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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
Ground Motion ParametersGround Motion Parameters
Amplitude parameters
Peak accelerationPeak velocityPeak displacementSustained maximum acceleration
3-cycle5-cycle
Ground Motion ParametersGround Motion Parameters
Amplitude parameters
Rocksite
Rocksite
Soilsite
Soilsite
Highest amax
Highest vmax
Fault Normal Fault Parallel
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
Frequency content parameters
Response spectrum
Ground Motion ParametersGround Motion Parameters
Examples fromProShake
Frequency content parameters
Spectral parameters
Predominant period
Bandwidth
Ground Motion ParametersGround Motion Parameters
Duration
Bracketed duration
Trifunac duration
Ground Motion ParametersGround Motion Parameters
+0.05g
-0.05g
5%
95%
Td
Td
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
Effects of source parameters on ground motions
Magnitude
Ground Motion ParametersGround Motion Parameters
Effects of source parameters on ground motions
Magnitude
Ground Motion ParametersGround Motion Parameters
Prediction
Predictive relationships (attenuation relationships)
Establish database
Select form of predictive equation
Perform regression analyses
Evaluate uncertainty
Ground Motion ParametersGround Motion Parameters
Prediction
Examples:
Ground Motion ParametersGround Motion Parameters
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
Prediction
Standard error - ln Y
Ground Motion ParametersGround Motion Parameters
log R
ln Y
M = M*
median +ln Y
median -ln Y
Prediction
Standard error
Ground Motion ParametersGround Motion Parameters
log R
ln Y
M = M*
R = R*
ln YY = Y*
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
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
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
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*]
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*]
Prediction
Common parameters
Peak acceleration
Spectral accelerations
Ground Motion ParametersGround Motion Parameters
T
Sa
0
amax
Prediction
Common parameters
Peak acceleration
Spectral accelerations
Ground Motion ParametersGround Motion Parameters
T
Sa
0
median
median +
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