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OCR for page 104
6
Recommended Criteria for Evaluating
Seismic Performance
BACKGROUND
To evaluate the seismic performance of a concrete dam subjected to
moderate or strong earthquakes, it is essential to have appropriate criteria.
As described in the preceding chapters, the seismic performance of concrete
dams in most cases is evaluated by using an analytical model of the dam
based on numerical techniques, usually the finite element method of analysis,
together with an appropriate characterization of the earthquake. To assess
seismic performance using results from finite element or other numerical
analyses, criteria are needed that relate the numerical results from such
analyses to the expected behavior of the dam.
As described in Chapter 3, when earthquakes were first considered in the
design and analysis of concrete dams, earthquake effects were characterized
in terms of "equivalent" static forces. The amplification of accelerations
through response of the dam was assumed to be either negligible or improbable,
and equivalent static forces for seismic conditions were simply added to
forces determined for true static loading conditions. The analytical results
for combined loading conditions including earthquake effects were not evaluated
any differently than results for normal static loading conditions. Consequently,
concrete dams were considered to be safe during earthquake loading conditions
if computed tensile stresses were small or nonexistent, if resultant forces in
two-dimensional sections through gravity dams fell within the central one-
third of their bases, and if compressive stresses were computed to be less
than an allowable working stress (usually 1,000 psi or less).
By the l950s the importance of the dynamic earthquake response of
typical structures such as buildings and bridges was recognized. However,
it was still commonly assumed that concrete dams were stiff enough that
104
OCR for page 105
105
amplification of earthquake ground motions through structural response was
insignificant. Although earthquake effects were still being characterized by
equivalent static forces, it was recognized that, given the relatively infrequent
occurrence and short duration of earthquakes, it was appropriate to apply
criteria having less conservatism for loading conditions that included earthquakes
than for loading conditions without earthquakes (3-9~.
However, in the late 1960s it was realized that although concrete dams
are relatively stiff structures, substantial amplitudes of earthquake ground
motions could occur at frequencies well within the frequency range of response
for concrete dams, and the resulting response amplification should not be
ignored. The dynamic response behavior of a concrete dam, together with
dam-water interaction, was recognized as a key factor in correctly understanding
and evaluating the dam's seismic performance. This increased understanding
was facilitated in part by the occurrence of the Koyna Dam earthquake in
1967, described in preceding chapters. However, it was not until the early
1970s that analytical tools, which included methods for modeling dynamic
response and reservoir water interaction, principally finite element procedures,
became readily available to those performing seismic stability analyses.
Improvements in analytical procedures required corresponding modifications
of the criteria used to evaluate analytical results. The criteria that had been
used to evaluate results from simplified pseudostatic analyses were not generally
appropriate for evaluating results from two- and three-dimensional dynamic
finite element analyses. More applicable criteria began to be developed
partly as a result of dynamic finite element analyses conducted for concrete
dams that successfully withstood the relatively large ground motions associated
with the 1971 San Fernando earthquake in California. Criteria were eventually
set forth whereby computed tensile stresses large enough to indicate the
initiation of cracking, and compressive stresses larger than the allowable
working stress level, were understood to not necessarily indicate structural
instability (6-1~. The existence of foundation characteristics that could
contribute to instabilities and the effects of strong earthquakes on foundation
stability also became better understood during the 1970s.
In the 1980s many of the research developments related to the numerical
analyses of concrete dams have focused on nonlinear material behavior and
nonlinear analytical techniques, as described in Chapter 4. Although some
nonlinear analyses have been performed to evaluate certain aspects of nonlinear
response, the analytical techniques and models necessary to reliably and
economically perform complete nonlinear analyses of concrete dams, together
with their associated reservoirs and foundations, are not yet sufficiently
developed to be applied during routine engineering analyses. Consequently,
criteria used to evaluate numerical results from earthquake analyses of concrete
dams, predominantly results from linear elastic finite-element analyses, remain
largely unchanged from those developed for linear response analyses in the
OCR for page 106
106
1970s. These criteria and their application and adequacy are the focus of
this chapter. However, some preliminaries concerning initial conditions
and analytical procedures must be addressed before these criteria can be
considered. Inappropriate recognition of initial conditions or misapplication
of analytical procedures may produce numerical results that cannot be
meaningfully related to expected seismic performance regardless of the criteria
used.
PRELIMINARY CONSIDERATIONS
Initial Conditions Resulting from Static Loads
Since the initial condition of a concrete dam prior to the occurrence of an
earthquake is the result of previously applied static loads, it is essential that
the effects of these static loads be adequately quantified before completing
a seismic evaluation. Thus, studies must be performed to determine the
effects of dead loads, water loads, and temperature distributions, in appropriate
combinations. In addition, the effects of any uncommon loads or conditions,
such as expansion due to alkali-aggregate reaction, must be included. Without
a thorough understanding of the existing static condition of a concrete dam,
an evaluation of the dam's seismic performance may be meaningless.
Effects of Construction Sequence
· · · . . . .
Generally, static dead load effects are easily accounted for in the analyses
of concrete dams, particularly when two-dimensional modeling is adequate.
However, when three-dimensional analyses are required, spurious stresses
may be indicated when the gravity loading is applied to the model as if dead
load effects occur only after construction of the dam is completed, rather
than on portions of the dam as they are constructed. Additional discrepancies
can occur when three-dimensional modeling neglects water loads from partial
Bllling of the reservoir prior to completion of construction. Further discrepancies
can arise when the successive grouting of portions of contraction joints
between partially completed monoliths of a conventionally constructed dam
is ignored. Neglecting these factors in a three-dimensional analysis can
lead to the indication of fictitious tensile stresses along abutments and horizontal
loads or thrusts that are incorrect, particularly in the case of double-curvature
arch dams.
