1. Modeling Decision Variables: Dollars, Deaths, and Downtime Judith Mitrani-Reiser (JHU) James L. Beck (Caltech) PEER Annual Meeting San Francisco, CA January 19, 2007

2. PEER Annual MeetingJanuary 19, 2007 Outline Methodology to estimate building safety for PEER’s PBEE framework (using ATC-20 guidelines). M ethodology 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.

3. PEER Annual MeetingJanuary 19, 2007 PBEE methodology for PEER: collaboration for benchmark study C. Goulet J. Stewart C. Haselton G. Deierlein J. Mitrani-Reiser J. Beck K. Porter

4. PEER Annual MeetingJanuary 19, 2007 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)

5. PEER Annual MeetingJanuary 19, 2007 Facility definition: benchmark building RC 4-story frame building Typical office building 4 x 6 bays (bay width = 30 ft) T 1 = 1 sec from Haselton

6. PEER Annual MeetingJanuary 19, 2007 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. S a (T 1 ) used as IM in benchmark study.

7. PEER Annual MeetingJanuary 19, 2007 Repair Cost: component contribution Repair costs for damageable building components.

8. PEER Annual MeetingJanuary 19, 2007 Repair Cost: vulnerability functions 10%-in-50yr2%-in-50yr Sum repair costs at each hazard level

9. PEER Annual MeetingJanuary 19, 2007 Repair Cost : expected annual loss where is the mean annual rate of events where: Spectral Acceleration (g) 1.51.0 0.1 0.5

10. PEER Annual MeetingJanuary 19, 2007 Results of Benchmark Study: EAL Design DescriptionEAL ($) A: Baseline perimeter frame design. 66,585 B: Same as A, but with code minimum strengths. 95,656 C: Same as A, but with uniform beam/column throughout. 51,933 D: Same as C, but no SCWB provision.112,930 E: Baseline space frame design. 49,422

11. PEER Annual MeetingJanuary 19, 2007 Results of Benchmark Study: EAL Design DescriptionEAL ($) A: Baseline perimeter frame design. 66,585 B: Same as A, but with code minimum strengths. 95,656 C: Same as A, but with uniform beam/column throughout. 51,933 D: Same as C, but no SCWB provision.112,930 E: Baseline space frame design. 49,422 43% increase

12. PEER Annual MeetingJanuary 19, 2007 Results of Benchmark Study: EAL Design DescriptionEAL ($) A: Baseline perimeter frame design. 66,585 B: Same as A, but with code minimum strengths. 95,656 C: Same as A, but with uniform beam/column throughout. 51,933 D: Same as C, but no SCWB provision.112,930 E: Baseline space frame design. 49,422 115% increase

13. PEER Annual MeetingJanuary 19, 2007 EAL Contributions Contribution from collapse ~ 1% Baseline Perimeter-Frame Design

14. PEER Annual MeetingJanuary 19, 2007 ATC 20 guidelines (ATC 1985, 1995, 1996) Event Tree Building Safety: virtual inspector

15. PEER Annual MeetingJanuary 19, 2007 ATC 20 guidelines (ATC 1985, 1995, 1996) Event Tree Building Safety: virtual inspector

16. PEER Annual MeetingJanuary 19, 2007 Building Safety: rapid evaluation results

17. PEER Annual MeetingJanuary 19, 2007 Building Safety: detailed evaluation results

18. PEER Annual MeetingJanuary 19, 2007 Life Safety Event Tree P[C|im] determined by structural analysis P[LC|im, NC] determined by virtual inspector p DM from epidemiological studies and expert opinion

19. PEER Annual MeetingJanuary 19, 2007 Life Safety P[C|im] determined by structural analysis P[LC|im, NC] determined by virtual inspector p DM from epidemiological studies and expert opinion Event Tree

20. PEER Annual MeetingJanuary 19, 2007 Life Safety: mean population at risk Mean # occupants determined from ATC-13 (1985).

21. PEER Annual MeetingJanuary 19, 2007 Building Characteristics Fatality Model Damage State (DM) For all construction types except light steel and wood frame. ATC-13 (1985) LC0.01 C0.20 Reinforced-concrete (non- near-field ground motions) Coburn et al. (1992) LC0.31 C0.49 Mid-rise concrete moment frame HAZUS 99- SR2 (2002) LC0.0001 C0.1 Mid-rise non-ductile reinforced-concrete frame Shoaf and Seligson (2005) LC0.015 C0.131 Life Safety: fatality probabilities

22. PEER Annual MeetingJanuary 19, 2007 Building Characteristics Fatality Model Damage State (DM)E[Y n |DM]Var[Y n |DM] For all construction types except light steel and wood frame. ATC-13 (1985) LC0.011.331.32 C0.2026.6821.34 Reinforced-concrete (non- near-field ground motions) Coburn et al. (1992) LC0.3141.3528.53 C0.4965.3733.2 Mid-rise concrete moment frame HAZUS 99- SR2 (2002) LC0.00010.01 C0.113.3412.01 Mid-rise non-ductile reinforced-concrete frame Shoaf and Seligson (2005) LC0.0152.001.97 C0.13117.4715.19 Life Safety: number of fatalities Use Binomial distribution to estimate mean and variance of fatalities.

