--

,,"\ '

~~

.::4-,I, ,:~.

ARMY COE LIBRARY SACRAMEN'

i11II iI1I1IIIII1II1I jIII~ 11111111111111111111111 91001012MISCELLANEOUS PAPER GL-84-13

RATIONALIZING THE SEISMIC COEFFICIENT METHOD

by

Mary E. Hynes-Griffin, Arley G. Franklin

Geotechnical Laboratory

DEPARTMENT OF THE ARMY Waterways Experiment Station, Corps of Engineers

PO Box 631 Vicksburg, Mississippi 39180

July 1984

Final Report

Approved For Public Release: Distnbution Unlimited

OCT 2 11991

I Richmond (;j~1" [~14 t'Hl4,~II·\')h;H~J

t

(S'10)

~ Prepared for DEPARTMENT OF THE ARMY

US Army Corps of Engineers Washington, DC 20314

Under CWIS Work Unit 31145

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8. CONTRACT OR GRANT NUMBER(.)7. AUTHOR(o)

Mary E. Hynes-Griffin and Arley G. Franklin

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19. KEY WORDS (Continue on ... ve,. •• • ~d. It n.c•••.",. .,d Identify by block number)

Dams--Earthquake effects--Mathematics (LC) Seismic coefficient method Embankments (LC) (WES) Earth dams (LC) Earthquakes and hydraulic structures (LC)

2Cl. AB5rRACT (Caatfauo ............... H _ _ Id ....ttr ",. bloc" n ..... t...)

The seismic stability of embankment dams may be evaluated by a rela­tively simple method, originally proposed by N. M. Newmark, in cases where there is no threat of liquefaction or severe loss of shear strength under seismic shaking. This method is based on idealization of the potential slide mass as a sliding block on an inclined plane which undergoes a history of earthquake-induced accelerations. The result is a computation of the expected final displacement of the block relative to the base. A necessary refinement

(Continued) FO_

EDITION OF' I NOV 65 IS OBSOLETEDO J ...... n 1m Unclassified SECURITY CLASSIFICAT'OH OF ,H'S PA:""...E (JPnNn Det. En/ered)

"'

I

Unclassified

SECURITY CLASSIFICATION OF THIS PAGE(l"l ... D.'. En'.red)

20. ABSTRACT (Continued).

is the consideration of amplification of the base motions in the embankment, which is evaluated by means of a linear elastic analysis. Sliding block anal­yses have been done for 348 horizontal components of natural earthquakes and 6 synthetic records. These computations, together with available results of amplification analyses, suggest that a pseudostatic seismic coefficient analy­sis would be appropriate for embankment dams where it is not necessary to con­sider (a) liquefaction or severe loss of shear strength, (b) vulnerability of the dam to small displacements, or (c) very severe earthquakes, of magnitude 8 or greater. A factor of safety greater than 1.0, with a seismic coefficient. equal to one-half the predicted bedrock acceleration, would assure that defor­mations would not be dangerously large.

Unclassified

SECURITY CLASSIFICATION OF THIS PAGE(When D.,. Entered)

PREFACE

The screening analysis reported herein is based on seismic stability

evaluations of several earth dams, in particular Richard B. Russell Dam in

Georgia and South Carolina and Ririe Dam in Idaho, and was performed by the

Earthquake Engineering and Geophysics Division (EE&GD), Geotechnical Labora­

tory (GL), U. S. Army Engineer Waterways Experiment Station (WES) , Vicksburg,

Miss.. This study was sponsored by the Office, Chief of Engineers (OCE) , U. S.

Army, under the Civil Works Investigational Studies (CWIS), Soils Research

Program (Work Unit 31145), "Liquefaction of Dams and Foundations During Earth­

quakes," for which Mr. R. F. Davidson was the OCE Technical Monitor.

The research was conducted and the report prepared by Ms. M. E.

Hynes-Griffin, EE&GD, and Dr. A. G. Franklin, Principal Investigator and

Chief, EE&GD. Appendix A was prepared by Mr. F. K. Chang, EE&GD. The study

was performed under the general supervision of Dr. W. F. Marcuson III, Chief,

GL.

COL Tilford C. Creel, CE, was Commander and Director of WES during the

preparation of this report. Mr. F. R. Brown was Technical Director.

1 "'

CONTENTS

Page

PREFACE . . . . . . . . . . . 1

APPENDIX A: TABLES OF SLIDING BLOCK CALCULATIONS FOR STRONG-MOTION DATA, EARTHQUAKES OF THE WESTERN UNITED STATES AND OTHER COUNTRIES, AND SYNTHETIC ACCELEROGRAMS ..... Al

PART I: INTRODUCTION . 3

PART II: PERMANENT DISPLACEMENT ANALYSIS 5

Stability Analysis . . . . . 5 Sliding Block Analysis 8 Embankment Response Analysis 13

PART III: CONCLUSIONS 19

REFERENCES 20

TABLE 1

2 ""'-,

RATIONALIZING THE SEISMIC COEFFICIENT METHOD

PART I: INTRODUCTION

1. Until the 1960's, seismic analysis of dams consisted essentially of

the seismic coefficient ~ethod, in which a static, horizontal inertia force

was applied to the potential sliding mass in an otherwise conventional static

limit analysis. The magnitude of the inertia force was chosen on the basis of

judgment and tradition; a rational basis was lacking. Alternatives to this

approach became available during the 1960's and 1970's. A method of analysi~

that dealt with the softening or liquefaction of granular soil? was evolved,

largely through work at the University of California at Berkeley, with Profes­

sor H. B. Seed playing the leading role. This approach is based on comparison

of dynamic shear stresses computed in a transient response analysis to the

cyclic strength (resistance to liquefaction) obtained from laboratory cyclic

shear tests or from empirical correlations of liquefaction occurrence (and non­

occurrence) with Standard Penetration Tests (Seed, et al. 1975a, bj Seed 1979j

Seed and Idriss 1983). A second alternative is to deal with the permanent de­

formations that might be anticipated if the embankment and foundation soils do

not suffer liquefaction or severe softening under cyclic loading, using as an

idealized model of the displaced part of the embankment a rigid block sliding

on an inclined plane. This approach was proposed by the late Professor N. M.

