modeling decision variables: dollars, deaths, and downtime judith mitrani-reiser (jhu) james l. beck...

Modeling Decision Variables: Dollars, Deaths, and Downtime

Judith Mitrani-Reiser (JHU)

James L. Beck (Caltech)

PEER Annual Meeting

San Francisco, CA

January 19, 2007

PEER Annual Meeting January 19, 2007

Outline

• Methodology to estimate building safety for PEER’s PBEE framework (using ATC-20 guidelines).

• Methodology to estimate probability of fatalities and downtime for PEER’s PBEE framework.

• Applied comprehensive damage and loss analysis to PEER’s benchmark study.

• Express all performance metrics in economic terms for a benefit-cost analysis.


PBEE methodology for PEER: collaboration for benchmark study

C. GouletJ. Stewart

C. HaseltonG. Deierlein

J. Mitrani-ReiserJ. Beck

K. Porter


Facility definition: benchmark site

LA Bulk Mail Facility, Bell, CA, 7 miles SE of downtown L.A.

Representative of urban area in highly seismic region.

Site is within 20 km of 7 known faults, but no one fault dominates the site hazard.

Near-fault effects are not a concern at this site.

High-quality geotechnical data is available for this site.

from USGS (by way of Goulet)


Facility definition: benchmark building

RC 4-story frame building Typical office building 4 x 6 bays (bay width = 30 ft) T1= 1 sec

from Haselton


Design Description

A: Baseline perimeter frame design.

B: Same as A, but with code min strengths.

C: Same as A, but with uniform beam/column throughout.

D: Same as C, but no SCWB provision.

E: Baseline space frame design.

Benchmark Building Design Variants

• Structural analysis performed using Opensees software.

• Fiber and lumped plasticity models used to estimate structural response for a range of hazard levels.

• Sa(T1) used as IM in benchmark study.


Repair Cost: component contribution

Repair costs for damageable

building components.


Repair Cost: vulnerability functions

Mean repair costMDF =

Replacement cost

Replacement cost $9M

.1 .19 .3 .44 .55 .82 1.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Design A, Baseline Perimeter-Frame DesignDesign E, Baseline Space-Frame Design

.26

Spectral Acceleration (g)

Mea

n D

amag

e Fa

ctor

10%-in-50yr 2%-in-50yr

Sum repair costs at each hazard level


Repair Cost : expected annual loss

0 [ | ] ( | )dcr

im

EAL E TC im p im im im im

where is the mean annual rate of events where:

0

0.1crIM im g

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

PGA (g)P

Hazard Curve

Spectral Acceleration (g)1.51.0 0.1 0.5


Results of Benchmark Study: EAL

Design Description EAL ($)

A: Baseline perimeter frame design. 66,585

B: Same as A, but with code minimum strengths.

95,656


51,933

D: Same as C, but no SCWB provision. 112,930

E: Baseline space frame design. 49,422






95,656


51,933



43% increase






95,656


51,933



115% increase


EAL Contributions

Contribution from collapse ~ 1%

Baseline Perimeter-Frame Design


ATC 20 guidelines (ATC 1985, 1995, 1996)

Event Tree

Building Safety: virtual inspector


Building Safety: rapid evaluation results


Building Safety: detailed evaluation results


Life Safety

Event Tree

P[C|im] determined by structural analysis

P[LC|im, NC] determined by virtual inspector

pDM from epidemiological studies and expert opinion


Life Safety

P[C|im] determined by structural analysis

P[LC|im, NC] determined by virtual inspector

pDM from epidemiological studies and expert opinion

Event Tree


Life Safety: mean population at risk

Mean # occupants determined from ATC-13 (1985).


DMpBuilding Characteristics

Fatality Model

Damage State (DM)

For all construction types except light steel and wood

frame.

ATC-13 (1985)

LC 0.01

C 0.20

Reinforced-concrete (non-near-field ground motions)

Coburn et al. (1992)

LC 0.31

C 0.49

Mid-rise concrete moment frame

HAZUS 99-SR2 (2002)

LC 0.0001

C 0.1

Mid-rise non-ductile reinforced-concrete frame

Shoaf and Seligson

(2005)

LC 0.015

C 0.131

Life Safety: fatality probabilities


DMpBuilding Characteristics

Fatality Model

Damage State (DM) E[Yn|DM] Var[Yn|DM]

For all construction types except light steel and wood

frame.

ATC-13 (1985)

LC 0.01 1.33 1.32

C 0.20 26.68 21.34

Reinforced-concrete (non-near-field ground motions)

Coburn et al. (1992)

LC 0.31 41.35 28.53

C 0.49 65.37 33.2

Mid-rise concrete moment frame

HAZUS 99-SR2 (2002)

LC 0.0001 0.01 0.01

C 0.1 13.34 12.01

Mid-rise non-ductile reinforced-concrete frame

Shoaf and Seligson

(2005)

LC 0.015 2.00 1.97

C 0.131 17.47 15.19

Life Safety: number of fatalities

Use Binomial distribution to estimate mean and variance of fatalities.


0 [ | ] ( | )dn cr

im

EANF E Y im p im im im im

Design DescriptionEANF(*10-3)

A: Baseline perimeter frame design. 1.4

B: Same as A, but with code-min strengths.

1.3

C: Same A, but with uniform beam/column throughout.

