REPORT NO.

UCB/EERC-77/14

JUNE 1977

PB 284 2011

EARTHQUAKE ENGINEERING RESEARCH CENTER

SEISMIC STRAININDUCED IN THE GROUNDDURING EARTHOUAKES

by

YOSHIHIRO SUGIMURA

Report to National Science Foundation

REPRODUCED BY' ..': :.

- NATIONAL TECHt4ICALINFORMATION SERVICE..... U.s. DEPARTMENT OFCOMMERC~·

SPRINGFIELD, VA. 22161

COLLEGE OF ENGINEERING

UNIVERSITY OF CALIFORNIA • Berkeley, California

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SEISMIC STRAIN

INDUCED IN THE GROUND

DURING EARTHQUAKES

by

Yoshihiro Sugimura

Report No. UCB/EERC-77/l4Earthquake Engineering Research Center

College of EngineeringUniversity of California

Berkeley, California

June 1977

Seismic Strain Induced in the Ground During Earthquakes

BIBLIOGRAPHIC DATASHEET

4. Title and Subtitle

Report No.NSF!RA-770558

• Re~rt~~t~ J ""- "'" ..June 1977

6.

7. Author( s)Yoshihiro Sugimura

9. Performing Organization Name and AddressEarthquake Engineering Research CenterUniversity of California, Richmond Field Station47th and Hoffman Blvd.Richmond, California 94804

12. Sponsoring Organization Name and Address

National Science Foundation1800 G Street, N.W.Washington, D. C. 20550

15. Supplementary Notes

16. Abstracts

8. Performing Organization Rept.NO' UCB!EERC-77!14

10. Project/Task/Work Unit No.

11. COntract/Grant No.

ENV 76-04264 A02

13. Type of Report & PeriodCovered

14.

This report develops a method of estimating seismic ground strain by ~sing tec~n~J··.:·...~i'....for strong motion data and presents some computed results from these technlques. S2m _

,····· ..1·

PlaneT::v:W:o:::t:::a:::l:::e::e:e:::i:h::c::::yf::v:ns:::~::t:::a:fd:::::n~ndstronJ:~'~liground motions. For these earthquakes the parallel and normal directions to thecausative fault line are shown to form a pair of orthogonal axes, along which the meansquare intensities of the components of ground motion have maximum and minimum values.

The velocity curves are transformed to this coordinate system. Then the seismicshear strain component at each frequency is evaluated by applying Fourier analysis andthe simple plane wave solution.

17b. Identifiers/Open-Ended Terms

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18. Availability Statement

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91

ABSTRACT

This report develops a method of estimating seismic

ground strain by using techniques for strong motion data and

presents some computed results from these techniques. Simple

plane wave forms are applied to seismic records for an esti-

mation of strain.

The two earthquakes selected for this study have shallow

focal depths and strong ground motions. For these earthquakes

the parallel and normal directions to the causative fault

line are shown to form a pair of orthogonal axes, along which

the mean square intensities of the components of ground

motion have maximum and minimum values.

The velocity curves are transformed to this coordinate

system. Then the seismic shear strain component at each

frequency is evaluated by applying Fourier analysis and the

simple plane wave solution.

TABLE OF CONTENTS

TABLE OF CONTENTS

ACKNO~JLEDGEMENTS

LIST OF FIGURES

LIST OF TABLES

INTRODUCTION .

DETERMINATION OF STRAIN

EARTHQUAKE WAVES USED AS EXAMPLES ..

LONGITUDINAL AND TRANSVERSE COMPONENTS

FOURIER ANALYSIS .

NORMAL AND PARALLEL COMPONENTS TO THE FAULT LINE.

ESTIMATION OF SEISMIC SHEAR STRAIN

CONCLUSIONS.

REFERENCES

APPENDIX ..

Preceding page blankiii

~

iii

v

. vi i

xi

1

1

4

5

8

10

12

13

45

49

ACKNOWLEDGEMENTS

This research was done with the kind support and assistance ofProfessor J. Penzien, University of California, Berkeley; the authorwishes to acknowledge his considerable help.

The author would also like to express his thanks to ProfessorY. Ohsaki, University of Tokyo, for the use of some subroutine sub-programs coded by him.

The author also wishes to thank Dr. Beverley Bolt for reviewingthe manuscript, Mrs. Abby Burton for typing the manuscript and Ms.

Gail Feazell for drafting the figures.

The financial support provided by the National Science Foundationunder grant No. ENV 76-04264 A02 is gratefully acknowledged.

v Preceding page blank

Fi g. 1

Fi g. 2

Fi g. 3

Fig. 4

Fi g. 5

Fi g. 6

Fi g. 7

Fig. 8

LIST OF FIGURES

Schematic location map of station, epicenterand causative fault (Imperial Valley Earthquake).

Schematic location map of station, epicenterand causative fault (Kern County Earthquake)

Transformation of coordinates. . ..

Relation between components of seismograph andtransformed coordinates (Imperial Valley Earthquake)

Relation between components of seismograph andtransformed coordinates (Kern County Earthquake). .

Reproduced acceleration curves in longitudinaland transverse directions (Imperial Valley Earthquake)

Reproduced velocity curves in longitudinal andtransverse directions (Imperial Valley Earthquake)

Reproduced acceleration curves in longitudinaland transverse directions (Kern County Earthquake)

15

16

17

18

18

19

19

20

Fi g. 9 Reproduced velocity curves in longitudinal andtransverse directions (Kern County Earthquake)

Fig. 10 Particle velocity orbit for first 6 seconds atImperial Valley Irrigation District. ..

20

21

Fi g. 11

Fi g. 12

Fig. 13a

Fig. l3b

Fig. 13c

Fi g. 14

Particle velocity orbit for first 4.8 seconds atTaft Lincoln School Tunnel

Fourier amplitudes of longitudinal and transversecomponents relative to the direction from theepicenter - El Centro 0 - 50 sec. . .. ..

Fourier amplitudes of longitudinal and transversecomponents relative to the direction from theepicenter - El Centro 0 - 10 sec. . ...

Fourier amp1it~des of longitudinal and transversecomponents relative to the direction from theepi center - El Centro 10 - 30 sec. .. ..

Fourier amplitudes of longitudinal and transversecomponents relative to the direction from theepicenter - El Centro 30 - 50 sec. . .

Fourier amplitudes of transverse and correctedlongitudinal compoents relative to the directionfrom the epicenter - Taft 0 - 50 sec. . .

22

23

23

24

24

25

Preceding page blank vii

Fig. 15a· Fourier amplitudes of transverse and correctedlongitudinal components relative to the directionfrom the epicenter - Taft 0 - 10 sec . 25

Fig. 15b Fourier amplitudes of transverse and correctedlongitudinal components relative to the directionfrom the epicenter - Taft 10 - 30 sec. .. .. 26

Fig. 15c Fourier amplitudes of transverse and correctedlongitudinal components relative to the directionfrom the epicenter - Taft 30 - 50 sec. . . . . . . . . . 26

Fig. 16 Reproduced acceleration curves in normal andparallel directions (Imperial Valley Earthquake) .... 27

Fi g. 17

Fi g. 18

Reproduced velocity curves in normal and paralleldirections (Imperial Valley Earthquake) .....

Reproduced acceleration curves in normal andparallel directions (Kern County Earthquake) . . . .

27

28

Fig. 19 Reproduced velocity curves in normal and paralleldi recti ons (Kern County Earthquake) . . . . . . . . 28

Fig. 20 Schematic explanation of coordinate transformation 29

Fig. 21

Fi g. 22a

Fourier amplitudes of parallel and correctednormal components in the direction of the faultline - El Centro 0 - 50 sec. . . . . .. . ..

Fourier amplitudes of parallel and correctednormal components in the direction of the faultline - E1 Centro 0 - 10 sec. . .

30

30

Fig. 22b Fourier amplitudes of parallel and correctednormal components in the direction of the faultline - El Centro 10 - 30 sec. . . . . . . . . . . . . . . 31

Fig. 22c

Fig. 23

Fig. 24a

Fourier amplitudes of parallel and correctednormal components in the direction of the faultline - E1 Centro 30 - 50 sec .

Fourier amplitudes of parallel and correctednormal components in the direction of the faultline - Taft 0 - 50 sec .

Fourier amplitudes of parallel and correctednormal components in the direction of the faultline - Taft 0 - 10 sec. . . . . . . . . . . . ..

31

32

32

Fig. 24b Fourier amplitudes of parallel and correctednormal components in the direction of the fault1i ne - Ta ft 10 - 30 sec. • . . . . . • . . . . . . . . . 33

vi i i

Fig. 24c Fourier amplitudes of parallel and correctednormal components in the direction of the faultline - Taft 30 - 50 sec. . . . . . . . . . . . . . . . . 33

ix

Table 1

LIST OF TABLES

Properties of Earthquakes and Stations ...~

· 35

Table 2 Subsurface Unit Thickness and Seismic Dataat Each Station (After Duke and Leeds, 1962) .... 36

Table 3 Maximum Value and Occurrence Time, Longitudinaland Transverse Components . . . . . . . . . . . . . 37

Table 4 Conditions of Computation and CorrespondingFigure Number . . . . . . . . . . . . . . . 38

Table 5 Peak Fourier Amplitude and Frequency of TransverseComponent at El Centro Site . . . . . . . . . . .. 39

Table 6 Peak Fourier Amplitude and Frequency of TransverseComponent at Taft Site . . . . . . . . 39

Table 7 Maximum Value and Occurrence Time, Normal andParallel Components . · . . · · · · · · · · · · · · 40

Table 8 Peak Fourier Amplitude and Frequency of ParallelComponent at El Centro Site · · · · · · · · · · · 41

Table 9 Peak Fourier Amplitude and Frequency of ParallelComponent at Taft Site. · · · · · 41

Table 10 Simplified Seismic Data at E1 Centro Site 42

Table 11 Simplified Seismic Data at Taft Site. · 42Table 12 Estimated Lower and Upper Limit of Shear Strain

at El Centro Site . · . . · · · · · · · · · · · · 43Table 13 Estimated Lower and Upper Limit of Shear Strain

at Taft Site. . . · · · · · · · · · · · · · · 43

Preceding page blankxi

INTRODUCTION

It is well-known that local soil conditions at sites subjectedto seismic shaking considerably affect damage to structures at the site.Many analytical studies and laboratory tests have been performed todetermine the dynamic characteristics of various types of soil deposits.In particular IIs train dependence ll of soils~ i.e.~ nonlinearity of shearmodulus and damping ratio with shear strain~ has been clarified mainlyby laboratory tests [l~ 2, 3~ 4, 5, 6J.* A clue to the relationshipbetween earthquake ground shaking and damage to structures may be foundif strains induced in the ground during an earthquake are evaluated andthen compared with results from laboratory tests.

An interesting question that also arises is as follows: IIHow largewill the actual strain level in soil layers induced by seismic ground motionbe~ particularly in the case of a great destructive earthquake?1I Straindata obtai ned di rectly from ins truments in soil depos its woul d provi dethe answer. However, except for some geophysical and geotechnical surveyssuch as triangulation which are mostly in a static sense, no suitableinstruments equivalent to strong-motion accelerographs for ground acceler-ation have been developed to measure local seismic strain waves.

This report develops a method of estimating seismic ground strainby using techniques for strong motion data and presents some computedresults from these techniques. Although the depth of soils~ especiallysoft soils, is a significant factor [7, 8J it is beyond the scope of thispaper.

DETERMINATION OF STRAIN

First, consider a plane wave in an elastic homogeneous body. If thewave is a shear wave, particle motion in the body is transverse to thedirection of propagation and if it is a compressional wave, particle motion

*Numbers in square brackets refer to corresponding references.

