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DAEN-ECE-D DAEN-ECE-G

Engineer Circular No. 1110-2-510

DEPARTMENT OF THE ARMY U.S. Army Corps of Engineers

Washington, DC 20314

S-29 June 1984

EC 1110-2-510

31 August 1983

EXPIRES 30 JUNE 1984 Engineering and Design

DRAFT OF ENGINEER MANUAL, RETAINING AND FLOOD WALLS

1. Purpose. This circular is to distribute a draft Engineer Manual 1110-2-XXXX, Retaining and Flood Walls, for interim guidance and review comments.

2. Applicability. This circular applies to all field operating activities having civil works responsibilities.

3. Discussion. This draft EM provides guidance for the design and analysis of retaining walls and flood walls of the gravity, reinforced concrete and sheet pile types. The draft EM combines EM 1110-2-2501, Flood Walls, and EM 1110-2-2502, Retaining Walls, into one manual.

4. Action Required. A review of the draft EM should be made by all applicable division and district design offices as well as applicable construction and operations elements. District comments are to be sent to their respective division office. Division offices will review all comments and forward them with their additional comments to

CDR USAGE (DAEN-ECE-DS) WASH DC 20314 by 29 June 1984. RCS exempt: AR 335-15, paragraph 5-2g.

FOR THE COMMANDER:

1 Appendix APP A - Draft EM

•*. ROBERT H. RYAN Colonel, Corps of Engineers Executive Director Directorate of Engineering &

Construction

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% DAEN-ECE-D DAEN-ECE-6

Engineer Manual No. 1110-2-XXXX

APPENDIX A

DEPARTMENT OF THE ARMY U.S. Army Corps of Engineers

Washington, D.C. 20314

DRAFT

EC 1110-2-510 31 Aug 83

Engineering and Design RETAINING AND FLOOD WALLS

Table of Contents

CHAPTER 1.

0 CHAPTER 2.

Section I.

Section II

Section III

Subject

INTRODUCTION

Purpose Applicability References Scope Terminology

GENERAL DESIGN CONSIDERATIONS

Types of Retaining Walls General Gravity Concrete Wall Cantilever Reinforced Concrete

Wall Sheet Pile Walls

Types of Flood Walls General , T-Type Wall Cantilever I-Type Wall , Other Types of Flood Walls . . . .

Differences between Retaining and Flood Walls

Purpose of Walls , Seepage and Leakage Control

Requirements Wall Stability Special Monoliths Design Philosophy

Paragraph

1-1 1-2 1-3 1-4 1-5

Page

2-1 2-2

2-3 2-4

2-5 2-6 2-7 2-8

2-9

2-10 2-11 2-12 2-13

2-1 2-1

2-1 2-1

2-3 2-3 2-3 2-3

2-3

2-6 2-6 2-6 2-6

0 DRAFT

V *

EC 1110-2-510 31 Aug 83

Section IV.

Section V.

Section VL

CHAPTER 3.

Section 1.

Section II.

Section III,

2-14 2-6 2-15 2-7

2-16 2-7 2-17 2-7 2-18 2-7 2-19 2-8

Subject Paragraph Page

Coordination between Disciplines

Stability Considerations Coordination ...... .

Foundation Infestigation and Laboratory Testing

General............... Field Investigation. ........ Sampling ...... . . Strength Testing . . Design Strengths

Strength Reduction Factors

General. 2-21 2-8

FORCES ON WALLS

Lateral Earth Pressures General. .............. 3-1 3-1 Single Wedge Equation. 3-2 3-1 Strength Reduction Factor 3-3 3-1 Wedge Geometry 3-4 3-5 Critical Value of Slip

Plane Angle. 3-5 3-8 Line of Action of Lateral Forces . . 3-i 3-12 Lateral Pressure Distribution. ... 3-7 3-14 Wedge Analysis in Layered Soil . . . 3-8 3-14 Irregular Backfill Configurations. . 3-9 3-14

Water Pressures General. .............. 3-10 3-17 Seepage Analysis by Line

of Seepage Method 3-11 3-17 Seepage Analysis by Method

of Fragments 3-12 3-17 Surge and Wave Loads ........... 3-13 3-21

Supplemental Forces Wind Loads 3-14 3-24 Lateral Earthquake Forces ..... 3-15 3-25

ii

•j

Subject

CHAPTER 4.

Section I.

Section II.

Section III.

Section IV.

Section V.

CHAPTER 5.

Section I.

STRUCTURAL STABILITY

EC 1110-2-510 31 Aug 83

Paragraph Page

Section II.

Loading Cases General 4-1 Retaining Walls 4-2 Inland Flood Walls 4-3 Coastal Flood Walls 4-4

Stability Requirements General 4-5 Stability Criteria 4-6

Overturning Stability Resultant Location 4-7 Criteria 4-8

Sliding Equilibrium Analysis Model 4-9 Introduction to Analysis Procedure . 4-10 Sliding Analysis for Design 4-11 Sliding Analysis for Investigation . 4-12 Basic Concept, Assumptions and Simplifications 4-13

Design Considerations 4-14

Base Pressures Computation of Base Pressures. ... 4-15 Allowable Base Pressures 4-16

FOUNDATION ANALYSES

Bearing Capacity of Wall Foundations General 5-1 General Bearing Capacity Equation. . 5-2 Bearing Capacity Factors 5-3 Embedment Factors 5-4 Inclination Factors. . 5-5 Base Tilt Factors 5-6 Ground Slope Factors 5-7 Effective Overburden Pressure. . . . 5-8 Example 5-9

Settlement General 5-10

4-1 4-1 4-1 4-2

4-2 4-3

4-3 4-3

4-3 4-3 4-9 4-9

4-15 4-16

4-17 4-18

5-1 5-1 5-2 5-2 5-2 5-4 5-4 5-5 5-5

5-5

m

EC 1110-2-510 31 Aug 83

Section III.

CHAPTER 6.

CHAPTER 7.

Section 1.

Section II.

Section III.

Section IV.

Section V.

Section VI.


Deep Seated Sliding General 5-11 5-5

DESIGN AND CONSTRUCTION DETAILS

Foundation Preparation 6-1 6-1 Concrete Mix Design 6-2 6-1 Constructability 6-3 6-1 Joints 6-4 6-1 Backfilling 6-5 6-3

SPECIAL CONSIDERATIONS FOR FLOOD WALLS

General Introduction 7-1 7-1 Background Behind Loading Cases. . . 7-2 7-1

Seepage Control General 7-3 7-2 Underseepage Control 7-4 7-2 Choice of Seepage Control Measures . 7-5 7-10

Foundation Considerations Base Types 7-6 7-10 Unsuitable Foundation Material

and Overbank Fills 7-7 7-11 Scour Protection 7-8 7-11

Types of Monoliths Change of-Alignment Monoliths. . . . 7-9 7-14 Closure and Abutment Monoliths . . . 7-10 7-14 Drainage Structure Monoliths .... 7-11 7-14 Transition Section Between Flood

Walls and Levees 7-12 7-14

Waterstops and Joints Waterstops 7-13 7-18 Contraction and Expansion Joints . . 7-14 7-18

Site Considerations Adjacent Structures and Rights-of-

Way 7-15 7-18 Architectural and Landscaping

Considerations 7-16 7-19

IV

/

Section VII.

Section VIII.

Section IX.

CHAPTER 8.

CHAPTER 9.

CHAPTER 10.

CHAPTER 11.

APPENDIX A.

APPENDIX B.

Subject 1

Instrumentation General .............. Types of Instrumentation. .....

O&M Manual Requirements General

Review of Existing Flood Walls Inspection. ............ Repair Measures ..........

GRAVITY CONCRETE WALLS

oenera i . ...... ...•*.. Foundation Investigation. ..... Materials ............. Design. ..............

CANTILEVER REINFORCED CONCRETE WALLS

General .............. Foundation Investigation. ..... Materials ............. Reinforcement Cover ........ Load Cases. ..... . . Structural Stability. ....... Reinforced Concrete Design Foundation Analyses ...

