Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

STUDY ON EARLY EARTHQUAKE DAMAGE EVALUATION
OF EXISTING BUILDINGS IN BUCHAREST, ROMANIA

Draft Report prepared by:Technical University of Civil Engineering, Bucharest

Draft Report prepared for:
Building Research Institute&International Institute for Seismology and Earthquake Engineering,
Tsukuba, Japan

MARCH 2006

Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

Table of Content
1. Vulnerability/Fragility Characteristics for Representative Building Types..........3
1.1 Description of Model Building Types.......................................................................3
1.2 Capacity Curves ........................................................................................................3
1.3 Fragility Curves.......................................................................................................10
1.3.1 Background .................................................................................................................10
1.3.2 Development of Damage State Medians ......................................................................11
1.3.3 Development of Damage State Variability ..................................................................11
1.3.4 Structural Damage........................................................................................................14
References Chapter 1.............................................................................................................17
2. Development of Seismic Risk Scenarios ..................................................................18
2.1 Introduction ...............................................................................................................18
2.2 Direct physical losses estimation; debris...................................................................19
2.3 Casualties and homeless estimation ..........................................................................23
2.4 Direct economic losses..............................................................................................28
2.5 Risk management ......................................................................................................30
References Chapter 2.............................................................................................................36
Annex A: Tables..............................................................................................................38
Annex B: Case study .......................................................................................................44
3. Full Probabilistic Risk Assessment of Current Buildings ......................................57
3.1 Introduction ...............................................................................................................57
3.2 Probabilistic seismic hazard assessment ...................................................................58
3.3 Probabilistic assessment of seismic structural response............................................60
3.3.1 The structural model.....................................................................................................60
3.3.2 Ground motions............................................................................................................61
3.3.3 Non-linear dynamic analyses .......................................................................................61
3.3.4 Probabilistic assessment of seismic structural vulnerability ........................................63
3.3.5 Risk analysis.................................................................................................................66
3.4 Conclusions ...............................................................................................................67
References Chapter 3.............................................................................................................67

Technical University of Civil Engineering

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1. Vulnerability/Fragility Characteristics for Representative Building Types
1.1

Description of Model Building Types

Table 1.1 lists the model building types included in this study and considered to be
representative for Bucharest building stock.
Table 1.1 Model Building Types
Height

No.
1
2
3
4
5
6

1.2

Label
RC1L
RC1M
RC1H
RC2L
RC2M
RC2H

Description

Concrete Moment Frame

Concrete Shear Walls

Range

TypicalName

Stories

Stories

MetersLow-Rise
Mid-RiseHigh-Rise
Low-Rise
Mid-RiseHigh-Rise

1-3
4-7
8+
1-3
4-7
8+

2
6
10
2
6
10

5.7
17.1
28.5
5.7
17.1
28.5

Capacity Curves

A building capacity curve (also known as a push-over curve) is a plot of a building’s lateral load
resistance as a function of a characteristic lateral displacement (i.e., a force-deflection plot). It isderived from a plot of static-equivalent base shear versus building (e.g., roof) displacement. In
order to facilitate direct comparison with earthquake demand (i.e. overlaying the capacity curvewith a response spectrum), the force (base shear) axis is converted to spectral acceleration andthe displacement axis is converted to spectral displacement.
The building capacity curves developed are based on engineering design parameters andjudgment. Three control points that define model building capacity describe each curve:• Design Capacity• Yield Capacity• Ultimate Capacity
Design capacity represents the nominal building strength required by current model seismic codeprovisions or an estimate of the nominal strength for buildings not designed for earthquake loads.
Yield capacity represents the true lateral strength of the building considering redundancies indesign, conservatism in code requirements and true (rather than nominal) strength of materials.
Ultimate capacity represents the maximum strength of the building when the global structural
system has reached a fully plastic state. Ultimate capacity implicitly accounts for loss of strength
due to shear failure of brittle elements. Typically, buildings are assumed capable of deforming
beyond their ultimate point without loss of stability, but their structural system provides noadditional resistance to lateral earthquake force.
Up to the yield point, the building capacity curve is assumed to be linear with stiffness based onan estimate of the true period of the building. The true period is typically longer than the codespecified period of the building due to flexing of diaphragms of short, stiff buildings, flexural
cracking of elements of concrete and masonry structures, flexibility of foundations and otherfactors observed to affect building stiffness. From the yield point to the ultimate point, thecapacity curve transitions in slope from an essentially elastic state to a fully plastic state. The

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capacity curve is assumed to remain plastic past the ultimate point. An example building
capacity curve is shown in Figure 1.1.

Sa

Ultimate
Capacity

Au

Ay

Yield
CapacityAd

DesignCapacity

Dd

Dy

Du

Sd

Figure 1.1 Example Building Capacity Curve
The building capacity curves are constructed based on estimates of engineering properties that
affect the design, yield and ultimate capacities of each model building type. These properties aredefined by the following parameters, Figure 1.1:
Cs
Te
α1
α2
γ
λ
µ

design strength coefficient (fraction of building’s weight),
true “elastic” fundamental-mode period of building (seconds),
fraction of building weight effective in push-over mode,
fraction of building height at location of push-over mode displacement,“overstrength” factor relating “true” yield strength to design strength,“overstrength” factor relating ultimate strength to yield strength, and“ductility” factor relating ultimate displacement to λ times the yielddisplacement (i.e., assumed point of significant yielding of the structure)

The design strength, Cs is based on the lateral-force design requirements of seismic codes. These
requirements are a function of the building’s seismic zone location and other factors including
type of lateral-force-resisting system and building period.
The major developments in four generations of seismic codes in Romania can be described asfollows:
Pre-code period (prior to 1941/45):
1941 Draft Instructions
1945 Instructions•

Development of first national seismic code
after the 1940 earthquake: lateral seismic
force was 5% of building weight.

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Low-code period (1963- 1977):
P13-63

P13-70••Control period of response spectra TC=0.3 s
Maximum dynamic amplification DAF = maxSA/PGA = 3
SA - structure absolute acceleration response spectra.

•••

Control period of response spectra TC=0.4 s
Max. dynamic amplification DAF = 2
Some ductility rules for RC frames.

Moderate-code period (1978 - 1990):
P100-78 • Development of the first seismic code based on the unique strong
ground motion recorded in soft soil of Bucharest during March 4,
1977 event: PGA = 0.2g and the long predominant period ofground vibration was Tp =1.6s.
P100-81 • Control period of response spectra TC=1.5 s• Maximum dynamic amplification DAF = 2• Ductility rules for RC shear wall & frame structures.
Moderate to High-code period (1990-present):
P100-90 • Control period of response spectra TC=1.5 s
P100-92 • Maximum dynamic amplification DAF = 2.5• Advanced ductility rules for RC shear wall and frame
structures and for steel structures.
The history of overall seismic design coefficient, Cs for shear wall and frames structures in
Bucharest, according to Romanian seismic codes during the time interval 1940-2002 is presented
in Figure 1.2. The geometry of Cs is self explanatory. One may note the gap of the Cs for flexible
buildings and structures during the period 1963-1978. However, even for rigid structures built
during that period, the maximum Cs was about 2/3 of the present day Cs.
It is emphasised that after the 1977 event, new ductility rules for RC structures were imported
from US practice and incorporated into Romanian seismic codes, P100. According to the
EUROCODE 8 requirements the rules were significantly improved after 1989.
Table 1.2 summarizes design capacity for each building type and design level. Building period,
Te, push-over mode parameters α1 and α2, the ratio of yield to design strength, γ, and the ratio of
ultimate to yield strength, λ, are assumed to be independent of design level. Values of theseparameters are summarized in Tables 1.3a&b for each building type. Values of the “ductility”
factor, µ, are given in Table 1.4 for each building type and design level. The values are given
only for medium and high-rise RC buildings considered to be representative for Bucharest.

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Shear walls
Frames

7.5%
7.2%
7.5%
6.8%

Seismic
designcoefficientCs , %

12.5 %
10%

10 %
8%

12
1.5 s

5%

10

Tc=0.4 s

0.3 s

Tc=1.5 s

RIGID 0.1
buildings 0.4

8-10

8

6-8

6

4-6

4

2-4

0.7
FLEXIBLE
buildings

1

2

1.3

2%

1.6
Building period
T,s

2.2%
1.8%

1.9

0
1978
1981

1970
1963

1941
1945

1990
1992

Year of code issue
Non ductile buildings

Ductile structures

Figure 1.2 Evolution of seismic design coefficient in Bucharest during period 1940-2002
Table 1.2 Code Building Capacity Parameters - Design Strength (Cs)
Building

Seismic Design Level (Percentage of Building Weight)Type

1941-1962 1963-1969 1970-1977 1978-1989 1990-2002

RC1M
RC1H
RC2M
RC2H

5
5
5
5

3.21
2.25
7.71
4.15

3.4
2.4
7.2
4.4

8
8
10
10

10
10
12.5
12.5

Table 1.3a Code Building Capacity Parameters - Period (Te), Pushover Mode
Response Factors (α1, α2) and Overstrength Ratios (γ, λ) - 1941-1977
Building

Height to Period, Te

Type

Roof (m)

(Sec)

RC1M
RC1H
RC2M
RC2H

17.1
28.5
17.1
28.5

0.7
1
0.4
0.7

Modal Factors

Overstrength Ratios

Weight, α1 Height, α2

Yield, γ Ultimate, λ

0.85
0.75
0.9
0.8

0.6
0.6
0.7
0.7

1.4
1.4
1.4
1.4

1.5
1.5
1.5
1.5

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Table 1.3b Code Building Capacity Parameters - Period (Te), Pushover Mode
Response Factors (α1, α2) and Overstrength Ratios (γ, λ) - 1978-2002
Building

Height to Period, Te

Type

Roof (m)

(Sec)

RC1M
RC1H
RC2M
RC2H

17.1
28.5
17.1
28.5

0.6
0.85
0.35
0.6

Modal Factors

Overstrength Ratios

Weight, α1 Height, α2

Yield, γ Ultimate, λ

0.85
0.75
0.9
0.8

0.6
0.6
0.7
0.7

1.5
1.5
1.5
1.5

2
2
2
2

Table 1.4 Code Building Capacity Parameter - Ductility (µ)
Building

Seismic Design Level (Percentage of Building Weight)Type

1941-1962 1963-1969 1970-1977 1978-1989 1990-2002

RC1M
RC1H
RC2M
RC2H

2
2
2
2

3
3
3
3

3
3
3
3

5
5
4
4

5
5
4
4

Building capacity curves are assumed to have a range of possible properties that are lognormally
distributed. Capacity curves described by the values of parameters given in Tables 1.2, 1.3 and1.4 represent median estimates of building capacity.
Tables 1.5a, 1.5b, 1.5c, 1.5d and 1.5e summarize yield capacity and ultimate capacity control
points.
Table 1.5a Code Building Capacity Curves - 1941-1962
Building

Yield Capacity PointType

Dy (cm)Ay (g)

RC1M
RC1H
RC2M
RC2H

1.00
2.32
0.31
1.07

0.082
0.093
0.078
0.088

Ultimate Capacity
Point
Du (cm)Au (g)
3.01
6.96
0.93
3.20

0.124
0.140
0.117
0.131

Table 1.5b Code Building Capacity Curves - 1963-1969
Building

Yield Capacity PointType

Dy (cm)Ay (g)

RC1M
RC1H
RC2M
RC2H

0.64
1.04
0.48
0.88

0.053
0.042
0.120
0.073

Ultimate Capacity
Point
Du (cm)Au (g)
2.90
4.70
2.15
3.98

0.079
0.063
0.180
0.109

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Table 1.5c Code Building Capacity Curves - 1970-1977
Building

Yield Capacity PointType

Dy (cm)Ay (g)

RC1M
RC1H
RC2M
RC2H

0.68
1.11
0.45
0.94

0.056
0.045
0.112
0.077

Ultimate Capacity
Point
Du (cm)Au (g)
3.07
5.01
2.00
4.22

0.084
0.067
0.168
0.116

Table 1.5d Code Building Capacity Curves - 1978-1989Type

Dy (cm)Ay (g)

Ultimate Capacity
Point
Du (cm)Au (g)

RC1M
RC1H
RC2M
RC2H

1.26
2.87
0.51
1.68

0.141
0.160
0.167
0.188

12.63
28.73
4.06
13.42

Building

Yield Capacity Point

0.282
0.320
0.333
0.375

Table 1.5e Code Building Capacity Curves - 1990-2002
Type

Dy (cm)Ay (g)

Ultimate Capacity
Point
Du (cm)Au (g)

RC1M
RC1H
RC2M
RC2H

1.58
3.59
0.63
2.10

0.176
0.200
0.208
0.234

15.79
35.91
5.07
16.77

Building

Yield Capacity Point

0.353
0.400
0.417
0.469

The values of yielding and ultimate displacement and acceleration given in Tables 1.5a to 1.5e
are represented in Figures 1.3, 1.4, 1.5 and 1.6 for building types RC1H and RC2H.
4.0

3.5

RC1H
RC2H

3.0

Dy , cm

2.5
2.0
1.5
1.0
0.5
0.0
1941-1962

1963-19691970-1977
Seismic code period

1978-1989

1989-2002

Figure 1.3. Yielding displacement according to seismic code period

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40
RC1H

35

RC2H

30

Du , cm

25
20
15
10
5
0
1941-1962

1963-19691970-1977

1978-1989

1989-2002

Seismic code period

Figure 1.4. Ultimate displacement according to seismic code period

0.25
RC1H
RC2H
0.20

Ay , 'g

0.15

0.10

0.05

0.00
1941-1962

1963-19691970-1977

1978-1989

1989-2002

Seismic code period

Figure 1.5. Yielding acceleration according to seismic code period

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0.50
RC1H
0.45

RC2H

0.40
0.35
Au , 'g

0.30
0.25
0.20
0.15
0.10
0.05
0.00
1941-1962

1963-19691970-1977

1978-1989

1989-2002

Seismic code period

Figure 1.6. Ultimate acceleration according to seismic code period

1.3

Fragility Curves

This section describes building fragility curves for Slight, Moderate, Extensive and Complete
structural damage states. Each fragility curve is characterized by median and lognormal standard
deviation (β) values.
1.3.1 Background
The probability of being in or exceeding a given damage state is modeled as a cumulative
lognormal distribution. For structural damage, given the spectral displacement, Sd, theprobability of being in or exceeding a damage state, ds, is modeled as:⎡ 1 ⎛ Sd ⎞ ⎤P ds Sd = Φ ⎢ln⎜⎟⎥⎣ β ds ⎝ Sd ,ds ⎠ ⎦[where: Sd,ds
βds
Φ

]

(1-1)

is the median value of spectral displacement at which the building reaches
the threshold of the damage state, ds,
is the standard deviation of the natural logarithm of spectral
displacement of damage state, ds, andis the standard normal cumulative distribution function.

