Civil Engineering Reference
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ground motion was computed in Section 16.4.3 to model the stiffness dete-
rioration). Next, we perform a linear regression analysis of the data in loga-
rithmic space as follows:
( )
+
ˆ
ˆ
⎧
θ
ln
Y
θ
+
σ
ε
Y
>
0
⎪
⎪
ZLC
1
t
ZLC
2
ZLC
ZLC
t
(
)
=
n
n
ln
Δ
DI
[16.36]
t
n
ˆ
0
Y
≤
0
t
n
where we obtain
θ
LC
1
=
−
6.0,
θ
LC
2
=
−
8.45, and
σ
ZLC
=
0.54, and
ε
ZLC
is a
standard normal random variable.
16.4.6 Analysis, results and discussion
Deterioration for different combinations of modes of failures, deterioration
mechanisms, and environmental conditions are analyzed. Depicting ND as
no deterioration, SD for seismic stiffness deterioration, AC for atmospheric
level corrosion and SC for splash level corrosion, we analyze the cases d
SD
,
d
(SD
AC)
, d
(SD
SC)
and
LC
, where
k
A
denotes failure in mode
k
considering
deterioration scenario
A
. For the analysis, it is assumed that
w
a
=
−
log(0.1)/
C
0
1.40. This value is adopted for
w
a
because if
W
t
> 1.40 then a small
deformation demand of approximately > 0.1% drift (i.e., 1/10th of drift at
yield) is suffi cient to collapse the structure. The accuracy in the value of
w
a
is not of signifi cance for the presented case because it is found that
t
F
is not
signifi cantly sensitive to
w
a
. Figure 16.10 shows the plots for
P
(
n
F
>
n
) for
the three mentioned scenarios. It is found that
P
(
n
F
>
n
) follows the order;
LC
> d
ND
> d
SD
> d
(SD
AC)
> d
(SD
SC)
. This is expected because the column is
likely to deteriorate faster when subject to both corrosion and seismic stiff-
ness deterioration than seismic stiffness deterioration alone. Furthermore
splash level exposure causes faster deterioration than atmospheric level
because corrosion is expected to start earlier under splash level exposure.
Similarly, Fig. 16.11 shows the plots for
P
(
t
F
>
t
) for the above mentioned
cases. It is found that
P
(
t
F
>
t
) follows the order as previously observed i.e.,
LC
> d
ND
> d
SD
> d
(SD
AC)
> d
(SD
SC)
, and that the slope of
P
(
t
F
>
t
) decreases
signifi cantly around
t
=
75 years. This happens due to the shape of the CDF
of
T
corr
(see Fig. 16.8) where the slope decreases signifi cantly indicating that
most of the deterioration is likely to occur for
t
< 75 years. This indicates
that for these cases, the CDF for
T
corr
primarily controls
P
(
t
F
>
t
).
=
16.5 Conclusions
Structural deterioration of infrastructure systems is a serious concern
because it might decrease the lifespan and reliability of the systems. In
addition, the prediction of structural deterioration can be helpful in opti-
mizing design of infrastructure systems accounting for their life cycle. In
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