seismic hazards and response spectrumresponse...
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Seismic Hazards andResponse SpectrumResponse Spectrum FundamentalsFundamentals Derrell ManceauxS SSenior Structural EngineerFHWA Resource Center
Learning OutcomesForce Displ. RetroTopic Applicability
g
Identify Upper & Lower Level EQ hazardsExplain how seismic hazard maps are usedDetermine Seismic Design Category (Zone)Define a response spectrum and factors that effect the spectrum shapeDescribe how a “three point” response spectrum is constructed
Upper & Lower Seismic HazardsForce Displ. RetroTopic Applicability
pp
Lower Seismic Hazard-100 year recurrenceLower Seismic Hazard 100 year recurrenceRetrofit
Upper Seismic Hazard-1000 year recurrenceUpper Seismic Hazard-1000 year recurrenceRetrofitGuide SpecificationGuide SpecificationLRFD 2008 Interims
Upper Seismic Hazard 500 year recurrenceUpper Seismic Hazard- 500 year recurrenceOld AASHTO
Force Displ. RetroTopic Applicability
Upper & Lower Seismic Hazards
Recurrence Period
Time( )
Probability of Exceedence
pp
Period(years)
(years) Exceedence
100 75 75%100 75 75%500 50 10%500 75 15%
1000 75 7%
≈ TimeReturn Period
Probability of Exceedence
Force Displ. RetroTopic Applicability
Upper & Lower Seismic Hazardspp
AASHTO Retrofitio
n (g
)A
ccel
erat
i
USGS
Gro
und USGS
100 500 1000 1500 2000 2500Return PeriodReturn Period
Seismic Hazard MapsForce Displ. RetroTopic Applicability
p
Seismic Hazard Maps display earthquakeSeismic Hazard Maps display earthquake ground accelerations for various probability levelsprobability levels
100 year return period (Retrofit) 1000 year return period (LRFD & GS)1000 year return period (LRFD & GS)Used to Determine:
Acc of structure (3 Points) on RockAcc of structure (3 Points) on Rock Seismic Design Category (Zones)
Seismic Hazard Maps(PGA 1 sec & 0 2 sec 1000 year)
Force Displ. RetroTopic Applicability
(PGA,1 sec & 0.2 sec-1000 year)
Seismic Hazard MapsForce Displ. RetroTopic Applicability
p
2500 year recurrence500 year recurrence
Seismic Hazard MapsForce Displ. RetroTopic Applicability
p
S2/50 Ln(S2/50)
Si Ln(Si)
475 P 2475R t P i d
S10/50
Ln(475) Ln(P) Ln(2475)N t l L (R t P i d)
Ln(S10/50)
Return Period Natural Log(Return Period)
)()( SLSLLinear Interpolation (ASCE 41-06)
))475()(()475()2475(
)()()( 50/1050/20 LnPLnLnLn
SLnSLnSLn i −×−−
=
Seismic Hazard MapsForce Displ. RetroTopic Applicability
p
Seismic Hazard Maps(PGA 500 year)
Force Displ. RetroTopic Applicability
(PGA-500 year)PGA Map
Acc Coefficient(PGA)
Seismic Zone
A≤ 0.09 10.09 < A≤ 0.19 20.19 < A≤ 0.29 3
0 29 < A 40.29 < A 4
K=∞ rockrock
Seismic Hazard MapsPGA 0 2 sec & 1 0 sec (1000 year)
Force Displ. RetroTopic Applicability
PGA, 0.2 sec & 1.0 sec (1000 year)
T=1-second
PGAT=0.2 second
rock rock rock
Seismic Hazard MapsPGA 1 sec & 0 2 sec (1000 year)
Force Displ. RetroTopic Applicability
PGA,1 sec & 0.2 sec (1000 year)Structure Acceleration on Rock
acc
Stru
ct a
PGA
rock rock rock0.2 second
1-second
Seismic Hazard MapsPGA 0 2 sec & 1 0 sec (1000 year) 0 2 d
Force Displ. RetroTopic Applicability
PGA, 0.2 sec & 1.0 sec (1000 year)PGA
0.2 second
Structure Acc1-second Structure Acc on Rock
Seismic Hazard MapsForce Displ. RetroTopic Applicability
p
SStructure Acc on Rock
Rock
Seismic Hazard MapsForce Displ. RetroTopic Applicability
p
Seismic Hazard
Structure acc on SoilS uc u e acc o So
RockRock