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1.3.2 Development of Damage State Medians
Median values of fragility curves are developed for each damage states (i.e., Slight, Moderate,
Extensive and Complete). Structural fragility is characterized in terms of spectral displacement.
Median values of structural component fragility are based on building drift ratios that describe
the threshold of damage states. Damage-state drift ratios are converted to spectral displacement
using Equation (1-2):
Sd ,Sds = δ R ,Sds ⋅ α 2 ⋅ h(1-2)

where: Sd ,Sds is the median value of spectral displacement, in cm, of structural
δR,Sdsα2hcomponents for damage state, ds,
is the drift ratio at the threshold of structural damage state, ds,
is the fraction of the building (roof) height at the location of push-overmode displacement, as specified in Tables 1.6, andis the typical roof height, in centimeters, of the model building type ofinterest (see Table 1.1 for typical building height).

For calibration of the drift ratio at the threshold of structural damage state one used a slightly
modified version of the Park&Ang damage index, in which the recoverable deformation isremoved from the first term, Eq. 1-3:
DI =Dm − Dy∫ dE+ βe ⋅Du − Dy
Fy ⋅ Du(1-3)

where Dm = maximum displacement attained during load history; Du = ultimate displacement; Dy= yielding displacement; βε = strength degrading parameter; Fy = yielding force and E = dissipated hysteretic energy.
To obtain discrete damage states, ranges for the above-mentioned damage index need to be
specified. In this respect the following classification suggested by Park, Ang & Wen was
adapted:Range of damage index
DI ≤ 0.1
0.1 < DI ≤ 0.25
0.20 < DI ≤ 0.40
0.40 < DI < 1.00
DI ≥ 1.00

Damage state
None
SlightModerate
Extensive
Complete

The roof displacement at threshold of damage states is obtained using the values of the damage
index at threshold of damage states and Equation 1-3. Finally, drift ratio at the threshold ofstructural damage state is computed by normalizing the roof displacement by the roof height.
1.3.3 Development of Damage State Variability
Lognormal standard deviation (β) values that describe the variability of fragility curves aredeveloped for each damage states (i.e., Slight, Moderate, Extensive and Complete).

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The total variability of each structural damage state, βSds, is modeled by the combination of threecontributors to structural damage variability, βC, βD and βM(Sds), as described in Equation (1-4):

β Sds = β C 2 + β D 2 + (β M ( Sds ) )2
where:βSds
βC
βD
βM(Sds)(1-4)

is the lognormal standard deviation that describes the total
variability for structural damage state, ds,
is the lognormal standard deviation parameter that describes thevariability of the capacity curve,
is the lognormal standard deviation parameter that describes thevariability of the demand spectrum,is the lognormal standard deviation parameter that describes theuncertainty in the estimate of the median value of the threshold ofstructural damage state, ds.

The variability of building response depends on demand and capacity (since capacity curves are
nonlinear). Demand spectra and capacity curves are described probabilistically by medianproperties and variability parameters, βD and βC, respectively.
The variability in capacity properties of the model building type is increasing as the structure isundergoing larger inelastic deformations. This assumption is supported by the results given in
Figure 1.7 and 1.8. The variability of the capacity properties is obtained through Monte-Carlosimulations.
0.7
RC!H
0.6

COVDR

0.5
0.4
0.3
0.2
0.1
0
0

0.5

1

1.5

2

2.5

Drift Ratio, DR , %He

Figure 1.7 Variability of drift ratio for RC1H building type3

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0.5
RC2M

0.45
0.4
0.35

COVDR

0.3
0.25
0.2
0.15
0.1
0.05
0
0

0.05

0.1

0.15

0.2

0.25

0.3

Drift Ratio, DR , %He

Figure 1.8 Variability of drift ratio for RC2M building type
Examples of the variability in response are given in Figure 1.9 for the relative displacement
response spectra computed for the seismic motions recorded in Bucharest during 1986 and 1990
Vrancea earthquakes. One can notice an average COV of 0.5.
0.7
0.6

COVSD

0.5
0.4
0.3
Bucharest'86
0.2

Bucharest'90

0.1
0.0
0.0

0.5

1.0

1.5

2.0

2.5

T, s

Figure 1.9 Variability of relative displacement response spectra

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The lognormal standard deviation parameter that describes the uncertainty in the estimate of themedian value of the threshold of structural damage state ds, βM(Sds), is assumed to be independentof capacity and demand, and is added by the square-root-sum-of-the-squares (SRSS) method tothe lognormal standard deviation parameters representing the demand and capacity variabilities.
Uncertainty in the damage-state threshold of the structural system is assumed to be βM(Sds) = 0.4,
for all structural damage states and building types.
1.3.4 Structural Damage
Structural damage fragility curves for buildings are described by median values of drift thatdefine the thresholds of Slight, Moderate, Extensive and Complete damage states. In general,these estimates of drift are different for each model building type (including height) and seismic
design level. A complete listing of damage-state drift ratios for all building types and heights areprovided for each seismic design level in Tables 1.6a, 1.6b, 1.6c, 1.6d and 1.6e, respectively.
Figure 1.10 provides an example of fragility curves for the four damage states used in thismethodology.
1
0.9
0.8
0.7

P(>ds|SD)

0.6
0.5
RC1H, 1990-2002
0.4
SlightModerate
Extensive
Complete

0.3
0.2
0.1
0
0

10

20

30

40

50

SD , cm

Figure 1.10 Example Fragility Curves for Slight, Moderate, Extensive and Complete Damage
Tables 1.6a, 1.6b, 1.6c, 1.6d and 1.6e summarize median and lognormal standard deviation (βSds)
values for Slight, Moderate, Extensive and Complete structural damage states.
.

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Table 1.6a Structural fragility curve parameters - 1941-1962

Building properties
Interstory drift at threshold of damage state, %Height (cm)Type
Roof Modal Slight Moderate Extensive Complete
RC1L
570
342
0.041
0.084
0.128
0.302
RC1M 1710 1026
0.037
0.076
0.115
0.272
RC1H
2850 1710
0.051
0.105
0.160
0.378
RC2L
570
399
0.004
0.008
0.012
0.027
RC2M 1710 1197
0.010
0.020
0.030
0.072
RC2H
2850 1995
0.020
0.041
0.063
0.149

SlightMedian
0.14
0.38
0.87
0.01
0.12
0.40

Beta
0.65
0.65
0.65
0.65
0.65
0.65

Spectral displacement, cm
Moderate
Extensive
MedianBeta
Median
Beta
0.29
0.75
0.44
0.85
0.78
0.75
1.18
0.85
1.80
0.75
2.73
0.85
0.03
0.75
0.05
0.85
0.24
0.75
0.36
0.85
0.83
0.75
1.26
0.85

Complete
Median
Beta
1.03
0.95
2.79
0.95
6.46
0.95
0.11
0.95
0.86
0.95
2.97
0.95

Beta
0.65
0.65
0.65
0.65
0.65
0.65

Spectral displacement, cm
Moderate
Extensive
MedianBeta
Median
Beta
0.41
0.75
0.62
0.85
0.71
0.75
1.08
0.85
1.15
0.75
1.75
0.85
0.08
0.75
0.12
0.85
0.53
0.75
0.80
0.85
0.98
0.75
1.48
0.85

Complete
Median
Beta
1.47
0.95
2.55
0.95
4.14
0.95
0.28
0.95
1.89
0.95
3.51
0.95

Beta
0.65
0.65
0.65
0.65
0.65
0.65

Spectral displacement, cm
Moderate
Extensive
MedianBeta
Median
Beta
0.43
0.75
0.66
0.85
0.75
0.75
1.14
0.85
1.23
0.75
1.87
0.85
0.06
0.75
0.09
0.85
0.49
0.75
0.75
0.85
1.04
0.75
1.57
0.85

Complete
Median
Beta
1.56
0.95
2.70
0.95
4.42
0.95
0.22
0.95
1.77
0.95
3.72
0.95

Table 1.6b Structural fragility curve parameters - 1963-1969
Building properties
Height (cm)
Type
Roof
Modal
RC1L 570
342
RC1M 1710
1026
RC1H 2850
1710
RC2L 570
399
RC2M 1710
1197
RC2H 2850
1995

Interstory drift at threshold of damage state, %Slight
0.058
0.033
0.033
0.009
0.021
0.024

Moderate
0.120
0.069
0.067
0.020
0.044
0.049

Extensive
0.182
0.105
0.102
0.030
0.067
0.074

Complete
0.430
0.249
0.242
0.070
0.158
0.176

SlightMedian
0.20
0.34
0.56
0.04
0.25
0.47

Table 1.6c Structural fragility curve parameters - 1970-1977
Building properties
Height (cm)
Type
Roof
Modal
RC1L 570
342
RC1M 1710
1026
RC1H 2850
1710
RC2L 570
399
RC2M 1710
1197
RC2H 2850
1995

Interstory drift at threshold of damage state, %Slight
0.061
0.035
0.035
0.008
0.020
0.025

Moderate
0.127
0.073
0.072
0.016
0.041
0.052

Extensive
0.193
0.112
0.109
0.024
0.062
0.079

Complete
0.456
0.264
0.258
0.056
0.148
0.186

SlightMedian
0.21
0.36
0.59
0.03
0.24
0.50

Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

Table 1.6d Structural fragility curve parameters - 1978-1989
Building properties
Height (cm)
Type
Roof
Modal
RC1L 570
342
RC1M 1710
1026
RC1H 2850
1710
RC2L 570
399
RC2M 1710
1197
RC2H 2850
1995

Interstory drift at threshold of damage state, %Slight
0.147
0.123
0.168
0.008
0.036
0.071

Moderate
0.324
0.272
0.371
0.017
0.077
0.152

Extensive
0.502
0.421
0.574
0.026
0.118
0.233

Complete
1.213
1.016
1.387
0.062
0.282
0.559

SlightMedian
0.50
1.26
2.87
0.03
0.43
1.41

Beta
0.65
0.65
0.65
0.65
0.65
0.65

Spectral displacement, cm
Moderate
Extensive
MedianBeta
Median
Beta
1.11
0.75
1.72
0.85
2.79
0.75
4.32
0.85
6.35
0.75
9.82
0.85
0.07
0.75
0.10
0.85
0.92
0.75
1.41
0.85
3.03
0.75
4.65
0.85

Complete
Median
Beta
4.15
0.95
10.43
0.95
23.72
0.95
0.25
0.95
3.37
0.95
11.15
0.95

Beta
0.65
0.65
0.65
0.65
0.65
0.65

Spectral displacement, cm
Moderate
Extensive
MedianBeta
Median
Beta
1.32
0.75
2.01
0.85
3.32
0.75
5.06
0.85
7.55
0.75
11.51
0.85
0.08
0.75
0.12
0.85
1.10
0.75
1.66
0.85
3.64
0.75
5.49
0.85

Complete
Median
Beta
4.78
0.95
12.03
0.95
27.35
0.95
0.29
0.95
3.90
0.95
12.89
0.95

Table 1.6e Structural fragility curve parameters - 1990-2002
Building properties
Height (cm)
Type
Roof
Modal
RC1L 570
342
RC1M 1710
1026
RC1H 2850
1710
RC2L 570
399
RC2M 1710
1197
RC2H 2850
1995

Interstory drift at threshold of damage state, %Slight
0.184
0.154
0.210
0.010
0.045
0.090

Moderate
0.386
0.324
0.442
0.020
0.092
0.182

Extensive
0.588
0.493
0.673
0.031
0.139
0.275

Complete
1.398
1.172
1.600
0.072
0.326
0.646

SlightMedian
0.63
1.58
3.59
0.04
0.54
1.79

Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

References Chapter 1
Aldea, A., Lungu, D., Demetriu, S., Cornea, T., Vacareanu, R. May 2005. “City of Bucharest: Distinctive
Features and Seismic Hazard”, Bulletin of the Technical University of Civil Engineering Bucharest, 2/2003, p.
43-75
Ang A.H-S., 1987. Basis for earthquake-resistant design with tolerable structural damage, Proc. 5thInternational Conference on Applications of Statistics and Probability in Soil and Structural Engineering(ICASP5), Vancouver BC, Canada, Vol.1, 407-416
ATC 40, 1996. Seismic Evaluation and Retrofit of Concrete Buildings, Report ATC-40, Applied
Technology Council, Redwood City CA.
HAZUS – Technical Manual 1997. Earthquake Loss Estimation Methodology, 3 Vol.
Lungu, D., Arion, C., Baur, M., Aldea, A., 2000. Vulnerability of existing building stock in Bucharest,
6ICSZ Sixth International Conference on Seismic Zonation, Palm Springs, California, USA, Nov.12-15,
p.837-846
Lungu, D., Demetriu, S., Arion, C. 1998. Seismic vulnerability of buildings exposed to Vrancea
earthquakes in Romania. In Vrancea Earthquakes. Tectonics, Hazard and Risk Mitigation, Kluwer Academic
Publishers, Wenzel F., Lungu D., editors, Proc. of First International Workshop on Vrancea Earthquakes,
p.215-224.
Park, Y.-J & Ang, A. H.-S.. Mechanistic seismic damage model for reinforced concrete. Journal of
Structural Engineering. ASCE vol. 111 (4): 722-739, 1985
Reinhorn A. M., Valles-Mattox R. E., Kunnath S. K. – Seismic Damageability Evaluation of a Typical R/C
Building in the Central U.S., NCEER Bulletin, Vol. 10, No. 4, October 1996
RISK-UE "An advanced approach to earthquake risk scenarios with applications to different European
towns", financed by European Commission, Fifth Framework, 2000-2004
Rubinstein, R. Y. Simulation and the Monte Carlo method. John Wiley & Sons, New York, 1981Văcăreanu R., 2000 - Monte Carlo Simulation Technique for Vulnerability Analysis of RC Frames – An
Example – Scientific Bulletin on Technical University of Civil Engineering of Bucharest, pg. 9-18;
Văcăreanu R., 1998 - Seismic Risk Analysis for a High Rise Building - Proceedings of the 11th European
Conference on Earthquake Engineering, Paris, Abstract Volume pg. 513
Văcăreanu R., Cornea T., Lungu D. Evaluation of seismic fragility of buildings, Earthquake Hazard andCountermeasures for Existing Fragile Buildings, Editors: Lungu D. & Saito T., Independent Film, Bucharest
Romania, 315p
Williams, M. S. & Sexsmith, R. G. 1995. Seismic Damage Indices for Concrete Structures: A State-of-theArt Review. Earthquake Spectra. Vol. 11(2): 319-345, 1997

