Cumulative demand of the earthquake ground motions in the near source

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2003; 32:1853–1865 (DOI: 10.1002/eqe.305)

Cumulative demand of the earthquake ground motionsin the near source

Gaetano Manfredi∗;†, Maria Polese and Edoardo Cosenza

Department of Structural Analysis and Design; University of Naples ‘Federico II’; via Claudio 21;80125 Napoli; Italy

SUMMARY

In this paper the e�ects of near-fault earthquakes are investigated through the study of parameters relatedto both input energy and plastic cycles demand. Based on the results of two di�erent regression analysesperformed with 128 near-fault and 122 far-�eld registrations, respectively, the Cosenza and Manfrediadimensional Id index was found to be the best seismological parameter correlated to the number n andamplitude m of plastic cycles in the vicinity of the source as well as far from it. Analytical formulationsfor n; m and for the equivalent number of plastic cycles neq are proposed for near-fault and far-�eldregions. The study of Id and neq shows the tendency of such parameters to increase as the distanceincreases. Copyright ? 2003 John Wiley & Sons, Ltd.

KEY WORDS: near fault; cumulative damage; attenuation law; input energy; plastic cycles

INTRODUCTION

In recent years, especially after extremely damaging events such as the 1995 Hyogo-Ken-Nambu (Kobe) earthquake (with more than 5000 victims and damage to structures estimatedas more than 96 billion dollars for reconstruction) attention on the e�ects of near-fault earth-quakes has been growing. In the whole territorial area surrounding an active fault system, andfor a distance from the fault surface projection that may reach the linear fault dimension, theground waves radiation pattern is strongly in�uenced by the source (i.e. fault rupture process).It has been observed [1] that near-fault records that match the forward directivity conditions(i.e., the rupture front propagates toward the site, and the direction of slip on the fault isaligned with the site) are characterized by a single large impulse of motion at the beginningof the seismogram. Ground shaking phenomenon in the near-fault area then may generatelarge velocity pulses (i.e. a great amount of energy demand to be dissipated nearly instanta-neously); as a consequence, structures may experience one or a few large plastic cycles, and

∗ Correspondence to: Gaetano Manfredi, Department of Structural Analysis and Design, University of Naples‘Federico II’, via Claudio 21, 80125 Napoli, Italy.

† E-mail: [email protected] 1 March 2002

Revised 16 December 2002Copyright ? 2003 John Wiley & Sons, Ltd. Accepted 22 January 2003

1854 G. MANFREDI, M. POLESE AND E. COSENZA

deformations will concentrate in their weaker parts, enhancing the risk of brittle failures andsoft-storey mechanisms.In this work, an attempt is made to better understand the earthquake e�ects on the structures

in the near-fault region. The presented results deal with the determination of the seismologicalparameter best correlated to the plastic cycles demand in the near source, and its variationwith the distance from the fault is investigated. The study con�rms that parameters governingthe earthquake phenomenon vary with distance from the fault, and a physically discriminativedistance can be assumed to be equal to fault length.

EQUIVALENT NUMBER OF PLASTIC CYCLES

Earthquakes transmit to structures an amount of input energy that has to be dissipated in orderto guarantee the system’s equilibrium. Depending on the earthquakes’ characteristics in relationto the global and local features of the main horizontal bearing system of the structure suchinput energy may (or at least should!) be absorbed in one or a few large plastic displacementcycles, or with a general hysteretic dissipation resource that is exploited through a greatnumber of plastic cycle reversals. In the �rst case, earthquake damage potential is mainlyrelated to maximum required ductility for the system, whilst in the second case it depends onhysteretic demand, i.e. on the number n and amplitude of subsequent plastic cycles that thestructure has to develop to absorb input energy. It is clear that a reasonable prediction of theexpected seismic input in relation to the number n and adimensional amplitude m (de�ned asthe mean value of the amplitudes of the n−1 cycles smaller than the plastic cycle of maximumamplitude �xmax = xmax − xy, scaled to �xmax [2]) may be a helpful tool for a meaningfulevaluation of structural behaviour due to seismic action. Analogously the equivalent numberof plastic cycles (neq) may be considered: it represents the number of plastic cycles at themaximum value of plastic excursion that the structure must develop in order to dissipatethe total amount of hysteretic energy EH [3]. For an elastic perfectly plastic system it isde�ned as:

neq =EH

Fy · (xmax − xy) (1)

where Fy is the yielding force. Clearly neq tends to 1 for impulsive type earthquakes, whilstit grows for earthquakes characterized by a great number of large plastic excursions. By thede�nition of n; m and neq it results that [4]:

neq = 1 + (n− 1) ·m (2)

