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increase, the costs associated with the inspec-
tion and maintenance decrease but this causes
a significant increase in the service failure cost.
The total LCC of the bridge has been shown in
Figure 12, considering the decreasing trend of
inspection and maintenance costs and increas-
ing trend of the service failure costs. From this
figure, it can be understood that the total LCC of
the bridge can be minimized if the inspection and
maintenance intervals are scheduled for every 2
or 3 years. This schedule optimizes the inspection
and maintenance costs while ensuring the safety
of the bridge.
where
C
ef
is the bridge failure cost due to earth-
quake event, and
C
e
u
, the user cost associated
with the probable bridge failure.
The failure cost is assumed to equal the cost
associated with the repair and replacement of the
damaged parts of a bridge during probable natural
hazards. Since the current chapter evaluates the
seismic performance of corroded bridges, the state
of damage after an earthquake event can be consid-
ered as an assessment measure for the estimation
of failure cost. Through a probabilistic approach,
the expected service failure cost is calculated for
each of the damage states and the results are then
combined with appropriate weighting factors.
This procedure is repeated over the entire life-
cycle of the bridge (
n
time intervals) to calculate
the total failure cost by taking into account the
failure probabilities which are updated at each
time interval based on the corrosion process. The
general formula for the estimation of failure cost
is as below:
6.4. Earthquake-Induced Failure Cost
This section focuses on the LCC analysis of RC
bridges considering the combined effects of natu-
ral hazards and environmental stressors on the
estimation of the LCC. The extent of structural
degradation and capacity loss due to the corrosion
process were discussed in the previous sections
and it is evident that an optimized plan for the
inspection and maintenance of bridges is necessary
to avoid any structural failure under the service
or seismic loads. To satisfy overall performance
requirements while minimizing the total resource
costs, the LCC of bridges is evaluated in this study
by taking into account the structural performance
criteria in addition to the key cost parameters.
As mentioned earlier the total LCC of the
bridge includes a one-time initial cost required
for the design and construction of the bridge,
some regular inspection and maintenance costs
necessary at certain time intervals, and the costs
associated with the serviceability failure of the
corroded bridge due to earthquake events. Based
on the mentioned costs, Equation 13 is updated
as follows to account for the earthquake-induced
failure cost for the degraded bridges.
n
4
∑∑
1
(
)
(
)
C
=
PI d i
,
∆
t r z i
∆
t C
(22)
ef
k
k
c
i
=
k
=
1
where
r
k
is the damage ratio (will be discussed
later) and
PI
is the performance index for the
damage state of
d
k
(
k
= 1, 2, 3, and 4) at
i
i-th time
interval. The performance index represents the
overall performance of a particular corroded state
of the bridge under a specified seismic hazard risk
and it can be determined in terms of the annual
probability of exceeding a given damage state
considering the effects of deteriorating mecha-
nisms. This index is calculated from Equation
23, as follows:
∞
∫
0
dH x
dx
( )
(
)
=
(
)
PI d i
,
∆
t
P DS
>
d
|
x
dx
k
k i
,
k
(23)
u
u
LCC C
=
+
C
+
C
+
C
+
C
+
C
]
(21)
[
]
[
c
IN
M
M
ef
ef
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