Framework for Performance-Based Earthquake Engineering. Helmut Krawinkler, Stanford U.

Transcription

1 Framework for Performance-Based Earthquake Engineering Helmut Krawinkler, Stanford U. PEER Summative Meeting June 13, 2007

2 Where were we 10 years ago? SEAOC Vision 2000, FEMA 273, ATC-40 Descriptive performance levels (IO, LS, CP, etc.) Associated with specific hazard levels Performance Objectives Qualitative (and a few quantitative) damage measures Limited consideration of uncertainties Implementation in terms of FORCES and DEFORMATIONS Earthquake Performance Level Fully Operational Operational Life Safe Near Collapse Earthquake Design Level Frequent (43 year) Occasional (72 year) Rare (475 year) Very Rare (970 year) Basic Objective Essential/Hazardous Objective Safety Critical Objective Unacceptable Performance (for New Construction)

3 Measures of Performance - PBEE Forces and deformation? Yes, but only for engineering calculations Intermediate variables Not for communication with clients and community Communication in terms of the three D s: Dollars (direct economic loss) Downtime (loss of operation/occupancy) Death (injuries, fatalities, collapse) Quantification Losses for a given shaking intensity Losses for a specific scenario (M & R) Annualized losses With or without rigorous consideration of uncertainties

4 Vision of PBEE Joe s Beer! Food! 1. Complete simulation 2. Defined performance objectives Quantifiable performance targets Annual probabilities of achieving them 3. Informed owners Joe s Beer! Food! Joe s Beer! Food! Sources: G. Deierlein, R. Hamburger

5 The Peer Framework Equation v ( DV ) = G DV DM dg DM EDP dg EDP IM dλ( IM ) Impact Performance (Loss) Models and Simulation Hazard Curse? Blessing

6 Performance-Based Methodology Bldgs. Measures of Performance Collapse & Casualties Direct Financial Loss Downtime Decision Decision Variable Variable Damage Damage Measure Measure drift as an EDP Engineering Engineering Demand Demand Parameter Parameter Intensity Intensity Measure Measure

7 Performance-Based Methodology Engineering Engineering Demand Demand Parameter Parameter Intensity Intensity Measure Measure Mean Annual Freq. of Exceedance, λ Sa MEAN SPECTRAL ACC. HAZARD CURVE -- T = 1.8 sec. Van Nuys, CA, Horizontal Component Spectral Acceleration S a (g) Medina & Krawinkler

8 Incremental Dynamic Analysis IM (e.g., S a (T 1 )) Individual records Median 84% IM Hazard curve (annual freq. of exceedance) EDP (e.g., max. interstory drift) λ EDP [ EDP y IM = x] dλ (x) ( y) = P IM

9 Performance-Based Methodology Decision Decision Variable Variable Performance Assessment types (ATC-58 definitions): Intensity-based: Scenario-based: Time-based: Prob. facility perf., given intensity of ground motion Prob. facility perf., given a specific earthquake scenario Prob. facility perf. In a specific period of time Damage Damage Measure Measure Damage Fragility Curves: P(DM>dm EDP) Drywall Partitions with Metal Frame + Cost Functions: P($>x DM) Drywall partitions Mean Loss Curve: E[Loss EDP] Drywall Partitions with Metal Frame DM 1 DM 2 DM EDP (IDR) Tape, Paste & Repaint Replacement of gypsum boards Partition replacement Cost of Repair / Cost New EDP (IDR) Aslani & Miranda Engineering Engineering Demand Demand Parameter Parameter Intensity Intensity Measure Measure Mean Annual Freq. of Exceedance, λ Sa MEAN SPECTRAL ACC. HAZARD CURVE -- T = 1.8 sec. Van Nuys, CA, Horizontal Component Spectral Acceleration S a (g) Medina & Krawinkler

10 Deaggregation of Expected Annual Loss Example: Van Nuys Testbed Building Collapse 29% Structural 12% Non-collapse 71% Non-tructural 88% Source: E. Miranda

11 Design Decision Support Hazard Domain Mean Hazard Curve Structural System Domain Mean IM-EDP Curves 10/50 EDP = Max. Interstory Drift EDP = Max. Floor Acceleration Loss Domain Mean Subsystem Loss Curves Expected $Loss NSDSS EDP = Max. Interstory Drift NSASS EDP = Max. Floor Acceleration Zareian & Krawinkler (2005)

12 Assessment of Collapse Potential NORM. STRENGTH VS. MAX. STORY DUCT. N=9, T 1 =0.9, ξ=0.05, α=0.03, θ=0.015, H 3, BH, K 1, S 1, NR94nya γ = V y W [S a (T 1 )/g] / γ Non-degrading system Degrading system Collapse Capacity µ si,max 15 20

13 Modeling of Deterioration Load (kips) UCI G12 OSB F y =8.2 kips, δ y =0.45 in, α s =0.047, α c =-0.081, α u =1.94, δ c /δ y = Displacement (in) Load (kips) UCI G12 OSB Pinching Model, κ=0.5, F y =8.2 kips, δ y =0.45 in α s =0.047, α c =-0.081, α c =1.94, δ c /δ y =5.44, γ s =270, γ c =270, γ k =, γ a = Displacement (in)

14 Collapse Capacity for a Set of Ground Motions 10 MAX. STORY DUCTILITY vs. NORM. STRENGTH N=9, T 1 =0.9, ξ=0.05, K 1, S 1, BH, θ=0.015, Peak-Oriented Model, α s =0.05, δ c /δ y =4, α c =-0.10, γ s =8, γ c =8, γ k =8, γ a =8, λ=0, LMSR 8 [S a (T 1 )/g]/γ Individual responses Maximum Story Ductility Over the Height, µ s,max

15 Collapse Fragility Curve 1 Obtaining the collapse fragility curve (MRF) N = 8, T 1 = 1.2, γ = 0.17, Stiff & Str = Shear, SCB = , ξ = 0.05 θ p = 0.03, θ pc /θ p = 5, λ = 20, M c /M y = 1.1 Probability of Collapse Data points Collapse fragility curve IM[Sa(T 1 )] Zareian & Krawinkler (2004)

16 Probability of Collapse at MCE, for MRFs with R = 8 P(Collapse) at MCE level P(Collapse) at MCE given R = 8 & Ω = 2.5 (MRF) Siff. & Str. = Shear, SCB = , ξ = 0.05, θ pc /θ p = 15.0, λ = 50, M c /M y = 1.1 Design Spectrum: Sa(T 1 )/g = /T < 1.0 θ p = 0.06 θ p = First Mode Period (sec.) Zareian & Krawinkler (2007)

17 Implementation of Framework ATC-58 Guidelines for Seismic Performance Assessment of Buildings ATC-63 Recommended Methodology for Quantification of Building System Performance TBI Tall Building Initiative LRFD for bridge design

18 Concluding Remarks Performance based engineering is here to stay It enforces a transparent design/assessment approach Much more emphasis must be placed on $ losses and loss of function (downtime) Performance based design should be reliability based We have a long road ahead of us