Civil Engineering Reference
In-Depth Information
the updating process is presented for
F
ˆ
k
(
t
,
S
a
); however the same process
can be used to update
F
ˆ
(
t
,
S
a
).
An estimate of
F
k
(
t
insp
,
S
a
) can be obtained as
F
ˆ
k
(
t
insp
,
S
a
)
=
Ĝ
F
,
k
(
x
0
,
t
insp
,
S
a
)
F
˜
k
(
x
0
,
S
a
) using
Ĝ
F
,
k
(
x
0
,
t
,
S
a
) to model the deterioration process but ignor-
ing the information from the fi eld observations. Alternatively,
F
k
(
t
insp
,
S
a
)
can be estimated by assessing the predictive fragility
F
˜
k
(
x
insp
,
S
a
) by conduct-
ing a reliability analysis using directly the current values of the geometry
and material properties obtained from the fi eld inspection, and without
using
Ĝ
F
,
k
(
x
0
,
t
insp
,
S
a
). Figure 19.8 shows the difference,
×
F
k
(
S
a
), between the
two estimates. An equivalent time
t
eq,
k
can be determined to update the
deterioration process modeled by
Ĝ
F
,
k
(
x
0
,
t
,
S
a
) so that the corresponding
fragility estimate matches the one based on
x
insp
, that is such that
F
ˆ
k
(
t
eq,
k
)
Δ
=
F
˜
k
(
x
insp
). The deterioration process might affect
the deformation and shear modes of failure differently, as a result, in general
t
eq,δ
F
˜
k
(
x
0
)
Ĝ
F
,
k
(
x
0
,
t
eq,
k
,
S
a
)
×
≈
t
eq,
v
.
If the updating of the deterioration process modeling is believed to be
due to an inaccurate estimate of the time of initiation of the deterioration,
then the fragility at a time
t
after the inspection (i.e.,
t
>
t
insp
) can be esti-
mated using
t
eq,
k
as
≠
ˆ
ˆ
[
]
×
(
)
(
)
=
()
>
FtS
,
G
x
,
t
+
Δ
t S
,
F
x
t t
[19.10]
k
a
F k
,
0
eq
,
k
a
k
0
insp
Predicted using
proposed increment
function computed
at
F
k
(
t, S
a
)
F
k
(
t, S
a
)
t
insp
Predicted using
properties from
field inspection
Predicted using
proposed increment
function computed
at
t
=
t
eq
t
=
t
=
t
insp
t
=
t
insp
Δ
F
k
t
S
a
S
a
F
k
(
t, S
a
)
F
k
(
t, S
a
)
Δ
F
k
Predicted using
proposed increment
function computed
at
t
=
t
insp
and
t
=
t
eq
t
t
S
a
t
insp
t
eq,
k
19.8
Defi nition of
t
eq,
k
(Gardoni and Rosowsky 2011). Reprinted by
permission of the publisher (Taylor & Francis Ltd, http://www.tandf.
co.uk/journals).
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