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U.S. Department of the InteriorU.S. Geological Survey
Risk-Targeted Ground Motions
Nicolas Luco (on behalf of SDPRG)Research Structural EngineerUSGS National Seismic Hazard Mapping Project
BSSC Annual Meeting & SDRPG WorkshopSeptember 10, 2009
Outline of Presentation
1.
Reminder of basis for current seismic design maps in 2003 NEHRP Provisions
2.
Explanation of basis for proposed "risk- targeted" adjustments and resulting maps
3.
Demonstration of preliminary risk-targeted adjustments for conterminous U.S.
Development of seismic design maps is explained in Chapter 21 of ASCE 7-05 (Site-Specific Ground Motion Procedures):
“The site-specific MCE [Maximum Considered Earthquake] spectral response acceleration at any period, SaM , shall be taken as the lesser of the spectral response accelerations from the probabilistic MCE of Section 21.2.1 and the deterministic MCE of Section 21.2.2.”
Focus herein is on proposed adjustments to probabilistic MCE ground motions
Current Seismic Design Maps
Current Probabilistic MCE Maps
Current probabilistic MCE ground motions have a 2% probability of being exceeding in 50 years (i.e., they are of �“uniform-hazard�”)
But as recognized in ATC 3-06 (1978), �…
"It really is the probability of structural failure with resultant casualties that is of concern, and the geographical distribution of that probability is not necessarily the same as the distribution of the probability of exceeding some ground motion"
*
Current Probabilistic MCE Maps
In other words, �…
Designing for uniform-hazard (e.g., 2% in 50 years) ground motions does not necessarily result in buildings with uniform probability of collapse in 50 years (i.e., �“uniform risk�”).
Proposed risk-targeted adjustments to uniform-hazard ground motions would result in expectation of uniform risk:
Collapse Risk Objective �–
1% in 50 years
*
Risk-Targeted vs. Uniform-Hazard
Why doesn�’t designing for uniform-hazard ground motions result in uniform risk?
It would IF the ground motion (spectral response acceleration) that a building can resist without collapsing – i.e., its collapse capacity – were simply equal to the mapped value at its location.
P [Collapse] = P [Collapse Capacity < GM Demand ] = P [MCE < GM Demand ]= P [GM Demand > MCE ]= 2% in 50 years
Risk-Targeted vs. Uniform-Hazard
Why doesn�’t designing for uniform-hazard ground motions result in uniform risk?
It would IF the ground motion (spectral response acceleration) that a building can resist without collapsing – i.e., its collapse capacity – were simply equal to the mapped value at its location.
A.
In reality, there is significant uncertainty in the collapse capacity.
B.
There are geographic differences in the shape of hazard curves from which uniform-
hazard ground motions are read.
Quantifying Risk of Collapse
�“Risk Integral�”
(e.g., ATC 3-06, ASCE 43-05)
where
P[Collapse] = annual prob. of collapse Risk
fCapacity (c) = collapse capacity PDF
P[SA>c] = annual prob. SA demand > c
0
d][)(][ ccSAPcfCollapseP Capacity
Capacity(or Fragility)
Hazard(Demand)*
A. Generic Collapse Capacity
Based on nonlinear response history analysis by the ATC-63 Project and others �…
Log. Std. Deviation of Collapse Capacity
0.8
10th-%ile Collapse Capacity c10%
MCE (T1
)
The latter is consistent with performance ex-pectation expressed in NEHRP Provisions.“If a structure experiences a level of ground motion 1.5 times the design level [i.e., the MCE level], the structure should have a low likelihood of collapse” (p. 320 of 2003 Provisions Commentary)
*
A. Generic Collapse Capacity
10-2
10-1
100
101
0
0.05
0.1
0.15
0.2
0.25Pr
obab
ility
Den
sity
Func
tion
(PD
F)Collapse Capacity Probability Distribution
Collapse Capacity / MCE Ground Motion
