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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
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
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
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
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
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
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
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-
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
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.
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,
115 is acceptable. However, it is still appropriate to require that there be no life-threatening uncontrolled release of reservoir water and no interruption to operating systems required for safety. Criteria for concrete dams presently used by the Bureau of Reclamation (6-1), the U.S. Army Corps of Engineers (6-9), and the Federal Energy Regulatory Commission (6-10) are generally consistent with this concept. Evaluating the seismic performance of concrete dams is considerably more complex than evaluating their static performance, particularly when the postulated earthquake motion is severe. For seismic analyses where all of the computed dynamic stresses summed with static stresses are below acceptable levels, the evaluation is straightforward. However, for MCE analyses when the ground motion is severe, such a simple evaluation usually is not possible, and considerably more effort is required to understand the dam's performance and provide a realistic evaluation. In such cases time history analyses are usually required, together with a considerable amount of postprocessing of the response data. If the computer program used to perform the analyses is not capable of calculating stresses in the planes of element faces, postprocessing should be performed to calculate face stresses in the appropriate local coordinate system. Postprocessing is also useful in determining locations (where stresses large enough to be of concern are expected to occur) that could experience large stresses at any particular time during an earthquake and the number of times the large stresses are expected to be repeated during the earthquake. In addition, the capability to produce plots showing time histories of stresses at particular locations, along with overall stress distributions at specific times, is especially useful. Arch and Gravity Dams When evaluating the seismic performance of a concrete dam, it is important that computed stresses at the dam faces be resolved into arch (or horizontal in the case of gravity dams) and cantilever components and that principal face stresses be calculated at significant instants of time during the earthquake. Other than foundation stability and bearing capacity of the foundation rock, the ultimate load-carrying capability of concrete dams is limited by the compressive strength of the concrete (and by sliding resistance for gravity dams). Thus, it is important to confirm that maximum computed earthquake compressive stresses do not approach the concrete's rapid-loading compressive strength. Computed compressive stresses will usually be well below this compressive strength limit; however, it is not unusual for computed tensile stresses to exceed the concrete's rapid-loading tensile strength when ground motion is severe. Unless the numerical model developed to perform the seismic analysis accounts for the existence of vertical contraction joints, horizontal tensile
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
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
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
119 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,
120 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
121 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
122 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
123 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,
124 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
125 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.
