Simulation of Synthetic Ground Motionsfor Specified Earthquake and Site Characteristics

7/27/2019 Simulation of Synthetic Ground Motionsfor Specified Earthquake and Site Characteristics

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Sanaz Rezaeian (Doctoral Candidate)

Armen Der Kiureghian (PI)

University of California, Berkeley

Simulation of Synthetic Ground Motions

for

Specified Earthquake and Site Characteristics

Sponsor: State of California through Transportation Systems Research Program of

Pacific Earthquake Engineering Research (PEER) Center


2/26

Our Goal: Earthquake and site characteristics Suite of simulated design time-histories

(F, M, Rrup, Vs30 ,)

Objective:

F: Faulting mechanismM: Moment magnitude

Rrup: Closest distance to ruptured area

Vs30: Shear wave velocity of top 30mControlling Fault

Site

What we have done so far:

Developed a stochastic site-based model for far-field strong ground motions. Developed empirical predictive equations for the model parameters. Compared elastic response spectra (median and variability) to NGA relations.Ongoing activity and what we plan to accomplish by May 2010:

Simulate orthogonal horizontal ground motion components. Extend the model to near-field ground motions. Scrutinize the simulated motions for inelastic structural responses.


3/26

Ground Motion Model:

0 5 10 15 200

Acceleration

High-pass Filtering

0 5 10 15 200

Time, sec

Unit-variance process

Controls spectral nonstationarity

0 5 10 15 200

Time, sec

Time modulating function

Controls temporal nonstationarity

0 5 10 15 200

Time, sec


4/26

Ground Motion Model Parameters:

t0 tn

Let:

0 tn

0 tn

: Arias intensity

: Time at the middle of strong shaking

: Effective duration


5/26

Ground Motion Model Parameters:

t0 tn

Let:

0 tn

0 tn

: Time at the middle of strong shaking

: Effective duration

If the model parameters are given, time-histories can be simulated.

: Arias intensity


6/26

Simulate a suite of ground motions for a given design scenario:

Simulate a given accelerogram:Applications in Practice:

GivenEarthquake/Site characteristics

(design scenario)

Generateseveral possible sets of

model parameters

Simulations0 5 10 15 20 25 30 35 40 45 50

-0.1

0

0.1

-0.1

0

0.1

0.1

-0.1

0

modelformulation

F, M, Rrup, Vs30

predictiveequations

Ia, tmid, D5-95

mid, ,

Matchstatistical

characteristicsRepresenting:

IntensityFrequencyBandwidth

Identifymodel parameters

mid, ,

Ia, tmid, D5-95Recorded0 40

-0.25

0

0.15

Time, secAcceleration,g

modelformulation

Simulations

-0.25

0

0.15

0-0.25

0

0.15

-0.25

0

0.15

40


7/26

Simulate a suite of ground motions for a given design scenario:

Simulate a given accelerogram:Applications in Practice:

GivenEarthquake/Site characteristics

(design scenario)

Generateseveral possible sets of

model parameters

Simulations0 5 10 15 20 25 30 35 40 45 50

-0.1

0

0.1

-0.1

0

0.1

0.1

-0.1

0

modelformulation

F, M, Rrup, Vs30

predictiveequations

Ia, tmid, D5-95Regression

Predictor variables

Response variables

Done for many records to get observational datafor predictor and response variables

mid, ,

Matchstatistical

characteristicsRepresenting:

IntensityFrequencyBandwidth

Identifymodel parameters

mid, ,

Ia, tmid, D5-95Recorded0 40

-0.25

0

0.15

Time, secAcceleration,g

modelformulation

Simulations

-0.25

0

0.15

0-0.25

0

0.15

-0.25

0

0.15

40


8/26

Ground Motion Database (far-field):