PLASTIC CYCLES DEMAND AND THE Id INDEX

The equivalent number of plastic cycles, neq, is a spectral quantity and it depends on thestructure’s fundamental period of vibration, damping and ductility level and on the seismicinput itself. Considering this, it is theoretically possible to distinguish the in�uence of structuraland seismological parameters on cyclic demand and to determine an analytical expression ofthe number n, and of the amplitude m, of plastic cycles demand, or, analogously, of the

Copyright ? 2003 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2003; 32:1853–1865

EARTHQUAKE GROUND MOTIONS IN THE NEAR SOURCE 1855

Table I. Earthquakes considered and fault dimensions.

Event Date Magnitude Fault length (km) Fault width (km)

Imperial Valley 15/10/1979 6.5 42 10.5Whittier 01/10/1987 5.9 10 10Loma Prieta 18/10/1989 6.9 40 20Northridge 17/01/1994 6.7 18 24Kobe 16/01/1995 6.9 20 + 40=60 20

number of equivalent cycles neq, in the function of selected signi�cant parameters. In orderto obtain a reliable estimate of n;m and neq, an extensive regression analysis based on anumber of strong motion records was performed; assuming an exponential-type formulation,the optimum elastic, plastic and seismic parameters were determined and their expression wasfound.Once chosen a di�erent set of records for each of the two cases of near-fault and far-�eld

conditions (128 near-fault and 122 far-�eld records – two horizontal components from 64and 61 recording stations, respectively; Tables I and AI, and Reference [5] for far-�eld) theanalysis was carried out separately for the two cases. The steps listed below were followed:

• a number of possible structural parameters (i.e., sti�ness, yielding force, reduction fac-tor R, damping percentage etc.) and seismological parameters (i.e., PGA; PGV; PGD,e�ective duration according to Trifunac and Brady te� [6], Arias intensity IA [7], Fajfarintensity IF [8], Cosenza and Manfredi Id index [9], number of zero crossing nzc [10],PGA=PGV ) correlated with n and m and, analogously, to neq, are introduced;

• an exponential type formulation for n; m and neq is adopted:

n=1+ A ·p�e; i ·p�p; i ·p�s; i (3)

m= B ·p�e; i ·p�p; i ·p�s; i (4)

and from (2)

neq = 1 + C ·p�e; i ·p’p; i ·p�s; i (5)

where pe; pp and ps are the possible structural, elastic and plastic, and seismological param-eters;

• a statistical regression is performed, comparing the values of n; m and neq obtained by astep-by-step integration of the equation of motion of the SDOF system with those givenby the proposed formulation;

• optimal parameters are de�ned by choosing those with higher partial correlation factors;• the best coe�cients A; B; �; �; �; �; �; �; �; , and � are those minimizing the standard error.It seems that the elastic behaviour of the system is adequately described by the percentage

� of proportional damping , normalized to the reference value 0 = 5% (�= =0), and bythe ratio �=T=T1, with T1 = initial period of medium period region in the Newmark and Hallspectral representation [11]. The plastic response is fully represented by (R−1), where R is the



Table II. Partial correlation factors obtained by regression for near-source registrations.

PGA PGV PGD IF IA Id te� znc PGA=PGV

n 0.55 0.61 0.52 0.53 0.46 0.68 0.63 0.53 0.44m 0.13 0.14 0.15 0.14 0.14 0.22 0.13 0.17 0.16

Table III. Partial correlation factors obtained by regression for far-�eld registrations.

PGA PGV PGD IF IA Id te� znc PGA=PGV

n 0.73 0.72 0.72 0.72 0.74 0.87 0.82 0.79 0.72m 0.33 0.35 0.36 0.33 0.27 0.39 0.26 0.27 0.32

reduction factor de�ned as:

R=ms · Sa(T )

Fy(6)

with Sa(T )= elastic spectral acceleration, ms=oscillator’s mass and Fy = yielding force [9].Regarding the seismological parameters, PGA; PGV , and PGD represent the peak groundacceleration, velocity and displacement, respectively. IA (the Arias intensity) is de�ned as:

