To transform earthquake engineering assessment and design ...
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To transform earthquake engineering assessment and design ... Perform.-Based
Approach
•Scientifically-defined seismic hazard
•Direct design approaches
•Defined outcomes with probabilities of achieving them
Traditional Approach
•Non-scientifically defined seismic hazard
•Indirect design approaches
•Undefined and uncertain outcomes
Performance-Based Earthquake Engineering
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Structurally
Stable
Assessment by Static Pushover Analysis (FEMA 273/356 and ASCE
41)
Life Safe
Joe’s
Beer!Beer!Food!Food!
Rare events(10%/50yrs)
Very rare events(2%/50yrs)
Operational
Frequent events(50%/50yrs)
Lateral Deformation
Base Shear
DemandJoe’s
Beer!Beer!Food!Food!
Occasional events(20%/50yrs)
Ref: R.O. Hamburger
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Base Shear
Deformation
Damage Threshold
CollapseOnset
OPEN
OPEN
OPEN
FEMA 356 Performance LevelsIO LS CP
Performance-Based Earthquake Engineering
PBEE today
$, % replacement0 25% 50% 100%
Downtime, days0
1 7 30 180
Casualty rate0.00.0001 0.001 0.01 0.25
PBEE tomorrow
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Damage Assessment: Nonstructural Fragilities
0.0
0.2
0.4
0.6
0.8
1.0
0 0.005 0.01 0.015 0.02 0.025
EPD (IDR)
P(DM|EPD) 5/8" Gypsum partition wall with 3-5/8" Wall Frame
Small cracks only
0.0
0.2
0.4
0.6
0.8
1.0
0 0.005 0.01 0.015 0.02 0.025
EPD (IDR)
P(DM|EPD) 5/8" Gypsum partition wall with 3-5/8" Wall Frame
Small cracks only
Wide cracks in gypsum boards
0.0
0.2
0.4
0.6
0.8
1.0
0 0.005 0.01 0.015 0.02 0.025
EPD (IDR)
P(DM|EPD) 5/8" Gypsum partition wall with 3-5/8" Wall Frame
Small cracks only
Wide cracks in gypsum boards
Severe damage to gypsum board and distorsion of metal frame
(Replace partition)
(Replace gypsum boards)
(Patch, Retape & Paint)
Ref: E. Miranda
Interstory Drift Ratio
Pro
bab
ilit
y o
f D
amag
e S
tate
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Engineering Demand Parameter
Engineering Demand Parameter
Intensity Measure Intensity Measure
Damage MeasureDamage Measure
Performance-Based Methodology
Decision VariableDecision Variable• Collapse & Casualties
• Direct Financial Loss
• Downtime
drift as an EDP
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6
0 0.05 0.1 0.150
0.5
1
1.5
2
2.5
3
3.5
4
Sa g.
m.(T
=1
.0s)
[g]
Maximum Interstory Drift Ratio
Incremental Dynamic Analysis – Collapse
STRUCTURAL RESPONSE (DRIFT)
GR
OU
ND
MO
TIO
N IN
TE
NS
ITY
44 Ground Motion Records
EQ: 11111, Sa: 2.06g EQ: 11112, Sa: 2.19g
EQ: 11121, Sa: 2.86g EQ: 11122, Sa: 2.32g
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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sag.m.
(T=1.0s) [g]
Cu
mm
ula
tive
Pro
ba
bili
ty o
f C
olla
pse
Empirical CDFLognormal CDF (RTR Var.)Lognormal CDF (RTR + Modeling Var.)
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
0.0016
0.0018
0.0020
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Sa at First Mode Period (g)
MA
F o
f Exc
ed
an
ce (
Po
isso
n r
ate
)Mean Annual Frequency of Collapse
Collapse CDF
Hazard Curve
Margin: Sa,collapse = 2.7 MCE
5% Probability of collapse
under design MCE = 5%
Mean Annual Frequency:
MAFcol = 1.0 x 10-4
(0.5% in 50 years)
2.7
Collapse Performance
5%
2/50
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Nonstructural Damage and Losses (Caltech)
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PBEE Methodology: IM-EDP-DM-DV
Ground Motion Hazard Characterization IM Definition (Sa, …) Selection and Scaling of Ground Motions
Simulation: IM – EDP Choice of EDPs (Drift, Floor Accel., other …) Fidelity of simulations to model collapse
Damage Modeling: EDP – DM Taxonomy of components Definition of conditional EDP-DM “damage
function”
Loss Modeling: DM – DV Definition of conditional DM-DV loss functions Downtime and injuries/fatalities are a challenge
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Performance Assessment Components
Decision Variable
Decision Variable
Intensity Measure
Intensity Measure
Damage Measure
Damage Measure
Engineering Demand
Parameter
Engineering Demand
Parameter
Relating Performance to Risk Decision Making
Quantifying Damage Measures
Simulation of System Response
Earthquake Hazard Characterization
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Integrative Testbeds
Buildings - Van Nuys - UC Sciences - SRB
UCB CampusBridges - Humboldt Bay - I-880 Viaduct
Bay Area Highway Network
0.2 0 0.2 0.4 0.6 Miles
Map 8.2Building Downtime in Months from a Rare Earthquake
StreetsHayward FaultTopo LinesNon-core Buildings
