This article was downloaded by: [RMIT University] On: 20 September 2013, At: 12:33 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Journal of Earthquake Engineering Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/ueqe20 Application of Wavelet Transforms on Characterization of Inelastic Displacement Ratio Spectra for Pulse- Like Ground Motions Saman Yaghmaei-Sabegh a a Department of Civil Engineering, University of Tabriz, Tabriz, Iran Published online: 15 May 2012. To cite this article: Saman Yaghmaei-Sabegh (2012) Application of Wavelet Transforms on Characterization of Inelastic Displacement Ratio Spectra for Pulse-Like Ground Motions, Journal of Earthquake Engineering, 16:4, 561-578, DOI: 10.1080/13632469.2011.640739 To link to this article: http://dx.doi.org/10.1080/13632469.2011.640739 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms- and-conditions
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This article was downloaded by: [RMIT University]On: 20 September 2013, At: 12:33Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Journal of Earthquake EngineeringPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/ueqe20
Application of Wavelet Transformson Characterization of InelasticDisplacement Ratio Spectra for Pulse-Like Ground MotionsSaman Yaghmaei-Sabegh aa Department of Civil Engineering, University of Tabriz, Tabriz, IranPublished online: 15 May 2012.
To cite this article: Saman Yaghmaei-Sabegh (2012) Application of Wavelet Transforms onCharacterization of Inelastic Displacement Ratio Spectra for Pulse-Like Ground Motions, Journal ofEarthquake Engineering, 16:4, 561-578, DOI: 10.1080/13632469.2011.640739
To link to this article: http://dx.doi.org/10.1080/13632469.2011.640739
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.
This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
Application of Wavelet Transforms onCharacterization of Inelastic Displacement Ratio
Spectra for Pulse-Like Ground Motions
SAMAN YAGHMAEI-SABEGHDepartment of Civil Engineering, University of Tabriz, Tabriz, Iran
In this article, a simple and effective wavelet-based procedure is implemented for describing principlefeatures of a special class of motions, pulse-like ground motions, on inelastic displacement ratiospectra (IDRS). The computed spectra supply a simple estimation of maximum inelastic displacementdemand from the corresponding elastic one. The results of analysis in this work provide a suitableplatform for quantification of pulse effects into IDRS and highlight the need to better understandingof this effect on demand estimation. It is concluded that the pulse has a significant influence on IDRSof pulse-like ground motions for systems with high ductility level.
Keywords Inelastic Displacement Ratio Spectra; Maximum Inelastic Displacement; Pulse-LikeMotions; Wavelet Transform and Ductility Level
1. Introduction
Displacement based-seismic design (DBSD) which was systematically proposed byPriestley [1995, 1998] is directed towards applying performance-based concepts bothin seismic design and performance assessment of structures. This procedure involvesdetermining the maximum expected displacement of structures rather than force whichtraditionally is used as a fundamental demand parameter in seismic design of structures.DBSD as an influential method for use in the future practice of seismic design has beengaining a good deal thought over the past 20 years and provided a reliable indication ofdamage potential by limiting the maximum displacement resulting from design level earth-quakes. While structures experience inelastic deformation during major earthquake groundmotions, accurate estimation of inelastic displacement demands of structures is recognizedas a main step for evaluation of structural performance.
Inelastic displacement ratio spectra (IDRS), first studied by Veletsos and Newmark[1960], are defined as ratio of maximum inelastic displacement demand to the correspond-ing elastic one and could be a useful connection for estimation of nonlinear demand ofSDOF systems from linear elastic analysis that has been conducted in this article. Manyresearch works have examined the evaluation of inelastic demands for structures under far-field ground motions [Miranda, 1993, 2000, 2001; Chopra and Goel, 2000; Miranda andJorge, 2002; Riddle et al., 2002; Decanini et al., 2003; Ruiz-Garcia and Miranda 2003,2006; Mollaioli and Bruno, 2008]. It is well known that characteristics of ground motionsclose to the earthquake source can be considerably different from those of far-field motionsin that they often contain a velocity pulse and permanent ground displacement [Somerville
Received 19 February 2011; accepted 10 November 2011.Address correspondence to Saman Yaghmaei-Sabegh, Department of Civil Engineering, University of
and Graves 1993]. Over the past two decades, severe substantial damages as well as fail-ures of engineered structures were observed within the near-fault regions in several majorearthquake events including the ones in Northridge, California, USA (1994), Kobe, Japan(1995), Chi-Chi, Taiwan (1999), and Bam, Iran (2003). These events revealed the vul-nerability of existing structures against pulse-like ground motions [Pitarka et al., 1998;Stephenson et al., 2000; Alavi and Krawinkler, 2001; Chi et al., 2002]. Other attemptswere also made to show the important effects of near-fault ground motions on the dynamicresponse of structures and estimating of seismic demand [Baker and Cornell, 2005; Fu,2005, Iwan et al., 2000, MacRae et al., 2001, Mortezaei et al., 2009]. As a consequence,the study of near-field ground motion characteristics and its effect on structural behavior isa very important theme in the field of seismology and earthquake engineering.
