Design Criteria for Concrete Arch and Gravity Dams

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A WATER RESOURCES TECHNICAL PUBLICATIONENGINEERING MONOGRAPti No. 19

Design Criteria for CoArch and Gr vity DamsUNITED STATES DEPARTMENTOF THE INTERIORBureau of Reclamation


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A WATER RESOURCES TECHNICAL PUBLICATIONEngineering Monograph No. 19

Design Criteria for ConcreteArch and.Gravity Dams

Office of Design and ConstructionEngineering and Research CenterDenver, Colorado 80225

United States Department of the InteriorBureau of Reclamation


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PrefaceThis revision of Engineering Monograph No. 19presents current Bureau of Reclamation designcriteria upon w hich are based design decisionsconcerning mass concrete dams. The basic consid-erations and specific design criteria set forth in thismonograph constitute the present-day standards forBureau designs.More than two decades have elapsed since thefirst issuance of this monograph in 1953. The intentof the publication at that time was to documentbasic concepts bearing on Bureau of Reclamationdesigns of concrete arch and gravity dams that hadevolved during the preceding 50 years. Compilationof the criteria that were essential to successfulconstruction and operation of many notable con-crete dams on Reclamation water resource projects,such as Hoover, Grand Coulee, Shasta, and Hun-gry Horse Dams, resulted in the first orderly recordof the Bureaus philosophy and basic criteria affect-ing the conception and development of concretedams. The Bureaus recognition of the importanceof keeping abreast of changing design technologywas evidenced by revision of the monograph in1%0.In the near ly 15 years following the first revisionof the monograph, design technology advanced at arapid rate. Such new knowledge as finite element

analysis, geologic advances leading to increasedunderstanding of foundations and abutments ofdams, improved techniques of seismic analyses,development of computer techniques for trial-load.analyses, and other advances accompanied by theprogress in computer technology opened new ave-nues to design and, in turn, brought about refine-ments in the basic concepts guiding dams design.Dams completed during this period, including GlenCanyon, Flam ing Gorge, Morrow Point, and Yel-lowtail Dams, reflect this progress.Concrete dams on Bureau of Reclamation proj-ects continue to be key elements in project develop-ment, as indicated by such major structures asGrand Coulee Forebay; Crystal, Nambe Falls, andAuburn Dams that are under construction or in

advanced stages of design.Assurance that Bureau design practices for con-crete dams remain upto-date and consistent withcurrently accepted good engineering practice can beachieved only through a program of continuingreview, evaluation, modification of standards, anddevelopment of new criteria as required. The reviewmust be made in light of developing technology inall fields associated with concrete dam design. Inthis effort, the Bureau of Reclamation is continu ingii i


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ContentsPage

Preface.. ..........................................................Introduction .......................................................Design Ph~osophy ...............................................

. . .111

11PART I-ARCH DAMS

Concrete Properties-Static ......................................... 5Strength ........................................................ 5Elastic Properties ................................................ 5Thermal Properties .............................................. 6

Concrete Propertiee-Dynamic ...................................... 6Strength ........................................................ 6Elastic Properties ................................................ 6

Average Properties.. ............................................... 6Foundation Properties .............................................. 7

Deformation Modulus ............................................ 7Shear Strength .................................................. 7Pore Pressure and Permeability ................................... 8Treatment ...................................................... 8Compressive and Tensile Strength ................................. 8V


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vi CONTENTSPage

Loads .............................................................Reservoir and Tailwater Loads ....................................Temperature ....................................................Internal Hydrostatic Pressures ....................................Dead Load .....................................................Ice ............................................................Silt ............................................................Earthquake .....................................................

Load Combinations ................................................Configuration of Dam and Foundation ...............................Cracking ..........................................................Factors of Safety ...................................................Bibliography .......................................................

PART II-GRAVITY DAMSConcrete Properties-Static .........................................

Strength ........................................................Elastic Properties ........................................ ........Thermal Properties ..............................................Concrete Properties-Dynamic ......................................

Strength ........................................................Elastic Properties ................................................AverageProperties .................................................Foundation Properties ..............................................

Deformation Modulus ............................................Shear Strength ..................................................Pore Pressure and Permeability ...................................Treatment ......................................................Compressive and Tensile Strength .................................Loads .............................................................

Reservoir and Tailwater Loads ....................................Temperature ....................................................Internal Hydrostatic Pressures ..................... .I. .............

9991011111111

1213131429

191919202020202020202122222222222324


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CONTENTS vi iPage

Dead Load .....................................................Ice ............................................................Silt ............................................................Earthquake .....................................................Load Combinations ................................................Configuration of Dam and Foundation ...............................Cracking ..........................................................Factors of Safety ...................................................Bibliography.....................................................

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FIGURESFigure1. Shear resistance on an existing joint in rock foundation of an archdam....................................................2. Arch abutment shaping criter ia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3. Shear resistance on an existing joint in rock foundation of a gravitydam....................................................4. Measured and computed uplift pressures for Shasta Dam . . . . . . . .5. Diagrams of base pressures acting on a gravity dam . . . . . . . . . . . .

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IntroductionDesign Philosophy

The Bureau of Reclamations philosophy of con-crete dam design is founded on rational and consist-ent criteria which provide for safe, economical,functional, durable, and easily maintained struc-tures. It is desirable, therefore, to establish, main-tain, and update design criteria. Under specialconditions, consideration can be given to deviatingfrom these standards. In those situations the de-signer bears the responsibility for any deviation and,therefore, should be careful to consider all ramifica-tions. Accordingly, each of the criteria definitions inthis monograph is preceded by a discussion of theunderlying considerations to explain the basis of thecriterion. This serves as a guide in appraising thewisdom of deviating from a particular criterion forspecial conditions.Loadings.-The designer can assure the safety ofconcrete dams by designing for all combinations ofloads including those whose simultaneous occur-rence is highly improbable and by using undulylarge safety factors. This may lead to overlyconservative, uneconomical designs. A structuredesigned for the loading combinations and corre-sponding safety factors listed in this monographshould be safe, yet economical.

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Design Data.-Modem methods of analysis arepowertirl and sophisticated; yet, without meaningfuland accurate input data, they may produce uselessand even erroneous results. Design data must bedetermined as accurately and completely as possi-ble. The data should be derived from field andlaboratory tests plus measurements taken from in-service dams. For occasional situations where thedata are incomplete, the designer may supplementthese data by referring to other dams with similarconditions. When data are absolutely unavailable,he may estimate them by using conservative engi-neering judgment. This approach may lead to overlyconservative designs and emphasizes the advantageof conducting comprehensive programs to obtainadequate design data.Safety Factors.-Safety factors have been estab-lished to limit the allowable stresses in the materialsas determined by analysis. The need for safetyfactors is due primarily to uncertainties in (1) theservice loads, (2) the variability of materials, (3)construction practices, and (4) the correctness ofanalyses. These uncertainties also preclude deter-mining the safety of the dam exactly; therefore,factors of safety are selected based upon experienceand judgment.


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Part I Arch Dams


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Arch DamsCONCRETE PROPERTIES-STATICStrength

Basic Considerations.-An arch dam should beconstructed of concrete that meets the designcriteria for strength, durability, permeability, andother required properties. Because of the sus tainedloading generally associated with them, the concreteproperties used for the analyses of static loadingconditions should include the effects of creep.Properties of concrete vary with age, the type ofcement, aggregates,and other ingredients, as well astheir proportions in the mix [3]. Since differentconcretes, gain strength at different rates, measure-ments must be made of specimens of sufficient ageto permit evaluation of ultimate strengths.Although the concrete mix is usually designedonly for compressive strength, appropriate testsshould be made to determine the tensile and shearstrength values.The mix should be proportioned to produceconcrete of sufficient strength to meet the designrequirements. Concrete strengths should be deter-mined by tests of the full mass mix in cylinders ofsufficient size to accommodate the largest sizeaggregate to be used. The compressive strength ofconcrete, determined as specified above, shouldsatisfy early load and construction requirements and

at some specific age should have a ratio to theallowable working stress as determined by thedesigner.The specific age is often 365 days, but it mayvary from one structure to another. The strengthshould be based on an evaluation of ultimate strengthand safety factor requirements discussed later inthese criteria.Tensile strength of the concrete mix should bedetermined as a companion test series to the testsfor the compressive strength.Shear strength is a combination of cohesivestrength and internal friction which varies with thenormal compressive stress. Companion series shearstrength tests should be conducted at several differ-ent normal stress values covering the range ofnormal stresses to be expected in the dam. Theseshould then be used to obtain a curve of shearstrength versus normal stress for test cylinders ofthe same age as required for compressive and ten-sile test cylinders.Elastic Properties

Basic Considerations.-Poissons ratio, the JUS-mined modulus of elasticity of the concrete, and thelatters ratio to the deformation modulus of thefoundation have significant effects on stress distnbu-5