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2. Development of Seismic Risk Scenarios
2.1 Introduction
Human, economic and ecological costs and losses associated with earthquake disasters are
increasing exponentially and these cost and losses pose a systemic risk to society’s politicaland economic bases. It is correspondingly difficult, in some cases impossible, for local,
national and global disaster management agencies to cope with the scope, magnitude andcomplexity of these disasters.
Even utilizing the most advanced technology, it is almost impossible, at the present state ofknowledge, to predict exactly when and where an earthquake will occur and how big it will
be. An earthquake suddenly hits an area where people are neither prepared nor alerted.
Hence, the earthquake often causes huge damage to human society. On the other hand, theother natural disasters like floods and hurricanes are almost predictable, providing some leadtime before they hit certain places. People could be alerted with a proper warning systemand precautionary measures could be taken to protect lives and properties.
It is therefore urgent and crucial to make the physical environment resistant against
earthquakes, strengthening buildings and infrastructure. Action should be taken for seismic
risk reductions. Different strategies may be taken to mitigate earthquake disasters, based on
appropriate risk assessment.
There is a tendency to think that disaster prevention would cost much more than relief
activities. However, the reality is the reverse. Our society has been spending a lot of
resources for response activities after disasters; these resources could have been drasticallyreduced if some had been spent for disaster prevention. There is also a tendency to look at
disasters mainly from a humanitarian angle, bringing us into the position of giving priority
to the response to disasters. However, relief activities can never save human lives that havealready been lost. Response activities can never help immediately resume functions of anurban infrastructure that has already been destroyed. The bottom line is that buildings
should not kill people by collapsing and infrastructure should not halt social and economic
activities of the city for a long time.
The damage caused by an earthquake could be magnified in areas where:
9 People are concentrated;
9 Economic and political functions are concentrated;
9 Buildings and infrastructure have been built to inadequate standards of design.
The larger an urban area is, the greater the damage would be. As the urban areas are
growing rapidly, the seismic risk in the urban areas is also growing rapidly. Even anintermediate earthquake could cause destructive damage to a city.
Risk is the expectancy of losses or of other negative future happenings derived on the basisof present knowledge. The risk analysis recognizes basically the impossibility ofdeterministic prediction of events of interest, like future earthquakes, exposure of elements
at risk, or chain effects occurring as a consequence of the earthquake-induced damage. Since
the expectancy of losses represents the outcome of a more or less explicit and accurate

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predictive analysis, a prediction must be made somehow in probabilistic terms, byextrapolating or projecting into the future the present experience.
The objective is to develop earthquake-risk model scenarios for physical and human loss
estimation. The model should take into account the following components:- Direct physical losses- Human losses- Direct economic losses- Problems due to homeless, debris
The worst case earthquake scenario – constant hazard scenario - is selected on probabilistic
basis, as uniform hazard acceleration spectra corresponding to a mean recurrence interval
MRI = 475 yr (10 % probability of exceedance in 50 yr).
2.2 Direct physical losses estimation; debris
The expected response of the built systems to given earthquake scenarios expressed in termsof acceleration – displacement spectra of uniform hazard is obtained by capacity spectrum
method, Figure 2.1. The expected spectral displacement Sd of an inelastic system isdetermined by the following steps:
1. The uniform hazard spectrum of absolute acceleration obtained in RISK-UE Project,
Figure 2.2, is converted into acceleration-displacement response spectrum, ADRS,
Figure 2.3. A demand constant-ductility spectrum is established by reducing theelastic acceleration-displacement spectrum by appropriate ductility-dependent
factors that depend on T.
2. The capacity curve is plotted on the same graph.
3. The yielding branch of the capacity curve intersects the demand spectra for severalµ values of ductility factor. One of these intersection points, which remains to be
determined, will provide the expected spectral displacement. At the one relevantintersection point, the ductility factor calculated from the capacity curve shouldmatch the ductility value associated with the intersecting demand spectrum.
4. The building fragility functions are determined. The conditional probability of beingin, or exceeding, a particular damage state, ds, given the spectral displacement, Sd, isdefined by the lognormal distribution of damage state conditional upon spectral
displacement.

LAT ERAL BUILDING FORCEBUILDING WEIGHTST RONGER CONST RUCT ION

WEAKER CONST RUCT IONMINORSHAKING

MODERAT ESHAKINGMAJORSHAKINGLAT ERAL BUILDING DISPLACEMENTNONE

SLIGHT

MODERAT E

EXTENSIVECOMPLET E

Figure 2.1. Capacity spectrum method (Source: www.fema.org)

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An example of the application of the capacity spectrum method within RISK-UE Project isgiven in Figure 2.4 and the computation of the probabilities of being in or exceeding
different damage states is presented for illustration in Figure 2.5.
Once the probabilities for being in various damage states are obtained (with Level I or Level
II methodology) the general methodology presented hereinafter is evenly applicable.
900

PSHA Bucharest - 475 yr. MRI

800
700

SA, cm/s

2

600
500
400
300
200
100
0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

T, s

Figure 2.2. Uniform hazard spectrum of absolute acceleration
900
800
700

SA, cm/s

2

600
500
400
300

PGA = 337 cm/s2

200
100

SA = 117 cm/s2

0
0

10

20

30

40

50

SD , cm

Figure 2.3. Acceleration – displacement spectrum of constant hazard
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900
800
700

µ=

2

600

2
4
6
Capacity500

SA , cm/s

WP4

1
3
5
8

400
300
200
100
0

Expected
displacement
0
10

20

30

40

50

T ,cm
s
SD,

Figure 2.4. Application of capacity spectrum method
1.0
0.9
0.8

C1M
1990-2002

P(>DS|SD)

0.7

WP4

0.6
SlightModerate

0.5
0.4
0.3
0.2
0.1

Expected
displacement 0.0
0

10

20

Ds
N
S
M
E
C

P(Ds|SD)
0.003
0.085
0.168
0.670
0.074

30

40

50

Extensive
Complete
Expected

60

70

80

SD , cm

Figure 2.5. Fragility functions and damage states exceedance probabilities
DebrisAn empirical approach that estimates two different types of debris is used (HAZUS, 1999):

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9 Debris that falls in large pieces, such as steel members or reinforced concreteelements - require special treatment to break into smaller pieces before they arehauled away;
9 Debris that is smaller and more easily moved with bulldozers and other machineryand tools - includes brick, wood, glass, building contents and other materials.
The following input is required for the evaluation of debris amount:
9 Probabilities of damage states for building typologies;
9 Floor area of building typologies analyzed.
Given the damage states, the debris estimates are based on observations of damage that has
occurred in past earthquakes and estimates of the weights of structural elements. Tables arecompiled to estimate generated debris from different damage states for each building
typology.
The debris generated from damaged buildings (in tons) is based on:
9 Unit weight of structural elements (tons/1000m2 of floor area) for each of thebuilding typologies, Table A.1, Annex A;
9 Probabilities of damage states;
9 Floor area of each of the building typologies;
9 Debris generated from different damage states (% of unit weight of element), Table
A.2 and Table A.3, Annex A.
The following notation is used:
i - the iteration variable for the types of debris, i = 1 to 2
where: 1- brick, wood and other2- reinforced concrete and steel components
j - the iteration variable for the damage states, j=1 to 5,
where: 1- None, 2- Slight; 3- Moderate; 4- Extensive; 5- Completek - the iteration variable for the building typology.
The input is the probabilities of different structural damage states. Thus, the first step in thedebris calculation is to combine the debris fraction generated from the different damage
states into the expected debris fraction for each building typology. The expected debris
fraction for building typology k and debris type i due to structural damage is given by:
5

EDFs (i, k) = ∑ Ps (j, k) ∗ DFs (i, j, k)

(2.1)

j =2

where:EDFs (i, k) - the expected debris fraction of debris type i due to structural damage forbuilding typology k
Ps (j,k)- the probability of structural damage state j for building typology kDFs (i, j, k) - the debris fraction of debris type i for building typology k in structural
damage state j (from Tables A.2 and A.3, Annex A)
These values indicate the expected percentage of debris type i generated due to structural
damage to building typology k. If one knows the total floor area of each building typology
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and weights of debris type i per 1000 m2 of building, then the amount of debris for thisparticular location can be obtained by multiplying the expected debris fraction of debris typei due to structural damage for building typology k with the weight of debris type i per 1000m2 of floor area for structural elements of building typology k (From Table A.1, Annex A)
and with the total floor area of each building typology and the summing for all k.
2.3 Casualties and homeless estimation
Direct Social Losses – Casualties
Earthquakes are devastating to people as individuals, to families, to social and economic
organization of the region affected and the country as a whole. Unquestionably the mostterrible consequence of earthquakes is the massive loss of human life that they cause.
The statistics recording the earthquake effects include a wide range of earthquake-induced
cause of human casualty and deaths. Although the principal cause of human casualty anddeaths is the collapse of the buildings, there are a wide range of other causes of death andinjury officially attributed to the earthquake occurrence, ranging from medical conditions
induced by the shock of experiencing ground motion, to accidents occurring during the
disturbance, epidemics among the homeless and shootings during martial law.
About 70% of fatalities and nearly 100% of injuries attributed to earthquakes are caused bycollapse of buildings (Spence et al., 1991). If a major earthquake occurs at night, catching
most people asleep in their homes, the mortality rate - the percentage of the population
killed - in the towns and villages of the epicentral area could be as high as 30% (Table 2.1).
The morbidity rate - the percentage of the population injured and requiring some level of
medical treatment - could be 60-80%.
Table 2.1. Breakdown of typical injury ratios for a population affected by a severe-caseearthquake scenario, Coburn and Spence, 2002
20 - 30%
Fatalities
Injuries requiring first aid/outpatient treatment

50 - 70%

Injuries requiring hospitalization

5 -10%

Injuries requiring major surgery

1 - 2%

When building collapses, not all the occupants are killed, injured or trapped inside. Manyare likely to escape just before the collapse and some, although even injured are able to freethemselves shortly after. In a high rise buildings, escape from upper floors is unlikely before
the collapse, and if it collapses completely about 70% of the its occupants are likely to be
killed, at best injured and trapped. In low-rise buildings, that have apparently 20-30 seconds
to collapse, more than three quarters of the occupants may be able to escape before thecollapse, and only one quarter are to be considered as casualty toll.
A wide range of types and severity of injury are caused by earthquakes. A significant
percentage of injuries are not only a direct consequence of building collapses and may be

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124 Lacul Tei Blvd., sector 2, Bucharest, Romania

result of many different earthquake-induced accidents. Some injuries are caused by nonstructural building damage, such as broken glass or the fall of architectural ornament orcollapse of parapet walls. But the majority of injures in a mayor earthquake are caused bybuilding damage.
Many more people tend to be injured in an earthquake than are killed. A ratio of threepeople requiring medical attention to every one person killed is typical (Ville de Goyet
1976; Alexander 1984), but this can vary very significantly with different types of
construction affected and with the size of the earthquake. Similarly light injuries requiring
outpatient hospitalization - typically there may be between 10 and 30 people requiring
outpatient treatment for every person hospitalized.
The relationship between the number of people killed and the number of buildings thatcollapse, the lethality ratio, is the important parameter to determine. If this ratio is known,
then human casualties can be estimated from estimates of the number of collapsed buildings.
The casualty model is stated as a series of these factors that are applied to building
typologies. For a building typology, or corresponding building (apartment) area, the numberof casualties due to collapse of building can be expressed as, Coburn and Spence, 2002:
Ks = C x [ M1 x M2 x M3 x ( M4 + M5 x (1 - M4))](2.2)

where C is total number (or floor area) of collapsed buildings in that typology class.
M1 is the occupancy rate (number of people / built m2). In low-rise residential building
stock, the population per building (P/B) is equivalent to the average family size living ineach house. In European cities, average residential P/B sizes are around 2 to 3. In cities with
rapidly expanding populations, a large immigration of population or a shortage of building
stock, P/B ratios can be much higher and can increase or decrease quite suddenly withchanges of population movement.
Factor M2 is the occupancy at time of earthquake. The time of day that an earthquake occurs
has long been known to affect the number of people killed, Figure 2.6. An earthquake
occurring when a lot of the population is indoors kills more people in the buildings thatcollapse.
Factor M3 represents the percentage of occupants trapped by collapse. Although there islittle detailed information or statistics to quantify it empirically, it is clear that not all theoccupants that are inside a building when an earthquake occurs are trapped if it collapses.
People escape before collapse, or the collapse of the structure is not total, or they are able tofree themselves relatively easily by their own efforts.
In single story structures, there is evidence that many people are able to get out of a building
before it collapses unless (as appears in the case for weak masonry buildings in the epicenterof strong earthquakes) collapse is instantaneous. In multi-story structures fewer people areable to leave the building once shaking has started. There is little documentation of the time
taken for buildings to collapse. A large magnitude earthquake can have a minute or more ofSeismic Risk Scenarios

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strong ground motion but the strongest amplitude shaking - the ones most likely to exceed
the strength of the structures - happen relatively early in the time history. A ductile building
may collapse over a period of several tens of seconds. A brittle building may collapse more
quickly. Tests of evacuation times show that people cannot get out of a building fromanywhere above the first floor in less than thirty seconds, even if they are capable ofwalking during the violent shaking. A reasonable assumption is that a certain percentage ofoccupants of the ground floor - e.g. 50% for a building of fairly shallow plan depth, will becapable of escape, all other occupants of the building will remain inside.

Figure 2.6. M2 - occupancy at time of earthquake, Coburn and Spence, 2002
Table 2.2. Factor M3 - Estimated average percentage of occupants trapped by collapse,
Coburn and Spence, 2002
Seismic Intensity (MSK Scale)
Building type
VII
VIII
IX
X
Masonry buildings (up to 3 stories)
Non earthquake resistant
5
30
60
70
Earthquake resistant
10
30
60
RC structures
Near-field high frequency ground70
motionDistant, long-period ground motion
50
Factor M4 gives the injury distribution at collapse. People caught in building collapses
suffer a range of types of injury (Table 2.3). A proportion of the buildings occupants are
killed outright when collapse occurs. This proportion (deaths at time 0 or T after theearthquake) is taken as the M4 factor in the casualty model. Others are injured to various
degrees of severity.

