Download - Hazard Analysis
Seismic Hazard Analysis
Revised 2/28/04
Seismic Hazard Analysis• Deterministic Procedures• Probabilistic Procedures• USGS Hazard Mapping• ASCE 7 Hazard Mapping• Site Amplification• IBC/ASCE 7 Response Spectrum
Revised 2/28/04
Hazard Analysis 3
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
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Large earthquakes less frequent
How does CEUS and WUS Seismic Risk Compare?
Large earthquakes frequent vs.
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Example of inadequately reinforced, non-ductile structure – 1989 LP EQ:
Cypress Overpass
Following photo sequence from I. Idriss…
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This Type of Non-Ductile Infrastructure is Common in CEUS!
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WUS and CEUS Risk Comparison Summary:• CEUS has potential for recurring large EQs• Attenuation lower in CEUS• Abundance of weak, non-ductile structures in
CEUS; weakest not “weeded out”• Immature seismic practice in CEUS• “Human inertia” in CEUS; little awareness• Much more uncertainty in CEUS• Areas with poor soils in CEUS
• Bottom line ⇒ seismic risk in CEUS and WUS is comparable!
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• Good analogy⇒ Kobe is to Tokyo, as CEUS is to the WUS
• Kobe M6.9 (> $140 billion losses); costliest natural disaster in world history; infrastructure weak and old, poor soil conditions
• Remember⇒ before Katrina, most expensive US natural disaster (Northridge, EQ ∼$30 billion) was moderate EQ on minor fault on fringe of LA
• Since 1800: CA has had 11 EQ’s > M7.3, CEUS has had 4 EQ’s > M7.3.
Issues to Think About
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Approaches to Seismic Hazard Analysis
Deterministic“The earthquake hazard for the site is a peak groundacceleration of 0.35 g 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 0.28 g, with a 2 percent probability of beingexceeded in a 50 year period.”
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Probabilistic Seismic Hazard Analysis
C. Allin Cornell“Engineering Seismic Risk Analysis”Bulletin of the Seismological SocietyVol. 58, No. 5, October, 1968
Hazard Analysis 17
F1 BalconesFault
AreaSource
Site
“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. ”
Fixed Distance R
Fixed Magnitude M
Magnitude M
Distance
Peak
Acc
eler
atio
n
2) Controlling Earthquake
Steps in Deterministic Seismic Hazard Analysis1) Sources
4) Hazard at Site3) Ground Motion
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Fault Fault
AreaSource
SiteFault
Localizing Structure
SeismotectonicProvince
SOURCE TYPES
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Maximum EarthquakeMaximum Possible EarthquakeAn upper bound to size (however unlikely) determinedby earthquake processes (e.g. Maximum Seismic Moment)
Maximum Credible EarthquakeThe maximum reasonable earthquake size basedon earthquake processes (but does not imply likelyoccurrence.
Maximum Historic EarthquakeThe maximum historic or instrumented earthquake. Often is a lower bound on Maximum Possible or Maximum CredibleEarthquake
Maximum Considered Earthquake (Described later)
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Ground Motion Attenuation
Reasons:• Geometric Spreading• Absorption (Damping)
Magnitude M
Distance
Gro
und
Mot
ion
Para
met
er
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Attenuation with Distance
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Comparison of Attenuation for Four Earthquakes
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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
Hazard Analysis 24
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)
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Ground Motion AttenuationRelationships for Different Conditions
• Central and Eastern US• 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)
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Ground Motion AttenuationRelationships
Seismological Research LettersVolume 68, Number 1January/February, 1997
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Earthquake Catalog for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)
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PGA Attenuation – 1989 Loma Prieta EQ
soft soil sites
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Attenuation Relation for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)
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)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
Attenuation Relation for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)
Table for Magnitude <= 6.5
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Attenuation Relation for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)
0.001
0.01
0.1
1
1 10 100 1000
Distance, KM
Peak
Gro
und
Acc
eler
atio
n, G
45678
Magnitude
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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, KM
1.0
Sec.