Earthquake #ofrecords

1 ImperialValley 22 Victoria,Mexico 2

3 Morganhill 10

4 Landers 4

5 BigBear 10

6 Kobe,Japan 4

7 Kocaeli,Turkey 4

8 Duzce,Turkey 29 Sitka,Alaska 2

10 Manjil,Iran 2

11 HectorMine 16

12 Denali,Alaska 4

13 SanFernando 14

14 Tabas,Iran 215 Coalinga 2

16 NPalmSprings 12

17 LomaPrieta 28

18 Northridge 38

19 ChiChi,Taiwan 48

Strike-slip

Reverse Momen

tMagnitude

Rrup , km

10 20 30 40 50 60 70 80 90 100

8.0

7.5

7.0

6.5

6.0

Strike-slipReverse

Vs30 > 600 m/sec

Two horizontal components

Shallow crustal earthquakes in

tectonically active regions

Total: 206Accelerograms


9/26

Predictive Equations (Regression):

Independent

Normally-distributed

errors

Observed DataFitted PDF

NormalizedFrequency(Total:206)

5 10 15 20 25 30 35 40 450

0.02

0.04

0.06

-2 -1.5 -1 -0.5 0 0.50

1

2

3

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

1

2

3

4

0 5 10 15 20 250

0.04

0.08

0.12

0.16

0 5 10 15 20 25 30 35 400

0.02

0.04

0.06

0.08

ln(Ia, sec.g) D5-95, sec

tmid, sec

'/(2), Hz/sec mid/(2), Hz

-7.5 -5.5 -3.5 -1.5 00

0.1

0.2

0.3

0.4Normal Beta Beta

Gamma Two-SidedExponential

Beta

Distributions assigned to the model parameters:

Regression model (for jth earthquake and kth record of that earthquake):

Predicted mean

conditioned on

earthquake and site characteristics

Model parameter

transformed to the

standard normal space


10/26

Standard deviation of

1.844 0.071 2.944 1.356 0.265 0.27 0.59 0.65

6.195 0.703 6.792 0.219 0.523 0.46 0.57 0.73

5.011 0.345 4.638 0.348 0.185 0.51 0.41 0.66

2.253 0.081 1.810 0.211 0.012 0.69 0.72 1.00

2.489 0.044 2.408 0.065 0.081 0.13 0.95 0.96

0.258 0.477 0.905 0.289 0.316 0.68 0.76 1.02

Regression Results (Predictive Equations):

if

if

Maximum Likelihood Estimation:

Formulation:


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Regression Results (Correlations):

1 0.36 0.01 0.15 0.13 0.01

1 0.67 0.13 0.16 0.20

1 0.28 0.20 0.22

1 0.20 0.28

1 0.01

1

Transformed model parameters:

Symmetric

(given the earthquake and site characteristics)


12/26

F = 1 (Reverse)M = 7.35

Rrup =14 km

VS30 = 660 m/sec

Example 1 : Acceleration

4 simulated motions and 1 real recording for the given design scenario:

Acceleration,g

Time, sec

0 5 10 15 20 25 30 35

-0.2

0

0.2

0 5 10 15 20 25 30 35-0.2

0

0.2

0 5 10 15 20 25 30 35-0.1

0

0.1

0 5 10 15 20 25 30 35-0.1

0

0.1

0 5 10 15 20 25 30 35

-0.1

0

0.1

Simulated

Recorded

Simulated

Simulated

Simulated

Realizaonsofmodelparameters:

0.01217.236.276.880.010.14

0.14512.306.785.900.120.26

0.05514.227.224.480.160.38

0.01414.076.3110.750.240.26

0.03614.878.324.360.150.03

Iasec.g

D5-95sec

tmidsec

/(2)

Hz/secmid/(2)

Hz

(1978 Tabas at Dayhook)


