Embed Size (px)
Citation preview
EM 1110-2-220030 June 1995
US Army Corpsof Engineers
ENGINEERING AND DESIGN
Gravity Dam Design
ENGINEER MANUAL
AVAILABILITY
Copies of this and other U.S. Army Corps of Engineers publi-cations are available from National Technical InformationService, 5285 Port Royal Road, Springfield, VA 22161.Phone (703)487-4650.
Government agencies can order directlyu from the U.S. ArmyCorps of Engineers Publications Depot, 2803 52nd Avenue,Hyattsville, MD 20781-1102. Phone (301)436-2065. U.S.Army Corps of Engineers personnel should use Engineer Form0-1687.
UPDATES
For a list of all U.S. Army Corps of Engineers publicationsand their most recent publication dates, refer to EngineerPamphlet 25-1-1, Index of Publications, Forms and Reports.
DEPARTMENT OF THE ARMY EM 1110-2-2200U.S. Army Corps of Engineers
CECW-ED Washington, DC 20314-1000
ManualNo. 1110-2-2200 30 June 1995
Engineering and DesignGRAVITY DAM DESIGN
1. Purpose. The purpose of this manual is to provide technical criteria and guidance for the planningand design of concrete gravity dams for civil works projects.
2. Applicability. This manual applies to all HQUSACE elements, major subordinate commands,districts, laboratories, and field operating activities having responsibilities for the design of civil worksprojects.
3. Discussion. This manual presents analysis and design guidance for concrete gravity dams.Conventional concrete and roller compacted concrete are both addressed. Curved gravity damsdesigned for arch action and other types of concrete gravity dams are not covered in this manual. Forstructures consisting of a section of concrete gravity dam within an embankment dam, the concretesection will be designed in accordance with this manual.
FOR THE COMMANDER:
This engineer manual supersedes EM 1110-2-2200 dated 25 September 1958.
DEPARTMENT OF THE ARMY EM 1110-2-2200U.S. Army Corps of Engineers
CECW-ED Washington, DC 20314-1000
ManualNo. 1110-2-2200 30 June 1995
Engineering and DesignGRAVITY DAM DESIGN
Table of Contents
Subject Paragraph Page Subject Paragraph Page
Chapter 1IntroductionPurpose . . . . . . . . . . . . . . . . . . . . . 1-1 1-1Scope. . . . . . . . . . . . . . . . . . . . . . . 1-2 1-1Applicability . . . . . . . . . . . . . . . . . . 1-3 1-1References . . . . . . . . . . . . . . . . . . . 1-4 1-1Terminology . . . . . . . . . . . . . . . . . . 1-5 1-1
Chapter 2General Design ConsiderationsTypes of Concrete Gravity Dams. . . . 2-1 2-1Coordination Between Disciplines . . . 2-2 2-2Construction Materials. . . . . . . . . . . 2-3 2-3Site Selection . . . . . . . . . . . . . . . . . 2-4 2-3Determining Foundation Strength
Parameters. . . . . . . . . . . . . . . . . . 2-5 2-4
Chapter 3Design DataConcrete Properties. . . . . . . . . . . . . 3-1 3-1Foundation Properties. . . . . . . . . . . . 3-2 3-2Loads . . . . . . . . . . . . . . . . . . . . . . . 3-3 3-3
Chapter 4Stability AnalysisIntroduction . . . . . . . . . . . . . . . . . . 4-1 4-1Basic Loading Conditions. . . . . . . . . 4-2 4-1Dam Profiles. . . . . . . . . . . . . . . . . . 4-3 4-2Stability Considerations. . . . . . . . . . 4-4 4-3Overturning Stability . . . . . . . . . . . . 4-5 4-3Sliding Stability . . . . . . . . . . . . . . . . 4-6 4-4Base Pressures. . . . . . . . . . . . . . . . . 4-7 4-10Computer Programs. . . . . . . . . . . . . 4-8 4-10
Chapter 5Static and Dynamic StressAnalysesStress Analysis . . . . . . . . . . . . . . . 5-1 5-1Dynamic Analysis . . . . . . . . . . . . . 5-2 5-1Dynamic Analysis Process. . . . . . . 5-3 5-2Interdisciplinary Coordination. . . . . 5-4 5-2Performance Criteria for Response to
Site-Dependent Earthquakes. . . . . 5-5 5-2Geological and Seismological
Investigation . . . . . . . . . . . . . . . . 5-6 5-2Selecting the Controlling Earthquakes 5-7 5-2Characterizing Ground Motions. . . . 5-8 5-3Dynamic Methods of Stress Analysis 5-9 5-4
Chapter 6Temperature Control of MassConcreteIntroduction . . . . . . . . . . . . . . . . . 6-1 6-1Thermal Properties of Concrete. . . . 6-2 6-1Thermal Studies. . . . . . . . . . . . . . . 6-3 6-1Temperature Control Methods. . . . . 6-4 6-2
Chapter 7Structural Design ConsiderationsIntroduction . . . . . . . . . . . . . . . . . 7-1 7-1Contraction and Construction Joints . 7-2 7-1Waterstops . . . . . . . . . . . . . . . . . . 7-3 7-1Spillway . . . . . . . . . . . . . . . . . . . . 7-4 7-1Spillway Bridge . . . . . . . . . . . . . . . 7-5 7-2Spillway Piers . . . . . . . . . . . . . . . . 7-6 7-2Outlet Works. . . . . . . . . . . . . . . . . 7-7 7-3Foundation Grouting and Drainage . . 7-8 7-3
i
EM 1110-2-190630 Sep 96
Subject Paragraph Page Subject Paragraph Page
Galleries . . . . . . . . . . . . . . . . . . . . . 7-9 7-3Instrumentation . . . . . . . . . . . . . . . . 7-10 7-4
Chapter 8Reevaluation of Existing DamsGeneral. . . . . . . . . . . . . . . . . . . . . . 8-1 8-1Reevaluation. . . . . . . . . . . . . . . . . . 8-2 8-1Procedures . . . . . . . . . . . . . . . . . . . 8-3 8-1Considerations of Deviation from
Structural Criteria . . . . . . . . . . . . . 8-4 8-2Structural Requirements for Remedial
Measure . . . . . . . . . . . . . . . . . . . . 8-5 8-2Methods of Improving Stability in
Existing Structures. . . . . . . . . . . . . 8-6 8-2Stability on Deep-Seated Failure
Planes . . . . . . . . . . . . . . . . . . . . . 8-7 8-3Example Problem. . . . . . . . . . . . . . . 8-8 8-4
Chapter 9Roller-Compacted ConcreteGravity DamsIntroduction . . . . . . . . . . . . . . . . . . 9-1 8-1Construction Method. . . . . . . . . . . . 9-2 9-1
Economic Benefits. . . . . . . . . . . . . 9-3 9-1Design and Construction
Considerations. . . . . . . . . . . . . . . 9-4 9-3
Appendix AReferences
Appendix BGlossary
Appendix CDerivation of the GeneralWedge Equation
Appendix DExample Problems - SlidingAnalysis for Single andMultiple Wedge Systems
ii
EM 1110-2-220030 Jun 95
Chapter 1Introduction
1-1. Purpose
The purpose of this manual is to provide technical criteriaand guidance for the planning and design of concretegravity dams for civil works projects. Specific areascovered include design considerations, load conditions,stability requirements, methods of stress analysis, seismicanalysis guidance, and miscellaneous structural features.Information is provided on the evaluation of existingstructures and methods for improving stability.
1-2. Scope
a. This manual presents analysis and design guidancefor concrete gravity dams. Conventional concrete androller compacted concrete (RCC) are both addressed.Curved gravity dams designed for arch action and othertypes of concrete gravity dams are not covered in thismanual. For structures consisting of a section of concretegravity dam within an embankment dam, the concretesection will be designed in accordance with this manual.
This engineer manual supersedes EM 1110-2-2200 dated25 September 1958.
b. The procedures in this manual cover only damson rock foundations. Dams on pile foundations should bedes igned acco rd i ng to Eng inee r Manua l(EM) 1110-2-2906.
c. Except as specifically noted throughout themanual, the guidance for the design of RCC and conven-tional concrete dams will be the same.
1-3. Applicability
This manual applies to all HQUSACE elements, majorsubordinate commands, districts, laboratories, and fieldoperating activities having responsibilities for the designof civil works projects.
1-4. References
Required and related publications are listed inAppendix A.
1-5. Terminology
Appendix B contains definitions of terms that relate to thedesign of concrete gravity dams.
1-1
EM 1110-2-220030 June 95
Chapter 2General Design Considerations
2-1. Types of Concrete Gravity Dams
Basically, gravity dams are solid concrete structures thatmaintain their stability against design loads from thegeometric shape and the mass and strength of the con-crete. Generally, they are constructed on a straight axis,but may be slightly curved or angled to accommodate thespecific site conditions. Gravity dams typically consist ofa nonoverflow section(s) and an overflow section or spill-way. The two general concrete construction methods forconcrete gravity dams are conventional placed mass con-crete and RCC.
a. Conventional concrete dams.
(1) Conventionally placed mass concrete dams arecharacterized by construction using materials and tech-niques employed in the proportioning, mixing, placing,curing, and temperature control of mass concrete (Amer-ican Concrete Institute (ACI) 207.1 R-87). Typical over-flow and nonoverflow sections are shown on Figures 2-1and 2-2. Construction incorporates methods that havebeen developed and perfected over many years of design-ing and building mass concrete dams. The cement hydra-tion process of conventional concrete limits the size andrate of concrete placement and necessitates building inmonoliths to meet crack control requirements. Generallyusing large-size coarse aggregates, mix proportions areselected to produce a low-slump concrete that gives econ-omy, maintains good workability during placement, devel-ops minimum temperature rise during hydration, andproduces important properties such as strength, imper-meability, and durability. Dam construction with conven-tional concrete readily facilitates installation of conduits,penstocks, galleries, etc., within the structure.
(2) Construction procedures include batching andmixing, and transportation, placement, vibration, cooling,curing, and preparation of horizontal construction jointsbetween lifts. The large volume of concrete in a gravitydam normally justifies an onsite batch plant, and requiresan aggregate source of adequate quality and quantity,located at or within an economical distance of the project.Transportation from the batch plant to the dam is gen-erally performed in buckets ranging in size from 4 to12 cubic yards carried by truck, rail, cranes, cableways, ora combination of these methods. The maximum bucketsize is usually restricted by the capability of effectivelyspreading and vibrating the concrete pile after it is
dumped from the bucket. The concrete is placed in liftsof 5- to 10-foot depths. Each lift consists of successivelayers not exceeding 18 to 20 inches. Vibration is gener-ally performed by large one-man, air-driven, spud-typevibrators. Methods of cleaning horizontal constructionjoints to remove the weak laitance film on the surfaceduring curing include green cutting, wet sand-blasting,and high-pressure air-water jet. Additional details ofconventional concrete placements are covered inEM 1110-2-2000.
(3) The heat generated as cement hydrates requirescareful temperature control during placement of mass con-crete and for several days after placement. Uncontrolledheat generation could result in excessive tensile stressesdue to extreme gradients within the mass concrete or dueto temperature reductions as the concrete approaches itsannual temperature cycle. Control measures involve pre-cooling and postcooling techniques to limit the peak tem-peratures and control the temperature drop. Reduction inthe cement content and cement replacement with pozzo-lans have reduced the temperature-rise potential. Crackcontrol is achieved by constructing the conventional con-crete gravity dam in a series of individually stable mono-liths separated by transverse contraction joints. Usually,monoliths are approximately 50 feet wide. Further detailson temperature control methods are provided inChapter 6.
b. Roller-compacted concrete (RCC) gravity dams.The design of RCC gravity dams is similar to conven-tional concrete structures. The differences lie in the con-struction methods, concrete mix design, and details of theappurtenant structures. Construction of an RCC dam is arelatively new and economical concept. Economic advan-tages are achieved with rapid placement using construc-tion techniques that are similar to those employed forembankment dams. RCC is a relatively dry, lean, zeroslump concrete material containing coarse and fine aggre-gate that is consolidated by external vibration using vibra-tory rollers, dozer, and other heavy equipment. In thehardened condition, RCC has similar properties to conven-tional concrete. For effective consolidation, RCC must bedry enough to support the weight of the constructionequipment, but have a consistency wet enough to permitadequate distribution of the past binder throughout themass during the mixing and vibration process and, thus,achieve the necessary compaction of the RCC and preven-tion of undesirable segregation and voids. The consisten-cy requirements have a direct effect on the mixture pro-portioning requirements (ACI 207.1 R-87). EM 1110-2-2006, Roller Compacted Concrete, provides detailed
2-1
EM 1110-2-220030 June 95
Figure 2-1. Typical dam overflow section
guidance on the use, design, and construction of RCC.Further discussion on the economic benefits and thedesign and construction considerations is provided inChapter 9.
2-2. Coordination Between Disciplines
A fully coordinated team of structural, material, and geo-technical engineers, geologists, and hydrological andhydraulic engineers should ensure that all engineering andgeological considerations are properly integrated into theoverall design. Some of the critical aspects of the analy-sis and design process that require coordination are:
a. Preliminary assessments of geological data, sub-surface conditions, and rock structure. Preliminarydesigns are based on limited site data. Planning andevaluating field explorations to make refinements indesign based on site conditions should be a joint effort ofstructural and geotechnical engineers.
b. Selection of material properties, design param-eters, loading conditions, loading effects, potential failure
mechanisms, and other related features of the analyticalmodels. The structural engineer should be involved inthese activities to obtain a full understanding of the limitsof uncertainty in the selection of loads, strength parame-ters, and potential planes of failure within the foundation.
c. Evaluation of the technical and economic feasi-bility of alternative type structures.Optimum structuretype and foundation conditions are interrelated. Decisionson alternative structure types to be used for comparativestudies need to be made jointly with geotechnical engi-neers to ensure the technical and economic feasibility ofthe alternatives.
d. Constructibility reviews in accordance withER 415-1-11. Participation in constructibility reviews isnecessary to ensure that design assumptions and methodsof construction are compatible. Constructibility reviewsshould be followed by a memorandum from the Director-ate of Engineering to the Resident Engineer concerningspecial design considerations and scheduling of construc-tion visits by design engineers during crucial stages ofconstruction.
2-2
EM 1110-2-220030 June 95
Figure 2-2. Nonoverflow section
e. Refinement of the preliminary structure configura-tion to reflect the results of detailed site explorations,materials availability studies, laboratory testing, andnumerical analysis. Once the characteristics of the foun-dation and concrete materials are defined, the foundinglevels of the dam should be set jointly by geotechnicaland structural engineers, and concrete studies should bemade to arrive at suitable mixes, lift thicknesses, andrequired crack control measures.
f. Cofferdam and diversion layout, design, andsequencing requirements.Planning and design of thesefeatures will be based on economic risk and require thejoint effort of hydrologists and geotechnical, construction,hydraulics, and structural engineers. Cofferdams must beset at elevations which will allow construction to proceedwith a minimum of interruptions, yet be designed to allowcontrolled flooding during unusual events.
g. Size and type of outlet works and spillway. Thesize and type of outlet works and spillway should be setjointly with all disciplines involved during the early stagesof design. These features will significantly impact on theconfiguration of the dam and the sequencing of construc-tion operations. Special hydraulic features such as water
quality control structures need to be developed jointlywith hydrologists and mechanical and hydraulicsengineers.
h. Modification to the structure configuration dur-ing construction due to unexpected variations in the foun-dation conditions. Modifications during construction arecostly and should be avoided if possible by a comprehen-sive exploration program during the design phase. How-ever, any changes in foundation strength or rock structurefrom those upon which the design is based must be fullyevaluated by the structural engineer.
2-3. Construction Materials
The design of concrete dams involves consideration ofvarious construction materials during the investigationsphase. An assessment is required on the availability andsuitability of the materials needed to manufacture concretequalities meeting the structural and durability require-ments, and of adequate quantities for the volume of con-crete in the dam and appurtenant structures. Constructionmaterials include fine and coarse aggregates, cementitiousmaterials, water for washing aggregates, mixing, curing ofconcrete, and chemical admixtures. One of the mostimportant factors in determining the quality and economyof the concrete is the selection of suitable sources ofaggregate. In the construction of concrete dams, it isimportant that the source have the capability of producingadequate quantitives for the economical production ofmass concrete. The use of large aggregates in concretereduces the cement content. The procedures for theinvestigation of aggregates shall follow the requirementsin EM 1110-2-2000 for mass concrete and EM 1110-2-2006 for RCC.
2-4. Site Selection
a. General. During the feasibility studies, thepreliminary site selection will be dependent on the projectpurposes within the Corps’ jurisdiction. Purposes appli-cable to dam construction include navigation, flood dam-age reduction, hydroelectric power generation, fish andwildlife enhancement, water quality, water supply, andrecreation. The feasibility study will establish the mostsuitable and economical location and type of structure.Investigations will be performed on hydrology and meteo-rology, relocations, foundation and site geology, construc-tion materials, appurtenant features, environmentalconsiderations, and diversion methods.
2-3
EM 1110-2-220030 June 95
b. Selection factors.
(1) A concrete dam requires a sound bedrock founda-tion. It is important that the bedrock have adequate shearstrength and bearing capacity to meet the necessary sta-bility requirements. When the dam crosses a major faultor shear zone, special design features (joints, monolithlengths, concrete zones, etc.) should be incorporated in thedesign to accommodate the anticipated movement. Allspecial features should be designed based on analyticaltechniques and testing simulating the fault movement.The foundation permeability and the extent and cost offoundation grouting, drainage, or other seepage and upliftcontrol measures should be investigated. The reservoir’ssuitability from the aspect of possible landslides needs tobe thoroughly evaluated to assure that pool fluctuationsand earthquakes would not result in any mass sliding intothe pool after the project is constructed.
(2) The topography is an important factor in theselection and location of a concrete dam and itsappurtenant structures. Construction as a site with a nar-row canyon profile on sound bedrock close to the surfaceis preferable, as this location would minimize the concretematerial requirements and the associated costs.
(3) The criteria set forth for the spillway, power-house, and the other project appurtenances will play animportant role in site selection. The relationship andadaptability of these features to the project alignment willneed evaluation along with associated costs.
(4) Additional factors of lesser importance that needto be included for consideration are the relocation ofexisting facilities and utilities that lie within the reservoirand in the path of the dam. Included in these are rail-roads, powerlines, highways, towns, etc. Extensive andcostly relocations should be avoided.
(6) The method or scheme of diverting flows aroundor through the damsite during construction is an importantconsideration to the economy of the dam. A concretegravity dam offers major advantages and potential costsavings by providing the option of diversion throughalternate construction blocks, and lowers risk and delay ifovertopping should occur.
2-5. Determining Foundation StrengthParameters
a. General. Foundation strength parameters arerequired for stability analysis of the gravity dam section.Determination of the required parameters is made by
evaluation of the most appropriate laboratory and/or insitu strength tests on representative foundation samplescoupled with extensive knowledge of the subsurface geo-logic characteristics of a rock foundation. In situ testingis expensive and usually justified only on very largeprojects or when foundation problems are know to exist.In situ testing would be appropriate where more precisefoundation parameters are required because rock strengthis marginal or where weak layers exist and in situproperties cannot be adequately determined from labora-tory testing of rock samples.
b. Field investigation. The field investigation mustbe a continual process starting with the preliminary geo-logic review of known conditions, progressing to adetailed drilling program and sample testing program, andconcluding at the end of construction with a safe andoperational structure. The scope of investigation andsampling should be based on an assessment of homogene-ity or complexity of geological structure. For example, theextent of the investigation could vary from quite limited(where the foundation material is strong even along theweakest potential failure planes) to quite extensive anddetailed (where weak zones or seams exist). There is acertain minimum level of investigation necessary to deter-mine that weak zones are not present in the foundation.Field investigations must also evaluate depth and severityof weathering, ground-water conditions (hydrogeology),permeability, strength, deformation characteristics, andexcavatibility. Undisturbed samples are required to deter-mine the engineering properties of the foundation mate-rials, demanding extreme care in application and samplingmethods. Proper sampling is a combination of scienceand art; many procedures have been standardized, butalteration and adaptation of techniques are often dictatedby specific field procedures as discussed inEM 1110-2-1804.
c. Strength testing.The wide variety of foundationrock properties and rock structural conditions preclude astandardized universal approach to strength testing. Deci-sions must be made concerning the need for in situ test-ing. Before any rock testing is initiated, the geotechnicalengineer, geologist, and designer responsible for formulat-ing the testing program must clearly define what the pur-pose of each test is and who will supervise the testing. Itis imperative to use all available data, such as resultsfrom geological and geophysical studies, when selectingrepresentative samples for testing. Laboratory testingmust attempt to duplicate the actual anticipated loadingsituations as closely as possible. Compressive strengthtesting and direct shear testing are normally required todetermine design values for shear strength and bearing
2-4
EM 1110-2-220030 June 95
capacity. Tensile strength testing in some cases as wellas consolidation and slakeability testing may also benecessary for soft rock foundations. Rock testing proce-dures are discussed in theRock Testing Handbook(US Army Engineer Waterways Experiment Station(WES) 1980) and in the International Society of RockMechanics, “Suggested Methods for Determining ShearStrength,” (International Society of Rock Mechanics1974). These testing methods may be modified as appro-priate to fit the circumstances of the project.
d. Design shear strengths.Shear strength valuesused in sliding analyses are determined from availablelaboratory and field tests and judgment. For preliminarydesigns, appropriate shear strengths for various types of
rock may be obtained from numerous available referencesincluding the US Bureau of Reclamation Reports SP-39and REC-ERC-74-10, and many reference texts (see bibli-ography). It is important to select the types ofstrengthtests to be performed based upon the probablemode of failure. Generally, strengths on rock discontinu-ities would be used for the active wedge and beneath thestructure. A combination of strengths on discontinuitiesand/or intact rock strengths would be used for the passivewedge when included in the analysis. Strengths alongpreexisting shear planes (or faults) should be determinedfrom residual shear tests, whereas the strength along othertypes of discontinuities must consider the strain charac-teristics of the various materials along the failure plane aswell as the effect of asperities.
2-5
EM 1110-2-220030 Jun 95
Chapter 3Design Data
3-1. Concrete Properties
a. General. The specific concrete properties used inthe design of concrete gravity dams include the unitweight, compressive, tensile, and shear strengths, modulusof elasticity, creep, Poisson’s ratio, coefficient of thermalexpansion, thermal conductivity, specific heat, and diffu-sivity. These same properties are also important in thedesign of RCC dams. Investigations have generally indi-cated RCC will exhibit properties equivalent to those ofconventional concrete. Values of the above propertiesthat are to be used by the designer in the reconnaissanceand feasibility design phases of the project are availablein ACI 207.1R-87 or other existing sources of informationon similar materials. Follow-on laboratory testing andfield investigations should provide the values necessary inthe final design. Temperature control and mix design arecovered in EM 1110-2-2000 and Em 1110-2-2006.
b. Strength.
