Geoscience Reference
In-Depth Information
5.2. EXTENT OF THELONG PERIOD, CONSTANT DISPLACEMENT RANGE
Because, on one hand, DDBD is rather recent and, on the other hand, only few struc-
tures require accurate response spectra at long periods
for design with the
traditional approach, studies that provide regional maps of parameters controlling the
responsespectraatsuchperiodsarealmostnon-existent.InBSSC(2003)thelongperiod
spectral response is governed by a corner period (that represents the transition from con-
stant spectral velocity to constant spectral displacement) named
T
L
. The meaning of this
parameter is obviously akin to that of
T
D
in Subsection2.5.
T
L
maps in BSSC (2003)
were prepared following a two-step procedure; in the first step the following correlation
was established between
M
and
T
L
:
(
T
>
4s
)
log
T
L
=−
1
.
25
+
0
.
3
M
(2.7)
This correlation was selected among several available formulas supported either by seis-
mic source theory (Brune, 1970) or by the evaluation of
T
L
from response spectra of
strongmotionaccelerogramswithreliablelongperiodcontent,recordedduringmoderate
and large magnitude earthquakes. The second step made use of deaggregation analyses
(for the 2% in 50-year exceedance level for
acceleration spectra
) aimed at constructing
maps of modal magnitude. From (2.7) and the knowledge of the magnitude that most
influences hazard at each site it was possible to construct a
T
L
map for the conterminous
United States.
While BSSC (2003) provides important clues as to practical ways of defining spectra
at long periods, only few records were used for calibrating (2.7) and, furthermore, the
deaggregation analysis assumed that the modal magnitude-distance bin controlling the
hazardat
T
=
2s(insomecaseseven1s)wouldremainthesamealsoatlongerperiods.
Using the Brune source model (Brune, 1970), with an average focal depth of 8km, an
average constant shear wave velocity of 3
0kms
−
1
, and a stress drop of 10MPa, the
values of the corner period listed in the second column of Table 2.6 were obtained. In
the third column, the values from (2.7) correlation are shown. These were compared, in
the remaining columns of the same table, with those estimated in this study: (a) directly
from (2.2) for ground types A and C; (b) from UH spectra (for ground types A and C)
computed at many different locations uniformly distributed in Italy;
1
(c) using the bi-
linear approximation discussed inSection2.5.
.
The corner period estimated from UH spectra on hard ground appears to be insensitive
tomagnitude(seealsoFigure2.16).Aspreviouslyindicated,thebi-linearapproximation
underestimates the corner periods, thus providing a conservative approximation to the
spectra at intermediate periods (see Section5.4).
5.3. OVERDAMPED, UNIFORM HAZARD (UH)
DRS
Overdamped UH spectra were calculated first directly through the attenuation relations
derivedfordampingratios0.10,0.20,and0.30.Then,spectrafordifferentlocationshave
