Stochastic Simulation of Ground Motion Components for a Specified Design Scenario
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Transcript of Stochastic Simulation of Ground Motion Components for a Specified Design Scenario
![Page 1: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/1.jpg)
Sanaz RezaeianArmen Der Kiureghian (PI)University of California, Berkeley
Stochastic Simulation of Ground Motion Components for a Specified Design Scenario
Sponsor: State of California through Transportation Systems Research Program of Pacific Earthquake Engineering Research (PEER)
![Page 2: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/2.jpg)
Outline:
Motivation
Ground motion model
Extend to simulate multiple components
o Principal axes of ground motions
o High correlations between model parameters
Example
Conclusion
![Page 3: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/3.jpg)
In seismic hazard analysis, development of design ground motions is a crucial step.
High levels of intensityExpected structural behavior: NonlinearApproach: Response-history dynamic analysisRequires: Ground motion time-series
Motivation:
![Page 4: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/4.jpg)
In seismic hazard analysis, development of design ground motions is a crucial step.
High levels of intensityExpected structural behavior: NonlinearApproach: Response-history dynamic analysisRequires: Ground motion time-series
Difficulties come from scarcity of previously recorded motions. Controversies come from methods of selecting and modifying real records. Alternative: Use simulated time-series in conjunction or in the place of real records.
Motivation:
![Page 5: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/5.jpg)
In seismic hazard analysis, development of design ground motions is a crucial step.
High levels of intensityExpected structural behavior: NonlinearApproach: Response-history dynamic analysisRequires: Ground motion time-series
Our Goal: Earthquake and site characteristics Suite of simulated time-series(F, M, Rrup, Vs30)
Motivation:
F: Faulting mechanismM: Moment magnitude
…
R: Closest distance to ruptured area
VS30: Shear wave velocity of top 30mControlling Fault
Site
![Page 6: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/6.jpg)
In seismic hazard analysis, development of design ground motions is a crucial step.
High levels of intensityExpected structural behavior: NonlinearApproach: Response-history dynamic analysisRequires: Ground motion time-series
Our Goal: Earthquake and site characteristics Suite of simulated time-series(F, M, Rrup, Vs30)
For 2D/3D structural analysis, need ground motion components.
Motivation:
F: Faulting mechanismM: Moment magnitude
…
R: Closest distance to ruptured area
VS30: Shear wave velocity of top 30mControlling Fault
Site
![Page 7: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/7.jpg)
t
fdwth
tt,qtx
)()](,[
)(1
)()( λα
Ground Motion Model:
Linear filterwith
time-varyingparameters
Timemodulating
filter
High-passfilter
Unit-variance process with spectral non-stationarity
Normalizationby
standarddeviation
White-noise)(tw
Fully non-stationary process)(tx
Simulated ground acceleration)(tz
Filteredwhite-noise
[Rezaeian and Der Kiureghian, 2008]
![Page 8: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/8.jpg)
t
fdwth
tt,qtx
)()](,[
)(1
)()( λα
Ground Motion Model:
Linear filterwith
time-varyingparameters
Timemodulating
filter
High-passfilter
Unit-variance process with spectral non-stationarity
Normalizationby
standarddeviation
White-noise)(tw
Fully non-stationary process)(tx
Simulated ground acceleration)(tz
Filteredwhite-noise
[Rezaeian and Der Kiureghian, 2008]
Acceleration time-series
![Page 9: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/9.jpg)
