Geology Reference
In-Depth Information
Table 2. Optimization results; units for c d are MN (sec/m) ad
Case
φ*
C (φ*)
Probabilities of failure for individual components
V p
z l
z r
v o
v l
v r
Nonlinear
Damper
c d
9.7
0.029
0.047
0.034
0.055
0.006
0.0205
0.0093
a d
0.66
Linear Damper
c d
19.5
0.034
0.059
0.037
0.071
0.006
0.0208
0.0102
a d
1.00
No Damper
c d
0
0.256
0.284
0.179
0.247
0.253
0.332
0.244
a d
-
Table 3. Sensitivity analysis results (normalised entropy) for total risk
No dampers (maximum relative entropy D m =0.565)
M
r
e v
e f
γ
v
A v
f p
m tl
m tr
x ol
x or
x o
k cl
0.410
0.270
0.243
0.055
0.010
0.001
1.000
0.653
0.007
0.028
0.013
0.016
0.011
0.011
k cr
k c
e cl
e cr
e cc
k al
k ar
ζ al
ζ ar
ζ p
k p
A p
μ p
δ yp
0.007
0.006
0.005
0.004
0.002
0.003
0.002
0.003
0.003
0.001
0.003
0.005
0.004
0.005
Optimal nonlinear dampers (maximum relative entropy D m =1.08)
M
r
e v
e f
γ
v
A v
f p
m tl
m tr
x ol
x or
x o
k cl
0.089
0.402
0.491
0.086
0.012
0.009
1.000
0.016
0.009
0.026
0.003
0.004
0.002
0.005
k cr
k c
e cl
e cr
e cc
k al
k ar
ζ al
ζ ar
ζ p
k p
A p
μ p
δ yp
0.006
0.007
0.003
0.001
0.001
0.031
0.026
0.003
0.002
0.005
0.004
0.003
0.004
0.002
significant degree of nonlinearity. This illustrates
the importance of a design methodology that can
efficiently address damper nonlinearities, so that
a truly optimal design is identified.
The results in Table 3 illustrate that the pulse
amplitude A v is the most influential parameter in
affecting the overall seismic risk. The uncer-
tainty in the pulse amplitude, e v , the moment
magnitude, M , and the epicentral distance, r , have
also a significant impact. As pointed out earlier
A v is actually influenced by all three previous ones,
so the higher importance for it is anticipated.
Similar remark holds for f p , which is shown, though,
to have considerable influence in the seismic risk
only for the bridge without the dampers. Since
both A v and f p are directly related to the impact of
the near-fault pulse on the structure (amplitude
of pulse and unison conditions, respectively),
these results, especially the high importance of
A v and e v , indicate that seismic risk does indeed
have a big correlation to the near-fault character-
Stochastic Sensitivity Analysis
Results for the sensitivity analysis are finally
discussed. Table 3 includes the maximum relative
entropy D m and the normalised entropy for each
parameter for the uncontrolled or optimal damper
configuration. The normalised entropy, D n , is de-
fined by scaling the entropy for each parameter by
the maximum, over all parameters, entropy. This
is an explicit measure of the relative importance
of each parameter to the seismic risk, with values
closer to unity indicating higher importance.
 
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