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MAXIMUM ACCELERATIONS DURING EARTHQUAKES By William K. Cloudl i A!!STRACT Presented is a resume of information on maximum accelerations during { ea rthquakes. Primarily the resume covers measurements obtained since 1933 1 from U.S. ' Coast and Geodetic Survey strong-motion seismographs. However, several estimates of maximum accelerations during great earthquakes are in-cluded. Measured accelerations are shown, and are discussed relative to attenu-ation with distance and to response spectra. ' FOREWORD
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For the scientific study of strong motion during earthquakes, measurement . , i of acceleration has at least two advantages over measurement of velocity or dis- ! placement. Acceleration describes strong. motion in more detail, and can be q directly and accurately recorded with simple, more rugged instruments. It also
- s provides additional data of engineering interest by way of integration and spectrum ,
analysis. For these reasons acceleration has always been the first choice for measurement and accelerometers the basic instruments in any strong-motion I research program. The Survey program is no exception. I As basic instrumentation the Survey uses short-period (0.04 to 0.08 sec) versions of the Wood-Anderson seismometer as accelerometers, and records pendulum motion directly on photographic tape by means of optical styll (Refer-ence 1).
'Ihe problem is to locate the instruments, which are limited in number by cost,, where results can be expected in a reasonable length of time. As ept- !
centers of future earthquakes cannot be predicted, the best that can be done is to select highly seismic areas and to try and outguess nature. 71us the Survey has attempted to do for the past 31 years, with the cooperation and advice of sels-mologists and engineers. g Starting with several newly designed three-component accelerographs in 1932, the network of acceleration measurement stations has gradually been ex-
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'panded to 72 locations in the following seismic areas: I en in l CD 1
,'O Montana - 4 o Arizona -1 Oregon - 1 l
[ sed r9 co California - 48 Nevada -4 Utah -1 000 T LL H ru cn O LU o'm e: 1 Chief, Seismological Field Survey, Coast and Geodetic Survey, U.S. . SSE Department of Commerce. , D@$N@hb
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e i MEASURED ACCELERATIONS (
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.During the 31 years that the thinly spread network has been in operation l
{ severaf hundred acceleration records of scientific interest have been obtained. However, 'as could be expected from the guesswork involved in location of instru- { ments, and from the ratio of small to large earthquakes, only a limited number of I these records are of engineering significance. l In Figure 1, horizontal accelerations recorded at ground-level stations , during 25 earthquakes illustrate the upper limits of recorded data to date. .The :
- highest two accelerations are from records shown in Figure 2. Symbols used in ,
j Figure i can be related to each of the 25 earthquakes by reference to Table 1., i As Table 1 shows, the earthquakes varied in magnitude from 5.0 to 7.7. . The earthquakes.also varied in depth of origin- shallow in United Statespfairly ) deep in Central and South America. Furthermore, foundation material under re- l cording stations varied-- rock at'Balbou Heights and Golden Gate Park, alluvium ! 4 or fill of various depths and. consolidation at all other stations. . l ' ,/ 1 l ATTENUATION OF ACCELERATION WITH DISTANCE Returning now to Figure 1, the dashed-line envelope merely represents an attempt to fit th.e data with a mathematical expression. As drawn the line is the graph of Log a = 6.17 - log (3900 + As ) where a = acceleration (cm/sec2) and A = distance (miles) I' I Between 7 and 200 miles predictions by the equation are in reasonable agreement with recorded data. At lesser or greate'r distances predictions are unsupported. Considering the previously mentioned variables, the equation would be of l
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little interest except for the attenuation-with-distance pattern it suggests. The ) pattern is similar to that inferred for single earthquakes. For example: An i unpublished report dated November 19, 1962, by the California State Department of Water Resources Consulting Board (Reference 2) contains the statement quoted l I below. Parts of the statement of present interest are underlined. !
