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FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 1
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 1
SEISMIC HAZARD ANALYSIS
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 2
Seismic Hazard Analysis• Deterministic procedures• Probabilistic procedures• USGS hazard maps• 2003 NEHRP Provisions design maps• Site amplification• NEHRP Provisions response spectrum• UBC response spectrum
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 4
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.”
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 5
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).
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 6
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
FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 2
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 7
Fault Fault
AreaSource
SiteFault
Localizing structure
Seismotectonicprovince
Source Types
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 8
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 9
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.
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 10
Ground Motion Attenuation
Reasons:• Geometric spreading• Absorption (damping)
Magnitude M
Distance
Gro
und
Mot
ion
Par
amet
er
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 11
Attenuation with Distance
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 12
Comparison of Attenuation for Four Earthquakes
FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 3
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 13
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 14
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)
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 15
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).
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 16
Ground Motion AttenuationRelationships
Seismological Research LettersVolume 68, Number 1January/February, 1997
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 17
Earthquake Catalog for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 18
Earthquake Catalog for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)
FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 4
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 19
Attenuation Relation for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 20
)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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 21
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 22
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
Attenuation Relation for Shallow Crustal Earthquakes(Sadigh, Chang, Egan, Makdisi, and Youngs)
Magnitude Magnitude
0.2 Second Acceleration 1.0 Second Acceleration
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 23
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 24
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
FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 5
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 25
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 26
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 27
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 28
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=?
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 29
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 30
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))
FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 6
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 31
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 32
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 33
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 34
Uniform Hazard Spectrum
Large distantearthquake
Small nearbyearthquake
Uniform hazard spectrum
Period
Response
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 35
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 36
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.”
FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 7
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 37
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.”
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 38
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 39
USGS Probabilistic Hazard Maps(and NEHRP Provisions Maps)
Earthquake Spectra, Seismic Design Provisions andGuidelines Theme Issue, Volume 16, Number 1,February 2000
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 40
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.
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 41
USGS Seismic Hazard Regions
Note: Different attenuation relationships used for different regions.
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 42
USGS Seismic Hazard WUS Faults
FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 8
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 43
USGS Seismic Hazard Curves for Various Cities
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 44
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)
2% in 50 years 10% in 50 years
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 45
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)
2% in 50 years 10% in 50 years
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 46
USGS Seismic Hazard Map of Coterminous United States
http://earthquake.usgs.gov/hazmaps/
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 47
USGS Seismic Hazard Map of Coterminous United States
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 48
USGS Seismic Hazard Map for Coterminous United States
FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 9
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 49
USGS Map for Central and Eastern United States
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 50
USGS Map for Central and Eastern United States
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 51
USGS Map for Central and Eastern United States
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 52
USGS Map for Western United States
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 53
USGS Map for Western United States
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 54
USGS Map for Western United States
FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 10
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 55
USGS Map for California
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 56
USGS Map for California
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 57
USGS Map for California
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 58
USGS Map for Pacific Northwest
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 59
USGS Map for Pacific Northwest
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 60
USGS Map for Pacific Northwest
FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 11
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 61
USGS Seismic Hazard Map of Coterminous United States
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 62
USGS Seismic Hazard Map of Coterminous United States
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 63
USGS Seismic Hazard Map of Coterminous United States
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 64
USGS Map for Central and Eastern United States
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 65
USGS Map for Central and Eastern United States
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 66
USGS Map for Central and Eastern United States
FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 12
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 67
USGS Map for Western United States
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 68
USGS Map for Western United States
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 69
USGS Map for Western United States
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 70
USGS Map for California
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 71
USGS Map for California
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 72
USGS Map for California
FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 13
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 73
USGS Map for Pacific Northwest
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 74
USGS Map for Pacific Northwest
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 75
USGS Map for Pacific Northwest
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 76
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.
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 77
Relative PGAs for the United States
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 78
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.
FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 14
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 79
Location of Deterministic Areas
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 80
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 81
NEHRP Provisions Maps0.2 Second Spectral Response (SS)
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 82
NEHRP Provisions Maps1.0 Second Spectral Response (S1)
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 83
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 84
A
B
A
B
Time
Acc
eler
atio
n
Rock
Shale
Sand
Site Amplification Effects
FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 15
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 85
Site Amplification Effects
• Amplification of ground motion
• Longer duration of motion
• Change in frequency content of motion
• Not the same as soil-structure interaction
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 86
Site Amplification (Seed et al.)
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 87
Site Amplification: Loma Prieta Earthquake
SoftRock
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 88
Site Amplification: Loma Prietaand Mexico City Earthquakes
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 89
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 90
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
FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 16
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 91
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 92
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”
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 93
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 94
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 95
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
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 96
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
FEMA 451B Topic 5a Handouts Seismic Hazard Analysis 17
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 97
Basis for Reduction ofElastic Spectra by R
Inelastic behavior of structures
Methods for obtaining acceptable inelastic response are presentedin later topics
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 98
Directionality and “Killer Pulse” EarthquakesFor sites relatively close to the fault, thedirection of fault rupture can have an amplifyingeffect on ground motion amplitude.
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 99
Towards
Away
Effect of Directionality on Response Spectra
Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 100
Effect of Directionality on Ground Motion
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