Quantifying risk by performance- based earthquake engineering, Cont’d Greg Deierlein Stanford University …with contributions by many 2006 IRCC Workshop on Use of Risk in Regulation

PBEE Assessment Components Decision Variable Intensity Measure Damage Measure Engineering Demand Parameter DV: COLLAPSE DM: Non-simulated failure, e.g., Loss of Vertical Carrying Capacity (LVCC) EDP: Interstory Drift Ratio IM: Sa(T 1 ) + Ground Motions

Deterioration Modes & Collapse Scenarios F 1.Deterioration Modes of RC Elements -Simulation vs. Fragility Models 2.Building System Collapse Scenarios -Sidesway Collapse (SC) -Loss in Vertical Load Carrying Capacity (LVCC) 3.Likelihood of Collapse Scenarios -Existing vs. New Construction -“Ordinary” versus “Special” seismic design

Realistic RC Component Simulation

Example: Criteria for RC Beams (FEMA 273)

Sidesway Collapse Modes - SMF 40% of collapses 27% of collapses 17% of collapses 12% of collapses 5% of collapses 2% of collapses

7 Incremental Dynamic Analysis – Collapse Median col = 2.2g σ LN, col = 0.36g STRUCTURAL RESPONSE (DRIFT) GROUND MOTION INTENSITY

8 Uncertainty – Plastic Rotation Capacity Mean (  ) Plastic Rotation Capacity Reduced (  Plastic Rot. Cap.

9 Correlation of Component Variabilities Type A: Correlation of parameters within an element Type B: Correlation between parameters of different elements

10 Collapse Capacity – with Modeling Uncert. Median = 2.2g  LN, Total = 0.36 σ LN, Total = 0.64 w/mod. P[collapse |Sa = 0.82g] = 5% 5% Margin 2.7x GROUND MOTION INTENSITY MCE 2% in 50 yrs

11 Mean Annual Frequency of Collapse Collapse CDF Hazard Curve Collapse Performance Margin: S a,collapse = 2.7 MCE Probability of collapse under design MCE = 5% MAF col = 1.0 x (about ¼ of the MCE 2% in 50 year ground motion) 2/50

Benchmarking Archetype Studies multiple realizations “design uncertainty” Facility Definition PBEE Assessment IM-EDP-DM-DV DV’s: p(collapse) p($ > X) p(D.T. > Y) 2003 Code Compliant - Strength - Stiffness - Capacity Design - Detailing … …

30 Archetype Realizations Height: 1, 2, 4, 8, 12 and 20 stories Bay Width: 6 & 9 meters Space vs. Perimeter Frame (A trib /A = 0.1 to 0.2) Strength/Stiffness Distribution (A) step sizes per typical practice (B) weak story (1 st or 1 st -2 nd stories) Perimeter Frame (A trib /A total = 0.16) Space Frame (A trib /A total = 1.0)

MAF x Likelihood & Mode of Collapse Mean Annual Frequency (MAF) of collapse: 5 to 25 x story2 stories4 stories8 stories12 stories20 stories Perimeter Frames Space Frames

Loading & EventMean Annual Frequency Gravity & Wind (LRFD limit state) 7x10 -4 Earthquake (collapse, new RC) 1 x Nuclear Reactor (earthquake hazard) 1 x Fire (flashover, 100m 2 office) 1 x Fire + (1.0D + 0.5L) (flashover, 100m 2 office) 1 x Relative Risk Levels

Concluding Remarks PB Methods == Means of Quantifying Performance scientific models and data role of judgment probabilistic vs. scenarios assumptions Performance Targets minimum life safety minimum “convenience” (societal value - cost/benefit) enhanced performance (cost-benefit) Implementation explicit assessment prescriptive methods (calibrated to performance targets) Consensus Guidelines and Standards design professionals, societal representatives, and stakeholders