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A number of injury severity scales have been proposed for quantifying earthquake injury
epidemiological studies. One of the simplest and most useful to emergency managers is thefour-point standard triage categorization of injuries. There is very little data to indicate the
distribution of severity of injury to occupants when a building collapses. However, studies
back-figuring injury types and survival times from mortality data of people retrieved frombuilding collapses several days later suggest that in reinforced concrete structures, the M4
injury distribution is bi-modal, with most people being either killed or only slightly injured,with very few people badly injured in-between. By contrast, injury distributions in masonrybuildings appear more uniform, with high percentages of trapped victims having serious
injuries.
Table 2.3. Factor M4 - Estimated injury distribution at collapses, in % of trapped occupants,
Coburn and Spence, 2002
Low strength
Triage injury category
RC
Masonry
masonry
Dead or unsavable
1020
40Life threatening cases needing
20
30
10
immediate medical attention
Injury requiring hospital treatment
30
30
40
Light
injurynotnecessitating
40
20
10
hospitalization
Factor M5 represents the mortality post-collapse. Those trapped in the rubble will die if they
are not rescued and given medical treatment. Those who have serious injuries will die
quickly. Less severely injured people can survive for longer. The unaffected community
usually rallies to the collapsed buildings and set to work to extricate trapped victims.
Effective emergency activities will save the lives of many of those trapped in building
collapses that would otherwise have died.
Time is critical and death rates increase with every hour that passes. The M5 factor - theadditional mortality of trapped victims after collapse - is a measure of the effectiveness of
post-collapse activities (Table 2.4). It is clear that in cases of extreme destruction, wherehigh percentages of the total population of a community are trapped in collapses (i.e. M2 x
M3 > 50%) the M5 factor becomes very high. The community itself loses its capability of
rescuing its own victims, both because its manpower is greatly reduced and because it ispsychologically and socially incapacitated by the disaster. In very high casualty earthquakes('hyper-fatality events') this appears to be a major factor in the escalation of casualty figures.
Table 2.4. Factor M5 - percentage of trapped survivors in collapsed buildings that
subsequently die, Coburn and Spence, 2002
Situation
MasonryRC
Community incapacitated95
Community capable of organizing rescue activities
60
90
Community + emergency squads after 12 hours
50
80
Community emergency squads SAR experts after
45
70
36 hours

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The possible output of the presented methodology is presented in Figure 2.7 for different
building typologies.
Low - code buildings, 1963-1969
100
90

Percentage of people living in

80
70
60
50
40
30
20
10
0

C1M

C1H

C2M

C2H

Figure 2.7. Casualties’ distribution for the given scenario
Homeless estimation
The following inputs are required to compute the number of uninhabitable dwelling units
and the number of displaced households, HAZUS, 1999:- Total Number of Single-Family Dwelling Units (#SFU)- Total Number of Multi-Family Dwelling Units (#MFU)- Damage state probability for moderate structural damage in the single-family residential
occupancy class (%SFM).
- Damage state probability for extensive structural damage state in the single-family
residential occupancy class (%SFE).
- Damage state probability for complete structural damage state in the single-family
residential occupancy class (%SFC).
- Damage state probability for moderate structural damage state in the multi- family
residential occupancy class (%MFM).
- Damage state probability for extensive structural damage state in the multi- family
residential occupancy class (%MFE).
- Damage state probability for complete structural damage state in the multi- family
residential occupancy class (%MFC).
The number of uninhabitable dwelling units due to structural damage is determined by
combining a) the number of uninhabitable dwelling units due to actual structural damage,and b) the number of damaged units that are perceived to be uninhabitable by theiroccupants.

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Based on comparisons with previous work (Perkins, 1992), the methodology considers all
dwelling units located in buildings that are in the complete damage state to be uninhabitable.
In addition, dwelling units that are in moderately and extensively damaged multi-family
structures are also considered to be uninhabitable due to the fact that renters perceive somemoderately damaged rental property as uninhabitable. On the other hand, those living insingle-family homes are much more likely to tolerate damage and continue to live in theirhome. Therefore, the total number of uninhabitable units (#UNUSD) due to structural
damage is calculated by the following relationship:%SF = wSFM × %SFM + wSFE × %SFE + wSFC × %SFC
%MF = wMFM × %MFM + wMFE × %MFE + wMFC × %MFC

(2.3)

# UNU SD = # SFU × %SF + # MFU × %MF
The values of weighting factors are 1.0 for wSFC and wMFC, 0.9 for wMFE and 0.0 for wSFM,
wSFE, wMFM.
2.4 Direct economic losses
The methodology described in HAZUS, 1999 is used and provides estimates of the repair
costs caused by building damage and the associated loss of building contents, Figure 2.8.
These losses are calculated from the building damage estimates.
Damaged Residential
Buildings
Over 10,000
5,000 to 10,000
1,000 to 5,000
500 to 1,000
0 to
500

IN
IN

IL
IL
MO
MO

KY
KY

TN
TN
AR
AR

Epicenter
Epicenter

AL
AL

MS
MS
Total Dam aged
Res idences~ 240,000

LA
LA
LA
LA

Top Three Counties
Shelby = 18,100
Craighead = 14,000
Poinsett = 7,500

00

50
50
50
50

100
100
100
100

miles
miles

Figure 2.8. Number of damaged residences (HAZUS, 1999)

Seismic Risk Scenarios

28Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

For building related items, methods for calculating the following monetary losses areprovided for:9 Building Repair and Replacement Costs
9 Building Contents Losses.
Building Repair and Replacement Costs
To establish monetary loss estimates, the damage state probabilities are converted tomonetary loss equivalents. For a given occupancy and damage state, building repair andreplacement costs are estimated as the product of the floor area of each building typology,
the probability of the building typology being in the given damage state, and repair costs ofthe building typology per square meter for the given damage state, summed over all building
typologies.
VenturVenturaaCountyCountyAngelesLos
Los Angeles
CountyCounty555
IIII-II-----555

III-405
I-405
-405
-405
I-405
I-405
-405

I-10
I-10
I-10
I-10
I-10
I-10

ttt
uuullltlltlt
FFFaaaaauuu
dddFFFoooo
odd
wwwoooooo
lleeleeeewww
ggg
g
nnng
-IInIIntt-t-IInooorrrtrrt-t-wppppppooo
w
w
w
w
eeew
N
NNN
Nee

Total Casualties[by census tract]
Over 20 [510 tracts]

10 - 20 [480 tracts]
5 - 10 [378 tracts]

Pacific
Pacific
Ocean
Ocean
Ocean
Ocean
Ocean

1 - 5 [625 tracts]
N one

0
00
00
0

10
10
10
10
10
10

20
20
20
20
20
20

Miles
M
M
iles
Miles
M
Miles
iles
iles

Figure 2.9. Expected casualties (HAZUS, 1999)
For structural damage, losses are calculated as follows:
CSds = ∑ Faj x PMBTSTRds,j x RCSds,j

(2.4)

j

5

CS = ∑ CSds

(2.5)

ds= 2

where:
CSds

Seismic Risk Scenarios

cost of structural damage (repair and replacement costs) for damage
state ds

29

Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

CS
FAj
PMBTSTRds,j
RCSds,jcost of structural damage (repair and replacement costs)
floor area of building type j (in m2)
probability of building type j being in structural damage state ds
structural repair and replacement costs (per m2) for building type jin damage state ds

Note that damage state "None" (ds = 1) does not contribute to the calculation of the cost of
structural damage and thus the summation in Equation 2.5 is from ds = 2 to ds = 5.
The cost of damage is expressed as a percentage of the complete damage state. The
assumed relationship between damage states and repair/replacement costs is as follows:
Slight damage:
2% of Complete
Moderate damage:
10% of Complete
Extensive damage:
50% of Complete
These values are consistent with and in the range of the damage definitions andcorresponding damage ratios presented in ATC-13, 1985, Earthquake Damage Evaluation
Data for California.
Structural Repair Costs for Complete Damage (Euro/m2) should be considered according to
the contractions and real estate markets in each region. For example, for Bucharest region it
was considered an amount equivalent to 300 Euro/m2 as structural repair cost for complete
damage.
Building Content Losses
Building content is defined as the furniture, equipment that is not integral with the structure,computers and other supplies. From Table 4.11 of ATC-13, 1985 it is assumed that contents
value of residential buildings represent 50 percent of building replacement value.
2.5 Risk management
Seismic risk is the outcome of the convolution of seismic hazard, exposure of elements at
risk and vulnerability of the elements at risk. The 20th century witnessed a painful history ofdevastating earthquakes. A list of most deadly earthquakes worldwide starting with year
1900 is given in Table A.4, Annex A.
Economic losses are another important feature of earthquake-induced phenomena.
Sometimes the economic burden and pressure induced by the consequences of anearthquake disaster caused irreparable economic crisis for poor countries. Table 2.5 presents
a combination of human and economic losses for earthquakes where monetary evaluations
were available.
Table 2.5. Human and economic losses produced by earthquakes in 20th century
No.

Date UTC

Location

1

1963 July 26

FYROM, Skopje

1,070

0.98

6.2

2

1972 Dec 23

Nicaragua, Managua

5,000

2

6.2

3

1976 Feb 4

Guatemala

23,000

1.1

7.5

4

1976 Jul 27

China, Tangshan

255,000

6

8

5

1977 Mar 4

Romania, Vrancea

1,500

2.0

7.2

Seismic Risk Scenarios

Deaths Losses ($bn) Magnitude

30

Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania
6

1979 Apr 15

7 1980 Nov 23

Montenegro

101

4.5

7

Italy, southern Campania

4,680

45

7.2

8

1985 Sep 19

Mexico, Michoacan

9,500

5

8.1

9

1986 Oct 10

El Salvador

1,000

1.5

5.5

10

1988 Dec 7 Turkey-USSR border region Spitak, Armenia 25,00017

7

11 1989 Oct 17

Loma Prieta

63

8

6.9

12 1990 Jun 21

Western Iran, Gilan

40,0007.2

7.7

Luzon, Philippine Islands

1,621

1.5

7.8

14 1994 Jan 17

Northridge

57

30

6.8

15 1995 Jan 16

Japan, Kobe

5,502

82.4

6.9

16 1999 Jan 25

Colombia

1,185

1.5

6.3

17 1999 Aug 17

Turkey17,11820

7.6

18 1999 Sep 20

Taiwan

2,297

0.8

7.6

13

1990 Jul 16

Human losses in Table 2.5 are represented as a function of magnitude in Figure 2.10. In
Figure 2.11 human losses are represented versus economic losses, also based on data in
Table 2.5.

Seismic Risk Scenarios

31Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

Major earthquakes in 20th

century

100,000

Iran, 1990
Armenia, 1988

Deaths, D

10,000Turkey, Kocaeli, 1999
Italy, 1980

Nicaragua, 1972
Japan, Kobe, 1995

1,000

Mexico, 1985

Taiwan, 1999
Philippines, 1990

Skopje, 1963
El Salvador, 1986

1.5M

D =0.06e

Guatemala, 1976

Romania, 1977

Colombia, 1999

Montenegro, 1979
100

USA, Northridge, 1994

USA, Loma Prieta, 1989

10

1
5.5

6

6.5

7

7.5

Magnitude, M

Figure 2.10. Human losses as a function of magnitude

Seismic Risk Scenarios

32

8

8.5

Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

Major earthquakes in 20th

century

1000

Economic losses, US$ bn.

100

Japan, Kobe, 1995
USA, Northridge, 1994

10

Italy, 1980

Turkey, Kocaeli, 1999
Armenia, 1988

USA, Loma Prieta, 1989
Mexico, 1985

Montenegro, 1979

Romania, 1977
El Salvador, 1986
Colombia, 1999
Philippines, 1990 Taiwan, 1999

1

Iran, 1990

Nicaragua, 1972
Guatemala, 1976

Skopje, 1963

0
10

100

1,000

10,000DeathsFigure 2.11. Human versus economic losses caused by earthquakes

Seismic Risk Scenarios

33

100,000

Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

Based on data in Table 2.5, the number of deaths from an earthquake can be related to themagnitude of the earthquake by the following relations:D = 0.002 ⋅ e1.5 M − lower bound value
D = 0.06 ⋅ e1.5 M− median value

D = 0 .4 ⋅ e− upper bound value

1.5 M

(2.6)

where
D is the number of deaths, andM is the magnitude of the earthquake.
The economic losses can be related to the number of deaths from an earthquake by thefollowing relations:lg L = −0.6 + 0.2 lg D − lower bound valuelg L = 0.06 + 0.2 lg D − median valuelg L = 0.9 + 0.2 lg D − upper bound value

(2.7)

where
L are the economic losses expressed in billion US$, andD is the number of deaths.
The general characteristics of earthquake-induced disasters as well as the generalcountermeasures for emergency management are presented in Table 2.6.
Table 2.6. General characteristics of earthquake disasters, general countermeasures andspecial problem areas for emergency management
Characteristics







Usually no warning,
Following a major
earthquake, secondary
shocksmay
give
warning of a further
earthquake.
Onset is sudden.
Earthquake-prone
areas are generally
well identified andwell known.
Major effects arise
mainly from violent
groundshacking(vibration), fracture orslippage;especiallythey include damage(usually very severe) to

Seismic Risk Scenarios

General counter measures







Special problem areas for
emergency management

Developmentof 
possiblewarning
indicators.
Land-use regulations.
Building regulations.
Relocationofcommunities.

Public awareness andeducation programs.


Severe and extensive
damage, creating theneedforurgentcounter-measures,
especially search andrescue, and medical
assistance.
Difficulty of accessand movement.
Widespread loss of ordamagetoinfrastructure, essential
servicesandlife
support systems.
Recovery requirements(e.g. restoration andrebuilding) may bevery extensive and34

Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

Characteristics
structures and lifeline
systems,plus
considerable casualty
due to lack of warning.

General counter measures

Special problem areas for
emergency managementcostly.
Rarity of occurrence insome areas may cause
problems
for
economies of countermeasures and publicawareness.
Response
problemsmaybesevere,extensive and difficult(e.g. rescue from ahighoccupancybuilding collapses, orin a circumstanceswhere additionally achemical or radiation
hazard exists, etc.).
Victim identification
may often be very
difficult.

