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Earthquake Input
EARTHQUAKE EXCITATION CONCEPTS
In evaluating the earthquake performance of concrete dams, it is evident
that descriptions of the earthquake ground motions and the manner in which
these motions excite dynamic response are of paramount importance. The
procedure that leads to the selection of the seismic input for concrete dams
is similar, in general, to that for other large important structures such as
nuclear power plants and longspan bridges. It involves the study of the
regional geologic setting, the history of seismic activity in the area, the
geologic structure along the path from source to site, and the local geotechnical
conditions. Ground motion parameters that may be utilized in characterizing
earthquake motions include peak acceleration (or effective peak acceleration),
duration, and frequency content of the accelerogram. However, the methods
of selecting such seismic parameters for the purpose of generating input
ground motions or response spectra are well documented (21) and are not
repeated here.
The focus of this chapter is on the specification of earthquake input
motions to be used in the analysis of concrete damreservoirfoundation
systems. Obviously, the level of sophistication to be used in defining the
seismic input is closely related to the degree of understanding of the dynamic
behavior of the dam system and to capabilities for modeling such behavior.
Thus, progress in defining seismic input has followed a long evolutionary
process parallel to that of the dynamic analysis capability. It is not surprising,
therefore, that the earliest method of defining earthquake input to concrete
dams was merely to apply a distributed horizontal force amounting to a
uniform specified fraction (typically 10 percent) of the weight of the dam
body. This force was intended to represent the inertial resistance of a rigid
16
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17
dam subjected to the horizontal motion of a rigid foundation. The procedure
was easily extended in an approximate sense to include the hydrodynamic
pressure effects of the reservoir water by invoking the added mass concept
(i.e., assuming that a portion of the reservoir water would move together
with the dam body).
Major improvements over the rigid dam approach resulted when the dynamic
effects of dam deformability, i.e., the free vibration behavior, were recognized.
The first improvement was to convert the equivalent static force from a
uniform distribution to a form related to the dam fundamental vibration
mode shape. The second improvement was to account for the amplification
of the base input motions in the response of the dam. Representing these
frequencydependent amplification effects by means of the earthquake response
spectrum provided an appropriate amplitude of equivalent static load distribution
to be used in the response analysis. The basic assumption of all these
methods of analysis is that the foundation rock supporting the dam is rigid,
so the specified earthquake motions are applied uniformly over the entire
damfoundation interface.
However, as the methods of response analysis improved, it became apparent
that the rigid base earthquake input no longer was appropriate. Because of
the great extent of the dam, and recognizing the wave propagation mechanisms
by which earthquake motions are propagated through the foundation rock, it
is important to account for spatial variation of the earthquake motions at the
damfoundation interface; these spatial variations also may result from "scattering"
of the propagating earthquake waves by the topography near the dam site.
A brief discussion of basic procedures for defining seismic input is presented
in a recent report (22~; the essential concepts contained in that report are
summarized in the following paragraphs.
Standard Base Input Model
The dam is assumed to be supported by a large region of deformable
rock, which in turn is supported by a rigid base boundary, as shown in
Figure 2la. The seismic input is defined as a history of motion of this
rigid base, but it is important to note that the motions at this depth in the
foundation rock are not the same as the freefield motions recorded at ground
surface.
Massless Foundation Rock Model
An improved version of the preceding model is obtained by neglecting
the mass of the rock in the deformable foundation region. This has the
effect of eliminating wave propagation mechanisms in the deformable rock,
so that motions prescribed at the rigid base are transmitted directly to the
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18
,~
CANYON —
WALL ~
DEFORMABLE FOUNDATION ROCK
__ _~ ~ ~ ~ ~ / ~ ~ ~ ~ ~ ~ / ~ ~ ~ / ~ ~ / ~ ~ A
RIGID BASE —~ Vgz ( t )
SEISM IC INPUT ~~ ~V9x ( t )
Vgy(t)
FREE FIELD MOTION (MEASURED BY
HORIZONTALLY L AYERE D
FOUNDATION ROCK
RIGID BASE MOTION (CALCULATED BY
DECONVOLUTION )

?'MED SUPPORTED
APPROPRI ATE LY FOR
EACH EARTHQUAKE
CO M PO N E N T
~\\~",' /
i: CANYON
_' WALL
DEFO RMA B L E FOU NDATI O N ROC K
DECONVOLVED RIGID BASE MOTION
LIMIT OF FLEXIBLE
WON
i._. ~
1 At'
~ \ \: ~ CANYON INPUT AT
CAM I~TF~FArF
/~/~/
L'
FIGURE 21 Proposed seismic input models for concrete dams (22). (a) Standard rigid base
input model; mass of foundation rock either included or neglected. (b) Deconvolution of free
field surface motions to determine rigid base motions. (c) Analysis of twodimensional free
field canyon motions using deconvolved rigid base motions as input. (d) Analysis of three
dimensional damfoundation system response using twodimensional freefield canyon motions
as input.