1.6

D: Same as C, but no SCWB provision. 22.8

E: Baseline space frame design. 1.0

Life Safety: expected annualnumber of fatalities


Design DescriptionEANF(*10-3)

EALF ($)

A: Baseline perimeter frame design. 1.4 4,900


1.3 4,550


1.6 5,600

D: Same as C, but no SCWB provision. 22.8 79,800

E: Baseline space frame design. 1.0 3,500

value of a statistical life = $3.5M (FHWA 1994, Mrozeck and Taylor 2002)

EALF VSL EANF

VSL

Life Safety: expected annual lossdue to fatalities


[ | , ] [ | ] ( | , )

[ | ] ( | , )

[ | ] ( | , )

TO TO G G

TO Y Y

TO R R

E R NC im E R TAG P TAG NC im

E R TAG P TAG NC im

E R TAG P TAG NC im

• ABAG’s building inspection data from over 700 buildings after the Loma Prieta earthquake, 10 days (Blecher and Comerio 2006).

• Estimate by expert, 1 month (Scawthorne 2006).

• Estimate from Stanford case study of closed buildings after Loma Prieta earthquake, 6 months (Comerio 2006).

Results from the Virtual Inspector.

Downtime: mobilization delay

Use Virtual Inspector results to determine

mobilization delay.


Baseline Perimeter-Frame Design

Downtime: mobilization delay & repair time

10%-in-5yr

DT ~ 4 months

2%-in-50yr

DT ~ 17 months


Design DescriptionDown-time Type

Sa(T1)

EALD ($USD)

0.1 0.19 0.26 0.3 0.44 0.55 0.82 1.2


Total(days) 24 52 114 157 284 388 518 655 20,519


Total(days) 28 89 221 238 363 426 543 635 28,362


Total(days) 26 57 94 124 245 335 485 642 22,207


Total(days) 30 94 220 239 386 491 726 942 32,726


Total(days) 26 42 85 119 217 332 577 949 19,517

Comerio (2006)

Downtime: economic losses


Comerio (2006) 16-32 months



Sa(T1)

EALD ($USD)

0.1 0.19 0.26 0.3 0.44 0.55 0.82 1.2


Total(days) 24 52 114 157 284 388 518 655 20,519


Total(days) 28 89 221 238 363 426 543 635 28,362


Total(days) 26 57 94 124 245 335 485 642 22,207


Total(days) 30 94 220 239 386 491 726 942 32,726


Total(days) 26 42 85 119 217 332 577 949 19,517




Sa(T1)

EALD ($USD)

0.1 0.19 0.26 0.3 0.44 0.55 0.82 1.2


Total(days) 24 52 114 157 284 388 518 655 20,519


Total(days) 28 89 221 238 363 426 543 635 28,362


Total(days) 26 57 94 124 245 335 485 642 22,207


Total(days) 30 94 220 239 386 491 726 942 32,726


Total(days) 26 42 85 119 217 332 577 949 19,517

28% increase in EALD for code-min design.




Sa(T1)

EALD ($USD)

0.1 0.19 0.26 0.3 0.44 0.55 0.82 1.2


Total(days) 24 52 114 157 284 388 518 655 20,519


Total(days) 28 89 221 238 363 426 543 635 28,362


Total(days) 26 57 94 124 245 335 485 642 22,207


Total(days) 30 94 220 239 386 491 726 942 32,726


Total(days) 26 42 85 119 217 332 577 949 19,517

47% increase in EALD for

non-code-conforming design.


Design DescriptionEAL($)

EALD ($)

EALF ($)

EALTOTAL

($)

A: Baseline perimeter frame design. 66,585 20,519 4,900 92,004

B: Same as A, but with code-min strengths. 95,656 28,362 4,550 128,568


51,933 22,207 5,600 79,740

D: Same as C, but no SCWB provision. 112,930 32,726 79,800 225,456

E: Baseline space frame design. 49,422 19,517 3,500 72,439

Summary of Results: “3 D” Losses


Design DescriptionEAL($)

EALD ($)

EALF ($)

EALTOTAL

($)E[PVL(50yr)]

($M)

A: Baseline perimeter frame design. 66,585 20,519 4,900 92,004 1.84

B: Same as A, but with code-min strengths. 95,656 28,362 4,550 128,568 2.50


51,933 22,207 5,600 79,740 1.64

D: Same as C, but no SCWB provision. 112,930 32,726 79,800 225,456 6.66

E: Baseline space frame design. 49,422 19,517 3,500 72,439 1.44

Summary of Results: “3 D” Losses


Benefit-Cost Analysis

Benefit = [ (50yr)] [ (50yr)] $403,500

Cost = [upfront cost] [upfront cost)] $100, 000

Benefit4

Cost

perimeter space

space perimeter

E PVL E PVL

E E

A risk-neutral decision maker will choose the space-frame design!


Summary

• Established framework for estimating the 3 D’s (dollars, deaths and downtime) as part of PEER’s PBEE framework.

• Used PEER benchmark study to illustrate this loss framework.

• Results show that all metrics are important in estimating overall building performance, and should all be included in a building loss estimation and BCA.

• We hope that this effort will contribute to the ongoing ATC-58 effort (downtime & deaths).


Thank You!

modeling decision variables: dollars, deaths, and downtime judith mitrani-reiser (jhu) james l. beck...

Documents

peer annual meetingjanuary

annual loss

baseline space frame

haselton slide

porter slide

increase slide

results of benchmark

peers benchmark study