Newmark in his Rankine Lecture (1965). Other contributions to a coherent pro­

cedure using this approach have been made by Professors Ambraseys and Sarma,

Imperial College, London (e.g. Ambraseys and Sarma 1967; Sarma 1975,1979),

the Berkeley group (Goodman and Seed 1966, Makdis~ and Seed 1977), and the

U. S. Army Engineer Waterways Experiment Station (WES) (Franklin and Chang

1977, Franklin and Hynes-Griffin 1981).

2. Sufficient experience has been gained in the application of the New­

mark approach to allow some conclusions to be drawn. In the absence of lique­

faction effects, dams with adequate static factors of safety against sliding

are not likely to be predicted by this analysis to be subject to deformations

so large as to endanger their reservoirs, through limited sliding deformations

may be predicted. This result suggests that many--perhaps most--permanent

displacement analyses do not really need to be done, and that some simple

screening method should be applied to separate those dams that are clearly

3

""

safe against earthquake-induced failure from those that require further anal­

ysis. A seismic coefficient analysis can serve this screening function, be­

cause the accumulated experience in permanent displacement analyses now pro­

vides a rational basis for choosing the value of the coefficient. The

rationale is based on assuring that deformations will be limited to tolerable

values, assuming the worst combination of earthquake loads and resonant em­

bankment response. A procedure that uses this approach is proposed in this

report.

4

PART II: PERMANENT DISPLACEMENT ANALYSIS

3. The major components of a permanent displacement analysis of the

Newmark type, as applied by the WES, are shown in Figure 1. The primary com­

ponent is the analysis of motions of a system consisting of a rigid block

sliding on an inclined plane, chosen to represent a potential sliding mass in

an embankment, as described by Newmark. A conventional limit analysis, or

slope stability analysis, with slight modifications, provides the shearing

resistance between the block and plane. Because bedrock motions may be ampl!­

fied upon being propagated upward through an embankment, a rigid-body model

may underestimate displacements, and an analysis of the amplification response

of the embankment is incorporated to account for amplified accelerations in

the embankment.

GEOLOGICAL AND

SEISMOLOGICAL EVALUATION

FIELD INVESTIGATION

Testing Sampling

LABORATORY INVESTIGATION

Routine Dynamic

SLIDING BLOCK

ANALYSIS

EMBANKMENT RESPONSE COMPUTE ANALYSIS u vs. h

lJ L I STABILITY r ...., ANALYSIS

Figure 1. Permanent displacement analysis

Stability Analysis

4. The concept of the traditional pseudostatic, seismic coefficient

method of analysis is illustrated in Figure 2. In an otherwise conventional

static stability analysis, such as a method of slices analysis, the earthquake

loading is represented by a statically applied horizontal force kW, where W

is the weight of the slice and k is the seismic coefficient, which is some

fraction of gravity. The value of k is generally prescribed by code or reg­

ulation, with values usually in the range of 0.05 to 0.20, depending on the

seismicity of the site. The procedure is described in EM 1110-2-1902 (U. S.

Army, Office, Chief of Engineers 1970) and in many standard texts.

5 "",

kW ... I +

Ei + 1

W

~

~c

Ft~N Figure 2. Earthquake stability analysis by pseudostatic

method using seismic coefficient.

5. For analysis of permanent displacements, the shearing resistance be­

tween the potential sliding mass and the underlying base is evaluated in terms

of a critical acceleration N , defined as the acceleration (of the ground or

embankment below the sliding surface) that will reduce the factor of safety

against sliding to unity, i.e., that will make sliding imminent. The value of

N , which is expressed as a fraction of gravity (g) , is obtained through a

stability analysis similar to conventional pseudostatic stability analyses,

but which includes two special features. One is that the stability is evalu­

ated in terms of a critical acceleration rather that a factor of safety, and

the other is that, because the amplified accelerations vary over the height of

the embankment, critical accelerations are determined for possible sliding

masses whose bases lie at various elevations in the section (Figure 3).

6. The analysis may be performed using conventional stability analysis

6

+

r::: o-CO > CD CD

'l" critical acceleration

Figure 3. Critical acceleration as a function of elevation

methods such as those of Bishop (1955) or Morgenstern and Price (1965). Trial

values of acceleration may be used to find the value that reduces the factor

of safety to unity. The Sarma method (Sarma 1975), which employs a slip sur­

face of arbitrary shape, determines the value of N directly.

7. In principle, the analysis can be performed on either a total or an

effective stress basis, but the problems of estimating pore pressures induced

by cyclic shearing are avoided by using a total stress analysis. The usual

Corps of Engineers practice for static stability analyses is to use a compos­

ite shear strength envelope based on the S test (consolidated-drained) at low

confining pressures and the R test (consolidated-undrained) at high confining

pressures (Figure 4). This strength envelope, which conservatively takes into

account possible dissipation of shear-induced negative pore pressures that

might occur in the field but cannot occur in an undrained test in the labora­

tory, is recommended for pervious soils. For soils of low permeability, in

which undrained conditions are more likely to exist during an earthquake, an

undrained (R) strength envelope would be appropriate.

