Quantifying risk by performancebased 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
DV: COLLAPSE
Damage
Measure
DM: Non-simulated failure,
e.g., Loss of Vertical
Carrying Capacity (LVCC)
Engineering
Demand
Parameter
Intensity
Measure
EDP: Interstory Drift Ratio
IM: Sa(T1) + Ground Motions
Deterioration Modes & Collapse Scenarios
A
A
F
E
D
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
Q
Qy
1.5
200
Experimental Results
Model Prediction
Non-Deteriorated
Backbone
150
100
0.5
Shear Force (kN)
Normalized Moment (M/My)
1
0
-0.5
50
0
Test 19 (kN, mm, rad):
-50
Ke = 3.1779e+007
Kinit = 7.4024e+007
s = 0.02
c = -0.04 (ND = 1)
y = 0.0091
cap,pl = 0.069 (LB = 1)
u,mono,pl = 0.116 (LB = 1)
-100
-1
-150
 = 85, c = 1.20
isPDeltaRemoved = 1
-1.5
-8
-6
-4
-2
0
2
Chord Rotation (radians)
4
6
8
-200
-100
-50
0
50
Column Top Horizontal Deflection (mm)
100
150
Example: Criteria for RC Beams (FEMA 273)
Sidesway Collapse Modes - SMF
11021,
Sa: 2.52g
EQ: EQ:
11151,
Sa: 2.51g
EQ: 11091, Sa: 2.19g
EQ: 11131, Sa: 2.19g
EQ: 11122, Sa: 2.32g
40% of collapses
EQ: 11161, Sa: 0.66g
EQ:11141,
11101,
Sa:
1.52g
EQ:
Sa:
1.79g
17% of collapses
5% of collapses
EQ: 11022,
Sa: 2.12g
EQ: 11152,
Sa: 2.26g
EQ: 11092, Sa: 3.06g
EQ: 11132, Sa: 2.12g
EQ: 11141, Sa: 1.79g
27% of collapses
EQ: 11162, Sa: 0.72g
11102,
Sa: 1.06g
EQ: EQ:
11142,
Sa: 1.32g
12% of collapses
2% of collapses
EQ
Incremental Dynamic Analysis – Collapse
4
Sa (T=1.0s)[g]
g.m. INTENSITY
GROUND MOTION
3.5
3
Mediancol = 2.2g
2.5
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
1.2
1.2
1.0
1.0
Normalized Moment (M/My)
Normalized Moment (M/My)
Uncertainty – Plastic Rotation Capacity
0.8
Mean (m) Plastic
Rotation Capacity
0.6
0.4
0.2
0.8
0.6
Reduced (m-s)
Plastic Rot. Cap.
Mean minus standard
deviation (lognormal)
for both plastic
rotation capacity and
post-capping stiffness
0.4
0.2
0.0
0.0
0.00
0.02
0.04
0.06
0.08
0.10
0.00
Total Chord Rotation (radians)
0.02
0.04
0.06
0.08
0.10
Total Chord Rotation (radians)
1.2
1.2
1
1
Sacomp(T=2.0s)[g]
Sacomp(T=2.0s)[g]
1.4
0.8
0.6
0.4
0.6
0.4
0.2
0.2
0
0
0.8
0.05
0.1
Maximum Interstory Drift Ratio
0.15
0
0
0.05
0.1
0.15
Maximum Interstory Drift Ratio
8
Correlation of Component Variabilities
Type A: Correlation
of parameters
within an element
Type B: Correlation
between parameters
of different elements
Type B Correlations - Between Parameters of Elementi and Elementj
Type A Correlations - Between
Different Parameters of the Same
Element
σLN, modeling
Full Correlation
Partial (ρij = 0.5) approx. method
No Correlation
Full Correlation
1.12
0.89
0.63
Full Correlation
between Variables
Expected to be
Correlated
0.63
0.50
0.33
No Correlation
0.43
0.34
0.23
9
Collapse Capacity – with Modeling Uncert.
1
Median = 2.2g
Cummulative Probability of Collapse
0.9
sLN, Total = 0.36
0.8
0.7
σLN, Total = 0.64 w/mod.
0.6
Margin 2.7x
0.5
0.4
0.3
P[collapse |Sa = 0.82g] = 5%
0.2
Empirical CDF
Lognormal CDF (RTR Var.)
Lognormal CDF (RTR + Modeling Var.)
0.1
5%
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Sag.m.(T=1.0s) [g]
MCE
2% in 50 yrs GROUND MOTION INTENSITY
4.5
5
10
Mean Annual Frequency of Collapse
1
Cummulative Probability of Collapse
0.9
Collapse Performance
Collapse
CDF
0.8
0.7
0.6
Margin: Sa,collapse = 2.7 MCE

Probability of collapse under
0.4
0.3
design MCE = 5%
0.2
Empirical CDF
Lognormal CDF (RTR Var.)
Lognormal CDF (RTR + Modeling Var.)
0.1
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Sag.m.(T=1.0s) [g]

0.0020
MAF of Excedance (Poisson rate)

0.5
MAFcol = 1.0 x 10-4 (about ¼
of the MCE 2% in 50 year
0.0018
Hazard
Curve
0.0016
0.0014
0.0012
ground motion)
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
Sa at First Mode Period (g)
4
4.5
5
11
Benchmarking Archetype Studies
…
…
DV’s:
Facility
Definition
p(collapse)
p($ > X)
p(D.T. > Y)
2003 Code Compliant
-
Strength
Stiffness
Capacity Design
Detailing
multiple realizations
PBEE
Assessment
“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
(Atrib/Atotal = 1.0)
Perimeter Frame
(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

collapse
MAF x 10
[10-4] -4
25
Perimeter
Frames
20
Mean Annual
Frequency (MAF)
of collapse:
5 to 25 x 10-4
15
Space
Frames
10
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
(collapse, new RC)
Nuclear Reactor
(earthquake hazard)
Fire
(flashover, 100m2 office)
Fire + (1.0D + 0.5L)
(flashover, 100m2 office)
1 x 10-4
1 x 10-5
1 x 10-6
1 x 10-7
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