EARTHQUAKE-INDUCED GROUND DISPLACEMENTS.pdf

7/27/2019 EARTHQUAKE-INDUCED GROUND DISPLACEMENTS.pdf

1/22

EARTHQUAKE ENGINEERING AN D STRUCTURAL DYNAMICS, VOL. 16,985-1006 (1988)

EARTHQUAKE-INDUCED GR O UN D DISPLACEMENTSN. N. AMBRASEYS AND J . M . MENU

Imperial College of Science and Technology, London, U.K.

S UMMARYThe paper brings up to date and amplifies earlier work on earthquake-induced ground displacements using near-fieldstrong-motion records, improved processing procedures and a hom ogenizing treatment of the seismo logical parameters.A review of upper bound limits to seismic displacements is given and a predictive procedure is examined that allows theprobabilistic assessment of the likelihood of exceedance of predicted displacements to be made in the near field ofearthquakes in the magnitude range 6.6 to 7.3. Using a considerable number of unscaled ground motion s obtained atsource distances of less than half of the source dim ensions , graphs and formulae are derived that allow the assessment ofpermanent displacements of foundations and slopes as a function of the critical acceleration ratio.

INTRODUCTIONFracturing and cracking of level ground and of natural and man-made slopes caused by earthquakes is not anuncommon phenomenon. Comparatively long, open cracks, extending to some depth in flat or slopingground, and compression ridges are features usually attributed to strong ground movements, strong enoughto overcome the yield resistance of a soil mass and cause permanent deformations. These permanentdisplacements are produced because the material through which acceleration pulses have to travel beforereaching the ground surface, be it alluvium or soft rock, has a finite strength, and stresses induced by strongearthquakes may bring about failure, with the result that accelerations, above a certain value in the frequencyrange of engineering interest,will be prevented from reaching the surface, and permanent deformations of theground will occur. Field observations show that soils and soft rocks in a strong earthquake will distort anddevelop cracks and deformations; the real design problem is to determine how much such materials willdeform and to establish what displacements or deformation are acceptable. The question of whether there isan upper bound for ground accelerations and ofwhether the associated permanent ground displacementscanbe calculated is indeed of importance to the engineer.

An early attempt to back-analyse the displacements observed in embankments and level ground affected bythe Tokachi-Oki earthquake of 4 March 1952 was made by Ambraseys,' Figure 1, but the procedure forevaluating potential slope and ground deformations due to earthquake shaking was developed by Newmark.2In this simple method it is assumed that slope or ground failure would be initiated and movements wouldbegin to develop if the seismic forces on a potential slide mass were large enough to overcome the yieldresistance and that movements would stop when the seismic forces were removed or reversed. Thus, bycomputing the acceleration at which yielding begins and summing up the displacements during the periods ofinstability, the final cumulative displacement of the slide mass can be evaluated. The calculation is based onthe assumption that the whole moving mass is displaced as a single rigid body with resistance mobilised alonga sliding surface. Newmark's sliding block method is based on the simple equation of rectilinear motion underthe action of a time-dependent force involving a resistance that may or may not be dependent on other factorssuch as displacement, rate of slip, pore water pressure or heat. When the input inertia forces and the yieldresistance can be determined, the method gives useful and realistic results.

One of the earliest applications of the sliding block method, that gave consistent and sensible answers, wasmade for the assessment of the ground motions associated with the Skopje earthquake of 1963. A largenumber of displacements of different objects of known 'yield resistance' was used to estimate the predominant009~8847/88/080985-22$11.000 988 by John Wiley & Sons, Ltd. Received 6 October 1987Revised 16 February 1988


2/22

986 N. N. AMBRASEYS AND J. M . MENUacceleration and periods of ground motion generated during the Skopje ear thq~ake.~he method wasrecommended as a check for the earthquake resistance of earth dams and foundations? and was applied to avariety of soil mechanics and foundation problems in which assessment of permanent earthquake-induceddisplacements was Studies of the character of displacement induced by stochastic inputs werealso published by, among others, Crandall et al.," Gazetas et ~ l . , ~ 'Ahmadi" and Constantinou andTadjbak hsh.*

In principle, the sliding block method is based on the time-history of the ground acceleration g ( t ) thatcontrols inertia forces, and on two parameters: namely keg, the minimum ground acceleration required tobring about incipient failure of a slope or foundation, a parameter controlled by yield resistance, and k,g, themaximum acceleration of the ground-motion time-history (k,g = g(t),,,). The critical acceleration coefficientk , is a function of the geometry and soil properties of the sliding mass corresponding to a factor of safety of one(F = ), and in calculatingk, for a given slip surface, the distortions within the mass, the pore water pressurechanges from static to failure conditions, and changes in the geometry of the mass must be taken into account.The critical coefficient k , is the most appropriate measure of the resistance to sliding of a soil mass subjected toan earthquake, k , playing the same role in the sliding block method as the factor of safety F does in thelimiting equilibrium method, the two coefficients being interrelated.

Given a design earthquake ground-motion time-historyg ( t ) of peak acceleration k,g and a potential slidemass in a foundation or slope material for which the horizontal acceleration required to cause failure underundrained conditions is k,g, it is possible, using a simple numerical model, to calculate the permanent

(a) 0Figure l(a ). Deformations ofembankm entscaused by the Tokachi-O ki earthquake of 4 March 1952 in Japan (Report on the Tokaki-Okiearthquake, Publ. Special. Comm. Inves., Sapporo, 1954)


3/22

EARTHQUAKE-INDUCEDGRO UND DISPLACEMENTS 987

. .-.- _/-- a-

Figure l(b). Deformations patterns produced by three shocks causing yielding (a, b and c) and final shape (d) after deformation of earthdam'

earthquake-induced displacement when k , > , . Figures2 and 3 describe briefly the sliding block method andFigure 4 shows a plot of the permanent displacements calculated for a variety of ground-motion time-histories recorded before 1972.Displacementsu in centimetres shown in this figure have been computed for anunsymmetrical yield resistance, that is we have allowed sliding only in one direction down-slope, and they areplotted as a function of the critical acceleration ratio k , / k , . The analysis was carried out with ground-motiontime-histories not scaled to a constant acceleration and velocity, assuming a constant yield resistance duringsliding expressed by the critical coefficient k , .The data points in this figure show a well-defined upper bound, and just as importantly, they exhibit aperfectly explained scatter below this upper limit, which is the result not onlyof the different energy content ofthe unscaled time-histories used, but also of directional and duration effects.The large dots in this figure showthe data points from the three orthogonal components of ground motion produced at Pacoima by the San-Fernando earthquake of 9 February 1971, and give some idea of the scatter due to directional effects. Theupper bound of the plot is given by

kckInlog(u) 2.3- .3-

where u is in centimetres, valid for down-slope displacements in the range 0.1 < k c / k , < 0 . 8 . 6Equation ( 1 ) may readily be used to assess the maximum permanent displacement of a slide mass of stable

materiai when its maximum resistance to sliding, expressed by k , , is exceeded by the peak acceleration k,g ofan earthquake time-history. Thus, if a slope shows F = 1 for, say, half as large an acceleration as its designvalue, i.e. k , / k , = 0.5, and also if the material loses little or no strength due to earthquake deformations, thenfrom Figure 4, or equation (l),we find that for the strongest ground motions recorded before 1972,permanent


