Using a Displacement-Based Approach for Loss Assessment

of Urban Areas

Julian Bommer

Rui Pinho

Helen Crowley

NATO ISTANBUL WORKSHOP, MAY-JUNE, 2005

DBELA

DISPLACEMENT-BASED EARTHQUAKE LOSS

ASSESSMENT

DEMAND – overdamped DISPLACEMENT

RESPONSE SPECTRA relate displacement

demand of a SDOF system to its fundamental

period of vibration

n Relationship between the frequency content

of the ground motion and dominant period of

the buildings

n Correlation of this ground motion parameter

to damage

∆LS ∆y

Keff

Vy

BUILDING CLASS CAPACITY – mechanics-derived

equations to relate limit state displacement capacity

of SDOF system to its fundamental period of vibration

MDOF Building

H

Limit state displacement

capacity, ∆c

SDOF System

Limit state

strains

Equivalent Linearisation

Direct Displacement-Based Design principles

∆c = f(Height, geometrical properties, limit state strains)

Period = f(Height)

∴ ∆c = f(Period, geometrical properties, limit state strains)

φ φy2 φy3 φy1

M M1

M2

M3

φ φy

M M1

M2

M3

Beam-sway Column-sway

ϑmt

ϑmt

ϑmt

ϑmt

ϑmt

ϑmt

ϑmt

ϑmt

ϑmt

ϑmt

∆m F4

F3

F2

F1

∆m

ϑmc

1 2

h

h

h

h

H

EXAMPLE OF PRE-YIELD CAPACITY

EQUATIONS

BEAM SWAY

COLUMN SWAY

PERIOD-HEIGHT

RELATIONSHIP

b

byThSy

h

lHef5.0 ε∆ =

c

s

yThSyh

hHef43.0 ε∆ =

Ty H1.0T =

EXAMPLE OF POST-YIELD CAPACITY

EQUATIONS

BEAM SWAY

COLUMN SWAY

PERIOD-HEIGHT

RELATIONSHIP

( )( ) ( )0.5 0.5 1.7 bSLsi h T y C Lsi S Lsi y h T

b

lef H ef H

hε ε ε ε∆ = + + −

sy)Lsi(S)Lsi(C

c

s

yThSLsi h)14.2(5.0h

hHef43.0 εεεε∆ −++=

LsiyLsi

�TT =

IF DEMAND > CAPACITY FAILURE OF LIMIT STATE

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0 1 2 3 4 5 6 7

Period (s)

Dis

pla

cem

ent

(m)

CAPACITY

Probabilistic distributions assigned to each

parameter in equation (e.g. Normal / Lognormal)

FORM – Produce the JPDF of displacement

capacity and period

UNCERTAINTY & VARIABILITY

Beam Length (m)

0 2 4 6 8

Fre

qu

ency

0

50

100

150

200

250

300

350

Mean = 3.41m S.D. = 1.16m Gamma Dist.

Storey Height (m)

1.5 2.0 2.5 3.0 3.5 4.0 4.5

Fre

qu

ency

0

10

20

30

40

50

60

70

Mean = 2.93 m S.D. = 0.23 m Normal Dist.

DEMAND – single scenario earthquakes

Cumultative distribution function computed using logarithmic standard deviation at each period

Reliability Formula

UNCERTAINTY & VARIABILITY

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0 1 2 3 4 5 6 7

Period (s)

Sp

ectr

al

Dis

pla

cem

ent

(m)

50-percentile

16-percentile

84-percentile

[ ] dxdy)y,x(f.)yT/x(F1PLSiLSi

T

x y

LsiDf ∆∫ ∫ =−=

DAMAGE BANDS (% of buildings)

SLIGHT – % slight = 1 – Pf1

MODERATE – % moderate = Pf1 – Pf2

EXTENSIVE –% extensive = Pf2 – Pf3

COMPLETE – % complete = Pf3

MEAN DAMAGE RATIO – weights applied to

each damage band to give composite measure

of damage: ratio between cost of repair/retrofit

to cost of rebuilding

SENSITIVITY STUDY – SEA OF MARMARA, TURKEY

Erdik et al. (2004) fault segmentation model, Mw = 7.2

Building Stock Data – 2000 Building Census

40º

30º29º28º27º

41º

Sea of Marmara

fault

rupture

TekirdagIstanbul

Kocaeli

Black Sea

BASE MODEL - GROUND MOTION PREDICTION

EQUATION

Boore et al. (1997)

Period (s)

0 2 4 6 8 10

Sp

ectr

al D

isp

lace

me

nt

(m)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

E: Soft soil

D: Stiff soil

C: Very dense soil

Soft rock

B: Rock

NEHRP GUIDELINES: 2

5

10

−

=wM

VDT

CORNER PERIOD =12.6 SECONDS

MW = 7.2

BASE MODEL – CAPACITY

(Poor, Column-sway frames)