CANTILEVER SHEET PILE WALLS

General .............. Materials ............. I-Walls .............. Design .............. Foundation Investigation .....

ANCHORED SHEET PILE WALLS General .............. Materials ............. Design ..............

REFERENCES

DERIVATION OF EQUATION FOR DEPTH OF TENSION CRACK

EC 1110-2-510 31 Aug 83

Paragraph Page

7-17 7-18

7-19

7-19 7-20

7-21

7-20 7-21 7-21 7-23

8-1 8-1 8-2 8-1 8-3 8-1 8-4 8-1

9-1 9-1 9-2 9-1 9-3 9-1 9-4 9-1 9-5 9-1 9-6 9-1 9-7 9-1 9-8 9-15

10-1 10-1 10-2 10-1 10-3 10-1 10-4 10-2 10-5 10-3

11-1 11-1 11-2 11-1

s

EC 1110-2-510 31 Aug 83


APPENDIX C. DERIVATION OF EQUATION FOR SLIP PLANE ANGLE

APPENDIX D. DETERMINATION OF LINE OF ACTION FOR HORIZONTAL FORCES

APPENDIX E. DERIVATION OF STRUCTURAL WEDGE EQUATION

APPENDIX F. DERIVATION OF GENERAL WEDGE EQUATION

APPENDIX G. CANTILEVER WALL DESIGN EXAMPLE

APPENDIX H. CANTILEVER WALL INVESTIGATION EXAMPLE

APPENDIX I. NOTATION - CHAPTERS 3, 4 and 5

APPENDIX J. NOTATION - CHAPTER 9

VI

DRAFT EC 1110-2-510 31 Aug 83

CHAPTER 1

INTRODUCTION

1-1. Purpose. The purpose of this manual is to provide guidance for the safe design and economical construction of retaining walls and flood walls This manual does not prohibit the use of other methods of analysis that maintain the same degree of safety and economy as structures designed by the methods outlined. However, if other methods of analysis are used, the final design should be checked by the methods outlined herein.

-2. Applicability. This manual applies to all HQUSACE/OCE elements and 11 field operating activities having responsibilities for the design of

1-2.

civil works projects.

1-3. References. References pertaining to this manual are listed in Appendix A.

1-4. Scope.

a. Types of Walls. This manual presents design guidance for retaining walls and inland and coastal flood walls.

b. Types of Foundations. This manual describes procedures for the design of retaining and flood walls on shallow foundations, i.e., bearing directly on either rock or soil. The substructure design of pile founded walls is not included.

c. Flood Wall Guidance. A flood wall is treated as a special case of a retaining wall. Unless specifically noted, the guidance herein applies to both retaining and flood walls.

d. Geotechnical and Structural Aspects. Both geotechnical and struc¬ tural aspects of design are considered. Coordination between soils and structural engineers and geologists in the design of retaining and flood walls is essential.

1-5. Terminology. The following definitions are essential to the use of this manual.

a. Retaining Wall. Any wall which restrains material to maintain a difference in elevation.

b. Flood Wall. Any wall having as its principal function the preven¬ tion of flooding of adjacent land.

c. Wedges. Those individual parts of the backfill, structure and foundation which can be separated into piece-wise linear approximations of the slip surface.

1-1

V

EC 1110-2-510 31 Aug 83 l-5d

d. Active-type Wedges. Those wedges exerting lateral forces on the structure that tend to cause movement of the structure.

e. Passive-type Wedges. Those wedges exerting lateral forces on the structure that tend to resist movement of the structure.

f. Strength Reduction Factor. The coefficient by which the shear strength of the sliding mass, consisting of the structural and active- and passive-type wedges, is multiplied to obtain the shear stress needed to bring the sliding mass into a state of equilibrium along a given set of slip planes. It is equal to the reciprocal of the safety factor

g. Load Factor. The coefficient by which a load is multiplied to design structural members by the strength design method.

h. Safety Factor. The factor determined by dividing the total resisting force or moment by the total applied force or moment.

1-2

DRAFT EC 1110-2-510 31 Aug 83

CHAPTER 2

GENERAL DESIGN CONSIDERATIONS

Section I. Types of Retaining Walls

2-1. General. The most common types of retaining walls are gravity, cantilever reinforced concrete, and cantilever and anchored sheet pile walls. These types are covered in the manual and are illustrated in Figure 2.1. Counterfort and buttressed reinforced concrete walls are used less commonly and are not included in the manual.

2-2. Gravity Concrete Wall. A gravity wall (Figure 2-1) consists of mass concrete without reinforcement. It is proportioned so that the resultant of the forces acting on any internal plane through the wall falls within, or close to, the kern of the section. A small tensile capacity is permissible for localized stresses due to extreme and temporary loading conditions.

2-3. Cantilever Reinforced Concrete Wall. A cantilever reinforced concrete wall (Figure 2-1) consists of a concrete stem and base slab, which form an inverted T. The structural members are fully reinforced to resist applied moments and shears. The base is made as narrow as possible, but must be wide enough to insure that the wall does not slide, settle excessively, or exceed the bearing capacity of the foundation. The toe of the base should be below the zone subject to freezing and thawing or other seasonal volume changes. This type of wall is usually more economical and is more widely used than any other type.

2-4. Sheet Pile Walls. Sheet pile walls (Figure 2-1) usually consist of standard steel or precast prestressed concrete sections.

a. Cantilever Sheet Pile Wall. The cantilever type is used where the difference in elevation between the fill and the dredge line is relatively small. Pile embedment below the dredge line must be sufficient to develop the total resisting force and moment required for overturning and sliding stability.

b. Anchored Sheet Pile Wall. The anchored type is used where the difference in elevation between the backfill surface and the dredge line is large enough to make the use of the cantilever type infeasible. A tie, anchored to a concrete deadman some distance from the wall, is used near the top of the wall. The wall acts as a beam overhanging one support, the tie, with the other support being the depth of embedment below the dredge line.

2-1

EC 1110-2-510 31 Aug 83

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/•• •/•./ v • i^" /•*."-'* ."'.' \ #v v>....:.

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GRAVITY SHEET PILING-

DREDGE LINE —3W5I mJr/ N

/MWW/

^■W:-->.:--:--..-*v:.-.-.*:

CONCRETE CANTILEVER

SHEET PILING

n TIE W*#t&/>

DREDGE LINE

//jwkrv

ANCHOR

iy^l

CANTILEVER SHEET PILE ANCHORED SHEET PftE

FIGURE 2-1. TYPES OF RETAINING WALLS

2-2

EC 1110-2-510 2-5 31 Aug 83

Section II. Types of Flood Walls

2-5. General« The most common types of flood walls are T-type walls and cantilever I-type walls.

2-6. T-Type Wall. Most flood protection walls are of the inverted T-type (Figure 2-2). The cross bar of the T serves as a base and the stem serves as the water barrier. When founded on earth, a vertical base key is sometimes used to increase passive resistence. A key is usually not included if the wall is founded on rock. When required, the wall can be supported on piles. A sheet pile cutoff can be included to limit seepage in a foundation of coarse grained material or for a pile-founded wall. T-type walls may be provided with a horizontal or sloped base. These walls are discussed in detail in Chapter 7. The advantages of sloped and horizontal bases are discussed in paragraph 7-6

2.7. Cantilever I-TypeWall. I-type flood walls consist of driven sheet piles capped by a concrete wall (Figure 2-2). I-walls are most often used in connection with levee and T-wall junctions or for protection in narrow restricted areas where the wall height is not over 10 feet. These walls are discussed In Chapter 10.