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6 DESIGN CRITERIA FOR CONCRETE ARCH AND GRAVITY DAMStion in the structure. Values of the modulus ofelasticity, although not directly proportional to con-crete strength, follow the same trend with the higherstrength concretes having a higher value for modu-lus of elasticity. As with the strength properties, theelastic modulus is influenced by mix proportions,cement, aggregate, admixtures, and age. The defor-mation that occurs immediately with application ofload depends on the instantaneous elastic modulus.The increase in deformation which occurs over aperiod of time with a constant load is the result ofcreep or plastic flow in the concrete. The effects ofcreep are generally accounted for by determining asustained modulus of elasticity of the concrete foruse in the analyses of static load ings.Instantaneous moduli of elasticity and Poissonsratios should be determined for the different ages ofconcrete when the cylinders are initially loaded. Thesustained modulus of elasticity should be deter-mined from these cylinders after specific periods oftime under constant sustained load. These periodsof loading are often 365 and 730 days. The cylindersto be tested should be of the same size and cured inthe same manner as those used for the compress ivestrength tests. The values of instantaneous modulusof elasticity, Poissons ratio, and sustained modulusof elasticity used in the analyses should be theaverage of all test cylinder values.Thermal Properties

Basic Considerations .-The effects of tempera-ture change in an arch dam are often a major part ofthe design considerations. Especially in the smallerdams, the stresses caused by temperature changescan be larger than those from the reservoir loading.The effects of temperature change depend on thethermal properties of the concrete. These propertiesare the coefftcient of thermal expansion, thermalconductivity, specific heat, and diffusivity [4].The coefficient of thermal expansion is the lengthchange per unit length for 1 degree temperaturechange. Thermal conductivity is the rate of heatconduction through a unit thickness over a unit areaof the material subjected to a unit temperaturedifference between faces. The specific heat isdefined as the amount of heat required to raise thetemperature of a unit mass of the material 1 degree.Diffusivity of concrete is an index of the facilitywith which concrete will undergo temperaturechange. The diffusivity is calculated from the valuesof the specific heat, thermal conductivity, anddensity [4].

Criteria.-Appropriate laboratory tests should bemade of the design mix to determine all concreteproperties.

CONCRETE PROPERTIES-DYNAMICStrength

The Reclamation laboratory is presently testingthe strength of concrete when the concrete issubjected to dynamic loading. However, data arenot yet available to indicate what the strengthcharacteristics are under dynamic loading.

Elastic PropertiesUntil dynamic modulus information is availablethe instantaneous modulus of elasticity determined

for concrete specimens at the time of initia l loadingshould be the value used for analyses of dynamiceffects.

AVERAGE PROPERTIESBasic Considera tions .-Necessary values of con-crete properties may be estimated from publisheddata for preliminary studies until laboratory test dataare available [5J Until long-term tests are made todetermine the effects of creep, the sustained modu-lus of elasticity should be taken as 60 to 70 percent

of the laboratory value for the instantaneous modu-lus of elasticity.Criteria.-If no tests or published data are availa-ble, the following average values for concreteproperties may be used for preliminary designs:Compressive strength-3,000 to 5,000 lb&r2 (20.7to 34.5 MPa)Tensi le strength-5 to 6 percent of the compres-sive strengthShear strength:Cohesion-about 10 percent of the compressivestrengthCoefficient of internal friction-l .OPoissons ratio-O .2Instantaneous modulus of elasticity-5.0 x 106 bs/in* (34.5 GPa)Sustained modulus of elasticity-3.0 x 106 bs/in*(20.7 GPa)Coefficient of thermal expansion-5.0 x lO-j/F(9.0 x 1OWZ)Unit weight-150 lbs/ft3 (2402.8 kg/m3)


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ARCH DAMS 7FOUNDATION PROPERTIESDeformation Modulus

Basic Considerations .-Foundation deformationscaused by loads from the dam affect the stressdistributions within the dam. Conversely, responseof the dam to external loading and foundationdeformability determines the stresses within thefoundation. Proper evaluation of the dam foundationinteraction requires as accurate a determination offoundation deformation characteristics as possible.Although the dam is considered to be homogene-ous, elastic, and isotropic, its foundation is gener-ally heterogeneous, inelastic, and anisotropic. Thesecharacteristics of the foundation have significanteffects on the deformation moduli of the foundation.The analysis of an arch dam should include theeffective deformation modulus and its variation overthe entire contact area of the dam with the founda-tion.The deformation modulus is defined as the ratioof applied stress to elastic strain plus inelastic strainand should be determined for each foundationmaterial. The effective deformation modulus is acomposite of deformation moduli for all materialswithin a particular segment of the foundation.Foundation investigations should provide informa-tion related to or giving deformation moduli andelastic moduli. The information includes elasticmodulus of drill core specimens, elastic modulusand deformation modulus from in situ jacking tests,deformation modulus of fault or shear zone mate-rials, and logs of the jointing that occurs inrecovered drill core. Information on the variation ofmaterials and their prevalence at different locationsalong the foundation is provided by the logs of drillholes and by tunnels in the foundation. Goodcompositional descriptions of the zones tested fordeformation modulus and adequate geologic loggingof the drill cores permit extrapolation of results tountested zones of similar material.Criteria .-The following foundation data shouldbe obtained for the analysis of an arch dam:

l The deformation modulus of each type of mate-rial within the loaded area of the foundation.The effects of joints, shears, and faults obtainedby direct (testing) or indirect (reduction factor)methods [lo].l An effective deformation modulus , as deter-mined when more than one type of material ispresent in a foundation.l The effective deforamtion modulus , as deter-

mined at enough locations along the foundationcontact to provide adequate definition of thevariation in deformability and to permit extrapo-lation to untested areas when necessary.Shear Strength

Basic Considerations .-Resistance to shearwithin the foundation and between the dam and itsfoundation depends upon the cohesion and internalfriction inherent in the foundation materials and inthe bond between concrete and rock at the contactwith the dam. These properties are determined fromlaboratory and in situ tests. The results of labora-tory triaxial and direct shear tests, as well as in situshear tests, are generally reported in the form of theCoulomb equation:

R = CA + N tan 4, or(Shear resistance) = (unit cohesion times area)+ (effective normal force timescoefficient of internal friction)

which defines a linear relationship between shearresistance and normal load. The value of shearresistance obtained as above should be limited touse for the range of normal loads used for the tests.Although this assumption of linearity is usuallyrealistic for the shear resistance of intact rock overthe range of normal loads tested, a curve of shearresistance versus normal load should be used formaterials other than intact rock. The shear resist-ance versus normal load relationship is determinedfrom a number of tests at different normal loads.The individual tests give the relationship of shear

Figure I.-Shea r resistance on an existing joint in rock founda-tion of an arch dam.


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8 DESIGN CRITERIA FOR CONCRETE ARCH AND GRAVITY DAMSresistance to displacement for a particular normalload. The results of these individual tests are usedto obtain a shear resistance versus normal loadcurve as shown on figure 1. The displacement usedto determine the shear resistance is the displace-ment that can be allowed on the possible slidingplane without causing unacceptable stress concen-trations w ithin the dam. Since specimens tested inthe laboratory or in situ are small compared to thefoundation, the scale effect should be carefullyconsidered in determining the values of shear resist-ance to be used.When a foundation is nonhomogeneous, the pos-sible sliding surface may consist of different mate-rials. Intact rock reaches its maximum break bondresistance with less deformation than is necessaryfor fractured materials to develop their maximumfrictional resistances. Therefore, the shear resistancedeveloped by each fractured material depends onthe displacement of the intact rock part of thesurface. If the intact rock shears, the shear resist-ance of the entire plane is equal to the combinationof the slid ing frictional resistance for al l materialsalong the plane.Criteria.-An adequate number of tests, as deter-mined by the designer for each material along thepossible sliding planes, should be made to obtain ashear resistance versus normal load relationship.The value of shear resistance recorded during testsshould be measured at displacements that corre-spond to those expected to occur along the in situpotential s liding planes.When the foundation along the plane of potentialsliding is nonhomogeneous, the total shear resist-ance is the summation of shear resistances of all thematerials along the plane.Pore Pressure and Permeability

Basic Considerations.-Analysis of a dam foun-dation requires knowledge of the hydrostatic pres-sure distribution in the foundation. Permeability iscontrolled by the characteristics of the rock type,the jointing systems, the shears and fissures, faultzones, and, at some damsites, by solution cavities inthe rock. The exit gradient for shear zone materialsthat surface near the downstream toe of the damshould also be determined to check against thepossibility of piping [ 11.Laboratory values for permeab ility of samplespecimens are applicable only to the portion orportions of the foundation that they represent.