The above-mentioned analysis often addresses the comparative effects of near-fault vs.far-field ground motions and the contribution of pulse portion of motion on inelastic dis-placement of a system has not been systematically quantified in the past. This article triesto present a new quantitative wavelet-based method for systematically analyzing the effectof pulse-like motions on inelastic demand of SDOF systems which will able to cover thisgap. Wavelet transform as a powerful mathematical tool is able to extract both time and fre-quency great information from ground motion records simultaneously and is used vastly forthe mining of earthquake records features [Baker, 2007; Yaghmaei-Sabegh, 2010a]. Thus,in the first part of this article (Secs. 2– 4), the large pulse of ground motions is extractedby applying continuous wavelet transforms, and then the residual motions are achieved bysubtracting of extracted pulse from the original motions. The elastic and inelastic displace-ments of SDOF systems were derived for the original and residual motions undergoingdifferent level of ductility. The preferred wavelet-based decomposition process aids quan-tification of the effect of extracted pulses on inelastic displacement ratio spectra (IDRS) bycomparing the results of original motions with those of the residual ground motions. Theprocedure developed in this article is applied to ground acceleration records classified byBaker [2007] as pulse-like motions and inelastic displacement ratios associated to meanvalues are derived. Displacement spectrum has been highlighted in this study, because itis known as a basic step in performance-based design just like to acceleration responsespectrum in traditional force-based design. As a result, inelastic displacement ratio spectra(IDRS) which have been derived for pulse-like ground motions could be used for predictingof inelastic demand of structures located in near-field area. In the second part (section 5),several parameters influencing on inelastic displacement ratio spectra for these types ofmotions are discussed.
2. Previous Studies on Wavelet Analysis and Applications
To illustrate the capacity of proposed method, a brief overview of the fundamental conceptsof wavelet analysis as well as its applications on earthquake and structural engineering ispresented herein. The wavelet name comes from the requirement that a function shouldintegrate to zero, waving above and below the axis [Suter 1997]. In 1982, the first dis-cussion about the idea of a wavelet was published by geophysicists involved in seismicsignal analysis [Morlet et al., 1982], although at this time it was a rather empirical scheme.Some researchers in wavelet field such as Graps believe that this idea basically is not new,because approximation using superposition of functions has existed since the early 1800’s,when Joseph Fourier found that superpose of sines and cosines could be used to repre-sent other functions, say earthquake ground motion records [Graps, 1995]. Conceptually,wavelet analysis is the breaking up of a signal but into shifted and scaled versions of awavelet prototype function, called “mother wavelet.” The basic idea behind wavelets is to
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analysis according to scale which plays an essential role in the wavelet analysis procedureand simply means stretching (or compressing) it. It is worth pointing out that Fourier basisfunctions are localized in the frequency domain, but not in time. Wavelet basis functionshave removed the shortcoming of Fourier analysis by switching from the time-frequencyto the time-scale and are inherently better suited to the analysis of earthquakes which areknown as transient and non stationary events. In this procedure, the signal can be decom-posed to a set of these of different frequencies taking place at different times. In addition,it is able to detect more costly information from the time series than other classical meth-ods of analysis which will use in this study for extracting of strong pulse of the nominatedrecords.
Wavelet analysis has been extended as a powerful method both in earthquake engi-neering and seismology field over the past decade and its domain is increasing rapidly. Itsapplications can be found in several studies that refer to dynamic analysis of structures,system identification and data mining operation, damage localization, health monitoring,derivation of evolutionary power spectra, early warning system (EWS), and processingof strong ground motion records [Basu and Gupta, 1997; Iyama and Kuwamura, 1999;Mukherjee and Gupta, 2002; Zhou and Adeli, 2003; Pazos et al., 2003; Iyama, 2005;Huang and Su, 2007; Jung and Koh 2009; Yan et al., 2010; Chunxiang and Jianhong, 2010].Todorovska et al. [2009] applied orthogonal wavelet series for reduced dimensionality rep-resentation of strong ground motion records. Earlier, the wavelet transform decompositionhas been used by Cao and Friswell [2009] to evaluate the effect of energy concentration ofearthquake ground motions on nonlinear response of reinforced concrete structures.
