lecture 13 building populations

Masonry Structures, lesson 13 slide 1

Seismic Design and Assessment ofMasonry Structures

Seismic Design and Assessment ofMasonry Structures

Lesson 13: Assessing Seismic Risk across Populations of Unreinforced Masonry Buildings

Notes Prepared by:Daniel P. Abrams

Willett Professor of Civil EngineeringUniversity of Illinois at Urbana-Champaign

October 28, 2004


Ömer O. Erbay

A Methodology to Assess Seismic Risk for Populations of

Unreinforced Masonry Buildings

University of Illinois at Urbana-Champaign, 2003

Ph.D. Advisor: Daniel P. Abrams


Research motivation

• Awareness

• Preparedness

Decision makers:City officials, building owners, insurance companies

Need: Simple and rapid assessments of seismic damage, economic loss and risk across their regions

• Mitigation

August 17, 1999, Kocaeli EQ, Turkey, M=7.4

Picture taken from Hurriyet Press, 1999

• Consequences

~ 50,000 injuries

~ 250,000 homeless

3-6.5 billion $


Inventory

Sample from NOVA Digital Systems, Inc.


Building specific damage estimates

Typical steps

• Identify building configurationand structural frame

• Estimate variation in material properties and load levels

f’m

qf

P

PL-shaped2-story

• Represent hazard char.at the building site

• Calculate buildingresponse variation

Res

pons

e va

riatio

n

0.3g 0.8g Sa

• Estimate buildingdamage state

Prob

abili

ty o

f Ex

ceed

ence

, %

Sa0.3g 0.8g


Loss from damage curves

NO-IO IO-LS LS-CP CP-TC Damage

Loss

, R

ep. C

ost R

atio

+

Hazard level, Sa

Loss

,(R

ep. C

ost R

atio

)

For a definedSa level

Hazard level, Sa

Prob

abili

ty o

f Ex

ceed

ence

, %


Regional versus building specific loss

=Expected Regional

Loss Σfor all buildings

in the region

Building Specific

Lossi

Building Specific

Loss= Lossi | Hazard Level = Sai

Lossi = RCRi x sfnAκ


Regional risk assessment

Scenario BasedSeismic Risk =

Expected Regional

LossX Defined

HazardProb

TotalSeismic Risk

= Σ Scenario BasedSeismic Risk

for all possible scenarios


The total loss/risk conceptIn

divi

dual

B

uild

ing

Loss

Actual

Estimate

Relative Error80%

75%

Cum

ulat

ive

build

ing

Loss

(To

tal L

oss)

14%8%

3%21%

9%

19%

12%33%

33% 60%49% 14% 57% 55%

57%


The total loss/risk concept: Mathematical

Seismic loss in a buildingrepresented by a randomvariable, L

Loss, L

Prob

abili

ty

2σL

µL

Let,

∑=iLTRL µµ

∑∑+∑=jii LLij

2L

2TRL σσρσσ

TRL

TRLTRL µ

σδ =

Correlated, ρij = 1.0

LTRL δδ =

Uncorrelated, ρij = 0.0

LTRL n1 δδ =

Total Regional Loss, TRL ∑

all bldgs= iL


The need: Sensitivity investigations

• Investigate the sensitivity of regional risk/loss estimated on regional and building specificparameters that are observed to be importantin past earthquakes.

Hazard representation

A rational approach to estimatebuilding damage states

Building population


Hazard representation: Ground motion selection

A suite of 18 ground motions

• Magnitude = 6.1 – 7.4

• Distance = 1 – 70 km

• Soil type = A – D (USGS soil categorization)

• PGA/PGV = 0.56 – 3.33 g.s/m

• Scaled up and down to representdifferent levels of hazard


Categorization of ground motions

0

0.5

0 1 2Period, s

Sa, g

0

0.5

0 1 2Period, s

Sa, g

0

0.5

0 1 2Period, s

Sa, g

PGAPGV = 1.4-3.3 g.s/m

PGAPGV = 0.8-1.4 g.s/m

PGAPGV < 0.8 g.s/m

High Medium Low

vs = 360 m/s

Near field, Rock

vs = 180-360 m/s

Stiff – Medium Stiff

vs < 180 m/s

Far field, Soft


Analytical modeling

Lumped mass and lumped stiffness model

Story Shear

Story Disp.

Sliding

Story Shear

Story Disp.