Permeability of the aforementioned geologic fea-tures can best be determined by in situ testing. Thepermeabilities obtained are used in the determina-tion of pore pressures for analyses of stresses,stability, and piping. Such a determination may bemade by several methods including two- and three-dimensional physical models, two- and three-dimen-sional finite element models, and electric analogs.If foundation grouting and drainage or othertreatment are to be used, their effects on the porepressures should be included.Criteria .-A sufficient number of tests, as deter-mined by the designer, should be made to determinethe permeability of the foundation rock, joints andfissures, fault zones, and solution cavities [6,7JAn adequate method of analysis should be usedto determine pore pressures within the foundation.The effects of any grouting, drainage, and otherfoundation treatment should be included.Treatment

Basic Considerations .-Foundation treatment isused to correct deficienc ies and improve physica lproperties by grouting, drainage, excavation ofinadequate materials, reinforcement, and backfillwith concrete. Some reasons for foundation treat-ment are: (1) improvement of deformation moduli,(2) prevention of sliding of foundation blocks, (3)prevention of relative displacement of foundationblocks, (4) prevention of piping and reduction ofpore pressures, and (5) provision of an artificialfoundation in the absence of adequate materials.Regardless of the reason for the foundationtreatment, its effects on the other foundation proper-ties should be considered in the analyses.Criteria .-Effects of treatment on foundationproperties should be considered.Compressive and Tensile Strength

Basic Considerations .-Compressive strength ofthe foundation rock can be an important factor indetermining thickness requirements for a dam at itscontact with the foundation. Where the foundationrock is nonhomogeneous, tests to obtain compres-sive strength values should be made for each typeof rock in the loaded portion of the foundation.A determination of tensile strength of the rock isseldom required because unhealed joints, shears,etc., cannot transmit tensile stress within the foun-dation.


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10 DESIGN CRITERIA FOR CONCRETE ARCH AND GRAVITY DAMStemperature loads are the differences between theclosure temperature and concrete temperatures tobe expected in the dam during operation [4].The closure temperature of an arch dam isdefined as the mean concrete temperature at thetime the structure is assumed to act monolithicallyand arch action begins. Generally, a monolithicstructure is obtained by grouting the vertical con-traction joints or by backtilling the closure slot.Natural cooling of the concrete will result invariations in closure temperatures, depending uponheight and thickness of the dam, climatic conditions,and the construction schedule.By artificially cooling the concrete with embeddedtemperature control systems, the closure temperaturecan be controlled to be uniform throughout the damor varied over the height of the structure to achievethe desired stress distribution. The closure tempera-ture or temperatures to be incorporated into thedesign should be determined from results of stressanalyses and modified as necessary by practicalconsiderations such as costs of temperature controlmeasures, site conditions, and construction pro-grams.Concrete temperatures to be expected duringoperation of the dam are determined from studieswhich include the effects of ambient air tempera-tures, reservoir water temperatures, and solar radia-tion.When the designer is m aking studies to determineconcrete temperature loads and temperature gra-dients, varying weather conditions can be applied.Similarly, a widely fluctuating reservoir water sur-face will affect the concrete temperatures. In deter-mining temperature loads, the following conditionsand temperatures are used.

(1) Mean air temperature .-The average airtemperature which is expected to occur at thesite. These are normally obtained from theNational Weather Service records of the meanmonthly air temperatures and the mean dailymaximum and minimum air temperatures.(2) Usual weather con&ions.-The combina-tion of the daily air temperatures, a l-weekcycle representative of the cold (hot) periodsassociated with barometric pressure changes,and the mean monthly air temperatures. Thiscondition will account for temperatures whichare halfway between the mean monthly airtemperatures and the minimum (maximum) re-corded air temperatures at the site.

(3) Extreme weather conditions.-The combnation of the daily air temperatures, a 2-weecycle representative of the cold (hot) periodassociated with barometric pressure changeand the mean monthly air temperatures. Thicondition will account for the minimum (maxmum) recorded air temperatures at the siteThis is an extreme condition and is seldomused.(4) Mean concrete temperatures.-The average concrete temperatures between the upstream and downstream faces which will resufrom mean air temperatures, reservoir watetemperatures associated with the design resevoir operation, and solar radiation.(5) Usual concrete temperatures .-Same aabove, except that usual weather conditions arapplied.(6) Extreme concrete temperatures .-Sameas above, except that extreme weather conditions are applied.Criteria .-For reconna issance and feasibility designs, temperature studies that give the range ofmean concrete temperatures are satisfactory. Finadesign studies should use such methods asSchmidts [4], or finite element methods to determine concrete temperatures and temperature gradients between the faces of the dam as they varythroughout the year in different parts of the struc-ture.

Internal Hydrostatic PressuresBasic Considera tions .-Hydrostatic pressurescaused by reservoir and tailwater ,pressures occurwithin the dam and foundation in pores, joints,cracks, and seams. The distribution and magnitudeof these internal pressures can be modified byplacing formed drains near the upstream face of thedam. When drains are used, the lateral spacing anddistance from the upstream face will depend on themaximum reservoir depth and thickness of the damDrains are constructed roughly paralle l to thevertically curved upstream face of recently designedBureau arch dams which are curved in both verticaland horizontal directions.Internal hydrostatic pressures reduce the compressive stresses acting within the concrete, therebylowering the frictional shear resistances. Unlikegravity dams, which depend on shear resistance forstability, arch dams resist much of the applied load


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ARCH DAMS 11by transferring it horizontally to the abutments byarch action.The effects of any internal hydrostatic pressuresin arch dams, therefore, will be distributed betweenboth vertical and horizontal elements. A recentanalysis of these effects on an arch dam of moder-ate height showed a stress change of approximately5 percent of the allowable stress. The capability ofanalyzing the effects of internal hydrostatic pressurehas not been incorporated as a regular part of theanalys is because of the minor change n stress.The internal pressure distribution through thefoundation depends on depth of drains, grout cur-tain, rock porosity, jointing, faulting, and any othergeologic features that may modify the flow. Deter-mination of such pressure distributions can be madefrom flow nets computed by several methods includ-ing two- and three-dimensional physical models,two- and three-dimensional finite element models,and electric analogs.Criteria.-Because of the small effect of internalhydrostatic pressure within an arch dam, it is notincluded in the design analyses. However, formeddrains in the dam should be utilized, where appro-priate, to minimize internal hydrostatic pressures.Foundation drainage and grouting should be in-cluded to reduce the internal hydrostatic pressureswithin the foundation.Dead Load

Basic Considerations.-Dead load is the weightof concrete plus such appurtenances as gates andbridges. The construction and grouting sequencecan affect the manner in which dead load istransmitted to the foundation. All dead load im-posed on the structure prior to the grouting ofcontraction joints is assumed to be transmittedvertically to the foundation without any transfer ofshear across the ungrouted joints. Dead load im-posed after grouting of contraction joints is assumedto be distributed between vertical and horizontalelements in much the same manner as other loads.Criteria .-The magnitude of dead load is consid-ered as the weight of concrete plus appurtenances.Effects of the construction and grouting sequenceshould be considered in determining the distributionof dead load.Ice

Basic Considerations .-Ice pressures can pro-duce a significant load against the face of a dam in

locations where winter temperatures are coldenough to cause a relatively thick ice cover. Icepressure is created by thermal expansion of the iceand by wind drag. Pressures caused by thermalexpansion of the ice depend on the temperature riseof the ice, thickness of the ice sheet, the coefficientof thermal expansion, the elastic modulus, and thestrength of the ice. W ind drag depends on the sizeand shape of the exposed area, the roughness of thesurface, and the direction and velocity of the wind.Ice pressures are generally considered to be atransitory loading. Many dams will be subjected tolittle, if any, ice pressure. The designer shoulddecide, after consideration of the above factors, ifan allowance for ice pressure is appropriate.Criteria.-The method of Monfore and Taylor[8] may be used to analyze anticipated ice pressuresif necessary basic data are available. An acceptableestimate of ice load to be expected on the face of astructure may be taken as 10,000 lbs/lin ft (146kN/m) of contact between the ice and the dam foran assumed ice depth of 2 feet (0.6 meter) or morewhen basic data are not available to computepressures.Silt

Basic Considerations.-Not all dams will besubjected to silt pressures, and the designer shouldconsider all available hydrologic data before decid-ing whether an allowance for silt pressure is neces-sary.Criteria .-Horizontal pressure exerted by thesaturated silt load is assumed to be equivalent tothat of a fluid weigh ing 85 Ibs/ft3 (1362 kg/m3).Vertical pressure exerted by saturated silt is deter-mined as if silt were a soil having a wet density of120 lbslft 3 (1922 kg/m 3, the magnitude of pressurevarying directly with depth.

EarthquakeBasic Considerations .-Concrete arch dams areelastic structures which may be excited to reso-

nance when subjected to seismic disturbances. Twosteps are necessary to obtain loadings on an archdam when such a disturbance occurs. The first stepis to estimate magnitudes and locations of earth-quakes to which the dam may be subjected and todetermine the resulting rock motions at the site. Thesecond step is to determine the response of the damto these earthquakes by either the response spec-trum or time-history methods.