(1) Concrete strength varies with age; the type ofcement, aggregates, and other ingredients used; and theirproportions in the mixture. The main factor affectingconcrete strength is the water-cement ratio. Lowering theratio improves the strength and overall quality. Require-ments for workability during placement, durability, mini-mum temperature rise, and overall economy may governthe concrete mix proportioning. Concrete strengths shouldsatisfy the early load and construction requirements andthe stress criteria described in Chapter 4. Design com-pressive strengths at later ages are useful in taking fulladvantage of the strength properties of the cementitiousmaterials and lowering the cement content, resulting inlower ultimate internal temperature and lower potentialcracking incidence. The age at which ultimate strength isrequired needs to be carefully reviewed and revised whereappropriate.
(2) Compressive strengths are determined from thestandard unconfined compression test excluding creepeffects (American Society for Testing and Materials(ASTM) C 39, “Test Method for Compressive Strength ofCylindrical Concrete Specimens”; C 172, “Method ofSampling Freshly Mixed Concrete”; ASTM C 31,“Method of Making and Curing Concrete Test Specimensin the Field”).
(3) The shear strength along construction joints or atthe interface with the rock foundation can be determined
by the linear relationshipT = C + δ tan φ in which C isthe unit cohesive strength,δ is the normal stress, and tanφ represents the coefficient of internal friction.
(4) The splitting tension test (ASTM C 496) or themodulus of rupture test (ASTM C 78) can be used todetermine the strength of intact concrete. Modulus ofrupture tests provide results which are consistent with theassumed linear elastic behavior used in design. Spittingtension test results can be used; however, the designershould be aware that the results represent nonlinear per-formance of the sample. A more detailed discussion ofthese tests is presented in theACI Journal (Raphael1984).
c. Elastic properties.
(1) The graphical stress-strain relationship for con-crete subjected to a continuously increasing load is acurved line. For practical purposes, however, the mod-ulus of elasticity is considered a constant for the range ofstresses to which mass concrete is usually subjected.
(2) The modulus of elasticity and Poisson’s ratio aredetermined by the ASTM C 469, “Test Method for StaticModulus of Elasticity and Poisson’s Ratio of Concrete inCompression.”
(3) The deformation response of a concrete damsubjected to sustained stress can be divided into two parts.The first, elastic deformation, is the strain measuredimmediately after loading and is expressed as the instanta-neous modulus of elasticity. The other, a gradual yieldingover a long period, is the inelastic deformation or creep inconcrete. Approximate values for creep are generallybased on reduced values of the instantaneous modulus.When design requires more exact values, creep should bebased on the standard test for creep of concrete in com-pression (ASTM C 512).
d. Thermal properties. Thermal studies are requiredfor gravity dams to assess the effects of stresses inducedby temperature changes in the concrete and to determinethe temperature controls necessary to avoid undesirablecracking. The thermal properties required in the studyinclude thermal conductivity, thermal diffusivity, specificheat, and the coefficient of thermal expansion.
e. Dynamic properties.
(1) The concrete properties required for input into alinear elastic dynamic analysis are the unit weight,Young’s modulus of elasticity, and Poisson’s ratio. The
3-1
EM 1110-2-220030 Jun 95
concrete tested should be of sufficient age to represent theultimate concrete properties as nearly as practicable.One-year-old specimens are preferred. Usually, upper andlower bound values of Young’s modulus of elasticity willbe required to bracket the possibilities.
(2) The concrete properties needed to evaluate theresults of the dynamic analysis are the compressive andtensile strengths. The standard compression test (seeparagraph 3-1b) is acceptable, even though it does notaccount for the rate of loading, since compression nor-mally does not control in the dynamic analysis. Thesplitting tensile test or the modulus of rupture test can beused to determine the tensile strength. The static tensilestrength determined by the splitting tensile test may beincreased by 1.33 to be comparable to the standard modu-lus of rupture test.
(3) The value determined by the modulus of rupturetest should be used as the tensile strength in the linearfinite element analysis to determine crack initiation withinthe mass concrete. The tensile strength should beincreased by 50 percent when used with seismic loadingto account for rapid loading. When the tensile stress inexisting dams exceeds 150 percent of the modulus ofrupture, nonlinear analyses will be required in consultationwith CECW-ED to evaluate the extent of cracking. Forinitial design investigations, the modulus of rupture can becalculated from the following equation (Raphael 1984):
(3-1)ft 2.3fc′2/3
where
ft = tensile strength, psi (modulus of rupture)
fc′ = compressive strength, psi
3-2. Foundation Properties
a. Deformation modulus. The deformation modulusof a foundation rock mass must be determined to evaluatethe amount of expected settlement of the structure placedon it. Determination of the deformation modulus requirescoordination of geologists and geotechnical and structuralengineers. The deformation modulus may be determinedby several different methods or approaches, but the effectof rock inhomogeneity (due partially to rock discontinu-ities) on foundation behavior must be accounted for.Thus, the determination of foundation compressibilityshould consider both elastic and inelastic (plastic) defor-mations. The resulting “modulus of deformation” is a
lower value than the elastic modulus of intact rock.Methods for evaluating foundation moduli include in situ(static) testing (plate load tests, dilatometers, etc.); labora-tory testing (uniaxial compression tests, ASTM C 3148;and pulse velocity test, ASTM C 2848); seismic fieldtesting; empirical data (rock mass rating system, correla-tions with unconfined compressive strength, and tables oftypical values); and back calculations using compressionmeasurements from instruments such as a borehole exten-someter. The foundation deformation modulus is bestestimated or evaluated by in situ testing to moreaccurately account for the natural rock discontinuities.Laboratory testing on intact specimens will yield only an“upper bound” modulus value. If the foundation containsmore than one rock type, different modulus values mayneed to be used and the foundation evaluated as a com-posite of two or more layers.
b. Static strength properties. The most importantfoundation strength properties needed for design of con-crete gravity structures are compressive strength and shearstrength. Allowable bearing capacity for a structure isoften selected as a fraction of the average foundation rockcompressive strength to account for inherent planes ofweakness along natural joints and fractures. Most rocktypes have adequate bearing capacity for large concretestructures unless they are soft sedimentary rock types suchas mudstones, clayshale, etc.; are deeply weathered; con-tain large voids; or have wide fault zones. Foundationrock shear strength is given as two values: cohesion (c)and internal friction (φ). Design values for shear strengthare generally selected on the basis of laboratory directshear test results. Compressive strength and tensilestrength tests are often necessary to develop the appropri-ate failure envelope during laboratory testing. Shearstrength along the foundation rock/structure interface mustalso be evaluated. Direct shear strength laboratory testson composite grout/rock samples are recommended toassess the foundation rock/structure interface shearstrength. It is particularly important to determine strengthproperties of discontinuities and the weakest foundationmaterials (i.e., soft zones in shears or faults), as these willgenerally control foundation behavior.
c. Dynamic strength properties.
(1) When the foundation is included in the seismicanalysis, elastic moduli and Poisson’s ratios for the foun-dation materials are required for the analysis. If the foun-dation mass is modeled, the rock densities are alsorequired.
3-2
EM 1110-2-220030 Jun 95
(2) Determining the elastic moduli for a rock founda-tion should include several different methods orapproaches, as defined in paragraph 3-2a.
(3) Poisson’s ratios should be determined from uniax-ial compression tests, pulse velocity tests, seismic fieldtests, or empirical data. Poisson’s ratio does not varywidely for rock materials.
(4) The rate of loading effect on the foundation mod-ulus is considered to be insignificant relative to the otheruncertainties involved in determining rock foundationproperties, and it is not measured.
(5) To account for the uncertainties, a lower andupper bound for the foundation modulus should be usedfor each rock type modeled in the structural analysis.
3-3. Loads
a. General. In the design of concrete gravity dams, itis essential to determine the loads required in the stabilityand stress analysis. The following forces may affect thedesign:
(1) Dead load.
(2) Headwater and tailwater pressures.
(3) Uplift.
(4) Temperature.
(5) Earth and silt pressures.
(6) Ice pressure.
(7) Earthquake forces.
(8) Wind pressure.
(9) Subatmospheric pressure.
(10) Wave pressure.
(11) Reaction of foundation.
b. Dead load. The unit weight of concrete generallyshould be assumed to be 150 pounds per cubic foot untilan exact unit weight is determined from the concretematerials investigation. In the computation of the deadload, relatively small voids such as galleries are normallynot deducted except in low dams, where such voids could
create an appreciable effect upon the stability of the struc-ture. The dead loads considered should include theweight of concrete, superimposed backfill, and appurte-nances such as gates and bridges.
c. Headwater and tailwater.
(1) General. The headwater and tailwater loadingsacting on a dam are determined from the hydrology, met-eorology, and reservoir regulation studies. The frequencyof the different pool levels will need to be determined toassess which will be used in the various load conditionsanalyzed in the design.
(2) Headwater.
(a) The hydrostatic pressure against the dam is afunction of the water depth times the unit weight of water.The unit weight should be taken at 62.5 pounds per cubicfoot, even though the weight varies slightly withtemperature.
(b) In some cases the jet of water on an overflowsection will exert pressure on the structure. Normallysuch forces should be neglected in the stability analysisexcept as noted in paragraph 3-3i.
(3) Tailwater.
(a) For design of nonoverflow sections. The hydro-static pressure on the downstream face of a nonoverflowsection due to tailwater shall be determined using the fulltailwater depth.
(b) For design of overflow sections. Tailwaterpressure must be adjusted for retrogression when the flowconditions result in a significant hydraulic jump in thedownstream channel, i.e. spillway flow plunging deep intotailwater. The forces acting on the downstream face ofoverflow sections due to tailwater may fluctuate sig-nificantly as energy is dissipated in the stilling basin.Therefore, these forces must be conservatively estimatedwhen used as a stabilizing force in a stability analysis.Studies have shown that the influence of tailwater retro-gression can reduce the effective tailwater depth used tocalculate pressures and forces to as little as 60 percent ofthe full tailwater depth. The amount of reduction in theeffective depth used to determine tailwater forces is afunction of the degree of submergence of the crest of thestructure and the backwater conditions in the downstreamchannel. For new designs, Chapter 7 of EM 1110-2-1603provides guidance in the calculation of hydraulic pressure
3-3
EM 1110-2-220030 Jun 95
distributions in spillway flip buckets due to tailwaterconditions.
(c) Tailwater submergence. When tailwater conditionssignificantly reduce or eliminate the hydraulic jump in thespillway basin, tailwater retrogression can be neglectedand 100 percent of the tailwater depth can be used todetermine tailwater forces.
(d) Uplift due to tailwater. Full tailwater depth willbe used to calculate uplift pressures at the toe of thestructure in all cases, regardless of the overflowconditions.
d. Uplift. Uplift pressure resulting from headwaterand tailwater exists through cross sections within the dam,at the interface between the dam and the foundation, andwithin the foundation below the base. This pressure ispresent within the cracks, pores, joints, and seams in theconcrete and foundation material. Uplift pressure is anactive force that must be included in the stability andstress analysis to ensure structural adequacy. Thesepressures vary with time and are related to boundaryconditions and the permeability of the material. Upliftpressures are assumed to be unchanged by earthquakeloads.
(1) Along the base.
(a) General. The uplift pressure will be considered asacting over 100 percent of the base. A hydraulic gradientbetween the upper and lower pool is developed betweenthe heel and toe of the dam. The pressure distributionalong the base and in the foundation is dependent on theeffectiveness of drains and grout curtain, where appli-cable, and geologic features such as rock permeability,seams, jointing, and faulting. The uplift pressure at anypoint under the structure will be tailwater pressure plusthe pressure measured as an ordinate from tailwater to thehydraulic gradient between upper and lower pool.
(b) Without drains. Where there have not been anyprovisions provided for uplift reduction, the hydraulicgradient will be assumed to vary, as a straight line, fromheadwater at the heel to zero or tailwater at the toe.Determination of uplift, at any point on or below thefoundation, is demonstrated in Figure 3-1.
(c) With drains. Uplift pressures at the base or belowthe foundation can be reduced by installing foundationdrains. The effectiveness of the drainage system willdepend on depth, size, and spacing of the drains; the
Figure 3-1. Uplift distribution without foundationdrainage
character of the foundation; and the facility with whichthe drains can be maintained. This effectiveness will beassumed to vary from 25 to 50 percent, and the designmemoranda should contain supporting data for theassumption used. If foundation testing and flow analysisprovide supporting justification, the drain effectivenesscan be increased to a maximum of 67 percent withapproval from CECW-ED. This criterion deviation willdepend on the pool level operation plan instrumentation toverify and evaluate uplift assumptions and an adequatedrain maintenance program. Along the base, the upliftpressure will vary linearly from the undrained pressurehead at the heel, to the reduced pressure head at the lineof drains, to the undrained pressure head at the toe, asshown in Figure 3-2. Where the line of drains intersectsthe foundation within a distance of 5 percent of the reser-voir depth from the upstream face, the uplift may beassumed to vary as a single straight line, which would bethe case if the drains were exactly at the heel. This con-dition is illustrated in Figure 3-3. If the drainage galleryis above tailwater elevation, the pressure of the line ofdrains should be determined as though the tailwater levelis equal to the gallery elevation.
(d) Grout curtain. For drainage to be controlledeconomically, retarding of flow to the drains from theupstream head is mandatory. This may be accomplishedby a zone of grouting (curtain) or by the natural impervi-ousness of the foundation. A grouted zone (curtain)should be used wherever the foundation is amenable togrouting. Grout holes shall be oriented to intercept themaximum number of rock fractures to maximize its effec-tiveness. Under average conditions, the depth of the groutzone should be two-thirds to three-fourths of theheadwater-tailwater differential and should be supple-mented by foundation drain holes with a depth of at least
3-4
EM 1110-2-220030 Jun 95
Figure 3-2. Uplift distribution with drainage gallery
Figure 3-3. Uplift distribution with foundation drainsnear upstream face
two-thirds that of the grout zone (curtain). Where thefoundation is sufficiently impervious to retard the flowand where grouting would be impractical, an artificialcutoff is usually unnecessary. Drains, however, should beprovided to relieve the uplift pressures that would buildup over a period of time in a relatively imperviousmedium. In a relatively impervious foundation, drainspacing will be closer than in a relatively permeablefoundation.
(e) Zero compression zones. Uplift on any portion ofany foundation plane not in compression shall be 100 per-cent of the hydrostatic head of the adjacent face, exceptwhere tension is the result of instantaneous loading result-ing from earthquake forces. When the zero compressionzone does not extend beyond the location of the drains,the uplift will be as shown in Figure 3-4. For the condi-tion where the zero compression zone extends beyond thedrains, drain effectiveness shall not be considered. Thisuplift condition is shown in Figure 3-5. When an existingdam is being investigated, the design office should submita request to CECW-ED for a deviation if expensive reme-dial measures are required to satisfy this loadingassumption.
Figure 3-4. Uplift distribution cracked base withdrainage, zero compression zone not extendingbeyond drains
Figure 3-5. Uplift distribution cracked base withdrainage, zero compression zone extending beyonddrains
(2) Within dam.
(a) Conventional concrete. Uplift within the bodyof a conventional concrete-gravity dam shall be assumedto vary linearly from 50 percent of maximum headwaterat the upstream face to 50 percent of tailwater, or zero, asthe case may be, at the downstream face. This simpli-fication is based on the relative impermeability of intactconcrete which precludes the buildup of internal porepressures. Cracking at the upstream face of an existingdam or weak horizontal construction joints in the body ofthe dam may affect this assumption. In these cases, upliftalong these discontinuities should be determined asdescribed in paragraph 3-3.d(1) above.
(b) RCC concrete. The determination of the percentuplift will depend on the mix permeability, lift joint treat-ment, the placements, techniques specified for minimizingsegregation within the mixture, compaction methods, and
3-5
EM 1110-2-220030 Jun 95
the treatment for watertightness at the upstream anddownstream faces. A porous upstream face and lift jointsin conjunction with an impermeable downstream face mayresult in a pressure gradient through a cross section of thedam considerably greater than that outlined above forconventional concrete. Construction of a test sectionduring the design phase (in accordance with EM 1110-2-2006, Roller Compacted Concrete) shall be used as ameans of determining the permeability and, thereby, theexact uplift force for use by the designer.
(3) In the foundation. Sliding stability must be con-sidered along seams or faults in the foundation. Materialin these seams or faults may be gouge or other heavilysheared rock, or highly altered rock with low shear resis-tance. In some cases, the material in these zones isporous and subject to high uplift pressures upon reservoirfilling. Before stability analyses are performed, engineer-ing geologists must provide information regarding poten-tial failure planes within the foundation. This includes thelocation of zones of low shear resistance, the strength ofmaterial within these zones, assumed potential failureplanes, and maximum uplift pressures that can developalong the failure planes. Although there are no prescribeduplift pressure diagrams that will cover all foundationfailure plane conditions, some of the most commonassumptions made are illustrated in Figures 3-6 and 3-7.These diagrams assume a uniform head loss along thefailure surface from point “A” to tailwater, and assumethat the foundation drains penetrate the failure plane andare effective in reducing uplift on that plane. If there isconcern that the drains may be ineffective or partiallyeffective in reducing uplift along the failure plane, thenuplift distribution as represented by the dashed line inFigures 3-6 and 3-7 should be considered for stabilitycomputations. Dangerous uplift pressures can developalong foundation seams or faults if the material in theseams or faults is pervious and the pervious zone is inter-cepted by the base of the dam or by an impervious fault.These conditions are described in Casagrande (1961) andillustrated by Figures 3-8 and 3-9. Every effort is madeto grout pervious zones within the foundation prior toconstructing the dam. In cases where grouting is imprac-tical or ineffective, uplift pressure can be reduced to safelevels through proper drainage of the pervious zone.However, in those circumstances where the drains do notpenetrate the pervious zone or where drainage is onlypartially effective, the uplift conditions shown inFigures 3-8 and 3-9 are possible.
Figure 3-6. Uplift pressure diagram. Dashed linerepresents uplift distribution to be considered forstability computations
Figure 3-7. Dashed line in uplift pressure diagramrepresents uplift distribution to be considered forstability computations
3-6
EM 1110-2-220030 Jun 95
Figure 3-8. Development of dangerous uplift pressurealong foundation seams or faults
Figure 3-9. Effect along foundation seams or faults ifmaterial is pervious and pervious zone is interceptedby base of dam or by impervious fault
e. Temperature.
(1) A major concern in concrete dam construction isthe control of cracking resulting from temperature change.During the hydration process, the temperature risesbecause of the hydration of cement. The edges of the
monolith release heat faster than the interior; thus the corewill be in compression and the edges in tension. Whenthe strength of the concrete is exceeded, cracks willappear on the surface. When the monolith starts cooling,the contraction of the concrete is restrained by the founda-tion or concrete layers that have already cooled and hard-ened. Again, if this tensile strain exceeds the capacity ofthe concrete, cracks will propagate completely through themonolith. The principal concerns with cracking are that itaffects the watertightness, durability, appearance, andstresses throughout the structure and may lead to undesir-able crack propagation that impairs structural safety.
(2) In conventional concrete dams, various techni-ques have been developed to reduce the potential fortemperature cracking (ACI 224R-80). Besides contractionjoints, these include temperature control measures duringconstruction, cements for limiting heat of hydration, andmix designs with increased tensile strain capacity.
(3) If an RCC dam is built without vertical contrac-tion joints, additional internal restraints are present.Thermal loads combined with dead loads and reservoirloads could create tensile strains in the longitudinal axissufficient to cause transverse cracks within the dam.
f. Earth and silt. Earth pressures against the dammay occur where backfill is deposited in the foundationexcavation and where embankment fills abut and wraparound concrete monoliths. The fill material may or maynot be submerged. Silt pressures are considered in thedesign if suspended sediment measurements indicate thatsuch pressures are expected. Whether the lateral earthpressures will be in an active or an at-rest state is deter-mined by the resulting structure lateral deformation.Methods for computing the Earth’s pressures are dis-cussed in EM 1110-2-2502, Retaining and Flood Walls.
g. Ice pressure. Ice pressure is of less importance inthe design of a gravity dam than in the design of gatesand other appurtenances for the dam. Ice damage to thegates is quite common while there is no known instanceof any serious ice damage occurring to the dam. For thepurpose of design, a unit pressure of not more than5,000 pounds per square foot should be applied to thecontact surface of the structure. For dams in this country,the ice thickness normally will not exceed 2 feet. Clima-tology studies will determine whether an allowance for icepressure is appropriate. Further discussion on types ofice/structure interaction and methods for computing iceforces is provided in EM 1110-2-1612, Ice Engineering.
3-7
EM 1110-2-220030 Jun 95
h. Earthquake.
(1) General.
(a) The earthquake loadings used in the design ofconcrete gravity dams are based on design earthquakesand site-specific motions determined from seismologicalevaluation. As a minimum, a seismological evaluationshould be performed on all projects located in seismiczones 2, 3, and 4. Seismic zone maps of the UnitedStates and Territories and guidance for seismic evaluationof new and existing projects during various levels ofdesign documents are provided in ER 1110-2-1806,Earthquake Design and Analysis for Corps of EngineersProjects.
(b) The seismic coefficient method of analysis shouldbe used in determining the resultant location and slidingstability of dams. Guidance for performing the stabilityanalysis is provided in Chapter 4. In strong seismicityareas, a dynamic seismic analysis is required for the inter-nal stress analysis. The criteria and guidance required inthe dynamic stress analysis are given in Chapter 5.
(c) Earthquake loadings should be checked for hori-zontal earthquake acceleration and, if included in thestress analysis, vertical acceleration. While an earthquakeacceleration might take place in any direction, the analysisshould be performed for the most unfavorable direction.
(2) Seismic coefficient. The seismic coefficientmethod of analysis is commonly known as the pseudo-static analysis. Earthquake loading is treated as an inertialforce applied statically to the structure. The loadings areof two types: inertia force due to the horizontal accelera-tion of the dam and hydrodynamic forces resulting fromthe reaction of the reservoir water against the dam (seeFigure 3-10). The magnitude of the inertia forces is com-puted by the principle of mass times the earthquake accel-eration. Inertia forces are assumed to act through thecenter of gravity of the section or element. The seismiccoefficient is a ratio of the earthquake acceleration togravity; it is a dimensionless unit, and in no case can it berelated directly to acceleration from a strong motioninstrument. The coefficients used are considered to be thesame for the foundation and are uniform for the totalheight of the dam. Seismic coefficients used in designare based on the seismic zones given in ER 1110-2-1806.
