Earthquake ground motion characterization using the Conditional Spectrum

Graduate researchers: Lynne Burks, Nirmal Jayaram, Ting Lin

Project sponsors: Applied Technology Council, Pacific Earthquake Engineering Research Center, U.S. Geological Survey

Calculation of the Conditional Mean Spectrum (from Baker, 2011)

A common goal of dynamic structural analysis is to predict the response of a structure subjected to ground motions having a specified spectral acceleration at a given period. This is important, for example, when coupling ground motion hazard curves from probabilistic seismic hazard analysis with results from dynamic structural analysis. The prediction is often obtained by selecting ground motions that match a target response spectrum, and using those ground motions as input to dynamic analysis. The commonly used Uniform Hazard Spectrum (UHS) conservatively implies that large-amplitude spectral values will occur at all periods within a single ground motion. An alternative, termed a Conditional Mean Spectrum (CMS), is presented here. The CMS provides the expected (i.e., mean) response spectrum, conditioned on occurrence of a target spectral acceleration value at the period of interest. The CMS may be a more appropriate target spectrum in some analysis situations, and is thus a useful tool for selecting ground motions as input to dynamic analysis.

Example software:

Simple Matlab script for computing the Conditional Mean Spectrum
Software for selecting and scaling ground motions to be consistent with a target Conditional Spectrum.

Selected publications

Short note regarding proposed terminology for the Conditional Spectrum and Conditional Mean Spectrum.
Baker, J. W., and Lee, C. (2018). “An Improved Algorithm for Selecting Ground Motions to Match a Conditional Spectrum.” Journal of Earthquake Engineering, 22(4), 708–723. Associated software.
Lin, T., Haselton, C. B., and Baker, J. W. (2013). “Conditional-Spectrum-based ground motion selection. Part I: Hazard consistency for risk-based assessments.” Earthquake Engineering & Structural Dynamics, 42(12), 1847–1865.
Lin, T., Haselton, C. B., and Baker, J. W. (2013). “Conditional-Spectrum-based ground motion selection. Part II: Intensity-based assessments and evaluation of alternative target spectra.” Earthquake Engineering & Structural Dynamics, 42(12), 1867–1884.
Lin, T., Harmsen, S. C., Baker, J. W., and Luco, N. (2013). “Conditional Spectrum Computation Incorporating Multiple Causal Earthquakes and Ground Motion Prediction Models.” Bulletin of the Seismological Society of America, 103(2A) 1103-1116.
Baker, J.W. (2011). "Conditional Mean Spectrum: Tool for ground motion selection," Journal of Structural Engineering, 137(3), 322-331.
Baker J.W. and Cornell C.A. (2006). "Spectral Shape, Epsilon and Record Selection," Earthquake Engineering & Structural Dynamics, 35 (9) 1077-1095.
Baker J.W. and Cornell C.A. (2005). "A Vector-Valued Ground Motion Intensity Measure Consisting of Spectral Acceleration and Epsilon," Earthquake Engineering & Structural Dynamics, 34 (10), 1193-1217.