Rocking

Wooddiaphragm

Out-of-planewalls

In-planewalls


Shaded Area

side xi

side xj

side yi side yj

nxi piers

nxj piers

nyj piersn y

ipie

rs

twx

twynyi can be different than nyj

nxi = nxj = nx

Lpx

Lpy

hpx hpy

hs

hs

αx = Floor AreaShaded Area

αy = Floor Areax y

Analytical modeling


Analytical modeling: Wall properties

Wall Stiffness

px

fmxj,xi h

AE1.0k α=

py

fm

yjyi

j,yiyj,yi h

AEnn

n2.0k

+= α

=

Wall Strength

y,fxy,px

y,pxy,srx P

hL

9.0H =

y,fxsldcy,xy,fx

fy,ssx P

PA

83H ⎟

⎟⎠

⎞⎜⎜⎝

⎛+= µτα

=

Rocking

Sliding


Analytical modeling: Diaphragm stiffness

Inertia force on the diaphragm

R

Assumed deformationshape

R

∆d

Lx

Ly

y

xd L

L=α

dddx G4k α=

dddy

1G4kα

=


From response to damage state: In-plane

hs

∆

Interstory Drift

xi+1

xi

s

i1i

s hxx

h−

= +∆

⎟⎟⎠

⎞⎜⎜⎝

⎛

shmax ∆


From response to damage state: Out-of-plane

R=P+Ww

O

Ww

Exci

tatio

ns c

omin

gfr

om d

iaph

ragm

s

sh

wt

2tw

R=P+Ww

Ww

P

4tw

6tw

R=P+Ww

Ww

P

O

wt9.0

ght

31a

s

wnlb,cr ⎟⎟

⎠

⎞⎜⎜⎝

⎛= g

ht

31

WP

65a

s

w

wlb,cr ⎟⎟

⎠

⎞⎜⎜⎝

⎛⎥⎦

⎤⎢⎣

⎡+=


From response to damage state: Out-of-plane

H∆

∆

H

⎟⎠⎞

⎜⎝⎛ +

2WP

ht9.0 w

s

w

ws

w Wht45.0

kPµ

2tw wt

s

bth

VV −

2VV bt +

Vt

Vb

hs

( )2b

2t

ww VV

gW

121KE +=

g2W

Paw

scon ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

µ

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

s

2w

wks

2w

w

wlb,f h

t45.0tht

439.0

WP

2WPE µ

⎥⎦

⎤⎢⎣

⎡=

s

2ww

nlb,f ht45.0

2WPE


Damage state assignment

In-plane, IP, damage state(based on interstory drift)

IO LS CP TC0.1% 0.6% 1.0% 2.0%

Out-of-plane, OP, damage state(based on floor accelerations and

velocities)IO CP TC

Crk. Col. NLBWall

Col. LBWall

Final Damage State

Higher of in-plane and out-of-plane

=


From damage state to loss quantification

Building replacement cost ratio for each damage state

IO-LS LS-CP CP-TC >TC2% 13% 66% 100%

NO-IO0%

0

2550

75

100

0 0-1 1-10 10-30 30-60 60-100Replacement cost ratio, %

Prob

abili

ty, %

None Intermediate Medium Heavy

Adopted from Abrams and Shinozuka, 1997


Investigated parameters

• Average length ofopenings, Lo

• Spacing between gravityload carrying members, Ls

Secondary, building

• Ground motion category, High, Medium, Low

• Size and type of buildingpopulation

Primary, regional• Number of stories, ns

• Floor area, Af

• Floor aspect ratio, αd

• Wall density, αw

• Distributed floor load, qf

• Story height, hs

• Elastic modulus, Em

Primary, building

• Shear modulus, Gd

• Pier height ratio, αh


Field surveys

City Source # of bldgs. Parameters

Urbana, IL

Carbondale, IL

Memphis, TN

San Francisco, CA Holmes et. al.,1990

Abrams & Shinozuka, 1997

Wu, Crelling & Olshansky, 2001

City of Urbana and Wu, 2001

Personal invest.54

72

517

2007

)L,(,,A,n ohdfs αα

fs A,n

),L,(,A,n dohfs αα

dsfs ,h,A,n α


Parameter distributions from field surveys

Urbana, IL

Carbondale, IL

Memphis, IL

San Francisco, CAThis study

0

40

80

1 2 3 4 5 6Number of Stories, ns

Perc

enta

ge

0

30

60

<1.5 1.5-4 4-7 7-10 10-15 >15Floor Area, Af, (1000 ft2)

Perc

enta

ge

0

40

80

<12 12-16 >16Story height, hs, (ft)

Perc

enta

ge

0

20

40

1-1.5 1.5-2 2-2.5 2.5-3 3-3.5 3.5-4 4-4.5 >4.5

Floor Aspect Ratio, α d

Perc

enta

ge


Assigned distributions

0

20

40

1 2 3 4 5 6Number of Stories, ns

Prob

abili

ty, %

0

1

2

3

0 5000 10000 15000Floor Area, Af, (ft2)

Prob

abili

ty, %

0

5

10

8 12 16 20Story height, hs, (ft)

Prob

abili

ty, %

0

20

40

60

0 1 2 3 4Floor Aspect Ratio, αd

Prob

abili

ty, %


Sensitivity investigations

Regional• Population size

• Ground motion category

Building specific• First order

• Second order


Framework for sensitivity analyses

{A} , Ai

Prob

.