"In the San Francisco 1906 shock A was 305 cm and T is estimated to have
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' been 5 seconds. For these values equation (3) gives a maximum acceleration of 4 yr*
305 x = 480 cm/sec2 . Equation (3) thus indicates that the slip started - 25 x-
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I' . 4 auddenly with an acceleration approximately one-half of the acceleration of gravity , and the movement was completed in about-5 seconds. For points away from the L fault the throw displacement and, acceleration decrease with distance in accordance - with equation (1). On the other hand.the oscillatory movements are presumed to have a corresponding increase with distance from the fault. De total acceler- .
--ation is thus roughly constant to a distance of 12 miles and from there out it decreases." '
Also'Steinbrugge and Cloud (Reference 3) referring to the Hebgen Lake, Montana, earthquake of August 17,1959, state: l "De intensity at West Yellowstone, as measured only by building damage, was not significantly different from that near the trace of the fault, considering comparable soils and comparable constmction. De small amount of damage , along the fault zone makes it difficult to determine lesser intensities e'Isewhere. -
.But there is still sufficient evidence to indicate that the intensity as measured by building damage was not greatly different along the fault zone from that,5 to 10 miles away." Also: " Damage observations and strong-motion seismograph re- , ,
.sults correlate only if the followl.ng assumptions are made: (a) That a sizeable area in'the ' epicentral region was subjected to almost the same level of acceler-ations; . ." - ,
} Measurements by the Survey to date neither prove nor disprove the existence of a. level zone of acceleration in the epicentral area of an earthquake. However, measurements.do indicate that at 'some distance from the epicenter attenuation with distance can be approximated by a = K A -2 where a = acceleration and A = distance usually within a factor.of better than 12.
' We equation also appears ,to hold for attenuation with distance of spectrttm intensity,2 as illustrated in Figure 3.
l Noticeable deviation from the curves at the shortest distances in Figure 3 may.or may not indicate transition toward a zone of about equal acceleration or intensity for the ' carthquake and toward zero for the explosion. Noticeable' dev'i-ations of acceleration at the largest distances for the explosion are probably due
,to the particular recording sites being deep in a potash mine. . Difference in 2 Defined by Housner as the arca under a relative maximum velocity response l ,J
! - spectrum between period limits of 0.1 and 2.5 seconds. However, for this l paper velocity rather than ' area is used and damping is specified as 10Tn <ritical. b
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l b deviation of acceleration and spectrum intensity here and elsewhere in Figure 3 is considered ilue to maximum acceleration being a single period quantity and spectrum intensity being a many-period quantity. l' , j Not evident in Figure 3 is the variation of foundation material under stations I recording the carthquake. In order of increasing distance from, epicenter, material under each site is: , 1 olden Gate Park - Rock. - State Building - Unconsolidated sand and gravel. (Mat foundation). ' i Southern Pacific Building - Water-soaked sediments covered by artificial ! fill. (Pile foundation). Alexander Building - Sand and sandy clay. (Mat foundation). Oakland City Hall - Unconsolidated alluvial fill. (Mat foundation). - For this earthquake at least, magnification of acceleration by foundation material was not large in spite of the variation; deviation from the curve in Figure 3 being in all cases less than a factor of 12.
# #' RESPONSE SPECTRA :
While it is common knowledge that both du ration of acceleration and maxi-
) mum acceleration are factors in stnictural response, a clear picture is sometimes hard to obtain. Figure 4, which has been prepared by means of a C.I.T. electric analog spectrum analyzer (Reference 4), represents an attempt to aid visualization.
In the upper half of the figure is shown the complete response of a linear oscillator to a single c.ycle of acceleration, and to the single cycle plus a nurrber of additional cycles. As oscillator damping is increased from 0 to 20% of critical rsotice that: (a) Duration of response decreases and approaches duration of acceleration. (b) Maximum amplitude of response decreases, with the rate of decrease less rapid for iesponse to the single cycle of acceleration. (c) Duration of acceleration plays an important role in response amplitude when the oscillator is undamped or lightly damped. In the lower half of Figu're 4 is shown the response spectra obtained from the same acceleration functions used in the upper half. liere the relative effect of the two acceleration functions on maximum response can be seen not only for the 0.757-second period oscillator but also for oscillators of other periods. Addi-tional data is thus made available by the spectra, but at the expense of information on exact duration of acceleration or on the number of times response reached or approached maxima. (Had zero-damped spectra been included in the illustration i duration or lack of duration of acceleration would havs been noticeable, but the l preceding statement as to loss of information would,still have been true.) l l .