Ground Motion Model:
Linear filterwith
time-varyingparameters
Timemodulating
filter
High-passfilter
Unit-variance process with spectral non-stationarity
Normalizationby
standarddeviation
White-noise)(tw
Fully non-stationary process)(tx
Simulated ground acceleration)(tz
Filteredwhite-noise
[Rezaeian and Der Kiureghian, 2008]
Temporal non-stationarity: Variation of intensity in time
Spectral non-stationarity: Variation of frequency content in time
t
fdwth
tt,qtx
)()](,[
)(1
)()( λα
![Page 10: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/10.jpg)
Ground Motion Model:
Linear filterwith
time-varyingparameters
Timemodulating
filter
High-passfilter
Unit-variance process with spectral non-stationarity
Normalizationby
standarddeviation
White-noise)(tw
Fully non-stationary process)(tx
Simulated ground acceleration)(tz
Filteredwhite-noise
[Rezaeian and Der Kiureghian, 2008]
Source of stochasticity
t
fdwth
tt,qtx
)()](,[
)(1
)()( λα
![Page 11: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/11.jpg)
t
fdwth
tt,qtx
)()](,[
)(1
)()( λα
Ground Motion Model:
Linear filterwith
time-varyingparameters
Timemodulating
filter
High-passfilter
Unit-variance process with spectral non-stationarity
Normalizationby
standarddeviation
White-noise)(tw
Fully non-stationary process)(tx
Simulated ground acceleration)(tz
Filteredwhite-noise
[Rezaeian and Der Kiureghian, 2008]
Impulse response function (IRF)corresponding to pseudo-acceleration response of a SDOF linear oscillator
![Page 12: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/12.jpg)
t
fdwth
tt,qtx
)()](,[
)(1
)()( λα
Ground Motion Model:
Linear filterwith
time-varyingparameters
Timemodulating
filter
High-passfilter
Unit-variance process with spectral non-stationarity
Normalizationby
standarddeviation
White-noise)(tw
Fully non-stationary process)(tx
Simulated ground acceleration)(tz
Filteredwhite-noise
[Rezaeian and Der Kiureghian, 2008]
Duhamel’s integral(superposition of filter responses to a sequence of statistically independent
pulses with the time of application τ)
![Page 13: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/13.jpg)
t
fdwth
tt,qtx
)()](,[
)(1
)()( λα
Ground Motion Model:
Linear filterwith
time-varyingparameters
Timemodulating
filter
High-passfilter
Unit-variance process with spectral non-stationarity
Normalizationby
standarddeviation
White-noise)(tw
Fully non-stationary process)(tx
Simulated ground acceleration)(tz
Filteredwhite-noise
[Rezaeian and Der Kiureghian, 2008]
![Page 14: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/14.jpg)
Ground Motion Model:
Linear filterwith
time-varyingparameters
Timemodulating
filter
High-passfilter
Unit-variance process with spectral non-stationarity
Normalizationby
standarddeviation
White-noise)(tw
Fully non-stationary process)(tx
Simulated ground acceleration)(tz
Filteredwhite-noise
[Rezaeian and Der Kiureghian, 2008]
t
fdwth
tt,qtx
)()](,[
)(1
)()( λα
![Page 15: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/15.jpg)
t
fdwth
tt,qtx
)()](,[
)(1
)()( λα
Ground Motion Model:
Linear filterwith
time-varyingparameters
Timemodulating
filter
High-passfilter
Unit-variance process with spectral non-stationarity
Normalizationby
standarddeviation
White-noise)(tw
Fully non-stationary process)(tx
Simulated ground acceleration)(tz
Filteredwhite-noise
[Rezaeian and Der Kiureghian, 2008]
0 time tn
![Page 16: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/16.jpg)
Ground Motion Model:
Linear filterwith
time-varyingparameters
Timemodulating
filter
High-passfilter
Unit-variance process with spectral non-stationarity
Normalizationby
standarddeviation
White-noise)(tw
Fully non-stationary process)(tx
Simulated ground acceleration)(tz
Filteredwhite-noise
[Rezaeian and Der Kiureghian, 2008]
Non-zero residuals!