(a) Inertia of concrete for horizontal earthquakeacceleration. The force required to accelerate the concretemass of the dam is determined from the equation:
Figure 3-10. Seismically loaded gravity dam, nonover-flow monolith
(3-2)Pex Max
Wg
αg Wα
where
Pex = horizontal earthquake force
M = mass of dam
ax = horizontal earthquake acceleration =g
W = weight of dam
g = acceleration of gravity
α = seismic coefficient
(b) Inertia of reservoir for horizontal earthquakeacceleration. The inertia of the reservoir water induces anincreased or decreased pressure on the dam concurrentlywith concrete inertia forces. Figure 3-10 shows the pres-sures and forces due to earthquake by the seismic coeffi-cient method. This force may be computed by means ofthe Westergaard formula using the parabolic approxima-tion:
(3-3)Pew23
Ce (α) y ( hy )
where
Pew= additional total water load down to depthy (kips)
3-8
Ce '51
1 & 0.72 h1,000 te
2
EM 1110-2-220030 Jun 95
3-9
(3-4)
Ce = factor depending principally on depth of water and i. Subatmospheric pressure. At the hydrostatic head the earthquake vibration period, t , in seconds for which the crest profile is designed, the theoreticale
h = total height of reservoir (feet) crest approach atmospheric pressure. For heads higher
Westergaard's approximate equation for Ce, which is obtained along the spillway. When spillway profiles aresufficiently accurate for all usual conditions, in pound- designed for heads appreciably less than the probablesecond feet units is: maximum that could be obtained, the magnitude of these
importance in their effect upon gates and appurtenances,where t is the period of vibration. they may, in some instances, have an appreciable effecte
(3) Dynamic loads. The first step in determining wind setup are usually important factors in determiningearthquake induced loading involves a geological and the required freeboard of any dam. Wave dimensions andseismological investigation of the damsite. The objectives forces depend on the extent of water surface or fetch, theof the investigation are to establish the controlling maxi- wind velocity and duration, and other factors. Informationmum credible earthquake (MCE) and operating basis relating to waves and wave pressures are presented in theearthquake (OBE) and the corresponding ground motions Coastal Engineering Research Center's Shore Protectionfor each, and to assess the possibility of earthquake- Manual (SPM), Vol II (SPM 1984).produced foundation dislocation at the site. The MCEand OBE are defined in Chapter 5. The ground motions k. Reaction of foundations. In general, the resultantare characterized by the site-dependent design response of all horizontal and vertical forces including uplift mustspectra and, when necessary in the analysis, acceleration- be balanced by an equal and opposite reaction at thetime records. The dynamic method of analysis determines foundation consisting of the normal and tangential compo-the structural response using either a response spectrum or nents. For the dam to be in static equilibrium, the loca-acceleration-time records for the dynamic input. tion of this reaction is such that the summation of forces
(a) Site-specific design response spectra. A response normal component is assumed as linear, with a knowledgespectrum is a plot of the maximum values of acceleration, that the elastic and plastic properties of the foundationvelocity, and/or displacement of an infinite series of material and concrete affect the actual distribution.single-degree-of-freedom systems subjected to an earth-quake. The maximum response values are expressed as a (1) The problem of determining the actual distribu-function of natural period for a given damping value. The tion is complicated by the tangential reaction, internalsite-specific response spectra is developed statistically stress relations, and other theoretical considerations.from response spectra of strong motion records of earth- Moreover, variations of foundation materials with depth,quakes that have similar source and propagation path cracks, and fissures that interrupt the tensile and shearingproperties or from the controlling earthquakes and that resistance of the foundation also make the problem morewere recorded on a similar foundation. Application of the complex.response spectra in dam design is described in Chapter 5.
(b) Acceleration--time records. Accelerograms, used generally determined by projecting the spillway slope tofor input for the dynamic analysis, provide a simulation of the foundation line, and all concrete downstream from thisthe actual response of the structure to the given seismic line is disregarded. If a vertical longitudinal joint is notground motion through time. The acceleration-time provided at this point, the mass of concrete downstreamrecords should be compatible with the design response from the theoretical toe must be investigated for internalspectrum. stresses.
pressures along the downstream face of an ogee spillway
than the design head, subatmospheric pressures are
pressures should be determined and considered in thestability analysis. Methods and discussions covering thedetermination of these pressures are presented inEM 1110-2-1603, Hydraulic Design of Spillways.
j. Wave pressure. While wave pressures are of more
upon the dam proper. The height of waves, runup, and
and moments are equal to zero. The distribution of the
(2) For overflow sections, the base width is
EM 1110-2-220030 Jun 95
(3) The unit uplift pressure should be added to thecomputed unit foundation reaction to determine the maxi-mum unit foundation pressure at any point.
(4) Internal stresses and foundation pressures shouldbe computed with and without uplift to determine themaximum condition.
3-10
EM 1110-2-220030 Jun 95
Chapter 4Stability Analysis
4-1. Introduction
a. This chapter presents information on the stabilityanalysis of concrete gravity dams. The basic loadingconditions investigated in the design and guidance for thedam profile and layout are discussed. The forces actingon a structure are determined as outlined in Chapter 3.
b. For new projects, the design of a gravity dam isperformed through an interative process involving a pre-liminary layout of the structure followed by a stability andstress analysis. If the structure fails to meet criteria thenthe layout is modified and reanalyzed. This process isrepeated until an acceptable cross section is attained. Themethod for conducting the static and dynamic stress anal-ysis is covered in Chapter 5. The reevaluation of existingstructures is addressed in Chapter 8.
c. Analysis of the stability and calculation of thestresses are generally conducted at the dam base and atselected planes within the structure. If weak seams orplanes exist in the foundation, they should also beanalyzed.
4-2. Basic Loading Conditions
a. The following basic loading conditions are gener-ally used in concrete gravity dam designs (see Fig-ure 4-1). Loadings that are not indicated should beincluded where applicable. Power intake sections shouldbe investigated with emergency bulkheads closed and allwater passages empty under usual loads. Load cases usedin the stability analysis of powerhouses and power intakesections are covered in EM 1110-2-3001.
(1) Load Condition No. 1 - unusual loadingcondition - construction.
(a) Dam structure completed.
(b) No headwater or tailwater.
(2) Load Condition No. 2 - usual loading condition -normal operating.
(a) Pool elevation at top of closed spillway gateswhere spillway is gated, and at spillway crest where spill-way is ungated.
(b) Minimum tailwater.
(c) Uplift.
(d) Ice and silt pressure, if applicable.
(3) Load Condition No. 3 - unusual loadingcondition - flood discharge.
(a) Pool at standard project flood (SPF).
(b) Gates at appropriate flood-control openings andtailwater at flood elevation.
(c) Tailwater pressure.
(d) Uplift.
(e) Silt, if applicable.
(f) No ice pressure.
(4) Load Condition No. 4 - extreme loadingcondition - construction with operating basis earthquake(OBE).
(a) Operating basis earthquake (OBE).
(b) Horizontal earthquake acceleration in upstreamdirection.
(c) No water in reservoir.
(d) No headwater or tailwater.
(5) Load Condition No. 5 - unusual loadingcondition - normal operating with operating basisearthquake.
(a) Operating basis earthquake (OBE).
(b) Horizontal earthquake acceleration in downstreamdirection.
(c) Usual pool elevation.
4-1
EM 1110-2-220030 Jun 95
Figure 4-1. Basic loading conditions in concrete gravity dam design
(d) Minimum tailwater.
(e) Uplift at pre-earthquake level.
(f) Silt pressure, if applicable.
(g) No ice pressure.
(6) Load Condition No. 6 - extreme loadingcondition - normal operating with maximum credibleearthquake.
(a) Maximum credible earthquake (MCE).
(b) Horizontal earthquake acceleration in downstreamdirection.
(c) Usual pool elevation.
(d) Minimum tailwater.
(e) Uplift at pre-earthquake level.
(f) Silt pressure, if applicable.
(g) No ice pressure.
(7) Load Condition No. 7 - extreme loadingcondition - probable maximum flood.
(a) Pool at probable maximum flood (PMF).
(b) All gates open and tailwater at flood elevation.
(c) Uplift.
(d) Tailwater pressure.
(e) Silt, if applicable.
(f) No ice pressure.
b. In Load Condition Nos. 5 and 6, the selected poolelevation should be the one judged likely to exist coinci-dent with the selected design earthquake event. Thismeans that the pool level occurs, on the average, rela-tively frequently during the course of the year.
4-3. Dam Profiles
a. Nonoverflow section.
(1) The configuration of the nonoverflow section isusually determined by finding the optimum cross section
4-2
EM 1110-2-220030 Jun 95
that meets the stability and stress criteria for each of theloading conditions. The design cross section is generallyestablished at the maximum height section and then usedalong the rest of the nonoverflow dam to provide asmooth profile. The upstream face is generally vertical,but may include a batter to increase sliding stability or inexisting projects provided to meet prior stability criteriafor construction requiring the resultant to fall within themiddle third of the base. The downstream face will usu-ally be a uniform slope transitioning to a vertical facenear the crest. The slope will usually be in the range of0.7H to 1V, to 0.8H to 1V, depending on uplift and theseismic zone, to meet the stability requirements.
(2) In the case of RCC dams not using a downstreamforming system, it is necessary for construction that theslope not be steeper than 0.8H to 1V and that in appli-cable locations, it include a sacrificial concrete because ofthe inability to achieve good compaction at the free edge.The thickness of this sacrificial material will depend onthe climatology at the project and the overall durability ofthe mixture. The weight of this material should not beincluded in the stability analysis. The upstream face willusually be vertical to facilitate construction of the facingelements. When overstressing of the foundation materialbecomes critical, constructing a uniform slope at thelower part of the downstream face may be required toreduce foundation pressures. In locations of slopechanges, stress concentrations will occur. Stresses shouldbe analyzed in these areas to assure they are withinacceptable levels.
(3) The dam crest should have sufficient thickness toresist the impact of floating objects and ice loads and tomeet access and roadway requirements. The freeboard atthe top of the dam will be determined by wave height andrunup. In significant seismicity areas, additional concretenear the crest of the dam results in stress increases. Toreduce these stress concentrations, the crest mass shouldbe kept to a minimum and curved transitions provided atslope changes.
b. Overflow section. The overflow or spillway sec-tion should be designed in a similar manner as the non-overflow section, complying with stability and stresscriteria. The upstream face of the overflow section willhave the same configuration as the nonoverflow section.The required downstream face slope is made tangent tothe exponential curve of the crest and to the curve at thejunction with the stilling basin or flip bucket. Themethods used to determine the spillway crest curves iscovered in EM 1110-2-1603, Hydraulic Design ofSpillways. Piers may be included in the overflow section
to support a bridge crossing the spillway and to supportspillway gates. Regulating outlet conduits and gates aregenerally constructed in the overflow section.
4-4. Stability Considerations
a. General requirements. The basic stability require-ments for a gravity dam for all conditions of loading are:
(1) That it be safe against overturning at any hori-zontal plane within the structure, at the base, or at a planebelow the base.
(2) That it be safe against sliding on any horizontalor near-horizontal plane within the structure at the base oron any rock seam in the foundation.
(3) That the allowable unit stresses in the concrete orin the foundation material shall not be exceeded.
Characteristic locations within the dam in which a stabil-ity criteria check should be considered include planeswhere there are dam section changes and high concen-trated loads. Large galleries and openings within thestructure and upstream and downstream slope transitionsare specific areas for consideration.
b. Stability criteria. The stability criteria for concretegravity dams for each load condition are listed inTable 4-1. The stability analysis should be presented inthe design memoranda in a form similar to that shown onFigure 4-1. The seismic coefficient method of analysis,as outlined in Chapter 3, should be used to determineresultant location and sliding stability for the earthquakeload conditions. The seismic coefficient used in the anal-ysis should be no less than that given in ER 1110-2-1806,Earthquake Design and Analysis for Corps of EngineersProjects. Stress analyses for a maximum credible earth-quake event are covered in Chapter 5. Any deviationfrom the criteria in Table 4-1 shall be accomplished onlywith the approval of CECW-ED, and should be justifiedby comprehensive foundation studies of such nature as toreduce uncertainties to a minimum.
4-5. Overturning Stability
a. Resultant location. The overturning stability iscalculated by applying all the vertical forces (ΣV) andlateral forces for each loading condition to the dam and,then, summing moments (ΣM) caused by the consequentforces about the downstream toe. The resultant locationalong the base is:
4-3
EM 1110-2-220030 Jun 95
Table 4-1Stability and stress criteria
LoadCondition
ResultantLocationat Base
MinimumSlidingFS
FoundationBearingPressure
Concrete Stress
Compressive Tensile
Usual Middle 1/3 2.0 ≤ allowable 0.3 fc′ 0
Unusual Middle 1/2 1.7 ≤ allowable 0.5 fc′ 0.6 fc′2/3
Extreme Within base 1.3 ≤ 1.33 × allowable 0.9 fc′ 1.5 fc′2/3
Note: fc′ is 1-year unconfined compressive strength of concrete. The sliding factors of safety (FS) are based on a comprehensive fieldinvestigation and testing program. Concrete allowable stresses are for static loading conditions.
(4-1)Resultant locationMV
The methods for determining the lateral, vertical, anduplift forces are described in Chapter 3.
b. Criteria. When the resultant of all forces actingabove any horizontal plane through a dam intersects thatplane outside the middle third, a noncompression zonewill result. The relationship between the base area incompression and the location of the resultant is shown inFigure 4-2. For usual loading conditions, it is generallyrequired that the resultant along the plane of study remainwithin the middle third to maintain compressive stressesin the concrete. For unusual loading conditions, the resul-tant must remain within the middle half of the base. Forthe extreme load conditions, the resultant must remainsufficiently within the base to assure that base pressuresare within prescribed limits.
4-6. Sliding Stability
a. General. The sliding stability is based on a factorof safety (FS) as a measure of determining the resistanceof the structure against sliding. The multiple-wedge anal-ysis is used for analyzing sliding along the base andwithin the foundation. For sliding of any surface withinthe structure and single planes of the base, the analysiswill follow the single plane failure surface of analysiscovered in paragraph 4-6e.
b. Definition of sliding factor of safety.
(1) The slidingFS is conceptually related to failure,the ratio of the shear strength (τF), and the applied shearstress (τ) along the failure planes of a test specimenaccording to Equation 4-2:
(4-2)FSτF
τ(σ tan φ c)
τ
whereτF = σ tan φ + c, according to the Mohr-CoulombFailure Criterion (Figure 4-3). The slidingFS is appliedto the material strength parameters in a manner that placesthe forces acting on the structure and rock wedges insliding equilibrium.
(2) The slidingFS is defined as the ratio of the maxi-mum resisting shear (TF) and the applied shear (T) alongthe slip plane at service conditions:
(4-3)FSTF
T(N tan φ cL)
T
where
N = resultant of forces normal to the assumed slidingplane
φ = angle of internal friction
c = cohesion intercept
L = length of base in compression for a unit strip ofdam
c. Basic concepts, assumptions, and simplifications.
(1) Limit equilibrium. Sliding stability is based on alimit equilibrium method. By this method, the shear forcenecessary to develop sliding equilibrium is determined foran assumed failure surface. A sliding mode of failurewill occur along the presumed failure surface when theapplied shear (T) exceeds the resisting shear (TF).
4-4
EM 1110-2-220030 Jun 95
Figure 4-2. Relationship between base area in com-pression and resultant location
(2) Failure surface. The analyses are based on failuresurfaces that can be any combination of planes andcurves; however, for simplicity all failure surfaces areassumed to be planes. These planes form the bases of thewedges. It should be noted that for the analysis to berealistic, the assumed failure planes have to be kinemati-cally possible. In rock the slip planes may be
Figure 4-3. Failure envelope
predetermined by discontinuities in the foundation. Allthe potential planes of failure must be defined andanalyzed to determine the one with the leastFS.
(3) Two-dimensional analysis. The principles pre-sented for sliding stability are based on a two-dimensionalanalysis. These principles should be extended to a three-dimensional analysis if unique three-dimensional geome-tric features and loads critically affect the sliding stabilityof a specific structure.
(4) Force equilibrium only. Only force equilibrium issatisfied in the analysis. Moment equilibrium is not used.The shearing force acting parallel to the interface of anytwo wedges is assumed to be negligible; therefore, theportion of the failure surface at the bottom of each wedgeis loaded only by the forces directly above or below it.There is no interaction of vertical effects between thewedges. The resulting wedge forces are assumedhorizontal.
(5) Displacements. Considerations regarding dis-placements are excluded from the limit equilibriumapproach. The relative rigidity of different foundationmaterials and the concrete structure may influence theresults of the sliding stability analysis. Such complexstructure-foundation systems may require a more intensivesliding investigation than a limit-equilibrium approach.The effects of strain compatibility along the assumedfailure surface may be approximated in the limit-equilibrium approach by selecting the shear strengthparameters from in situ or laboratory tests according tothe failure strain selected for the stiffest material.
(6) Relationship between shearing and normal forces.A linear relationship is assumed between the resistingshearing force and the normal force acting on the slipplane beneath each wedge. The Coulomb-Mohr FailureCriterion defines this relationship.
4-5
EM 1110-2-220030 Jun 95
d. Multiple wedge analysis.
(1) General. This method computes the sliding FSrequired to bring the sliding mass, consisting of the struc-tural wedge and the driving and resisting wedges, into astate of horizontal equilibrium along a given set of slipplanes.
(2) Analysis model. In the sliding stability analysis,the gravity dam and the rock and soil acting on the damare assumed to act as a system of wedges. The damfoundation system is divided into one or more drivingwedges, one structural wedge, and one or more resistingwedges, as shown in Figures 4-4 and 4-5.
(3) General wedge equation. By writing equilibriumequations normal and parallel to the slip plane, solving forNi and Ti, and substituting the expressions forNi and Ti
into the equation for the factor of safety of the typical
wedge, the general wedge and wedge interaction equationcan be written as shown in Equation 4-5 (derivation isprovided in Appendix C).
Figure 4-4. Geometry of structure foundation system
(4-5)FS Wi Vi cos αi HLi HRi sin αi Pi 1 Pi sin αi Ui tan φi
CiLi / HLi HRi cos αi Pi 1 Pi cos αi Wi Vi sin αi
Figure 4-5. Dam foundation system, showing driving, structural, and resisting wedges
4-6
EM 1110-2-220030 Jun 95
Solving for (Pi-1 - Pi) gives the general wedge equation,
(4-6)Pi 1 Pi Wi Vi tan φdi cos αi sin αi Ui tan φdi HLi HRi
tan φdi sin αi cos αi cdiLi / cos αi tan φdi sin αi
where
i = number of wedge being analyzed
(Pi-1 - Pi) = summation of applied forces acting horizon-tally on the i th wedge. (A negative value forthis term indicates that the applied forcesacting on the i th wedge exceed the forcesresisting sliding along the base of the wedge.A positive value for the term indicates thatthe applied forces acting on thei th wedge areless than the forces resisting sliding along thebase of that wedge.)
Wi = total weight of water, soil, rock, or concretein the i th wedge
Vi = any vertical force applied above top ofi th
wedge
tan φdi = tan φi /FS
αi = angle between slip plane ofi th wedge andhorizontal. Positive is counterclockwise
Ui = uplift force exerted along slip plane of thei th
wedge
HLi = any horizontal force applied above top orbelow bottom of left side adjacent wedge
HRi = any horizontal force applied above top orbelow bottom of right side adjacent wedge
cdi = ci /FS
Li = length along the slip plane of thei th wedge
This equation is used to compute the sum of the appliedforces acting horizontally on each wedge for an assumedFS. The sameFS is used for each wedge. The derivationof the general wedge equation is covered in Appendix C.
(4) Failure plane angle. For the initial trial, the fail-ure plane angle alpha for a driving wedge can beapproximated by:
α 45°φd
2
where φd tan 1
tan φFS
For a resisting wedge, the slip plane angle can be approx-imated by:
α 45°φd
2
These equations for the slip plane angle are the exactsolutions for wedges with a horizontal top surface with orwithout a uniform surcharge.
(5) Procedure for a multiple-wedge analysis. Thegeneral procedure for analyzing multi-wedge systemsincludes:
(a) Assuming a potential failure surface based on thestratification, location and orientation, frequency anddistribution of discontinuities of the foundation material,and the configuration of the base.
(b) Dividing the assumed slide mass into a number ofwedges, including a single-structure wedge.
(c) Drawing free body diagrams that show all theforces assuming to be acting on each wedge.
(d) Estimate theFS for the first trial.
(e) Compute the critical sliding angles for eachwedge. For a driving wedge, the critical angle is the
4-7
EM 1110-2-220030 Jun 95
angle that produces a maximum driving force. For aresisting wedge, the critical angle is the angle that pro-duces a minimum resisting force.
(f) Compute the uplift pressure, if any, along the slipplane. The effects of seepage and foundation drainsshould be included.
(g) Compute the weight of each wedge, including anywater and surcharges.
(h) Compute the summation of the lateral forces foreach wedge using the general wedge equation. In certaincases where the loadings or wedge geometries are compli-cated, the critical angles of the wedges may not be easilycalculated. The general wedge equation may be used toiterate and find the critical angle of a wedge by varyingthe angle of the wedge to find a minimum resisting ormaximum driving force.
(i) Sum the lateral forces for all the wedges.
(j) If the sum of the lateral forces is negative,decrease theFS and then recompute the sum of the lateralforces. By decreasing theFS, a greater percentage of theshearing strength along the slip planes is mobilized. Ifthe sum of the lateral forces is positive, increase theFSand recompute the sum of the lateral forces. By increas-ing the FS, a smaller percentage of the shearing strengthis mobilized.
(k) Continue this trial and error process until the sumof the lateral forces is approximately zero for theFS used.This procedure will determine theFS that causes thesliding mass in horizontal equilibrium, in which the sumof the driving forces acting horizontally equals the sum ofthe resisting forces that act horizontally.
(l) If the FS is less than the minimum criteria, aredesign will be required by sloping or widening the base.
e. Single-plane failure surface. The general wedgeequation reduces to Equation 4-7 providing a directsolution for FS for sliding of any plane within the damand for structures defined by a single plane at the inter-face between the structure and foundation material withno embedment. Figure 4-6 shows a graphical representa-tion of a single-plane failure mode for sloping and hori-zontal surfaces.
(4-7)FS[W cos α U H sin α] tan φ CL
H cos α W sin α
where
H = horizontal force applied to dam
C = cohesion on slip plane
L = length along slip plane
Figure 4-6. Single plane failure mode
4-8
EM 1110-2-220030 Jun 95
For the case of sliding through horizontal planes, gener-ally the condition analyzed within the dam, Equation 4-7reduces to Equation 4-8:
(4-8)FS(W U) tan φ CL
HL
f. Design considerations.
(1) Driving wedges. The interface between the groupof driving wedges and the structural wedge is assumed tobe a vertical plane that is located at the heel of the struc-tural wedge and extends to its base. The magnitudes ofthe driving forces depend on the actual values of thesafety factor and the inclination angles of the slip path.The inclination angles, corresponding to the maximumactive forces for each potential failure surface, can bedetermined by independently analyzing the group of driv-ing wedges for a trial safety factor. In rock, the inclina-tion may be predetermined by discontinuities in thefoundation. The general equation applies directly only todriving wedges with assumed horizontal driving forces.
