Seismic hazard analysis - Memphis...FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 5...

FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 1

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SEISMIC HAZARD ANALYSIS


Seismic Hazard Analysis• Deterministic procedures• Probabilistic procedures• USGS hazard maps• 2003 NEHRP Provisions design maps• Site amplification• NEHRP Provisions response spectrum• UBC response spectrum


Seismic hazard analysisdescribes the potential for dangerous,earthquake-related natural phenomenasuch as ground shaking, fault rupture,or soil liquefaction.

Seismic risk analysisassesses the probability of occurrence of losses(human, social, economic) associated withthe seismic hazards.

Hazard vs Risk


Approaches to Seismic Hazard Analysis

Deterministic“The earthquake hazard for the site is a peak groundacceleration of 0.35g resulting from an earthquakeof magnitude 6.0 on the Balcones Fault at a distance of12 miles from the site. ”

Probabilistic“The earthquake hazard for the site is a peak groundacceleration of 0.28g with a 2 percent probability of beingexceeded in a 50-year period.”


Probabilistic Seismic Hazard Analysis

First addressed in 1968 by C. Allin Cornell in“Engineering Seismic Risk Analysis,” and articlein the Bulletin of the Seismological Society(Vol. 58, No. 5, October).


F1 BalconesFault

AreaSource

SiteFixed distance R

Fixed magnitude M

“The earthquake hazard for the site is a peak ground acceleration of 0.35 g resulting from an earthquake of magnitude 6.0 on the Balcones Fault at a distance of 12 miles from the site. ”

Magnitude M

Distance

Peak

Acc

eler

atio

n

(2) Controlling Earthquake

Steps in Deterministic Seismic Hazard Analysis(1) Sources

(4) Hazard at Site(3) Ground Motion



Fault Fault

AreaSource

SiteFault

Localizing structure

Seismotectonicprovince

Source Types


Localizing structure: An identifiable geological structure that is assumed to generate or “localize”earthquakes. This is generally a concentration of known or unknown active faults.

Seismotectonic province: A region where there is a known seismic hazard but where there are no identifiable active faults or localizing structures.

Source Types


Maximum Earthquake

Maximum possible earthquake: An upper bound to size (however unlikely) determined by earthquake processes (e.g., maximum seismic moment).Maximum credible earthquake: The maximum reasonable earthquake size based on earthquake processes (but does not imply likely occurrence). Maximum historic earthquake: The maximum historic or instrumented earthquake that is often a lower bound on maximum possible or maximum credible earthquake.

Maximum considered earthquake: Described later.


Ground Motion Attenuation

Reasons:• Geometric spreading• Absorption (damping)

Magnitude M

Distance

Gro

und

Mot

ion

Par

amet

er


Attenuation with Distance


Comparison of Attenuation for Four Earthquakes



Ground Motion AttenuationSteps to Obtain Empirical Relationship

1. Obtain catalog of appropriate ground motion records

2. Correct for aftershocks, foreshocks

3. Correct for consistent magnitude measure

4. Fit data to empirical relationship of type:

εln)(ln),(ln)(ln)(lnˆln 43211 +++++= iPfRMfRfMfbY


Ground Motion AttenuationBasic Empirical Relationships

εln)(ln),(ln)(ln)(lnˆln 43211 +++++= iPfRMfRfMfbY

1b

)(1 Mf

)(2 Rf

),(3 RMf

)(4 iPfε

Scaling factor

Function of magnitude

Function of distance

Function of magnitude and distance

Other variables

Error term

Y Ground motion parameter (e.g. PGA)


Ground Motion AttenuationRelationships for Different Conditions

• Central and eastern United States• Subduction zone earthquakes• Shallow crustal earthquakes• Near-source attenuation• Extensional tectonic regions• Many others

May be developed for any desired quantity (PGA, PGV, spectral response).


Ground Motion AttenuationRelationships

Seismological Research LettersVolume 68, Number 1January/February, 1997


Earthquake Catalog for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)


Earthquake Catalog for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)



Attenuation Relation for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)


)2())exp(ln()5.8()ln( 7654321 +++++−++= ruprup rCMCCrCMCMCCy

T C1 C2 C3 C4 C5 C6 C7

PGA -0.624 1.000 0.000 -2.100 1.296 0.250 0.0000.07 0.110 1.000 0.006 -2.128 1.296 0.250 -0.0820.1 0.275 1.000 0.006 -2.148 1.296 0.250 -0.0410.2 0.153 1.000 -0.004 -2.080 1.296 0.250 0.0000.3 -0.057 1.000 -0.017 -2.028 1.296 0.250 0.0000.4 -0.298 1.000 -0.028 -1.990 1.296 0.250 0.0000.5 -0.588 1.000 -0.040 -1.945 1.296 0.250 0.0000.75 -1.208 1.000 -0.050 -1.865 1.296 0.250 0.0001 -1.705 1.000 -0.055 -1.800 1.296 0.250 0.0001.5 -2.407 1.000 -0.065 -1.725 1.296 0.250 0.0002 -2.945 1.000 -0.070 -1.670 1.296 0.250 0.0003 -3.700 1.000 -0.080 -1.610 1.296 0.250 0.0004 -4.230 1.000 -0.100 -1.570 1.296 0.250 0.000