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19
dam interface. With this assumption it is reasonable to prescribe recorded
freefield surface motions as the rigid base input.
Deconvolution Base Rock Input Model
In this approach, as illustrated in Figure 2lb, a deconvolution analysis
is performed on a horizontally uniform layer of deformable rock to determine
motions at the rigid base boundary that are consistent with the recorded
freefield surface motions. The resulting rigid base motion is then used in
the standard base input model. This procedure tends to be computationally
expensive because the mathematical model includes a large volume of foundation
rock in addition to the concrete dam.
FreeField Input Model
A variation of the preceding procedure is to apply the deconvolved rigid
base motion to a model of the deformable foundation rock without the dam
in place, in order to determine the freefield motions at the interface positions
where the dam is to be located. These calculated interface freefield motions
account for the scattering effects of the canyon topography on the earthquake
waves and are used as input to the combined damfoundation rock system.
In many cases of the form shown in Figure Alec), it may be reasonable to
assume twodimensional behavior in modeling the scattering effects and
then to apply these twodimensional freefield motions as input to a three
dimensional damcanyon system, as indicated by Figure 2l~d).
In the abovementioned report (22) these seismic input models are discussed
in the context of arch dam analysis, but they are equally applicable for
gravity dams when the foundation topography warrants a threedimensional
analysis. If the dam is relatively long and uniform, so that its response may
be considered to be twodimensional, the canyon scattering effect need not
be considered, but the seismic input still may vary spatially due to traveling
wave effects. It is important to note that all four of the input models listed
above include a rigid boundary at the base of the deformable foundation
rock; thus, vibration energy is not permitted to radiate from the model.
Elimination of this constraint is one of the key issues in present research on
seismic input procedures.
Of these four input models the freefield model usually is the most reasonable,
so a key element in the input definition is the determination of appropriate
freefield motions. Research progress in this area is discussed in the next
section.
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20
PRESENT STATUS OF KNOWLEDGE
Prediction of FreeField Motion
Definition of seismic input is very closely related to the way the dam
reservoirfoundation system is modeled. Although existing finite element
programs for the dynamic analysis of concrete dams (23, 24, 25) use
uniform base motion as input, these programs can be modified to accept
nonuniform earthquake excitation at the interface between dam and canyon
wall. In this case the freefield motion is defined as the motion of the dam
foundation contact surface due to seismic excitation without the presence of
the dam.
TwoDimensional Case Method
If the canyon where the dam is to be located has an essentially constant
cross section for some distance upstream and downstream, it may be treated
as a linearly elastic halfplane, and the problem of evaluating the earthquake
freefield motion can be formulated as a wavescattering problem with the
canyon as the scatterer. Various approaches have been used to obtain solutions
to the problem.
The case involving earthquake SH waves (i.e., horizontal shear waves) is
somewhat simpler in the sense that only outofplane displacements occur.
Closedform solutions have been obtained for semicircular canyons (26)
and for semielliptical canyons (27~. For cases with more general geometry,
further assumptions must be made in the formulation or He numerical solution
techniques. By using the method of images and integral equation formulation,
results have been obtained for SH wave scattering due to arbitrarily shaped
canyons by solving the integral equation numerically (28~. The same problem
also has been solved using a different integral equation formulation (29~;
in this approach the free boundary condition at the canyon wall is satisfied
in the least squares sense.
An integral equation approach that imposes an approximately satisfied
boundary condition also has been used in the solution of problems involving
P and SV waves (210) (i.e., compression and vertical shear waves). Similar
procedures have been used by others in solving P. SV, and Rayleigh wave
problems (211, 212~. A solution for incident SH, P. and SV waves also
has been obtained by assuming periodicity in the surface topography and a
downwardonly scattered wave (213~.
Direct numerical solution using a finite difference formulation has been
employed to evaluate the scattering effects of various surface irregularities
for example, a ridge with incident SH wave (214), vertically incident SV
and P waves on a step change in surface (215), and the use of nonreflecting
boundary conditions with other surface irregularities (216~.