4/22

988 N. N. AMBRASEYS AND J. M. MENU

A

I L U - l , a

B I C

1

Figure 2. Application of simplified sliding block method for the stability analysis of slopes. (A) Forces acting on a slice C l of a soil masswithin the critical slip surface AB. AB is defined as the sliding surface between levelsa-a an d b-b that obtains for a factor of safety of one(F = ) and also for the minimum horizontal acceleration k,g. Th e critical coefficient k , of the soil mass between these two levels is afunction of the soil strength parameters c' an d 6', lope geometry and pore pressure changes du e to th e application of seismic forcescausing failure, and it can be calculated using a stand ard stability analysis. (B) Vector diagram of forces at F= 1 for the critical slip surfaceAB. It should be noted that Figure B refers to the overall stability of the sliding mass within A-B (Figure A) for a facto r of safety of one,and not of the sliding element C i .Note tha t for dry, purely frictional materials B = 9 0 deg. For all other cases of practical interest 8 variesbetween 85 deg and 10 0 deg. (C)Sliding block model satisfying diagram (B). Fo r k > k, , sliding takes place on a plane AB inclined to thehorizontal by an angle B , defined in diagram (B). In its simplified version the model assumes th at du ring deeoupling the mass m ovesprogressively down the slip surface generated at F = 1 without any fu rther change of the yield resistance. Resolving forces in the directionof sliding o-a, it can be shown that the equation of motion down-slope is given by

cos6'U(t) = X ( t ) - k , gco s (6'- )

where u(t) is the displacement of the mass relative to the slip surface AB, x(t) = -g(t) is the absolute groun d acceleration time-history, andk , is the critical acceleration of the mass, which is consta nt. If k , is the maximum horizontal groun d acceleration [g(t)lmnX. convienientway of expressing the results of the analysis for different ground motion time-histories would be in terms of the quantity.cos 9'

U(= u cos(6' - )cos Band the critical acceleration ratio kJk, , where now displacements are measured in a horizontal direction. For a one-way, down-slopemotion we may write ui= u , , and for a two-w ay, horizontal motio n, i.e. for j = O , we may write ui=u2. Notice tha t for practical purposes,the multiplier of u may be taken equal to one.

displacements will be less than 5 cm. If, on the other hand, because of earthquake-induced stresses the soilloses part of its strength, say to a value as low as kc /k , = 0.1, the corresponding displacements would bealmost one metre.

An upper bound limit for displacement based on four strong earthquakes and several explosions wasderived by Sa~ma.~.4

The upper bound for the unsymmetrical displacement is given bylog(&)= 1-07-3.83- kC

km

in which u, in centimetres, is the permanent displacement, T is the predominant half-period of the ground inseconds and C is a factor that depends on the slope and material properties of the sliding material.

Charts for the evaluation of permanent displacements as a function of critical acceleration ratio for six realand one synthetic scaled ground motions have been presented by Makdisi and Seed,13 and, from a muchlarger body of scaled data, by Franklin and Chang."


5/22

E AR T HQUAKE -INDUC E D GR OUN D DIS PL AC E M E NTS 989Parkfield Array 2 (N65E) Kc/Km = 0.3

Accelerat ion of Ground-A

- BuuYield Index

-

Absolute Displacement of BlockFigure 3. Ground acceleration time-history x(t)= -g(t) of one of the horizontal components of motion recorded at Parkfield, ofmaximum acceleration k,g =0.495g. If a sliding block system with a critical coefficientk, = 03k,(/3 = 15 deg and W = 32 deg) is subjectedto the ground motion shown in A it will slide down-slope in two stages shown by the yield index in Figure B. The resulting absolutedisplacement of the block is shown in Figure C (continuous line) and the relative displacements between block and sliding surface isshown by the dashed time-history. In this case u, =20.3 cm and the actual displacement down the slope would be 22.9 cm

Figure 4. Data points and upper bound envelope (A-A) of permanent displacement for the unsymm etrical (one-way) case, u being thehorizontal displacemen t in cm, plotted ag ainst critical acceleration ratio kJk, for natural earthquakes and explosions. The envelope isgiven by log (u) =2.3 -3.3 k,/k,. Large dots show displacements calculated for the three orthogonal components of grou nd accelerationrecorded at Pacoima during the earthquake of 9 February 1971.


6/22

990 N. . MBRASEYS AND J. M. EN UDATA AND ANALYSIS

Since 1971, when equation (1) was first derived, additional strong-mo tion records have become available. Thepresent study is made to investigate whether this additional body of da ta alters the upper bou nd defined bythis equation, and also to develop a better correlation between permanent displacement and earthquakecharacteristics for near-field conditions.Referring to Figure 4, we notice that different ground motions may produce very different permanentdisplacements, varying by a factor of 25, and that this spread becomes larger as m ore da ta points a re includedin this plot, suggesting that the actual scatter is probably even larger th an shown in F igure 4. However, itshould be noted here that equation (1) in Figure 4 has been derived as an upper boun d solution to a problemfor which, because of the many variables which are no t considered, a unique functional relationship betweenpermanent displacement and critical acceleration ratio does not exist. These variables include the size of th eearthquake in terms of its magnitude M , o r M,, the source distance R, the duration of shaking D, th efrequency at w hich the bulk of the seismic energy radiates a t the site, directional effects associated with the twoor three orthog onal components of ground motion, base-line correction errors of the input m otion associatedwith sm all values of the critical acceleration ratio, scaling effects an d oth er facto rs that vary from site to site.W hat is impo rtant in Figure 4 s tha t the scatter, regardless of the number of da ta points, is confined below anupper bound of the displacement u , a bound tha t shows a well-defined dependence on th e cube of the criticalacceleration ratio, a significant dependence t ha t allows the assessment of extreme values of u to be made fromequation (1) with some confidence.To re-examine the behaviour of permanent displacement as a function of critical acceleration ratio, weconcentrated our analysis on near-field data. This reduces magnitude, attenuation and duration problemsarising from site-specific cond itions in the far field, an d fur ther en hance s th e role of acceleration or p articlevelocity as a variable. Ground motions were selected, therefore, from near-field data generated by shallowearthquakes, within source distances com parable w ith the source dim ensions of causative earthquakes. Th ese t of 26 two-component horizontal groun d m otions chosen, produced by 11earthquakes, is shown in TablesI and I1 together with the main earthquake parameters and ground motion characteristics used in theanalysis. It should be noted that the magnitude range for which we have near-field data is very limited andthat our investigation in terms of magnitude is, therefore, restricted within the narrow range of M , = 6.9( & 0.3).In order to reduce uncertainties associated with earthquake characteristics, source parameters in Table Iwere carefully revised. We have chosen to define the size of earthquakes in terms of surface-wave (M,) ormoment magnitude (M,) and no t in terms of local magnitude (ML)hich is determined from high frequencyradiation, but has the disadvantage that for larger events instruments may overload, and it is difficult tointerpret when the source size becomes comparable with station distance. Values of M , therefore were re-comp uted uniform ly using the Prag ue formula.34 Mo men t m agnitudes w ere calculated from publishedteleseismic mom ent estimates using the re lation of Kanam ori and Anderson.22Source dimensions were takento be of the ord er of the length of surface fauIting L, which, together w ith relative fault displacements, weretaken from field reports and special studies.The 50 strong -mo tion records listed in Tab le 11, of peak acceleration between 6 an d 115per cent g were base-line corrected and low -pass-filtered. Frequency cut-offs were chosen from v isual examina tion of the am plitudeFourier spectrum of uncorrected time-histories, and applied to frequencies below those that showed anunrealistic energy increase due to digitization noise and instrument distortions. Source distances of therecording stations were re-examined, and Arias intensities were calculated in th e usual way. The du ratio n ofthe record D in seconds was calculated as the time elapsed between the 0.05 and 0.95 of the Arias plot.35 Thepredominant period of the records, P in second, was estimated by tak ing th e sum of the zero crossings in thepositive and negative directions and by dividing the du ration of the digitized record by half of the sum.

