Civil Engineering Reference
In-Depth Information
the smallest based on the attenuation formula, equation (23.28) can be
rewritten as
[
]
[
]
∪
(
)
=
mode
mode
mode
p
=
P D
Z
P Z
S
M R G
,,
s
[23.29]
f
EQ
EQ
EQ
1
⊂
(
)
sS MRG
k
,,
[
(
)
=
] [
]
PS M
,
RRG
,
sEQ P EQ
1
1
1
n
[
]
[
]
∑
∪
(
)
=
+
PD
E
mode
Z
E
mode
PZ
E
mode
S MRG
,,
s
k
⊂
(
)
k
2
ssS MRG
,,
,,
k
PS MRG
[
(
)
=
] [
]
sEQ PEQ
k
k
k
N
=
∑
[
]]
[
]
(
)
=
∪
mode
mode
mode
+
PD
Z
PZ
S MRG
,,
s
EQ
EQ
EQ
k
⊂
(
)
kn
1
sS MRG
,,
k
[
(
)
=
]] [
]
PS MRG
,,
sEQ
PEQ
k
k
k
In this equation, the fi rst term corresponds to the critical scenario
earthquake, and the second term is a group of earthquakes that are of
moderately severe seismic intensity generated from known active faults;
the last term denotes a group of earthquakes that will be less seismically
severe.
Currently, the majority of research groups have estimated seismic risk
from all active faults. But in actual design schemes, seismic assessment for
all active faults is impractical. A simple approach would be preferable to
the current approach (Equation (23.29)). The worst spectral method (JARL,
1992), dealing with many earthquakes caused by unknown faults, is adopted
in the present study as a conservative estimate for dealing with this issue.
Since each seismic intensity
S
k
(
M
,
R
,
G
) is less than the worst seismic inten-
sity
S
worst
shown as
(
)
≤
SMRG S
k
,,
worst
[23.30]
the probability of failure in Equation (23.29) can be replaced by
[
]
[
]
∪
(
)
=
p
=
P D
E
mode
Z
E
mode
P Z
E
mode
S
M R G
,,
s
[23.31]
f
1
⊂
(
)
sS MRG
k
,,
[
(
)
=
] [
]
PS M
,
RRG
,
sEQ P EQ
1
1
1
n
[
]
[
]
∑
∪
(
)
=
+
PD
mode
Z
mode
PZ
mode
S MRG
,,
s
EQ
EQ
EQ
k
k
2
ssS MRG
⊂
(
,,
,,
)
k
PS MRG
[
] [
]
(
)
=
sEQ PEQ
k
k
k
[
]]
[
]
∪
(
)
=
+
PD
E
mode
Z
E
mode
PZ
E
mode
S MRG
,,
s
k
⊂
(
)
sS MRG
k
,,
[
]
[
]
PS
=
sEQ
PEQ
worst
worst
wo
rst
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