Basic HTML Version
299
IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 3
R. A. C. LOPES | E. P. SANTOS
|
L. A. C. M. VELOSO
(10.1)
θ=
2πt
d
365
, 1
≤ ≤
t
d
365
where:
t
d
is the number of days elapsed from the beginning of the year until
the date of observation in the same year;
b
1
, b
2
, b
3
, b
4
are adjustable parameters.
According to [14], the effect of creep over time can be represented
through the elements of a Dirichlet series, which has the form:
(11)
U
F
(
t
)
=c
1
[
1-exp(-10
-3
t)
]
+ c
2
[
1-exp(-10
-4
t)
]
where:
t represents the number of days elapsed from the date of first ob-
servation;
c
1
and c
2
are adjustable parameters.
Considering that the displacement of the block crest is influenced
by the variables mentioned above, the function used in the predic-
tion has the following form:
(12)
E = U
h
+ U
T
+ U
F
+ε
Figures [1], [2] and [3] show the contribution of the upstream level,
temperature and concrete creep in overall displacement of the
dam crest.
4.3 Control chart
According to [15], the ultimate goal of the statistical process con-
trol is the elimination of variability in the process. Although it may
4.2 Selection of independent variables
The independent variables were chosen based on the correlation of each
with the dependent variable and based on existing literature on dam be-
havior prediction models. The variables selected for the prediction mod-
els for displacement of the TA-2 concrete block are described below.
According to [5], the estimated effects E depend on two compo-
nents, one of an elastic nature Er, formed by the portions related to
hydrostatic pressure and temperature, and another of an inelastic
nature Et, which represents the effect of creep over time. Thus, E
is expressed as follows:
(8)
E= E
r
+ E
t
According to [8], the contribution from the upstream level is often
represented by a polynomial function of the form:
(9)
U
h
(h)
= a
1
h
4
+ a
2
h
3
+ a
3
h
2
+ a
4
h
where:
h is the upstream level in meters;
a
1
, a
2
,..., a
4
are adjustable parameters.
In the operation phase of the dam, the concrete temperature varia-
tions depend mainly on environmental temperature variations. Ac-
cording to [8], the annual influence of thermal effects on the con-
crete block can be represented by the sum of annual harmonic
functions. The annual temperature function can be given by:
(10)
U
T
(
θ
)
=b
1
cos
(
θ
)
+b
2
sen
(
θ
)
+b
3
sen
2
(
θ
)
+b
4
cos
(
θ
)
sen(θ)
Figure 1 – Contribution of the upstream level to displacement of the dam crest