Review of GMSM Solicitation and Methods Nicolas Luco, On behalf of The PEER GMSM Program

Review of GMSM Solicitation and Methods

Nicolas Luco,

On behalf ofThe PEER GMSM Program

2nd Annual PEER Ground Motion Selection & Modification (GMSM) Program Workshop29 October 2007

NSF Year 7 Site Visit

Outline of PresentationOutline of Presentation

Review of GMSM Objectives (Solicited)

List of GMSM Methods for Objectives 3 & 4

Summaries of GMSM Methods for Objectives 3 & 4

List of GMSM Methods for Objectives 1 & 2


GMSM ObjectivesGMSM Objectives

Average (or average & dispersion) of structural response for a given response spectrum

Why not? Because probability of exceedance in T years (PE) of response spectrum is not typically known.

Median & probability distribution (CDF) of structural response for a given Sa(T1), M, R (and S, F)*

Why? Because PE of Sa(T1) and associated M, R are typically known (e.g., via PSHA and deaggregation).

Median and probability distribution (CDF) of structural response for a given M, R (and S, F)*

Why? For scenarios or "attenuation relations" for structural response.

* Hereafter M, R, S, & F will be abbreviated to M, R.


GMSM Methods for Objectives 3 & GMSM Methods for Objectives 3 & 44

Index # Name Developer(s) Objective(s)

4, 53 "Sa(T1) Scaling" Shome 3 and 4

67 "ATC-58 [35% Draft] -- Near-Field Set" Whittaker et al (Zareian) 3 and 4

9980-9989 "Building Code Selection Mini-Study" Baker 4

16 "Semi-Automated Selection & Scaling …" Rathje & Kottke 4

17 "Building Code (purposefully extreme selection)" Watson-Lamprey 4

10 "Conditional Mean Spectrum Selection w/ Scaling" Baker 4

15 "Genetic Algorithm Selection (based on CMS)" Naeim, Alimoradi 4 or 3?

24 "Semi-Automated Selection & Scaling - to match CMS" Rathje, Kottke 4 or 3?

45 "Design Ground Motion Library (DGML)" Power, Youngs, Wang 3 and 4

20 "Target Spectrum Based on Epsilon Correlations ..." Stewart, Skyers, Goulet 3? and 4

31 "ε Selection with Sde(T1) Scaling" Tothong, Luco 3? and 4

57, 58 "Sa(T1) Scaling Considering Spectral Shape" Shome 3, 4

43, 48 "ATC-63 - Far[/Near]-Field set with the ε correction" Haselton, Kircher 4

6 "Vector of Record Properties Identified by Proxy" Watson-Lamprey 4

11 "Inelastic Response Surface Scaling - Basic set" Shantz 4

26, 27 "Sdi(T1, dy) Scaling" Tothong, Luco 3, 4

34, 35 "IM1I&2E Selection/Scaling" Luco, Tothong 3, 4

51 "Inelastic Response Surface Scaling - With post-processing" Shantz 3

"Sa(T1) Methods"

"Uniform Hazard Spectrum (UHS) Methods"

"Conditional Mean Spectrum (CMS) Methods"

"Spectral Shape Proxy Methods"

"Inelastic Ground Motion Parameter Methods"


"Sa(T1) Methods""Sa(T1) Methods" (4 & 53, 67) (4 & 53, 67)

Selection: GMs consistent with given M, R Scaling: Match given Sa(T1)

(Source: ATC-58 35% Draft for Method #67)


"Sa(T1) Methods""Sa(T1) Methods" (4 & 53, 67) (4 & 53, 67)

Selection: GMs consistent with given M, R Scaling: Match given Sa(T1)

(Source: Shome for Methods #4 & 53)


"UHS Methods""UHS Methods" (9980-9989) (9980-9989)

Selection: GMs with spectral shape similar to UHS, perhaps consistent with given M, R

Scaling: "Closely match" UHS

(Source: Haselton for Method #9980)


UHS for our M, R, Sa(T1) ScenarioUHS for our M, R, Sa(T1) Scenario

Suppose that the only fault near the S=400m/s site is F=Strike-Slip at R=10km capable of M=7 every 50yrs

In this case, 2500yr Sa(Ti) is equal to 98%-ile Sa(Ti) for given M, R, S, F (since 1/50yrs*2%=1/2500yrs)

0.01

0.10

1.00

10.00

0.01 0.10 1.00 10.00

Period [seconds]

Sa

[g]

Median Spectrum from Attenuation Relation

98%-ile Spectrum from Attenuation Relation

2500yr UHS


"CMS Methods" – Objective 4 "CMS Methods" – Objective 4 (10, 15?, (10, 15?, 24?)24?)

