Existing Gravity Dam Stability Anaysis

8/13/2019 Existing Gravity Dam Stability Anaysis

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Hosted byU.S. Army Corps of Engineers

Modernization and Optimizationof Existing Dams and Reservoirs

27th Annual USSD ConferencePhiladelphia, Pennsylvania, March 5-9, 2007


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On the CoverThe Corps of Engineers Beltzville Lake in East-Central Pennsylvania. In this south-facing photo, from the bottomto the top, features include the project office, the emergency spillway, the 4,560-foot long embankment, the intaketower, and a series of ridges of the Appalachian front. Beltzville Lake is on Pohopoco Creek, which drains into theLehigh River. The Lehigh Rivers water gap through Blue Mountain can be seen in the background of the photo.(Photo by Anthony S. Bley.)

The information contained in this report regarding commercial projects or firms may not be used for advertising or promotional purposes and may not be construed as an endorsement of any product or

from by the United States Society on Dams. USSD accepts no responsibility for the statements madeor the opinions expressed in this publication.

Copyright 2007 U.S. Society on DamsPrinted in the United States of America

Library of Congress Control Number: 2007921375ISBN 978-1-884575-40-2

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Providing public awareness of the role of dams in the management of the nation's water resources;

Enhancing practices to meet current and future challenges on dams; and

Representing the United States as an active member of the International Commission onLarge Dams (ICOLD).


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Existing Gravity Dam Stability Analysis 341

CURRENT STATE-OF-THE-PRACTICE FOR EXISTING GRAVITY DAMSTABILITY ANALYSIS

Robert A. Kline, Jr., PE 1 Boyd Howard, PE 2

Steven M. Davidheiser, EIT 3

ABSTRACT

For over 150 years, engineers have been wrestling with a proper analytical understandingof the structural stability of concrete dams on rock foundations. During this period, boththe analytical methods and engineers appreciation of various factors that affect structuralstability have evolved. A concurrent evolution has occurred in the application of safetyfactors that address uncertainties in structural loadings, material strengths, constructionquality, and analysis methods.

Within the past five years, the Federal Energy Regulatory Commission (FERC) and the

U.S. Army Corps of Engineers (Corps) have again formally revised their gravity damstability requirements. For almost the past ten years, the U.S. Bureau of Reclamation(Reclamation) and more recently the Corps have adopted a risk-based approach, wherethe site specific risks of each dam are evaluated. Establishing analysis and the remedialdesign criteria for existing dams is not always straightforward since each facility hasvarying degrees of available information concerning its original construction, foundationconditions, and performance history, especially during notable floods or seismic events.Furthermore, interpretation of the available facility information and published guidancemay differ among engineers.

This paper summarizes the evolution of gravity dam stability analyses and safety factors

used by engineers in the United States over the past 150 years with an emphasis oncurrent practices adopted by key federal agencies including the Corps, FERC, andReclamation.

HISTORIC DESIGN AND CONSTRUCTION PRACTICES

When considering the stability of existing dams, especially those constructed prior to theadvent of modern extreme flood and earthquake estimation techniques in the 1970s, it ishighly beneficial to have an awareness of the typical design and construction practices in

place at the time an existing dam was built. This is particularly true when few specificrecord documents are available. Such awareness aids the engineer in better pinpointing

likely deficiencies and in developing sound remedial solutions.

1 Senior Associate, Dams and Hydraulics Section; Gannett Fleming, Inc.; PO Box 67100, Harrisburg,Pennsylvania 171062 Project Manager, Dams and Hydraulics Section; Gannett Fleming, Inc.; PO Box 67100, Harrisburg,Pennsylvania 171063 Project Engineer; Lahkani & Jordan Engineers, P.C.; GF Field Office, Harrisburg, Pennsylvania 17106


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342 Modernization and Optimization of Existing Dams and Reservoirs

Unfortunately, great time and effort can be expended in researching historic practicessince no single publication presently exists that compiles all the available information. Inthe following text, some of the more noteworthy practices are presented, which willhopefully prove to be of value to the reader. It should be understood that even though

published guidance existed in the past, a particular designer may not have adopted it for

any number of reasons. Inexperience in dam design, lack of current knowledge of thefield, or disagreement with such practices contributed to past (and present)inconsistencies. Page limitations do not allow this paper to be exhaustive on this subject

but only serve as a general guide.

