DEPARTMENT OF THE ARMY EP 1110-2-12U.S. Army Corps of Engineers

CECW-ED Washington, DC 20314-1000

PamphletNo. 1110-2-12 30 September 1995

Engineering and DesignSEISMIC DESIGN PROVISIONS FOR ROLLER

COMPACTED CONCRETE DAMS

1. Purpose

The purpose of this engineer pamphlet (EP) is toprovide preliminary guidance and direction for theearthquake-resistant design of new roller compactedconcrete (RCC) dams, and for the evaluation of safetyand serviceability of existing RCC dams subjected toearthquake loading.

2. Applicability

This EP applies to all HQUSACE elements andUSACE commands having responsibilities for thedesign of civil works projects.

3. Discussion

a. This EP presents preliminary guidanceconcerning the design of new RCC dams and theevaluation of existing RCC dams located in zones ofhigh seismic activity. References are included inAppendix A.

b. Appendices B-D present examples ofapplying this guidance to the design of a new RCCdam.

c. Both the preliminary guidance containedherein and the example problems are based onEM 1110-2-2200 and ER 1110-2-1806. Both of thesedocuments are under revision and the final guidancecontained in these documents may vary somewhatfrom the provisions of this EP. Draft copies of thesedocuments may be obtained from CECW-ED for usein the design of RCC structures.

d. A dynamic stress analysis shall be performedas part of the design procedure for all new RCCdams, or the evaluation of existing RCC dams,located in areas of strong seismicity. Dams shall beshown capable of satisfying general performancerequirements for design earthquake seismic eventsdescribed herein. Linear-elastic analysis methodsshall be used in performing dynamic stress analysis.

e. Consultation and approval of CECW-ED arerequired prior to performing a nonlinear dynamicstress analysis based upon the theory of fracturemechanics to qualify a new design or to evaluate anexisting RCC dam with regard to dam safety.

FOR THE COMMANDER:

ROBERT H. GRIFFINColonel, Corps of EngineersChief of Staff

DEPARTMENT OF THE ARMY EP 1110-2-12CECW-ED U.S. Army Corps of Engineers

Washington, DC 20314-1000

PamphletNo. 1110-2-12 30 September 1995

Engineering and DesignSEISMIC DESIGN PROVISIONS FOR ROLLER

COMPACTED CONCRETE DAMS

Table of Contents

Subject Paragraph Page

Chapter 1IntroductionGeneral. . . . . . . . . . . . . . . . . . . . . 1-1 1-1References . . . . . . . . . . . . . . . . . . 1-2 1-1Explanation of Terms. . . . . . . . . . . 1-3 1-1Background. . . . . . . . . . . . . . . . . . 1-4 1-1Design Philosophy. . . . . . . . . . . . . 1-5 1-1Design Earthquakes. . . . . . . . . . . . 1-6 1-1Acceptance Criteria. . . . . . . . . . . . 1-7 1-2Important Factors. . . . . . . . . . . . . . 1-8 1-2Analysis Methods and Procedure . . . 1-9 1-3Coordination . . . . . . . . . . . . . . . . .1-10 1-3

Chapter 2Seismic Design CriteriaStability . . . . . . . . . . . . . . . . . . . . 2-1 2-1Response to Ground Shaking. . . . . . 2-2 2-1Foundation Fault Displacement. . . . 2-3 2-2Refined Dynamic Analyses Methods 2-4 2-6

Chapter 3Material Properties of RCCSimilarities of RCC and

Conventional Concrete. . . . . . . . . 3-1 3-1Compressive Strength. . . . . . . . . . . 3-2 3-1Tensile Strength. . . . . . . . . . . . . . . 3-3 3-1Shear Strength. . . . . . . . . . . . . . . . 3-4 3-3Modulus of Elasticity . . . . . . . . . . . 3-5 3-3Poisson’s Ratio. . . . . . . . . . . . . . . 3-6 3-4Tensile Stress/Strain Relationship . . . 3-7 3-5Dynamic Tensile Strength (DTS) . . . 3-8 3-6Allowable Tensile Stresses. . . . . . . 3-9 3-7

Subject ParagraphPage

Chapter 4Design EarthquakesDefinition . . . . . . . . . . . . . . . . . . . . 4-1 4-1Operating Basis Earthquake (OBE) . . 4-2 4-1Maximum Credible Earthquake

(MCE) . . . . . . . . . . . . . . . . . . . . . 4-3 4-1

Chapter 5Design Response Spectra andAcceleration Time HistoriesDefining the Design Earthquake. . . . 5-1 5-1Developing Design Response

Spectra. . . . . . . . . . . . . . . . . . . . . 5-2 5-1Developing Acceleration Time

Histories . . . . . . . . . . . . . . . . . . . . 5-3 5-1Dynamic Analysis by Modal

Superposition . . . . . . . . . . . . . . . . 5-4 5-2Types of Design Response Spectra . . . 5-5 5-2Horizontal and Vertical Design

Response Spectra. . . . . . . . . . . . . . 5-6 5-3

Chapter 6Earthquake Load CasesLoad Combinations. . . . . . . . . . . . . 6-1 6-1Dynamic Loads To Be Considered . . . 6-2 6-1Static Loads To Be Considered. . . . . 6-3 6-1Static Loads Not To Be Considered . . 6-4 6-2

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Subject Paragraph Page

Chapter 7Factors Significantly AffectingDynamic ResponseEvaluation Procedure and Objectives 7-1 7-1Design Response Spectra. . . . . . . . 7-2 7-1Dam-Foundation Interaction,

Damping Effect. . . . . . . . . . . . . . 7-3 7-1Dam-Foundation Interaction,

Foundation Modulus Effect. . . . . . 7-4 7-3Hydrodynamic Effect. . . . . . . . . . . 7-5 7-5Reservoir Bottom Absorption. . . . . 7-6 7-7Method of Combining Modes. . . . . 7-7 7-8Vertical Component of Ground

Motion . . . . . . . . . . . . . . . . . . . . 7-8 7-8

Chapter 8Dynamic Analysis Methods andProceduresAttributes of Dynamic Analysis

Methods . . . . . . . . . . . . . . . . . . . 8-1 8-1Comparison of Dynamic Analysis

Methods . . . . . . . . . . . . . . . . . . . 8-2 8-3Dynamic Analysis Procedure. . . . . . 8-3 8-4Preliminary Design of New Dams . . 8-4 8-5Final Design of New Dams. . . . . . . 8-5 8-6Evaluating Existing Dams. . . . . . . . 8-6 8-6

Subject ParagraphPage

Appendix AReferences

Appendix BDesign Example Problem

Appendix CDesign Example - Chopra’s Simplified Method

Appendix DDesign Example - Finite Element Method

Appendix ETensile Strength of Roller CompactedConcrete

Appendix FGlossary

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Chapter 1Introduction

1-1. General

Roller compacted concrete (RCC) dams are designedin accordance with EM 1110-2-2200. Theproportions of the RCC dam are derived by stabilityanalysis in a manner identical to that for aconventional concrete gravity dam and are governedby the static forces to be resisted and not by thedynamic forces generated during seismic activity.After the geometric proportions are determined basedon the static loads a dynamic analysis is conducted.Zones requiring superior RCC mixes are established,and vibratory compaction methods and jointpreparation methods which affect the RCC tensilestrength are also established based on the criteriaprovided in this engineer pamphlet (EP).

1-2. References

Required and related publications are listed inAppendix A.

1-3. Explanation of Terms

Abbreviations, symbols, and notations usedthroughout this EP are explained in the glossary.

1-4. Background

Basic criteria and guidance for the design of RCCdams are provided in EM 1110-2-2200. ER 1110-2-1806 provides guidance on analysis methods andprocedures for new designs and an investigativeprogram for existing dams. ETL 1110-2-301 givesadditional information on specifying earthquakeground motions for a particular site. ETL 1110-2-303provides guidance on finite element dynamic analysismethods and on evaluating the severity of crackingbased on tensile stresses from the linear analysis.EM 1110-2-2006 provides guidance concerning RCCusage and mix design.

1-5. Design Philosophy

a. Response spectrum analysis.The nonlinear-ities associated with concrete behavior under seismicloading are difficult to assess and beyond practicalanalyzing capabilities of most design offices.Procedures which permit the use of a linear-elastictype of dynamic analysis adjusted to provide areasonable but conservative approximation of thenonlinear behavior are adequate in almost all designsituations. The philosophy of design followed in thisEP will be to establish the procedures applicable tothe majority of design situations. This consists ofproviding in some detail the requirements forperforming the linear-elastic response spectrumanalysis and the criteria for evaluating the results.

b. Refined analyses.For the few occasionswhere this approach does not produce a satisfactorydesign or where an existing dam does not satisfycriteria, the designer is then advised to pursue themore refined analysis methods. Should the evenmore complex nonlinear analysis become necessary, itshould be performed under the guidance of arecognized expert in this specialized field and shouldonly be undertaken with approval of CECW-ED.

1-6. Design Earthquakes

The linear-elastic response spectrum method ofanalysis is the simplest dynamic analysis method andprovides adequate results for most designs. Theground motion is usually defined by design responsespectra scaled to peak ground accelerations (PGA) forthe two design earthquakes described below.

a. Operating basis earthquake.The operatingbasis earthquake (OBE) is defined as the earthquakeproducing the greatest level of ground motion that islikely to occur at the site during the economic life ofthe dam.

b. Maximum credible earthquake.Themaximum credible earthquake (MCE) is defined asthe earthquake which produces the greatest level ofground motion at the site as a result of the largestmagnitude earthquake that could reasonably occuralong the recognized faults or within a particularseismic source.