8. Makdisi and Seed (1977) point out that substantial permanent strains

may be produced by cyclic loading of soils to stresses near the yield stress,

while essentially elastic behavior is observed under many (>100) cycles of

loading at 80 percent of the undrained strength. They recommend the use of

80 percent of the undrained strength as the "dynamic yield strength" for soils

that exhibit small increases in pore pressure during cyclic loading, such as

clayey materials, dry or partially saturated cohesionless soils, or very dense

saturated cohesionless materials.

7 --.,

f-­

til til <J.) .... til

.... eo <J.)

s: til

normal stress (J

Figure 4. Composite "S-R" strength envelope

Sliding Block Analysis

9. Figure 5 presents the elements of the sliding block analysis (Frank­

lin and Chang 1977). The potential sliding mass in Figure Sa is in a condi­

tion of impending failure, so that the factor of safety equals unity. This

condition is caused by the acceleration of both the base and the mass toward

the left of the sketch with an acceleration of Ng. The acceleration of the

mass is limited to this value by the limit of the shear stresses that can be

exerted across the contact, so that if the base acceleration were to increase,

the mass would move downhill relative to the base. By D'Alembert's principle,

the limiting acceleration is represented by an inertia force NW applied

pseudostatically to the mass in a direction opposite to the acceleration.

10. Figure 5b shows the force polygon for this situation. The angle of

inclination 8 of the inertia force may be found as the angle that is most

critical; this is, the angle that minimizes N. Its value is usually within

a few degrees of zero, and since the results of the analysis are not sensitive

to it, it can generally be ignored. The angle ~ is the direction of the re­

sultant S of the shear stresses on the interface and is determined in the

course of the stability analysis. The same force polygon applies to the model

of a sliding block on a plane inclined at an angle ~ to the horizontal (Fig­

ure 5c). Hence, the sliding block model is used to represent the sliding mass

in an embankment.

8

o

S

pf -1l

\ p

..-- W\ NW

a. POTENTIAL SLIDING MASS b. FORCE POLYGON FOR F.S.=-1.0

Q)

o I­

oW -

Nd W

UPHILL

•

DOWNHILL ..

displacement

NuW

c. SLIDING BLOCK MODEL d. FORCE-DISPLACEMENT RELATION

time

OF SLIDING MASS

RELA TlVE DISPLACEMENT

DURING ONE CYCLE

GROUND VELOCITY VgCt)

o" e \ & , f:.t0..~, fI:.\.¥ ..

o o iJ.)

>

>.-

e. COM PUT A TION OF DISPLACEMENT

Figure 5. Elements of the sliding block analysis

9

....

11. The force-displacement relation in Figure 5d is assl~ed to apply to

this system. The force in this diagram is the inertia force corresponding to

the instantaneous acceleration of the block, and the displacement is the slid­

ing displacement of the block relative to the base. It is usually assumed

that resistance to uphill sliding is large enough that all displacements are

downhill. This assumption, in addition to simplifying the calculations, 1S

both realistic and conservative (Franklin and Chang 1977).

12. If the base (i.e., the inclined plane) is subjected to some se­

quence of acceleration pulses (the earthquake) large enough to induce s~iding

of the block, the result will be that after the motion has abated, the block

will come to rest at some displaced position down the slope. The amount of

permanent displacement, which will be called u, can be computed by using

Newton's second law of motion, F = rna , to write the equation of motion for

the sliding block relative to the base, and then numer1cally or graphically

integrating (twice) to obtain the resultant displacement. During the time

intervals when relative motion is occurring, the acceleration of the block

relative to the base is given by

cos (~ - e - ~) u = = (abase N) (1)a r e l cos ~

- (a N)\ . a- \ base ­

where

a = relative acceleration between the block and the inclined planer e l

a = acceleration of the inclined plane, a function of timebase N = critical acceleration level at which sliding begins

~ = direction of the resultant shear force and displacement, and the inclination of the plane

e = direction of the acceleration, measured from the horizontal

~ = friction angle between the block and the plane

The acceleration a is the earthquake acceleration acting at the level ofbase

the sliding mass in the embankment. It is assumed to be equal to the bedrock

acceleration multiplied by an amplification factor that accounts for the

q~asi-elastic response of the embankment.

13. The permanent displacement is determined by twice integrating the

relative accelerations over the total duration of the earthquake record. It 1S

assumed that ~, ~,and e do not change with time; thus, the coefficient

10 "'

a is a constant and is not involved in the integration. In the final stage

of analysis, the result of the integration is multiplied by the coefficient

a , the determination of which requires knowledge of the embankment properties

and the results of the pseudostatic stability analysis. For most practical

problems, the coefficient a differs from unity by less than 15 percent (Fig­

ure 6). For the purposes of this report, a value of unity will be assumed.

45, » .. } ,. I I II

en CD CD "­CD CD

"C

Q:)

I

~ 15

a= 1.0 1.3

o r I ! I

o 15 30 45

¢. degrees

Figure 6. Values of the coefficient a

14. The integration can be easily visualized on a plot of base velocity

versus time, obtained by a single integration of the acceleration record (Fig­

ure 5e). Since the slope of the velocity curve is the acceleration, the

limiting acceleration Ng of the block defines .the velocity curve for the

block by straight lines in those parts of the plot where the critical accel­

eration has been exceeded in the base. The area between the curves gives the

relative displacement.

15. In this analysis, the characteristics of the sliding mass in the

embankment are represented only by the critical acceleration N and the am­

plification factor, the latter being simply a constant multiplying factor.

The permanent displacement u for a particular earthquake record can be de­

termined as a function of N/A ,where Ag is the peak value of the earth­

quake acceleration, and the u versus N/A curve can be determined from the

earthquake record without reference to a particular embankment.

