Ground Motions for Design

Nicolas Luco Research Structural Engineer

U.S. Department of the Interior Thailand Seismic Hazard Workshop U.S. Geological Survey January 18, 2007 Outline of Material

ƒ Derivation of "International" Building Code (IBC) Design Maps from USGS Hazard Maps

ƒ Use of IBC Design Maps (i.e., procedure)

ƒ Computer software for IBC Design Maps

ƒ Potential updates of IBC Design Maps Derivation of IBC Design Maps

ƒ The ground motions for design that are mapped in the IBC are based on, but not identical to, the USGS Probabilistic Seismic Hazard Analysis (PSHA) Maps for …

ƒ 2% in 50 years probability of exceedance

ƒ 0.2- and 1.0-second spectral acceleration (SA)

ƒ (Vs30=760m/s, i.e., boundary of Site Classes B/C) The design maps in the IBC are based on, but not identical to, the USGS PSHA Maps … The design maps in the IBC are based on, but not identical to, the USGS PSHA Maps … Derivation of IBC Design Maps

ƒ The ground motions for design that are mapped in the IBC are based on, but not identical to, the USGS Probabilistic Seismic Hazard Analysis (PSHA) Maps for …

ƒ 2% in 50 years probability of exceedance

ƒ 0.2- and 1.0-second spectral acceleration (SA)

ƒ The site-specific ground motion procedure in the building code explains the link between the two. Derivation of IBC Design Maps

ƒ "The probabilistic MCE [Maximum Considered Earthquake] spectral response accelerations shall be taken as the spectral response accelerations represented by a 5 percent damped acceleration response spectrum having a 2 percent probability of exceedance within a 50-yr. period." Derivation of IBC Design Maps

ƒ "The deterministic MCE response acceleration at each period shall be calculated as 150 percent of the largest median 5 percent damped spectral response acceleration computed at that period for characteristic earthquakes on all known active faults within the region." Derivation of IBC Design Maps

ƒ "…, the ordinates of the deterministic MCE ground motion response spectrum shall not be taken lower than the corresponding ordinates of the response spectrum determined in accordance with Fig. 21.2-1 [on the next slide],

where Fa and Fv are [the site coefficients], with the value of [the 0.2-second SA] taken as 1.5 and the value of [the 1.0-second SA] taken as 0.6."

ƒ 0.6g = 1.5 * 0.4g (from UBC), 1.5g = 2.5 * 0.6g Derivation of IBC Design Maps

ƒ Note: For the USGS Hazard Maps, Fa & Fv = 1 Derivation of IBC Design Maps

ƒ "The site-specific MCE spectral response acceleration at any period … shall be taken as the lesser of the spectral response accelerations from the probabilistic MCE … and the deterministic MCE." Near-Fault Criteria

Sa Probabilistic - 2% in 50 years

Plateau - 1.5 x UBC Design (0.6 or 1.5g)

Deterministic - 1.5 x Median

X

Fault

(Source: E.V. Leyendecker) Near-Fault MCE

Sa

Deterministic

Plateau - 1.5 x UBC Design (0.6 or 1.5g)

Probabilistic - 2% in 50 Years

X

Fault

(Source: E.V. Leyendecker)

Maximum Considered Earthquake (MCE) Ground Motion for 0.2-sec Spectral Acceleration

Reno, NV 1.54g

Salt Lake City, UT 1.76g

Memphis, TN 1.43g San Francisco, CA 1.50g

Charleston, SC 1.60g Design Maps vs. Hazard Maps (0.2s) Design Maps vs. Hazard Maps (0.2s)

San Francisco Bay Area New Madrid Seismic Zone Outline of Material

ƒ Derivation of "International" Building Code (IBC) Design Maps from USGS Hazard Maps

ƒ Use of IBC Design Maps (i.e., procedure)

ƒ Computer software for IBC Design Maps

ƒ Potential updates of IBC Design Maps

Use of IBC Design Maps

ƒ The Maximum Considered Earthquake (MCE) Ground Motion Maps in the IBC are in terms of …

Ss = "short-period" (0.2-second) spectral acceleration

S1 = 1.0-second spectral acceleration

ƒ Ground motions for other periods, and hence other buildings, are derived from these two spectral accelerations (as explained later) Use of IBC Design Maps

ƒ The Ss and S1 values from the MCE ground motion maps are modified by "site coefficients"

Fa and Fv that account for site class (soil or rock condition) amplification or deamplification, i.e., …