(2) Structural wedge. The general wedge equation isbased on the assumption that shearing forces do not acton the vertical wedge boundaries; hence there can be onlyone structural wedgebecause concrete structures transmitsignificant shearing forces across vertical internal planes.Discontinuities in the slip path beneath the structuralwedge should be modeled by assuming an average slipplane along the base of the structural wedge.
(3) Resisting wedges. The interface between thegroup of resisting wedgesand the structural wedge isassumed to be a vertical plane that is located at the toe ofthe structural wedge and extends to its base. The magni-tudes of the resisting forces depend on the actual valuesof the safety factor and the inclination angles of the slippath. The inclination angles, corresponding to the mini-mum passive forces for each potential failure mechanism,can be determined by independently analyzing the groupof resisting wedges for a trial safety factor. The generalwedge equation applies directly only to resisting wedgeswith assumed horizontal passive forces. If passive resis-tance is used, then rock that may be subjected to highvelocity water scouring should not be used unless ade-quately protected. Also, the compressive strength of therock layers must be sufficient to develop the wedge resis-tance. In some cases, wedge resistance should not beincluded unless rock anchors are installed to stabilize thewedge.
(4) Effects of cracks in foundation. Sliding analysesshould consider the effects of cracks on the driving sideof the structural wedge in the foundation material result-ing from differential settlement, shrinkage, or joints in arock mass. The depth of cracking in massive strong rockfoundations should be assumed to extend to the base ofthe structural wedge. Shearing resistance along the crackshould be ignored, and full hydrostatic pressure should beassumed to act at the bottom of the crack. The hydraulicgradient across the base of the structural wedge shouldreflect the presence of a crack at the heel of the structuralwedge.
(5) Uplift. The effects of uplift forces should beincluded in the sliding analysis. Uplift pressures on thewedges and within any plane within the structure shouldbe determined as described in Chapter 3, Section 3.
(6) Resultant outside kern. As previously stated,requirements for rotational equilibrium are not directlyincluded in the general wedge equation. For some loadcases, the normal component of the resultant applied loadswill lie outside the kern of the base area, and not all ofthe structural wedge will be in contact with the foundationmaterial. The sliding analysis should be modified forthese load cases to reflect the following secondary effectsdue tocoupling of the sliding and rational behavior.
(a) The uplift pressure on the portion of the base notin contact with the foundation material should be a uni-form value that is equal to the maximum value of thehydraulic pressure across the base (except for instanta-neous load cases such as those resulting from seismicforces).
(b) The cohesive component of the sliding resistanceshould include only the portion of the base area in contactwith the foundation material.
(7) Seismic sliding stability. The sliding stability of astructure for an earthquake-induced base motion should bechecked by assuming the specified horizontal earthquakeand the vertical earthquake acceleration, if included in theanalysis, to act in the most unfavorable direction. Theearthquake-induced forces on the structure and foundationwedges may then be determined by the seismic coefficientmethod as outlined in Chapter 3. Lateral earthquakeforces for resisting and driving wedges consisting of soilmaterial should be determined as described inEM 1110-2-2502, Retaining and Flood Walls.
4-9
EM 1110-2-220030 Jun 95
(8) Strain compatibility. Shear resistance in a damfoundation is dependent on the strength properties of therock. Slide planes within the foundation rock may passthrough different materials, and these surfaces may beeither through intact rock or along existing rock disconti-nuities. Less deformation is required for intact rock toreach its maximum shear resistance than for discontinuitysurfaces to develop their maximum frictional resistances.Thus, the shear resistance developed along discontinuitiesdepends on the amount of displacement on the intact rockpart of the shear surface. If the intact rock breaks, theshear resistance along the entire length of the shear planeis the combined frictional resistance for all materialsalong the plane.
4-7. Base Pressures
a. Computations of base pressures. For the dam tobe in static equilibrium, the resultant of all horizontal andvertical forces including uplift must be balanced by anequal and opposite reaction of the foundation consistingof the total normal reaction and the total tangential shear.The location of this force is such that the summation ofmoments is equal to zero.
b. Allowable base pressure. The maximum computedbase pressure should be equal to or less than the allow-able bearing capacity for the usual and unusual load con-ditions. For extreme loading condition, the maximumbearing pressure should be equal to or less than 1.33times the allowable bearing capacity.
4-8. Computer Programs
a. Program for sliding stability analysis of concretestructures (CSLIDE).
(1) The computer program CSLIDE has the capabilityof performing a two-dimensional sliding stability analysisof gravity dams and other concrete structures. It uses theprinciples of the multi-wedge system of analysis as dis-cussed in paragraph 4-6. Program documentation is cov-ered in U.S. Army Engineer Waterways ExperimentStation (WES) Instruction Report ITL-87-5, “SlidingStability of Concrete Structures (CSLIDE).”
(2) The potential failure planes and the associatedwedges are chosen for input and, by satisfying limit equi-librium principles, theFS against sliding failure is com-puted for output. The results also give a summary offailure angles and forces acting on the wedges.
(3) The program considers the effects of:
(a) Multiple layers of rock with irregular surfaces.
(b) Water and seepage effects. The line-of-creep andseepage factor/gradient are provided.
(c) Applied vertical surcharge loads including line,uniform, strip, triangular, and ramp loads.
(d) Applied horizontal concentrated point loads.
(e) Irregularly shaped structural geometry with a hori-zontal or sloped base.
(f) Percentage of the structure base in compressionbecause of overturning effects.
(g) Single and multiple-plane options for the failuresurfaces.
(h) Horizontal and vertical induced loads because ofearthquake accelerations.
(i) Factors requiring the user to predetermine thefailure surface.
(4) It will not analyze curved surfaces or disconti-nuities in the slip surface of each wedge. In those cases,an average linear geometry should be assumed along thebase of the wedge.
b. Three-dimensional stability analysis and designprogram (3DSAD), special purpose modules for dams(CDAMS).
(1) General. The computer program called CDAMSperforms a three-dimensional stability analysis and designof concrete dams. The program was developed as a spe-cific structure implementation of the three-dimensionalstability analysis and design (3DSAD) program. It isintended to handle two cross-sectional types:
(a) An overflow monolith with optional pier.
(b) A nonoverflow monolith.
The program can operate in either an analysis or designmode. Load conditions outlined in paragraph 4-1 can beperformed in any order. A more detailed description andinformation about the use of the program can be found in
4-10
EM 1110-2-220030 Jun 95
Instruction Report K-80-4, “A Three-Dimensional Stabil-ity Analysis/Design Program (3DSAD); Report 4, SpecialPurpose Modules for Dams (CDAMS)” (U.S. Army Corpsof Engineers (USACE) 1983).
(2) Analysis. In the analysis mode, the program iscapable of performing resultant location, bearing, andsliding computations for each load condition. A review ismade of the established criteria and the results outputted.
(3) Design. In the design mode, the structure isincrementally modified until a geometry is established thatmeets criteria. Different geometric parameters may bevaried to achieve a stable geometry. A design memoran-dum plate option is also available.
4-11
EM 1110-2-220030 Jun 95
Chapter 5Static and Dynamic Stress Analyses
5-1. Stress Analysis
a. General.
(1) A stress analysis of gravity dams is performed todetermine the magnitude and distribution of stressesthroughout the structure for static and dynamic load con-ditions and to investigate the structural adequacy of thesubstructance and foundation. Load conditions usuallyinvestigated are outlined in Chapter 4.
(2) Gravity dam stresses are analyzed by eitherapproximate simplified methods or the finite elementmethod depending on the refinement required for theparticular level of design and the type and configurationof the dam. For preliminary designs, simplified methodsusing cantilever beam models for two-dimensional analy-sis or the trial load twist method for three-dimensionalanalysis are appropriate as described in the US Bureau ofReclamation (USBR), “Design of Gravity Dams” (1976).The finite element method is ordinarily used for the fea-ture and final design stages if a more exact stress investi-gation is required.
b. Finite element analysis.
(1) Finite element models are used for linear elasticstatic and dynamic analyses and for nonlinear analysesthat account for interaction of the dam and foundation.The finite element method provides the capability ofmodeling complex geometries and wide variations inmaterial properties. The stresses at corners, around open-ings, and in tension zones can be approximated with afinite element model. It can model concrete thermalbehavior and couple thermal stresses with other loads.An important advantage of this method is that compli-cated foundations involving various materials, weak jointson seams, and fracturing can be readily modeled. Specialpurpose computer programs designed specifically foranalysis of concrete gravity dams are CG-DAMS (Ana-tech 1993), which performs static, dynamic, and nonlinearanalyses and includes a smeared crack model, and MER-LIN (Saouma 1994), which includes a discrete crackingfracture mechanics model.
(2) Two-dimensional, finite element analysis is gener-ally appropriate for concrete gravity dams. The designershould be aware that actual structure response is three-dimensional and should review the analytical and realistic
results to assure that the two-dimension approximation isacceptable and realistic. For long conventional concretedams with transverse contraction joints and without keyedjoints, a two-dimensional analysis should be reasonablycorrect. Structures located in narrow valleys betweensteep abutments and dams with varying rock moduliwhich vary across the valley are conditions that necessi-tate three-dimensional modeling.
(3) The special purpose programs Earthquake Analy-sis of Gravity Dams including Hydrodynamic Interaction(EADHI) (Chakrabarti and Chopra 1973) and EarthquakeResponse of Concrete Gravity Dams Including Hydrody-namic and Foundation Interaction Effects (EAGD84)(Chopra, Chakrabarti, and Gupta 1980) are available formodeling the dynamic response of linear two-dimensionalstructures. Both programs use acceleration time recordsfor dynamic input. The program SDOFDAM is a two-dimensional finite element model (Cole and Cheek 1986)that computes the hydrodynamic loading using Chopra’ssimplified procedure. The finite element programs suchas GTSTRUDL, SAP, ANSYS, ADINA, and ABAQUSprovide general capabilities for modeling static anddynamic responses.
5-2. Dynamic Analysis
The structural analysis for earthquake loadings consists oftwo parts: an approximate resultant location and slidingstability analysis using an appropriate seismic coefficient(see Chapter 4) and a dynamic internal stress analysisusing site-dependent earthquake ground motions if thefollowing conditions exist:
a. The dam is 100 feet or more in height and thepeak ground acceleration (PGA) at the site is greater than0.2 g for the maximum credible earthquake.
b. The dam is less than 100 feet high and the PGA atthe site is greater than 0.4 g for the maximum credibleearthquake.
c. There are gated spillway monoliths, wide road-ways, intake structures, or other monoliths of unusualshape or geometry.
d. The dam is in a weakened condition because ofaccident, aging, or deterioration. The requirements for adynamic stress analysis in this case will be decided on aproject-by-project basis in consultant and approved byCECW-ED.
5-1
EM 1110-2-220030 Jun 95
5-3. Dynamic Analysis Process
The procedure for performing a dynamic analysis includethe following:
a. Review the geology, seismology, and con-temporary tectonic setting.
b. Determine the earthquake sources.
c. Select the candidate maximum credible and operat-ing basis earthquake magnitudes and locations.
d. Select the attenuation relationships for the candi-date earthquakes.
e. Select the controlling maximum credible and oper-ating basis earthquakes from the candidate earthquakesbased on the most severe ground motions at the site.
f. Select the design response spectra for the control-ling earthquakes.
g. Select the appropriate acceleration-time recordsthat are compatible with the design response spectra ifacceleration-time history analyses are needed.
h. Select the dynamic material properties for theconcrete and foundation.
i. Select the dynamic methods of analysis to be used.
j. Perform the dynamic analysis.
k. Evaluate the stresses from the dynamic analysis.
5-4. Interdisciplinary Coordination
A dynamic analysis requires a team of engineering geolo-gists, seismologists, and structural engineers. They mustwork together in an integrated approach so that elementsof conservatism are not unduly compounded. An exampleof undue conservatism includes using a rare event as theMCE, upper bound values for the PGA, upper boundvalues for the design response spectra, and conservativecriteria for determining the earthquake resistance of thestructure. The steps in performing a dynamic analysisshould be fully coordinated to develop a reasonably con-servative design with respect to the associated risks. Thestructural engineers responsible for the dynamic structuralanalysis should be actively involved in the process ofcharacterizing the earthquake ground motions (see
paragraph 5-6) in the form required for the methods ofdynamic analysis to be used.
5-5. Performance Criteria for Response toSite-Dependent Earthquakes
a. Maximum credible earthquake. Gravity damsshould be capable of surviving the controlling MCE with-out a catastrophic failure that would result in loss of lifeor significant damage to property. Inelastic behavior withassociated damage is permissible under the MCE.
b. Operating basis earthquake. Gravity dams shouldbe capable of resisting the controlling OBE within theelastic range, remain operational, and not require exten-sive repairs.
5-6. Geological and Seismological Investigation
A geological and seismological investigation of all dam-sites is required for projects located in seismic zones 2through 4. The objectives of the investigation are toestablish controlling maximum and credible operatingbasis earthquakes and the corresponding ground motionsfor each and to assess the possibility of earthquake-induced foundation dislocation at the site. Selecting thecontrolling earthquakes is discussed below. Additionalinformation is also available in TM 5-809-10-1.
5-7. Selecting the Controlling Earthquakes
a. Maximum credible earthquake. The first step forselecting the controlling MCE is to specify the magnitudeand/or modified Mercalli (MM) intensity of the MCE foreach seismotectonic structure or source area within theregion examined around the site. The second step is toselect the controlling MCE based on the most severevibratory ground motion within the predominant fre-quency range of the dam and determine the foundationdislocation, if any, capable of being produced at the siteby the candidate MCE’s. If more than one candidateMCE produce the largest ground motions in differentfrequency bands significant to the response of the dam,each should be considered a controlling MCE.
b. Operating basis earthquake.
(1) The selection of the OBE is based upon thedesired level of protection for the project from earth-quake-induced damage and loss of service project life.The project life of new dams is usually taken as100 years. The probability of exceedance of the OBE
5-2
EM 1110-2-220030 Jun 95
during the project life should be no greater than50 percent unless the cost savings in designing for a lesssevere earthquake outweighs the risk of incurring the costof repairs and loss of service because of a more severeearthquake.
(2) The probabilistic analysis for the OBE involvesdeveloping a magnitude frequency or epicentral intensityfrequency (recurrence) relationship of each seismicsource; projecting the recurrence information fromregional and past data into forecasts concerning futureoccurrence; attenuating the severity parameter, usuallyeither PGA of MM intensity, to the site; determining thecontrolling recurrence relationship for the site; and finally,selecting the design level of earthquake based upon theprobability of exceedance and the project life.
5-8. Characterizing Ground Motions
a. General. After specifying the location and magni-tude (or epicentral intensity) of each candidate earthquakeand an appropriate regional attenuation relationship, thecharacteristics of vibratory ground motion expected at thesite can be determined. Vibratory ground motions havebeen described in a variety of ways, such as peak groundmotion parameters, acceleration-time records (accelero-grams), or response spectra (Hayes 1980, and Krinitzskyand Marcuson 1983). For the analysis and design ofconcrete dams, the controlling characterization of vibra-tory ground motion should be a site-dependent designresponse spectra.
b. Site-specific design response spectra.
(1) Wherever possible, site-specific design responsespectra should be developed statistically from responsespectra of strong motion records of earthquakes that havesimilar source and propagation path properties as thecontrolling earthquake(s) and are recorded on a foundationsimilar to that of the dam. Important source propertiesinclude magnitude and, if possible, fault type and tectonicenvironment. Propagation path properties include dis-tance, depth, and attenuation. As many accelerograms aspossible that are recorded under comparable conditionsand have a predominant frequency similar to that selectedfor the design earthquake should be included in thedevelopment of the design response spectra. Also, accel-erograms should be selected that have been corrected forthe true baseline of zero acceleration, for errors in digiti-zation, and for other irregularities (Schiff and Bogdanoff1967).
(2) Where a large enough ensemble of site-specificstrong motion records is not available, design responsespectra may be approximated by scaling that ensemble ofrecords that represents the best estimate of source, propa-gation path, and site properties. Scaling factors can beobtained in several ways. The scaling factor may bedetermined by dividing the peak or effective peak acceler-ation specified for the controlling earthquake by the peakacceleration of the record being rescaled. The peakvelocity of the record should fall within the range of peakvelocities specified for the controlling earthquake, or therecord should not be used. Spectrum intensity can beused for scaling by using the ratio of the spectrum inten-sity determined for the site and the spectrum intensity ofthe record being rescaled (USBR 1978). Accelerationattenuation relationships can be used for scaling by divid-ing the acceleration that corresponds to the source dis-tance and magnitude of the controlling earthquake by theacceleration that corresponds to the source distance andmagnitude of the record being rescaled (Guzman andJennings 1970). Because the scaling of accelerograms isan approximate operation at best, the closer the character-istics of the actual earthquake are to those of the control-ling earthquake, the more reliable the results. For thisreason, the scaling factor should be held to within a rangeof 0.33 to 3 for gravity dam.
(3) Guidance for developing design response spectra,statistically, from strong motion records is given inVanmarcke (1979).
(4) Site-dependent response spectra developed fromstrong motion records, as described in paragraphs 5-8b,should have amplitudes equal to or greater than the meanresponse spectrum for the appropriate foundation given bySeed, Ugas, and Lysmer (1976), anchored by the PGAdetermined for the site. This minimum response spectrummay be anchored by an effective PGA determined for thesite, but supporting documentation for determining theeffective PGA will be required (Newmark and Hall 1982).
(5) A mean smooth response spectrum of theresponse spectra of records chosen should be presentedfor each damping value of interest. The statistical levelof response spectra used should be justified based on thedegree of conservatism in the preceding steps of the seis-mic design process and the thoroughness of the develop-ment of the design response spectra. If a rare event isused as the controlling earthquake and the earthquakerecords are scaled by upper bound values of groundmotions, then use a response spectrum corresponding to
5-3
EM 1110-2-220030 Jun 95
the mean of the amplification factors if the response spec-trum is based on five or more earthquake records.
c. Accelerograms for acceleration-time historyanalysis. Accelerograms used for dynamic input shouldbe compatible with the design response spectrum andaccount for the peak ground motions parameters, spectrumintensity, and duration of shaking. Compatibility isdefined as the envelope of all response spectra derivedfrom the selected accelerograms that lie below the smoothdesign response spectrum throughout the frequency rangeof structural significance.
5-9. Dynamic Methods of Stress Analysis
a. General. A dynamic analysis determines the struc-tural response based on the characteristics of the structureand the nature of the earthquake loading. Dynamicmethods usually employ the modal analysis technique.This technique is based on the simplifying assumptionthat the response in each natural mode of vibration can becomputed independently and the modal responses can becombined to determine the total response (Chopra 1987).Modal techniques that can be used for gravity damsinclude a simplified response spectrum method and finiteelement methods using either a response spectrum oracceleration-time records for the dynamic input. Adynamic analysis should begin with the response spectrummethod and progress to more refined methods if needed.A time-history analysis is used when yielding (cracking)of the dam is indicated by a response spectrum analysis.The time-history analysis allows the designer to determinethe number of cycles of nonlinear behavior, the magnitudeof excursion into the nonlinear range, and the time thestructure remains nonlinear.
b. Simplified response spectrum method.
(1) The simplified response spectrum method com-putes the maximum linear response of a nonoverflowsection in its fundamental mode of vibration due to thehorizontal component of ground motion (Chopra 1987).The dam is modeled as an elastic mass fully restrained ona rigid foundation. Hydrodynamic effects are modeled asan added mass of water moving with the dam. Theamount of the added water mass depends on the funda-mental frequency of vibration and mode shape of the damand the effects of interaction between the dam and reser-voir. Earthquake loading is computed directly from thespectral acceleration, obtained from the design earthquakeresponse spectrum, and the dynamic properties of thestructural system.
(2) This simplified method can be used also for anungated spillway monolith that has a section similar to anonoverflow monolith. A simplified method for gatedspillway monoliths is presented in WES Technical ReportSL-89-4 (Chopra and Tan 1989).
(3) The program SDOFDAM is available to easilymodel a dam using the finite element method andChopra’s simplified procedure for estimating the hydrody-namic loading. This analysis provides a reasonable firstestimate of the tensile stress in the dam. From that esti-mate, one can decide if the design is adequate or if arefined analysis is needed.
c. Finite element methods.
(1) General. The finite element method is capable ofmodeling the horizontal and vertical structural deforma-tions and the exterior and interior concrete, and it includesthe response of the higher modes of vibrations, the inter-action effects of the foundation and any surrounding soil,and the horizontal and vertical components of groundmotion.
(2) Finite element response spectrum method.
(a) The finite element response spectrum method canmodel the dynamic response of linear two- and three-dimensional structures. The hydrodynamic effects aremodeled as an added mass of water moving with the damusing Westergaard’s formula (Westergaard 1933). Thefoundations are modeled as discrete elements or a halfspace.
(b) Six general purpose finite element programs arecompared by Hall and Radhakrishnan (1983).
(c) A finite element program computes the naturalfrequencies of vibration and corresponding mode shapesfor specified modes. The earthquake loading is computedfrom earthquake response spectra for each mode of vibra-tion induced by the horizontal and vertical components ofground motion. These modal responses are combined toobtain an estimate of the maximum total response.Stresses are computed by a static analysis of the damusing the earthquake loading as an equivalent static load.
(d) The complete quadratic combination (CQC)method (Der Kiureghian 1979 and 1980) should be usedto combine the modal responses. The CQC methoddegenerates to the square root of the sum of squares(SRSS) method for two-dimensional structures in which
5-4
EM 1110-2-220030 Jun 95
the frequencies are well separated. Combining modalmaxima by the SRSS method can dramatically overesti-mate or significantly underestimate the dynamic responsefor three-dimensional structures.
(e) The finite element response spectrum methodshould be used for dam monoliths that cannot be modeledtwo dimensionally or if the maximum tensile stress fromthe simplified response spectrum method (paragraph 5-9b)exceeds 15 percent of the unconfined compressivestrength of the concrete.
(f) Normal stresses should be used for evaluating theresults obtained from a finite element response spectrumanalysis. Finite element programs calculate normalstresses that, in turn, are used to compute principalstresses. The absolute values of the dynamic response atdifferent time intervals are used to combine the modalresponses. These calculations of principal stress overesti-mate the actual condition. Principal stresses should becalculated using the finite element acceleration-time his-tory analysis for a specific time interval.
(3) Finite element acceleration-time history method.
