A Multi-Hazard Framework for Optimum Life-Cycle Cost Design of Reinforced Concrete Bridges - Structural Seismic Design Optimization and Earthquake Engineering - page 101

Table 9. Suggested values for A(d k ) in Equation 25

Seismic Hazard Risk

Damage State Low Medium High

slight 3.26 × 10 -05 5.44 × 10 -05 9.93 × 10 -05

moderate 5.53 × 10 -06 1.05 × 10 -05 2.38 × 10 -05

extensive

1.66 × 10 -06 3.74 × 10 -06 9.12 × 10 -06

complete 5.46 × 10 -07 1.43 × 10 -06 3.66 × 10 -06

predict the progress of corrosion in reinforced
concrete members. Through this study, the effects
of various influential parameters, such as water
to cement ratio, ambient temperature, relative
humidity, concrete age, free chloride content, and
binding capacity, are carefully considered for an
accurate estimation of the chloride penetration
profile in deteriorating structural members over
the time.
The corrosion initiation time is estimated by
comparing the chloride content values in the vi-
cinity of reinforcing bars with critical thresholds.
After the determination of the corrosion initiation
time, the rate of reduction in geometry and material
properties due to the corrosion process is calculated
at different time steps. This chapter specifically
considers the reduction rate of diameter and yield
strength of reinforcing bars in corroded members.
The crack initiation and propagation in concrete
cover is also investigated in order to modify the
confinement assumptions required for capac-
ity evaluation. Based on the updated structural
characteristics of corroded members, the capacity
loss of a group of RC bridges with short, medium,
and long spans is evaluated. In addition to the
structural degradation, the effects of the corrosion
process on the life-cycle cost of bridges are also
studied. From the detailed calculation of construc-
tion, inspection, maintenance, and service failure
costs of the bridges, this chapter examines various
inspection and maintenance strategies and sug-
gests the optimized inspection and maintenance
intervals. The proposed procedure minimizes the

total life-cycle cost of the bridge while maintains
its expected structural performance.
This chapter also provides a multi-hazard
framework that evaluates the life-cycle perfor-
mance and cost of reinforced concrete highway
bridges. The bridges under consideration are lo-
cated in seismic areas and they are continuously
exposed to the attack of chloride ions. As a result,
it is necessary to study the combined effects of a
natural hazard and an environmental stressor over
the time. The time-dependent seismic fragility
curves of the bridges are then generated using a
set of damage states for the purpose of seismic
risk assessment. In addition to the probabilistic
structural evaluation, the results of fragility analy-
sis are employed to estimate the total life-cycle
cost of the bridges. To consider both earthquake
and corrosion scenarios, a performance index is
introduced which represents the vulnerability of a
corroded bridge under a specified seismic hazard
risk. Comparing the life-cycle costs calculated with
and without the effects of corrosion, it is found
that the suggested performance index plays a key
role in obtaining more realistic estimates of the
total costs and it provides valuable information to
optimize the inspection and maintenance intervals.
The time-dependent variation of this index is also
formulated to be directly used in the life-cycle cost
analysis of similar cases without going through
the detailed corrosion models.