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21
Direct finite element solutions also have been used to solve scattering
problems of P and SV waves incident on a mountain and on an alluvium
filled canyon (217), using more than one solution to obtain the canceling
effect on nonreflecting boundaries (218~. Standard planestrain soil dynamics
finite element programs with special treatment at nonreflecting boundaries
(219, 220, 221) reportedly have been used for P. SV, and SH waves with
a simple modification (2221. A particle model combined with finite element
modeling to account for an irregular surface has been used for SV waves
incident to cliff topography (223~. The freefield motions at Vshaped and
closetoVshaped canyons also have been studied using a combination of
finite and infinite elements in a model with finite depth that extends to
infinity horizontally (224~. In this case earthquake motions prescribed at
the rigid base of the foundation are taken as input to the system.
TwoDimensional Case Results
Results for a semicircular canyon are used as the basis of discussion here
because the most information is available for this simple geometry; some
reference also is made to cases involving other geometries, as depicted in
Figure 22. Results expressed in the frequency domain are described in
many cases to indicate the effects of wave frequency. Motions at the canyon
walls generally are found to be dependent on the ratio of canyon width to
wave length (wave frequency), on the angle of wave incidence, and on the
wave type. The effect of scattering is more significant when the wave
length is of the same order as or smaller than the canyon width. In comparison
with the freefield motion without any canyon, the freefield motion at the
canyon surface can be either amplified or reduced depending on the location
of the observation point, as shown in Figure 23. In general, motions near
the upper corner of the canyon facing the incident wave are amplified; the
amplification increases as the wave length decreases and as the direction of
incidence tends toward the horizontal. For incident SH, P. SV, and Rayleigh
waves, the maximum amplification is found to be 2 for semicircular and
semielliptical canyons (26, 27, 2121. However, this amplification factor
can be higher if the canyon surface has local convex regions, which tend to
trap energy (2~. Motion from SH and Rayleigh waves generally is reduced
near the bottom of the canyon. For Rayleigh waves and closetohorizontally
incident SH waves, the motion at the back side of the canyon also is often
reduced, but this shielding effect disappears for SV and P waves. For
vertically incident SH waves, the wall slope of a triangular canyon has
significant effects on the motion at the wall surface (29~; steeper slopes
lead to greater reductions in motion near the bottom of the canyon.
The amplification of motion at some locations and the attenuation of
motion at others results in a large frequencydependent spatial variation of
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22
SH, P. SV, RAYLEIGH

SH




\
SH, P. SV, RAYLEIGH
/
\
~ 1
SH, P. SV
FIGURE 22 Valley shapes and input wave types for which twodimensional analyses of wave
scattenng effects have been reported.
motion along the canyon walls. This spatial variation is more abrupt when
the canyonwidthtowavelength ratio is larger than 1 (higher frequency)
for all types of waves. Calculated relative motion ratios of 2 to 3 are
common in many cases of differing incident angles and wave types. For the
more irregular geometry of a real canyon, a calculated relative motion ratio
as high as 6 was reported for Pacoima Dam, California (2~.
The relative phase of motions along the canyon walls has been reported
for the case of SH waves incident to a semicircular canyon (26~. It seems
that the phase variation is close to what can be predicted from simple traveling
wave considerations for most of the canyon wall. Near the upper corners of
the canyon, however, more abrupt variations of phase angle appear.
From the above brief description of theoretical results, it is clear that the
spatial variation of freefield motion is very complex and frequency dependent.
In an effort to obtain an averaged index of motion intensity, a Topographical
Effects Index was defined using the Arias Intensity Concept (225~; however,
this index is still dependent on location and angle of incidence.
ThreeDimensional Case
Analytical solutions for threedimensional canyon topography are much
more difficult to obtain. For the simple case of a hemispherical cavity at
the surface of an elastic halfspace, series solutions have been obtained for
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23
5
C] 4

~ 3
id
LL
~ 2
LL
a:
CO
1
4:
3
2
1
o
1 2 3 6 7 8 7= 30
.
  ~ mar
\4 5/
SH /
/
;~
0~
0 1 2 3
5
1 2 3 6 7 8
' ' 1 ~ I ' '
SH \4 5J
\/ ~
~ =60
_ A
1 ~
0 1 2 3
FIGURE 23 Calculated amplification of incident plane SH waves by a semicylindrical canyon
surface (26). A flat freefield surface gives a displacement amplitude of 2; ~ represents the SH
wave velocity.
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24
incident P and S waves (226~. A boundary element method that satisfies
the free surface condition at and near the canyon walls in a least squares
sense has also been applied to axisymmetric cavity problems (227), although
results are given only for a hemispherical cavity with a vertically incident P
wave.
