Civil Engineering Reference
In-Depth Information
the equations, which are a function of magnitude and distance only, are not presented. Since ductility-
equivalent damping, employed in direct deformation-based design, may be up to 30% for fi xed - base
structures, displacement spectra specifi c to such applications are required (Borzi
et al.
, 2001 ).
In order to derive attenuation relationships for the prediction of response spectra to use in deforma-
tion-based design, it is necessary to compile a data set of high-quality accelerograms for which the
associated source, path and site parameters are uniformly and accurately determined. It would be
preferable to employ recordings from digital accelerographs (Tolis and Faccioli, 1999 ). However, the
number of available digital accelerograms is relatively low and hence while these data may provide
more accurate values for the spectral ordinates, it would be diffi cult to fi nd correlations between these
ordinates and the parameters characterizing the earthquake source, travel path and recording site. The
data set presented by Ambraseys
et al.
(1996) consists of 422 triaxial accelerograms generated by
157 shallow earthquakes with surface magnitude
M
s
between 4.0 and 7.9 and is the basis for the
attenuation relationships discussed herein. In view of the fact that the study reported in Bommer and
Elnashai (1999) was concerned with the long-period response spectrum and that small- magnitude
earthquakes do not produce signifi cant long-period ground motion, it was decided to impose a higher
magnitude limit on the data set. The removal of weak- and low-amplitude records from the data set,
in order to obtain better signal-to-noise ratios, would not be acceptable since it would introduce a
statistical bias. However, the removal of all the earthquakes with magnitude below the chosen lower
limit of
M
s
= 5.5 does partially achieve this objective. Thus, the fi nal data set consisted of 183 accel-
erograms from 43 shallow earthquakes. For three of the recording stations, each of which contributed
only one record, the site classifi cation is unknown. For the remaining 180 accelerograms, the distribu-
tion among the three site classifi cations, i.e. rock, stiff soil and soft soil, is 25:51:24, which compares
favourably with the distribution of the original data set of Ambraseys
et al.
( 1996 ) which is 26:54:20.
Regression analyses were performed on the horizontal displacement spectral ordinates for damping
ratios of 5, 10, 15, 20, 25 and 30% of critical damping. The regression model used for
S
D
ordinates
(expressed in centimetres) was the same as that employed by Ambraseys
et al.
( 1996 ) for acceleration
spectral ordinates. At each period, the larger spectral ordinate from the two horizontal components
of each accelerogram was used as the dependent variable. Each component record was only used for
regressions up to a period of 0.1 second less than the long-period cut-off employed in processing that
record. As a result, for periods greater than 1.8 seconds, there was a reduction in the number of data
points available for each regression. At a response period of 3.0 seconds, the data set was reduced
from 183 to 121 accelerograms. It was decided not to perform the regressions for periods longer than
3.0 seconds since the number of usable spectral ordinates becomes insuffi cient. Regression analysis
was also performed on the larger values of peak ground displacement (in cm) from each record, using
the same attenuation model as above. Although it is not possible to make direct comparisons because
of the use of different defi nitions for the parameters, this regression predicts values of PGD very
similar to those presented by Bolt (1999) for the near- fi eld, but more rapid attenuation with distance
was observed.
From inspection of a large number of displacement response spectra for the six specifi ed damping
levels of 5, 10, 15, 20, 25 and 30%, it was concluded that a general, idealized format would be as shown
in Figure 3.12. The smoothed spectrum for each damping level comprises six straight-line segments
and is defi ned by four control periods along with their corresponding amplitudes. The amplitude cor-
responding to
T
E
is the peak ground displacement. Only that part of the spectrum up to periods of 3.0
seconds is considered because longer periods would require use of hitherto unavailable digital record-
ings of a suffi ciently large number. For displacement attenuation over longer periods, the reader is
referred to Tolis and Faccioli (1999), where the 1995 Kobe strong motion was used to derive longer-
period ordinates. The results of the work by Bommer and Elnashai (1999) are summarized in Tables
3.6 and 3.7 .
Inspection of the predicted spectral ordinates shows that the shape of the spectra is strongly infl uenced
by magnitude and site classifi cation, but far less so by distance. It was observed that the decrease of
