Transcript PBEE Process Organization

Framework for Performance-Based
Earthquake Engineering
Helmut Krawinkler, Stanford U.
PEER Summative Meeting – June 13, 2007
Where were we 10 years ago?
SEAOC Vision 2000, FEMA 273, ATC-40
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Descriptive performance levels (IO, LS, CP, etc.)
Associated with specific hazard levels → Performance Objectives
Qualitative (and a few quantitative) damage measures
Limited consideration of uncertainties
Implementation in terms of FORCES and DEFORMATIONS
Earthquake Performance Level
Fully Operational
Operational
Life Safe
Near Collapse
Frequent
Earthquake Design Level
(43 year)
Occasional
(72 year)
Rare
(475 year)
Very Rare
(970 year)
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Unacceptable
Performance
(for New Construction)
Ba
sic
Es
sen
Ob
tia
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l/H
tiv
Sa
az
e
fet
ar
yC
do
us
rit
Ob
ica
lO
jec
bje
tiv
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cti
ve
Measures of Performance - PBEE
Forces and deformation?
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Yes, but only for engineering calculations
Intermediate variables
Not for communication with clients and community
Communication in terms of the three D’s:
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Dollars (direct economic loss)
Downtime (loss of operation/occupancy)
Death (injuries, fatalities, collapse)
Quantification
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Losses for a given shaking intensity
Losses for a specific scenario (M & R)
Annualized losses
With or without rigorous consideration of uncertainties
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Vision of PBEE
1. Complete simulation
2. Defined performance
objectives
Joe’s
Beer!
Food!
•
Quantifiable
performance targets
•
Annual probabilities
of achieving them
3. Informed owners
Joe’s
Beer!
Food!
Beer!
Food!
Sources: G. Deierlein, R. Hamburger
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The Peer Framework Equation - 1999
vDV    G DV DM | dG DM EDP | dG EDP IM | d ( IM )
Impact
Performance (Loss) Models and Simulation
Curse?
Blessing
Hazard
Performance-Based Methodology – Bldgs.
Measures of Performance
• Collapse & Casualties
• Direct Financial Loss
• Downtime
Decision Variable
Damage Measure
drift as an EDP
Engineering Demand
Parameter
Intensity Measure
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Performance-Based Methodology
Intensity Measure
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Mean Annual Freq. of Exceedance, Sa
Engineering Demand
Parameter
MEAN SPECTRAL ACC. HAZARD CURVE -- T = 1.8 sec.
Van Nuys, CA, Horizontal Component
10
1
0.1
0.01
0.001
Medina & Krawinkler
0.0001
0
0.2
0.4
0.6
Spectral Acceleration Sa(g)
0.8
1.0
IM (e.g., Sa(T1))
Incremental Dynamic Analysis
Individual records
Median
84%
IM Hazard curve
(annual freq. of exceedance)
EDP (e.g., max. interstory drift)
 EDP ( y)   PEDP  y | IM  x  | d IM ( x ) |
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Performance-Based Methodology
Decision Variable
Performance Assessment types (ATC-58 definitions):
Intensity-based: Prob. facility perf., given intensity of ground motion
Scenario-based: Prob. facility perf., given a specific earthquake scenario
Time-based:
Prob. facility perf. In a specific period of time
Damage Fragility Curves:
Cost Functions:
Drywall Partitions with Metal Frame
P(DM>dm | EDP)
P($>x | DM)
1.0
Damage Measure
Mean Loss Curve:
Drywall partitions
E[Loss | EDP]
1.4
Drywall Partitions with Metal Frame
1.0
1.2
0.8
0.8
+
0.6
0.4
DM 1
0.2
1.0
0.6
0.8
0.4
0.6
Tape, Paste & Repaint
Replacement of gypsum boards
Partition replacement
0.2
DM 2
DM 3
0.0
0.000
0.0
0.005
0.010
0.015
0.020
0.0
0.4
EDP (IDR)
0.8
1.2
1.6
Cost of Repair / Cost New
2.0
2.4
0.4
0.2
0.0
0.000
0.005
0.010
0.015
0.020
0.025
0.030
EDP (IDR)
Aslani & Miranda
Intensity Measure
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Mean Annual Freq. of Exceedance, Sa
Engineering Demand
Parameter
MEAN SPECTRAL ACC. HAZARD CURVE -- T = 1.8 sec.
