Geology Reference
In-Depth Information
variables with mean value 0.6 and coefficient of
variation 20%.
The time-history for future near-fault ground
motions is described by the excitation model pre-
sented earlier. The details for the functions A ( f ; M,r )
and e ( t ; M,r ) are the same as in (Taflanidis et al.,
2008). The uncertainty in moment magnitude for
seismic events, M , is modeled by the Gutenberg-
Richter relationship truncated to the interval [ M min ,
M max ]=[6, 8]. Smaller than M min earthquakes are
not expected to have significant impact on the
base isolated structure [and also do not frequently
contain a near-fault pulse component (Bray &
Rodriguez-Marek, 2004)] whereas it is assumed
that the regional faults cannot produce seismic
events with larger than 8 magnitude. This choice
leads to a truncated exponential PDF (Kramer,
2003):
moment magnitude and the epicentral distance,
also uncertain parameters, through the conditional
median values given by Equations 21 and 22.
The second set corresponds to a more abstract
representation but is independent of any other
model parameters. Throughout the discussion in
this paper both representations will be utilized,
according to convenience, but the risk integral
was actually formulated with respect to e f and e v .
The probability models for the rest of the pulse
model parameters, the number of half cycles and
phase, are chosen, respectively, as truncated in [1,
∞) Gaussian with mean value 2 and coefficient
of variation 15%, and uniform in the range [-π/2,
π/2]. These probability models are based on the
values reported in (Mavroeidis & Papageorgiou,
2003) when tuning the analytical relationship in
Equation 18 to a wide range of recorded near-fault
ground motions.
The uncertain model parameter vector in this
design problem consists of the bridge model pa-
rameters θ s =[ k p α p μ p δ yp ζ p k all k ar ζ all ζ ar m tl m tr x o , x ol
x or e cc e cl e cr k cc k cl k cr ] the seismological parameter
θ g =[ M r ], the additional parameters for the near-
fault pulse θ p =[ e v e f γ p v p ] (with the former two
related to A v and f p ) and the white-noise sequence,
Z w , so θ =[ θ s θ g θ p Z w ] T . Table 1 reviews these
parameters along with their probability models.
b
exp(
b M
)
p M
(
)
=
M
M
exp(
b M
)
exp(
b M
)
M
min
M
max
(32)
The selection for the regional seismicity fac-
tor is b Μ =0.9log e (10), corresponding to fairly
significant seismic activity. For the uncertainty
in the event location, the epicentral distance, r ,
for the earthquake events is assumed to be a log-
normal variable with median r m =10 km and large
coefficient of variation 50%. For the near-field
pulse, the pulse frequency f p and the peak ground
velocity A v are selected according to the probabi-
listic models for the characteristics of near-field
pulses in rock sites given earlier by Equations
19 and 20. This is equivalent to f p and A v being
log-normal variables with median value the ones
in Equations 21 and 22 and coefficient of varia-
tion 0.4 and 0.39, respectively. Note that either
f p and A v , or e f and e v can be used as the uncertain
parameters addressing the uncertainty in the pulse
frequency and ground velocity amplitude; the first
set corresponds to a representation with an unam-
biguous physical meaning but is correlated to the
Damper Configuration and
Performance Characteristics
Nonlinear viscous dampers are applied to the con-
nection of each of the two spans to its correspond-
ing abutment, as illustrated in Figures 1 and 3.
They are modeled by Equation 16 with maximum
force capability for each damper, representing cost
constraints (Taflanidis & Beck, 2009a), selected
as 4000 kN. Coefficients a d and c d correspond to
the design variables for the problem and for cost
reduction (bulk ordering) are chosen the same
for all dampers. The initial design space for each
of them is defined as a d
[0.3,2] and c d
[0.1, 30]
MN (sec/m) ad .
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