IA =�2g

∫ d

0a2(t) dt (7)

with a=ground acceleration and d=seismic event duration. The e�ective duration by Trifunacand Brady, te� , is de�ned as the time interval in which IA varies between 5% and 95% of itsmaximum value, while IF (the Fajfar intensity) is given by:

IF =PGV · t0:25e� (8)

The Cosenza and Manfredi Id index is de�ned as:

Id=IE

PGA ·PGV =2g�

· IAPGA ·PGV (9)

with IE =∫ d0 a

2(t) dt.Finally, the number of zero crossing, nzc, represents the number of the accelerogram’s sign

inversion in the te� interval.By applying such a procedure, it is found that the Id index is the seismological parameter

that best describes the phenomenon in the near-fault as well as in the far-�eld, having thehigher partial correlation factors with n;m and neq, respectively. Partial correlation factors withn and m for all the analysed seismological parameters are compared in Tables II and III forboth near-fault and far-�eld cases.The resulting expressions of nn:f :; mn:f :; nf :f : and mf :f :, where n.f. and f.f. refer to near-fault

and far-�eld conditions, respectively, for an elastic perfectly plastic 5% damped oscillator, are



listed in Equations (10) to (13):

nn:f : =1+ 1:25 · �−2=3 · (R− 1)1=2 · I 4=5d (10)

mn:f : =0:19 · �1=6 · (R− 1)−1=10 · I 1=5d (11)

nf :f : =1+ 1:05 · �−2=3 · (R− 1)4=5 · I 4=5d (12)

mf :f : =0:17 · �1=6 · (R− 1)−1=5 · I 1=5d (13)

The mean and standard errors of the estimate (versus the mean) obtained with Equations (10)and (11) are 0.46 and 0.53 for n, and 0.36 and 0.50 for m, respectively. The mean andstandard errors (versus the mean) obtained with Equations (12) and (13) are 0.11 and 0.46for n, and 0.15 and 0.47 for m, respectively. The errors are slightly greater in the near-fault,probably due to the major complexity of the phenomenon near the source and to the di�cultyin describing it. Moreover, it is interesting to note that:

• with reduction factor R decreasing a smaller number of cycles n is obtained, whilst theaverage value m increases;

• for increasing period, in the �eld of low periods, the number of cycles decreases, whilsttheir average amplitude increases;

• dependence of n on Id is nearly linear;• the in�uence of (R− 1) on n is greater for far-�eld than for near-fault earthquakes.

An analogous expression to those of Equations (10) and (12) is found for neq; consideringEquation (2), the same formulas can also be obtained by combining Eqs (10) and (11), or(12) and (13), respectively, for near-fault and far-�eld.

neq;n:f : =1+ 0:23 · �−1=2 · (R− 1)2=5 · Id (14)

neq; f :f : =1+ 0:18 · �−1=2 · (R− 1)3=5 · Id (15)

In Figures 1 and 2 the comparison between e�ective neq (mean value in the medium periodsrange for a reduction factor R=4) and neq calculated with Equations (14) and (15) is shown.As can be seen, Equations (14) and (15) give a good estimate of neq in the near-fault and inthe far-�eld, respectively. There is a little di�erence in the parameters and exponent values oncomparing the equations, but in both conditions the dependence of neq on the seismologicalparameter Id is linear. It can be concluded that Id is a very stable parameter, representingdamage potential connected to the plastic cycles demand in the far-�eld as well as in thenear-fault.The study of its variation with the distance from the fault contributes to giving a qualitative

and rational explanation of the diversity of seismic demand for sites located in the proximityof the fault compared to those in far-�eld conditions, as observed by several researchers[12–14].



0

2

4

6

8

10

12

0 2 4 6 8 10 12

approximate neq

effe

ctiv

e n e

q

Figure 1. Comparison between e�ective neq;n:f : (mean value in the medium periods range for a reductionfactor R=4) and neq;n:f : calculated with Equation (14).

0

2

4

6

8

10

12

0 2 4 6 8 10 12

approximate neq

effe

ctiv

e n e

q

Figure 2. Comparison between e�ective neq; f :f : (mean value in the medium periods range for a reductionfactor R=4) and neq; f :f : calculated with Equation (15).

