Overview of GMSM Methods Nicolas Luco

Overview of GMSM Methods

Nicolas Luco

1st Workshop on Ground Motion Selection and Modification (GMSM) for Nonlinear Analysis – 27 October 2006

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GMSM Methods Currently being Compared

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Nonlinear Analysis Results being Compared(Objectives of GMSM Methods Currently being

Compared)

1. Cumulative Distribution Function (CDF) of the Engineering Demand Parameter (EDP) for a given earthquake magnitude (M), source-to-site distance (R), 30m shear wave velocity (S), and style of faulting (F).

2. Median EDP | M, R, S, F.

3. CDF of EDP | M, R, S, F and a given pseudo spectral acceleration at the estimated fundamental period of the structure (and a 5% damping ratio), SA(T1).

4. Median EDP | M, R, S, F and SA(T1).

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Specifics of Current Comparison Case

Structure = 4-Story Reinforced Concrete (RC) Special Moment Frame (SMF) Building, T1 ≈ 1 sec.

EDP = maximum (over height) peak (over time) inter-story drift ratio (MIDR)

M = 7 (moment magnitude)

R = 10 km (closest distance to rupture)

S = 400 m/sec (30m shear wave velocity)

F = strike-slip (style of faulting)

SA(T1) = +2 sigma level (=2) based on Campbell & Bozorgnia (2006) GM prediction equation

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Specifics of Current Comparison Case

10-2

10-1

100

101

10-2

10-1

100

101

Period [sec]

Sp

ect

ral A

cce

lera

tion

[g

]M = 7, R = 10km, S = 400m/s, F = SS

Median Spectrum+2 Sigma Spectrum

SA(T1)=1.08g

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Categories of Methods for Objective #1( i.e., CDF of EDP | M, R, S, F )

Select GMs for a M-R-S-F "bin" chosen to be consistent with the given M, R, S, F (no scaling).(Watson-Lamprey)

Scale (in amplitude) each GM in bin so as to "correct" for ranges of M, R, S, F values vs. given values.(Bozorgnia)

Select GMs that, with scaling, will both …(i) closely match the median response spectrum(ii) sample the variability of the response spectra(Rathje, Youngs/DGML, Almoradi)

Adjust resulting variability of EDP for effects of scaling.(Shome)

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Example GMSM Method for Objective #1( i.e., CDF of EDP | M, R, S, F )

Selection Procedure1. Gather GMs for bin consistent with given M, R, S, F.2. Select from combinations of scaled GMs generated

by modification procedure

Modification Procedure1. Scale GMs such that their median matches the

median response spectrum for given M, R, S, F, and such that their variability matches the variability in SA(T).

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Example GMSM Method for Objective #1( i.e., CDF of EDP | M, R, S, F )

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Categories of Methods for Objective #2( i.e., Median of EDP | M, R, S, F )

Select GMs according to M-R-S-F bin and scale to median value of scalar EDP-proxy (e.g., SA(T1) or inelastic spectral displacement) for given M, R, S, F.(Shome, Haselton, Cornell, Bozorgnia)

Select GMs to match, with scaling allowed, median of EDP-proxy (e.g., elastic response spectrum or inelastic spectral displacement) for given M, R, S, F.(Youngs/DGML, Alimoradi, Baker, Watson-Lamprey, Shantz)

Select GMs according to M-R-S-F bin (or randomly select?) and spectral-match them to median elastic or inelastic response spectrum.(Bazzurro/RASCAL, Watson-Lamprey/RSPMATCH, Bozorgnia)

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Example GMSM Method for Objective #2( i.e., Median of EDP | M, R, S, F )

Selection Procedure1. Gather GMs for bin consistent with given M, R, S.2. After scaling (procedure below), select GMs with

smallest Mean Squared Error (MSE) w.r.t. median spectrum for given M, R, S, F.

Modification Procedure1. Scale GMs to minimize MSE w.r.t. median

spectrum for given M, R, S, F.

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Example GMSM Method for Objective #2( i.e., Median of EDP | M, R, S, F )

1 2 3 40.90.80.70.60.5

Pe rio d (se c)

0.1

1

0.2

0.5

2

5

0.05

Sca

led

(S

A /

PG

A)

S caled Fau lt-N orm al C omponents P eriod R ange: 0 .5 to 4 .0 seconds

Target: FN

12 sca led FN s

5% dam ping

(Source: Youngs, Power & Chin; 2006)

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Categories of Methods for Objective #3( i.e., CDF of EDP | M, R, S, F, and SA(T1) )

Select GMs for bin that is consistent with given M, R, S, F, and SA(T1) (no scaling).

