In review (limited distribution) July 2007 1 Bai, J. W., Hueste, M., and Gardoni, P. “Probabilistic Assessment of Structural Damage due to Earthquakes for Buildings in Mid-America,” ASCE Journal of Structural Engineering, submitted for review, June 2007. Probabilistic Assessment of Structural Damage due to Earthquakes for Buildings in Mid-America Jong-Wha Bai 1 , Mary Beth D. Hueste 2 , and Paolo Gardoni 3 Abstract This paper provides an approach to conduct a probabilistic assessment of structural damage due to seismic events with an application to typical building structures in Mid-America. The developed methodology includes modified damage state classifications based on the ATC-13 and ATC-38 damage states and the ATC-38 database of building damage. Damage factors are assigned to each damage state to quantify structural damage as a percentage of structural replacement cost. To account for the inherent uncertainties, these factors are expressed as random variables with a Beta distribution. A set of fragility curves, quantifying the structural vulnerability of a building, is mapped onto the developed methodology to determine the expected structural damage. The total structural damage factor for a given seismic intensity is then calculated using a probabilistic approach. Prediction and confidence bands are also constructed to account for the prevailing uncertainties. The expected seismic structural damage is assessed for three types of building structures in the Mid-America region using the developed 1 Graduate Research Assistant, Zachry Dept. of Civil Engineering, Texas A&M University, College Station, TX, 77843-3136, USA. E-mail: [email protected]2 E.B. Snead II Associate Professor, Zachry Dept. of Civil Engineering, Texas A&M University, College Station, TX, 77843-3136, USA. E-mail: [email protected]3 Assistant Professor, Zachry Dept. of Civil Engineering, Texas A&M University, College Station, TX, 77843-3136, USA. E-mail: [email protected]
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In review (limited distribution) July 2007
1
Bai, J. W., Hueste, M., and Gardoni, P. “Probabilistic Assessment of Structural Damage due to Earthquakes for Buildings in Mid-America,” ASCE Journal of Structural Engineering, submitted for review, June 2007.
Probabilistic Assessment of Structural Damage due to Earthquakes
for Buildings in Mid-America
Jong-Wha Bai1, Mary Beth D. Hueste2, and Paolo Gardoni3 Abstract
This paper provides an approach to conduct a probabilistic assessment of structural damage due
to seismic events with an application to typical building structures in Mid-America. The
developed methodology includes modified damage state classifications based on the ATC-13 and
ATC-38 damage states and the ATC-38 database of building damage. Damage factors are
assigned to each damage state to quantify structural damage as a percentage of structural
replacement cost. To account for the inherent uncertainties, these factors are expressed as
random variables with a Beta distribution. A set of fragility curves, quantifying the structural
vulnerability of a building, is mapped onto the developed methodology to determine the expected
structural damage. The total structural damage factor for a given seismic intensity is then
calculated using a probabilistic approach. Prediction and confidence bands are also constructed
to account for the prevailing uncertainties. The expected seismic structural damage is assessed
for three types of building structures in the Mid-America region using the developed
1 Graduate Research Assistant, Zachry Dept. of Civil Engineering, Texas A&M University, College Station, TX,
Fig. 1. Possible relationship between fragility curves and damage states
Fig. 2. Probability distribution for each damage factor, kL
Fig. 3. Illustration for computing the probability of being in each damage state
Fig. 4. Illustration of expected damage factor with prediction and confidence bands
Fig. 5. Elevation of the case study structures
Fig. 6. Fragility curves for case study structures
Fig. 7. Probabilities of each damage state as a function of aS for case study structures
Fig. 8. Expected total damage factor with prediction bands for case study structures
Fig. 9. Expected total damage factor with confidence bands for case study structures
In review (limited distribution) July 2007
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List of Tables
Table 1. ATC-38 damage state classification [adapted from ATC (2000)]
Table 2. ATC-13 damage states and corresponding damage factor ranges [adapted from ATC
(1985)]
Table 3. Damage factor distributions by number of buildings in the ATC-38 database
Table 4. LAMB loss factors for repair cost [adapted from Abrams and Shinozuka (1997)]
Table 5. Comparison of ATC-38 and proposed damage states
Table 6. Proposed damage state descriptions
Table 7. Relationship between damage states and performance levels
Table 8. Relationship between proposed damage states and ATC-13 damage categories
Table 9. Statistical description of damage factors, Lk
Table 10. Data for case study structures
Table 11. Statistics of total damage factors for case study structures
Table 12. Results of the sensitivity analysis for the total damage factor for case study structures
In review (limited distribution) July 2007
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0
1
Earthquake Intensity (IM)Pr
obab
ility.
PL1PL2PL3
IM
HC
Fig. 1. Possible relationship between fragility curves and damage states
In review (limited distribution) July 2007
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0.000
0.005
0.010
0.015
0.020
0.025
0.0 0.2 0.4 0.6 0.8 1.0
Prob
abili
ty.
0.0 5.0 10.0 15.0 20.0 25.0 30.0
0.000
0.005
0.010
0.015
0.020
0.025
30.0 40.0 50.0 60.0 70.0 80.0Damage Factor (%)
Prob
abili
ty.
