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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 3
W. R. L. da Silva | L. R. Prudencio Jr
|
A. L. de Oliveira
a value for the total number of tests n equal to six (n = 6). Note that
the value resulting from equation (1) is equal to 5.1. Nevertheless,
this figure was rounded to the next highest whole number. Hence,
12 tests were performed in each concrete plate (6 at 13 days old
and 6 at 36 days old).
3.2
Stage 1: Determination of the correlation curve
of probe penetration test
The definition of the correlation between the results of the probe
penetration test and the concrete compressive strength was de-
termined by tests performed on two concrete plates. The concrete
plates measuring 0.60×0.60×0.15 m were moulded with shotcrete,
whose composition corresponds to that used in the tunnel in ques-
tion and agrees with the dosage that was used in stage 1.
Prior to conducting the probe penetration test, four core sam-
ples with 75.0 mm diameters were extracted from the concrete
plates. Due to the variation in the thickness of the concrete plates
resulting from the process of producing the same in the tunnel, the
height of the core samples ranged from 93.0 mm to 159.8 mm. A
total of 12 probe penetration tests were performed in each of the
concrete plates. This number of tests is based on the results of the
study to determine the coefficient of variation of the probe penetra-
tion test described in section 3 .1.
The compression strength tests were performed at different times;
in this case, two core samples were tested at 13 days, and two
at 36
days. This measurement was performed to cover a wider
range of compressive strengths to define the correlation curve. It
is important to note that the quality and integrity of the core sam-
ple must be evaluated before being tested. Samples that present
moulding failures, known as concrete lenses in the case of shot-
crete, should be discarded and the extraction of an additional core
sample should be performed.
After conducting the tests proposed in this section, the correlation
curve between the exposed probe penetration length and the com-
pressive strength was determined by a linear regression using the
model described in equation (2). The prediction errors, E
r,
, for the
individual and mean values of the correlation curve were calculat-
ed using equations (3) and (4), respectively. The significance value
α, which is necessary to determine the confidence interval of the
correlation curve, is equivalent to the value employed in the cal-
culation of the concrete characteristic strength, i.e., α = 5.0% [19].
Among the various references, detailed descriptions of the linear
regression process as well as the equations used for the determi-
nation of the prediction error can be found in [18].
(2)
p
Exba y
± × +=
(3)
(4)
, )
( 1
) (
2
)2 (,2/
xx
i
e
n
i
medio
p
s
x x
n
S
t
x
E
-
+ × ×
±=
-
-
a
where x and y correspond, respectively, to the dependent and in-
dependent variables; a and b correspond, respectively, to the lin-
ear coefficient and the slope; E
p–individual
is the predicted error for the
individual values and E
p–medio
is the predicted error for the mean
values; S
e
corresponds to the standard error of the estimate and
is calculated using equation (5), n refers to the sample size, i.e.,
the number of points used to define the correlation curve; x corre-
sponds to the average value of the variable x; and S
xx
is the sum of
the residues of the variable x given by equation (6).
(5)
,
2
))
(
(
2
1
-
× + -
=
å
=
n
xba y
S
i
n
i
i
e
(6)
(
(.
1
=
å
=
x x– –
S
i
n
i
xx
In addition to the correlation curve, the results obtained in the tests
carried out on the plates were used to verify the second coefficient
of variation of the assay. To do so, the coefficient of variation of
the results of each of the plates for different ages and the average
coefficient of variation CVwere calculated using equation (7).
(7)
,
m
m
m
x
s
CV
=
Table 2 – Average penetrated length of
the probe and average gunpowder mass
Average penetrated length, [mm]
Probe penetration test
Gunpowder mass
39.10
Standard deviation, [mm]
3.20
Coefficient of variation, [%]
8.1
Number of tests
10
Average mass, [g]
0.324
Standard deviation, [g]
0.009
Coefficient of variation, [%]
2.7
Number of tests
10