IT, v 77:r r WTechnicalW Reot&REM4T-JI

Octobm I M

US ArmyCorps AD-A273 009of EngineersWaterways Experiment iii 1 II! i II!i IIStation

Repair, Evaluation, Maintenance, and Rehabilitation Research Program

Incorporation of Wall Movementand Vertical Wall Friction in theAnalysis of Rigid ConcreteStructures on Rock Foundations

by Shannon and Wilson, Inc.Engineering and Applied Geosciences

NOV2 419933

Approved For Public Release; Distribution Is Unlimited

93-28748

93 11 23049

Prepared for Headquarters, U.S. Army Corps of Engineers

The following two letters used as part of the number designating technical reports of research publishedunder the Repair, Evaluation, Maintenance, and Rehabilitation (REMR) Research Program identify theproblem area under which the report was prepared:

Problem Area Problem Area

CS Concrete and Steel Structures EM Electrical and MechanicalGT Geotechnical El Environmental ImpactsHY Hydraulics OM Operations ManagementCO Coastal

The contents of this report are not to be used for advertising,publication, or promotional purposes. Citation of tradenames does not constitute an official endorsement or approval ofthe use of such commercial products.

SPRINTED ON RECYCED PAPER

Repair, Evaluation, Maintenance, and Technical Report REMR-GT-21Rehabilitation Research Program October 1993

Incorporation of Wall Movementand Vertical Wall Friction in theAnalysis of Rigid ConcreteStructures on Rock Foundationsby Shannon and Wilson, Inc.

Engineering and Applied Geosciences Accesion ForSt. Louis, MO 63141-7126 NTIS CR'E& ;I

DTIC ,,

By

AvjL1::i- •ty C(c,.es

Aw,!. • .i t orDiSt

Final report

Approved for public release; distribution is unlimited

Prepared for U.S. Army Corps of EngineersWashington, DC 20314-1000

Under Contract No. DACW39-86-M-4062Work Unit 32648

Monitored by Geotechnical and Structures LaboratoriesU.S. Army Engineer Waterways Experiment Station3909 Halls Ferry Road, Vicksburg, MS 39180-6199

US Armny Corpsof EngineersWaterways Experiment -Station,•w

LI~luclmm • UIM •

WATMIAWm MA

Waterways Experiment Station Cataloging-in-Publicatlon Data

Incorporation of wall movement and vertical wail friction in the analysis ofrigid concrete structures on rock foundations I by Shannon and Wilson,Inc., Engineering and Applied Geosciences ; prepared for U.S. ArmyCorps of Engineers ; monitored by Geotechnical and StructuresLaboratories, U.S. Army Engineer Waterways Experiment Station.49 p. : ill. ; 28 crn. -- (Technical report ; REMR-GT-21)Includes bibliographical references.1. Structural stability. 2. Concrete construction. 3. Foundations.

4. Rock mechanics. I. Shannon & Wilson. II. United States. Army.Corps of Engineers, Ill. U.S. Army Engineer Waterways Experiment Sta-tion. IV. Repair, Evaluaton, Maintenance, and Rehabilitation ResearchProgram. V. Series: Technical report (U.S. Army Engineer WaterwaysExperiment Station) ; REMR-GT-21.TA7 W34 no.REMR-GT-21

Contents

Preface ........................................... iv

Conversion Factors, Non-SI to SI Units of Measurement ........ .. v

I--Introduction ..................................... 1

2-Summary of Findings ............................... 2

Strain Compatibility ................................ 2Wall Friction .................................... 2Case Study ...................................... 3

3-Elastic Movements of Rigid Structures ................... 4

Elastic Rotation .................................. 4Elastic Translation ......... ....................... 5Elastic Stresses Behind a Rigid Yielding Wall .............. 5Development of Passive Pressures in the Elastic Range ........ 8

4-Wall Friction .................................... 9

Interface Friction .................................. 9Deformation Condition ............................. 11Long-Term Effects ................................ 13

5-Proposed Changes to Methods of Analysis ................ 15

6-Practical Application of Suggested Methods ............. .. 16

7-Future Studies ................................... 19

References ........................................ 20

Plates 1-5

Appendix A: Sample Calculations ....................... Al

SF 298

iii

Preface

The study reported herein was authorized by Headquarters, U.S. ArmyCorps of Engineers (HQUSACE), as part of the Geotechnical ProblemArea of the Repair, Evaluation, Maintenance, and Rehabilitation (REMR)Research Program. The work was performed under Civil Works ResearchWork Unit 32648, "Geomechanical Modeling for Stability of ExistingGravity Structures." The REMR Technical Monitor was Mr. WayneSwartz (CECW-EG).

Mr. William N. Rushing (CERD-C) was the REMR Coordinator at theDirectorate of Research and Development, HQUSACE. Mr. James F.Crews (CECW-O) and Dr. Tony C. Liu (CECW-EG) served as the REMROverview Committee. The REMR Program Manager was Mr. William F.McCleese. U.S. Army Engineer Waterways Experiment Station (WES).Mr. Jerry S. Huie, Geotechnical Laboratory (GL), WES, was the ProblemArea Leader.

The study was performed by Shannon and Wilson, Inc., under ContractNo. DACW39-86-M-4062 to WES. Mr. Robert D. Bennett was PrincipalInvestigator. This work was conducted under the direct supervision ofMr. Huie and under the general supervision of Dr. Don C. Banks, Chief,Soil and Rock Mechanics Division, GL. Dr. Paul F. Hadala was AssistantDirector, GL, and Dr. William F. Marcuson III was Director, GL.

At the time of publication of this report, Director of WES wasDr. Robert W. Whalin. Commander was COL Bruce K. Howard, EN.

iv

Conversion Factors, Non-SI to SIUnits of Measurement

Non-SI units of measurement used in this report can be converted to SIunits as follows:

Multiply By To Obtain

degrees (angle) 0.01745329 radians

feet 0.3048 meters

pounds (force) per foot 14.5939 newtons per meter

pounds (force) per square foot 47.88026 pascals

pounds (force) per square inch 6.894757 kilopascals

pounds (mass) per cubic foot 16.01846 kilograms per cubic meter

square feet 0.09290304 square meters

V

1 Introduction

The following Phase II report for the U.S. Army Engineer WaterwaysExperiment Station supplements the initial report entitled, "Evaluation ofOverturning Analysis for Concrete Structures on Rock Foundations"(Shannon and Wilson, Inc., in preparation). The purpose of the Phase Istudy was to review the overturning stability method presently used by theU.S. Army Corps of Engineers. Apparent short-comings in this method ofanalysis have resulted in computed safety factors of less than 1.0 for his-torically stable structures. The topics to be expanded upon in this reportinclude the effects of strain compatibility and wall friction on the stabilityof rigid concrete gravity structures. These areas were singled out for addi-tional review because they are ignored in present methods of analysis.