VARIATION OF Id AND neq WITH THE DISTANCE FROM THE FAULT

The study of the variation of Id and neq with the distance from the fault has been conductedspeci�cally for the cases of the Kobe and Northridge earthquakes. These earthquakes were



0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5

r j.b./Flength

I d,g

h/I d

,gh,

max

Northridge

Kobe

Near Fault limit

Near Faultregion

Figure 3. Variation of Id;gh=Id;gh;max with adimensionalized distance from fault rj:b:=Flength for the casesof the Kobe and Northridge earthquakes.

chosen due to the great number of near-source registrations available. Earthquakes and record-ing station characteristics, and the relative distance rj:b: from the fault, are listed in Tables Iand AII, where rj:b: is de�ned as the shortest distance between the recording site and thevertical projection of the rupture zone on the surface of the earth (j.b. stands for Joyner andBoore de�nition of distance [15]). As can be seen from Table I, the Kobe faulting systemis formed by two separate faults, the lengths of which, however, may be summed for thepurpose of de�ning the area in�uenced by the source, i.e., to determine the near-fault area.For each recording station both horizontal components of acceleration were considered; the�rst, labelled 1, is the fault normal component, while the one labelled 2 is the fault parallelcomponent. The variation with rj:b was determined for Id;gh, that is the value of Id associatedwith the global horizontal acceleration, and is de�ned as:

Id;gh =√I 2d1 + I

2d2 (16)

where Id1 and Id2 are the values of Id determined for the two horizontal components; neq isthe mean value of neq;1 and neq;2; neq;1 and neq;2 being the equivalent number of plastic cyclesfor components 1 and 2, each averaged in the medium periods �eld, for a reduction factorR=4.In Figures 3 and 4 the variation of Id;gh and neq with rj:b, for both studied earthquakes, is

shown; the distance rj:b is scaled with respect to fault length, whilst neq and Id;gh are scaled tothe relative maximum value determined for each of the two earthquakes. As can be seen fromFigure 3, Id increases with distance from the fault and tends to become constant at a distancecorresponding to the fault dimension. The same trend can be observed in Figure 4 for neq,despite some irregularities, probably due to site e�ects. The parameter Id, then, adequatelydescribes the variation and the increase of plastic cycles demand with the distance from thefault rj:b, as was observed for real buildings [12]. The increase of plastic cycles demand with



0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5

r j.b. /Flength

n eq/n

eq,m

ax

Northridge

KobeNear Fault limit

Near Faultregion

Figure 4. Variation of e�ective neq (mean value in the medium periods range for a reduction factorR=4) scaled to its maximum value neq;max, with distance from fault scaled to its length rj:b:=Flength for

the cases of the Kobe and Northridge earthquakes.

the distance from the source can also be qualitatively con�rmed applying an attenuation lawas proposed by Chou and Uang [16] for the parameter Na, de�ned as the ratio of absorbedenergy Ea versus the energy absorbed at the elastic limit Ey:

Na =EaEy

(17)

It is possible to show that neq is directly related to Na as introduced in Reference [16]. Infact, considering that:

Ea = Ey + EH (18)

Ey = 12Fyxy (19)

�xmax = xmax − xy = ( − 1) · xy (20)

with system’s ductility, it results in:

Na = 1 + 2 · ( − 1) · neq (21)

Although the attenuation formula proposed in Reference [16] is strictly valid just in the far-�eld, its application may be helpful to comprehend the phenomenon. In fact, it is interestingto observe the tendency of Na to increase with distance from the fault for high values ofductility, and to become constant for large distances. In Figure 5 the trend is shown wherethe value of Na, for a system’s period T =0:7 s and a spectral reduction factor R=4, are



0.4

0.6

0.8

1

1.2

0 1 2 3 4 5

r j.b./Flength

Na/

Na

max

(T

=0.

7 s;

R=

4)

North r idge

Kobe

Near Fault limit

Near fault region

Figure 5. Variation of Na=Na;max, for T =0:7 s and R=4, with adimensionalized distance from faultrj:b:=Flength for the cases of the Kobe and Northridge earthquakes.

calculated for the same records as those used to investigate the variation of Id and neq. Na isscaled with respect to its maximum value for both earthquakes, and rj:b is scaled with respectto fault length.The analysis of the trend of the Id index allows a consistent interpretation of �eld ob-

servations and numerical studies performed by di�erent researchers. In fact, considering theformulation proposed for the input energy in Reference [5]:

