Upload
anonymous-ep7le5zdp5
View
226
Download
0
Embed Size (px)
Citation preview
7/25/2019 CE 7014 Chap2 Part1
1/51
In this chapter you will learn:
Amplitude Parameters
Frequency Content Parameters
Duration Parameters
Near-fault Eects Directi!ity and Flin"#
$rientation-Independent %round &otion&easures
7/25/2019 CE 7014 Chap2 Part1
2/51
Earthqua'e en"ineers mostly interested in stron" "roundmotion motion su(cient stren"th to aect people and
the en!iroment#
Earthqua'e eects on a site stron" "round motion
objective andquantitative way of
describing is needed
Complicated
)u"e amount of information
*hree components of motion
7/25/2019 CE 7014 Chap2 Part1
3/51
+tron" "round
motions are mostymeasured ,yacceleographs.Severalagencies placedacceleo"raphs all
around *ur'eyespecially close tothe acti!e faults.
/aw stron" "round motion data may include errors from se!eral sources thatrequire correction to produce accurate stron" motion records. +tron" motion
processin" is often required to minimi0e ,ac' "round noise correct for thedynamic response of the transducer and to correct for measurement errors.
http:11daphne.deprem."o!.tr1
For information a,outthe acti!e faults you
can chec'www.mta."o!.tr
Remember:
7/25/2019 CE 7014 Chap2 Part1
4/51
Fortunately, it is not necessary to reproducee!ery time history to descri,e the "roundmotions adequately for en"ineerin" purposes.
Instead we can descri,e the important
characteristics of "round motions:
Amplitude Frequency content ground motion
parameters Duration
2e need to 'now somethin" a,out more thanone of them to descri,e a "round motion
7/25/2019 CE 7014 Chap2 Part1
5/51
*he common way ofdescri,in" a "roundmotion is time history
*he motion parametermay ,e acceleration!elocity or displacement.
*ypically one of theseparameters are measuredand the others will ,ecomputed ,y inte"rationor dierentation.
=
=
dttvtd
dttatv
)()(
)()(
&ost popular "round motion parameter foramplitude is pea hori!ontal acceleration
"#$%& which is the lar"est acceleration fromthe histor .
P)A
7/25/2019 CE 7014 Chap2 Part1
6/51
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
7/25/2019 CE 7014 Chap2 Part1
7/51
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
7/25/2019 CE 7014 Chap2 Part1
8/51
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
7/25/2019 CE 7014 Chap2 Part1
9/51
*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.
7/25/2019 CE 7014 Chap2 Part1
10/51
*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
7/25/2019 CE 7014 Chap2 Part1
11/51
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
7/25/2019 CE 7014 Chap2 Part1
12/51
*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
=
7/25/2019 CE 7014 Chap2 Part1
13/51
*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
7/25/2019 CE 7014 Chap2 Part1
14/51
7/25/2019 CE 7014 Chap2 Part1
15/51
7/25/2019 CE 7014 Chap2 Part1
16/51
7/25/2019 CE 7014 Chap2 Part1
17/51
(uration of stron" "round motion can ha!e a stron" in
7/25/2019 CE 7014 Chap2 Part1
18/51
(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.
7/25/2019 CE 7014 Chap2 Part1
19/51
*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.
7/25/2019 CE 7014 Chap2 Part1
20/51
*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.
7/25/2019 CE 7014 Chap2 Part1
21/51
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
7/25/2019 CE 7014 Chap2 Part1
22/51
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
7/25/2019 CE 7014 Chap2 Part1
23/51
+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
7/25/2019 CE 7014 Chap2 Part1
24/51
-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
7/25/2019 CE 7014 Chap2 Part1
25/51
*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
7/25/2019 CE 7014 Chap2 Part1
26/51
7/25/2019 CE 7014 Chap2 Part1
27/51
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
7/25/2019 CE 7014 Chap2 Part1
28/51
7/25/2019 CE 7014 Chap2 Part1
29/51
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
7/25/2019 CE 7014 Chap2 Part1
30/51
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
7/25/2019 CE 7014 Chap2 Part1
31/51
7/25/2019 CE 7014 Chap2 Part1
32/51
7/25/2019 CE 7014 Chap2 Part1
33/51
-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
7/25/2019 CE 7014 Chap2 Part1
34/51
0.001
0.01
0.1
1
0.01 0.1 1 1
SpectralAccelera
tion(g)
Period (sec)
IZT-NS
IZT-EW
7/25/2019 CE 7014 Chap2 Part1
35/51
-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
7/25/2019 CE 7014 Chap2 Part1
36/51
0.001
0.01
0.1
0.01 0.1 1 1
SpectralAcceler
ation(g)
Period (sec)
ARC-NS
ARC-EW
7/25/2019 CE 7014 Chap2 Part1
37/51
-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
7/25/2019 CE 7014 Chap2 Part1
38/51
24
.
TCU072
TCU074
TCU089
TCU084
TCU071
TCU078
TCU129
TCU068
TCU052
TCU067TCU065
TCU075
TCU076
CHY028
TCU087
TCU049TCU101
TCU102
7/25/2019 CE 7014 Chap2 Part1
39/51
S
S N
7/25/2019 CE 7014 Chap2 Part1
40/51
-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
7/25/2019 CE 7014 Chap2 Part1
41/51
-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)
7/25/2019 CE 7014 Chap2 Part1
42/51
-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
7/25/2019 CE 7014 Chap2 Part1
43/51
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
7/25/2019 CE 7014 Chap2 Part1
44/51
%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
7/25/2019 CE 7014 Chap2 Part1
45/51
7/25/2019 CE 7014 Chap2 Part1
46/51
%&/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.
7/25/2019 CE 7014 Chap2 Part1
47/51
*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.
7/25/2019 CE 7014 Chap2 Part1
48/51
*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 >>
7/25/2019 CE 7014 Chap2 Part1
49/51
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 >>
7/25/2019 CE 7014 Chap2 Part1
50/51
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.
7/25/2019 CE 7014 Chap2 Part1
51/51
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'.