Civil Engineering Reference
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retrieving the relationship between PGA and moment magnitude (more
specifi cally, their joint distribution) through seismic deaggregation results
(Kramer and Mayfi eld, 2007; Juang
et al.
, 2008). Alternatively, using Monte
Carlo simulation, a simpler method can be devised by conducting probabi-
listic liquefaction triggering assessment for individual earthquakes included
in a synthetic catalogue (Goda
et al.
, 2011). A brief summary of the latter
approach based on the Standard Penetration Test (SPT) data is given in
the next paragraph, and an example case study of PLHA is discussed
subsequently.
The Seed-Idriss simplifi ed method based on the SPT data is capable of
predicting the occurrence of liquefaction triggering by comparing cyclic
resistance ratio with cyclic stress ratio at a specifi c depth of a soil column.
One of the recent probabilistic models for liquefaction triggering is the one
developed by Cetin
et al.
(2004), which takes key uncertainties associated
with the input data/parameters and the adopted model into account. Cetin
et al.
's model computes the probability of liquefaction initiation
P
L
at a
depth of interest as:
(
)
−
(
)
−
(
)
N
160
1
+
0 004
.
FC
13 32
.
ln
CSR
29 53
.
ln
M
⎛
⎞
,
eq
w
⎜
⎜
⎜
(
)
+
⎟
⎟
⎟
−
370
.
ln
σ
′
P
005
.
FC
+
1685
.
v
a
P
=−
Φ
,
[1.5]
L
27
.
⎝
⎠
where
is the standard normal function;
N
1,60
is the corrected SPT blow
count (but not adjusted for fi nes content);
FC
is the fi nes content (in per-
centage);
CSR
eq
is the cyclic stress ratio (but not adjusted for moment
magnitude);
Φ
σ
′
v
is the vertical effective stress; and
P
a
is the atmospheric
pressure (
100 kPa). The correction of the
in-situ
N
values to
N
1,60
can
be done by using a set of correction factors, as suggested by Youd
et al.
(2001) and Cetin
et al.
(2004). The value of
CSR
eq
for a given depth
d
is
calculated by:
=
PGA
g
σ
σ
v
CSR
=
065
.
r
,
[1.6]
eq
d
′
v
where
PGA
is the geometric mean of PGAs of two horizontal components
at ground surface (Youd
et al.
, 2001);
σ
v
is the total vertical stress; and
r
d
is
the nonlinear stress reduction factor. Cetin
et al.
(2004) conducted extensive
site response analyses to derive a new probabilistic relation for
r
d
(note: the
calculation of
r
d
requires the average shear wave velocity in the top 12 m
V
S12
in addition to
PGA
and
M
w
; see Cetin
et al.
, 2004, for details). Using
Equations [1.5] and [1.6], a value of
P
L
at a depth
d
can be evaluated for a
given scenario (i.e. a pair of
PGA
and
M
w
). It is noted that the cyclic resis-
tance ratio (
CRR
eq
) for a given
P
L
can be obtained as:
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