SMS = Fa x Ss and SM1 = Fv x S1

where Fa and Fv vary with Ss and S1, i.e., … Use of IBC Design Maps Reference Site Class = B (or B-C) Reference Use of IBC Design Maps

Site Coefficients Site Coefficients 4 4 A A B B 3.5 3.5 C C D D 3 E 3 E

2.5 2.5 a v F F 2 2

1.5 1.5

1 1

0.5 0.5 0.2 0.4 0.6 0.8 1 1.2 0.1 0.2 0.3 0.4 0.5 S [g] S [g] s 1 Use of IBC Design Maps Default Site Class = D Default Site Use of IBC Design Maps

ƒ The "final" design ground motions, SDS and SD1, are simply 2/3rds of SMS and SM1, i.e., …

SDS = 2/3 x SMS and SD1 = 2/3 x SM1

ƒ Why 2/3rds? … Use of IBC Design Maps

ƒ Goal: Prevent building collapse under values of SA with 2% in 50 years probability of exceedance. ƒ Assumption: Buildings designed for SA=DGM actually have the capacity to prevent collapse at 1.5*DGM. ƒ Result: 1.5*DGM = 2%-in-50yrs SA Î DGM = 2/3 * (2%-in-50yrs SA) Use of IBC Design Maps

ƒ Design ground motions for other periods are found using an approximate Uniform-Hazard Response Spectrum (UHRS) shape, i.e., …

(Note: UHRS is a plot of, e.g., 2%-in-50yrs SA values versus the vibration periods T.) IBC Ground Motions for Design Use of IBC Design Maps

ƒ Design ground motions for other periods are found using an approximate Uniform-Hazard Response Spectrum (UHRS) shape, i.e., …

(Note: UHRS is a plot of, e.g., 2%-in-50yrs SA values versus the vibration periods T.)

ƒ Ss and S1 were deemed by code developers to be sufficient to delineate the short-to-moderate period portion of the UHRS Long-Period Transition Period, TL (sec) IBC Ground Motions for Design

ƒ TL is used to define the long-period part of the design response spectrum because USGS hazard maps are only produced for …

0 (PGA), 0.1, 0.2, 0.3, 0.5, 1.0, & 2.0-sec SA

ƒ The maximum period is 2.0 seconds because of the available attenuation relations IBC Ground Motions for Design

ƒ The Pacific Earthquake Engineering Research (PEER) Center project entitled "Next Generation Attenuation (NGA)" has recently developed attenuation relations for periods up to 10 seconds.

ƒ The difficulty in developing attenuation relations for long periods is that many of the available ground motion recordings are filtered at long periods when the raw data is processed IBC Ground Motions for Design

ƒ The TL maps were produced by building code developers via the following procedure:

ƒ A relationship between earthquake magnitude (M) and TL was established, based on seismic source theory, ground motion recordings, and simulations IBC Ground Motions for Design

ƒ The TL maps were produced by building code developers via the following procedure:

ƒ A relationship between earthquake magnitude (M) and TL was established, based on seismic source theory, ground motion recordings, and simulations

ƒ A map of modal M was constructed via deaggregation of the 2%-in-50yrs, 2.0-second hazard

ƒ See "Development of Seismic Ground-Motion Criteria for the ASCE 7 Standard" by C.B. Crouse et al. for details Outline of Material

ƒ Derivation of "International" Building Code (IBC) Design Maps from USGS Hazard Maps

ƒ Use of IBC Design Maps (i.e., procedure)

ƒ Computer software for IBC Design Maps

ƒ Potential updates of IBC Design Maps GROUND MOTION TOOL

http://earthquake.usgs.gov/ research/hazmaps/

SEISMIC DESIGN VALUES FOR BUILDINGS Ss and S1, Hazard Curves, Uniform Hazard Spectra, and Residential Design Category

(Source: E.V. Leyendecker) Review of IBC Seismic Design Maps

Outline of Material

ƒ Derivation of "International" Building Code (IBC) Design Maps from USGS Hazard Maps

ƒ Use of IBC Design Maps (i.e., procedure)

ƒ Computer software for IBC Design Maps

ƒ Potential updates of IBC Design Maps Development of IBC Design Maps

ƒ IBC Section 1613 on Earthquake Loads references “ASCE 7”

Æ references Æ

(ASCE = American Society of Civil Engineers) Development of IBC Design Maps

ƒ ASCE 7 is based on the “NEHRP Provisions”

Æ based on Æ

(NEHRP = National Earthquake Hazard Reduction Program) Development of IBC Design Maps