The wavelet transform of a ground motion, g(t), with respect to mother waveletfunction ψ(•) is defined by:
WT[g; a, b
] = 1√|a|
∞∫−∞
g(t)ψ∗(t − b
a)dt, (1)
where a �= 0 and b are real values called the scale and translation or location parameters,respectively, and symbol ∗ denotes complex conjugation. Dilation by the scale a which isinversely proportional to frequency represents the periodic nature of the signal. WT
[g; a, b
]as results of the wavelet transform is representing a time-scale map (or Scalogram). Thefactor 1
/√|a| is used to normalize the energy to keep the energy at the same level fordifferent values of a and b. By taking Fourier transform of ψ(t), it is possible to reconstructg(t) from its wavelet transform, WT
[g; a, b
], as:
g(t) = 1
2πCψ
∞∫−∞
∞∫−∞
1
a2WT[g, a, b]ψ(
t − b
a)dadb (2)
Cψ =∞∫
−∞
∣∣∣ψ̂(ω)∣∣∣2
|ω| dω, (3)
where ψ̂(ω) is the Fourier transform of ψ(t) and the coefficient of Cψ is a constant dependson the selected mother wavelet.
It is acknowledged that the continuous wavelet transform (CWT) which has been usedin the present study computes the wavelet coefficients associated with every integer value
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564 S. Yaghmaei-Sabegh
of the scale and location parameters. More detailed description about mathematics back-ground of continuous wavelet transform can be found in text books of the subject [Newland,1997; Walnut, 2003].
3. Inelastic Displacement Ratio
The inelastic displacement ratio (C) is defined as ratio of maximum inelastic displacementdemand (�inelastic) to the corresponding elastic one (�elastic) on a SDOF oscillator with thesame mass and initial stiffness while subjected to the same earthquake ground motion. Thisratio is expressed mathematically as
C = �inelastic
�elastic. (4)
For the purpose of earthquake design, maximum inelastic displacement demands (�inelastic)corresponding to specific values of μ were calculated by iteration process on the lateralstrength of the system until the displacement ductility demand was, within a tolerance,equal to the specified ductility ratio. This tolerance named as “ductility convergencetolerance” and is taken to be 0.01 in the present work.
The provided spectra in this article describe constant-ductility inelastic spectral ordi-nates and will provide a functional connection for estimating of maximum inelasticdisplacement demand of SDOF systems based on maximum elastic displacement. Here,the force-displacement relationship of system is elastic-perfectly plastic, damping ratio isassumed 5% of critical damping and inelastic ratios were computed for five different levelsof ductility ratios: 2, 3, 4, 5, and 6. To outline inelastic displacement ratio spectra (IDRS),C was computed for a set of 200 natural vibration periods between 0.02 and 4 s.
4. Description of the Procedure
The availability of instrumented measured ground motions in near-field areas duringthe recent destructive earthquakes—1994 Northridge, California; 1995 Kobe, Japan;1999 Kocaeli, Turkey; 1999 Chi-Chi, Taiwan—provided great information of the veloc-ity pulses recorded on different site conditions and has brought significant fine-tuning inthe practice of structural engineering.
In this article, the large pulse of selected ground motions is extracted by applying con-tinuous wavelet transforms, and then the residual motions are achieved by subtracting ofextracted pulse from the original motions (Sec. 4.1). This database enabled us to captureeffect of pulse-like ground motions on estimating of inelastic demand of structures withdifferent ductility level. For this purpose, the elastic and inelastic displacements and there-fore IDRS of SDOF systems were derived for the original and residual motions undergoingdifferent level of ductility (Sec. 4.2). Thus, by means of solving a linear elastic systemwhich is generally accurate enough for engineering purposes, inelastic demands will bedetermined directly for different level of ductility under pulse-like motions without anynonlinear time history analysis.
4.1. Preparing of Seismic Input
Recently, Baker [2007] presented a wavelet-based method for identifying ground motionscontaining strong velocity pulse caused by near-field directivity. In this process, the largestvelocity pulse from a given ground motion is extracted and the size of original motion is
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Application of Wavelet Transforms 565
compared with the residual of motion after this extraction. Comparisons were made bymeans of a pulse indicator (PI) which proposed by Baker [2007] as the following form:
The above equation consists of two predictor variables: (1) PGV ratio that is the peakground velocity of the residual record divided by the original record’s PGV; and (2) energyratio which is obtained by dividing the energy of the residual record to the original record’senergy. Hereby, one pulse indicator is assign for each record and records with score above0.85 are classified as pulse-like motion. For complete details of this approach the readershould refer to Baker [2007]. Ninety-one large-velocity pulses of 3,500 fault-normal strongground motion recordings of Next Generation Attenuation (NGA) project library (www.peer.berkeley.edu), classified by Baker [2007] as pulse-like ground has been selected asseismic input in this article. It is worth noting that Daubechies wavelet of order 4 (db4) hasbeen used as the mother wavelet in this classification.
