Geology Reference
In-Depth Information
Figure 5. Sample near-fault ground motion; acceleration and velocity time histories
for the characteristics of A ( f ; M , r ) and e ( t ; M , r ). The
following procedure describes the final model:
coincides with the phase of the time history
generated in step 2.
6. Finally superimpose the time histories gener-
ated in steps 2 and step 5.
1. Generate the high-frequency component of
the acceleration time history by the stochastic
method.
2. Generate a velocity time history for the near-
field pulse using Equation 18. The pulse is
shifted in time to coincide with the peak of
the envelope e ( t ; M , r ). This defines the value
of the time shift parameter t o . Differentiate
the velocity time series to obtain an accel-
eration time series.
3. Calculate the Fourier transform of the ac-
celeration time histories generated in steps
1 and 2.
4. Subtract the Fourier amplitude of the time
series generated in step 2 from the spectrum
of the series generated in 1.
5. Construct a synthetic acceleration time his-
tory so that its Fourier amplitude is the one
calculated in step 4 and its Fourier phase
Figure 5 illustrate a near-fault ground motion
sample for an earthquake M =6.7, r =5km and pa-
rameters for the near-fault pulse γ p =1.7, ν p =π/6.
Both the acceleration and velocity time histories
of the synthetic ground-motion are presented. The
existence of the near-fault pulse is evident when
looking at the velocity time history.
STOCHASTIC ANALYSIS,
OPTIMIZATION, AND SENSITIVITY
Stochastic Analysis
Since the nonlinear models considered for the
bridge and the excitation are complex and include
a large number of uncertain model parameters the
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