CORRELATION OF MAXIMUM DISPLACEMENT WITH CRITICAL ACCELERATION RATIOT o determine the extent to which displacements can be predicted in terms of critical ratio, the d at a in Table I1were used to calculate displacements, and the results were expressed in terms of k , / k , . In the computation of


7/22

Te1Lsoeh

unays

F

H

Mo

L

d

w

N

Eh

De

Ece

(km

M

M

rn

x

M,(km

(mF

2

1ImVe

1Ma137N14W"17203*16469

560b

71

659S

2

2KnCy1Ju230N10W"277&03*17273

2Wb

75

721TH

7r

3HmCy1D248N10Wa

66f02*16568

13

67

2

w s s s

9T

1S133N5E173+*5-64

1W

74

1Moeo

1A140N10E17103*5

68

62

4w

71

7

TH

z

11ImVe

1O138N114Wd

69f03*4'6

56

05

65

308

S

U E

STSrkSpTH=R

*=addao=Nmosaou

'dr & 3lo P zU

4Pked

1Ju238N14Wd964&3*955

52

02

62

300S

5BeMo

1A932N11Wd170+2*26765

06

65

304

S

6SFn

1F93N14Wd960*364

62

12

67

121TH

7L

1NOV.438N22E15703*5-51

0

58

1

TH

8G

1Ma14N63E171+31

6

21

69

333TH

8

15TH

-

0 C v

b=KmaA

o

d=ISCf=KsyetaLZ5;HzZ

h=A

o

j=J

aB

*

a=UG

e=BuaAen

g=NaaKm2

i=enaTch

k=BaMie

I=Dd

L

m=DewkaWo

~

c=Baeta2


8/22

992 N. N . AMBRASEYS AND J . M. MENUTable 11. List of earthquake strong-motion characteristics

R Ari D P ,No. Code Earthquake Station A,,, M, (km) (kAr) (sec) (sec) G1 CENTL702 CENTT703 KER2L704 KER2T705 EURlL706 EURlT707 EUR2L708 EUR2T709 PAR2L7010 BORlL7011 BORlT7012 SFElL7013 SFElT7014 LEUlL7015 LEUlT70

16 GAZL7O17 GAZT7O18 DAYL7119 DAYT7120 BOST7121 TB4L7122 TB4T7123 MONlL7124 MONlT7125 MON3L7126 MON3T7127 MON4L7128 MON4T7129 MONSL7130 MONST7131 IV13L7032 IV13T7033 IV14L7034 IV14T7035 IV15L7036 IV15T7037 IV16L7038 IV16T7039 IV17L7040 IV17T7041 IV18L7042 IV18T7043 IV19L7044 IV19T7045 IV20T7046 IV20T7047 IV21L7048 IV21T7049 IV22L7050 IV22T70

Imperial ValleyImperial ValleyKern CountyKern CountyHumbolt CountyHumbolt CountyHumbolt CountyHumbolt CountyPark ie dBorrego MountainBorrego MountainSan FernandoSan FernandoLeukasLeukasGazliGazliTabasTabasTabasTabasTabasMontenegroMontenegroMontenegroMontenegroMontenegroMontenegroMontenegroMontenegroImperial ValleyImperial ValleyImperial ValleyImperial ValleyImperial ValleyImperial ValleyImperial ValleyImperial ValleyImperial ValleyImperial ValleyImperial ValleyImperial ValleyImperial ValleyImperial ValleyImperial ValleyImperial ValleyImperial ValleyImperial ValleyImperial ValleyImperial Valley

El-CentroEl-CentroTaftTaftFed. Build.Fed.BuildFerndaleFerndaleArray 2El-CentroEl-CentroPacoimaPacoimaLeukasLeukasGazliGazliDayhookDayhookBoshrooyehTabasTabasPetrovacPetrovacUlcinj-2Ulcinj-2BarBarHerceg NovHerceg NovHustonHustonBonds CornBonds CornCruicksh.Cruicksh.JamesJamesDogwoodDogwoodAndersonAndersonBrowleyBrowleyHoltvilleHoltvilleKeystoneKeystoneCalexicoCalexico

0.3440.2170.1560.1890.1640.272016502050.4950.1430.0581.1521.1200.5130.2450.6 130.73403400.37800920.9370.8530.45303020.1810.2240.3670.36602180.2490.41204240375074805970.3920.4860.3610.4770.3460.4850.3350.2190.1640.2050.2450.2230.1710.1980,265

7.27.27.77.76.76 66.66 66.47.07.06.76.75.75.77.17.17.37.37.37.37.37.17.17.17.17.17.17.17.16.96.96.96.96.96.96.96.96.96.96-96.96.96.9696 96.96.96.96.9

12.012.042.042.024.024.040.040.01o45.045.03.03.020.020.05.05.021.021.054.08.08.011.011.010.010013.013.032.0

32.01 o1o303.04.04.04-04.05.05.07.07.07.07.08.08.016.016.011.011.0

116.4583.3338.6335.3621.2223.7634.59112.7215.26967548.73505.2374.0326.10

303.20322.65102.34102.7918.09742.97797.02275.00120.8738.6145.55120.25183.2428.5688.7 1106.76230.683560092-6285.9697.129934125.93101.21795356.3 1264317.9850.405 1.5742.0334.5343.7 150.44

