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Intensity of Earthquake Ground Shaking Near Causative Fault
ML20235B873
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Site: 05000000, Bodega Bay
Issue date: 01/31/1965
From: Housner G
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NEAR THE CAUSATIVE FAULT *  ! by George W. Housner N - F Abstract . . 1 Data and analyses ' indicate an upper bound for intensity of ground - shaking that is approximately 50% greater than at El Centro during the I earthquake of 18 May 1940. Upper bounds of 50%g for maximum ground j acceleration and 45 seconds for duration of strong shaking are indicated. - l The intensity immediately adjacent to a fault is not especially severe but is, in general, somewhat less than at a distance of several miles. The maximum intensity of shaking associated with a Magnitude 8. 5 earthquake , is less and that associated with a Magnitude 5 earthquake is greater than j has been commonly supposed. The strain energy that is released in the form of seismic waves during slip on a fault will affect most strongly a region in the general vicinity of the fault, whereas at greater distances the intensity of ground shaking will be attenuated. In the past, misunderstandings of the signifi- ' cance of the seismological terms " earthquake Magnitude"~and " Modified Mercalli Intensity" have led to erroneous conclusions about the intensity of ground shaking. The only precise measure of the intensity of ground shaking is the spectrum intensity that has been calculated from instru-mental recordings made on the spot, either from accelerograms or from readings of properly designed seismoscopes. For engineering purposes, a significant quantity is the maximum intensity of ground shaking that may be  ! associated with an earthquake as this represents an upper bound for the l forces that structures may be called upon to resist. The estimation of { the maximum intensity must be based on ground motion records and ob-servations of past earthquakes, and upon knowledge of the mechanics of fault slip and wave propagation. i l Nature of Earthquake Faulting. In California, faults on which large earth- I quakes have occurred are well defined and the nature of the fault slip ' during the earthquakes is well understood. Since the most intense hori-zontal ground shaking is associated with horizontal (strike-slip) fault displacements, the San Andreas fault can be taken as the classical example of a strong-motion generating fault. The 1906 San Francisco earthquake resulted from horizontal slip over approximately 250 miles of this fault N Professor of Civil Engineering and Applied Mechanics, California Institute of Technology, Pasadena, California, U. S. A.

           * (To be presented at the Third World Conference on Earthquake Engineering, January,1965, Auckland, New Zealand. )

8709240263 PDR FOIA 851217

           , FIRESTOBS-665         PDR                                       -

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     , ,.       m              ,
                                    . _ _   .m  a mm.x .m u.m.m.#.m u m:mm.w.n.w. ma :

2. m with a maximum relative displacement of the two sides of the fault of , 21 feet (2). There was, of course, no recording of ground accelerations , during this carthquake. The 18 May 1940 El Centro earthquake was the

                                                                                                                       ~

most severe so far recorded. This earthquake resulted from slip on a ' ,' southern branch of the San Andreas fault system (Imperial fault). The slip extended over a length of approximately 50 miles of fault and with a maximum relative displacement of the two sides of the f ault of 15 f eet (3). The El Contro, 1940 carthquake is a good illustrative exampic of a strong-motion earthquake in that it was a relatively large shock with well- l defined faulting in a region having deep alluvium, and with ground motion recorded not far distant from the fault, and with a number of towns in the l region of strong shaking. At El Centro there is more than 5000 feet of clay,

  • loam, sand, and gravel underlaid by ' sandstone. The trace of the fault and ,

the location of the adjacent towns are shown in Fig.1. The maximum relative surface fault displacement occurred just east of Calexico. The i southern extremity of the fault was not well defined. Presumably the l maximum relative fault displacement in the rock beneath the alluvium was ' somewhat greater than 15 feet. The accelerometer that recorded the j ground motion was located in the town of El Centro at a distance of ap- . proximately 4 miles from the fault trace. A Modified Mercalli Intensity of IX was assigned to all of the towns shown in Fig.1 by U,1 rich (3). In a

  • 1ater publication (4) the following MM. intensities were assigned: B rawley and Imperial IX; El Centro and Holtville VIII; Calexico and Heber VII. A significant portion of the damage at Imperial and Brawicy is reported to 3 have occurred during a smaller aftershock, so that greater credence should be given to Ulrich's estimates of intensity which were made on the basis of personal inspection. It was noted that some rather poorly con-structed farm buildings located within a few hundred feet of the fault trace suffered no damage.

