ground motion parameters measured by triaxial accelerographs 2 orthogonal horizontal components 1...
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Ground Motion ParametersGround Motion Parameters
Measured by triaxial accelerographs2 orthogonal horizontal components1 vertical component
Digitized to time step of 0.005 - 0.01 secFor 60 sec record,
N = 3 x 60 / 0.01 = 18,000 values
Important characteristicsAmplitudeFrequency contentDuration
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Ground Motion ParametersGround Motion Parameters
Amplitude parameters
Peak accelerationPeak velocityPeak displacementSustained maximum acceleration
3-cycle5-cycle
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Ground Motion ParametersGround Motion Parameters
Amplitude parameters
Rocksite
Rocksite
Soilsite
Soilsite
Highest amax
Highest vmax
Fault Normal Fault Parallel
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Frequency content parameters
Fourier spectrum
Plot of cn vs n gives Fourier spectrum
cn
Ground Motion ParametersGround Motion Parameters
nnn
no tcctx
sin)(
1
n
Example fromProShake
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Frequency content parameters
Response spectrum
Ground Motion ParametersGround Motion Parameters
Examples fromProShake
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Frequency content parameters
Spectral parameters
Predominant period
Bandwidth
Ground Motion ParametersGround Motion Parameters
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Duration
Bracketed duration
Trifunac duration
Ground Motion ParametersGround Motion Parameters
+0.05g
-0.05g
5%
95%
Td
Td
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Other ground motion parameters
rms acceleration
Arias intensity
Spectral intensity
Ground Motion ParametersGround Motion Parameters
dttaT
aT
drms
d
0
2)]([1
dttag
I a
0
2)]([2
5.2
0),()( dTTPSVSI
All are influencedby amplitude,frequency content,and duration
All are influencedby amplitude,frequency content,and duration
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Effects of source parameters on ground motions
Magnitude
Ground Motion ParametersGround Motion Parameters
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Effects of source parameters on ground motions
Magnitude
Ground Motion ParametersGround Motion Parameters
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Prediction
Predictive relationships (attenuation relationships)
Establish database
Select form of predictive equation
Perform regression analyses
Evaluate uncertainty
Ground Motion ParametersGround Motion Parameters
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Prediction
Examples:
Ground Motion ParametersGround Motion Parameters
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Prediction
Standard error - ln Y
Ground Motion ParametersGround Motion Parameters
log R
ln Y
M = M*
R = R*
ln Y ln Yln Y
Accounts for uncertaintyin prediction of effects ofearthquake
Accounts for uncertaintyin prediction of effects ofearthquake
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Prediction
Standard error - ln Y
Ground Motion ParametersGround Motion Parameters
log R
ln Y
M = M*
median +ln Y
median -ln Y
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Prediction
Standard error
Ground Motion ParametersGround Motion Parameters
log R
ln Y
M = M*
R = R*
ln YY = Y*
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Prediction
Standard error
Ground Motion ParametersGround Motion Parameters
log R
ln Y
M = M*
R = R*
ln YY = Y*
Most ground motion parameters are lognormally distributed
Most ground motion parameters are lognormally distributed
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Lognormal distribution
Ground Motion ParametersGround Motion Parameters
x ln x
The logarithm of a lognormally distributed random variable is normally distributed
The logarithm of a lognormally distributed random variable is normally distributed
Median of ln x is equal to mean of ln x
Median of x is less than mean of x
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Standard normal distribution
Standard normal variate, z
Mean: z = 0
Standard deviation: z = 1
Ground Motion ParametersGround Motion Parameters
x
xXz
Values of probability distribution for z obtained from widely used tables
Values of probability distribution for z obtained from widely used tables
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Prediction
Standard error
Ground Motion ParametersGround Motion Parameters
log R
ln Y
M = M*
R = R*
ln YY = Y*
P[Y > Y*| M=M*, R=R*]
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Prediction
Standard error
Ground Motion ParametersGround Motion Parameters
log R
ln Y
M = M*
R = R*
ln YY = Y*
P[Y > Y*| M=M*, R=R*]
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Prediction
Common parameters
Peak acceleration
Spectral accelerations
Ground Motion ParametersGround Motion Parameters
T
Sa
0
amax
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Prediction
Common parameters
Peak acceleration
Spectral accelerations
Ground Motion ParametersGround Motion Parameters
T
Sa
0
median
median +