Downtime for Building in Months0 - 12 - 45 - 1213 - 2425 - 40
N
EW
S
#
OXFORD
#
HEARSTBarker Hall Tolman Hall
Giannini Hall
Hesse Hall
Warren Hall
Mulford Hall
Campbell Hall
McLaughlin Hall
Latimer Hall
Lewis Hall
Hildebrand Hall
Wurster Hall
2251 COLLEGE AVE
Berkeley Art Musuem
Art Gallery
Barrows Hall
2223 Fulton
2111 BANCROFT WAY
Doe Annex
0.2 0 0.2 0.4 0.6 Miles
Map 8.2Building Downtime in Months from a Rare Earthquake
StreetsHayward FaultTopo LinesNon-core Buildings
Downtime for Building in Months0 - 12 - 45 - 1213 - 2425 - 40
N
EW
S
#
OXFORD
#
HEARSTBarker Hall Tolman Hall
Giannini Hall
Hesse Hall
Warren Hall
Mulford Hall
Campbell Hall
McLaughlin Hall
Latimer Hall
Lewis Hall
Hildebrand Hall
Wurster Hall
2251 COLLEGE AVE
Berkeley Art Musuem
Art Gallery
Barrows Hall
2223 Fulton
2111 BANCROFT WAY
Doe Annex
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Performance Assessment Components
Decision Variable
Decision Variable
Intensity Measure
Intensity Measure
Damage Measure
Damage Measure
Engineering Demand
Parameter
Engineering Demand
Parameter
Relating Performance to Risk Decision Making
Quantifying Damage Measures
Simulation of System Response
Earthquake Hazard Characterization
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Performance Assessment Components
Decision Variable
Decision Variable
Intensity Measure
Intensity Measure
Damage Measure
Damage Measure
Engineering Demand
Parameter
Engineering Demand
Parameter
DV: $ loss, functionality, downtime, casualties
DM: physical condition & consequences/ramifications
EDP: Drift Ratio (peak, residual), Floor Acceleration, Local Indices (p, strain, …)
IM: Sa(T1), multiple Sa’s, epsilon, Sdinelastic, duration
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)(||| IMdIMEDPdGEDPDMdGDMDVGDVv
PBEE – Probability Framework Equation
Performance (Loss) Models and Simulation HazardImpact
IM – Intensity Measure
EDP – Engineering Demand Parameter
DM – Damage Measure
DV – Decision Variable
(DV) – Probabilistic Description of Decision Variable
(e.g., Mean Annual Probability $ Loss > 50% Replacement Cost)
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REF: Yang, Conte, Elgamal (UCSD)
Comprehensive System Simulation
S chemat ic of the F inite E lement M odel
2 D , 4 D
N o n - l in e a r p -y e le m e n t
N o n - l in e a r
N o n - lin e a r p -y e le m e n t
N o n - l in e a r F ib e r B e a m E le m e n t
D ra g
C lo s u re
P la s t ic E la s t ic
G a p
P ile N o d e
N e a r f ie ldP la s t ic R e s p o n s e
F a r - f ie ldE la s t ic
S te e l F ib e rs
U n c o n fin e d
C o n c re te F ib e rs
R e s p o n s e
C o n c re te F ib e rs
C o n fin e d C o re
F ib e r B e a m E le m e n t
= 1 4 D
1 4 E le m e n tsa t 1 .0 D o .c .
C o m p re s s io nA x ia l
E x te n d e d
G ro u n d L e v e l
PV
P ile S h a fto r 6 D
D is p la c e m e n t T im e h is to ry in p u tsfro m 1 -D n o n l in e a r s ite re s p o n s e
A
REF: Boulanger (UCDavis)
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NS Components & Contents
Problem Insight – Small Equipment
Floor-level motion
Ground-level motion
Floor-level motion
Bench-level motion
Movement
Multi-Story Building
Equipment
SupportElement
-Cascade approach-Transmissibility
importantIM = Sa(T1)
EDP = PFA
DM
Hutchinson
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Integrated Simulation/Assessment Platform
Algorithms,Solvers,Parallel/distributedcomputing
Simulation & Reliability Models for Materials, Components, and Systems
http://opensees.berkeley.edu
Computation InformationTechnology
Software framework,Databases, Visualization,Internet/grid computation
Models
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Integrative Testbeds
Buildings
Van Nuys
UC Sciences
UCB Campus
Bridges
Humboldt Bay
I-880 Viaduct
Bay Area Highway Network
0.2 0 0.2 0.4 0.6 Miles
Map 8.2Building Downtime in Months from a Rare Earthquake
StreetsHayward FaultTopo LinesNon-core Buildings
Downtime for Building in Months0 - 12 - 45 - 1213 - 2425 - 40
N
EW
S
#
OXFORD
#
HEARSTBarker Hall Tolman Hall
Giannini Hall
Hesse Hall
Warren Hall
Mulford Hall
Campbell Hall
McLaughlin Hall
Latimer Hall
Lewis Hall
Hildebrand Hall
Wurster Hall
2251 COLLEGE AVE
Berkeley Art Musuem
Art Gallery
Barrows Hall
2223 Fulton
2111 BANCROFT WAY
Doe Annex
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Evolution of PBEE Concept
Groups of Buildings:
• Portfolio Analysis• Regional Loss
Studies• Mitigation Studies
e.g., ATC 13, HAZUS
CasualtiesRepair Costs
Downtime
Individual Buildings:
•Evaluation•Retrofit
e.g., FEMA 273/356
Performance Objectives
Building Ratings:•Probable Maximum Loss•Other
e.g., ST-RISK
Percentage or Dollars
Ref. W. Holmes