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12 DESIGN CRITERIA FOR CONCRETE ARCH AND GRAVITY DAMSMethods of determining a design earthquakewhich represents an operating basis event arepresently under development. These methods willconsider: (1) historical records to obtain frequencyof occurrence versus magnitude, (2) useful life ofthe structure, and (3) a statistical approach todetermine probable occurrence of different magni-

tudes of earthquakes during the l ife of the structure.When future developments produce such methods,suitable safety factors will be included in thecriteria.Maximum Credible Earthquake .-Mostearthquakes are the result of crustal movementsof the earth along faults. Geolog ic examinationsof the area should be made to locate any faults,determine how recently activity has occurred,and estimate the probable length of the fault.Records of seismologica l activity in the areashould also be studied to determine magnitudeand location of any recorded earthquakes whichmay affect the site. Based on these geologicaland historical data, hypothetical earthquakes,usually having magnitudes greater than thehistorical events, are estimated for any activefaults in the area. These earthquakes areconsidered the most severe associated with thefaults and are assumed to occur at the pointson those faults closest to the site. This definesthe Maximum Credible Earthquake in termsof Richter magnitudes and distances to the site.

The field of earthquake engineering is currentlythe subject of much research and development. Thefollowing criteria represent the current conceptsused by the Bureau to obtain earthquake loads forconcrete arch dams.Criteria.-The dam should be analyzed for theMaximum Credible Earthquake.(1) Response spectrum .-A response spec-trum at the site should be determined for eachMaximum Credible Earthquake by all threemethods described in appendix D of reference[9]. The composite of the three spectra be-

comes the design response spectrum.(2) Time history .-The required accelero-grams may be produced by appropriate adjust-ment of existing or artific ially generated acce-lerograms. The response spectrum computedfrom an adjusted accelerogram must correspondto the above-defined design response spectrum.(3) Structural response .-The analyticalmethods used to compute natural frequencies,

mode shapes, and structural response are described in another Reolamation publication [I].LOAD COMBINATIONS

Basic Considerations .-Arch dams should bedesigned for all appropriate load combinations usinthe proper safety factor for each. Combinations oftransitory loads, each of which has only a remoteprobability of occurrence at any given time, have anegligible probability of simultaneous occurrenceand should not be considered as an appropriate loadcombination. When large fluctuations of the waterlevel and temperature may be expected, the designshould give an acceptable balance of stresses or thedifferent applicable load combinations.Criteria.-An arch dam should be designed fothe applicable load combinations using the safetyfactors prescribed under Factors of Safety in thismonograph. The loading combinations to be considered are as follows:

(1) Usual loading cor&inations.+a) Effectsof minimum usual concrete temperatures andthe most probable reservoir elevation occurringat that time with appropriate dead loads, tailwater, ice, and silt.(b) Effects of maximum usual concrete temperatures and the most probable reservoir elevation occurring at that time with appropriatedead loads, tailwater, and silt.(c) Normal design reservoir elevation and theeffects of usual concrete temperatures occurringat that time with appropriate dead loads, tailwater, ice, and silt.(d) Minimum design reservoir elevation and theeffects of concrete temperatures occurring athat time with appropriate dead loads, tailwater,ice, and silt.(2) Unusual loading combinations.-Maxi-mum design reservoir elevation and the effectsof mean concrete temperatures occurring athat time with appropriate dead loads, tailwaterand silt.

(3) Extreme load ing combinations .-Any othe usual loading combinations plus effects othe Maximum Credible Earthquake.(4) Other loadings and investigations.-(a)Any of the above loadings plus hydrostaticpressures within the foundation for foundationstability studies.(b) Dead load.(c) Any of the above loadings revised to reflec


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ARCH DAMS 13the chronological application of loadings toinclude the effects of construction and groutingsequences if the contraction joints are to begrouted in stages.(d) Any other loading combination which, inthe designers opinion, should be analyzed for aparticular dam.

CONFIGURATION OF DAM AND FOUNDATIONBasic Considerations.-The shape of an archdam and the configuration of its foundation contactsare extremely important in providing stability andfavorable stress conditions. Proper curvatures of thedam in both horizontal and vertical directions aredesirable to obtain acceptable stresses and aneconomic design. The greatest degree of horizontalcurvature cons istent with the limitation on maxi-mum central angle at the crest and other require-

ments for the site will generally provide the mosteffective arch action for circular horizontal.arches inrelatively narrow sites. When the economy of thestructure is considered, the maximum practicableangle is between 90 and 110 for the top arch.Similarly, effective arch action can be achieved byusing polycentered horizontal arches in the widersites.Added thickness at the abutments of the dam canbe used to control and distribute stresses transmit-ted to the foundation by the use of abutment pads,fillets, 6r variable thickness arches.The angle of incidence of a tangent to theintrados with contours for the competent rockshould be large enough to provide adequate founda-tion rock cover in the direction of the resultantforce. The contact of the dam with the canyonshould be smooth without any abrupt changes eitherin configuration of arch abutments or in slope alongthe abutment contact profile, to minimize stressconcentrations.The following criteria are generally applicable forthe design of most arch dams. Special studies forunusual cases, however, may indicate that increasedeconomy and adequate safety can be achieved bydeviating from the criteria.Criteria .-The maximum degree of horizontalcurvature com patible with site conditions should beused. The maximum central angle of the crest,however, should be between 90 and 110. Theangle of incidence of a tangent to the intrados withcontours for competent rock should not be less than

30.

The arches should have abutments radial to theaxis center where feasible. If this results in exces-sive excavation on the upstream face, full radialabutments at the top of the dam should be mergedwithout abrupt changes into half radial abutments,as shown on figure 2(a). If radial abutments wouldresult in excessive excavation on the downstreamface, the abutment may be greater than radial, asshown on figure 2(b). These nonradial abutmentsshould be merged smoothly into radial abutments.

CRACKINGBasic Considerations .-Horizontal crackingshould be assumed to occur in an arch damwherever vertical tensile stresses resulting fromdynamic response of the structure to an earthquakeexceed the tensile strength of the concrete. Crack-

ing would be initiated at the point of maximumtensile stress first. The cracks should be assumed toextend to the point of zero stress within the dam.Although internal hydrostatic pressures may existwithin the dam, pressure in the crack duringearthquake is assumed to be zero. This assumptionaccounts for the rapidly cycling nature of openingand closing of the cracks and the inability of internalhydrostatic pressure to develop rapidly. The verticalcontraction joints are assumed to open wheneverhorizon tal tensile stresses are indicated. If stressesindicate their possible existence, effects of bothhorizontal cracks and opening of the vertical jointsduring an earthquake should be evaluated. Horizon-tal or peripheral formed joints may be used toeliminate tensile stresses in a manner similar to thestress relief during cracking.Methods of determining the depth of crack,resulting stresses, etc., are discussed in other Bu-reau of Reclamation publications [l].Criteria .-Wherever computed tensions exceedthe tensile strength of the concrete, cracking shouldbe assumed to exist. The depth of crack extends tothe point of zero stress within the section.After the change in static flexibility caused by thecracking and opening of contraction joints or otherformed joints has been included, another analysisshould be made. Any changes in depth of crackingor openings that result should be incorporated andthe procedure repeated until stresses computed atthe ends of the cracks or opened joints are zero andfurther changes n depth are not indicated.


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14 DESIGN CRITERIA FOR CONCRETE ARCH AND GRAVITY DAMS

Angle 2 30 J Axis Center1(a)---Half Radial Arch Abutment

Parallel toreference plane Crown

(b)---Greater Than Radial AbutmentFigure 2 .-Arch abutment shaping criteria.

FACTORS OF SAFETYBasic Considerations.-All loads to be used inthe design should be chosen to represent, as nearlyas can be determined, the actual loads that will acton the structure during operation, in accordancewith the criteria under Load Combinations.Methods of determining load-resisting capacity ofthe dam should be the most accurate available. Alluncertainties regarding loads or load-carrying capac-ity must be resolved as far as practicable by field orlaboratory tests, thorough exploration and inspec-tion of the foundation, good concrete control, and

good construction practices. On this basis, thefactor of safety will be as accurate an evaluation asposs ible of the capacity of the structure to resistapplied loads. All safety factors listed are minimumvalues.Like other important structures, dams should befrequently inspected. Particularly where uncertain-ties exist regarding such factors as loads, resistingcapacity, or characteristics of the foundation, it isexpected that adequate observations and measure-ments will be made of the structural behavior of thedam and its foundation to assure that the structureis at all times functioning as designed.Although somewhat lower safety factors may bepermitted for limited local areas, overall safetyfactors for the dam and its foundation after benefi-ciation should meet the requirements for the loadingcombination being analyzed.For other loading combinations where the safetyfactors are not specified, the designer is responsib lefor the selection of safety factors consistent withthose for the loading combination categories previ-ously discussed. Somewhat higher safety factorsshould be used for foundation studies because of thegreater amount of uncertainty involved in assessingfoundation load-resisting capacity.Safety factors for the dam are based on analysesusing the Trial Load Method or its computerizedversion, the Arch Dam Stress Analysis System(ADSAS) [ 11. Those for the foundation slidingstability are based on an assumption of uniformshear stress distributed on the plane being analyzed.