23. PEER Annual MeetingJanuary 19, 2007 Design Description EANF (*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 annual number of fatalities

24. PEER Annual MeetingJanuary 19, 2007 Design Description EANF (*10 -3 ) EALF ($) A: Baseline perimeter frame design. 1.44,900 B: Same as A, but with code-min strengths. 1.34,550 C: Same A, but with uniform beam/column throughout. 1.65,600 D: Same as C, but no SCWB provision.22.879,800 E: Baseline space frame design.1.03,500 Life Safety: expected annual loss due to fatalities

25. PEER Annual MeetingJanuary 19, 2007 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.

26. PEER Annual MeetingJanuary 19, 2007 Baseline Perimeter-Frame Design Downtime: mobilization delay & repair time 10%-in-5yr DT ~ 4 months 2%-in-50yr DT ~ 17 months

27. PEER Annual MeetingJanuary 19, 2007 Design Description Down- time Type S a (T 1 ) EALD ($USD) 0.10.190.260.30.440.550.821.2 A: Baseline perimeter frame design. Total (days) 245211415728438851865520,519 B: Same as A, but with code- min strengths. Total (days) 288922123836342654363528,362 C: Same A, but with uniform beam/column throughout. Total (days) 26579412424533548564222,207 D: Same as C, but no SCWB provision. Total (days) 309422023938649172694232,726 E: Baseline space frame design. Total (days) 26428511921733257794919,517 Comerio (2006) Downtime: economic losses

28. PEER Annual MeetingJanuary 19, 2007 Comerio (2006) 16-32 months Downtime: economic losses Design Description Down- time Type S a (T 1 ) EALD ($USD) 0.10.190.260.30.440.550.821.2 A: Baseline perimeter frame design. Total (days) 245211415728438851865520,519 B: Same as A, but with code- min strengths. Total (days) 288922123836342654363528,362 C: Same A, but with uniform beam/column throughout. Total (days) 26579412424533548564222,207 D: Same as C, but no SCWB provision. Total (days) 309422023938649172694232,726 E: Baseline space frame design. Total (days) 26428511921733257794919,517

29. PEER Annual MeetingJanuary 19, 2007 Downtime: economic losses Design Description Down- time Type S a (T 1 ) EALD ($USD) 0.10.190.260.30.440.550.821.2 A: Baseline perimeter frame design. Total (days) 245211415728438851865520,519 B: Same as A, but with code- min strengths. Total (days) 288922123836342654363528,362 C: Same A, but with uniform beam/column throughout. Total (days) 26579412424533548564222,207 D: Same as C, but no SCWB provision. Total (days) 309422023938649172694232,726 E: Baseline space frame design. Total (days) 26428511921733257794919,517 28% increase in EALD for code-min design.

30. PEER Annual MeetingJanuary 19, 2007 Downtime: economic losses Design Description Down- time Type S a (T 1 ) EALD ($USD) 0.10.190.260.30.440.550.821.2 A: Baseline perimeter frame design. Total (days) 245211415728438851865520,519 B: Same as A, but with code- min strengths. Total (days) 288922123836342654363528,362 C: Same A, but with uniform beam/column throughout. Total (days) 26579412424533548564222,207 D: Same as C, but no SCWB provision. Total (days) 309422023938649172694232,726 E: Baseline space frame design. Total (days) 26428511921733257794919,517 47% increase in EALD for non-code-conforming design.

31. PEER Annual MeetingJanuary 19, 2007 Design Description EAL ($) EALD ($) EALF ($) EAL TOTAL ($) A: Baseline perimeter frame design. 66,58520,5194,90092,004 B: Same as A, but with code-min strengths. 95,65628,3624,550128,568 C: Same A, but with uniform beam/column throughout. 51,93322,2075,60079,740 D: Same as C, but no SCWB provision. 112,93032,72679,800225,456 E: Baseline space frame design. 49,42219,5173,50072,439 Summary of Results: “3 D” Losses

32. PEER Annual MeetingJanuary 19, 2007 Design Description EAL ($) EALD ($) EALF ($) EAL TOTAL ($) A: Baseline perimeter frame design. 66,58520,5194,90092,004 B: Same as A, but with code-min strengths. 95,65628,3624,550128,568 C: Same A, but with uniform beam/column throughout. 51,93322,2075,60079,740 D: Same as C, but no SCWB provision. 112,93032,72679,800225,456 E: Baseline space frame design. 49,42219,5173,50072,439 Summary of Results: “3 D” Losses

33. PEER Annual MeetingJanuary 19, 2007 Design Description EAL ($) EALD ($) EALF ($) EAL TOTAL ($) E[PVL(50yr)] ($M) A: Baseline perimeter frame design. 66,58520,5194,90092,0041.84 B: Same as A, but with code-min strengths. 95,65628,3624,550128,5682.50 C: Same A, but with uniform beam/column throughout. 51,93322,2075,60079,7401.64 D: Same as C, but no SCWB provision. 112,93032,72679,800225,4566.66 E: Baseline space frame design. 49,42219,5173,50072,4391.44 Summary of Results: “3 D” Losses

34. PEER Annual MeetingJanuary 19, 2007 Benefit-Cost Analysis A risk-neutral decision maker will choose the space-frame design!

35. PEER Annual MeetingJanuary 19, 2007 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).

36. PEER Annual MeetingJanuary 19, 2007 Thank You!