CE 7014 Chap2 Part1

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    In this chapter you will learn:

    Amplitude Parameters

    Frequency Content Parameters

    Duration Parameters

    Near-fault Eects Directi!ity and Flin"#

    $rientation-Independent %round &otion&easures

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    Earthqua'e en"ineers mostly interested in stron" "roundmotion motion su(cient stren"th to aect people and

    the en!iroment#

    Earthqua'e eects on a site stron" "round motion

    objective andquantitative way of

    describing is needed

    Complicated

    )u"e amount of information

    *hree components of motion

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    +tron" "round

    motions are mostymeasured ,yacceleographs.Severalagencies placedacceleo"raphs all

    around *ur'eyespecially close tothe acti!e faults.

    /aw stron" "round motion data may include errors from se!eral sources thatrequire correction to produce accurate stron" motion records. +tron" motion

    processin" is often required to minimi0e ,ac' "round noise correct for thedynamic response of the transducer and to correct for measurement errors.

    http:11daphne.deprem."o!.tr1

    For information a,outthe acti!e faults you

    can chec'www.mta."o!.tr

    Remember:

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    Fortunately, it is not necessary to reproducee!ery time history to descri,e the "roundmotions adequately for en"ineerin" purposes.

    Instead we can descri,e the important

    characteristics of "round motions:

    Amplitude Frequency content ground motion

    parameters Duration

    2e need to 'now somethin" a,out more thanone of them to descri,e a "round motion

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    *he common way ofdescri,in" a "roundmotion is time history

    *he motion parametermay ,e acceleration!elocity or displacement.

    *ypically one of theseparameters are measuredand the others will ,ecomputed ,y inte"rationor dierentation.

    =

    =

    dttvtd

    dttatv

    )()(

    )()(

    &ost popular "round motion parameter foramplitude is pea hori!ontal acceleration

    "#$%& which is the lar"est acceleration fromthe histor .

    P)A

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    2hy P)A is so important3

    21 )()( HH PHAPHAPHA =

    'ote:*he P)A representin" the hori0ontal motion is found ,y thegeometric meanof two hori0ontal "round motion components.

    Can ,e correlated with the si0e ofthe earthqua'e...As the ma"nitude increases...

    As the &&I increases...

    gumkuucum =++

    4ar"est component of the forceinduced on the structure5

    Is P)A directly correlatedwith the dama"e3 )ow

    a,out the duration...

    P)A

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    Pea' hori0ontal !elocity P)6# and pea' hori0ontal

    displacement P)D# are de7ned as the lar"est !elocityand displacement !alues ta'en from the time history.

    A "ood measure for potentialdama"e to tall ,uildin"s ,rid"es etc.

    Correlated to earthqua'e ma"nitude

    or intensity

    P)6 P)D

    4ess popular measure ofamplitude

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    2e 'now that the response of the structures is !ery

    sensiti!e to the frequency of the loadin"...

    Earthqua'es produce complicated loadin" withcomponents of motion o!er a ,road ran"e offrequencies.

    Frequency content descri,es how the amplitude of"round motions is distri,uted amon" dierentfrequencies.

    Frequency content is measured ,y the threedierent spectra of the "round motion: Fourier +pectra Power +pectra /esponse +pectra

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    *he Fourier spectrum consists of series of harmonicterms with dierent amplitude frequency and phase.

    )sin()( 0 tQtQ =

    amplitude frequency

    )sin()( 0 += tQtQ

    phase

    &any 8t#terms willadd up to "ettheacceleration-time history.

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    *he Fourier amplitude spectrum may ,e narrow or

    ,road.

    A narrow Fourierspectrum implies thatthe motion has a

    dominant frequency anda smooth almostsinusoidal time history9

    A ,road spectrum shows

    that the amplitude ofthe motion is distri,utedwith respect tofrequency and more

    a""ed irre"ular time

    history9

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    2hen the Fourier amplitude spectrum is plotted on lo"-lo" scale thecharacteristic shape can ,e seen more easily.