Design Practice Prior to 1900

The theories and design practices developed by French engineers, Sazilly and Delocreand British scholar, Rankine between the 1850s and 1880s established three fundamentalrequirements for masonry (gravity) dams: 1) compressive stresses must not exceed setlimits, 2) tensile stresses should be avoided by using the middle third rule and 3) the

structure must resist horizontal sliding. This earlier work by the French and Britishinfluenced the work of Edward Wegmann, who was involved with the design of NewYork Citys, New Croton Dam, and who first published The Design and Construction of

Dams in 1888 and subsequent revisions and updates in seven more editions, the last being published in 1927. This document was the primer for gravity dam design in the UnitedStates over a span of more than 40 years.

One significant goal of each engineer who built on the original work of Sazilly (1853)was to determine a means to reduce the minimum profile area needed by a masonry damto safely withstand the reservoir empty and reservoir full loading cases in an effort toachieve greater economy. This reduction was accomplished by 1) increasing the

maximum allowable compressive stress from Delocres range of 86-114 psi toWegmanns range of 114-208 psi, 2) abandoning Sazillys equal resistance rule by usinghigher stress limits for the upstream face in comparison to the downstream face asopposed to equal limits for both faces, and 3) increasing the unit weight of masonryfrom 125 pcf to a less conservative but likely more realistic value of 146 pcf.

Furthermore, all the profiles produced by Wegmanns predecessors had a stepped, polygonal, or curvilinear shape for both the upstream and downstream faces. Wegmannargued that for dams less than 200 feet in height, a simple right triangle with its verticalside facing upstream was much more practical to construct. To combat shock fromfloating debris and wave action at the crest, he allowed for a vertically-sided crest (orchimney section) with a width ranging between 5 to 20 feet depending upon accessneeds. This practical profile, as Wegmann deemed it, has served as the basic profileused by U.S. engineers for over the past 100 years. For a 50-meter-high dam,Wegmanns practical profile reduced the minimum area by 16% and 11% in comparisonwith Delocres (1861) and Rankines (1881) profiles, respectively.


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By the end of the 19 th century, much was gained in the understanding of gravity damdesign. At the same time, engineers were also aware that rigid bodies and linear stressdistribution, although the basis for the classical analysis method was not exact, albeitstill reasonable and that a short, high dam behaved differently than a long, low one,leading to the development in 1929 of the trial-load method.

Construction Practice Prior to 1900

The last fifty years of the 19 th century also witnessed a dramatic evolution in thematerials and methods used to construct gravity dams. Until the 1860s, gravity damswhere mainly constructed of cut stone masonry (Ashlar) bonded by lime mortar or a lesscostly alternative involving a rubble masonry core with cut stone masonry and mortarfacades. By the 1870s, lime was being replaced by cement mortar mixed to a ratio of 1:2to 1:3 cement:sand and as early as 1900 cut stone was being replaced by pre-cast concrete

blocks. Care was exercised to avoid creating horizontal courses of cut stone or stonerubble that would create horizontal weak planes that are more susceptible to sliding. Due

to a scarcity of suitable nearby rubble stone, Crystal Springs Dam (formerly known asSan Mateo Dam) near San Francisco, California became the first use of mass concrete inthe U.S. Completed in 1888, this dam withstood the infamous 1906 San Franciscoearthquake and is still in service today.