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c. Types of design spectra.Design responsespectra for the OBE are usually developed using aprobabilistic approach, and design response spectrafor the MCE are developed using a deterministicapproach. Design response spectra are furtherclassified into two types: (1) site-specific or(2) standard. The seismic zone location of the site,the height of the dam, and the proximity to activefaults are the factors used to determine if it isnecessary to develop a site-specific design responsespectra or if the standard spectra may be used in thedynamic analysis. When standard design responsespectra are acceptable, Chapter 5 provides theappropriate spectra along with the PGA values to beused for scaling. These standard design spectra arebased on the mean level of the ground motionparameters for the records selected in thedevelopment of the standard spectra.

d. Ground motion time histories.The morerefined analysis methods require a ground motiontime history representation of the design earthquakes.These may be developed using actual past earthquakeground motion records, synthetically, or by modifyingan actual record. Ground motion time histories aredeveloped so their response spectrum closely matchesthe site-specific design response spectrum.

1-7. Acceptance Criteria

a. Cracking of RCC.The ground motion that isproduced during a seismic event can cause cracks tooccur in an RCC dam. As cracking progresses,serviceability is eventually impaired. If groundshaking is extremely severe, or if strong groundshaking combines with a foundation fault displace-ment, it is conceivable that continued propagation ofthe system of cracks could eventually lead to a failuremechanism where the dam is no longer capable ofcontaining the pool. This EP establishes acceptancecriteria which maintain serviceability during an OBE,and provide a reasonable safety factor againstdeveloping a failure mechanism during a MCE.Because of the complexity and the great number ofvariables involved in seismic design, the EP criteriashould be supplemented with the judgment ofstructural engineers experienced in seismic design.

b. Direct tensile strength.The direct tensilestrength of the RCC is the design parameter used forestablishing the acceptance criteria. Unlikeconventional concrete, tensile strength of RCC

depends on mix consistency and placement andcompaction methods as well as mix proportions.Tensile strength of both the lift joint and the parentconcrete shall be determined from cores taken fromtest fill placements for new dam design and from thein-place RCC for existing dams. Although splittingtensile tests may be used, the test results shall beadjusted to reflect direct tensile strength. From thedirect tensile strength, the allowable design tensilestresses shall be established for both lift joints andparent concrete by applying adjustment factors toaccount for high strain rate associated with dynamicloading and certain nonlinear characteristics of thestress/strain curve. Adjustment factors shall beselected to maintain serviceability during an OBE andto produce a reasonable safety factor for a MCE.

1-8. Important Factors

Discussed below are recommendations regardingfactors which are important because they have asignificant impact on the dynamic response.Recommendations that differ from those contained inETL 1110-2-303 and ER 1110-2-1806 are identified.

a. Effective damping.The material andradiation damping of the foundation contributesignificantly to the damping of the combineddam-foundation system, and must be considered inthe analysis. This requires calculating an effectiveviscous damping ratio to reflect the dampingcontribution of both the dam and the foundation.This will result in a considerably higher dampingratio for a foundation having a very low modulusthan the damping ratio used previously.

b. Hydrodynamic effect. Added mass shall becalculated using standard hydrodynamic pressurefunction curves which consider compressibility of thewater, stiffness characteristics of the dam, andreservoir bottom absorption (Fenves and Chopra1986). Appendix D provides an example showing therequired procedure.

c. Mode combination methods.The completequadratic combination method (CQC) of combiningmodes shall be used for final design of dams undercritical seismic design conditions and for evaluationof existing dams. Critical conditions are consideredto exist when site-specific design response spectra arerequired by this EP. Either the square root of thesum of the squares method (SRSS) or the CQC

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method is acceptable for all preliminary designs andfor final designs under noncritical seismic conditions.Since the modal frequencies are fairly well separatedin gravity dams, the simpler SRSS method producesadequate results which are in balance with the generallevel of precision required for preliminary ornoncritical analyses.

d. Seismic zone map.The seismic zone map,Figure 5-1, shall be used in the dynamic stressanalysis phase of the seismic design. The peakground accelerations for use in scaling standarddesign response spectra are contained in Table 5-2and are based on the zone map. The seismic zonemaps and the seismic coefficients contained inER 1110-2-1806 shall be used only in the stabilityanalysis phase of seismic design.

1-9. Analysis Methods and Procedure

In general a dynamic stress analysis shall beperformed, and the results shall be evaluated todetermine if the response of the RCC dam to thedesign earthquakes is acceptable. If the response isnot acceptable, the design of a new dam may bemodified and reanalyzed using the same analysismethod, or a more refined analysis method may beemployed. For an existing dam, progressively morerefined methods of analysis are employed.

a. Method attributes.There are four attributesthat characterize a particular dynamic analysismethod.

(1) Material behavior. Options are (a) linear-elastic or (b) nonlinear behavior.

(2) Design earthquake definition. Options are(a) design response spectrum or (b) time historyground motion record input.

(3) Dimensional representation. Options are(a) two-dimensional representation or (b) three-dimensional representation.

(4) Model configuration. Options are(a) Chopra’s “standardized” model, (b) compositefinite element-equivalent mass system model, or(c) finite element-substructure model.

b. Computer programs.Various computerprograms are available which are identified withcertain analysis methods. Also, Chopra’s Simplified

Method may be either hand-calculated or done by acomputer program. Some computer programs, suchas the general purpose finite element programs, allowthe attribute options to be changed so that one ofseveral possible methods may be employed for thedynamic analysis. This often allows a transition to amore refined method without necessarily abandoningall the previous computer model input effort. Othercomputer programs, such as the EAGD-84 program,and Chopra’s Simplified Method are single methodprograms since they have fixed attributes. Chapter 8discusses dynamic analysis methods in more detail.

c. Preliminary and final design.The two-dimensional, linear-elastic, response spectrum methodshall be used for the preliminary design analysis.Either Chopra’s Simplified Method or a general-purpose finite element program shall be employeddepending on the design conditions. The simplestfinal design analysis utilizes a composite finiteelement-equivalent mass system model and general-purpose finite element program.

1-10. Coordination

A fully coordinated team of structural engineers,geotechnical and materials engineers, geologists, andseismologists should ensure that all factors relevant tothe dynamic analysis are correct and that the resultsof the analysis are properly evaluated. Some of thecritical analysis and design aspects requiring coordi-nation are discussed below.

a. Design response spectra.Developing site-specific design response spectra when required.

b. Tensile strength of RCC.Obtainingrepresentative cores from test-fill placements for newdams or from the in-place concrete for existing damsfor use in determining the direct tensile strength anddynamic tensile strength of both the lift joints and theparent RCC.

c. Foundation properties.Obtaining explora-tory corings and evaluating tests to determine thefoundation deformation modulus and other foundationproperties.

d. Foundation fault displacement.Evaluatinggeoseismic conditions at the site to determine iffoundation fault displacement is possible, and to mapthe location, strike, and dip of the potential faults.

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Chapter 2Seismic Design Criteria

2-1. Stability

a. Resultant location and sliding.RCC damsshall satisfy the overturning and sliding stabilityrequirements for gravity dams using inertia forcescalculated by the seismic coefficient method as setforth in EM 1110-2-2200 and ETL 1110-2-256. Theseismic coefficients shall be as shown on the seismiczone maps provided in ER 1110-2-1806.

b. Extreme stability conditions.When intenseground shaking causes serious tensile cracking at thedam-foundation interface, a nonlinear time historyanalysis shall be performed to evaluate cracking,potential permanent displacements, and the effectthese have on sliding stability. Certain stipulationsregarding nonlinear analyses are covered inparagraph 2-2g.

