Transcript GEM Vulnerability: Uncertainty in Nonstructural Guidelines

GEM Vulnerability: Uncertainty
in Nonstructural Guidelines
GVC team meeting
Oakland CA 1 Aug 2012
K Porter & K Farokhnia | GEM Vulnerability Consortium
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
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
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.
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 σ1bld
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 σb2b
Schematically, combining them & assuming independence,
 class   b22b   12bld
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-tobuilding 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.
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
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 log10 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 log10 multiplicative effect that major features have on probability of
collapse (95% in real, not log10, space). Component fragility may surpass
these 3 in importance. So our recommended top 3: design level, vertical irregularity, and
component fragility.
Feature
Post-Benchmark
Vertical Irregularity
Pre-Code
High Rise (> 7 stories)
Plan Irregularity
Mid Rise (4 to 7 stories)
W1
2.4
-2.5
0.0
N/A
-0.5
N/A
W2
2.4
-2.0
-1.0
N/A
-0.5
N/A
S1
1.4
-1.0
-1.0
0.6
-0.5
0.2
S2
1.4
-1.5
-0.8
0.8
-0.5
0.4
S3
N/A
N/A
-0.6
N/A
-0.5
N/A
S4
1.6
-1.0
-0.8
0.8
-0.5
0.4
S5
N/A
-1.0
-0.2
0.8
-0.5
0.4
C1
1.4
-1.5
-1.2
0.6
-0.5
0.4
C2
2.4
-1.0
-1.0
0.8
-0.5
0.4
C3
N/A
-1.0
-0.2
0.3
-0.5
0.2
PC1
2.4
N/A
-0.8
N/A
-0.5
N/A
PC2
N/A
-1.0
-0.8
0.4
-0.5
0.2
RM1
2.8
-1.0
-1.0
N/A
-0.5
0.4
RM2
2.6
-1.0
-0.8
0.6
-0.5
0.4
URM |AVG| "CDF"
N/A
2.08
38%
-1.0
1.27
61%
-0.2
0.69
74%
N/A
0.63
85%
-0.5
0.50
94%
0.0
0.31 100%
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 10th and 90th percentiles of mean
performance within the class. By 3-point moment matching, we can weight them wpoor
= wsuperior = 0.3, and median is weighted wtyp = 0.4. Let’s denote their mean
vulnerability functions as y(s).
yclass  s   wpoor  y poor  s   wtyp  ytypical  s   wsuperior  ysuperior  s 
2
2
  w  y2  s   w  y2  s   w