From the 1860s to the 1920s, a hybrid material referred to as cyclopean masonry was invogue. Cyclopean masonry consists of large plum stones embedded in concrete mortarto form a homogeneous monolithic matrix of stone and concrete mortar. During the spanof this 70 year period, the trend moved toward reducing the volumetric percentage of

plum stones from about 50 to 10 percent, with the smaller percentage involvingapplication of plum stones only at the concretes horizontal lift joints to improve shear

resistance.During this era, the typical concrete mix was a ratio of 6:3:1 to 4:2:1 stone:sand:cementwith an intended ultimate compressive strength of 2,600 to 3,300 psi, respectively. Theultimate strength of stone masonry and rubble was typically assumed to be 1,700 to2,100 psi. Despite the relatively slow and small material production, delivery and

placement rates compared to todays standards, the final in-place strength of the stonemasonry and mortar, cyclopean masonry, or mass concrete for many dams of this era has

been proved by modern sampling and laboratory testing to be of reasonably uniform andadequate strength.

Standard practice was to take special care in ensuring proper bonding of the structure tothe foundation rock by washing the foundation with pressurized water, isolating andcapping springs, hand cleaning and backfilling any surface fissures with concrete or groutand placing a grout or mortar bedding on the foundation rock in advance of the masonry.

A listing of the more noteworthy gravity dams constructed between the 16 th and 19 th centuries is provided in Table 1. Of interest is the apparent confidence engineers placed


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in the advent of mathematical design methods with the trend toward ever increasingstructural heights in wider stream valleys without the added benefit of arch action.

Table 1. Gravity Dams Over 100 Feet High Constructed Prior to 1920 [Wegmann]

Dam LocationDate

ofConstructio

n

HeightFt

CrestWidth

ft

BaseWidth

ft

Base/Ht

Ratio

CrestLength

ftPlan

Alicante Spain 1579-1594 135 67.25 111.0 0.82 190 CurvedPuentes Spain 1785-1791 164 35.73 145.0 0.88 925 PolygonalFurens France 1862-1866 183 9.9 161.0 0.88 328 CurvedHabra Algeria 1865-1873 125 14.1 95.0 0.76 1,476 StraightSan Mateo U.S. 1887-1888 170 20.0 176.0 1.04 700 CurvedVyrnwy England 1882-1889 146 20.0 117.8 0.81 1,350 Straight

New Croton U.S. 1892-1907 297 22.0 206.0 0.69 2,168 StraightWachusett U.S. 1900-1906 228 25.8 187.0 0.82 1,476 StraightKensico U.S. 1910-1917 307 28.0 235.0 0.77 1,843 Straight

CURRENT PRACTICE

Jumping ahead from the initial origins of gravity dam design practices in the U.S. to the present day practice of analyzing existing dams, it is important to note that the threefundamental requirements of preventing overturning (moment equilibrium) and slidingand satisfying internal stress limits remain the main focus. However, differences instability criteria persist among the Reclamation, FERC, and Corps. The following is a

brief summary of the noteworthy differences and further discussion on the evolution ofthe modern analysis approach.

Failure Modes and Risk Analyses

Perhaps the most notable development that has occurred within the past ten years has been the inclusion of potential failure mode and risk analyses in dam safety evaluations.These analyses place more emphasis on an existing dams site specific characteristics andvulnerabilities that could lead to failure and the associated public risk as opposed tosatisfying a finite, one size fits all, set of safety standards. Since the majority of U.S.dams are reaching their intended design life and since associated costs to fullyrehabilitate these facilities are well beyond the funding capacity of most dam owners, riskassessments are being used to either prioritize repairs or decide whether or not the risk isgreat enough to substantiate the repair. In some cases, improved instrumentation andmonitoring programs are considered to be a more effective solution to reduce public riskin comparison with more costly structural repairs. The Corps has integrated specific siteknowledge and risk into the traditional stability load cases and safety factors.Reclamations new risk-based approach is yet to be formally published but supersedes thestability criteria found in previous Reclamation design manuals like Design of SmallDams (1987) and should be noted when consulting their literature and the comparisontables in this paper.


