Framework for Performance-Based Earthquake...

Framework for Performance-Based Earthquake Engineering

Helmut Krawinkler, Stanford U.

PEER Summative Meeting – June 13, 2007

NSF-PEER Summative Meeting

Where were we 10 years ago?

SEAOC Vision 2000, FEMA 273, ATC-40 Descriptive performance levels (IO, LS, CP, etc.)Associated with specific hazard levels → Performance ObjectivesQualitative (and a few quantitative) damage measuresLimited consideration of uncertaintiesImplementation in terms of FORCES and DEFORMATIONS

Unacceptable Performance

(for New Construction)Basic Objective

Essential/Hazardous Objective

Safety Critical Objective

Fully Operational Operational Life Safe Near Collapse

Frequent

(43 year)

Occasional

(72 year)

Rare

(475 year)

Very Rare

(970 year)

Earthquake Performance Level

Ear

thqu

ake

Des

ign

Lev

el






Frequent

(43 year)

Occasional

(72 year)

Rare

(475 year)

Very Rare

(970 year)


Ear

thqu

ake

Des

ign

Lev

el






Frequent

(43 year)

Occasional

(72 year)

Rare

(475 year)

Very Rare

(970 year)







Frequent

(43 year)

Occasional

(72 year)

Rare

(475 year)

Very Rare

(970 year)











Basic Objective



Basic Objective




Frequent

(43 year)

Occasional

(72 year)

Rare

(475 year)

Very Rare

(970 year)


Ear

thqu

ake

Des

ign

Lev

el


Measures of Performance - PBEE

Forces and deformation?Yes, but only for engineering calculationsIntermediate variables Not for communication with clients and community

Communication in terms of the three D’s:Dollars (direct economic loss)Downtime (loss of operation/occupancy)Death (injuries, fatalities, collapse)

QuantificationLosses for a given shaking intensityLosses for a specific scenario (M & R)Annualized lossesWith or without rigorous consideration of uncertainties


Vision of PBEE

Joe’s

Beer!Beer!Food!Food!

1. Complete simulation

2. Defined performance objectives

• Quantifiable performance targets

• Annual probabilities of achieving them

3. Informed owners

Joe’sBeer!Beer!Food!Food!

Joe’sBeer!Beer!Food!Food!

Sources: G. Deierlein, R. Hamburger

The Peer Framework Equation - 1999

( ) ∫∫∫= )(||| IMdIMEDPdGEDPDMdGDMDVGDVv λ

Performance (Loss) Models and Simulation HazardImpact

BlessingCurse?


Performance-Based Methodology – Bldgs.

Engineering Demand Parameter


Intensity MeasureIntensity Measure

Damage MeasureDamage Measure

drift as an EDP

Decision VariableDecision Variable• Collapse & Casualties• Direct Financial Loss• Downtime

Measures of Performance


Performance-Based Methodology

Intensity MeasureIntensity Measure0.0001

0.001

0.01

0.1

1

10

0 0.2 0.4 0.6 0.8 1.0Spectral Acceleration Sa(g)M

ean

Ann

ual F

req.

of E

xcee

danc

e, λ

Sa MEAN SPECTRAL ACC. HAZARD CURVE -- T = 1.8 sec.Van Nuys, CA, Horizontal Component

0.0001

0.001

0.01

0.1

1

10


ean

Ann

ual F

req.

of E

xcee

danc

e, λ




Medina & Krawinkler


Incremental Dynamic Analysis

EDP (e.g., max. interstory drift)

IM (e

.g.,

S a(T

1))

IM Hazard curve(annual freq. of exceedance)

Individual recordsMedian84%

[ ] |)x(d|xIM|yEDPP)y( IMEDP λ=≥=λ ∫


Performance-Based Methodology

Decision VariableDecision Variable



Intensity MeasureIntensity Measure0.0001

0.001

0.01

0.1

1

10


ean

Ann

ual F

req.

of E

xcee

danc

e, λ


0.0001

0.001

0.01

0.1

1

10


ean

Ann

ual F

req.

of E

xcee

danc

e, λ


Medina & Krawinkler

Damage MeasureDamage Measure

Drywall Partitions with Metal Frame

0.0

0.2

0.4

0.6

0.8

1.0

0.000 0.005 0.010 0.015 0.020EDP (IDR)

DM 1 DM 2 DM 3

P(DM>dm | EDP)