2

is parallel to the direction of propagation (longitudinal). If the x andy axes are chosen in the longitudinal and transverse directions, respective-lY,and u and v are the corresponding particle displacements, then the funda-mental wave propagation equations can be represented as follows:

For a longitudinal wave,

32. u = c 2.32. u

3t2. 1 3x2.

and for a transverse wave,

32. v c 2. 32 v

3t2. = 3x2.2

where

[~ l-v ]k:2-

c1 = Vp = (l+v)( 1-2v)

and

c2. = Vs = [~J~

(1)

(2)

(3 )

(4)

are the longitudinal (or compressional) wave velocity and transverse(or shear) wave velocity, respectively. E, G, and v are Young's modulus,the shear modulus and Poisson's ratio of the elastic body, respectively.Equations (1) and (2) have similar solutions of the form

o = f(x-ct) + g(x+ct) (5)

where 0 and c are either u and c1

or v and c2.' respectively. The firstterm on the right hand side of eq. (5) represents a forward moving wave andthe second term a backward moving wave. If the elastic body is infinite orif the effects of reflected waves from a boundary can be neglected, thenit is only necessary to consider the forward wave to determine the behaviorof an arbitrary point in the body, so that

o = f(x-ct) . (6)

3

The particle velocity and strain at that location are obtained bydifferentiating eq. (6) with respect to t and x as shown below,

Hence

• _ dO _ (o - dt - -cf~ x-ct)

E = ~~. = f~(x-ct)

(7)

(8)

E = oc (9)

Thus the strain can be simply expressed as the ratio of particle velo-city to wave velocity. Therefore, axial and shear strains are shown,respectively, as follows:

.= u ( 10)EX c1.

V (11 )Yxy = --c2.

It is obvious, furthermore, that the maximum shear velocity v of aparticle and the maximum shear strain Yxy occur simultaneously when thesolution v is expressed by the sinusoidal wave form.

In the case of seismic waves propagating through the earth, conditionsare considerably different from the case of plane waves. The followingdifficulties must be considered.

(1) The energy source may move along a line or on a plane, i.e., anearthquake fault, so that the source is a function of time as well as space.

(2) A variety of properties might be contained within the waves them-selves induced from the source. The structure is so complicated that inmost cases it is not possible to represent the wave motion exactly by aphysical model, therefore measurements of seismic waves will be consideredas random quantities.

4

(3) There exist many soil layers and topographic boundaries in theactual ground at which reflection and refraction of seismic waves mightoccur.

(4) Parameters such as Young1s modulus and the shear modulus of soilswill not be constant during a destructive ground shaking since, in general,soils are not elastic.

If an observation station, however, is located far enough from thesource, seismic records at that location can be decomposed into differentwave components according to the different wave velocities c

1' c

2and so on.

Based on this possibility, decomposition technique has been used regularlyin seismology to overcome to some extent the difficulties (1) and (2). Dif-ficulties (3) and (4) are principally derived from local site conditionsextremely near the surface of the earth so that they might not affect signi-ficantly arrival times of waves in earlier parts of seismic records. Theseeffects cannot be neglected, however, if it is necessary to consider theamplitudes of recorded waves. It has been pointed out, for instance, thatmaximum values of ground response to seismic shaking scatter in a remarkablywide range under the influence of local soil conditions [1, 2J. In particu-lar, because of the interdependence between elastic modulus and amplitude ofthe particle velocity, strains cannot be determined directly from seismicrecords.

In spite of all these difficulties and uncertainties, the applicationof the simple plane wave forms (eqs. (10) and (11)) to seismic recordsfor an estimation of strain appears to be, at present, the best availablefirst approximation for engineering use.

EARTHQUAKE WAVES USED AS EXAMPLES

Since the San Fernando earthquake in 1971 during which many seismicrecords were obtained in Southern California strong motion data from theWestern states, including these records, have been processed at the Earth-quake Engineering Research Laboratory, California Institute of Technology[9]. Some data processing techniques such as IIbaseline ll correction and

5

high-frequency correction [10, 11] were applied to these data and, finally,the results were published as corrected accelerograms and integrated groundvelocity and displacement curves [12J. The object of the base line cor-rection was to prevent divergence of the resultant curves, which may occurif the original data are integrated simply and directly. The object ofthe high-frequency correction was to account for the fall-off of basic trans-ducer response in the accelerographs [10, 11, 13J.

These corrected data are suitable for the purpose of this work. Twoearthquake records were selected from among them and used as shown in Table1. Schematic maps of locations of the epicenters and recording stations forthese earthquakes are shown in Figs. 1 and 2, respectively. Both earth-quakes selected have strong ground motions and shallow focal depths as isgenerally the case in California and the Western states.

Geotechnical data from the sites of the stations are given by C. M.Duke and D. J. Leeds, 1962 [14J; W. R. Hansen et al., 1973 [15]; and theU.S. Department of the Interior, Geological Survey, 1976 [16J. Subsurfaceunit thickness and seismic data from Duke and Leeds are shown in Table 2,and will be used as basic in subsequent sections.

LONGITUDINAL AND TRANSVERSE COMPONENTS

Since earthquakes occur at random locations, the direction of eachcomponent of a seismogram at a station does not ordinarily coincide withthe direction to the focus. Therefore, records are initially decomposedinto longitudinal and transverse components. Let us consider u, v and was vector components in the longitudinal, transverse and vertical directions,respectively, and u"', v'" and w'" as former components. If ai (i = 1,2,3)are direction cosines, then

Simil arly,

v = b u'" + b v'" + b w'"1 2 3

(12)

( 13)

6

and

(14)

in which bi(i = 1,2~3) and ci(i = 1,2,3) are direction cosines of v and wto u~, v~ and w~, respectively.

If the depth of the focus can be neglected or is assumed not toaffect the direction of wave propagation, direction cosines as' bs' c1 andc2 are zero and Cs = 1. Then, eqs. (12) to (14) reduce to the followingsimple forms.

u = a u~ + a v~1 2

v = b u~ + b v~I 2

w = w~

(15 )

(16)

(17)

Furthermore, since the coordinate systems are Cartesian, eqs. (15) and(16) can be written as

(-90 0 < e < 90 0 ) • ( 18)

We note that it does not necessarily follow that the positive directionof the longitudinal axis coincides with the direction from the station to thefocus. For instance, for the Imperial Valley earthquake, the positive di-rection on the longitudinal axis coincides with the direction to the focusbut vi ce versa for the Kern County earthquake, as shown in Fi gs. 4 and 5,respectively.

Acceleration and velocity curves in both cases generated by eq. (18)are shown in Figs. 6 to 9. Table 3 shows the maximum values and occurrencetimes for these curves compared with those of the original records. Forthe Taft record, there are only slight changes in the maximum values andwave shape, but no change in the occurrence time of the maximum values

7

since the direction cosines are nearly equal to zero or unity during thecoordinate transformation; that is, the new longitudinal curves correspondto the original E-W component and the new transverse curves to the N-Scomponents. On the other hand, in the case of the El Centro record afterthe coordinate transformation the new curves are different from those of theoriginal records.

Figure 10 shows the particle orbit for the first six seconds based onboth components of the transformed velocity curves at the Imperial Irriga-tion District station in El Centro. Similarly, the particle velocity orbitdescribed for the first 4.8 seconds at Taft Lincoln School Tunnel stationis shown in Fig. 11. Approximate directions along the fault lines observedon the ground surface during these earthquakes are also shown in thesefigures [17, 18J. The direction is shown by a single solid line at theEl Centro site because the Imperial fault is running nearly straight (seeFig. 4). For the White Wolf fault in Kern County, the direction can beestimated as almost straight but slightly curved at the southern end nearthe epicenter (see Fig. 5). Thus two lines are shown in Fig. 11. The solidline shows the direction judged from the whole and the dashed line shows thedirection estimated from the vicinity of the observed fault end. What isevident and interesting from these two figures is that large shaking compon-ents are induced along the direction of the fault line rather than along thelongitudinal or transverse directions to the focus. Horizontal dislocationwas predominant in the activity of both the Imperial fault and the WhiteWolf fault, thus causing strongest motions along their fault lines [19, 20,21J. Distinctive characteristics of short or medium distance shocks shouldbe considered for these earthquakes because the epicentral distances fromthe stations are about 7.3 miles (El Centro) and 25.6 miles (Taft), respect-ively. This fact suggests that for these earthquakes an important factoraffecting the ground motion will be the direction of slip of the fault.Hence, it might be more informative to transform the coordinate system tothe directions normal and parallel to the fault line. In any case, in orderto confirm this suggestion, further research is necessary as well as improvedmethods of analyzing large quantities of data.

8

FOURIER ANALYSIS

Fburier analysis provides a powerful means of investigating thecharacteristics of a random wave in the frequency domain. Let us considernow the components in the frequency domain in the longitudinal and trans-verse directions. The Fourier amplitudes and phase angles for N discretedata samples Xmwith time interval 6t, where N is even, are shown by

where

1X = [A 2 + B 2J~

k k k

2 N-l 2 kAk = N l: Xm cos-2I....!!!.m=O N

2 N-l 2 kBk =N l: Xm sin-!JRm=O N

N,k=O,l,2,····'2 (19 )

(20)

Then, the time history of each component of the Fourier transform wave isexpressed by

(21)

where

is the frequency of the kth Fourier transform wave. Recalling the defini-ti on of

then

0,1,2, ... , N-l (23)

NAk + iBk = AN- k - iBN_k, k = 0,1,2, ... , 2 (24)

9

so that eg. (21) can be expressed in terms of discrete complex Fourier co-efficients given by the equation,

N-l . ( )C = 1 '" X e- 1 2 km/N k 0 1 2 N 1k N '-' m ' =" , ••. , -

m=O

The discrete Fourier coefficients Ak and Bk are shown as follows:

(25)

Nk = 0, 1,2, ... , 2" (26)

(This method is the fast Fourier transformation (FFT) [22J.) Coeffic-ients Ck were computed first by using a subroutine program of the FFT codedby Y. Ohsaki (see program list in Appendix), then the Fourier amplitudesand phase angles were obtained by eq. (19). These results are shown inFigs. 12 to 13c for the El Centro site, and in Figs. 14 to 15c for the Taftsite.

Two approaches were attempted in this computation process: (1) Thetime duration during which the Fourier analysis is applied is divided intofour different parts; viz., the total fifty seconds from the initial time;zero to ten seconds; ten to thirty seconds; and thirty to fifty seconds.The results from the latter three parts correspond to the so-called runningFourier spectrum. (2) Using the phase angle, a correction was made to theFourier amplitude of the longitudinal component at each frequency so as tosatisfy simultaneously the maximum value of the transverse component. Theresults of these calculations are tabulated in Table 4.

The purpose of these computations is to consider whether there existsa frequency at which either the longitudinal or transverse component showsa high peak and the other a low trough. If this were found in the figures,it could be used to distinguish the kind or type of wave which is the domin-ant component in the ground motion. For instance, if the transverse com-ponent is more dominant than the longitudinal, such a frequency component

might be identified as a shear wave and so forth. This idea can also beapplied by a statistical approach corresponding to the concept of II principal

10

axes of ground motion ll presented by T. Kubo and J. Penzien [23J, althoughin a slightly different sense.

Each shaded part in Figs. 12 to 15c shows the range where the trans-verse component becomes larger than the longitudinal. The selection ofseveral peaks for the transverse component from this range was attempted.The results are summarized in Table 5 and Table 6. What is evident hereis that the same or a very close frequency component for each peak inthe total fifty seconds is clearly confirmed in each of the three inter-vals. The classification of the wave type, however, is fairly complicatedbecause a low value of the longitudinal component does not always corres-pond to the peak of the transverse component.

