Seismic reliability of deteriorating reinforced concrete (RC) bridges - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 515

representative of current construction in California. Specifi cally, Mackie
and Stojadinovic (2001) designed the bridge following the Caltrans Bridge
Design Specifi cation and Seismic Design Criteria (Caltrans 1999). For the
parameters that affect the corrosion initiation and propagation, Choe et al.
(2009) assumed that the concrete has a water-to-cement ratio (w/c) of 0.5
and 1 day curing time, and that the bridge is located in a tidal zone (thus
affected by chlorides) with humid-dry cycles.
Three variables are assumed to be random: the compressive strength of
concrete, f

c and the yield stress of the longitudinal reinforcement, f y , are
modeled as a random variable to capture the uncertainty in the material
properties, and the third random variable is the bridge dead load, r , is used
to model the variability in the axial load. Specifi cally, it was assumed that
f

′

c follows a lognormal distribution with mean 27.6 MPa and 10% coeffi cient
of variation; f y follows a lognormal distribution with mean 448.2 MPa and
5% coeffi cient of variation; and r follows a normal distribution with mean
equal to 10% of the dead weight and a 25% coeffi cient of variation. Addi-
tional variables needed to model the corrosion initiation and propagation
(such as the reference diffusion coeffi cient, etc.) were taken to be random
in accordance with DuraCrete (2000).
Figure 19.4 shows the deformation and shear capacity of the RC column
and the corresponding seismic demands as a function of time, where the
demands are computed for S a

′

2.0 g. The solid lines show the mean capaci-
ties along with the confi dence bands computed as the mean

=

± 1 standard

deviation of the model error, σ Ck , whereas the dashed lines show the mean

demands along with the confi dence bands computed as the mean

Dk . The
mean deformation and shear capacities decrease over time while the mean
deformation and shear demands remain approximately constant. In addi-
tion, the mean shear capacity decays at a faster rate than the mean defor-
mation capacity. The next section discusses the effects of the deterioration
on the seismic reliability of RC bridges.

± σ

19.3.2 Effects of deterioration on seismic reliability
of RC bridges
Time-dependent deterioration models can be used to assess the reliability
of RC structures over time (Mori and Ellingwood 1993; Enright and Fran-
gopol 1998a,b; Stewart and Rosowsky 1998; Li and Melchers 2005; Choe
et al. 2009, 2010). Fragility estimates can be developed to quantify the reli-
ability of a bridge structure or sub-structure at time t . The fragility is defi ned
as the conditional probability that any demand measure, D ik ( t ), is larger
than or equal to the corresponding capacity measure, C ik ( t ), for a given S a .
The fragility estimates can be computed using methods of structural reli-
ability, such as fi rst- and second-order reliability methods (FORM and