1Chapter 1 Introduction

2 Summary of Findings

This report presents recommendations for modifications to the presentCorps of Engineers' stability analysis for concrete gravity structures.These modifications are intended for use in conjunction with the currentanalysis procedures for a more accurate assessment of the factor of safetyof existing structures. It is concluded from this study that the effects ofwall friction and strain compatibility are significant when the foundationrock modulus is relatively low.

Strain Compatibility

The elastic rotation and translation of a rigid structure can be separatedto obtain initial estimates of deformations produced by external momentsand forces. Equations to compute these deformations are provided, andonce determined, they can be used to estimate the reduction in earth pres-sure behind a wall that yields in the active sense. Although the equationsare valid only for smooth, translating retaining walls, it has been shownthat the influence of wall friction on earth pressures will be small and thata translating wall should produce similar reductions as does a rotatingwall for the same deformation at the top of the wall.

No reasonable procedure is available for determining the partial pas-sive pressure resistance of walls moving into a backfill. However, be-cause usually only small heights of backfill are in front of a wall, thisresistance may be ignored and at-rest earth pressures used.

Wall Friction

The works of Potyondy (1961) and Goh and Donald (1984) have pre-sented reasonable estimates of maximum wall friction values that can de-velop as a function of the internal friction angle and cohesion of thebackfill soil. These estimated values compare favorably to actual fieldand model test results at the limiting cases. For the present study, it is

2 Chapter 2 Summary of Findings

sufficient to assume that the frictional resistance provided by the wall willbe equivalent to the resistance through the soil on a vertical surface abovethe base of the structure.

The development of wall friction versus time is difficult to determine.From instrumented walls it appears that the development of the limitingfriction angle is linear up to slippage between the wall and soil from aninitial value. This initial value is dependent on the method of backfillplacement and the height of the wall. A tentative correlation in determin-ing mobilized wall friction is provided. It currently appears, based on in-strumented case histories, that this resistance can be counted on forlong-term effects. However, this point still needs consideration.

Case Study

The case study of a hypothetical concrete gravity structure is providedto show how the effects of strain compatibility and wall friction can be in-corporated into the current Corps of Engineers' analysis procedures. Itwas concluded that the effect of these additional resistances is significantwhen the foundation rock modulus is low and significant deformation ofthe structure can occur.

3Chapter 2 Summary of Findings

3 Elastic Movements ofRigid Structures

From the theory of superposition, the solutions for elastic rotation andelastic translation can be used for determining backfill deformations forthe overturning and sliding analyses, respectively. Whereas actual defor-mations may result from combined rotation and translation, the separationof these two forms of elastic movement will give conservative estimatesof backfill deformations for the appropriate case of analysis.

Elastic Rotation

The elastic rotation of a rigid structure under an applied unit momentwas presented in the Phase I report and is repeated here for completeness.The angle of rotation cx is obtained from the solution below, where ot is inradians:

CE = 4m (I _ IL2) )

zEb2

where

m = Applied moment in units of moment per length

p = Poisson's ratio

E = Young's modulus

b = Half width of base of structure

This solution was obtained from Muskhelishvili (1954) for the momentloading of a smooth, infinite strip on a semi-infinite mass (elastic half-space). It is redefined below for the general cases where the base may notbe infinitely long:

4 Chapter 3 Elastic Movements of Rigid Structures

m (1- A2) J6 (2)Qt = B2E

where

B = Width of base (equal to 2b)

le = Constant dependent on LIB

L = Length of base

It should be noted that for large U/B ratios, i.e., approaching an infinitestrip, the solution defined above is equal to the solution from Muskhelish-viii. The factor 1O can be determined from the curve shown in Plate 1.

Elastic Translation

The translation of a rigid structure on an elastic medium acted upon byan applied horizontal force is obtained from Barkan (1962). This solutionis not as rigorous as the solution for rotation. The average horizontal dis-placement d of the base is computed by assuming a uniform distributionof shear stress over the contact area and is given by:

d (- -2P ((LB)", (3)

where

P = Applied horizontal force in units of force per length

BX = Constant dependent on ji and L/B

The factor Bx can be determined from the curve shown in Plate 2 for gt= 0.3.

Elastic Stresses Behind a Rigid Yielding Wall

Justification for the use of an elastic theory for stresses behind a yield-ing wall comes from the widespread use of the theory for various otheranalyses (settlement analysis, vertical pressure distribution, etc.). Finn(1963) published an article dealing with the development of stresses be-hind a rigid yielding retaining wall based on the theory of elasticity. Finnhoped to determine the pressure exerted by a soil mass behind a wall when

5Chapter 3 Elastic Movements 01 Rigid Structures

the boundary displacements were such that the classical plastic methodswould not apply.

Finn's analysis was based on the classical concept of the "trap door"analysis, i.e., a soil mass with a yielding base. As the door is releasedaway from the boundary, the pressure above it decreases due to soil arch-ing. Finn applied this "trap door" analysis to that of a yielding retainingwall. He derived solutions for stresses developing behind rigid retainingwalls rotating away from the backfill about their top and translating awayfrom the backfill. He derived these solutions for cases where friction actsalong the base (perfectly rough) and where it does not act along the base(perfectly smooth).

The pressure behind a smooth retaining wall that moves laterally awayfrom the backfill was derived by Finn and is as follows:

K,7z + 4zh2Ed (4)

(1 - 112) it (z + h)3 (z - h)

where

0r = Horizontal pressure at depth z

Ko = At-rest earth pressure

y = Unit density

z = Depth from top of soil backfill

h = Height of backfill

E = Young's modulus of soil backfill

d = Horizontal displacement

R. = Poisson's ratio

This equation can be integrated to determine the net force P acting on thewall:

~ Z!K~2+ Edp= z 1o 2)o 2 nI -•2

IIn h + I 1 (5)2 + +1+ 20

6 Chapter 3 Elastic Movements of Rigid Structures

The resultant of this force can be determined upon further integration andis stated below:

O'zKo13 + hU In +[2- 3+ I°z3 K0ý X,, - P 2) (2 + I) (I + •

P h (6)

where

Z7h = Ratio of the depth at which the pressure behind the wallbecomes negative to the height of the soil backfill(Appendix A, Sheet 6)

A stress singularity (division by zero, see Equation 5) develops at the

point z = h where infinite tension develops in the backfill. However, be-cause the backfill cannot take a net tension, the stresses are assumed to goto zero below the depth where the tension adjustment to the earth pressureexceeds the at-rest pressure. It should be noted that the above equationsare valid only for a backfill with a horizontal top surface and in which the

backfill is either dry or completely submerged. It should be furtherpointed out that this equation is valid only for small displacements as isusually understood in the theory of elasticity such that slip surfaces willnot occur.