Table for Magnitude <= 6.5



0.001

0.01

0.1

1

1 10 100 1000

Distance, KM

Peak

Gro

und

Acc

eler

atio

n, G

45678

Magnitude


0.001

0.01

0.1

1

10

1 10 100 1000

Distance, KM

0.2

Sec.

Spe

ctra

l Acc

eler

atio

n, G

45678

0.001

0.01

0.1

1

10

1 10 100 1000

Distance, KM1.

0 Se

c. S

pect

ral A

ccel

erat

ion,

G

45678


Magnitude Magnitude

0.2 Second Acceleration 1.0 Second Acceleration


Source 1

Source 2Source 3

Site Source M D PGA(km) (g)

1 7.3 23.7 0.422 7.7 25.0 0.573 5.0 60.0 0.02

Example Deterministic Analysis (Kramer)

D1

D2D3

From attenuation relationshipClosest distanceMaximum on source


F1 BalconesFault

AreaSource

Site

M1

Distance

Peak

Acc

eler

atio

n

Steps in Probabilistic Seismic Hazard Analysis(1) Sources

(4) Probability of Exceedance(3) Ground Motion

Magnitude M

Log

# Q

uake

s > M

(2) Recurrence

M2M3

Uncertainty

Prob

abili

ty o

f Exc

eeda

nce

Ground Motion Parameter



0.0001

0.001

0.01

0.1

1

10

100

1000

0 2 4 6 8 10

Magnitude

Mea

n A

nnua

l Rat

e of

Exc

eeda

nce

Empirical Gutenberg-RichterRecurrence Relationship

bmam −=λlog

mλ = mean rate ofrecurrence(events/year)

a and b to be deter-mined from data

λ m

mλ/1 = return period


0.000001

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

0 2 4 6 8 10

Magnitude

Mea

n A

nnua

l Rat

e of

Exc

eeda

nce

UnboundedBounded

Bounded vs UnboundedRecurrence Relationship


Uncertainties Included inProbabilistic Analysis

Attenuation laws Recurrence relationship

Distance to site

][][],*[1 1 1

* kjkj

N

i

N

j

N

kiy rRPmMPrmyYPv

S M R

==>=∑∑∑= = =

λ


Source 1

Source 2Source 3

Site

D1=?D2=?D3

Source 1

Source 2

Source 3

Site

Example Probabilistic Analysis (Kramer)

M2=?

M3=?

M1=?A1=?

A3=?

A2=?


Source 1

Source 2Source 3

Site

0.0 0.2 0.4 0.6 0.8

10-6

10-4

10-2

10-0

10-7

10-5

10-3

10-1

10-1

10-8

Peak Horizontal Acceleration (g)Mea

n An

nual

Rat

e of

Exc

eeda

nce

Source 1

Source 2

Source 3

All Source Zones

SEISMIC HAZARD CURVE

Result of Probabilistic Hazard Analysis


1

10

100

1000

10000

0 20 40 60 80 100

Period of Interest (years)

Ret

urn

Perio

d (y

ears

)

2%10%20%30%40%50%

2475

474

50

Relationship Between Return Period, Period of Interest,and Probability of Exceedance

Return period = -T/ln(1-P(Z>z))



0.0 0.2 0.4 0.6 0.8

10-6

10-4

10-2

10-0

10-7

10-5

10-3

10-1

10-1

10-8

Peak Horizontal Acceleration (g)

Mea

n An

nual

Rat

e of

Exc

eeda

nce SEISMIC HAZARD CURVE

PGA=0.33g

10% probability in 50 yearsReturn period = 475 yearsRate of exceedance = 1/475=0.0021

Use of PGA Seismic Hazard Curve

Period, T (sec)

Acc

eler

atio

n, g

0.0 0.5 1.0 1.5

0.2

0.4

0.6

0.810% in 50 yearelastic responsespectrum


0.0 0.2 0.4 0.6 0.8

10-6

10-4

10-2

10-0

10-7

10-5

10-3

10-1

10-1

10-8

0.2 Sec Spectral Acceleration (g)

Mea

n An

nual

Rat

e of

Exc

eeda

nce SEISMIC HAZARD CURVE

PGA = 0.55g

10% probability in 50 yearsReturn period = 475 yearsrate of exceedance = 1/475=0.0021

