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

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

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 of optimum ground motion intensity measures that can be used in the PEER framework equation to assess the performance of R/C frame building structures.

4. 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 Seismological Variables Ground Motion Parameters Magnitude Closest Distance (R) Faulting Mechanism Local Site Condition Rupture Directivity Index PGA, PGV, PGD Duration Mean Period T mean Arias Intensity,I a,max Spectral Acceleration S a (T 0,  = 5%) Average scaled spectral acceleration [ from S a (T 0,  ) to S a (2T 0,  )] Ground Motion Database

5. 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 Nonlinear SDOF Analysis System Parameter Initial Period T 0 Damping Ratio  Normalized Strength C y = R y /(mg) Strain Hardening Ratio 

6. Ground Motion Intensity Measures Primary Intensity Measure: S a (T 0,  ) 84-percentile S a level Median S a level 16-percentile S a level Secondary Intensity Measures: Proposed Intensity Measures Maximum Value of 1 Measures of damage effectiveness of a given ground motion record Obtained using Bilinear Inelastic SDOF system with  = 0 Ground Motions scaled to three levels of S a : Median S a, 16-percentile and 84-percentile. Distortion of earthquake records minimized by restricting the scale factors to reasonable values, namely 3.0Factor Scale3.0  T 0 [sec] S a [g]

7. Statistical Correlation Analysis Results PGV [in/sec] Duration [sec] CyCy Good correlation as measured by a high correlation coefficient  Poor correlation as measured by a low correlation coefficient  CyCy T 0 = 0.2 sec;  = 0.05 ;  = 0 ;  = 8 ; Model: Bilinear Inelastic Inverse Analysis: CyCy R [km] Medium correlation as measured by a medium correlation coefficient 

8. Statistical Correlation Analysis Results Magnitude  T 0 = 0.2 sec.;  = 0.05;  = 0; C y  = =  ; Model: Bilinear Inelastic   Direct Analysis: Response - Seismological Variable Correlation Response - SDOF-Based Intensity Measure Correlation Inter-Response Correlation

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. ) ( rev  ) ( * max, PL  ) ( N rev, y ) ( ) ( N y ve  ) (  ) ( *, E end I ) ( P * max, I ) ( P *, H ) ( E * h ) ( rev  ) ( * max, PL  ) ( N rev, y ) ( ) ( N y ve  ) (  ) ( *, E end I ) ( P * max, I ) ( P *, H ) ( E * h  [Response vs. IM] T 0 = 1.0 sec  = 0.05  = 0 C y = 0.028 Response Parameters computed using Bilinear Inelastic Model SDOF-based Intensity Measures (IM) computed using Bilinear Inelastic Model ) ( rev  ) ( * max, PL  ) ( N rev, y ) ( ) ( N y ve  ) (  ) ( *, E end I ) ( P * max, I ) ( P *, H ) ( E * h  [Response vs. IM] Correlation analysis to evaluate optimum intensity measures: STEP-I T 0 = 1.0 sec  = 0.05  = 0 C y = 0.028 Option 1: Option 2:         F S I 100 E a M * h              F F S I 25 N 8 a M rev,y

11. ) (  ) ( * max, PL  ) ( N rev, y ) ( ) ( N y ve  ) (  ) ( *, E end I ) ( P * max, I ) ( P *, H ) ( E * h ) ( rev  ) ( * max, PL  ) ( N rev, y ) ( ) ( N y ve  ) (  ) ( *, E end I ) ( P * max, I ) ( P *, H ) ( E * h  [Response vs. IM] T 0 = 1.0 sec  = 0.05  = 0 C y = 0.028 Response Parameters computed using Slip Model SDOF-based Intensity Measures (IM) computed using Bilinear Inelastic Model ) ( rev  ) ( * max, PL  ) ( N rev, y ) ( ) ( N y ve  ) (  ) ( *, E end I ) ( P * max, I ) ( P *, H ) ( E * h  [Response vs. IM] T 0 = 1.0 sec  = 0.05  = 0 C y = 0.028 Option 1: Option 2:         F S I 100 E a M * h              F F S I 25 N 8 a M rev,y Correlation analysis to evaluate optimum intensity measures: STEP-II

12. Relative Correlation of Response Parameter, here Ductility (  to Various Candidate Intensity Measures PGA PGVPGD I a,max Dur T mean Mag RF  = 2 F  = 4 F  = 6 F  = 8 F 25 E * h  F 5 E * h  F 50 E * h  F 100 E * h    Vs. IM] (T 0 = 3.0 sec)   Vs. IM] (T 0 = 1.0 sec)   Vs. IM] (T 0 = 0.2 sec) Candidate Intensity Measures (IM) System Parameters and Model: Damping ratio (  ) = 5% Strain hardening ratio (  ) = 0 Model: Clough’s Stiffness Degrading Model Strength: C y = 0.125 Strength: C y = 0.028 Strength: C y = 0.005

13. PGA PGVPGD I a,max Dur T mean Mag RF  = 2 F  = 4 F  = 6 F  = 8 F 25 E * h  F 5 E * h  F 50 E * h  F 100 E * h  Candidate Intensity Measures (IM) System Parameters and Model: Damping ratio (  ) = 5% Strain hardening ratio (  ) = 0 Model: Clough’s Stiffness Degrading Model   vs. IM] (T 0 = 0.2 sec)   vs. IM] (T 0 = 1.0 sec)   vs. IM] (T 0 = 3.0 sec) Relative Correlation of Response Parameter, here Max. Plastic Deformation (  to Various Intensity Measures * max,PL  Strength C y = 0.125 Strength C y = 0.028 Strength C y = 0.005

14. Total number of ground motion records = 550 Total number of ground motion records = 210 Total number of ground motion records = 91 S a = 0.416 g (Median S a ) c.o.v. = 1.09 c.o.v. = 0.57 c.o.v. = 0.44 System Parameters and Model: Initial Period (T 0 ) = 0.2 sec. Damping ratio (  ) = 5% Strength C y = 0.125 Strain hardening ratio (  ) = 0 Model: Bilinear Inelastic N N N Ductility (  ) S a = 0.416 g (Median S a ) 36.024.0 F N rev,y  Reduction in Dispersion of Normalized Hysteretic Energy (  when are Specified in Addition to S a (T 0,  ) E * h FF N rev, y and 

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

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

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

18. 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:         F S I 100 E a M * h              F F S I 25 N 8 a M rev,y 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. Main regression lines for both subsets Confidence interval for LMSR subset Confidence interval for SMSR subset Log (residuals) T 0 = 1.0 sec;  = 0.05;  = 0 C y = 0.028, Model: Bilinear inelastic Nonlinear Regression Analysis SMSR subset LMSR subset