    Fccorner frequency4ar"est o!er theintermediate

    frequencies

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    *he frequency content of a "round motion can also ,edescri,ed ,y power spectrum.

    *he total intensity of a "round motion in the time domain isdescri,ed ,y the area under the time history of squaredacceleration.

    [ ]=dT

    o dttaI0

    2)(

    It is also e;pressed in frequency domain: =n

    dQIo

    0

    2

    01

    *he a!era"e intensity is equalto:

    [ ] ===

    n nd

    dGdQTdttaT od

    T

    do

    0 0

    2

    0

    2

    )(

    1

    )(

    1

    where *d is the duration of theearthqua'e n is the hi"hestfrequency in the Fourier series and%# is the power spectral density.

    2

    0

    1)( Q

    TG

    d

    =

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    *he response spectrum descri,es the ma;imumresponse of a +D$F system to a particular input motionas a function of natural frequency and dampin".

    Remember, theresponse spectrarepresents only thema;imumresponses of anum,er ofdierentstructures5

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    (uration of stron" "round motion can ha!e a stron" in

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    (uration of stron" "round motion is directly related

    to the time required to release the accumulated strainener"y ,y the rupture alon" the fault.

    As areaor lengthof the fault rupture increases thetime required to rupture and the duration increases.)ow a,out the magnitude3

    For en"ineerin" applications only stron" "roundmotion portion of the acceleo"ram is of interest.

    )otal duration*)start+ )end

    *end is di(cult to determine since the wea' motioncontinues for a lon" time in far 7eld.

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    *he braceted duration is de7ned as the time

    ,etween the 7rst and last e;ceedences of a tresholdacceleration usually >.>? "#

    umulative -nergy (uration")rifunac and rady, /012& isde7ned as the time inter!al,etween the points at which ?@and ?@ of the total intensity

    has ,een recorded.

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    *he total intensity of the "round motion is"i!en ,y: [ ]=

    dT

    o dttaI0

    2)(

    *he average intensityis :

    [ ]=dT

    d

    o dttaT

    0

    2)(

    1 which is also de7ned as

    mean-squaredacceleration

    [ ] rms

    T

    d

    o adttaT

    d

    == 0

    2)(

    1 *he armsis the root mean-squared

    acceleration.

    A parameter closely related to arms is the %rias

    intensity Ia#:

    [ ] )/()(2 0

    2smdtta

    g

    Ia

    =

    *he predominant period ")p& is de7ned as the period of !i,ration

    correspondin" to the hi"hest fourier amplitude.

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    Directi!ity /elated to the direction of the rupture

    front

    Forward directi!ity: rupture toward the

    sitesite away from the epicenter#

    Bac'ward directi!ity: rupture away fromthe site site near the epicenter#

    Flin"

    /elated to the permanent tectonicdeformation at the site

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    Forward Directi!ity

    *wo-sided !elocity pulse due to constructi!einterference of +) wa!es from "enerated fromparts of the rupture located ,etween the siteand epicenter

    Constructi!e interference occurs if slip

    direction is ali"ned with the rupture direction $ccurs at sites located close to the fault ,ut

    away from the epicenter for stri'e-slip Flin"

    $ne-sided !elocity pulse due to tectonicdeformation

    $ccurs at sites located near the fault ruptureindependent of the epicenter location

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    +ense of +lip+ense of +lip Directi!ityDirecti!ity Flin"Flin"

    +tri'e-+lip+tri'e-+lip Fault NormalFault Normal Fault ParallelFault Parallel

    Dip-+lipDip-+lip Fault NormalFault Normal Fault NormalFault Normal

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    -0.4

    -0.3-0.2-0.100.1

    0.2.