poor
poor
typ
typical
superior  y superior  s    yclass  s 


COVb 2b  s  
2


yclass  s 


 0.35
Let’s assume
COVclass  s  
COV1bld  s   COVb 2b  s 
 COV  s     COV  s  
2
1bld
b 2b
2
 2  COVb 2b
Is sqrt(2) a reasonable factor? Consider ratio of COV from HAZUS to COV from CUREE-Caltech
3.0
COVtotal/COV1bld
Ratio of HAZUS-MH COV (for a building class) to
CUREE-Caltech COV (for an individual building
within a class), for the same MDF
2.0
1.0
sqrt(2), which would reflect uncertainty due to
building-to-building variability being equal to
within-building uncertainty
0.0
0.00
0.25
0.50
0.75
Mean damage factor
1.00
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:
4
3
2
y = 0.28x-0.25
R² = 0.75
1
0
0.00
0.05
0.10
0.15
Mean damage factor
ATC-13 all types
(unpublished; uses
ATC-13 data)
0.20
COV of damage factor
Coefficient of variation
COV of damage factor
5
5
5
4
3
-0.48
y = 0.24x
R2 = 0.85
2
1
0
0.00
4
3
Townhouse, poor
Townhouse, typical
Townhouse, superior
Townhouse, limited drift
Typical quality
y = 0.19x-0.33
R2 = 0.89
2
1
0
0.05
0.10
0.15
Mean damage factor
HAZUS-MH
(Porter 2010)
0.20
0.00
0.05
0.10
0.15
Mean damage factor
CUREE-Caltech Woodframe
(Porter et al. 2006)
ESTIMATING THE NON-STRUCTURAL SEISMIC
VULNERABILITY OF BUILDING CATEGORIES
GVC Non-Structural Presentation
Keith Porter, Karim Farokhnia
University of Colorado at Boulder
August 2012
Topic 2: tests of how well the top-5 (by cost) nonstructural components’
vulnerability reflects the total nonstructural vulnerability
Why top 5 components by construction cost & not top 5 by some measure
of fragility or contribution to loss?
Contribution to repair cost varies by level of seismic excitation (figure)
A priori, contribution to loss is unknown
This method is simple to understand & seems to be practical in US and elsewhere
In a number of tests it seems to work
1.00
0.75
Paint
Interior shearwall
Glazing
Drywall
Exterior shearwall
0.50
0.25
0.00
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
Fraction of total cost
(1)
(2)
(3)
(4)
Spectral acceleration, g
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
Index Building
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
Figure 2 & 3 . William Village apartments at the University of Colorado at
Boulder
Step 1: Select index building and identify top non-structural components
Figure 4. RSMeans 2007, Building model
M.030
Rank order contribution to total construction cost
RS Means
model no.
M.030
1
2
Exterior walls
Elevators and
lifts
3
Partitions
4
Plumbing
fixtures
5
Construction
Total non-
Fraction of
cost of top 5
structural
total
components per construction
construction
sq. ft ($)
cost ($)
cost new
66.48
119.46
0.42
Fraction of
total nonstructural
constructi
on cost
Cooling
generating
system
Table 2. Non-structural rank order contribution to total construction cost, William
Village
0.56
Step 2: Aggregating vulnerability functions for different damage states
and different sizes or capacities of a non-structural component h
𝑁𝑖
𝑁𝑑
𝐸 𝐶 𝑆 = 𝑠, 𝐻 = ℎ] =
𝑃 𝐷 = 𝑑𝑖 𝑆 = 𝑠] ∙ 𝐸 𝐶 𝐷𝑖 = 𝑑] ∙ 𝑊ℎ (𝑖)
(1)
𝑖=1 𝑑=1
𝑃 𝐷𝑖 = 𝑑 𝑆 = 𝑠] = 𝜑
𝑃 𝐷𝑖 = 𝑑 𝑆 = 𝑠] = 𝜑
ln
ln
𝑠
𝜃𝑖𝑑
𝛽𝑖𝑑
−𝜑
ln
𝑠
𝜃𝑖𝑑 +1
𝛽𝑖𝑑 +1
𝑠
𝜃𝑖𝑑
𝛽𝑖𝑑
𝑓𝑜𝑟 𝑑 < 𝑁𝑑
(2)
𝑓𝑜𝑟 𝑑 = 𝑁𝑑
(3)
Vulnerability Distribution Curves
Component category C1010, interior partitions, 13′x100′
35000
E[C|X=x]
30000
25000
DS1
20000
DS2
15000
DS3
10000
Sum
5000
0
-5000
0
0.05
0.1
0.15
0.2
PTD
Figure 5. Component vulnerability function for 100 linear feet of interior
partition.
0.25
Step 3: Story-level nonstructural component vulnerability functions
a) Component sensitive to peak transit drift;
E[𝐶𝑃𝑇𝐷,𝑛 | 𝑆𝑃𝑇𝐷 = 𝑠, 𝑀 = 𝑚] =
𝑁𝑁𝐻 ,𝑃𝑇𝐷
ℎ=1
𝐸 𝐶 | 𝑆𝑃𝑇𝐷 = 𝑠, 𝐻 = ℎ ∙ 𝑄 ℎ 𝑀 = 𝑚)
𝐹 𝑚
(4)
Story-level vulnerability of drift-sensitive components in M.030
300000
250000
E[C|X=x]
200000
150000
100000
50000
0
0
0.05
0.1
0.15
Peak transient drift ratio
0.2
0.25
b) Component sensitive to peak floor acceleration;
E[𝐶𝑃𝐹𝐴,𝑛 | 𝑆𝑃𝐹𝐴,𝑛 = 𝑠, 𝑀 = 𝑚] =
𝑁𝐻,𝑃𝐹𝐴
ℎ=1
𝐸 𝐶 | 𝑆𝑃𝐹𝐴,𝑛 = 𝑠, 𝐻 = ℎ ∙ 𝑄 ℎ 𝑀 = 𝑚)
𝐹 𝑚
(5)
Story-level vulnerability of acceleration-sensitive components in M.030
120000
100000
E[C|X=x]
80000
60000
40000
20000
0
0.00
0.20
0.40
0.60
0.80
1.00
1.20
Peak floor acceleration, g
1.40
1.60
1.80
2.00
Step 4: Building-level non-structural components vulnerability function;
Implications for drift by story & accel. By floor
Total nonstructural repair cost:
𝐸 𝐶 𝑀 = 𝑚 , 𝑋 = 𝑥]
𝑁𝑠 +1
𝑛
𝐸 𝐶𝑃𝑇𝐷,𝑛 𝑀 = 𝑚 , 𝑆𝑃𝑇𝐷,𝑛 = 𝜑𝑚
(𝑋)] + 𝐸 𝐶𝑃𝐹𝐴,𝑛 𝑀 = 𝑚 , 𝑆𝑃𝐹𝐴,𝑛
=
𝑛 =1
𝑁𝑠+𝑛
= 𝜑𝑚
(𝑋)]
(6)
0.50
GVC nonstructural
GVC nonstructural + HAZUS structural
0.40
Mean damage factor
ATC-13 RC/SW-MRF/HR
HAZUS C2H-m-RES3AF-DF
0.30
0.20
0.10
0.00
0.00
0.25
0.50
Sa(1.0 sec, 5%), g
0.75
1.00
sensitivity test: Effect of mode
shape
• Building spec:
12-story, concrete
shearwall, dormitory
•
•
•
•
+/-13% difference
High: Frame
Low: Shearwall
Moderate: Mixed
Validation and sensitivity test
Min DF
Max DF
7 Top Comp.
Different Top
Comp.
0.18
0.19
0.19
0.2
Anchored/Isolated
0.12
0.19
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
Cooling
Plumbing Exterior generating
meduim rise (4-7) M.020
fixtures (m) walls (m2) system
(unit)
Iran const. Cost
Manual,cost/unit
(Rials)
cost per story
(Rials)
Rank
35000
145500
3253000
interior
doors
(unit)
Lighting & Domestic
Elevators
Energy supply Partitions
branch
water Wall finishes
and lifts
(unit)
(m3)
wiring distributio
(m2)
(unit)
(unit)
n (m)
855800
120000000
301556000
612000
281000
31600
23600
18,480,000 69,840,000 26,024,000 41,078,400 120,000,000 301,556,000 47,001,600 6,744,000 8,342,400 33,984,000
8
3
7
5
2
1
4
10
9
6
Second sample building: (Shiraz, Iran)
Building vulnerability function comparison:
0.50
GVC nonstructural
GVC nonstructural + HAZUS structural
0.40
Mean damage factor
ATC-13 RC/SW-MRF/MR
HAZUS C3M-I-RES3AF-DF
0.30
0.20
0.10
0.00
0.00
0.25
0.50
Sa(1.0 sec, 5%), g
0.75
1.00