11

16. Kutter (1982) has done limited experimental testing of this method

by means of model embankments shaken by simulated earthquakes in the Cambridge

University geotechnical centrifuge. For these tests, the sliding block model

gave poor predictions of very small displacements «1 em), but if strength

degradation was provided for, it produced good predictions when the displace­

ments at prototype scale were greater than about 1 cm.

17. The following example, drawn from Kutter's test results for embank­

ment model D and earthquake I , demonstrates the application of the dis­

placement calculation procedures described herein. If the yield acceleration

for the embankment model is calculated on the basis of 80 percent of the mea­

sured shear strength, and the measured amplification of the base motion is in­

cluded, the predicted displacement is 15.0 em and the corresponding measured

displacement is 16.4 em at the prototype scale.

18. Sliding block analyses have been done at the WtS for 348 horizontal

earthquake components and 6 synthetic records. These calculations are tabu­

lated in Appendix A. The results are summarized in Figure 7, which shows the

mean, mean plus one standard deviation (a), and upper bound curves, for all

natural records and all synthetic records representing magnitudes smaller than

8.0. (Caution is recommended in interpreting these curves quantitatively In

terms of relative probability, because the data base is biased by over­

representation of a single earthquake, the 1971 San Fernando earthquake, which

produced records at many locations.)

19. The question of how much deformation is tolerable has no single

answer; it depends on such factors as the size and geometry of the dam, the

zonation, the location of the sliding surface, and the amount of freeboard

available. The authors have arbitratily chosen 1 m of permanent displacement

as a tolerable upper limit. Such a deformation would surely be considered

serious damage, but it could be tolerated in most dams without immediately

threatening the integrity of the reservoir. The unusual cases where a dam

could not tolerate 1 m of displacement, because of small freeboard or vulner­

ability of critical design features to small displacements, should be evalu­

ated by other methods.

20. When Figure 7 is entered at 100 em (1 m) of displacement, the cor­

responding N/A value is 0.17. Thus, deformations will be limited to less

than 1 m of displacement if the critical acceleration is as much as 0.17 times

the peak acceleration on the sliding surface.

12

1000' I I

"'.0;061

"'6

-E o 100'

0", /)0'

I" 11

""= "I"" I-::s

1 0 I I

0.01 0.1 1.0

N/A

Figure 7. Permanent displacement u versus N/A , based on 348 horizontal components and 6 synthetic accelerograms

Embankment Response Analysis

21. Amplification of ground motions in the embankments may be examined

by analysis of a shear-beam model of the embankment-foundation system. A

closed-form solution has been obtained by Sarma (1979) for the problem illus­

trated by Figure 8. The model considered is an untruncated triangular wedge

of height hI with a shear-wave velocity SI and density PI ' underlain by

a foundation layer with thickness h ' shear-wave velocity S2 ' and density2 P2' Both the wedge and foundation are linearly visco-elastic and have the

Isame damping ratio D. The earthquake motions are considered to be rigid-body

I

I 13

T 81 , P 1 ,D

h2 8 2 , P2 ,D

~f~~~~~~~~ -- at t)

Figure 8. Mathematical model for viscoelastic shear beam analysis of embankment and foundation response

by the Sarma method

motions in the rock underlying the foundation layer, and it is assumed that

all motions are horizontal (hence, a shear-beam model). Shear-wave veloc­

ities and damping values are chosen so as to be consistent with expected

strain levels. The computation of accelerations is carried out in the time

domain.

22. Geometry and material properties are described in terms of the

dimensionless parameters m and q , which are defined as

P1 S1 Sl h2 m =-- and q =-- (2)

P2S2 S2h 1

23. For use with the sliding block analysis, accelerations are averaged

over a wedge that is selected to be approximately equivalent in volume and

location to a potential sliding mass with its base at some chosen elevation,

as shown in Figure 9. The average acceleration acting on the wedge at any

instant is taken as

a av

=JAa(z) A

dA (3)

where a(z) is the acceleration of the area element dA, at elevation z ,

and A is the total area of the wedge.

24. The largest average acceleration that acts on the wedge at any time

during the earthquake shaking is produced as the output of the computer pro­

gram, and the ratio of that acceleration value to the peak bedrock accelera­

tion is taken as the amplification factor for the wedge. In Figure 10, values

of the amplification factor are plotted against the embankment fundamental pe­

riod T for one record of the Parkfield earthquake of 27 June 1966. Curves o

14 "'.

c o /C'J o::> ill

ill

TT1

~...8?~/:::V~/~~f~Aa amplification factor

Figure 9. Computation of average acceleration acting on the sliding mass

3.0

-o

I ­

02.0

C'J-C 0--C'J o

- 1.0 a. E ca

0

m = 0.5

q =O. 5

damping =20%

0.1 0.5 1.0 4.0

fundamental period, seconds

Figure 10. A~plification curves for the S 25 Wcomponent, Temblor No. 2 Record, Parkfield earthquake of 27 June 1966

(damping = 20 percent)

are shown for wedges with their bases at various distances y/h (defined1

in Figure 9) from the crest, for a single combination of m and q values

(m = 0.5, q = 0.5).

25. Amplification curves have been obtained from 27 strong-motion

earthquake records and a wide range of m and q values (representing em­

bankments on rock and on foundation layers of varied thickness, and with a

variety of relative embankment-foundation stiffnesses). Damping values used

ranged from 15 to 20 percent. Also, numerous computed amplification values

have been obtained from finite element analyses and from the literature.

15 "

Figure 11 presents a summary of computed resonant response, obtained by plot­

ting the values at the peaks of the amplification curves. Table 1 shows these

peak amplification values. Amplification values obtained from finite element

analyses, which do not necessarily represent resonant conditions, are gener­

ally lower than these curves indicate.