NORMAL AND PARALLEL COMPONENTS TO THE FAULT LINE

In this section let us consider the normal and parallel waves tothe fault line reproduced from the original records. The procedure is thesame as that described in the preceding sections with the appropriate angleof transformation; i.e., e = +54°.5 for the El Centro site and e = -40°.4for the Taft site, as shown in Table 7. Note that for the Taft site, thedirection of the dashed line in Fig. 11 was assumed to be the direction offault slip in the area nearest to the station.

Figures 16 and 17 show the acceleration and velocity waves for theImperial Valley earthquake; those of the Kern County earthquake are shownin Figs. 18 and 19. Consider the parallel components of these waves andcompare them schematically with the longitudinal and transverse curvesshown before (Figs. 6, 7 for the El Centro site and Figs. 8, 9 for theTaft site) and the original north-south and east-west records. Initiallywe will call these waves SH (parallel), LO (longitudinal), TR (transverse),NS (original north-south) and EW (original east-west).

In the case of the Imperial Valley, if the sign is reversed the formof the SH wave is similar to that of LO even though the values of theamplitudes are different from each other. This tendency is particularlyconspicuous in the velocity curves. Now LO was quite different from

11

either NS or EW, as mentioned before, hence SH bears no resemblance toei ther NS or EW.

In the case of the Kern County earthquake, it can be seen from Figs.8 and 18, or Figs. 9 and 19 that SH is not like LO or TR. In particular,the amplitudes are different. Meanwhile LO resembles EW closely and TRresembles NS, as before. Therefore, it can be said that SH bears noresemblance to either NS or EW.

This result can be justified theoretically as follows: Assumingu~ = v~ = 1 and solving eq. (18) for u with 0° < e < 45°, the result shownin Fig. 20 is obtained. The new component u or the ratio r = u/u~ (inwhich u~ = 1) can be expressed by the length of the chord for values ofe and changes on the continuous curve described in this figure. Therange of r is r = 1 at e = 0° to r = 2 at e = 45°. Three pairs of com-ponents corresponding to the smallest rotation angle were selected fromamong the three coordinates of SH, LO-TR and NS-EW and each ratio wascalculated. The results are summarized below.

El Centro site

Case 1

Case 2

Case 3

Taft site

Case 4

Case 5

Case 6

SH to LO

SH to NS

LO to EW

SH to LO

SH to EW

LO to EW

35° .5

36° .0

40°.4

r = 1.266

r = J.395

r = 1 .397

r = 1.413

r = 1 .409

r = 1.044

All the other combinations of components have larger ratios thanthese cases. It is clear from the above that the pairs of waves aresimilar to each other in Case 1 and especially in Case 6 because of theirsmall ratios, but look quite different from each other in Cases 2, 3, 4and 5.

(27)

12

Attention should also be paid to the fact that for e = 45° onecomponent becomes zero. This fact suggests that there may exist a setof directions of the predominant and minor ground motion that are prin-cipal axes. At the same time, it also suggests that it might not bereasonable to use directly the values measured by a seismograph as theground motion at the site because only in rare cases do the directionsof the seismograph agree with these principal axes.

The computed Fourier amplitudes of the parallel and normal velocitywaves are shown in Figs. 21 to 22c for the El Centro site and in Figs. 23to 24c for the Taft site. The computations are the same as before(Table 4); in particular, comparing Fig. 21 with Fig. 12 or Fig. 23 withFig. 14, for these curves the shaded part is more clearly defined thanbefore. The selection of peaks of the parallel components from amongthese figures was performed in the same manner as before. The resultsare summarized in Table 8 and Table 9 for the El Centro and Taft sites,respectively. The peak of the parallel component corresponds to the lowtrough of the normal component at almost all the frequencies so that thecomponent waves can be identified as shear waves or, at least, waves ofshear type. Hence, a coordinate transformation to the normal and paralleldirections to the causative fault line rather than to the longitudinaland transverse directions to the epicenter seems to be more satisfactoryfor explaining the characteristics of ground motion at a station site.

ESTIMATION OF SEISMIC SHEAR STRAIN

From the preceding section, it seems reasonable to assume as a firstapproximation that each predom~nant frequency component in the paralleldirection is a shear wave. In this section, an estimate of the seismicshear strain in the ground at each site is attempted by applying eq. (11).First the seismic data shown in Table 2 are simplified as follows: At eachsite some equivalent single soil layers are considered with an averageshear wave velocity shown by,

r.V .H.s, ,V. =-~.......:...s, EH.,

in which i is the stratum number from the surface and Vsi and Hi are the

13

shear wave velocity and the thickness of each stratum, respectively. Thenthe natural frequency of each equivalent layer is expressed by

4L:H.f. =----V1 (28)

1 si

The average velocity and frequency calculated for each layer fromeqs. (27) and (28), respectively, are summarized in Table 10 and Table 11.Five equivalent single layers exist at the El Centro site and four at theTaft sHe. Next, taki ng these frequencies as representati ve boundaryvalues, peak frequency components shown in Table 8 and Table 9 are classi-fied into several groups. Then, shear strains at each site are calculatedbyeq. (11) for each case using the value Vs of the adjacent lower frequen-cy (lower limit of shear strain) and higher frequency (upper limit of shearstrain). The results are summarized in Table 12 and Table 13, respectively.Finally, the average value of shear strain corresponding to each frequencywill change within the range between these lower and upper limits. Theorder of these strain levels is estimated as about 10-3 (%) at the ElCentro site and about 10-4 (%) at the Taft site.

-The above approach provides a basis for the assumption that eachpeak seen in Fig. 21 or Fig. 23 corresponds to a single soil layer of somedepth for which the first vibration mode corresponds to the particularpeak frequency. As is generally known, the first mode of a soil layer isto some extent predominant in the ground motion at a site. Therefore, asa fi rst approximation thi s assumpti on wi 11 be an effecti ve method of i n-vestigating the ground motion. It should be kept in mind, however, thatsuch a method (1) gives the average value through the whole soil deposit;(2) shows only the discrete Fourier amplitude corresponding to each fre-quency; and (3) gives no consideration to the higher modes of the ground.Hence, further studies such as improvement of the method and analysis ofmore data are necessary to cl ari fy the real shear strai n wave induced inthe local part of the ground during earthquakes.

CONCLUSIONS

The conclusions achieved in this work can be divided into the folloWing

14

two ca tegori es .

(1) The mean square intensity of a single orthogonal component ofground motion at a site depends on the direction of that component. Thereexists a pair of orthogonal axes (principal axes) along which the meansquare intensities of the components of motion have maximum and minimumvalues. The parallel and normal directions to the causative fault linewere shown to correspond to such a coordinate system for the two examplesof earthquake and station, i.e., Imperial Valley earthquake (1940) record-ed at El Centro site and Kern County earthquake (1952) recorded at Taftsite. This is consistent with the characteristics of these causativefaults, namely that they (a) slip mainly horizontally, and (b) are regard-ed as nearly straight lines. A more difficult situation will arise in thecase of earthquakes caused by faults with more complicated characteristics.

(2) Provided that the velocity curves are transformed to the coordin-ate system mentioned above and that the predominant components in the paral-lel direction are assumed to be of shear wave type) it is possible toevaluate the seismic shear strain component at each frequency by applyingFourier analysis and the simple plane wave solution. The order of theaverage shear strain component at each frequency caused by ground shakingcan be estimated at about 10-3(%) at the El Centro site and about 10-4(%)at the Taft site as a first approximation. It should be noted, however,that additional detailed study is necessary to determine the shear straininduced in the ground during an earthquake.

33

°00

'NI

II

3~45'

" "S

90

W--

lR:

//

/

o5

10M

ILE

SI

I,

o5

1015

KM

II

II

N j

ME

XIC

O

11

5°4

5'

11

5°3

0'

1150

'5'W

Fig.

1Sc

hem

atic

loca

tion

map

ofst

atio

n,

epic

ente

ran

dca

usat

ive

fau

lt(I

mpe

rial

Val

ley

Ear

thqu

ake)

U1

35

015

'Njiii

O'l

3~00' 11

9°3

0'

N21

E f

<5

6 .4f11..~S

119°

15'

o5

1015

MIL

ES

II

II

o10

20

KM

II

I

;I'

~;I'

((~-

0/((

/~O

v/;I

'N

~1";,/

1--/~

.k

"

EP

ICE

NT

ER

11

9°0

0'

1180

30

'W

Fig

.2

Sche

mat

iclo

cati

onm

apof

stat

ion

,ep

icen

ter

and

caus

ativ

efa

ult

(Ker

nC

ount

yE

arth

quak

e)

17

.O'l.....u..

V>

~rclC....."0s-oou

4-oCo.....+>

~o4-V>c~I-

I-+

I-+

~~

oW+

-1+

en~

oZ+

Cf)~

oZ+

NO

RT

H

+S

90

W--

..--

--

-.....

.......:---------

~ EP

ICE

NT

ER

DIR

EC

TIO

N

Fig.

4R

elat

ion

betw

een

com

pone

nts

ofse

ism

ogra

phan

dtr

ansf

orm

edco

ordi

nate

s(I

mpe

rial

Val

ley

Ear

thqu

ake)

NO

RT

H

'-~

"i-S

69~

::::::--.

........

-.....

.~~

EP

ICE

NT

ER

DIR

EC

TIO

N

Fig.

5R

elat

ion

betw

een

com

pone

nts

ofse

ism

ogra

phan

dtr

ansf

orm

edco

ordi

nate

s(K

ern

Cou

nty

Ear

thqu

ake)

--'

ex>

'LC

EHTR

O1

91

0.5

.18

IMP

ER

IAL

VA

LLE

Y

30

0.0

TRA

NS

VE

RS

EA

CC

.(G

AL

IM

AX

:2

11

.5

30

0.0

o1

0.0

20

.03

0.0

40

.05

0.0

(SE

C)

30

0.

0--

LON

GIT

UO

IHA

LA

CC

.(G

AL

IM

AX

:2

59

.1

J00

.0o

10

.02

0.0

30

.0,

40

.05

0.0

(S

EC

)

Fig

.6

Rep

rodu

ced

acce

lera

tion

curv

esin

long

itud

inal

and

tran

sver

sed

irec

tion

s(I

mpe

rial

Val

ley

Ear

thqu

ake)

ELC

EHTR

O1

91

0.5

.18

IMP

ER

IAL

VA

LLE

Y

50

.0TR

AH

SV

ER

SE

VE

L.(K

IHE

IM

AX

:2

7.8

38

Fig

.7

Rep

rodu

ced

velo

city

curv

esin

long

itud

inal

and

tran

sver

sed

irec

tion

s(I

mpe

rial

Val

ley

Ear

thqu

ake)

\0

.0o

50

.0·

-

\o.0

o

j0

.0

10

.0

20

.0

20

.0

30

.0

30

.0

40

.0

40

.0

LON

GIT

UO

IHA

LV

EL.

(KIH

EJ

MA

X:

18

.50

6

50

.0(

SE

C)

50

.0(S

EC

I-l

,1

.0

TA

fTLI

NC

OLN

SCH

OO

LTU

NN

EL

19

52

.7.2

1KE

RN

CO

UN

TY

N o

20

0.

0TR

AN

SV

ER

SE

AC

C.I

GA

L)

MAX

=1

51

.8

-2

00

.0o

20

0.0

10

.02

0.0

30

.0'0

.05

0.0

(S

EC

)

LON

GIT

UO

INA

LA

CC

.IG

AL

)M

AX=

17

0.1

Fig

.8

Rep

r.odu

ced

acce

lera

tion

curv

esin

long

itud

inal

and

tran

sver

sed

irec

tion

s(K

ern

Cou

nty

Ear

thqu

ake)

-20

0.0

o1

0.0

20

.03

0.0

'0..