Reduction of vulnerability to earthquakes is, clearly, an urgent goal for the coming decades. It
is, moreover, one that is realizable as policy makers now have many earthquake mitigation
options available. These include insurance, construction codes and standards, strengthening
and retrofit, demolition of hazardous structures, relocations, sitting and land-use criteria,
training and exercises. The key to success will be to integrate risk assessment and risk
management as an ongoing strategy aimed at avoidance of flaws in planning, design, sitting,construction and use which create or increase vulnerability.
Mitigation strategies
i. Regulating, strengthening, or removing unsafe structures
ii. Enhancing critical utility networks and facilities [e.g., redundancy, backup power]iii. Improving land use planning
It is the local governments, first of all, that should recognize the risk of disasters within their
domain. Decision makers and local government officials have the actual power to make thephysical environment resistant against disasters through development policies such as urban
planning, construction of infrastructure, land-use control, and building regulations. If urban
infrastructures were to be destroyed by disasters, urban activities would be halted for a longtime, severely damaging economic and social activities.
It is the communities and citizens that should recognize the risk of loss of their own houses
and lives. They are supposed to build and maintain their houses in good physical condition,
while local governments are not able to reinforce a huge number of inappropriately
constructed buildings, most of which are owned privately, in developing countries. It is said

Seismic Risk Scenarios

35

Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

that earthquakes do not kill people but collapsed buildings and houses do. Unless people takeaction concerning their existing houses, casualties cannot be reduced by much.
Semi-public companies, which maintain basic urban infrastructures such as the telephone, andwater supply, should be prepared for disasters as their disruption could cause serious damage
to urban activities. Business leaders and related companies such as building owners,
developers, real estate agents, and insurance/reinsurance companies should also understandthe seismic risk to their properties, to avoid human loss caused by their collapse and tominimize the damage their businesses.
From experience, it can be said that even if scientists were to lay stress on such seismic risk to
local governments, the officials would not take it into account. Only when the government
officials can understand the possible damage through their own efforts, are they likely to takethe necessary action.
Similarly, although most of the buildings seem highly vulnerable to earthquakes, and although
it is obvious that certain houses would be easily destroyed, communities and residents are, insome instances, indifferent to the seismic risk. They will take appropriate action for thereinforcement of their houses only when they understand that they would be killed by theirhouses or lose their fortunes.
References Chapter 2
Ang A.H-S., 1987. Basis for earthquake-resistant design with tolerable structural damage, Proc. 5thInternational Conference on Applications of Statistics and Probability in Soil and Structural Engineering(ICASP5), Vancouver BC, Canada, Vol.1, 407-416
ATC-13, 1985. Earthquake Damage Evaluation Data for California, Applied Technology Council, Redwood
City, CA.
ATC 40, 1996. Seismic Evaluation and Retrofit of Concrete Buildings, Report ATC-40, Applied Technology
Council, Redwood City, CA.
Coburn, A., Spence, R., 2002. Earthquake Protection. Second Edition, John Wiley and Sons Ltd., Chichester,
England
HAZUS – Technical Manual 1999. Earthquake Loss Estimation Methodology, 3 Vol.
Lungu, D., Arion, C., Baur, M., Aldea, A., 2000. Vulnerability of existing building stock in Bucharest,
6ICSZ Sixth International Conference on Seismic Zonation, Palm Springs, California, USA, Nov.12-15, p.837846
Lungu, D., Demetriu, S., Arion, C. 1998. Seismic vulnerability of buildings exposed to Vrancea earthquakes
in Romania. In Vrancea Earthquakes. Tectonics, Hazard and Risk Mitigation, Kluwer Academic Publishers,
Wenzel F., Lungu D., editors, Proc. of First International Workshop on Vrancea Earthquakes, p.215-224.
Lungu, D. & Aldea, A., 1999. Understanding Urban Risk Around the World. United Nations RADIUS
Project at Geohazards Int., Ca., USA. Documents for the City of Bucharest seismic profile, 29p.+25p.+8p.
National Institute of Statistics, Romanian Statistical Yearbook 2000.
Park, Y.-J & Ang, A. H.-S.. Mechanistic seismic damage model for reinforced concrete. Journal of StructuralEngineering. ASCE vol. 111 (4): 722-739, 1985
Perkins, J. B. - Estimates of Uninhabitable Dwelling Units in Future Earthquakes Affecting the San
Francisco Bay Region. ABAG: Oakland, California, 89 pp., 1992
Reinhorn A. M., Valles-Mattox R. E., Kunnath S. K. – Seismic Damageability Evaluation of a Typical R/C
Building in the Central U.S., NCEER Bulletin, Vol. 10, No. 4, October 1996
RISK-UE "An advanced approach to earthquake risk scenarios with applications to different European
towns", financed by European Commission, Fifth Framework, 2000-2004
Rubinstein, R. Y. Simulation and the Monte Carlo method. John Wiley & Sons, New York, 1981Văcăreanu R., 2000 - Monte Carlo Simulation Technique for Vulnerability Analysis of RC Frames – An
Example –Bulletin on Technical University of Civil Engineering Bucharest, pg. 9-18;
Vacareanu, R., Lungu, D., Aldea, A., Arion, C. May 2005. “WP7 Handbook – Seismic Risk Scenarios”,
Bulletin of the Technical University of Civil Engineering Bucharest, 2/2003, p. 97-117
Văcăreanu R., 1998 - Seismic Risk Analysis for a High Rise Building - Proceedings of the 11th European

Seismic Risk Scenarios

36Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania
Conference on Earthquake Engineering, Paris, Abstract Volume pg. 513
Văcăreanu R., Cornea T., Lungu D. Evaluation of seismic fragility of buildings, Earthquake Hazard andCountermeasures for Existing Fragile Buildings, Editors: Lungu D. & Saito T., Independent Film, Bucharest
Romania, 315p
Williams, M. S. & Sexsmith, R. G. 1995. Seismic Damage Indices for Concrete Structures: A State-of-theArt Review. Earthquake Spectra. Vol. 11(2): 319-345, 1997

Seismic Risk Scenarios

37Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

Annex A: Tables
Table A.1. Suggested unit weight for structural elements as building debris, adapted from
HAZUS, 1999, in t/ m2
Building
Typology

Brick, Woodand Other

Reinforced Concreteand Steel

0.38

0.45 – 0.6 t/m

0.2 – 0.25

0.85 – 1.05 t/m

M1.1, M1.2,
M1.3, M2,
M3.1, M 3.2,
M3.3, M3.4
M4, M5,RC3.1, RC3.2

2

2

RC1, RC2,
RC4, RC6
RC5

01.05 – 1.3 t/m

0.1

0.45 t/m

S1, S20.45 – 0.5

0.5 t/m

S3

0.25

0.5 t/m

S4, S50

0.7 t/mW

0.1

0.17 t/m

2

2

2
2
2
2

Table A.2. Suggested brick, wood, and other debris generated from damaged structuralelements, adapted from HAZUS, 1999, in fraction of weight
Building

Structural Damage State

Typology
M1.1, M1.2
M1.3, M2
M3.1, M 3.2
M3.3, M3.4
M4, M5RC3.1, RC3.2
RC1, RC2,
RC4, RC6,
S1, S2, S4, S5
RC5SlightModerate

Extensive

Complete

0.05

0.25

0.55

1

0.05

0.25

0.6

1

0

0

0

1

0

0.06

0.32

1

S3

0.05

0.25

0.6

1

W

0

0.05

0.34

1

Seismic Risk Scenarios

38Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

Table A.3. Suggested reinforced concrete and wrecked steel generated from damaged
structural elements, adapted from HAZUS, 1999, in fraction of weight
Structural Damage State

Building
Typology
M1.1, M1.2
M1.3, M2
M3.1, M 3.2,
M3.3, M3.4
M4, M5
RC1
RC2
RC3.1, RC3.2
RC4, RC5, RC6
S1, S2, S3
S4, S5W

SlightModerate

Extensive

Complete

0

0.02

0.25

1

0
0
0.01
0
0.02
0
0.02
0

0.03
0.05
0.08
0.04
0.1
0.04
0.1
0.03

0.305
0.33
0.35
0.32
0.35
0.3
0.4
0.27

1
1
1
1
1
1
1
1

Table A.4. Earthquakes with 1,000 or More Deaths from 1900 (Source: USGS,
www.usgs.gov)
No. Date UTC
Location
1 1902 Apr 19
Guatemala, 14 N 91 W
2 1902 Dec 16
Turkestan, 40.8 N 72.6 E
3 1903 Apr 19
Turkey, 39.1 N 42.4 E
4 1903 Apr 28
Turkey, 39.1 N 42.5 E
5 1905 Apr 4
India, Kangra, 33.0 N 76.0 E
6 1905 Sep 8
Italy, Calabria, 39.4 N 16.4 E
7 1906 Jan 31
Colombia, 1 N 81.5 W
8 1906 Mar 16 Formosa, Kagi, (Taiwan), 23.6 N 120.5 E
9 1906 Aug 17
Chile, Santiago, 33 S 72 W
10 1907 Jan 14
Jamaica, Kingston, 18.2 N 76.7 W
11 1907 Oct 21
Central Asia, 38 N 69 E
12 1908 Dec 28
13
14
15
16
17

1909 Jan 23
1912 Aug 91915 Jan 13
1917 Jan 21
1917 Jul 30

18 1918 Feb 13
19 1920 Dec 16
20 1923 Mar 24
21 1923 May 25
22

1923 Sep 1

Italy, Messina, 38 N 15.5 E
Iran, 33.4 N 49.1 E
Marmara Sea, 40.5 N 27 E
Italy, Avezzano, 42 N 13.5 E
Indonesia, Bali, 8.0 S 115.4 E
China, 28.0 N 104.0 E
China, Kwangtung, (Guangdong)
23.5 N 117.0 E
China, Gansu, 35.8 N 105.7 E
China, 31.3 N 100.8 E
Iran, 35.3 N 59.2 E
Japan, Kanto, Tokyo-Yokohama
35.0 N 139.5 E

Deaths Magnitude
Comments
2,000
7.5
4,500
6.4
1,700
2,200
6.3
19,000
8.6
2,500
7.9
1,000
8.9
1,300
7.1
20,000
8.6
1,600
6.5
12,0008.1
70,000Deaths from earthquake and7.5
to 100,000
tsunami.
5,500
7.3
1,950
7.8
29,9807.5
15,0001,800
6.5
10,0007.3

200,000
5,000
2,200

8.6
7.3
5.7

143,000

8.3

23 1925 Mar 16

China, Yunnan, 25.5 N 100.3 E

5,000

7.1

24 1927 Mar 7
25 1927 May 22
26 1929 May 1
27 1930 May 6
28 1930 Jul 23
29 1931 Mar 31
30 1932 Dec 25
31 1933 Mar 2

Japan, Tango, 35.8 N 134.8 E
China, near Xining, 36.8 N 102.8 E
Iran, 38 N 58 E
Iran, 38.0 N 44.5 E
Italy, 41.1 N 15.4 E
Nicaragua, 13.2 N 85.7 W
China, Gansu, 39.7 N 97.0 E
Japan, Sanriku, 39.0 N 143.0 E

3,020
200,000
3,300
2,500
1,430
2,400
70,000
2,990

7.9
8.3
7.4
7.2
6.5
5.6
7.6
8.9

Seismic Risk Scenarios

Major fractures, landslides.
Great Tokyo fire.
Talifu almost completely
destroyed.
Large fractures.

39

Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania
Location
Deaths Magnitude
Comments
China, 32.0 N 103.7 E
10,000
7.4
India, Bihar-Nepal, 26.6 N 86.8 E
10,7008.4
Formosa, 24.0 N 121.0 E
3,280
7.1
Quetta almost completely
30,0007.5
35 1935 May 30
Pakistan, Quetta, 29.6 N 66.5 E
destroyed.
to 60,000
36 1935 Jul 16
Taiwan, 24.4 N 120.7 E
2,700
6.5
37 1939 Jan 25
Chile, Chillan, 36.2 S 72.2 W
28,0008.3
38 1939 Dec 26
Turkey, Erzincan, 39.6 N 38 E
30,0008.0
39 1940 Nov 10
Romania, 45.8 N 26.8 E
1,000
7.3
40 1942 Nov 26
Turkey, 40.5 N 34.0 E
4,000
7.6
41 1942 Dec 20
Turkey, Erbaa, 40.9 N 36.5 E
3,000
7.3
Some reports of 1,000 killed.
42 1943 Sep 10
Japan, Tottori, 33.6 N 134.2 E
1,190
7.4
43 1943 Nov 26
Turkey, 41.0 N 33.7 E
4,000
7.6
Reports of as many as 8,000
44 1944 Jan 15
Argentina, San Juan, 31.6 S 68.5 W
5,000
7.8
killed.
Reports of as many as 5,000
45 1944 Feb 1
Turkey, 41.4 N 32.7 E
2,800
7.4
killed.
46 1944 Dec 7
Japan, Tonankai, 33.7 N 136.2 E
1,000
8.3
47 1945 Jan 12
Japan, Mikawa, 34.8 N 137.0 E
1,900
7.1
48 1945 Nov 27
Iran, 25.0 N 60.5 E
4,000
8.2
49 1946 May 31
Turkey, 39.5 N 41.5 E
1,300
6.0
50 1946 Nov 10
Peru, Ancash, 8.3 S 77.8 W
1,400
7.3
Landslides, great destruction.
51 1946 Dec 20
Japan, Tonankai, 32.5 N 134.5 E
1,330
8.4
52 1948 Jun 28
Japan, Fukui, 36.1 N 136.2 E
5,390
7.3
USSR, (Turkmenistan, Ashgabat)
53 1948 Oct 5
110,000
7.3
38.0 N 58.3 E
Large landslides,
54 1949 Aug 5
Ecuador, Ambato, 1.2 S 78.5 E
6,000
6.8
topographical changes.
Great topographical changes,
55 1950 Aug 15
India, Assam, Tibet, 28.7 N 96.6 E
1,530
8.7
landslides, floods.
56 1954 Sep 9Algeria, Orleansville, 36 N 1.6 E
1,250
6.8
57 1957 Jun 27
USSR, (Russia), 56.3 N 116.5 E
1,200
58 1957 Jul 2
Iran, 36.2 N 52.7 E
1,200
7.4
59 1957 Dec 13
Iran, 34.4 N 47.6 E
1,130
7.3
10,000Occurred at shallow depth just
60 1960 Feb 29
Morocco, Agadir, 30 N 9 W
5.9
to 15,000
under city.
More then 2,000 killed, 3,000
injured, 2,000,000 homeless,and $550 million damage inHawaii; 138 deaths and $50
4,000
9.5*
million damage in Japan; 32
61 1960 May 22
Chile, 39.5 S 74.5 W
to 5,000dead and missing in thePhilippines; and $500,000
damage to the west coast of
the United States
62 1962 Sep 1
Iran, Qazvin, 35.6 N 49.9 E
12,230
7.3
Occurred at shallow depth just
63 1963 Jul 26
Yugoslavia, Skopje, 42.1 N 21.4 E
1,100
6.0
under city.
64 1966 Aug 19
Turkey, Varto, 39.2 N 41.7 E
2,520
7.1
12,0007.3
65 1968 Aug 31
Iran, 34.0 N 59.0 E
to 20,000
66 1969 Jul 25
Eastern China, 21.6 N 111.9 E
3,000
5.9
67 1970 Jan 4 Yunnan Province, China, 24.1 N 102.5 E 10,000
7.5
68 1970 Mar 28
Turkey, Gediz, 39.2 N 29.5 E
1,100
7.3
$530,000 damage, great rock69 1970 May 31
Peru, 9.2 S 78.8 W
66,0007.8
slide, floods.
70 1972 Apr 10
Southern Iran, 28.4 N 52.8 E
5,054
7.1

No. Date UTC
32 1933 Aug 25
33 1934 Jan 15
34 1935 Apr 20

Seismic Risk Scenarios

40Technical University of Civil Engineering

No. Date UTC
71 1972 Dec 23
72 1974 May 10
73 1974 Dec 28
74 1975 Feb 4
75 1975 Sep 676 1976 Feb 4
77 1976 May 6