4458

4478

24.4 0.318 S24.5 0.340 S28.7 0.302 R30.4 0.278 R14.6 0.785 S10.0 0-810 S19.6 0593 S18.0 0.631 S7.1 0.475 S49.2 0.693 S52.9 0.653 S7.1 0181 R7.3 0.162 R5.1 0.412 S8.0 0.385 S6.5 0.091 R6.8 0.082 R32.8 0.162 S33.6 0.181 S21.5 026115.7 0.186 S17.2 0.174 S12.0 0.261 S13.4 0.247 S12.4 0.155 R12.3 0.188 R21.5 0.209 S18.9 0.223 S11.0 0163 R

12.2 0129 R11.5 0-254 S8.6 0.270 S9.7 0.278 S9.8 0.418 S6-8 0.227 S5.9 0.220 s8-6 0-247 S9.3 0.286 S6.6 0.201 S7.5 0,241 S6.7 0.265 S10.3 0.322 S14.6 0.229 S15.3 0.243 S13.7 0.269 S12.0 0.328 S12.1 0.266 S13.2 0.305 S16.0 0.272 S11.2 0.276 S

unsymmetrical displacements, two values were calcu lated, one for each of the two horizontal components ofground acceleration, using both sides of the record. In order to avoid problems of scaling when widelydifferent records are used, the 50 records in Tab le I1 were not normalized, and at this stage no attempt was


9/22

EARTHQUAKE-INDUCED GROUND DISPLACEMENTS 993made to compute displacements by combining the two horizontal components of ground motion in real timeor include in the computation vertical motion.

The results of the computation, valid in the range 0.1 < k , / k , < 0.9,are plotted in Figure 5 together withthe best fit expressed, in its simplest form, by the regression

with a goodness of fit of 0.9 and a variance of 0.13.The results corresponding to symmetrical motion are shown in Figure 6 together with the best fit given by

klog(u,)= 1.72- .38 km (4)with a variance of log (uz)of 0-17 and a goodness of fit of 083.

Figures 5 and 6 show the regression of log (ui) on (k, /k, ) and also the scatter of the data points which issignificant. This is partly due to other variables which are not and perhaps cannot be considered, and partlydue to directional effects associated with the two different components of acceleration used for each station.However, these figures show that, in both regressions the critical acceleration ratio is the predominantvariable.As with equation (l),when we were investigating an upper bound, here also with the mean we find u idepending on the third or fourth power of k , / k , that dominates over the weaker influence of other variables.

Comparing Figures 4 nd 5 we notice that the upper bound equation ( l ) , corresponds approximately toequation (3) with a confidence limit of about 65 per cent for small critical acceleration ratios, while for largerratios the limit rises to 99 per cent ,confirming the upper bound nature of this relationship.

Returning to equations (3) and (4 ) we notice that, strictly speaking, these formulae do not satisfy thenecessary conditions at k , / k , =O and 1. For a critical ratio of 1.0, both equations should give zerodisplacement, while for k , / k , = O u 1 hould tend to infinity and u z should approach the maximum absoluteground displacement. In reality, only the first condition of k , / k , = 1-0is satisfied approximately by bothequations, giving values of about 0 02 cm, which for all practical purposes are zero. However, the secondcondition is not obviously satisfied, and the lack of known or accurately determined absolute ground

.. '.., ..90 Z confidence

Meanm

t o B 30. 0 0.'2 0!4 0: s O h 170Ratio Kc/Km

Figure 5. Estimated regressions for unsymmetrical displacements u l. log (u,)= 2.27-4.08 k,/k,. Mean from equation (3), andconfidence limits for 900%. The variance of log(#,) is, in fact, a quadratic function of the dependent variables; in the range0.1< k,/k, < 0.9, the sample is large enough to allow us to assume that s 2 is constant


10/22

994 N. N . AMBRASEYS AND J. M. MENU

.0' . . - 1 o0 o 0.2 0:4 0:1 o:,

Ratio Kc/KmFigure 6. Estimated regression for symmetrical displacements u2. og(u,) = 1.72- 3 3 8 k , / k , . Mean from equ ation(4), and confidencelimits for 90.0%and 975%displacement makes it difficult to impose on the functional relationship for u2 he appropriate values at k , =O .

Nevertheless, an improvement of the model may be made by introducing into the regression the analyticalexpressions for ui in terms of k , / k , for inputs of pulses of simple shape such as (1- ,/k,)"' or ( l /kc /km)". Thefirst expression with rn = 2 or rn = 3, for instance, corresponds to a square or triangular pulse respectively, anexpression suitable for large values of k,/k,, while the second expression, with n = 0 or n = 1, is more suitablefor small values of the critical acceleration ratio. For the symetrical case,n = 0 is obviously required to providea finite value of the displacement at k , =O .A combination of these two expressions was used therefore to regress log (uJ with the following results:

log (u )= 0.77+ og(K,log (14%)= 1.17 +log ( K 2 )

( 5 )

(6 )for unsymmetrical displacements, with variance of log (ul) of 0.11, and

for symmetrical displacements, with variance of log (uz) of 0.14, where2 . 5 8 k -1.16

K , = ( --i:) c) a n d K,=These equations show an improvement on equations (3) and (4), and they are valid in the range0.1


11/22

EARTHQUAKE-INDUCED GROUN D DISPLACEMENTSTable 111. Results of regression analyses of log@,) on various combinations of variables,equations (5) and (6)Case Equation a b m n rz sz Figure

995

2.27 4.08 - - 0.90 0.13 52.33 3.96 - - 0.91 0.112.42 4.00 - - 0.92 0.101.72 3.38 - 0.83 017 61.85 3.34 - - 0.84 0.15- 0.85 0140.77 1.00 2.58 1.16 0.92 0.110.90 1.00 2.53 1.09 0.93 0.09 ll(A)-120.96 1.00 2.54 1.12 0.94 0.08 13(C)1.17 1-00 3-00 000 0.85 0.141.31 1.00 2.96 0.00 0.86 0.13 ll(Bk-121.38 1.00 2.98 0.00 0.88 0.12

u 1-A-I (3)~1-B-I (3)u ,-c-I (3)uZ-A-I (4)u,-B-I (4)u 1-A-I1 ( 5 )ul-B-11 ( 5 )u,-c-I1 ( 5 )uZ-A-11 (6)uZ-B-11 (6)u,-c-I1 (6)

-u,-c-I (4) 1.91 3.36 -

Notes.U,: unsymmetrical (one-way) displacemen t.U2: symmetrical (two -way) displacement.A : permanent displacement calculated for each of the two horizontal components of each record(two values per acceleration record).B: permanent displacement calculated for each record (one value per acc eleration record).C: permanent displacemen t computed from the two horizontal maxima combined vectorially, foreach record.I: regression equation; log (ui)= + b(k , /k ,) i = 1, 211: regression eq uation; log (u,)=a+b log (1 -k,/k,)" (k,/k,)-".r 2 : goodness of fit.2 : variance of log (ui).