To reduce these inaccuracies in a three-dimensional linear elastic analysis
of a conventionally constructed concrete dam, alternate monoliths in the
model of the completed dam can be assigned zero mass and zero stiffness.
The gravity loading can be applied to the remaining monoliths, which will
support the gravity load through simple cantilever action. The analysis can
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107
then be repeated with the other monoliths to obtain the gravity load state of
stress for the entire dam. In some cases this simplified approach will be
sufficient. However, in other cases,~especially for large double-curvature
arch dams, it may be necessary to perform a sequence of analyses (as many
as five or more) to simulate construction of the dam in blocks, partial
grouting of contraction joints, changing temperature distributions after grouting,
and staged filling of the reservoir (6-2~. Similarly, a series of analyses that
simulate the sequence of construction for some roller-compacted concrete
dams may be necessary to adequately account for construction of these
dams in horizontal layers.
Temperature Effects
The effects of changing temperature distributions can also influence the
seismic performance of concrete (and even masonry) dams and often are not
fully considered, especially when older existing structures are analyzed.
After concrete or masonry hardens, it expands and contracts in response to
temperature changes. Temperature changes in concrete dams occur because
of variations in the temperature of the surrounding air, variations in reservoir
water temperatures, and, to a lesser extent, solar radiation at exposed surfaces.
These temperature changes cause strains, which if restrained result in stresses.
Thermally induced stresses and strains can be significant and as a result can
affect the strain capacity available to resist earthquake inertia forces without
the concrete being damaged.
For concrete gravity dams and buttress dams that are essentially two-
dimensional in their behavior, concrete temperature changes can usually be
ignored. However, for concrete dams whose behavior is three-dimensional,
including some concrete gravity dams (see section below titled Two-Dimensional
Versus Three-Dimensional Analytical Models), the effects of temperature
changes must be assessed in order to adequately evaluate seismic performance.
When concrete temperatures are important to consider, it often is not sufficient
to characterize them as uniform distributions. Rather, it is usually necessary
to consider nonuniform, linearly varying temperature distributions. In some
cases, particularly for thin concrete arch dams, it may even be necessary to
consider nonlinearly varying temperature distributions.
Creep Effects
Concrete is a brittle material that exhibits significant variations in its
elasticity depending on its age when loaded, the rate of loading, and the
duration of loading. Most of the laboratory tests conducted to determine
modulus of elasticity and compressive strengths of concrete are performed
with loading applied at a rate of about 30 to 40 psi/see, such that tested
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108
samples are taken from zero load to failure in 2 to 3 min. The resulting
modulus and strength values can appropriately be termed instantaneous or
short-term static values. However, static loads that are actually experienced
by concrete dams may exist for many years. Under sustained loads concrete
exhibits pronounced creep (increasing strain with time at constant load),
which affects displacements due to external loads, such as gravity and reservoir
water loads, and stresses due to internal loads, such as those induced by
thermal strains. Creep effects should be accounted for in all analyses, but
are particularly significant if nonlinear behavior is being considered.
For linear elastic analyses it is not appropriate to represent stress-strain
behavior with a single modulus-of-elasticity value obtained from short-term
laboratory loads. The most common means of accounting for creep in
linear elastic analyses of concrete dams is to use a sustained-load modulus
of elasticity, which is less than the short-term static modulus typically measured
in the laboratory. Based on results from numerous uniaxial laboratory tests
(6-3), a reduction of about 25 to 30 percent from the short-term value
appears to be appropriate, depending on the duration of significant components
of static loads. However, more research concerning the creep behavior of
the mass concrete used to construct dams is needed, particularly for multiaxial
loading conditions.
Uplift
Another factor that can have a significant influence on the seismic performance
of a concrete dam is uplift. Uplift is the result of interstitial water, which
carries a portion of the normal compressive loads applied to mass concrete
in dams and their foundations. Under static loading conditions the effect of
these pore pressures is to reduce the normal compressive stresses acting
within the concrete and to increase any normal tensile stresses, should they
exist. The exception is an open crack, in which case water in the crack
produces external loads along both faces of the crack.
The stresses that should usually be considered when evaluating the stability
of concrete dams, except for thin arch dams, are "effective" stresses. At a
particular location the effective stress equals the difference of the total
stress due to external loads and the pore pressure or uplift at that location.
Since uplift has not been shown to significantly affect the stress distribution
in thin arch dams, and since the stability of arch dams is dependent on their
ultimate capability to carry loads in compression, normally it is not considered
necessary to reduce compressive total stresses to effective stresses when
evaluating the stability of most arch dams. Except for thick arch dams,
normal practice is to neglect uplift pressures and to base evaluations of
numerical results on total stresses rather than effective stresses.
For concrete gravity dams subjected to static loads, uplift increases the
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109
tendency for cracking along the upstream face of the dam and reduces
compressive normal stresses within the dam structure and along the dam-
foundation contact, which correspondingly reduces sliding stability. To
include the effects of uplift in a static analysis using the finite element
method, an analysis can be performed in the usual manner, neglecting pore
pressures and calculating total stresses. Pore pressures, based on appropriate
considerations regarding the presence and effectiveness of drainage systems
within the dam and its foundation, can then be summed with total stresses
to calculate effective stresses (6-4, 6-5~.