Over estimates response spectrum at long periods!
t
fdwth
tt,qtx
)()](,[
)(1
)()( λα
![Page 17: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/17.jpg)
Ground Motion Model:
Linear filterwith
time-varyingparameters
Timemodulating
filter
High-passfilter
Unit-variance process with spectral non-stationarity
Normalizationby
standarddeviation
White-noise)(tw
Fully non-stationary process)(tx
Simulated ground acceleration)(tz
Filteredwhite-noise
[Rezaeian and Der Kiureghian, 2008]
Critically damped oscillator
)(2 2 txzzz cc
t
fdwth
tt,qtx
)()](,[
)(1
)()( λα
![Page 18: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/18.jpg)
Ground Motion Model:
Linear filterwith
time-varyingparameters
Timemodulating
filter
High-passfilter
Unit-variance process with spectral non-stationarity
Normalizationby
standarddeviation
White-noise)(tw
Fully non-stationary process)(tx
Simulated ground acceleration)(tz
Filteredwhite-noise
[Rezaeian and Der Kiureghian, 2008]
t
fdwth
tt,qtx
)()](,[
)(1
)()( λα
![Page 19: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/19.jpg)
t
fdwth
tt,qtx
)()](,[
)(1
)()( λα
Model Parameters:
![Page 20: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/20.jpg)
t
fdwth
tt,qtx
)()](,[
)(1
)()( λα
Model Parameters:
midω
'ω
: Frequency at the middle of strong shaking
: Damping ratio
: Rate of change of frequency over time
Modulating function parameters: Filter parameters:
midt
955D
: Time at the middle of strong shaking, at 45% Ia
: Effective duration, between 5% to 95% Ia
nta tt
gI
02 d))( (accel
2
: Arias intensity
![Page 21: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/21.jpg)
t
fdwth
tt,qtx
)()](,[
)(1
)()( λα
Model Parameters:
midω
'ω
: Frequency at the middle of strong shaking
: Damping ratio
: Rate of change of frequency over time
Modulating function parameters: Filter parameters:
midt
955D
: Time at the middle of strong shaking, at 45% Ia
: Effective duration, between 5% to 95% Ia
nta tt
gI
02 d))( (accel
2
: Arias intensity
![Page 22: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/22.jpg)
t
fdwth
tt,qtx
)()](,[
)(1
)()( λα
Model Parameters:
midω
'ω
: Frequency at the middle of strong shaking
: Damping ratio
: Rate of change of frequency over time
Modulating function parameters: Filter parameters:
midt
955D
: Time at the middle of strong shaking, at 45% Ia
: Effective duration, between 5% to 95% Ia
nta tt
gI
02 d))( (accel
2
: Arias intensity
Model parameters are identified for many recorded motions to develop predictive equations in terms of F, M, R, VS30
Match statistical
characteristicsRepresenting:• Intensity• Frequency• Bandwidth
Identify model parameters
ωmid, ω’ , ζIa, tmid, D5-95
Recorded0 40-0.25
0
0.15
Time, secAcc
eler
atio
n, g
![Page 23: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/23.jpg)
Two Horizontal Components:
Component 1:
Component 2:
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 1111 λα
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 2222 λα
![Page 24: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/24.jpg)
Two Horizontal Components:
Component 1:
Component 2:
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 1111 λα
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 2222 λα
source of stochasticity
w1(τ) and w2(τ) are statistically independent if along the principal axes.
![Page 25: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/25.jpg)
Two Horizontal Components:
Component 1:
Component 2:
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 1111 λα
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 2222 λα
source of stochasticity
w1(τ) and w2(τ) are statistically independent if along the principal axes.
Principal Axes of Ground Motion:A set of orthogonal axes along which the components are uncorrelated.
Expected Epicenter
Site
Horizontal Plane
Major
Intermediate
Minor
Penzien and Watabe (1975)
![Page 26: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/26.jpg)
Two Horizontal Components:
Component 1:
Component 2:
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 1111 λα
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 2222 λα
source of stochasticity
w1(τ) and w2(τ) are statistically independent if along the principal axes.