CORRELATION OF M AXIM UM DISPLACEM E NT WITH CRITICAL ACCELERATION RATIOAND SEISMIC PARAMETERSIn orde r to investigate the influence of other variables on permanent displacements that could explain theobserved scatter and arrive at a better prediction model, the effects of magnitude M,, source distance R,predominant period P, duration of shaking D and peak acceleration A were introduced in a multipleregression model that includes the effects of critical ratio in the form of equations ( 5 ) and (6).The technique used is a conventional multiple regression procedure, rendered linear by appropriatetransformations. The expansion of the constant term in equations ( 5 ) an d (6) was performed using dummyvariables Zir36o that the equations can be written

where Z i , = 1, 2, . . . , n are the dummy variables, the index i being associated with inputs from a givenearthquake at a specific source distance. The method allows for the decoupling of the critical accelerationratio dependence from other variables and therefore it is convenient to separate the expan sion terms from theinfluence of k , / k , . Once the coefficients A,, B, C and y i are determined, y i is retained and fitted to theexpansion variables. The subsequent step of the technique givesf i Z i = p + q l o g ( A ) + r l o g ( P ) + s l o g ( D ) ( 8 4i = 1

orn1 izi p' +q ; M , +q;R +r ' lo g ( P ) + s ' log D (8b)i = 1


12/22

996 N. N. AMBRASEYS AN D J . M. MENU

0.4

h 0.0M4

E-1 0.1P)8 8.8

(a)

The results of the analysis show that as expected magnitude M, and duration D play an insignificant role inthe prediction of the permanent displacement. Figures 7(a) and 7(b) show the ill-defined variation of y i withthese two variables, resulting from the fact that the bulk of the earthquakes used centre at M ,= 6. 9( kO.35).

80 0 i i " 5 00

' I .! a 0one-sided sllding .

a

VARIATION OF y I WITH MAGNITUDE Ms

r= 0.0.z -0.43Ec.rp , -0.m

(b) -1.1

I .o

h 0 4111C.f 0.0E

&I

8.

. m . aeg m.s aone -s ided s l id ing

aib Jb 8bb 604

D

a

0i two-sided sliding

VARIATION OF y , WITH DURATION D

. 0two-sided sl idlng

0-1.0 ib xb Jb abDuration D rb


13/22

E AR T HQUAKE -INDUC E D GR OU ND DIS PL AC E M E NTS 997More significant are found to be the variables A, P and R, the effects of which may be included in aregression of a more general character. Combining equations (7) and (8) we have

log&)=a +b lo g (Ki)+ log ( P ) + d log (A)+ e R (9)Th e coefficients of equa tion (9) are shown in Table IV for the combination of the variables that show the

Table IV. Results of regression analysis of log (a)n various combinations of variables equations (9)Case Equation a b C d e m n r 2 SZu,-A-111 (9.1) 1.04 1.00 0.46 0 0 2.58 1.16 0.96 0-08uI-B-111 (9.2) 1.16 1.00 0 4 4 0 0 2.53 1.09 0.97 0.07u,-c-111 (9.3) 1.43 1.00 0-48 0.44 0 2.54 1.12 098 0.061.41 1.00 0 4 4 0.26 -0 005 2.54 1.12 0.98 0 0 6u,-A-111 (9.4) 1.54 1.00 0.63 0 0 3.00 0 0-83 017uZ-B-111 (95) 1.66 1.00 0.59 0 0 2.96 0 0.84 0.15u,-c-111 (9.6) 1.96 1.00 0 7 2 0 - 0 0 1 298 0 085 0.140 085 0.14.94 1.00 0.59 0.26 -0.007 2.98Notes. Cases as in Table 111.111: regressionequation-equation(9),log u i ) = a + b o g ( K , ) + c log ( P ) + d log(A)+eR, where K i isdefined inequations(5)and(6).P: Predominant period of ground motion in sec.A: Peak acceleration in g.R: Source distance in km.

"i equat ion 9.3 a'U

10

a0

1b0:2 0 :4 0 . 0:mR a t i o Kc/Km equat ion 9. aa

Rat io Kc/KmFigure 8(a). Variation of the ratio LI of displacem ent calculated from a sliding block mode l to predicted displace ment from equ ation (9.1)(plot a) and equa tion (9.3) (plot b) with critical ratio. For all practical purposes scatter of CI is bracketed by a factor of 3


14/22

998 N. N . AMBRASEYS AND I. M. MENU

.'Oj equation 9.6 QU

n16' 1 .b:o 0 0 :4 0 :a 0:sR a t i o K c / b PJ

R a t i o K c / K mFigure 8(b). Variation of the ratio U ofdisplacement calculate d from a sliding block m odel to predicted displac emen t from equation{9 .4)(plot a) and equation (9.6)(plot b) with critical ratio. For all practical purposes scatter of U s bracketed by a factor of 3

highest significance. These eq uatio ns [(9.1) to (9.6)] show a somewh at reduced variance an d predict relativelywell displacements calculated from a sliding block model. The plots of the ratio of calculated to predictedpermanent displacement versus critical acceleration ratio depicted in Figures 8(a) an d 8(b) show t hat thescatter arising from the use of equation (9) is now bracketed within a ratio of 3 which, for all practicalpurposes, is independent of the critical acceleration ratio.EXTREME VALUES

Perm anent displacements generated by earthqua kes are variables whose largest values, such as those given byequation (l),are of practical interest in design. An extreme values model, therefore, may be used to bracketdesign values for displacements within acceptable limits.For both unsymmetrical and symmetrical motions, permanent displacements calculated from a slidingblock model by combining vectorially the two horizontal maxima for each record (case C in Tables I11 andIV), were classified into n ine se ts for values of the critical ratio s 0.9,0.8,. . . ,0.1. Fo r each subset permanentdisplacements were ranked and several probability distributions were tested. A Weibull distribution, withlower limit equal t o zero (Gum bel's type III), was found to fit all subsets rem arkably well, on e of which, fork, /k ,=0 .2 , is shown in Figure 9. We used, therefore, the inverse Weibull distributionu i= a,[n-(1 z ) ] - l ' b i

where the dependent variable is the percentage of confidence z, with ui > 0. The characteristic value of the


15/22

EARTHQUAKE-INDUCEDGRO UND DISPLACEMENTS 999DISTRIBUTION OF ONE-SIDED M A X I M U M DISPLACEMENTS7

li d . . . . . . . . . . . . .-2.b - I r -0!4 0 !ar-.rl r -Ln ( 1 - 0 1-4 .o

Kc/Km = 0.2

Cumulative Probability F,,(Urnax)Figure 9. Fitting ofmaximum displacements ui oan extreme value distribution .The figures show an ex amp leof the fitting for the case ofthe symmetrical k,/k ,=0.2 subset. The slope and intercept of the linearized plot give the coefficients oi and bi of equation (10)

distribution a, is an indicator associated with a confidence of 63 per cent, and the exponent b, , when constant,reflects an invariance in the shape of the distribution. Means and standard deviations are proportional to a,.

