Quantifying risk by performance-based earthquake engineering, Cont’d

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 DV: COLLAPSE Decision Variable Damage Measure DM: Non-simulated failure, e.g., Loss of Vertical Carrying Capacity (LVCC) Engineering Demand Parameter EDP: Interstory Drift Ratio Intensity Measure IM: Sa(T1) + Ground Motions

Deterioration Modes & Collapse Scenarios F • Deterioration Modes of RC Elements • Simulation vs. Fragility Models • Building System Collapse Scenarios • Sidesway Collapse (SC) • Loss in Vertical Load Carrying Capacity (LVCC) • 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

Incremental Dynamic Analysis – Collapse Mediancol = 2.2g σLN, col = 0.36g GROUND MOTION INTENSITY STRUCTURAL RESPONSE (DRIFT)

Uncertainty – Plastic Rotation Capacity Mean (m) Plastic Rotation Capacity Reduced (m-s) Plastic Rot. Cap.

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

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

Mean Annual Frequency of Collapse Collapse Performance • Margin: Sa,collapse = 2.7 MCE • Probability of collapse under design MCE = 5% • MAFcol = 1.0 x 10-4 (about ¼ of the MCE 2% in 50 year ground motion) Collapse CDF Hazard Curve 2/50

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

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

MAF x 10-4 Likelihood & Mode of Collapse Perimeter Frames Mean Annual Frequency (MAF) of collapse: 5 to 25 x 10-4 Space Frames 1 story 2 stories 4 stories 8 stories 12 stories 20 stories

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

Quantifying risk by performance-based earthquake engineering, Cont’d