2-8. Other Types of Flood Walls.

a. Braced Sheet Pile Wall. This wall consists of a row of vertical pre-stressed concrete sheet piles, backed by batter piles connected to the sheet piles by a cast-in-place horizontal concrete beam (Figure 2-2). This type of wall has been used for coastal flood walls. It is ideal for wet areas because no excavation or dewatering is required to construct the wall. The disadvantage is that it does not lend itself to a rigorous analysis. The design of this wall will not be included in this draft.

b. Other Types. There are various other types of walls that may be used for flood walls, such as: buttress, counterfort, gravity, cellular, and inclined-deck walls (Figure 2-3). These walls will not be further discussed in this chapter, but details concerning the design of these walls may be found elsewhere in this manual or in standard textbooks or trade journals.

Section III. Differences Between Retaining and Flood Walls

2-9. Purpose of Walls. A retaining wall is any wall which retains material to maintain a change in elevation; whereas, the principle function of a flood wall is to prevent flooding (inundation) of adjacent land. It is subject to hydraulic loading on one side which is resisted by little or no earth loading on the other side.

2-3

EC 1110-2-510 31 Aug 83

SHEET PILE

HORIZONTAL ftASE KEYED HORIZONTAL BASE ' SLOPED lASE INTO STROtfrCR SOIL

INVERTED T-TYPE WALLS

HhN TINT

TYPE. I TYPE 2 TYPE 3

CANTILEVER I-TYPE SHEET RLE WALL

7ir\\ w—wr-—w

FHar. %™ ING LES

BRACED SHEET PILE COASTAL FLOOD WALL

FIGURE 2-2. TYPES OF FLOOD WALLS

2-4

EC 1110-2-510 31 Aug 83

SHEET PILE

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SHEET P>LE

INCLINED DECK

w. s.

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SHEET PILE-

L.S.

SHEET PILE

BUTTRESS AND COUNTERFORT

GRAVITY

FIGURE 2-3. LESS COMMONLY USED FLOOD WALL TYPES

2-5

EC 1110-2-510 31 Aug 83

2-10. Seepage and Leakage Control Requirements. All water-retaining structures are subject to seepage through, under and around them. Inadequate control of the seepage may affect the stability of a flood wall from uplift or loss of support resulting from erosion. Properly controlled seepage, even if quantities of flow remain large, presents little or no hazard. Control of through-seepage is provided by waterstops. Retaining walls rarely need seepage protection other than to relieve the hydrostatic load on the fill side of the wall Waterstops are used in retaining walls to prevent water in the backfill from passing through the vertical joints. Seepage control and waterstops are more fully discussed in Chapter 7.

2-11. Mall Stability. Generally, it is more difficult to stabilize flood walls than retaining walls. By their very nature, floodwalls are usually built in a flood plain which has poor foundation conditions. Uplift is always a critical item with flood walls and seldom a problem with retaining walls. The loads acting on a retaining wall are usually soil backfills. The water load on a flood wall is more severe, especially when wave loadings are applicable. When the ground water surface is above the wall footing, a corrmon occurrence with flood walls, the allowable bearing capacity of the soil is reduced.

2-12. Special Monoliths. For flood walls special monoliths are required often. Special monoliths are those which have design conditions that require the monolith to be designed as a total unit.

2-13. Design Philosophy. Retaining walls are normally built as an appurtenance to other structures; such as a dam, a hydroelectric power house, a pump station, etc. The consequences of failure of a retaining wall are seldom high, unless, of course, the wall failure could trigger the failure of a more significant structure such as failure of an embankment dam. Also, retaining walls are seldom more than a few hundred feet long; so if they are designed conservatively, the added costs are of limited significance. Flood walls, on the other hand, are usually the primary feature of a local protection project. They must be designed for the most economical cross-section per unit length of wall, because they often extend for great distances. Added to this need for an economical cross-section is safety. The consequences of failure for a flood wall are normally very great since it is protecting valuable property and human life. Thus, the design of retaining and flood walls is a complex process involving safety and economy which must be executed in a logical, conservative manner based on the function of the wall.

Section IV. Coordination, Between Disciplines

2-14. Stability Considerations. An adequate assessment of stability must account for the basic structural behavior, the mechanism of transmitting compressive and shearing loads to the foundation, the reaction of the foundation to such loads, and the secondary effects of the foundation behavior on the structure.

2-6

EC 1110-2-510 2-15 31 Aug 83

2-15. Coordination. A fully coordinated team of soils and structural engineers and geologists should insure that the results of stability analyses are properly integrated into the overall design. Some of the critical aspects of design which require coordination are;

a. Preliminary estimates of geotechnical data, subsurface conditions, and types of structures which are suitable for the foundation.

b. Seclection of loading conditions, loading effects, potential failure mechanisms and other related features of the analytical models.

c. Evaluation of the technical and economic feasibility of alternative type structures.

d. Constructabilityreviews, in accordance with ER 1110-1-803.

e. Refinement of the preliminary structure configuration to reflect the results of detailed geotechnical site exploration, laboratory testing and numerical analysis.

f. Modification to the structure configuration during construction due to unexpected variations in the foundation conditions.

Section V. Foundation Investigation and Laboratory Testing

2-16. General. Of all the geotechnical elements needed to assess the stability of any wall, the strength parameters for the foundation are the most difficult to determine. This determination is made by analysis of laboratory and field tests coupled with intimate knowledge of the geological structure of a rock foundation or inhomogeneities of a soil foundation.

2-17. Field Investigation. A field investigation must be a continual process starting with the preliminary geological review of conditions progressing to a detailed boring and sample testing program, and concluding at the end of construction with a safe operational structure. The scope of investigations and sampling should be based on an assessment of the inhomogeneity or geologicial complexity. For example the extent of the investigation could vary from quite limited where the foundation material is strong even along the weakest potential failure planes to quite intensive and detailed where weak zones or seams exist. However, it must be recognized that a certain minimum of investigation is necessary to determine that weak zones are not present in the foundation.

2-18. Sampling. Representative soil and rock samples including undisturbed soil samples are required to determine the engineering properties of the materials. Rock and soil sampling are discussed in EM 1110-1-1801, Geologic Investigations, EM 1110-2-1803, Subsurface Investigations, Soils, and EM 1110-2-1907, Soil Sampling.

2-7

EC 1110-2-510 31 Aug 83

2-19. Strength Testing. The nearly infinite number of combinations of soil and rock properties and rock structural conditions preclude a standard universal approach to strength testing. Soils engineers and geologists must clearly define the purpose of each test to those who will supervise the testing. All available data from geological and geophysical studies must be used in selecting representative samples for testing. Decisions must be made concerning the need for in-situ testing. Soil testing procedures are discussed in EM 1110-2-1906, Laboratory Soils Testing. Rock testing procedures are discussed in the Rock Testing Handbook^ and in the International Society of Rock Mechanics, Suggested Methods for Determining Shear Strengths.28 These methods may be modified as appropriate to fit the circumstances of the project.

2-20. Design Strengths. Strength values used in stability analyses are determined from the available tests and through judgement. Information in EM 1110-2-1902 should be used in selecting design strengths for soils, where appropriate. There is no equivalent engineering manual which provides information on appropriate types of rock tests and selection of strengths. It is important that the types of tests be based upon the probable mode of failure. Generally, strengths on rock discontinuities would be used for an active-type wedge and beneath the structure. Where a passive-type wedge exists, strengths on discontinuities or intact rock, or a combination of the two, would be used. Refer to the stability criteria tables 4-1 through 4-3 (notes 1 through 4) for design strength and testing guidance.

Section VI. Strength Reduction Factors

2-21. General. Appropriate values of strength reduction factors depend on;

a. The design condition being analyzed.

b. Degree of confidence in design strength shear values.

c. Consequence of failure.

d. Thoroughness of investigation.

e. Nature of structure-foundation interaction.

f. Quality of construction control.

g. Judgement based on past experierice with similar structures.

In the final analysis, the consequence of failure with respect to human life, property damage, and impairment of functions are important considerations in establishing acceptable strength reduction factors for specific projects. Tables 4-1 through 4-3 list maximum strength reduction factors for the various design conditions and applicable types of shear tests.