ƒ The NEHRP Provisions are prepared by the Building Seismic Safety Council (BSSC) with funding from FEMA (Federal Emergency Management Agency). Development of IBC Design Maps

ƒ In 1997: BSSC Seismic Design Procedures Group derived first MCE Ground Motion Maps from 1996 USGS Hazard Maps

ƒ In 2003: MCE Maps were updated to reflect 2002 USGS Maps

ƒ In 2007: BSSC Seismic Design Procedures Review Group is revisiting the methodology for deriving the MCE Maps ("Project '07") Update of IBC Design Maps

ƒ 2007 Update of USGS Hazard Maps

2008 2010 2012 Update of IBC Design Maps

ƒ "Project ‘007, License to Build"

ƒ C. Kircher (Chair) C.B. Crouse B. Ellingwood J. Hooper E.V. Leyendecker J. Kimball N. Luco (Task 1 Leader) R. Hamburger A. Whittaker (Task 2 Leader) W. Holmes J. Harris (Task 3 Leader) Update of IBC Design Maps

ƒ Task 1: Consider "risk-targeted" instead of uniform-hazard basis for maps of ground motions for design

ƒ Task 2: Consider using maximum instead of geometric mean of two horizontal components for deterministic MCE ground motions

ƒ Task 3: Consider alternative ways to define the shape of the design response spectrum Update of IBC Design Maps (Task 1)

ƒ What is the probability of collapse (e.g., in 50 years) for buildings designed using the current design ground motions? Quantifying Risk of Collapse

“Risk Integral” (total probability theorem app.) ∞ dH (a) P = P (a) da f ∫ f 0 da where

Pf = probability of “failure” (e.g., collapse) = Risk

Pf (a) = conditional (on a) prob. of failure = Fragility H(a) = prob. of exceeding ground motion a = Hazard ( dH(a)/da = prob. (density) of equaling g.m. a ) Example: "San Francisco vs. Memphis"

Memphis Metro Area 1.5DGM = 1.4g San Francisco Bay Area 1.5DGM = 1.5g ReviewExample: of IBC Seismic Hazard CurvesDesign Maps

Example Hazard Curves, H(a)

0 10

-2 10

2% in 50 yrs

-4 10

-6 10

-8 10 San Francisco Mean Annual Frequency of Exceedance of AnnualMean Frequency Memphis 1.5*DGM = g g -10 1.4 1.5 10 -2 -1 0 1 10 10 10 10 Spectral Acceleration (0.2 sec) [g] Quantifying Fragility, Pf (a)

ƒ From 1998 NEHRP Provisions Commentary …

“The collective opinion of the SDPG was that the seismic margin contained in the 1997 NEHRP Provisions provides, as a minimum, a margin of about 1.5 times the design earthquake ground motions. In other words, if a structure is subjected to a ground motion 1.5 times the design level, the structure should have a low likelihood of collapse. The SDPG recognized that quantification of this margin is dependent on the type of structure, detailing requirements, etc., but the 1.5 factor was considered a conservative judgment appropriate for structures designed in accordance with the 1997 NEHRP Provisions. This seismic margin estimate is supported by Kennedy et al. (1994), Cornell (1994), and Ellingwood (1994), who evaluated structural design margins and reached similar conclusions.”

ƒ Corresponding assumption (ref. ATC-63):

Pf (a = 1.5 DGM ) = 10% Quantifying Fragility, Pf (a)

ƒ Time-honored lognormality assumption: ⎡ln a − (ln1.5 DGM + 1.28 )⎤ Pf (a) = Φ⎢ ⎥ ⎣ β β ⎦

where β = variability/uncertainty of ground motion value that induces failure

ƒ Assumption (again, ref. ATC-63): β = 0.8 Example Fragilities, Pf (a)

1 San Francisco 1.5*DGM = 1.4g 1.5g 0.9 Memphis (a) f 0.8 (β = 0.8) 0.7

0.6

ility of Failure, P Failure, of ility 0.5

0.4

0.3

0.2 10%

Conditional Probab 0.1

0 -2 -1 0 1 10 10 10 10 Spectral Acceleration (0.2 sec), a [g] MCE-Based Design Ground Motions 0 10 ∞ 2% in 50 yrs dH(a) -5 10 Pf = Pf (a) da Hazard ∫ da 0 1.5*DGM = g g -10 1.4 1.5 10 -2 -1 0 1 10 10 10 10