2-2. Response to Ground Shaking

RCC dams shall be capable of resisting the strongmotion ground shaking associated with designearthquakes within the allowable tensile stress designcriteria specified in Chapter 4. Dynamic stressanalysis methods and procedures are described inChapter 8. The dynamic analyses shall incorporatethe dynamic characteristics of the dam, foundation,reservoir, and backfill or silt deposition whenapplicable.

a. Defining ground motion.The free fieldground motions are used to define the ground motionthat would be felt at the site due to two designearthquakes. Free field ground motion associatedwith each shall be represented by design responsespectra and, when required, design acceleration timehistories. The design earthquakes are operating basisearthquake (OBE), and maximum credible earthquake(MCE). Both are discussed in detail in Chapter 4.

b. Propagation of cracks in RCC.Most damswith earthquake resistant provisions will probablysurvive the most severe earthquake shaking possibleat the site with little or no damage, although highdams located near major faults have experiencedextensive cracking during major earthquakes (Chopraand Chakrabarti 1973). Concrete cracking due to

ground shaking combined with cracking due tofoundation fault displacement could propagate to anextent where a failure mechanism is formed thusimpairing the ability of the dam to contain the pool.Criteria defining an acceptable response of the dam todesign earthquakes are based on initiation andpropagation of tensile cracking within the RCC.

c. Analyzing response to ground shaking.Theprocess of cracking and the propagation of the cracksresult in nonlinear behavior of the dam. There arealso nonlinearities associated with dam-foundationinteraction and dam-reservoir interaction which aredifficult to assess. Approximate linear relationshipsaccount for some of the nonlinear dynamic behaviorand allow the response of the dam to the designearthquake ground motion to be determined using alinear-elastic analysis method. Tensile stresses canthen be evaluated based on tensile strength parametersadjusted to be compatible with linear-elastic analysismethods.

d. Analysis methods.The simplest of the linear-elastic methods uses a response spectrum to definethe ground motion as outlined in Chapter 5. MostRCC dams will be found adequate using this method.For the few exceptions, the next level of refinementin determining the dynamic response is the linear-elastic time history method, and in rare cases anonlinear time history finite element analysis may berequired.

e. Allowable tensile stress.The tensile strengthof the RCC is the single concrete material propertyused to evaluate cracking, and to establish acceptableresponse. Allowable tensile stresses are defined inparagraph 4-2c and paragraph 4-3c for the OBE andMCE, respectively.

f. Evaluating time-history response.Whendynamic response is determined by the linear-elastictime-history method, the allowable tensile stress is theprincipal criterion for evaluating acceptable response,but additional criteria are also required to qualifyother response characteristics such as the number ofstress cycles approaching or exceeding the allowablestress, and the magnitude and pattern of theseexcursions beyond the specified limits.

g. Evaluating nonlinear analyses.Whendynamic response is determined by the nonlineartime-history method, criteria for evaluating acceptableresponse are based on the theory of fracture

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mechanics. This type of analysis should only beundertaken in consultation with and as approved byCECW-ED.

2-3. Foundation Fault Displacement

a. General. Most RCC dam sites are notsubject to any significant differential displacement ofthe ground surface at the dam-foundation interfaceduring a seismic event. Dam sites should always beavoided when located near a major active faultsystem with the potential to trigger sympatheticfoundation displacements at the site. Occasionally itis not possible to avoid these sites, and it becomesnecessary to evaluate the response of the dam shouldsuch a foundation fault displacement occur.

(1) Considerable judgment is required in theevaluation process. At best, analysis methods forfoundation fault displacement are approximate and aregenerally unsupported by past observations of theresponse of existing dams to fault displacementsoccurring at the dam foundation. Furthermore,considerable judgment is required in the prediction offuture fault movement and in the magnitude of thefault displacement. For example, the estimate of themagnitude of potential fault displacement provided bydifferent experts for a specific site could vary from afew inches to several feet. This necessitatesconsulting several geotechnical firms to provide site-specific fault displacement estimates, and thencarefully scrutinizing these estimates before finallyestablishing the design fault displacement.

(2) Experts in plate tectonics, geology,seismology, and finite element analysis techniquesshould be consulted to provide guidance for any damlocated on a site subject to foundation faultdisplacement. Because of the many uncertainties andthe risk involved, approval by CECW-ED is requiredfor any RCC dam which is located on a site subjectto foundation fault displacement.

b. Types of faults.Fault slip is the relativedisplacement of two adjacent tectonic plates withrespect to each other. This refers to large active faultsystems such as the San Andreas or Hayward faultsin California. On a smaller scale, the foundation rockmass beneath a dam contains various discontinuities,joint sets, and shear and fault zones. Normally this isa system of historically inactive discontinuities;however, there is a potential for fault slippage

particularly when triggered by a great earthquake on anearby large active fault. The three general types offault slips are strike-slip, normal-slip (dip-slip), andreverse-slip (thrust-slip). Refer to Figure 2-1 forillustrations of the various types of faults and how themagnitude of slip is measured. The strike of the faultis the trace the fault makes with respect to the groundsurface, and it may be at any orientation with respectto the dam axis.

c. Design fault displacement.The design faultdisplacement (DFD) is defined as the maximumpossible free field fault slip movement that couldreasonably occur in the dam foundation as measuredat the ground surface. The return period that wouldbe associated with the DFD is similar to that of theMCE. Therefore, the DFD and the free field groundmotion together specify the site-specific seismicactivity associated with the MCE. To fully describethe DFD, three factors must be specified: magnitude,type of slip, and strike of the fault.

(1) The geology of the dam foundation iscomplex, and the foundation may be crossed by anumber of discontinuities with fault displacementpotential. Experts in the fields of geology andseismology should be consulted to study thefoundation fault system, determine which faults arecapable of surface displacement, and finallyrecommend which faults are critical and specify theDFD for each critical fault.

(2) Normally, foundation fault displacements arenot considered to occur concurrently with strongmotion shaking associated with the OBE. The activefault near the dam site that produces a seismic eventof OBE magnitude is not likely to trigger sympatheticslippage in the fault system in the dam foundation.The probability of sympathetic foundation faultdisplacement is normally several orders of magnitudeless than the recurrence rate for the strong motionshaking associated with the OBE; therefore, theprobability of the OBE being accompanied bysignificant foundation displacement is usuallyconsidered negligible.

(3) On rare occasions, the probability logicdiscussed above may not apply when considering if itis appropriate to combine foundation faultdisplacement with ground shaking in specifying theOBE. For example, unusual geology of thefoundation could make it susceptible to a reservoir-induced foundation fault displacement or to other

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unusual causes of foundation fault displacement

Figure 2-1. Types of fault slips

discussed later in this chapter. In these situations thestrong motion shaking accompanying the local faultslip may be nearly as intense or even more intensethan the gound motion shaking associated with anOBE produced by a major active fault slip occurringsome distance from the site. When this is the case, areduced value of the DFD would be included withfree field ground motion to describe the OBE.

d. Combined DFD and ground shaking.Stresses associated with the DFD result from highlycomplex nonlinear behavior; however, simplified faultdisplacement analysis procedures, such as the onedescribed below, are normally used to investigateconcrete stresses that may occur due to fault displace-

ment. Stresses due to ground shaking are determinedby methods discussed earlier in this chapter. Thus,stresses due to fault displacement and stresses due toground shaking are obtained from two separate, inde-pendent, and approximate analyses. The response tothe design earthquake is then obtained by direct addi-tion of the two sets of stresses without accounting forany interaction. Actually, the fault displacement maycause inelastic behavior at the dam-foundation inter-face, cracking within the RCC, or other inelasticresponse which changes the dynamic characteristicsof the dam, which in turn interacts with and effectsthe ground shaking response. Because these simpli-fied and approximate procedures have not been sup-ported by nonlinear finite element analyses thatproperly combine the effects of fault displacement

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and ground shaking, they should be used withcaution.

e. Simplified DFD analysis procedure.Thesimplified procedure described below was used toinvestigate concrete stresses due to fault displacementin the Auburn Dam in California (U.S. Department ofthe Interior, Bureau of Reclamation 1980). The damand foundation are modeled with finite elements withthe mesh geometry adjusted to allow the fault to beproperly oriented. Refer to Figure 2-2. Thefoundation model consists of a fixed block withconventional boundary supports, and a movable blockwith special boundary conditions that allow forces tobe applied at the boundary parallel to the fault toproduce the DFD. The fixed and movable block areseparated by elastic orthotropic elements which allowthe sharp displacement discontinuity to take place asthe movable block displaces upward.

(1) The finite element model is first loaded withthe gravity loads followed by the hydrostatic loads,and finally the movable block is forced to undergothe DFD. Each loading is applied incrementally.After each loading increment, tensile stresses areevaluated and elements are softened in areas wherethe tensile strength is exceeded. Elements are soft-ened by reducing their elastic modulus until thetensile stress is eliminated. Most elements requiringsoftening are located in the foundation because joint-ing and discontinuities in the rock prevent it fromsustaining high tensile stress. When the DFD isreached, the extent of the tensile failure areas isevaluated. The dam tends to bridge over the fracturezone in the foundation. Resulting stresses induced inthe RCC are obtained from the finite element analysisfor the final increment of loading which produced theDFD.

(2) The method of incremental loading and soft-ening of element properties allows the use of asimplified static, linear-elastic finite element analysisapproach. Disadvantages of the procedure are that itgives only an approximation of the complex nonlinearbehavior associated with fault displacement, it is timeconsuming, and it requires considerable judgment.

(3) The example shown in Figure 2-2 is typicalfor a normal or reverse fault where the fault strike isapproximately parallel to the dam axis so a two-dimensional analysis is adequate. If the fault strike isnot close to parallel to the dam axis, or for a strike-slip fault, a three-dimensional analysis is required.

The three-dimensional analysis is even more timeconsuming and complex, but the principles andgeneral procedure are similar to the two-dimensionalanalysis described.

f. Acceptable response to DFD.When the seis-mic activity associated with the design earthquakeconsists of both fault displacement and ground shak-ing, stresses for the combined response described inparagraph 2-3d must satisfy the allowable tensilestress criteria of paragraph 2-2e. Beyond thesetensile stress requirements, additional consideration isrequired regarding general performance requirementsof Chapter 4 related to dam safety and operations inthe event of foundation fault displacement. Thepotential fault displacement and the effect it has onthe dam must be evaluated on a case-by-case basis.The analysis procedures described above forevaluating the effect of fault displacement are roughapproximations, but they do provide an indication ofthe extent of the fracture zones that could occur inthe foundation or lower portions of the RCC dam.The analysis results must be coupled withconsiderable judgment to determine if this damagecould lead to the erosion of the foundation or RCCmaterials to the extent that finally causes anuncontrolled release of the reservoir.

g. Dam failures caused by fault displacements.To help identify some of the judgment factorsinvolved in evaluating sites with fault displacementpotential, the following is a brief review of historicalinformation on dams that failed directly or indirectlyas a result of fault displacement. Differential dis-placements across a fault have been recorded due to:triggering of the fault by a seismic event; a differencein consolidation of materials on either side of thefault; a reduction in resistance to fault movementcreated by the lubricating effects of water, or theerosion of fault materials by flowing water; andincrease in hydrostatic pressures along the fault.