124 Lacul Tei Blvd., sector 2, Bucharest, Romania
Location
Deaths Magnitude
Nicaragua, Managua, 12.4 N 86.1 W
5,000
6.2
China, 28.2 N 104.0 E
20,000
6.8
Pakistan, 35.0 N 72.8 E
5,300
6.2
China, 40.6 N 122.5 E
10,000
7.4
Turkey, 38.5 N 40.7 E
2,300
6.7
Guatemala, 15.3 N 89.1 W
23,000
7.5
Northeastern Italy, 46.4 N 13.3 E
1,000
6.5

78 1976 Jun 25 West Irian, (New Guinea), 4.6 S 140.1 E

422

7.1

80 1976 Aug 16
81 1976 Nov 24
82 1977 Mar 4
83 1978 Sep 16

255,000(official)
8,000
5,000
1,500
15,000

7.9
7.3
7.2
7.8

84

3,500

7.7

4,680
3,000
1,500
2,800
1,342
9,500
1985 Sep 19 Mexico, Michoacan, 18.2 N 102.5 W(official)
1986 Oct 10
El Salvador, 13.8 N 89.2 W
1,000+
1987 Mar 6
Colombia-Ecuador, 0.2 N 77.8 W
1,000+
1988 Aug 20 Nepal-India border region, 26.8 N 86.6 E 1,450
Turkey-USSR border region Spitak,1988 Dec 7
25,000Armenia, 41.0 N 44.2 E

7.2
6.9
7.3
6.0
6.9

79

85
86
87
88
89
90
91
92
93
94

1976 Jul 27

China, Tangshan, 39.6 N 118.0 E

Philippines, Mindanao, 6.3 N 124.0 E
Iran-USSR border, 39.1 N 44.0 E
Romania, 45.8 N 26.8 E
Iran, 33.2 N 57.4 E
Algeria, El Asnam, (formerly
1980 Oct 10
Orleansville), 36.1 N 1.4 E
1980 Nov 23 Italy, southern Campania, 40.9 N 15.3 E
1981 Jun 11
Southern Iran, 29.9 N 57.7 E
1981 Jul 28
Southern Iran, 30.0 N 57.8 E
1982 Dec 13 Western Arabian Peninsula, 14.7N 44.4 E
1983 Oct 30
Turkey, 40.3 N 42.2 E

95 1989 Oct 17

Loma Prieta

63

40,000to 50,000
1,621
97 1990 Jul 16 Luzon, Philippine Islands, 15.7 N 121.2 E(2,600)98 1991 Oct 19
Northern India, 30.8 N 78.8 E
2,000
96 1990 Jun 21

Western Iran, Gilan, 37.0 N 49.4 E

99 1992 April 26

Cape Mendocino

100 1992 June 28

Big Bear

8.0

8.1

6.9
7.7
7.8

Estimated death toll as high as
30,000.

3,757injuries
5,900Property
Damage ($ Million)
Landslides.
Landslides, subsidence, andsand blows.

7.0
6.5

101 1992 Dec 12 Flores Region, Indonesia, 8.5 S 121.9 E

2,500

7.5

102 1993 Sep 29

Southern India, 18.1 N 76.5 E

9,748

6.3

103 1994 Jan 17

Northridge

57

6.8

5,502

6.9

1,989

7.5

106 1997 May 10

Northern Iran, 33.9 N 59.7 E

1,560

7.5

107 1998 Feb 04

Afghanistan-Tajikistan Border Region,
37.1 N 70.1 E

2,323

6.1

108 1998 May 30 Afghanistan-Tajikistan Border Region,

4,000

6.9

Seismic Risk Scenarios

Deaths estimated.

7.0

6.6

Japan, Kobe, Near S. Coast of Western
Honshu, 34.6 N 135 E
105 1995 May 27
Sakhalin Island, 52.6 N 142.8 E

5,000 to 9,000 missing andpresumed dead.
Estimated death toll as high as
655,000.

5.5
7.0
6.6

1

104 1995 Jan 16

Comments

356 injuries
48.3
Property Damage ($ Million)
402 injuries
91.1
Property Damage ($ Million
Tsunami ran inland 300
meters; wave height 25
meters.
9,000 injuries
10,000Property Damage ($ Million)
Landslide, liquefaction.
4,460 injured, 60,000
homeless.
818 injured, 8,094 houses
destroyed, 6,725 livestock
killed.
Many thousands injured and41

Technical University of Civil Engineering

No. Date UTC

109 1998 Jul 17

110 1999 Jan 25

111 1999 Aug 17

112 1999 Sep 20

113 2001 Jan 26

114 2002 Mar 25

115 2003 May 21

124 Lacul Tei Blvd., sector 2, Bucharest, Romania
Location
Deaths Magnitude
Comments
37.1 N 70.1 E
homeless.
Thousands injured, about
9,500 homeless and about 500
Papua New Guinea, Near N. Coast,
2,183
7.1
missing as a result of a2.96 S 141.9 E
tsunami with maximum wave
heights estimated at 10 meters.
At least 1,185 killed, over 700
missing and presumed killed,
Colombia, 4.46 N 75.82 W
1,185
6.3
over 4,750 injured, and over
250,000 homeless.
More than 17,000 killed,
50,000 injured, thousands
Turkey, 40.7 N 30.0 E
17,118
7.6
missing, and about 600,000
homeless. Damage estimatedat 3 to 6.5 billion U.S. dollars.
At least 2,400 killed, over
8,700 injured, 82,000 housing
units damaged, and 600,000
Taiwan, 23.7 N 121.0 E
2,297
7.6
left homeless. Damaged
estimated at 14 billion U.S.
dollars.
At least 20,005 people killed,
166,836 injured,approximately 339,000
buildings destroyed and783,000 damaged in the BhujAhmadabad-Rajkot area andother parts of Gujarat. Many
bridges and roads damaged in
Gujarat. At least 18 people
killed and some injured insouthern Pakistan. Felt
throughout northern India andmuch of Pakistan. Also felt in
India, 23.3 N 70.3 E
20,023
7.7
Bangladesh and western
Nepal. The earthquake
occurred along anapproximately east-west
trending thrust fault at shallow
depth. The stress that caused
this earthquake is due to theIndian plate pushingnorthward into the Eurasianplate. Complex earthquake. A
small event is followed by alarger one about 2 seconds
later..
4,000 injured, 1,500 houses
destroyed in the Nahrin area.
Hindu Kush Region, Afghanistan,
1,000
6.1
35.9 N 69.2 E
Approximately 20,000 people
homeless.
At least 2,000 people killed,
1,136 missing, 9,085 injured,
200,000 homeless andNorthern Algeria
2000
6.8
extensive damage (X) in the
Algiers-Bourmerdes-Thenia
area. A tsunami generated
with an estimated wave height

Seismic Risk Scenarios

42Technical University of Civil Engineering

No. Date UTC

Seismic Risk Scenarios

124 Lacul Tei Blvd., sector 2, Bucharest, Romania
Location
Deaths Magnitude

Comments
of 2m caused damage to boats
and underwater telephone
cables off the Balearic Islands,
Spain. Also felt in Monaco
and southwestern Spain.

43

Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

Annex B: Case study
Case study on mid-rise and high-rise RC residential buildings built in Bucharest
in-between 1978 and 1990 – corresponding to moderate earthquake resistant code period
The following categories of buildings were considered:
RC1M – mid rise RC frames
RC1H – high rise RC frames

Figure B.1. Typical RC frame apartment building, built in 80's
RC2M – mid rise RC shear walls
RC2H – high rise RC shear wall

Figure B.2. Typical RC shear wall apartment building

Seismic Risk Scenarios

44Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

Seismic action
The seismic action is described by the acceleration spectrum with 475 yr. MRI defined in
RISK-UE Project, Figure B.3.
900

PSHA Bucharest - 475 yr. MRI

800
700

SA, cm/s

2

600
500
400
300
200
100
0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

T, s

Figure B.3. Elastic acceleration response spectrum, MRI = 475 yr.
The spectrum was converted into ADRS format, Figure B.4.
900
800
700

SA, cm/s

2

600
500
400
300
200
100
0
0

10

20

30

40

50

SD , cm

Figure B.4. ADRS format for seismic action

Seismic Risk Scenarios

45Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

The acceleration spectrum was reduced for inelastic effects, Figure B.5 using strength
reduction factors and converted back to ADRS format, Figure B.6.
900

SA , cm/s

2

1
800

2

700

3
µ=

4

600

5

500

6
8

400
300
200
100
0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

T, s

Figure B.5. Inelastic acceleration response spectrum
900
800
700

µ=

SA , cm/s

2

600

1

2

3

5

6

8

4

500
400
300
200
100
0
0

10

20

30

40

50

SD, cmFigure B.6. Elastic and inelastic ADRS

Seismic Risk Scenarios

46Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

Direct physical losses
Capacity spectrum method was applied to get the expected response of building types (Figure
B.7, Figure B.9, Figure B.11 and Figure B.13) and fragility functions (Figure B.8, Figure
B.10, Figure B.12 and Figure B.14) were derived.
900
800
700

1
3
5
8

µ=

SA , cm/s

2

600

2
4
6
Capacity

500
400
300
200
100
0
0

10

20

30

40

50

SD , cm

Figure B.7. Expected response of RC1M building type
1.0
0.9
0.8

C1M
1978-1989

P(>DS|SD)

0.7
0.6
0.5

SlightModerate

0.4

Extensive
Complete

0.3

Expected

0.2
0.1
0.0
0

10

20

30

40

50

60

70

80

SD , cm

Figure B.8. Fragility functions of RC1M building type

Seismic Risk Scenarios

47

Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

900
800
1
3
5
8

700

SA , cm/s

2

600

µ=

2
4
6
Capacity

20

30

500
400
300
200
100
0
0

10

40

50

SD , cm

Figure B.9. Expected response of RC1H building type

1.0
0.9
0.8

C1H
1978-1989

P(>DS|SD)

0.7
0.6

SlightModerate
Extensive
Complete

0.5
0.4
0.3

Expected

0.2
0.1
0.0
0

10

20

30

40

50

60

70

80

SD , cm

Figure B.10. Fragility functions of RC1H building type

Seismic Risk Scenarios

48Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

900
800
1
3
5
8

700

SA , cm/s

2

600

µ=

2
4
6
Capacity

20

30

500
400
300
200
100
0
0

10

40

50

SD , cm

Figure B.11. Expected response of RC2M building type

1.0
0.9
0.8

C2M
1978-1989

0.7
0.6
0.5

SlightModerate

0.4

Extensive
Complete
Expected

0.3
0.2
0.1
0.0
0

20

40

60

80

100

120

Figure B.12. Fragility functions of RC2M building type

Seismic Risk Scenarios

49Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

900
800
700

2

600
SA , cm/s

2
4
6
Capacity

1
3
5
8

µ=

500
400
300
200
100
0
0

10

20

30

40

50

SD , cm

Figure B.13. Expected response of RC2H building type

1.0
0.9
0.8

C2H
1978-1989

0.7
0.6
0.5

SlightModerate

0.4

Extensive
Complete
Expected

0.3
0.2
0.1
0.0
0

20

40

60

80

100

120

Figure B.14. Fragility functions of RC2H building type

Seismic Risk Scenarios

50Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

Given the expected response and the fragility functions, the following damage probability
matrix was obtained for the analysed building typologies, Table1.1.
Table B.1. Damage probability matrix
P(ds|Sd)ds
RC1M RC1H RC2M RC2H
0.001 0.001 0.002 0.002
N
0.052 0.038 0.060 0.066
S
0.137 0.116 0.145 0.152
M
0.686 0.692 0.676 0.671
E
0.125 0.153 0.118 0.109
C
The building stock in Bucharest built in between 1977 and 1990 corresponding to theanalyzed building types is expressed in millions of m2 of floor area as follows in Table B.2:
Table B.2. Total floor area, in millions of m2
RC1M RC1H RC2M RC2H
0.43 2.225236 0.3 5.1922182
Assuming a ratio of 0.05 persons/m2 one gets the number of people living in each building
type, Table B.3.
Table B.3. Number of inhabitants in each building type
RC1M RC1H RC2M RC2H
21500 111262 14333 259611
Debris
The expected debris fraction for model building type k and debris type i due to structural
damage is given by, HAZUS, 1999:
5

EDFs (i, k) = ∑ Ps (j, k) ∗ DFs (i, j, k)

(B.1)

j =2

where:EDFs (i, k) - the expected debris fraction of debris type i due to structural damage forbuilding type k, Table B.5
Ps (j,k)- the probability of structural damage state j for building type k at thelocation being considered, given in Table B.1
DFs (i, j, k) - the debris fraction of debris type i for building type k in structural damage
state j, given in Table B.4
The expected debris fraction of debris type i due to structural damage for building type k isgiven in Table B.5. These values indicate the expected percentage of debris type i generated
due to structural damage to building type k. If one knows the total floor area of each building
type and weights of debris of type i per 1000 m2 of building, then the amount of debris forthis particular location can be obtained by multiplying the expected debris fraction of debris
type i due to structural damage for building type k, Table B.5 with the weight of debris type i

Seismic Risk Scenarios

51Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

per 1000 m2 of floor area of model building type k (From Table B.6) and with the total floorarea of each building type, Table B.2 and the summing for all k in Table B.8.
Table B.4. Reinforced concrete and wrecked steel generated from damaged structuralelements, in percentage of weight
Building
type
RC1M
RC1H
RC2M
RC2H

Structural damage state
SlightModerateExtensiveComplete
0
0
1
1

5
5
8
8

33
33
35
35

100
100
100
100

Table B.5. Expected fraction of debris, in percentage of weight
RC1M 35.83
RC1H 38.73
RC2M 36.66
RC2H 35.71
Table B.6. Unit weight for structural elements, adapted from HAZUS, 1999, in t/1000m2
Building Reinforced Concrete and
Type
Steel
RC1M
1055
RC1H
1055
RC2M
1206
RC2H
1206
Table B.7. Reinforced concrete and wrecked steel generated from damaged structuralelements, in t/1000m2
RC1M 377.98
RC1H 408.56
RC2M 442.11
RC2H 430.61
Table B.8. Reinforced concrete and wrecked steel generated from damaged structural, in t
RC1M 162533
RC1H 909147
RC2M 126737
RC2H 2235809
The total amount of debris is 3,434,225 tons.
Casualties
The number of casualties due to collapse of buildings can be expressed as, Coburn andSpence, 2002:

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52Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

Ks = C x [ M1 x M2 x M3 x ( M4 + M5 x (1 - M4))](B.2)

where C is total number (or floor area) of collapsed buildings in that typology class. C isgiven in Table B.9 and is obtained multiplying the floor area of each building type, Table B.2
by the corresponding complete damage state probability in Table B.1.
Table B.9. Floor area of collapsed buildings, in m2
RC1M
RC1H
RC2M
RC2H
53837 340620 33733 567566
M1 is the occupancy rate (number of people/built m2) and it is assumed to be 0.05 for
Bucharest.
M2 is the occupancy at time of earthquake; in this scenario it is considered the earthquake
strikes at 6 AM and the assumed value of M2 is 0.65.
M3 represents the percentage of occupants trapped by collapse; assumed value of M3 = 0.50.
M4 gives the injury distribution at collapse according to Table B.10.
Table B.10. Injury distribution at collapse
Triage injury category
M4
dead
0.4
life threatening
0.1
injured - required hospit
0.4
lightly injured
0.1
M5 represents the mortality post-collapse – assumed in this scenario to be 0.70.
The casualties, expressed in number of persons, in the case of this scenario are given in Table
B.11. Table B.12 gives the breakdown of casualties in percentages.
Table B.11. Breakdown of casualties for buildings typology
Human casualties, no.
RC1M RC1H RC2M RC2H
Dead
717
4539
449
7563
life threatening
639
4041
400
6733
injured - required hospit
717
4539
449
7563
lightly injured
639
4041
400
6733
Uninjured
18788 94103 12634 231020
Table B.12. Breakdown of casualties in percentage
Human casualties, %RC1M RC1H RC2M RC2H
dead
3.33
4.08
3.14
2.92
life threatening
2.97
3.63
2.79
2.59
injured - required hospit
3.34
4.08
3.14
2.91
lightly injured
2.97
3.63
2.79
2.59
uninjured
87.39 84.58 88.14 88.99
Homeless estimation
The total floor area of uninhabitable dwelling units (#UNU) is the output of this portion of themodel.

