Civil Engineering Reference
In-Depth Information
simulation results are assumed to occur with equal likelihood, i.e., equal
annual frequency of occurrence, the annual frequency of occurrence for
each set of Monte Carlo simulation results is one
n
mc
th of that for the asso-
ciated scenario earthquake. Consider, for example, the Scenario 175 Verdugo
earthquake, the annual occurrence frequency of which is 9.65E
04. Then,
the annual occurrence frequency for a SSI of 0.81, associated with the simu-
lation results in
Plate IV
(between pages 452 and 453), is 9.65E
−
−
06, if
n
mc
=
100. The similar process was applied to all 59
n
mc
sets of simulation results,
i.e., SSI, each of which is associated with its own annual occurrence fre-
quency. The 59
×
n
mc
SSI were then sorted in an increasing order of SSI, and
the annual frequency of exceeding a given SSI, SSI
0
, is calculated by a sum-
mation of the annual occurrence frequencies for those SSI
×
≤
SSI
0
,
≤
∑
(
)
=
(
)
F
SSI
f
SSI
[24.2]
0
SSI
SSI
0
where
F
(SSI
0
) is the annual frequency of exceeding SSI
0
, and
f
(SSI) is the
annual occurrence frequency of SSI.
Figure 24.5 shows the system risk curves plotting the variation of annual
exceedance frequency as a function of SSI. The system risk curve without
a 24-hour period of running tanks is shown by open triangles and that with
a 24-hour period of running tanks is shown by open squares. The system
risk curve without a 24-hour period of running tanks varies almost linearly
in the semi-logarithmetic scale, with a minimum SSI of 0.64 corresponding
to an annual frequency of 0.0001, or 10 000-year recurrence interval. The
1.0000
SSI =
∑
Q
/
∑
Q
0
∑
Q
: Total water demands satisfied after earthquakes
∑
Q
0
: Total water demands satisfied before earthquakes
0.1000
Without running tank effects
With running tank effects
0.0100
0.0010
0.0001
1
0.8
0.6
0.4
0.2
0
System serviceability index, SSI
24.5
System risk curves (after Wang and O'Rourke 2008).
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