Criteria .-( 1) Compress ive stress .-The maxi-mum allowable compressive stress for concretein an arch dam subjected to any of the UsualLoading Combinations should be equal to thespecified compressive strength divided by asafety factor of 3.0. However, in no caseshould the allowable stress for Usual LoadingCombinations exceed 1,500 lbs/i$ (10.3MPa).The maximum allowable compressive stressfor the Unusual Loading Combinationsshould be equal to the specified compressivestrength divided by a safety factor of 2.0, andin no case should this value exceed 2,250 lbs/in*(15.5 MPa).The maximum allowable compressive stressfor the Extreme Loading Combinationsshould be determined in the same way, using asafety factor greater than 1.0.Safety factors of 4.0, 2.7, and 1.3 should beapplied to the foundation compressive strength


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ARCH DAMS 15in determining the allowable compression in thefoundation for Usual, Unusual, and Ex-treme Loading Combinations, respectively.

(2) Tensile stress.-Whenever practicable,tensile stresses should be avo ided by redesignof the dam. However, limited amounts oftensile stress may be permitted in localizedareas for the Usual Loading Combinationsat the discretion of the designer. Under nocircumstances should this tensile stress exceed150 lbs/in* (1.03 MPa) and for the UnusualLoading Combinations should be no greaterthan 225 lbs/in* (1.55 MPa).For the lowGeservoir-high-temperatureloading combination or for dead load duringconcrete placement when tensile stresses mayoccur on the downstream face, a somewhathigher tensile stress may be permitted in local-ized areas that are under compression duringfull reservoir loading. An allowable tensilestress equal to the tensile strength of concreteat the lift surface may be permitted at thediscretion of the designer. The point of applica-tion of the resultant dead load force must alsoremain within the base of the vertical section tomaintain stability during construction.For the Extreme Loading Combinations,which includes the Maximum Credible Earth-quake, the concrete should be assumed tocrack when the tensile strength is exceeded.The cracks are assumed to propagate to thepoint of zero stress as required under Crack-ing in this monograph. The structure may bedeemed safe for the Extreme Loading Combi-nations if, after cracking effects have beenincluded, the stresses do not exceed thestrength and the stability of the structure ismaintained.

(3) Shear stress and sliding stability .-Themaximum allowable average shearing stress onany plane within the dam should be determinedby dividing the shear strength by 3.0 for theUsual Loading Combinations, and by 2.0 forthe Unusual Loading Combinations. Asafety factor greater than 1.0 is required for theExtreme Loading Combinations.Where cracking for the Extreme LoadingCombinations is included, the remaining por-

tion of the untracked section shou ld bechecked for stability against sliding. The shear-friction factor of safety, which is a measure ofstability against sliding, should be used tocheck the reliability of the remainder of thepartially cracked section. The expression forthe shear-friction factor of safety (Q) is theratio of resisting to driving forces, as follows:

Q= CA + (XN + CU) tan 4XVwhere:C = unit cohesionA = untracked areaXN = summation of normal forcesCU = summation of uplift forcestan 4 = coefficient of interna l friction

XV = summation of shear forcesAll parameters must be specified in consistentunits. Uplift is negative according to the signconvention given in reference [ 11.To assure safety against sliding during thisextreme loading, the shear-friction factor shouldhave a value greater than 1.0. The sameequation can be used to determine the slidingstability at the concrete-rock contact or at anyplane within the dam for the other loadingcombinations instead of checking the allowableshear stress. Adequate shear-friction factors ofsafety are 3.0 for the Usual, 2.0 for theUnusual, and greater than 1.0 for the Ex-treme Loading Combinations.Methods of determining stability against slid-ing within the foundation are discussed inchapter 4 of reference [ 11.The factor of safety against sliding of theentire structure along planes of possible weak-ness within the foundation should be no lessthan 4.0 for the Usual, 2.7 for the Unu-sual, and 1.3 for the Extreme LoadingCombinations. If the computed safety factoris less than required, foundation treatment canbe included to increase the safety factor to therequired value.


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Part II Gravity Dams


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CONCRETE PROPERTlE%STATlCStrength

Basic Considerations.-A gravity dam should beconstructed of concrete that will meet the designcriteria for strength, durability, permeability, andother required properties. Because of the sustainedloading generally associated with them, the concreteproperties used for the analyses of static loadingconditions should include the effect of creep. Prop-erties of concrete vary with age, the type of cement,aggregates, and other ingredients as well as theirproportions in the mix [3]. Since different concretesgain strength at different rates, measurements mustbe made of specimens of suffkient age to permitevaluation of ultimate strengths.Although the concrete mix is usually designed foronly compressive strength, appropriate tests shouldbe made to determine the tensile and shear strengthvalues.Elastic Properties

Basic Considerations.-Poissons ratio, the sus-tained modulus of elasticity of the concrete, and thelatters ratio to the deformation modu lus of thefoundation have significant effects on stress distribu-

tion in the structure. Values of the modulus ofelasticity, although not directly proportional to con-crete strength, do follow the same trend, with thehigher strength concretes having a higher value formodulus of elasticity. As with the strength proper-ties, the elastic modulus is influenced by mixproportions, cement, aggregate, admixtures, andage. The deformation that occurs immediately withapplication of load depends on the instantaneouselastic modulus. The increase in deformation whichoccurs over a period of time with a constant load isthe result of creep or plastic flow in the concrete.The effects of creep are generally accounted for bydetermining a sustained modulus of elasticity of theconcrete for use in the analyses of static loadings.

Instantaneous moduli of elasticity and Poissonsratios should be determined for the different ages ofconcrete when the cylinders are initially loaded. Thesustained modulus of elasticity should be deter-mined from these cylinders after specific periods oftime under constant sustained load. These periodsof loading are often 365 and 730 days. The cylindersto be tested should be of the same size and cured inthe same manner as those used for the compressivestrength tests. The values of instantaneous modulusof elasticity, Poissons ratio, and sustained modulus19


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20 DESIGN CRITERIA FOR CONCRETE ARCH AND GRAVITY DAMSof elasticity used in the analyses should be theaverage of all test cylinder values.Thermal Properties

Basic Conside rations .-The effects of tempera-ture change in gravity dams are not as important inthe design as those in arch dams. However, duringconstruction, the temperature change of the con-crete in the dam should be controlled to avoidundesirable cracking. Thermal properties necessaryfor the evaluation of temperature changes are thecoefficient of thermal expansion, thermal conductiv-ity, specific heat, and diffusivity [4].The coefficient of thermal expansion is the lengthchange per unit length for 1 degree temperaturechange. Thermal conductivity is the rate of heatconduction through a unit thickness over a unit areaof the material subjected to a unit temperaturedifference between faces. The specific heat isdefined as the amount of heat required to raise thetemperature of a unit mass of the material 1 degree.Difisivity of concrete is an index of the facilitywith which concrete will undergo temperaturechange. The diflusivity is calculated from the valuesof spec ific heat, thermal conductivity, and density.Criteria .-Appropriate laboratory tests should bemade of the design mix to determine all concreteproperties.

CONCRETE PROPERTIES-DYNAMICStrength

The Reclamation laboratory is presently testingfor the strength of concrete when the concrete issubjected to dynam ic loading. However, no data areyet available to indica te what the strength character-istics are under dynamic loading.Elastic Properties

Until dynamic modulus information is available,the instantaneous modulus of elasticity determinedfor concrete specimens at the time of initial loadingshould be the value used for analyses of dynamiceffects.AVERAGE PROPERTIES

Basic Considerations.-Necessary values of con-crete properties may be estimated from publisheddata for preliminary studies until laboratory test dataare available. Until long-term tests are made to

determine the effects of creep, the sustained modulus of elasticity should be taken as 60 to 70 percenof the laboratory value for the instantaneous modulus of elasticity.Criteria-If no tests or published data are avaiable, the following average values for concreteproperties may be used for preliminary designs unti

test data are available for better results.Compressive strength-3,000 to 5,000 Ibs/i$(20.7 to 34.5 MPa)Tensile strength-5 to 6 percent of the compressive strengthShear strength:Cohesion-about 10 percent of the compressive strengthCoefficient of internal friction-l .OPoissons ratio-O.2Instantaneous modulus of elasticity-5.0 x 10lbs/in2 (34.5 GPa)Sustained modulus of elasticity-3.0 x 106 bsin2 (20.7 GPa)Coefficient of thermal expansion-5.0 x 10-6/(9.0 x lo-6PC)Unit weight-150 Ibs/ft3 (2402.8 kg/m3)FOUNDATION PROPERTIESDeformation Modulus

Basic Considerations .-Foundation deformationscaused by loads from the dam affect the stressdistributions within the dam. Conversely, responseof the dam to external loading and foundationdeformability determines the stresses within thefoundation. Proper evaluation of the dam andfoundation interaction requires as accurate a deter-mination of foundation deformation characteristicsas possible.Although the dam is considered to be homogene-ous, elastic, and isotropic, its foundation is generallyheterogeneous, inelastic, and anisotropic. Thesecharacteristics of the foundation have significanteffects on the deformation moduli of the foundation.The analysis of a gravity dam should include theeffective deformation modulus and its variation overthe entire contact area of the dam with the founda-tion .The deformation modulus is defined as the ratioof applied stress to e lastic strain plus inelastic strainand should be determined for each foundationmaterial. The effective deformation modulus is acomposite of deformation moduli for all materialswithin a particular segment of the foundation.