(a) The acceleration-time history method requires ageneral purpose finite element program or the specialpurpose computer program called EADHI. EADHI can
model static and dynamic responses of lineartwo-dimensional dams. The hydrodynamic effects aremodeled using the wave equation. The compressibility ofwater and structural deformation effects are included incomputing the hydrodynamic pressures. EADHI wasdeveloped assuming a fixed base for the dam. The mostcomprehensive two-dimensional earthquake analysis pro-gram available for gravity dams is EAGD84, which canmodel static and dynamic responses of lineartwo-dimensional dams, including hydrodynamic andfoundation interaction. Dynamic input for EADHI andEAGD84 is an acceleration time record.
(b) The acceleration-time history method computesthe natural frequencies of vibration and correspondingmode shapes for specified modes. The response of eachmode, in the form of equivalent lateral loads, is calculatedfor the entire duration of the earthquake acceleration-timerecord starting with initial conditions, taking a small timeinterval, and computing the response at the end of eachtime interval. The modal responses are added for eachtime interval to yield the total response. The stresses arecomputed by a static analysis for each time interval.
(c) An acceleration-time history analysis isappropriate if the variation of stresses with time isrequired to evaluate the extent and duration of a highlystressed condition.
5-5
EM 1110-2-220030 Jun 95
Chapter 6Temperature Control of Mass Concrete
6-1. Introduction
Temperature control of mass concrete is necessary toprevent cracking caused by excessive tensile strains thatresult from differential cooling of the concrete. The con-crete is heated by reaction of cement with water and cangain additional heat from exposure to the ambient con-ditions. Cracking can be controlled by methods that limitthe peak temperature to a safe level, so the tensile strainsdeveloped as the concrete cools to equilibrium are lessthan the tensile strain capacity.
6-2. Thermal Properties of Concrete
a. General. The properties of concrete used in ther-mal studies for the design of gravity dams are thermaldiffusivity, thermal conductivity, specific heat, coefficientof thermal expansion, heat of hydration of the cement,tensile strain capacity, and modulus of elasticity. Themost significant factor affecting the thermal properties isthe composition of the aggregates. The selection of suit-able aggregates is based on other considerations, so littleor no control can be exercised over the thermal propertiesof the aggregates. Type II cement with optional low heatof hydration limitation and a cement replacement arenormally specified. Type IV low-heat cement has notbeen used in recent years, because in most cases heatdevelopment can be controlled by other measures andtype IV cement is not generally available.
b. Thermal conductivity. The thermal conductivity ofa material is the rate at which it transmits heat and isdefined as the ratio of the flux of heat to the temperaturegradient. Water content, density, and temperature signifi-cantly influence the thermal conductivity of a specificconcrete. Typical values are 2.3, 1.7, and 1.2 Britishthermal units (Btu)/hour/foot/Fahrenheit degree (°F) forconcrete with quartzite, limestone, and basalt aggregates,respectively.
c. Thermal diffusivity. Diffusivity is described as anindex of the ease or difficulty with which concrete under-goes temperature change and, numerically, is the thermalconductivity divided by the product of specific heat anddensity. Typical diffusivity values for concrete rangefrom 0.03 square foot/hour for basalt concrete to0.06 square foot/hour for quartzite concrete.
d. Specific heat. Specific heat or heat capacity is theheat required to raise a unit weight of material 1 degree.Values for various types of concrete are about the sameand vary from 0.22 to 0.25 Btu’s/pound/°F.
e. Coefficient of thermal expansion. The coefficientof thermal expansion can be defined as the change inlinear dimension per unit length divided by the tempera-ture change expressed in millionths per °F. Basalt andlimestone concretes have values from 3 to 5 millionths/°F;quartzite concretes range up to 8 millionths/°F.
f. Heat of hydration. The reaction of water withcement is exothermic and generates a considerable amountof heat over an extended period of time. Heats of hydra-tion for various cements vary from 60 to 95 calories/gramat 7 days and 70 to 110 calories/gram at 28 days.
g. Tensile strain capacity. Design is based on maxi-mum tensile strain. The modulus of rupture test(CRD-C 16) is done on concrete beams tested to failureunder third-point loading. Tensile strain capacity is deter-mined by dividing the modulus of rupture by the modulusof elasticity. Typical values range from 50 to200 millions depending on loading rate and type ofconcrete.
h. Creep. Creep of concrete is deformation thatoccurs while concrete is under sustained stress. Specificcreep is creep under unit stress. Specific creep of massconcrete is in the range of 1.4 × 10-6/pounds per squareinch (psi).
i. Modulus of elasticity. The instantaneous loadingmodulus of elasticity for mass concrete ranges from about1.5 to 6 × 106 psi and under sustained loading from about0.5 to 4 × 106 psi.
6-3. Thermal Studies
a. General. During the design of gravity dams, it isnecessary to assess the possibility that strain induced bytemperature changes in the concrete will not exceed thestrain capacity of the concrete. Detailed design proce-dures for control of the generation of heat and volumechanges to minimize cracking may be found in theACIManual of Concrete Practice, Section 207. The followingconcrete parameters should be determined by a divisionlaboratory: heat of hydration (CRD-C 229), adiabatictemperature rise (CRD-C 38), thermal conductivity(CRD-C 44), thermal diffusivity (CRD-C 37), specific
6-1
EM 1110-2-220030 Jun 95
heat (CRD-C 124), coefficient of thermal expansion(CRD-C 397, 125, and 126), creep (CRD-C 54), andtensile strain capacity (CRD-C 71). Thermal propertiestesting should not be initiated until aggregateinvestigations have proceeded to the point that the mostlikely aggregate sources are determined and the availabil-ity of cementitious material is known.
b. Allowable peak temperature. The peak tempera-ture for the interior mass concrete must be controlled toprevent cracking induced by surface contraction. Theallowable peak temperature commonly used to preventserious cracking in mass concrete structures is the meanannual ambient temperature plus the number of degreesFahrenheit determined by dividing the tensile strain capac-ity by the coefficient of linear expansion. This assumesthat the concrete will be subjected to 100-percent restraintagainst contraction. When the potential temperature riseof mass concrete is reduced to this level, the temperaturedrop that causes tensile strain and cracking is reduced toan acceptable level.
6-4. Temperature Control Methods
The temperature control methods available for consider-ation all have the basic objective of reducing increases in
temperature due to heat of hydration, reducing thermaldifferentials within the structure, and reducing exposure tocold air at the concrete surfaces that would createcracking. The most common techniques are the control oflift thickness, time interval between lifts, maximum allow-able placing temperature of the concrete, and surfaceinsulation. Postcooling may be economical for largestructures. Analysis should be made to determine themost economic method to restrict temperature increasesand subsequent temperature drops to levels just safelybelow values that could cause undesirable cracking. Forstructures of limited complexity, such as conventionallyshaped gravity dams, satisfactory results may be obtainedby use of the design procedures in ACI 207 “Mass Con-crete for Dams and Other Massive Structures.” Rollercompacted concrete thermal control options include theinstallation of contraction joints, winter construction,mixture design, and increased heat dissipation. Contrac-tion joints can be created by inserting a series of cuts ormetal plates into each lift to produce a continuous verticaljoint. Using very high production and placement rates,RCC construction can be limited to colder winter monthswithout excessive schedule delays. The normal lift heightof 1 to 2 feet provides for an increased rate of heat dissi-pation during cool weather.
6-2
EM 1110-2-220030 Jun 95
Chapter 7Structural Design Considerations
7-1. Introduction
This chapter discusses the layout, design, and constructionconsiderations associated with concrete gravity dams.These general considerations include contraction andconstruction joints, waterstops, spillways, outlet works,and galleries. Similar considerations related to RCCgravity dams are addressed in Chapter 9.
7-2. Contraction and Construction Joints
a. To control the formation of cracks in mass con-crete, vertical transverse contraction (monolith) joints willgenerally be spaced uniformly across the axis of the damabout 50 feet apart. Where a powerhouse forms an inte-gral part of a dam and the spacing of the units is inexcess of this dimension, it will be necessary to increasethe joint spacing in the intake block to match the spacingof the joints in the powerhouse. In the spillway section,gate and pier size and other requirements are factors inthe determination of the spacing of the contraction joints.The location and spacing of contraction joints should begoverned by the physical features of the damsite, detailsof the appurtenant structures, results of temperature stud-ies, placement rates and methods, and the probable con-crete mixing plant capacity. Abrupt discontinuities alongthe dam profile, material changes, defects in the founda-tion, and the location of features such as outlet works andpenstock will also influence joint location. In addition,the results of thermal studies will provide limitations onmonolith joint spacing for assurance against cracking fromexcessive temperature-induced strains. The joints arevertical and normal to the axis, and they extend continu-ously through the dam section. The joints are constructedso that bonding does not exist between adjacent monolithsto assure freedom of volumetric change of individualmonoliths. Reinforcing should not extend through a con-traction joint. At the dam faces, the joints are chamferedabove minimum pool level for appearance and for mini-mizing spalling. The monoliths are numbered, generallysequentially, from the right abutment.
b. Horizontal or nearly horizontal construction joints(lift joints) will be spaced to divide the structure intoconvenient working units and to control constructionprocedure for the purpose of regulating temperaturechanges. A typical lift will usually be 5 feet consisting ofthree 20-inch layers, or 7-1/2 feet consisting of five18-inch layers. Where necessary as a temperature control
measure, lift thickness may be limited to 2-1/2 feet incertain areas of the dam. The best lift height for eachproject will be determined from concrete production capa-bilities and placing methods. EM 1110-2-2000 providesguidance on establishing lift thickness.
7-3. Waterstops
A double line of waterstops should be provided near theupstream face at all contraction joints. The waterstopsshould be grouted 18 to 24 inches into the foundation orsealed to the cutoff system and should terminate near thetop of the dam. For gated spillway sections, the tops ofthe waterstops should terminate near the crest of the ogee.A 6- to 8-inch-diameter formed drain will generally beprovided between the two waterstops. In the nonoverflowmonolith joints, the drains extend from maximum poolelevation and terminate at about the level of, and draininto, the gutter in the grouting and drainage gallery. Inthe spillway monolith joints, the drains extend from thegate sill to the gallery. A single line of waterstops shouldbe placed around all galleries and other openings crossingmonolith joints. EM 1110-2-2102 provides further detailsand guidance for the selection and use of waterstops andother joint materials.
7-4. Spillway
a. The primary function of a spillway is to releasesurplus water from reservoirs and to safely bypass thedesign flood downstream in order to prevent overtoppingand possible failure of the dam. Spillways are classifiedas controlled (gate) or uncontrolled (ungated). The over-flow (ogee) spillway is the type usually associated withconcrete gravity dams. Other less common spillway typessuch as chute, side channel, morning glory, and tunnel arenot addressed in this manual.
b. An overflow spillway profile is governed in itsupper portions by hydraulic considerations rather than bystability requirements. The downstream face of the spill-way section terminates either in a stilling basin apron orin a bucket type energy dissipator, depending largely uponthe nature of the site and upon the tailwater conditions.The design of the spillway shall include the stability andinternal stress analysis and the structural performance.Loadings should be consistent with those discussed inChapter 4. Operating equipment should be designed to beoperational following a maximum credible earthquake.
c. Discharge over the spillway or flip bucket sectionmust be confined by sidewalls on either side, terminatingin training walls extending along each side of the stilling
7-1
EM 1110-2-220030 Jun 95
basin or flip bucket. Height and length of training wallsare usually determined by model tests or from previoustests of similar structures. Sidewalls should be of suffi-cient height to contain the spillway design flow, with a2-foot freeboard. Negative pressures (see EM 1110-2-1603) due to flowing water should be considered in thedesign of the sidewalls, with the maximum allowance (seeEM 1110-2-2400) being made at the stilling basin,decreasing uniformly to no allowance at the crest. Side-walls are usually designed as cantilevers projecting out ofthe monolith. A wind load of 30 pounds/square foot orearthquake loading should be assumed for design of rein-forcing in the outer face of the walls. The spillway sec-tion surfaces should be designed to withstand the highflow velocities expected during peak discharge andreduced pressures resulting from the hydrodynamiceffects.
d. The dynamic loads occurring in the energy dissipa-tors will include direct impact, pulsating loads from turbu-lence, multidirectional and deflected hydraulic flows,surface erosion from high velocities and debris, and cavi-tation. The downstream end of the dissipator shouldinclude adequate protection against undermining fromturbulence and eddies. Concrete apron, riprap, or othermeasures have been used for stabilization.
7-5. Spillway Bridge
a. Bridges are provided across dam spillways to fur-nish a means of access for pedestrian and vehicular trafficbetween the nonoverflow sections; to provide access orsupport for the operating machinery for the crest gates; or,usually, to serve both purposes. In the case of an uncon-trolled spillway and in the absence of vehicular traffic,access between the nonoverflow sections may be providedby a small access bridge or by stair shafts and a gallerybeneath the spillway crest.
b. The design of a deck-type, multiple-span spillwaybridge should generally conform to the following criteria.The class of highway design loading will normally not beless than HS-20. Special loadings required for performingoperation and maintenance functions and those that thebridge is subjected to during construction should be takeninto account, including provisions for any heavy concen-trated loads. Heavy loadings for consideration shouldinclude those due to powerhouse equipment transportedduring construction, mobile cranes used for maintenance,and gantry cranes used to operate the regulating outletworks and to install spillway stoplogs. If the structurecarries a state or county highway, the design will usually
conform to the standard specification for highway bridgesadopted by the American Association of State Highwayand Transportation Officials (AASHTO).
c. Materials used in the design and construction of thebridge should be selected on the basis of life cycle costsand functional requirements. Floors, curbs, and parapetsshould be reinforced concrete. Beams and girders may bestructural steel, precast or cast-in-place reinforced con-crete, or prestressed concrete. Prestressed concrete isoften used because it combines economy, simple erectionprocedures, and low maintenance.
7-6. Spillway Piers
a. For uncontrolled spillways, the piers function assupports for the bridge. On controlled spillways, the pierswill also contain the anchorage or slots for the crest gatesand may support fixed hoists for the gates. The piers aregenerally located in the middle of the monolith, and thewidth of pier is usually determined by the size of thegates, with the average width being between 8 and10 feet. The spillway piers in RCC dams are constructedwith conventional concrete.
b. Since each pier supports a gate on each side, thefollowing pier loading conditions should be investigated:
(1) Case 1--both gates closed and water at the top ofgates.
(2) Case 2--one gate closed and the other gate wideopen with water at the top of the closed gate.
(3) Case 3--one gate closed and the other open withbulkheads in place and water at the top of the closed gate.
c. Cases 1 and 3 result in maximum horizontal shearnormal to the axis of the dam and the largest overturningmoment in the downstream direction.
d. Case 2 results in lower horizontal shear and down-stream overturning moment, but in addition the pier willhave a lateral bending moment due to the water flowingthrough the open gate and to the hoisting machinery whenlifting a closed gate. A torsional shear in the horizontalplane will also be introduced by the reaction of the closedgate acting on one side of the pier. When tainter gateswith inclined end frames are used, Cases 2 and 3introduce the condition of the lateral component of thethrust on the trunion as a load on only one side of thepier in addition to the applicable loads indicated above.
7-2
EM 1110-2-220030 Jun 95
7-7. Outlet Works
a. The outlet works for concrete dams are usuallyconduits or sluices through the mass with an intake struc-ture on the upstream face, gates or valves for regulationcontrol, and an energy dissipator on the downstream face.Multiple conduits are normally provided because of eco-nomics and operating flexibility in controlling a widerange of releases. The conduits are frequently located inthe center line of the overflow monoliths and dischargeinto the spillway stilling basin. Outlet works located innonoverflow monoliths will require a separate energydissipator. All conduits may be at low level, or somemay be located at one or more higher levels to reduce thehead on the gates, to allow for future reservoir silting, orto control downstream water quality and temperature.The layout, size, and shape of the outlet works are basedon hydraulic and hydrology requirements, regulationplans, economics, site conditions, operation and mainte-nance needs, and interrelationship to the construction planand other appurtenant structures. Conduits may be pro-vided for reservoir evacuation, regulation of flows forflood control, emergency drawdown, navigation, environ-mental (fish), irrigation, water supply, maintaining mini-mum downstream flows and water quality, or for multiplepurposes. Low-level conduits are used to aid waterquality reservoir evacuation and are sometimes desirablefor passage of sediment. These openings are generallyunlined except for short sections adjacent to the controlgates. For lined conduits, it is assumed that the liner isdesigned for the full loading. In conduits where velocitieswill be 40 feet/second or higher, precautions will be takento ensure that the concrete in the sidewalls and invertswill be of superior quality. If the dam includes a powerintake section, penstocks will be provided and designed inaccordance with EM 1110-2-3001.
b. The effect of project functions upon outlet worksdesign and hydraulic design features, including trashrackdesign and types for sluice outlets, are discussed inEM 1110-2-1602. A discussion of the structural featuresof design for penstocks and trashracks for power plantintakes is included in EM 1110-2-3001. The structuraldesign of outlet works is addressed in EM 1110-2-2400.
7-8. Foundation Grouting and Drainage
It is good engineering practice to grout and drain thefoundation rock of gravity dams. A well-planned andexecuted grouting program should assist in disclosingweaknesses in the foundation and improving any existingdefects. The program should include area grouting forfoundation treatment and curtain grouting near the
upstream face for seepage cutoff through the foundation.Area grouting is generally done before concrete place-ment. Curtain grouting is commonly done after concretehas been placed to a considerable height or even after thestructure has been completed. A line of drainage holes isdrilled a few feet downstream from the grout curtain tocollect seepage and reduce uplift across the base.Detailed information on technical criteria and guidance onfoundation grouting is contained in EM 1110-2-3506.
7-9. Galleries
A system of galleries, adits, chambers, and shafts isusually provided within the body of the dam to furnishmeans of access and space for drilling and grouting andfor installation, operation, and maintenance of the acces-sories and the utilities in the dam. The primary consider-ations in the arrangement of the required openings withinthe dam are their functional usefulness and efficiency andtheir location with respect to maintaining the structuralintegrity.
a. Grouting and drainage gallery. A gallery forgrouting the foundation cutoff will extend the full lengthof the dam. It will also serve as a collection main forseepage from foundation drainage holes and the interiordrainage holes. The location of the gallery should be nearthe upstream face and as near the rock surface as feasibleto provide the maximum reduction in overall uplift. Aminimum distance of 5 feet should be maintained betweenthe foundation surface and gallery floor and between theupstream face and the gallery upstream wall. It has beenstandard practice to provide grouting galleries 5 feet wideby 7 feet high. Experience indicates that these dimen-sions should be increased to facilitate drilling andgrouting operations. Where practicable, the width shouldbe increased to 6 or 8 feet and the height to 8 feet. Agutter may be located along the upstream wall of thegallery where the line of grout holes is situated to carryaway drill water and cuttings. A gutter should belocatedalong the downstream gallery wall to carry awayflows from the drain pipes. The gallery is usuallyarranged as a series of horizontal runs and stair flights.The stairs should be provided with safety treads or anonslip aggregate finish. Metal treads are preferablewhere it is probable that equipment will be skidded up ordown the steps since they provide protection against chip-ping of concrete. Where practicable, the width of treadand height of riser should be uniform throughout allflights of stairs and should never change in any one flight.Further details on the grouting and drainage gallery arecovered in EM 1110-2-3506.
7-3
EM 1110-2-220030 Jun 95
b. Gate chambers and access galleries. Gate cham-bers are located directly over the service and emergencysluice gates. These chambers should be sized to accom-modate the gate hoists along with related mechanical andelectrical equipment and should provide adequate clear-ances for maintenance. Access galleries should be suffi-cient size to permit passage of the largest component ofthe gates and hoists and equipment required for mainte-nance. Drainage gutters should be provided and the floorof the gallery sloped to the gutter with about 1/4 inch/footslope.
7-10. Instrumentation
Structural behavior instrumentation programs are providedfor concrete gravity dams to measure the structural
integrity of the structure, check design assumptions, andmonitor the behavior of the foundation and dam duringconstruction and the various operating phases. The extentof instrumentation at projects will vary between projectsdepending on particular site conditions, the size of thedam, and needs for monitoring critical sections. Instru-mentation can be grouped into those that either directly orindirectly measure conditions related to the safety of thestructure. Plumbing, alignment, uplift, and seismic instru-ments fall into the category of safety instruments. In theother group, the instruments measure quantities such asstress and strain, length change, pore pressure, leakage,and temperature change. Details and guidance on theplanning of instrumentation programs, types of instru-ments, and the preparation, installation, and collection ofdata are provided in EM 1110-2-4300.
7-4
EM 1110-2-220030 Jun 95
Chapter 8Reevaluation of Existing Dams
8-1. General
Existing gravity dams and foundations should be reevalu-ated for integrity, strength, and stability when:
a. It is evident that distress has occurred because ofan accident, aging, or deterioration.
b. Design criteria have become more stringent.
c. Excavation is to be performed near existingstructures.
d. Structural deficiencies have been detected.
e. Actual loadings are, or anticipated loadings willbe, greater than those used in the original design. Load-ings can increase as a result of changed operational proce-dures or operational deficiencies, an increase in damheight, or an increase in the maximum credible earth-quake as a result of seismological investigations. Condi-tions such as excessive uplift pressures, unusual horizontalor vertical displacements, increased seepage through theconcrete or foundation, and structural cracking are indica-tions that a reevaluation should be performed.
8-2. Reevaluation
The reevaluation should be based on current design crite-ria and prevailing geological, structural, and hydrologicalconditions. If the investigations indicate a fundamentaldeficiency, then the initial effort should concentrate onrestoring the dam to a safe and acceptable operating con-dition. Efforts could include measures to reduce exces-sive uplift pressures, reduce leak, repair cracks, or restoredeteriorated concrete. Should restoration costs be unrea-sonable or should the fundamental deficiency be due tochanges in load or stability criteria, a detailed analysisshould be performed in accordance with the followingprocedures. The evaluation and repair of concrete struc-tures is covered by EM 1110-2-2002. Reevaluation ofstructures not designed to current standards should be inaccordance with the requirements of ER 1110-2-100.