Using the expressions for u i n terms of K, see equations ( 5 )and (6)], the distributions parameters are foundto be given by:

-0 .12b l = 1 * 1 8 ( 2 )

and b2 = 1.16 (1 1 4The dependence of a, and bi on critical ratio is shown in Figure 10. The constant value of b, implies aninvariance in the shape of the distribution in the case of symmetrical displacements, while equation (1 lb)shows some dependence on the nature of the ground motions.

Equations (10) and (11) may be used to predict permanent displacements associated with a givenprobability of not being exceeded. As an example, Table V lists the predicted values of ui or confidence levelsof 90-0 and 96.2 per cent and compares the values of the latter with the actual maxima in the data subsetswhich have a size of 26.


16/22

loo0 N. N. AMBRASEYS AN D J. M . M E N U

2 4 0

*1-76+J$'z 1 - 6 0

cQ)0 1.26u

1.00

0:2 0:4 D :6 -x----.D1.0 ri'l:o - . . .0:) Or 4 D :e 0:a -*?1210:o Ratio K c / K m Ratio Kc/Km2.00

N4 76U

/::; 0 O O " *' O D.- . . . . . . . ......... . . . . - . . . . ......... . . . . . - 1.000 .0 0 :2 0:4 0s 0:0 1.0 0 . 0 0!2 0:4 0:s v20Table V. Maximum displacements calculated from extreme value distribution

Unsymmetrical displacements Symmetrical displacementsU I(4 uz(cm)A B C A B Ck J k , (90.0%) (96'2%) (96.2%) (90.0%) (96.2%) (96.2%)

0.10.20.30 40.50.60.70.80.9

194.169.732.616.48.23.91.60.50.1

242.088.542.021.310.85.12.10.70.1

128.093.138.119.711.05.11.70.80.2

47.633.522514.28.34.21.80 50 1

63.945.030.219.111.15.72.40.70.1

85.271.832.714.87.84.01.70.80.2Notes. Extreme value prediction of permanent displacement ui computed for vectorially combinedmaxima in two horizontal directions.A: Displacements with a 10 per cent probability of exceedance computed from equations (10)and (11).B: Displacements with a 3.8 per cent probability of exceedance computed from equations (10)and (1 I) . .C Extreme values of the data subsets of size 26.

DISCUSSIONTh e near-field dat a used in this study have served to establish empirically the behaviou r of permanent groun ddisplacements in the epicentral area of strong earthquakes. We have used only acceleration time-historiesrecorded at source distances of up to 45 per cent of the source dimensions of events in the magnitude ran ge


17/22

EARTHQUAKE-INDUCED GR OU ND DISPLACEMENTS 10016.4 < M , < 7.7, a range often used for the design of structures in areas of high seismicity. In our analysis wehave made the crucial assumption that the yield resistance to sliding remains constant and equal to thatmobilized at a factor of safety of one. The influence of pore pressure and rapid loading effects ondisplacements3' awaits further study. Site effects have not been considered and we have limited our regressionanalyses to critical ratios between0.1and 0.9. The reason for this is that, for ratios smaller than 0.1,errors dueto other factors, such as the length of the record used in analysis and base-line corrections, become important.

The purpose of equations (4) to (6)and (9) is prediction of the mean value of permanent displacement.Estimates of displacement have been calculated by regressing log (ui) on critical acceleration ratio and onother variables, and these estimates are interpreted as'most likely, rather than maximum values, which couldbe exceeded 50 per cent of the time. However, estimates at other probability levels may be calculated using therelevant variances. It must be stressed that these regressions are not major axis solutions, and as such theyshould not be used to estimate a variable from ui .

From Tables 111 and IV we notice that the main variable in the prediction displacement is the criticalacceleration ratio, and that although additional variables in equations (5) and (6)do improve their predictivevalue, improvements are not all that great. Predominant period P and to a lesser extent peak accelerationAdo seem to have some significance on predicted displacements, but the data set analysed shows that theremaining variables, source distance R, magnitudeM, nd duration of shaking D are even less significant inthe narrow M, imits investigated.Figure 11 shows a plot of unsymmetrical (A) and symmetrical (B) displacements in the direction ofmaximum acceleration for a 50 per cent probability of exceedance as a function of the critical ratio, predictedfrom equations (5-B-11) nd (64-11) respectively (Table 111). This figure shows that, other things beingequal, the difference between displacements induced down-slope and on level ground decreases withincreasing values of the critical ratio. At k,/k,=O.l , down-slope displacements are on average 5 times largerthan on level ground, becoming practically equal for ratios greater than about 06. This is perfectly acceptable,since for values of the critical ratio greater than about 0.6, the significant part of the ground accelerationrecord inducing sliding is reduced (essentially to a single triangular pulse on one side of each accelerationc ~ m p o n e n t . ~ ~his also suggests that the dependence coefficients n equation (7) should be in fact a function ofthe critical ratio and not constants. However, the data are insufficient to allow such a refinement of the modelto be tested.Equations (5-C-11) and (64-11) in Table I11 may be used to calculate displacements induced by groundaccelerations n two horizontal components combined vectorially. Alternatively, these displacements may beassessed from Figure 11, by multiplying the values from curves (A) and (B) by 1.25 and 1.15 respectively. Asalready pointed out, directional effects are not significant. Figure 1 1 is valid for M, 6.9(

Equations (5-B-11), (6-B-11), (5-C-11) and (6C-11) may also be used to predict displacements withprobabilities of exceedance smaller than 50per cent. This may be done by adding to the expressions for log (ui)the term t x s,where s are the relevant variance given in Tables 111and IV, and t can be obtained from a tableof the normal distribution function. Figure 12 shows predicted unsymmetrical (A) and symmetrical (B)displacements in the direction of maximum acceleration, for different probabilities of exceedance. However,the data are insufficient to warrant probabilities smaller than about 10 per cent, and caution is indicated inusing these equations for t values larger than about 1.3. Extreme values of permanent displacement computedfrom equations (10) and (1 1) offer a better alternative in this case and hold true in the magnitude range of thedata investigated.

It is of interest that, regardless of the method of analysis in the regression of log@,) on one variable, theexponentsm and n in the expressions for K i re, for all practical purposes, invariant (Table VI), and equal tom = 2-54 and n = 1-12 for the unsymmetrical case, and m=2.98 and n = 0 for the symmetrical case.

Of the regression equations that involve variables in addition to the critical ratio (Table IV), equation (9.3),which predits displacements induced by vectorially combined ground accelerations, is of particular interest.From Table IV we notice that the coefficients of the terms that involve accelerationA and periods P are, for allpractical purposes, identical so that they may be replaced by a single velocity term. If we define by V the groundvelocity that corresponds to 4 V = A x P(cgs), and replace A and P in equation (9.3) n terms of V,we find thatdisplacements may now be predicted in terms of critical acceleration ratio and ground velocity only. Figure 13

0.3).


18/22

1002 N. N. AMBRASEYS AN D J. M.MENU

10050U(cml10

5

1.00.5

0.1O.O!

