Ground Motion Parameters

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
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
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
PY gt Y MM, RR
ln Y
Y Y
ln Y
M M
R R
log R
20
Ground Motion Parameters
Prediction Standard error
ln Y
PY gt Y MM, RR
ln Y
Y Y
M M
R R
log R
21
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