Van Nuys, CA, Horizontal Component
10
1
0.1
0.01
0.001
Medina & Krawinkler
0.0001
0
0.2
0.4
0.6
Spectral Acceleration Sa(g)
0.8
1.0
Deaggregation of Expected Annual Loss
Example: Van Nuys Testbed Building
Collapse
29%
Non-collapse
71%
Structural
12%
Non-tructural
88%
Source: E. Miranda
Design Decision Support
Hazard
Domain
Structural System Domain
Mean IM-EDP Curves
Mean Hazard Curve
10/50
EDP = Max. Interstory Drift
EDP = Max. Floor Acceleration
Loss Domain
Expected $Loss
Mean Subsystem Loss Curves
NSDSS
EDP = Max. Interstory Drift
NSASS
EDP = Max. Floor Acceleration
Zareian & Krawinkler (2005)
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Assessment of Collapse Potential
NORM. STRENGTH VS. MAX. STORY DUCT.
N=9, T 1=0.9, x=0.05, a=0.03, q=0.015, H 3, BH, K 1, S1, NR94nya
20
W
[Sa(T1)/g] / g
g=
Vy
Non-degrading system
Degrading system
15
10
Collapse
Capacity
5
0
0
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5
10
msi,max
15
20
Modeling of Deterioration
UCI G12 OSB
UCI G12 OSB
Fy=8.2 kips, y=0.45 in, as=0.047, ac=-0.081, au=1.94, c/y=5.44
Pinching Model, =0.5, Fy=8.2 kips, y=0.45 in
10
8
6
4
2
0
-2
-4
-6
-8
-10
Load (kips)
Load (kips)
as=0.047, ac=-0.081, ac=1.94, c/y=5.44, gs=270, gc=270, gk=, ga=270
-4
-2
0
Displacement (in)
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2
4
10
8
6
4
2
0
-2
-4
-6
-8
-10
-4
-2
0
Displacement (in)
2
4
Collapse Capacity for a Set of Ground Motions
MAX. STORY DUCTILITY vs. NORM. STRENGTH
N=9, T1=0.9,x=0.05, K1, S1, BH, q=0.015, Peak-Oriented Model,
as=0.05, c/y=4, ac=-0.10, gs=8 , gc=8 , gk=8 , ga=8 , =0, LMSR
10
[Sa(T1)/g]/ g
8
6
4
2
Individual responses
0
0
10
20
Maximum Story Ductility Over the Height, ms,max
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30
Collapse Fragility Curve
Obtaining the collapse fragility curve (MRF)
N = 8, T1 = 1.2, g = 0.17, Stiff & Str = Shear, SCB = 2.4-2.4, x = 0.05
qp = 0.03, qpc/qp = 5,  = 20, Mc/My = 1.1
Probability of Collapse
1
0.75
0.5
Data points
0.25
Collapse fragility curve
0.1
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
IM[Sa(T1)]
Zareian & Krawinkler (2004)
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Probability of Collapse at MCE,
for MRFs with R = 8
P(Collapse) at MCE given R = 8 & W = 2.5 (MRF)
Siff. & Str. = Shear, SCB = 2.4-1.2, x = 0.05, qpc/qp = 15.0,  = 50, Mc/My = 1.1
P(Collapse) at MCE level
0.8
0.7
Design Spectrum:
Sa(T1)/g = 0.32 ≤ 0.6/T < 1.0
qp = 0.06
0.6
qp = 0.03
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
3
3.5
First Mode Period (sec.)
Zareian & Krawinkler (2007)
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Implementation of Framework
ATC-58 – Guidelines for Seismic
Performance Assessment of Buildings
ATC-63 – Recommended Methodology
for Quantification of Building System
Performance
TBI – Tall Building Initiative
LRFD for bridge design
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Concluding Remarks - 1999
• Performance based engineering is here to stay
• It enforces a transparent design/assessment approach
• Much more emphasis must be placed on $ losses and
loss •of function (downtime)
• Performance based design should be reliability based
• We have a long road ahead of us
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