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Ground Motion Intensity Measures for Performance-Based Earthquake Engineering

Ground Motion Intensity Measures for Performance-Based Earthquake Engineering. Hemangi Pandit Joel Conte Jon Stewart John Wallace. Earthquake Database Seismological Variables Ground Motion Parameters. MDOF Nonlinear Finite Element Model. SDOF Structural Model

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Ground Motion Intensity Measures for Performance-Based Earthquake Engineering

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  1. Ground Motion Intensity Measures for Performance-Based Earthquake Engineering Hemangi Pandit Joel Conte Jon Stewart John Wallace

  2. Earthquake • Database • Seismological • Variables • Ground Motion • Parameters MDOF Nonlinear Finite Element Model • SDOF Structural Model • System Parameters • Hysteretic Model • Parameters Nonlinear Response History Analysis MDOF Response/ Demand Parameters Hysteretic Models • Bilinear Inelastic • Clough’s Stiffness Degrading • Slip Model Inverse Analysis Direct Analysis • Statistical Study • Marginal Statistics • Correlation Analysis SDOF Response/Demand Parameters • Statistical Analysis • Marginal Probability Distributions • Second-Order Statistics Regressionbetween Proposed Nonlinear SDOF-Based Intensity Measuresand MDOF Response Parameters • Correlation and Regression Analysis • New Intensity Measures vs. Ground Motion Parameters • Nonlinear SDOF Response vs. New Intensity Measures Simplified and Efficient Methods to evaluate PEER Hazard Integral for MDOF Inelastic Models of R/C Frame buildings Proposed Vector of Ground Motion Intensity Measures

  3. Project Vision PEER Framework Equation: • A critical issue in the PEER probabilistic framework is the choice of ground motion intensity measures, either a single intensity measure or a vector of intensity measures • The choice of this vector has a profound impact on the simplifying assumptions and methods that can be used to evaluate accurately and efficiently the PEER hazard integral for actual R/C frame buildings. Primary objective of this project: • Identify a set ofoptimum ground motion intensity measures that can be used in the PEER framework equation to assess the performance of R/C frame building structures.

  4. Ground Motion Database Source of ground motion records • Pacific Engineering and Analysis Strong Motion (PEASM) • Database including Northridge and Kobe earthquakes • Big Bear, Hector Mine, Petrolia and Northridge aftershocks • 1999, Chi-chi,Taiwan and 1999, Ducze and Kocaeli, Turkey, • earthquakes Shallow crustal earthquakes in active tectonic regions Selection criteria for records Final set of 881 qualified records • 689 from PEASM and additional records • 159 from Taiwan, 1999, and 33 from Turkey, 1999 Ground Motion Parameters Seismological Variables • PGA, PGV, PGD • Duration • Mean Period Tmean • Arias Intensity ,Ia,max • Spectral Acceleration Sa(T0, x = 5%) • Average scaled spectral acceleration • [ from Sa (T0, x) to Sa (2T0, x)] • Magnitude • Closest Distance (R) • Faulting Mechanism • Local Site Condition • Rupture Directivity Index

  5. Nonlinear SDOF Analysis u D D R R u R , p1 , p3 u D , p1 k k k p 2 p p R R R 1 1 10 1 1 y y y 9 k 0 1 u D k k , p2 u u 0 u 0 4 3 8 11 1 U 7 1 U U y y y u u D D , , p1 p3 5 6 u D u D , p2 , p2 Bilinear Inelastic Model Clough’s Stiffness Degrading Model Slip Model • Key Response/Demand Parameters • Displacement Ductility • Residual Displacement Ductility • Maximum Normalized Plastic Deformation Range • Number of Positive Yield Excursions • Number of Yield Reversals • Normalized Earthquake Input Energy • Normalized Hysteretic Energy Dissipated • Maximum Normalized Earthquake Input Power • Maximum Normalized Hysteretic Power • System Parameter • Initial Period T0 • Damping Ratio x • Normalized Strength • Cy = Ry /(mg) • Strain Hardening Ratio a

  6. Ground Motion Intensity Measures £ £ 0 . 3 Scale Factor 3.0 84-percentile Sa level Primary Intensity Measure: Sa(T0, x) • Ground Motions scaled to three levels of Sa : Median Sa, 16-percentile and 84-percentile. • Distortion of earthquake records minimized by restricting the scale factors to reasonable values, namely Sa [g] Median Sa level 16-percentile Sa level Secondary Intensity Measures: T0 [sec] • ProposedIntensity Measures • Maximum Value of 1 • Measures of damage effectiveness of a given ground motion record • Obtained using Bilinear Inelastic SDOF system with a = 0