    5 10 15 20 25 30 3

    Acc(g)

    YPT EW

    YPT NS

    -100

    0

    100

    5 10 15 20 25 30 35

    e

    cm

    s

    YPT EW

    YPT NS

    -100

    0

    100

    200

    300

    5 10 15 20 25 30 35

    Dis(cm)

    Time (sec)

    YPT EW

    YPT NS

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    *wo Eects on %round &otion Amplitudes Chan"es in the a!era"e hori0ontal component as

    compared to standard attenuation relations

    Increase in the amplitude of lon" period"round motion for rupture toward the site

    Decrease in the amplitude of lon" period"round motion for rupture away from the site

    +ystematic dierences in the "round motions onthe two hori0ontal components

    Fault normal component is lar"er than thefault parallel component at lon" periods

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    Additional Parameters /equired +tri'e-+lip Fault simple model#

    + len"th of rupture toward site

    fraction of fault rupture ,etween theepicenter and the site

    an"le ,etween the fault stri'e and theepicentral direction from the site

    Comple; model /adiation pattern

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    0

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    1.4

    1.6

    1.8

    0.01 0.1 1 1

    ScaleFactor

    Period (sec)

    X Cos(theta) = 0

    X Cos(theta) = 0.1

    X cos(theta) = 0.2

    X cos(theta) = 0.3

    X Cos(theta) >= 0.4

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    0.5

    0.6

    0.7

    0.8

    0.9

    1

    1.1

    1.2

    1.3

    1.4

    .

    0.1 1 1

    ScaleFactor

    Period (sec)

    theta = 0

    theta = 15

    theta = 30

    theta = 45

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    -0.25

    0

    .

    0 5 10 15 20 25 30 3

    cc

    g

    IZT NS

    IZT EW

    -50

    0

    50

    0 5 10 15 20 25 30 35

    Vel(cm/s)

    IZT NS

    IZT EW

    -30

    0

    30

    0 5 10 15 20 25 30 35

    Dis(cm)

    Time (sec)

    IZT NS

    IZT EW

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    0.001

    0.01

    0.1

    1

    0.01 0.1 1 1

    SpectralAccelera

    tion(g)

    Period (sec)

    IZT-NS

    IZT-EW

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    -0.25

    0

    .

    5 10 15 20 25 30 3

    cc

    g

    ARC EW

    ARC NS

    -50

    0

    50

    5 10 15 20 25 30 35

    Vel(cm/s

    )

    ARC EW

    ARC NS

    -60

    -30

    0

    30

    60

    5 10 15 20 25 30 35

    Dis(cm)

    Time (sec)

    ARC EW

    ARC NS

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    0.001

    0.01

    0.1

    0.01 0.1 1 1

    SpectralAcceler

    ation(g)

    Period (sec)

    ARC-NS

    ARC-EW

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    -0.4

    -0.3-0.2-0.10

    0.10.2.

    5 10 15 20 25 30 3

    Acc

    (g)

    YPT EW

    YPT NS

    -100

    0

    100

    5 10 15 20 25 30 35

    e

    cms

    YPT EW

    YPT NS

    -100

    0

    100

    200

    300

    5 10 15 20 25 30 35

    Dis(cm)

    Time (sec)

    YPT EW

    YPT NS

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    24

    .

    TCU072

    TCU074

    TCU089

    TCU084

    TCU071

    TCU078

    TCU129

    TCU068

    TCU052

    TCU067TCU065

    TCU075

    TCU076

    CHY028

    TCU087

    TCU049TCU101

    TCU102

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    S

    S N

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    -0.4

    -0.3-0.2-0.100.1

    0.20.3.

