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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 DV: COLLAPSE
Variable
Damage DM: Non-simulated failure,
Measure
e.g., Loss of Vertical
Engineering Carrying Capacity (LVCC)
Demand EDP: Interstory Drift Ratio
Parameter
Intensity IM: Sa(T1) + Ground Motions
Measure
Deterioration Modes & Collapse Scenarios
A
A
E D
F C
B
E
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
QCap,pl
M
My
Ke Ke
Qy Q
1.5 200
Experimental Results
Non-Deteriorated Model Prediction
Backbone 150
1
Normalized Moment (M/My)
100
0.5
50
Shear Force (kN)
0
0
-50 Test 19 (kN, mm, rad):
-0.5
Ke = 3.1779e+007
Kinit = 7.4024e+007
s = 0.02
-100
c = -0.04 (ND = 1)
-1 y = 0.0091
cap,pl = 0.069 (LB = 1)
u,mono,pl = 0.116 (LB = 1)
-150
= 85, c = 1.20
isPDeltaRemoved = 1
-1.5
-8 -6 -4 -2 0 2 4 6 8 -200
-100 -50 0 50 100 150
Chord Rotation (radians) Column Top Horizontal Deflection (mm)
Example: Criteria for RC Beams (FEMA 273)
Sidesway Collapse Modes - SMF
11151, Sa: Sa:
EQ: EQ: 11021,2.51g2.52g EQ: Sa: 2.26g
EQ: 11152, 11022, Sa: 2.12g
EQ: 11091, Sa: 2.19g EQ: 11092, Sa: 3.06g
EQ: 11131, Sa: 2.19g EQ: 11132, Sa: 2.12g
EQ: 11122, Sa: 2.32g EQ: 11141, Sa: 1.79g EQ
40% of collapses 27% of collapses
EQ: 11161, Sa: 0.66g EQ: 11162, Sa: 0.72g
EQ: 11101, Sa: 1.52g
EQ: 11141, Sa: 1.79g 11142, Sa: Sa:
EQ: EQ: 11102,1.32g1.06g
17% of collapses 12% of collapses
5% of collapses 2% of collapses
Incremental Dynamic Analysis – Collapse
4
3.5
GROUND MOTION INTENSITY
3
Sag.m.(T=1.0s)[g]
2.5 Mediancol = 2.2g
σLN, col = 0.36g
2
1.5
1
0.5
0
0 0.05 0.1 0.15
Maximum Interstory Drift Ratio
STRUCTURAL RESPONSE (DRIFT)
7
Uncertainty – Plastic Rotation Capacity
1.2 1.2
1.0 1.0
Normalized Moment (M/My)
Normalized Moment (M/My)
0.8 0.8
Mean (m) Plastic
0.6 0.6
Reduced (m-s)
Mean minus standard
deviation (lognormal)
Rotation Capacity
0.4 0.4 for both plastic
Plastic Rot. Cap.
rotation capacity and
post-capping stiffness
0.2 0.2
0.0 0.0
0.00 0.02 0.04 0.06 0.08 0.10 0.00 0.02 0.04 0.06 0.08 0.10
Total Chord Rotation (radians) Total Chord Rotation (radians)
1.4
1.2 1.2
1 1
Sacomp(T=2.0s)[g]
Sacomp(T=2.0s)[g]
0.8 0.8
0.6 0.6
0.4 0.4
0.2 0.2
0 0
0 0.05 0.1 0.15 0 0.05 0.1 0.15
Maximum Interstory Drift Ratio Maximum Interstory Drift Ratio
8
Correlation of Component Variabilities
Type A: Correlation
of parameters Type B: Correlation
within an element between parameters
of different elements
Type B Correlations - Between Parameters of Elementi and Elementj
σLN, modeling Full Correlation
Partial (ρij = 0.5) -
No Correlation
approx. method
Different Parameters of the Same
Type A Correlations - Between
Full Correlation 1.12 0.89 0.63
Full Correlation
Element
between Variables
Expected to be 0.63 0.50 0.33
Correlated
No Correlation 0.43 0.34 0.23
9
Collapse Capacity – with Modeling Uncert.
1
Median = 2.2g
0.9
sLN, Total = 0.36
Cummulative Probability of Collapse
0.8
σLN, Total = 0.64 w/mod.
0.7
0.6
Margin 2.7x
0.5
0.4
0.3
P[collapse |Sa = 0.82g] = 5%
0.2
Empirical CDF
0.1 Lognormal CDF (RTR Var.)
5% Lognormal CDF (RTR + Modeling Var.)
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
MCE Sag.m.(T=1.0s) [g]
2% in 50 yrs GROUND MOTION INTENSITY 10
Mean Annual Frequency of Collapse
1
0.9
Collapse Performance
Cummulative Probability of Collapse
Collapse
0.8
0.7
0.6 CDF Margin: Sa,collapse = 2.7 MCE
0.5
0.4
0.3 Probability of collapse under
design MCE = 5%
0.2
Empirical CDF
0.1 Lognormal CDF (RTR Var.)
Lognormal CDF (RTR + Modeling Var.)
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.0020
Sag.m.(T=1.0s) [g]
MAFcol = 1.0 x 10-4 (about ¼
of the MCE 2% in 50 year
MAF of Excedance (Poisson rate)
0.0018
Hazard
0.0016
0.0014 ground motion)
0.0012 Curve
0.0010
0.0008
0.0006
0.0004
2/50
0.0002
0.0000
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Sa at First Mode Period (g)
11
Benchmarking Archetype Studies
… …
DV’s:
Facility p(collapse)
Definition
p($ > X)
p(D.T. > Y)
2003 Code Compliant
- Strength
- Stiffness
PBEE
- Capacity Design multiple realizations Assessment
- Detailing “design uncertainty” IM-EDP-DM-DV
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)
Space Frame Perimeter Frame
(Atrib/Atotal = 1.0) (Atrib/Atotal = 0.16)
• Strength/Stiffness Distribution
(A) step sizes per typical practice
(B) weak story (1st or 1st-2nd stories)
Likelihood & Mode of Collapse
30
25 Perimeter Mean Annual
Frames
collapse[10-4] -4
Frequency (MAF)
MAF x 10
20
15
of collapse:
Space 5 to 25 x 10-4
10
Frames
5
Space Frames
Perimeter Frames
0
0 5 10 15 20
Number of Stories
1 story 2 stories 4 stories 8 stories 12 stories 20 stories
Relative Risk Levels
Loading & Event Mean Annual Frequency
Gravity & Wind
7x10-4
(LRFD limit state)
Earthquake
1 x 10-4
(collapse, new RC)
Nuclear Reactor
1 x 10-5
(earthquake hazard)
Fire
1 x 10-6
(flashover, 100m2 office)
Fire + (1.0D + 0.5L)
1 x 10-7
(flashover, 100m2 office)
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