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Load Combinations

During the 1970s, loading combinations were divided into three principle categories:usual, unusual, and extreme in which the cases for each have grown well beyond thereservoir empty (construction) and reservoir full (flood) cases used in the latter half of the

19th

century. Table 2 provides the loading combinations required for analysis by thethree most prominent Federal agencies. Between these agencies, no two agenciesapproach the loading combinations in the same way. Most noteworthy is thecategorization of the maximum flood case by Reclamation and FERC as an unusual loadcombination; whereas, the Corps categorizes it as extreme for spillway design floods witha return period greater than 300 years, which is typically the case for the probablemaximum flood (PMF). This divergence in approach is most significant whenconsidering the associated minimum stability criteria for overturning (momentequilibrium), sliding, and stresses.

Oddly, all three agencies neglect including a loading combination that consists of

evaluating the record flood or earthquake experienced by an existing dam during itsservice life to determine if the structure may have sustained any damage. For example, past tensile cracking at the upstream face may warrant increasing uplift pressureconditions or reducing shear resistance for other loading combinations. Such damagewould be undetectable except by stability analysis or a decidedly more costly coresampling and testing program.

Table 2. Standard Federal Agency Load CombinationsLoad CombinationsLoad

Category Reclamation 1987 FERC 2002 Corps 2005Usual (1) Normal Pool Level + dead

load, uplift, silt, ice, silt,tailwater, and minimum usualtemperature load.(4) Case (1) + drains inoperative.

Case I Normal Pool Case 2 Normal Operation +uplift, ice, silt with 10-Year Flood

Unusual (2) Maximum Pool Level + deadload, silt, tailwater, uplift, andminimum usual temperatureload.(4) Case (2) + drains inoperative.(4) Dead load only.

Case II Flood withlowest safety factorCase IIA Case I +ice

Case 1 ConstructionCase 3 Infrequent FloodCase 5 Coincident Pool withOperational Basis Earthquake(OBE)

Extreme (3) Usual + Maximum CredibleEarthquake (MCE)

Case III Postearthquake

Case 4 Construction + OBECase 6 Coincident Pool withMaximum Design Earthquake(MDE)Case 7 Maximum Design Flood(>300-Year Return Period)

Note: Within the past ten years, Reclamation uses a site specific risk-based approach in place of the 1987criteria shown here in Table 2.


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Forces

By 1900, the need to account for less understood forces such as ice pressure, uplift pressure, and earthquake accelerations as part of or in addition to the standard loadingcases of reservoir empty (construction) and reservoir full (flood) was increasingly

recognized. The following is a brief discussion of how these forces evolved into thecurrent practice.

Ice and Uplift Pressure

Longstanding practice has been to use a pressure of 5,000 psf per foot of ice thickness(Reclamation assumes a 2-foot-thickness as standard) at the contact surface of the normalreservoir level with the structure in regions where applicable. In the U.S., only one damin Minnesota in 1899 has been known to fail as a result of ice pressure and was largelydue to restraint provided by a retaining wall parallel to and 350 feet opposite the dam.For run of river dams, ice impact loading is also another important consideration.

In 1895, another French engineer, Maurice Levy, proposed a principle, rejected by his peers that equated to applying full headwater pressure at the heel to tailwater pressure atthe toe to the full area of any horizontal joint. Opponents held that 100% uplift could not

be true because a large portion of the joint or base area must be in contact to support theload and that most existing dams would have failed since their design neglected upliftentirely. However, with the failures of the Colorado Dam in Austin, Texas in 1900 andthe Bayless Dam in Austin, Pennsylvania in 1911, U.S. engineers were starting to givemore credence to the need to account for uplift pressure, albeit for only high dams withhigh-hazard potential like Wachusett and Kensico.

The typical practice, which continued from the 1890s into the 1950s, was to use fullheadwater at the heel to tailwater at the toe acting over half or two-thirds of the area, witha two-thirds intensity factor being the most common. By the mid-1950s, throughadvocates like Karl Terzhagi and L.F. Harza, the industry began adopting the present

practice first proposed by Levy. Even while uplift was being debated, design featureswere included to reduce seepage and uplift with the use of cutoff walls, grout curtainsand/or drain curtains at or near the heel. Medina Dam (1911-12) in San Antonio, Texaswas the first U.S. dam to have drainage in both the structure and foundation. By 1915,nearly all high gravity dams incorporated structure and foundation drain systems.

