The use of risk in design:
ATC 58 performance assessment
procedure
Craig D. Comartin
Outline
Traditional code design procedures
Performance-based design
Risk analysis
Risk as a measure of performance
Performance assessment procedure
Example
Traditional code-based design
Building
Future earthquakes
Rock
Fault
Soil
Building
Site
SITE
RESPONSE
Motion can be
amplified by soil
conditions.
ATTENUATION
Seismic waves lengthen
and diminish in strength
as they travel away
from the epicenter.
Elastic structural model
Forces reduced from 500 yr. shaking
V
T
Are the elastic forces less than the component capacities ?
Yes: code requirement satisified
No:
make stronger
Performance based design
Building Damage States
Force
parameter
Immediate
occupancy
Life
safety
Collapse
prevention
Performance Levels
Demand for specific hazard level
Displacement
parameter
Qualitative range of performance
Performance level
Collapse
Prevention
Demand for
specific hazard
level
Life Safety
Damage
Control
Immediate
Occupancy
Damage
Downtime
•• Severe structural damage
• Incipient Collapse
• Probable falling hazards
• Possible restricted egress
Probable
total loss
• Probable structural damage
• No Collapse
• No falling hazards
• Adequate emergency egress
Possible
total loss
• Slight structural damage
• Life safety attainable
• Essential systems repairable
• Moderate overall damage
2 to 3
weeks
•
•
•
••
Negligible structural damage
Life safety maintained
Essential systems operational
Minor overall damage
24
hours
Expected losses for an event
(HAZUS procedure)
Inelastic analysis results
slight
moderate
extensive
complete
Earthquake force
on building
Pushover curve
Global displacement
of building
Fragility relationships
Probability
Expected losses for event
•Casualties
•Repair/replacement costs
•Downtime
Displacement
Quantitative range of performance
Force parameter
Displacement
parameter
0
0.0
0
25%
0.0001
1
7
50%
0.001 0.01
30
180
100%
$, % replacement
0.25
Casualty rate
Downtime, days
What do we mean by performance?
Building
Future extreme event (e.g. earthquake)
Rock
Fault
Soil
Building
Site
SITE
RESPONSE
Motion can be
amplified by soil
conditions.
ATTENUATION
Seismic waves lengthen
and diminish in strength
as they travel away
from the epicenter.
What can happen?
Deaths (safety)
P
Dollars (damage)
Downtime (loss of use)
= RISK
Pacific Earthquake Engineering Research Center
PEER framing equation
Decision variable
• risk of losses
v(DV )= G DV DM | dG DM EDP | dG EDP IM | dl ( IM )
Damage measure
• casualties
• capital loss
• downtime
Engineering demand
parameter
• displacement
• drift
• etc
Intensity measure
• hazard curve
• level of shaking
DV
DM
EDP
IM
Performance assessment procedure
Determine the hazard.
Analyze the structure.
Characterize the damage.
Compute the loses.
DV
DM
EDP
IM
Example building description
Height:
3 stories; 14 ft. floor
to floor; 42 ft total
above grade; no
basement
Area:
22,736 sq.ft. per
floor; 68,208 sq.ft.
total (actual building
slightly larger)
Occupancy:
General office space
(B2)
The example application uses the building shown above as a prototype. This building is located
in Berkeley, California, near the campus of the University of California. It is repres entative of
modern Class A office space in the Great er Bay Area of California. Construction was completed
in 2004. Some of the features of the actual building were modified and simplified for application
in this example.
Site-specific hazard curve
IM
Equal hazard spectra
IM
Deaggregation of hazard
IM
Ground motion scaling
IM
Response Spectrum 10% in 50 years (SMRFX T1 = 1.139 sec)
4.5
Target (maxAg,SF)
LPlgpc (0.51g,0.79)
LPsrtg (0.46g,1.28)
LPcor (0.81g,1.67)
LPgav (1.11g,3.79)
LPgilb (0.66g,2.35)
LPlex1 (0.21g,0.47)
KBkobj (0.42g,0.49)
TOhino (0.59g,0.56)
EZerzi (0.59g,1.23)
4
3.5
Sa-FN (g)
3
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
Period (sec)
2.5
3
3.5
4
Structural analysis
EDP
Nonlinear model
Multiple response history analyses
Sets of demands for 10 individual
records
Statistically generated sets of correlated
demands for 200 realizations
Sets of demands
EDP
10%/50yrs
Du1-2 max
(%)
Du2-3 max
(%)
Du3-R max
(%)
a1 max (g)
a2 max (g)
a3 max (g)
aRmax (g)
GM 1
1.26
1.45
1.71
0.54
0.87
0.88
0.65
GM 2
1.41
2.05
2.43
0.55
0.87
0.77
0.78
GM 3
1.37
1.96
2.63
0.75
1.04
0.89
0.81
GM 4
0.97
1.87
2.74
0.55
0.92
1.12
0.75
GM 5
0.94
1.80
2.02
0.40
0.77
0.74
0.64
GM 6
1.73
2.55
2.46
0.45
0.57
0.45
0.59
GM 7
1.05
2.15
2.26
0.38
0.59
0.49
0.52
GM 8
1.40
1.67
2.10
0.73
1.50
1.34
0.83
GM 9
1.59
1.76
2.01
0.59
0.94
0.81
0.72
GM 10
0.83
1.68
2.25
0.53
1.00
0.90
0.74
Performance groups
Name
Location
EDP
SH12
between levels 1 and 2
d1-2
SH23
between levels 2 and 3
d2-3
SH3R
between levels 3 and R
d3-R
EXTD12
between levels 1 and 2
d1-2
EXTD23
between levels 2 and 3
d2-3
EXTD3R
between levels 3 and R
d3-R
INTD12
between levels 1 and 2
d1-2
INTD23
between levels 2 and 3
d1-2
INTD3R
between levels 3 and R
d3-R
INTA2
below level 2
a1
INTA3
below level 3
a2
INTAR
below level R
a3
CONT1
at level 1
a1
CONT2
at level 2
a2
CONT3
at level 3
a3
EQUIPR
at level R
aR
Components
Structural lateral: lateral load
resisting system; damage oriented
fragility (direct loss calculations)
Exterior enclosure: panels, glass,
etc.
