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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