05

0.0

(SE

C)

TA

FT

LIN

CO

LNSC

HO

OL

TUN

NE

L1

95

2.7

.21

KERN

CO

UN

TY

20

.0TR

AN

SV

ER

SE

VE

L.I

KIN

E)

MAX

=1

6.3

06

-20

.0o

20

.0

10

.02

0.0

30

.0'0

.05

0.0

ISE

CJ

-2

0.0

o1

0.0

20

.03

0.0

'0.0

50

.0I

SE

C)

Fig

.9

Rep

rodu

ced

velo

city

curv

esin

long

itud

inal

and

tran

sver

sed

irec

tion

s(K

ern

Cou

nty

Ear

thqu

ake)

-30

L 50 (KINE)

-30

Fig. 10 Particle velocity orbit for first 6 secondsat Imperial Valley Irrigation District

21

22L 20 (KINE)

L

-15

I (KINE)

-2

-10

Fig. 11 Particle velocity orbit for first 4.8 secondsat Taft Lincoln School Tunnel

T

" 10" (KINE)

""

23

EL CENTRO 1910.5.18 IMPERIAL VALLEY

1.0

w

~ 3. 0

-J0..I:«: 2.0=w

ORI.-COR.VEL. TR 0-50 SECVEL. LO 0-50 SECMAX= 2.230

1.0

1.5 3.5 1.0 1.5 5.0

Fig. 12 Fourier amplitudes of longitudinal and transversecomponents relative to the direction from the epicenter -El Centro 0 - 50 sec.

EL CENTRO 1910.5.18 IMPERIAL VALLEY

10.0

~ 8.0>~ 6.0-J0..

I:<

=w

.5 1.0 1.5 2.0 2.5 3.0FREQUENCY (HZ)

3. 5 1.0 1. 5 5.0

Fig. 13a Fourier amplitudes of longitudinal and transversecomponents relative to the direction from the epicenter -El Centro 0 - 10 sec.

24

10. 0

~ 8.0:>:...,Q

=>

I- 6.0....Ja..>::

=LL.

EL CENTRO 1940.5.18 IMPERIAL VALLEY

ORI.-COR.VEL. TR 10-30 SECVEL. LO 10-30 SECMAX= 5.613

2. 0

. 5 1.0 1.5 2.0 2.5 3.0FREQUENCY [HZ)

3. 5 1.0 4.5 5. 0

Fig. 13b Fourier amplitudes of longitudinal and transversecomponents relative to the direction from the epicenter -El Centro 10 - 30 sec.

EL CENTRO 1940.5.18 iMPERIAL VALLEY

4.0

wz~ 3.0

....Ja..

~ 2.0

""...,

""=>=LL.

1.0

OR 1. -COR.VEL. TR 30-50 SECVEL. LO 30-50 SECMAX: 2.371

oL.L----.:~--!....::~~~~~~~~~~~~l:l::eo.~""""""..-..---...o .5 1.0 1.5 2.0 2.5 3.0 3.5 La 1.5 5.0

FREQUENCY [HZ)

Fig. 13c Fourier amplitudes of longitudinal and transversecomponents relative to the direction from the epicenter -El Centro 30 - 50 sec.

25

TAFT LINCOLN SCHOOL TUNNEL 1952.7.21 KERN COUNTY

2.0

wz~ 1. 5

>:

26

2. a

wz'" 1. 5

-'"'-

~ l. 0

TAFT lINCOLN SCHOOL TUNNEL 1952.7.21 KERN COUNTY

OR I. -COR.VEL. TR la-3D SECVEL. lO 10-30 SECMAX= 1.775

=u.J

. 5

..~'.:

. 5 1.0 1 . 5 2.0 2.5 3.0FREQUENCY (HZ)

3.5 La L5 5. 0

Fig. 15b Fourier amplitudes of transverse and corrected longitudinalcomponents relative to the direction from the epicenter -Taft 10 - 30 sec.

TAFT lINCOLN SCHOOL TUNNEL [952.7.21 KERN COUNTY

LO

wz'" 3.0

-'"'-

~ 2.0

ORI.-CoR.VEL. TR 30-50 SECVEL. La 30-50 SECMAX= 2.816

=u.J

1.0

.5 1.0 1.5 2.Q 2.5 3.0FREQUENCY (HZ)

3.5 4,0 4,5 5. a

Fig. 15c Fourier amplitudes of transverse and corrected longitudinalcomponents relative to the direction from the epicenter -Taft 30 - 50 sec.

ELC

ENTR

O1

91

0.5

.18

IMP

ER

IAL

VA

LLE

Y

10

0.0

PA

RA

LLE

LTO

fAU

LT

AC

C.l

GA

L)

MAX~

31

2.7

'10

0.0

o1

0.0

20

.0

30

.0

10

.05

0.0

(S

EC

)

100'0~

NO

RM

ALTO

fAU

LT

AC

C.L

GA

L)

MAX~

20

1.

2

OiJJL~

-!~I\

'UMIIAt!.!QU.r.AI"NlI.~.f1II.!l.dl!

LMLM

OO

I\iIA

1\1

\1,.

,0,0

,A~,

A~o,

l\~

.,0

~"'I

"A

,.

o"j

6=

0I

-~~~L_~_

_-..,

iJ11/'

vv'lW

"VY"

WfN

V'I"Q

'w'N

VvV

W"V

VV

,-rV

\TVV

\Vv'

\I'V

lIIT

V"V

orVJV

rrw

r,M

","'v

Ol'

=V

-F

-loo

.oL o

10

.02

0.0

30

.01

0.0

50

.0(S

EC

)

Fig

.16

Rep

rodu

ced

acce

lera

tion

curv

esin

norm

alan

dp

aral

lel

dir

ecti

ons

(Im

peri

alV

alle

yE

arth

quak

e)

ELC

ENTR

O1

9\0

.5.1

6IM

PE

RIA

LV

ALL

EY

50

.0

-5

0.0

o

50

.0

10

.02

0.0

30

.04

0.0

PA

RA

LLE

LTO

fAU

LT

VE

L.(

KIN

El

MAX~

17

.19

5

50

.0(S

EC

)

NO

RM

ALTO

fAU

LT

VE

L.(

KIN

E)

MAX~

26

.57

0

Fig

.17

Rep

rodu

ced

velo

city

curv

esin

norm

alan

dp

aral

lel

dir

ecti

ons

(Im

peri

alV

alle

yE

arth

quak

e)

-5

0.0

o1

0.0

20

.0

30

.04

0.0

50

.0(

SE

C)

N '-J

30

0.0

TAFT

LIN

CO

LNSC

HO

OL

TUN

NE

L1

95

2.7

.21

KER

NC

OU

NTY

N ex>

PA

RA

LLE

LTO

FAU

LTA

CC

.(G

All

MAX

=2

14

.2

-30

0.0

o

30

0.0

10

.02

0.0

30

.01

0.0

50

.0(S

EC

)

NO

RM

ALTO

FAU

LTA

CC

.(G

AL

)M

AX=

14

1.1

-30

0.0

o1

0.0

20

.03

0.0

10

.05

0.0

(SE

C)

30

.0

Fig

.18

Rep

rodu

ced

acce

lera

tion

curv

esin

norm

alan

dp

aral

lel

dir

ecti

ons

(Ker

nC

ount

yE

arth

quak

e)

TA

FT

LIN

CO

LNSC

HO

OL

TUN

NE

L1

95

2.7

.21

KER

NC

OU

NTY

PA

RA

LLE

LTO

FAU

LTY

EL

.(K

INE

JM

AX=

21

.17

7

-3

0.0

o

30

.0

10

.02

0.0

30

.01

0.0

50

.0(S

EC

)

NO

RM

ALTO

FA

ULT

VE

L.(K

INE

JM

AX=

10

.86

2

-3

0.0

o1

0.0

20

.03

0.0

10

.05

0.0

(SE

C1

Fig

.19

Rep

rodu

ced

velo

city

curv

esin

norm

alan

dp

aral

lel

dir

ecti

ons

(Ker

nC

ount

yE

arth

quak

e)

29

1.5 ,....------------------------,

40

v l =I

u· =1

20 30

8 (DEGREE)10

1.1

1.4

I.0 L..-_-'--_---'-__.L..-_-'--_---'-__.L..-_-'--_--'-_---'o

1.3

1.2

r

Fig. 20 Schematic explanation of coordinate transformation

30

1.0

wzi2 3.0

.....Co

~ 2.0a:....-a::::>C>.....

1.0

EL CENTRO 1910.5.18 IMPERIAL VALLEY

OR I. -COR.VEL. SH 0-50 SECVEL. [0 0-50 SECMAX= 2.759

.5 1.0 1.5 2.0 2.5 3.0FREQUENCY (HZ)

3.5 1.0 1.5 5.0

Fig. 21 Fourier amplitudes of parallel and corrected normal componentsin the direction of the fault line - El Centro 0 - 50 sec.

EL CENTRO 1910.5.18 IMPERIAL VALLEY

10.0

~ 8.0i2....Cl:::>

!: 6.0.....Co~

<a:....

ORI.-COR.VEL. SH 0-10 SECVEL. CO 0-10 SECMAX= 5.962

a::::>C>.....

.5 1.0 1.5 2.0 2.5 3.0FREQUENCY (HZ)

3.5 l.Q 1.5 5.0

Fig. 22a Fourier amplitudes of parallel and corrected normal componentsin the direction of the fault line - El Centro 0 - 10 sec.

31

EL CENTRO 19iO.S.18 IMPERIAL VALLEY

10.0 ORI.-COR.VEL. SH 10-30 SECvEL. CO 10-30 SECMAX= 3.i19

~ 8.0::.::....=:=>

~ 6.0-Ja..E:<

""....- i.O"":=>o...

2.0

.5 1.0 1.5 2.0 2.5 3.0FREQUENCY (HZ)

3.5 LO LS 5.0

Fig. 22b Fourier amplitudes of parallel and corrected normal componentsin the direction of the fault line - El Centro 10 - 30 sec.

EL CENTRO 19iO.5.18 IMPERIAL VALLEY

LO ORI.-COR.VEL. SH 30-50 SECVEL. CO 30-50 SECMAX= 2.i65

wz~ 3.0....o:=>~--Ja..

~ 2.0

""....-"":=>o...

1.0

5.0LSLOoL!.........:~~~~~~~~~~O::=-~~~~ __-.Jo .5 1.0 1.5 2.0 2.5 3.0 3.5

FREOUENCY (HZ)

Fig. 22c Fourier amplitudes of parallel and corrected normal componentsin the direction of the fault line - El Centro 30 - 50 sec.

32

2.0

wz~ 1. 5

-'a..

~ 1. 0

TAFT LINCOLN SCHOOL TUNNEL 1952.7.21 KERN COUNTY

ORI.-COR.VEL. SH 0-50 SECVEL. CO 0-50 SECMAX= 1.139

a::::>c::>....

O~~~~~VWJ~~~~~o .5 1.0 1.5 2.0 2.5 3.0 3.5 1.0 1.5 5.0

FREQUENCY (HZ)

Fig. 23 Fourier amplitudes of parallel and corrected normal componentsin the direction of the fault line - Taft 0 - 50 sec.

TAFT LINCOLN SCHOOL TUNNfL 1952.7.21 kERN COUNTY

1.0

wz~ 3.0

-'a..

~ 2.0

OR!. -COR.VEL.. SH 0-10 SECVEL. CO 0-10 SECMAX= 1.900

""..........""::>c::>....

1.0

.5 1.0 1.5 2.0 2.5 3.0FREQUENCY (HZ)

3.5 1.0 1.5 5.0

Fig. 24a Fourier amplitudes of parallel and corrected normal componentsin the direction of the fault line - Taft 0 - 10 sec.