0
0
0
80.0 85.0 90.0 95.0 100.0Damage Factor (%)
0.25*Range0.20*Range0.15*Range
Fig. 2. Probability distribution for each damage factor, kL
I M
H C
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0
1
Earthquake Intensity (IM)
Prob
abili
ty.PL1PL2PL3
P I|IM = 1.0 - PPL1
P M|IM =PPL1 - PPL2
PPL1
PPL2
PPL3
P H|IM = PPL2 - PPL3
P C|IM = PPL3
Fig. 3. Illustration for computing the probability of being in each damage state
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0
100
Intensity Measure (IM)
Tot
al D
amag
e Fa
ctor
s (%
). Prediction band
Confidence band
ˆL IMµ
Fig. 4. Illustration of expected damage factor with prediction and confidence bands
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Fig. 5. Elevation of the case study structures
RC Steel URM
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0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0S a (g )
Prob
abili
ty.S a =0.104g
S a =0.535g
0.0 0.2 0.4 0.6 0.8 1.0
S a (g )
S a =0.0935g
S a =0.433g
0.0 0.2 0.4 0.6 0.8 1.0
S a (g )
PL1PL2PL3
S a =0.232g
S a =0.664g
Fig. 6. Fragility curves for case study structures
RC Steel
URM
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0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0Sa (g )
Prob
abili
ty.
0.0 0.2 0.4 0.6 0.8 1.0Sa (g )
0.0 0.2 0.4 0.6 0.8 1.0Sa (g )
IMHC
Fig. 7. Probabilities of each damage state as a function of aS for case study structures
RC
Steel
URM
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0
20
40
60
80
100
0.0 0.2 0.4 0.6 0.8 1.0S a (g )
Tot
al D
amag
e Fa
ctor
s (%
) .
50% Predic tionband
ˆL IMµ
90% Predic tionband
0.0 0.2 0.4 0.6 0.8 1.0S a (g )
90% Predic tion band
50% Predic tion band
ˆL IMµ
0.0 0.2 0.4 0.6 0.8 1.0S a (g )
50% Predic tion band
ˆL IMµ
90% Predic tionband
Fig. 8. Expected total damage factor with prediction bands for case study structures
RC Steel URM
In review (limited distribution) July 2007
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0
20
40
60
80
100
0.0 0.2 0.4 0.6 0.8 1.0S a (g )
Tot
al D
amag
e Fa
ctor
s (%
) .
90% Confidence band
50% Confidence band
ˆL IMµ
0.0 0.2 0.4 0.6 0.8 1.0S a (g )
90% Confidence band
50% Confidence band
ˆL IMµ
0.0 0.2 0.4 0.6 0.8 1.0S a (g )
90% Confidence band
50% Confidence band
ˆL IMµ
Fig. 9. Expected total damage factor with confidence bands for case study structures
RC Steel URM
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Table 1. ATC-38 damage state classification [adapted from ATC (2000)] Damage state Description
None (N)
None. No damage is visible, either structural or nonstructural.
Insignificant (I)
Damage requires no more than cosmetic repair. No structural repairs are necessary. For nonstructural elements this would include spackling, partition cracks, picking up spilled contents, putting back fallen ceiling tiles, and righting equipment.
Moderate (M)
Repairable structural damage has occurred. The existing elements can be repaired essentially in place, without substantial demolition or replacement of elements. For nonstructural elements this would include minor replacement of damaged partitions, ceilings, contents, and equipment or their anchorages.
Heavy (H)
Damage is so extensive that repair of elements is either not feasible or requires major demolition or replacement. For nonstructural elements this would include major or complete replacement of damaged partitions, ceilings, contents, equipment or their anchorages.
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Table 2. ATC-13 damage states and corresponding damage factor ranges [adapted from ATC (1985)]
Table 5. Comparison of ATC-38 and proposed damage states ATC-38
damage states Proposed
damage states Comments
None (N)
Insignificant (I) Insignificant (I)
None (N) and Insignificant (I) damage states in ATC-38 are merged into Insignificant (I) damage state.
Moderate (M) Moderate (M) Same
Heavy (H) Heavy (H)
Complete (C)
Heavy (H) damage state in ATC-38 is divided into Heavy (H) and Complete (C) damage states.
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Table 6. Proposed damage state descriptions Damage state Description
Insignificant (I)
Damage requires no more than cosmetic repair. No structural repairs are necessary. For nonstructural elements, repairs could include spackling, partition cracks, picking up spilled contents, putting back fallen ceiling tiles, and righting equipment.
Moderate (M)
Repairable structural damage has occurred. The existing elements can be repaired essentially in place, without substantial demolition or replacement of elements. For nonstructural elements, repairs would include minor replacement of damaged partitions, ceilings, contents, and equipment or their anchorages.
Heavy (H)
While the damage is significant, the structure is still standing. Structural damage would require major repairs, including substantial demolition or replacement of elements. For nonstructural elements, repairs would include major replacement of damaged partitions, ceilings, contents, equipment or their anchorages.
Complete (C)
Damage is so extensive that repair of most structural elements is not feasible. Structure is destroyed or most of the structural members have reached their ultimate capacities.
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Table 7. Relationship between damage states and performance levels
Damage state Performance level
Insignificant (I) Moderate (M)
Heavy (H) Complete (C)
PL1 PL2 PL3
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Table 8. Relationship between proposed damage states and ATC-13 damage categories Proposed