26. To use these curves in a permanent displacement analysis, pick off

the amplification factor for the depth of sliding being investigated, and mul­

tiply the peak bedrock acceleration by that value before entering the plot of

displacement versus N/A. This step involves an assumption that the sliding

block analysis and the amplification analysis can be decoupled. In fact,

there is good reason to believe that decoupling results in overestimates of

the amplification when very strong shaking is involved. The amplification may

be large in cases where the motions are small and the embankment behavior is

nearly elastic (Gazetas, et al. 1981), but this assumption is not compatible

with inelastic embankment response. If accelerations are high enough to pro­

duce sliding on a deep surface, then the embankment is incapable of propa­

gating these large accelerations to higher elevations. The critical accelera­

tion on a slip surface defines the magnitude of acceleration that can be prop­

agated beyond it. At the same time, the critical acceleration always de­

creases with depth, in a homogeneous section with constant slopes.

27. A note of caution is in order for dams with abrupt changes in sec­

tion or zoning that would cause a reduction in yield accelerations for slip

surfaces above the base of the embankment. For example, some dams have slopes

that steepen abruptly near the crest. However, for upstream slip surfaces,

the reduction in yield acceleration due to steeper slopes is usually more

than offset by an increase due to lower pore pressures if the steeper

section lies above the pool elevation. Upstream or downstream berms will also

result in relatively reduced yield accelerations for slip surfaces that lie

entirely above the berms. For these or similar cases, a profile of yield ac­

celerations can be developed from stability analyses; Figure 11 can be used to

estimate amplification factors; and potential displacement can be calculated

from Figure 7 for each of the potential slip surfaces identified in the sta­

bility analyses.

28. The authors conclude that, except for a few special cases, deep

sliding surfaces are of greatest significance when evaluating the possibility

of displacements that could threaten the integrity of the structure, and

16

l-

l l I·

· i

· .,

:1

u J

CREST 0 u 1 u

I

I J

u 0.4

y Ih 1

0.6

, I

..I

1 I 0.8

J

u

BAS E 1.0 !

I I I I I

0.2 l- t

/S!l ~~~~~

I

o 1.0 2.0 3.0 4.0 u

amplification factor

i

5.0 I , , ! , !

Figure 11. Amplification factors for linearly viscoelasticJ embankments at resonance

...

17

-l

accordingly, they look for a limiting amplification factor representing slid­

i.rig surfaces at the base of the embankment. Figure 11 shows that the value al

the mean plus 2a limit is approximately 3.0. Applying this amplification fac­

tor to the N/A value, 0.17, which gives an upper bound of 1-m displacement

for the rigid-plastic sliding block, the ratio of critical acceleration to

peak bedrock acceleration is 0.5.

r

~

~

18

1 ]

PART III: CONCLUSIONS

29. The results of analysis of earthquake strong-motion records using a , j

sliding block model and a decoupled elastic response analysis

manent displacements for deep-seated sliding surfaces limited

show that per­

to less than 1 m

n carr be assured if tbe ratio of critical acceleration to peak bedrock accelera­

tion is at least 0.5. This value is considered to be very conservative and

subject to downward revision as better understanding of elastic-plastic ampli­

fication response of embankments is developed.

30. Furthermore, a pseudostatic, seismic coefficient analysis can serve

as a useful screening procedure to separate dams that are clearly safe against ~

earthquake-induced sliding failure from those that require further analysis.

The permarrent displacement analyses described in this report provide a ra­

tional basis for choosing the value of the seismic coefficient.

31. The suggested procedure is as follows:

a. Carry out a conventional pseudostatic stability analysis, using - a seismic coefficient equal to one-half the predicted peak bed­

rock acceleration.

b. Use a composite S-R strength envelope for pervious soils, and - the R (undrained) strength for clays, multiplying the shear

strength in either case by 0.8.

c. Use a minimum factor of safety of 1.0.

32. This procedure should not be used in the following cases:

a. wbere areas are subject to great earthquakes (of magnitude 8.0 or greater).

b. wbere materials in either the embankment or foundation are sus­ceptible to liquefaction under the design cyclic loading.

c. wbere the available freeboard is small, or where the dam has safety-related features that are vulnerable to small deformations.

19

-------.."""""-,-"""~-...~~~~~.J~~::.~~"':'~~~~:.,~:'>'~~::~_~~

REFERENCES

Ambraseys, N. N., and Sarma, S. K. 1967. "The Response of Earth Dams to Strong Earthquakes," Geotechnique, Vol 17, No.2, pp 181-213.

Bishop, A. W. 1955. "The Use of the Slip Circle in the Stability Analysis of Slopes," Geotechnique, Vol 5, No.1, pp 7-17.

Franklin, A. G., and Chang, F. K. 1977. "Earthquake Resistance of Earth and Rock-Fill Dams; Permanent Displacements of Earth Embankments by Newmark Slid­ing Block Analysis," Miscellaneous Paper S-71-17, Report 5, U. S. Army Engi­neer Waterways Experiment Station, CE, Vicksburg, Miss.

Franklin, A. G., and Hynes-Griffin, M. E. 1981. "Dynamic Analysis of Embank­ment Sections, Richard B. Russel Dam," Proceedings, Earthquakes and Earthquake Engineering - The Eastern United States Conference, Knoxville, Tenn.

Gazetas, G., Debchaudhury, A., and Gasparini, D. A. 1981. "Random Vibration Analysis for the Seismic Response of Earth Dams," Geotechnique, Vol 31, No.2, pp 261-277.

Goodman, R. E., and Seed, H. B. 1966. "Earthquake-Induced Displacements in Sand Embankment," Journal of the Soil Mechanics and Foundations Division, A~erican Society of Civil Engineers, Vol 92, No. SM2, pp 125-146.

Jennings, P. C., Housner, G. W., and Tsai, N. C. 1968. "Simulated Earthquake Motions," Earthquake Engineering Research Laboratory Report, California Institute of Technology.

