Overview of GMSM Methods Nicolas Luco

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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)
• 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).
• Median EDP M, R, S, F.
• 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).
• 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 (e2) based on Campbell
  Bozorgnia (2006) GM prediction equation

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Specifics of Current Comparison Case

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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 Procedure
• Gather GMs for bin consistent with given M, R, S,
  F.
• Select from combinations of scaled GMs generated
  by modification procedure
• Modification Procedure
• 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 Procedure
• Gather GMs for bin consistent with given M, R, S.
• 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
• 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 )

(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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Example GMSM Method for Objective 3

• ( i.e., CDF of EDP M, R, S, F, and SA(T1) )
• Selection Procedure
• Gather GMs for bin consistent with M, R, S, F,
  SA(T1).
• Modification Procedure
• For each GM (unscaled), calculate
• Iteratively scale each GM such that
• IM1I2E scalar combination of first-mode
  inelastic spectral displacement and SA(T2)
  (Luco Cornell, 2002)

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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
  IM1I2E is available from Tothong Cornell
  (2007).
• GMPEs for Inelastic Spectral Displacement (part
  of IM1I2E) are available for
• constant strength, dy (Tothong Cornell,
  2006)
• constant ductility, m (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 IM1I2E.

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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 Procedure
• 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 Procedure
• 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)

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GMSM Methods Currently being Compared
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Additional GMSM Methods to be Compared
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(No Transcript)
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Example GMSM Method for Objective 1

• ( i.e., CDF of EDP M, R, S, F )
• Selection Procedure
• Decide on "bin" consistent with given M, R, S, F.
• (e.g., M 6.75 to 7.25, R 0 to 20 km)
• Gather GMs for chosen bin.
• Modification Procedure
• Scale each GM by
• where the Median SA(T1) is from a GM
  Prediction Equation (GMPE).