Geology Reference
In-Depth Information
n
fic is assumed to be 100,000 hour.vehicle.year
-1
,
which makes the user cost of the maintenance
program equal to $875,000. It is also assumed
here that the inspection procedure is so short that
it leads to negligible disruptions on bridge traffic,
and as a result, it causes no user cost.
∑
1
C
=
Mz i
(
∆
t
(16)
M
i
=
where
M
is the cost of maintenance activity in
base year prices. The maintenance cost is usually
assumed between 0.5% to 1.0% of the construction
cost, but since it is expected that the maintenance
cost increases as the bridge ages, it is assumed here
that the maintenance cost has a linear increasing
trend from 0.5% to 1.0% during the structure's
service life time.
In addition to the direct maintenance costs, the
user cost associated with the temporary closure
of facilities should also be considered. The actual
user cost during the regular maintenance work
depends on the extent and duration of service
disruption (Chang and Shinozuka, 1996). This
can be expressed as:
6.2. Service Failure Costs
The expected value for the service failure cost
of a bridge can be calculated using Equation 18:
n
∑
1
(
)
C
=
C z i
∆ ∆
t
p i
( )
(18)
sf
f
f
i
=
where
C
f
is the repair cost due to the service
failure, assumed to be equal to 20% of the con-
struction cost. In order to obtain the expected
service failure cost, the repair cost should be
multiplied by the relevant probability of failure
during each time interval of the bridge life-cycle.
Since the current chapter studies the effects of the
corrosion process on LCC of bridges, the prob-
ability of failure due to the corrosion process
between (
i
-1)-th and
i
i-th time intervals, Δ
p
f
(
i
),
has been calculated using a recursive formula
suggested by Val and Stewart (2003) in Box 1:
where
p
is the cumulative distribution function
for the time of service failure. Since the crack
initiation and propagation time (calculated in
Section 4.2) is small comparing to the corrosion
initiation time, the service failure is assumed to
occur after the corrosion initiation time. The
values of Δ
p
f
(
i
) have been calculated for different
inspection intervals and are shown in Figure 10
for the entire life-cycle of the bridge, which is
n
∑
1
m m
u
C
=
t b uz i
(
∆
t
(17)
M
i
=
where
t
m
is the duration of maintenance activities,
and
b
m
, the index of usage disruption (0 ≤
b
m
≤
1). For example, if maintenance entails closure
of one of the two lanes of a bridge,
b
m
would be
0.5. In Equation 17,
u
is the unit user cost which
depends on the volume and type of traffic crossing
the bridge as well as the availability of convenient
alternative routes. The user cost also typically
includes the increased costs associated with travel
delays and accidents. In the current study, it is
assumed that for the maintenance program, only
1/4 of bridge is closed at each period of time for
one week. Hence, the average hourly user cost is
calculated to be $8.75 per vehicle. The annual traf-
Box 1.
−
∑
i
1
{
}
+
−
=
(
)
−
(
)
(
)
(
)
∆
p i
( )
p i
∆
t
p i
−
1
∆
t
∆
p j
( )
p i
−
j
∆
t
p i
[
−
j
−
1
∆
t
]
(19)
f
f
j
=
1
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