The current practice for analyzing existing dams allows for application of an uplift

pressure that is less than the accepted full headwater to tailwater rule for the usualloading category; but only for instances where it can be fully substantiated by a thoroughinstrumentation and monitoring program. Extrapolating historical uplift data to predictuplift pressures for unprecedented flood conditions is viewed with caution andskepticism. This constraint should not negate the practice of routinely monitoring uplift

pressure to at least verify that analysis assumptions are valid and safe conditions persist.For dams with tension in the base, full headwater pressure must be applied throughout the


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non-compression (cracked) zone. Several publications provide more detaileddescriptions and diagrams of the various potential uplift conditions to be used foranalysis.

Earthquake Acceleration

A detailed discussion of earthquake forces and associated analysis are well beyond thescope of this paper. However, some interesting points will be briefly noted. It is notclear when earthquake forces were first applied in design, but as early as 1931,Westergaard suggested using an acceleration of 0.10g in earthquake regions. And as lateas 1958, published guidance still suggested use of 0.10g in moderate to severe earthquakeregions and a value of 0.05g in more favorable regions. A pseudo-static method ofanalysis was first used to evaluate earthquake loadings, and for some cases is still used.In the 1960s, Anil Chopra began developing the pseudo-dynamic and dynamic methods.Todays technology includes linear and non-linear finite element computer analyses forhigh dams in high seismic regions. In the past two decades, seismologists estimates of

potential earthquake forces have moderately to significantly increased in certain activeseismic regions, causing the need for remediation for some dams.

A recent departure from the traditional seismic analysis approach is FERCs policychange in which evaluation of stability under seismic loading is replaced by criteria for

post-seismic static conditions. This new approach uses a dynamic analysis to determinethe degree of cracking resulting from the earthquake to determine if the structure meetscertain stability criteria in a cracked state. This approach includes a separate stabilityevaluation of cracked sections by means of a block rocking analysis. FERC does notallow the use of the pseudo-static method with the view that conventional momentequilibrium is not valid for oscillatory type loadings.

Material Strength Properties

Critical material strength properties are typically unit weight of the masonry or concreteand the shear strength of the foundation rock, the foundation/dam interface and to a lesserdegree the masonry or concrete within the dam, all of which are best determined bysampling and laboratory testing. For stone rubble or cyclopean masonry dams, aweighted average by percent volume of the stone and concrete should be used to estimatea bulk unit weight.

Regarding concrete joint shear strength, an accepted assumption is to use zero cohesion

and a 45 friction angle. For the dam/foundation interface, construction photos, ifavailable, can be very helpful in selecting shear strength. Foundation rock shear strengthis the most difficult parameter to select and requires the expertise of both an experiencedgeologist and geotechnical engineer. In 1976, Don Deere noted that a reasonable

preliminary estimate of rock shear strength is to assume cohesion is zero and frictionangle for a smooth surface is 30 to 35 for hard, massive rock; 25 to 30 for hard, shaleyor schistose rocks; and 20 to 25 for softer laminated or schistose rocks to which must be


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added an asperity ( i) angle for the geologic discontinuity. He also noted that these valuesare for unweathered rock and should be reduced 5 to 10 for weathered surfaces.