Spe
ctra
l Acc
eler
atio
n, G
45678
Attenuation Relation for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)
Magnitude Magnitude
0.2 Second Acceleration 1.0 Second Acceleration
Hazard Analysis 33
Source 1
Source 2
Site
Source 3
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
D1
D2D3
Example Deterministic Analysis (Kramer)
From Attenuation RelationshipClosest DistanceMaximum on Source
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F1 BalconesFault
AreaSource
Site
M1
Distance
Peak
Acc
eler
atio
n
Steps in Probabilistic Seismic Hazard Analysis1) Sources
4) Probability of Exceedance3) Ground Motion
Magnitude M
Log
# Q
uake
s > M
2) Recurrence
M2M3
Uncertainty
Prob
abili
ty o
f Exc
eeda
nce
Ground Motion Parameter
Hazard Analysis 35
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
Hazard Analysis 36
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
Hazard Analysis 37
Poisson Distribution (for one event)
PE = 1 - e-λt
where λ = rate of exceedance (events/year) ⇐ key!!t = exposure interval (50 years typical)
1/λ = return period
Hazard Analysis 38
Common Probabilistic Design Levels
• (1) 10% PE in 50 years, a.k.a.“500-year motion*” (actually is 475-yr. event; rate is 1/475 or 0.0021 events/yr.).
• (2) 5% PE in 50 years, a.k.a. “1000-year motion” (actually is 975-yr. event; rate is 1/975 or events/year or 0.001 events/yr).
• (3) 2% PE in 50 years a.k.a. “2500-year earthquake” (actually is 2475-yr. event; rate is1/2,475 or 0.0004 events/yr).
_______*Does not mean EQ occurs once every 500 yrs., etc.!Rather, the EQ with chance of 1/500 of occurring in 1 year.
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0.0 0.4
10-6
10-4
10-2
10-7
10-5
10-3
10-1
10-8
0.2 0.6 0.8
10-0
10-1
Peak Horizontal Acceleration (g)M
ean
Ann
ual R
ate
of E
xcee
danc
e 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
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0.0 0.6
10-6
10-4
10-2
10-7
10-5
10-3
10-1
10-8
0.2 0.4 0.8
10-0
10-1
0.2 Sec Spectral Acceleration (g)M
ean
Ann
ual R
ate
of E
xcee
danc
e SEISMIC HAZARD CURVE
.2 Sec accn = 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
Hazard Analysis 41
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 Elastic Response Spectrum (UHS)
UHS is envelope of maximums
Each point on curve could be from a different earthquake sources
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Uniform Hazard Spectrum (UHS)
Large DistantEarthquake
Small NearbyEarthquake
Uniform Hazard Spectrum
Period
Response
Hazard Analysis 43
Uniform Hazard Spectrum (UHS)
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
Hazard Analysis 44
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”.
Hazard Analysis 45
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.
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U.S.G.S. 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
Hazard Analysis 47
U.S.G.S. PROBABILISTIC HAZARD MAPS(and NEHRP MAPS)
Earthquake SpectraTheme Issue : Seismic Design Provisions and GuidelinesVolume 16, Number 1February, 2000
Hazard Analysis 48
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.
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U.S.G.S. SEISMIC HAZARD REGIONS
Note: Different attenuation relationships used for different regions
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U.S.G.S. SEISMIC HAZARD SOURCE ZONES
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U.S.G.S. SEISMIC HAZARD WUS FAULTS
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USGS Seismic Hazard Curves for Various Cities
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Uniform Hazard Spectra for San Francisco, CA
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 Analysis 54
Uniform Hazard Spectra for Charleston, S.C.
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)
2% in 50 years 10% in 50 years
Hazard Analysis 55
http://eqhazmaps.usgs.gov/2002April03/US/USpga2500v4.gif
USGS SEISMIC HAZARD MAP (PGA)
2% in 50 years
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USGS SEISMIC HAZARD MAP OF US (0.2 sec)
2% in 50 years
Hazard Analysis 57
USGS SEISMIC HAZARD MAP OF US (1.0 sec)
2% in 50 years
Hazard Analysis 58
U.S.G.S. SEISMIC HAZARD MAP OF U.S.A. [PGA]
2% in 50 years
http://eqint.cr.usgs.gov/eq/html/zipcode.shtml
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U.S.G.S. SEISMIC HAZARD MAP OF U.S.A. [0.2 sec]
2% in 50 years
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U.S.G.S. SEISMIC HAZARD MAP OF U.S.A. [1.0 sec]
2% in 50 years
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U.S.G.S. SEISMIC HAZARD MAP ofSouthern California [PGA]
2% in 50 years
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U.S.G.S. SEISMIC HAZARD MAPof Southern California [0.2 sec]
2% in 50 years
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U.S.G.S. SEISMIC HAZARD MAPof Southern California [1.0 sec]
2% in 50 years
Hazard Analysis 64
http://eqint.cr.usgs.gov/eq/html/zipcode.htmlUSGS Web Site: Zip Code Lookup
Hazard Analysis 65
USGS Seismic Hazard Maps• Probabilistic analysis used for maps• Most recent published versions: April 2003• Hazard in some areas increased in new maps
relative to older-generation maps (i.e., 1996) • Maps developed for motions on B-C boundary
rock)• Maps developed for 2%, 5%, and 10% PE• Maps adopted by ASCE 7 and used as basis for
building code maps; USGS and ASCE 7 identical in all US areas other than CA and AK
• Maps do not account for regional geological effects such as deep sediment profiles
Hazard Analysis 66
Relative PGA’s in the USA key point to remember….
