World Journal of Engineering
1405
Neural network modeling of strength enhancement of CFRP confined concrete cylinders
Mojtaba Fathi
a
Mostafa Jalal
b
a
Department of Civil Engineering, Razi University, Kermanshah, Iran
Email:
fathim74@yahoo.com
b
Department of Civil Engineering, Razi University, Kermanshah, Iran
Email:
m.jalal.civil@gmail.com
Abstract
In the present study, a new approach is developed to obtain
compressive strength of concrete cylind
ers confined with carbon
fiber reinforced polymer (CFRP) using a relatively large number of
experimental data by applying artificial neural networks (ANNs).
Having parameters used as input nodes in ANN modeling such as
characteristics of concrete and CFRP,
the output node was CFRP

confined compressive strength of concrete. The idealized neural
network was employed to generate empirical curves and equations
for use in design. The comparison of the new approach with existing
empirical and experimental data sh
ows good precision and accuracy
of the developed ANN

based model in predicting the CFRP

confined compressive strength of concrete.
Keywords:
concrete,
CFRP
, artificial neural networks,
compressive strength, confinement
1.
introduction
External confinement
of concrete using FRPs has become a
common method of column retrofitting, especially for
circular columns
[
1
]
and many recent studies have been
conducted on the compressive strength of FRP

confined
concrete and various models have been developed
[
2

7
]
.In
recent years, artificial neural networks have been of interest
to researchers in the modeling of various civil engineering
systems among which the earlier work of the authors can be
mentioned
[
8
]
.
Artificial neural networks automatically
manage the relatio
nships between variables and adapt based
on the data used for their training. So it is important to
collect
a large number of experimental data. In this study, a large test
database built from an extensive survey of existing tests on
FRP

confined circular
concrete specimens is carefully
examined to establish the effect of various variables. Finally,
a new model is proposed based on artificial neural networks
and then verified against experimental data and existing
models.
2.
Modeling
From the test results
and also the general form for many of
existing strength models Eq. (1), it can be concluded that the
compressive strength of confined concrete is definitely
affected by the compressive strength of the unconfined
concrete (
f’
c
), the lateral confining streng
th Eq. (2) including
the ultimate circumferential strain in the FRP jacket (
rup
), the
total thickness of FRP (
t
) and the diameter of the circular
concrete specimen (
d
). The input of specimen height (
h
) as a
separate parameter is also necessary in order to
take into
account the effect of the length

to

diameter ratio (
h/d
) of the
specimens which is considered by some researchers in their
empirical models. Finally, the elastic modulus of FRP (
E
frp
)
was selected as the last input parameter since its effect on
f’
cc
has been considered in some existing models such as
formula proposed by Karbhari and
Gao
[
9
]
.
So the
parameters used as the input nodes in the ANN modeling
are summarized as:

d
(mm): Diameter of the circular concrete specimen

h
(mm): Height of the
circular concrete specimen

t
(mm): Total thickness of CFRP jacket

rup
(mm): Ultimate circumferential strain in the CFRP
jacket

E
frp
(MPa): Elastic modulus of CFRP

f’
c
(MPa): Compressive strength of the unconfined
concrete
(1)
(2)
3.
NN Performance
Two criteria as
Mean Square Error (MSE) and Regression
values (R

values) were considered as the basis for selecting
the idealized network.
NN 6

5

1
that is a network with 6
inputs, one hidden layer
with 5 neurons and one output
was
chosen since it present
ed
good results with respect to the
least value of MSE and the maximum R

values among all
networks
.
Fig. 1 shows the training and testing process of
the optimal network.
Fig. 1. Training and test
ing process of the network
4.
Comparison of ANN with
some
empirical models
The simulated compressive strengths of the CFRP

confined
concrete from idealized neural network compared to the
five existing strength models are plotted against the
experimental v
alues in Fig.
2
. If there is perfect agreement
between the model and experimental results, all the points
will lie along the 45° line.
Actually, about 85% of the simulated results are within
20% of the experimental values for ANN mod
el but the
accuracy of other models is lower than 75% in the same
World Journal of Engineering
1406
range. This is an indication that the network has learned to
generalize the information well.
Fig
.
2
. Comparison of various predicted values of
f’
cc
versus
experimental data for different
strength models
5.
Proposed approach
for
f’
cc
prediction
The pattern formula used here for predicting the compressive
strength of CFRP

confined concrete was introduced by Leung
et al.
[
10
]
for determining ultimate FRP strain of FRP

strengthened concrete b
eams
.
As the first step,
f’
cc
is first
plotted against
E
frp
in Fig.
3
assuming the other five input
parameters to be kept constant at their respective reference
values.
Fig.
3
. Variations of
against
assuming
other input
parameters to be in their reference value.
To account for the effect of these parameters on
f’
cc
, a
correction function has to be derived. The correction function
can be written in the following form:
(3)
Afte
r finishing the process, the following equations for
correction factors are summarized as:
(4)
(5)
(6)
(7)
(8)
Consequently, the compressive strength of CFRP

confined
concrete will be obtained from Eq. (11)
.
(9)
Considering the whole data from experimental database, the
proposed ANN model is compared with the five existing
models in Fig.
4
.
Fig.
4
. Comparison
of
f’
cc
predictions
versus experimental data for
proposed ANN equation
with some
existing models
6.
Conclusions
The average error for the ANN model for predicting the
experimental results was about 10% while the aver
age
errors for the other three models were more than 14%. On
the other hand, about 85% of the simulated results were
within 20% of the experimental values for ANN model but
the accuracy of other models was lower than 75% in the
same range In order to use t
he simulated results obtained
from ANN model in prediction of compressive strength of
CFRP

confined concrete conveniently for design purposes
in the absence of the idealized network, an equation was
derived which predicts the compressive strength
independe
ntly from the network. The precision of the
proposed equation was verified by available experimental
data and showed good agreement
.
References
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[
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[9] Karbhari VM, Gao Y. Composite jacketed concrete under
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