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1984 Hynes-Griffin and Franklin - Seismic Coefficient
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Transcript of 1984 Hynes-Griffin and Franklin - Seismic Coefficient
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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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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_
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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.
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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
1. 6
8 W
este
rn
Was
hing
ton
Ear
thqu
ake,
U
. S.
A
rmy
Bas
e ST
A 00
00,
S 02
W,
4/13
/49
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
Uni
on S
choo
l,
S 50
W,
10/1
5/79
1.
0
. 0.
5 2.
78
2.71
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
.3,
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
) U
p 2
9.3
4.
1 3
.0
1.00
4 K
ern
Cou
nty
[ulh
qu
d,r
.
)-2
1-1
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---------------------------------_
._
--
(Sh
Ul
11 or
11)
Tab
le
A2
S
yn
theti
c
Ear
thq
uak
e R
eco
rds
Sim
ula
ted
E
arth
qu
ake
T~
Ap
pro
xim
ate
Mag
nitu
de
A
Max
imum
A
ccele
rati
on
2
em/s
ec
V
Max
imum
V
elo
cit
y
em/s
ec
D
Max
imum
D
isp
lace
al
ent
em
AD
V2
V2
AD
Ap
pro
xim
ate
Pre
do
min
ant
Per
iod
se
c
To
tal
Du
rati
on
se
c 0
.02
V
alu
es
of
u (e
m)
0.1
fo
r N
/A
0.5
Cl1
'*
A-I
8+
3
82
.77
5
8.9
9
39
.83
4
.38
0
.22
8
0.5
0
120
15
01
.85
(1
57
0.9
5)t
4
53
.64
(4
39
.10
)t
15
.72
(8
.09
)t
A-2
8+
4
41
. 64
55
.05
7
2.9
7
10
.63
0
.09
4
0.3
5
120
14
09
.44
(1
40
9.4
4)
38
9.0
7
(39
1.8
1)
2.5
3
(5.5
5)
B-1
7
36
8.1
2
45
.72
3
3.1
7
5.8
4
0.1
71
0
.20
50
5
95
.09
1
69
.78
3
.57
B-2
7
30
8.7
0
48
.26
2
2.2
2
2.9
4
0.3
39
0
.22
50
4
92
.66
15
9. 1
9 5
.13
C-l
6
66
.93
6
.65
1.
36
2.0
6
0.4
86
0
.15
12
2
2.5
9
9.9
1
0.8
2
C-2
6
57
.23
6
.09
0
.88
1.
36
0.7
36
0
.20
12
2
6.8
9
9.9
1
0.4
6
D-l
5
47
0.4
0
26
.67
4
.88
3
.23
0
.31
0
0.1
5
10
80
.89
2
4.4
9
I. 5
4
D-2
5
49
0.0
0
28
.94
6
.84
4
.00
0
.24
5
0.1
5
10
74
.69
1
7.6
0
0.5
9
See
d
8-1
/4
41
2.2
1
57
.76
-
--
0.4
0
73
12
56
.10
(1
26
9.8
6)
45
1.6
1
(42
4.9
0)
8.0
1
(11
.65
) Id
riss
**
NRC
34
3.0
0
51
. 40
34
5.8
4
13
3.2
5
3.6
2
* ** r
Jen
nin
gs,
H
ou
sner
, an
d T
sai
(19
68
).
Seed
an
d ld
riss
(19
69
).
Val
ues
in
p
are
nth
ese
s are
fo
r re
ver
sed
d
irecti
on
o
f sh
akin
g.
}