2-8

DRAFT EC 1110-2-510

31 Aug 83

CHAPTER 3

FORCES ON WALLS

Section I. Lateral Earth Forces

3-1. General. The method of analysis described below for computing lateral earth forces is an adaption of the multiple wedge sliding equilibrium analysis described in paragraph 4-12b. Instead of computing the lateral earth forces from an iterative solution of a multiple wedge system, the lateral earth forces can be computed approximately from the single wedge equation shown in Figure 3-1. This approach allows the designer to compute the soil loadings prior to performing a sliding analysis.

3-2. Single Wedge Equation. The single wedge equation can be used for calculating the force due to an active or passive-type wedge. The sign convention is described in Figure 3-1. The single wedge equation is the same as the general wedge equation given in Figure 4-4 if only one wedge is being analyzed, i.e., (P-j-i-P-j) = P. The forces acting on the active and passive-type wedges are shown in Figure 3-2.

3-3. Strength Reduction Factor (SRF).

a. Definition. The SRF term in the wedge equation is the ratio of the applied shear stress (T) to the shear strength (Vpr) of the wedge material along the assumed sliding plane according to equations (3-2) and (3-3).

SRF = Tr/^F (3-2)

Since X=^TAN^ + C, according to the Mohr-Coulomb failure criterion (Figure 3-3),

T = SRF ( CTTAN fti ) + SRF (C) (3-3)

The quanity SRF ( 2jr) can be considered as a degree of strength mobilization.

b. Developed Shear Stress Parameters. The SRF reduces the shear strength parameters (TAN 0 and C) for the wedge materials to the developed shear stress parameters (TAN jzfj and C^) which would exist if the wedges acting on the wall are in sliding equilibrium. The developed shear stress parameters are related to the actual shear strength parameters by the SRF, as follows;

SRF = TAN ffj/TAN # = Cd/C (3-4)

3-1

p = (W +V) [(SRF)TAN^ COSa + SIN a]-U(SRF)TAN^+ (HL - HR ) [(SRF)TAN^ SIN a -COSa] + (SRF) CL

COS a -(SRF)TAN^ SIN a

WHERE:

P = LATERAL (HORIZONTAL) FORCE PRODUCED BY WEDGE,

W = TOTAL WEIGHT OF MATERIAL IN WEDGE, INCLUDING WATER.

V = ANY VERTICAL FORCE APPLIED TO THE WEDGE.

A = ANGLE BETWEEN THE SLIP PLANE OF THE WEDGE AND THE HORIZONTAL,

U = UPLIFT FORCE ACTING ON AND NORMAL TO THE SLIP PLANE OF THE WEDGE.

HL = ANY EXTERNAL HORIZONTAL FORCE APPLIED TO THE WEDGE, ACTING TO THE RIGHT.

HR = ANY EXTERNAL HORIZONTAL FORCE APPLIED TO THE WEDGE, ACTING TO THE LEFT.

<t> = ANGLE OF INTERNAL FRICTION ON THE SLIP PLANE OF THE WEDGE.

SRF= STRENGTH REDUCTION FACTOR

C = COHESION ON THE SLIP PLANE OF THE WEDGE .

EQ.(3-I)

L = LENGTH ALONG THE SLIP PLANE OF THE WEDGE.

SIGN CONVENTIONS TO BE FOLLOWED IN USING THIS EQUATION ARE".

a HAS A NEGATIVE SIGN WHEN ROTATION FROM THE HORIZONTAL, AT THE BASE OF THE WEDGE,

TO THE SLIP PLANE IS IN A CLOCKWISE DIRECTION (POSITIVE IS COUNTER-CLOCKWISE). H|_ AS

DEFINED IS POSITIVE. HR AS DEFINED IS POSITIVE. V IS POSITIVE WHEN ACTING DOWNWARD.

ALL OTHER VALUES |N THE EQUATION ARE ALWAYS POSITIVE.

FIGURE 3-1. SINGLE WEDGE EQUATION

EC 1110-2-510 31 Aug 83

TENSION CRACK

HR

FORCES ON ACTIVE-TYPE WEDGE

HL

FORCES ON PASSIVE-TYPE WEDGE

FIGURE 3-2. FORCES ON WEDGE;S

3-3

EC 1110-2-510 31 Aug 83

T

TF = o-TAN (t> +C

•m* <T

SHEAR STRENGTH ENVELOPE

FIGURE 3-3. MOHR-COULOMS eMUURE CRITERION

3-4

EC 1110-2-510 3-3b 31 Aug 83

In a single wedge analysis, the SRF applies only to that wedge of the sliding mass.

c. SRF for Computing Medge Forces. The actual value of the SRF for multiple wedges is determined by a trial and error procedure (applying the general wedge equation to each wedge), which continues until the sum of the horizontal forces acting on the wedges is equal to zero. To simplify this procedure for computing the forces exerted by the soil wedges on the structure, an SRF of 2/3 will be used for computing the critical slip plane angle (paragraph 3-5) and the corresponding force P (paragraph 3-2).

(1) Active-type Wedge Forces. The soil wedge forces computed using an SRF of 2/3 will give greater than active earth pressures since the shear strength of the soil is not fully mobilized. For a wedge with a horizontal surface and shear strength parameters of $ =: 30° and C = 0, an SRF of 2/3 gives a wedge force P equivalent to the force computed using an earth pressure coefficient of 0.47. (An SRF of 1 corresponds to an earth pressure coefficient of 0.33 as shown in Figure 3-4). The validity of using greater than active earth pressures for retaining walls, whether or not the wall can yield by an amount sufficient to reduce the lateral earth pressure to the minimum active state initially, is discussed by Casagrande29 and Matsuo, Kenmochi and Yagi30.

(2) Passive-type Wedge Forces. For a passive-type wedge with a horizontal surface and shear strength parameters of 0 = 30° and C = 0, an SRF of 2/3 gives a passive force equivalent to that computed using an earth pressure coefficient of 2.13. (An SRF of 1 corresponds to an earth pressure coefficient of 3.0 as shown in Figure 3-4). Since no shear strength needs to be mobilized, i.e., 0 = 0 and C = 0, to produce a passive force determined by an earth pressure coefficient of 1.00, the earth pressure coefficient of 2.13 represents a 56.5 percent (2.13-1.00)/(3.00-1.00) mobilization of the full shear strength resistance for the wedge described. However, if in the designer^ judgement, the wall deformations will not be sufficient to mobilize this partial passive resistance, a lower SRF than 2/3 can be used in order to be compatible with expected deformations. The minimum passive resistance for a soil wedge should be the weight of the wedge defined by alpha («*< ) = 45°. This is equivalent to an earth pressure coefficient of LOO. See Figure 3-4.

(3) The rationale for assigning the SRF values something other than 2/3 should be developed in consultation with and approved by HQUSACE (DAEN-ECE).

3-4. Wedge Geometry, The geometries of a typical active-type and a typical passive-type wedge are shown in Figure 3-5. The active-and passive-type wedges should always be oriented as shown in these figures, in order that the lateral forces produced by active-type sedges will always be negative and those produced by passive-type wedges will always be positive. The absolute value of alpha is used in calculating the

3-5

EC 1110-2-510 31 Aug 83

p=KArh

SRF=

1 ^/-V-*'^'*-5-"*--''!