Principal Axes of Ground Motion:A set of orthogonal axes along which the components are uncorrelated.
Rotate recorded motions in the database.
SiteHorizontal Plane
θa2,θ
a1,θ
a2
a1
ρ a1 , a2 ≠ 0ρ a1,θ , a2,θ = 0
![Page 27: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/27.jpg)
Rotating Recorded Motions: Northridge earthquake recorded at Mt. Wilson Station
Time, s
Acc
eler
atio
n, g
As-RecordedComponent 1
0 5 10 15 20 25 30 35 40
As-RecordedComponent 2
Time, s
PrincipalComponent 1
PrincipalComponent 2
-0.2-0.1
00.10.20.3
0 5 10 15 20 25 30 35 40
Cor
rela
tion
Coe
ffici
ent
Bet
wee
n Th
e Tw
oC
ompo
nent
s
Rotation Angle, degrees
(0,-0.42)
(55,0)
0 10 20 30 40 50 60 70 80 90
-0.5
0
0.5
-0.3
-0.2-0.1
00.10.20.3
-0.3
-0.2-0.1
00.10.20.3
-0.3
-0.2-0.1
00.10.20.3
-0.3
![Page 28: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/28.jpg)
Two Horizontal Components:
Component 1:
Component 2:
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 1111 λα
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 2222 λα
![Page 29: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/29.jpg)
Two Horizontal Components:
Component 1:
Component 2:
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 1111 λα
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 2222 λα
Predictive equations:
εηβββββpFp m/s 750
Vln
km 25
Rln
7.0M
)F( )]([ s304
rup3210
-1
εηβββββpFp m/s 750
V
km 25
R
0.7M
)F( )]([ s304
rup3210
1
fmidmid- ζ,ω',ω,t,Dp 955 if
if ,intmaj, , aa IIp
![Page 30: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/30.jpg)
Two Horizontal Components:
Component 1:
Component 2:
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 1111 λα
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 2222 λα
Predictive equations:
εηβββββpFp m/s 750
Vln
km 25
Rln
7.0M
)F( )]([ s304
rup3210
-1
εηβββββpFp m/s 750
V
km 25
R
0.7M
)F( )]([ s304
rup3210
1
fmidmid- ζ,ω',ω,t,Dp 955 if
if ,intmaj, , aa IIp
Model parameter p transformed to the
standard normal space
![Page 31: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/31.jpg)
Two Horizontal Components:
Component 1:
Component 2:
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 1111 λα
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 2222 λα
Predictive equations:
εηβββββpFp m/s 750
Vln
km 25
Rln
7.0M
)F( )]([ s304
rup3210
-1
εηβββββpFp m/s 750
V
km 25
R
0.7M
)F( )]([ s304
rup3210
1
fmidmid- ζ,ω',ω,t,Dp 955 if
if ,intmaj, , aa IIp
Independent normally-distributed
errors
Predicted meanconditioned on
earthquake and site characteristics
![Page 32: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/32.jpg)
Two Horizontal Components:
Component 1:
Component 2:
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 1111 λα
t
hdττwτ,th
tσt,qtx )()]([
)(1
)()( 2222 λα
Predictive equations.
High correlations expected between parameters of the two components.