The strongest component of horizontal ground acceleration recorded in El Centro (4) is shown in Fig. 2. This shows only the strong phase of shaking, following waich there were several minutes of less strong shaking that gradually attenuated. There are listed below the amplitude At and duration t of some l of the larger pulses of the El Centro ground acceleration. The values l given will indicate the nature of the acceleration pulses during strong l l i l (2)Lawson, et. al. , " Report of the State Earthquake Investigation Com- l mis sion, " Carnegie Institution of Washington, Vol.1,1908; Vol. 2,1910. . l (3)Ulrich, F. P. , "The Imperial Valley Earthquakes of 1940, " Bulletin of Seis. Soc. Am. , Vol. 31, No. 1, 1941.

                                                                                                                         'l
                      ' 54)U. S. Coast and Geodetic Survey, "U. S. Earthquakes - 1940, " U. S.

I Government Printing Office, 1942. s s l o- l

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S- ground motion. The area of each pulse (velocity increment) is also given. The size of a single acceleration pulse, however, is not a reliable indica- , tion of the intensity of shaking as regards its effect on structures for the intensity depends upon the cumulative effect of the sequence of pulses. A (%g) , t:(secs. ) . Velocity Increment _ (ft per sec. ) 33 0.23 1.6 27 0.14 0. 8 31' O.10 0.6 - ' 23 0.29 1. 4 l 30 0.18 1.1 Figure 3 shows the integrated velocity and displacement for both ' components of ground motion (5). The recording instrument was suffi-ciently close t'o the fault so that a permanent displacement is shown in Fig. 3. The resultant permanent displacement is approximately 12 inches in the northwest direction. The magnitude of surf ace slip at the adjacent part of .the fault was reported to be approximately 4 feet. The maximum transient displacement in Fig. 3 is 20 inches, and this was attained at the end of the first 5 seconds of motion. A maximum velocity of 1. 25 ft/sec ' was attained at the end of the first two seconds of motion in each component, , it being the cumulative effect of the first 5 acceleration pulses. As suming - that the maximum velocities of the two components of ground motion are O> the components of a resultant vector ground velocity, there is obtained a ' value of 1.75 ft/sec for the peak ground velocity. ' Figure 3 indicates a permanent EW displacement of 10 inches - which would also be the approximate displacement of the underlying rock. j It may be inferred that the transient displacement of 20 inches represents an amplification of about 2 at the surface of the alluvial layer. This would indicate a maximum velocity of the underlying rock of 1. 7 5 + 2 = 0. 9 f t/ s e c. If the underlying rock reached a peak velocity of 0. 9 ft/sec and underwent i a permanent displacement of 15 2 = 7. 5 feet, the total duration of slipping 1 at that point would be 8 seconds. Slipping progressed beyond this point some 15 miles south, and assuming that strong shaking would be produced by waves originating 15 miles away the total duration of strong shaking might be expected to be approximately 8 + 15 = 23 secs. This is based on a velocity of propagation of slip along the fault of 2 miles per second and taking the same value for velocity of shear waves. The El Centro accelero-gram shows 25 seconds of strong shaking.

  • Although no recordings of ground accelerations were made during the 1906 San Francisco shock, a very complete description of this earth-quake has been given (2) which is in agreement with the characteristics j - (5) Berg, G. V. and Housner, G. W. , " Integrated Velocity and Displacement of Strong Earthquake Ground Motion, " Bulletin Seis. Soc. Am. ,

Vol. 51, No. 2, 1961. s) l

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             , .-                           ..     .- --..~ .._.-.- -         e.     .-- - ,.- ~ m anwc.mm a m.w a ra.w g j     M y   4 t

4. m d of the El Centro shock. The strongest ground shaking, as deduced from damage to buildings, was reported for the town of Santa Rosa which was , located approximately 20 miles from the fault. An inspection of photo-graphs of buildings indicates that the damage was similar to that observed in Santa Barbara (1925), in I,ong Beach (1933), and in El Centro (1940), and it is inferred that the intensity of shaking in Santa Rosa was not i significantly greater than in the El Centro (1940) earthquake.- Strong shaking ' was also reported for the northeastern part of San Francisco which was some 10 miles from the f ault; this region of severe damage coincided ap-proximately with the region of soft alluvium and the region of oldest l commercial buildings. Photographs of damaged buildings indicate that . i the intensity of ground shaking was not more severe than has been experi- l enced in subsequent California earthquakes. This conclusion has also been j stated by Byerly (6) who thought that the 1906 shock, the El Centro, 1940, the Dixic Valley, Nevada, 1954, and the Kern County,1952, all had ap-proximately the same maximum intensity: "I feel that intensity 9 is as high as we should go in any of the shocks even if faults did break in some of them and even if incipient landslides were set off and loose earth disturbed by them. " It may also be seen that in 1906 the intensity of shaking immediately