•—, »

.33rh L

.47Xh

SINGLE ACTIVE WEDGE

Jj ^

P = Kprcl'

TS^r

SRF = T

SRF=I ■ ,T

-V

rd

z.isrd

s/d

SINGLE PASSIVE WEDGE

FIGURE 3-4. SINGLE ACTIVE AND PASSIVE WEDGES

3-6

EC 1110-2-510 31 Aug 83

TENSION CRACK ACTIVE WEDGE ONLY-

h-dc COS a _ SlN (a-jfel)

a . (h-dc)COSa SIN(a-)Q)

TRIG. IDENT.: SIN (0-0) = SIN a

h-dc TAN a COSp -SIN£

L _ o COS/3 _ COS a " SIN a - TAN

k/3 aCOS)S =

h-dc TAN a -TAN )Qu

o

-

<£>

1 o

1

JC

ACTIVE TYPE WEDGE

TAN a - TAN B

c-SLIP PLANE

PASSIVE TYPE WEDGE

JIT I I i GUBE 3-5. WEDGE GEOMETRY

3-7

EC 1110-2-510 31 Aug 83 3-4

dimensions in Figure 3-5, and beta (/S) is taken as positive for top surfaces sloping upward away from the vertical faces of the wedges. The value of dc (the depth of the tension crack) is given by:

[1 - (SRF) TAN <(> TAN a] (SRF) c x-gx

"y [1 + (SRF) TAN + COT a] [ (SRF) TAN + SIN2a — SIN a COS a]

The proper sign convention for alpha is used in calculating dc. See Appendix B for the derivation of Equation 3-5.

3-5. Critical Value of Slip Plane Angle.

a. General. The magnitude of the horizontal force P for either the typical active-tyt)e or passive-type wedges is a function of the orientation of the slip plane as defined by alpha. The critical angle alpha for the active-type wedge is that angle which gives the maximum force P. The critical angle alpha for the passive-type wedge is that angle which gives the minimum force P. For a backfill with an irregular surface, a trial and error process varying alpha is usually needed to determine the critical alpha. But for the special case of a backfill with an unbroken top surface, and a strip surcharge V, the following equation can be used to compute the critical alpha for an active-type wedge:

Y-c, " \/c?+ 4cA a=TAN",l ! -) (3-6)

The critical angle alpha for a passive-type wedge with an unbroken top surface, supporting a strip surcharge V, is given by the equation:

•ci + V c7+ 4c- a=TAN

/77 (3-7)

3-8

>

EC 1110-2-510 3-5a 31 Aug 83

For the active-type wedge the general equations for cj, and C2 are,

(1) for a cohesionless backfill:

c, = 2(SRF)TAN f ; (3-8a)

(SRF)TAN<K1 - (SRF)TAN <(. TAN/?] -TAN/3 ,. ... C2 = ■ (3-8bJ

(SRF)TAN <}>

(2) for a cohesive or cohesionless backfill with a strip surcharge:

4(SRF)C [(SRF) TAN + + TAN p] 4V TAN p [1 + (SRFrTAN^]

2(SRF)2TAN^ + y(h + dc) , y(h2-dc2) (3-9a)

c, =.

2(SRF)C [1 - (SRF)TAN j TAN p]

(SRFJTAN f [1 - (SRF)TAN p] -TAN/J +| y (h + dc) j C2 =; :

A l

2V TAN/?2 [1 + (SRF)2 TAN2<t>] ,2 _ J 2 rW-dS) (3-9b)

where

A = (SRF)TAN + + 2(SRF>C [' - (SRF)TAN + TAN p] _ 2V[1 +(SRF)Z TAN2<H y (h + dc) y (h2 - dc

2)

3-9

EC 1110-2-510 31 Aug 83 3-5a

For a passive-type wedge, the equations for cj, and C2 are the same as for the active-type wedge except that the value of dc is always taken as zero. See Appendix C for the derivation of Equations 3-6 and 3-7.

b. Limitations of Critical Slip Plane Equations. The equatii :i and eg are valid except when the strip surcharge, V, is too lai ions for

ci and eg are valid except when the strip surcharge, V, is too large or when the slope of the top surface is too great. The maximum value for the strip surchage is determined by setting the denominator of the equation for ci or C2 equal to zero and solving for V. This value is:

VM _ r (h2 - dc2KSRF)TAN + + 2(SRF)C(h - dc)[l -(SRF)TAN + TAN ffi (3-10)

2[1 + (SRF)2 TAN2<}>]

When V^V^ the value of alpha is set by the location of the strip surcharge as shown in Figure 3-6, and given by the equation:

[ABSOLUTE VALUE] a = TAN "h -dc + (S)TAN<n p.-Q)

Even when }J<ym9 a check should be made to be certain that the entire strip surcharge lies on the top surface of the wedge defined by the calculated value of alpha. Also when {c|+4c2)< 0, alpha is indeterminate. This is an indication that the slope of the top surface is too great to be sustained by the strength parameters (SRFJTAN # and (SRF)C.

c. Critical Slip Plane Equations for Backfills with Horizontal Top Surface. The critical value of alpha for an active-type wedge with a horizontal top surface and with or without a uniform surcharge can be computed as follows:

a= 45° + 2£ WHERE 2

(3-12)

+d = TAN-HCSRFJTAN^]

For a passive-type wedge with a horizontal top surface alpha can be computed as follows:

3-10

* M

EC 1110-2-510 31 Aug 83

EDGE OF STRIP SURCHARGE

V>Vvi

SLIP PLANE

h-dc TAN a - TAN £

TAN a ■^S_ + TAN/? h - dc + S TAN /3

S

D ABSOLUTE VALUE a = TA ■] a = TAN"1 f- h-dc + STA JLL)

FIGURE 3-6. SURCHARGE EFFECT ON CRITICAL SLIP PLANE

3-11

EC 1110-2-510 31 Aug 83 3-5c

a=450-ii (3-13) 2

3-6. Line of Action of Lateral Forces. A typical wedge is shown in Figure 3-7. The total lateral force, P, produced by this wedge may be separated into five parts; Py due to the surcharge, P^ due to the moist weight of the material in the wedge, P^s due to the difference in weight between saturated and moist material in the saturated part of the wedge, Py due to uplift on the slip plane, and PQI due to the cohesive resistance along the slip plane.

Then P = Py + PWM + Pws + Pu + PCL (3-14)

where

p V[(SRF)TAN 4 COS a + SIN a] (3.14a) V COS a - (SRF)TAN <|> SINa

PWM = WM[(SRF)TAN + COS a + SIN a] (3-14b) COS a - (SRF)TAN 4 SIN a

WS[(SRF)TAN <}> COS a + SIN a) (3- 14;C) COS a - (SRF)TAN 4 SIN a

Pu = -U(SRF)TAN4 (3-14d) COS a -(SRF)TAN ^SIN a

(SRF)CL (3-14e) ret =

COS a - (SRF)TAN <|> SIN a

Setting the summation of moments about point C equal to zero we obtain

["(h - dc)(h2+ 2dc)1 /h - dc\ 3 Py Hy + PWM h + dc J + Pws Hs + Pu Hs + 3 PCLV 2 /

3P

and the line of action of the force P is determined. The derivation for the location of the line of action of P^m is given in Appendix D.

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EC 1110-2-510 31 Aug 83

CRACK; ACTIVE WEDGE- COHESIVE MATERIAL ONLY.

S-X

SLIP PLANE FOR ENTIRE WEDGE

CM

SLIP PLANES FOR STRIP SURCHARGE

-SATURATED PART OF WEDGE

l>-

FIGURE 3-7. LINES OF ACTION FOR FORCES

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EC 1110-2-510 31 Aug 83 3-7

3-7. Lateral Pressure Distribution, The line of action of the lateral force produced by a wedge is determined as described in paragraph 3-6. However, the distribution of lateral pressure on the wall must also be determined in order that the structural design of the wall can be completed. A partially saturated wedge, behind a retaining wall, is shown in Figure 3-8. A relatively simple method for finding the pressure distribution on the wall is illustrated in Figure 3-8. The total force (P) may be considered equal to the area of the trapezoidal pressure diagram with its centroid at a distance "a" below point E, as shown in pressure diagram (1) of Figure 3-8. From the geometry of a trapezoid.

(3-16) PE = 2P (2hw - 3a)

l4

Pc = 2P(3a-hw)

(3-17)

If a vertical pressure exists on the top surface at "E," that is if the surcharge on the top surface extends to the wall the trapezoidal distri¬ bution in (1) of Figure 3-8 is the distribution on the wall. If the vertical pressure at point E is zero, as in Figure 3-8, the pressure diagram should be modified. The unshaded part of (1) is replaced by (2), which has the same area and centroid. Then the shaded part of (1) is added to (2) to obtain the pressure distribution (3) on the wall, as shown in Figure 3-8. This is not the only manner in which the distribu¬ tion of pressure on the wall can be obtained; any other reasonable method of distribution may be used_if the area of the pressure diagram is equal to P and its centroid lies y distance above point C.