Lognormal50%2.25 %Limit state 3 steel strain, εs2

Lognormal50%0.75 %Limit state 3 concrete strain, εc2

Lognormal50%1.25 %Limit state 2 steel strain, εs3

Lognormal50%0.45 %Limit state 2 concrete strain, εc3

Normal10%263 MPaSteel yield strength

Lognormal10%0.55 mBeam depth

Lognormal25%4.0 mBeam length

Lognormal35%0.6 mColumn section depth

Lognormal35%3.6 mGround floor storey height

Probabilistic

Distribution

Coefficient of

variation

Mean valueCapacity Parameter

BASE MODEL DAMAGE PREDICTIONS

Slight Moderate Extensive Complete MDR

Pro

po

rtio

n o

f R

C F

ram

e B

uild

ing

Sto

ck

0.0

0.2

0.4

0.6

0.8

1.0

'Poor'_Column-sway

'Poor'_Beam-sway

'Good'_Beam-sway

All

MEAN DAMAGE

RATIO (MDR)

2% SLIGHT

10% MODERATE

50% EXTENSIVE

100% COMPLETE

-25 -20 -15 -10 -5 0 5 10 15 20 25

NEHRP factors applied to Boore et al. (1997)

rock spectra

Site class B to C

Site class E to D

Site class B to C and E to D

Gradient increase 10%

Gradient decrease 20%

Constant spectral displacement at 5 s

85% aleatory variability

% Variation of MDR from Base Model

SENSITIVITY TO DEMAND VARIABLES

BASE MODEL – CAPACITY

(Poor, Column-sway frames)

Lognormal50%2.25 %Limit state 3 steel strain, εs2

Lognormal50%0.75 %Limit state 3 concrete strain, εc2

Lognormal50%1.25 %Limit state 2 steel strain, εs3

Lognormal50%0.45 %Limit state 2 concrete strain, εc3

Normal10%263 MPaSteel yield strength

Lognormal10%0.55 mBeam depth

Lognormal25%4.0 mBeam length

Lognormal35%0.6 mColumn section depth

Lognormal35%3.6 mGround floor storey height

Probabilistic

Distribution

Coefficient of

variation

Mean valueCapacity Parameter

SENSITIVITY TO CAPACITY VARIABLES

Combined increase / decrease (10-20%) capacity

parameters – upper bound / lower bound

-100.0 -50.0 0.0 50.0 100.0

slight

moderate

extensive

complete

MDR

% Variation from Base Model

Upper boundcapacity

Lower boundcapacity

LOSS ASSESSMENT

Single earthquake scenario – useful for disaster

management, communicating seismic risk to public

ALL possible earthquake scenarios

insurance / reinsurance industry

Seismic code drafting committees

Loss versus annual frequency of exceedance

0.0001

0.001

0.01

0 2000 4000 6000 8000 10000 12000 14000

Loss (millions $)

An

nu

al

Fre

qu

ency

of

Exce

edan

ce

LOSS EXCEEDANCE CURVES

n Need to perform a seismic hazard assessment

of area and convolute results with vulnerability.

n Aleatory variability modelled in hazard and thus

removed from reliability formula.

n Inter-event and intra-event components of

aleatory variability need to be modelled

separately in loss model.

n Need to use thousands of scenario earthquakes

(which can be generated using Monte Carlo

Simulation in conjunction with seismicity model)

to obtain robust loss exceedance curves.

CONCLUSIONS / FUTURE RESEARCH

n DBELA is a MECHANICS-BASED loss assessment

methodology and the demand and capacity can be plotted on the same displacement-period plane.

n Capacity equations can be EASILY CALIBRATED for

different regions by adapting (µ, σ, DISTRIBUTION) of parameters.

nFurther developments:

INFILL PANELS, SHEAR FAILURE, other STRUCTURAL

TYPES, improved parameters used in EQUIVALENT LINEARISATION, improvement of DISPLACEMENT

SPECTRA (especially at long periods).

n CALIBRATION of the methodology and COMPARISON

of results with damage data.

Thank you!

CALIBRATION OF SEISMIC DESIGN CODES

Quantitative comparison of incremental cost of adding seismic resistance and the associated losses that can be

avoided within an urban area

n DBELA is ideal as structural parameters in displacement capacity equations can easily be adapted to model increasing levels of seismic resistance (e.g. stiffness and ductility).

n Owners and regulators need to decide on a minimum allowable resistance of the building stock considering the return period of ‘tolerable’ levels of death, injury and persons rendered homeless.

n Loss curves derived for various resistance levels of each building class are produced and compared with cost of resistance to define ‘optimum’ resistance.

BASE MODEL DAMAGE PREDICTIONS FOR EACH NUMBER OF STOREYS FOR POOR,

COLUMN-SWAY

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

slight moderate extensive complete

Pro

po

rtio

n o

f R

C f

ram

e b

uil

din

g s

tock

1 storey

2 storey

3 storey

4 storey

5 storey

6 storey

7-9 storey

SENSITIVITY TO GROUPING OF STOREY

NUMBERS

-25.0 -15.0 -5.0 5.0 15.0 25.0

slight

moderate

extensive

complete

MDR

% Variation from Base Model

Building classes [1-9] , Number of storeys = 3