(Eim

)max

=0:45 · (1 + 0:23 · Id) ·AV 2 ·PGV 2 (22)

the amount of the input energy demand is due to the product of three factors: the square ofthe peak ground velocity (PGV), the square of the spectral ampli�cation factor of the velocity(AV) and (1+ 0:23 · Id), which represents the e�ect of the duration of the earthquake relatedto the equivalent number of plastic cycles, neq.Therefore, although input energy is very high in the vicinity of the source, its peak value

is mainly due to peak velocity, that rapidly decreases with distance from the fault, whilst, atthe same time, the number of plastic cycles tends to increase with distance from the fault.Damage in the near-fault is mainly caused by the peak ground velocity and maximum

incremental velocity. Near-source impulse-type ground motion may force structures to absorba large amount of energy with a single or a few large plastic cycles, and that may be criticaleven for structures designed according to advanced seismic criteria.As a consequence, the relative importance of cyclic damage for structures grows at greater

distances from the fault, whilst in near-source conditions the structural response is governedby the peak demand. On the other hand, with increasing distance from the fault peak de-mands rapidly decrease, while plastic cyclic demand becomes more important; this penalizesstructures that are more vulnerable to cyclic damage, such as masonry structures or poorlydetailed RC structures.



CONCLUSIONS

In this work the e�ects of near-fault earthquakes are investigated through the study of structuraland seismological parameters related to both input energy and plastic cycles demand. Basedon the results of two di�erent regression analyses performed with 128 near-fault and 122far-�eld registrations, respectively, it was observed that:

• the Cosenza and Manfredi adimensional Id index was found to be the best seismologicalparameter correlated to the number n and amplitude m of plastic cycles in the vicinityof the source as well as far from it.

• analytical formulations for n;m and for the equivalent number of plastic cycles neq areproposed for near-fault and far-�eld regions; these equations are similar for dependenceon structural and seismological parameters.

On the other hand, the study of the variation of the Id index and neq with distance fromthe fault shows their tendency to increase with distance; in fact, after a sharp increase in thenear-fault area, the trend of the Id index becomes constant.As a consequence, the relative importance of the cyclic damage for structures grows at

higher distances from the fault, whereas in near-source conditions structural response is gov-erned by peak demand, con�rming the damage observations after destructive earthquakes.

APPENDIX A

Table AI. Records used in the regression analysis – near fault stations.

Event Station name Station ID1 Soil type2

Imperial Valley El Centro Array# 1 E01 Deep broad soilImperial Valley El Centro Array# 3 E03 Deep broad soilImperial Valley El Centro Array# 4 E04 Deep broad soilImperial Valley El Centro Array# 5 E05 Deep broad soilImperial Valley El Centro Array# 6 E06 Deep broad soilImperial Valley El Centro Array# 7 E07 Deep broad soilImperial Valley El Centro Array# 8 E08 Deep broad soilImperial Valley El Centro Array# 10 E10 Deep broad soilImperial Valley El Centro Array# 11 E11 Deep broad soilImperial Valley Holtville Post O�ce HVP Deep broad soilImperial Valley Aeropuerto Mexicali AEP Deep broad soilImperial Valley Agrarias AGR Deep broad soilImperial Valley Brawley Airport BRA Deep broad soilImperial Valley Bonds Corner BCR Deep broad soilImperial Valley Compuertas CMP Deep broad soilWhittier Calexico Fire Station CXO Deep broad soilWhittier Whittier N. Dam upstream WHD Deep broad soilWhittier El Monte – Fairview Ave FAI Deep broad soilWhittier San Gabriel – Grand Ave GRN Rock

Continued



Table AI. Continued.

