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Ground Motion Parameters

Ground Motion Parameters. Measured by triaxial accelerographs 2 orthogonal horizontal components 1 vertical component Digitized to time step of 0.005 - 0.01 sec For 60 sec record, N = 3 x 60 / 0.01 = 18,000 values Important characteristics Amplitude Frequency content Duration.

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Ground Motion Parameters

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  1. Ground Motion Parameters • Measured by triaxial accelerographs • 2 orthogonal horizontal components • 1 vertical component • Digitized to time step of 0.005 - 0.01 sec • For 60 sec record, • N = 3 x 60 / 0.01 = 18,000 values • Important characteristics • Amplitude • Frequency content • Duration

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

  3. Ground Motion Parameters Amplitude parameters Highest amax Fault Parallel Fault Normal Rock site Soil site Highest vmax

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

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

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

  7. +0.05g -0.05g Ground Motion Parameters • Duration • Bracketed duration • Trifunac duration Td 95% Td 5%

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

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

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

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

  12. Ground Motion Parameters • Prediction • Examples:

  13. 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

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

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

  16. 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

  17. 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

  18. 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

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

  20. 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

  21. Sa amax 0 T Ground Motion Parameters • Prediction • Common parameters • Peak acceleration • Spectral accelerations

  22. Ground Motion Parameters • Prediction • Common parameters • Peak acceleration • Spectral accelerations Sa median + s median 0 T

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