8-3. Procedures
The following procedures shall be used in evaluatingcurrent structural conditions and determining the
necessary measures for rehabilitation of existing concretegravity dams.
a. Existing data. Collect and review all the availableinformation for the structure including geologic and foun-dation data, design drawings, as-built drawings, periodicinspection reports, damage reports, repair and maintenancerecords, plans of previous modifications to the structure,measurements of movement, instrumentation data, andother pertinent information. Any unusual structuralbehavior that may be an indication of an unsafe conditionor any factor that may contribute to the weakening of thestructure’s stability should be noted and investigatedfurther.
b. Site inspection. Inspect and examine the existingstructure and site conditions. Any significant differencein structure details and loading conditions between exist-ing conditions and design plans and any major damagedue to erosion, cavitation, undermining, corrosion, crack-ing, chemical reaction, or general deterioration should beidentified and evaluated.
c. Preliminary analyses. Perform the preliminaryanalyses based on current structural criteria and availabledata. If the structure does not meet the current criteria,list the possible remedial schemes and prepare a prelimi-nary cost estimate for each scheme. ER 1130-2-417should be followed as applicable.
d. Design meeting. Schedule a meeting when thepreliminary analyses indicate that the structure does notmeet current criteria. The meeting should include repre-sentatives from the District, Division, CECW-E, andCECW-O to decide on a plan for proposed analyses, theextent of the sampling and testing program, the remedialschemes to be studied, and the proposed schedule. Thismeeting will facilitate the design effort and should obviatethe need for major revisions or additional studies whenthe results are submitted for review and approval.
e. Parametric study. Perform a parametric study todetermine the effect of each parameter on the structure’ssafety. The parameters to be studied should include, butnot be limited to, unit weight of concrete, groundwaterlevels, uplift pressures, and shear strength parameters ofrock fill material, rock foundation, and structure-foundation interface. The maximum variation of eachparameter should be considered in determining its effect.
f. Field investigations. Develop an exploration, sam-pling, testing, and instrumentation program, if needed, to
8-1
EM 1110-2-220030 Jun 95
determine the magnitude and reasonable range of variationfor the parameters that have significant effects on thesafety of the structure as determined by the parametricstudy. The Division Material Laboratory should be usedto the maximum extent practicable to perform the testingin accordance with ER 1110-1-8100.
g. Detailed structural analyses. Perform detailedanalyses using data obtained from studies, field investiga-tions, and procedures outlined in Chapters 4 and 5.Three-dimensional modeling should be used as appropri-ate to more accurately predict the structural behavior.
h. Refined structural analysis. The conventionalmethods described in Chapters 4 and 5 may be more con-servative than necessary, especially when making a deter-mination as to the need for remedial strengthening toimprove the stability of an existing dam. If the conven-tional analyses indicate remedial strengthening is required,then a refined finite element analysis should be per-formed. This refined analysis should accurately modelthe strength and stiffness of the dam and foundation todetermine the following:
(1) The extent of tensile cracking at the dam founda-tion interface.
(2) The base area in compression.
(3) The actual magnitude and distribution of foun-dation pressures.
(4) The magnitude and distribution of concretestresses.
Information relative to refined stability analysis proce-dures can be found in Technical Report REMR-CS-120(Eberling et al., in preparation).
i. Review and approval. Present the results ofdetailed structural analyses and cost estimates for remedialmeasures to the Division Office for review and approval.If a deviation from current structural criteria was made inthe analyses, the results should be forwarded toCECW-ED for approval. The required basis for deviatingfrom current structural criteria is given in paragraph 8-4b.
j. Plans and specifications. Develop design plans,specifications, and a cost estimate for proposed remedialmeasures in accordance with ER 1110-2-1200.
8-4. Considerations of Deviation fromStructural Criteria
a. The purpose of incorporating a factor of safety instructural design is to provide a reserve capacity withrespect to failure and to account for strength variability ofthe dam and foundation materials. The required margindepends on the consequences of failure and on the degreeof uncertainties due to loading variations, analysis simpli-fications, design assumptions, variations in materialstrengths, variations in construction control, and otherfactors. For evaluation of existing structures, a higherdegree of confidence may be achieved when the criticalparameters can be determined accurately at the site.Therefore, deviation from the current structural criteria foran existing structure may be allowed under the conditionslisted in paragraph 8-4b.
b. In addition to the detailed analyses and cost esti-mates as listed in paragraph 8-3h, the following informa-tion should also be presented with the request for a devia-tion from the current structural criteria:
(1) Past performance of the structure, includinginstrumentation data and a description of the structurecondition such as cracking, spalling, displacements, etc.
(2) The anticipated remaining life of the structure.
(3) A description of consequences in case of failure.
c. Approval of the deviation depends upon the degreeof confidence in the accuracy of design parameters deter-mined in the field, the remaining life of the structure, andthe potential adverse effect on lives, property, and ser-vices in case of failure.
8-5. Structural Requirements forRemedial Measure
When it is determined that remedial measures are requiredfor the existing structure, they should be designed to meetthe structural criteria of Chapter 4.
8-6. Methods of Improving Stability inExisting Structures
a. General. Several methods are available forimproving the rotational and sliding stability of concretegravity dams. In general, the methods can be categorized
8-2
EM 1110-2-220030 Jun 95
as those that reduce loadings, in particular uplift, or thosethat add stabilizing forces to the structure and increaseoverturning or shear-frictional resistance. Stressed foun-dation anchor systems are considered one of the mosteconomical methods of increasing rotational and slidingresistance along the base of the dam. Foundation groutingand drainage may also be effective in reducing uplift,reducing foundation settlements and displacements,thereby increasing bearing capacity. Regrouting thefoundation could adversely affect existing foundationdrainage systems unless measures are taken to preventplugging the drains; otherwise, drain redrilling will berequired. Various methods of transferring load to morecompetent adjacent structures or foundation materialthrough shear keys, buttresses, underpinning, etc., are alsopossible ways of improving stability.
b. Reducing uplift forces. In many instances, mea-sured uplift pressures are substantially less than thoseused in the original design. These criteria limit drain effi-ciency to a maximum of 50 percent. Many designs arebased on efficiencies less than 50 percent. Existing drain-age systems can produce efficiencies of 75 percent ormore if they extend through the most pervious layers ofthe foundation, if the elevation of the drainage gallery isat or near tailwater, and if the drains are closely spacedand effectively maintained. If measured uplift pressuresare substantially less than design values, then parametricstudies should determine what benefit it may havetowards improving stability. Uplift pressures less thandesign allowables should be data from reliable instrumen-tation which assures that the measured uplift is indicativeof pressures within the upper zones and along the entirefoundation. Uplift pressures can be reduced by additionalfoundation grouting and re-establishing drains. Upliftmay also be reduced by increasing the depth of existingdrains, adding new drains, or rehabilitating existing drainsby reaming and cleaning.
c. Prestressed anchors. Prestressed anchors withdouble corrosion protection may be used to stabilize exist-ing concrete monoliths, but generally should not be usedin the design of new concrete gravity dams. They areeffective in improving sliding resistance, resultant loca-tion, and excessive foundation pressure. Anchors may beused to secure thrust blocks or stilling basins for the solepurpose of improving sliding stability. The anchor forcerequired to stabilize a dam will depend largely on theorientation of the anchors. Anchors should be orientedfor maximum efficiency subject to constraints of access,embedded features, galleries, and stress concentrationsthey induce in the dam. Analyses of tensile stressesunder anchor heads should be made, and reinforcing
should be provided as required. Tendon size, spacing,and embedment length should be based on the requiredanchor force, and should be provided the geotechnicalengineer for determination of the required embedmentlength. Design, installation, and testing of anchors andanchorages should be guided by information in “Recom-mendations for Prestressed Rock and Soil Anchors” (Post-Tensioning Institute (PTI) 1985). Allowable bond stressesused to determine the length of embedment between groutand rocks are recommended to be one half of the ultimatebond stress determined by tests. The typical values ofbond strength given in the above referenced PTI publica-tion may be used in lieu of test values during design, butthe design value should be verified by test before or dur-ing construction. The first three anchors installed and aminimum of 2 percent of the remaining anchors selectedby the engineer should be performance tested. All otheranchors must be proof tested upon installation inaccordance with the PTI recommendations. Additionally,initial lift-off readings should be taken after the anchor isseated and before the jack is removed. Lift-off tests ofrandom anchors selected by the engineer should be made7 days after lock-off and prior to secondary grouting.Long-term monitoring of selected anchors using load cellsand unbonded tendons should be employed where unusualconditions exist or the effort and expense can be justifiedby the importance of the structure. In addition to stabilityalong the base of the dam, prestressed anchors may berequired for deep-seated stability problems as discussed inthe following paragraph. Non-prestressed anchors shallnot be used to improve the stability of dams.
8-7. Stability on Deep-Seated Failure Planes
A knowledge of the rock structure of a foundation iscrucial to a realistic stability analysis on deep-seatedplanes. If instability is to occur, it will take place alongzones of weakness within the rock mass. A team effortbetween the geotechnical and structural engineers isimportant in evaluating the foundation and its significanceto the design of the dam. Deep-seated sliding is of pri-mary interest as it is the most common problem encoun-tered. Significant foundation features are: rock surfacejoint patterns that admit water to potential deep-seatedsliding planes; inclination of joints and fracturing thataffect passive resistance; relative permeability of founda-tion materials that affect uplift; and discontinuities such asgouge zones and faulting which affect both strength anduplift along failure planes. Strength values for failureplanes are required for design. As these values are oftendifficult to define with a high level of confidence, theyshould be described in terms of expected values andstandard deviations. Analyses of resultant location and
8-3
EM 1110-2-220030 Jun 95
maximum bearing pressure will also be required. Criteriafor these loading conditions will be the same as inChapter 4 for the dam.
a. Method and assumptions.Stability on deep-seatedplanes is similar to methods described in Chapter 4 forthe dam. Tensile strength within the foundation isneglected except where it can be demonstrated by explo-ration and testing. Vertical and near vertical joints areassumed to be fully pressurized by the pool to which theyare exposed. Normally a pressurized vertical joint will beassumed to exist at or near the heel of the dam. Uplift onflat and inclined bedding planes will be dependent ontheir state of compression and the presence of drainspassing through these planes as described for dams inChapter 3. Passive resistance will be based on the rockconditions downstream of the dam. Adversely inclinedjoints, faults, rock fracturing, or damage from excavationby blasting will affect available passive resistance.
b. Anchor penetration. Required anchor penetrationdepends on the purpose of the anchor. Anchors providedto resist uplift of the heel must have sufficient penetrationto develop the capacity of the anchors. Anchors providedto resist sliding must be fully developed below the lowestcritical sliding plane. Critical sliding planes are thoserequiring anchors to meet minimum acceptable factors ofsafety against sliding.
c. Anchor resistance.The capacity of the anchor toresist uplift should be limited to the force that can bedeveloped by the submerged weight of the rock engagedby the anchor. Rock engaged will either be shaped ascones or intersecting cones depending on the length andspacing of the anchors. The anchor force that can bedeveloped should be based on the pullout resistance of acone with an apex angle of 90 deg. Tensile stresses willoccur in the anchorage zone of prestressed anchors. Thepossibility of foundation cracking as a result of thesetensile stresses must be considered. It is possible thatcracks in the foundation could open at the lower terminalpoints of the anchors and propagate downstream. Toalleviate this potential problem, a sufficient weight ofsubmerged rock should be engaged to resist the anchorforce, and the anchor depths should be staggered.
8-8. Example Problem
The following example is a gated outlet structure for anearth fill dam. The existing gated spillway monoliths are
deficient in sliding resistance along a weak seam in thefoundation which daylights in the stilling basin. A cross-section of the spillway monoliths is shown in Figure 8-1.The spillway monoliths are founded at elevation 840 onmoderately hard silty shale. A continuous soft, plasticclay shale seam approximately 1/2 inch in thickness existsat elevation 830. A free body diagram showing forcesacting on the gravity structure and foundation above theweak seam is shown in Figure 8-2. Even though thefoundation drains penetrate the potential sliding plane,the drains are assumed ineffective as they are insufficientto drain a thin clay seam. The sliding plane is in fullcompression, and uplift is assumed to vary uniformlyfrom upper pool head to zero in the stilling basin. Adrained shear strength of 20° 30′ has been assigned to thispotential sliding surface, and a sliding factor of safety of0.49 has been calculated for loading condition No. 2, i.e.,pool to top of closed spillway gates. The tailwater isbelow the level of the sliding surface. A summary ofloads and the resulting factor of safety for this criticalloading condition is shown in Table 8-1. The design ofanchors to provide a required factor of safety of 1.70 issummarized in Table 8-2. The anchors are located asshown in Figure 8-3. Details of the anchors are shown inFigure 8-4. The 45-deg angle for the anchors wasselected to minimize drilling and to provide a large com-ponent of resisting force without creating a potentialupstream sliding problem during low pools. Tips ofanchors are staggered to avoid tensile stress concentra-tions in the foundation. The anchors are embedded belowthe lowest sliding plane requiring anchors to meetrequired safety factors. Reinforcement similar to thatused in post-tensioned beams is provided under the bear-ing plates to resist the high tensile bursting stresses asso-ciated with large capacity anchors. The anchors weretensioned in the sequence shown in Figure 8-4 to avoidunacceptable stress concentrations in the concrete mono-liths. The anchors were designed, installed, and tested inaccordance with PTI (1985). The anchors are designedfor a working load of 826 kips and were locked-off at910 kips (i.e., working load plus 10 percent) to allow forcalculated relaxation of the anchors, creep in the concretestructure, and consolidation of the foundation. Prooftesting of all anchors to 80 percent of ultimate strengthconfirmed the adequacy of the anchors for a working loadof 826 kips per anchor (approximately 60 percent of ulti-mate strength). Each anchor successfully passed a 14thday lift-off test, secondary grouting was accomplished,and anchor head recesses were filled with concrete torestore the spillway profile.
8-4
EM 1110-2-220030 Jun 95
8-5
EM 1110-2-220030 Jun 95
Figure 8-2. Free body diagram, R y = resultant of vertical forces, R H = resultant of horizontal forces, andXR = distance from heel to resultant location on sliding plane
Table 8-1Summary of Forces on the Sliding Plane. Loading Condition No. 2 (Pool at Top of Gates, Tailwater Below Sliding Surface)
Σ Vert, kips Σ Horz, kips
Concrete 11,910
Rock (Saturated Weight) 13,160
Machinery 10
Gates 70
Water Down 870
Water Up - 90
Uplift - 16,830
Horizontal Water 6,990
________ _____
Totals, Loading Condition No. 2 9,100 6,990
Sliding FS, Without Anchors TAN 20.5° × 9,1006,990
0.49
8-6
EM 1110-2-220030 Jun 95
Table 8-2Summary of Forces on the Sliding Plane. Loading Condition No. 2, With Anchors
Σ Vert, kips Σ Horz, kips
Concrete 11,910
Rock 13,160
Machinery 10
Gates 70
Water Down 870
Water Up - 90
Uplift - 16,830
Horizontal Water 6,990
Anchors (Vertical) 7 x 826 x 0.707 4,088
Anchors (Horizontal) - 4,088
________ _______
Totals, Loading Condition No. 2 13,188 2,902
Sliding FS, With Anchors TAN 20.5° × 13,1886,990 4,088
1.70
8-7
EM 1110-2-220030 Jun 95
Figure 8-3. Location of anchors
8-8
EM 1110-2-220030 Jun 95
8-9
EM 1110-2-220030 Jun 95
Chapter 9Roller-Compacted Concrete GravityDams
9-1. Introduction
Gravity dams built using the RCC construction method,afford economies over conventional concrete throughrapid placement techniques. Construction proceduresassociated with RCC require particular attention be givenin the layout and design to watertightness and seepagecontrol, horizontal and transverse joints, facing elements,and appurtenant structures. The designer should takeadvantage of the latitude afforded by RCC constructionand use engineering judgment to balance cost reductionsand technical requirements related to safety, durability,and long-term performance. A typical cross section of anRCC dam is shown in Figure 9-1. RCC mix design andconstruction should be in accordance withEM 1110-2-2006.
Figure 9-1. Typical RCC dam section
9-2. Construction Method
Construction techniques used for RCC placement oftenresult in a much lower unit cost per cubic yard comparedwith conventional concrete placement methods. The dry,nonflowable nature of RCC makes the use of a widerange of equipment for construction and continuous
placement possible. End and bottom dump trucks and/orconveyors can be used for transporting concrete from themixer to the dam. Mechanical spreaders, such as cater-pillars and graders, place the material in layers or lifts.Self-propelled, vibratory, steel-wheeled, or pneumaticrollers along with the dozers perform the compaction.The thickness of the placement layers, ranging from 8 to24 inches, is established by the compaction capabilities.With the flexibility of using the above equipment andcontinuous placement, RCC dams can be constructed atsignificantly higher rates than those achievable with con-ventional mass concrete. A typical work layout for theRCC placement spreading operation is illustrated inFigure 9-2.
9-3. Economic Benefits
RCC construction techniques have made gravity dams aneconomically competitive alternative to embankmentstructures. The following factors tend to make RCC moreeconomical than other dam types:
a. Material savings. Construction cost histories ofRCC and conventional concrete dams show the unit costper cubic yard of RCC is considerably less. The unit costof concrete for both types of dam varies with the volumeof the material in the dam. As the volume increases, theunit cost decreases. The cost savings of RCC increase asthe volume decreases. RCC dams have considerably lessvolume of construction material than embankments of thesame height. As the height increases, the volume versusheight for the embankment dam increases almost expo-nentially in comparison to the RCC dam. Thus, thehigher the structure, the more likely the RCC dam will beless costly than the embankment alternative.
b. Rapid construction. The rapid construction tech-niques and reduced concrete volume account for the majorcost savings in RCC dams. Maximum placement rates of5,800 to 12,400 cubic yards/day have been achieved.These production rates make dam construction in oneconstruction season readily achievable. When comparedwith embankment dams, construction time is reduced by1 to 2 years. Other benefits from rapid constructioninclude reduced construction administration costs, earlierproject benefits, and possible selection of sites withlimited construction seasons. Basically, RCC constructionoffers economic advantages in all aspects of dam con-struction that are related to time.
c. Spillways and appurtenant structures. The locationand layout alternatives for spillways, outlet and hydro-power works, and other appurtenant structures in
9-1
EM 1110-2-220030 Jun 95
Figure 9-2. Typical work layout for RCC placement spreading operation
RCC dams provide additional economic advantages com-pared with embankment dams. The arrangements of thesestructures is similar to conventional concrete dams, butwith certain modifications to minimize costly interferenceto the continuous RCC placement operation. Gatestructures and intakes should be located outside the dammass. Galleries, adits, and other internal openings shouldbe minimized. Details on the layout and design of spill-ways and appurtenant structures are discussed in para-graph 9-4. Spillways for RCC dams can be directlyincorporated into the structure. The layout allows dis-charging flows over the dam crest and down the down-stream face. In contrast, the spillway for an embankmentdam is normally constructed in an abutment at one end ofthe dam or in a nearby natural saddle. Generally, theembankment dam spillway is more costly. For projectsthat require a multiple-level intake for water quality con-trol or for reservoir sedimentation, the intake structure canbe readily anchored to the upstream face of the dam. Foran embankment dam, the same type of intake tower is afreestanding tower in the reservoir or a structure built intoor on the reservoir side of the abutment. The economic
savings for an RCC dam intake is considerably cheaper,especially in high seismic areas. The shorter base dimen-sion of an RCC dam compared with an embankment damreduces the size and length of the conduit and penstockfor outlet and hydropower works.
d. Diversion and cofferdam. RCC dams provide costadvantages in river diversion during construction andreduce damages and risks associated with cofferdam over-topping. The diversion conduit will be shorter comparedwith embankment dams. With a shorter constructionperiod, the size of the diversion conduit and cofferdamheight can be reduced. These structures may need to bedesigned only for a seasonal peak flow instead of annualpeak flows. With the high erosion resistance of RCC, ifovertopping of the cofferdam did occur, the potential for amajor failure would be minimal and the resulting damagewould be less.
e. Other advantages. The smaller volume of an RCCdam makes the construction material source less of adriving factor in site selection of a dam. Furthermore, the
9-2
EM 1110-2-220030 Jun 95
borrow source will be considerably smaller and moreenvironmentally acceptable. The RCC dam is also inher-ently safer against internal erosion, overtopping, and seis-mic ground motions.
9-4. Design and Construction Considerations
a. Watertightness and seepage control. Achievingwatertightness and controlling seepage through RCC damsare particularly important design and construction consid-erations. Excessive seepage is undesirable from theaspect of structural stability and because of the adverseappearance of water seeping on the downstream dam face,the economic value associated with lost water, and possi-ble long-term adverse impacts on durability. RCC thathas been properly proportioned, mixed, placed, and com-pacted should be as impermeable as conventional con-crete. The joints between the concrete lifts and interfacewith structural elements are the major pathways for poten-tial seepage through the RCC dam. This condition isprimarily due to segregation at the lift boundaries anddiscontinuity between successive lifts. It can also be theresult of surface contamination and excessive time inter-vals between lift placements. Seepage can be controlledby incorporating special design and construction proce-dures that include contraction joints with waterstops mak-ing the upstream face watertight, sealing the interfacebetween RCC layers, and draining and collecting theseepage.
b. Upstream facing. RCC cannot be compactedeffectively against upstream forms without the forming ofsurface voids. An upstream facing is required to producea surface with good appearance and durability. Manyfacings incorporate a watertight barrier. Facings withbarriers include the following:
(1) Conventional form work with a zone of conven-tional concrete placed between the forms and RCCmaterial.
(2) Slip-formed interlocking conventional concreteelements. RCC material is compacted against the curedelements.
(3) Precast concrete tieback panels with a flexiblewaterproof membrane placed between the RCC and thepanels.
A waterproof membrane sprayed or painted onto a con-ventional concrete face is another method; however, itsuse has been limited since such membranes are not elasticenough to span cracks that develop and because of
concerns about moisture developing between the mem-brane and face and subsequent damage by freezing.
c. Horizontal joint treatment. Bond strength andpermeability are major concerns at the horizontal liftjoints in RCC. Good sealing and bonding are accom-plished by improving the compactibility of the RCC mix-ture, cleaning the joint surface, and placing a beddingmortar (a mixture of cement paste and fine aggregate)between lifts. When the placement rate and setting timeof RCC are such that the lower lift is sufficiently plasticto blend and bond with the upper layer, the bedding mor-tar is unnecessary; however, this is rarely feasible innormal RCC construction. Compactibility is improved byincreasing the amount of mortar and fines in the RCCmixture. The lift surfaces should be properly moist curedand protected. Cleanup of the lift surfaces prior to RCCplacement is not required as long as the surfaces are keptclean and free of excessive water. Addition of thebedding mortar serves to fill any voids or depressions leftin the surface of the previous lift and squeezes up into thevoids in the bottom of the new RCC lift as it is com-pacted. A bedding mix consisting of a mixture of cementpaste and fine and 3/8-in.-MSA aggregate is also appliedat RCC contacts with the foundation, abutment surfaces,and any other hardened concrete surfaces. EM 1110-2-2006 contains additional guidance on this issue.
d. Seepage collection. A collection and drainagesystem is a method for stopping unsightly seepage waterfrom reaching the downstream face and for preventingexcessive hydrostatic pressures against conventional con-crete spillway or downstream facing. It will also reduceuplift pressures within the dam and increase stability.Collection methods include vertical drains with waterstopsat the upstream face and vertical drain holes drilled fromwithin the gallery near the upstream or downstream face.Collected water can be channeled to a gallery or the damtoe.
e. Nonoverflow downstream facing. Downstreamfacing systems for nonoverflow sections may be requiredfor aesthetic reasons, maintaining slopes steeper than thenatural repose of RCC, and freeze-thaw protection insevere climate locations. Facing is necessary when theslope is steeper than 0.8H to 1.0V when lift thickness islimited to 12 inches or less. Thicker lifts require a flatterslope. Experience has demonstrated that these are thesteepest uncompacted slopes that can be practically con-trolled without special equipment or forms. The exposededge of an uncompacted slope will have a rough stair-stepped natural gravel appearance with limited strengthwithin 12 inches of the face. Downstream facing systems
9-3
EM 1110-2-220030 Jun 95
include conventional vertical slipforming placement andhorizontal slipforming similar to that used on theupstream face. When this type of slope is used, thestructural cross section should include a slight overbuildto account for deterioration and unraveling of materialloosened from severe weather exposure over the projectlife (see Figure 9-3). Several recent projects have com-pacted downstream faces using a tractor-mounted vibrat-ing plate.