Earlier, behavior of the different types of mother wavelets on classification perfor-mance and estimation of pulse period for velocity time series of ground motions wereinvestigated by Yaghmaei-Sabegh [2010a]. From analysis, it was revealed that the choice ofmother wavelets and its associated scaling function are very significant to obtain the mostreliable wavelet transforms and it depends on the characteristic of velocity pulse whichfrequently appears in near-fault ground motions. The comparisons among different motherwavelets also showed the better performance of BiorSpline (bior1.3) basis from biorthognalwavelet families. Consequently, this mother wavelet is used in this article for pulse extrac-tion of a total of 91 pulse-like ground motions in NGA database. Example of the extractionprocedure are presented in Figs. 1 and 2 which show the acceleration and velocity timehistory of original ground motions, and the associated extracted pulse for 1998 Northridgeearthquake recorded in Rinaldi Receiving station along with the residual ground motionachieved after the pulse extraction. Key properties regarding the recording stations andearthquakes characteristics are listed in Table 1 which are used as seismic excitation in thenext section of the article.
4.2. Inelastic Displacement Ratio Spectra for Pulse-Like Ground Motions
This section describes main characteristics of inelastic displacement ratio spectra (IDRS)derived for pulse-like motions along with the contribution of pulse in displacement demandof structures. For this purpose, IDRS for two sets of ground motions, original pulse-likemotions, and residual ground motions, corresponding to five ductility levels 2, 3, 4, 5, and6 are computed. Figure 3 shows the mean IDRS by separately averaging of results for twosets of ground motions. This figure will provide a suitable condition for: (1) predictingmaximum inelastic displacement of a SDOF system from the corresponding elastic one fordifferent level of ductility under pulse-like motions; and (2) evaluating the contribution ofstrong pulse portion of such motions on IDRS. In order for better visualization of structuralinfluence of pulse for different natural vibration period, the ratio of mean IDRS for originalpulse-like ground motions to residual ones is presented in Fig. 4. Plotting of IDRS curvesin Fig. 4 will provide a suitable implement to quantify the effect of pulse portion of motionson actual demand estimation of structures. As shown in this figure, the effect of pulse isobvious as 5, 10, 15, 20, and 30% increasing in IDRS for different structural ductility levelof 2, 3, 4, 5, and 6, respectively. This means that this ratio generally becomes much larger
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566 S. Yaghmaei-Sabegh
Original Ground Motion
–1
–0.8
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25
Time(Sec)
Acce
lera
tion
(g)
Original Ground Motion
–200
–150
–100
–50
0
50
100
150
0 5 10 15 20 25
Time(Sec)
Ve
locity
(cm
/se
c)
FIGURE 1 Acceleration, velocity time history of original ground motion of1994 Northridge event recorded in Rinaldi Receiving station.
by increasing the ductility level. The largest ratio, nearly 30%, is observed for ductilitylevel of 6 and smallest effect of pulse on IDRS exists for ductility ratio of 2.
5. Effect of Ground Motion Parameters on IDRS
The effect of several ground motion parameters on derived pulse-like ground motioninelastic displacement ratio spectra is investigated herein. For this purpose, the thresholdvalue of different ground motion parameters was selected as an average of those calculatedusing all of ground motions. Then the database is separated into two groups, lower andlarger than these thresholds, and the corresponding ratio of the inelastic displacement ratiospectra for each group is evaluated.
Near-field ground motions generally include large amplitude pulses in both velocityand displacement that can cause significant levels of interstory drift in structural systems[Yaghmaei-Sabegh, 2010b]. Thus, peak ground velocity (PGV) and peak ground displace-ment (PGD), two most important parameters in near-field area, are evaluated for differentlevel of ductility in Figs. 5 and 6. These figures show results for PGV>65cm/s andPGD>40 cm to those with PGV<65 cm/s and PGD<40 cm. The largest difference ofIDRS for the two PGV and PGD parameters are 1.26 and 1.65, respectively, and occur
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Application of Wavelet Transforms 567
Extracted Pulse
–1
–0.8
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25Time(Sec)
Accele
ration(g
)
Residual Ground Motion
–1
–0.8
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25
Time(Sec)Accele
ration(g
)
FIGURE 2 Associated extracted pulse and residual ground motion of 1994 Northridgeevent recorded in Rinaldi Receiving station.
around 2.4 s. Comparison of these figures also shows that PGD has more effect on theIDRS for pulse-like ground motions particularly at long periods.