    15 20 25 30 35 40 45 50 55 6

    Acc(g)

    TCU 049 E

    TCO052 E

    -200

    -100

    0

    100

    15 20 25 30 35 40 45 50 55 60

    ecms

    TCU 049 E

    TCO052 E

    -600

    -400

    -200

    0

    200

    15 20 25 30 35 40 45 50 55 60

    Dis(cm)

    Time (sec)

    TCU 049 E

    TCO052 E

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    -150

    0

    150

    0 2 4 6 8 10 12

    sp(cm

    Time (sec)

    -0.1

    0

    0.1

    0 2 4 6 8 10 12

    Acc(g)

    Time (sec)

    -80

    -40

    0

    40

    80

    0 2 4 6 8 10 12

    Vel(cm/s)

    Time (sec)

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    -0.25

    0

    0.25

    .

    30 35 40 45 50 55 6

    ccg

    fling

    TCU052E

    -200-150-100-50050100

    30 35 40 45 50 55 60

    e

    cm

    s

    fling

    TCU052E

    -500-400-300-200-1000100

    30 35 40 45 50 55 60

    Dis(cm)

    Time (sec)

    fling

    TCU052E

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    Amplitude of Flin"

    From fault slip and "eodetic data

    Duration period# of Flin" From stron" motion data

    Arri!al *ime of Flin"

    From numerical modelin"

    /elati!e timin" of

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    %ood measure : 4ess aleatory uncertaintycompared to other measures.

    It has one important disad!anta"e it isdependent on orientation of the ortho"onalcomponents of accelero"raph Boore et al.G>>H#.

    Boore et al. G>>H# de7ned two orientation-independent measures for "round motionintensity %&/otDpp and %&/otIpp

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    %&/otDpp and %&/otIpp

    where

    %&stands for "eometric mean

    /ot means rotations are used o!erall non-redundant an"les

    D states that period dependentrotations are used whereas Istates

    that the rotations are periodindependent

    ppstands for percentile !alue of themeasure.

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    *hese measures are calculated throu"hrotated response spectra of as- recordedmotions as summari0ed ,elow:

    Calculation of %&/otIpp requires the use of%&/otDpp. +o latter one is calculated 7rst.

    Initially response spectra for eachindi!idual component are calculated forrotation an"le ,ein" equal to J>K.

    *hen these response spectral !alues arerotated ,y an increment L.

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    *hen the "eometric means are calculated from these rotatedresponse spectra for the new an"le usin" ,elow Equations :

    where

    /sMt# : /esponse +pectra of N-+

    /sGt# : /esponse spectra of E-2

    /esponse spectra /sMt# and /sGt# are defined for a"i!en oscillator dampin" and usa,le period ran"e.

    *his %& /esponse spectrum is assi"ned to the specific an"le .

    *his process is then repeated for the an"le L until >>

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    After o,tainin" "eometric mean response spectra for allan"le increments spectral !alues for each period are ran'ed,y the ascendin" order.

    %&/otDpp is o,tained for the pp thpercentile of ran'ed!alues.

    For e;ample %&/otD?> corresponds to the median of the ran'ed!alues for a "i!en period.

    All %&/otDpp !alues are normali0ed ,y %&/otDpp for ade7ned pp !alue that will ,e used in %&/otIpp calculation.

    *his %& /esponse spectrum is assi"ned to the speci7can"le .

    *his process is then repeated for the an"le Luntil >>

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    After that a penalty function is calculated usin" the formula"i!en ,elow:

    where

    *i : Osa,le spectra period %&*i# : %eometric mean of response spectra for period

    *i at an"le .

    *his penalty function is calculated for all !alues and therotation an"le that "i!es the minimum penalty !alue is

    determined . Osin" the selected rotation an"le as-recorded motions are

    rotated *hen response spectra are calculated from each rotated

    component motion. Finally the "eometric mean of these response spectra is

    calculated and this spectrum is de7ned as %&/otIpp.

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    Comparison of

    GMRotI50 andGMRotD50. Also shown

    by the gray

    !r"es are GMRotD00

    and GMRotD#00 $the

    minim!m and ma%im!m

    geometrimeans !sing period&

    dependent rotation

    angles'.