Seismic Hazard Analysis Jonathan P. Stewart, Ph.D., P.E. Professor - PowerPoint PPT Presentation

Non-Ergodic Site Response in Seismic Hazard Analysis Jonathan P. Stewart, Ph.D., P.E. Professor and Chair Civil & Environmental Engineering Dept. University of California, Los Angeles ESG 5 August 15, 2016 Taipei, Taiwan

Acknowledgements Co-Author: Kioumars Afshari, UCLA OpenSHA assistance from: Kevin Milner, Christine Goulet, SCEC Financial Support: PEER, Caltrans, CSMIP EERI, SSA: Sponsorship of Joyner Lecture 2

Objectives Understand differences between non-ergodic and ergodic site response Present framework for developing site-specific GMPE for use in ground motion hazard analysis Effects on hazard Takes some effort, but tools available … and worth it 3

Outline • Ergodic site amplification • Non-ergodic (location-specific) site amplification • Implementation in PSHA • Summary 4

Notation • IM = intensity measure • X = Reference site IM • Z = soil site IM • Y = Z / X (site amplification) 5

Ergodic Models • Ergodic : Ground motions evaluated from diverse (global) data set • Examples: – V S30 - and depth-dependent site terms in GMPEs – Site amplification coefficients in building codes 6

GMPE       ln Z F F F ln E P S n Z Ergodic source & path F S : ergodic effect of site Two components: F S = F lin + F nl 7

GMPE       ln Z F F F ln E P S n Z Ergodic source & path F S : ergodic effect of site Actual for site j : F S + h Sj 8

GMPE       ln Z F F F ln E P S n Z Ergodic source & path F S : ergodic effect of site Actual for site j : F S + h Sj      2 2 ln ln Z Z  ln Z : ergodic total standard deviation Between-event variability 9

GMPE       ln Z F F F ln E P S n Z Ergodic source & path F S : ergodic effect of site Actual for site j : F S + h Sj      2 2 ln ln Z Z  ln Z : ergodic total standard deviation Within-event variability      2 2 2 Modified from Al Atik et al. (2010) 10 10 2 2 ln P P S S Y

Importance of  Consider example site Figure: P. Zimmaro. 11

Importance of  Consider example site Hazard with as-published ergodic  & sensitivity Figure: P. Zimmaro. Similar to Bommer and Abrahamson, 2006 12

Importance of  Consider example site Hazard with as-published ergodic  & sensitivity Ergodic  difficult to reduce as GMPEs evolve… After Strasser et al., 2009 13

Outline • Ergodic site amplification • Non-ergodic (location-specific) site amplification • Implementation in PSHA • Summary 14

Non-Ergodic Site Amplification • Non-Ergodic : Amplification is site-specific – Bias removal – Reduced dispersion • Evaluation from: – On-site recordings – Geotechnical simulations • Site response model: m lnY ,  lnZ 15

Dispersion reduction        2 2 2 2 Recall ln 2 2 ln Z P P S S Y  lnZ from GMPE If site effect non-ergodic, can remove S2S-component:     2 2 Approach 1: use ln 2 Z S S     2 2 2 Approach 2: replace with 2 2 P P S S SS 16

Approach 1 17

Approach 2 GMPE (ergodic) vs single-station (  SS ) (GeoPentech, 2015) 18

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Evaluation from Recordings Install sensors at Site j Record eqks in M -R range of GMPE (Site j and others) Compute residuals:   m ln R z ln , ij ij Z ij Partition residuals:  h   R W ij Ei ij

Evaluation from Recordings Install sensors at Site j Record eqks in M -R range of GMPE (Site j and others) Compute residuals:   m ln R z ln , ij ij Z ij Partition residuals:  h   R W ij Ei ij Mean of  W ij is  h Sj

Evaluation from Recordings Mean linear site response:  h F lin Sj Ergodic linear site term F nl term can be added from simulations Adjusts mean ground motion m ln Z

Evaluation from Simulations z Geotechnical 1D GRA Output V s What is simulated, what is not. Y=Z/X G/G Max D g x Rock GMM Input 23

Evaluation from Simulations Geotechnical 1D GRA What is simulated, what is not. Use range of input motions, X. For each, compute Y=Z/X (Detailed procedures in 2014 PEER report) Limited effectiveness for many sites ( e.g., Thompson et al. 2012 ) 24