Seismic Hazard MapsForce Displ. RetroTopic Applicability
p
SD1 =S1xFvPOF
Seismic Hazard MapsForce Displ. RetroTopic Applicability
p
How are Seismic Hazard Maps used?How are Seismic Hazard Maps used?To get 3 points to build the “rock” response spectrum (“Struct acc on rock”)spectrum ( Struct. acc on rock )To determine Seismic Design Category (Zone),SD1, using acc,S1, modified with Site (soil)(Zone),SD1, using acc,S1, modified with Site (soil) factor, Fv
Seismic Design Category (Zone)Force Displ. RetroTopic Applicability
Calculate associated soil factors L P i d F
g g y ( )
Long Period, Fv
Site Class
Mapped Spectral Acc at 1.0 s
S1 ≤ 0.1 S1 = 0.2 S1 = 0.3 S1 = 0.4 S1 ≥ 0.5
B 1.0 1.0 1.0 1.0 1.0C 1 7 1 6 1 5 1 4 1 3C 1.7 1.6 1.5 1.4 1.3D 2.4 2.0 1.8 1.6 1.5E 3.5 3.2 2.8 2.4 2.4
Seismic Design Category (zone)Force Displ. RetroTopic Applicability
g g y ( )
New Seismic Zones (SDC) 500 1000
2007 4th Edition LRFDA l ti S i i Z
500 year 1000 year2008 Interims & Guide Specs
A l ti S i i ZAcceleration Coefficient
Seismic Zone
A≤ 0.09 1
Acceleration Coefficient
Seismic Zone (SDC)
SD1 ≤ 0.15 10.09 < A≤ 0.19 20.19 < A≤ 0.29 3
D1
0.15 < SD1 ≤ 0.30 20.30 < SD1 ≤ 0.50 3
0.29 < A 4 0.50 < SD1 4A=PGA SD1 =Structure acceleration=S1xFv
Seismic Design Category (Zone)Force Displ. RetroTopic Applicability
1 Second Rock Acceleration Coefficient (S1)
g g y ( )
PGA2008 Interims & Guide Specs (1000 year)
Soil Site B Soil Site C Soil Site D Soil Site E Seismic Z
2007 4th Edition (500 year)
Acceleration Zone
S1 < 0.15 S1 < 0.09 S1 < 0.07 S1 < 0.04 1
Coefficient
APGA < 0.09
0.15 < 0.30 0.09 < 0.20 0.07 < .15 0.04 < .09 2
0.30 < 0.50 0.20 < 0.35 0.15 < .27 0.09 < .15 3
0.09<APGA ≤ 0.19
0.19<APGA ≤ 0.29
0.50 < S1 0.35 < S1 0.27 < S1 0.15 < S1 4 0.30 < APGA
Seismic Design CategoryForce Displ. RetroTopic Applicability
Seismic Zones vs Acceleration,S1
g g y
1
1.2
0 4
0.6
0.8 Zone 4Zone 3Zone 2Zone 1
S1 (g)
0
0.2
0.4 Zone 1
B C D E
Soil Type
Seismic Design CategoryForce Displ. RetroTopic Applicability
SDC-Zones
g g y
Zone 1-SDC “A”Zone 2-SDC “B”Zone 3-SDC “C”Z 4 SDC “D”
Soil (Site) Class
Zone 4-SDC “D”
( )“B” (Rock)“C” (N> 50 blows/ft)“D” (15<N<50 blows/ft)“E” (N<15 blows/ft)
Seismic Design CategoryForce Displ. RetroTopic Applicability
g g y
Seismic Design Category (zone)(500 year Return Period)
Force Displ. RetroTopic Applicability
(500 year Return Period)
Zone 1-SDC “A”Zone 2-SDC “B”Zone 3-SDC “C”Zone 4-SDC “D”
Seismic Design Category (zone)(1000 Year Return Period)
Force Displ. RetroTopic Applicability
(1000 Year Return Period)
Zone 1-SDC “A”Zone 2-SDC “B”Zone 2-SDC BZone 3-SDC “C”Zone 4-SDC “D”
SITE CLASS “B”
Seismic Design Category (zone)(1000 Year Return Period)
Force Displ. RetroTopic Applicability
(1000 Year Return Period)
Zone 1-SDC “A”Zone 2-SDC “B”Zone 2-SDC BZone 3-SDC “C”Zone 4-SDC “D”
SITE CLASS “C”
Seismic Design Category (zone)(1000 Year Return Period)
Force Displ. RetroTopic Applicability
(1000 Year Return Period)
Zone 1-SDC “A”Zone 2-SDC “B”Zone 3-SDC “C”Zone 4-SDC “D”
SITE CLASS “D”
Seismic Design Category (zone)(1000 Year Return Period)
Force Displ. RetroTopic Applicability
(1000 Year Return Period)
Zone 1-SDC “A”Zone 1 SDC AZone 2-SDC “B”Zone 3-SDC “C”Zone 4-SDC “D”
SITE CLASS “E”
Seismic Design Category (zone)(1000 Year Return Period)
Force Displ. RetroTopic Applicability
How to Calculate Seismic Design Category
(1000 Year Return Period)
How to Calculate Seismic Design Category (zone)?