Figure 9-3. Compaction of RCC at downstream face
f. Transverse contraction joints. Transverse contrac-tion joints are required in most RCC dams. The potentialfor cracking may be slightly lower in RCC because of thereduction in mixing water and reduced temperature riseresulting from the rapid placement rate and lower liftheights. In addition, the RCC characteristic of point-to-point aggregate contact decreases the volume shrinkage.Thermal cracking may, however, create a leakage path tothe downstream face that is aesthetically undesirable.Thermal studies should be performed to assess the needfor contraction joints. Contraction joints may also berequired to control cracking if the site configuration andfoundation conditions may potentially restrain the dam. Ifproperly designed and installed, contraction joints will not
interfere or complicate the continuous placement operationof RCC. At Elk Creek Dam, contraction joints wereinstalled with no impact to RCC placement operations byinserting galvanized steel sheeting into the uncompactedRCC for the entire thickness and height of the dam. Thesheets were pushed vertically into the RCC by means of atractor-mounted vibratory blade, as shown in Figure 9-4.
Figure 9-4. Contract joint placement using a vibratingblade to insert galvanized steel sheeting
g. Waterstops. Standard waterstops may be installedin an internal zone of conventional concrete placed aroundthe joint near the upstream face. Waterstops and jointdrains are installed in the same manner as for conven-tional concrete dams. Typical internal waterstops andjoint drain construction in RCC dams are shown inFigure 9-5. Around galleries and other openings crossingjoints, waterstop installation will require a section ofconventional concrete around the joint.
9-4
EM 1110-2-220030 Jun 95
Figure 9-5. Typical internal waterstops and joint drain construction in RCC dams
9-5
EM 1110-2-220030 Jun 95
Figure 9-6. RCC spillway details
9-6
EM 1110-2-220030 Jun 95
Appendix AReferences
A-1. Required Publications
Note: References used in this EM are available on inter-library loan from the Research Library, ATTN: CEWES-IM-MI-R, U.S. Army Engineer Waterways ExperimentStation, 3909 Halls Ferry Road, Vicksburg, MS39180-6199.
TM 5-809-10-1Seismic Design Guidelines for Essential Buildings
ER 415-1-11Biddability, Constructibility and Operability
ER 1110-1-8100Laboratory Investigations and Materials Testing
ER 1110-2-100Periodic Inspection and Continuing Evaluation of Com-pleted Civil Works Structures
ER 1110-2-1200Plans and Specifications for Civil Works Projects
ER 1110-2-1806Earthquake Design and Analysis for Corps of EngineersProjects
ER 1130-2-417Major Rehabilitation Program and Dam Safety AssuranceProgram
EM 1110-1-1804Geotechnical Investigations
EM 1110-2-1602Hydraulic Design of Reservoir Outlet Works
EM 1110-2-1603Hydraulic Design of Spillways
EM 1110-2-1612Ice Engineering
EM 1110-2-2000Standard Practice for Concrete for Civil Works Structures
EM 1110-2-2002Evaluation and Repair of Concrete Structures
EM 1110-2-2006Roller Compacted Concrete
EM 1110-2-2102Waterstops and Other Joint Materials
EM 1110-2-2400Structural Design of Spillways and Outlet Works
EM 1110-2-2502Retaining and Flood Walls
EM 1110-2-2906Design of Pile Foundations
EM 1110-2-3001Planning and Design of Hydroelectric Power PlantStructures
EM 1110-2-3506Grouting Technology
EM 1110-2-4300Instrumentation for Concrete Structures
A-2. Related Publications
EM 1110-1-1802Geophysical Exploration
EM 1110-2-1605Hydraulic Design of Navigation Dams
EM 1110-2-1901Seepage Analysis and Control for Dams
EM 1110-2-1902Stability of Earth and Rock Fill Dams
ACI Committee 116“Cement and Concrete Terminology,” ACI 116R-85,ACIManual of Concrete Practice, 1988.
ACI Committee 207“Mass Concrete for Dams and Other Massive Structures,”ACI Journal, Proceedings V. 67, No. 4, April 1970,pp 273-309.
ACI Committee 207“Cooling and Insulating Systems for Mass Concrete,”Part 1, 207.4R-80,ACI Manual of Concrete Practice,1988.
A-1
EM 1110-2-220030 Jun 95
ACI Committee 207“Roller Compacted Concrete,” ACI 207.5R-80,ACI Man-ual of Concrete Practice, 1988.
ACI Committee 207“Mass Concrete,” ACI 207.1 R-87.
ACI Committee 224“Control of Cracking in Concrete Structures,” ACI 224R-80 Revised 1984, ACI Journal, December 1972,pp 717-753.
ACI Committee 439“Effect of Steel Strength and of Reinforcement Ration onthe Mode of Failure and Strain Energy Capacity of Rein-forced Concrete Beams,”ACI Journal, March 1969,pp 164-172.
ASTM C 31“Test Methods for Making and Curing Concrete TestSpecimens in the Field,”Annual Book of ASTM Stan-dards, Vol. 04.02, Concrete and Mineral Aggregates.
ASTM C 39“Test Method for Compressive Strength of CylindricalConcrete Specimens,”Annual Book of ASTM Standards,Vol. 04.02, Concrete and Mineral Aggregates.
ASTM C 78“Test Method of Flexural Strength of Concrete UsingSimple Beam with Third-Point Loading,”Annual Book ofASTM Standards, Vol. 04.02, Concrete and MineralAggregates.
ASTM C 138“Test Method for Unit Weight, Yield, and Air ContentGravimetric of Concrete,”Annual Book of ASTM Stan-dards, Vol. 04.02, Concrete and Mineral Aggregates.
ASTM C 172“Method of Sampling Freshly Mixed Concrete,”AnnualASTM Standards, Vol. 04.02, Concrete and MineralAggregates.
ASTM C 469“Test Method for Static Modulus of Elasticity andPoisson’s Ratio of Concrete in Compression,”AnnualBook of ASTM Standards, Vol. 04.02, Concrete and Min-eral Aggregates.
ASTM C 496“Test Method for Splitting Tensile Strength of CylindricalConcrete Specimens,”Annual Book of ASTM Standards,Vol. 04.02, Concrete and Mineral Aggregates.
ASTM C 512“Test Methods for Creep of Concrete in Compression,”Annual ASTM Standards, Vol. 04.02, Concrete and Min-eral Aggregates.
ASTM C 2848“Method for Laboratory Determination of Pulse Velocitiesand Ultrasonic Elastic Constants of Rock,”Annual Bookof ASTM Standards, Vol. 04.08, Soil and Rock; BuildingStones.
ASTM C 3148“Test Method of Elastic Moduli of Intact Rock CoreSpecimens of Uniaxial Compression,”Annual Book ofASTM Standards, Vol. 04.08, Soil and Rock; BuildingStones.
American Society of Civil Engineers 1974American Society of Civil Engineers. 1974.Foundationfor Dams, Engineering Foundation Conference.
Anatech Corp. 1993Anatech Corp. 1993. “Concrete Gravity Dam AnalysisModular Software,” EPRI Project RP 2917-2, LaJolla,CA.
Bey and Selim 1945Bey, S. L., and Selim, M. A. 1945.Uplift Pressure inand Beneath Dam a Symposium, American Society ofCivil Engineers Transactions Paper No. 2304, pp 444-526.
Cannon 1985Cannon, R. W. 1985.Design Considerations for RollerCompacted Concrete and Rollcrete in Dams, ConcreteInternational, pp 50-58.
Carlson 1951Carlson, R. W. 1951. “Permeability, Pore Pressure, andUplift in Gravity Dams,” Report to Office of the Chief ofEngineers.
Carlson, Houghton, and Polivka 1979Carlson, R. W., Houghton, D. L., and Polivka, M. 1979.“Causes and Control of Cracking in Unreinforced MassConcrete,”ACI Journal, pp 831-837.
A-2
EM 1110-2-220030 Jun 95
Casagrande 1961Casagrande, A. 1961. First Rankine Lecture “Control ofSeepage through Foundations and Abutment of Dam.”
Chakrabarti and Chopra 1972Chakrabarti, P., and Chopra, A. K. 1972. “Hydro-dynamic Pressures and Response of Gravity Dams toVertical Earthquake Component,”Journal of the Interna-tional Association for Earthquake Engineering, 1:325-335.
Chakrabarti and Chopra 1973Chakrabarti, P., and Chopra, A. K. 1973.A ComputerProgram for Earthquake Analysis of Gravity DamsIncluding Reservoir Interaction, EERC 73-7, EarthquakeEngineering Research Center, University of California,Berkeley AD 766 271 A04.
Chakrabarti and Chopra 1973Chakrabarti, P., and Chopra, A. K. 1973. “EarthquakeAnalysis of Gravity Dams Including Hydrodynamic Inter-action EADHI,” Earthquake Engineering and StructuralDynamics, 2:143-160.
Chakrabarti and Chopra 1974Chakrabarti, P., and Chopra, A. K. 1974. “Hydro-dynamic Effects in Earthquake Response of GravityDams,” ASCE Journal of the Structural Division,106ST6:1211-1225.
Chang and Chen 1982Chang, M. F., and Chen, W. F. 1982.Lateral EarthPressures on Rigid Retaining Walls Subjected to Earth-quake Forces, SM Archives 7, pp 315-362.
Chopra 1970Chopra, A. K. 1970. “Earthquake Response of ConcreteGravity Dams,” Journal of the Engineering MechanicsDivision, American Society of Civil Engineers,96EM4:443-454.
Chopra 1980Chopra, A. K. 1980. Dynamics of Structures, A Primer,Earthquake Engineering Research Institute, Berkeley, CA.
Chopra 1987Chopra, A. K. 1987. “Simplified Earthquake of ConcreteGravity Dam,” ASCE Journal of the Structural Division,113ST8:1688-1708.
Chopra and Chakrabarti 1972Chopra, A. K., and Chakrabarti, P. 1972 Oct-Dec. “TheEarthquake Experience at Koyna Dam and Stresses in
Concrete Gravity Dams,”Journal of the InternationalAssociation for Earthquake Engineering, 12.
Chopra and Chakrabarti 1981Chopra, A. K., and Chakrabarti, P. 1981. “EarthquakeAnalysis of Concrete Gravity Dams Including Dam-Water-Foundation Rock Interaction,”Earthquake Engi-neering and Structural Dynamics, 9:262-383.
Chopra, Chakrabarti, and Gupta 1980Chopra, A. K., Chakrabarti, P., and Gupta, S. 1980.Earthquake Response of Concrete Gravity Dams IncludingHydrodynamic and Foundation Interaction Effects,EERC 80-01, Earthquake Engineering Research Center,University of California, Berkeley ADA 087297.
Chopra and Gupta 1982Chopra, A. K., and Gupta, S. 1982. “Hydrodynamic andFoundation Interaction Effects in Frequency ResponseFunctions for Concrete Gravity Dams,”Earthquake Engi-neering and Structural Dynamics, 10:89-106.
Chopra and Tan 1989Chopra, A. K., and Tan, H. 1989. “Simplified Earth-quake Analysis of Gated Spillway Monoliths of ConcreteGravity Dams,” Technical Report SL-89-4, U.S. ArmyEngineer Waterways Experiment Station, Vicksburg, MS.
Clough and Zienkiewicz 1982Clough, R. W., and Zienkiewicz, O. C. 1982.FiniteElement Methods in Analysis and Design of Dams, Com-mittee on Analysis and Design of Dams.
Cole and Cheek 1986Cole, R. A., and Cheek, J. B. 1986. “Seismic Analysisof Gravity Dams,” Technical Report SL-86-44, U.S. ArmyEngineer Waterways Experiment Station, Vicksburg, MS.
Cosschalk and Brook 1976Cosschalk, E. M., and Brook K. M. 1976. “Methods ofDetermining Effects of Shrinkage Creek and Temperatureon Concrete for Large Dams,”International Commissionof Large Dams, Bulletin 26.
Der Kiureghian 1979Der Kiureghian, A. 1979. On Response of Structures toStationary Excitiation, Report No. EERC 79-32, Earth-quake Engineering Research Center, University ofCalifornia, Berkeley.
A-3
EM 1110-2-220030 Jun 95
Der Kiureghian 1980Der Kiureghian, A. 1980. “Probabilistic Modal Com-bination for Earthquake Loading,”7th World Conferenceon Earthquake Engineering, Proceedings, 6:729-736.
Dumanoglu and Severn 1984Dumanoglu, A. A., and Severn, R. T. 1984. “DynamicResponse of Dams and Other Structures to DifferentialGround Motions,” Proc. Lustn Civ Engrs, Part 2,pp 333-352.
Ebeling et al.Ebeling, R. M., Clough, G. W., Duncan, J. M., Brandon,T. M. 1992 Technical Report REMR-CS-29, “Methods ofEvaluating the Stability and Safety of Earth RetainingStructures Founded on Rock,” U.S. Army Engineer Wa-terways Experiment Station, Vicksburg, MS.
Fanelli and Giuseppetti 1975Fanelli, D. I. M., and Giuseppetti, G. 1975 Jun-Jul.“Techniques to Evaluate Effects of Internal Temperaturesin Mass Concrete,”Water Power and Dam Construction,pp 226-230.
Federal Emergency Management Agency (FEMA)1985Federal Emergency Management Agency (FEMA). 1985.Federal Guidelines for Earthquake Analysis and Designof Dams, FEMA 65.
Federal Energy Regulatory Commission (FERC) 1987Federal Energy Regulatory Commission (FERC). 1987.Engineering Guidelines for the Evaluation of HydropowerProjects, FERC 0119-1.
Fenves and Chopra 1983Fenves, G., and Chopra, A. K. 1983. “Effects of Reser-voir Bottom Absorption on Earthquake Response of Con-crete Gravity Dams,”Earthquake Engineering and Struc-tural Dynamics, 11.
Fenves and Chopra 1984Fenves, G., and Chopra, A. K. 1984. “Earthquake Anal-ysis of Concrete Gravity Dams Including Reservoir Bot-tom Absorption and Dam-Water-Foundation Rock Interac-tion,” Earthquake Engineering and Structural Dynamics,12:663-680.
Fenves and Chopra 1985Fenves, G., and Chopra, A. K. 1985. “Effects of Reser-voir Bottom Absorption and Dam-Water-Foundation RockInteraction on Frequency Response Functions for ConcreteGravity Dams,” Earthquake Engineering and StructuralDynamics, 13:13-31.
Fenves and Chopra 1985Fenves, G., and Chopra, A. K. 1985. “Reservoir BottomAbsorption Effects in Earthquake Response of ConcreteGravity Dams,”ASCE Journal of Structural Engineering,American Society of Civil Engineeers, 1113:545-562.
Golzé 1977Golzé, A. R. 1977. Handbook of Dam Engineering, VanNostrand Rienhold Company, New York.
Guedes, Rosso, and Franco 1981Guedes, Q. M., Rosso, J. A., and de B. Franco, H. C.1981. “Analysing Displacement Measurements in GravityDams,” Water Power & Dam Construction, pp 43-46.
Guzman and Jennings 1970Guzman, R. A., and Jennings, P. C. 1970. “DesignSpectra for Nuclear Power Plants,”Journal of the PowerDivision, American Society of Civil Engineers,102P02:165-178.
Hall and Chopra 1982Hall, J. F., and Chopra, A. K. 1982.HydrodynamicEffects in the Dynamic Response of Concrete GravityDams, Earthquake Engineering and Structural Dynamics,10:333-345.
Hall and Radhakrishnan 1983Hall, R. L., and Radhakrishnan, N. 1983.Case Study ofSix Major General-Purpose Finite Element Programs,Technical Report K-83-4, U.S. Army Engineer WaterwaysExperiment Station, Vicksburg, MS.
Harza 1976Harza, L. F. 1976. “The Significance of Pore Pressure inHydraulic Structures,”American Society of Civil Engi-neers Transactions, Paper No. 2368, pp 193-289.
Hayes 1980Hayes, W. W. 1980. Procedures for Estimating Earth-quake Ground Motions, Geological Survey ProfessionalPaper 1114.
Henny 1934Henny, D. C. 1934. “Stability of Straight Concrete Gra-vity Dams,” Transactions, American Society of CivilEngineers, 99.
Houghton 1969Houghton, D. L. 1969 Oct. “Concrete Volume Changefor Dworshak Dam,” ASCE Journal of the PowerDivision, pp 153-166.
A-4
EM 1110-2-220030 Jun 95
Houghton 1976Houghton, D. L. 1976 Dec. “Determining Tensile StrainCapacity of Mass Concrete,”ACI Journal, pp 691-700.
Humar and Roufaiel 1983Humar, J., and Roufaiel, M. 1983. “Finite ElementAnalysis of Reservoir Vibration,”ASCE Journal of Engi-neering Mechanics, 1091:215-230.
Iida, Hoko, and Matsumoto 1979Iida, R., Hoko, K., and Matsumoto, N. 1979.SafetyMonitoring of Dams During First Filling of Reservoirs,International Congress on Large Dams, pp 385-405.
Iliev and Kalchev 1981Iliev, S., and Kalchev, L. 1981 Dec. “Selecting theOptimum Cross Section of a Concrete Gravity Dam,”Water Power and Dam Construction, pp 23-27.
International Commission of Large Dams 1975International Commission of Large Dams. 1975.AReview of Earthquake Resistant Design of Dams,Bulletin 27.
International Society for Rock Mechanics, Commissionon Standardization of Laboratory and Field Tests 1974International Society for Rock Mechanics, Commission onStandardization of Laboratory and Field Tests. 1974.Suggested Methods for Determining Shear Strength,Document No. 1.
Jansen 1988Jansen, R. B. 1988. Advanced Dam Engineering forDesign, Construction, and Rehabilitation, Van NostrandReinhold, New York.
Johnson and Heller 1973Johnson, S. J., and Heller, L. W. 1973. “Lectures andDiscussions by Professor N.W. Ambrareys on EngineeringSeismology and Earthquake Engineering,” U.S. ArmyEngineer Waterways Experiment Station, MiscellaneousPaper S-74-15, Vicksburg, MS.
Joshi 1980Joshi, C. S. 1980. Designing the Profile of GravityDams, Water Power and Dam Construction, pp 28-30.
Kenner 1950Keener, K. B. 1950.Uplift Pressures in Concrete Dams,American Society of Civil Engineers Transactions, PaperNo. 2464, pp 1218-1264.
Krinitzsky and Marcuson 1983Krinitzsky, E. L., and Marcuson III, W. F. 1983.Princi-ples for Selecting Earthquake Motions in EngineeringDesign, Bulletin of the Association of Engineering Geolo-gists, XX3:253-265.
Liu and McDonald 1978Liu, T. C., and McDonald, J. E. 1978 May. “Predictionof Tensile Strain Capacity of Mass Concrete,”ACI Jour-nal, pp 192-197.
Logie 1985Logie, C. V. 1985. “Economic Considerations in Selec-tion of a Roller Compacted Concrete Dam,”Proceedingsof ASCE Symposium, Roller Compacted Concrete,May 1-2, American Society of Civil Engineers,pp 111-122.
Mlakar, Vitaya-Udom, and Cole 1985Mlakar, P. F., Vitaya-Udom, K. P., and Cole, R. A.1985. “Dynamic Tensile-Compressive Behavior of Con-crete,”ACI Journal, pp 484-491.
Morgenstern and Price 1965Morgenstern, N. R., and Price, V. E. 1965. “The Analy-sis of the Stability of General Slip Surfaces,”Geotechnique, 15.
Newmark and Hall 1982Newmark, N. M., and Hall, W. J. 1982.EarthquakeSpectra and Design, Earthquake Engineering ResearchInstitute, Berkeley, CA.
Post-Tensioning Institute 1985Post-Tensioning Institute. 1985.Recommendations forPrestressed Rock and Soil Anchors, Phoenix, AZ.
Price 1982Price, W. H. 1982. Control of Cracking in Mass Con-crete Dams, Concrete International, pp 36-44.
Raphael 1984Raphael, J. M. 1984 Mar-Apr. “Tensile Strength ofConcrete,”ACI Journal, pp 158-165.
Rea, Liaw, and Chopra 1975Rea, D., Liaw C. Y., and Chopra, A. K. 1975. “Mathe-matical Models for the Dynamic Analysis of ConcreteGravity Dams,” Earthquake Engineering and StructuralDynamics, 3:249-258.
A-5
EM 1110-2-220030 Jun 95
Richter 1958Richter, C. F. 1958. Elementary Seismology, W. H.Freeman and Company, Inc., San Francisco and London.
Saini, Betless, and Kiewica 1978Saini, S. S., Betless, P., and Kiewica, Z. 1978. “CoupledHydrodynamic Response of Concrete Gravity Dams UsingFinite and Infinite Elements,”Earthquake Engineeringand Structural Dynamics, 6:363-374.
Schiff and Bogdanoff 1967Schiff, A., and Bogdanoff, J. L. 1967.Analysis of Cur-rent Methods of Interpreting Strong-Motion Accelero-grams, Bulletin of the Seismological Society of America,575:857-874.
Schrader 1977Schrader, E. K. 1977 Sep-Oct. “Roller CompactedConcrete,”The Military Engineer, pp 314-317.
Schrader 1979Schrader, E. K. 1979. “Mass Concrete ConstructionPrinciples,”The Military Engineer, pp 318-321.
Seed, Ugas, and Lysmer 1976Seed, H. B., Ugas, C., and Lysmer, J. 1976.Site-Dependent Spectra for Earthquake-Resistant Design,Bulletin of the Seismological Society of America,661:221-243.
Serafim and Guerreiro 1969Serafim, J. L., and Guerreiro, M. 1969. “Autogenousand Hygrometric Expansion of Mass Concrete,”ACIJournal, pp 716-720.
Severn 1978Severn R. T. 1978. “The Aseismic Design of ConcreteDams,” Water Power and Dam Construction, pp 41-46.
Shore Protection Manual 1984Shore Protection Manual. 1984. 4th Ed., 2 Vol,U.S. Army Engineer Waterways Experiment Station,U.S. Government Printing Office, Washington, DC.
