Seismic Ground Motion - Dynamic Behavior of Concrete and Seismic Engineering - page 107

Its final value W f , is directly linked to the energy contained in the signal a(t). It
can also be connected to the spectral content using Parseval's relation (see above).
For this reason, Arias used it to define the “Arias intensity”, viz: I A = S/2g. W f .

This is also used to define a “high phase duration”, D (H 1 , H 2 ), given by:

D (İ , İ ) = T (İ )T İ )

12 2 1

where T(H i ) is defined by: W(T(H i )) = H i . W f .

If H 1 is nearly always chosen as equal to 5%, the values of H 2 are either 75%
(which involves quite short a duration) or 95% (which, on the contrary, leads to a
rather long duration).

Correlatively, as soon as duration has been determined, we can define an
“average quadratic acceleration”, a rms (H 1 , H 2 ) for this duration:

a İ , İ ) = İİ W/Dİ ,İ ª f º

¬ ¼

rms 1 2 2 1 1 2

Thus, once a duration has been defined, we can estimate time parameters owing
to the Fourier spectrum.

3.3.4. Caveats regarding differential motions

In addition to considering pure translation motions, the rapid space variations
shown by seismic motions should not be neglected either. These variations have
multiple origins, including the differences due to wave propagation, decorrelations
related to heterogenity or the complex wave field and local site effects.

Thus, the origin of spatial variability of seismic motions is multiple:

- whenever the angle of incidence is oblique (Tz 0°), their horizontal
propagation speed is finite and equal to c / sin T. From then on, at two sites separated
by a distance d (projected along the propagation direction), the signal (despite its
shape and amplitude being identical for both sites) will be delayed by W = d sin T/c.
The delay has to be compared with the predominant period of the signal T = 1/f and
can induce significant effects when the ratio W = d sin T/c exceeds a threshold of 0.1.
The “horizontal propagation” effect will become increasingly significant when the