13/26

F = 1 (Reverse)M = 7.35

Rrup =14 km

VS30 = 660 m/sec


Velocity,m/sec

Time, sec

0 5 10 15 20 25 30 35

-0.2

0

0.2

0 5 10 15 20 25 30 35-0.2

0

0.2

0 5 10 15 20 25 30 35-0.05

0

0.05

0 5 10 15 20 25 30 35-0.1

0

0.1

0 5 10 15 20 25 30 35-0.1

0

0.1

Example 1 : Velocity

Simulated

Recorded

Simulated

Simulated

Simulated


0.01217.236.276.880.010.14

0.14512.306.785.900.120.26

0.05514.227.224.480.160.38

0.01414.076.3110.750.240.26

0.03614.878.324.360.150.03

Iasec.g

D5-95sec

tmidsec

/(2)

Hz/secmid/(2)

Hz


14/26

F = 1 (Reverse)M = 7.35

Rrup =14 km

VS30 = 660 m/sec


Displacement,m

Time, sec

0 5 10 15 20 25 30 35

-0.1

0

0.1

0 5 10 15 20 25 30 35

-0.1

0

0.1

0 5 10 15 20 25 30 35-0.05

0

0.05

0 5 10 15 20 25 30 35-0.05

0

0.05

0 5 10 15 20 25 30 35

-0.05

0

0.05

Example 1 : Displacement

Simulated

Recorded

Simulated

Simulated

Simulated


0.01217.236.276.880.010.14

0.14512.306.785.900.120.26

0.05514.227.224.480.160.38

0.01414.076.3110.750.240.26

0.03614.878.324.360.150.03

Iasec.g

D5-95sec

tmidsec

/(2)

Hz/secmid/(2)

Hz


15/26


0.14512.306.785.900120.26

0.14512.799.867.480.520.13

0.14522.1116.248.050.090.12

0.1458.145.317.340.020.30

0.14511.0110.304.430.120.29

Example 2 :

F = 1 (Reverse)M = 7.35

Rrup =14 km

VS30 = 660 m/sec

If desired, a fixed value may be assigned to one or more of the model parameters:

Acceleration,g

Time, sec

0 5 10 15 20 25 30 35 40-0.5

0

0.5

0 5 10 15 20 25 30 35 40-0.5

0

0.5

0 5 10 15 20 25 30 35 40-0.5

0

0.5

-0.5

0

0.5

0 5 10 15 20 25 30 35 40-0.5

0

0.50 5 10 15 20 25 30 35 40

Recorded

Simulated

Simulated

Simulated

Simulated

Iasec.g

D5-95sec

tmidsec

/(2)

Hz/secmid/(2)

Hz


16/26

Example 3 : Response Spectrum (5% damped)

2 horizontal components of a recorded motion (1994 Northridge at LA Wonderland Ave)

Vs.

50 simulated motions

Corresponding to earthquake and site characteristics:

Period, sec

De

format

ion

Response

Spec

trum,

m

10-1 10010-4

10-3

10-2

10-1

100

510010-1

10010-3

10-2

10-1

100

101

5100

Period, sec

Pseu

do-Accel

era

tion

Response

Spec

trum,

g

Recorded

Simulated

F = 1 (Reverse)

M = 6.69

Rrup = 20.3 km

VS30 = 1223 m/sec


17/26

Comparison with NGA Models:

10-3

10-2

10-1

100

M=6.0, R=20km

Campbell-Bozorgnia (z2.5 = 1km)

Abrahamson-Silva (z1.0 = 34m)

Chiou-Youngs (z1.0 = 24m)

Boore-Atkinson

5%

Damp

edPseu

do-Acce

lera

tion

Resp

onse

Spec

trum,

g

10-3

10-2

10-1

100

M=7.0, R=20km M=7.0, R=20km

M=7.0, R=10km

Period, sec

0.1 1.0

M=7.0, R=40km

5.0

F = 0 (Strike-Slip)

Vs30 = 760 m/sec

Avg NGA 500 Simulations

Median

Median 1 logarithmic stdv.

Median +1 logarithmic stdv.

NGA Parameters: Rupture width = 20kmRupture depth = 1km

Selected NGA Models:

Note:Models based on different subsets of NGA database.