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GRAVITY DAMS 21Foundation investigations should provide informa-tion related to or giving deformation moduli andelastic moduli. The information includes elasticmodulus of drill core specimens, elastic modulusand deformation modulus from in situ jacking tests,deformation modulus of fault or shear zone material,and logs of the jointing that occurs in recovered drillcore. Information on the variation of materials andtheir prevalence at different locations along thefoundation is provided by the logs of drill holes andby tunnels in the foundation. Good compositionaldescription of the zone tested for deformationmodulus and adequate geologic logging of the drillcores permit extrapolation of results to untestedzones of similar material.Criteria .-The following foundation data shouldbe obtained for the analysis of a gravity dam:l The deformation modulus of each type of mate-

rial within the loaded area of the foundation.l The effects of joints, shears, and faults obtainedby direct (testing) or indirect (reduction factor)methods [lo].l An effective deformation modulus, as deter-mined when more than one type of material ispresent in a foundation.l The effective deformation moduli, as deter-mined at enough locations along the foundationcontact to provide adequate definition of thevariation in deformability and to permit extrapo-lation to untested areas when necessary.

Shear StrengthBasic Considera tions .-Resistance to shearwithin the foundation and between the dam and itsfoundation depends upon the cohesion and internalfriction inherent in the foundation materials and inthe bond between concrete and rock at the contactwith the dam. These properties are determined fromlaboratory and in situ tests. The results of labora-tory triaxial and direct shear tests, as well as in situshear tests, are generally reported in the form of the

Coulomb equation:R=CA+Ntan+,or(Shear resistance) = (unit cohesion times area)+ (effective normal force timescoefficient of internal friction)

which defines a linear relationship between shearresistance and normal load. The value of shear

resistance obtained as above should be limited touse for the range of normal loads used for the tests.Although this assumption of linearity is usuallyrealistic for the shear resistance of intact rock overthe range of normal loads tested, a curve of shearresistance versus normal load should be used formaterials other than intact rock. The shear resist-ance versus normal load relationship is determinedfrom a number of tests at different normal loads.The individual tests give the relationship of shearresistance to disp lacement for a particular normalload. The results of these individual tests are usedto obtain a shear resistance versus normal loadcurve, as shown on figure 3. The displacement usedto determine the shear resistance is the maximumdisplacement that can be allowed on the possiblesliding plane without causing unacceptable stressconcentrations within the dam. Since specimenstested in the laboratory or in situ are small com-pared to the foundation, the scale effect should becarefully considered in determining the values ofshear resistance to be used.

Figure 3.-Shear resistance on an existing joint in rock founda-tion of a gravity dam.

When a foundation is nonhomogeneous, the pos-sible sliding surface may consist of several differentmaterials, some intact and some fractured. Intactrock reaches its maximum break bond resistancewith less deformation than is necessary for fracturedmaterials to develop their maximum frictiona l resist-ances. Therefore, the shear resistance developed byeach fractured material depends upon the displace-ment of the intact rock part of the surface. If theintact rock shears, the shear resistance of the entireplane is equal to the combined sliding frictionalresistance for all m aterials along the plane.


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22 DESIGN CRITERIA FOR CONCRETE ARCH AND GRAVITY DAMSCriteria.-An adequa te number of tests, as deter-mined by the designer, should be made to obtain ashear resistance versus normal load relationship foreach material along the possible sliding planes. Thevalue of shear resistance recorded during testsshould be measured at displacements which corre-spond to those expected to occur along the in situpotential sliding planes.When the foundation along the plane of potentialsliding is nonhomogeneous, the total shear resist-ance is the summation of shear resistances of all thematerials along the plane.

Pore Pressure and PermeabilityBasic Considerations.-Analysis of a dam foun-dation requires a knowledge of the hydrostaticpressure distribution in the foundation. Permeabilityis controlled by the characteristics of the rock type,

the jointing systems, the shears and fissures, faultzones, and, at some damsites, by solution cavities inthe rock. The exit gradient for shear zone materialsthat surface near the downstream toe of the damshould also be determined to check against thepossibility of piping [2].Laboratory values for permeability of samplespecimens are applicable only to the portion orportions of the foundation that they represent.Permeability of the aforementioned geologic fea-tures can best be determined by in situ testing. Thepermeabilities obtained are used in the determina-tion of pore pressures for analyses of stresses,stability, and piping. Such a determination may bemade by several methods including two- and three-dimensional physical models, two- and three-dimen-sional finite element models, and electric analogs.If foundation grouting and drainage or othertreatment are to be used, their effects on the porepressures should be included.Criteria .- A sufficient number of tests, as deter-mined by the designer, should be made to determinethe permeability of the foundation rock, joints,fissures, fault zones, and solution cavities [6,7JAn adequate method of analysis should be usedto determine pore pressures within the foundation.The effects of any grouting, drainage, and otherfoundation treatment should be included.Treatment

Basic Considerations .-Foundation treatment isused to correct deficiencies and improve physicalproperties by grouting, drainage, excavation of

inadequate materials, reinforcement and backfilwith concrete. Some reasons for foundation treatment are: (1) improvement of deformation moduli(2) prevention of sliding of foundation blocks, (3prevention of relative displacement of foundationblocks, (4) prevention of piping and reduction opore pressures, and (5) provision of an artificialfoundation in the absence of adequate materials.Regardless of the reason for the foundationtreatment, its effects on the other foundation proper-ties should be considered in the analyses.Criteria .-Effects of treatment on foundationproperties should be considered.Compressive and Tensile Strength

Basic Considerations .-Compressive strength othe foundation rock can be an important factor indetermining thickness requirements for a dam at itscontact with the foundation. Where the foundationrock is nonhomogeneous, tests to obtain compressive strength values should be made for each typeof rock in the loaded portion of the foundation.A determination of tensile strength of the rock isseldom required because unhealed joints, shearsetc., cannot transmit tensile stress within the foun-dation.Criteria.-A sufficient number of tests, as determined by the designer, should be made to obtaincompressive strength values for each type of rock inthe loaded part of the foundation.LOADS

Factors to be considered as contributing to theloading combinations for a gravity dam are: (1)reservoir and tailwater loads, (2) temperature, (3)internal hydrostatic pressure, (4) dead weight, (5)ice, (6) silt, and (7) earthquake. Such factors asdead weight and static water loads can be calculatedaccurately. Others such as earthquake, temperature,ice, silt, and internal hydrostatic pressure must bepredicted on the basis of assumptions of varyingreliability.Reservoir and Tailwater Loads

Basic Considerations .- Reservoir and tailwaterloads to be applied to the dam are obtained fromreservoir operation studies and tailwater curves.These studies are based on operating and hydrologicdata such as reservoir capacity, storage allocation,streamflow records, flood hydrographs, and reser-


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GRAVITY DAMS 23voir releases for all purposes. A design reservoircan be derived from these operation studies whichwill reflect a normal high water surface, seasonaldrawdowns, and the usual low water surface.Definitions of the water surface designations are:

(1) Maximum water surface .-The highestacceptable water surface elevation with allfactors affecting the safety of the structureconsidered. Normally, it is the highest watersurface elevation result ing from a computedrouting of the inflow design flood through thereservoir on the basis of established operatingcriteria. It is the top of surcharge capacity.(2) Top of exclus ive lood control capacity.-The reservoir water surface elevation at the topof the reservoir capacity allocated to exclusiveuse of regulating flood inflows to reduce dam-age downstream.

(3) Maximum controllable water surface ele-vation .-The highest reservoir water surfaceelevation at which gravity flows from thereservoir can be completely shut off.(4) Top ofjoint use capacity.-The reservoirwater surface eleva tion at the top of thereservoir capacity allocated to joint uses offlood control and conservation purposes.(5) Top of active conservation capacity.-The reservoir water surface elevation at the topof the capacity allocated to storage of water forconservation purposes only.(6) Top of inactive capacity .-The reservoirwater surface elevation below which the reser-voir w ill not be evacuated under normal condi-tions.(7) Top of dead capacity.-The lowest eleva-tion in the reservoir from which water can bedrawn by gravity.(8) Streambed at the dam axis.- The eleva-tion of the lowest point in the streambed at theaxis of the dam prior to construction. Thiselevation normally defines the zero for area-capacity tables.