Results from Finn's analysis generally show that when using elasticpressure theory, the pressure distribution against the wall departs from itslinear shape with increasing deformation such that pressure shifts fromthe bottom of the wall toward the center of the wall. This shift produces arise in the center of pressure above the lower one-third point. Finn's find-ings are confirmed by results from both Terzaghi (1934) and Sherif,Ishibashi, and Lee (1982) which show the center of pressure to be be-

tween 0.40 and 0.44 times the height of the wall above the base at the ac-tive state.

The equations shown above are for the case of a perfectly smooth walltranslating away from the backfill. The results using a rough wall are sim-

ilar but will result in lower earth pressures. Although, later in this report,

wall friction will be shown to vary with deformation, its incorporationinto this model would present complexities that are not easily resolved.

Therefore, assuming a smooth wall will suffice for this study.

The model proposed by Finn is based on wall translation away fromthe backfill. Finn proposes no method to compute stresses when a wall

rotates about its base. However, studies by Sherif, Ishibashi, and Lee

(1982) and similar results by Terzaghi (1934), as well as finite element

analyses by Clough and Duncan (1971), have shown that results produced

by rotation about the base are similar to results where translation occursfor equal values of deformation at the top of the wall.

7Chapter 3 Elastic Movements of Rigid Structures

Development of Passive Pressures in theElastic Range

Finn's work was restricted to wall movement in the active sense. A lit-erature search was unsuccessful in finding a method that could easily pro-vide theoretical solutions for partial passive resistance. There appears tobe no satisfactory method available to compute passive pressure resistanceas a function of deformation.

Based on model tests and finite element studies, it appears that a signif-icant amount of passive resistance is mobilized by small deformations(i.e., deformations sufficient to place the outer backfill into the activestate). Results from Terzaghi on model retaining walls and finite elementanalyses by Clough and Duncan show that, in general, passive pressuresare mobilized at a much faster rate than active pressures for the same walldeformation. Thus, this resistance may prove more beneficial in increas-ing apparent stability where thick backfills are present than the reductionof pressure on the active side. Future studies may be able to determine asatisfactory elastic method for computing passive pressures.

8 Chapter 3 Elastic Movements of Rigid Structures

4 Wall Friction

Wall friction is mobilized any time shear deformations occur along thecontact between the wall and soil. This deformation occurs either throughrelative displacement between the wall and soil backfill (in the case of arigid foundation this would imply settlement of the backfill) or through lat-eral earth pressures inducing movement of the wall. The frictional resis-tance that develops as a result of this displacement is dependent on thetype of backfill, the nature of the wall, and the amount of wall movement.

Interface Friction

The soil-structure interaction behavior between various soil types andconstruction materials can be regarded as the initial step in understandingthe role of wall friction on the stability of concrete gravity structures.The development of skin frictional resistance between a wall and soilbackfill is excluded from the present Corps of Engineers' stability analy-sis. While skin friction is generally acknowledged as developing duringshear deformations along this contact, there is some question to the long-term benefit of such a shearing force. Whether this force tends to dissi-pate with time, as a result of the creep of cohesive soils or vibrationaleffects on cohesionless soils, is currently unclear. Thus, for conservativedesign analyses, this resistance is ignored in practice.

Even if it is possible to verify that friction is sustained for long periodsof time and during vibrations or cyclic loadings, the amount of wall defor-mation necessary to fully mobilize this force must be determined. Theoret-ically, the fully mobilized force should correspond to the initiation ofslippage between the backfill soil and wall. For typical rigid gravity struc-tures founded on a competent rock foundation, it can be shown that elasticdeformations may be quite small. Thus, the wall friction may not be fullymobilized, and it becomes necessary to develop a relationship between thedegree of wall movement and the mobilization of wall friction.

Previous investigators have generally incorporated the use of frictionbetween soil or rock and construction materials as developing as a percent-age of the soil's or rock's shear strength. Along rough contacts, such as

9Chapter 4 Wall Flctilon

the base of concrete structures where concrete is cast directly against thesoil or rock, the sliding surface is acknowledged to occur just below thebase through the soil or on a joint just below the surface of the rock. Thisis the case because the concrete enters the irregularities of the soil or rockmaking this boundary surface stronger. Because the failure surface occursbelow the base, the full friction angle or cohesion of the soil or rock dis-continuity is developed. The same does not hold true for backfill soilsplaced against vertical concrete walls that are usually constructed byforms. In this instance, the wall is relatively smooth and provides lessshearing resistance than a failure through the backfill material. Thus, theweakest link is along this contact, and the vertical friction angle or cohe-sion will be less than the maximum values the soil could develop.

For retaining wall design, Huntington (1957) suggests using an angleof wall friction 8 equal to two-thirds of the friction angle ý and a wall ad-hesion value cA equal to two-thirds of the soil cohesion c for analysis atthe limiting equilibrium active and passive states. These values, althoughwidely neglected for conservatism, have been accepted for design.

Potyondy (196 1) performed a series of shear tests in both strain- andstress-controlled shear boxes to determine the skin friction between vari-ous construction materials and soil backfill types. Potyondy reported theratio of the angle of wall friction to the soil's angle of internal friction(6/0) and the ratio of wall adhesion to soil cohesion (cA/c). Unfortunately,there was no mention of the amount of shear deformation necessary to mo-bilize these values nor of the long-term effects of this friction.

Goh and Donald (1984) expanded upon Potyondy's testing. They feltthat the direct shear device used by Potyondy contained numerous short-comings in determining the value of skin friction and therefore modifiedthe NGI Direct Simple Shear Device to overcome these problems. Thenew device was also able to reproduce the approximate shear mechanismbehind a retaining wall and the approximate compaction procedures thatwould develop in the field. The results of these tests were fairly consis-tent to the 8/0 vales obtained by Potyondy. However, the values of CA/Cwere approximately twice as high in the latter study for the cohesive mate-rials. The authors attributed this difference to the compaction of the cohe-sive material against the concrete resulting in higher adhesive strengths.

A summary of the results of the above-mentioned tests for differentbackfill soils against concrete walls, in terms of the ratio of maximum de-veloped interface friction to soil friction (at slippage), is presented inTable 1.

