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loss of information and accuracy. Systematic assessment of a measure of
model quality can be made; thus, it is possible to differentiate between the
accuracy of alternative candidate models. These explanatory functions
provide the means for gaining insight into the underlying behavioral phe-
nomena and selecting ground motion parameters that are most relevant to
the seismic demands. The approach can take into account information
gained from scientifi c/engineering laws, observational data from laboratory
experiments, and data from simulated dynamic responses. The demand
models are unbiased and properly account for all the predominant uncer-
tainties, including model errors, arising from an inaccurate model form or
missing variables, measurement errors, and statistical uncertainty. Addi-
tional examples of such probabilistic demand models can be found in, for
example, Zhong
et al.
(2009) and Huang
et al.
(2010).
Following Gardoni
et al.
(2003) the deformation demand for RC bridges
in terms of ln(
D
)
is the probabilistic deformation demand model,
S
a
is the pseudo spectral
acceleration corresponding to
T
N
of the structure and 5% damping,
x
rep-
resents the structural properties, and
Δ
/
H
), at time
t
n
is
D
d
[
x
t
n
,
S
a
(
S
t
n
,
x
t
n
),
Θ
D
], where
D
d
(
x
,
S
a
,
Θ
Θ
D
is a set of model parameters. To
compute the probability distribution for
D
d
(
x
,
S
a
,
D
) the probability dis-
tribution for
S
a
is needed. The CDF
F
S
a
(
s
) for
S
a
for a given region and
T
N
is given by
F
S
a
(
s
)
Θ
H
(
s
)/
H
(0), where
H
(
s
) is the regional seismic hazard
curve for the given
T
N
. A seismic hazard curve defi nes the relation between
a value of
S
a
and the annual probability of the value being exceeded. Figure
16.4 shows
H
(
s
) for San Francisco for
T
N
=
1
−
=
0.5 s, 0.75 s and 1.0 s obtained
10
0
H
(0) = 0.1614
10
-2
10
-4
10
-6
T
N
= 1.0 s
T
N
= 0.75 s
T
N
= 0.50 s
10
-8
10
-10
10
-3
10
-2
10
-1
10
0
10
1
s
(g)
16.4
Seismic hazard curves for San Francisco, CA.
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