Earthquakes and Ground Motions - Earthquake Engineering for Structural Design - page 262

consideration of one or maximum two half-cycle pulses is a good value to be used
in seismic evaluation (Stewart et al, 2001).
7.5.3 Analytical Models for Velocity Pulses
To generate an analytical model for velocity pulses, one must specify the values of
several parameters which control the ground motion in the above-mentioned near-
source areas (peak ground velocity, pulse period and number of pulses). The
analytical models use the so-called wavelet analysis to extract the largest velocity
pulse from a given ground motion (Baker, 2007). The analytical expression of the
time variation of velocity must be established so that it fits the recorded variation
(Fig. 7.40) (Fu and Menun, 2002).
Some proposals for analytical model of wavelet are the following:
- Polygonal variation (Fig. 7.41a) is proposed by Alavi and Krawinkler (2000)
for symmetrical waves and by Mateescu and Gioncu (2000) for symmetrical and
asymmetrical waves;
- Sinusoidalvariation (Fig. 7.41b) (Sasani and Bertero, 2000);
- Polynomialvariation (Fig. 7.41c) (Gyorgyi et al, 2006);
- Four different trigonometrical functions for the four pulse types (Makris and
Chang, 1998, Agrawal and He, 2002, He and Agrawal, 2008);
- Five-parameter mathematical expression (Mavroeidis and Papageorgiou,
2002, Menun and Fu, 2002a,b, Fig. 7.42).
Some conclusions can be drawn from the comparison among those
representative analytical models. The polygonal and sinusoidal function are the
simplest, but much different from the earthquake motions. The polynomial
variation is constructed to be symmetrical with reference to the maximum velocity
pulse. The model adopted by Makris and Chang does not consider the alterable
amplitudes of velocities. The Mavroeidis and Papageorgiou (2002) and Menun and
Fu (2002 a,b) and Fu and Menun (2002) proposals may consider this variation of
pulse amplitudes.
Analytical
approximation
Recorded variation
Figure 7.40 Analytical and recorded velocities (after Fu and Menun, 2002)