33

TAfT LINCOLN SCHOOL TUNNEL 1952.7.21 KERN COUNTY

2.0

wZ;;:: 1. 5......"~

I--.........~ 1.0

ORI.-COR.VEL. SH 10-30 SECVEL. CO 10-30 SECMAX= 1.905

ex.....

.5.... ;:

.5 1.0 1.5 2.0 2.5 3.0fREQUENCY (HZ)

3.5 LO L5 5.0

Fig. 24b Fourier amplitudes of parallel and corrected normal componentsin the direction of the fault line - Taft 10 - 30 sec.

TAfT LINCOLN SCHOOL TUNNEL 1952.7.21 KERN COUNTY

1.0

wz;;:: 3. 0......"~

I--.........~ 2.0 ..ex.....

ORI.-COR.VEL. SH 30-50 SECVEL. CO 30-50 SECMAX= 3.385

Fig. 24c Fourier amplitudes of parallel and corrected normal componentsin the direction of the fault line - Taft 30 - 50 sec.

Table 1 Properties of Earthquakes and Stations

35

Example 1 Example 2

Name of earthquake Imperi alVa11 ey, Kern Coun ty ,California Cal i forni a

Date and (local) time May 18, 1940 July 21, 195220:37 PST 4:53 PDT

Epicenter location 32° 44 1 00" N 35° DO' 00" N115° 27' 00" W 119° 02' 00" W

Richter Magnitude 7.1 7.7

Approximate length ofsurface faulting (miles) 40 minimum 14

Number and name of 117 El Centro, Imperi a1 095 Taft, Lincolnstation Valley Irrigation District School Tunnel

Station location 32° 47 1 43 11 N 35° 09' 0011 N1150 32'1 55" W 119° 27 I 00" W

Site characteristics Alluvium, more than 300 m Alluvium

Structure type/size 2-story bldg. l-story bldg.

Instrument location(s) Ground level Tunnel and roof

Components of instrument SOOE N21Elocation S90E S69E

Modified MercalliIntensity near station VII to VIII VII

Preceding page blank

36

Table 2 Subsurface Unit Thickness and Seismic Data at Each Station(After Duke and Leeds, 1962)

Imperial Valley Irrigation District

Thi ckness Vp Densi ty Vs Vs(feet) (fps) (pcf) Vp (fps)

100 522 128 1.0 522

1000 2810 139 1.0 2810

3000 3620 139 1.0 3620

3500 4050 147 1.0 4050

3500 7200 147 1.0 7200

10000 172 1.0 10000

Taft Lincoln School

ThicknessVp Densi ty Vs Vs

(feet) (fps) (pcf) Vp (fps)

40 1190 140 0.45 535 .

160 5000 144 0.48 2399

500 6500 144 0.48 3119

3300 8000 148 0.48 3839

15500 170 0.61 9454

Tab

le3

Max

imum

Val

uean

dO

ccur

renc

eTi

me,

Lon

gitu

dina

lan

dT

rans

vers

eC

ompo

nent

s

Acc

eler

atio

nV

eloc

ity

Dir

ecti

onM

ax.

Va1

(gal

)O

cc.

Tim

e(s

ec)

Max

.V

al(k

ine)

Occ

.Ti

me

(sec

)

ElC

entr

o,Im

peri

alV

alle

yIr

rig

atio

nD

istr

ict,

May

18,

1940

,Im

peri

alV

alle

y

Lon

gitu

dina

lS5

4E25

9.1

2.08

·48

.52.

16u

u

Tra

nsve

rse

S36W

241

.52.

12·

27.8

4.36

vv

N-S

SOOE

....34

1.7

2.12

U..33

.42.

18u

E-W

S90W

v"21

0.1

11.4

4v"

-36.

92.

14

Taf

tL

inco

lnSc

hool

Tun

nel,

July

21,

1952

,K

ern

Cou

nty

Lon

gitu

dina

lN6

6.4W

-170

.13.

70·

17.1

3.56

uu

Tra

nsve

rse

N23

.6E

154.

89.

10·

-16.

33.

40v

v

N-S

N21E

....15

2.7

9.10

U..

-15.

73.

40u

E-W

S69E

....17

5.9

3.70

·..-1

7.7

3.56

vv

W -.....J

38

Table 4 Conditions of Computation and Corresponding Figure Number

Time (sec) o - 50 o - 10 10 - 30 30 - 50

Number of data 1251 251 501 501(n)

Number used in 2048 512 512 512FFT* (N)

Frequency interval 0.012 0.049 0.049 0.049(Hz)

Nyquist frequency 12.5 12.5 12.5 12.5(Hz)

E1 Centro si te Fi g. 12 Fi g. 13a Fig. 13b Fi g. 13c

Taft site Fi g. 14 Fig. 15a Fig. 15b Fig. 15c

*Remaining parts of data (N-n) are set to be equal to zero

39

Table 5 Peak Fourier Amplitude andFrequency of Transverse Component at El Centro Site

o - 50 sec. o - 10 sec. 10 - 30 sec. 30 - 50 sec.

0.11 (1.76) ----- Q.10 (5.61) 0.10 (1.40)

0.18 (2.23) 0.15 (2.83) 1.20 (5.40) 0.20 (2.37)

0.32 (1 .37) 0.34 (2.35) ---- 0.34 (1.01)

0.72 (0.95) ---- ---- 0.73 (0.48)

0.84 (0.82) 0.88 (1.68) ---- 0.83 (0.44)

1.17 (0.69) 1.17 (1.55) 1.17 (1. 31 ) ----Note: Numerals without parentheses are frequency (Hz) and those in

parentheses are peak values of transverse components (kine)

Table 6 Peak Fourier Amplitude andFrequency of Transverse Component at Taft Site

o - 50 sec. o - 10 sec. 10 - 30 sec. 30 - 50 sec.

0.09 (1.00) 0.10 (0.97) 0.10 (1.78) ----

0.17 (0.99) ---- ---- 0.20 (2.72)

0.26 (0.76) 0.24 (1. 22) 0.24 (0.88) ----

0.35 (0.52) ---- 0.34 (1.00) ----0.45 (0.39) 0.44 (0.83) ---- ----

0.60 (0.47) ---- 0.59 (0.60) 0.59 (0.71)

0.72 (0.41) 0.73 (1.03) 0.78 (0.78) -----

1.17 (0.42) 1.07 (1.04) 1. 17 (0.77) ----

1.37 (0.40) ---- 1.37 (1.04) ----Note: Numerals without parentheses are frequency (Hz) and those in

parentheses are peak values of transverse components (kine)

Tab

le7

Max

imum

Val

uean

dO

ccur

renc

eTi

me,

Nor

mal

and

Par

alle

lC

ompo

nent

s

~ o

Acc

eler

atio

nV

eloc

ityDi

rect

ion

Max

.Va

l(g

al)

Occ

.Ti

me

(sec

)M

ax.

Val

(kin

e)O

cc.

Tim

e(s

ec)

ElC

entr

o,Im

peri

alV

alle

yIr

riga

tion

Dis

tric

t,M

ay18

,19

40,

Impe

rial

Val

ley

Nor

mal

tofa

ult

S54.

5Wu

204.

24.

30U

26.6

26.1

6

Par

alle

lto

fau

ltS3

5.5E

v-3

12.7

2.12

v-4

7.5

2.16

N-S

SOOE

U...

341.

72.

12·...

33.4

2.18

u

E-W

S90W

v'"21

0.1

11.4

4·...

-36.

92.

14v

Taf

tli

ncol

nSc

hool

Tun

nel,

July

21,

1952

,K

ern

Cou

nty

Nor

mal

tofa

ult

N19.4

W-1

41.4

4.20

·-1

0.9

9.76

uu

Para

l1el

tofa

ult

N70

.6E

v21

4.2

3.70

·-2

1.5

3.56

v

N-S

N21E

U...

152.

79.

10·...

-15.

73.

40u

E-W

S69E

v'"17

5.9

3.70

·...-1

7.7

3.56

v

Table 8 Peak Fourier Amplitude andFrequency of Parallel Component at El Centro Site

41

o - 50 sec o - 10 sec. 10 - 30 sec. 30 - 50 sec.

0.07 (1.43) ---- ---- 0.10 (2.43)

0.18 (1 .42) 0.20 (4.78) 0.24 (1.94) 0.24 (0.74)

0.37 (1. 78) 0.34 (5.96) ---- 0.34 (0.61)

0.45 (1. 33) 0.49 (3.97) 0.44 (1. 79) ----

0.81 (0.87) 0.83 (2.24) 0.88 (1.68) 0.88 (0.48)

1.16 (0.83) 1.17 (2.30) 1.17 (1.44) ----

1.47 (0.69) 1.47 (1.70) 1.47 (1.28) ----

1.54 (0.52) 1.61 (1. 09) 1.61 (1.10) ----

1. 76 (0.52) 1. 76 (1. 60) ---- ----

1.83 (0.50) 1.90 (1.33) 1.81 (0.83) ----

Note: Numerals without parentheses are frequency (Hz) and those inparentheses are peak values of parallel components (kine)

Table 9 Peak Fourier Amplitude andFrequency of Parallel Component at Taft Site

o - 50 sec. o - 10 sec. 10 - 30 sec. 30 - 50 sec.

0.11 (1 .44) 0.10 (1. 42) 0.10 (1.91) 0.15 (3.39)

0.26 (0.97) 0.24 (1. 90) 0.24 (1.46) ----

0.31 (0.88) ---- ---- 0.29 (1. 60)

0.45 (0.58) 0.39 (1.40 ) 0.44 (1.03) 0.49 (0.95)

0.60 (0.70) 0.59 (1.90) ---- 0.64 (0.84)

0.73 (0.45) 0.73 (1.01) 0.73 (0.73) 0.78 (0.64)

1.14 (0.47) 1. 12 (1. 25) 1.07 (0.65) ----

1. 54 (0.40) 1.51 (0.78) ---- ----

Note: Numerals wi thout parentheses are frequency (Hz) and those inparentheses are peak values of parallel components (kine)

42

Table 10 Simplified Seismic Data at El Centro Site

Case Depth (ft) Vs (fps) f (Hz)

1 100 522 1.31

2 1100 2602 0.59

3 4100 3347 0.20

4 7600 3671 0.12

5 11100 4784 0.11

Table 11 Simplified Seismic Data at Taft Site

Depth (ft) - (fps) f (Hz)Case Vs

1 40 535 3.34

2 200 2026 2.53

3 700 2807 1.00

4 4000 3658 0.23

43

Table 12 Estimated Lower and Upper Limit of Shear Strain at E1 Centro Site

Fourier Amplitude Shear Strain x10-3 (%)

f (Hz) Amp (kine) f (Hz) Lower Limit T (Hz) Upper Lim; t

0.07 1.43 -- -- 0.11 0.98

0.18 1.42 0.12 1.27 0.20 1.40

0.37 1.78 0.20 1.75 0.59 2.25

0.45 1.33 0.20 1.31 0.59 1.68

0.81 0.87 0.59 1.10 1.31 5.48

1.16 0.83 0.59 1.05 1.31 5.23

1.47 0.69 1.31 4.35 -- --

1.54 0.52 1.31 3.28 -- --

1.76 0.52 1.31 3.28 -- --

1.83 0.50 1.31 3.15 -- --

Table 13 Estimated Lower and Upper Limit of Shear Strain at Taft Site

Fourier Amplitude Shear Strain x10-4 (%)

f (Hz) Amp (kine) f (Hz) Lower Limit f (Hz) Upper Limit

0.11 1.44 -- -- 0.23 12.95

0.26 0.97 0.23 8.72 1.00 11.37

0.31 0.88 0.23 7.91 1.00 10.31

0.45 0.58 0.23 5.22 1.00 6.80

0.60 0.70 0.23 6.29 1.00 8.20

0.73 0.45 0.23 4.05 1.00 5.27

1.14 0.47 1.00 5.51 2.53 7.63

1.54 0.40 1.00 4.69 2.53 6.49

45

REFERENCES

1. Ohsaki, Y., "The Effects of Local Soil Conditions upon EarthquakeDamage," Soil Dynamics, Proc. of Specialty Session 2, 7th ICSMFE,Mexico, 1969