For seismic loading conditions, where a dam oscillates rapidly, the present
state of practice for linear elastic analyses is to not attribute any additional
significance to pore pressures beyond their effects during static loading
conditions. During seismic loading conditions, as the dam moves upstream,
the upstream portions of the dam carry the inertia load in compression,
resulting in higher pore pressures, while the stresses in the downstream
portions of the dam tend toward tension, causing reductions in pore pressures.
When the movement of the dam reverses, pore pressures tend to be reduced
in the upstream portions of the dam while increasing in the downstream
portions. Since the increase in pore pressures in compressive zones is usually
accompanied by a larger increase in total stress, higher pore pressures do
not significantly affect stability during seismic loading conditions. Should
cracking occur in portions of the upstream face during an earthquake, it is
usually assumed that oscillations occur quickly enough to prevent significant
penetration of water into the cracks. Consequently, pore pressures are usually
treated as though they are constant during both static and dynamic loading
conditions. However, research to more accurately characterize the effects of
pore pressures during earthquakes is needed, especially when the response
. .
IS non. [near.
Deformation Modulus of Foundation Rock
The deformation of foundation rock due to loads applied from a concrete
dam influences seismic response and the stresses that develop in the dam,
particularly near the dam-foundation contact. The fundamental property
that represents the deformation characteristics of a dam's foundation is termed
the deformation modulus.
In linear elastic analyses, the deformation modulus is an effective elastic
modulus that represents both elastic strain of the rock mass and also the
inelastic deformation of discontinuities. Values for deformation modulus
can be determined from in situ testing, laboratory testing, empirical relationships,
comparisons of analytical results with measured prototype behavior, or various
combinations of these methods. The appropriate approach for determining
deformation moduli will vary depending on the size of the dam, the severity
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110
of anticipated loading conditions, the availability of data characterizing foundation
conditions, and the status of the dam as an existing structure or one under
design. Often, the deformation characteristics of the foundation underneath
a concrete dam will vary spatially. In such cases, more than a single deformation
modulus may be necessary to adequately represent differing deformation
behavior in various zones of the foundation.
There are no known data that indicate that deformation moduli increase
significantly during seismic loading conditions. Therefore, the same values
of deformation moduli are usually used for seismic response analyses as for
corresponding static analyses. If deformation moduli should increase by 25
percent, for example, during seismic loading conditions as compared with
static loading conditions, this would not appreciably affect the frequency
characteristics of the dam-foundation system, the seismic response of the
system, or the stresses near the dam-foundation contact.
Two-Dimensional Versus
Three-Dimensional Analytical Models
It is commonly accepted that three-dimensional analyses are necessary to
adequately evaluate concrete arch dams. Probably the only situation in
which two-dimensional analyses might be appropriate for an arch dam would
be a "worst-case" evaluation for a gravity arch structure. Concrete gravity
dams, on the other hand, are usually evaluated on the basis of two-dimensional
analyses. Wh.,le two-dimensional analyses are appropriate in many cases,
there are situations where three-dimensional analyses should be considered.
In some of these cases concrete gravity dams, particularly roller-compacted
concrete gravity dams, are located in relatively narrow sites, having crest-
length-to-height ratios of 5 to 1 or less. In other cases concrete gravity
dams are located at sites that are extremely irregular in shape from abutment
to abutment. Such sites can provide additional restraint or can result in
structural movements from applied loads that cannot be accounted for in
two-dimensional analyses. Generally, two-dimensional analyses for static
loading conditions are conservative; but while this conservatism may be
appropriate for static loads, it may be misleading for seismic loading conditions.
For example, in the case of a relatively narrow site where additional restraint
is provided by the abutments, the restraint can increase compressive stresses
near the heel of the dam along the upstream face during static loading
conditions, thereby reducing the magnitude of tensile stresses developing
during seismic conditions. Two-dimensional analyses will almost always
indicate the development of high tensile stresses during large earthquakes at
these locations, whereas three-dimensional analyses may indicate much lower
stresses (6-4~. In such cases two-dimensional analyses may predict stresses
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111
large enough to cause cracking, while three-dimensional analyses may indicate
that cracking will not occur at all.
It should be noted that in relatively narrow sites the fact that a concrete
gravity dam has numerous vertical contraction joints that are unkeyed is not
sufficient justification by itself for performing two-dimensional analyses
rather than three-dimensional analyses. In relatively narrow sites the horizontal
forces perpendicular to the contraction joints can be large enough to develop
significant shear friction resistance, so that adjacent monoliths do not respond
to loading independently of one another, as is often assumed. These horizontal
forces can result from three factors: (1) small displacements parallel to the
abutments toward the bottom of the site caused by gravity, (2) twisting of
adjacent monoliths caused by water loads, and (3) thermal strains.
GUIDELINES FOR EVALUATING RESULTS
FROM LINEAR ANALYSES
At present, seismic safety evaluations of concrete dams are usually based
on numerical results from linear dynamic finite element response analyses.
The evaluations are in large part based on comparisons of computed levels
of stress with levels of stress deemed to be acceptable considering concrete
strengths and the probability, at least in a qualitative sense, that the postulated
earthquake ground motion will occur.
The following paragraphs are intended to aid in understanding concrete
behavior during earthquake loading and to provide a means for estimating
reasonable concrete strengths. However, these are simply guidelines for
making estimates. When performing a seismic safety evaluation of a concrete
dam, it is imperative that an appropriate amount of work be conducted to
investigate the characteristics and strengths of the specific concretes used or
proposed for a particular dam. The following guidelines are not intended to
replace those necessary investigations.