Use of 0.2 Sec. Seismic Hazard Curve

Period, T (sec)

Acc

eler

atio

n, g

0.0 0.5 1.0 1.5

0.2

0.4

0.6

0.8

10% in 50 yearElastic ResponseSpectrum


Period, T (sec)

Acc

eler

atio

n, g

0.0 0.5 1.0 1.5

0.2

0.4

0.6

0.8

10% in 50 Year ElasticResponse Spectrum


Uniform Hazard Spectrum

Large distantearthquake

Small nearbyearthquake

Uniform hazard spectrum

Period

Response


Uniform Hazard Spectrum

All ordinates have equal probability of exceedance

Developed from probabilistic analysis

Represents contributions from small local,large distant earthquakes

May be overly conservative for modal responsespectrum analysis

May not be appropriate for artificial ground motiongeneration


Probabilistic vs DeterministicSeismic Hazard Analysis

“The deterministic approach provides a clear andtrackable method of computing seismic hazard whoseassumptions are easily discerned. It providesunderstandable scenarios that can be related to theproblem at hand.”

“However, it has no way for accounting for uncertainty.Conclusions based on deterministic analysis can easilybe upset by the occurrence of new earthquakes.”



Probabilistic vs DeterministicSeismic Hazard Analysis

“The probabilistic approach is capable of integratinga wide range of information and uncertainties intoa flexible framework.”

“Unfortunately, its highly integrated framework canobscure those elements which drive the results, and itshighly quantitative nature can lead to false impressionsof accuracy.”


USGS Probabilistic Hazard Maps (Project 97)

0.0

0.5

1.0

1.5

2.0

2.5

0 0.5 1 1.5 2 2.5

Period (sec)

Spec

tral

Res

pons

e A

ccel

erat

ion

(g)

2% in 50 years 10% in 50 years

HAZARD MAP RESPONSE SPECTRA


USGS Probabilistic Hazard Maps(and NEHRP Provisions Maps)

Earthquake Spectra, Seismic Design Provisions andGuidelines Theme Issue, Volume 16, Number 1,February 2000


Maximum Considered Earthquake (MCE)

The MCE ground motions are defined asthe maximum level of earthquake shakingthat is considered as reasonable to designnormal structures to resist.


USGS Seismic Hazard Regions

Note: Different attenuation relationships used for different regions.


USGS Seismic Hazard WUS Faults



USGS Seismic Hazard Curves for Various Cities


Uniform Hazard Spectra for San Francisco

0.0

0.5

1.0

1.5

2.0

2.5

0 0.5 1 1.5 2 2.5

Period (sec)

Spec

tral

Res

pons

e A

ccel

erat

ion

(g)



Uniform Hazard Spectra for Charleston, SC

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 0.5 1 1.5 2 2.5

Period (sec)

Spec

tral

Res

pons

e A

ccel

erat

ion

(g)



USGS Seismic Hazard Map of Coterminous United States

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




USGS Seismic Hazard Map for Coterminous United States



USGS Map for Central and Eastern United States






USGS Map for Western United States







USGS Map for California






USGS Map for Pacific Northwest













USGS Website for Map Valueshttp://earthquake.usgs.gov/research/hazmaps/design/

The input zipcode is 80203. (DENVER)ZIP CODE 80203LOCATION 39.7310 Lat. -104.9815 Long.DISTANCE TO NEAREST GRID POINT 3.7898 kmsNEAREST GRID POINT 39.7 Lat. -105.0 Long.Probabilistic ground motion values, in %g, at the Nearest Grid

point are:

10%PE in 50 yr 5%PE in 50 yr 2%PE in 50 yrPGA 3.299764 5.207589 9.642159

0.2 sec SA 7.728900 11.917400 19.9215910.3 sec SA 6.178438 9.507714 16.1337111.0 sec SA 2.334019 3.601994 5.879917

CAUTION: USE OF ZIPCODES IS DISCOURAGED; LAT-LONG VALUES WILL GIVE ACCURATE RESULTS.


Relative PGAs for the United States


2000 NEHRP Recommended Provisions Maps

• 5% damped, 2% in 50 years, Site Class B (firm rock)

• 0.2 second and 1.0 second spectral ordinates provided

• On certain faults in California, Alaska, Hawaii, and CUSProvisions values are deterministic cap times 1.5. Outsidedeterministic areas, Provisions maps are the sameas the USGS maps.

• USGS longitude/latitude and zipcode values areprobabilistic MCE. To avoid confusion, ALWAYSuse Provisions (adopted by ASCE and IBC) maps for design purposes.