Multiply Rock Spectrum (S ) x Site Class (F )Multiply Rock Spectrum (S1) x Site Class (Fv) Amplification Factor @ 1.0 secSD1 =Structure acceleration=S1xFSD1 =Structure acceleration=S1xFv
SDC is variable at any single locationN i l i i d t i SDCNo single seismic map can determine SDC
Response Spectrum Force Displ. RetroTopic Applicability
What is the Response Spectrum?Th t id thThe response spectrum provides the maximum acceleration a single degree f f d t t ill iof freedom structure will experience
when it is subjected to a ground motion.
Response SpectrumForce Displ. RetroTopic Applicability
p pEl Centro (1942)
How is it created?
Response SpectrumForce Displ. RetroTopic Applicability
p p
Actual Spectra vs. Smoothed Spectra
Range one structure may experiencefor a variety of ground motionsfor a variety of ground motions.
Amplification zone
Response SpectrumForce Displ. RetroTopic Applicability
p p
“Dynamics of Structures”by Anil K Chopra
Response SpectrumForce Displ. RetroTopic Applicability
Response Spectrum2007 Design Response Spectrum
Three Point Response Spectrum Force Displ. RetroTopic Applicability
Determine Rock AccelerationsSs = Rock Acceleration @ 0.2 sS1 = Rock Acceleration @ 1.0 sSPGA =Rock Acceleration @ 0.0 s
Three Point Response SpectrumForce Displ. RetroTopic Applicability
p pDetermine Soil (Site) Coefficients
F = Site Coefficient @ 0 2 sFa = Site Coefficient @ 0.2 sFPGA = Site Coefficient @ 0.0 s
Site Class
Mapped PGA and Spectral Acc at 0.2 s (Fa, FPGA)
PGA ≤ 0.1S ≤ 0 25
PGA = 0.2S 0 50
PGA = 0.3S 0 75
PGA = 0.4S 1 00
PGA ≥ 0.5S ≥ 1 25Ss ≤ 0.25 Ss = 0.50 Ss = 0.75 Ss = 1.00 Ss ≥ 1.25
B 1.0 1.0 1.0 1.0 1.0C 1.2 1.2 1.1 1.0 1.0D 1.6 1.4 1.2 1.1 1.0E 2.5 1.7 1.2 0.9 0.9
Three Point Response SpectrumForce Displ. RetroTopic Applicability
p pDetermine Soil (Site) Coefficients
F = Site Coefficient @ 1 0 sFv = Site Coefficient @ 1.0 s
Site Class
Mapped Spectral Acc at 1.0 s
S1 ≤ 0.1 S1 = 0.2 S1 = 0.3 S1 = 0.4 S1 ≥ 0.51 1 1 1 1
B 1.0 1.0 1.0 1.0 1.0C 1.7 1.6 1.5 1.4 1.3D 2.4 2.0 1.8 1.6 1.5E 3.5 3.2 2.8 2.4 2.4
Three Point Response Spectrum Force Displ. RetroTopic Applicability
PGA
PG
AF P
Three Point Response Spectrum South West Indiana
Force Displ. RetroTopic Applicability
South West IndianaSs = Acceleration @ 0.2 s= 0.5 gS1 = Acceleration @ 1.0 s= 0.13 gS1 Acceleration @ 1.0 s 0.13 g
X X1 second spectral response (5% damp)0.2 second spectral response p p ( p)p p
(5% damp)
Three Point Response Spectrum Force Displ. RetroTopic Applicability
Ss=0.5g Fa = 1.7 S1=0.13g Fv = 3.3
Spectral S1(1 0 )
Ss 0.5g Fa 1.7 S1 0.13g Fv 3.3
Spectral Acc at SS(0 2 )
S1 >S1 =S1 =S1 =S1 <
5g4g3g2g1g
(1.0 sec)SiteSite
(0.2 sec)SS < SS = SS = SS = SS >
.25g .50g .75g 1.0g 1.3g
1.01.01.01.01.0B0.80.80.80.80.8A
.5g.4g.3g.2g.1gg g g g g
A 0.8 0.8 0.8 0.8 0.8
B 1.0 1.0 1.0 1.0 1.0