Concrete Strengths During Earthquake Loading
As previously discussed, concrete is a brittle material that exhibits significant
variations in its elasticity depending on the rate of loading. For the rapid
loading rates that occur during oscillatory inertia loads associated with
earthquakes, the concrete modulus-of-elasticity values increase. Typically,
concrete in a dam during an earthquake can experience minimum strain
followed by maximum strain in 0.1 sec or less. By conducting tests under
similar conditions, it has been shown that the dynamic uniaxial modulus-of-
elasticity values for concrete in constructed dams are about 25 percent higher
than the values obtained from typical short-term laboratory tests (5-3, 5-
OCR for page 112
112
22~. Although failure strains remain about the same as for short-term static
loads, the material stiffening that occurs during rapid loading, shown by
increased modulus of elasticity, affects concrete strengths and thus the acceptable
levels of computed stresses.
Compression
Concrete core samples have been obtained by drilling from a number of
dams in the United States and used to perform laboratory compression tests
at loading rates comparable to inertia loading rates during earthquakes. For
these concretes the uniaxial compressive strengths measured during rapid
loading rates were 12 to 52 percent larger than compressive strengths of
comparable samples measured during typical short-term tests (4-12~. Since
only two of the rapid loading test results published to date indicated compressive
strengths substantially higher than about 30 percent above typical standard
static test values, increases in uniaxial compressive strengths of 25 to 30
percent above static strengths appear reasonable.
T.
enszon
Core samples obtained by drilling at a number of dams have also been
used to perform laboratory tensile tests at loading rates comparable to those
attained during earthquakes. For these dams uniaxial and modulus-of-rupture
tensile strengths measured during rapid loading rates were 31 to 83 percent
larger than tensile strengths of comparable samples measured during typical
short-term tests (4-12~. Based on these results and others (3-18), an increase
of 50 percent above static tensile strengths appears reasonable.
The general relationship between tensile strength and compressive strength
of concrete is not linear. However, for the range of compressive strengths
common for concretes used to construct dams, the intact uniaxial static
tensile strength is approximately 10 percent of the static uniaxial compressive
strength (4-12~. When increased 50 percent for rapid loading conditions,
intact uniaxial concrete tensile strengths approximately equal to 15 percent
of static uniaxial compressive strengths are presently considered appropriate
for evaluating the seismic performance of concrete dams. However, it is
important to note that very few data exist concerning failure strains and
stresses during rapid strain-rate multiaxial loading conditions.
Because concrete does not demonstrate a linear relationship between stress
and strain, except at relatively low levels of applied loading, and because
most seismic evaluations are based on linear elastic analyses rather than
nonlinear analyses, some investigators have proposed the use of an apparent
tensile strength rather than actual tensile strength for such evaluations (4-
12, 6-6, 6-7~. The apparent tensile strength is equal to the tensile stress
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113
corresponding to actual uniaxial tensile strain at failure assuming a strictly
linear relationship between stress and strain. Under rapid loading conditions
the apparent tensile strength is approximately 25 percent greater than the
actual uniaxial tensile strength. This results in apparent rapid loading tensile
strengths that are approximately 20 percent of static uniaxial compressive
strengths for the range of compressive strengths common for concretes used
to construct dams.
While the concept of an apparent tensile strength is valid for evaluating
the results from linear elastic numerical analyses for severe seismic conditions,
it is important to remember that for all concrete dams the limiting tensile
strength of the concrete is that which exists across lift surfaces (the horizontal
surfaces between concrete placements that are typically spaced at intervals
of 1 to 10 ft over the height of the dam, depending on the type of dam and
the type of construction) and across the contact surfaces between the dam
and its rock foundation. Even in cases where particular efforts are implemented
during construction to prepare concrete and foundation contact surfaces for
bonding, uniaxial tensile strengths across bonded lift surfaces and foundation
contacts should be expected to be at least 10 to 20 percent less than corresponding
intact tensile strengths without lift or contact surfaces (3-18~. While the
decrease in tensile strength across bonded lift surfaces and foundation contacts
is an independent effect and has no relationship to the nonlinearity of the
stress-strain curve, under ideal conditions the two effects essentially offset
one another in terms of the tensile strength appropriate for evaluating the
results from linear elastic analyses. For dams where no specific construction
techniques, such as high-pressure water jetting, were employed to achieve
bond between lift surfaces and foundation contacts, significant portions of
the surfaces will probably not be bonded, and additional reductions in the
tensile strength used to evaluate seismic performance should be considered,
beyond the 10 to 20 percent indicated by the limited data available for ideal
. .
cone loons.
It is interesting to note that in some countries outside the United States
the tensile strength of concrete is discounted or routinely assumed to be
zero when evaluating the performance of concrete dams (6-8~. Since computed
tensile stresses are expected from linear elastic analyses of concrete dams
during significant earthquake excitation, discounting tensile strength necessitates
performing nonlinear analyses (6-8~. However, given the amount of data
suggesting that some reasonable tensile capacity can be expected in most
cases, as well as the uncertainties in the results from nonlinear analyses
performed to date, it is not recommended at present that the tensile capacity
of concrete be ignored in favor of performing nonlinear analyses.
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114
Shear
The shear resistance of concrete in dams, and along contacts with rock
foundations, is usually assumed to follow Mohr-Coulomb relationships.