0.0

Figure 1 1 . Predicted unsymmetrical (A) and symmetrical (B) displacementsfor 50% probability of exceedance as a function of criticalratio (equations 5-5-11 and 6B-II in Table 111). M, 6.9( +_ 0.3)

shows a plot of the unsymmetrical displacement u 1 as a function of the critical ratio and V, for groundvelocities of 10, 100and 200 cm/sec. The same figure shows a plot of equation (5-C-11) for comparison (C).Curve (C) implies that displacements predicted from equation (5-C-11) are almost identical to those predictedby equation (9.3) for an average ground velocity of 25 cm/sec.

The present analysis demonstrates that, provided the yield resistance to sliding does not deteriorate withdisplacement, that is k , remains constant, soil masses may resist with negligibly small displacements (of theorder of millimetres), ground motions generated in the near field, even when peak accelerations exceed criticalvalues by 40 per cent. This implies (i) hat, provided k J k , 2 0-7,effective design accelerations may be reducedto 0 7 k , in a static analysis, and (ii) that recorded ground accelerations on soil sites may include such yieldeffects.The use in design of a reduced peak acceleration, of say 0.7 k,, implies that surface cracking of severalmillimetres to a few centimetres is acceptable and of little consequence for the stability of a slope or afoundation. However, such cracking, particularly near the top of a slope, aided by tensile stresses, dryingeffects and aftershock activity may extend to a considerable depth, particularly in materials of low plasticity,fine silty soils or poorly compacted fills. Although these cracks by themselves may have little detrimental effecton stability, subsequent flooding by seepage, rain or reservoir water may bring about instability and failure ofa slope sometime after the earthquake. There is some evidence that landslides, particularly those in clays with


19/22

EARTHQUAKE-INDUCED GROUND DISPLACEMENTS 1003

Figure 12. Predicted values of unsymmetrical (A ) and symmetrical (B) displacemen ts in the direction of maximum acc eleration as afunction ofcr itical ratio for probabilitiesofexceedenceof 1,5,16 and 50per cent, from equatio ns5-&I1 and 6 8 - 1 1 . Dashed curves showextrapolation of the prediction to be used with caution. M, 6.9(+0.3)

Table VI. Values of m and n derived from different modelsm n Equation

Unsymmetrical case: 2.58 1.162.53 1.092.54 1.122.58 1.16253 1.092.54 1.122.50 1.123.00 02.96 02.98 03.00 02.96 02 98 02.98 0

Symmetrical case:

(5-A-11)(5-511)(54-11)(9- A-111)(9-B-111)(9-C-111)(6-A-11)(CB-11)(9- A-I 11 )(9-B-111)(9-C-111)

( 1 la )(CC-11)

ma, = 2 5 4 ( +_ 0.03)nav= 1.12(k0.03)

( 1 lc) ma, = 2.98(+_ 0 0 2 ) nnv= 0

pree xisting slip surfaces, take place some time after the earthquake. In such cases, the shock can have only anindirect effect on stability, and this may very well be due to cracking and subsequent flooding of cracksinduced by permanent displacement^.^^ Piping failures may originate from embankment cracks, and in


20/22

1004 N. N. AMBRASEYS A ND J . M. MENU

Figure 13. Predicted vectorially combined maximum displacements for the unsymmetrical case as a function of critical ratio, equa tion5-C-111, curve (C). Curves (A)and (B) show predictions in terms ofequation (9.3) n which we have substituted 4V= A x P, where Vis theground velocity, for V = 10 cm/sec and V= 100 cm/sec. Input data range M ,= 69 , standard deviation 0.35

allowing small permanent displacements to develop in earth dams (an effect implicit in the reduction of thepeak acceleration), care must be taken to safeguard against secondary effects that may lead to instability. Forconcrete faced dams, the amount of damage which may ensue from cracking and requirements for effectiverepair are difficult to assess and great caution must be exercised in protecting such structures from piping.

CONCLUSIONSSeveral prediction equations for permanent displacement are presented in terms of critical ratio, predominantperiod, ground acceleration and source distance, for near-field conditions and for earthquake magnitude M,= 6.9( +_0*3),regardless of site conditions.

Critical acceleration ratio is the fundamental parameter, and the most appropriate prediction equations forunsymmetrical u1and symmetrical u 2 displacements in the direction of the maximum acceleration are

10g(u,)=090+10g (5-B-11)and

1.31+,,,[ ( - P ) . ~ ~ ] + ~ . ~ ~ ~ 6-B-111)where t is zero for a probability of exceedance of 50 per cent. For smaller probabilities t could be obtained


21/22

E AR T HQUAKE-INDUCE D GR OU ND DIS P LAC E M E NT S 1005from a table of the normal distribution function. These equations are shown on Figure 12 and they are validfor 0.1 < k , /k , < 0.9.

Displacements resulting from two components combined vectorially may be obtained from equations(54-11) and (6-B-II), the former shown in Figure 13, curve (C)for t = 0.Directional effects are relatively smalland would increase values derived from (54-11) and (6-B-11) by 1.25 and 1.15 respectively.

For the narrow range of magnitudes used,M , is not statistically significant. It is of interest to note that, forthe narrow range of M , used, duration of shaking D , a measure of the size of seismic event, is also notsignificant for displacements.

The examination of the sensitivity of the prediction equations to other variables shows that predominantperiod and to a lesser extent peak acceleration and source distance have some significance for displacements,resulting in a small improvement in the total variance. Equation (9) and Table IV provide somewhatimproved regressions for displacements,one of which, based on ground velocity, is shown in Figure 13. FromTable IV we notice that the source distance coefficiente is of the order of magnitude that one would expect inan attenuation relationship valid in the near field of strong earthquakes and that the period coefficientc is thesame, to one decimal place, as that for accelerationd, suggesting a velocity dependence. However, for designpurposes, equations (9) involve additional assumptions to be made regarding P, A, R or V that undulycomplicate the confidence that can be placed on predicted displacements and it seems quite reasonable thatpreference should be given to equations (543-11) and (MI-11).For critical acceleration ratios greater than about 0.6, maximum displacements on sloping and level groundare almost identical. However, down-slope displacements ncrease more rapidly with decreasing values of thecritical acceleration ratio, becoming about 5 times larger than on horizontal ground for values of the ratioapproaching 0.1.

Finally, equation (1) is still valid and comparison of Figures 3 and 12 suggests that this equation in factrepresents displacements that have a probability of about 25 per cent of being exceeded.

However, any reliable prediction model for displacements must involve data from a wider range ofmagnitudes and distances and in particular more realistic yield resistance characteristics. Until then,equations (5-B-11) and (6B-11) may be used for design purposes, provided k, is based on residual strengthand M, ies between 6.6 and 7-3.

AC KNOW L E DGE M E NT SThis work was supported by the Science and Engineering Research Council under Grant No. GR/D/38620.We thank Drs. S. Sarma, P. Viughan and J. Hutchinson for comments and constructive criticisms.

1.2.3.4.5.6.7.8.9.10.