                        ,,.e adjacent to the slipped portion of the fault was less severe than at greater distances, as evidenced by damage to structures (2).
      ,                                                 The maximum permanent ground displacement in 1906 was 10. 5 f t
        ')                                  (on rock or shallow alluvium) some 10 miles north of San Francisco. This may be compared with the permanent displacement of 7. 5 ft during the El Centro earthquake. Assuming a maximum ground velocity (rock) of                e
0. 9 f t/sec, as during the El Centro shock, 11 seconds would be required to move through 10. 5 feet. As strong shaking might be expected if the slipping portion of the fault was not more than about 25 miles distant, the l total duration of strong shaking might be expected to be approximately l 8 + 25 = 33 seconds. It would, of course, be followed by several minutes of less intense, gradually attenuating ground motion. This is in agreement with the description of ground motion during the 1906 shock: "What has been called the violent part of the shock did not last longer than 40 or 50 seconds, whereas the principal part cortainly lasted many minutes. " (2)(Vol. II, p. ll4).

1 i Properties of Strong Ground Motion. The properties of recorded strong ground motions are given in Table I, where thers are listed the Magnitudes of the shocks, the spectrum intensities of the ground motion, the maximum recorded ground acceleration, and the duration of the strong phase of shaking. It should be noted that the maximum acceleration is not a good l 1 (6)Byerly, P. , " Seismicity of n 'estern United States," Proc.1st World Conf. Earthquake Engineerh.g,1956. m 1

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                . measure of the intensity of shaking as regards effects on structures. The only precise measure of the effect of ground shaking is given by the spectrum (7) of the ground motion. The spectrum intensity (SI)n is                              ,

defined (8) as the area under '.he Velocity Response Spectrum curve:

                                                          ,2. 5
                                                     =

(SI)n s S (n, T)dt v (1) ,

0. I where S y(n, T) is the velocity response spectrum, which is a function of natural period of vibration T and fraction of critical damping. - ,

A properly designed seismoscope will give a point on the Sy(n, T) curve for a particular set of values n and T and, hence, an estimate of (SI)n ' C",n be made (9).

                          ' The commonly used Modified Mercalli Intensity is a completely subjective description and hence is not suitable for engineering purposes.                           l The defects of the Modified Mercalli Intensity are exhibited by comparing                     -

the Long Beach, California (10 March 1933) earthquake with the Helena, Montana (31 October 1935) shock. The Long Beach ' quake was recorded ) at Vernon which was approximately 15 miles horizontally (estimated) ] from the nearest point of the slipped f ault. The recording at Helena is i estimated to have been 5 to 10 miles horizontally from the nearest point i of the slipped fault. From Table I the following comparison can be made. Q

   .                                                          Long Beach       Helena                      -

(Vernon) Magnitude 6.3 6.O Max. Acceleration O.19g O.16g

  • Duration 6 secs 4 secs Spectrum Intensity:
0. O Damping (SI)o 4.62 ,

1.82

0. 2 Damping (SI)0. 2 1.70 1.02 Modified Mercalli (10) VII VIII UI Alford, J. L. , Housner, G. W. , and Martel, R. R. , " Spectrum Analys es of Strong-Motion Earthquakes," Earthquake Research Laboratory * '

Report, California Institute of Technology,1951. , (8) Housner, G. W. , " Spectrum Intensities of Strong-Motion Earthquakes, " l Proc. Symp. Earthquake and Blast Effects on Strt.ctures, Earthquake Engineering Research Institute, 1952. I9) Cloud, W. K. , and Hudson, D. E. , "A Simplified Instrument for Recording Strong-Motion Earthquakes," Bulletin Seism. Soc. Am. , i Vol. 51, No. 2, 1961. (10)U. S. Coast and Geodetic Survey, "U. S. Earthquakes 1933-1935." l, i l

v . - n. 1 ,r

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t 6. KL ,

 .)'                        It is seen that the ground motion at Helena was significantly less intense.