Consequently, the shear resistance across a plane consists of the sum of two
forces: intact shear strength (usually termed cohesion) multiplied by intact
area, and frictional resistance (coefficient of friction or tan 0) multiplied by
normal load. Cohesion values, or zero normal load intact shear strengths,
are typically about 10 percent of static uniaxial compressive strengths based
on direct shear tests of concrete core samples, and coefficients of friction
are typically near 1. These static values are not usually increased to account
for rapid loading rates, because there is a lack of data documenting any
change in shear strength.
Evaluating Seismic Performance
At present the process of evaluating the seismic performance of concrete
dams using results from linear elastic numerical analyses, finite element or
other, is in most cases deterministic. The process involves comparing computed
levels of stress with levels that are considered acceptable based on considerations
of concrete strength and the likelihood of significant earthquakes occurring.
If computed levels of stress are generally less than or equal to levels considered
acceptable, the seismic performance and safety of the dam are considered
acceptable. If computed levels of stress exceed acceptable levels, the seismic
performance of the dam may be considered unacceptable. If computed
levels of stress exceed material strengths, a rational analysis of the seismic
performance of the dam is considerably more difficult and may not be
possible based on the results of linear analyses alone.
An earthquake that causes the largest ground motion expected to occur at
a dam site at least once during the economic life of the dam, usually taken
to be 100 years, is commonly termed a design basis earthquake (DBE). A
DBE should be considered a design loading condition, although in most
cases it is appropriate to consider it as an unusual loading condition. When
evaluating the performance of a concrete dam for a DBE, it is appropriate to
apply factors of safety to concrete strengths and require that there be no
excessive damage, no irreparable damage, no life-threatening uncontrolled
release of the reservoir water, and no interruption to systems or components
needed to maintain safe operation.
An earthquake capable of producing the largest ground motion that could
ever be expected at a dam site is commonly termed the maximum credible
earthquake (MCE). An MCE should be considered to be an extreme loading
condition. When evaluating the performance of a concrete dam for an
MCE, criteria based on factors of safety applied to concrete strengths are
not applicable since extensive damage, including extensive irreparable damage,
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116
stresses will usually be indicated near and above the reservoir water surface
elevation. These tensile stresses may occur on only one face of the dam at
any given time or on both faces simultaneously, particularly for loading
conditions involving minimum concrete temperatures. Generally, these tensile
stresses are not of concern unless accompanied by vertical tensile stresses
acting in the cantilever directions over a significant portion of the dam.
Since vertical contraction joints have little or no tensile capacity, it is reasonable
to assume that the indicated horizontal tensions would be replaced by slight
openings of the contraction joints. When contraction joint openings are
thought to occur, the potential for and consequences of any subsequent load
redistribution should be assessed. Since the analyses discussed in this section
are assumed to be linear elastic, load redistributions and the resulting increases
in other stresses cannot be precisely quantified. However, on a qualitative
basis it is possible to estimate whether sufficient reserve load-carrying capacity
exists in the adjacent sections and whether the stability of the dam can be
considered adequate.
When tensile stresses that approach or exceed the rapid-loading tensile
strength are computed in directions other than normal to contraction joints,
cracking should be assumed to occur. However, so long as the tensile
stresses occur over a very limited extent of the dam, do not repeatedly
exceed the tensile strength, or are the result of modeling anomalies (such as
the contact between the dam and its foundation), it is reasonable to conclude
that the cracking does not necessarily indicate unacceptable performance
for extreme events. However, the extent of such cracking must be estimated,
and computed stress distributions must indicate that adequate compressive
capability exists to accommodate subsequent load redistributions. In addition,
the overall distributions of principal stresses that develop at particular instants
of time should be evaluated to confirm that indicated regions of tensile
cracking are not likely to join together to form surfaces along which partial
sliding failures could occur, if such failures would result in a significant
life-threatening reservoir release.
In the case of arch dams analyzed assuming linear elastic material behavior,
the structure may exhibit a tendency toward developing a partial failure,
usually resembling the shape of a semicircular or rectangular notch in the
upper central portion of the dam, if the calculated seismic stresses are large.
Whether such partial failures could actually occur is unknown, since they
have not actually been observed. However, if the partial failures are credible,
their development would primarily depend on the extent of cracking, the
orientation of cracking, and whether arch action can restrain the notch-
shaped portions separated by cracking.
In the case of gravity dams, unless both the upstream and downstream
faces are sloped or the dam is unusually stiff, nest structures exhibit a
tendency toward developing horizontal cracks on both the upstream and
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117
downstream faces in the upper half of the dam when large stresses are
produced by earthquake inertia loading. Whether such cracking indicates
that sliding stability is significantly impaired depends primarily on the extent
of the indicated cracking and the duration of time when the cracking tendency
is indicated.
Potentialfor Sliding Failures: Except for the cases of sliding associated
with the partial notch-shaped failures described above, or for sliding failures
developing within or along rock foundations, which are discussed in a separate
section, sliding is not a credible failure mode for arch dams. For gravity
dams the potential for sliding or shear failures within the dam depends
primarily on the extent of cracking that develops during an earthquake. If
extensive cracking and a significant reduction in sliding resistance are indicated,
sliding stability can be checked using time histories of nodal point forces,
which are available as part of the output from most finite element programs
presently used to perform time history dynamic analyses. If the particular
finite element program used does not provide time histories of forces directly,
relatively simple modifications to the program are usually possible to obtain
them.