2. Seed, H. B., liThe Influence of Local Soil Conditions on EarthquakeDamage'" Soil Dynamics, Proc. of Specialty Session 2, 7th ICSMFE,Mexi co, 1969

3. Hardin, B. O. and Drnevich, V. P., IIShear Modulus and Damping inSoils, I - Measurement and Parameter Effects," Technical ReportUKY 26-70-CE2, University of Kentucky, 1970

4. Hardin, B. O. and Drnevich, V. P., "Shear Modulus and Damping inSoils, II - Design Equations and Curves," Technical ReportUKY 27-70-CE3, University of Kentucky, 1970

5. Richart, F. E., Jr., Hall, J. R., Jr., and Woods, R. D., IIVibrationsdf Soils and Foundations,1I Prentice-Hall, 1970

6. Seed, H. B. and Idriss, r. M., "Soil Moduli and Damping Factors forDynamic Response Analyses," Report No. EERC 70-10, EarthquakeEngineering Research Center, University of California, Berkeley,California, 1970

7. Seed, H. B., Ugas, C. and Lysmer, J., "Site-Dependent Spectra forEarthquake-Resistant Design,1I Report No. EERC 74-12, EarthquakeEngineering Research Center, University of California, Berkeley,California, 1974

8. Seed, H. B., Whitman, R. V., Dezfulian, H., Dorby, R. and Idriss,I. M., "Relationships between Soil Conditions and Building Damagein the 1967 Caracas Earthquake, II Journal of the Soil Mechanics andFoundations Division, ASCE, 1972

9. California Institute of Technology, Earthquake Engineering ResearchLaboratory, "Strong Moti on Earthquake Acce1erograms, Di gitized andPlotted Data," Volume I - Uncorrected Accelerograms, Part A,Report of Earthquake Engineering Research Laboratory, EERL 70-20,California Institute of Technology, Pasadena, California, 1969

10. Trifunac, M. D., IILow Frequency Digitization Errors and a NewMethod for Zero Base-Line Correcti on of Strong-Moti on Accelerograms, 1/Report of Earthquake Engineering Research Laboratory, EERL 70-07,California Institute of Technology, Pasadena, California, 1970

11. Trifunac, M. D., Udwadia, F. E. and Brady, A. G., "High FrequencyErrors and Instrument Corrections of Strong-Motion Accelerograms,"Report of Earthquake Engineering Research Laboratory, EERL 71-05,California Institute of Technology, Pasadena, California, 1971

Preceding page blank

46

12. California Institute of Technology, Earthquake Engineering ResearchLaboratory, "Strong Motion Earthquake Acce1erograms, Digitized andPlotted Data," Volume II - Corrected Acce1erograms and IntegratedGround Velocity and Displacement Curves, Part A, Report of Earth-quake Engineering Research Laboratory, EERL 71-50, California Insti-tute of Technology, Pasadena, California, 1971

13. Hudson, D. E., Preface to the Series in "Strong-Motion EarthquakeAccelerograms Digitized and Plotted Data,1I Volume II - CorrectedAccelerograms and Integrated Ground Velocity and DisplacementCurves, Part A, Report of Earthquake Engineering Research Laboratory,EERL 71-50, California Institute of Technology, Pasadena,California, 1971

14. Duke, C. M. and Leeds, D. J., "Site Characteristics of SouthernCalifornia Strong-Motion Earthquake Stations," Report No. 62-55,Department of Engineering, University of California, Los Angeles,California, November 1962

15. Hansen, W. R., Weiss, R. B., Idriss, 1. M. and Cluff, L. S.,IIGeotechnical Data Compilations for Selected Strong-Motion Seismo-graph Sites in California," prepared for National Oceanic and At-mospheric Administration, Woodward-Lundgren &Associates, Consult-ing Engineers and Geologists, Oakland, California, December 1973

16. United States Department of the Interior, Geological Survey, "Strong-Motion Acce1erograph Station List - 1975," Open File Report No.76-79, March 1976

17. State of California, The Resources Agency, Department of Conservation,"Geologic Map of California, San Diego - El Centro Sheet," Compila-tion by R. G. Strand, 1962, Second Printing, 1973

18. State of California, The Resources Agency, Department of Conservation,IIGeologic Map of California, Bakersfield Sheet,1I Compilation byA. R. Smith, 1964

19. Richter, C. F., IIE1ementary Seismology," W. H. Freeman and Company,1958

20. Bonilla, M. G., "Surface Faulting and Related Effects,1I in "Earth-quake Engineering," edited by R. L. Wiegel, Chapter 3, Prentice-Hall,1970

21. Coffman, J. L. and von Hake, C. A., IIEarthquake History of theUnited States," Publication 41-1, Revised Edition, U.S. Departmentof Commerce, National Oceanic and Atmospheric Administration, 1973

22. Cooley, J. W. and Tukey, J. W., "An Algorithm for the Machine Calcu-lation of Complex Fourier Series,1I Mathematics of Computation,Vol. 19, No. 90, pp. 297-301, The American Mathematical Society, 1965

47

23. Kubo, T. and Penzien, J., "Time and Frequency Domain Analyses ofThree Dimensional Ground Motions, San Fernando Earthquake," ReportNo. EERC 76-6, Earthquake Engineering Research Center, Universityof California, Berkeley, California, 1976

APPENDIX

Computer Program Listings

Preceding page blank

49

50

PROGRAM COR I 1'1 ( IMPUT. OUTPUT. TAPE I •TAPE5 -IMPUT. TAPE6-0UTPUT. PUMCH)COMMON /l)ATAN/x(250 I, 2) .XD(2500.2) .XMAXC2.2)COMMOM /lill/liAME(B)

C CORRECTION OF ORIGII'lAL TWO HORIZONTAL DIRECTION DATA INTOC LONGITUDINAL AND TRANSEVERSE COMPONEMTS TOWl'IRD THE EPICEMTERC INPUT DATAC MAME - NAME OF EARTHQUAKEC TT· DURATION (SEC) AND TT.LE.50.0C TETA - ANGLE OF 1'1 TO L OR E TO TC +-CLOCKWISE. --COUNTERCLOCKWISEC IMD 1 • NE.0 IF PR INT OUT DATA ARE NECESSARYC IND2 • NE.0 IF PUMCH OUT DATA ARE MECESSARYC IMD3 • NE.a IF PLOT OUT DATA ARE NECESSARYC CAUTION - OR IG HlAL DATA SHOULD BE AS A RIGHTHAMD SYSTEM.!. E••C IF 1'1 SIDE IS POSITIVE. E SIDE SHOULD BE POSITIVE.C IF S SIDE IS POSITIYE. W SIDE SHOULD BE POSITIVE.

READC5.46) NAMEREAD(5.100) TTREADC5.100) TETAREAD(5.10D INDI. IND2. IMD3MA'IF IX(TT/0.02)+1MY-MA/2+1CALL 5ETFX8(5LTAPE I .2500.11'8)CALL lMPUT(MA)TETA -TETA *8.8174533~XI-8.8

xmX2·8.8XI 'COS

51

c ~'***''*******************************'''********C SUBROUTINE FOR FAST FOURIER TRANSFORMC ********,,

52

C "'**"""*************"'***~C SUBROUTINE FOR PRINT OF SPECTRA AND AUTOCORRELATIONC ***********************'101I:********************************

SUBROUTINE SPAR(NAMLN.Y.ND.DX. IND. IAXIS.NAMl

NA~1EC B)N

Y(ND)NDDX

IND

IAXIS

DIMENSION NAME( S).Y(ND)DIMENSION NAM(2)DIM~NSION L< Hll) .SMAX(4) .STEP(4) .LSTEP (4) .FMT(3) .FMT3(6) .NUM(9)DATA SMAX/2 •• 4 •• S•• 18J.STEP/.S.I •• 1..2J.LSTEP/le.le.s.s/DATA FMT3/4H.l) .4H.2) .4H.3) .4H.4) .4H.S) .4H.6) /DATA NUM/1Hl.IH2.IH3.1H4.1HS.IH6.IH7.1H8.IH9/

CC HEADINGC

WRlTE(6.6eJ) NAMEWRITE(6.7Ell) NAMIFCIND.EQ.IElEl) WRITEC6.SEl2)IF( IND.EQ.ElIEl) WRITE(6.S03)IFUND.EQ.ElaJ) I"l

PROGRAM CORFA( INPUT. OUTPUT. TAPES-INPUT. TAPE6-0UTPUT. TAPE99)C INPUT DATAC DT - TIME INTERVAL OF EARTHQUAKE DATAC FMAX - MAXIMUM FREQUENCY ON FIGURE OF FOURIER SPECTRUMC NG - NUMBER OF DIVIDED INTERVALSC NF - NUMBER OF NPC NP - 1-2 FOR NS-EW. LO-TR OR CO-SHC 2-3 FOR EW-COR. NS. TR-COR. LO OR SH-COR. COC 1-4 FOR NS-COR. EW. LO-COR. TR OR CO-COR. SHC N - NUMBER OF COMPLEX FOURIER FREQUENCIESC YHAL.DIVY- MAX. VALUE AND NUM8ER OF EQUAL DIVISIONS ON ORDINATEC NAME - NAME OF STATION AND EARTHQUAKEC NAM - NAME OF EACH DIVIDED INTERVALC AMP - FOUR IER AMPLITUDEC PHA I - PHASE DIFFERENCEC FMAX CAN BE SELECTED ARBITRARILY.C PUNCHED CARDS BY PROGRAM (RUNF I) CAN 8E USED AS NAf1E TO PHA IC DIRECTLY.C AMP(K.I) - ORIGINAL FOURIER AMPLITUDE NS OR LOC AMP(K.2) - ORIGINAL FOURIER AMPLlTLIDE EW OR TRC AMP(K.3) - CORRECTED FOURIER AMPLITUDE NS OR LOC AMP(K.4) • CORRECTED FOURIER AMPLITUDE EW OR TR

DIMENSION NAME( 8.2) .NAM(2.2) • AMP (204B.4) .PHAI(2MB.4)DIMENSION NAMI ( 8) .. NAf12(2)DIMENSION X(2048). Y(204S) .DIVY(S). YMALCS) .NP(2. 3)DIMENSlON SPECS(35)READ(S.I"2) DTREAD(S.102) FMAXREAD(S.100) NGREAD(S.100) NFDO I I-J .NF

1 READ(S.J80) (NP(J.IJ.J-J.2)100 FORMATCSIS)

XFRM-I.SDO 999 I I - 1. NGREAD(S.100) NREAD(S.102) YMALCII).DIVY(II)N2-N/2AN-FLOAT(N)DO 10 1-1.2READ(S.IOI) (NAMEU.I).J·I.B)

101 FORMAT

54

CCCCCCCCCCCCCCCCC

~~~G~A~A~:rYE (INPUT• OUTPUT• TAPES- INPUT. TAPES-OUTPUT. TAPE99)

ILN - -I CASE OF COORDINATE TRANSFORMATION mLONGITUDINAL AND TRANSYERSE DIRECTION mlJARDEPICENTER

-2 CASE OF COORDINATE TRAHSFORMATIOH TOHORMAL AND PARALLEL DIRECTlOH TO FAULT LINE

NAME - NAME OF STATION AND EARTHQUAKEXl'tAX(I. IJ)- MAXIMUM VALUE OF ACCELERATION (GAllHA - TOTAL NUMBER OF XX - ACCELERAT!ON DATAXMAX(2.Il)- MAXIMUM VALLIE OF VELOCITY (KINE)HV - TOTAL HUMBER OF XDXD - YELOC 1TV DATA