1 San Francisco Memphis ( β = 0.8 )

0.5

Fragility 10% 0 -2 -1 0 1 10 10 10 10

-4 x 10 3 P = 1.2% in 50 yrs f

2 P = 0.7% in 50 yrs f

Risk Integral 1

0 -2 -1 0 1 10 10 10 10 Spectral Acceleration (0.2 sec) [g] MCE-Based Design Ground Motions 0 10

2% in 50 yrs ∞ dP (a) a -5 f

10 d Pf = H(a) da Hazard ∫ da 0 1.5*DGM = g g ) -10 1.4 1.5 10 a -2 -1 0 1 ( 10 10 10 10 a d H 1 San Francisco d Memphis ( β = 0.01 ) ) 0.5 a ( Fragility f 10% P 0 -2 -1 0 1 10 10 10 10

-4 0 ∞ x 10 ∫ P = 2.0% in 50 yrs f 4

P = 2.0% in 50 yrs = f

2 f Risk Integral P 0 -2 -1 0 1 10 10 10 10 Spectral Acceleration (0.2 sec) [g] Risk (Pf ) at Additional Locations

2 Contra Costa County 1.8 Shelby County 1.6

1.4

1.2

1

0.8

0.6

0.4 Probability of Failure in 50 years (%) years 50 in Failure of Probability 0.2

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sorted & Normalized Grid Point #

(Assuming DGM = 2/3 * 2%-in-50yrs S.A.) Risk (Pf ) at Additional Locations

4.5 Contra Costa County 4 Shelby County

3.5

3

2.5

2

1.5

1

Probability of Failure in 50 years (%) years 50 in Failure of Probability 0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sorted & Normalized Grid Point #

(For DGM = 2/3 * MCE S.A.) Risk (Pf ) at Additional Locations

2

1.8

1.6 Los Angeles 1.4 Sacramento Salt Lake City 1.2 San Francisco Seattle 1 Boston 0.8 Charleston Chicago 0.6 Memphis 0.4 St. Louis Probability of Failure in 50 years (%) years 50 in Failure of Probability 0.2

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sorted & Normalized Grid Point #

(Assuming DGM = 2/3 * 2%-in-50yrs S.A.) Risk (Pf ) at Additional Locations

4.5

4

3.5 Los Angeles Sacramento 3 Salt Lake City San Francisco 2.5 Seattle 2 Boston Charleston 1.5 Chicago Memphis 1 St. Louis

Probability of Failure in 50 years (%) years 50 in Failure of Probability 0.5

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sorted & Normalized Grid Point #

(Assuming DGM = 10%-in-50yrs S.A.) Risk (Pf ) at Additional Locations

4.52

1.84

1.6 3.5 LosLos AngelesAngeles 1.4 SacramentoSacramento 3 SaltSalt LakeLake City 1.2 SanSan FranciscoFrancisco 2.5 SeattleSeattle 1 Boston 2 Boston 0.8 CharlestonCharleston 1.5 ChicagoChicago 0.6 MemphisMemphis 1 St. Louis 0.4 St. Louis Probability of Failure in 50 years (%) years 50 in Failure of Probability Probability of Failure in 50 years (%) years 50 in Failure of Probability 0.20.5

00 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 SortedSorted & & Normalized Normalized GridGrid Point Point # #

(Assuming DGM = 5%-in-50yrs S.A.) Question

ƒ What design ground motion (DGM) values would lead to uniform probability of collapse (e.g., in 50 years) across locations and spectral acceleration vibration periods? MCE-Based Design Ground Motions 0 10 ∞ 2% in 50 yrs dH(a) -5 10 Pf = Pf (a) da Hazard ∫ da 0 1.5*DGM = g g -10 1.4 1.5 10 -2 -1 0 1 10 10 10 10

1 San Francisco Memphis ( β = 0.8 )

0.5

Fragility 10% 0 -2 -1 0 1 10 10 10 10

-4 x 10 3 P = 1.2% in 50 yrs f

2 P = 0.7% in 50 yrs f

Risk Integral 1

0 -2 -1 0 1 10 10 10 10 Spectral Acceleration (0.2 sec) [g] Risk Integral Fragility Hazard 10 10 10 0.5 -10 -5 0 0 1 2 3 0 1 x 10 P P 10% f f -4 = 1.2% in 50yrs = 1.2% in 50yrs 10 10 10 -2 -2 -2 Memphis FranciscoSan MCE-Based Design Ground Motions Spectral Acceleration (0.2 sec) [ sec) (0.2 Acceleration Spectral 10 10 10 -1 -1 -1 1.5*DGM =