Scale (individually) GMs in bin to "correct" for ranges of M, R, S, F, and SA(T1) values vs. given values.(Luco/Bozorgnia/Tothong)

Select GMs for M-R-S-F-consistent bin and scale them to given SA(T1).(Shome)

Select GMs for Objective #1 (CDF of EDP | M, R, S, F) and scale them to given SA(T1).(Alimoradi, Youngs/DGML)

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( i.e., CDF of EDP | M, R, S, F, and SA(T1) )

Selection Procedure1. Gather GMs for bin consistent with | M, R, S, F, SA(T1).

Modification Procedure1. For each GM (unscaled), calculate …

2. Iteratively scale each GM such that …

IM1I&2E = scalar combination of first-mode inelastic spectral displacement and SA(T2) (Luco & Cornell, 2002)

Example GMSM Method for Objective #3

GM of for Geomean

GM for

)(,,,,)(

&

&&

121

2121 TSAFSRMIM

IMIM

EI

EIEI

)(,,,,)( &&& 1212121 TSAFSRMIMIMIM EIEIEI Given for GeomeanGM for

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Example GMSM Method for Objective #3( i.e., CDF of EDP | M, R, S, F, and SA(T1) )

Ground Motion Prediction Equation (GMPE) for IM1I&2E is available from Tothong & Cornell (2007).

GMPEs for Inelastic Spectral Displacement (part of IM1I&2E) are available for …

… constant strength, dy (Tothong & Cornell, 2006)

… constant ductility, (Bozorgnia et al., 2006)

… constant strength reduction factor, R (???)

Combine with GMPE for SA(T2) and its correlation with SA(T1) to approximate GMPE for IM1I&2E.

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Categories of Methods for Objective #4( i.e., Median of EDP | M, R, S, F and SA(T1) )

Select GMs for Objective #2 (Median of EDP | M, R, S, F) and scale them to given SA(T1).(Youngs/DGML)

Select GMs to match, with scaling allowed, median (or other target) of EDP-proxy (e.g., elastic or inelastic response spectrum) for given M, R, S, F, and SA(T1).(Alimoradi, Baker, Watson-Lamprey, Shantz, Rathje)

Select GMs according to M-R-S-F bin (or randomly select?) and spectral-match them to elastic or inelastic response spectrum consistent with SA(T1).(Bazzurro/RASCAL, Watson-Lamprey/RSPMATCH, Bozorgnia)

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Example GMSM Method for Objective #4( i.e., Median of EDP | M, R, S, F, and SA(T1) )

Selection Procedure1. Gather GMs for bin consistent with given M, R, S, F,

and/or SA(T1) (e.g., M = 6.75 to 7.25, R = 0 to 20 km).

Or … randomly select GMs?

Modification Procedure1. Spectral-match each GM to Conditional Mean

Spectrum (CMS – Baker & Cornell, 2006) for given M, R, S, F and SA(T1).

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Example GMSM Method for Objective #4( i.e., Median of EDP | M, R, S, F, and SA(T1) )

e.g., from Bazzurro using RASCAL (Silva & Lee, 1987)

10-2

10-1

100

101

10-2

10-1

100

101

Target Spectrum = Conditional

Period [sec]

Sp

ect

ral A

cce

lera

tion

[g

]

10-2

10-1

100

101

10-2

10-1

100

101

Target Spectrum = Conditional

Period [sec]

Sp

ect

ral A

cce

lera

tion

[g

]

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GMSM Methods Currently being Compared

NSF Year 7 Site Visit

Additional GMSM Methods to be Compared

NSF Year 7 Site Visit

NSF Year 7 Site Visit

Example GMSM Method for Objective #1( i.e., CDF of EDP | M, R, S, F )

Selection Procedure1. Decide on "bin" consistent with given M, R, S, F.

(e.g., M = 6.75 to 7.25, R = 0 to 20 km)2. Gather GMs for chosen bin.

Modification Procedure1. Scale each GM by …

… where the Median SA(T1) is from a GM Prediction Equation (GMPE).

GM of for Median

given for Median

FSRMTSA

FSRMTSASF

,,,)(

,,,)(

1

1