than at Vernon. The 20% damped Spectrum Intensity is a good measure of the amount of damage to be expected and the ratio of (SI)0. 2 shows that the Vernon ground motion was 70% more intense than the Helena ground motion. However, a Modified Mercalli Intensity of VIII was assigned to Helena and only VII to Vernon. This discrepancy indicates

                                          ~

that a casual observation of damage, as is required to assign MMI + numbers, is not a reliab1'e method of estimating the intensity of ground s haking.. The Modified Mercalli Intensity should not be used for engi-neering purposes. Seismologists sometimes estimate the maximum ground accelera-tion from the Modified Mercalli Intensity by means of the following empirical formula, or its equivalent: (2) log 10A = h-f . where ' A' is the maximum ground acceleration in gals and I is the MMI number. This formula gives: MMI Max. Accel. (%g) VII . 7

                 .                                 VIII                                 15

'd' IX *32 - Equation (2) was adjusted to fit El Centro 1940 which had MMI = IX, max, accel. = 33%g, but it is approximately 200% in error in predicting the Vernon ground acceleration. It would be illogical, of course, to suppose that maximum ground accelerations can be calculated from MMI numbers that are assigned on the basis of casual observations of building damage. The use of Eq, (2) to calculate very high ground accelerations for.MMI numbers X and XI is completely irrational as these larger MMI numbers are assigned on the basis of ground cracking, landslides, and other phenomena that are not associated with intensity of ground shaking. It should also be noted that the Magnitude of an carthquake is not a direct indication of theintensity of ground shaking in the epicentral r egion. The numerical value. of the Magnitude is defined as the logarithm of the maximum amplitude (in millimeters) of a 0. 8 sec period instrument having 60% damping and 2800 magnification, the instrument to bc located 100 kms from the epicenter. To calculate the Magnitude from the reading is to use the instrument as a seismoscope to give a measure of the in-tensity of ground shaking 100 kms from the epicenter. The frequency characteristics of the ground motion at this distance are quite different from those close to the epicenter. In the case of a very large shock, such as the Alaskan earthquake of 28 March 1964 whose slipped length of fault was approximately 1400 kms, the 'seismoscopes' upon whose readings s the Magnitude was determined were several thousand miles away. The i '

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7. A large Magnitude (M = 8.5) given by these instrumental readings is in-o dicative of the large area of slipped fault but is not indicative of the shaking near the f ault. It must be emphasized that the Magnitude is merely an estimate of the intensity of shaking at large distances from the epicenter. l It can be used to estimate the size of the earthquake (langth of fault), but ) is not of itself a good indication of the intensity of strong shaking near the fault. ,- Maximurn Intensity of Shaking. A plot can be made of the (SI)0. 2 8 pe ctrum intensity versus Magnitude using the values given in Table I. This plot , is shown in Fig. 4 with the dashed line indicating the upper bound (SI)0. 2 max. Points close to this line represent ground motions relatively close l to the causative fault. Points farther from the line represent ground  ! motions recorded at greater distances from the fault. It is seen that l (SI)0 2 max does not vary strongly with Magnitude, being equal 1. 2 at l M = $ and 3. O at M = 7.1. The dashed line extrapolates to (SI)0. 2 max l equal to 4. 25 at M = 8. 5. This is approximately 50% greater than for i El Centro, 1940. The ground motions of Table I were almost all recorded on relatively deep alluvium. It is noteworthy that the Port Hueneme earthquake had (SI)0. 2 equal , to 1. 2 and M = 5. This c'arthquake consisted essentially of a single dis-placement pulse (11). The accelerogiam was recorded close to the l epicenter and the focus was relatively shallow. Using (SI)0. 2 as a j q measure of intensity of shaking, the El Centro 1940 ground shaking was I ../ only 2. 5 times as intense as the Port Hueneme. This is consistent with the observation that the Agadir, Morocco earthquake of 29 February 1960, ,. which produced such great damage, had a ground motion similar to the  ! Port Hueneme shock (12). The duration of the strong phase of ground shaking is closely correlated with the Magnitude of shock. Figure 5 is a plot of duration i of strong phase versus Magnitude. Since the duration of the strong phase I of shaking can be distinguished only for ground motions recorded rela- i tively close to the causative f ault, there are fewer data points in Fig. 5 ' than in Fig. 4. The dashed line in Fig. 5 indicates an upper bound and it 1 shows a strong variation with Magnitude, extrapolating to 45 seconds at ] Magnitude 8. 5 which is an upper bound. The 1906 San Francisco shock I hat an assigned Magnitude of 8. 2 for which Fig. 5 indicates a duration . I of 43 seconds. This is not inconsistent with the estimate of 33 secs based on the time required to complete the slipping, and it is also consistent with the report of not more than 40 or 50 secs (2). I )Housner, G. W. and Hudson, D. E. , "The Port Hueneme Earthquake of March 18, 1957," Bulletin seism. Soc. Am. , Vol. 48, No. 2,1958. (12)Clough, R. W. , "The - Agadir Morocco Earthquake," Am. Iron and