Selection: GMs with spectral shape similar to CMS, perhaps consistent with given M, R

Scaling: Match given Sa(T1) (Method #10) or "closely match" CMS (Methods #24,

15?)


10-1

100

101

10-2

10-1

100

101

Period [sec]

Spe

ctra

l Acc

eler

atio

n [g

]

Scenario: M7, Method: 10, Building: C, Record Set: Combined, Obj.: 4

Median + 2 Prediction

Conditional MeanMedian of Rec. Set

Individual Records





15?)


10-1

100

101

10-2

10-1

100

101

Period [sec]

Spe

ctra

l Acc

eler

atio

n [g

]

Scenario: M7, Method: 15, Building: C, Record Set: Combined, Obj.: 3,4



Individual Records





15?)


10-1

100

101

10-2

10-1

100

101

Period [sec]

Spe

ctra

l Acc

eler

atio

n [g

]

Scenario: M7, Method: 24, Building: C, Record Set: Combined, Obj.: 3,4



Individual Records


"CMS Methods" – Objective 3 "CMS Methods" – Objective 3 (45)(45)

Selection: GMs with spectral shape approximating distribution about CMS (Obj. 3) or similar to

CMS (Obj. 4), and with consistent M, R Scaling: Match given Sa(T1)

(Source: Geomatrix Consultants for Method #45)


Review of Conditional Mean Review of Conditional Mean SpectrumSpectrum

CMS ≡ expected spectrum for given Sa(T1), M, R

where = correlation between lnSa(Ti) and lnSa(T1)

],|)1([ln)1(

],|)([ln],),1(|)([ln

RMTSaT

RMTiSaERMTSaTiSaE

(Source: Baker for Method #10)

e.g., …M = 7R = 10kmSa(T1) = "2"


"Proxy Methods" – "Proxy Methods" – (T1) (T1) (20, 31) (20, 31)

Selection: GMs consistent with given (T1) and M, R

Scaling: Match given Sa(T1)


10-1

100

101

10-2

10-1

100

101

Period [sec]

Spe

ctra

l Acc

eler

atio

n [g

]




Individual Records

e.g., for …(T1) = 1-3M = 6.7-7.3R = 0-42kmS = 215-560m/s


"Proxy Methods" – "Proxy Methods" – (T1) (T1) (20, 31) (20, 31)




10-1

100

101

10-2

10-1

100

101

Period [sec]

Spe

ctra

l Acc

eler

atio

n [g

]




Individual Records


"Proxy Methods" – Sa(Ti) Vector "Proxy Methods" – Sa(Ti) Vector (57 (57 & 58)& 58)

Selection: GMs consistent with expected (Obj. 4) or distribution of (Obj. 3) Sa(0.5T1) & Sa(2T1) for given Sa(T1), M, R, and consistent with given M, R


(Source: Shome for Methods #57 & 58)


"Inelastic Methods" – Obj. 4 "Inelastic Methods" – Obj. 4 (6) (6)

Selection: GMs with expected Sdi(T1,R)/Sde(T1) consistent with that and DurUNI, PGV, Sa(2T1) for given Sa(T1), M, R


DurUNI, PGV, Sa(2T1) from available ground motion prediction equations (a.k.a., attenuation relations)

Expected Sdi(T1,R)/Sde(T1) for DurUNI, PGV, Sa(T1), Sa(2T1) computed as part of method


"Inelastic Methods" – Obj. 4 "Inelastic Methods" – Obj. 4 (11) (11)

Selection: GMs with Inelastic Displacement Surface similar to that expected for given Sa(T1), M, R

Scaling: Optimal fit to expected (i.e., target) IDS

1 2 3 4 5Periods 2

4

6

8

2

4

6

Dmaxcm

1 2 3 4 5Periods

(Source: Shantz for Method #11)

CMS x CR(R,T,)

Sdi(T,R)/Sde(T)


"Inelastic Methods" – Obj. 4 "Inelastic Methods" – Obj. 4 (27, 35) (27, 35)

Selection: Random Scaling: Match expected Sdi(T1,dy) (Method #27)

or IM1I&2E (Method #35) for given Sa(T1), M, R

dy from Nonlinear Static Pushover curve

Expected Sdi(T1,dy) from Tothong & Cornell (2006)

Expected IM1I&2E from expected Sdi(T1,dy) and Tothong & Cornell (2006)

222

2112&1 )]([)],([ TSPFdTSPFIM deydiEI

(Luco, 2002)


Selection: Random Scaling: Approximate distribution of Sdi(T1,dy)

(Method #26) or IM1I&2E (Method #34) for given Sa(T1), M, R

Distribution of Sdi(T1,dy) or IM1I&2E also from Tothong & Cornell (2006)

-4 -3 -2 -1 0 1 2 3 40

0.1

0.2

0.3

0.4

# Std. Dev. from Mean of ln(IM)

PD

F o

f ln

(IM

)