Ai

Prob

.

H

L

H

L

H

L

H

L

c1

c2

c3

cn

Hazard Level

Tota

l Nor

m

Reg

. Los

s

{A}

Narrow Range

Full Range{A}FR

{A}NRc1 c2 c3 cn

Randomize {A}FR

{A}NR

Hazard Level

Diff

. or S

TD


Sensitivity investigations: Population size

10 10 10

53

2 2

0

5

10

15

5 10 25 50 100 250 500Number of buildings

Num

ber o

f gen

erat

ed

build

ing

popu

latio

ns



0.0

0.5

1.0

0 1 2 3Sa, g

TNR

L

0.0

0.5

1.0

0 1 2 3Sa, g

TNR

L

0.0

0.5

1.0

0 1 2 3Sa, g

TNR

L

0.0

0.5

1.0

0 1 2 3Sa, g

TNR

L

5 10

5025



0.0

0.5

1.0

0 1 2 3Sa, g

Tota

l Nor

mal

ized

R

egio

nal L

oss

100A100B100C250A250B500A500B


-0.3

0.0

0.3

0 1 2 3-0.3

0.0

0.3

0 1 2 3

-0.3

0.0

0.3

0 1 2 3-0.3

0.0

0.3

0 1 2 3


-0.3

0.0

0.3

0 1 2 3

-0.3

0.0

0.3

0 1 2 3

5 10 25

50 100 250

Sa, g Sa, gSa, g

Diff

eren

ceD

iffer

ence


0.0

0.5

1.0

0 1 2 3Sa, g

Tota

l Nor

mal

ized

R

egio

nal L

oss

MeanHighMedLow

Sensitivity investigations: GM category

-0.2

0.0

0.2

0 1 2 3Sa, g

Diff

eren

ce w

ithth

e m

ean

curv

e

HighMedLow

Pop size = 250


0.0

0.5

1.0

0 1 2 3Sa, g

0.0

0.5

1.0

0 1 2 3Sa, g

0.0

0.5

1.0

0 1 2 3Sa, g

0.0

0.5

1.0

0 1 2 3Sa, g

Sensitivity investigations: First order

0.0

0.5

1.0

0 1 2 3Sa, g

0.0

0.5

1.0

0 1 2 3Sa, g

ns αd αw

hs Em Af

TNR

L or

ER

CR

TNR

L or

ER

CR

Pop. Size = 50 Unbiased 10% 90%


0.0

0.5

1.0

0 1 2 3Sa, g

0.0

0.5

1.0

0 1 2 3Sa, g

qf

Gd

Sensitivity investigations: First order

0.0

0.5

1.0

0 1 2 3Sa, g

0.0

0.5

1.0

0 1 2 3Sa, g

TNR

L or

ER

CR

TNR

L or

ER

CR

Lo

αh

22%

qf

Lo

Gd

αh

ns

αd

αw

hs

Em

Af

12%

6%

7%

10%

11%

14%

18%

6%

4%

Par. Max Diff.


Sensitivity investigations: Second order

low 30

med 40

up 30

Prob

abili

ty

Original distribution and associated cumulative distribution

A1 = A2 = A3 = 1.0A1

A2

A3

Prob

.Pr

ob.

Prob

.

Low

erR

ange

Med

ium

Ran

geU

pper

Ran

ge

Distribution segments for sub-intervals



Parameter Range 1 Range 2 Range 3

GM category

αd

αw (%)

hs (ft)

Af (ft2)

Em (ksi)

High Medium Low

1 story 2-3 stories 4-5-6 stories

1.0-1.75 1.75-2.75 2.75-3.5

50-62 62-78 78-90

9.0-12.5 12.5-14.8 14.8-20.0

500-710 710-990 990-1200

1000-2300 2300-4750 4750-30000

Total # of cases = 37 = 2187 Investigated cases = 432

ns


0 1 2 30.0

0.5

1.0

Sa, g

TNRLorERCR

1 2 3Sa, g

TNR

L or

ER

CR

00.0

0.5

1.0

Scatter


0.0

0.5

1.0

0 1 2 3Sa, g

TNR

L or

ER

CR

10

49

8

7

6 32

1

5


Sensitivity investigations: Second orderGM ns αd αw hs Em Af

Group1Group2Group3Group4Group5Group6Group7Group8Group9Group10

Uniform Range 1 Range 2 Range 3


The methodology: Main steps

Part IData Collection

Seismic Hazard Building Inventory

Part IIGrouping

DCB

A

Part IIIRisk estimation

Seismic Risk = TRL x Probability(Hazard)