Perhaps the most relevant solution for threedimensional canyon topography
is that obtained by finite element analysis of Pacoima Dam and its adjacent
canyon (228), shown in Figure 24. Part of the foundation rock was included
with the finite element model of the dam, taking account of the variations in
the rock properties. Threedimensional modeling was considered necessary
because of the complex topography, which is apparent near the dam, consisting
of a thin, spiny ridge at the left abutment and a broad, massive right abutment.
A rigid base motion was assumed at the finite element base boundary, and
its three components of motion were calculated by a process of deconvolution
from the three components of earthquake motion recorded on the ridge
above the left abutment. The strongmotion accelerograph was located at
the crest of the ridge, as indicated in the photograph. The peak acceleration
of the filtered left abutment record was 1.15 g, and that of the calculated
base motion was 0.40 g. This result indicates that the amplification may be
larger than expected because of the assumed rigid energytrapping boundary
at the base; also, the assumption of uniform motion at the base may have
contributed to the conservative results.
Applicability of the Results
The theoretical freefield motion results have limitations in their application
due to the various simplifying assumptions made in their derivation. In the
twodimensional analyses it was assumed that the change of topography
along the upstreamdownstream direction was negligible; therefore, the results
are valid only for prismatically shaped canyons. Moreover, the results
apply only to specific wave types, and the amplification effect of wave
scattering is very much dependent on the type of incident wave. Unless the
composition of an actual incident earthquake wave is known in terms of its
wave types, such results are not directly applicable.
Often a complicated canyon geometry requires that freefield motion varying
in three dimensions be considered, and it is doubtful that any method other
than a numerical one can be expected to produce realistic results for such
cases. Even with a numerical approach the various assumptions made in
treating the finite boundary and in modeling the inhomogeneous media may
introduce errors; thus, both two and threedimensional results need to be
compared with actual freefield earthquake records to assess their applicability
(229~. 7 '
Because of the many uncertainties involved in modeling the geometry,
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25
FIGURE 24 Pacoima Dam, California, was subjected to the 1971 San Femando earthquake;
the seismic motions were recorded by a seismograph on the narrow rock ridge above the left
abutment, at the point indicated (228).) (Courtesy of George W. Housner)
the foundation material properties, and the incident earthquake motion, it is
probable that a stochastic approach to defining the freefield motions will
be needed in addition to the deterministic procedures reviewed in this report.
Random field theory (230, 231) is quite relevant to the problem of spatial
variation of earthquake input motion. Using the stochastic approach, some
work already has been done for freefield motions over a flat, open surface
(232, 233, 234, 235~. To date, no results have been reported on the
probabilistic nature of seismic motions along a canyon wall.
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26
Measured Motions of Foundation Rock
Reports of actual earthquake motion recorded at the walls of a canyon
are very scarce; however, the importance of differential input motion at a
dam site is well recognized, and a few such reports do exist, mostly for
abutment motion of existing dams. As early as 1964, differential motion at
the two abutments of the Tonoyama (arch) Dam in Japan was reported (2
36, 237~. The dam is 65 m high, with a crosscanyon width at the crest
level of about 150 m. The maximum recorded acceleration at the center of
the dam crest during an earthquake in 1960 was 0.018 g, and those at the
two abutments were less than 0.010 g. In general, the records at the two
abutments appeared to be quite similar in magnitude and phase. However,
Fourier analysis revealed that the amplitude of motion at the right abutment
was two to three times that at the left abutment for frequencies greater than
4 [Iz. Other observations made in Japan at the Tagokura (gravity) Dam (2
38) and at the Kurobe (arch) Dam (239) also indicate differing motions at
the opposite abutments; however, in both of these cases there was amplification
of motion over the height of the abutments.
Eight aftershock measurements were made in the vicinity of Pacoima
Dam after the San Fernando earthquake (240~. Comparison of the records
obtained at the south abutment near the original strongmotion station with
those obtained at a downstream canyon floor location some distance from
the dam revealed an average amplification of about 1.5 for horizontal motions
at the top of the ridge. The amplification was about 4.2 near a frequency of
5 Hz but decreased to a ratio near 1 for lower frequencies. In a separate
study four aftershocks of the San Fernando earthquake were recorded at two
stations, one near the dam base and the other near the top of Kagel Mountain
(241~. The two stations were approximately 3,000 ft apart and were selected
to represent the freefield motions at the base and top of the mountain. The
highest timedomain horizontal acceleration ratio (toptobase) was about
1.75, but the frequencydomain ratio, as measured by the pseudorelative
velocity spectra, was as high as 30 at a frequency of about 2 Hz.