![Page 33: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/33.jpg)
1 −0.38 −0.04 −0.21 −0.25 −0.06 +0.92 −0.30 −0.03 −0.13 +0.09 +0.02
1 +0.68 −0.07 −0.21 −0.26 −0.31 +0.89 +0.68 −0.17 −0.11 −0.17
1 −0.24 −0.22 −0.26 +0.04 +0.65 +0.96 −0.30 −0.24 −0.21
1 −0.19 +0.28 −0.13 −0.15 −0.29 +0.94 −0.10 +0.29
1 −0.06 +0.19 −0.21 −0.22 −0.10 +0.52 −0.13
1 −0.01 −0.23 −0.29 +0.32 −0.02 +0.75
1 −0.31 +0.01 −0.08 +0.07 −0.005
1 +0.69 −0.20 −0.18 −0.17
1 −0.34 −0.24 −0.22
1 −0.19 +0.28
1 −0.05
1
tf,aI
Symmetric
tf,955D tf,midt tf,midω tfω' tfζ
tf,aI
tf,955D tf,midt
tf,midω
tfω'
tfζ
Correlation Matrix:
tf,aI tf,955D tf,midt tf,midω tfω' tfζ
tf,aI
tf,955D tf,midt
tf,midω
tfω'
tfζ
Major Component (larger Arias intensity) Intermediate Component (smaller Arias intensity)
Intermediate C
omponent
Major C
omponent
Two Horizontal Components:
![Page 34: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/34.jpg)
1 −0.38 −0.04 −0.21 −0.25 −0.06 +0.92 −0.30 −0.03 −0.13 +0.09 +0.02
1 +0.68 −0.07 −0.21 −0.26 −0.31 +0.89 +0.68 −0.17 −0.11 −0.17
1 −0.24 −0.22 −0.26 +0.04 +0.65 +0.96 −0.30 −0.24 −0.21
1 −0.19 +0.28 −0.13 −0.15 −0.29 +0.94 −0.10 +0.29
1 −0.06 +0.19 −0.21 −0.22 −0.10 +0.52 −0.13
1 −0.01 −0.23 −0.29 +0.32 −0.02 +0.75
1 −0.31 +0.01 −0.08 +0.07 −0.005
1 +0.69 −0.20 −0.18 −0.17
1 −0.34 −0.24 −0.22
1 −0.19 +0.28
1 −0.05
1
tf,aI
Symmetric
tf,955D tf,midt tf,midω tfω' tfζ
tf,aI
tf,955D tf,midt
tf,midω
tfω'
tfζ
Correlation Matrix:
tf,aI tf,955D tf,midt tf,midω tfω' tfζ
tf,aI
tf,955D tf,midt
tf,midω
tfω'
tfζ
Major Component (larger Arias intensity) Intermediate Component (smaller Arias intensity)
Intermediate C
omponent
Major C
omponent
Two Horizontal Components:
![Page 35: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/35.jpg)
1 −0.38 −0.04 −0.21 −0.25 −0.06 +0.92 −0.30 −0.03 −0.13 +0.09 +0.02
1 +0.68 −0.07 −0.21 −0.26 −0.31 +0.89 +0.68 −0.17 −0.11 −0.17
1 −0.24 −0.22 −0.26 +0.04 +0.65 +0.96 −0.30 −0.24 −0.21
1 −0.19 +0.28 −0.13 −0.15 −0.29 +0.94 −0.10 +0.29
1 −0.06 +0.19 −0.21 −0.22 −0.10 +0.52 −0.13
1 −0.01 −0.23 −0.29 +0.32 −0.02 +0.75
1 −0.31 +0.01 −0.08 +0.07 −0.005
1 +0.69 −0.20 −0.18 −0.17
1 −0.34 −0.24 −0.22
1 −0.19 +0.28
1 −0.05
1
tf,aI
Symmetric
tf,955D tf,midt tf,midω tfω' tfζ
tf,aI
tf,955D tf,midt
tf,midω
tfω'
tfζ
Correlation Matrix:
tf,aI tf,955D tf,midt tf,midω tfω' tfζ
tf,aI
tf,955D tf,midt
tf,midω
tfω'
tfζ
Major Component (larger Arias intensity) Intermediate Component (smaller Arias intensity)
Intermediate C
omponent
Major C
omponent
Two Horizontal Components:
![Page 36: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/36.jpg)
1 −0.38 −0.04 −0.21 −0.25 −0.06 +0.92 −0.30 −0.03 −0.13 +0.09 +0.02
1 +0.68 −0.07 −0.21 −0.26 −0.31 +0.89 +0.68 −0.17 −0.11 −0.17
1 −0.24 −0.22 −0.26 +0.04 +0.65 +0.96 −0.30 −0.24 −0.21
1 −0.19 +0.28 −0.13 −0.15 −0.29 +0.94 −0.10 +0.29
1 −0.06 +0.19 −0.21 −0.22 −0.10 +0.52 −0.13