"Inelastic Methods" – Obj. 3 "Inelastic Methods" – Obj. 3 (26, 34) (26, 34)

10

GM

s

7 G

Ms

7 G

Ms

2 G

Ms

2 G

Ms

0 G

Ms

0 G

Ms




3 "Bin Selection with Scaling by Elastic GMPE" Stewart (Tothong) 1 and 2

5, 25 "Sdi(T1, dy) Scaling" Tothong, Luco 1 and 2, 2

22 "Malhotra 2007 Method" Malhotra 1 and 2

28, 29 "ε Selection with Sde(T1) Scaling" Tothong, Luco 1 ans 2, 2

32, 33 "IM1I&2E Selection/Scaling" Luco, Tothong 1 and 2, 2

36 "Bin Selection with no Scaling" Tothong 1 and 2

41 "Building Code …" Baker 2

49, 50 "ATC-63 - Far[/Near]-Field set with the ε correction" Haselton, Kircher 1 and 2

52, 56 "Sa(T1) Scaling Considering Spectral Shape" Shome 1 and 2, 2

54, 55 "Sa(T1) Scaling" Shome 1 and 2, or 2


61, 70 "Design Ground Motion Library (DGML)" Power, Youngs, Wang 1 and 2, 2

62 "Conditional Mean Spectrum Selection with Scaling" Baker 2


65 "Inelastic Response Surface Scaling - With post-processing " Shantz 1 and 2

66 "Genetic Algorithm Selection (based on median spectrum)" Naeim, Alimoradi 1? and 2

68 "ATC-58 - Near-Field Set" Whittaker et al (Zareian) 1 and 2




4, 53 "Sa(T1) Scaling" Shome 3 and 4

67 "ATC-58 [35% Draft] -- Near-Field Set" Whittaker et al (Zareian) 3 and 4

9980-9989 "Building Code Selection Mini-Study" Baker 4

16 "Semi-Automated Selection & Scaling …" Rathje & Kottke 4

17 "Building Code (purposefully extreme selection)" Watson-Lamprey 4

10 "Conditional Mean Spectrum Selection w/ Scaling" Baker 4

15 "Genetic Algorithm Selection (based on CMS)" Naeim, Alimoradi 4 or 3?

24 "Semi-Automated Selection & Scaling - to match CMS" Rathje, Kottke 4 or 3?

45 "Design Ground Motion Library (DGML)" Power, Youngs, Wang 3 and 4

20 "Target Spectrum Based on Epsilon Correlations ..." Stewart, Skyers, Goulet 3? and 4

31 "ε Selection with Sde(T1) Scaling" Tothong, Luco 3? and 4

57, 58 "Sa(T1) Scaling Considering Spectral Shape" Shome 3, 4

43, 48 "ATC-63 - Far[/Near]-Field set with the ε correction" Haselton, Kircher 4



26, 27 "Sdi(T1, dy) Scaling" Tothong, Luco 3, 4

34, 35 "IM1I&2E Selection/Scaling" Luco, Tothong 3, 4

51 "Inelastic Response Surface Scaling - With post-processing" Shantz 3

"Sa(T1) Methods"

"Uniform Hazard Spectrum (UHS) Methods"

"Conditional Mean Spectrum (CMS) Methods"

"Spectral Shape Proxy Methods"

"Inelastic Ground Motion Parameter Methods"


Extra Slides …Extra Slides …


"Proxy Methods" – Objective 3 "Proxy Methods" – Objective 3 (30)(30)


Scaling: To given Sa(T1)


10-1

100

101

10-2

10-1

100

101

Period [sec]

Spe

ctra

l Acc

eler

atio

n [g

]Scenario: M7, Method: 30, Building: C, Record Set: Combined, Obj.: 3



Individual Records


Old Presentation …Old Presentation …


GMSM Methods Currently being GMSM Methods Currently being ComparedCompared

Notes: A, B, C = Class of GMSM Method for given Objective.#1D = Adjust resulting variability of EDP for effects of scaling. ( √ √ ) = Median for Objective #2 or 4 obtained via CDF from Objective #1 or 3, respectively.


Additional GMSM Methods to be Additional GMSM Methods to be ComparedCompared


Summary of Categorization of GMSM Summary of Categorization of GMSM MethodsMethods

4 Objectives

1. CDF of EDP | M, R, S, F2. Median of EDP | M, R, S, F3. CDF of EDP | M, R, S, F and SA(T1)

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

3 Classes (A, B, C) per objective

30+ specific GMSM Methods under consideration

Any other objectives, classes, specific methods?

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Review of GMSM Solicitation and Methods Nicolas Luco, On behalf of The PEER GMSM Program

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