1. GEM Vulnerability: Uncertainty in Nonstructural Guidelines GVC team meeting Oakland CA 1 Aug 2012 K Porter & K Farokhnia | GEM Vulnerability Consortium

2. 2 topics to discuss today 1.We propose to treat uncertainty with 3 options that differ by how many index buildings represent the class. – They increase in effort and rigor, and presumably in accuracy. 2.Tests support the hypothesis that one can estimate total nonstructural repair cost for an index building by just considering the top 5 nonstructural components, and scaling up loss by their fraction of total nonstructural construction cost. – “Top 5” components contribute most to nonstructural construction cost – Needed to do just top 5 to limit the effort to what is practical in GEM context – Using the top 5 is new territory (research & application) hence the need for tests

3. Topic 1: Using one or more index buildings represent the class We will use index buildings to represent the class We will lump uncertainties into 2 groups: Within-building uncertainty (like ATC-58) Building-to-building variability

4. Using index buildings to estimate the coefficient of variation of damage factor We want seismic vulnerability functions that reflect mean and coefficient of variation of loss, conditioned on a building class and a level of seismic excitation In analytical methodologies, we always use index buildings (in one guise or another) to represent the class. Don’t know if there is another way other than index buildings. But an index building is not the class, and the performance of one index building is not the same thing as the performance of the class. Geometry (height, area, structural configuration, etc.) and material properties vary between specimens in the class, and we want our vulnerability function for the class to reflect that variability. How to reconcile? 3 options are considered here.

5. Option 4: propagate all ATC-58 uncertainties + building-to-building variability ATC-58 uncertainties (one index building) Ground-motion time history, component fragility, component repair costs For less engineering buildings, material uncertainties may matter let’s denote by σ 1bld Building-to-building feature variabilities Vertical & plan irregularity, number of stories, structural material properties and geometry variability (member sizes, etc.), redundancy, foundation type, pounding… let’s denote by σ b2b Schematically, combining them & assuming independence, Little or no scholarly work exists to support such an approach. Porter et al. (2001), Crowley et al. (date?), & maybe others have explicitly addressed the effect of some building-to- building variabilities on damage or loss, but a large research program is needed to understand their relative contribution to overall uncertainty. GVC is not that research program.

6. Option 3: use several index buildings that span the “top” uncertainties Like CEA Premium Incentives project, use several index buildings that span several quantifiable features with known distributions. Here, we use 7 index buildings that sample over the top 3 uncertainties using moment matching. (With 7 buildings we can only span the top 3 uncertainties with 3-point moment matching.) Do Monte Carlo simulation a la PEER methodology to explicitly capture uncertain behavior of an individual specimen. 3-point moment matching: replace the continuous joint distribution of n random variables with 2n + 1 weighted delta functions. The moments of a function of the continuous joint distribution are estimated using the moments of the weighted samples of the function evaluated at the delta functions

7. What are the “top 3” uncertainties? Very little precedent. CEA project assumed the available features with the important ones. ST-Risk and cat models address these modifiers for repair cost, but are unavailable. In the public domain, we are only aware of FEMA 154, which uses the HAZUS-MH conditional probability of collapse to quantify the effect of a feature. The score modifiers are log 10 factors—the ratio of collapse probability with the feature to the collapse probability without the feature. Top 3 structural attributes: design level, vertical irregularity, and height represent 75% of the possible log 10 multiplicative effect that major features have on probability of collapse (95% in real, not log 10, space). Component fragility may surpass these 3 in importance. So our recommended top 3: design level, vertical irregularity, and component fragility.