A correlation study on ground motion intensity and site elevation was
carried out for the general area of Kagel Mountain and Pacoima Dam using
the San Fernando earthquake data (242~. On a larger scale it was found
that there was an almost linear relationship between the peak recorded motion
of a site and the recorder elevation, as the profile rises from the lower San
Fernando dam site (approximately 1,200 ft) to the Pacoima dam site
(approximately 2,000 It) to the peak of Kagel Mountain (approximately
3,500 ft). Based on this linear relationship, it was calculated that the base
rock acceleration at the Pacoima dam site was about 0.99 g, but it is evident
that this calculation ignores local topographic features such as the abutment
ridge.
In a somewhat similar case, aftershocks of the 1976 Friuli earthquake in
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27
Italy were measured at the Ambiesta (arch) Dam (243~. The dam is 60 m
high, and the canyon width at the crest level is about 140 m. Records were
obtained at three locations along the damfoundation interface, two at crest
level at the abutment and one at the base of the dam. The average ratio of
horizontal peak velocity at the crest level to that at the base of the dam
ranged from 3.11 to 1.88. The predominant frequency of motion at the base
of the dam was about 4 Hz, based on more than 35 records having peak
velocities greater than 0.002 cm/sec.
Observed motion at the Chirkey (arch) Dam in the Soviet Union was
reported in a translated paper (244~. The motion at the left abutment was
recorded at three heights during a magnitude 3.5 earthquake that occurred
on 4 February 1971 at an epicentral distance of 46 km. The peak velocities
at heights of 160, 220, and 265 m were 0.4, 0.63, and 0.62 cm/see, respectively.
In the frequency domain it was found that the maximum spectral value
increased by a factor of 2.5 when the height of the observation point increased
by 100 m.
The Whittier, California, earthquake of 1 October 1987 triggered all 16
of the accelerometers that had been installed on Pacoima Dam. Preliminary
reports indicated that the accelerations at the dam base were on the order of
0.001 g, while those at about 80 percent height of the dam on the dam
abutment interface were on the order of 0.002 g (245~.
All of the abovementioned records were of small amplitude due to low
intensity shaking. A largeramplitude record was obtained at the Techi dam
site in Taiwan during an earthquake on 15 November 1986 (246~. This
arch dam is 180 m high, and the canyon width is about 250 m at crest level.
The peak acceleration recorded at the center of the crest in the upstream
downstream direction was 0.170 g. Three strongmotion accelerographs
had been installed along the damfoundation interface, one at the base of
the dam and the others at about midheight on the opposite abutments.
Unfortunately, one of the midheight instruments malfunctioned, leaving only
one operational. The peak acceleration obtained at the dam base in the
upstreamdownstream direction was 0.014 g, while that at midheight of the
damabutment interface was 0.022 g. In the crosscanyon direction the
peak acceleration at the dam base was 0.012 g, versus 0.017 g at the midheight
abutment location. These records clearly demonstrate a large spatial variation
of motion along the foundation interface, but it is probable that dam interaction
contributed significantly to the recorded motion. Consequently, these data
are not representative of freefield canyon wall motions.
A 1984 earthquake of amplitude comparable to the Techi event was reported
recently for the Nagawado (arch) Dam in Japan (247, 248~. The dam is
155 m high with a crest length of 355.5 m. The peak recorded radial
accelerations of the dam crest were 0.197 g at midspan and 0.245 g at the
quarter point from the left abutment. The recorded peak accelerations in
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28
the foundation rock 17 m below the base of the dam were 0.016 g in the N
S direction and 0.029 g in the EW direction; the dam axis lies approximately
in the NS direction. At a level about 25 m above the base of the dam, an
accelerograph installed deep in the right abutment rock away from the dam
recorded accelerations of 0.018 g (NS) and 0.021 g (EW). Almost directly
above this accelerograph, also deep in the right abutment, an instrument at
crest level recorded peak accelerations of 0.031 g (NS) and 0.026 g (EW).
Across the canyon at crest level deep in the left abutment, another recorder
indicated peak accelerations of 0.026 g (NS) and 0.021 g (EW). The
spatial variation revealed by these data is quite indicative of the lack of
uniformity in the earthquake motions of the rock supporting the dam.
In a translated paper (249) the findings of a model test of Toktogul Dam
are reported. The model had a length scale of 1:4,000 and it simulated the
topography of the Toktogul dam site, which covers an area of 6 x 6 km and
was 4 km deep. The model was subjected to excitation initiated at different
points on the model, and the motion along the canyon wall was recorded up
to a height from the bottom of the canyon equal to twice that of the dam.