Resultant Location (Overturning) Criteria

Prior to 1900, engineers mainly focused on maximum compressive stresses and satisfyingthe middle third rule and largely ignored sliding stability. Current practice for existinggravity dams continues to be use of the middle third rule for the usual load combinationswith less stringent requirements for the unusual and extreme loading combinations aslong as minimum sliding and stress criteria are met. FERC allows tension in the heel(cracked base) for all loading categories as long as the crack stabilizes, the resultantremains within the base, and sliding stability and stress criteria are still satisfied. FERCincludes the caveat that remedial measures should attempt to satisfy the middle third rulefor static loadings. Table 3 provides the most recently published resultant locationcriteria for Reclamation, FERC, Corps, and New York State Dam Safety, one of the fewstates with separate stability criteria. However, it should be noted that with

Reclamations adoption of a risk-based approach within the past ten years, this criteria isviewed as a starting point and is not considered an absolute requirement.

Sliding Criteria

Prior to 1933, the shear or cohesion (C) strength of stone masonry, concrete, and rockwas viewed as indeterminate and ignored, thus only the friction component of slidingresistance was considered. The elimination of cohesion from the Coulomb-Mohrequation was viewed as an added, albeit unquantifiable, margin of safety. With this viewin mind, the sliding factor became the requirement that the ratio of the sum of thehorizontal forces to the sum of the vertical forces must not exceed the friction factor

(tana

); typically varying among practitioners from 0.67 to 0.75 (i.e., 33.8 to 36.9friction angle).

In 1933, D.C. Henny proposed a means of determining cohesion through compressiontesting of concrete and rock specimens culminating into the shear-friction formula. Heindicated that the typical cohesion strength of sound rock is on the order of 800 psi butultimately proposed a value of 400 psi for use in design with the view that the weak planewas in horizontal concrete lift joints and not foundation rock. An example problem inHennys 1933 paper used a safety factor of 4 for the maximum flood case whichinadvertently became the industry standard in use as late as the early 1960s. Hennyconceded that the shear-friction formula was not applicable for dams founded on

horizontal or near-horizontally bedded rock, arguably since he understood that cohesionat the bedding planes could be substantially less than 400 psi and even approach zero.

As late as the early 1960s, both the sliding factor (friction only) and the shear-frictionmethods were used in conjunction by Reclamation and the Corps. If a dam did notsatisfy the sliding factor requirement, the alternative was to evaluate it using the shear-friction method. Until the 1970s, cohesion and friction values for foundation rock tended


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to be unconservatively high since they were based on intact samples and not on weaker joints and fault planes. For example, Reclamation typically used a cohesion value of 300to 700 psi based on intact foundation rock. By the 1970s, renewed recognition was beinggiven to the complexity of assigning a reasonably valid cohesion value for foundationrock.

The shear-friction method was widely used until the 1980s when the Corps migrated tousing what is referred to as the limit equilibrium method, which is largely based on soilmechanics. This method requires that the ratio of available to mobilized shear strength

be above a minimum safety factor and that the mobilization of strength be such that allsegments of the potential failure plane have an equal factor of safety. Limit equilibriumappears to be best suited for dams with steeply sloping multi-wedge (passive wedge)foundation conditions. The shear-friction and limit equilibrium methods only yieldequivalent safety factors for the special cases of a horizontal failure plane with no passivewedge and when tan is equal to V/ H. Presently, Reclamation and FERC stillendorse the use of the shear-friction method, but with the caveat that strain compatibility

may need to be considered for such features as shear keys and passive restraint.

Due to present limitations in availability of qualified testing laboratories, the high cost ofsampling and shear testing, and the limited degree to which such testing may fullyrepresent actual conditions, FERC has recently implemented an alternate set of slidingsafety factors if cohesion is ignored in the interface and foundation. This alternateapproach basically reverts back to the friction-only criteria in use since the 1890s. Thetrend over the past three decades has been to lower sliding safety factors to better matchthe concurrent advances in rock mechanics that is yielding lower and likely more realisticshear strengths. Table 4 provides a comparison of the most recently published slidingcriteria.

Stress Criteria

The concrete used for most gravity dams has a minimum ultimate compressive strengthof 3,000 to 5,000 psi. For older gravity dams, moderate to significant strength gains canoccur over a long service life due to favorably moist curing conditions. Maximum

principal stresses are typically well below the concretes ultimate compressive strength,with exceptions occurring under cracked base and/or high seismic loading conditions.Table 5 provides a comparison of the most recently published stress criteria.