Kutter, B. L. 1982. "Centrifugal Modelling of the Response of Clay Embank­ments to Earthquakes," Ph.D. dissertation, Cambridge University.

Makdisi, F. I., and Seed, H. B. 1977. "Simplified Procedure for Estimating Darn and Embankment Earthquake-Induced Deformations," Journal of the Geotech­nical Engineering Division, American Society of Civil Engineers, Vol 104, No. GT7, pp 849-867.

Morgenstern, N. R., and Price, V. E. 1965. "The Analysis of the Stability of General Slip Surfaces," Geotechnique, Vol 15, No.1, pp 79-93.

Newmark, N. M. 1965. "Effects of Earthquakes on Dams and Embankments," Geo­technique, Vol 15, No.2, pp 139-160.

Sarma, S. K. 1975. "Seismic Stability of Earth Dams and Embankments," Geo­technique, Vol 25, No.4, pp 743-761.

1979. "Response and Stability of Earth Dams During Strong Earth­quakes," Miscellaneous Paper GL-79-13, U. S. Army Engineer Waterways Experi­ment Station, CE, Vicksburg, Miss. .

Seed, H. B. 1979. "Considerations in the Earthquake-Resistant Design of Earth and Rockfill Dams," Geotechnigue, Vol 29, No.3, pp 215-263.

Seed, H. B., and Ld r i s s , I. M. 1969. "Rock Motion Accelerograms for High Magnitude Earthquakes," EERC 69-7, Earthquake Engineering Research Center, University of California, Berkeley, Calif.

1983. "Evaluation of Liquefaction Potential Using Field Per­formance Data," Journal of the Geotechnical Engineering Division, American Society of Civil Engineers, Vol 109, No.3, pp 458-482.

20

Seed, H. B., Idriss, 1. 11., Lee, K. 1., and Hakdisi, F. 1. 19753. "Dynamic Analysis of the Slide in the Lower San Fernando Darn During the Earthquake of 9 February 1971," Journal of the Geotechnical Engineering Division, American Society of Civil Engineers, Vol 101, No. GT9, pp 889-911.

1975b. "The Slides in the San Fernando Darns During the Earthquake of February 9, 1971," Journal of the Geotechnical Engineering Division, American Society of Civil Engineers, Vol 101, No. GT7, pp 651-688.

U. S. Army, Office, Chief of Engineers. 1970. "Engineering and Design - Sta­bility of Earth and Rock-Fill Dams," Engineer l1anual 1110-2-1902, Washington, D. C.

21

Tab

le

1

Am

pli

fica

tio

n F

acto

rs

for

Em

bank

men

t R

espo

nse

at

Res

onan

ce

Am

plI

fica

tio

n F

acto

r

'L

y -

hi

+ h

2 h

I h 2

Dam

ping

m

~

0

.2

0.4

0

.6

0.8

1

.0

1.2

1.

r-1

.6

--­

--­

1.8

2

.0

Per

cen

t A

ccel

erog

ram

0 0

2,6B

2

.50

2

.31

2

.06

1.

77

-­20

0,5

0.

125

2.8

9

2.5

8

2.4

1

2.1B

1.

63

1. 5

6

0,5

0.

25

3.3

4

2.9

2

2.5

5

2.3

5

2.1

0

1. 6

4 I.

56

I. 4

4

0.5

0.

375

3.5

0

3.1

6

2.7

7

2.5

4

2.2

9

2.0

3

I. 8

0 I.

61

I. 4

9 -­

Max

imum

of

9

reco

rds:

0.5

0

.5

3.47

3

.20

2.

B8

2.6

6

2.4

'\

2.2

0

1. 9

9 I.

BO

1. 6

1 1.

51

a.

San

Fer

nand

o 19

71,

Pac

oim

a,

0.5

0.

75

3.15

2.

9B

2. B

I 2

.65

2.

51

2.3

3

2.1

7

2.0

3

1. 9

2 I.

79

3 co

mpo

nent

s

0.5

1.

00

2.7f

'. 2.

71

2.64

2.

57

2.49

2

.37

2

.26

2.

15

2,07

I.

9B

b.

El

Cen

tro

1940

, 2

com

pone

nts

1. 0

0 0.

25

2.6

6

2.5

5

2.43

2

.26

2.

07

1. B

5 1.

78

-­c.

K

oyna

196

7,

2 co

mpo

nent

s

I.00

0

.50

2

.54

2

.49

2.

41

2,3

2

2.1

7

2.0

2

1. B

5 1.

75

-­d.

Pa

rkf

i eId

19

66,

Cho

l am

e ,

I co

mpo

nent

I. 0

0 0

.75

2

.46

2

.44

2.

39

2.3

2

2.2

2

2.11

1.

98

1. 8

4 1.

71

-­e.

P

ort

Hue

nem

e 19

57,

1 co

mpo

nent

1. 0

0 1.

00

2.42

2

.40

2

.36

2.

31

2.2

3

2.15

2

.06

1.

94

1. B

3 I.

70

.1.0

0 1.

50

2.37

2

.36

2.

33

2,31

2

.26

2

.20

2

.14

2.

07

1. 9

9 1.

92

1. 0

0 2

.00

2

.36

2

.35

2.

33

2.3

0

2.2

7

2,24

2

.19

2.

13

2,O

B

2.0

3

0.8

O

.B

2.57

2

.53

2.

47

2,40

2

.30

2,

IB

2.0

7

1. 9

3 1.

79

I.66

0 0

2.5B

2

.29

1.

B9

1.66

1.

43

-­H

elen

a 19

35,

Car

roll

C

oll

ege,

E-

W

o 5

0.18

5 3

.16

2

,65

2.