The normal design reservoir elevation is the Topof Joint Use Capacity, if joint use capacity isincluded. If not, it is the 6Top of Active Conserva-tion Capacity.The minimum design reservoir elevation is de-fined as the usual low water surface as reflected inseasonal drawdowns. Unless the reservoir is drawndown to Top of Inactive Capacity at frequent

intervals, the minimum design reservoir elevationwill be higher than that level.Maximum design reservoir elevation is the highestanticipated water surface elevation and usuallyoccurs in conjunction with routing of the inflowdesign flood through the reservo ir.For computation of the reservoir and tailwaterloads, water pressure is considered to vary directlywith depth and to act equally in al l directions.Criteria .-Reservoir levels should be selectedfrom reservoir operation studies for the loadingcombinations being analyzed.The minimum tailwater level associated with eachreservoir level should be used. Tailwater surfaceelevations should be obtained from tailwater curvesassociated with operating studies. Water pressuresshould be computed as varying directly with depth.Water loads are considered to be applied at, andact normal to, the contact surfaces.Temperature

Basic Considerations.-Volumetric increasescaused by temperature rise will transfer load acrosstransverse contraction joints if the joints aregrouted. Horizontal thrusts which are caused byvolumetric changes as temperature increases willresult in a transfer of load across grouted contrac-tion joints, increas ing twist effects and the loadingof the abutments as discussed in another Bureaupublication [2]. Ungrouted contraction joints areassumed to offer no restraint on volumetric increasecaused by temperature rise and no associatedtransfer of load, providing the mean concrete tem-peratures remain below the closure temperature.When the designer is making studies to determineconcrete temperature loads, varying weather condi-tions can be applied. Similarly, a widely fluctuatingreservoir water surface will affect the concretetemperatures. In determining temperature loads, thefollowing conditions and temperatures are used:

(1) Usual weather conditions .-The combina-tion of the daily air temperatures, a l-weekcycle representative of the cold (hot) periodsassocia ted with barometric pressure changes,and the mean monthly air temperatures. Thiscondition will account for temperatures whichare halfway between the mean monthly airtemperatures and the minimum (maximum) re-corded air temperatures at the site.(2) Usual concrete temperatures.-The aver-age concrete temperatures between the up-


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GRAVITY DAMS 25Criteria .-The magnitude of a dead load is con-sidered as the weight of concrete plus appurte-nances.

iceBasic Considerations .-Ice pressures can pro-

duce a significant load against the face of a dam inlocations where winter temperatures are coldenough to cause relatively thick ice cover. Icepressure is created by thermal expansion of the iceand by wind drag. Pressures caused by thermalexpansion of the ice depend on the temperature riseof the ice, thickness of the ice sheet, the coefficientof thermal expansion, the elastic modulus, and thestrength of the ice. W ind drag depends on the sizeand shape of the exposed area, the roughness of thesurface, and the direction and velocity of the wind.Ice pressures are generally considered to be atransitory loading, Many dams will be subjected tolittle, if any, ice pressure. The designer shoulddecide, after consideration of the above factors, ifan allowance for ice pressure is appropriate.Criteria .-The method of Monfore and Taylor [S]may be used to analyze anticipated ice pressures ifnecessary basic data are available. An acceptableestimate of ice load to be expected on the face of astructure may be taken as 10,000 lbsllin ft (146kN/m) of contact between the ice and the dam foran assumed ice depth of 2 feet (0.6 meter) or morewhen basic data are not available to computepressures.Silt

Basic Considerations.-Not all dams will besubjected to silt pressure, and the designer shouldconsider all available hydrologic data before decid-ing whether an allowance for silt pressure is neces-sary.Criteria .-Horizontal pressure exerted by thesaturated silt load is assumed to be equivalent tothat of a fluid weighing 85 lbs/ft (1362 kg/m 3.Vertical pressure exerted by saturated silt isdetermined as if silt were a soil having a wet densityof 120 lbslft (1922 kg/m3), the magnitude ofpressure varying directly with depth.Earthquake

Basic Considerarions .-Concrete gravity damsare elastic structures which may be excited toresonance when subjected to seismic disturbances.Two steps are necessary to obtain loadings on a

gravity dam caused by such a disturbance. The firststep is to estimate magnitude and locations ofearthquakes to which the dam may be subjected anddetermine the resulting rock motions at the site. Thesecond step is to determine the response of the damto these earthquakes by either the response spec-trum or time-history methods.Methods of determining a design earthquakewhich represents an operating basis event arepresently under development. These methodsshould consider: (I) historical records to obtainfrequency of occurrence versus magnitude, (2) use-ful life of the structure, and (3) a statistical approachto determine probable occurrence of earthquakes ofdifferent magn itudes during the life of the structure.When future developments produce such methods,suitable safety factors will be included in thecriteria.

Maximum Credible Earthquake .-Mostearthquakes are the result of crustal movementsof the earth along faults. Geologic examinationsof the area should be made to locate any faults,determine how recently activity has occurred,and estimate the probable length of the fault.Records of seismological activity in the areashould also be studied to determine magnitudeand location of any recorded earthquakes thatmay affect the site. Based on these geologicaland historical data, hypothetical earthquakes,usually having magnitudes greater than thehistorical events, are estimated for any activefaults in the area. These earthquakes areconsidered to be the most severe associatedwith the faults and are assumed to occur at thepoints on those faults closest to the site. Thisdefines the Maximum Credible Earthquakein terms of Richter magnitudes and distances tothe site.Earthquake engineering is currently the subject ofmuch research and development. The followingcriteria represent the current concepts used by theBureau to obtain earthquake loads for concrete

gravity dams.Criteria.-The dam should be analyzed for theMaximum Credible Earthquake.(1) Response spectrum .-A response spectrumat the site should be determined for each Maxi-mum Credible Earthquake by all three methodsdescribed in appendix D of reference [9]. Thecomposite of the three spectra becomes thedesign response spectrum.


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26 DESIGN CRITERIA FOR CONCRETE ARCH AND GRAVITY DAMS(2) Time history .-The required accelerogramsmay be produced by appropriate adjustments ofexisting or artificially generated accelerograms.The response spectrum computed from an ad-justed accelerogram must correspond to theabove-defined design response spectrum.(3) Structural response .-The analytical meth-

ods used to compute natural frequencies, modeshapes, and structural response are described inanother publication [2].LOAD COMBINATIONS

Basic Considerations .- Gravity dams should bedesigned or all appropriate load combinations, usingthe proper safety factor for each. Combinations oftransitory loads, each of which has only a remoteprobability of occurrence at any given time, havenegligible probability of simultaneous occurrenceand shou ld not be considered as an appropriate loadcombination. Temperature loadings should be in-cluded when applicable, as previously discussed inthis monograph.Criteria.-Gravity dams should be designed forthe loading combinations which follow using thesafety factors subsequently prescribed under Fac-tors of Safety in this monograph.

( 1) Usual loading combinations .-Normaldesign reservoir elevation with appropriate deadloads, uplift, silt, ice, and tailwater. If tempera-ture loads are applicable, use minimum usualtemperatures occurring at that time.(2) Unusual loading combinations .-Maxi-mum design reservoir elevation with appropri-ate dead loads, silt, tailwater, uplift, and mini-mum usual temperatures occurring at that time,if applicable.

(3) Extreme loading combinations .-Theusual loading plus effects of the MaximumCredible Earthquake.(4) Other loadings and investigations.-(a)The usual or unusual loading combination withdrains inoperative.

(b) Dead load.(c) Any other loading combination which, inthe designers opinion, should be analyzed for aparticular dam.CONFIGURATION OF DAM AND FOUNDATION

Basic Considerations .-The shape of a gravitydam, its thickness at the contact with the founda-tion, and the slope of the concrete-rock contact are

important factors providing stability for the structure. Transversely, the foundation contact should beither horizontal or sloping upward toward thedownstream face. Longitudinally, the profile shoulvary smoothly without abrupt changes to minimizestress concentrations.Abrupt changes of slope on either face of the damcan cause unacceptable stress concentrations andshould be avoided whenever possible.Although a vertical downstream face near the topof the dam to provide a crest thickness for access usually acceptable, the point of intersection with thsloping downstream face should be carefullychecked for possible stress concentrations. Minimiz-ing the mass near the top of the dam is beneficial inreducing the effects of earthquake.

Criteria .-The foundation contact should beeither horizontal or sloping upward toward thedownstream face in a direction normal to the axisIn addition, the foundation contact should varysmoothly along the axis profile of the dam withoutany abrupt changes.Abrupt changes in slope on either face should bavoided where unacceptable stress concentrationsmay occur.The minimum crest thickness consistent withother requirements should be used to reduce earthquake effects.