(1) Earth-fill dams, concrete gravity dams, andconcrete arch dams have failed due to fault move-ments. Failures of the Baldwin Hills earth-fill dam,the Malpasset concrete arch dam, and the St. Francisconcrete gravity dam (James et al. 1988) can all beattributed in part to forces and movements occurringalong fault surfaces. Although these forces andmovements were not triggered by seismic activity, itcan be surmised that if a seismic event had occurred,it would have likely triggered similar failures. Theseexamples show that fault movement can cause a

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failure mechanism to form in the dam structure whichresults in dam failure; however, it is more likely thatthe fault movement would create flow paths thatcould lead to a release of the impounded reservoir.Seepage can erode dam or foundation materials whicheventually results in failure because capability forcontrolled release of the pool is lost.

(2) An earth-fill dam with a flexible core is nor-mally considered less susceptible to failure due tofoundation fault displacement because it would tendto conform to the displaced shape of the foundation.Although this flexibility of the dam material willreduce voids and flow paths in the dam and founda-tion it will not completely eliminate them. Thus, anearth-fill dam is susceptible to erosion of core orfoundation material from water flowing through faultsor through voids in the dam or foundation created byfault movements. For this reason, an earth-fill dam isnot necessarily superior to a concrete gravity dam inresisting the effects of fault movement.

h. Defensive design features.Defensive designfeatures which can be employed in the design of anRCC dam susceptible to foundation displacement arediscussed below.

(1) The arching action provided by laying out thedam axis on a curve may better distribute the forceson a gravity dam due to foundation fault displace-ment, and reduce the tensile stresses and cracking ofthe RCC. This defensive feature is only effective ifthe heave of the foundation block is generally in adownstream direction, and providing the fault move-ment does not occur at either abutment.

(2) Special sliding joints may also be used toreduce cracking of the RCC due to fault displace-ment. For example, vertical joints may be located inthe RCC to accommodate potential strike-slip faultdisplacements where the strike is generally in theupstream-downstream direction.

(3) A design feature for controlling the reservoirrelease is to provide a buttress fill against theupstream face of the dam. This requires the reservoirwater to pass through a succession of filters andcrack stoppers in a manner analogous to the behaviorof the transitions and filters in a zoned embankment

dam. This defensive measure would be effective forflood-control projects where the reservoir pool eleva-tion is low enough that the required height of thebuttress fill is economically feasible, and does notimpair the stability of the dam.

2-4. Refined Dynamic Analyses Methods

a. Need for refinement.When the simplifiedlinear-elastic analysis methods described above for anexisting RCC dam produce tensile stresses in excessof the allowables discussed in paragraph 2-2e, morerefined analyses methods shall be pursued before thedam is judged unsafe. Also, if all practical and eco-nomical adjustments to the design of a new dam havebeen exhausted in the attempt to satisfy the allowa-bles based on simplified linear-elastic methods, themore refined analyses methods may be pursued tobetter evaluate nonlinear structural behavior. Refinedanalyses consist of linear or nonlinear time historyanalyses as discussed in paragraph 2-2d, with someadditional details of the nonlinear analysis providedbelow. The response produced by refined analysesshall be evaluated in accordance with the stipulationsof paragraphs 2-2f and 2-2g.

b. Fracture mechanics.Nonlinear dynamicanalysis is based on fracture mechanics theory whichis presently in the research phase. It is also difficultto determine just what level of structural damage canbe sustained safely by the dam and still consider it tosatisfy the performance requirements. The nonlinearattribute requires this type of dynamic analysis beperformed in a time domain (time history analysis)rather than a frequency domain (response spectrumanalysis), and use a direct integration solution. Theanalysis accounts for: energy dissipation by cracking,strength of cracked concrete, changes in vibrationcharacteristics caused by cracking, changes in damp-ing, and changes in strength due to strain rate andloading history.

c. Nonlinear analysis requirements.Because itis very complex, costly, and requires a considerableamount of judgment to interpret the results, an expertin fracture mechanics and nonlinear analysis tech-niques should be consulted to provide guidance whenpursuing a nonlinear analysis.

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Chapter 3Material Properties of RCC

3-1. Similarities of RCC and ConventionalConcrete

The strength and elastic properties of RCC vary de-pending on the mix components and mix proportionsin much the same manner as that for conventionalmass concrete. Aggregate quality and water-cementratio are the principal factors affecting strength andelastic properties. Properties important to the seismicanalysis of RCC dams include compressive strength,tensile strength, shear strength, modulus of elasticity,Poisson’s ratio, and unit weight. Except for unitweight, all these properties are strain rate sensitive,and the strain rates that occur during major earth-quakes are in the order of 1,000 times greater thanthose used in standard laboratory testing. Guidanceconcerning the determination of RCC material proper-ties is given in EM 1110-2-2006 and ETL 1110-2-343.

3-2. Compressive Strength

The relationship between water-cement ratio andcompressive strength is the same for RCC as forconventional mass concrete. Normally, for durabilityreasons, the RCC mix will be designed to provide aminimum strength of 2,000 psi; however, for seismicreasons higher compressive strengths are oftenrequired to achieve the desired tensile and shearstrength. The compressive strength at seismic strainrates will be 15 to 20 percent greater than that at thequasi-static rates used during laboratory testing (ACICommittee-439 1969); however, compressive strengthis never the governing factor in seismic design.

3-3. Tensile Strength

The tensile strength of RCC shall be based on thedirect tensile strength tests of core samples. For thefinal design of new dams, cores shall be taken fromtest-fill placements made with the proposed designmixes, and placed with the proposed consolidationand joint treatment methods. When an existing damis evaluated for compliance with the requirements ofthis EP, cores shall be taken directly from the struc-ture. Cores should be taken vertically so that testscan be made which reflect weaknesses inherent at lift

joint surfaces in addition to the tests to determine thetensile strength of the parent concrete.

a. Location of critical tensile stress.Criticaltensile stresses are located at the upstream and down-stream faces of the dam. The tensile stress distribu-tion within the dam mass is of interest to helpestablish zone boundaries for superior, higher strengthRCC mixes that may be required to control crackingnear the faces.

(1) Usually the tensile stress in the lift joints inthe direction normal to the joint surface is criticalnear the upstream face of the dam. This is becausethe direction of the principal tensile stress near theupstream face is very nearly normal to the joint sur-face, thus there is little difference between the jointstress and the maximum principal stress in the parentconcrete. Since tensile strength of the lift joint isnotably less than the parent RCC, it will control thedesign near the upstream face.

(2) Near the downstream face, the direction ofthe principal tensile stress is nearly parallel to theface which results in significantly higher principaltensile stresses in the parent concrete compared to thetensile stresses in the lift joints normal to the jointsurface. The ratio of the tensile strength of parentconcrete to the tensile strength of the lift joints variesaccording to several parameters including workabilityof the mix, joint preparation, and maximum sizeaggregate. Thus, it usually becomes necessary toinvestigate both the principal tensile stress and thecomponent tensile stress normal to the lift joints todetermine which is critical near the downstream face.

b. Preliminary design.For preliminary design,the tensile strength of the RCC may be obtained fromFigures 3-1 through 3-6 for the proposed concretecompressive strength (f’c). These figures show boththe tensile strength of the parent material and thetensile strength of the lift joint based on the proposedconsolidation and joint treatment method. Thesefigures were developed from Tables E2 and E3,Appendix E.

c. Tensile strength tests.Splitting tensile testsare easier to perform and provide more consistentresults than direct tensile tests. However, splittingtensile test results tends to overpredict actual tensilestrengths, and should be adjusted by a strength reduc-tion factor to reflect results that would be obtainedfrom direct tensile tests. When splitting tensile tests

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are used as the basis for determining the tensile

Figure 3-1. Tensile strength range, RCC, MSA ≤ 1.5 inches, consistency < 30 seconds vibration, mortarbedding

strength of RCC, the test results shall be reduced by astrength reduction factor of 75 percent as recom-mended in Appendix E.

d. Factors affecting tensile strength.The tensilestrength of RCC, as well as of conventionally placedmass concrete, is dependent on many variablesincluding paste and aggregate strength, aggregate size,loading history, and load deformation rates. Seeparagraph 3-9 concerning strain rate sensitivity anddynamic tensile strength.

(1) RCC differs from conventionally placed massconcrete due to the many horizontal planes of weak-ness (construction joints) created during placement.RCC is placed and compacted in layers ranging from6 to 24 inches with each layer creating a joint withtensile strength less than that of the parent concrete.

The joint strength can be improved by placing a layerof high slump bedding mortar on each lift; however,the resulting joint strength is always somewhat lessthan the parent concrete. The consistency of RCCcan also affect tensile strength with lower strengthvalues for harsh mixes with low paste contents.Refer to Chapter 2 for additional discussion of thesefactors.

