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