19

1.8

2

1. 6

2 -­

Hel

ena

1935

, C

arro

ll

Co

lleg

e,

E-W

o 5

0.5

2.

9B

2.77

2.

41

2.2

3

1.95

-­

Hel

ena

1935

, C

arro

ll

Co

lleg

e,

E-W

0 0

2.9B

2

.70

2

.62

1.

91

1. 5

7 --

Par

kfi

eld

19

66,

Tem

blor

No

.2,

S 25

W

0.5

0,

185

3.3

4

3.0

4

2.5

8

2.19

1.

79

--P

ark

fiel

d

1966

, T

embl

or

No

.2,

S 25

W

0.5

0

.5

3.3

8

3.2

3

2.97

2

.66

2.

31

--P

ark

fiel

d

1966

, T

embl

or N

o.2

, S

25 W

()

0 2

55

2.4

4

2.25

2.

01

1.71

--

Oro

vil

le

1975

, O

rov

ille

Dam

, N

53

W

0.5

0.

185

2 68

2

.56

2.

41

2.2

0

1. 9

5 --

Oro

vil

le

1975

, O

rov

ille

Dam

, N

53

W

0.5

0

.5

2 69

2.

67

2.61

2.

51

2.35

--

Oro

vil

le

1975

, O

rov

ille

Dam

, N

53

W

0 0

2.31

2.

04

1. 9

6 1.

82

I. 6

3 --

San

Fer

nand

o 19

71,

Gri

ffit

h P

ark

, N-

W

O. "

()

185

2.61

>

2.31

2.

07

I. 9

5 1.

7B

-­

San

Fer

nand

o 19

71,

Gri

ffit

h

Par

k,

N-W

0,5

0

.5

2.61

2.

44

-­-­

--Sa

n F

erna

ndo

1971

, G

riff

i t h

Par

k,

N-W

(Con

tinu

ed)

(Sh

e,o

l I

of

3)

-)

---

Tab

le

1 (C

onti

nued

)

Y-

hI

t L

hh 2

hI

2

Dam

ping

m

0

.2

0.4

0

.6

0.8

1

.0

1.2

1.4

1.6

1.8

2

.0

Per

cen

t A

ccel

erog

ram

--

..!L­

0 0

2.01

1.

90

1. 7

3 1.

54

1. 3

1 --

20

San

Fern

ando

19

71,

Cas

taic

N 6

9 W

0.5

0.18

5 2.

26

2.13

1.

88

1.68

1.

48

--Sa

n Fe

rnan

do

1971

, C

asta

ic N

69

W

0.5

0

.5

2.47

2.

38

2.24

2.

02

1. 8

2 --

San

Fern

ando

19

71,

Cas

taic

N 6

9 W

0 0

2.19

1.

96

--Sa

n Fe

rnan

do

1971

, C

asta

ic N

21

E

0.5

0.18

5 2.

57

2.22

--

San

Fern

ando

19

71,

Cas

taic

N 2

1 E

0.5

0.5

2.09

2.

52

2.26

--

San

Fern

ando

19

71,

Cas

taic

N 2

1 E

0.5

0.

5 4.

36

4.02

3.

61

3.19

2.

73

2.21

1.

84

1.65

1.

53

1. 4

4 15

E

l C

entr

o A

rray

N

o.

10,

Key

ston

e R

oad,

N

50

E,

10/1

5/79

I.

00

0.5

3.43

3.

26

3.03

2.

78

2.50

2.

15

1. 9

7 1.

79

1.73

1.

67

El

Cen

tro

Arr

ay

No.

10

, K

eyst

one

Roa

d,

N 5

0 E

, 10

/15/

79

0.5

0.

5 3.

30

3.14

2.

85

2.55

2.

39

2.16

1.

97

1.84

1.

75

1. 6

6 Im

peri

al V

alle

y E

arth

quak

e,

Ho

ltv

ille

P

ost

Off

ice,

S 4

5 W

, 10

/15/

79

1.0

0.

5 2.

70

2.60

2.

54

2.44

2.

30

2.13

2.

02

1. 9

1 1.

85

1. 7

8 Im

peri

al V

alle

y E

arth

quak

e,

Ho

ltv

ille

P

ost

Off

ice,

S

45 W

, 10

/15/

79

0.5

0.

5 4.

58

4.40

4.

12

3.78

3.

38

2.91

2.

44

2.17

1.

99

1. 8

5 Im

peri

al V

alle

y E

arth

quak

e,

Ho

ltv

ille

P

ost

Off

ice,

N

45

W,

10/1

5/79

1.

0

0.5

3.92

3.

81

3.63

3.

41

3.15

2.

86

2.67

2.

47

2.38

2.

29

Impe

rial

V

alle

y E

arth

quak

e,

Ho

ltv

ille

P

ost

Off

ice,

N

45

W,

10/1

5/79

0.

5

0.5

4.

01

3.81

3.

49

3.08

2.

64

2.19

1.

79

1. 6

0 1.

50

1. 3

9 I

Wes

tern

Was

hing

ton

Ear

thqu

ake,

U

. S.

A

rmy

Bas

e ST

A 00

00,

S 02

W,

4/13

/49

1.0

0.

5 3.

24

3.08

2.

85

2.59

2.

38

2.14

1.

99

1. 8

3 1.

76

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8 W

este

rn

Was

hing

ton

Ear

thqu

ake,

U

. S.

A

rmy

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e ST

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W,

4/13

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0.5

0.

5 3.

95

3.75

3.

44

3.09

2.

72

2.26

1.

83

1. 6

0 1.

51

1.44

Im

peri

al V

alle

y E

arth

quak

e,

El

Cen

tro

Arr

ay

No

.3,

Pine

U

nion

Sch

ool,

S

40 E

, 10

/15/

79

I 1.