  7. Statistical Correlation Analysis Results Good correlation as measured by a high correlation coefficient r Medium correlation as measured by a medium correlation coefficient r Poor correlation as measured by a low correlation coefficient r Cy Cy Cy PGV [in/sec] R [km] Duration [sec] T0 = 0.2 sec; x = 0.05 ; a = 0 ; m = 8 ; Model: Bilinear Inelastic Inverse Analysis:

  8. Statistical Correlation Analysis Results Inter-Response Correlation Response - Seismological Variable Correlation Response - SDOF-Based Intensity Measure Correlation m m m Magnitude T0 = 0.2 sec.; x = 0.05; a = 0; Cy= = 0.125; Model: Bilinear Inelastic Direct Analysis:

  9. Three Steps To Determine Effectiveness / Optimality of Proposed Intensity Measures STEP I: Good Correlation with SDOF response parameters obtained from the same hysteretic model as that used to determine , namely the Bilinear Inelastic Model. STEP II: Good Correlation with SDOF response parameters obtained from other hysteretic models, namely Clough’s Stiffness Degrading Model and Slip Model. STEP III: Good Correlation with MDOF response parameters obtained from nonlinear finite element models of RC building or bridge structures.

  10. Correlation analysis to evaluate optimum intensity measures: STEP-I é ù S a = I ê ú M F ë û * = 100 E h m m m ( ( ( ) ) ) é ù m m m ( ( ( ) ) ) S rev rev rev a * * * ( ( ( ) ) ) D D D ê ú PL PL PL , , , max max max = ( ( ( ) ) ) I ê F ú N N N m = + + + ( ( ( ) ) ) y y y M 8 ve ve ve ( ( ( ) ) ) N N N ê ú y y y , , , rev rev rev F * * * ) ) ) ( ( ( = E E E ë û 25 N I I I , , , end end end y , rev * * * ( ( ( ) ) ) E E E h h h * * * ( ( ( ) ) ) P P P I I I , , , max max max * * * ( ( ( ) ) ) P P P H H H , , , max max max Response Parameters computed using Bilinear Inelastic Model SDOF-based Intensity Measures (IM) computed using Bilinear Inelastic Model Option 1: r [Response vs. IM] T0 = 1.0 sec x = 0.05 a = 0 Cy = 0.028 Option2: r [Response vs. IM] T0 = 1.0 sec x = 0.05 a = 0 Cy = 0.028

  11. Correlation analysis to evaluate optimum intensity measures: STEP-II é ù S a = I ê ú M F ë û * = 100 E h m m m ( ( ( ) ) ) é ù m m m ( ( ( ) ) ) S rev rev rev a * * * ( ( ( ) ) ) D D D ê ú PL PL PL , , , max max max = ( ( ( ) ) ) I ê F ú N N N m = + + + ( ( ( ) ) ) y y y M 8 ve ve ve ( ( ( ) ) ) N N N ê ú y y y , , , rev rev rev F * * * ) ) ) ( ( ( = E E E ë û 25 N I I I , , , end end end y , rev * * * ( ( ( ) ) ) E E E h h h * * * ( ( ( ) ) ) P P P I I I , , , max max max * * * ( ( ( ) ) ) P P P H H H , , , max max max Response Parameters computed using Slip Model SDOF-based Intensity Measures (IM) computed using Bilinear Inelastic Model Option 1: r [Response vs. IM] T0 = 1.0 sec x = 0.05 a = 0 Cy = 0.028 Option2: r [Response vs. IM] T0 = 1.0 sec x = 0.05 a = 0 Cy = 0.028

  12. Relative Correlation of Response Parameter, here Ductility (m), to Various Candidate Intensity Measures F * = 100 E h F * = 25 E h F * = F 5 E * h = 50 E h r [m Vs. IM] (T0 = 0.2 sec) Strength: Cy = 0.125 r [m Vs. IM] (T0 = 1.0 sec) Strength: Cy = 0.028 r [m Vs. IM] (T0 = 3.0 sec) Strength: Cy = 0.005 System Parameters and Model: Damping ratio (x) = 5% Strain hardening ratio (a) = 0 Model: Clough’s Stiffness Degrading Model Fm = 6 PGA Ia,max PGV PGD Fm = 2 Fm = 8 Fm = 4 Mag Tmean Dur R Candidate Intensity Measures (IM)