Calculate Total Regional

Loss, TRL

Soil Variation


The methodology: Loss calculationRegional grouping

of buildings

DCB

A

Hazard level, Sa

Loss

,(R

ep. C

ost R

atio

)

Further sub-grouping for hazard variation


Test-bed application: S. G. D. Puglia, Molise

Molise earthquakesOct & Nov 2002

Mw = 5.7

PGA ~ 0.36g

Population ~ 1160

# of Bldgs ~ 100-150

%URM ~ 45-65%

Epicenter ~ 5km


Test-bet application

Part IData collection


Part I: HazardHistoric seismicity

Picture taken from Mola et. al. 2002


Part I: Hazard

Figu

re ta

ken

from

Mol

aet

. al.

2002


Part I: Soil variation

Figure taken fromSSN’s web site, 2002


Part I: Building inventoryC.

O.M

.

Aerial photo of the region after the eventsPicture taken from the site engineer


Part I: Building inventory

Investigated buildings

Green tagged buildings

Red tagged buildings

Collapsed buildings

Map taken from the site engineer


Part I: Parameter distributions

0

30

60

1 2 3 4ns

Perc

enta

ge

0

30

60

1.0-1.

5

1.5-2.

0

2.0-2.

5

2.5-3.

0

3.0-3.

5>3

.5

αd

Perc

enta

ge

0

25

50

<50

50-60

60-70

70-80

80-90 >9

0

αw

Perc

enta

ge

0

45

90

<12 12-16 >16hs (ft)

Perc

enta

ge

0

20

40

<5 5-10 10-15 15-20 20-25 25-30 30-35 >35Af (100 ft2)

Perc

enta

ge


Test-bed application

Part IIGrouping


Part II: Soil variation under building population

Buildings are primarily located over artificially filled regions


Part II: Building parameters and GM category

G3G7

G3

G3G6G1

G3

G1

G3

GM ns αd αw hs Em Af GM

cont

inue

d

ns αd αw hs Em Af

Range 1 Range 2 Range 3


0.0

0.5

1.0

0 1 2 3Sa, g

TNR

L or

ER

CR

1

3

67

Part II: Total regional loss estimate

A B C D

Group #Value, %ERCRLoss, %

1 3 6 76.5 79.7 10.2 3.6

0.82 0.60 0.85 0.455.3 47.8 8.4 1.6

Sa = 0.36g x 2.0 = 0.72g

TNRL = 63.1%


Test-bed application

Part IIIRisk estimation


Part III: Risk estimate

• Assuming earthquake occurrencefollows a Poison’s distribution

Tr = 500 years

Seismic Risk = TRL x P(n = 1 | Sa = 0.72g)

year/%5.12e!1

year1500

1

1.63year1

5001

1

=⎟⎠⎞

⎜⎝⎛ ⋅

×=⎟⎠⎞

⎜⎝⎛ ⋅−


Observed damage: CategorizationEMS-98 Damage Scale

FEMA-356 Damage Categories

Grade 1: NO - IO Grade 2: IO - LS

Grade 3: LS Grade 4: CP

Grade 5: TC


Observed damage: In-plane


Observed damage: Soft-story and sliding


Observed damage: Out-of-plane


Observed damage: Load bearing wall failure


Observed damage: Undamaged buildings


Damage Distribution

Computed normalized loss ~ 43%

Estimated loss = 63%

0

20

40

IO - LS LS - CP CP - TC > TC

Damage

Perc

enta

ge o

fM

ason

ry B

uild

ings

, %


Summary

• To develop a regional risk/loss assessmentmethodology for unreinforced masonrybuildings through rational and systematicinvestigation of building and region specificparameters.

• Sensitivity investigations on building andregion specific parameters are conductedaround the concept of total loss/risk.


Conclusions

• Hazard-loss relationships that areunacceptably scattered for individualbuilding loss calculations can beutilized to estimate regional losses.

• Number of stories, floor aspect ratio,wall density, and ground motioncategories are the most significantparameters in regional loss estimatesof unreinforced masonry buildings


Conclusions

• There exist an essential need forcollection of complete damage datafrom real events. In data collectionprocess, together with buildingdamage states, building parametersthat are found to be significant for lossestimates have to be collected.

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