Optimal Design of Nonlinear Viscous Dampers for Protection of Isolated Bridges - Structural Seismic Design Optimization and Earthquake Engineering - page 391

istics of the excitation for base-isolated bridge.
All other excitation and structural parameters have
negligible importance in affecting seismic risk.
Only the gap sizes, contact stiffnesses, and live
loads from the trucks seem to have some, small,
significance.
The sensitivity pattern does change between
the no-damper and optimal-damper-configuration
cases. This is another important outcome of this
study; it shows that addition of the dampers not
only alters the seismic risk but also influences the
risk factors that contribute more to this risk. Since
addition of the dampers provides an overall reduc-
tion of seismic pounding occurrences (identified
from the results of Table 2) the characteristics
that have a stronger connection to this pound-
ing are impacted more. It is interesting that the
second most important model parameter for the
no-damper case, the pulse frequency, has small

only importance for the system with optimized
viscous dampers. This is an interesting outcome
and can be attributed to resonance characteristics;
the rigid type of connection to the abutments
introduced through the dampers influences the
vibration properties of the isolated-bridge and
thus alters the frequencies of the near fault-pulse
that have higher impact on it.
Sensitivity analysis results for individual com-
ponents of the total performance are presented in
Table 4. In particular the maximum pier shear V p ,
the maximum displacement for right abutment z r ,
and the maximum velocity for impact between the
left span and abutment v l are reported. Only the
interesting model parameters are included in this
table. For obtaining these results the risk occur-
rence measure in Equation 34 is substituted by the
fragility of the corresponding component. Since
this fragility has been already computed when

Table 4. Sensitivity analysis results for different response quantities

No Dampers Optimal Nonlinear Dampers

V z r v l V p z r v l

D m 0.227 0.701 0.494 1.179 0.672 2.740

D n M 0.48 0.404 0.551 0.144 0.071 0.125

r 0.30 0.251 0.214 0.372 0.540 0.245

e v 0.19 0.246 0.176 0.407 0.453 0.525

e f 0.15 0.042 0.080 0.034 0.155 0.053

γ 0.01 0.007 0.005 0.012 0.010 0.006

ν 0.03 0.001 0.007 0.004 0.008 0.021

A v 1.00 1.000 1.000 1.000 1.000 1.000

f p 0.81 0.646 0.919 0.039 0.022 0.070

m tl 0.031 0.007 0.010 0.004 0.009 0.003

m tr 0.073 0.023 0.016 0.012 0.011 0.005

k p 0.02 0.002 0.003 0.006 0.004 0.001

x ol 0.011 0.011 0.024 0.004 0.005 0.008

x or 0.012 0.016 0.028 0.002 0.006 0.018

x o 0.04 0.011 0.021 0.001 0.002 0.010

k cl 0.027 0.009 0.007 0.011 0.007 0.001

k cr 0.040 0.005 0.008 0.005 0.006 0.002

k c 0.09 0.004 0.006 0.005 0.010 0.003