~~~~~~ Y~ARDS BY PROGRAM (COR IN) CAN BE USED AS HAME TO XD

IJ -I-LONG I TUD iNAL DATA. -2-TRANSVERSE DATAI IJ -! -ACC. DATA. -2-\/EL. DATADIMENSIOH >'l'1AL(2).XSC(7)COMMON /DATAWX(3aEl0.2) .XD( 1500.2) .XMAX(2.2)CONi'iON /N 11/1;AI'£ (S)COMMON /ILONO/ILNDATA XSC/18 •• 2l3 •• 3El •• 4El •• SEl .. SEl •• JElEl./READ(S.!l ILNDO Ie IJ-1.2READ(S.Iee) NAME.XMAX(I.Ill.HAREAD(S.lOll (X(K.Ill.K-l.NA)READ(S.IEl2) XMAX(2.1I1.HVREAD(S.IEl!l (XD(K.Ill.K-I.NV)

tel CONTI HUEXN-El.aDO sa IJ J -1.2DO 2a IJ·I.2XM-AMAXI (XN.XNAX( I I I. Ill)

2a CONTINUEIF(j I I.EQ.ll XN-XN*0.1XNM-!a0.JF(XM.GE.XNM) GO TO 4ElXNM-!El.IF(XN.LE.XNM) GO TO 40DO 3El KK-I.7IF(XM.GT.XSC(KK) GO TO 3ElXf1M-XSC(KK)GO TO 40

3El CONTINUE4C IF( IJ I.EO. 1) XNM-X~U'1>l

55

EARTHQUAKE ENGINEERING RESEARCH CENTER REPORTS

NOTE: Numbers in parenthesis are Accession Numbers assigned by the National Technica 1 In formation Service: tl:c, se are'followed by a price code. Copies of the reports may be ordered from the National Technical Information Service, 52HSPort Royal Road, Springfield, Virginia, 22161. Accession Numbers should be quoted on orders for reports (PB --- ---)and remittance must accompany each order. Reports without this information were not available at time of printinq.Ur0n request, CERC will mail inquirers this information when it becomes available.

ECRC 67-1

EERe 68-1

CERC 68-2

EERC 68-3

EERC 68-4

EERC 68-5

EERe 69-1

EERC 69-2

EERC 69-3

EERC 69-4

EERC 69-5

E2RC 69-6

EERC 69-7

EERC 69-8

"Feasibility Study Large-Scale Earthquake Simulator Facility," by J. Penzien, J .G. Bouwkamp. R. W. Clouqha!ld O. Rea - 1967 (PH 187 905)1'.07

Unassigned

"Inelastic Behavior of Beam-to-Column Subassemblages Under Repeated Loading." by V. V. Bertero - 1968(PB 184 888) 1'.05

"A Graphical ~lethod for Solving the Wave Reflection-Refraction Problem." by H.D. McNiven and Y. "ler,yi - 1%8(PB 187 943) 1'.03

"Dynamic Properties of McKinley School Buildings," by D. Rea, J.G. Bouwkamp and R.W. Clough - 1968(PB 187 902)1'.07

"Characteristics of Rock Motions During Earthquakes," by H.B. Seed, 1./01. Idriss and F.I'. Kiefer -1')6

56EERC 70-5 "A Computer Program for Earthquake Analysis of Dams," by A.K. Chopra and P. Chakrabarti -1970 (AD 723 994)1\f)'i

EERC 70-6 "The Propagation of Love Waves Across Non-Horizontally Layered Structures," by J. Lysmer and L.A. Drake1970 {PB 197 896)A03

EERC 70-7 "Influence of Base Rock Characteristics on Ground Response," by J. Lysmer, H.B. Seed and P.B. Schnabel1970 {PB 197 897)A03

EERC 70-8 "Applicability of Laboratory Test Procedures for Measuring Soil Liquefaction Characteristics under CyclicLoading," by H.B. Seed and w.n. Peacock - 1970 (PB 198 016)A03

EERC 70-9 "A Simplified Procedure for Evaluating Soil Liquefaction Potential," by II. B. Seed and 1./1. Idriss - 1970(PB 198 009)A03

EERC 70-10 "Soil Moduli and Damping Factors for Dynamic Response Analysis," by H.B. Seed and 1.M. Idriss -1970(PB 197 869)A03

EERC 71-1 "Koyna Earthquake of December 11, 1967 and the Performance of Koyna Dam," by A.K. Chopra and P. Chakrabarti1971 (AD 731 496)A06

EERC 71-2 "Preliminary 'In-Situ Measurements of Anelastic Absorption in Soils Using a Prototype Earthquake Simulator,"by R.D. Borcherdt and P.W. Rodgers - 1971 (PB 201 454)A03

EERC 71- 3 "Static and Dvnamic Analysis of Inelastic Frame Structures," by F. L. Porte~' and- G. H. Powell - 1971(PB 210 135)A06

EERe 71-4 "Research Needs in Limit Design of Reinforced Concrete Structures," by V.V. Bertero -1971 (PB 202 943)A04

EERC 71-5 "Dynamic Behavior of a High-Rise Diagonally Braced Steel Building," by D. Rea, A.A. Shah and .J.G. 8ou''''h11''p1971 (PB 203 584)A06

EERC 71-6 "Dynamic Stress Analysis of Porous Elastic Solids Saturated with Compressible Fluids," by J. Ghaboussi andE. L. Wilson -1971 (PB 211 396)AQ6

EERC 71-7 "Inelastic Behavior of Steel Beam-to-Column Subassemblages," by H. Krawinkler, V.V. Bertero and E.P. Popov1971 (PB 211 335)A14

EERC 71-8 "Modification of Seismograph Records for Effects of Local Soil Conditions," by P. Schnabel, H.B. Seed andJ. Lysmer -1971 (PB 214 450)A03

EERC 72-1 "Static and Earthquake Analysis of Three Dimensional Frame and Shear Wall Buildings," by E.L. Wilson andH.H. Dovey -1972 (PB 212 904)A05

EERC 72-2 "Accelerations in Rock for Earthquakes in the Western United States," by P.B. Schnabel and H.B. Seed-1972(PB 213 100)A03

EERC 72-3 "Elastic-Plastic EarthqUake Response of Soil-Building Systems," by T. Minami - 1972 (PB 214 868) A08

EERC 72-4 "Stochastic Inelastic Respons" of Offshore Towers to Strong Me>tion Earthquakes," by M.K. Kaul-1972(PB 215 713) A05

EERC 72-5 "Cyclic Behavior of Three Reinforced Concrete Flexural Members with High Shear," by E.P. Popov, V.V. Berteroand H. Krawinkler - 1972 {FB 214 555)A05

EERC 72-6 "Earthquake Response of Gravity Dams Including Reservoir Interaction Effects," by F. Chakrabarti andA.K. Chopra - 1972 (AD 762 330)A08

EERC 72-7 "Dynamic Properties of Pine Flat Dam," by D. Rea, C.Y. Liaw and A.K. Chopra -1972 {AD 763 928)A05

EERC 72-8 "Three Dimensional Analysis of Building Systems," by E.L. Wilson and H.H. Dovey -1972 (PB 222 438)A06

EERC 72-9 "Rate of Loading Effects on Uncracked and Repaired Reinforced Concrete Members," by S. Mahin, V.V. Bertero,

D. Rea and M. Atalay - 1972 (FB 224 520) AC8

EERC 72-10 "Computer Program for Static and Dynamic Analysis of Linear Structural Systems," by E.L. Wilson, K.-J. Bathe.J,E. peterson and H.H,DoveY-1972 (FB 220 437)A04

EERC 72-11 "Literature Survey - Seismic Effects on Highway Bridges," by T. Iwasaki, J. l?enzien and R.W. Clough -1972(l?B 215 613) A19

EERC 72-12 "S!lAl

EERC 73-3

EERC 73-4

EERC 73-5

57

"Computer Aided Ultimate Load Design of Unbraced Multistory Steel Frames," by M.B. EI-Hafez and G.H. Powell1973 (PB 248 315)A09

"Experimental Investigation into the Seismic Behavior of Critical Resions of Reinforced Concrete Componentsas Influenced by Moment and Shear," by M. Celebi and J. Penzien - 1973 (PB 215 884)/109

"Hysteretic Behavior of Epoxy-Repaired Reinforced Concrete Beams," by M. Celebi and J. Penzien - 1973(PB 239 568)A03

EERC 73-6 "General Purpose Computer Program for Inelastic Dynamic Response of Plane Structures," by A. Kanaan andG.H. Powell- 1973 (PB 221 260)A08

EERC 73-7 "A Computer Program for Earthquake Analysis of Gravity Dams Including Reservoir Interaction," byP. Chakrabarti and A.K. Chopra-1973 (AD 766 271)A04

EERC 73-8 "Behavior of Reinforced Concrete Deep Beam-Column Subassemblages Under Cyclic Loads," by O. Kustu andJ.G. Bouwkamp -1973 (PB 246 117)A12

EERC 73-9 "Earthquake Analysis of Structure-Foundation Systems," by A.K. Vaish and r,.K. Chopra -1973 (AD 766 272)A07

EERC 73-10 "Deconvolution of Seismic Response for Linear Systems," by R.B. Reimer -1973 (PB 227 179)A08

EERC 73-11 "SAP IV: A Structural Analysis Program for Static and Dynamic Response of Linear Systems," by K.-J. Bathe.E.L. Wilson and F.E. Peterson -1973 (PB 221 967)A09

EERC 73-12 "Analytical Investigations of the Seismic Response of Long, Multiple Span Highway Bridges," by W.S. Tsengand J. Penzien - 1973 (PB 227 816) AlO

EERC 73-13 "Earthquake Analysis of Multi-Story Buildings Including Foundation Interaction," by A.K. Chopra andJ .A. Gutierrez - 1973 (FB 222 970) A03

EERC 73-14 "ADAP: A Computer Program for Static and Dynamic Analysis of Arch Dams." by R.W. Clough, J.M. Raphael andS. Mojtahedi - 1973 (PB 223 763)A09

EERC 73-15 "Cyclic Plastic Analysis of Structural Steel Joints," by R.B. Pinkney and R.W. Clough -1973 (PB 226 843)/108

EERC 73-16 "QT.'AD-4: A Computer Program for Evaluating the Seismic Response of Soil Structures by Variable DampingFinite Element Procedures," by 1.M. Idriss, J. Lysmer, R. Hwang and H.B. Seed -1973 (PB 229 424)/105

EERC 73-17 "Dynamic Bf'l1avior of a Multi-Story Pyramid Shaped Building," by R.M. Stephen, J.P. Hollings andJ.G. Bouwkamp -1973 (PB 240 718)1\06

EERC 73-18 "Effect of Different Types of Reinforcing on Seismic Behavior of Short Concrete Columns," by V.V. Bertero,J. Hollings, O. Kustu, R.M. Stephen and J.G. Bouwkamp -1973

EERC 73-19 "Olive View Medical Center Materials Studies, Phase I," by B. Bresler and V.V. Bertero -1973 (PB 235 986)/106

EERC 73-20 "Linear and Nonlinear Seismic Analysis Computer Programs for Long MUltiple-Span Highway Bridges," byW.S. Tseng and J. Penzien-1973

EERC 73-21 "Constitutive Models for Cyclic Plastic Deformation of Engineering Materials," by J.M. Kelly and P.P. Gillis1973 (PB 226 024)A03