(2) Inherent in some RCC mixes are certainanisotropic material properties. In the RCC compac-tion process, the flatter coarse aggregate particles inthese mixes have a tendency to align themselves inthe horizontal direction. When this occurs, thestrength of vertical cores will be less, and the strengthof horizontal cores greater than the average tensilestrength. The variance from average could be as highas 20 percent, although in general these effects will

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Figure 3-2. Tensile strength range, RCC, MSA > 1.5 inches, consistency < 30 seconds vibration, mortarbedding

be small. If the coarse aggregate particle shape indi-cates the possibility of significant anisotropy, bothvertical and horizontal cores obtained from the labo-ratory test placement should be tested.

3-4. Shear Strength

The shear strength along lift joint surfaces is alwaysless than the parent concrete; therefore, final shearstrength determination should be based on tests ofrepresentative samples from the dam or test fill.Both the bond strength and the tangent of the angleof internal friction can be increased by 10 percent toaccount for the apparent higher strengths associatedwith seismic strain rates.

3-5. Modulus of Elasticity

RCC will usually provide a modulus of elasticityequal to, or greater than, that of conventional massconcrete of equal compressive strength. The modulusof RCC in tension is equal to that in compression.The static modulus of elasticity, in the absence oftesting, can be assumed equal to (ACI Committee-2071973):

E 57,000 fc

where E static modulus of elasticity

fc static compressive strength of RCC

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The relationship between strain rate and modulus of

Figure 3-3. Tensile strength range, RCC, MSA ≤ 1.5 inches, consistency > 30 seconds vibration, mortarbedding

elasticity is as follows (Bruhwieler 1990):

E E(Er)0.020

where E static modulus of elasticity

E seismic modulus of elasticity at thequasi static rate

Erhigh seismic strain rate

quasi static rate

For a seismic strain rate equal to 1,000 times thequasi-static rate the seismic modulus of elasticity is1.15 times the static modulus. For long-term load-ings where creep effects are important, the effectivemodulus of elasticity may be only 2/3 the static mod-

ulus of elasticity calculated by the above formula(Dunstan 1978). The modulus of elasticity mayexhibit some anisotropic behavior due to the coarseaggregate particle alignment as discussed inparagraph 3-3d(2); however, the effects on themodulus will be small and can be disregarded whenperforming a dynamic stress analysis.

3-6. Poisson’s Ratio

Poisson’s ratio for RCC is the same as for conven-tional mass concrete. For static loads, values rangebetween 0.17 and 0.22, with 0.20 recommended whentesting has not been performed. Poisson’s ratio is alsostrain rate sensitive, and the static value should bereduced by 30 percent when evaluating stresses dueto seismic loads (Bruhwieler 1990).

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3-7. Tensile Stress/Strain Relationship

Figure 3-4. Tensile strength range, RCC, MSA > 1.5 inches, consistency > 30 seconds vibration, mortarbedding

As mentioned in paragraph 2-2b, concrete cracking,crack propagation, and the energy dissipated in theprocess are complex and nonlinear in nature. For asimplified linear-elastic analysis, a constant modulusof elasticity is required. Thus, a linear stress/strainrelationship is used for the analysis with a tensilemodulus equal to the modulus of elasticity for con-crete in compression.

a. Compression and tension differences.Although a linear relationship is assumed for theanalysis, in actuality the stress/strain relationshipbecomes nonlinear after concrete stresses reachapproximately 60 percent of the peak stress (Raphael1984). In compression this does not cause a problembecause, in general, concrete compressive stresseseven during a major earthquake are quite low with

respect to the peak stress or ultimate capacity. Intension, it is a different matter since tensile stress canapproach and exceed the peak tensile stress capacityof the concrete and in some cases cracking willoccur.

b. Tensile stress/strain curve.The actual non-linear stress/strain relationship for RCC concrete isshown in Figure 3-7. The assumed linear relationshipused for finite element analysis was developed fromthe work done by Raphael (1984). The actual nonlin-ear performance of concrete in tension consists of alinear region from zero stress up to 60 percent of thepeak stress, a nonlinear ascending region from60 percent of peak stress to peak stress (this point onthe curve corresponds to the direct tensile strengthtest value described in paragraph 3-3c), and a nonlin-ear descending region from peak stress back to zero

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stress. The last region is termed the “tensile soften-

Figure 3-5. Tensile strength range, RCC, MSA ≤ 1.5 inches, consistency > 30 seconds vibration, no mortarbedding

ing zone.” In this region, where deformationincreases with decreasing stress, deformation con-trolled stable test procedures are required to capturethe stress/strain behavior (Bruhwieler 1990), whereconventional test procedures will cause the strain tofall off abruptly to zero strain at a point on the curvejust beyond the peak stress point. The area under thetensile softening region of the stress/strain curverepresents additional energy absorbed by the RCCstructure during the crack formation process. Assuch, this region is quite instrumental in dissipatingthe energy imparted to the dam through seismicground motion. The transition from linear to nonlin-ear in the ascending region of the stress/strain curverepresents the development of microcracking withinthe concrete. These microcracks eventually coalesceinto macrocracks as the tensile softening zone isreached.

3-8. Dynamic Tensile Strength (DTS)

The tensile strength of concrete is strain rate sensi-tive. During seismic events strain rates are related tothe fundamental period of vibration of the dam withthe peak stress reached during a quarter cycle ofvibration. The high strain rates associated with damresponse to ground motion produce tensile strengths50 to 80 percent higher than those produced duringdirect tensile strength testing where the strain rate isvery slow. For this reason, the dynamic tensilestrength (DTS) of RCC shall be equivalent to thedirect tensile strength multiplied by a factor of 1.50(Cannon 1991, Raphael 1984). This adjustment fac-tor applies to both the tensile strength of the parentmaterial and to the tensile strength at the lift joints.

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3-9. Allowable Tensile Stresses

Figure 3-6. Tensile strength range, RCC, MSA > 1.5 inches, consistency > 30 seconds vibration, no mortarbedding

When the response to ground motion increasesbeyond the elastic limit, energy is dissipated throughcrack development and crack propagation in accor-dance with the stress/strain relationship shown inFigure 3-7. To account for all nonlinear responseincluding that in the tensile softening zone of thestress/strain curve requires a complex nonlinear anal-ysis. The simpler linear-elastic analysis may be uti-lized in a manner which accounts for response in thelinear region, and the nonlinear pre-peak region.

a. Comparing linear and nonlinear curves.Since a linear-elastic analysis converts strains tostress using a constant modulus of elasticity, thestresses from the analysis will be higher than actualstresses when in the nonlinear pre-peak and post-peakstrain regions. This may be compensated for by

establishing an allowable tensile stress which isgreater than the actual peak tensile stress as shown inFigure 3-7. In this figure, the dashed line representsthe tensile stress/strain relationship assuming linear-elastic behavior as opposed to the actual nonlinearstress/strain relationship which is shown as a heavysolid line. The amount the peak tensile stress isincreased in establishing the allowable stress dependson the extent of tensile cracking that can be tolerated,which in turn is based on the performance require-ments for the design earthquake under consideration.The economics of the design also becomes a factor inthe higher seismic zones. In these zones, a somewhatgreater amount of cracking can be justified economi-cally because there is a point where the cost of pro-ducing RCC mixes with high tensile strengths toresist cracking will exceed the cost of repairing thecracks as long as the cracking is not too extensive.

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b. Key points on stress/strain curve.Several

Figure 3-7. Tensile stress/strain diagram for RCC

points on the stress/strain curve are of interest whenestablishing the allowable tensile stresses that areused in linear-elastic analyses (refer to para-graphs 4-2c and 4-3c). Based onf ′t = actual peaktensile stress (tensile stress that corresponds to thatwhich would be attained by a direct tensile strengthtest), andft = the stress level based on linear-elasticbehavior (refer to the dashed line in Figure 3-7), thefollowing key values offt are of interest:

(1) ft = 0.60 f ′t -- the end of the elastic rangeand the beginning of microcracking.

(2) ft = 0.90 f ′t -- this point was selected becausethe stress/strain dashed line for linear-elastic behavioris just beginning to significantly separate from theactual stress/strain curve. If the tensile stresses for alinear-elastic analysis stay within the stress level for

this point, the response can still be judged as primar-ily linear.

(3) ft = 1.25 f ′t -- the area under the dashed linefor linear-elastic behavior up to this stress level isapproximately equal to the area under the solid linefor the actual stress/strain curve up to the peak tensilestress point (this point is the end of microcrackingand the beginning of macrocracking). Thus, theenergy absorbed in a linear-elastic analysis to thispoint of stress is equal to the actual energy absorbedthrough the microcracking pre-peak region.

(4) ft = 1.33 f ′t -- the strain corresponding to thispoint of stress based on linear-elastic behavior isequal to the strain corresponding to the actual peaktensile stress. This strain point signifies the end ofmicrocracking and the beginning of macrocracking.This point also represents a practical limit for the

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linear-elastic response spectrum analysis described inparagraph 2-2c. Beyond this point in the tensilesoftening zone, the stress/strain relationship based onlinear-elastic behavior diverges so rapidly from theactual stress/strain curve that a linear-elastic analysis

will no longer provide an acceptable approximation ofeither the energy absorbed by the dam-foundationsystem, or the strain deformation of the system.Cracking could be extensive enough to change thedynamic properties of the dam structure.