  • i Steel Institute, New York, 1962.
              ,5   ',                                                                                                                [

t 8.

   .-                                The maximum record nd acceleration can also be plotted versus the Magnitude and this has been done in Fig. 6. The data points in this                                     ,

graph represent a more complete cet of U. S. Coast and Geodetic Survey values (13). The dashed line indicates an upper bound. The points close to the line represent ground motions recorded relatively close to the causative fault, whereas those at greater distances from the line repre-sent ground motions at greater distances from the fault. The line extra- ,

                        - polates to a maximum acceleration of 50%g for M = 8.5. This agrees with the.cstimate of 50%g made by Cloud (13) and with the estimato of 50%g made by H. Benioff as quoted by Cloud (13).

It is, of course, to be expected that the maximum acceleration and the maximum intensity of ground shaking sheuld not be very much greater for a Magnitude 8. 5 earthquake than for a Magnitude 7. O shock. The M = 7 shock (El Centro 1940) might release strain energy over a length of fault of approximately 50 miles and the M = 8 shock might - release energ'y over a 200-mile length of f ault. Since the point of strongest ground shaking for the M = 7 shock would be approximately 25 miles from cach end of the surface trace of the slip, the additional 150 miles of slipped j f ault would begin 25 miles away and, hence, its effect upon the maximum acceleration should not be large, particularly as the superposition of ground accelerations emanating from two points on the f ault is as the square root of the sum of the squares.. The same data points plotted in Fig. 6 are used in Fig. 7 to plot '

       )                 Magnitude versus distance to epicenter (or fault). The dotted lines in Fig. 7 indicate approximately the variation of maximum acceleration with distance from epicenter.

Acceleration Adjacent to Fault Plane. The fact that the data in the pro-coding section indicated an upper bound (50%g) for the maximum ground acceleration is not surprisi..g since the maximum acceleration reflects the magnitude of stress relief afforded by the fault slip. It is well known l that the rock on the two sides of the San Andreas fault is being displaced j in such a way as to build up shear stress on the fault plane. When this stress reaches a failing value there will be a slip whose extent will depend upon the state of stress on adjacent portions of the f ault. The i value of failing stress will be less than the strength of the rock since the j f ault has experienced many movements in the past and the material along '

                                                                                                                                          ]

the fault is weaker than the pristine rock. l (13) Cloud, W. K. , " Maximum Accelerations During Earthquakes, " Proc. Chilean Conf. on Seism, and Earthquake Engineering, " Univ. of Chile, 1963. . W l

4. ..  ;  !.

t ,

9. ,

l i 3' During a large earthquake, such as the 1906 San Francisco shock, ) there may be as much as 21 ft relative displacement of the two sides of j the fault. An analysis will be made of the maximum ground acceleration i that might be experienced by a point sufficiently close to the fault to parti - j cipate in the 10. 5 ft permanent displacement. An idealized situation will j be anatyzed in which the granitic basement rock extends to the surface of the ground, with no alluvium or sedimentary rock cover. It .is suppos ed, , also, that the slip extends over several hundred miles of fault. .