3-8. Hedge Analysis in Layered Soil. When the backfill behind a wall consists of two or more types of soils, the methods discussed in paragraphs 3-1 through 3-7 remain valid. This condition is illustrated in Figure 3-9. The impervious blanket on the top surface is considered to be a uniform surcharge on wedge 1. The impervious blanket, moist granular material, and saturated granular material are considered to be a uniform surcharge on wedge 2. The lateral forces produced by the surcharges, weight of wedges, and uplifts on the slip planes are calculated in the manner already described. See Appendix G for an example.

3-9. Irregular Backfill Configurations. When the top surface of a wedge has an irregular shape, it is often possible to perform an approximate analysis using the provisions of paragraph 3-5 to calculate the critical slip plane angle alpha, thereby avoiding an iterative solution which varies alpha until the maximum horizontal force P is found. Even when

3-14

EC 1110-2-510 31 Aug 83

S2-X2

<\j

> X

t ,'

X

'.:'?:.• -./••'b'; .'♦, •/:» .• o '.' ' /''■;v'. v v

P = Pvi + PV2 + pWM + PWS + pU

r(h-dc)(h-f2dcn.t;r u D .h-dcx -. 3(PV1HV| + PV2HV2) + PWML h+dc . J*PWSHS + PU Hs+3PCL(-Lg£)

3P

T I-

1

II o

(>:

■.•.k'.: •Vli"

FIGURE 3-8. LATERAL PRESSURE DISTRIBUTION

3-15

EC 1110-2-510 31 Aug 83

CRACK

UJ > m UJ x o o

WEDGE I WEDGE 2

#

(X <

z < CD 2

^ SATURATION £ LINE-^N.

MMMt

IMPERVIOUS BLANKET

zz

.6'

6 :V-y.-../.."^-.;.-.*.-^;':! 'WW*

FIGURE 3-9. WEDGE ANALYSIS IN LAYERED SOIL

3-16

EC 1110-2-510 3-9 31 Aug 83

the irregularity is very complex, the methods of paragraph 3-5 can be used to furnish an approximation for alpha, thus shortening any iterative procedure required for a more exact determination. Two examples of broken surfaces are shown in Figure 3-10. In the top view of Figure 3-10 11 h" is set equal to the distance from the bottom of the wedge to the level top surface and the shaded area is considered a negative strip surcharge; the equations for ci and C2 can then be used to find alpha. In the bottom view of Figure 3-10 "h" is set as shown and the shaded area is considered a positive surcharge; again the equations for ci and C2 are used to find alpha.

SECTION II. WATER PRESSURES

3-10. General. Static pressures due to water above the ground surface is equal to the density of the water multiplied by the depth of water. Forces due to water below the ground surface are included in the wedge analysis by using the saturated weight for the weight of the wedge, the weight of any water above the surface of the wedge as a surcharge load, and the uplift force along the wedge slip plane. (See Figure 3-7 and the example in Appendix G).

3-11. Seepage Analysis by Line of Seepage Method. If seepage exists, the line of seepage method affords a relatively simple approximate method for determining water pressures along wedge slip planes This method is sufficiently accurate in most cases. A seepage path along wedge slip planes is shown in Figure 3-11, and the method of calculating water pressures at points on this path is given.

3-12. Seepage Analysis by Method of Fragments.

a. General. The method of fragments is a more accurate approximate method for performing a seepage analysis than the line of seepage method. This method was developed by Pavlovsky in 1935 (Reference 31). The underlying assumption of the method is that equipotential lines at various critical points in the flow region can be approximated by straight vertical lines. These vertical lines divide the flow region into parts called fragments. Figure 3-12 shows the flow region for a typical retaining wall divided into three such fragments. The head loss in any fragment is determined as

1+ % - 5- (3-18)

where:

3-17

EC 1110-2-510 31 Aug 83

0 = 0 ASSUMED TOP SURFACE

u

ACTUAL TOP SURFACE

FIGURE 3-10. WEDGE ANALYSIS FOR IRREGULAR BACKFILL

3-18

EC 1110-2-510 31 Aug 83

WEDGE I

SLIP PLANE

WEDGE 2 WEDGE

• SLIP PLANE

SLIP PLANE

TOTAL LENGTH OF SEEPAGE PATH = Ls = Lsi +LS2 + LS3

"' ■ [hsl" -^rf1}r"

ua = fh hsi - Ah (LSI .SI+LS2"1 LS J

XW

WHERE rw = UNIT WEIGHT OF WATER

FIGURE 3-11. LINE OF SEEPAGE METHOD

3-19

EC 1110-2-510 31 Aug 83

//*#Mt

in

A^

©

-jimrnrT,

//&//

CS-' ■^••.

^A UB

iw/m/f CVJ

CO

nB CVJ

/// //

TOP OF IMPERVIOUS LAYER 'n- i

/////////

'^j = 0| + ^2 + ^3

</>, AND </>3 ARE OBTAINED FROM FIGURE 3-10

02 = -L ^^ a

UA = rw

UB s rw

S. -

S| - h (0| +02)"

2 0] . rw s2 + TIT 2 0j

FIGURE 3-12. FLOW REGION FOR METHOD OF FRAGMENTS

3- 20

EC 1110-2-510 3-12a 31 Aug 83

hj = Head loss through the fragment.

h = Total head differential across wall

fy = Form factor for the fragment.

24j = Summation of form factors for all fragments in the flow region.

For a detailed explanation of this method see reference 31.

b. Form Factors.

(1) Fragment ?f in Figure 3-12, is called a Type I fragment. The form factor for Type I fragments is:

♦;-ii 0-19)

(2) Fragments 1 and 3f in Figure 3-12, are called Type II fragments. The form factor for this type fragment may be obtained from Figure 3-13.

c. Mater Pressures. The manner in which water pressures are calculated at critical points is illustrated in Figure 3-12.

d. Toe Drain Effect. A wall with a toe drain is shown in Figure 3-14. The effect of the drain is to lower the water surface on the toe side, to the bottom of the drain, thereby reducing seepage pressures and the chance for boils. Fragments 1 and 3 are again Type II, and fragment 2 is Type I. However, calculations for head losses and water pressures for the stability analysis should use a water surface assuming a zero effectiveness of the toe drain. This assumption is due to the uncertainity of the toe drain effectiveness over a long period of time.

3-13. Surge and Wave Loads.

a. General. Wave and water level predictions for the design of walls shall be determined with the criteria in the Shore Protection Manual^ of the U.S. Army Coastal Engineering Research Center. Design forces acting upon the wall shall be determined for the water levels and the waves predicted, taking into account the most severe fetch and the effects of shoaling, refraction, and diffraction. A distinction is made between the action of nonbreaking, breaking and broken waves.

3-21

EC 1110-2-510 31 Aug 83

FIGURE 3-13. FORM FACTORS FOR TYPE IE FRAGMENTS

3-22

EC 1110-2-510 31 Aug 83

L

»Mmii WW i;.1

-^r

*»' 1 sz C/5 .'fc!