The ratio of peak ground velocity to peak ground acceleration (PGV/PGA) as a repre-sentative of frequency content, has a significant effect not only on peak inelastic responsebut also on hysteretic energy dissipation and stiffness deterioration of stiffness degradingsystems [Zhu et al., 1988]. Also, Liu et al., [2006] found that the maximum of momentaryinput energy spectra is insensitive to this ratio which is a very important parameter to char-acterize the damage potential of ground motions. Hence, its influence on IDRS is presentedin Fig. 7 for pulse-like ground motions as a ratio of results for PGV/PGA>0.2 to thosewith PGV/PGA<0.2. Several important remarks can be made from Fig. 7, meaning thatthe mean IDRS for ground motions with PGV/PGA>0.2 has been significantly amplifiedto those with PGV/PGA<0.2 at long period ranges. This amplification increases when theductility level is increasing and can reach 45% for a ductility level of six at 2.28 s.
Arias intensity [Arias, 1970] as a measure of earthquake intensity that strongly corre-lated with the level of damage and local intensity [Margottini et al., 1992; Cabanas et al.,1997] is defined for ground motion in the x direction as follows:
Ia = π
2g
Td∫
0
(aX(t))2dt, (6)
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Arr
ay#6
6.2
36.3
C0.
2435
.46.
50.
8426
Taiw
anSM
AR
T1(
40)
1986
SMA
RT
1C
006.
368
.2D
0.2
31.2
6.8
0.32
27Ta
iwan
SMA
RT
1(40
)19
86SM
AR
T1
M07
6.3
67.2
D0.
2336
.18.
170.
35
28N
.Pal
mSp
ring
s19
86N
orth
Palm
Spri
ngs
6.1
10.6
D0.
6873
.611
.82.
1729
San
Salv
ador
1986
Geo
tech
Inve
stig
Cen
ter
5.8
7.9
C0.
8562
.310
3.07
30W
hitti
erN
arro
ws-
0119
87D
owne
y-
Co
Mai
ntB
ldg
6.0
16.0
D0.
234
30.4
40.
48
31W
hitti
erN
arro
ws-
0119
87L
B-
Ora
nge
Ave
6.0
20.7
D0.
2532
.94.
80.
5532
Supe
rstit
ion
Hill
s-02
1987
Para
chut
eTe
stSi
te6.
516
.0D
0.42
106.
850
.53.
5533
Lom
aPr
ieta
1989
Ala
med
aN
aval
Air
Stn
Han
ger
6.9
90.8
D0.
2232
.210
0.4
34L
oma
Prie
ta19
89G
ilroy
Arr
ay#2
6.9
29.8
D0.
4145
.712
.51.
5135
Lom
aPr
ieta
1989
Oak
land
-O
uter
Har
bor
Wha
rf6.
994
.0D
0.33
49.2
13.1
0.97
36L
oma
Prie
ta19
89Sa
rato
ga-
Alo
haA
ve6.
927
.2C
0.36
355
.629
.41.
437
Erz
ican
,Tur
key
1992
Erz
inca
n6.
79.
0D
0.47
95.4
32.1
2.03
38C
ape
Men
doci
no19
92Pe
trol
ia7.
04.
5C
0.62
82.1
25.5
3.67
39L
ande
rs19
92B
arst
ow7.
394
.8C
0.14
30.4
27.7
0.26
3
(Con
tinu
ed)
569
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nloa
ded
by [
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] at
12:
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0 Se
ptem
ber
2013
TAB
LE
1(C
ontin
ued)
#E
vent
Yea
rSt
atio
nM
w
Epi
cent
ral
dist
ance
NE
HR
Pcl
assi
ficat
ion
PGA
(g)
PGV
(cm/s)
PGD
(cm
)
Ari
asin
tens
ity(m/s)
40L
ande
rs19
92L
ucer
ne7.
344
.0C
0.7
140.
324
36.
7441
Lan
ders
1992
Yer
mo
Fire
Stat
ion
7.3
86.0
D0.
2253
.245
.30.
9642
Nor
thri
dge-
0119
94Je
nsen
Filte
rPl
ant
6.7
13.0
C0.
5267
.442
2.65
43N
orth
ridg
e-01
1994
Jens
enFi
lter
Plan
tG
ener
ator
6.7
13.0
C0.
5267
.442
.62.
