A Multi-Hazard Framework for Optimum Life-Cycle Cost Design of Reinforced Concrete Bridges - Structural Seismic Design Optimization and Earthquake Engineering - page 93

assumed to be 50 years after the corrosion initia-
tion time. It is evident that as the number of in-
spections decreases, the probability of failure due
to the corrosion process increases. According to
Chang and Shinozuka (1996), the expected user
cost associated with the probable service failure
can be calculated as below:

tion and maintenance costs as well as the service
failure costs of all the bridges are calculated and
the average costs are summarized in Table 5. The
values of Table 5 are obtained with the assumption
of 4% annual inflation rate and scheduling an-
nual inspection and maintenance program. This
table shows that the user associated costs, C u
and C s u , do not change for different bridge types,
which indicates that they are independent of the
construction cost.
In order to evaluate the effects of inspection
and maintenance intervals on the LCC of bridges,
different inspection and maintenance strategies
have been examined. In this study, it is assumed
that the inspection and maintenance intervals are
the same and can be scheduled every 1, 2, 3, 4, or
5 years. Table 6 indicates the average inspection,
maintenance, and service failure costs for the
medium-span bridge inspected and maintained
according to the proposed time schedules. The ratio
of different cost types to the initial construction
cost are depicted in Figure 11. Referring to Table
6 and Figure 11, when the inspection intervals

n

∑ 1

( )

u

C = t b u z i ∆ ∆ t p i ( ) (20)

sf sf sf f

i =

where t sf is the duration of repair activities after
failure, and b sf , the usage disruption parameter
due to the service failure. In this study, it is as-
sumed that it takes one month for the bridge to
be repaired and during this time half of the bridge
will be closed to traffic.

6.3. Optimized Inspection and
Maintenance Intervals

Based on the total construction cost of the short-,
medium-, and long-span bridge cases, the inspec-

Figure 10. Probability of service failure due to the corrosion process for various inspection intervals