CONCLUSIONS AND RECOMMENDATIONS

Even after over 150 years have passed since the advent of the modern gravity dam era,different design approaches and associated standards still remain and will likely continueto remain in the United States. This situation is the biggest challenge for privateconsultants and state dam safety officials whose practice usually requires them to bewell-versed in all design approaches and standards.


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Partly driven by current funding constraints in both the private and government sectors,recent design standard revisions have placed more emphasis on possible failure modesand their associated probabilities of occurrence so that remedial measures can be focusedon more likely problems, thus maximizing the value of limited available funding.

When using modern techniques for estimating unusual and extreme load cases such asfloods and earthquakes, many existing gravity dams violate current stability safetymargin minimums. However, these same dams have demonstrated good long-term

performance that is largely a testament to past design practices erring on the side ofconservatism with known parameters, unwittingly counterbalancing shortcomings in lessunderstood or unknown parameters, in combination with the implementation of soundconstruction practices. Since some parameters will always remain less understood,todays engineers would do well to continue this practice.

The following are recommendations to further improve the practice:

1)

Establish a better defined method for assigning seismic forces in less seismicallyactive regions such as the east coast region and eliminate the earthquake analysisrequirement in less active regions when the pga is less than say 0.20g. In the eastcoast, the flood case typically governs due to the relatively higher potential forextreme rainfall events as opposed to extreme seismic events in contrast with morearid and seismically active western regions where the opposite may be true.

2) Require an analysis of the record flood and/or seismic load cases taking into account,to the extent practical, changes in material strength properties throughout thestructures life to assess the potential for otherwise difficult to detect crackingdamage.

3) Establish a better defined approach and formulation for addressing deep-seated failure planes within foundation rock and the associated passive wedge resistance.

4) Place more emphasis on substantiating loading and material strength parameters incomparison to satisfying minimum stability criteria since the typical bias is tomanipulate parameters to meet criteria.

5) Place more emphasis on parametric analyses of critical load and strength parameters.6) Determine load conditions necessary for marginal stability/failure as a reality check

and as an alternate method of evaluating the degree of safety similar in part to theReclamations new risk analysis procedures.

REFERENCES

Wegmann, The Design and Construction of Dams , John Wiley & Sons, 1927.

The complete reference list is too long to mention and can be provided upon request.


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T a b l e 3 . R e s u l t a n t L o c a t i o n C r i t e r i a C o m p a r i s o n

R e c

l a m a t

i o n

1 9 8 7

F E R C 2 0 0 2

N e w

Y o r

k D a m

S a f e t y

1 9 8 9

L o a

d C a s e

N e w

D a m

E x i s t

i n g

D a m

E x i s t

i n g D a m

R e p a i r

D e s

i g n

C o r p s

2 0 0 5

N e w

D a m

E x i s t i n g

D a m

U s u a l

M i d d l e 1 / 3 A

M i d d l e 1 / 3 A

W i t h i n B a s e

M i d d l e 1 / 3 C

M i d d l e

1 / 3

M i d d l e 1 / 3

M

i d d l e 1 / 3

U n u s u a l

M i d d l e 1 / 3 A

W i t h i n B a s e A , B

W i t h i n B a s e

M i d d l e 1 / 3 C

M i d d l e

1 / 2

M i d d l e 1 / 3

M

i d d l e 1 / 2

E x t r e m e

W i t h i n B a s e A

W i t h i n B a s e A

N / A

N / A

W i t h i n B a s e

W i t h i n B a s e

W i t h i n B a s e

N o t e s : A I n f e r r e d b y s t r e s s c r i t e r i a , B D

r a i n s I n o p e r a t i v e ,

C T o

e x t e n t p o s s i b l e ,

T a b l e 4 . S l i d i n g S a f e t y F a c t o r s C r i t e r i a C o m p a r i s o n