C 1 2 1 2 1 1 1 0 1 0
2.42.42.83.23.5E1.51.61.82.02.4D1.31.41.51.61.7CC 1.2 1.2 1.1 1.0 1.0
D 1.6 1.4 1.2 1.1 1.0
E 2.5 1.7 1.2 0.9 0.9
SD1=0.13*3.3 =0.43>0.3 Zone “3”
Three Point Response SpectrumForce Displ. RetroTopic Applicability
1000 EQ vs 500 EQ
South Indiana (1000 vs 500 year return period)
0.8
Acc1000 year / Φ (.9)S il “C”
0.6
cc (F
ract
ion
of g
)Soil “C”
0.2
0.4
Spec
Ac
Acc1000 year / Φ (.9)
Acc500 year / Φ ( 9)
0 1 2 3 4 50
P i d (S )Acc500 year / Φ (.75)
Acc500 year / Φ (.9)
Period (Sec)500 year (.75)
Soil type“E” – Zone “3”
Three Point Response Spectrum Force Displ. RetroTopic Applicability
1000 EQ vs 500 EQ
West Tennessee (1000 vs 500 year return period)
1000 EQ vs 500 EQ
1.5
21000 EQ vs 500 EQ
Acc1000 year / Φ (.9)1.5
21000 EQ vs 500 EQ
1
ec A
cc (F
ract
ion
of g
)
Acc500 year / Φ (.5)1
ec A
cc (F
ract
ion
of g
)
0
0.5
Spe
Acc500 year / Φ (.9)
0
0.5
Spe
0 0.5 1 1.5 2 2.5 30
Period (Sec)
Soil=“B”
0 0.5 1 1.5 2 2.5 30
Period (Sec)
Soil=“E”
Three Point Response Spectrum East Idaho (1000 vs 500 year return period)
Force Displ. RetroTopic Applicability
East Idaho (1000 vs 500 year return period)
21000 EQ vs 500 EQ
Acc500 year / Φ (.5)
21000 EQ vs 500 EQ
1
1.5
c (F
ract
ion
of g
)
Acc1000 year / Φ (.9)1
1.5
c (F
ract
ion
of g
)
0.5
Spec
Ac
Acc500 year / Φ ( 9)
0.5
Spec
Ac
0 0.5 1 1.5 2 2.5 30
Period (Sec)
Acc500 year / Φ (.9)
Soil=“E”
0 0.5 1 1.5 2 2.5 30
Period (Sec)
Soil=“B”
Three Point Response Spectrum North New Jersey (1000 vs 500 year return period)
Force Displ. RetroTopic Applicability
North New Jersey (1000 vs 500 year return period)
1000 EQ vs 500 EQ 1000 EQ vs 500 EQ
0.4
0.5
g)
Acc500 year / Φ (.75)
Acc500 year / Φ (.9) 0 4
0.5
)
0 2
0.3
0.4
pec
Acc
(Fra
ctio
n of
g
0 2
0.3
0.4
ec A
cc (F
ract
ion
of g
)0
0.1
0.2Sp
Acc1000 year / Φ (.9)0.1
0.2Sp0 0.5 1 1.5 2 2.5 3
0
Period (Sec)
Soil=“E”Soil=“B”
0 0.5 1 1.5 2 2.5 30
Period (Sec)
Three Point Response Spectrum Force Displ. RetroTopic Applicability
Determine Rock AccelerationsSs = Rock Acceleration @ 0.2 sSs Rock Acceleration @ 0.2 sS1 = Rock Acceleration @ 1.0 sSPGA =Rock Acceleration @ 0.0 s
Determine Soil (Site) CoefficientsDetermine Soil (Site) CoefficientsCalculate Ratios SD1/SDSPlot Response SpectrumPlot Response Spectrum
AP
GA
F PG
A
Conclusion
New recurrence period from 500 to 1000New recurrence period from 500 to 1000 year does not:
double the demanddouble the demandnecessarily increase population of seismic bridgesbridges
Seismic Design Categories (Zones) are: I t d b S il (Sit ) C ffi i tImpacted by Soil (Site) CoefficientsDetermined by structural acceleration on soil
ConclusionNew Response Spectrum is:
Less conservative in long period rangeLess conservative in long period range
0.6
0.8
T/10.4
T
3/2/1 T
0 10 20 30 40 500
0.2
0 10 20 30 40 50
What questions do you have?