Civil Engineering Reference
In-Depth Information
major scenarios are sorted in a descending order in terms of expected
seismic intensity measure. Specifi cally, the plotting position for the earth-
quake scenarios for the event-based seismic hazard curve
Q
is given by:
Qq
=
for
j
=
1
j
j
[27.2]
m
(
)
(
)
=−
=
∏
(
)
Q
=− −
11
q
1
−
Q
1
1
−
q
for
j
>
1
j
j
j
−
1
j
j
1
where
q
j
is the assigned probability of occurrence for the
j
th scenario (
j
=
1 corresponds to the largest event in terms of seismic intensity measure);
usually,
q
j
is expressed as the annual occurrence probability. Then, the con-
ditional probability distribution of the seismic risk measure
c
is assessed for
each scenario. This conditional probability distribution of
c
incorporates the
uncertainty associated with the considered scenario, such as uncertainty of
source magnitude and location, ground motion, site amplifi cation, and
seismic damage/loss. Finally, the event-based seismic risk curve is converted
into an integrated seismic risk curve as follows:
c
m
⎡
⎢
⎤
⎥
max
∏
=
()
=−
∫
()
Gc
1
1
−
q
f
ς
j
d
ς
[27.3]
C
j
C
j
1
c
where
m
is the number of scenarios considered in the assessment,
f
C
(
c
|
j
) is
the conditional seismic loss density function expressed in terms of earth-
quake scenario, rather than ground motion intensity level as in Equation
27.1 (note: the unconditional density function
f
Cj
(
c
j
)
f
C
(
c
|
j
)). This equa-
tion represents the integrated form of seismic risk curve resulting from all
of the scenario earthquakes. The event-based seismic risk curve is illustrated
in Fig. 27.2. Generally speaking, event-based seismic risk curves are jagged
in appearance, because of discrete values of the assigned occurrence prob-
abilities to individual scenario events.
=
q
j
×
0.05
NEL; event risk curve
PML; event risk curve
0.04
0.03
0.02
Risk curve
0.01
PML1
1/475=0.0021
PML3
0.00
0.00
0.10
0.20
0.30
0.40
0.50
Ratio of seismic loss to the replacement cost
27.2
Seismic event risk curves and integrated seismic risk curves.
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