Three configurations were tested: without the dam, with the dam but without
water, and with both dam and water; generally the greatest motion occurred
for the empty canyon case.
More recently model test results were reported for an existing arch dam
and for a proposed arch dam, both in China (250~. The model scales were
1:600 and 1:2,000, respectively, and input to the models was both random
excitation and impact. The model test results were found to be consistent
with those from finite element analyses and from ambient vibration surveys.
An amplification factor of between 2 and 3 was observed for abutment
motion at the crest level relative to motion at the bottom of the canyon.
Predicted Response to Spatially Varying Input
Dynamic Excitation
Direct application of measured earthquake motions to predict dam response
has been reported for the Ambiesta (arch) Dam (251~. Three records are
available, one at the base of the dam and two at the crest level near opposite
damabutment interfaces. In the analysis the interface was divided into three
zones by drawing a horizontal line near midheight on an elevation view of
the downstream face. Within each zone a uniform boundary motion identical
to what was recorded in that zone was used as interface input. It was
reported that agreement between the calculated accelerations along the crest
of the dam and the corresponding measured quantities was startlingly good,
while poor agreement resulted if uniform input motion was used along the
entire interface.
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29
Using prescribed input motions at the foundation rock boundary, the
effects of differential input motion on the responses of a gravity dam and an
arch dam have been studied by finite element analysis (252~. A two
dimensional planestrain analysis was performed of the gravity dam and its
supporting block of foundation rock, assuming a travelingwave input along
the horizontal foundation base boundary. To reduce the amount of computation,
the boundary was divided into four regions, with uniform motion assumed
in each. The dam was 46 m high, and the length of the horizontal base
boundary was approximately twice the height of the dam. The input wave
form was that of the S16E component of the 1971 San Fernando earthquake
recorded at Pacoima Dam, and three wave speeds were used: 2,000 m/see,
4,000 m/see, and infinite. Stress analysis results indicated that as the wave
speed was reduced the stresses in the dam increased.
In the case of the 110mhigh arch dam, which had a crest length of 528
m, a threedimensional analysis was performed. The left half of the foundation
boundary was assumed to move uniformly according to the prescribed San
Fernando earthquake record, while the right half was held fixed. It was
reported that different stress patterns in the dam were obtained for the
variable base input as compared with the uniform base input.
In a recent study on travelingwave effects, a small portion of the foundation
rock was treated as an extension of the dam body, and shell equations were
used to model the extended arch dam (253~. Crosscanyon traveling waves
in the form of harmonic motion or earthquake motion were then assigned to
the periphery of the shell; reservoir effects were neglected. Results indicated
that stresses in the dam increased when the period of the input harmonic
wave approached the fundamental period of the shell.
In a separate study the effects of traveling waves on arch dams were
examined using a finite element approach (254~. The model was similar to
the freefield input model described above, but the freefield motion was
taken as a prescribed traveling earthquake wave. It was found that the
effects of a wave traveling in the upstream direction were not significant
when compared with the rigid base input. However, a traveling wave in the
crosscanyon direction caused an average stress increase of 40 to 50 percent
and a doubling of the maximum computed stress.
Travelingwave effects also have been studied, with emphasis on the
energy input to the reservoir water. A twodimensional solution was reported
for the problem of a rigid gravity dam with infinite reservoir excited by a
vertical traveling ground motion (255~. Three cases were studied: infinite
wave speed, wave leaving the dam moving upstream, and wave approaching
the dam from upstream. The vertical component of the E1 Centro 1940
earthquake was used, and in the latter two cases the wave propagation speed
was taken to be three times the speed of sound in water. It was found that
maximum pressure on the dam occurred when the wave approached from
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30
upstream, and it was lowest when the wave propagated away from the dam.
In terms of maximum total force or overturning moment, the larger traveling
wave response was almost twice that resulting from the infinite wave speed.
A similar conclusion, but with much less difference between the cases for
infinite and finite wave speeds, was obtained by a finite difference study of
a flexibledam finitereservoir model (256~. Later a finite difference solution
scheme was applied to an improved model that included energytransmitting
boundaries and elastic foundation (257~. It was reported, however, that
traveling waves did not produce more critical stress conditions in the gravity
dam than did the wave with infinite propagation speed.