These results were compared with results from model retaining walls atthe active and passive states. Terzaghi (1934) obtained 8/0 values for drysand against a model wall that ranged from 0.65 to 0.85 at the active statefor four different testing conditions. Fukuoka et al. (1977) obtained avalue of /0/ equal to 0.8 for sand against a large-scale concrete wall thatyielded into the active state. Sherif, Ishibashi, and Lee (1982) obtained a

10 Chapter 4 Wall Friction

Table 1Wall Friction Values Between concrete Structures and Varioussoil Types (after Goh and Donald 1984)

Soil Type 8/* CA/C

Sand 0.8

Uncompacted silt 0.5

Compacted silt 0.8

Non-swelling clay 0.7 0.4

Uncompacted cohesive granular 0.4 0.4

Compacted cohesive granular 0.6 0.8

value of 8/I of approximately 0.65 for a sand backfill that had developedits active earth pressure against an aluminum wall (estimated range of 8/Ifrom Potyondy for aluminum of 0.54 to 0.76). For a cohesive granularsoil against a steel retaining wall, Fukuoka et al. (1977) obtained maxi-mum wall friction values at the limiting active condition that resultedfrom a combination of friction and cohesion. Although no attempt wasmade to separate the individual contributions, the total force was found tobe in the range that would be estimated from Potyondy's values for steel(8/I = 0.40 to 0.65, cA/c = 0 to 0.35). The results of the aforementionedinvestigators suggest that the testings performed by Potyondy (196 1) andGoh and Donald (1984) are reasonable for maximum wall friction valueswhich will develop at the active state for various types of construction ma-terials. Therefore, the values presented in Table 1 are proposed as maxi-mum friction values that can be mobilized against concrete walls.

Deformation Condition

Fukuoka et al. (1977) concluded from a 2-year study of an instru-mented retaining wall that "the existence of wall friction is so large that itcould not be neglected in design." In order to rely on the full effects ofwall frictional resistance, however, sufficient deformation of the backfillmust occur. As tK_ soil stretches during movement of the structure, thewall friction increases from an initial value to its maximum value. Thismaximum value will develop at or before the initiation of slippage be-tween the backfil; and the wall at the limiting equilibrium cases (i.e. ac-

tive and passive states). The initial value of wall friction is difficult todetermine as it depends on the properties of the backfill, the nature of

placement (e.g., loosely placed as in siltation as compared with denselyplaced by compaction) and the wall material.

11Chapter 4 Wall Frict.,,..

Results from Terzaghi (1934) and Sherif, Ishibashi, and Lee (1982) onrigid retaining wall models resting on solid foundations and yielding inthe active direction show that a substantial initial value of wall frictionmay be dependent on the method of backfill placement behind the wall.For sands placed loosely behind a wall, Terzaghi presented experimentaldata that showed the initial value of tan 8 is slightly less than the maxi-mum value which it can attain. For dense sands, where density wasachieved by a heavy compactive effort, the initial value of tan 8 ap-proached zero. Fukuoka et al. (1977) obtained similar results for bothloose and compacted dense sand behind a yielding rigid wall. Sherif,Ishibashi, and Lee (1982) obtained an initial value of tan 8 that wasslightly less than one-half of its maximum value from using a shakingtable to obtain high densities of the sand.

The results above may be explainable in terms of the effects of the com-pactive effort on the values of 5, ý, and K. The initial value of tan 8 willusually decrease as a result of the compaction procedure for small walls.Compaction of backfill against a rigid wall will lock in additional horizon-tal stresses (as a function of the compaction-induced vertical stresses) thatdo not relax after the vertical stresses are removed. This is especially truefor small walls (less than 25 ft1 in height) where the compaction effortwill have a substantial influence over the entire height of the wall. Forhigh walls (greater than 50 ft in height), the horizontal stresses from thebackfill overburden will be higher than the induced compaction stressesover much of the wall and thus control the value of the wall friction, i.e.,the compaction-induced stresses will have a smaller influence over theheight of the wall.

As the horizontal earth pressure increases from locked in compactionstresses 8 tends to decrease if all other factors remain the same, thus, re-ducing the value of tan 8 before earth pressure-related movement. This ar-gument is strengthened by the results of Sherif, Ishibashi, and Lee (1982)with tests using sand that was densified rather than compacted. In thiscase, the locked in horizontal stresses are expected to be less significantbecause a shaking table was used rather than heavy compaction equip-ment. Thus, the initial value of tan 8 is expected to be lower and in this in-stance approached one-half of its maximum value.

The above-mentioned investigations also show that, in general, thevalue of tan 8 increases linearly with wall deformation towards its maxi-mum value at or slightly before the active state is reached. Terzaghi's(1934) limited data on movement toward the passive state show that thismovement has a small effect on the wall frictional resistance, and it is,therefore, negligible.

A table of factors for converting non-Sl units of measurement to SI units is presentedon page vi.

12 Chapter 4 Wall Friction

In summary, the initial value of the wall friction cannot be determinedaccurately. However, from literature it appears that the tangent of thewall friction angle generally increases linearly with increasing deforma-tion of the wall for cohesionless soils. Thus, it is reasonable to accountfor some frictional resistance by assuming that tan 8i varies linearly froman initial value to its maximum value (determined as some percentage of*) as a function of the amount of wall movement necessary to develop thelimiting equilibrium active case. Plate 3 is proposed, which takes into ac-count friction angle development as a function of wall height and compac-tive effort.

Only limited data are available on wall friction values of cohesivesoils; however, there is reason to believe that similar conditions exist.Gould (1970) presented test results from numerous investigators thatshowed an increase in the at-rest earth pressure with overconsolidationpressure resulting from compaction-induced stresses. Thus, the wall fric-tion value would be expected to decrease with the overconsolidation ratioas the earth pressure increases. However, to be conservative, because ofonly limited experimental data, the wall friction (or adhesion) should bevaried linearly from zero at the at-rest condition to its maximum values atthe active state regardless of the initial placement conditions.

Long-Term Effects

The uncertainty of the long-term effects of wall friction subjects thistype of resistance to scrutiny. Terzaghi's early results showed that at inter-mediate states (during displacement of the wall), if the wall was held con-stant, there was almost invariably a decrease of the coefficient of wallfriction and an increase in the horizontal earth pressure. This phenome-non was explained in terms of the rotation of individual grains into less fa-vorable positions such that the force required to keep them in this positiondecreases. In other words, the frictional resistance decreases, thereby in-creasing the net vertical reaction. Because the horizontal earth pressure isdirectly related to the vertical force, it also increases. Thus, as reasonedearlier, the wall friction should decrease. This result may be one reasonfor the current disregard of any wall frictional component. The decreasesTerzaghi referred to, however, were in general relatively small. Further-more, model wall tests since have demonstrated sustained friction forces.

