concrete under uniaxial compression—Verification of
simple design equations. J Mater Civ Eng 1997;9:185–93.
[15] Mirmiran A, Shahawy M. A new concrete-filled hollow FRP composite column. Compos Part B
Eng 1996;27:263–8.
[16] Thériault M, Neale KW. Simplified design equations for reinforced concrete columns confined
with FRP Wraps. FRP Compos Civ Eng Int Conf FRP Compos Civ Eng HELD DECEMBER
2001, HONG KONG-VOLUME I, 2001.

[17] ACI A. 440.2 R-02: Guide for the design and construction of externally bonded FRP systems for
strengthening concrete structures. Am Concr Institute, Farmingt Hills, USA 2002.
[18] Lam L, Teng JG. Strength models for circular concrete columns confined by FRP composites 2001.
[19] Bisby LA, Dent AJS, Green MF. Comparison of confinement models for fiber-reinforced polymer-
wrapped concrete. ACI Struct J 2005;102:62.
[20] Kaveh A, Servati H. Design of double layer grids using backpropagation neural networks. Comput
Struct 2001;79:1561–8.
[21] Kaveh A, SERVATI H, FAZEL DD. Prediction of moment-rotation characteristic for saddle-like
connections using FEM and BP neural networks 2001.
[22] Kaveh A, Khalegi A. Prediction of strength for concrete specimens using artificial neural networks.
Asian J Civ Eng 2000;2:1–13.
[23] Iranmanesh A, Kaveh A. Structural optimization by gradient‐based neural networks. Int J Numer
Methods Eng 1999;46:297–311.
[24] Oreta AWC, Kawashima K. Neural network modeling of confined compressive strength and strain
of circular concrete columns. J Struct Eng 2003;129:554–61.
[25] Naderpour H, Kheyroddin A, Ghodrati Amiri G, Hoseini Vaez SR. Estimating the behavior of
FRP-strengthened RC structural members using artificial neural networks. Procedia Eng
2011;14:3183–90. doi:10.1016/j.proeng.2011.07.402.
[26] Naderpour H, Nagai K, Fakharian P, Haji M. Innovative models for prediction of compressive
strength of FRP-confined circular reinforced concrete columns using soft computing methods.
Compos Struct 2019;215:69–84. doi:10.1016/j.compstruct.2019.02.048.
[27] Cui C, Sheikh SA. Analytical Model for Circular Normal- and High-Strength Concrete Columns
Confined with FRP. J Compos Constr 2010;14:562–72. doi:10.1061/(ASCE)CC.1943-
5614.0000115.
[28] Fathi M, Jalal M, Rostami S. Compressive strength prediction by ANN formulation approach for
CFRP confined concrete cylinders. Earthq Struct 2015;8:1171–90. doi:10.12989/eas.2015.8.5.1171.
[29] Behfarnia K, Khademi F. A comprehensive study on the concrete compressive strength estimation
using artificial neural network and adaptive neuro-fuzzy inference system. Iran Univ Sci Technol
2017;7:71–80.
[30] Naderpour H, Alavi SA. A proposed model to estimate shear contribution of FRP in strengthened
RC beams in terms of Adaptive Neuro-Fuzzy Inference System. Compos Struct 2017;170:215–27.
doi:10.1016/j.compstruct.2017.03.028.
[31] Hosseini G. Capacity Prediction of RC Beams Strengthened with FRP by Artificial Neural
Networks Based on Genetic Algorithm. Soft Comput Civ Eng 2017;1:93–8.
doi:10.22115/scce.2017.48392.
[32] Sharifi Y, Lotfi F, Moghbeli A. Compressive Strength Prediction Using the ANN Method for FRP
Confined Rectangular Concrete Columns. J Rehabil Civ Eng 2019;7:134–53.
doi:10.22075/JRCE.2018.14362.1260.
[33] Khan QS, Sheikh MN, Hadi MN. Predicting strength and strain enhancement ratios of circular
fiber-reinforced polymer tube confined concrete under axial compression using artificial neural
networks. Adv Struct Eng 2019;22:1426–43. doi:10.1177/1369433218815229.

[34] Naderpour H, Nagai K, Haji M, Mirrashid M. Adaptive neuro‐fuzzy inference modelling and
sensitivity analysis for capacity estimation of fiber reinforced polymer‐strengthened circular
reinforced concrete columns. Expert Syst 2019:e12410.
[35] Lorenzis L De, Tepfers R. Comparative Study of Models on Confinement of Concrete Cylinders
with Fiber-Reinforced Polymer Composites 2003.
[36] Naderpour H, Kheyroddin A, Amiri GG. Prediction of FRP-confined compressive strength of
concrete using artificial neural networks. Compos Struct 2010;92:2817–29.
doi:10.1016/j.compstruct.2010.04.008.
[37] Kartam N, Flood I, Garrett JH. Artificial neural networks for civil engineers: fundamentals and
applications, American Society of Civil Engineers; 1997.
[38] Fahlman SE. Faster-learning variations of back-propagation: An empirical study. Proc 1988
Connect Model Summer Sch, Morgan Kaufmann; 1988, p. 38–51.
[39] Harmon TG, Slattery KT. Advanced composite confinement of concrete. Adv Compos Mater Bridg
Struct, 1992, p. 299–306.
[40] Watanabe K, Nakamura H, Honda Y, Toyoshima M, Iso M, Fujimaki T, et al. Confinement effect
of FRP sheet on strength and ductility of concrete cylinders under uniaxial compression. Non-
Metallic Reinf Concr Struct 1997;1:233–40.
[41] Micelli F, Myers JJ, Murthy S. Effect of environmental cycles on concrete cylinders confined with
FRP. Proc CCC2001 Int Conf Compos Constr Porto, Port, 2001.
[42] Matthys S, Taerwe L, Audenaert K. Tests on axially loaded concrete columns confined by fiber
reinforced polymer sheet wrapping. Spec Publ 1999;188:217–28.
[43] Shahawy M, Mirmiran A, Beitelman T. Tests and modeling of carbon-wrapped concrete columns.
Compos Part B Eng 2000;31:471–80.
[44] Rousakis T, Tepfers R. Experimental investigation of concrete cylinders confined by carbon FRP
sheets, under monotonic and cyclic axial compressive load. Res Rep 2001;44:1–87.
[45] NeuralWare UN. A Tutorial for NeuralWorks Professional II/Plus and NeuralWorks Explorer,
NeuralWare. Inc, Pittsburgh, Pennsylvania 1993.

Modeling of Confined Circular Concrete Columns Wrapped by Fiber Reinforced Polymer Using Artificial Neural Network

More Related Content

Similar to Modeling of Confined Circular Concrete Columns Wrapped by Fiber Reinforced Polymer Using Artificial Neural Network (20)

More from Journal of Soft Computing in Civil Engineering (20)

Recently uploaded (20)

Modeling of Confined Circular Concrete Columns Wrapped by Fiber Reinforced Polymer Using Artificial Neural Network