Applications of an energytransmitting boundary approach to a freefield
input model were reported recently (258~. A numerical example was given
to illustrate the computation procedure for a uniform freefield input motion
assumed along the damfoundation interface. In another study a new input
procedure that included the influence of the infinite foundation domain was
developed (259~. The analysis procedure was divided into two stages:
first, the stresses were computed on a fictitious fixed boundary facing the
incident wave; these stresses were then released in the second stage, when
the complete domain was modeled by finite elements near the canyon and
by infinite elements away from the canyon. Numerical results were obtained
for a threedimensional dam topography, considering an SH wave propagating
across the canyon. The displacement amplitudes at the crest and on the
crown cantilever were found to be much reduced from those obtained using
a uniform base input. The presence of the dam body was found to have the
general effect of reducing the motion at the canyon wall, as compared with
the freefield values at the same locations.
A recent study (260) of an arch dam used freefield motions for the
seismic input that were computed for a canyon embedded in a twodimensional
half space and subjected to incident SH, SV, and P waves. These freefield
motions were applied to a threedimensional finite element model containing
the dam, a massless foundation region, and an infinite reservoir of compressible
water. Frequencydomain responses were converted into the time domain
in the form of standard deviations of the response to a random input with an
earthquakelike frequency content. As shown by an analysis of Pacoima
Dam, inclusion of nonuniformity in the stream component of the excitation
reduces the dam response, while the effect of nonuniformity in the cross
stream and vertical components varies, with the potential for some increase.
For various cases of nonuniform input, the average arch stress along the
crest ranged from 62 to 122 percent of that for uniform input.
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Fault Displacement
All the abovementioned analyses were for vibratory seismic input motions.
The case of a faultdisplacement offset occurring directly beneath the base
of a concrete gravity dam also has been studied. In a twodimensional
nonlinear analysis of a damfoundation system (261), a reverse fault was
simulated by applying concentrated forces along an assumed fault zone that
extended from the finite element boundary of the modeled foundation rock
to the base of the dam body. Results for the particular case studied indicated
that the dam did not crack as a result of fault displacement but partially
separated from the foundation. It was recommended that the combined
effect of fault displacement and vibratory seismic input could be accounted
for in preliminary studies by performing a dynamicresponse analysis with a
linear finite element model, using a softened foundation.
More recently a model test study of a proposed 185mhigh arch dam in
Greece was carried out to determine the effects of fault displacements occurring
directly beneath the base of the dam (262~. Selection of the dam type and
location was based on economic considerations. A thorough seismotectonic
investigation concluded that fault displacement at the dam base of as much
as several decimeters could not be ruled out; consequently, design measures
were taken to accommodate such possible movement. Among these was a
sophisticated joint system to alleviate the adverse effects of the fault displace
ment. A 1:250 scale model was built and tested at the Laboratorio Nacional
de Engenharia Civil (LNEC) in Lisbon. The horizontal movement of the
fault was simulated by imparting to the left abutment a gradual displacement
upstream to compress the arch. Results of the test indicated that the joint
system worked very well in protecting the dam from collapse for a displacement
of up to 1 m in prototype scale. It was also concluded that the joint system
would enable the dam body to withstand a fault displacement of the order of
5 to 10 cm without damage.
There have been two cases where concrete gravity dams have actually
been constructed in which the plane of an underlying fault has been extended
through the entire dam section in the form of a sliding joint to accommodate
possible fault movement (263~. These are Morris Dam (264) in California,
which was completed in 1934, and the recently finished Clyde Dam (265)
in New Zealand. In both cases the fault ran along the river channel perpendicular
to the axis of the dam and dipped about 60 degrees off horizontal. Figure 2
5 is a photograph of Morris Dam. The joint is located near the gallery
entrance, which can be seen on the downstream face. The sliding joints in
both dams were oriented vertically and were designed for displacements on
the order of 2 m. This required an interesting geometric solution, details of
which were quite different in the two cases. To date, no movement has
occurred on either fault.
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Other methods of defensive design of concrete gravity dams for fault
displacement include the placement of a zoned selfhealing berm of embankment
material at the heel of the dam and a buttressing berm of freedraining
granular fill against the downstream face (263~. Reference 263 also states
that an acceptable defense may not exist for thin arch dams against fault
displacements.
STATUS OF STRONGMOTION INSTRUMENT NETWORKS
The topic of strongmotion instrumentation placed at concrete dam sites
for the purpose of studying the spatial variation of ground motion has not
received sufficient attention. Traditionally, for recording the input motion
it was considered adequate to have one strongmotion recorder at either the
toe of the darn or one of the abutments. As early as 1975, however, it was
recommended that there be a minimum of two accelerographs located at the
dam site to `'record earthquake motions in the foundation" (266, p. 1,099~.