( β = 0.8 ) 0.8 = 1.0 g 10 10 10 0 0 0 g ] 1.5 g 10 10 10 1 1 1

∞ dH(a) P = P (a) da f ∫ f 0 da Risk-Targeted Design GMs

ƒ For Pf = 1.2% in 50yrs; vs. 2/3 * 2%-in-50yrs DGM

1.3 Contra Costa County Shelby County 1.2

1.1

1

0.9

0.8 Ratio of Spectral Acclerations Spectral Ratio of 0.7

0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sorted & Normalized Grid Point # Risk-Targeted Design GMs

ƒ For Pf = 1.0% in 50yrs; vs. 2/3 * 2%-in-50yrs DGM

1.3

1.2

Los Angeles 1.1 Sacramento Salt Lake City 1 San Francisco Seattle Boston 0.9 Charleston Chicago 0.8 Memphis St. Louis Ratio of Spectral Acclerations Spectral Ratio of 0.7

0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sorted & Normalized Grid Point # Risk-Targeted Design GMs

ƒ Resulting risk ( Pf ) …

2

1.8

1.6 Los Angeles 1.4 Sacramento Salt Lake City 1.2 San Francisco

1 Seattle Boston 0.8 Charleston Chicago 0.6 Memphis 0.4 St. Louis

Probability of Failure in 50 years (%) years 50 in Failure of Probability 0.2

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sorted & Normalized Grid Point # Simplification ala ASCE 43-05?

(ASCE 43-05 = Standard for Seismic Design Criteria for Structures, Systems, and Components in Nuclear Facilities) ƒ GM Hazard Return Period = 10,000yrs ƒ "Design Factor" (applied to UHRS):

0.8 DF = max{ 1.0, 0.6AR }

where AR = 1 / (log hazard curve slope, k) ƒ Recently adopted in NRC Draft Regulatory Guide 1146 (A Performance-Based Approach to Define the Site-Specific Earthquake Ground Motion) Simplification ala ASCE 43-05?

ƒ Re-calibrate DF for building codes? ƒ Regional k-values, e.g., from FEMA 350 …

ƒ Allow for site-specific evaluation Update of IBC Design Maps (Task 1)

ƒ Current 2/3 * 2%-in-50yrs DGMs … ƒ do not result in uniform risk (probability of collapse, e.g., in 50 years) ƒ result in risks that are closer to uniform than 10%-in-50yrs DGMs ƒ Risk-targeted DGMs can be defined via … ƒ maps of "design factors" to apply to uniform- hazard maps that account for hazard curve shapes ƒ return period(s), and potentially factor(s), that result in somewhat uniform risk Update of IBC Design Maps (Task 2)

ƒ The spectral accelerations from the attenuation relations used for both probabilistic and deterministic MCE ground motions are geometric means of the SA's for the two orthogonal horizontal components, i.e., … SAY

Geomean(SA) = SAX ⋅ SAY SA ln SA + ln SA X = exp( X Y ) 2 = exp( Mean(ln SA) ) Update of IBC Design Maps (Task 2)

ƒ Particularly near-fault (where the deterministic MCE governs), the maximum SA across the two horizontal components can be substantially larger than the geometric mean, i.e., …

Max(SA) >> Geomean(SA)

ƒ The use of the maximum SA for the deterministic MCE ground motions is under consideration by Project '07. Update of IBC Design Maps (Task 2)

Max(SA) ÷ Geomean(SA)

7

6 ave _ 5

4

3

2

1 Max demand/GMRotI50

0 012345 Period (sec) Update of IBC Design Maps (Task 3)

ƒ Recall that the Design Response Spectrum is defined by Ss, S1, and TL.

Ss

S1 Update of IBC Design Maps (Task 3)

ƒ Project '07 is considering alternative definitions of the design response spectrum, e.g., …

ƒ Use of PGA, 0.3-second, or 0.1-second instead of 0.2- second SA.

ƒ Use of more periods to better define the shape of the design response spectrum.

ƒ A separate response spectrum for elastic modal response analysis and/or the selection and scaling of ground motion recordings is also being considered. Other Potential Updates

ƒ The BSSC Provisions Update Committee (PUC) Technical Subcommittee on Ground Motions is considering the following:

ƒ Vertical ground motions

ƒ Changes to the Site Class Coefficients Outline of Material

ƒ Derivation of "International" Building Code (IBC) Design Maps from USGS Hazard Maps

ƒ Use of IBC Design Maps (i.e., procedure)

ƒ Computer software for IBC Design Maps

ƒ Potential updates of IBC Design Maps