CRACKINGBasic Considerations .-Horizontal crackingshould be assumed to occur in a gravity damwherever the vertical normal stress (Xi on figure5(b)) for dynamic response to an earthquake doesnot meet minimum safety factor requirements. Thedepth of crack is assumed to extend along ahorizontal section to the point where compressivestress computed without uplift and the internalhydrostatic pressure are equal.When the ana lysis for the extreme loading combi-nation of normal reservoir plus effects of theMaximum Credible Earthquake indicates thatcracking should occur, uplift pressures within the

crack are assumed to be zero. This assumptiontakes into account the rapidly cycling nature of theopening and closing of the crack and the inability ofinternal hydrostatic pressure to develop rapidly.Determination of the depth of crack becomes aniterative process in which the remaining upliftdepends on the depth of crack and the depth ofcrack depends partially on the uplift acting in theuntracked portion. If the compressive stress at the


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GRAVITY DAMS 27upstream face is less than the uplift (internalhydrostatic) pressure minus the tensile strength ofthe concrete, the pressure diagram should be re-vised as on figure 5(d). For the initial determinationof cracking effects, an assumption of crack depthequal to one-half the thickness can be used. Uplifteffects in the untracked portion can then be deter-mined and the depth of crack computed. This cycleof determining uplift and crack depth changesshould be repeated until a satisfactory degree ofaccuracy has been obtained. Uplift pressure ordi-nates at the end of the crack are obtained byinterpolation using an uplift pressure diagram, asshown on figure 5(c) and discussed under InternalHydrostatic Pressures in this monograph.For cracking computations, the eccentricity of theresulting stress diagram (e) is obtained by takingmoments about the center of gravity of the originalsection. The following expression should be used:

e = CM + M,7XW - A4(T,)where:CM = summation of moments of all externalforcesM, = moment of the tentative uplift force(A4 w T,)XW = summation of vertical forcesA4 = internal hydrostatic pressure ordinateat the end of the crack (see figure

5(c))T1 = remaining untracked portion of thethicknessTo compute a revised T, based on the e valueobtained from the above expression, use thefollowing expression:

T,=3 i--e( )where:T = the original thickness (see fig. 5(a)).

After the value of T, has been determined withsufficient accuracy (0.5 percent change from theprevious value), the resulting stress at the down-stream face (B5 on fig. 5(d)) should be computedusing the following expression:-i--B5= WW-(A4*T,)) -Tl + A4

where all terms are as described above.

The shear-friction factor of safety shou ld becomputed for the remaining untracked portion, T,.The remaining untracked area should be used indetermining total cohesion, and (ZW - A4 l TJshould be used as the summation of normal forces.Safety requirements for both stress and slidingstability are discussed under Factors of Safety inthis monograph.Criteria .-Cracking should be assumed to occurin a gravity dam for the Extreme Loading Combi-nations whenever the vertical normal stress com-puted at the face does not meet the criteriaestablished under Factors of Safety in this mono-graph. The crack should be assumed to extend tothe point where the compressive stress is equal tothe internal hydrostatic pressure within the un-cracked portion at the end of the crack. Upliftpressures in the crack when it is opened byearthquake should be assumed to be zero.

Resewor water surfore, n

Center of growty of

ZVLkiizbaseAl12 i

6

(a ) VERTICAL CROSS-SECTION

(b) PRESSUR E DIAGRAM WITHOUT UPLIFT

V me of drams3(C) UPLIFT PRESSUR E DtAGRAM

T3

(d) COMBINED PRESSUR E AND USLIFT PRE SSURE DIAGRAM

Figure L-Diagrams of base pressures acting on a gravity dam.


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28 DESIGN CRITERIA FOR CONCRETE ARCH AND GRAVITY DAMSFACTORS OF SAFETY

Basic Considerations.-All loads to be used indesign should be chosen to represent, as nearly ascan be determined, the actual loads that will occuron the structure during operation, in accordancewith the criteria under Load Combinations.Methods of determining load-resisting capacity ofthe dam should be the most accurate available. Alluncertainties regarding loads or load-carrying capac-ity should be- esolved as far as practicable by fieldor laboratory tests and by thorough exploration andinspection of the foundation. Thus, the factor ofsafety should be as accurate an evaluation aspossib le of the capacity of the structure to resistapplied loads. All safety factors listed are minimumvalues.Like other important structures, dams should beregularly and frequently inspected. Adequate obser-vations and measurements should be made of thestructural behavior of the dam and its foundation toassure that the structure is functioning as designed.Although somewhat lower safety factors may bepermitted for limited local areas within the founda-tion, overall safety factors for the dam and itsfoundation after beneticiation should meet require-ments for the loading combination being analyzed.For other loading combinations where safetyfactors are not specified , the designer is responsiblefor selection of safety factors consistent with thosefor loading combination categories previously dis-cussed. Somewhat higher safety factors should beused for foundation studies because of the greateramount of uncertainty involved in assessing ounda-tion load-resisting capacity.Safety factors for gravity dams are based on theuse of the gravity method of analys is and those forfoundation sliding stability are based on an assump-tion of uniform stress distribution on the plane beinganalyzed.

Criteria.--(I) Compressive stress.-The maxi-mum allowable compressive stress for concretein a gravity dam subjected to any of the UsualLoading Combinations should not be greaterthan the specified compressive strength dividedby a safety factor of 3.0. Under no circum-stance should the allowable compressive stressfor the Usual Loading Combinations exceed1,500 bs/in2 (10.3 MPa).A safety factor of 2.0 should be used indetermining the allowable compressive stressfor the Unusual Loading Combinations. The

maximum allowable compressive stress for thUnusual Loading Combinations should in ncase exceed 2,250 lbs/in2 (15.5 MPa). Thmaximum allowable compressive stress for thExtreme Loading Combinations should bdetermined in the same way using a safetfactor greater than 1.0.Safety factors of 4.0, 2.7, and 1.3 should bused in determining allowable compressivstresses in the foundation for Usual, Unusual, and Extreme Loading Combinations,respectively.(2) Tensi le stress.-In order not to exceethe allowable tensile stress, the minimum allowable compressive stress computed without internal hydrostatic pressure should be detemined from the following expression whictakes into account the tensile strength of thconcrete at the lift surfaces:

UZ =where:uz, =

P=

p l w l h - (f,/s)minimum allowable stress at the faca reduction factor to account fodrainsw= unit weight of waterh= depth below water surfaceft = tensile strength of concrete at lif

s=surfaces

safety factor.All parameters must be specified using consistent units.The value of p should be 1.0 if drains are nopresent or if cracking occurs at the downstreamface and 0.4 if drains are used. A safety factoof 3.0 should be used for Usual and 2.0 foUnusual Loading Combinations. The allowable value of o Zu or Usual Loading Combinations should never be less than 0. Crackin

should be assumed to occur if the stress athe upstream face is less than uZ, computedfrom the above equation with a safety factoof 1.0 for the Extreme Loading Combinations. The structure should be deemed saffor this loading if, after cracking has beeincluded, stresses in the structure do noexceed the specified strengths and slidingstability is maintained.


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(3) Sliding stability .-The shear-friction BIBLIOGRAPHYfactor of safety provides a measure of thesafety against sliding or shearing on any [1] Bureau of Reclamation, Design of Archsection. The following expression is the ratio Dams, 1977.of resisting to driving forces and appl ies to [2] Bureau of Reclamation, Design of Gravityany section in the structure or at its contact Dams, 1976.with the foundation for the computa tion of [3] Bureau of Reclamation, Concrete Manual,the shear-friction factor of safety, Q: 8th Edition, 1975.[4] Bureau of Reclamation, Control of Crack-Q= CA+ @N+ cUltan+ ing in Mass Concrete Structures, Engi -XV neering Monograph No. 34, October1965.

where: [5] Bureau of Reclamation, Properties of MassC = unit cohesion Concrete in Bureau of ReclamationA = area of section considered Dams, Concrete Laboratory Report No.2.N = summation of normal forces C-1009, December 6, 1961.CU = summation of uplift forces [6] Bureau of Reclamation, Permeability Teststan 4 = coefficient of internal friction Using Drill H oles and Wells, GeologyXV = summation of shear forces Report No. G-97, January 3, 1951.[7] Bureau of Reclamation, Drill Hole WaterTests Technical Instructions-Provi-All parameters must be specified using con-sistent units. Uplift is negative according to sional, Engineering Geology, July 1970.[8] Monfore, G. E. and Taylor, F. W. Thethe sign convention in reference [2]. Problem of an Expanding Ice Sheet,The minimum shear-friction factor w ithin Bureau of Reclamation Technical Memo-the dam or at the concrete-to-rock contact randum, March 18, 1948.shou ld be 3.0 for Usual, 2.0 for Unu- [9] Boggs, H. L., et al., Method for Estimatingsual, and greater than 1 .0 for the Extreme Design Earthquake Rock Motions, Engi-Load ing Combinations. The factor of safety neering and Research Center, Bureau ofagainst sliding

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Design Criteria for Concrete Arch and Gravity Dams