*
B. WUS vs. CEUS Hazard Curves
0.0001
0.001
0.01
0.1
0.01 0.1 1 101-Second Spectral Acceleration (g)
Annu
al F
requ
ency
of E
xcee
danc
e
San Francisco (94101)Los Angeles (90012)Seattle (98101)Salt Lake City (84105)Memphis (38111)Charleston (29412)St. Louis (63104)New York City (10034)Chicago (60604)
10% in 50 Years
2% in 50 Years
Figure 4. Hazard Curves for Selected United States Cities and Zip Codes - (USGS, 1996)
(Figure from C. Kircher)
Example: "San Francisco vs. Memphis"
Memphis Metro AreaMCE = 1.3g
San Francisco Bay AreaMCE = 1.4g
Review of IBC Seismic Design MapsExample: Hazard Curves
0
d][)(][ ccSAPcfCollapseP Capacity
10-2
10-1
100
101
10-10
10-5
100
P[SA
>c]
(in 1
yr)
2% in 50 yrs
MCE = 1.38g1.29g
Designing for Current MCE Ground Motions
10-2
10-1
100
101
0
0.05
0.1
0.15
0.2
f Capa
city
( c)
San Francisco LocationMemphis Location
10-2
10-1
100
101
0
1
2
3x 10
-4
Collapse Capacity, c [g]
P[SA
> c]
f Capa
city
( c)
P[Collapse] = 1.1% in 50yrsP[Collapse] = 0.7% in 50yrs
2% in 50yrs
1.38g1.29g
Risk-Targeted
Risk C
oefficient
*
0
d][
)(
][
cc
SAP
cf
Colla
pse
PCa
paci
ty
10-2
10-1
100
101
10-10
10-5
100
P[SA
>c]
(in 1
yr)
MCE = 1.44g1.04g
Designing for Risk-Targeted Ground Motions
10-2
10-1
100
101
0
0.1
0.2
0.3
f Capa
city
( c)
San Francisco LocationMemphis Location
10-2
10-1
100
101
0
1
2
3x 10
-4
Collapse Capacity, c [g]
P[SA
> c]
f Capa
city
( c)
P[Collapse] = 1.0% in 50yrsP[Collapse] = 1.0% in 50yrs
2% in 50yrs
1.38g1.29g
Risk-Targeted
Risk C
oefficient
1.44g1.04g
1.040.81
*
RTE
Map of Risk Coefficients
Risk Coefficient
0.55 -
0.65
0.65 -
0.75
0.75 -
0.85
0.85 -
0.95
0.95 -
1.05
1.05 -
1.15
1.15 -
1.25
1.25 -
1.35
1.35 -
1.45
1.45 -
1.55
1.55 -
1.65
FIGURE 22-22 RISK COEFFICIENT, 1.0 SEC. SPECTRAL RESPONSE PERIODFOR THE CONTERMINOUS UNITED STATES
*
Map of Risk Coefficients
125 W 120 W 115 W 110 W 105 W 100 W 95 W 90 W 85 W 80 W 75 W 70 W 65 W
25 N
30 N
35 N
40 N
45 N
50 N
Risk-Targeted (1% in 50yrs, = 0.8) Uniform-Hazard (2% in 50yrs) ; 0.2sec SA
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6
125 W 120 W 115 W 110 W 105 W 100 W 95 W 90 W 85 W 80 W 75 W 70 W 65 W
25 N
30 N
35 N
40 N
45 N
50 N
Risk-Targeted (1% in 50yrs, = 0.8) Uniform-Hazard (2% in 50yrs) ; 0.2sec SA
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6
Map of Risk Coefficients
< 0.85
125 W 120 W 115 W 110 W 105 W 100 W 95 W 90 W 85 W 80 W 75 W 70 W 65 W
25 N
30 N
35 N
40 N
45 N
50 N
Risk-Targeted (1% in 50yrs, = 0.8) Uniform-Hazard (2% in 50yrs) ; 0.2sec SA
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6
Map of Risk Coefficients
> 1.15
Notes on Risk Coefficients
Risk-targeted design ground motions (here for 1%-in-50yrs prob. of collapse) are normalized by uniform-hazard ground motions (here for 2% in 50yrs) merely as a matter of convenience.
Since same generic fragility is used everywhere, risk coefficients mainly reflect geographic differences in shape of hazard curves.
Resulting risk coefficients are generally 0.85-1.15, but as low as 0.7 near New Madrid and Charleston.
Summary
Designing for the uniform-hazard (probabilistic) ground motions on the current seismic design maps does not result in uniform risk.
Proposed risk-targeted adjustments do, by capturing (A) uncertainty in collapse capacity and (B) geographic differences in shape of hazard curves.
For a 1%-in-50-years risk (i.e., prob. of collapse) target, adjustments are generally 0.85-1.15, but as low as 0.7 near New Madrid and Charleston.
Questions?
Example Fragilities, Pf (a)
10-2 10-1 100 1010
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Spectral Acceleration (0.2 sec), a [g]
Con
ditio
nal P
roba
bilit
y of
Fai
lure
, P f (a
)
( = 0.8)
1.5*DGM = 1.5g1.4g
10%
San FranciscoMemphis
MCE
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