Instrumentation of the Port Allen Locks (Kaufman and Sherman 1964)led the authors to the conclusion that substantial wall friction was avail-able at small deflections. Although not actually measured, the wall fric-tion was essential in obtaining realistic moment computations inback-calculating forces. These forces were generated by filling and emp-tying the locks and were measured through pressure cells installed on thelock walls. Frictional forces were believed to exist over the 2 years inwhich continuous monitoring was employed. Fukuoka et al. (1977) con-structed a rigid cantilever retaining wall and backfilled it with clayey soil.

13Chapter 4 Wall Friction

For over 2 years, this retaining wall was monitored. Twice, the wall wasallowed to stand undisturbed for 9 months and 1 year, respectively. Bothtimes, the load cells measured sustained frictional values. As a matter offact, the frictional forces increased slightly throughout this period, mostlikely as a result of backfill settlement.

Frictional forces are also used for other applications. As explained inthe Phase I report (Shannon and Wilson, Inc., in preparation), footingfoundations on clay and sand are designed with a factor of safety relativeto shear strength with no concern that these stresses will dissipate withtime. Also, friction piles are designed with long-term friction componentsof resistance.

14 Chapter 4 Wall Friction

5 Proposed Changes toMethods of Analysis

It is proposed that the stability of concrete gravity structures be ana-lyzed using earth pressures computed based on elastic theory and that ver-tical friction between the soil and concrete also be included. Rotation andtranslation may be computed based on earth pressure at rest as a first ap-proximation. The earth pressures are then computed using the deforma-tions from above and the equations developed by Finn (Part 3.13). Thedeformations may then be recomputed for the revised earth pressure distri-bution. Next, the amount of wall friction mobilized is estimated based onthe deformations and the relationships proposed in Plate 3. With theseforces defined, the rigid body equilibrium of the structure may be ana-lyzed. An example calculation is provided in Appendix A and a discussionfollows.

15Chapter 5 Proposed Changes to Methods of Analysis

6 Practical Application ofSuggested Methods

Appendix A presents example calculations for a typical concrete grav-ity structure (Plate 4) using the recommendations stated previously.Plate 5 shows the forces acting on this structure. Assumptions for the soiland rock properties are presented on page Al. Pages A2 and A3 show theexternal forces and moments acting on the wall. Page A4 computes theelastic rotation and translation of the structure from the influence of theforces and moments. Note that these deflections would be considered tol-erable. Sherif, Fang, and Sherif (1984) presented results which showedthat the active earth pressure was obtained, regardless of density or inter-nal angle of friction of the backfill soil, at a horizontal translation of0.001 times the height of the wall. From page A4 it can be seen that themovement of the structure is less than this value. Therefore, slip shouldnot have occurred, and the deformation is small enough to use the theoryof elasticity.

Page A6 shows the earth pressure distribution (no water pressureshown) for the elastic movements calculated above. For conservatism thesmaller value of the elastic deformation due to rotation and translationwas used. Also shown on this graph are the linear distributions for the at-rest earth pressure and the active earth pressure, with no friction actingalong the wall. The distribution is seen to be non-linear and comparableto results of Taylor (1948) and Terzaghi (1934). The resultant force andlocation can be calculated based on equations derived from Finn and arepresented on pages A7 and A8. Two interesting points should be made.First of all, the resultant earth pressure of 21,550 plf is between the activeand at-rest pressures calculated, which is expected. Second, the center ofpressure is located at 0.36 times the height of the wall. This finding con-firms results of Terzaghi (1934) and Sherif, Ishibashi, and Lee (1982),which showed the center of pressure of the active condition to be abovethe one-third point, acting at 0.40 to 0.44 times the height of the wall (thecenter of pressure for the example is lower than these values because thefull active condition has not been reached). It should be noted that the re-sultant force acting on the wall and its location were obtained through inte-gration from the top of the wall down to 39.5 ft where the pressure behindthe wall becomes zero.

16 Chapter 6 Practical Application of Suggested Methods

If further calculations are made, it can be shown that the resultant earthforce decreases non-linearly with increasing deformation of the wall awayfrom the backfill. This non-linear variation is such that the largest forcedecreases occur under very small movements, after which only smallchanges in the earthen force are experienced with further deformation ofthe backfill up to the active state. This is consistent with the results ofTerzaghi (1934) and Clough and Duncan (1971). It can also be shown thatthe center of pressure for the above case will increase to approximately0.40 times the wall height if deformations of 0.001 times the height of thewall occur, the resultant force will be approximately equal to the activeearth force as computed by the Coulomb theory for no wall friction. Itshould be noted, however, that large deformations such as these are be-yond the scope of the elastic realm.

Page A9 presents a summary of the procedure suggested to determinethe friction acting along the wall. Note that it is necessary to compute ini-tial forces, moments, and deformations before calculating approximatewall friction values. From Plate 3, the mobilized wall friction value canbe determined based on the suggested 8/1 value from Table 1. In this caseonly 53 percent of the tangent of the wall friction angle is mobilized.After computing an initial wall friction value, it is necessary to recomputethe forces and moments acting on the wall with the incorporated wall fric-tion force. Pages A10 and AI I present a summary of these calculations.Also, the elastic movements must be recomputed. Note that the change inthe elastic deformation for rotation is substantially smaller than thechange in deformation for translation. This is because of the long momentarm effect of the wall frictional force. Note, however, that the design de-formation is only slightly less than that used previously because thesmaller of the two deformations (from rotation and translation) are used.For structure and loading configurations in which the translation deforma-tion is the larger component, a more significant change in the design defor-mation will be seen.

Pages A1 2 through A15 present calculations for the factor of safetyagainst overturning (in terms of the location of the base resultant) and slid-ing (by using the limit equilibrium method of the Corps of Engineers,ETL 1110-2-256) using current Corps of Engineers' procedures and bymodifying these procedures with the use of strain compatibility effectsand a wall friction force. This work is summarized in the table on pageA 16. Also shown are the tiedown forces needed for a tiedown installed5 ft from the backfill edge at the top of the wall at a 20-deg angle in the di-rection of the backfill. Note that the tiedown forces needed using bothcases are approximately the same for the sliding analysis. However, thereis up to a 30-percent change in the required remedial force in meetingoverturning requirements. Once again, this effect is a direct result of thelong moment arm for the friction force. It can be concluded that for over-turning analysis, wall friction may have a significant influence on the loca-tion of the base resultant and remedial forces needed to meet Corps ofEngineers' criteria.

