Civil Engineering Reference
In-Depth Information
4.4.2
IM
s which can be presently considered in ground
motion selection
There are a large number of ground motion intensity measures which have
been proposed over several decades as indicators of the severity of a ground
motion for various seismic response analysis problems. In theory, any of
these ground motion intensity measures can be considered in the proposed
ground motion selection framework. Several practical requirements
however, which remove many intensity measures from consideration at
present, are that if a set of
N
IM
i
ground motion
IM
s,
IM
, wish to be consid-
ered then: (i) GMPEs must be available to predict the marginal mean and
standard deviation of (the logarithm of) each of the
N
IM
i
IM
i
s in
IM
(i.e.
μ
ln
IM
i
|
Rup
); (ii) correlation equations must be available to predict
the correlation between each of the
N
IM
i
IM
i
s in
IM
and
IM
j
(i.e.
ln
IM
i
|
Rup
and
σ
ρ
ln
IM
i
,ln
IM
j
|
Rup
);
and (iii) correlation equations are also required between the
N
IM
i
(
N
IM
i
−
1)/2
combinations of
IM
i
pairs in
IM
itself (i.e.
ρ
ln
IM
i
,ln
IM
k
|
Rup
). Points (i) and (ii)
above are required to obtain the conditional mean and standard deviation
vectors (i.e. Equation (4.6)), while (iii) is further required to determine the
correlation matrix of the vector
IM
|
Rup
,
IM
j
(i.e. Equation (4.7)). Because
the availability of GMPEs for a particular
IM
i
is required in order to
develop correlation equations involving this
IM
i
(e.g. see Bradley, 2011a),
then it follows that the availability of correlation equations between various
IM pairs is the governing restriction on which IMs may be considered in
the proposed ground motion selection methodology.
Table 4.1 illustrates various intensity measure pairs for which, as far as
the author is aware, empirical ground motion correlation equations have
been developed. It can be seen that correlation equations are available
between common peak-amplitude-based IMs such as
SA
(
T
),
PGA
and
PGV
. Correlation equations are also available for the response-spectrum-
based
IM
s: acceleration spectrum intensity,
ASI
(Von Thun
et al.
, 1988),
spectrum intensity,
SI
(Housner, 1952), and displacement spectrum inten-
sity,
DSI
(Bradley, 2011b), which can be considered to represent the average
high-, moderate, and low-frequency intensity of a ground motion, respec-
tively (Bradley, 2011b). In addition to these aforementioned peak-
amplitude-based
IM
s, Table 4.1 also illustrates that correlations are available
for
IM
s such as cumulative absolute velocity,
CAV
(EPRI, 1988) and arias
intensity,
IA
(Arias, 1970), which are strongly infl uenced by cumulative
ground motion features, and also the signifi cant duration parameters,
Ds575
and
Ds595
(Bommer and Martinez-Pereira, 1999; Bradley, 2011a).
In the subsequent ground motion selection examples to follow, the inten-
sity measure vector
IM
{
SA
(
T
),
PGA
,
PGV
,
ASI
,
SI
,
DSI
,
CAV
,
Ds
575,
Ds
595} will be adopted (where
SA
(
T
) is considered at nine periods
T
=
=
{0.05, 0.1, 0.2, 0.3, 0.5, 1.0, 2.0, 5.0, 10.0}), i.e. a total of 17
IM
i
s were consid-
ered. The following GMPEs were used for predicting these various
IM
i
s:
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