Civil Engineering Reference
In-Depth Information
0.8
0.7
t
= 100 years
0.6
0.5
t
= 0 years
0.4
0.3
t
= 100 years
t
= 0 years
0.2
0.1
0.0
0
1
2
3
4
5
S
a
19.6
F
˜
(
t
,
S
a
) for the example RC bridge considering deformation
(dashed), shear (dash-dotted), and deformation and shear (solid)
failure modes (Choe
et al.
2009). Reprinted with permission from
Elsevier © 2009.
faster rate than the deformation fragility. However, because the deforma-
tion failure mode controls (i.e., it is signifi cantly more likely than the shear
failure mode), then
F
˜
(
t
,
S
a
) varies at a rate close to the one of the deforma-
tion fragility.
Figure 19.6 compares the fragilities of the undeteriorated (
t
=
0 years)
and the deteriorated bridge at
t
100 years considering the deformation
failure mode only (dashed lines), the shear failure mode only (dashed-
dotted lines), and considering that either the deformation or the shear
demands might exceed the corresponding capacities (solid lines). It can be
observed that at
t
=
0 years the deformation failure mode is the most likely
mode of failure, which is consistent with Caltrans specifi cations used to
design the example bridge. At
t
=
100 years, consistently with chat observed
in Fig. 19.5,
F
˜
(
t
,
S
a
), increases for a given
S
a
, however, at least for this
example bridge, the deformation failure mode remains the most likely one.
Additional work and examples of the effects of corrosion on the reliability
of RC bridges can be found in Zhong
et al.
(2012a), and Simon
et al.
(2010),
while those on the reliability of post-tensioned (PT) bridges can be found
in Trejo
et al.
(2009), Gardoni
et al.
(2009), and Pillai
et al.
(2009, 2010a,b).
=
Seismic fragility increment functions for deteriorating RC bridges
In the formulation described so far, a reliability analysis has to be
performed at each time
t
using the corresponding capacity and demand
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