1 −0.01 −0.23 −0.29 +0.32 −0.02 +0.75
1 −0.31 +0.01 −0.08 +0.07 −0.005
1 +0.69 −0.20 −0.18 −0.17
1 −0.34 −0.24 −0.22
1 −0.19 +0.28
1 −0.05
1
tf,aI
Symmetric
tf,955D tf,midt tf,midω tfω' tfζ
tf,aI
tf,955D tf,midt
tf,midω
tfω'
tfζ
Correlation Matrix:
tf,aI tf,955D tf,midt tf,midω tfω' tfζ
tf,aI
tf,955D tf,midt
tf,midω
tfω'
tfζ
Major Component (larger Arias intensity) Intermediate Component (smaller Arias intensity)
Intermediate C
omponent
Major C
omponent
Two Horizontal Components:
![Page 37: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/37.jpg)
F = 1 (Reverse) , M = 7.35 , R =14 km , VS30 = 660 m/s Design scenario:
Example:
![Page 38: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/38.jpg)
F = 1 (Reverse) , M = 7.35 , R =14 km , VS30 = 660 m/s Design scenario:
Example:
Ia
s.g
D5-95
s
tmid
s
ωmid/(2π)
Hz
ω’/(2π)
Hz/s ζf
Recorded 0.0165 16.7 18.3 3.9 –0.08 0.12
Simulated 0.0147 17.3 10.1 8.1 –0.12 0.420.0099 27.2 17.1 3.2 –0.03 0.20
Ia
s.g
D5-95
s
tmid
s
ωmid/(2π)
Hz
ω’/(2π)
Hz/s ζf
0.0135 17.0 17.8 4.1 –0.02 0.110.0047 21.0 10.7 8.6 –0.18 0.500.0034 24.8 16.9 3.7 –0.13 0.35
Major Component Intermediate Component
![Page 39: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/39.jpg)
F = 1 (Reverse) , M = 7.35 , R =14 km , VS30 = 660 m/s Design scenario:
Example:
Ia
s.g
D5-95
s
tmid
s
ωmid/(2π)
Hz
ω’/(2π)
Hz/s ζf
Recorded 0.0165 16.7 18.3 3.9 –0.08 0.12
Simulated 0.0147 17.3 10.1 8.1 –0.12 0.420.0099 27.2 17.1 3.2 –0.03 0.20
Ia
s.g
D5-95
s
tmid
s
ωmid/(2π)
Hz
ω’/(2π)
Hz/s ζf
0.0135 17.0 17.8 4.1 –0.02 0.110.0047 21.0 10.7 8.6 –0.18 0.500.0034 24.8 16.9 3.7 –0.13 0.35
Major Component Intermediate Component
-0.1
0
0.1Simulated
-0.05
0
0.05Simulated
-0.1
0
0.1Recorded
Simulated
Simulated
Recorded
Acc
eler
atio
n, g
0 20 40 60 80 0 20 40 60 80Time, s Time, s
![Page 40: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/40.jpg)
F = 1 (Reverse) , M = 7.35 , R =14 km , VS30 = 660 m/s Design scenario:
Example:
Ia
s.g
D5-95
s
tmid
s
ωmid/(2π)
Hz
ω’/(2π)
Hz/s ζf
Recorded 0.0165 16.7 18.3 3.9 –0.08 0.12
Simulated 0.0147 17.3 10.1 8.1 –0.12 0.420.0099 27.2 17.1 3.2 –0.03 0.20
Ia
s.g
D5-95
s
tmid
s
ωmid/(2π)
Hz
ω’/(2π)
Hz/s ζf
0.0135 17.0 17.8 4.1 –0.02 0.110.0047 21.0 10.7 8.6 –0.18 0.500.0034 24.8 16.9 3.7 –0.13 0.35
Major Component Intermediate Component
-0.01
0
0.01
-0.05
0
0.05
-0.05
0
0.05
Simulated
Simulated
Recorded
Simulated
Simulated
Recorded
Velo
city
, m/s
0 20 40 60 80 0 20 40 60 80Time, s Time, s
![Page 41: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/41.jpg)
F = 1 (Reverse) , M = 7.35 , R =14 km , VS30 = 660 m/s Design scenario:
Example:
Ia
s.g
D5-95
s
tmid
s
ωmid/(2π)
Hz
ω’/(2π)
Hz/s ζf
Recorded 0.0165 16.7 18.3 3.9 –0.08 0.12
Simulated 0.0147 17.3 10.1 8.1 –0.12 0.420.0099 27.2 17.1 3.2 –0.03 0.20
Ia
s.g
D5-95
s
tmid
s
ωmid/(2π)
Hz
ω’/(2π)
Hz/s ζf