Interior nonstructural drift
sensitive: partitions, doors,
glazing,etc
Interior nonstructural acceleration
sensitive: ceilings, lights, sprinkler
heads, etc
Contents: General office on first and
second floor, computer center on third
Equipment on roof
DM
Fragilities
DM
P ( DS  DSi )
1.0
None
Complete
0.5
DS1
DS2
DS3
DSj
EDP1
EDP 2
EDP 3
EDP j
0
EDP
 1
 EDP
P ( DS  DSi EDP ) =  
ln 

 DSi  EDPDSi




Consequence function for repair costs
Unit Cost, $
Uncertainty
Ci
Qi
Quantity
DM
BASIC COMPOSITION
No of square feet of flexurally controlled RC
concrete shear walls in each direction
DESCRIPTION
DM
DAMAGES STATES
DS1
Flexural cracks < 3/16"
Shear (diagonal) cracks < 1/16"
No significant spalling
No fracture or buckling of r/f
Not structurally significant
DS2
Flexural cracks > 1/4"
Shear (diagonal) cracks > 1/8"
Moderate spalling/ loose cover
No fracture or buckling of r/f
Insignificant residual drift/shortening
Repairable in place
DS3
Max. crack widths >3/8"
Significant spalling/ loose cover
Fracture or buckling some r/f
Significant residual drift/shortening
Repair in place impractical
ILLUSTRATION
(example photo or drawing)
MEDIAN EDP
(interstory drift)
1.5%
3.0%
5.0%
BETA
0.2
0.3
0.4
70%
CORRELATION (%)
REPAIR MEASURES
Patch cracks each side with caulk
Paint each side
Remove loose concrete
Patch spalls with NS grout
Patch cracks each side with caulk
Paint each side
Shore
Demo existing wall
Replace
Patch and paint
$4.00 per sq ft up to 800 sq ft
$2.00 per sq ft over 4000 sq ft
0.2
$10.00 per sq ft up to 800 sq ft
$5.00 per sq ft over to 4000 sq ft
0.3
$50.00 per sq ft up to 200 sq ft
$30.00 per sq ft over 2000 sq ft
0.3
CONSEQUENCE FUNCTION
Cost per sq ft of wall for repair
Max. cost up to lower quantity
Min cost over upper quantity
Beta (cost)
DV
Distribution of losses
P(Total Repair Cost <= $C)
1.0
0.9
0.8
0.7
95% in 50 yrs
90% in 50 yrs
75% in 50 yrs
50% in 50 yrs
10% in 50 yrs
5% in 50 yrs
0.6
0.5
0.4
0.3
0.2
0.1
00
0.5
1
1.5
2
2.5
$C (dollar)
3
3.5
4
x 106
DV
1
0.9
P(losses < DV | IM= 475 yr.)
0.8
0.7
0.6
0.5
Median loss
= $1.1M
0.4
0.3
0.2
0.1
0
0
1
2
3
4
DV (capital loss, $M)
5
6
DV
1
0.9
P(losses < DV | IM= 475 yr.)
0.8
0.7
0.6
0.5
0.4
Loss for 90%
confidence
$1.9M
0.3
0.2
0.1
0
0
1
2
3
4
5
DV (capital loss, $M)
6
DV
1
0.9
P(losses< DV | IM= 475 yr.)
0.8
0.7
60% Chance
that loss
exceeds $1M
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
DV (capital loss, $M)
6
DV
1
0.9
P(losses < DV | IM= 475 yr.)
0.8
0.7
80% chance
losses are
between $0.7M
and $1.9M
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
DV (capital loss, $M)
5
6
DV
Aggregated loss function
SMRFX - Sa (0.1395g ~ 0.8305g)
Annual rate of exceeding capital loss
0.25
0.2
0.15
0.1
0.05
0
0
0.5
1
1.5
2
2.5
Capital loss
3
3.5
4
x 106
DV
From hazard
To loss
SMRFX - Sa (0.1395g ~ 0.8305g)
Anual Rate of Exceeding Total Repair Cost = $C
0.25
0.2
0.15
0.1
0.05
0
0
0.5
1
1.5
2
$C (dollar)
2.5
3
3.5
4
6
x 10
Annualized loss
DV
Annual probability of
being exceeded
0.25
0.2
0.15
Area represents expected losses
per year (annualized loss)
0.1
0.05
0
0.5
1
1.5
2
2.5
3
3.5
4
Capital losses ($M)
Benefit of retrofit
DV
Annual probability of
being exceeded
0.25
0.2
0.15
Annualized loss before
retrofit= $100k
0.1
Annualized loss after
retrofit= $60k
0.05
0
0.5
1
1.5
2
2.5
3
3.5
4
Capital losses ($M)
Design decisions
DV
Exterior envelope
41%
Contents (3rd flr. computer center)
25%
Interior nonstructural (drift sensitive)
12%
Interior nonstructural (accel. sensitive)
8%
5%
Contents (Ist and 2nd flr. offices)
Structure
4%
Roof top equipment
4%
0%
5%
10%
15%
20%
25%
30%
35%
40%
Portion of annualized capital loss
45%