Overview of GMSM Methods Nicolas Luco 1 st Workshop on Ground Motion Selection and Modification (GMSM) for Nonlinear Analysis – 27 October 2006

NSF Year 7 Site Visit GMSM Methods Currently being Compared

NSF Year 7 Site Visit 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(T 1 ). 4. Median EDP | M, R, S, F and SA(T 1 ).

NSF Year 7 Site Visit Specifics of Current Comparison Case Structure =4-Story Reinforced Concrete (RC) Special Moment Frame (SMF) Building, T 1 ≈ 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(T 1 ) =+2 sigma level (  =2) based on Campbell & Bozorgnia (2006) GM prediction equation

NSF Year 7 Site Visit Specifics of Current Comparison Case SA(T 1 )=1.08g

NSF Year 7 Site Visit 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)

NSF Year 7 Site Visit Example GMSM Method for Objective #1 ( i.e., CDF of EDP | M, R, S, F ) Selection Procedure 1. Gather GMs for bin consistent with given M, R, S, F. 2. Select from combinations of scaled GMs generated by modification procedure Modification Procedure 1. 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).

NSF Year 7 Site Visit Example GMSM Method for Objective #1 ( i.e., CDF of EDP | M, R, S, F )

NSF Year 7 Site Visit 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(T 1 ) 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)

NSF Year 7 Site Visit Example GMSM Method for Objective #2 ( i.e., Median of EDP | M, R, S, F ) Selection Procedure 1. 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 Procedure 1. Scale GMs to minimize MSE w.r.t. median spectrum for given M, R, S, F.

NSF Year 7 Site Visit Example GMSM Method for Objective #2 ( i.e., Median of EDP | M, R, S, F ) (Source: Youngs, Power & Chin; 2006)

NSF Year 7 Site Visit Categories of Methods for Objective #3 ( i.e., CDF of EDP | M, R, S, F, and SA(T 1 ) ) Select GMs for bin that is consistent with given M, R, S, F, and SA(T 1 ) (no scaling). Scale (individually) GMs in bin to "correct" for ranges of M, R, S, F, and SA(T 1 ) values vs. given values. (Luco/Bozorgnia/Tothong) Select GMs for M-R-S-F-consistent bin and scale them to given SA(T 1 ). (Shome) Select GMs for Objective #1 (CDF of EDP | M, R, S, F) and scale them to given SA(T 1 ). (Alimoradi, Youngs/DGML)

NSF Year 7 Site Visit ( i.e., CDF of EDP | M, R, S, F, and SA(T 1 ) ) Selection Procedure 1. Gather GMs for bin consistent with | M, R, S, F, SA(T 1 ). Modification Procedure 1. For each GM (unscaled), calculate … 2. Iteratively scale each GM such that … IM 1I&2E =scalar combination of first-mode inelastic spectral displacement and SA(T 2 ) (Luco & Cornell, 2002) Example GMSM Method for Objective #3

NSF Year 7 Site Visit Example GMSM Method for Objective #3 ( i.e., CDF of EDP | M, R, S, F, and SA(T 1 ) ) Ground Motion Prediction Equation (GMPE) for IM 1I&2E is available from Tothong & Cornell (2007). GMPEs for Inelastic Spectral Displacement (part of IM 1I&2E ) are available for … … constant strength, d y (Tothong & Cornell, 2006) … constant ductility,  (Bozorgnia et al., 2006) … constant strength reduction factor, R (???) Combine with GMPE for SA(T 2 ) and its correlation with SA(T 1 ) to approximate GMPE for IM 1I&2E.

NSF Year 7 Site Visit Categories of Methods for Objective #4 ( i.e., Median of EDP | M, R, S, F and SA(T 1 ) ) Select GMs for Objective #2 (Median of EDP | M, R, S, F) and scale them to given SA(T 1 ). (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(T 1 ). (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(T 1 ). (Bazzurro/RASCAL, Watson-Lamprey/RSPMATCH, Bozorgnia)

NSF Year 7 Site Visit Example GMSM Method for Objective #4 ( i.e., Median of EDP | M, R, S, F, and SA(T 1 ) ) Selection Procedure 1. Gather GMs for bin consistent with given M, R, S, F, and/or SA(T 1 ) (e.g., M = 6.75 to 7.25, R = 0 to 20 km). Or … randomly select GMs? Modification Procedure 1. Spectral-match each GM to Conditional Mean Spectrum (CMS – Baker & Cornell, 2006) for given M, R, S, F and SA(T 1 ).

NSF Year 7 Site Visit Example GMSM Method for Objective #4 ( i.e., Median of EDP | M, R, S, F, and SA(T 1 ) ) e.g., from Bazzurro using RASCAL (Silva & Lee, 1987)

NSF Year 7 Site Visit GMSM Methods Currently being Compared

NSF Year 7 Site Visit Additional GMSM Methods to be Compared

NSF Year 7 Site Visit

Example GMSM Method for Objective #1 ( i.e., CDF of EDP | M, R, S, F ) Selection Procedure 1. 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 Procedure 1. Scale each GM by … … where the Median SA(T 1 ) is from a GM Prediction Equation (GMPE).