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Chapter 4Design Earthquakes

4-1. Definition

The term “design earthquake” refers to the specifica-tion of the free field ground motion that would be feltat the dam site due to a particular seismic event thatis used as the basis for earthquake resistant design ofnew RCC dams, or to evaluate the response of exist-ing RCC dams.

4-2. Operating Basis Earthquake (OBE)

The OBE is defined as the earthquake producing thegreatest level of ground motion that is likely to occurat the site during the service life of the dam. Theservice life shall be taken as 100 years for both newdams and existing dams. The seismic risk or adverseconsequences of failure of an existing dam is notreduced as long as the dam is in operation; therefore,the “remaining service life” of an existing dam shallnot be substituted for the 100-year service life speci-fied above. The OBE is determined using probab-ilistic methods and, as such, is defined as the earth-quake with a 50 percent chance of exceedance in theservice life of the dam.

a. General performance requirements.Allstructural, mechanical, and control equipment used toregulate the reservoir shall be capable of remainingfully operational during and after an OBE. NewRCC dams located in low seismic regions shall bedesigned to prevent the initiation of cracking in theconcrete structure. Tensile cracking in new RCCdams located in high seismic regions and in existingdams in all seismic regions is allowed; however, itshall be limited to only “minor cracking” that requireslittle or no repair.

b. Structural criteria. The following generalstructural criteria shall be the basis for satisfying theconcrete cracking performance requirements statedabove.

(1) Initiation of cracking is prevented when thetensile stresses are less than 0.60f ′t as shown inFigure 3-7.

(2) The level of cracking is considered to be“minor cracking” when the tensile stresses are lessthan 1.25f ′t as shown in Figure 3-7.

c. Allowable tensile stress.The allowable ten-sile stressesft (allowable) for the OBE are establishedbelow. The formulae apply to the calculation of bothallowable tensile stress of the parent material andallowable tensile stress of the lift joints. DTS =Dynamic Tensile Strength, andf ′t = direct tensilestrength.

(1) Existing dams:

ft (allowable) = 1.25 × DTS = 1.875 ×f ′t

(2) New dams in seismic zones 0, 1, 2A,and 2B:

ft (allowable) = 0.60 × DTS = 0.90 ×f ′t

(3) New dams in seismic zones 3 and 4:

ft (allowable) = 0.90 × DTS = 1.35 ×f ′t

d. Damping. Studies on dams under severeground motion which cause stresses in the upperreaches of the elastic range indicate a dampenedresponse which corresponds to a damping factor ofabout 5 percent of critical. On this basis the OBEshall be analyzed using a damping ratio equal to5.0 percent of critical damping for the concrete damstructure only. This factor must be modified as out-lined in paragraph 7-3 to account for foundationdamping.

4-3. Maximum Credible Earthquake (MCE)

The MCE is defined as the largest possible earthqu-ake that could reasonably occur along the recognizedfaults or within a particular seismic source. Oftenseveral fault sources must be investigated to deter-mine which will produce the critical site groundmotion. By definition the MCE has a very low prob-ability of occurence. Ground motion associated withthe MCE is established using the deterministicapproach.

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a. General performance requirements.Bothnew RCC dams and existing dams shall be capable ofsurviving the MCE without a failure of a type thatwould result in the loss of life or significant damageto downstream property caused by an uncontrolledrelease of the reservoir pool. Nonlinear behaviorwith associated damage is permissible, but the postearthquake damaged condition of the dam shall allowfor controlled lowering of the pool to facilitate repair.

b. Structural criteria. The upper limit of linearelastic analysis is considered to be that point on thestraight stress/strain line corresponding to a linearstress level of 1.33f ′t (see Figure 4-7). When tensilestrains exceed the strain associated with this linearstress limit, macrocracking occurs and the RCC willbe subject to some degree of structural damage. Asthe strain level increases well into the tensile soften-ing zone, response becomes markedly nonlinear and itis clear that a linear-elastic analysis no longer approx-imates the response. Although crack damage

increases in this zone, performance requirements maystill be satisfied. Thus, the structural criteria for theMCE, when using linear-elastic analysis, are set bylimitations of the method of analysis rather than oncriteria that relate to an acceptable level of structuralconcrete damage.

c. Allowable tensile stresses.The allowabletensile stressft (allowable) for the MCE is establishedbelow. DTS = Dynamic Tensile Strength, andf ′t =the direct tensile strength.

ft (allowable) = 1.33 × DTS = 2.000 ×f ′t

d. Damping. The linear-elastic analysis for theMCE shall utilize a damping ratio equal to 7.0 per-cent of critical damping for the concrete dam struc-ture only. The increase in the damping ratio from5 percent for the OBE to 7 percent for the MCEhelps account for some additional nonlinear behaviorwhile using a linear-elastic approach.

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Chapter 5Design Response Spectra andAcceleration Time Histories

5-1. Defining the Design Earthquake

In a linear-elastic response spectrum analysis,response spectra define the free field ground motionfor the design earthquake. A response spectrum givesthe maximum damped response (expressed as dis-placement, velocity, or acceleration) of all possiblelinear single degree-of-freedom systems using thenatural frequency (or period) to describe the system.Viscous damping expressed as a percentage of criticaldamping is used to develop a response spectra. Adesign earthquake is often defined by a set ofresponse spectra for various damping ratios. Theresponse spectra produced by recorded earthquakeevents are characterized by a jagged shape made upof peaks and valleys of varying magnitude; however,design response spectra are smoothed so that they arenot frequency sensitive.

5-2. Developing Design Response Spectra

a. Deterministic and probabilistic approaches.Design response spectra are developed by using eithera “deterministic approach” or a “probabilisticapproach.” The probabilistic approach is based onprobabilistic seismic hazard analysis methodologywhich in essence uses the same elements as the deter-ministic approach, but adds an assessment of thelikelihood that ground motion will occur during aspecified time period.

b. Procedures.There are two basic proceduresfor developing design response spectra using eitherthe deterministic or probabilistic approach. They are:(1) anchoring the spectral shape to the peak groundacceleration; and (2) estimating the spectrum directly.Although procedure (1) is more often used, the use ofprocedure (2) is increasing, and for some situations ispreferred because it incorporates factors besides justthe local site conditions.

c. Obtaining design response spectra.It isbeyond the scope of this EP to present the detailedprocedures for developing design response spectra, orfor forecasting PGA’s for design earthquakes. Referto ETL 1110-2-301, ETL 1110-2-303, and “Tentative

Provisions for the Development of Seismic Regula-tions for Buildings” (Applied Technology Council1984) for further information on developing designresponse spectra to define the design earthquakes.

5-3. Developing Acceleration TimeHistories

a. Matching design response spectrum.Themore refined methods of analysis discussed in para-graph 2-2d are of the time-history type. Time histo-ries usually express the ground motion as a record ofacceleration with respect to time. Acceleration timehistories should be developed so their response spec-trum is consistent with the previously established site-specific design response spectrum described inparagraph 5-5c. The time histories should also have astrong motion duration appropriate to the particulardesign earthquake.

b. Procedures.There are two basic proceduresfor developing acceleration time histories: (1) select-ing a suite of past recorded earthquake groundmotions, and (2) synthetically developing or modify-ing one or more ground motions.

(1) When selecting a suite of time-historyrecords for the first procedure, the intent is to coverthe valleys of the spectrum produced by one record,which fall significantly below the site-specific designresponse spectrum, with better matching spectralvalues at these frequencies as produced by the otherrecords in the suite. It is also necessary that thespectra produced by the suite of records not signifi-cantly exceed the site-specific design response spec-trum. Primary advantage of this procedure is that thestructure is analyzed by real, natural ground motionsthat are representative of what the structure couldexperience.

(2) When using the second procedure, it is possi-ble to either completely synthesize an accelerogram,or modify an actual recorded earthquake accelero-gram so that the response spectrum of the resultantaccelerogram closely fits or matches the site-specificdesign response spectrum. The primary advantage ofthis procedure is that a good fit to the designresponse spectrum can be achieved with a singleaccelerogram, thus only a single dynamic analysis isrequired.

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5-4. Dynamic Analysis by ModalSuperposition

a. Frequencies and mode shapes.The linear-elastic response spectrum method utilizes modalsuperposition dynamic analysis to determine the struc-tural response.

b. Time-history analysis.Once the modes arederived, the response of the complex multiple degree-of-freedom system is reduced to the solution of thesimple, single basic equation of motion for a singledegree-of-freedom (SDOF) system. For time-historyanalysis, the response is easily obtained using step-by-step integration of the equation of motion for theSDOF system for each significant mode based on thefrequency (eigenvalue) of the mode. In essence theresponse contribution of each mode is determined fora series of time steps using a prescribed time-stepinterval, and the response at each time step is simplythe superposition, or addition, of characteristic modeshapes adjusted by coefficients obtained from theintegration procedure. Normally, only a few modeshapes are found to contribute significantly to theresponse, so that the modal superposition methodproduces a precise response with minimum computa-tional effort.

c. Response spectrum analysis.In a responsespectrum analysis, the step-by-step integration part ofthe dynamic analysis, described above for time-history analysis, is performed in the process of devel-oping the response spectrum. The response spectrummay be envisioned as a display of the results of thispart of the modal analysis, and it is presented in theform of “maximum” response versus frequency (orperiod). In the response spectrum modal analysis,eigenvalues, eigenvectors, and modal participationfactors are computed and used in the analysis proce-dure just as they are in a time-history modal analysis.Precise “maximum” modal responses are easily calcu-lated from a simple equation that relates these param-eters and the appropriate spectral value thatcorresponds to the modal frequency.

d. Combining modal responses.The final stepin a response spectrum analysis consists of correctsuperpositioning of the “maximum” modal responses;however, there is not a unique solution to this finalstep in the response spectrum method. This isbecause the exact mode contributions at the criticalpoint in time when the response peaks are not avail-able from a response spectrum representation of a

particular ground motion. One advantage of asmooth design response spectrum is that it is a statis-tical representation, or an envelope, of the manypossible ground motions that could occur at the siterather than only a single ground motion. The super-position of the maximum modal responses is accom-plished by use of one of several statistical methodsdescribed in Chapter 7.