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53Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

The following inputs are required to compute the number of uninhabitable dwelling units andthe number of displaced households, HAZUS, 1999:
9 Total Number of Dwelling Units (#MFU)
9 Damage state probability for moderate structural damage state in the building type(%MFM).
9 Damage state probability for extensive structural damage state in the building type(%MFE).
9 Damage state probability for complete structural damage state in the building type(%MFC).
The probabilities %SFM, %SFE, %SFC, %MFM, %MFE, and %MFC are provided in Table
B.1.
The number of uninhabitable dwelling units due to structural damage is determined by
combining a) the number of uninhabitable dwelling units due to actual structural damage, andb) the number of damaged units that are perceived to be uninhabitable by their occupants.
Based on comparisons with previous work (Perkins, 1992), the methodology considers all
dwelling units located in buildings that are in the complete damage state to be uninhabitable.
In addition, dwelling units that are in moderately and extensively damaged multi-family
structures are also considered to be uninhabitable due to the fact that renters perceive somemoderately damaged rental property as uninhabitable. Therefore, the total floor area of
uninhabitable units (#UNUSD) due to structural damage is calculated by the following
relationship, HAZUS, 1999:%MF = wMFM x %MFM + wMFE x %MFE + wMFC x %MFC
#UNUSD = #MFU x %MF
The values of weighting factors are provided in Table B.13.

(B.3)

Table B.13. Default Values for Damage State Probabilities
Default
WeightValue
Factor
0.0
wMFM
0.9
wMFE
1.0
wMFC
The percentage of uninhabitable units is given in Table B.14 and the total floor ofuninhabitable dwelling units is given in Table B.15.
Table B.14. Percentage of uninhabitable units
RC1M 0.74
RC1H 0.78
RC2M 0.73
RC2H 0.71
Table B.15 Total floor are of uninhabitable dwelling units, 1000 m2
RC1M 319.16
RC1H 1726.65
RC2M 208.25
RC2H 3704.38

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54Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

The total floor area of uninhabitable units amounts at 5,958.44 thousands of sq.m.
Direct economical losses
For building related items, methods for calculating the following monetary losses areprovided for:9 Building Repair and Replacement Costs
9 Building Contents Losses.
Building Repair and Replacement Costs
To establish monetary loss estimates, the damage state probabilities are converted tomonetary loss equivalents. For a given occupancy and damage state, building repair andreplacement costs are estimated as the product of the floor area of each building type within
the given occupancy, the probability of the building type being in the given damage state, andrepair costs of the building type per square meter for the given damage state, summed over allbuilding types within the occupancy.
For structural damage, losses are calculated as follows, HAZUS, 1999:
CSds = ∑ Faj x PMBTSTRds,j x RCSds,j

(B.4)

j
5

CS = ∑ CSds

(B.5)

ds= 2

where:
cost of structural damage (repair and replacement costs) for damage
state ds
CS
cost of structural damage (repair and replacement costs)
FAjfloor area of building type j (in m2), based on the total floor area andthe distribution of floor area between building types, Table B.2
PMBTSTRds,j probability of building type j being in structural damage state ds,
Table B.1
RCSds,jstructural repair and replacement costs (per m2) for building type j indamage state ds
Note that damage state "None" (ds = 1) does not contribute to the calculation of the cost of
structural damage and thus the summation in Equation B.3 is from ds = 2 to ds = 5.
CSds

The cost of damage is expressed as a percentage of the complete damage state. The assumed
relationship between damage states and repair/replacement costs, for both structural and nonstructural components, is as follows, ATC 13, 1985:
Slight damage:Moderate damage:
Extensive damage:

2% of complete
10% of complete
50% of complete

Structural repair costs for complete damage is considered 300 Euro/m2.

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55Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

The direct economic losses from buildings repair and replacement costs are given in Table
B.16.
Table B.16. Building Repair and Replacement Costs, EuroMonetary losses, Euro RC1M
RC1H
RC2M
RC2H
0
0
0
0
N
132,974
508,888
102,7312,048,190
S
1,762,418
7,752,412 1,243,442 23,644,605
M
44,220,524 231,004,651 29,086,539 522,802,448
E
16,151,066 102,185,939 10,119,863 170,269,821
C
Total monetary losses 62,266,982 341,451,889 40,552,575 718,765,064
Total monetary losses due to building repair and replacement costs are in excess of 1.16
billion Euros.
Building Content Losses
Building content is defined as the furniture, equipment that is not integral with the structure,computers and other supplies. From Table 4.11 of ATC-13, 1985 it is assumed that forresidential buildings contents value represent 50 percent of building replacement value.
Thus, the building content loss is half of the building repair and replacement cost rising up to
more than 581 million Euros.
Overall, the direct economic losses are in excess of 1.74 billion Euros.

Seismic Risk Scenarios

56

Technical University of Civil Engineering

124 Lacul Tei Blvd., sector 2, Bucharest, Romania

3. Full Probabilistic Risk Assessment of Current Buildings
3.1 Introduction
Seismic risk represents the expectancy of damage or losses (expressed in probabilistic terms)
in relation to the performance of a definite built system, as a function of duration.
The risk analysis recognizes basically the impossibility of deterministic prediction of eventsof interest, like future earthquakes, exposure of elements at risk, or chain effects occurring asa consequence of the earthquake-induced damage. Since the expectancy of losses represents
the outcome of a more or less explicit and accurate predictive analysis, a prediction must be
made somehow in probabilistic terms, by extrapolating or projecting into the future thepresent experience. A probability-based prediction relies on two major premises:
1. the conceptual and methodological framework of the theory of probabilities;
2. the assumption that there exists some intrinsic stability and stationarity of objective
processes determining the input and outcome of phenomena and events dealt with (Sandi,
1986).
The general relation for the determination of the total risk can be expressed as (Whitman &Cornell, 1976):
P[ Ri ] = ∑ P[ Ri /Sj]⋅P[Sj]

(3.1)

j

in which P[ ] signifies the probability of the event indicated within the brackets, Ri denotes
the event that the state of system is i, Sj means that the seismic input experienced is level j,and P[Ri/Sj] states the probability that the state of the system will be Ri given that the seismic
input Sj takes place.
The probabilistic risk assessment is not a straightforward matter and involves a highcomputational effort. The probabilistic risk assessment is aiming at computing the annual
probability of exceedance of various damage states for a given structural system. The consistentprobabilistic approach is based on the idea of (Cornell & Krawinkler, 2000) using the total
probability formula applied in a form that suits the specific needs:P( ≥ d s ) =∫ ∫ Φ( ≥ d | Sd) ⋅ f(Sd|PGA) ⋅ f(PGA)d (Sd )d ( PGA)
s

(3.2)

PGA Sdwhere:- P(≥ ds) – annual probability of exceedance of damage state ds− Φ(≥ ds | Sd) – standard normal cumulative distribution function of damage state ds
conditional upon spectral displacement Sd- f(Sd | PGA) - probability density function of spectral displacement Sd given the occurrenceof peak ground acceleration PGA- f(PGA) – probability density function of peak ground acceleration PGA
One can change Eq. (3.2) to solve for the mean annual rate of exceedance of various damage
states for a given structural system:λ( ≥ d s ) = ∑∑ P( ≥ d s|Sd) ⋅ P(Sd|PGA) ⋅ λ(PGA)(3.3)

PGA SdSeismic Risk Scenarios

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where:− λ(≥ ds) – mean annual rate of exceedance of damage state ds- P(≥ ds | Sd) – probability of exceedance of damage state ds conditional upon spectral
displacement Sd- P(Sd | PGA) - probability of reaching spectral displacement Sd given the occurrence peakground acceleration PGA− λ(PGA) – mean annual rate of occurrence of peak ground acceleration PGA.
Consequently, the probabilistic assessment of seismic risk involves the:1. probabilistic seismic hazard assessment, λ(PGA)
2. probabilistic assessment of seismic structural response, P(Sd | PGA)
3. probabilistic assessment of seismic structural vulnerability, P(≥ ds | Sd)
Equations (3.2) and (3.3) are disaggregating the seismic risk assessment problem into threeprobabilistic analysis of: hazard, structural response and vulnerability. Then it aggregates therisk via summation (or integration) over all levels of the variables of interest.
3.2 Probabilistic seismic hazard assessment
According to the 20th century seismicity, the epicentral Vrancea area is confined to a rectangleof 40x80km2 having the long axis oriented N45E and being centered at about 45.6o Lat.N and26.6o Long. E.
The average number per year of Vrancea subcrustal earthquakes with moment magnitude equal
to and greater than Mw is (Lungu et.al., 2000, Lungu et. al. 1999):
log n(≥Mw) = 3.76 - 0.73 Mw(3.4)

The values of surface rupture area (SRA) and surface rupture length (SRL) from Wells andCoppersmith (1994) equations for "thrust" rupture were used to estimate maximum credible
Vrancea magnitude, (Lungu et. al. 1997). According to Romanian geologists Sandulescu &Dinu, in Vrancea subduction zone: SRL ≤ 150÷200 km, SRA≤8000 km2. Based on thisestimation, one gets:(3.5)

Mw,max= 8.1.

If the source magnitude is limited by an upper bound magnitude Mw,max, the recurrence
relationship can be modified in order to satisfy the property of a probability distribution(McGuire & Arabasz, 1990):n(≥ M w ) = eα − βM w

1− e
1− e

− β (M w, max − M w )− β (M w , max − M w0 )(3.6)

and, in the case of Vrancea source (Elnashai and Lungu 1995):n(≥ M w ) = e 8.654 − 1.687 M w

1 − e −1.687 (8.1− M w )1 − e − 1.687 (8.1− 6.3)

(3.7)

In Eq.(3.5), the threshold lower magnitude is Mw0=6.3, the maximum credible magnitude of
the source is Mw,max=8.1, and α = 3.76 ln10 = 8.654, β = 0.73 ln10 =1.687.

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The depth of the Vrancea foci has a great influence on the experienced seismic intensity. The
damage intensity of the Vrancea strong earthquakes is the combined result of both magnitude
and location of the focus inside the earth.
The relationship between the magnitude of a destructive Vrancea earthquake (Mw≥6.3) and thecorresponding focal depth shows that higher the magnitude, deeper the focus (Lungu et.al., 2000,
Lungu et. al., 1999):(3.8)

ln h = - 0.866 + 2.846 lnMw - 0.18

where P is a binary variable: P=0 for the mean relationship and P=1.0 for mean minus one
standard deviation relationship.
The following model was selected for the analysis of attenuation (Mollas & Yamazaki, 1995):
ln PGA = c0 + c1 Mw + c2 lnR +c3R +c4 h + ε(3.9)

where: PGA is peak ground acceleration at the site, Mw- moment magnitude, R - hypocentral
distance to the site, h - focal depth, c0, c1, c2, c3, c4 - data dependent coefficients and ε - randomvariable with zero mean and standard deviation σε = σln PGA, Table 3.1. Details are given
elsewhere (Lungu et.al., 2000, Lungu et. al. 2001).
Table 3.1. Regression coefficients inferred for horizontal components of peak groundacceleration during Vrancea subcrustal earthquakes, Equation (3.9)
c0
3.098

c1
1.053

c2
-1.000c3-0.0005c4-0.006σlnPGA
0.502

For a given earthquake recurrence, the probability of exceeding a particular value of peakground acceleration, PGA*, is calculated using the total probability formula (Cornell, 1968,
Kramer, 1996):(3.10)λ ( PGA > PGA*) = ∫ ∫ P( PGA > PGA* | m , r ) ⋅ f ( m ) ⋅ f ( r )dmdr
where:− λ(PGA>PGA*) – mean annual rate of exceedance of PGA* ;- P(PGA>PGA*|m,r) – probability of exceedance of PGA* given the occurrence of anearthquake of magnitude m at source to site distance r. This probability is obtained from
attenuation relationship (3.9) assuming log-normal distribution for PGA;
- f(m) – probability density function for magnitude;- f(r) – probability density function for source to site distance.
The probability density function for magnitude is obtained from Eq. (3.6) (McGuire &Arabasz, 1990). The probability density function for source to site distance is considered, forthe sake of simplicity, uniform over the rectangle of 40x80km2 having the long axis oriented
N45E and being centered at about 45.6o Lat.N and 26.6o Long. E.
The mean annual rate of exceedance of PGA – the hazard curve - for Bucharest site and
Vrancea seismic source is represented in Figure 3.1.

