Geoscience Reference
In-Depth Information
broad band velocity meters and SM accelerographs confirmed the reliability of the basic
processing applied to acceleration records. The shortest period taken into account in
deriving the attenuation relations is 0.1s, thus making it unnecessary to apply a high-
cutfilter,commonlychosentohavearoll-offat50Hzandcut-offat100Hz,fordigitally
recorded data (Ambraseys et al., 2005). From the acceleration histories, baseline cor-
rected as just described, the
DRS
ordinates were computed up to 20s period for both
horizontal and for the vertical component of each accelerogram. The horizontal ground
motion is represented in this study by the geometric mean of the
DRS
ordinates of the
two recorded horizontal components at a given period, and by the single ordinate of the
vertical response spectrum. The spectral ordinates areexpressed incm.
2.2. PREDICTION EQUATIONS FOR DISPLACEMENT SPECTRAL RESPONSE
The empirical equations for the prediction of the
DRS
(
T
) ordinates were initially taken
in the form(e.g. Ambraseys et al., 1996):
log
DRS
(
T
)
=
a
1
+
a
2
M
+
a
3
log
R
+
a
4
S
1
+
a
5
S
2
+
ε
(2.2)
where
T
denotes a
random error term, assumed as normally distributed with zero mean and standard devi-
ation
(
s
)
=
vibration period, and
a
1
...
a
5
are numerical coefficients,
ε
σ
log
DRS
.
S
1
and
S
2
are dummy variables accounting for the main local ground
categories contemplated in both the Eurocode 8 and the Italian current norms (CEN,
2004; Ministero delle Infrastrutture e dei Trasporti, 2005), with the following values:
S
1
=
800m s
−
1
;
S
1
=
S
2
=
0 for type A (rocklike) ground, with
V
s
30
≥
1 and
S
2
=
0
for type B (stiff) ground, with 360m s
−
1
800m s
−
1
;
S
1
=
≤
V
s
30
≤
0
,
S
2
=
1 for type
C ground, with 180m s
−
1
360m s
−
1
, and
S
1
=
≤
V
s
30
≤
S
2
=
1 for type D (very soft)
180m s
−
1
. Note that accounting for local ground conditions with
twodummyvariablesonly,asin(2.2),doesnotallowtodiscriminatebetweentheampli-
fication ratios D/B and C/A, both equal to 10
a
5
S
2
, and between B/A and D/C. To avoid
such ambiguity, a third dummy variable
S
3
should be introduced, so that the portion on
the rhs of (2.2) accounting for ground conditions would become
a
4
S
1
+
ground, with
V
s
30
<
a
5
S
2
+
a
6
S
3
.
In such case,
S
1
=
and the other two
dummy variables wouldbesetequal to0 for theother ground types. Table 2.1shows the
distributionof thecalibration data in termsof
M
and ground type.
S
2
=
S
3
=
0 for ground A, while
S
i
=
1
(
i
=
1
,
2
,
3
)
Table 2.1. Distribution of acceleration records in the database in terms of magnitude and ground
types (CEN, 2004)
M
A
B
C
D
Unknown
5.0-5.4
17
95
97
13
34
5.5-5.9
11
141
131
38
0
6.0-6.3
8
127
135
21
16
6.4-6.6
23
96
59
15
49
6.7-7.2
9
13
11
0
22