5-5. Types of Design Response Spectra

a. Probability level. Design response spectraare usually based statistically either on the mean,median (50th percentile probability level), or themedian plus one standard deviation (84th percentileprobability level), of the ground motion parametersfor the records chosen. Design response spectra usedfor design of new RCC dams or for evaluation of thesafety and serviceability of existing dams shall bebased on the mean level of the ground motionparameters.

b. Type of spectrum required.Either a “site-specific” or a “standard” design response spectra shallbe used to describe the design earthquakes. The typerequired shall be based on the seismic zone, the prox-imity of the seismic source, and the maximum heightof the dam.

c. Site-specific design response spectra.Thesite-specific design response spectra should bedeveloped based on earthquake source conditions,propagation path properties, and local foundationcharacteristics associated with the specific site. Thistype of design spectra may be established by anchor-ing a selected response spectral shape for the site tothe estimated peak ground acceleration, or by estimat-ing the design spectra directly using response spectralattenuation relationships, performing statistical analy-sis of strong-motion records, or applying theoretical(numerical) ground motion modeling. In the require-ments that follow, a site is classified as a “high seis-mic risk site” when it is located within 20 kilometersof an active fault or area source in the western UnitedStates (WUS), or within a tectonic province in theeastern United States (EUS) where the source orprovince has a maximum local magnitude of 6.0 orgreater. The boundary between the WUS and theEUS is defined as the eastern boundary of the RockyMountains. Site-specific design response spectra arerequired for:

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(1) Dams greater than 100 feet in height locatedat a site classified as a “high seismic risk site.”

(2) Dams greater than 100 feet in height locatedin Seismic Zone 2B, 3, or 4 even though the site isnot classified as a “high seismic risk site.”

(3) Dams not greater than 100 feet in heightlocated in Seismic Zone 2B, 3, or 4 when the site isclassified as a “high seismic risk site.”

d. Standard design response spectra.Standarddesign response spectra are based on fixed spectralshapes established for very general site classificationssuch as rock or soil site. They ignore the effects ofearthquake magnitude and distance, and the specificfoundation characteristics at the site. The standarddesign spectra are usually “anchored” to the estimatedpeak ground acceleration (PGA) established for thedesign earthquake. The fixed spectral shape is usu-ally presented such that it is normalized to a 1.0 gvalue of maximum ground acceleration. This normal-ized value can be easily checked by observing thespectral acceleration value from the spectrum plot forfrequencies above about 50 cps where the responseand the maximum ground acceleration coincide.Standard design response spectra are adapted to theseverity of ground motion associated with the OBE orMCE by using the PGA as a scaling factor. Thestandard design response spectra can be used for:

(1) Dams greater than 100 feet in height locatedin Seismic Zone 0, 1, or 2A when the site is notclassified as a “high seismic risk site.”

(2) Dams not greater than 100 feet in heightlocated in Seismic Zone 0, 1, or 2A.

(3) Dams not greater than 100 feet in heightlocated in Seismic Zone 2B, 3, or 4 when the site isnot classified as a “high seismic risk site.”

e. Required design spectrum.When it isacceptable to use a standard design response spectrumto define the design earthquakes, the standard designspectrum shown in Figure 5-2 shall be used (AppliedTechnology Council 1984). This spectrum is consid-ered conservative but reasonable for essential struc-tures such as dams. It is fully described by only five

control points on a tripartite plot. Table 5-1 presentsthe spectrum in equation format so it is easily devel-oped for any damping value. The standard designspectrum shown in Figure 5-2 and defined in equationformat in Table 5-1 is normalized to 1.0 g PGA. Thestandard spectrum shall be anchored to the PGA forthe OBE and the MCE by using the appropriate scal-ing factors provided in Table 5-2. The correct scal-ing factors are selected based on the seismic zonelocation of the site using the seismic zone map shownin Figure 5-1.

5-6. Horizontal and Vertical DesignResponse Spectra

a. Site-specific design response spectra.Whensite-specific design response spectra are required inaccordance with paragraph 5-5c, two independentdesign response spectra shall be developed, one todefine the horizontal component of ground motion,and the second to define the vertical component. Thevertical component of ground motion usually containsmuch higher frequency content than the horizontalcomponent, therefore the spectral shape is quite dif-ferent than that of the horizontal component. ThePGA associated with the vertical component will alsobe different than the PGA of the horizontal compo-nent. Both values of PGA are dependent on the dis-tance from the source, but for short distances, thePGA of the vertical component may actually exceedthe PGA of the horizontal component.

b. Standard design response spectra.When itis acceptable to use standard design response spectrato define the design earthquakes, the horizontal com-ponent of ground motion shall be defined by anchor-ing the standard design response spectra for theappropriate damping factor developed from Table 5-1with the scaling factor provided in Table 5-2. Thevertical component of ground motion shall utilize thesame standard design response spectrum used for thehorizontal component, but it shall be scaled using theappropriate ratio of the PGA for the vertical compo-nent to the PGA for the horizontal component asprovided in Figure 5-3. This ratio is based on thesite to source distance (R) and the fundamental natu-ral period of vibration of the structure.

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Figure 5-1. Seismic zone map of the United States. (Uniform Building Code, 1988 Edition)

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Figure 5-2. Standard design response spectra for horizontal component of ground motion - normalized toPGA = 1.0 g. (Applied Technology Council ATC-3-06 Tentative Provisions, 1984)

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Table 5-2Peak Ground Accelerations (PGA’s) for Use in Scaling the Standard Design ResponseSpectra

PGA

Seismic ZoneOperating BasisEarthquake (OBE)

Maximum CredibleEarthquake (MCE)

0 0.030 0.130

1 0.050 0.210

2A 0.095 0.360

2B 0.115 0.430

3 0.210 0.550

4 0.270 0.610

NOTES:

1. Refer to Figure 5-1 for the seismic zone maps.2. PGA’s are expressed as the decimal ratio of the acceleration due to gravity (g).3. PGA’s are obtained from curves of “Annual Risk of Exceedance vs. PGA” in Figure C1-7 of ATC-3 Tentative Provisions,

April 1984.4. The PGA for the OBE is based on a 50 percent chance of exceedance in 100 years.5. The MCE is considered to be the event with a 5,000-year return period (annual risk of exceedance = 0.0002

chance/year).

Figure 5-3. Ratio of PGA for the horizontal component to the PGA for the vertical component as a functionof source to site distance (R) and the fundamental period of vibration of the structure

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Chapter 6Earthquake Load Cases

6-1. Load Combinations

The cyclic and oscillatory nature of vibratoryresponse can cause critical tensile stresses to occur ineither the upstream or the downstream face of thedam. Therefore, the earthquake load cases mustconsider combinations of the design earthquake load-ing with other loads which lead to critical tension inboth the upstream and downstream faces. Usuallytwo or more OBE load cases and two or more MCEload cases must be evaluated. The discussion ofearthquake load cases that follows refers to seismiccriteria regarding ground shaking and foundation faultdisplacement as discussed in paragraphs 2-2 and 2-3,respectively, and not stability criteria described inparagraph 2-1. Load case requirements for stabilityare covered in EM 1110-2-2200.

6-2. Dynamic Loads To Be Considered

The design earthquake imposes several types of dy-namic loads on the dam. The greatest dynamic loadis the inertia load caused by the response of the con-crete mass to ground motion accelerations. Next isthe hydrodynamic load created by a high reservoirand tailwater condition. Hydrodynamic forces areimposed on the dam due to motions of the dam react-ing with the surrounding water, and motions of thereservoir bottom. Finally, backfill or silt depositsagainst the faces of the dam will interact with thestructural mass of the dam in a manner similar to thehydrodynamic load.

6-3. Static Loads To Be Considered

The effects on the dam structure due to static loads,as discussed below, are determined by conventionalstatic analysis methods. The results of the dynamicand static analyses are combined by superposition todetermine the total stresses for the earthquake loadcase.

a. Reservoir and tailwater loads.Load casesshall be included to cover both the highest and thelowest reservoir pool elevations that can be judged on

a statistical basis to have a reasonable chance ofoccurrence at the time of the design earthquake.

(1) Flood frequency data from project flood flowand flood routing studies provide a basis for estab-lishing reasonable high pool elevations. Each dammust be evaluated based on its own set of uniqueconditions.

