Ground Motion Parameters Measured by triaxial accelerographs 2

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

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

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

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

Ground Motion Parameters Frequency content parameters Response spectrum Examples from Pro. Shake

Ground Motion Parameters Frequency content parameters Spectral parameters Predominant period Bandwidth

Ground Motion Parameters Duration Bracketed duration +0. 05 g -0. 05 g Td Trifunac duration 95% Td 5%

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

Ground Motion Parameters Effects of source parameters on ground motions Magnitude

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

Ground Motion Parameters Prediction Examples:

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

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

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

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

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

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

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

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

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

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