65
44N
orth
ridg
e-01
1994
LA
-W
adsw
orth
VA
Hos
pita
lNor
th6.
719
.6C
0.27
32.4
10.4
0.79
45N
orth
ridg
e-01
1994
LA
Dam
6.7
11.8
C0.
576
77.1
201.
846
Nor
thri
dge-
0119
94N
ewha
ll-
WPi
coC
anyo
nR
d.6.
721
.6D
0.43
87.8
551.
44
47N
orth
ridg
e-01
1994
Paco
ima
Dam
(dow
nstr
)6.
720
.4A
0.5
50.4
6.4
1.3
48N
orth
ridg
e-01
1994
Paco
ima
Dam
(upp
erle
ft)
6.7
20.4
A1.
3710
7.1
2310
.17
49N
orth
ridg
e-01
1994
Rin
aldi
Rec
eivi
ngSt
a6.
710
.9D
0.87
167.
228
.88.
250
Nor
thri
dge-
0119
94Sy
lmar
-C
onve
rter
Sta
6.7
13.1
D0.
613
0.3
546.
3
51N
orth
ridg
e-01
1994
Sylm
ar-
Con
vert
erSt
aE
ast
6.7
13.6
C0.
8411
6.6
39.4
4.32
52N
orth
ridg
e-01
1994
Sylm
ar-
Oliv
eV
iew
Med
FF6.
716
.8C
0.73
122.
731
.73.
8
53K
obe,
Japa
n19
95Ta
kara
zuka
6.9
38.6
D0.
6472
.620
.74
2.93
54K
obe,
Japa
n19
95Ta
kato
ri6.
913
.1D
0.68
169.
645
10.5
570
Dow
nloa
ded
by [
RM
IT U
nive
rsity
] at
12:
33 2
0 Se
ptem
ber
2013
55K
ocae
li,T
urke
y19
99G
ebze
7.5
47.0
B0.
2452
.044
.10.
5356
Chi
-Chi
,Tai
wan
1999
CH
Y00
67.
640
.5D
0.31
64.7
21.4
257
Chi
-Chi
,Tai
wan
1999
CH
Y03
57.
643
.9D
0.26
42.0
7.8
1.38
58C
hi-C
hi,T
aiw
an19
99C
HY
101
7.6
32.0
D0.
4585
.457
.32.
4559
Chi
-Chi
,Tai
wan
1999
TAP0
037.
615
1.7
E0.
0933
.018
.20.
3860
Chi
-Chi
,Tai
wan
1999
TC
U02
97.
679
.2C
0.22
62.3
51.8
0.76
61C
hi-C
hi,T
aiw
an19
99T
CU
031
7.6
80.1
D0.
1159
.948
.90.
5762
Chi
-Chi
,Tai
wan
1999
TC
U03
47.
687
.9C
0.23
42.8
34.7
0.8
63C
hi-C
hi,T
aiw
an19
99T
CU
036
7.6
67.8
D0.
135
62.4
640.
7764
Chi
-Chi
,Tai
wan
1999
TC
U03
87.
673
.1D
0.14
50.9
650.
7565
Chi
-Chi
,Tai
wan
1999
TC
U04
07.
622
.1E
0.14
553
.056
.30.
6566
Chi
-Chi
,Tai
wan
1999
TC
U04
27.
626
.3D
0.21
47.3
37.7
1.11
67C
hi-C
hi,T
aiw
an19
99T
CU
046
7.6
16.7
B0.
1444
.035
.60.
4768
Chi
-Chi
,Tai
wan
1999
TC
U04
97.
63.
8C
0.28
44.8
661.
3769
Chi
-Chi
,Tai
wan
1999
TC
U05
37.
66.
0C
0.22
541
.956
0.96
70C
hi-C
hi,T
aiw
an19
99T
CU
054
7.6
5.3
D0.
1760
.963
171
Chi
-Chi
,Tai
wan
1999
TC
U05
67.
610
.5D
0.12
743
.549
0.91
72C
hi-C
hi,T
aiw
an19
99T
CU
060
7.6
8.5
D0.
2133
.749
0.68
73C
hi-C
hi,T
aiw
an19
99T
CU
065
7.6
0.6
D0.
8212
7.7
937.
7174
Chi
-Chi
,Tai
wan
1999
TC
U06
87.
60.
3C
0.56
191.
137
33.
5775
Chi
-Chi
,Tai
wan
1999
TC
U07
57.
60.
9C
0.33
88.4
86.6
2.97
76C
hi-C
hi,T
aiw
an19
99T
CU
076
7.6
2.8
C0.
363
.732
3.52
77C
hi-C
hi,T
aiw
an19
99T
CU
082
7.6
5.2
D0.