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c ESTIMATED ACCELERATION I As no great earthquake has occurred in United States since installation of
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were located beyond the limits of great earthquakes that did occ*ur, the question of , . [ maximum possible accelerations has yet to be answered by measurement. However, , a number of estimates have been made, several of which follow. - ! From' carefully documente:i evidence of boulders lifted out of the ground with-out. cutting the edges of their former seats, of posts shot from the ground, and from ' - ' other effects observed after the great (magnitude 8.7) Assam, India,' earthquake of-
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- June 12,1897, R. D. Oldham estimated vertical accelerations in excess of gravity. I However, for horizontal accelerations his estimate was considerably less-- slight-ly over 40% of gravity, based on overthrow of columns (Reference 5-a).,
1 For the great Mino-Owarf, Japan, earthquake of October 28,1891, Milne i and Omori made a similar estimate of horizontal acceleration (Reference 5-b).
, In both cases the following formula, credited to C. D. West, was used to j relate overturning of columns to acceleration: )
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a=g_ . J h ' where h = height to center of gravity of column and b = distance from center of line of column to overturn edge. Accuracy of the estimates are, thus, questionable. For as pointed out by Kirk-patrick (Reference 6), maximum acceleration relates to start of overturn rather than actual overturn. . However, it is interesting that the estimates are in the same range of ac-celeration as some recent estimates for California earthquakes. For example, , ,
- the Consulting Board report, previously quoted (Reference 2), suggests that, had *
, faulting during the El Centro shock of May 18, 1940, started 40 miles northwest of the city and continued 40 miles southeast of the city, a total distance of 80 miles
- instead of the 40 miles actually obseived- ". . . the intensity of oscillatory
' ground shaking might have been greater by .i factor of approximately /2 and the duration of strong shaking might have been lengthened by a factor of 2." Also: .
"It would be reasonable to take for a large earthquake on the San Andreas fault a horizontal ground shaking that has in the vicinity of the fault a maximum acceler-ation of 50% g and a duration of 60 seconds."
With the preceding estimates in mind, Figure.5 represents the result of ; 'N speculation on what effect a 50% increase in maximum acceleradon would have on ! spectrum amplitudes. In the figure, the form and duration of accelera, tion is ! l
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2 .= ratio of assumed acceleration to recorded acceleration at . Had the more reasonable assumption been made that a 50% increase in maximum ' acceleration would change both the form and duration of the acceleration function, then the lightly damped spectra would probably be considerably different,from that shown in Figure 5, but the more heavily damped spectra would probably remain somewhat.as shown. . CONCLUSIONS
/ .
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- J . Whue the Survey has recorded maximum horizontal accelerations of approxi-
- mately 35% of gravity with duration of strong motion lasting approximately 30 '
seconds, the data can be considered to indicate maxima only for earthquakes up to
-l magnitude 7.1.
For earthquakes of greater magnitude many estimates have been made, but to the author, those in the range of 50% of gravity for maximum acceleration and of 60 seconds for du' ration seem most reasonabic for engineering use. Should higher accelerations actually occur, it seems likely that they would be associated with such extremely small displacements as to cause little damage except to very brittle structures. As to attenuation of acceleration with distance, a zone of approximately equal acceleration near the epicenter of earthquakes seems probable. However, measurements have been too limited to supply proof. Outside the immediate epi- i central or faulted zone of earthquakes recorded, maximum accelerations appear to' attenuate roughly as the inverse square of distance, no consideration being . given to periods of the accelerations. ACKNOWLEDGMENTS The author is indebted to Professor George W.'Housner for permission to
$/ quote from Reference $; to Mr. Robert F. Rigling for preparing spectral data; and to Mrs. Nina H. Scott for typing and assembling the paper.