0.0135 17.0 17.8 4.1 –0.02 0.110.0047 21.0 10.7 8.6 –0.18 0.500.0034 24.8 16.9 3.7 –0.13 0.35
Major Component Intermediate Component
-0.02
0
0.02
-0.05
0
0.05
0 20 40 60 80-0.05
0
0.05
0 20 40 60 80
Simulated
Simulated
Recorded
Simulated
Simulated
Recorded
Dis
plac
emen
t, m
Time, s Time, s
![Page 42: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/42.jpg)
Conclusion:
Developed a stochastic model for earthquake ground motion components
Created a database of principal ground motion components
Identified model parameters for the records in the database predictive equations for model parameters in terms of F , M , R , VS30
Identified correlation coefficients between model parameters of the components
For given F , M , R , VS30 , correlated model parameters are randomly simulated and used along with statistically independent white-noise processes to generate a pair of horizontal ground motion components in the directions of principal axes.
The proposed methods can be easily extended to simulate the vertical component.
![Page 43: Stochastic Simulation of Ground Motion Components for a Specified Design Scenario](https://reader035.fdocuments.in/reader035/viewer/2022062811/56815f3e550346895dce1339/html5/thumbnails/43.jpg)
Rezaeian S, Der Kiureghian A. "A stochastic ground motion model with separable temporal and spectral nonstationarities”, Earthquake Engineering and Structural Dynamics, 2008, Vol. 37, pp. 1565-1584.
Rezaeian S, Der Kiureghian A. "Simulation of synthetic ground motions for specified earthquake and site characteristics”, Earthquake Engineering and Structural Dynamics, 2010, Vol. 39, pp. 1155-1180.
Related Publications:
Rezaeian S, Der Kiureghian A. "Simulation of orthogonal horizontal ground motion components for specified earthquake and site characteristics”, Submitted to Earthquake Engineering and Structural Dynamics.
1.
2.
3.
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44
Thank YouThis project was made possible with support from:
State of California through Transportation Systems Research Program of Pacific Earthquake Engineering Research Center (PEER TSRP).
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Small number of parameters that have physical meaning and can be easily identified by matching with features of a given accelerogram
Completely separable temporal and spectral nonstationary characteristics, which facilitates identification and interpretation of the parameters
No need for sophisticated processing of the target accelerogram, e.g. Fourier analysis or estimation of evolutionary PSD
Simple simulation of sample functions, requiring little more than generation of standard normal random variables
Ground Motion Model: Advantages
k
iii utstqtx
1
)()()(ˆ
,...,nititwhere i 0 1 kk tttfor
)1,0(~ N iuwhere
Form of the model facilitates nonlinear random vibration analysis (e.g., by using TELM).
Extra