0

0.5

3.25

3.

14

2.97

2.

75

2.50

2.

22

2.05

1.

87

1. 7

9 1.

71

I Im

peri

al V

alle

y E

arth

quak

e,

El

Cen

tro

Arr

ay

No

.3,

Pine

U

nion

Sch

ool,

S

40 E

, 10

/15/

79

0.5

0.

5 3.

32

3.21

3.

02

2.78

2.

49

2.14

I.

84

1.65

I.

53

I. 4

3 I

Impe

rial

V

alle

y E

arth

quak

e,

£1 C

entr

o A

rray

N

o.3

, Pi

ne

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on S

choo

l,

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1.

0

. 0.

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78

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2.

62

2.48

2.

30

2.09

1.

98

I.86

I.

81

I. 7

5 I

Impe

rial

V

alle

y E

arth

quak

e,

El

Cen

tro

Arr

ay

No

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Pine

U~ion

S

choo

l,

S 50

W,

10/1

5/79

0.

5

0.5

3.13

2.

93

2.63

2.

35

2.09

1.

80

1. 5

3 1.

40

1. 3

2 1.

25

I E

l C

entr

o A

rray

N

o.

10,

Key

ston

e R

oad,

N

40

W,

10/1

5/79

1.

0 0.

5 2.

41

2.35

2.

24

2. 1

1 1.

95,

1.77

I.

66

I.54

I.

50

I. 4

6 I

£1 C

entr

o A

rray

N

o.

10,

Key

ston

e R

oad,

N

40

W,

10/1

5/79

(C

onti

nued

) (S

heet

2

of

3)

:= :11

--

iIiii

i;;;

----

-....

iiiiiii

Tab

le

1 (C

oncl

uded

)

~

0.4

L hI

0.6

0

.8

1.0

1

.2

y

-!..:

..L

-hI

+

h2

h 2 1

.6

1.8

2

.0

Sum

mar

y V

alue

s o

f A

mp

lifi

cati

on

Fac

tors

Ave

rage

2

.95

2

.77

2

.61

2

.40

2

.17

2

.14

1.

98

1. 8

3 1

. 76

1

.69

(a)

Ave

rage

+

a

(0.5

8)

3.5

3

(0.5

4)

3.3

1

(0.5

0)

3.1

1

(0.4

6)

2.8

6

(0.4

4)

2.6

1

(0.2

9)

2.4

3

(0.2

5)

2.2

3

(0.2

5)

2.D

8

(0.2

5)

2.0

1

(0.2

5)

1. 9

4

Max

imum

4

.58

4

.40

4

.12

3

.78

3

.38

2

.91

2

.67

2

.47

2

.38

2

.29

(Sh

eet

3 o

f 3)

APPENDIX A

TABLES OF SLIDING BLOCK CALCULATIONS FOR STRONG-MOTION DATA FROM E~~.THQUAKES OF THE WESTERN L~ITED STATES AlfD OTHER COVNTRIES, AND

SYNTHETIC ACCELEROGRAMS

•••Tab

le

AI

Str

on

l-M

oli

on

D

.la

l E

e r

rhq

uek

es

ol

Wes

tern

U

nil

ed

Sta

tes

(Un

llo

r.l

y

Pro

cess

ed

at

C.l

ilo

rn

la

Ins

tit

ut

e o

f T

ech

no

lou

L

and

Oth

er

Co

un

triu

'ITA

V

P

eak

Pl"

'.kCI

T S

illf

D

ale

P

eak

Dil

ph

ce­

Ep

i cen

t re

I R

ich

ler

Ho

dd

ied

Acr

e le

r e t

i oe

fi It

C

l...

tfi­

of

[pi

cen

te r

l11s

lrL

iale

nl

Velo

cit

y

..0'

Ili s

t an

ce

tba

nil

ud

e H

erce

llI

D

ure

t io

n V

.lu

es

ol

u (c

m)

lor

N/'"

;:

~~

R

eto

rdJ

08

S

ldlo

n

cal

ion"

* E

Ulh

qu

ak

e L

ora

lio

n _

C

o.p

onen

t

c.

__

H__

In

len

l il

y

~.

0.

1 O~I

.~~

.s

siss

s:

~--

""-­

AO

OI

[1

Cen

tro

S

ite,

lep

er

i el

Va

lley

1

-18

-.0

J2

°44

1 S

00

· £

3.1

.1

B.'

1

0.9

9

.3

6.7

V

III

JO

16

\.3

(1

90

.7)'

J8

.81

(1

1.8

7)'

I.J

' (0

.19

),

11

5'2

1'

S 90

° \II

2

10

.1

36

.9

19

.8

13

19

1.8

(2

13

.9)

17

.68

(.

9.9

) 1

.88

(1

23

) U

p 2

06

.3

10

.8

1.6

1.00

2 N

ort

hw

es

t C

el i

Icrr

ue

Ea

r t h

­10

-)-

11

4

0·1

7'

N

S •

•'

W

10

2.0

4

.8

2.•

1

6.3

q

uak

e,

Fern

da

le

Cit

y

Hal

l 1

2'°

'8'

W

H .

6'

W

10

9.1

7

.'

2.7

U

p 26

.•

2.2

1

.6

1.00

3 K

ern

Cou

nty

[Ulh

qu

..ke

,

)-2

1-1

2

35

·00

. S

000

[ .6

.1

6.2

2

.7

12

6.0

7

.7

VII

10

(8

0.3

1)

(27

.03

) (0

.94

) A

lhR

U"

"

11

9'0

2 '

S 9

0'

W

12

.1

9.1

2

.9

50

8••

08

(13

1.1

3)

3'.

17

(.

1.1

11

1

.\1

(2

.\ 7

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