EERC 73-22 "DRAIN - 20 User's Guide," by G.H. Powe11-l973 (PB 227 016)1105

EERC 73-23 "Earthquake Engineering at Berkeley - 1973," (PB 226 033)All

EERC 73-24 Unassigned

EERC 73-25 "Earthquake Response of Axisymmetric Tower Structures Surrounded by Water," by C.Y. Liaw and A.K. Chopra1973 (,\0 773 052)1109

EERC 73··26 "Investigation of the Failures of the Olive View Stairtowers During the San Fernando Earthquake and TheirImplications on Seismic Design," by V.V. Bertero and R.G. Collins -1973 (PB 235 106)A13

EERC 73-27 "Further Studies on Seismic Behavior of Steel Beam-Column Subassemblages," by V.V. Bertero, H. Krawinklerand E.P. Popov -1973 (PB 234 172)A06

EERC 74-1 "Seismic Risk Analysis," by C.S. Oliveira -1974 (PB 235 920)1106

EERC 74-2 "Settlement and Liquefaction of Sands Under Multi-Directional Shaking," by R. Pyke, C.K. Chan and H.B. Seed1974

EERC 74-3 "Optimum Design of Earthquake Resistant Shear Buildings," by D. Ray, K.S. Pister and /I.K. Chopra - 1974(PB 231 172)1106

EERC 74-4 "LUSH - A Computer Program for Complex Response Analysis of Soil-Structure Systems," by J. Lysmer, '. Udaka,H.B. Seed and R. Hwang-1974 (PE 236 796)1105

58

EERC 74-5 "Sensitivity Analysis for Hysteretic Dynamic Systems: Applications to Earthquake Engineering." by D. Ray1974 {PB 233 213)A06

EERC 74-6 "Soil Structure Interaction Analyses for Evaluating Seismic Response," by H.B. Seed, J. Lysmer and R. Hwang1974 (PB 236 519)A04

EERC 74-7 Unassigned

EERC 74-8 "Shaking Table Tests of a Steel Frame - A Progress Report," by R. W. Clough and D. Tang - 1974 (PB 240 Pr'9) AD:'

EERC 74-9 "Hysteretic Behavior of Reinforced Concrete Flexural Members with Special Web Reinforcement," byV.V, Bertero, E.P. Popov and T.Y. Wang - 1974 (PB 236 797)A07

EZRC 74-10 "Applications of Reliability-Based, Global Cost Optimization to Design of Earthquake Resistant Structures."by E. Vitiello and K.S. Pister -1974 {PB 237 231)A06

EERC 74-11 "Liquefaction of Gravelly Soils Under Cyclic Loading Conditions," by R.T. Wong, H.B. Seed and C.K. Chan1974 (PB 242 042)A03

EERC 74-12 "Site-Dependent Spectra for Earthquake-Resistant Design," by H.B. Seed, C. Ugas and J. Lysmer -1974(PB 240 953)A03

EERC 74-13 "Earthquake Simulator Study of a Reinforced Concrete Frame," by P. Hidalgo and R.W. Clough -1974(PB 241 9~4)A13

EERC 74-14 "Nonlinear Earthquake Response of Concrete Gravity Dams," by N. Pal-1974 {AD/A 006 583)A06

EERC 74-15 "Modeling and Identification in Nonlinear Structural Dynamics - I. One Degree of Freedom Models," byN. Distefano and A. Rath - 1974 (PB 241 548) A06

EERC 75-1 "Determination of Seismic Design Criteria for the Durnbarton Bridge Replacement Structure, Vol. I: Description.Theory and Analytical Modeling of Bridge and Parameters," by F. Baron and S.-H. Pang -1975 (PB 259407'A15

EERC 75-2 "Determination of Seismic Design Criteria for the Durnbarton Bridge Replacement Structure. Vol. II: NumericalStudies and Establishment of Seismic Design Criteria," by F. Baron and S.-H. Pang -1975. (PB 259 408)All(For set of EERC 75-1 and 75-2 (pa 259 406))

EERC 75-3 "Seismic Risk Analysis for a Site and a Metropolitan Area." by C.S. Oliveira -1975 (PB 248 l34)A09

EERC 75-4 "Analytical Investigations of Seismic Response of Short, Single or Multiple-Span Highway Bridges." byM. -C. Chen and J. Penzien - 1975 (PB 241 454) A09

EERC 75-5 "An Evaluation of Some Methods for Predicting Seismic Behavior of Reinforced Concrete Buildings." by S.A.Mahin and V.V. Bertero -1975 (PB 246 306)A16

EERC 75-6 "Earthquake Simulator Study of a Steel Frame Structure, Vol. I: Experimental Results," by R.I•. Clough andD.T. Tang -1975 {PB 243 981)A13

EERC 75-7 "Dynamic Properties of San Bernardino Intake Tower," by D. Rea, C.-Y. Liaw and A.K. Chopra-1975 (AD/A008406)A05

EERC 75-8 "Seismic Studies of the Articulation for the Durnbarton Bridge Replacement Structure. Vol. I: Description,Theory and Analytical ~lodeling of Bridge Components," by F. Baron and R.E. Harnati -1975 (PB 251 539)A07

EERC 75-9 "Seismic Studies of the Articulation for the Durnbarton Bridge Replacement Structure, Vol. 2: NumericalStudies of Steel and Concrete Girder Alternates," by F. Baron and R.E. Hamati - 1975 (PB 251 540)AIO

EERC 75-10 "Static and Dynamic Analysis of Nonlinear Structures," by D.P. Mondkar and G.H. Powell-1975 (PB 242 434)A08

EERC 75-11 "Hysteretic Behavior of Steel Columns," by E.P. Popov, V.V. Bertero and S. Chandramouli-1975 {PB252 3f'5)All

EERC 75-12 "Earthquake Engineering Research Center Library Printed Catalog," - 1975 (PB 243 711) A26

EERC 75-13 "Three Dimensional Analysis of Building Systems {Extended Version)," by E.L. Wilson, J.P. Hollings andH.H. Dovey - 1975 (PB 243 989)A07

EERC 75-14 "Determination of Soil Liquefaction Characteristics by Large-Scale Laboratory Tests," by P. De Alba,C.K. Chan and H.B. Seed -1975 (NUREG 0027)A08

EERC 75-15 "A Literature Survey - Compressive, Tensile, Bond and Shear Strength of Masonry," by R.L. Mayes and R.W.Clough - 1975 (FB 246 292)AIO

EERC 75-16 "Hysteretic Behavior of Ductile Moment Resisting Reinforced Concrete Frame Components," by V.V. Bertero andE.P. Popov-1975 (PB 246 388)A05

EERC 75-17 "Relationships Between Maximum Acceleration, Maximum Velocity, Distance from Source, Local Site Conditionsfor Moderately Strong Earthquakes," by H.B. Seed, R. Murarka, J. Lysmer and LM. Idriss-1975 {PB 248 172)A03

EERC 75-18 "The Effects of Method of Sample Preparation on the Cyclic Stress-St;rain Behavior of Sands," by J. ~lulilis,C.K. Chan and H.B. Seed - 1975 (Summarized in EERC 75-28)

59

EERC 75-19 "The Seismic Behavior of Critical Regions of Reinforced Concrete Components as Influenced by Moment, Shearand Axial Force," by M.B. Atalay and J. Penzien -1975 (PB 258 842)All

EERC 75-20 "Dynamic Properties of an Eleven Story Masonry Building," by R.M. Stephen, J.P. Hollings, J.G. Bouwkamp andD. Jurukovski - 1975 (PB 246 945)A04

EERC 75-21 "State-of-the-Art in Seismic Strength of Masonry - An Evaluation and Review," by R.L. Mayes and R.W. Clough1975 (PB 249 040)A07

EERC 75-22 "Frequency Dependent Stiffness Matrices for Viscoelastic Half-Plane Foundations," by A.K. Chopra,P. Chakrabarti and G. Dasgupta -1975 (PB 248 l21)A07

EERC 75-23 "Hysteretic Behavior of Reinforced Concrete Framed Walls," by T.Y. Wong, V.V. Bertero and E.P. Popov -1975

EERC 75-24 "Testing Facility for Subassernblages of Frame-Wall Structural Systems," by V.V. Bertero, E.P. Popov andT. Endo-1975

EERC 75-25 "Influence of Seismic History on the Liquefaction Characteristics of Sands," by H.B. Seed, K. Mori andC.K. Chan - 1975 (Swmnarized in EERC 75-28)

EERC 75-26 "The Generation and Dissipation of Pore Water Pressures during Soil Liquefaction," by H.B. Seed, P.P. Martinand J. Lysmer - 1975 (PB 252 648) A03

EERC 75-27 "Identification of Research Needs f"r Improving Aseismic Design of Building Structures," by V.V. Bertero1975 (PB 248 136)A05

EERC 75-28 "Evaluation of Soil Liquefaction Potential during Earthquakes," by H.B. Seed, I. Arango and C.K. Chan - 1975(NUREG 0026}Al3

EERC 75-29 "Representation of Irregular Stress Time Histories by Equivalent Uniform Stress Series in LiquefactionAnalyses," by H.B. Seed, I.M. Idriss, F. Makdisi and N. Banerjee -1975 (PB 252 635)A03

EERC 75-30 "FLUSH - A Computer Program for Approximate 3-D Analysis of Soil-Structure Interaction Problems," byJ. Lysmer, T. Udaka, C.-F. Tsai and H.B. Seed-1975 (PB 259 332)A07

EERC 75-31 "ALUSH - A Computer Program for Seismic Response Analysis of Axisymmetric Soil-Structure Systems," byE. Berger, J. Lysmer and H.B. Seed-1975

EERC 75-32 "TRIP and TRAVEL - Computer Programs for Soil-Structure Interaction Analysis with Horizontally TravellingWaves," by T. Udaka, J. Lvsmer and ILB. Seed -1975

EERC 75-33 "Predicting the Performance of Structures in Regions of High Seismicity," by J. Penzien -1975 (PB 248 l30lA03

EERC 75-34 "Efficient Finite Element Analysis of Seismic Structure -Soil-Direction," by J. Lysmer, H.B. Seed, T. Udaka,R.N. Hwang and C.-F. Tsai -1975 (PB 253 570)A03

EERC 75- 35 "The Dynamic Behavior of a First Story Girder of a Three-Story Steel Frame Subjected to Earthquake Loading,"by R.W. Clough and L.-Y. Li - 1975 (PB 248 84l)A05

EERC 75- 36 "Earthquake SimUlator Study of a Steel Frame Structure, Volume II - Analytical Results," by D. T. Tang - 1975(PB 252 926) A10

EERC 75-37 "ANSR-I General Purpose Computer Program for A11alysis of Non-Linear Structural Response," by D.P. Mondkarand G.H. Powell-1975 (PB 252 386)A08

EERC 75-38 "Nonlinear Response Spectra for PrObabilistic Seismic Design and Damage ASSessment of Reinforced ConcreteStructures," by M. Murakami and J. Penzien -1975 (PB 259 530)A05

EERC 75-39 "Study of a Method of Feasible Directions for Optimal Elastic Design of Frame Structures Subjected to Earth-quake Loading," by N.D. Walker and K.S. Pister-1975 (PB 257 781)A06

EERC 75-40 "An Alternative Representation of the ElastiC-Viscoelastic Analogy," by G. Dasgupta and J .L. Sackman - 1975(PB 252 173) AD3

EERC 75-41 "Effect of Multi-Directional Shaking on Liquefaction of Sands," by H.B. Seed, R. Pyke and G.R. Martin -1975(PB 258 781) A03

EERC 76-1 "Strength and Ductility Evaluation of Existing Low-Rise