1. Ground-Motion Parameters
CEE 431/ESS465

2. Ground Motion Parameters
Measured by triaxial accelerographs
2 orthogonal horizontal components
1 vertical component
Digitized to time step of sec
For 60 sec record,
N = 3 x 60 / = 18,000 values
Important Characteristics
Amplitude
Frequency content
Duration

3. Ground Motion Parameters
Amplitude Parameters
Peak acceleration
Peak velocity
Peak displacement
Sustained maximum acceleration
-3-cycle
-5-cycle

4. Ground Motion Parameters
Amplitude parameters
Highest amax
Rock
site
Soil
site
Highest vmax

5. Ground Motion Parameters
Frequency content parameters
Fourier spectrum
Plot of cn vs wn gives Fourier spectrum cn
Example from
ProShake wn

6. Ground Motion Parameters
Frequency content parameters
Response spectrum
Examples from
ProShake

7. Ground Motion Parameters
Frequency content parameters
Spectral parameters
Predominant period
Bandwidth

8. Ground Motion Parameters
Duration
Bracketed duration
Trifunac duration
+0.05g
-0.05g Td
95% Td 5%

9. Ground Motion Parameters
Other ground motion parameters
rms acceleration
Arias intensity
Spectral intensity
All are influenced
by amplitude,
frequency content,
and duration

10. Ground Motion Parameters
Effects of source parameters on ground motions
Magnitude

11. Ground Motion Parameters
Effects of source parameters on ground motions
Magnitude

12. Ground Motion Parameters
Prediction
Predictive relationships (attenuation relationships)
Establish database
Select form of predictive equation
Perform regression analyses
Evaluate uncertainty

13. Ground Motion Parameters
Prediction
Examples:

14. Ground Motion Parameters
Prediction
Standard error - sln Y
Accounts for uncertainty
in prediction of effects of
earthquake
ln Y
sln Y
ln Y
sln Y
M = M*
R = R*
log R

15. Ground Motion Parameters
Prediction
Standard error - sln Y
log R
ln Y
M = M*
median + sln Y
median - sln Y

16. Ground Motion Parameters
Prediction
Standard error
ln Y
Y = Y*
ln Y
M = M*
R = R*
log R

17. Ground Motion Parameters
Prediction
Standard error
Most ground motion parameters are lognormally distributed
ln Y
Y = Y*
ln Y
M = M*
R = R*
log R

18. Ground Motion Parameters
Lognormal distribution
Median of x is less than mean of x
Median of ln x is equal to mean of ln x x
ln x
The logarithm of a lognormally distributed random variable is normally distributed

19. Ground Motion Parameters
Standard normal distribution
Standard normal variate, z
Mean: z = 0
Standard deviation: sz = 1
Values of probability distribution for z obtained from widely used tables

20. Ground Motion Parameters
Prediction
Standard error
ln Y
P[Y > Y*| M=M*, R=R*]
Y = Y*
ln Y
M = M*
R = R*
log R

21. Ground Motion Parameters
Prediction
Standard error
ln Y
P[Y > Y*| M=M*, R=R*]
ln Y
Y = Y*
M = M*
R = R*
log R

22. Ground Motion Parameters
Prediction
Common parameters
Peak acceleration
Spectral accelerations T Sa
amax

23. Ground Motion Parameters
Prediction
Common parameters
Peak acceleration
Spectral accelerations Sa
median + s
median T