Site Response Model Site-specific amplification function    x f m   3 IMref   ln f f ln 1 2 Y   f 3 F lin F nl

Site Response Model Site-specific amplification function Fit GRA results Approximate fits possible if fewer runs

Site Response Model Site-specific amplification function Fit GRA results Approximate fits possible if fewer runs As available, note empirical amplification

Site Response Model Site-specific amplification function Fit GRA results Approximate fits possible if fewer runs As available, note empirical amplification Shift to match empirical for weak motion (semi- empirical approach)

Site Response Model Site-specific amplification    x f m   IMref 3   ln f f function ln Y 1 2  f  3 Standard deviation term  ln Z reduced from  ln X due to: 2     f x •         Nonlinearity 2 2 2  2  1 F  ln ln 2 ln Z X S S Y   x f 3

Site Response Model Site-specific amplification    x f m   IMref 3   ln f f function ln Y 1 2  f  3 Standard deviation term  ln Z reduced from  ln X due to: 2     f x •         Nonlinearity 2 2 2  2  1 F  ln ln 2 ln Z X S S Y   x f Non-ergodic  ln 3 • Approach 1

Site Response Model Site-specific amplification    x f m   IMref 3   ln f f function ln Y 1 2  f  3 Standard deviation term  ln Z reduced from  ln X due to: 2   f x •       Nonlinearity 2 2  2  1  ln ln Z SS Y   x f Non-ergodic  ln 3 • Approach 2

Site Response Model Site-specific amplification    x f m   IMref 3   ln f f function ln Y 1 2  f  3 Standard deviation term  ln Z reduced from  ln X due to: 2     f x •         Nonlinearity 2 2 2  2  1 F  ln ln 2 ln Z X S S Y   x f Non-ergodic  ln 3 • Include uncertainty in site amplification,  ln Y  0.3

Site Response Model Site-specific amplification function Standard deviation term Epistemic uncertainty Should consider center & range of possible: • Mean amplification functions  ln Z models •

Outline • Ergodic site amplification • Non-ergodic (location-specific) site amplification • Implementation in PSHA • Summary 39

Hybrid term from Cramer, 2003, and others         For any given probability, P : ln ln ln z Y x x IMref Mean site amplification Read from given x from hazard curve hazard curve Dominant approach in practice (basis for building code ground motions) 40

Convolution Bazzurro and Cornell, 2004 Given: (1) Hazard curve for reference condition     | P X x t   m   (2) Site amplification function: f x ln Y IMref ln Y    z          |  |  P Z z t P Y x f x dx  IMref  X x 0 Abs. value of slope Simple probability of hazard curve operation given PDF for Y Advantage relative to hybrid: uncertainty in Y considered 41

Hybrid & Convolution - Summary Advantages: • Simple to implement. Only requires rock PSHA and amplification model. Drawbacks: • PSHA based on  lnX not  lnZ • No allowance for non-ergodic standard deviation • Controlling sources and epsilons based on rock GMPE • Nonlinearity driven by X hazard (  X > 0). 42

Modify GMPE in hazard integral m  m  m • Mean: ln | x ln ln Z X Y IMref • Adjusted  ln Z By default, x IMref taken as mean value (  = 0) Pending technical issue: correlation of z and x IMref (unknown presently) Consider epistemic uncertainties using logic trees – high uncertainty sites should have wider bounds 43

OpenSHA Implementation Non-ergodic site response GMPE can be selected as ‘intensity measure relation’ Select GMPE for reference condition and its V S30 V S30 and depth parameters for site Coefficients entered for mean and st dev site model for range of periods. Fitted interpolation between periods with specified coefficients Option to adjust to ergodic model at long periods. http://www.opensha.org/ 44

Example Applications 45

Los Angeles – Obregon Park 46

Los Angeles – Obregon Park 47

Los Angeles – Obregon Park 48

Los Angeles – Obregon Park Simulations for nonlinear parameters: UHS: 2% Prob. exc. 50 yr 49

Los Angeles – Obregon Park Simulations for nonlinear parameters: UHS: 2% Prob. exc. 50 yr 50