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19
IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 1
A. D. de Figueiredo | A. de la Fuente | A. Aguado | C. Molins | P. J. Chama Neto
4. Contrasting experimental
and numerical results
With the aim of verifying the suitability of the MAP model for the
simulation of the mechanical response of FRCP subjected to CT,
the experimental results presented in the first part of this work (see
Figueiredo
et al
. [19]) were contrasted. So, a comparison of the
curves
F
-
v
c
captured during the test for the pipes with
D
i
of 600
mm from series 2 (displacement measured in the spigot) is done.
All the pipes in these series of tests were manufactured with the same
concrete composition, although there were some modifications in the
water consumption in order to improve the workability due to the use
of fibres (DRAMIX® RC-80/60-BN). The pipes were manufactured
and tested at the same age with the aim of reaching, at least, the
resistance class EA2 established in NBR 8890:2007 [20].
4.1 Modeling the materials
The modeling of the compressive behavior of SFRC was performed
with the equation suggested by Barros
et al
. [28], considering a char-
acteristic compressive strength (
f
ck
) of 50 MPa at 28 days according
to the tests performed during the regular quality control in the factory.
On the other hand, for the simulation of its tensile response, the
trilinear diagram proposed by Vandewalle
et al
. [16] was used (see
Figure [3b]). However, due to the lack of flexural tests (see Vande-
walle
et al
. [35]), in order to determine the values of concrete ten-
sion stress
σ
i
, the expressions (Eqs. 23-24) calibrated in Barros
et al
. [36] have been used to determine the values of the residual
flexural strength
f
Ri
as a function of
C
f
. In this regard, the type of
fibres used both in this campaign and in the one carried out by
Barros
et al
. [36] are the same: (DRAMIX® RC-80/60-BN). Table
[1] shows the values established for σ
i
, ε
i
and
E
cm
in order to model
the tensile behavior of SFRC.
(23)
f
R,1
= 0.0945C
f
+ 0.702
(24)
f
R,4
= 0.926 f
R,1
4.2 Results obtained
Figures 6a, 6b and 6c show the curves
F
-
v
c
obtained both experi-
mentally (individual and average values) and numerically for pipes
with
C
f
of 10, 20 and 40 kg/m
3
, respectively.
With reference to what has been previously explained in section 3
and to the requirements of the EA2 class of the NBR 8890:2007,
the load
F
cr
must be equal or higher than the load
F
c
(90 kN), and
F
u
must be equal or higher than 135 kN for this type of pipes. Fi-
nally, the maximum post-failure load
F
max,pos
measured in the curve
F
-
v
c
must reach, at least, the 105% of
F
c
(94.5 kN). In this sense,
since the test was carried out in a continuous manner, it was estab-
lished that the value of
F
max,pos
is associated to a
v
c
of 3 mm (see
Figueiredo
et al
. [19]), and is called
F
3mm
.
Based on the results presented in Fig. 6a, it is deduced that the
MAP model fits properly to the experimental results for the amount
of 10 kg/m
3
, particularly in the linear elastic regime and in the
post-failure regime. For the latter, the numerical results tend to-
ward the experimental maximum values for displacements higher
than 3 mm. This might indicate that the values
f
R,i
and/or
σ
i
of the
constitutive equation of tensioned SFRC (see Fig. 3b) are slightly
higher than the real ones. The values for
F
cr
,
F
u
and
F
3mm
obtained
numerically are 98 kN, 114 kN and 88 kN, respectively. Therefore,
neither
F
u
nor
F
3mm
reach
the minimum values stipulated by NBR
8890:2007 for the EA2 class. Thus, it can be stated that, according
to the model, the amount of 10 kg/m
3
is not enough to guarantee
that level of requirements.
The results gathered in Fig. 6b, concerning the dosage of 20 kg/
m
3
, highlight that the simulation by means of the numerical model
guarantees values close to the experimental ones. Still, the model
exceeds the experimental results with displacements higher than
5.5 mm, which can be due to the considered excessive values of
f
R,i
and/or
σ
i
, as in the case of pipes with 10 kg/m
3
of fibres for this
range of displacements. The values for
F
cr
,
F
u
and
F
3mm
obtained
numerically are: 98 kN, 123 kN and 108 kN, respectively. Con-
sequently, according to the model, with 20 kg/m
3
the EA2 class
would not be reached, since the load
F
u
(123 kN) is lower than the
required 135 kN.
Finally, for the pipes with 40 kg/m
3
of fibres (Fig. 6c), it can be
noticed that the numerical model adjusts suitably to the average
experimental results at all the stages. In this case,
F
cr
is 98 kN
and
F
u
is 156 kN, values higher than those specified for a pipe of
600 mm from the EA2 class (NBR 8890:2007). It should be noted
that, due to the hardening behavior, there is no way to assess the
Table 1 – Parameters to simulate the tensile behavior of the SFRC for the pipe of D = 600 mm
i
C
f
3
(Kg/m )
f
R,1
(MPa)
f
R,4
(MPa)
E
cm
(MPa)
s
*
1
(MPa)
e
1
(mm/m)
s
2
(MPa)
e
2
(mm/m)
s
3
(MPa)
e
3
(mm/m)
10
1.647
1.525
37000
4.071
0.104
0.741
0.204
0.564
25.000
20
2.592
2.400
37000
4.071
0.104
1.166
0.204
0.888
25.000
40
4.482
4.150
37000
4.071
0.104
2.017
0.204
1.536
25.000
2/3
* This value is obtained by using the expression
σ
= 0.30*(f ) gathered in the EHE-08 [37].
1
ck