17Chapter 6 Practical Application of Suggested Methods

As a final point, it should be emphasized that the example calculationsin the appendix were based on a Young's modulus for the foundation of100,000 psi, which is relatively low for a rock foundation. This low valuecould indicate highly fractured rock or a very weak intact rock (possiblyweathered). For hard intact rock, modulus values of over 100 times thevalue used in the example would be expected, and thus all elastic move-ments would be negligible.

18 Chapter 6 Practical Application of Suggested Methods

7 Future Studies

The development of friction or adhesion between a cohesive backfillsoil and wall should be investigated further. It is probable that a substan-tial wall adhesion value is available, especially for normally consolidatedmaterial, which can increase apparent stability at movements that are notsufficient to develop the full active pressure condition. Also, long-term ef-fects of wall friction should be researched to confirm that they exist in thefield. Finally, the development of wall friction on curved surfaces or onsurfaces that are not vertical above the base should be investigated to de-termine if higher resistances along these surfaces exist.

Future studies should also consider the development of passive earthpressures, as these pressures would provide substantially higher resist-ances for equal values of backfill height and backfill deformation than dothe active pressures. Because backfills on the front of a wall are usuallysmall or nonexistent, ignoring this development is usually insignificant.

19Chapter 7 Future Studies

References

Barkan. (1962). "Dynamics of bases and foundations," McGraw-Hill,New York, 434.

Clough, G. W., and Duncan, J. M. (1971). "Finite element analyses of re-taining wall behavior," Journal of the Soil Mechanics and FoundationDivision, ASCE, 97(SM12), 1657-!673.

Finn, W. D. L. (1963). "Boundary value problems of soil mechanics,"Journal of the Soil Mechanics and Foundation Division, ASCE, Proc.Paper 3648, 89(SM5), 39-72.

Fukuoka, M., Akatsu, T., Katagiri, S., Iseda, T., Shimazu, A., andNakagaki, M. (1977). "Earth pressure measurements on retainingwa11s," Proceedings of the Ninth International Conference on Soil Me-chanics and Foundation Engineering, Tokyo.

Goh, A. T. C., and Donald, I. B. (1984). "Investigation on soil-cement in-terface behaviour by simple shear apparatus," Preprint Proceedings,Fourth Australia-New Zealand Conference on Geomechanics, Perth,Western Australia.

Gould, J. P. (1970). "Lateral pressures on rigid permanent structures,"Proceedings of the ASCE Specialty Conference on Lateral Stresses inthe Ground and the Design of Earth Retaining Structures, Cornell Uni-versity, Ithaca, NY.

Huntington, W. C. (0957). "Earth pressures and retaining walls," JohnWiley & Sons, Inc., New York, 534.

Kaufman, R. I., and Sherman, W. C., Jr. (1964). "Engineering measure-ments for Port Allen lock," Journal of the Soil Mechanics and Founda-tion Division, ASCE, 90(SM5), 221-247.

Morgenstern, N. R., and Eisenstein, Z. (1970). "Methods of estimatinglateral loads and deformations," Proceedings of the ASCE SpecialtyConference on Lateral Stresses in the Ground and the Design of EarthRetaining Structures, Cornell University, Ithaca, NY.

20 References

Muskhelishvili, N. I. (1954). "Some basic problems of the mathematicaltheory of elasticity," P. Noordhoff Ltd. Groningen-The Netherlands,Fourth, Corrected and Augmented Edition, Translated from Russian byJ. R. M. Radok, Moscow.

Potyondy, J. G. (1961). "Skin friction between various soils and construc-tion materials," Geotechnique, London, 11, 339-353.

Poulos, H. G., and Davis, E. H. (1974). Elastic solutions for soil androck mechanics, John Wiley & Sons, Inc., New York.

Shannon and Wilson, Inc. "Evaluation of overturning analysis for con-crete structures on rock foundations," Technical Report REMR-CS-, inpreparation, prepared by Shannon and Wilson, Inc., for U.S. Army En-gineer Waterways Experiment Station, Vicksburg, MS.

Sherif, M. A., Fang, Y. S., and Sherif, R. I. (1984). "KA and KO behindrotating and non-yielding walls," Journal of Geotechnical Engineering,ASCE, 110(1), 41-56.

Sherif, M. A., Ishibashi, I., and Lee, C. D. (1982). "Earth pressuresagainst rigid retaining walls," Journal of the Soil Mechanics and Foun-dation Division, ASCE, 108(GT5), 679-695.

Terzaghi, K. (1934). "Large retaining wall tests. I. Pressure of drysand," Engineering News Record, III, 136-140.

Tomlinson, M. J. (1957). "The adhesion of piles driven into clay soils,"Proceedings of the Fourth International Conference on Soil Mechanicsand Foundation Engineering, London, 2, 66-71.

References 21

7

6

5

10

4.

A3I

Phs II tuie

COEFFICIENT IQ for RIGIDRECTANGULAR FOOTING

Plate 1

I. 1 1 I

1.06. 01. Q

-BIONA OOIGL'

W.....!A .....RATI ,....0.

Waeray Exeimn Stto

Phas II Studie

-MMRECANGULA FOOTINGL /

Plae

Loose (No Compaction) All Wall Heights

1.0 I

Itt tee%°0.8

Wall * oFRICTION 0.6 ., t,"

ton 6, tn Sm oton 6b) max VIA nteAt

0.4 --- .,.Lq_

0.2-_-•,•

0 0.2 0.4 0.6 0.8 I .0At-*rest Act iveState d/d Active state

Deformation between the At-rest and

Active States for Cohesionless Soils.

Waterways Experiment StationPhase R" Studies

Proposed Correlation BetweenWall Deformation and the

Development of Wall Friction

Plate 3

SOIL BACKFILL:

# - 30°C-0"7 125 pcf

40'

CONCRETEGRAVITY

STRUCTURE

7c = 150 pcf

10'

ROCK: E - 100,000 psi

- 0.3

Waterways Experiment StationPhase II Studies

TYPICAL GRAVITYSTRUCTURE CONFIGURATION

Plate 4

SoI Bockfill0•* s130

1"= I2Spcf

jT-Ww

WWeweI

1

30- X x

30

ROCK: E= Il0,O00psiv= 0.3

Waterways Experiment StationPhase II Studies

External Forces Actingon a Gravity Structure

Plate 5

Appendix ASample Calculations

AlAppendix A Samdle Calculations

I .I

~' - . - -4 t.- - 4 . I t . ~ -

I'.M

-K V'- S;-,-

rj77 56 Z§ *

Z4 1i-1-t _J_7 r~

.14 4

A2 Apeni A Sample Calculations.7k

OSUBJCT V~~-Pk-,,. Z.

my O-2 ATS U2 Sff7 ~ 8099

PCi

7. 74-

44 It4 . 4C4)1L

Vj~ o6N~ 1-J)('O4.)