Normally, if cracking through the thickness of the dam is not indicated
and if substantial intact concrete remains at cracked locations, the sliding
stability will be acceptable (sliding factor of safety greater than 1.0 for
extreme loading conditions). If unacceptable factors of safety are calculated
at more than a few instants of time, nonlinear analyses incorporating a joint
element to represent the sliding plane of interest can be performed to estimate
the amount of sliding that will result, as recommended by the current criteria
of the U.S. Army Corps of Engineers and the Federal Energy Regulatory
Commission (6-9, 6-10~. However, at present, analyses incorporating joint
elements are limited to two-dimensional cases. If a dam has keyed contraction
joints or there are other three-dimensional effects offering restraint to potentially
unstable portions of the dam, results from two dimensional analyses incorporating
joint elements may have little practical meaning.
Potential for Overturning Failures: Because of their inherent resistance
to overturning and the extremely short duration of dynamic overturning
forces during earthquake excitation, overturning failures of well-proportioned
concrete dams during earthquakes are not possible. However, appurtenant
structures, such as parapet walls and gate support piers, could experience
overturning in severe earthquakes, and reinforcement that is designed to
resist the expected earthquake input should be provided for such components.
Buttress Dams
No major buttress dam has been constructed in the United States since
about the mid-1970s. Given the economics of roller-compacted concrete
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118
construction, it is unlikely that any significant buttress dams will be constructed
in the future. However, existing buttress dams have required, and undoubtedly
will continue to require, seismic evaluations.
Certain types of buttress dams are more susceptible to damage from
cross-channel earthquake ground motion than are arch or gravity dams.
However, the concrete comprising buttress dams is usually well reinforced,
unlike the unreinforced mass concrete used to construct arch and gravity
dams. Because of this reinforcement and because so few buttress dams
have been constructed during the past 20 to 30 years, there are no updated
criteria intended specifically for such dams that are comparable to available
criteria for arch and gravity dams. Consequently, to evaluate the seismic
performance of concrete buttress dams based on results from numerical
analyses, it is recommended that the most recent criteria developed by the
American Concrete Institute (6-11) be used, as set forth in code requirements
for reinforced concrete structures.
GUIDELINES FOR EVALUATING RESULTS FROM
NONLINEAR ANALYSES
No complete nonlinear time history earthquake analysis of a concrete
dam, together with its associated reservoir and foundation, has been done to
date. However, nonlinear analyses for selected aspects of nonlinear earthquake
response of concrete dams have been performed, and research applicable to
the nonlinear behavior of concrete and nonlinear analysis techniques continues
to be done.
Depending on the type of nonlinearity modeled, the criteria used to relate
the results from nonlinear analyses to expected performance may require a
different approach than that for linear analyses. If a nonlinear mechanism
primarily affecting the distribution of loads is modeled, such as vertical
contraction joints, results can be evaluated in much the same manner as
results from linear elastic analyses. However, for nonlinear mechanisms
providing for inelastic deformations, such as cracks forming potential sliding
surfaces, results that include accumulated displacements must be evaluated.
For these cases acceptable limits of accumulated displacements must be
established for which the dam would still be considered stable and capable
of safely resisting the loads acting after the earthquake has ended.
No detailed criteria for use in evaluating the results from nonlinear seismic
analyses of concrete dams are known to have been developed. Part of the
difficulty in setting forth detailed criteria for nonlinear seismic analyses is
that few definitive data exist concerning the development of failure mechanisms
in concrete dams. Research to identify all of the credible potential failure
mechanisms for concrete dams and to determine how failures could develop
during earthquakes is needed. Such research would not only lead to the
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development of rational criteria for evaluating the results from nonlinear
analyses of concrete dams but would also provide a basis for improving
criteria used for evaluating results from linear analyses.
GUIDELINES FOR EVALUATING FOUNDATION STABILITY
In addition to failures resulting from exceeding the bearing capacity of
the foundation rock, two types of potential foundation instability during
seismic events can be evaluated using results from finite element analyses.
The first type is potential sliding along the contact between the dam and
foundation rock, and the second is potential sliding of rock blocks or wedges
within the foundation and in contact with the dam. These potentially unstable
blocks or wedges are formed by intersecting planes associated with rock
discontinuities, such as faults and rock joints, and have sliding planes that
daylight downstream from the dam.
Sliding Stability Along Concrete-Foundation Contacts
Usually, sliding stability along the concrete-foundation contact of a concrete
arch dam is not a problem because of the wedging produced by arch action.
However, gravity and buttress dams usually do not have the benefit of this
wedging action, although they sometimes are designed to be curved in plan
to provide increased stability. Additionally, there can be cases where the
geometry of the abutment surfaces is not conducive to sliding stability,
adequate drainage is not provided along the contact, and the concrete is not
thoroughly bonded to the foundation rock. In such cases the results obtained
from time history finite element analyses, together with results from static
analyses that include the effects of uplift, can be used to calculate factors of
safety against sliding along the abutments.
Since loads acting at nodal points can be obtained from finite element
analyses on an element-by-element basis, time histories of loads acting on a
portion of the foundation surface corresponding to the bottom faces of one
or more elements can be readily determined. For most of the locations
along the modeled abutments, loading on a particular portion of the foundation
surface originates from elements in the modeled dam whose bottom faces
are in direct contact with the foundation. Depending on how the dam is
modeled, one or more elements in the dam may have an edge in contact
with the foundation as well. In addition to these edge forces, nodal forces
corresponding to any applied loads at the contact must be added to the
element nodal loads to satisfy equilibrium of forces at the node points.