R e c

l a m a t

i o n

1 9 8 7

( S h e a r - F r i c t

i o n )

F E R C 2 0 0 2

( S h e a r -

F r i c t i o n )

C o r p s

2 0 0 5

( L i m i t E q u i l i b r i u m

)

N e w

Y o r

k D a m

S a f e t y 1 9 8 9

( S h e a r - F r i c t

i o n )

F o u n

d a t i o n

O r d

i n a r y

N e w

D a m

E x i s t

i n g

D a m

L o a

d C a s e

D a m

/

I n t e r

f a c e

C > 0

C =

0

C

> 0

C =

0

W e l

l -

D e f

i n e d

E Q

N o

E Q

C > 0

C =

0

C > 0

C =

0

U s u a l

3 . 0

4 . 0

2 . 0

3 . 0

1 . 5

1 . 7

2 . 0

2 . 0

2 . 0

1 . 5

2 . 0

1 . 5

U n u s u a l

1

2 . 0

2 . 7

1 . 5

2 . 0

1 . 3

1 . 3

1 . 5

1 . 7

2 . 0

1 . 5

1 . 5

1 . 2 5

E x t r e m e 2

1 . 0

1 . 3

1 . 0

1 . 3

1 . 3

1 . 1

1 . 1

1 . 3

1 . 5

1 . 2 5

1 . 2 5

1 . 0

N o t e s :

1 F E R C a l l o w s S F o f 1 . 3 i f t h e S D F = P M F , C = 0 .

N Y S a l l o w s t h e S D F = P M F f o r e x i s t i n g d a m s a n d r e q u i r e s S D F = P M F f o r n e w

d a m s .

2 C o r p s p r o j e c t s i n w h i c h n o s i t e - s p e c i f i c s e i s m i c d a t a i s a v a i l a b l e , t h e u n u s u a l a n d e x t r e m e S F m u s t b e i n c r e a s e d t o 1 . 7 a n d 1 . 3 , r e s p e c t i v e l y .

T a b l e 5 . I n t e r n a l S t r e s s C r i t e r i a C o m p a r i s o n

R e c

l a m a t

i o n

1 9 8 7

F E R C 2 0 0 2

L o a

d C a s e

D a m

I n t e r f a c e /

F o u n d a t

i o n

I n t a c t

/ D a m

C r a c k e d /

D a m

I n t e r f a c e /

F o u n

d a t i o n

C o r p s

2 0 0 5

U s u a l

c

< f ' c / 3 . 0

c

< 1 , 5 0 0 p s i

t = 0

c

<

u l t / 4 . 0

t = 0

c

< f ' c / 3 . 0

t = 1 . 7 f ' c 2 / 3

c

< f ' c / 3 . 0

< 1 . 4

n

t = 0

c

<

u l t

/ 3 . 0

t = 0

=

a l l o w a b l e w /

s a f e t y f a c t o r

U n u s u a l

c

< f ' c / 2 . 0

c

< 2 , 2 5 0 p s i

t = 0

c

<

u l t / 2 . 7

t = 0

c

< f ' c / 2 . 0

t = 1 . 7 f ' c 2 / 3

c

< f ' c / 2 . 0

< 1 . 4

n

t = 0

c

<

u l t

/ 2 . 0

t = 0

=

1 1 5 % o f

u s u a l a l l o w a b l e

E x t r e m e

c

< f ' c / 1 . 0

t a l l o w e d

c

<

u l t / 1 . 3

t = 0

N / A

P o s t - S e i s m i c

N / A


N / A


=

1 5 0 % o f

u s u a l a l l o w a b l e

G e n e r a l

N o t e : W i t h i n t h e p a s t t e n y e a r s , R e c l a m a t i o n u s e s a s i t e s p e c i f i c r i s k - b a s e d a p p r o a c h i n p l a c e o f t h e 1 9 8 7 c r i t e r i a / a n a l y s i s m e t h o d s s h o w n h e r e

i n T a b l e s 3 , 4 , a n d 5 .


14/14

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