Transcript Instrumentation needs for PBEE

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