Location of Deterministic Areas


Deterministic Cap

Applies only where probabilistic values exceedhighest design values from old (Algermissen and Perkins)maps.

The deterministic procedure for mapping applies:• For known “active” faults• Uses characteristic largest earthquake on fault• Uses 150% of value from median attenuation

Use deterministic value if lower than 2% in 50 year value


NEHRP Provisions Maps0.2 Second Spectral Response (SS)


NEHRP Provisions Maps1.0 Second Spectral Response (S1)


0.00

0.20

0.40

0.60

0.80

1.00

0 1 2 3 4 5

Period, sec.

Spec

tral

Acc

eler

atio

n, g

.

2% in 50 Year 5% Damped MCE Elastic SpectraSite Class B (Firm Rock)

S1 = 0.30g

Ss = 0.75g

Curve is S1/T

PGANot mapped

Constantdisplacement region beyondtransition period TL


A

B

A

B

Time

Acc

eler

atio

n

Rock

Shale

Sand

Site Amplification Effects



Site Amplification Effects

• Amplification of ground motion

• Longer duration of motion

• Change in frequency content of motion

• Not the same as soil-structure interaction


Site Amplification (Seed et al.)


Site Amplification: Loma Prieta Earthquake

SoftRock


Site Amplification: Loma Prietaand Mexico City Earthquakes


A Hard rock vs > 5000 ft/sec

B Rock: 2500 < vs < 5000 ft/sec

C Very dense soil or soft rock: 1200 < vs < 2500 ft/sec

D Stiff soil : 600 < vs < 1200 ft/sec

E Vs < 600 ft/sec

F Site-specific requirements

NEHRP Provisions Site Classes


NEHRP Site Amplification for Site Classes A through E

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 0.25 0.50 0.75 1.00 1.25 1.50

Short Period Ss (sec)

Am

plifi

catio

n Fa

ABCDE

Site Class

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0.00 0.25 0.50 0.75 1.00 1.25 1.50

Long Period S1 (sec)

Am

plifi

catio

n Fv

ABCDE

Site Class



0.00

0.21

0.42

0.63

0.84

1.05

0 1 2 3 4 5

Period, sec.

Spec

tral

Acc

eler

atio

n, g

.

SMS = FASS = 1.2(0.75)=0.9g

SM1 = FVS1 = 1.8(0.30) = 0.54g

2% in 50 Year 5% Damped MCE Elastic SpectraModified for Site Class D

Basic

Site Amplified


Buildings designed according to current proceduresassumed to have margin of collapse of 1.5

Judgment of “lower bound” margin ofcollapse given by current design procedures

Design with current maps (2% in 50 year) butscale motions by 2/3

Results in 2/3 x 1.5 = 1.0 deterministic earthquake(where applicable)

Scaling of NEHRP Provisions Spectraby 2/3 for “Margin of Performance”


0.00

0.20

0.40

0.60

0.80

1.00

0 1 2 3 4 5

Period, sec.

Spec

tral

Ace

lera

tion,

g.

2% in 50 Year 5% Damped ElasticDesign Spectra (Scaled by 2/3)

SDS = (2/3)(0.90) = 0.60g

SD1 = (2/3)(0.54) = 0.36g

Basic

Site Amplified

Scaled


0.0

0.5

1.0

1.5

2.0

2.5

0 0.5 1 1.5 2 2.5

Period (sec)

Spec

tral

Res

pons

e A

ccel

erat

ion

(g)

2% in 50 years 10% in 50 years 2/3 of 2% in 50 years

Effect of Scaling in Western United States


0.0

0.5

1.0

1.5

2.0

2.5

0 0.5 1 1.5 2 2.5

Period (sec)

Spec

tral

Res

pons

e A

ccel

erat

ion

(g)

2% in 50 years 10% in 50 years 2/3 of 2% in 50 years

Effect of Scaling in Eastern United States


0.00

0.20

0.40

0.60

0.80

1.00

0 1 2 3 4 5

Period, sec.

Spec

tral

Acc

eler

atio

n, g

.

2% in 50 Year 5% DampedInelastic Design Spectra (R=6, I=1)

Site Class D

CS = SD1/R = 0.90/6 = 0.15g

CS = SDS/R = 0.36/6 = 0.06g

Basic

Site Amplified

Scaled

Inelastic



Basis for Reduction ofElastic Spectra by R

Inelastic behavior of structures

Methods for obtaining acceptable inelastic response are presentedin later topics


Directionality and “Killer Pulse” EarthquakesFor sites relatively close to the fault, thedirection of fault rupture can have an amplifyingeffect on ground motion amplitude.


Towards

Away

Effect of Directionality on Response Spectra


Effect of Directionality on Ground Motion

Seismic hazard analysis - Memphis...FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 5...

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