Geology Reference
In-Depth Information
Box 3.
a
f
sgn
(
x
−
x
)
; if
if
c x
−
x
d
>
f
max
sl
al
d
sl
al
max
f
=
(16)
dl
a
d
a
c
sgn
(
x
−
x
)
x
−
x
;
c x
−
x
≤
f
d
d
sl
al
sl
al
max
d
sl
al
Box 4.
a
f
sgn
(
x
−
x
)
; if
if
c x
−
x
d
>
f
max
sr
ar
d
sr
ar
max
f
=
(17)
a
d
dr
a
c
sgn
(
x
−
x
)
x
−
x
;
c x
x
f
−
d
≤
d
sr
ar
sr
ar
d
sr
ar
max
have focused on the estimation of the spatial
variability of the seismic ground motions which
is a result of the transmission of the waves from
the source through the different earth strata to the
ground surface (Zerva, 2008). The latter effect
is considered to be very crucial in the design of
elongated structures such as long - span bridges.
An important factor of the spatial variability is
the site response effect (i.e. the difference at the
local soil conditions at two stations), especially
for structures situated in regions with rapidly
changing local soil conditions and for bridges with
short or medium length spans (Der Kiureghian,
1996). Moreover, other researchers have devel-
oped models that address the nonstationarity of the
ground motions by accounting the time variation
of both intensity and frequency content (Conte &
Peng, 1997; Rezaeian & Der Kiureghian, 2008).
An alternative tool for modeling uncertainty of
future earthquake loads is the critical excitation
method in which the ground motion is represented
as a product of a Fourier series and an envelope
function and in general involves estimating the
excitation producing the maximum response
from a class of allowable inputs (Abbas, 2011;
Takewaki, 2002).
For the proposed probabilistic framework, a
complete stochastic model for characterizing the
acceleration time-history of near-fault excitations
is required, that addresses all important sources of
uncertainty. Such a model was proposed recently in
(Taflanidis, Scruggs, & Beck, 2008) and is briefly
discussed next. According to it the high-frequency
and long-period components of the motion are
independently modeled and then combined to
form the acceleration time history. It is pointed
out that the spatial variation of the seismic input
is not been taken into account, because the bridge
systems we focus on are relatively short-spanned.
High - Frequency Component
The fairly general, point source stochastic
method (Boore, 2003) is selected for modeling
the higher-frequency (>0.1-0.2 Hz) component
of ground motions. This approach corresponds
to 'source - based' stochastic ground motion
models, developed by considering the physics
of the fault rupture at the source as well as the
propagation of seismic waves through the entire
ground medium till the structural site. It is based
on a parametric description of the ground motion's
radiation spectrum
A
(
f
;
M,r
), which is expressed as
a function of the frequency,
f
, for specific values
of the earthquake magnitude,
M
, and epicentral
distance,
r
. This spectrum consists of many factors
which account for the spectral effects from the
source (source spectrum) as well as propagation
through the earth's crust up to the structural site.
The duration of the ground motion is addressed
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