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

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

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

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

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

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

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

Nonstructural Damage and Losses (Caltech)

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

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

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

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

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

)(||| 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)

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)

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

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

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

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