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Annual exceedance rate, λ (PGA )1.E-01

PSHA - Bucharest

1.E-02

1.E-03

1.E-04
100

150

200

250
300
2
PGA , cm/s

350

400

Figure 3.1. Hazard curve for Bucharest from Vrancea seismic source
The hazard curve can be approximated by the form H = ko ⋅ a g− k (Fajfar et al, 1994), where ag
is peak ground acceleration, and ko and k are constants depending on the site (in this caseko=1.176E-05, k=3.0865).
3.3 Probabilistic assessment of seismic structural response
3.3.1 The structural model
The building analyzed has a reinforced concrete moment resisting frame structure and it waserected in early ‘70’s. It is a thirteen-storey building, the first two storeys being of 3.60 m, all
the rest of 2.75 m height. The building has two spans of 6.00 m each in the transversal
direction and five spans of 6.00 m each in the longitudinal direction. The concrete is of class
Bc 20 and the steel is of quality PC 52. Some details regarding the structural members are
given in Table 3.2. Further details can be found elsewhere (Vacareanu, 1998).
Table 3.2.Description of the structural members
Storey #

1,2
3-5
6–9
10 – 13

Columns
(BxD)

(mm)
700 x
900
700 x
750
600 x
750
600 x
600

Overall
reinforcement
ratio

Hoop
bar
diameter

Hoopbarspacing

(%)
1.75

(mm)
8

(mm)
150

1.70

8

200

Seismic Risk Scenarios

1.40
1.00

200
6

200

Beams
(BxD)

(mm)
350 x
700
350 x
700
300 x
700
300 x
600

Bottomreinforcement
ratio

Top
reinforcement
ratio

Stirrupdiameter

Stirrupspacing

(%)
0.70

(mm)
6

(mm)
200

0.32

0.75

6

200

0.32

0.60

6

250

0.30

0.50

6

250

(%)
0.30

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3.3.2 Ground motions
In this paper, the seismic motion intensity is quantified by peak ground acceleration (PGA).
The seismic motions used in the analyses consist of seven classes of random processes
comprising ten samples each. Elastic acceleration spectra are used to simulate samples. The
input seismic motions are simulated using a stationary Gaussian model based on elastic
acceleration spectra (Shingal & Kiremidjian, 1997). The time histories are generated such as
to fit the given response spectrum. The probability distributions of the dynamic amplification
factors are used to obtain an ensemble of response spectra corresponding to a given level ofseismic motion (Vacareanu, 2000).
For parametric analysis purpose, the accelerograms are simulated at predefined values of PGA,
as follows: 0.10g, 0.15g, 0.20g, 0.25g, 0.30g, 0.35g, 0.40g (g – acceleration of gravity).
3.3.3 Non-linear dynamic analyses
The structural model in the transversal direction consists of six - two spans - reinforced
concrete moment resisting frames acting together due to the action of horizontal diaphragms
located at each storey. The computer program IDARC 2D (Valles et. al., 1996) is used for
performing inelastic dynamic analyses.
To trace the hysteretic response of structural elements, the piece-wise linear three-parametermodel that included stiffness degradation, strength deterioration and slip is used to model the
response of reinforced concrete structural elements. The trilinear hysteretic model relies onfour parameters that scale the main characteristics represented in the model: stiffness degradation, strength deterioration and pinching. In this paper, for analysis purpose, the default
values (HC = 2.0 ; HBD = 0.0; HBE = 0.10 ; HS = 1.0) are used, these values allowing fornominal stiffness degradation and strength deterioration and no pinching effects.
Nonlinear dynamic analyses are performed for 10 simulated ground motions generated at eachvalue of PGA. An integration time step of 0.002s is used in the analyses. The accelerograms
last for 20 s and the total duration of the analysis is 21 s. The damping coefficient is 5 % of
the critical damping and the structural damping is assumed to be mass proportional.
In damage analysis, the uncertainties associated with seismic demands and structural
capacities need to be modelled. The Monte-Carlo technique involves the selection of samplesof the random structural parameters and seismic excitations required for nonlinear analyses,
the performance of nonlinear analyses and the computation of the structural response.
In brief, the Monte-Carlo simulation technique implies the following steps:• simulation of structural parameters and seismic excitations;• random permutations of structural parameters and of excitations;• performing nonlinear analyses using generated samples;• sample statistics of results of analyses.
The direct Monte-Carlo technique requires a large number of simulation cycles to achieve an
acceptable level of confidence in the estimated probabilities. The Latin hypercube techniquemight be used to reduce the number of simulation cycles. Using the Latin hypercube

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technique for selecting values of the input variables, the estimators from the simulation areclose to the real values of the quantities being estimated. The Latin hypercube technique uses
stratified sampling of the input variables, which usually results in a significant decrease in thevariance of the estimators (Rubinstein, 1981).
The compressive strength of concrete and the yield strength of steel are the only parameters
treated as structural random variables in this paper. Following Galambos et al. (1982), normal
probability distribution for concrete strength and lognormal probability distribution for steel
strength are used in this research. Concrete strength has a mean of 25 MPa and a coefficient ofvariation of 15%. Steel strength has a mean of 397 MPa and a coefficient of variation of 7%.
For simulation purposes 10 values for concrete and reinforcement strengths are randomly
generated and used for each PGA value considered within the analysis. Latin hypercube
technique is used for randomly combine the generated strength variables and accelerations.
Spectral displacements are calculated using nonlinear dynamic analyses. Data regarding therandomness of the seismic response of the structural system are obtained. The statistic
indicators of the spectral displacement obtained at each PGA value are used to get theparameters of a lognormal distribution function for that level of intensity of ground motion.
The computed mean and standard deviation of the spectral displacements are reported inTable 3.3.
Table 3.3 Mean and standard deviation of DI
PGA, 'g
0.1
0.15
0.2
0.25
0.3
0.35
0.4

µ Sd|PGA

σ Sd|PGA

13.1
22.8
30.0
39.5
49.8
59.0
68.7

2.2
3.3
4.0
3.8
5.3
6.4
6.9

Finally, the lognormal probability density function of spectral displacement conditional upon
PGA is evaluated:f ( Sd | PGA ) =

1
1
1
⋅
⋅
⋅e
2π Sd σ ln( Sd|PGA )1 ⎛ ln( Sd )− µ ln( Sd |PGA ) ⎞⎟
− ⎜
⎟
2 ⎜⎝
σ ln( Sd |PGA )⎠2(3.11)

Examples of lognormal probability density functions of Sd conditional upon PGA= 0.1g, 0.2g
and 0.3g are presented in Figure 3.2. Using the density functions one obtains probability ofreaching spectral displacement Sd given the occurrence of peak ground acceleration, PGA,
P(Sd | PGA).

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80

80

Sd

70

Sd , cm

60

60
50

50

Sd
40

40
30

30

30

Sd

20
15

10 f[Sd|PGA]

10
0
0.05

f[Sd|PGA]20

PGA , 'g
0
0.1

0.15

0.2

0.25

0.3

0.35

0.4

Figure 3.2. Mean and standard deviation of the spectral displacement
3.3.4 Probabilistic assessment of seismic structural vulnerability
The probabilistic assessment of seismic structural vulnerability involves the determination of
the building vulnerability functions. These functions describe the conditional probability of
being in, or exceeding, a particular damage state, ds, given the spectral displacement, Sd, andis defined as HAZUS (1997) :⎡⎤1 ⎛⎜ S d ⎞⎟⎥P[ds S d ] = Φ ⎢ln −⎢ β ds ⎜ S ⎟⎥⎝ d ,ds ⎠⎦⎣(3.12)

where:- Sd,ds is the median value of spectral displacement at which the building reaches the thresholdof the damage state, ds,- βds is the standard deviation of the natural logarithm of spectral displacement for damage
state ds, and− Φ is the standard normal cumulative distribution function.
For the spectral (maximum) displacement, Sd, expected for the demand earthquake, one
determines the structural damage state probabilities using vulnerability functions (Eq. 3.12).
HAZUS (1997) includes the vulnerability function parameters, Sd,ds and βds appropriate foreach type of building corresponding to USA practice of design and construction. In order tocalibrate the vulnerability function parameters appropriate for structural systems which are
different from USA practice, the Monte-Carlo simulation technique can be used. For
simulation purposes 10 values for concrete and for reinforcement strengths are randomly
generated and randomly combined for each push-over analysis.
The outcome of the pushover analyses is a family of capacity curves, which can be describedas mean and mean plus/minus one standard deviation capacity curves, Figure 3.3 (Vacareanu
et. al., 2001).
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For calibration of vulnerability function parameters it is necessary to establish a correlation between
Park&Ang (1985) damage index and interstory drift ratio at threshold of damage state. The more
recent slightly modified version of Park&Ang index, in which the recoverable deformation isremoved from the first term might be used:
0.12
13 stories
0.10

SA, ' g

0.08

µ
µ−σ
µ+σ

0.06
0.04
0.02
0.00
0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

SD , %He

Figure 3.3. Capacity curve, Monte-Carlo simulation∫ dE(3.13)Du − Dy
Fy ⋅ Du
where Dm = maximum displacement; Du = ultimate displacement; Dy = yielding
displacement; βe = strength deterioration parameter; Fy = yielding force and E = dissipatedhysteretic energy. The correlation between Park&Ang damage index and damage state isgiven in Table 3.4 (Williams & Sexsmith, 1995):
D=

Dm − Dy+ βe ⋅

Using the definition of Park&Ang damage index (Eq. 3.13) and the structural behavior
described by the capacity curve, one can determine the correlation between Park&Ang
damage index and mean (± 1 standard deviation) interstory drift ratio values, Figure 3.4(Vacareanu et. al., 2001).
Table 3.4. Relations between damage index and damage state
Range of damage index

Damage stateD ≤ 0.1None

0.1 < D ≤ 0.25

Slight0.25 < D ≤ 0.40

Moderate

0.40 < D ≤ 1.00

ExtensiveD > 1.00

Complete

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Making vertical sections in Figure 3.4 for the threshold values of Park&Ang damage index
given in Table 3.4 one can identify the mean and standard deviation values of interstory drift
at threshold of damage state, Table 3.5, Figure 3.5. The median value of spectral displacement
at which the building reaches the threshold of the damage state, Sd,ds is obtained bymultiplying the interstory drift by the height of the building and by the fraction of the buildingheight at the location of push-over mode displacement, Table 3.6. The standard deviation of
the natural logarithm of spectral displacement for damage state ds, βds is obtained using thestandard deviation of structural displacement.
5.0
13 stories

4.5
4.0

µ
µ−σ
µ+σ

Drift Ratio, %

3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Park&Ang Damage Index

Figure 3.4. Correlation between Park&Ang damage index and interstory drift ratio
0.08
13 stories
0.07
0.06

SA, 'g0.05
0.04
Mean behaviour
0.03

Elasto-plastic
Slight threshold

0.02

Moderate threshold
Extensive threshold

0.01

Collapse threshold
0.00
0.0

0.5

1.0

1.5

2.0

2.5

3.0

Sd, %He

Figure 3.5. Median capacity curve and thresholds of damage states

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One can notice from Figure 3.5 that the complete damage state corresponds to the collapse
prevention limit state and the extensive damage state corresponds roughly to the life safety
limit state.
Once the parameters of vulnerability function, Sd,ds and βds, are obtained one can compute andplot the functions using Eq. 3.12, Figure 3.6.
Table 3.5. Mean interstory drift ratio at threshold of damage state
Slight0.0028Mean interstory drift ratio; Monte-Carlo Simulation
Moderate
Extensive
0.00640.0100Complete
0.0244

Table 3.6. Vulnerability function parameters (Monte-Carlo Simulation)
Damage state
Moderate
Extensive
Sd,ds, cm
Sd,ds, cm
βds
βds
17.88
0.66
27.94
0.76

SlightSd,ds, cm
βds
7.82
0.66
1.0

Complete
Sd,ds, cm
βds
68.16
0.91

P(>ds|Sd)

0.9
0.8
0.7
0.6
0.5
SlightModerate
Extensive
Complete

0.4
0.3
0.2
0.1

SD , cm

0.0
0

20

40

60

80

100

120

Figure 3.6. Vulnerability functions, Monte-Carlo simulation
3.3.5 Risk analysis
Given the results of the probabilistic seismic hazard assessment, λ(PGA), the probabilistic
assessment of seismic structural response, P(Sd | PGA), and the probabilistic assessment ofseismic structural vulnerability, P(≥ ds | Sd) one can aggregate the risk via summation (orintegration) over all levels of the variables of interest using Equation 3.3. The results on risk
are presented as mean annual rate of exceedance of damage state ds, λ(≥ ds), in Table 3.7.
Also, in Table 3.7 is presented the exceedance probability of various damage states in 1 year,
50 years and 100 years assuming that the damage states follows a Poisson distribution:

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Pexc ( d s ,T ) = 1 − e− λ ( ≥ d s )⋅T(3.14)

where:- Pexc(ds, T) - exceedance probability of damage state ds in time T.
Table 3.7. Results of seismic risk analysis
Damage state ds

Annual exceedance rate, λ(≥ ds)

SlightExceedance prob., Pexc(ds, T) in:
T=1 year

T=50 years

T=100 years

5.1E-02

5.0E-02

9.2E-01

9.9E-01

Moderate

2.6E-02

2.6E-02

7.3E-01

9.3E-01

Extensive

1.2E-02

1.2E-02

4.4E-01

6.9E-01

Complete

4.7E-03

4.7E-03

2.1E-01

3.7E-01

One can notice from Table 3.7 the exceedance probability of complete damage state in 1 yearof 4.7⋅10-3 which is much higher that the commonly accepted probabilities of failure of 10-4 to
10-5 as in the case of non-seismic loads. The main reason for this high probability comes fromthe design of the building which was accomplished taking into account an inferior code forearthquake resistant design (P13-70) combined with the low level of seismic hazard
considered in the design process.
3.4 Conclusions
1. The approach used is fully probabilistic and is the only one that incorporates
uncertainties and enables quantification of the safety level on a consistent theoretical basis.
2. Interstory drift at threshold of damage states can be analytically evaluated for different
structural typologies. The actual values of the interstory drifts could be different with respect
to that specified in HAZUS for USA design and construction practice.
3. Monte-Carlo simulation is a very powerful tool that can validate and complete thedatabase on seismic behavior and vulnerability of buildings.
4. The unsatisfactory building safety level against seismic actions is put to evidence. The
reasons for the un-conservative safety margins against earthquake action are the inferior code(P13-70) used for earthquake resistant design of building and the low level of seismic hazard
considered in design.
5. The state of the practice in seismic design and seismic assessment of structural
performances has to incorporate, in an appropriate and correct manner, the basic concepts ofseismic vulnerability and risk.
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Kramer, S. L., 1996 – Geotechnical Earthquake Engineering – Prentice Hall, Inc., p. 653
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EAEE WG 5/10 to the 8-th European Conference on Earthquake Engineering, Lisbon, 1986
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Engineering Research, State University of New York at Buffalo
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Technical University of Civil Engineering of Bucharest, 1/2002, BucharestVăcăreanu R., Cornea T., Lungu D., 2001 - Evaluarea comportarii structurale si a vulnerabilitatii seismice
folosind metodologiile HAZUS si ATC-40 modificat (in Romanian) – Proceedings of the 2nd National
Conference on Earthquake Engineering, Vol. 2, p. 2.16-2.31
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