Civil Engineering Reference
In-Depth Information
The accumulation of energy in earthquake records can be computed as the integral of the square of
the ground acceleration, velocity or displacement. If the integral of the ground acceleration is employed
then the quantity is related to the Arias intensity,
AI
(Arias, 1970), given by the following:
2
t
r
∫
2
AI
=
a
()
t
d
t
(3.34)
g
0
where
a
(
t
) is the acceleration time history,
t
r
is the total duration of the accelerogram and g is the
acceleration due to gravity. Generally, the signifi cant duration is assumed equal to the build-up of the
Arias intensity between two arbitrary limits; this is referred to as a ' Husid plot ' (Husid, 1969 ).
All the aforementioned defi nitions can be based upon either absolute or relative criteria. For
example, the bracketed and uniform durations may be defi ned for a specifi ed absolute level of threshold
acceleration, or alternatively for a bound which is a fraction of the peak acceleration. By adopting
absolute criteria, the values of the acceleration thresholds
a
0
for bracketed and uniform durations
can vary between 0.05 g and 0.10 g (Bolt, 1973). Trifunac and Brady (1975) and Dobry
et al.
( 1978 )
assumed, as the absolute arbitrary limits in the defi nition of signifi cant duration, the interval between
the times at which 5% and 95% of the total integral of square of the acceleration is attained. Com-
prehensive studies by Somerville
et al.
(1997) have shown that more reliable estimates of earthquake
signifi cant durations can be derived by assuming the limits of 5% and 70% of the total Arias
intensity.
It is unwise to rely upon a single, universal defi nition for strong-motion duration, since different
defi nitions may be more or less appropriate in different situations. Furthermore, Bommer and Martinez-
Pereira ( 1999) demonstrated that all three defi nitions of strong-motion durations as given above are
fl awed in some instances. For example, the bracketed duration takes into consideration only the fi rst
and the last peaks that cross the specifi ed threshold, ignoring completely the characteristics of the strong
shaking phase. The latter can result in long durations being estimated for earthquakes with small sub-
events occurring after the main shock motion has passed. In addition, the defi nition can be rather
unstable if low thresholds of acceleration are employed and, for some accelerograms, a change of the
threshold, e.g. from 0.03 g to 0.02 g, can result in an increase of the bracketed duration by 20 seconds
or more. The former defi nition does not include a continuous time window during which the shaking
can be considered to be strong. On the other hand, the signifi cant duration considers the characteristics
of the entire accelerogram and defi nes a continuous time window in which the motion may be con-
sidered strong.
To investigate the differences between the defi nitions of strong-motion duration and their sensitivity
to threshold values, Bommer and Martinez-Pereira (1999) calculated the duration for the set of accel-
erograms summarized in Table 3.26. The sample horizontal components of earthquakes included very
strong, moderate and very weak motions, and multiple seismic events. The durations calculated using
a few representative examples of the different defi nitions are summarized in Table 3.27 .
The computed results show that both bracketed and uniform durations are very sensitive to accelera-
tion thresholds
a
0
; this is not the case for signifi cant durations. The uniform durations are characterized
by low values for high thresholds. Strong-motion records generated from multiple ruptures exhibit
unrealistic values of bracketed durations, especially if low values of
a
0
are employed. For example, for
the 23 November 1980 Irpinia (Italy) earthquake - a multiple seismic event - the bracketed durations
are as high as 40-50 seconds if relatively low threshold values of accelerations, e.g. 0.05 g, are used
and the second event is included in the strong shaking phase. When the threshold is raised from 0.05 g
to 0.10 g, the duration is reduced by almost 35 seconds, i.e. about 70-80% lower. To identify the limits
of the strong shaking sequence of the 1971 San Fernando earthquake (Table 3.26), relative criteria in
the defi nition of durations should be used. The bracketed durations based on absolute thresholds of
0.05 g and 0.10 g result in values of zero for this earthquake ground motion, whereas non-zero durations
are derived by adopting the defi nitions based on relative criteria.