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( 7, REFERENCES
- 1. Cloud, W. K., and D. S. Carder, "The Strong-Motion Program of the Coast and Geodetic Survey," Proc. First World Conference on Earthquake Engineering, pp. 2-1-2-10. Berkeley, California, June 1956.
- 2. Departme'nt of Water Resources Consulting Board for Earthquake Analysis, i Members of the consulting board include Hugo Benloff; Chairman; l George W. Housner, and H. B. Seed. An unpublished report to A. R. Golze', Chief Engineer, Department of Water Resources, Sacra-mento, California, November 19,1962 (p. 3),
- 3. Steinbrugge, Karl V., and W. K. Cloud, "The Earthquake at Hebgen Lake, Montana, August 17, 1959 - Epicentral Intensities and Damage," ,
Bull. Seism. Soc. Am., 52, No. 2: 181-234 (pp. 229 and 231).
'4. Caughey, T. K., D. E. Hudson, and R. V. Powell, "The C.hT. Mark IL Response Spectrum Analyzer for Earthquake Engineering Studies,"
Proc. Second World Conference on Earthquake Engineering, Vol. II: . j 1137-1148. Japan,1960.
- 5. Davidson, Charles, " Great Earthquakes," Thomas Murby & Co., Publishers, London,1936 (pp.138-157). Davidson quotes as his references:
(a) Oldham, R. D., " Report on the Great Earthquake of 12th June,1897," India Geol. Sury. Mem., Vol. 29,1899, pp.1-379. (b) Omori, F., " Note on the Great Mino-Owarl Earthquake of October 28th,1891," Imp. Earthq. Inv. Com. Publ., No.4,1900, pp.13-24.
- 6. Kirkpatrick, Paul, " Seismic Measurements b'y the Overthrow of Columns,"
Bull. Seism. Soc. Am., 17: 95-109 (p. 97). e
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. TABLE 1.-- Legend for use with Figure 1.- ,
(- Symbols used Earthquake in Figure 1 Nearest recording station .
. Date
. M1 l
i 4 , 5 Oct 1950 , ' 7.7 San Jose, Costa Rica
^
l O 21 July 1952 ~7.6 Taft, Calif.
-6 23 Oct 1950 7.3 Guatemala City, Guatemala 0' 18 May 1940 7.1 El Centro, Calif.
t -4 ,13 Apr 1949 7.1 Olympia, Wash. X' 17 Aug 1959 7.1 Bozeman, Mont.- *
- 3. 13 Sept 1945 - 7.1 Santiago, Chile
'w 16 Dec 1954 7.0- Bishop, Calif.
.5 ' 18 Nov.1948. 7.0 San Jose, Costa Rica -
8 6 Jan 1951 6.9 Balboa Heights, Panama
- n' 21'Nov 1952 - 6.8 San Luis Obispo, Calif.
2- 23 Nov 1954 6.8 Hawthorne, Nev. e 9 Feb 1956 6.8' El Centro, Calif. p 6.8 Ferndale, Calif. . 25 Novf1954 l 7 - 17 Mar 1945 6.75 Balboa Helghts, Panama
- 7 b 21 Dec 1954 6.6 - Eureka, Calif.
H' u 3 Oct 1941 6.4 Eureica, Caftf. A 10 Mar 1933 6.2 Long Beach, Calif.
+ 30 June 1941 5.9 Santa Barbara, Calif.
o 8 Apr 1961 5.6 Hollister, Calif. m 25 Oct 1943 5.5 San Jose, Calif. c 4 Sept 1955 5.5 San Jose, Calif. s 22 Mar 1957 5.3 Golden Gate Park,
. San Francisco, Calif.
~t 2 Oct 1933 5.3 Long Beach, Calif.
v 18 Mar 1957 5.0 Port Hueneme, Calif. i 1 Gutenberg-Richter Magnitude _ 4 i O l _ _ _ _ . . _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ __ _ _ _ _ _ . _ _ _ - - - - - - - _ - - _ - - - - - - - - - - - --}}