Geology Reference
In-Depth Information
Box 7.
{
}
a
(
)
KN
(33)
Φ :
[ . ,
]
/
d
;
[ . ,
];
,
c
0 1 30
MN sec m
a
0 3 2
f
f
4000
di
di
dl
dr
Box 8.
ln(
V
)
ln(
µ
)
ln( )
z
ln(
µ
)
ln(
z
)
ln(
µ
)
1
6 Φ
+
+
p
p
h
( , )
ϕ θ =
[
Φ
Φ
l
z
r
z
g
β
g
β z
g
β
(34)
p
z
ln(
v
)
ln
(
µ
)
ln( )
v
ln(
µ
)
ln(
v
)
ln(
µ
) ]
+
+
+
Φ
o
v
Φ
l
v
Φ
r
v
g
g
g
β
β
β
v
v
v
Optimal Design
design configuration for both nonlinear and linear
damper implementation, the overall objective
function C ( φ ) as well as the expected fragility
for each of the components. The results illustrate
that the addition of the viscous dampers leads to
significant improvement of fragility of the bridge;
there is a big difference between the optimal
C ( φ *) and the uncontrolled performance C ( 0 ).
All six components contributing to the overall
fragility are characterized by a considerable
reduction, with the maximum pounding veloci-
ties having by far the largest one. This illustrates
that the viscous dampers can significantly reduce
the undesirable collisions between the different
spans, which can have devastating effects for the
serviceability of the bridge, while simultaneously
efficiently controlling other modes of failure for
the bridge, as the pier shear or the abutment dis-
placements. It should be also pointed out that the
optimal linear damper configuration provides still
a significant improvement over the uncontrolled
bridge performance. Implementation, though, of
nonlinear dampers provides a further reduction
in the seismic risk for the bridge, especially with
respect to the pier and abutment failure criteria.
The exponent coefficient for the dampers under
optimal design is 0.66, which corresponds to a
The bridge model, described by system of Equa-
tions 4, is created and analyzed in SIMULINK
(Klee, 2007). The computations are performed
for this study on the “Persephone” cluster at the
HIgh Performance system Analysis and Design
(HIPAD) laboratory at the University of Notre
Dame (www.nd.edu/~hipad). The cluster is com-
posed of 42 nodes, each having eight 2.56GHz
Nehalem cores. All stochastic simulations are
performed in parallel mode, taking advantage of
the multi-core capacities of the high-performance
computing cluster.
SPSA is used for the design optimization
with selection of N= 2000 for the estimate of
Equation 23 and importance sampling densities
established only for the moment magnitude, M ,
which is anticipated to be the most influential
parameter within the ones included in vector θ ,
based on results from previous studies on the risk
assessment of flexible structures under near-fault
excitations (Taflanidis & Jia, 2011). A truncated
in [6 8] Gaussian with mean 6.8 and standard
deviation 0.6 is selected for M .
Cumulative results from the optimization are
presented in Table 2 which includes the optimal
 
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