Event Station name Station ID1 Soil type2

Whittier Arcadia – Campus drive CAM Deep broad soilWhittier Alhambra – Fremont sch. ALH Deep broad soilWhittier Bell Gardens – Jaboneria JAB Deep broad soilWhittier LA – Obregon Park OBR Deep broad soilWhittier San Marino – SW Academy SMA Deep broad soilWhittier Baldwin Park – Holly Ave NHO Deep broad soilWhittier LA – Figueroa st. FIG Deep narrow soilNorthridge Los Angeles Dam LDM Deep broad soilNorthridge Sylmar – Olive view SYL Deep broad soilNorthridge Arleta – Nordho� Fire st. ARL Deep broad soilNorthridge Newhall Fire st. NWH Deep broad soilNorthridge Sun Valley – Roscoe Blvd R03 Deep broad soilNorthridge Canyon Country – W lost cany LOS Deep broad soilNorthridge Canoga Park – Topanga CNP Deep broad soilNorthridge Rinaldi Receiving Station RRS Deep narrow soilNorthridge Beverly Hills – Mulhol MU2 Deep narrow soilNorthridge Big Tujunga TUJ Deep narrow soilNorthridge – WPI Deep narrow soilNorthridge Paci�c Palisades SUN Sti� soilNorthridge Topanga Fire st. TPF RockLoma Prieta Gilroy Array# 1 G01 RockLoma Prieta Gilroy Array# 2 G02 Deep broad soilLoma Prieta Gilroy Array# 3 G03 Deep broad soilLoma Prieta Saratoga – Aloha Ave STG Deep broad soilLoma Prieta Gilroy – Gavilan Coll GIL Sti� soilLoma Prieta Corralitos CLS Sti� soilLoma Prieta Capitola CAP Deep narrow soilLoma Prieta Saratoga W Valley WVC Deep broad soilLoma Prieta Anderson Dam AND Deep broad soilLoma Prieta Gilroy Historic Building GOF Deep broad soilLoma Prieta Agnews State Hospital AGW Deep broad soilKobe Abeno ABN Deep broad soilKobe Amagasaki AMA Deep broad soilKobe Yae YAE Deep broad soilKobe Kobe University KBU RockKobe Kakogawa KAK Soft soilKobe Nishi-Akashi NIS Soft soilKobe Shin-Osaka SHI Soft soilKobe Sakai SKI Soft soilKobe Takarazuka TAZ Soft soilKobe Takatori TAK Soft soilKobe Osaka OSA Soft soilKobe Port Island (0 m) PRI Soft soilKobe Fukushima FKS Soft soil

1 ID by PEER (Paci�c Earthquake Engineering Research); records are taken from PEER database.2 Soil type de�nition by PEER.



Table AII. Recording station used.

Event Station name Station ID1 rj:b: Soil type2

(km)

Kobe Abeno ABN 29 Deep broad soilKobe Amagasaki AMA 16 Deep broad soilKobe Yae YAE 32 Deep broad soilKobe Kobe University KBU 5 RockKobe Kakogawa KAK 20 Soft soilKobe Nishi-Akashi NIS 4 Soft soilKobe Shin-Osaka SHI 21 Soft soilKobe Sakai SKI 32 Soft soilKobe Takarazuka TAZ 4 Soft soilKobe Takatori TAK 6 Soft soilKobe Osaka OSA 26 Soft soilKobe Port Island (0 m) PRI 8 Soft soilKobe Fukushima FKS 22 Soft soilKobe Fukui FUK 155 Deep broad soilKobe Chihaya CHY 54 RockKobe Maizuru MZH 66 Sti� soilKobe Okayamon OKA 87 Sti� soilKobe Tottori TOT 117 Sti� soilKobe Hik HIK 96 –Northridge Los Angeles Dam LDM 0 Deep broad soilNorthridge Sylmar – Olive view SYL 4 Deep broad soilNorthridge Arleta – Nordho� Fire st. ARL 3 Deep broad soilNorthridge Newhall Fire st. NWH 5 Deep broad soilNorthridge Sun Valley – Roscoe Blvd R03 8 Deep broad soilNorthridge Canyon Country – W lost cany LOS 13 Deep broad soilNorthridge Canoga Park – Topanga CNP 2 Deep broad soilNorthridge Rinaldi Receiving Station RRS 0 Deep narrow soilNorthridge Beverly Hills – Mulhol MU2 13 Deep narrow soilNorthridge Big Tujunga TUJ 20 Deep narrow soilNorthridge – WPI 2 Deep narrow soilNorthridge Paci�c Palisades SUN 16 Sti� soilNorthridge Topanga Fire st. TPF 13 RockNorthridge Arcadia – Campus Dr CAM 41 Deep broad soilNorthridge Bell Gardens – Jaboneria JAB 42 Deep broad soilNorthridge Baldwin Park – N. Holly Ave NHO 48 Deep broad soilNorthridge Anaheim – W Ball Rd WBA 67 Deep broad soilNorthridge – BIR 47 Deep broad soilNorthridge Compton – Castelgate St CAS 44 Deep broad soilNorthridge – SYC 83 Deep broad soilNorthridge Elizabeth Lake ELI 37 Deep broad soilNorthridge Glendale – Las Palmas GLP 22 Deep narrow soil

1 ID by PEER (Paci�c Earthquake Engineering Research); records are taken from PEER database.2 Soil type de�nition by PEER.



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Cumulative demand of the earthquake ground motions in the near source

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