Use of Response Spectra Properties for Ground Motion Validation

J. Baker 1 Use of elastic & inelastic response spectra properties to validate simulated ground motions Jack Baker Civil & Environmental Engineering Stanford University

J. Baker 2 Ground motions for illustration Illustrative results are presented for several sets of Puente Hills broadband simulations at 648 sites in the Los Angeles region (Graves and Somerville 2006) One-second elastic spectral accelerations (from Graves and Somerville 2006)

J. Baker 3 Elastic response spectra Often serve as the link between seismic hazard analysis and structural response calculation. Basis of significant engineering intuition Looking at these in a statistical sense is important (means, standard deviations, and correlations)

J. Baker 4 Spectral correlations are important and easily measurable Hypothetical response spectra from ground motion simulations with a fixed M & R. All sets of spectra have the same means and standard deviations. Correct correlation Empirical models for correlation are available, and are surprisingly stable across magnitude, distance, site condition, tectonic regime, etc. Over-correlated Under-correlated

J. Baker 5 Nonlinear response spectra One step up in complication and realism Also tied to engineering intuition Can still be tied to statistics of recorded ground motions Predictive model available (e.g., Tothong and Cornell, 2006) Relatively insensitive to most parameters besides magnitude and site nonlinearity Force fy Displacement Expected level of nonlinearity

J. Baker 6 Nonlinear response spectra

J. Baker 7 Nonlinear response spectra

J. Baker 8 Nonlinear response spectra

J. Baker 9 A more advanced topic: sources of variability The latest empirical ground motion prediction models are attempting to separate sources of ground motion variability more carefully = + + + Source ln ( ) ( , , ,etc.) Sa T f M R V 30 s Site Path mean prediction variability Simulated motions could be analyzed in the same way, and it would be interesting to compare the breakdown of variability between the simulations and observations Empirical data: Hard to get repeated observations from a given source and path Source variability is correct by definition Simulations: Possible to get repeated observations from a given source and path Modeling of source variability is actively evolving

J. Baker 10 Conclusions A few easy and useful ground motion properties to look at: Mean values of elastic response spectra (for mean structural response) Standard deviations of response spectra (for hazard, and variability in structural response) Correlations of response spectra at multiple periods (for excitation of nonlinear and multiple modes) Nonlinear response spectral ratios (for nonlinear structural response)