2556
.171
.61.
3478
Chi
-Chi
,Tai
wan
1999
TC
U08
77.
67.
0C
0.1
53.7
650.
4179
Chi
-Chi
,Tai
wan
1999
TC
U09
87.
647
.7C
0.11
32.7
27.6
0.46
80C
hi-C
hi,T
aiw
an19
99T
CU
101
7.6
2.1
D0.
2268
.471
.81.
0881
Chi
-Chi
,Tai
wan
1999
TC
U10
27.
61.
5D
0.29
106.
687
282
Chi
-Chi
,Tai
wan
1999
TC
U10
37.
66.
1C
0.13
262
.285
0.67
(Con
tinu
ed)
571
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nloa
ded
by [
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rsity
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ptem
ber
2013
TAB
LE
1(C
ontin
ued)
#E
vent
Yea
rSt
atio
nM
w
Epi
cent
ral
dist
ance
NE
HR
Pcl
assi
ficat
ion
PGA
(g)
PGV
(cm/s)
PGD
(cm
)
Ari
asin
tens
ity(m/s)
83C
hi-C
hi,T
aiw
an19
99T
CU
104
7.6
12.9
C0.
1131
.447
.30.
4884
Chi
-Chi
,Tai
wan
1999
TC
U12
87.
613
.2C
0.18
778
.796
.40.
7985
Chi
-Chi
,Tai
wan
1999
TC
U13
67.
68.
3C
0.17
51.8
600.
786
Nor
thw
estC
hina
-03
1997
Jias
hi6.
1−
D0.
2737
.06.
80.
7487
You
ntvi
lle20
00N
apa
Fire
Stat
ion
#35.
0−
D0.
643
.04.
41.
0688
Chi
-Chi
,Tai
wan
-03
1999
CH
Y02
46.
219
.7C
0.18
733
.119
.60.
489
Chi
-Chi
,Tai
wan
-03
1999
CH
Y08
06.
222
.4C
0.47
369
.913
.91.
890
Chi
-Chi
,Tai
wan
-03
1999
TC
U07
66.
214
.7C
0.52
59.4
9.6
191
Chi
-Chi
,Tai
wan
-06
1999
CH
Y10
16.
336
.0D
0.12
636
.313
.80.
5
572
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nloa
ded
by [
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Application of Wavelet Transforms 573
0
1
2
3
4
5
6
0.01
µ = 6
µ = 5
µ = 4
µ = 3
µ = 2
0.1 1 10Period(sec)
C
FIGURE 3 Mean IDRS for original pulse-like motions (bold lines) and residual groundmotions (dash lines) (color figure available online).
0.8
1
1.2
1.4
0 1 2 3 4 5
Period(Sec)
C(O
rig
ina
l)/C
(Re
sid
ua
l)
µ = 6µ = 5
µ = 4
µ = 3µ = 2
FIGURE 4 Ratio of mean IDRS of original pulse-like motions to those of residual motions(color figure available online).
where Ia is the Arias Intensity in units of length per time, aX is the acceleration time historyin the x direction in units of g, Td is the total duration of ground motion, and g is theacceleration of gravity. The effect of this parameter on mean IDRS of pulse-like groundmotions is shown in Fig. 8 because it is able to obtain more reliable estimating of the levelof expected damage by incorporating amplitude, frequency content, and duration of strongground-motion in near field-area. The comparison between the results corresponding toeach ductility level reveals the interesting finding that the ratio of IDRS for ground motionswith Ia ≥ 2 m/s is larger than those with Ia < 2 m/s for ductility level of 4, 5, and 6. Also,there is a large difference with maximum value of 1.5 between the results of low ductilitysystems (i.e., 2 and 3) and systems with high level of ductility (i.e., 4, 5, and 6). It can beconcluded that the arias intensity has a significant influence on IDRS for pulse-like groundmotions for systems with high ductility level.
The evaluation of the effect of local site condition on IDRS of pulse-like groundmotions is the final part of this section. To this end, the pulse like-ground motions in thisstudy are classified into two groups, rock and soil site condition, which is consistent withsoil classification of NEHRP of B, C and D, E, respectively. Figure 9 shows the ratio of
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574 S. Yaghmaei-Sabegh
0.8
1
1.2
1.4
1010.10.01Period(Sec)
C(P
GV
>6
5)/
C(P
GV
<6
5)
µ = 6µ = 5
µ = 4µ = 3
µ = 2
FIGURE 5 Ratio of IDRS for pulse-like motions with PGV>50 cm/s to those withPGV<50 cm/s (color figure available online).