In the case of an arch dam or a gravity dam constructed with keyed
contraction joints, instability at a particular location will cause the transfer
of excess driving forces acting on the unstable portion to adjacent portions,
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provided the adjacent portions have sufficient reserve load-carrying capability.
Therefore, even if one or more local instabilities exist, the dam could remain
stable. While such load transfers may be acceptable for infrequent, extreme
loading conditions, such as earthquakes, they should generally be considered
unacceptable for design loading conditions.
Sliding Stability Within Foundations
Potential foundation instabilities formed by intersecting rock discontinuities
(joints, shear zones, bedding planes, etc.) can also be evaluated using results
obtained from time history finite element analyses combined with results
from static analyses (6-12~. Typically, two modes of instability can be
considered: a block or wedge of rock formed by rock discontinuities underneath
the dam sliding along the surface of one plane of the discontinuity, and a
block or wedge of rock underneath the dam sliding along the line of intersection
of two of these discontinuities. In order for sliding to occur, the direction
of sliding must intersect a free surface downstream from the dam; sliding
instability is not likely if the direction of sliding is into the dam itself.
As for the evaluation of sliding stability along the foundation contact, if
all of the calculated factors of safety are greater than or equal to an acceptable
value, sliding stability can be considered adequate. If some of the calculated
factors of safety are less than an acceptable value, adequate stability may
still exist. However, the adjacent portions of the dam must be capable of
bridging the unstable foundation block and transferring excess driving forces
to adjacent portions of the foundation. Depending on the number of time
intervals when instability is indicated by a linear time history analysis and
the extent of the instability, a time history sliding-block analysis may be
required to fully evaluate stability. While load transfers involving significant
blocks within the foundation may be acceptable for infrequent, extreme
loading conditions, they should generally be considered unacceptable for
design loading conditions.
STABILITY FOLLOWING FAULT DISPLACEMENT
Generally concrete dams have not been sited at locations where there
were faults classified as active. However, as described in Chapter 2, two
gravity dams (Morris in California and Clyde in New Zealand) have been
constructed across faults in the foundation rock, using sliding joints in the
structure to accommodate possible fault movement. It is worth noting that
the fault under Morris Dam has since been classified as inactive.
In the future there may be sites considered suitable for concrete dams
where there is some possibility of fault displacements occurring underneath
the dam. In addition, there may be situations where an existing dam was
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constructed over a fault thought to be inactive and later determined to be
active. For these cases nonlinear analyses and criteria will be required to
assess the capability of concrete dams to safely withstand fault displacements.
Only one such analysis is known to have been performed (2-61~. Although
portions of the analysis were conducted using a nonlinear finite element
model, the analysis was greatly simplified.
Research is needed to develop criteria that can be used to evaluate the
results from numerical analyses simulating fault displacements. With sufficient
research, defensive design measures could be identified that would allow
concrete dams to safely withstand fault displacements. Defensive measures
have been satisfactorily incorporated into the design of embankment dams
and have been accepted as providing adequate protection against failure.
Conceptually, defensive measures for concrete dams also could be developed
that should be just as acceptable and safe.
EVALUATION OF CRITERIA
Present Criteria
Most of the seismic evaluations of concrete dams performed in the United
States are based on criteria set forth by the Bureau of Reclamation (6-1),
the U.S. Army Corps of Engineers (6-9), or the Federal Energy Regulatory
Commission (6-10~. The concepts discussed in this chapter are generally
consistent with these criteria. However, there are portions of the presently
used criteria that should be reviewed and possibly revised.
For example, past research and observations of prototype behavior have
clearly shown that pseudostatic stability analyses using simple seismic coefficients
will not realistically predict the response of concrete gravity dams to strong
earthquakes. Yet some of the criteria presently in use continue to allow or
even require pseudostatic analyses for the evaluation of the seismic response
of gravity dams, even though simple methods that provide more reliable
results are available (3-29, 3-30~. Except for gravity dams that are extraordinarily
stiff and less than about 100 ft in height, the results from pseudostatic
analyses are not likely to be comparable to expected prototype responses to
earthquakes. Because the results from these analyses are rarely meaningful,
pseudostatic analyses using seismic coefficients should be discontinued,
even for preliminary screening studies. For preliminary studies, starting
with an earthquake design spectrum, a rational simplified analysis (3-29, 3-
30) can be performed manually or implemented on a small computer.
Another aspect of some of the criteria presently being used that needs
further review is the treatment of uplift pressures. Several methods of
accounting for the effects of uplift have been proposed and are presently in
use. However, there are some significant differences between the various
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approaches, and these differences should be resolved. Comprehensive uplift
measurements from actual dams, similar to those assembled by the Bureau
of Reclamation (6-13), could be used to help resolve these differences.
Similarly, various criteria contain differing requirements concerning levels
of tensile stress considered acceptable, particularly along the interface between
the dam and its foundation. For instance, some criteria require that the
interface between foundation rock and concrete in gravity dams always be
assumed to have zero tensile strength. Although there are obviously cases
where zero tensile strength across the interface should be assumed, this
assumption is not appropriate in all cases. Most well-designed, well-constructed
concrete gravity dams analyzed two dimensionally for their response to significant
earthquake excitation will exhibit the tendency to develop tensile stresses
near and along the foundation contact. If the dam is well proportioned, if
an appropriate amount of foundation preparation has been performed, and if
appropriate construction techniques have been employed, sufficient tensile
capacity across the interface may exist to resist these tensile stresses. The
possibility that a discontinuity exists in the rock foundation within the first
few feet below a dam may by itself be insufficient justification for requiring
an assumption of zero tensile strength across the interface for two reasons.