                             . An' extreme case for the violence of motion associated with the fling of the rock on one side of the fault 'would be if the entire fault were                    ,                  i to slip simultaneously with comple'te release of shear stress on the fault                                          {

plane (lubricated slipping). In this case the movement of the rock would i experience no restraint and would be completely free to move as strongly as possible. The acceleration in this case will consist of a single positive acceleration pulse of short duration and large amplitude, fc11 owed by a negative acceleration pulse of long duration and small amplitude which brings the movement to rest, as shown in Fig. 8. Let the relative displacement across a fault be 2L ft so that the absolute displacement of one side of the fault is L ft. Suppose the I ac celeration, G , of a point adjacent to the fault, as shown in Fig. 8, is expressed by: . U = A sin n 2 tg (0 < t < tg) 3-(3) *

                                             =   -Aa sin ta    E t'                          (0 < t < tz)                           ,

The velocity 6 is given by: 6 = A t1 1 - cos (0 < t < tg)

                                                                                          ,,                       (4) 2_ A_ t 3 , A_2t ;    I - cos
                                             =

w w ta (0 < t < ta) At t=t, the velocity must be zero (h = 0) which requires:

                                                                  .A tti   =     Azt:

The maximum velocity is given by: 6 = 2A tll (5) max w en W

        . r..--..-      . m-.          .         ..                     ..         ,.       . - . ,   4 . . , , ,    , . . .
4. 4 *

!/ m & likZ Xi G 5Xn MTE2 F;w M.GGLB W R E.6222ndn & M 2.: . t,'

    . , e.                          oo                                                                                                     I 10.

']; The displacement of the point is given by: r A_,1h,,Lsin"t) u = w w 1 (0 < t < t ) 3 (6) i t

                                                                    . A t:2 w , 2A  w t li $13w t Dwsin "ta (0 < t < tz)

At t=t it is required that u = L, from which condition there is obtainc8. - Ag tg = "k g (7) k_ The quantities 6 max ' to, and (Atit ) are unknowns and if one of them can be specified the other two can be determined from the preceding equations. An upper bound for 6 max can be found as follows. The in-stantaneous release of stress on the fault willinitiate a shear wave which propagates normal to the fault plane. A point on the surface of the ground near the fault will experience essentially a motion generated by the passage of a step-function, plane shear wave. If the change in shear strain is y and the velocity of propagation of a shear wave is c, the point will be given a step-function increase in velocity: , 6, = ye (8) Substituting this value of maximum velocity in equations (3) and (5) gives: Ati = yye (9) ' 2L

                                                                                         *o ye                             ( 0)

The velocity of propagation, c, of shear waves is known to be approxi-mately 10,000 ft per sec and, hence, if y is known.the acceleration pulse At can be determine d. The report on the 1906 carthquake states that 3 the measurements after the carthquake indicated that, adjacent to the fault, there was y = 0. 00015 on the ocean side and y = 0. 00025 on the continental side (2)(Vol.1, p.134). The different values of y on the two sides were attributed to the fact that the ocean side of the fault was all granite whereas on the continental side the granite was overlaid by - several thousand feet of sedimentary rock. This would indicate that a value y= 0. 0002 would be reasonable. The measurements required to determine the value of y adjacent to a fault are rather difficult and it is questionable. Various authors have made appears estimatesthat andtheir accuracy (also of doubtful accuracy) and have come up calculations with various values of y. Equation (10) gives the following values of duration of slip t for various values of y: o y t o(secs. ) O.0001 20 0.0002 10 0.0003 6. 7 j 0.0004 -5

frrcMar>9.r.E & 4-hekttngWgi.sh M6;g g nigsg h h h_ . w c 11.

   'm              It is concluded from this that y = 0. 0003 gives too short a duration and y = 0. 0001 gives too long a duration and, hence, y = 0. 0002 is taken as a reasonable . estimate for the maximum shear strain. This value would not be inconsistent with measurements made after the El Centro, 1940 earthquake (14)(15), and with independent estimates (16).

For y = 0. 0002, c = 10,000 f t/see there is obtained for the amplitude-duration product: At = 3. I ft/sec. Such a pulse would have an area equal 3 to 2.0 ft/see and would correspond to A = 50%g, t = 0. 2 secs; or Ag=40%g, l t = 25, s e c s . These may be compared with the El Centro, 1940 pulses, the maximum of which had A = 33%g, tg = 0. 23 secs. The computed pulse was 3 for the acceleration of granite under idealized slip conditions, which over-estimate the resulting acceleration so that a pulse in rock of Ag = L%g, ti = 0. 25 secs is a reasonable estimate of the maximum. If the rock were . . . overlain by a deep layer of firm alluvium the maximum acceleration at the surface of the alluvium as the wave is reflected would be doubled, that is, Ai = 50%g, t2 = 0. 25 secs. This is in agreement with the estimate of 50%g that was deduced from Fig. 6. The foregoing analysis makes clear why there is an upper bound for the maximum acceleration.