Singh 1985Singh, M. 1985. “State-of-the-Art Finite Element Com-puter Programs for Thermal Analysis of Mass ConcreteStructures,”Civil Engineering for Practicing and DesignEngineers, 4:129-136.
Stelle, Rubin, and Buhas 1983Stelle, W. W., Rubin, D. I., and Buhas, H. J. 1983.“Stability of Concrete Dam: Case History,”ASCE Jour-nal of Energy Engineering, 1093:165-180.
Structural Engineers Association of California, Seis-mology Committee 1985Structural Engineers Association of California, Seis-mology Committee. 1985. Tentative Lateral ForceRequirements and Commentary.
Saouma et al. 1994Saouma, V., et al. 1994. “A Three-Dimensional FiniteElement Program for Problems in Elasticity, Plasticity,Linear and Nonlinear Fracture Mechanics, Steady Stateand Transient Linear Heat Transfer, and Steady State andTransient Linear Seepage Flow,” EPRI Project RP2917-08, University of Colorado, Boulder, CO.
Tarbox, Dreher, and Carpenter 1979Tarbox, G. S., Dreher, K. J., and Carpenter, L. R. 1979.“Seismic Analysis of Concrete Dams,”Thirteenth Interna-tional Congress on Large Dams, Transactions, NewDelhi, India.
Tatro and Schrader 1985Tatro, S. B., and Schrader, E. K. 1985. “Thermal Con-siderations for Roller-Compacted Concrete,”ACI Journal,pp 119-128.
Thompson and Emery 1976Thompson, C. D., and Emery, C. D. 1976. “Geotechni-cal Design Aspects for Large Gravity Retaining StructuresUnder Seismic Loading,”Canadian Geotechnical Journal,13:231-242.
Tuthill and Adams 1976Tuthill, L. H., and Adams, R. F. 1976 Aug. “CrackingControlled in Massive, Reinforced Structural Concrete byApplication of Mass Concrete Practices,”ACI Journal,pp 481-491.
U.S. Army Corps of Engineers 1980U.S. Army Corps of Engineers. 1980 Mar.Supplement 2to Design Memorandum No. 7, Dynamic Analysis of LibbyReregulating Dam.
A-6
EM 1110-2-220030 Jun 95
U.S. Army Corps of Engineers 1983U.S. Army Corps of Engineers. 1983. “A Three-Dimensional Stability Analysis/Design Program 3DSAD;Report 4, Special Purpose Modules for Dams CDAMS,”Instruction Report K-80-4, Office, Chief of Engineers,Washington, DC.
U.S. Army Engineer Waterways Experiment Station1980U.S. Army Engineer Waterways Experiment Station.1980. “Standard and Recommended Methods,”RockTesting Handbook, U.S. Army Engineer WaterwaysExperiment Station, Vicksburg, MS.
U.S. Army Engineer Waterways Experiment Station1987U.S. Army Engineer Waterways Experiment Station.1987. “Sliding Stability of Concrete Structures CSLIDE,”Instruction Report ITL-87-5, Vicksburg, MS.
U.S. Bureau of Reclamation 1953U.S. Bureau of Reclamation. 1953.Physical Propertiesof Some Typical Foundation Rocks, Concrete LaboratoryReport No. SP-39, Engineering Laboratories Branch.
U.S. Bureau of Reclamation 1965Bureau of Reclamation. 1965.Control of Cracking inMass Concrete Structures, Engineering MonographNo. 34.
U.S. Bureau of Reclamation 1974U.S. Bureau of Reclamation. 1974.Rock MechanicsProperties of Typical Foundation Rock Types, REC-ERC-74-10, Engineering and Research Center.
U.S. Bureau of Reclamation 1976U.S. Bureau of Reclamation. 1976.Design of GravityDams.
U.S. Bureau of Reclamation 1977Bureau of Reclamation. 1977.Design Criteria for Con-crete Arch and Gravity Dam, Engineering MonographNo. 19.
U.S. Bureau of Reclamation 1978U.S. Bureau of Reclamation. 1978.Design and Analysisof Auburn Dam, Vol. 4, Dynamic Studies, Engineeringand Research Center, Denver, CO.
U.S. Tennessee Valley Authority 1951U.S. Tennessee Valley Authority. 1951. “The KentuckyProject,” Technical Report No. 13.
Vanmarcke 1979Vanmarcke, E. H. 1979. “Representation of EarthquakeGround Motion: Scaled Accelerograms and EquivalentResponse Spectra, State-of-the-Art for Assessing Earth-quake Hazards in the United States,” Report 14, Miscella-neous Paper 5-73-1, U.S. Army Engineer WaterwaysExperiment Station, Vicksburg, MS.
Warner 1974Warner, L. A. 1974. “Dams, Dam Foundations,”Devel-opments in Geotechnical Engineering, Vol 6, ElsevierScientific Publishing Company, Amsterdam, The Nether-lands.
Westergaard 1933Westergaard, H. M. 1933. “Water Pressures on DamsDuring Earthquakes,”Transaction, American Society ofCivil Engineers, 98:418-433.
Wilson 1980Wilson, E. L. 1980. “SAP-80 Structural Analysis Pro-grams for Small or Large Computer Systems,” CEPA1980 Fall Conference and Annual Meeting, NewportBeach, CA.
Wylie 1975Wylie, E. B. 1975 Mar. “Seismic Response of Reser-voir-Dam Systems,”ASCE Journal of the HydraulicsDivision, 111Hy 3:403-419.
Yeh, Chau-Shioung1976Yeh, Chau-Shioung. 1976 Aug. “Dynamic Response ofRetaining Walls During Earthquake,”International Sym-posium on Earthquake Structural Engineering,pp 287-392.
Zienkiewica and Gerstner 1961Zienkiewicz, O. C., and Gerstner, R. W. 1961. “StressAnalysis and Special Problems of Prestressed Dams,”Journal of the Power Division, American Society of CivilEngineers.
Zienkiewica, Paul, and Hinton 1983Zienkiewicz, O. C., Paul, D. K., and Hinton, E. 1983.“Cavitation in Fluid-Structure Response With ParticularReference to Dams Under Earthquake Loading,”Journalof Earthquake Engineering and Structural Dynamics,11:463-481.
A-7
EM 1110-2-220030 Jun 95
Appendix BGlossary
ABUTMENT. The foundation along the sides of thevalley or gorge against which the dam is constructed.
ACCELEROGRAM. The record from an accelerometershowing acceleration as a function of time.
AGGREGATE. The natural sands, gravels, and crushedstones used in the manufacture of concrete. Aggregatefor concrete commonly is obtained from alluvial streamdeposits or from rock quarries.
ANISOTROPIC. Exhibiting properties with different val-ues when measured along axes in different directions.
APPURTENANT FEATURE. Any physical feature otherthan the dam, such as the spillway, outlet, powerhouse,penstock, tunnels, etc.
AUTOGENOUS VOLUME CHANGE. Change in vol-ume produced by continued hydration of cement exclusiveof effects of external forces or change of water content ortemperature (ACI 116R-85).
BEDROCK. The solid rock foundation of a dam, usuallyoverlain by soil or other unconsolidated superficialmaterial.
BOND. The adhesion of concrete or mortar to otherconcrete layers, rock, and other surfaces.
BOND STRENGTH. Resistance to separation of concreteor mortar and other contact surfaces.
BOND STRESS. The force per unit area of contactbetween two bonded surfaces.
COEFFICIENT OF THERMAL EXPANSION. Thechange in linear dimension per unit length divided by thetemperature change (see also paragraph 6-2).
COFFERDAM. A temporary structure constructed aroundpart or all of the excavation for a dam or other appurte-nant features to facilitate construction in the dry.
COMPRESSIVE STRENGTH. The maximum resistanceof a concrete or mortar specimen to axial loading,expressed as force per unit cross-sectional area, or thespecified resistance used in design calculations, in the UScustomary units of measure expressed in pounds per
square inch and designated f′c (ACI 116R-85) (see alsoChapter 3).
CONCRETE. A composite material that consists essen-tially of a binding medium which is embedded particles orfragments of aggregate; in portland cement concrete, thebinder is a mixture of portland cement and water (ACI116R-85).
CONSTRUCTION JOINT. The surface between twoconsecutive placements of concrete that develops bondstrength (see also paragraph 7-1).
CONTRACTION JOINT. A formed surface, usuallyvertical, in a dam to create a plane for the regulation ofvolumetric changes (see also paragraph 7-1).
CONTRACTION JOINT GROUTING. Injection of groutinto contraction joints.
CREEP. Deformation over a long period of time under acontinuous sustained load.
CRUSHED GRAVEL. Gravel created by the artificialcrushing of stone.
CURING. The process of humidity and temperaturemaintenance performed after concrete placement to assuresatisfactory heat of hydration and properhardening of the concrete.
CUTOFF. An impervious construction placed beneath adam to intercept seepage flow.
DAMPING. Resistance that reduces vibration by energyabsorption. There are different types of damping such asviscous and Coulomb damping.
DAMPING RATIO. The ratio of the actual damping tothe critical damping, critical damping being the minimumamount of damping that prevents free oscillatoryvibration.
DEAD LOAD. The constant load on the dam resultingfrom the mass of the concrete and other attachments.
DEFLECTION. Linear deviation of the structure due tothe effect of loads or volumetric changes.
DEFORMATION. Alteration of shape or dimension dueto stress.
B-1
EM 1110-2-220030 Jun 95
DENSITY. Weight per unit volume.
DESIGN RESPONSE SPECTRA. Smooth, broad-bandedspectra appropriate for specifying the level of seismicdesign force, or displacement, for earthquake-resistantdesign purposes.
DIVERSION CHANNEL OR TUNNEL. A structure totemporarily divert water around a damsite duringconstruction.
DURABILITY. The ability of concrete to resist weather-ing action, chemical attack, abrasion, and other conditionsof service.
DYNAMIC MODULUS OF ELASTICITY. The modulusof elasticity computed from the size, weight, shape, andfundamental frequency of vibration of a concrete testspecimen, or from pulse velocity (ACI 116R-85).
EFFECTIVE PEAK GROUND ACCELERATION. Thatacceleration which is most closely related to structuralresponse and to damage potential of an earthquake. Itdiffers from, and is less than, the peak free-field groundacceleration (Newmark and Hall 1982).
ELASTIC DESIGN. Design based on a linear stress-strain relationship and elastic properties of the materials.
ELASTIC LIMIT. The limit of stress without undergoingpermanent deformation.
EXPANSION JOINT. A joint between parts of a con-crete structure to allow for thermal changes to occurindependently.
EXTENSIBILITY. The maximum tensile strain of con-crete before cracking.
FOREBAY. The impoundment of water above a dam orhydroelectric plant.
FOUNDATION. The surface and the natural material onwhich a dam and appurtenant features are constructed.
FOUNDATION DRAINAGE SYSTEM. A line of holesdrilled downstream of the grout curtain designed to inter-cept and control seepage through or beneath a dam so asto reduce uplift pressures under a dam (see alsoparagraph 7-8).
GALLERY. A long, narrow passage inside a dam usedfor access, inspection, grouting, or drilling of drain holes.
GROUND MOTION. A general term including allaspects of ground motion, namely particle acceleration,velocity, or displacement, from an earthquake or otherenergy source.
GROUT. A mixture of water and cement or a chemicalsolution that is forced by pumping into foundation rocksor joints in a dam to prevent seepage and to increasestrength.
GROUT CURTAIN. A row of holes filled with groutunder pressure near the heel of the dam to control seepageunder the dam (see also paragraph 7-8).
HEAT OF HYDRATION. Heat generated by chemicalreactions of cementitious materials with water, such asthat evolved during the setting and hardening of portlandcement.
HEEL OF DAM. The location where the upstream faceof the dam intersects the foundation.
HOMOGENEOUS. Uniform in structure or composition.
INSTANTANEOUS MODULUS OF ELASTICITY. Themodulus of elasticity of concrete that occurs immediatelyafter loading (see also Chapter 6).
INSTRUMENTATION. Devices installed on andembedded within a dam to monitor the structural behaviorduring and after construction of the dam.
INTAKE STRUCTURE. The structure in the forebay thatis the entrance to any water transporting facility such as aconduit or tunnel.
ISOTROPIC. Having identical properties in all directions.
LIFT. The concrete placed between two consecutivehorizontal construction joints.
MAGNITUDE. A measure of the strength of an earth-quake, or the strain energy released by it, as determinedby seismographic observations. C. F. Richter first definedlocal magnitude as the logarithm, to the base 10, of theamplitude, in microns, of the largest trace deflection thatwould be observed on a standard torsion seismograph at adistance of 100 kilometers from the epicenter (Richter1958). Magnitudes determined at teleseismic distancesare called body-wave magnitude and surface-wave magni-tude. The local, body-wave, and surface-wave magni-tudes of an earthquake do not necessarily have the samenumerical value (see also Chapter 5).
B-2
EM 1110-2-220030 Jun 95
MASS CONCRETE. Any volume of concrete withdimensions large enough to require that measures be takento cope with generation of heat of hydration of the cementand attendant volume change to minimize cracking(ACI 116R-85).
MAXIMUM CREDIBLE EARTHQUAKE (MCE). Thelargest earthquake associated with a specific seismo-tectonic structure or source area within the region exam-ined (see also Chapter 5).
MODIFIED MERCALLI (MM) INTENSITY. A numeri-cal index, developed in 1931, describing the effects of anearthquake on mankind, on structures built by mankindand on the Earth’s surface. The grades of the scale areindicated by Roman numerals from I to XII (see alsoChapter 5) (Hayes 1980).
MODULUS OF ELASTICITY. The ratio of normalstress to strain.
MONOLITH. A section or block of the dam that isbounded by transverse contraction joints.
NONOVERFLOW SECTION. The section of the damthat is designed not to be overtopped.
OPERATING BASIS EARTHQUAKE (OBE). Theearthquake, usually smaller than the MCE, associated witha specific seismotectonic structure or source area withinthe region examined which reflects the level of earthquakeprotection desired for operational or economic reasons(see also Chapter 5).
ORTHOTROPIC. Having elastic properties with consid-erable variations of strength in two or more directionsperpendicular to each other.
OUTLET STRUCTURE. A structure at the outlet of acanal, conduit, or tunnel for the purpose of dischargingwater from the reservoir.
OVERFLOW SECTION. That portion of a dam, usuallyoccupied by a spillway, which allows the overflow ofwater. Also referred to as spillway section.
PEAK GROUND ACCELERATION (PGA). That accel-eration representing the peak acceleration of free-fieldvibratory ground motion, that is, motion which is notinfluenced by topography or man-made structures.
PERMEABILITY (LABORATORY) (TO WATER,COEFFICIENT OF). The rate of discharge of water
under laminar flow conditions through a unit cross-sectional area of a porous medium under a unit hydraulicgradient and standard temperature conditions, usually20 degrees Centigrade.
PLACEMENT. The process of depositing, distributing,and consolidating of newly mixed concrete.
POISSON’S RATIO. The ratio of transverse strain toaxial stress resulting from uniformly distributed axialstress below the proportional limit of the material.
PORE PRESSURE. The interstitial pressure of waterwithin the mass of rock or concrete. Also called neutralstress and pore-water pressure.
POROSITY. The ratio of the volume of voids to the totalvolume of the material.
PREDOMINANT PERIOD(S) OF VIBRATION. Theperiod(s) at which maximum spectral amplitudes areshown on response spectra.
PRINCIPAL STRESS. Maximum and minimum stressoccurring at right angles to a principal plane of stress.
RESPONSE SPECTRUM. A plot of the maximumresponse of a series of single-degree-of-freedom dampedoscillators (elastic systems) as a function of their naturalperiods, or frequencies, when the oscillators are subjectedto a vibratory ground motion.
RESTRAINT (OF CONCRETE). Internal or externalrestriction of free movement of concrete in one or moredirections.
ROLLER-COMPACTED CONCRETE (RCC). A rela-tively dry concrete material that has been consolidatedthrough external vibration from vibratory rollers.
SPECTRUM INTENSITY. The integral of the pseudo-velocity response spectrum taken over the range of signif-icant structural vibration periods of the structure beinganalyzed.
SPILLWAY. The structure over or through which reser-voir flood flows are discharged.
SPILLWAY CHUTE. The outlet channel for the spillwaydischarge.
STILLING BASIN. A basin to dissipate the energy inthe water discharged from the spillway or outlet structure.
B-3
EM 1110-2-220030 Jun 95
STRUCTURAL CONCRETE. Concrete used forstructural load and forms a part of the structure.
SUSTAINED MODULUS OF ELASTICITY. The mod-ulus of elasticity of concrete that occurs with a constantsustained load over a period of time (see also Chapter 6).
TAILRACE. The channel or canal that carries wateraway from a dam. Also sometimes called afterbay.
TAILWATER ELEVATION. The elevation of the watersurface downstream from a dam or hydroelectric plant.
TEMPERATURE RISE. The increase in temperature inconcrete resulting from the hydration of cement.
TEMPERATURE STRESS. Stresses created in concretefrom the changes or differentials in temperature.
TENSILE STRENGTH. The maximum stress that amaterial is capable of resisting under an axial tensile load.
THERMAL CONDUCTIVITY. The measure of theability of concrete to conduct heat (see also Chapter 6).
THERMAL DIFFUSIVITY. The measure of the facilitywith which temperature changes take place with a mass ofconcrete (see also Chapter 6).
TOE OF DAM. The location where the downstream faceof the dam intersects the foundation.
TRANSVERSE CRACKS. Cracks that develop at rightangles to the longitudinal axis of the dam.
TRANSVERSE JOINT. A joint normal to the longitudi-nal axis of the dam.
UPLIFT PRESSURE. The upward water pressure in thepores of concrete or rock or along the base of the dam(see also Chapter 3).
WATER STOP. A thin sheet of metal, rubber, plastic, orother material placed across joints in concrete dams toprevent seepage of water through the joint (see alsoChapter 7).
B-4
EM 1110-2-220030 Jun 95
Appendix CDerivation of the General WedgeEquation
The equations for sliding stability analysis of a generalwedge system are based on the right-hand sign conventionthat is commonly used in engineering mechanics. Theorigin of the coordinate system for each wedge is locatedin the lower left-hand corner of the wedge. The x- andy-axes are horizontal and vertical, respectively. Axesthat are tangent (t) and normal (n) to the failure plane are
Figure C-1. Sign convention for geometry
oriented at an angle (α) with respect to the +x- andy-axes. A positive value of α is a counter-clockwiserotation; a negative value ofα is a clockwise rotation.
Figure C-2. Geometry of the typical i th wedge andadjacent wedges
Figure C-3. Distribution of pressures and resultantforces acting on a typical wedge
C-1
EM 1110-2-220030 Jun 95
Figure C-4. Free body diagram of the i th wedge
C-2
EM 1110-2-220030 Jun 95
Figure C-5. Derivation of the general equation (Sheet 1 of 3)
C-3
EM 1110-2-220030 Jun 95
Figure C-5. (Sheet 2 of 3)
C-4
EM 1110-2-220030 Jun 95
Figure C-5. (Sheet 3 of 3)
C-5
EM 1110-2-220030 Jun 95
Figure C-6. Free body diagram of the i th wedge with anchor
The free body diagram above varies from that shown inFigure C-4 in that the above free body diagram containsan anchor force “Ai” oriented at an angle,βi with thevertical. The equilibrium equations and governing wedgeequation on the following pages will include this anchorforce.
C-6
EM 1110-2-220030 Jun 95
Figure C-7. Derivation of the general equation for a wedge containing an anchor force (Sheet 1 of 3)
C-7
EM 1110-2-220030 Jun 95
Figure C-7. Derivation of the general equation for a wedge containing an anchor force (Sheet 2 of 3)
C-8
EM 1110-2-220030 Jun 95
Figure C-7. Derivation of the general equation for a wedge containing an anchor force (Sheet 3 of 3)
Note: Solutions of factors of safety and forces on freebodies determined by the above equations, or by computeranalyses should be verified by an independent method ofanalysis. Vector diagrams may be used to check theresults graphically. In multi-wedge analyses, consider-ation should be given to the stress-strain compatibility ofdifferent rock materials on the failure plane.
C-9
EM 1110-2-220030 Jun 95
Appendix DExample Problems - Sliding Analysis forSingle and Multiple Wedge Systems
D-1. Examples of typical static loading conditions forsingle and multiple wedge systems are presented in thisappendix.
D-2. These examples are provided to clearly demon-strate the procedure for applying the general wedge equa-tion to the sliding analysis of single and multiple wedgesystems. The variations of uplift pressure, orientation offailure planes, etc., used in the examples were onlyselected to simplify the calculations and are not intendedto represent the only conditions to be considered duringthe design of a hydraulic structure.
D-1
EM 1110-2-220030 Jun 95
D-2
EM 1110-2-220030 Jun 95
D-3
EM 1110-2-220030 Jun 95
D-4
EM 1110-2-220030 Jun 95
D-5
EM 1110-2-220030 Jun 95
D-6
EM 1110-2-220030 Jun 95
D-7
EM 1110-2-220030 Jun 95
D-8
EM 1110-2-220030 Jun 95
Sliding Stability AnalysisExample: Five Wedge System
Summary: Wedge Forces for Trial Safety Factors
FS = 1.5
i αi Li HLi HRi Vi Wi Ui (Pi-1 - Pi )
1 -51.82 6.36 0 0 6.14 1.15 10.93 -9.01
2 -55.53 12.13 0 0 10.73 8.20 26.53 -24.56
3 9.5 30.3 19.53 0 0 122.4 47.33 32.97
4 34.47 8.83 0 0 0 7.02 4.14 7.59
5 30.38 9.89 0 0 0 2.82 1.54 3.32
∆PR = 10.31
FS = 2.5
i αi Li HLi HRi Vi Wi Ui (Pi-l - Pi )
1 -49.14 6.61 0 0 6.75 1.27 11.36 -9.10
2 -51.5 12.78 0 0 12.43 9.50 27.95 -25.48
3 9.5 30.3 19.53 0 0 122.4 47.33 19.65
4 38.5 8.0 0 0 0 6.06 3.76 6.26
5 35.72 8.56 0 0 0 2.29 1.34 2.45
∆PR = -6.20
FS = 2.0
i αi Li HLi HRi Vi Wi Ui (Pi-1 - Pi )
1 -50.16 6.51 0 0 6.52 1.22 11.19 -9.06
2 -53.05 12.51 0 0 11.73 8.97 27.37 -25.13
3 9.5 30.3 19.53 0 0 122.4 47.33 24.53
4 36.95 8.33 0 0 0 6.43 3.9 6.73
5 33.62 9.03 0 0 0 2.48 1.41 2.75
∆PR = -0.18
D-9
EM 1110-2-220030 Jun 95
D-10
![Gravity Dam Design[1]](https://img.pdfslide.us/doc/110x75/545a2372b1af9f37608b5959/gravity-dam-design1.jpg)