Observe:

Except for M=6.0 (lower bound of database),

deviations are much smaller than the variability

present in the NGA prediction equations.

Synthetics are in close agreement with NGA.

Period, sec

10-3

10-2

10-1

10

0

M=8.0, R=20km

0.1 1.0 5.0


18/26

Current & Future Developments:

Simulating correlated orthogonal horizontal ground motion components.Component 1:

Component 2:

Motions in the database are rotated to the principal axes so that w1() and w2() are statistically independent.

Model is fitted to the rotated database to estimate correlations: 1,2 and 1,2


19/26


Simulating near-field ground motions.Separately model and superimpose:

1) The directivity pulse

Long period pulse in the velocity time-series of thefault-normalcomponent.

Develop prediction equations for characteristics of the pulse in terms of earthquake/site parameters.

Collaboration with Jack Baker:

Using wavelet analysis, directivity pulse extracted from a database of near-field motions,

this database will be used to develop prediction equations.

2) The fling step

Permanent displacement may exist in thefault-parallelcomponent.

Incorporate the available seismological models (e.g., Somerville 1998, Abrahamson 2001).

3) The residue motion

The total motion minus the directivity pulse and the fling step.

Model by a modified version of the far-field stochastic ground motion process.


20/26


Scrutinize the simulated motions for inelastic structural responses.Compare inelastic response spectra (for given ductility ratios) of synthetic motions with real recordings and

existing prediction equations (e.g., Bozorgnia et. al., 2010).

Case Study:

Compare inelastic response of a multi-degree-of-freedom structure to simulated and recorded motions.


21/26

Related Publications:

Rezaeian, S. and A. Der Kiureghian,

"A stochastic ground motion model with separable temporal and spectral nonstationarities,"

Earthquake Engineering and Structural Dynamics, July 2008, Vol. 37, pp. 1565-1584.

Rezaeian, S. and A. Der Kiureghian,

"Simulation of synthetic ground motions for specified earthquake and site characteristics,"

Earthquake Engineering and Structural Dynamics, 2009. Submitted.

MATLAB software to be made available

Current abilities:

Fitting the stochastic model to a target accelerogram.Simulating far-field strong motions on firm-ground for specified F, M, Rrup, Vs30.

Will be added by May 2010:

Two component simulation.

Near-field simulation.


22/26

Thank You


23/26

Cumulative energy

Cumulative number of zero-levelup crossings a measure of

dominant frequency

Cumulative number of positive minima andnegative maxima a measure of bandwidth

Features of target accelerogram

0 5 10 15 20 25 30 35 4000.0050.01

0.0150.02

0.0250.03

Cumulativeenergy

0 5 10 15 20 25 30 35 40020406080100120140160

Cumulativenumberofzero-levelup

-crossin

gs

Time, sec

0 5 10 15 20 25 30 35 40020406080100

120140

Cumulativenumberofnegativemaxima

andpositiveminima


24/26

Response spectrum

Discretizedwhite noise(input)

Unit-variance process withspectral nonstationarity

Lineartime-varyingfilter

Fully non-stationarityprocess

Time modulation

High-passfilter

Simulatedground motion(output)

Post-processing is needed for long

-period range. A critically damped

oscillator is used as a high-pass filter.

corner frequency

10 100 10110-310101010

T (sec)

A(g)

-1

-1

-2

0

1

After high-pass filtering

10 100 101T (sec)

-110-310101010

A(g)

-1

-2

0

1


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Acceleration,g

Recorded motion

0 5 10 15 20 25 30 35 40-0.2-0.1

00.10.2

0 5 10 15 20 25 30 35 40-0.20

0.2

0 5 10 15 20 25 30 35 40-0.2-0.1

00.10.2

Time (sec)

Simulation

Simulation

Northridge earthquake


26/26

Acceleration,g

Recorded motion

Time (sec)

Simulation

Simulation

Kobe earthquake

Simulation of Synthetic Ground Motionsfor Specified Earthquake and Site Characteristics

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