  13. * D PL , max r [ vs. IM] (T0 = 0.2 sec) F * = 100 E h F * = 25 E h F * = F 5 E * h = 50 E h Relative Correlation of Response Parameter, here Max. Plastic Deformation ( ), to Various Intensity Measures Strength Cy = 0.125 r [ vs. IM] (T0 = 1.0 sec) Strength Cy = 0.028 r [ vs. IM] (T0 = 3.0 sec) Strength Cy = 0.005 System Parameters and Model: Damping ratio (x) = 5% Strain hardening ratio (a) = 0 Model: Clough’s Stiffness Degrading Model Fm = 6 Fm = 8 PGA Ia,max PGV PGD Fm = 2 Fm = 4 Mag Tmean Dur R Candidate Intensity Measures (IM)

  14. Reduction in Dispersion of Normalized Hysteretic Energy ( ) when are Specified in Addition to Sa(T0, x) * E h £ £ 0 . 24 0 . 36 F N y , rev and F F m N y rev , Total number of ground motion records = 550 Sa = 0.416 g (Median Sa) N c.o.v. = 1.09 System Parameters and Model: Initial Period (T0) = 0.2 sec. Damping ratio (x) = 5% Strength Cy = 0.125 Strain hardening ratio (a) = 0 Model: Bilinear Inelastic Total number of ground motion records = 210 Sa = 0.416 g (Median Sa) N c.o.v. = 0.57 Total number of ground motion records = 91 Sa = 0.416 g (Median Sa) N c.o.v. = 0.44 Ductility (m)

  15. Reduction in Dispersion of Normalized Hysteretic Energy ( ) when are Specified in Addition to Sa(T0, x) * E h and F F m N y rev , Total number of ground motion records = 550 Sa = 0.416 g (Median Sa) N c.o.v. = 0.67 System Parameters and Model: Initial Period (T0) = 3.0 sec. Damping ratio (x) = 5% Strength Cy = 0.005 Strain hardening ratio (a) = 0 Model: Slip Total number of ground motion records = 201 Sa = 0.416 g (Median Sa) N c.o.v. = 0.41 Total number of ground motion records = 26 Sa = 0.416 g (Median Sa) N c.o.v. = 0.33 Ductility (m)

  16. Reduction in Dispersion of Normalized Hysteretic Energy ( ) when are Specified in Addition to Sa(T0, x) * E h and F F m N y rev , Total number of ground motion records = 94 Sa = 0.416 g (Median Sa) N c.o.v. = 1.01 System Parameters and Model: Initial Period (T0) = 0.2 sec. Damping ratio (x) = 5% Strength Cy = 0.125 Strain hardening ratio (a) = 0 Model: Bilinear Inelastic SUBSET: LMLR Total number of ground motion records = 39 Sa = 0.416 g (Median Sa) N c.o.v. = 0.48 Total number of ground motion records = 27 Sa = 0.416 g (Median Sa) N c.o.v. = 0.45 Ductility (m)

  17. Reduction in Dispersion of Normalized Hysteretic Energy ( ) when are Specified in Addition to Sa(T0, x) * E h and F F m N , rev y Total number of ground motion records = 84 Sa = 0.416 g (Median Sa) N c.o.v. = 0.86 System Parameters and Model: Initial Period (T0) = 0.2 sec. Damping ratio (x) = 5% Strength Cy = 0.125 Strain hardening ratio (a) = 0 Model: Slip SUBSET: LMSR Total number of ground motion records = 29 Sa = 0.416 g (Median Sa) N c.o.v. = 0.48 Total number of ground motion records = 19 Sa = 0.416 g (Median Sa) N c.o.v. = 0.45 Ductility (m)

  18. é ù S a = I ê ú M F ë û * = 100 E h é ù S a ê ú = I ê F ú m = M 8 ê ú F = ë û 25 N y , rev Conclusions • Performed extensive parametric and statistical study of correlation between: • Seismological variables • Ground motion parameters • Nonlinear SDOF response parameters • Defined new nonlinear SDOF-based ground motion intensity measures • Evaluate effectiveness of newly defined nonlinear SDOF-based intensity measures at the SDOF level • Identify promising vectors of intensity measures: • Work in progress: Nonlinear regression analysis between • Proposed intensity measures and nonlinear SDOF response parameters • Seismological variables and proposed intensity measures • Future work: • Evaluation of effectiveness of nonlinear SDOF-based intensity measures at the MDOF level

  19. Nonlinear Regression Analysis SMSR subset LMSR subset Log (residuals) Main regression lines for both subsets Confidence interval for LMSR subset T0 = 1.0 sec; x = 0.05; a = 0 Cy = 0.028, Model: Bilinear inelastic Confidence interval for SMSR subset

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