Seismic Hazards and Response SpectrumResponse...

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


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)


(PGA,1 sec & 0.2 sec-1000 year)


p

2500 year recurrence500 year recurrence


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 −×−−

=


p

Seismic Hazard Maps(PGA 500 year)


(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)


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)


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


PGA, 0.2 sec & 1.0 sec (1000 year)PGA

0.2 second

Structure Acc1-second Structure Acc on Rock


p

SStructure Acc on Rock

Rock


p

Seismic Hazard

Structure acc on SoilS uc u e acc o So

RockRock


p

SD1 =S1xFvPOF


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


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)


g g y

Seismic Design Category (zone)(500 year Return Period)


(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)


(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”




Zone 1-SDC “A”Zone 2-SDC “B”Zone 2-SDC BZone 3-SDC “C”Zone 4-SDC “D”

SITE CLASS “C”




Zone 1-SDC “A”Zone 2-SDC “B”Zone 3-SDC “C”Zone 4-SDC “D”

SITE CLASS “D”




Zone 1-SDC “A”Zone 1 SDC AZone 2-SDC “B”Zone 3-SDC “C”Zone 4-SDC “D”

SITE CLASS “E”



How to Calculate Seismic Design Category


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?


p p

Actual Spectra vs. Smoothed Spectra

Range one structure may experiencefor a variety of ground motionsfor a variety of ground motions.

Amplification zone


p p

“Dynamics of Structures”by Anil K Chopra


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


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


PGA

PG

AF P

Three Point Response Spectrum South West Indiana


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)


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”


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”


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


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)


East Idaho (1000 vs 500 year return period)

21000 EQ vs 500 EQ


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)


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)


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)


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

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