"TT" !JM/M// ^^T' !t&/W/

y^ ^V^^ -CBCC «IIPPArP \-

- TOE DRAIN -^

C/)

O ® ! © ® H TOP OF IMPERVIOUS

1 1 | LAYER -^\

' »

FIGURE 3-14. TOE DRAIN EFFECT

3-23

EC 1110-2-510 31 Aug 83 3-13b

b. Wave Heights. Wave heights for design are obtained from the statistical distribution of all waves in a wave train, and are defined as f o 11ows:

Hs = Average of the highest 1/3 of all waves

Hi = 1.67 Hs = Average of highest 1 percent of all waves

Hb = Height of wave which breaks in water depth db

c. Nonbreaking Wave Condition. When the depth of water is such that waves do not break, a nonbreaking condition exists. This occurs when the water depth at the wall is greater than approximately 1.5 times the maximum wave height. The Hj wave shall be used for the nonbreaking condition. Design nonbreaking wave pressures shall be computed using the Miche-Rudgren Method, as described in the Shore Protection Manual Whenever the maximum Stillwater level results in a nonbreaking condition, lower Stillwater levels should be investigated for the possibility that shallow water may produce breaking wave forces which are larger than the nonbreaking forces.

d. Breaking Wave Condition, The breaking condition occurs when the steepness of the wave and the bottom slope in front of the wall have certain relationships to each other. Typically, breaking waves occur when the water depth (at a distance of approximately one-half but not over 3/4 a wave length in front of a wall) is between 1.3 and 1.5 times the wave weight. The design breaker height (Hb) is the highest wave which breaks within a distance of 7 to 8 wave heights in front of the wall. Design breaking wave pressures should be determined by the Minikin Method, presented in the Shore Protection Manual. Theoretically, a breaking wave produces a force on the structure that cannot be exceeded.

e. Broken Wave Condition. Broken waves are those that break in a zone lying within a distance between one half and one wave length from the wall. The design breaker height in this case (Hb) is the highest wave which will be broken in the break zone. Design wave forces for the height (Hb) should be determined by the method presented in the Shore Protection Manual.

f. Seepage Pressures. Seepage pressures are based on the elevation of the surge Stillwater level (See para. 4-4).

SECTION III. SUPPLEMENTAL FORCES

3-14. Wind Loads. Wind loads should be considered on retaining walls during construction, prior to placing backfill. Wind loads can act on a floodwall for the entire life of the structure. In locations subjected to hurricanes the wind load used should be 50 psf on exposed surfaces; in other locations 30 psf should be used.

3-24

EC 1110-2-510 3-15 31 Aug 83

3-15. Lateral Earthquake Forces. The geometry and weights of the active- and passive-type wedges will be determined using an SRF equal to 0.90 for computing the static and seismic lateral forces. The static lateral forces produced will be determined from the single wedge equation given in Figure 3-1. The line of action for the static forces will be as obtained by the method given in paragraph 3-6. The lateral forces produced by horizontal and vertical seismic accelerations acting on these wedges will be applied, in addition to the static forces, to the structural wedge to calculate sliding and overturning stabilities.

a. Wedge Lateral Forces for Horizontal Seismic Acceleration. A typical active-type wedge is shown in Figure 3-15. The lateral force due to seismic action is K^W where K^ is the coefficient of horizontal earthquake acceleration and W is the weight of material in the wedge including water. This force can be treated as an HL force (See Figures 3-1 and 3-2). The line of action of this force passes through the center of gravity of the wedge. A typical passive-type wedge is shown in Figure 3-15, and the earthquake induced force and its line action are determined in the same manner as they were for the active-type wedge. This force can be treated as an HL force also. The seismic coefficients listed in Table 1 of ER 1110-2-1806, dated 16 May 1983, should be used for Kh.

b. Wedge Lateral Forces for Vertical Seismic Acceleration. A typical active-type wedge is shown in Figure 3-16. The lateral force due to vertical seismic acceleration is obtained by substituting KVW for W in the single wedge equation and solving for P^. Ky is the coefficient of vertical seismic acceleration and W is the weight of the material in the wedge including water. The line of action of this force is the same as the line of action of the static lateral force. A typical passive-type wedge is shown in Figure 3-16, and the force and its line of action are determined in the same manner as they were for the active-type wedge. These forces can be treated as HL forces (See Figures 3-1 and 3-2). Kv can be taken as 2/3 K^.

c. Seismic Force Due to Water Above Ground. Water standing above ground can have its static pressure, acting against a wall, increased or decreased due to seismic action. Figure 3-17 shows the pressures and forces due to earthquake for free standing water. The dynamic force is given by Westergaard^ equation as:

PE = (2/3) CE Khh2 (3-20)

where CE is a factor depending upon the depth of water, h, in feet, and the earthquake foundation period of vibration, T, in seconds. Wester- gaard's approximate equation for C^ in kip-second-foot units is:

3-25

EC 1110-2-510 31 Aug 83

C.G. OF MATERIAL IN WEDGE (INCLUDING WATER)

LATERAL FORCE FOR ACTIVE TYPE WEDGE- HORIZONTAL ACCELERATION


SLIP PLANE

KhW = PE

LATERAL FORCE FOR PASSIVE TYPE WEDGE- HORIZONTAL ACCELERATION

FIGURE 3-15. WEDGE FORCES DUE TO HORIZONTAL EARTHQUAKE ACCELERATION

3-26

EC 1110-2-510 31 Aug 83


SLIP PLANE

LATERAL FORCE FOR ACTIVE TYPE WEDGE- VERTICAL ACCELERATION


SLIP PLANE

LATERAL FORCE FOR FWSSIVE TYPE WEDGE VERTICAL ACCELERATION

FIGURE 3-16. WEDGE FORCES DUE TO VERTICAL EARTHQUAKE ACCELERATION

3-27

EC 1110-2-510 31 Aug 83

TOP OF GROUND

WATER SURFACE

PE

•*f

*/.

d imm

WATER SURFACE

f^/^/f

'}(•}. ■■•:••*::: -^

PE TOP OF GROUND

FIGURE 3-17. HYDRODYNAMIC FORCES FOR FREE STANDING WATER

3-28

EC 1110-2-510 3-15c 31 Aug 83

r 0.051

Yl - 0.72 (H/1000T)2

Normally, for retaining and flood walls, Cg can be taken as 0.051. The pressure distribution is parabolic, and the pressure at any point y below the top surface is:

PE = CE KhYhy" (3-21)

The line of action of force P^ is 0.4h above the ground surface.

d. Structural Wedge. In addition to the forces due to the active- and passive-type wedges, horizontal and vertical forces caused by seismic action are applied at the center of gravity of the structural wedge. These forces are KfoW and KVW; where W is the weight of the structural wedge. Applying all forces to the free body of the structural wedge, a sliding analysis is performed in accordance with paragraph 4-11 for design or paragraph 4-12 for investigation.

3-29

DRAFT EC 1110-2-510 31 Aug 83

CHAPTER 4

STRUCTURAL STABILITY

Section I. Loading Cases

4-1. General. The following loading cases are generally representative oft conditions affecting retaining walls and inland and coastal flood walls. The loading cases for a specific wall should be chosen, as applicable, from the lists below. Loadings which are not listed below should be included where applicable.

4-2. Retaining Malls.

a. CASE Rl, Usual Loading. Backfill in place to final elevation; surcharge loading (if any exists) acting; backfill dry, moist, or partially saturated as the case may be; lateral and uplift pressures due to water (if any exist) acting. This case also includes the usual loads possible during construction which are not considered short duration 1oads.

b. CASE R2, Extreme Loading. Same as for Case Rl except that backfill is partially or completely saturated, as the case may be, for a short duration, or another type of loading of short duration is applied, i.e., high wind loads, equipment surcharges during construction, etc.

c. CASE R3, Earthquake Loading. Case Rl with earthquake-induced lateral and vertical loads added, if applicable; uplift same as for Case Rl.

4-3. Inland Flood Walls.

a. CASE II, Usual Flood Loading. Backfill in place to final elevation; water level at the design water level (top of wall less freeboard) on the unprotected side; uplift.

b. CASE 12, Extreme Flood Loading. Same as for Case II except the water level is at the top of unprotected side of wall.

c. CASE 13, Earthquake Loading. Backfill in place to final elevation; water at the usual level during the non-flood stage; uplift, if applicable; earthquake-induced lateral and vertical loads, if applicable. (Note: If the wall has no significant load during the non- flood stage, no earthquake case is necessary.)