0.8
1
1.2
1.4
1.6
1.8
0.01 0.1 1 10Period(Sec)
C(P
GD
>4
0)/
C(P
GD
<4
0)
µ = 6
µ = 5
µ = 4
µ = 3
µ = 2
FIGURE 6 Ratio of IDRS for pulse-like motions with PGD>40 cm to those withPGD<40 cm (color figure available online).
0.8
1
1.2
1.4
1.6
0.01 0.1 1 10Period(Sec)
C(P
GV
/PG
A>
0.2
)/C
(PG
V/P
GA
<0.2
µ = 6
µ = 5
µ = 4
µ = 3
µ = 2
FIGURE 7 Ratio of IDRS for pulse-like motions with PGV/PGA>0.2 to those withPGV/PGA<0.2 (color figure available online).
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Application of Wavelet Transforms 575
0.8
1
1.2
1.4
1.6
0.01 0.1 1 10
Period(Sec)
C(I
>2
)/C
(I<
2)
µ = 6
µ = 5
µ = 4
µ = 3
µ = 2
FIGURE 8 Ratio of IDRS for pulse-like motions with Ia ≥ 2 to those with Ia < 2 (colorfigure available online).
0.8
1
1.2
0.01 0.1 1 10
Period(Sec)
C(R
ock s
ites)/
C(S
oil
sites)
µ = 2µ = 3
µ = 5
µ = 6
µ = 4
FIGURE 9 Ratio of IDRS for pulse-like motions with rock condition to those with soilcondition (color figure available online).
IDRS for rock site to those with soil site condition. As seen in Fig. 9, in most period ranges,the IDRS for rock site conditions are smaller than those for soft soil condition; however, themaximum difference between two groups is about 15%. It means that the effect of local sitecondition on IDRS for pulse-like motion is lower than other aforementioned parameters inthis section of article. It should be noted that Figs. 3–9 were derived as average of thosecalculated using all of ground motions used in this article. Consequently, the results of thispaper can help us in prediction of mean inelastic displacement demands of structures frommean value of elastic displacement obtained by time history analyses over an ensemble of260 recorded accelerograms.
6. Summary and Conclusions
This study was aimed at studying the application of wavelet transforms on characteriza-tion of inelastic displacement ratio spectra (IDRS) for pulse-like ground motions which isknown as a very important subject in seismic performance evaluation of structures. IDRS
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576 S. Yaghmaei-Sabegh
are defined as the ratio of the maximum inelastic to the maximum elastic displacement of aSDOF system provide a simple estimation of its maximum inelastic displacement demandfrom the corresponding elastic one for different level of ductility. The results of this arti-cle lead to the presentation of a quantitative method for analyzing the effect of pulse-likemotions on inelastic demands of SDOF systems which has not been studied systematicallyin the past.
In the preferred procedure of this article, continuous wavelet transform as a quantitativeapproach is applied to extract strong near-fault velocity pulse of selected motions. Ninety-one large-velocity pulses of 3,500 fault-normal strong ground motion recordings of NextGeneration Attenuation (NGA) project library, classified by Baker [2007] as pulse-likeground, were used in this procedure. The largest velocity pulse from normal-fault compo-nent of selected earthquakes is extracted. IDRS for two sets of ground motions, originalpulse-like motions, and residual ground motions, corresponding to five ductility levels, 2,3, 4, 5, and 6 were computed. As this ratio generally becomes much larger by increasing theductility level, the largest ratios of near 30% is observed for ductility level of 6 and smallesteffect of pulse on IDRS exist for lower ductility ratio of 2. It means that designer shouldbe aware about this effect on inelastic displacement of structures, particularly for buildingswith higher ductility level. As another result, while the fundamental period moves awayfrom the pulse period of the records, the increase in IDRS tend to decrease.
The effect of various ground motion parameters on derived pulse-like ground motioninelastic displacement ratio spectra was investigated herein. These parameters wereincluded as PGV, PGD, ratio of PGV/PGA, arias intensity, and local site condition. It wasrevealed from comparative analysis that the arias intensity and PGV/PGA ratio has a signif-icant effect on IDRS, therefore on the maximum inelastic displacement of SDOF systemsunder pulse-like motions, in particular for systems with high ductility level and should beconsidered in seismic design of the structures constructed in near-field areas.
It should be mentioned that unlike of the ordinary records, there is a limited numberof records for this special class of motions. Consequently, the results in this study can besignificantly improved if additional high quality data become available, including adequateinformation on soil site conditions and characteristics of seismic source.
Acknowledgment
The writer thanks Soheil Yaghmaei-Sabegh for his kind assistance in preparing this article.
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