A Multi-Hazard Framework for Optimum Life-Cycle Cost Design of Reinforced Concrete Bridges - Structural Seismic Design Optimization and Earthquake Engineering - page 83

Table 2. Reduction in the mass, diameter, and yield strength of reinforcing bars at 5-year time intervals

Time* (year) 0 5 10 15 20 25 30 35 40 45 50

(M loss /M 0 )x100 0.00 6.38 12.24 18.10 23.96 29.82 35.68 41.54 47.40 53.26 59.12

D (mm)

35.80 34.75 33.61 32.46 31.32 30.17 29.03 27.88 26.74 25.59 24.45

f y /f y0 1.00 0.97 0.94 0.91 0.88 0.85 0.82 0.79 0.76 0.73 0.70

*after corrosion initiation

where Δ A s (t) is the steel loss of the rebar cross
section during the corrosion process (mm 2 ), Δ A 0 ,
the steel loss of the cross section needed for crack
initiation (mm 2 ), and K crack , an empirical coeffi-
cient equal to 0.0577. Assuming the crack width
of 0.3 mm as one of the first serviceability limits,
the time in which this limit is exceeded has been
calculated to equal 117 days (0.32 year). Compar-
ing the time to crack initiation (0.14 year) and the
time to exceed the crack width of 0.3 mm (0.32
years) with the time to corrosion initiation (10.40
years), it can be clearly seen that the two former
times are negligible within the whole life-cycle
of the bridge. Hence, considering the fact that the
crack initiation occurs shortly after the corrosion
initiation time, it is assumed that the time corre-
sponding to the serviceability threshold is equal
to the corrosion initiation time. Furthermore, it is
widely accepted that a crack width of more than
1 mm indicates the performance failure of the
concrete cover. The time required for reaching
this crack width limit has also been calculated to
equal 542 days (1.48 year) after corrosion initia-
tion. Since the capacity of structures under study
will be evaluated every 5 years after the corrosion
initiation time, it is assumed that the concrete
cover is destroyed from the first analysis interval.

This group consists of two-span bridges with three
variations in the span lengths, representing the
short-, medium-, and long-span bridges. All the
bridges have two columns at each bent and their
height varies from 7.5 to 12.5 m. This provides a
range of span length-to-column height ratios from
1.2 to 6.0. For the purpose of this study, the effect
of skewness is not considered and as a result, the
skew angle is assumed to equal zero degrees.
A schematic view of the bridges under study is
illustrated in Figure 4 and their dimensions are
summarized in Table 3.
OpenSees (2009) is used in this study to carry
out a series of static and dynamic analyses which
can provide a comprehensive performance assess-
ment of the bridges subjected to the time-depen-
dent corrosion process. At different bridge ages,
the remained structural capacity and expected
seismic response are calculated by analyzing the
bridge mathematical models which consist of a
variety of elements defined for the superstructure,
pier, abutment, and foundation. The developed
models are representative of the bridge geometric
characteristics, boundary conditions, material
properties, mass distribution, and nonlinear be-
havior of selected components. The detailed as-
sumptions made for each of the bridge components
are discussed below.

4. BRIDGE MODELING

1. Material Properties: The compressive
strength of concrete, f c ' , is assumed to equal
35 MPa for the bridge columns and super-
structure. The Poisson's ratio is 0.2 and the
concrete modulus of elasticity, E c , is calcu-
lated for the normal weight concrete using:

To develop the probabilistic life time fragility pa-
rameters of RC bridges located in chloride-laden
environments, a group of 9 box girder bridge
models are developed and analyzed in this study.