*- w i - kw 0

-H-

O]:12tIjr P12Mx7 *(0 -...-.PY , -is

-0.11204 .I r r~ T -'-'-A3

Appendi [A= ? Sapl Calcuation

3. +1. :-j03."

7r-- -7

1,1,1 5 -7r. -i.

-~~----------`l4&. - 4 JcLH I L ..

. F L . L ... I * I . I

A - Appndi A Sampl + oal ai.CLa -

By C• DAT. .AJ-Pl!.•F

3 ' . to-I

-- - - -- :i .. . .. t . . . - i r. . . - ' • '+ I - . . .. . .

tT •- , ' -- -

.1 - - _ _"

:4 --,

: • • ] • _ _ •: . ... ... .. 1_ ,_ - - I ! - __ )-

-7-.0. C A" . A t

---

_;* ; l - . 4.-i-,•10"•, -i' --T--.t-+ !-- ' -

T L •.... -, - ", . • " ,-1 . . --- -:- " I±: ..7 . .

. . "F I__ _• ! J.i ; :... 1_. -- . -• . . . - __ _L _-- _i ± . . . . .

• • i " • . " ' ,- - r--- , -

1 I '. . -., - ,

I - i :_

. • ._ ..• _ ,3•_• = '

Appendix A Sample Calculations A

-- • , . .I i i .: ' ,, . ) •* i _ _ __ _

.-•- ----7 i-I - -T..-tt- --t-.--r-rw r ..... '" --- -T ---.1 --,-- t • - * • -

S. .I ' . I . ,O~ 1IJ O n o .

_j • := :iL _ •_ -- - - -L •--I • --" - - '÷ __ - ,. , ---.....

"-.T " -•- 1-- -- •:.. ..'t...___ -T_ •- , "; -- I- •-f- .. . .. . .--& 1 l .oe...... -.... .

.. • • t • ' • I | L ! ! ..L.

-i ? i J. I :2 " , . 4 '-- • -

S, ! , "I , . -' . I : I

-C I

, - .10 I I • • I . ' --_1 - -_-

I _

, - - - -1 -.. ... . . ... . . . .. ..

- V .-- .---I--~-- ~ I4- --.-- -_. .... _ __ _ ___ __ • j. :

-- + r ; : -" - . .C. .. .I- I I-

k. i S

A6 Appen x A S

A Append.. .x A Sample, Calculations:,.

-SJejir K -II XII IIDV C..A: F*r 0 ..-6_ swe aT r.. ,,

II.-'T 3l l I , I 1 | ' ' • , . . - - • -

• - 1I j _ _, _. _, I ' I _ _ _ _ _'_ _ _ _

-35-

. .1 : , " •

- ---- --- \ -- ,- •.-- ----H.. .. - -• .... . •-----.- .... . ." I" , \ l ' 1 / , '

-" .- 1 I : .. i. ' ........

--- ,. ' -- ---1-•G----- ,-2- 2.-- - .. ... -I-- .... . .

'I . "~ I \ . ' I " ' i " -... i ' " 1 ---Z - -I - -- - t- ;--�-t- ¶- - -. .. . . . .

-- " - i l \ \X , l I ' _ i 4 . -_._ .. . ..

-. J.' ; -- \+-_--"_'------ ,- • - --__I-_ _ ;_ •-- _ I -- __- ____

; I. - . . -. .. . -

Appendix A Sample Calculations A

*~~~ ~~~~ -* ..-- -. j- os_ _ _ _

-il --

2 p I

1-4

Tof 1-- - Jc, .- -

A8 Apendi A Sr~leCalcla-n

W e . . .-. **" 3O O._ _ __ _

*By OATE L&U, S _S ... ,,

"a" a I . . • '

. - . . 1 * .. .-. '- . .S, . a , , . : :

-.. .C. _ .. . . 73 _b.sX z:). 3! .t -.. .... ;

T C Z- ,/

SIT)

r r• : . . , J , . , a

-,-- 7-" - - -J- -- - - - " - '- --

-4 i I : : : ! I

I . ...- j ..

" -- -... ... '-"-I .. b$ 4.L'-' .... o, j4 4 tn._. ....... .• _.. :'•:• •I , j• - .'.~ _

.- ; .• 4 , I • ! I _ _ _. C . . .. . .... . . . .:"-'- ,........ - .i'- / -----------

I • I :

S. ... * . . . . . - - " - - * . . -a. . .. T . .. . . . -... . . . . .--. . -... . .. -- ... ......-- ... .. 4--:- --- . . . . - . .. .

S..... -....... ..... i........-..J.......__.... ._.:.. .... . .... ~~

S• • • .I

A9Appendix A Sample Calculations

eY_________ DATE -ILW- SH4IRT .

OA 4...4

I. .I11

I SI C

A10 ~ ~ Appendi A apeCluain

Mum.sC. a TucT M,- P S..Et *3 'gy Ser- OATE 8I6 HICE7 fMITJ..E&

FTTI

-*1 4

-__L I__. __,_ ii

SAL"- -Z-- - T - -4-'r -----

50;. f .. . .

- ~ij~ -i j '¾;

111. _ _ -.-. -2 , __ __ t l,7 I' ".' r

_____ , I_- -, --- .- _ --- ---___ _ -- '--___ , •_

S! F ti ___i_________ ______ _ .__.__ .____T__

* I _ _I I _ _ _

- -7-i-. ' - W--s.. - -.

* . I. j j

______ I__.., )I

i I-"i i SamIpl Cacua n A

-- *'-.-------'--"-' --"i _ - .-- --, ... . . .... i i V±Q.'_Q.•-(... " '...... -. .. ..I " fiL ; '-

_-_- L•.i .... •,. • ;,• ;,- •:- -z~-•,__,.,, o, =-, o ' : All.

Ap.e....A.ampl Calculations /,"!4•x,,I "

*• ., . t- ,, . .

By

! .OATS 86L41DI ML

1ji --W .I

-- -- d---•-~ -. .-----

.- ..

iii : O; I I

: I 'I I

I

' •. • I ,I. ! i .! .