                                                                                                         .            J Intensity of Motion Immediately Adjacent to a Fault.       It was reported that the intensity of ground shaking immediately adjacent to the fault, du ring                 ,

the El Centro earthquake, was very much less than at several miles distant from the fault. Similar reports have been made about other earthquakes and it has been attributed to the way shear waves propagate from the face q of the fault, the amplitude being greatest along a ray perpendicular to the fault and being least along a ray that makes a small angle with the ' f ace of the fault (cosine law). Ground motions have been observed only on alluvium or sedimentary rock and never on granite that slips against granite; this means that the shear waves must travel directly upward from the point of origia some distance before reaching the surf ace cf the ground adjacent to the fault. The intensity of shaking in the immediate vicinity of a fault was discussed by Louderback (17) who stated:

                          "The occurrence of an observable fault trace, or shearing of the ground, does not necessarily indicate high intensity of earthquake action in the past or point to such action in the future. . . . . The idea held by many that moving the location of a proposed structure a thousand yards                                ,

or even a few miles from the outcrop of a known active, strong-earthquake- ' generating fault will render the structure much less liable to earthquake Whitten, C. A. , " Horizontal Earth Movements in California, " Journal of Coast and Geodetic Survey, No. 2, April 1949. o (15)Whitten, C. A. , " Coastal Movements in California and Nevada," Trans. Am. Geophysical Union, Vol. 37, No. 4. - (16)Chinnery, M. A.," Strength of the Earth's Crust Under Horizontal Shear Stress, " Jour. Geophysical Research, Vol. 69, No.10, May 15,1964.

   ]~             @I Louderback, G. D. , " Faults and Earthquakes, " Bulletin of the Seism.

Soc. Am. , Vol. 32, No. 4, 1942. i

J. ..., P" 12. damage, is not borne out by theory or experience. " o tJ Observations of large earthquakes having surface faulting agree that the intensity of shaking close to the fault was not particularly severe: ' 1906 San Francisco (2); 2 October 1915 Nevadi (18); 16 December 1954, Nevada (19); 17 August 1959, Montana (20): 1 September 1962, Iran (21). These observations all indicate that the intensity of ground shaking at El Centro (4 ' miles from the fault) could not have been significantly less than at points closer to the fault. Summary. Data and analyscs indicate an upper bound for the intensity of ground shaking on reasonably firm deep alluvium that is 50% greater than , that at El Centro during the earthquake of 18 May 1940. An upper bound is indicated for the maximum acceleration during the ground motion on firm, deep alluvium of 50%g, and on rock of 25%g. An upper bound is indicated for the duration of the strong phase cf shaking during 'a Magnitude 8. 5 earthquake of 45 seconds. The intensity of ground shaking immediately adjacent to a f ault is not especially severe but is, in general, somewhat less than at a distance of several miles from the fault. The maximum intensity of shaking associated with a great earthquake of Magnitude 8. 5 is only approximately 50% greater than for a Magnitude 7 earthquake, and this is less intense than has been sometimes supposed.

 ,)               The maximum intensity of ground shaking associated with a Magnitude 5 earthquake is 1/3 to 1/2 that of a Magnitude 7 earthquake and therefore is more severe than has been sometimes supposed.

The Modified Mercalli Intensity is not suitable for engineering purposes and in particular it should not be used to estimate maximum ground acceleration. The spectrum intensity is the best measure of the intensity of ground shaking and it should be used for engineering purposes. (18) Jones, J. C. , "The Pleasant Valley, Nevada Earthquake of October 2, 1915, " Bulletin Seism. Soc. Am. , Vol. 5, No. 4, 1915. ( 9}Tocher, Steinbrugge, et. al. , "The Dixie Valley-Fairview Peak, Nevada Earthquakes of December 16, 1954," Bulletin Seism. Soc. Am. , Vol. 47, No. 4, p. 335 et seq. ( 0)Steinbrugge, K. and Cloud, W. K. , "The Earthquake at Hebgen Lake, Montana, August 17, 1959 - Epicentral Intensities and Damage, " Bulletin Seism. Soc. Am. , Vol. 52, No. 2, 1962. (21)Ambraseys, N., "The Buyin-Zara (Iran) Earthquake of September 1962,

                .      A Field Report, " Bulletin Seism. Soc. Am. , Vol. 53, No. 4, July,1963.

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