First, a thorough geologic investigation of a site, even for existing dams,
may provide evidence that continuous rock discontinuities that could be
potentially troublesome do not exist. Second, even if such a discontinuity
did exist, its effect on the stability and seismic performance of a concrete
gravity dam may be quite different from the effect of an unhanded foundation
interface.
Deformation-Based Criteria
As discussed in the preceding sections, presently accepted criteria used
in the United States to evaluate the seismic performance of concrete dams
are based on comparing levels of computed stresses with concrete strengths.
This is a longstanding practice that is not likely to change in the near future.
However, as discussed in the section titled Creep Effects and Concrete
Strengths During Earthquake Loading in this chapter, the behavior of mass
concrete is highly strain-dependent. In fact, its behavior is more strain- or
deformation-dependent than stress- or load-dependent. In addition, the primary
unknowns calculated from finite element analyses are deformations and
strains. Calculated stresses are secondary variables, the computation of which
often involves extrapolation of strains and can result in some inconsistencies.
Although the use of stress-based criteria is appropriate for the linear
elastic analyses commonly performed at present to assess the seismic performance
of concrete dams, it may be inappropriate to use such criteria to evaluate
the results from analyses using nonlinear techniques that will continue to be
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developed. Since the behavior of mass concrete is more strain-dependent
than stress-dependent, strain-based criteria will likely be necessary in the
future to adequately evaluate results from nonlinear analyses. Evaluation of
results from linear analyses could also be improved through application of
suitable strain-based criteria. Consequently, as additional research is performed
concerning the behavior of mass concrete, researchers should consciously
begin to form the basis for developing deformation/strain-based criteria suitable
for evaluating the performance of mass concrete in dams.
Probability-Based Criteria
It is evident from the discussions in the preceding sections that the criteria
presently used to evaluate the seismic performance of concrete dams are
deterministic. Since characterizing the occurrence of earthquakes is most
meaningful in terms of probabilities of occurrence, use of probability-based
criteria to evaluate the seismic performance of concrete dams is an appropriate
approach. At present the uncertainties (expressed in probabilistic terms) of
site characteristics, material flaws, construction flaws, and other factors
influencing the seismic performance of dams are too significant to provide
for meaningful probabilistic evaluations. However, some work of this type
has been done, and conceptual principles have been considered (6-8~. It is
expected that such work will continue and that probabilistic safety evaluations
will become more common in the future.
RESEARCH NEEDS
1. Criteria and Guidelines
Guidelines similar to those described in this chapter have been used for
evaluating the seismic performance of concrete dams for at least the past 10
years. However, the criteria used remain relatively crude in comparison
with the complexity of dam-reservoir-foundation systems. To address this
disparity some investigators have chosen to attempt more complex analytical
solutions, but without improvements in the ability to relate numerical results
to prototype behavior; more complex analytical solutions remain outside the
realm of application. In fact, analytical techniques may have already advanced
beyond our present ability to develop input data consistent with the detail,
preciseness, and complexity of those solutions.
Before the reliability of evaluating the seismic performance and safety of
concrete dams can be significantly increased, the criteria used must be improved.
Criteria presently in use are considered adequate only in the context of the
present limited understanding of seismic excitation, material properties of
dam-reservoir-foundaiion systems, and resulting system response. Consequently,
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significant enhancements in criteria cannot be devised without preceding
improvements occurring in the understanding of prototype seismic response
of dam-reservoir-foundation systems. To achieve better understanding of
the seismic response of concrete dam systems and develop subsequent
improvements in criteria, more complete data concerning prototype seismic
response of concrete dams are needed. The data needed include:
significant levels of ground acceleration at various locations along the
abutments of concrete dams and at locations upstream and downstream from
the dams,
- hydrodynamic pressures at various locations along the upstream face
of concrete dams.
response accelerations at various locations along the dams,
joint openings of contraction joints near the upstream and downstream
faces in the upper central portions of concrete dams, and
—dynamic uplift pressures, particularly along the foundat~on-dam interface
of concrete gravity dams.
2. Continued Research
In addition to collecting and evaluating data from prototype behavior,
much can be gained by continuing research at suitably equipped research
centers. Therefore, the following research is also recommended:
—further characterization of the creep behavior of the mass concrete
used to construct dams, together with analytical improvements in accounting
for creep in numerical analyses,
studies of stress-strain relationships during rapid multiaxial loading
conditions, especially including tension,
—identification of failure mechanisms for concrete dams and Heir foundations
during earthquakes and delineation of the conditions that would cause various
failure mechanisms to develop, and
Development of defensive design measures to safely accommodate fault
displacements.
3. Creep Behavior and Stress-Strain Relationships of Mass Concrete
Conducting research in the above areas not only would allow further
improvements in analytical techniques but would also provide for improvements
in criteria relating analytical results to acceptable prototype behavior. Research
to further characterize creep behavior and stress-strain relationships of mass
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concrete during multiaxial loading conditions would be of particular value
for developing deformation or strain-based criteria. Such criteria should be
a priority for research and development because it offers the potential for
more realistic evaluation of mass concrete behavior under a variety of loading
conditions, especially those including seismic events.
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Representative terms from entire chapter:
loading conditions
