Civil Engineering Reference
In-Depth Information
where
EQ
1
EQ
k
, and
EQ
worst
are the critical scenario earthquake, the
k
th
earthquake belonging to the 2nd group, and the worst earthquake,
respectively.
The probability of the earthquake from an active fault can be predicted
using the Brownian passage time (BPT; Ellsworth
et al.
, 1999) distribution
model as
TT
+
T
⎡
⎣
⎤
⎦
PD
P
[
]
=
∫
(
)
∫
(
)
PEQ
f tT
;
,
κ
d
t
1
−
f tT
;
,
κ
d
t
[23.32]
R
R
T
0
P
are the return period of the earthquake, the
non-occurrence period, the design period, probability density function of
the BPT model, and the coeffi cient of variation of the return period, respec-
tively. The probability density function of the BPT model is given by:
in which
T
R
T
P
,
T
D
,
f
, and
κ
(
)
2
⎡
⎢
⎤
⎥
μ
πκ
t
−
μ
μκ
(
)
=
ft
;
μα
,
exp
−
[23.33]
23
2
2
t
2
t
In particular, with the return period and non-occurrence period of the worst
earthquake, it might be assumed that
T
R
middle point
of the return period as the average non-occurrence period of many
earthquakes.
=
475 years and
T
P
=
23.3.3 Structural failure
Let us defi ne the damage modes for structural components in the following
way;
R
,
D
,
L
,
S
,
C
S
,
T
p
are the residual strength for each damage mode, dead
load, live load, seismic load, retrofi tting investment, and present time,
respectively:
(
)
=
(
)
−+
(
)
−⋅ <
ZCTRCTDLS
Z
E
minor
,
minor
,
1
0
Sp
Sp
Q
(
)
=
(
)
−+
(
)
−⋅ <
moderate
C
,
T
R
moderate
C
,
T
DL
S
1
0
[23.34]
EQ
S
p
Sp
Q
(
)
=
(
)
−+
major
(
)
−⋅ <
ZCTRC
,
major
,
TDLS
1
0
Sp
SSp
Q
EQ
where,
1
0
:
:
an earthquake occurs at
an earthquake does not
t
occur at
EQ
⎩
EQ
1
=
[23.35]
EQ
t
The expected value of 1
EQ
equals the probability of an earthquake occur-
ring in the residual service period (
T
D
-
T
p
), and it is given by the following
equation using the return period of the possible future earthquake:
[ ]
=
[
]
E
1
EQ
P EQ
[23.36]
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