8. Option 2: Use 3 index buildings: “poor,” “typical,” and “superior” specimens Like CUREE-Caltech Woodframe Project. Specimens represent the analyst’s idea of the overall variation in vulnerability within the class. Say poor and superior are intended to represent the 10 th and 90 th percentiles of mean performance within the class. By 3-point moment matching, we can weight them w poor = w superior = 0.3, and median is weighted w typ = 0.4. Let’s denote their mean vulnerability functions as y(s). Let’s assume

9. Is sqrt(2) a reasonable factor? Consider ratio of COV from HAZUS to COV from CUREE-Caltech

10. Option 1: Use 1 index building with mean characteristics to represent mean behavior of the class Follow the examples of HAZUS-MH and CAPSS Soft Story study: use 1 index building with mean characteristics to represent the mean behavior of the class. (World Housing Encyclopeadia often offers 1 example building to represent a class.) Calculate mean damage factor (MDF) versus IM for the index building. That function represents the mean performance of the entire class. Then apply a class-level COV = 0.25*MDF -0.5. Here’s why: ATC-13 all types (unpublished; uses ATC-13 data) HAZUS-MH (Porter 2010) CUREE-Caltech Woodframe (Porter et al. 2006)

11. ESTIMATING THE NON-STRUCTURAL SEISMIC VULNERABILITY OF BUILDING CATEGORIES GVC Non-Structural Presentation Keith Porter, Karim Farokhnia University of Colorado at Boulder August 2012

12. Topic 2: tests of how well the top-5 (by cost) nonstructural components’ vulnerability reflects the total nonstructural vulnerability

13. Why top 5 components by construction cost & not top 5 by some measure of fragility or contribution to loss? (1)Contribution to repair cost varies by level of seismic excitation (figure) (2)A priori, contribution to loss is unknown (3)This method is simple to understand & seems to be practical in US and elsewhere (4)In a number of tests it seems to work

14. Proposed Methodology Step 1: Select index building and identify top non-structural components Step 2: Deriving component vulnerability functions Step 3: Deriving story-level nonstructural component vulnerability functions Step 4: Building-level non-structural components vulnerability function

15. Index Building Figure 2 & 3. William Village apartments at the University of Colorado at Boulder William Village apartments High-rise shear-wall reinforced concrete Located at the University of Colorado at Boulder 12 stories Approximately 6400 sq ft/story Reinforced concrete shear-wall system, Residential occupancy

16. Step 1: Select index building and identify top non-structural components Figure 4. RSMeans 2007, Building model M.030 RS Means model no. Rank order contribution to total construction cost Construction cost of top 5 components per sq. ft ($) Total non- structural construction cost ($) Fraction of total construction cost new Fraction of total non- structural constructi on cost 12345 M.030Exterior walls Elevators and lifts Partitions Plumbing fixtures Cooling generating system 66.48 119.46 0.420.56 Table 2. Non-structural rank order contribution to total construction cost, William Village

17. Step 2: Aggregating vulnerability functions for different damage states and different sizes or capacities of a non-structural component h Figure 5. Component vulnerability function for 100 linear feet of interior partition.

18. Step 3: Story-level nonstructural component vulnerability functions a) Component sensitive to peak transit drift;

19. b) Component sensitive to peak floor acceleration;

20. Step 4: Building-level non-structural components vulnerability function; Implications for drift by story & accel. By floor Total nonstructural repair cost:

21. sensitivity test: Effect of mode shape Building spec: 12-story, concrete shearwall, dormitory +/-13% difference High: Frame Low: Shearwall Moderate: Mixed

22. Validation and sensitivity test Min DFMax DF 7 Top Comp.0.180.19 Different Top Comp.0.190.2 Anchored/Isolated0.120.19

23. Second sample building: (Shiraz, Iran) 4 stories (Mid-rise), Approximately 2000 sq ft/story Reinforced concrete shear-wall system, Residential occupancy, Design era: 2011 Available info:  Architect., Structural & MEP drawings  Iran’s building construction cost manual meduim rise (4-7)M.020 Plumbing fixtures (m) Exterior walls (m2) Cooling generating system (unit) interior doors (unit) Elevators and lifts (unit) Energy supply (unit) Partitions (m3) Lighting & branch wiring (unit) Domestic water distributio n (m) Wall finishes (m2) Iran const. Cost Manual,cost/unit (Rials) 3500014550032530008558001200000003015560006120002810003160023600 cost per story (Rials) 18,480,00069,840,00026,024,00041,078,400120,000,000301,556,00047,001,6006,744,0008,342,40033,984,000 Rank83752141096

24. Second sample building: (Shiraz, Iran) Building vulnerability function comparison: