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and trapping of surface waves inside the basin. In any case, none of the results seems
clearly predictable. The most severe peaks exhibited by the simulated
DRS
occur in all
cases for
T
1s and the attenuation relation (2.4), even when corrected with the resid-
uals provided in Choi et al. (2005), cannot always account for their amplitude, in some
cases quite high. This seems to confirm, albeit in a different range of periods, the previ-
ous case of the Gubbio Plain response, adding further support to the need of a separate,
appropriate quantification of
DRS
on alluvium basins. Additional simulations for higher
magnitudes are being carried out toreach more definitive conclusions.
<
4. Overdamped spectra
With reference to the illustration in Figure 2.1, the response spectra for viscous damping
ratios
(ξ)
different from 5% are currently obtained by applying a damping correction
factor
to the 5% damped spectrum, defined in the past in several ways (see e.g. Tolis
and Faccioli, 1999; Bommer et al., 2000).
(η)
InCEN(2004)thespectralreductionfactorhasbeentakenfromBommeretal.(2000)at
intermediateperiods(between
T
B
and
T
E
)
whileatshorterandlongerperiods
η
increases
linearlysoastoreachthevalue1at
T
=
0sand
T
=
T
F
(
T
B
,
T
E
,
T
F
aredefinedinCEN,
2004 and depend on siteconditions).
In order to define a reliable correction factor transforming the 5% damped
DRS
into the
overdampedspectra,acomparisonhasbeenmadebetweentheavailablefactorsandthose
derivedfromUHspectrafordifferentdampingratios(calculatedasexplainedinSection5
for about 50 locations equally distributed in Italy). The ratios of spectral ordinates for
T
7s are constant, see Figure 2.14; in this interval the formulation of CEN (2004)
provides the best agreement with the median ratios derived from the UH spectra. At
T
<
7s the ratios linearly increase, as theory predicts, and tend to reach the value 1 at
anapproximateperiodof25s.Thismeansthatatsuchaperiodtherelativedisplacement
of the oscillator roughly equals the ground displacement. Hence, the expressions for the
scaling factors proposed in thisstudy are:
>
10
5
SRS
(ξ)
η
0
=
=
T
B
≤
T
≤
7s
(2.6)
SRS
(
5%
)
+
ξ
1
18
[
η
=
(
1
−
η
0
)
T
+
25
η
0
−
7] 7s
≤
T
≤
25s
Figure 2.14 shows the comparison between the correction factors (2.6) and the UH
median ratios. Although the fit of (2.6) to the data is not optimal for damping ratios
of 0.20 and 0.30, the slight overestimation of the reduction factor leads to a conservative
prediction of spectral ordinates, and hence it isdeemed acceptable.
