r - The Hong Kong Polytechnic University

M original data
S scaled data with target at T=0.3 sec only
S scaled data with target at T=0.3 and 2.0 secs
S scaled data with target at T=0.3, 0.6, 1, 2 and 4 sec
target spectrum
Figure 21 The impact of the geomean scaling method for the θ and β of spectral acceleration
The records in Bin 1a were scaled with target values at a) T = 0.3 second only, b) T = 0.3 and 2 seconds, and c)
T = 0.3, 0.6, 1, 2 and 4 seconds. The median spectra for the original (or pre-scaled) motions and the three sets
of the amplitude-scaled motions were normalized to the target spectrum at a period of 0.3 second and presented
in Figure 21a. The dispersions β in the spectral acceleration for the four sets are presented in Figure 21b.
Some key observations are:
a. The shape of the median spectrum after geomean scaling of pairs of ground motions is independent of the
target spectral values and is identical to the shape of the pre-scaled median spectrum. If a UHS is used for
design where the period range of interest is broad (for example, if the structure has significant higher
mode effects that should be considered in the analysis) and different magnitude-distance pairs dominate
the UHS across the subject period range, it will be difficult to select a set of ground motions whose
median spectrum closely matches the target spectrum.
b. The dispersions in the spectral acceleration for the pre-scaled (seed) motions were reduced at periods
smaller than 3 seconds for all three sets of target spectral ordinates of Figure 21. Whether sufficient
dispersion is preserved by the geomean scaling method depends on the dispersion in the seismic hazard of
interest, which can be the dispersion in the spectral demand predicted by an attenuation relationship for a
magnitude-distance pair, or the epistemic or model uncertainty in the spectral acceleration at an annual
frequency of exceedance associated with a family of hazard curves. The geomean scaling method does not
guarantee that the dispersion preserved in the spectral ordinates is sufficient.
Figure 22 presents the 16th, 50th and 84th percentiles and β of peak displacement for the oscillators
introduced earlier and for Bin 1a. These statistical representations were computed using Eqs. (8) through (11)
except that y
i
is the peak displacement for a given oscillator subjected to the ith ground motion. The dashed
line in panels a, c and e of both figures identifies the yield displacement for each oscillator. The value of β for
the displacements shown in Figure 22 varies mainly between 0.3 and 0.7.
The studies for Methods 2 and 3 use the median spectrum of Figure 20a as the target spectrum to scale the
ground motions in Bin 1a but have different treatments for the dispersion preserved in the spectral ordinates of
Figure 20a. The results of response-history analysis presented in Figure 22 using the 50 motions in Bins 1a are
used to benchmark the results for Methods 2 and 3 to investigate the impact of scaling procedures on the
distribution of structural responses. In Figure 22, the periods presented in the X axes in panels a through d are
computed using the pre-yield stiffness and those in panels e and f are computed using the post-yield stiffness.
-385-