Damage Fragility Curves:Drywall partitions

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.4 0.8 1.2 1.6 2.0 2.4Cost of Repair / Cost New

Tape, Paste & RepaintReplacement of gypsum boardsPartition replacement

P($>x | DM)

Cost Functions:

+

Drywall Partitions with Metal Frame

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.000 0.005 0.010 0.015 0.020 0.025 0.030EDP (IDR)

E[Loss | EDP]

Mean Loss Curve:

Aslani & Miranda

Performance Assessment types (ATC-58 definitions):Intensity-based:Scenario-based:Time-based:

Prob. facility perf., given intensity of ground motionProb. facility perf., given a specific earthquake scenarioProb. facility perf. In a specific period of time

Deaggregation of Expected Annual Loss

Example: Van Nuys Testbed Building

Source: E. Miranda

Collapse29%

Non-collapse71%

Structural12%

Non-tructural88%


Design Decision SupportStructural System Domain

Loss Domain

Hazard Domain

NSDSS NSASS

EDP = Max. Interstory Drift EDP = Max. Floor Acceleration

Mean Subsystem Loss Curves

EDP = Max. Interstory Drift EDP = Max. Floor Acceleration

Mean IM-EDP Curves

Mean Hazard Curve

10/50

Expe

cted

$Lo

ss

Zareian & Krawinkler (2005)


Assessment of Collapse Potential

NORM. STRENGTH VS. MAX. STORY DUCT.N=9, T1=0.9, ξ=0.05, α=0.03, θ=0.015, H3, BH, K1, S1, NR94nya

5

10

15

20

[Sa(

T1)

/g] /

γ

γ = Vy

W Non-degrading systemDegrading system

Collapse Capacity

00 5 10

µsi,max

15 20


Modeling of Deterioration

UCI G12 OSBFy=8.2 kips, δy=0.45 in, αs=0.047, αc=-0.081, αu=1.94, δc/δy=5.44

-10-8-6-4-202468

10

-4 -2 0 2 4Displacement (in)

Load

(kip

s)

UCI G12 OSBPinching Model, κ=0.5, Fy=8.2 kips, δy=0.45 in

αs=0.047, αc=-0.081, αc=1.94, δc/δy=5.44, γs=270, γc=270, γk=∞, γa=270

-10-8-6-4-202468

10

-4 -2 0 2 4Displacement (in)

Load

(kip

s)


Collapse Capacity for a Set of Ground Motions

M AX. STORY DUCTILITY vs. NORM . STRENGTHN=9, T1=0.9, ξ=0.05, K 1, S1, BH, θ=0.015, Peak-Oriented M odel,

α s=0.05, δc/δy=4, α c=-0.10, γs=8 , γc=8 , γk=8 , γa=8 , λ=0, LM SR

0

2

4

6

8

10

0 10 20 30M aximum Story Ductility Over the Height, µs,max

[Sa(

T1)

/g]/ γ

Individual responses


Collapse Fragility Curve

Obtaining the collapse fragility curve (MRF)N = 8, T1 = 1.2, γ = 0.17, Stiff & Str = Shear, SCB = 2.4-2.4, ξ = 0.05

θp = 0.03, θpc/θp = 5, λ = 20, Mc/My = 1.1

0

0.25

0.5

0.75

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5IM[Sa(T1)]

Prob

abili

ty o

f Col

laps

e

Data points

Collapse fragility curve


0.1


Probability of Collapse at MCE, for MRFs with R = 8

P(Collapse) at MCE given R = 8 & Ω = 2.5 (MRF)Siff. & Str. = Shear, SCB = 2.4-1.2, ξ = 0.05, θpc/θp = 15.0, λ = 50, Mc/My = 1.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.5 1 1.5 2 2.5 3 3.5First Mode Period (sec.)

P(C

olla

pse)

at M

CE

leve

l

θp = 0.06

θp = 0.03

Design Spectrum:Sa(T1)/g = 0.32 ≤ 0.6/T < 1.0



Implementation of Framework

ATC-58 – Guidelines for Seismic Performance Assessment of BuildingsATC-63 – Recommended Methodology for Quantification of Building System PerformanceTBI – Tall Building InitiativeLRFD for bridge design


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 andloss of function (downtime)•

• Performance based design should be reliability based

• We have a long road ahead of us

Framework for Performance-Based Earthquake...

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