11 .

12.13.

REFERENCESN. N . A mbraseys, The seismic stability of earth dams, Ph.D. Thesis University of London, Vol. 1, F.3 & Vol. 2 uppl. Ch. 13, 1959.N. M. Ne wm ark, Effects of earthq uake s on dams and embarkments. Geotechnique 15, 139-160 (1965).T. Kirijas, Opredeluuanje nu Zemjotresot uo Skopje od 26 Juli 1963, Publ. Inst. Seis. Zemjotr. Inzen. Plan., Skopje, 1968, p. 197.N. Am braseys, The seismic stability of dams, Proc. 2nd Symp. earthquake eng. Roorkee 11-21 (1962).N. Ambraseys and S. Sarma, The response of earth dams to strong earthquakes Geotechnique, 17, 181-213 (1967).N. Ambraseys, Behaviour of foundation materials during stron g earthquakes, Proc. 4th Eur. symp. earthquake eng. London, 7,ll-12(1972).N. Ambraseys, Feasibility of simulating earthquake effects on earth dams using underground nuclear events. Appendix A,Earthquake Resistance of earth dams, Miscellaneous Paper 971-17, U S . Army Engineer Waterways Experiment Station,

~Vicksburg, 1972.S.K. Sarm a and M . V. Bhave. Critical acceleration versus static factor of safety in stability analysis ofe art h dam s and emba nkments,~Geotechnique 24,661-665 (1974).S. K. Sarma, Seismic stability of earth dams and embankments GPotechnique 25, 743-761 (1975).C. Plichon, Hooped rubber bearings and frictional plates: a modern antiseismic engineering technique, Proc. speciality meetingantiseismic d esign nuclear installations, Paris (1 75).A. G . Franklin and F. K. Chang, Earthquake resistance of earth and rockfill dams; permanent displacements of embankments byNewmark sliding block analysis, Miscellaneous Puper S . 71 . 17, U S. A rmy Engineers Waterways Experiment Station, Vicksburg,1977.C. Plichon and F. Jolivet, (1978)Aseismic found ation sy stems for nuclear pow er plants, Proc. SMIR T con5 London, Paper No.C190/1978.F. Makdisi and H. 8.Seed, Simplifiedprocedure for estimating dam and em bankment earthquake-induce d deformation,1. eotech.eng. diu. ASCE 104,849-867 (1978).


22/22

1006 N. N. AMBRASEYS AN D J. M. ENU14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.29.30.31.32.33.34.35.36.37.38.39.

S. K. Sarma, Response and stability of earth dams during strong earthquakes, Miscellaneous Paper G L7 9- 13 .US. rmy EngineerWaterways Experiment Station, Vicksburg, 1979.R. Richards an d D. G. Elms, Seismic behavior of gravity retaining wall, J . geotech. eng. diu. ASC E 105, 44 94 64 (1979).S. K. Sarma, A simplified method for the ea rthquake resistant design of earth dams, in Dams and Earthquakes, TTL, London, 1980,R. V. Whitman and S. Liao Seismicdesign of gravity ret aining walls, Proc. 8 th world con$ earthquake eng. San Francisco 3,533-540(1984).S. H. Crandall, S. S. Lee and J. H. Williams Accumulated slip of a friction-controlled mass excited by ear thq uak e motions, J . appl.mech. ASME 41, 10941098 (1974).G.Gazetas, A. Debchaudhury and D.A. Gasparin i, Random vibration analysis for the seismic response ofe art h dams, GLotechniqueG. Ahm adi, Stochastic earthquak e response of structures on sliding foundations, Int. j . eng. sci. 21.93-102 (1983).M. C. Constantinou and I. G. Tadjbakhsh, Response of a sliding structure to filtered random excitation, J . struct. mech. 12,401-418 (1984).H. Kanam ori a nd D. Anderson, Theoretical basis of some empirical relations in seismology, Bull. seism. soc. Am. 65, 1073-1095(1975).M. Bonilla, R. Mark and J. Lienkaernper, Statistical relations amon g ear thq uak e magnitude, su rface rupture, length, etc., Bull. seism.soc. Am. 74, 2379-2411 (1984).J. Brune and C. Allen, A low stress-drop, low-magnitude earthquake with surface faulting; the Imperial Valley, Californiaearthquake of March 4, 1966, Bull. seism. soc. Am. 57 , 501-514 (1967).M. risty, L. Burdick and D. Simpso n, The focal mechanism of the Gazli USSR earthquake Bull. seism soc. Am. 70, 1737-1750(1980).S. Hartzell, Faulting process of the May 17, 1976 Gazli, USSR earthquake, Bull. seism. soc. Am. 70 , 1715-1736 (1980).M. iazi and H. Kanamori, Source parameters of the 1978 Tabas and 1979 Qainat earthquakes from long-period surface waves,Bull. seism. soc. Am. 71, 1201-1213 (1981).H. J. Anderson, Seismotectonicof the w estern Mediterranean, Ph.D. Dissertation, University of Cambridge, 1985.R. Stein and W . Thatcher, Seismic and aseism ic deformations associated with th e 1952 Kern County earthquake. J. geophys. res. 86,4913-4928 (1981).W. Joyner and D. Boore, Peak horizontal acceleration and velocity from strong -motion records, Bull. seism. oc . Am. 71,2011-2038(1981).B. Bolt and R.Miller, Catalogue of Earthquakes in Northern ColiJornia 1910-1972. Publ. Seism. Station, University of California,Berkeley, CA, 1975.S. Dede, The Earthquake ofApril 15. 1979. Publ. Acad. Sci. SOC.Republ. Albania, Tirana, 1980.A. Dziewonski and J. Woodhouse, An experiment in systematic study of global seismicity: centroid-moment tensor solu tions for 201moderate and large earthquakes in 1981. J. geophys res. 88 , 3247-3271 (1983).J. Vanek, A. Zatopek et al. Standardization of magnitude scales, iruest . akad. sci. U SS R Geophys. series no. 2,108, Moscow (1962).M. D. Trifunac and A. G. Brady, A study on the duration of strong earthquake ground motion, Bull. seism. soc. Am . 65,581426(1975).H. R. Draper and H. Smith, Applied Regression Analysis, Wiley, New York, 1966.P. R.Vaughan, L. Lemos and T. Tika Strength loss o n shear surfaces du e to rapid loading. Session 7B: Seismic stability of n aturalslopes, 11th int. con5 soil mech. found. eng. San Francisco (1985).S. K. Sarma and K. S. Yang, An evaluation of strong m otion records an d a new p arameter A9S, Earthquake. eng. struct. dyn . 15,V. Geogiannou, T he effect of vertic al cracks on slope stability,M.Sc . Dissertation, Engineering Seismology Section, Imperial Collegeof Science and Technology, Lon don, 1985.

pp . 155-158.

31, 261-277 (1981).

119-132 (1987).

Documents

EARTHQUAKE-INDUCED GROUND DISPLACEMENTS.pdf