_ II Ii

.hLL

-ý14

- ---- - , I

7I I

,

i !! If' i , ' i i I

_ _ , _ _ _

_' " ' .,• ._ :_'__ _•__ __• _L _ _._ -; _ _.. . _._ _. _ . -• . . I '_ _ _ _ _ _ _ _ _ - I- , _ _ _ '

__"___•

!__-

-7

A12 Appendix A.- . Caciai o-- -.... n

-I 4

A12 Appendix A Sample Calculations

- - .. I, NO ,•oe __ NO_,__._

A I

I-- I!

•.. S -F ; S L fý. .i '

-I-.t- .-J-• -

F i. o . ,- -F -l - - -

It

-7-

-T--

tt -j .

Appendix A Sample Calculat i iA

S.r!I __ "-__ -'

S , ,- ' ! I I i i ! ; I I '; I ,~i

I 7 .-- -.-. . ... . . .. . - -. -.... ,. ........... i-

' I I ___,______

~iil i! ] I ; 'i. , . i I~ ~ - I _ _ I " . __ _ _

S. . . -' l : " : " I I , I -. . . . .. ,_ . ..... .. .. __ . . ..... __... . _- -S* : I . __ __ _ __

!.4. - , L 1. - ,. ;___ , I ____

T 13Append-i---x A amleCacuato

-Jo No.,

a N c~r A 301 81466 -1,L of ____

'4-

I t

T- I

4'4 JI4. zL--V- 0 -18.

2AA

4-- o 11-7 13,4 z!IFS

-~~~I . aIr3El7J -I-7~! -,-.1--.-l I

Z3. i~~c

A t14 Apeni A- Sapl Caclain

- :- •-. : -'J - no. -.

mm.. su VJL,.- r L.. .

ey AT 51L. 11- , IT ý.

-I I-z!.1-0 1 4

S, j j:! [

_, _ •_ -- •. I i o

-. G

0 .-. 4,,Z ?. A,

S i AD I I _L7,. , F :/ . I pa U. P.

r .l - . .- . .' I __ _ ; S' ; ' __ .

' I I I , ,

,. ;-t - _ _ - - --- /22.1--1_.. .._ " . . .. I 1±.: . .. ... .__

• ... ii ± ... x :7 .L __ *

~4Li I L~h7'~:-~

fiI i i ,

,I i i I- " - -'- - , .. . ---. . -4"''-.. .• . .. . ... ...- -..- . .... .. .

, ! , ,I _ _ _ _ _ _ _ _ . _ _ ,_ _

t i

-- .. . .. • . . ... ;-4 . . .. .. . - ----- - - - -• ..... . ... .. .. . • -

A15Appendix A Sample Calculations

JoeNo.

• -I iI - L , " 1; 'I

i -I- +i I • , , l ui ! • I '-i : I I . . • ',

; -L• ---~ I , * I I .; • I T' •-I, I I f : ;I ' : . i

_I -- I 1 �- -- :.i • , TAl l: .Z

* L . I _ I i K 4'. I 1 • • ,• ;.

,__ _ _ _ _ _I ,_ _ _ ; ._ € • .L l• •L ; • ,L • -. ,

• ,• '".. . -

__ __ __ :, , • i I 5Z i a, z ! o' ! • 0 / i I , , g; 2-I-~(A /l313~(OJ~,'- ' "• '• - •- - -- • .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

. . . ... .

•.•-- • ..4------I i ---- :---•- . , l -f3 L -, ~ "C " -I

I•,

61- lo ;k

-g eD -r .- 2o (to)

, - -,--

.1 1L. . .. -T

A16 Appendix A Sample Calculations

-~ -4-:

•44;1YIVsoJI 7

-- T_ __ _ -- -----T .- --.--

- - I..~~~2 . ** . -

-J.. , 1U JL;_.

Appendix__ ___ __ A Sa peCacltin21

REPORT DOCUMENTATION PAGE Do fNo. 0o70418

"P.Mic oo•wing burdn for this collectiOn of information is estimated to avrae 1 hour plf reueonw including the time foe revieming instructions, searching exiting data source.gathering an mIantaiong the data needed, and compileting and reu9ewin the collection Of information Send comments, regarding this burden estimate or anv other aloe" of tficoltion of information. ncfuding wggeslions for reducing this burldnW.e(0 *aAngton of eaqartir" Stervices. Oirectorate for information Operations aid Reports. 1211 miffenonODais Hlighway, Suite 1204. Arlington, VA 22202-4302 and to the Office of Management and Budget. *apelork Reduction Prtfect (0704-CN). Wathington. DC 2M003

i. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVEREDI Otmher 199"4 I Fnal renowrt

4. TITLE AND SUBTITLE S. FUNDING NUMBERS

Incorporation of Wall Movement and Vertical Wall Friction in the Contract No.Analysis of Rigid Concrete Structures on Rock Foundations DACW39-86-M-4062

6. AUTHOR(S) WU 32648

Shannon and Wilson. Inc.

7. PERFORMING ORGANIZATION NAME(S) AN£ ADORESS(ES) B. PERFORMING ORGANIZATIONREPORT NUMBER

Engineering and Applied GeosciencesSt. Louis, MO 63141-7126

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESSRES) 10. SPONSORING/MONITORING

U.S. Army Corps of Engineers AGENCY REPORT NUMBER

Washington, DC 20314-1000;U.S. Army Engineer Waterways Experiment Station Technical ReportGeotechnical and Structures Laboratories REMR-GT-21"2Q0,A•s &.olf , Ina Vir.Irehivr.. - M QR112__i4100

11. SUPPLEMENTARY NOTES

This report is available from National Technical Information Service, 5285 Port Royal Road, Springfield,VA 22161.

12a. DISTRIBUTION / AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Approved for public release; distribution is unlimited.

13. ABSTRACT (Maximum 200 words)

This report presents recommendations for modifications to the present Corps of Engineers' si. hilityanalysis for concrete gravity structures. These modifications are intended for use in conjunction with thecurrent analysis procedures for a more accurate assessment of the factor of safety of existing structures. Itis concluded from this study that the effects of wall friction and strain compatibility are significant whenthe foundation rock modulus is relatively low.

14. SUBJECT TERMS 15. NUMBER OF PAGES

Gravity structures Strain compatibility AGStability Wall friction 16. PRICE CODE

17. SECURITY CLASSIFICATION IS. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACTOF REPORT O 4IS PAGE OF ABSTRACT

UNCLASSIIIED UNCLASSIFIEDNSN 7540-01-280-5500 Standard Form 298 (Rev 2-89)

Prescribed by ANSI SWt Z39-16298-102