Hazard Analysis 67
Soil is the great equalizer:Many CEUS areas with poor soils
Hazard Analysis 68
ASCE 7-05 Seismic Hazard Maps5% 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, and Hawaii,ASCE 7 values are deterministic cap times 1.5. Outsideof deterministic areas, NEHRP maps are the sameas the USGS maps.
USGS Zip Code and Longitude/Latitude Values areProbabilistic MCE. To Avoid Confusion, ALWAYSUse ASCE-7 Maps for Design Purposes
Hazard Analysis 69
NEHRP Seismic Hazard Maps0.2 Second Spectral Response (SS)
Hazard Analysis 70
NEHRP Seismic Hazard Maps1.0 Second Spectral Response (S1)
Hazard Analysis 71
Deterministic CapApplies only where probabilistic values exceedhighest design values from old (Algermissen & Perkins)maps.
Deterministic Procedure for Mapping:applies for known “active” faultsuses characteristic largest earthquake on faultuses 150% of value from median attenuation
Use deterministic value if lower than 2% in 50 year value
Hazard Analysis 72
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
Hazard Analysis 73
A
B
A
B
Time
Acc
eler
atio
n
Rock
Shale
Sand
Site Amplification Effects
Hazard Analysis 74
Site Amplification Effects
• Amplification of Ground motion
• Longer Duration of Motion
• Change in Frequency Content of Motion
• Not the Same as Soil-Structure Interaction
Hazard Analysis 75
Site Amplification; Seed et al
Hazard Analysis 76
Site Amplification; Loma Prieta Earthquake
SoftRock
Hazard Analysis 77
Site Effects on Ground Motions
• Conservation of energy drives amplification
Hazard Analysis 78
Soft Soils Commonly Amplify Motions Relative To Bedrock
(1989 Loma Prieta EQ)
Hazard Analysis 79
Site Amplification; Loma Prieta& Mexico City Earthquakes
Hazard Analysis 80
Cypress Structure Collapse
Hazard Analysis 81
Hazard Analysis 82
Cypress Structure Collapse
Hazard Analysis 83
A Hard Rock vs > 5000 ft/sec
B Rock: 2500 < vs < 5000 ft/sec
C Very Dense Soil or Soft Rock: 1200 < vs < 5000 ft/sec
D Stiff Soil : 600 < vs < 1200 ft/sec
E Vs < 600 ft/sec
F Soft Clays or Liquefiable sands -- Site Specific Requirements
ASCE 7 SITE CLASSES (based on top 30 m)
Hazard Analysis 84
NEHRP/IBC– General Procedure• Determine Fa & Fv values from Ss, S1 and site class:
Hazard Analysis 85
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
Hazard Analysis 86
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
Hazard Analysis 87
Buildings designed according to current proceduresassumed to have margin of collapse of 1.5
Judgement 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 Spectra by 2/3for “Margin of Performance”
Hazard Analysis 88
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
Hazard Analysis 89
Basis for Reduction of Elastic Spectrum by R
Inelastic Behavior of Structures
Methods for obtaining acceptable inelastic response are presented in later topics
Hazard Analysis 90
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, Western U.S.
Hazard Analysis 91
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, Eastern U.S.
Hazard Analysis 92
Old Maps vs New MapsCharleston, S.C.
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Period, T, sec
Seis
mic
Coe
ffici
ent,
Cs(
g)
94 Site B00 Site B
Hazard Analysis 93
Directionality and “Killer Pulse” EarthquakesFor sites relatively close to the fault, thedirection of fault rupture can have an amplifyingeffect on ground motion amplitude
Hazard Analysis 94
Forward directivity
Backward directivity
Rupture direction
Rupture direction
The areas under the far-field displacementpulses are equal, but the amplitudesand durations differ. This has majoreffects on the ground velocity and acceleration.
Ground Displacement
To Receiver
To Receiver
Hazard Analysis 95
Towards
Away
Effect of Directionality on Response Spectra
Hazard Analysis 96
Effect of Directionality on Ground Motion