(2) The conservation pool elevation for the proj-ect shall be used for earthquake load cases involvinglow pool conditions. If there is no established con-servation pool, use the lowest average pool elevationthat can best be judged to exist for a 30-day period ina normal yearly flow cycle.

(3) Where tailwater is applicable for an earth-quake load case, the elevation shall be selected whichincreases the response while being consistent with thereservoir conditions.

b. Backfill load. Earth or rock fill placedagainst either face of the dam has both a static anddynamic load effect during an earthquake. Theseloads shall be included in all earthquake load cases.Static loading shall be based on at-rest pressures.Dynamic loading may be approximated by theMononobe and Okabe method utilizing the inertiaforce acting on the Coulomb sliding wedge in theappropriate direction as discussed in EM 1110-2-2502. For finite element analyses the dynamic effectmay be approximated by added mass based on theCoulomb sliding wedge.

c. Siltation load. During the life of the dam,silt may build up against the upstream face to a depthwhich may cause a moderate increase in the tensilestresses in load cases where tension in the upstreamface is critical. For these load cases, siltation loadingshall be considered based on the full depth expectedduring the life of the dam. In load cases where ten-sion in the downstream face is critical, the siltationload will decrease the tensile stresses. For these loadcases a zero depth of silt shall be assumed. Whensilt is included, both static and dynamic loadingeffects should be incorporated using the same meth-ods as discussed for backfill loads.

d. Gravity loads. Gravity loads shall includethe weight of the RCC, weight of backfill or silt onbattered faces of the dam, and weight of equipment ifsignificant.

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6-4. Static Loads Not To Be Considered

There are several types of loads where the magnitudeof the load and the load pattern that would exist atthe time of the design earthquake event cannot bedefined on a logical basis or to any degree of accur-acy. However, based on the general nature and rangeof magnitude normally associated with loads of thistype, and in comparing these loads with the dynamicand static loads already discussed, these loads nor-mally do not contribute significantly to the results ofthe analyses for earthquake load cases. However, thedesigner should at least make a cursory evaluation ofthese loads to be sure that no unusual site conditionsexist that would warrant including one or more ofthem in the earthquake load cases. For this reason, abrief discussion of these loads is included.

a. Pore pressure.When evaluating dam stabil-ity using the seismic coefficient method described inparagraph 2-1, uplift is considered to act over the

entire interface area. Under the MCE, any crackingin the concrete would only extend just beyond themicrocracking level. These fine cracks are open andsubject to buildup of internal water pressure for ashort period of time due to the oscillatory nature ofthe dynamic response. Therefore, uplift or internalwater pressure within concrete cracks would be quitesmall and may be ignored in the dynamic analysisphase of design.

b. Temperature stresses.Except under extremeclimatic conditions, temperature stresses need not beincluded as part of the earthquake load cases.

c. Wind load. Wind load on an RCC dam is sosmall it can be considered insignificant.

d. Ice load. Ice loading need not be included aspart of an earthquake load case except for unusualclimatic conditions which would cause a great depthof ice to exist over an extended period of time.

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Chapter 7Factors Significantly AffectingDynamic Response

7-1. Evaluation Procedure and Objectives

There are many important factors in a dynamic stressanalysis that can greatly affect the response of a dam.The influence which the various material and strengthparameters and loads have on the final results mustbe evaluated. This can be done by executing themodel using a typical dam cross-section and typicalmaterial properties, then modifying the loads andparameters one-by-one to give an indication of theinfluence each factor has on the dynamic response.Once the important factors have been identified, thedesign effort should concentrate on the more criticalfactors that form the input to the dynamic analysis.Following is a discussion of the impact some of theparameters have on the response of a dam.

7-2. Design Response Spectra

a. Spectral shape.Both the shape of the spec-trum and the PGA used to anchor the spectrum affectthe dam response and should be established carefully.The dynamic response in a linear-elastic analysis isdirectly proportional to the PGA, but minor changesin the shape of the spectra may not result in propor-tional changes in the response.

b. Comparison of standard spectra.For com-parison purposes, three widely accepted standarddesign response spectra will be considered, eachrepresenting the same site conditions. The designspectra are: (1) Applied Technology Council spec-trum for rock of any characteristic whether shalelikeor crystalline in nature (ATC 1984), (2) H. B. Seedspectrum for rock based on 28 records (Seed 1974),and (3) Newmark-Hall spectrum using recommendedvalues for maximum ground velocity and displace-ment for competent crystalline rock (Newmark andHall 1987). Figure 7-1 shows all three spectra nor-malized to 1.0 g PGA for the same rock foundationsite conditions. The Newmark-Hall spectrum is basedon the median or 50th percentile cumulative probabil-ity, where the other two spectra are based on themean of the records used in their development. Thisdifference in probability level is reflected in the spec-tral shape. The primary cause for the difference in

shape of these three spectra can be attributed to theassumptions and techniques used in smoothing thejagged spectra produced from the statistical combina-tion of real earthquake records.

c. Spectral accelerations.Referring toFigure 7-1, the range of interest of natural periodwould be for periods of less than 1.0 second. Thisrange would cover the mode shapes that producesignificant response. In this range the spectral accel-eration values for a given period vary between spectraup to as much as 65 percent. The ATC spectrumenvelopes the other two design spectra, and is rec-ommended for use as the standard design responsespectrum. In linear-elastic response spectrum analy-ses, dynamic response of a particular system eval-uated by two different response spectra is directlyproportional to the spectral ordinates taken from thetwo spectra at the natural period of the system. Thusthe shape of the design response spectrum greatlyinfluences the results of the dynamic analysis.

7-3. Dam-Foundation Interaction, DampingEffect

a. Properties of the foundation.The two prop-erties of the foundation rock that have a significantinfluence on the dynamic response are the dampingratio and the deformation modulus. The dampingcharacteristics of the foundation contribute signifi-cantly to the damping of the combined dam-foundation system and must be considered in theanalysis. When the foundation deformation modulusis low, the damping ratio of the combined system isconsiderably higher than the damping ratio of theRCC dam structure alone.

b. Effective damping ratio.There are twosources of damping for the foundation rock:(1) material (hysteretic) and (2) radiation. In contrastto this type of damping is the viscous type of damp-ing (directly proportional to velocity) used in pro-ducing design response spectra. Therefore, it isnecessary to develop an effective viscous dampingratio to represent the combined dam-foundation sys-tem in a response spectrum analysis. This isaccomplished by using the curves provided in Fig-ure D-6 of Appendix D, and the following equation isfor an empty reservoir condition which allows theeffects of foundation damping to be isolated. Thismethod, developed by A. K. Chopra, is based on the

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Figure 7-1. Comparison of design response spectra for rock foundations

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fundamental mode of vibration, and has been shownto be reasonably close for the significant highervibration modes (Fenves and Chopra 1986). In Fig-ure D-6, damping for the foundation rock is expres-sed by the constant hysteretic damping factor.

ξ11

(Rf)3ξ1 ξf

where

ξ1 = the effective viscous damping ratio for theempty reservoir condition

ξ1 = the viscous damping ratio for the RCC damstructure only

ξ1 = 5.0 percent for the OBEξ1 = 7.0 percent for the MCE

Rf = ratio of the fundamental period of the dam on arigid foundation to the fundamental period ofthe dam on a foundation with a deformationmodulus =Ef

ξf = added damping ratio due to dam-foundationrock interaction taken from Figure D-6

c. Effect of damping on response.To determinethe effect that the damping ratio has on the responseof a dam, the fundamental frequency of the compositefinite element dam-foundation model must be deter-mined. It is noted that for the response spectrummethod, the effects of damping are contained only inthe response spectrum itself. Thus, the ratio of theresponse of a dam/foundation system responding atone damping factor to the same system responding ata second damping factor is equal to the ratio of thespectral ordinates taken from the two spectra eval-uated at the fundamental frequency of the system.

d. Conclusion. The damping characteristics ofthe foundation can have a great influence on thedynamic response. This indicates the need to care-fully determine the value of the constant hystereticdamping factor for the foundation rock. This can bedetermined from experimental tests of appropriaterock samples subject to harmonically varying stressand strain. From such tests, the inelastic energy lostand the strain energy stored per cycle are determinedand the hysteretic damping factor is calculated.

7-4. Dam-Foundation Interaction, Founda-tion Modulus Effect

a. Modulus of deformation.The flexibility ofthe jointed rock foundation is characterized by themodulus of deformation which represents the relation-ship between applied load and the resulting elasticplus inelastic deformation. It is best determined byin-situ testing, but may be estimated from the elasticmodulus of the rock by applying an appropriatereduction factor. In a linear-elastic analysis, themodulus of deformation is synonymous with Young’smodulus of elasticity (Ef).

b. Dynamic characteristics affected.The elasticmodulus of the foundation influences the responsebecause it directly affects the following dynamiccharacteristics of the dam-foundation system:

(1) Modal frequencies. As the modulus of defor-mation decreases, the modal frequencies of the com-posite dam/foundation system also decrease.

(2) Mode shapes. As the modulus of deforma-tion decreases, the mode shapes are affected byincreased rigid body translations and rotation of thedam on the elastic foundation.

(3) Effective damping ratio. As the modulus ofdeformation decreases, the effective damping ratio ofthe dam/foundation system increases.

c. Effect of foundatio