The purpose of requiring two instruments was "to give some indication of
the uniformity of conditions, and to ensure some useful information in the
event of an instrument malfunction." In the 1978 International Workshop
on StrongMotion Instrument Arrays, various aspects of instrumentation
were discussed, and useful suggestions were made specifically for study of
the spatial variation of seismic ground motions (267~. One of the array
types suggested was the "local effect array" that could be used to study the
"variation of ground motions across valleys." But in that suggestion the
emphasis was clearly on the motion of the overburden soil in a valley rather
than that along a canyon wall. In a followup meeting of U.S. researchers
in 1981 (268, p. 8), the following recommendation was made: "Lifeline
and other systems should be instrumented along with building structures.
These should include highway bridges and overpasses, dams, and other
utility system facilities. The degree of instrumentation should be sufficient
to obtain information equivalent to that for building structures." However,
few if any concrete dams in the United States are currently instrumented to
the extent needed to study the seismic input problem. Of the 45 concrete
dams listed in a survey report (269), only Pacoima Dam has strongmotion
instruments installed at both the toe and two abutments (as well as at other
locations on the dam). Although the survey list is not complete, very few
other concrete dams have seismographs installed near the toe. Even though
the measuring of freefield and interface input motion has been recognized
to be as important as that of the dam response (270), current strongmotion
instrumentation for concrete dams in the United States is inadequate for the
purpose of defining seismic input.
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RESEARCH NEEDS
Various theoretical models have been developed for prediction of free
field motion at the surface of a valley or canyon to be used as input to a
dam system; however, no verification of such input predictions has yet been
achieved by comparison with actually recorded earthquake motions. The
existing strongmotion instrumentation at concrete dams is not designed to
provide such essential data. It is clear, therefore, that an improved instrumenta
tion program for observation of earthquake motions at sites of existing or
proposed dams is needed. Similarly, further theoretical work is needed on
the deterministic and stochastic modeling of input motion to provide the
basis for realistically modeling seismic input to concrete dams. Specific
recommendations for research on earthquake input to concrete dams follow:
1. Deployment of StrongMotion Instrumentation
(a) Arrays of strongmotion instruments should be deployed at selected
dam sites. The locations of the instruments at each site should include at
least three elevations along the abutment interfaces and selected locations
within the abutment rock, the face of the canyon downstream of the dam,
and several positions along the reservoir bottom. Triggering of these instruments
should be synchronized so that travelingwave effects can be detected. The
seismographs should be made part of an overall instrumentation system that
includes pressure transducers at the dam surface in the reservoir and
accelerographs at selected locations within and on the dam body.
(b) An array of strongmotion instruments should be deployed at sites
being considered for construction of concrete dams to obtain the freefield
motions at a canyon location without the interference of an existing dam.
2. StrongMotion Instrumentation Program
.
(a) The necessity of obtaining actual records and the high cost of
instrumentation point to the need for a concerted joint effort between the
dam owner/operator and the research community. A permanent or semiperma
nent instrumentation program should be established after a careful study of
potential sites for instrumentation.
(b) A joint program of strongmotion instrumentation for concrete dams
In areas of high seismicity should be developed in cooperation with other
countries having similar hazards.
3. Use of Recorded Seismic Motion Records
Seismic motions actually recorded at a damfoundation interface should
be utilized in analyses intended to verify the various input methods. Because
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the recorded motions would be affected by damfoundation interaction, a
system identification approach may be needed to determine the freefield
input motion.
4. Enhancement of TwoDimensional Analyses
Currently available twodimensional theoretical freefield canyon or valley
wall motions are presented in terms of the incident wave angle and wave
type and are in a frequencydependent form. Even though they are of
limited applicability because of assumptions regarding two~imensional geometry
and homogeneity of the medium, these results should be synthesized to
provide guidelines for defining realistic input for concrete dams.
5. Enhancement of ThreeDimensional Models
The deterministic prediction of freefield motion at a dam site with three
dimensional topography can be performed by numerical methods such as
finite elements, boundary elements, finite differences, or some combination
of the three. The development of nonreflective boundaries for such three
dimensional models remains a highpriority requirement.
6. Stochastic Approach
In view of the many uncertainties involved, the simulation of spatially
varying freefield motion may require the application of stochastic theory;
therefore, methods should be developed for simulating stochastic inputs for
valley and canyon topographies.
7. Effects of Fault Displacement
Further studies should be carried out focusing on the effects of fault
displacements on the safety of concrete dams, using both numerical simulation
procedures and physical model testing. The effectiveness of joint systems
in a dam at the location of the fault break should be included in these
studies.