World Journal of Engineering
Neural network modeling of strength enhancement of CFRP confined concrete cylinders
Mojtaba Fathia Mostafa Jalalb
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 cylinders 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 CFRPconfined 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 shows good precision and accuracy
of the developed ANN-based model in predicting the CFRPconfined 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 relationships 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 strength 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 (Efrp)
was selected as the last input parameter since its effect on f’cc
1405
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
- Efrp (MPa): Elastic modulus of CFRP
- f’c (MPa): Compressive strength of the unconfined
concrete
f cc′= f c′
+ k1 f l
fl =
2ntE frp rup
(1)
d
(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 presented 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 testing 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 values 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 model but the
accuracy of other models is lower than 75% in the same
World Journal of Engineering
range. This is an indication that the network has learned to
generalize the information well.
Fig. 4. Comparison of f’cc predictions versus experimental data for
proposed ANN equation with some existing models
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 FRPstrengthened concrete beams. As the first step, f’cc is first
plotted against Efrp in Fig. 3 assuming the other five input
parameters to be kept constant at their respective reference
values.
180
f'cc simulated by the network (MPa)
170
160
150
140
130
120
110
100
90
References
80
70
60
50
40
0
50
100
150
200
250
300
350
400
450
500
550
600
E frp (GPa)
Fig. 3. Variations of
f cc′against EFRP
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)
F (d , h, t ,  rup , f c)  C (d )  C (h)  C (t )  C ( rup )  C ( f c)
After finishing the process, the following equations for
correction factors are summarized as:
d 4
d 3
d 2
d
C (d ) = 4.1001(
) 13.086(
) + 16.781(
) 10.779(
) + 3.9514
130
130
130
130
C (h) = 0.0665(
h 4
h 3
h 2
h
) 0.2904(
) + 0.2598(
) + 0.0895(
) + 0.8739
300
300
300
300
C (t ) = 0.7144 e
C ( rup )  0.0267(
6. Conclusions
The average error for the ANN model for predicting the
experimental results was about 10% while the average
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 the 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
independently from the network. The precision of the
proposed equation was verified by available experimental
data and showed good agreement.
 rup
0.2664(
t
)
0.5
)5 0.1082(
 rup
) 4  0.0855(
 rup
) 2  0.025(
 rup
)  0.0475(
 rup
(4)
(5)
(6)
)  0.9236
(7)
(8)
Consequently, the compressive strength of CFRP-confined
concrete will be obtained from Eq. (11).
f cc′ = ( f cc′
)curve × C(d) × C(h) × C(t) × C( rup) × C( f c′
)
(9)
Considering the whole data from experimental database, the
proposed ANN model is compared with the five existing
models in Fig. 4.
0.009
0.009
0.009
0.009
0.009
C ( f c′
) = 1.0266 ( f c′
/ 40) 0.5465
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