4-1

EC 1110-2-510 31 Aug 83 4-3d

d. CASE 14, Construction Short Duration Loading. Flood wall in place with loads added which are possible during the construction period but are of short duration such as from strong winds and construction equipment surcharges.

4-4. Coastal Flood Walls.

a. CASE CI, Surge Stillwater Loading. Backfill in place to final elevation; water at the surge Stillwater level on the unprotected side; no wave force; uplift.

b. CASE C2a, Nonbreaking Wave Loading. Case CI with a nonbreaking wave loading added, if applicable; uplift same as for Case CI.

c. CASE C2b, Breaking Wave Loading. Case CI with a breaking wave loading added, if applicable; uplift same as for Case CI.

d. CASE C2c, Broken Wave Loading. Case CI with a broken wave loading added, if applicable; uplift same as for Case CI.

e. CASE C3, Earthquake Loading. Backfill in place to final elevation; water at the usual (non-storm) level; uplift, if applicable; earthquake-induced lateral and vertical loads, if applicable. (Note: If the wall has no significant load during the usual (non-storm) stage, no earthquake case is necessary.)

f. CASE C4, Construction Short Duration Loading. Flood wall in place with loads added which are possible during the construction period but are of short duration, such as from strong winds and construction equipment surcharges.

\j

g. CASE C5, Wind Loading. Backfill in place to final elevation; water at the usual (non-storm) level on the unprotected side; wind load of 50 psf on protected side of wall.

Section II. Stability Requirements

4-5. General. The basic requirements for the stability of a retaining or flood wall for all loading conditions are:

a. That it be safe against sliding at the base of the wall, or through any soil layer or rock seam below the base.

b. That it be safe against overturning at the base of the wall, and, in the case of gravity walls, at any horizontal plane within the wall.

c. That it be safe against bearing failure and excessive differential settlement in the foundation.

4-2

EC 1110-2-510 4-6 31 Aug 83

4-6. Stability Criteria. The stability criteria for retaining walls and inland and coastal flood walls by loading case are listed in Tables 4-1 through 4-3.

Section III. Overturning Stability

4-7. Resultant Location. The overturning stability is computed by applying all the vertical and lateral forces to a free body of the structural wedge, and summing moments caused by these forces about a common point on the assumed plane of sliding. The resultant location along the sliding plan with respect to the common point assumed for the moment computations is:

Resultant Location = SuTwnation of Moments (4.1) Summation of Vertical Forces

The methods to be used in determining the lateral and uplift forces are described in Chapter 3.

4-8. Criteria. The overturning stability requirements in Tables 4-1 through 4-3 are given as minimum base areas in compression. Figure 4-1 illustrates the relationship between the base area in compression and the resultant location. See Section V for the computation of the base pressures, q.

Section IV. Sliding Equilibrium

4-9. Analysis Model. In the sliding equilibrium analysis the retaining or flood wall and the soil acting on the wall are assumed to act as a system of wedges. The soil-structure system is divided into one or more active-type wedges, one structural wedge, and one or more passive-type wedges, as shown in Figure 4-2. This is called the multiple wedge model.

4-10. Introduction to Analysis Procedure.

a. General Approach. A trial and error process is required, if the system consists of two or more wedges, to find the actual value of the strength reduction factor (SRF). The SRF is defined mathematically as the developed shear stress parameters divided by the shear strength parameters, as follows:

SRF = TAN ^d/TAN J0 » Cd/C (4-2)

An in depth explanation of the SRF is provided in paragraph 3-3. The multiple wedge analysis usually requires at least three iterations to compute the SRF for which horizontal equilibrium is obtained.

4-3

Table 4-1. RETAINING WALL STABILITY CRITERIA

Maximum Strength Minimum Case Loading Reduction Factor, SRF Shear Strength Test Required Minimum Base Area In Compression Bearing Capacity No. Condition (Factor of Safety, FS) Soil Foundation(l) Rock Foundation(4) Soil Foundation Rock Foundation Safety Factor

Rl Usual

R2 Extreme

R3 Earthquake

2/3 (1.5) (Q &/or S)(2) Direct Shear

0.75 (1.33) (Q &/or S)(2M3) Direct Shear

0.90 (1.1) (Q &/or S)(2H3) Direct Shear

100%

75%

Resultant Within Base

75%

50%


3.0

2.0

1.1

1. For a sliding analysis at the base of the structure, the value of cohesion used should not exceed the adhesion between concrete and the foundation material.

2. For soil foundations which are not free draining (permeability <10 x IQ-^cm/sec), analyze for both Q and S strengths. For free draining soil foundations (permeability > 10 x lO'^cm/sec), analyze for S strengths only.

3. For construction loadings in cases Rl or R2, use Q strengths when excess pore water pressure in the soil foundation is anticipated and S strengths when it is not anticipated.

4. The sliding analysis of a wall on rock should be based on the frictional resistance (tan^) of concrete on rock or rock on rock. The values should be obtained from direct shear tests of pre-cut samples of concrete on rock and rock on rock, or direct shear tests on natural rock joints or bedding planes.

C I-1 UD »—» o 00 I CO I>0

cn i—» o

Table 4-2. INLAND FLOOD WALL STABILITY CRITERIA

Case No.

Loading Condition

Maximum Strength Reduction Factor, ! (Factor of Safety,

SRF FS)

Shear Strength Soil Foundation

Test Required (1) Rock Foundatior i(4)

Minimum Base Soil Foundat-

Area In Compression ion Rock Foundation

Minimum Bearing Capacity

Safety Factor

11 Usual Flood 2/3 (1.5) (Q &/or S)(2) Direct Shear 100% 75% 3.0

12 Extreme Flood

2/3 (1.5) (Q &/or S)(2) Direct Shear 75% 50% 2.0

13 Earthquake 0.90 (1.1) (Q &/or S)(2) Direct Shear Resultant Within Base


1.1


2. For soil foundations which are not free draining (permeability< 10 x 10"4cm/sec)» analyze for both Q and S strengths For free draining soil foundations (permeability > 10 x lO"^/^^ analyze for S strengths only.

3. For the construction loading case, use Q strengths when excess pore water pressure in the soil foundation is anticipated and S strengths when it is not anticipated.

4. The sliding analysis of a wall on rock should be based on the frictional resistance (tan^) of concrete on rock or rock on rock. The values should be obtained from direct shear tests of pre-cut samples of concrete on rock and rock on rock, or direct shear tests on natural rock joints or bedding planes

Oil I-* *-* i—» o

y* i c ro

%n i on

oo t-* oi o

Table 4-3. COASTAL FLOOD WALL STABILITY CRITERIA

Maximum Strength Reduction Factor, SRF (Factor of Safety, FS)

____ Mini mum Shear Strength Test Required Minimum Base Area In Compression Bearing Capacity

Soil Foundation(l) Rock Foundation^) Soil Foundation Rock Foundation Safety Factor Case Loading No. Condition

35" ^ C I—» in !—» o

oo I OU IV

I CI Surge Stillwater

2/3 (1.5)

C2 Wave

C2a Nonbreak¬ ing

2/3 (1.5)

C2b Breaking 0.80 (1.25)

C2c Broken 2/3 (1.5)

C3 Earthquake 0.90 (1.1)

(Q &/or S)(2) Direct Shear 100% 75%

C5 Wind 2/3 (1.5)

(Q k/or S)(2) Direct Shear 75% 50%

(Q i/or S)(2) Direct Shear 60% 40%

(Q &/or S)(2) Direct Shear 75% 50%

(Q &/or S) Direct Shear Resultant Within Base


(Q Ei/or S)(3) Direct Shear 75% 50%

3.0

2.0

1.5

2.0

i.l

2.0

2.0


2. For soil foundations which are not free draining (permeability^10 x lQ-4cm/sec), analyze for both Q and S strengths. For free draining soil foundations (permeability > 10 x 10-4cm/sec)s analyze for S strengths only.

3. For construction loading case, use Q strengths when excess pore water pressure in the soil foundation is anticipated and S strengths when it is not anticipated.

4. The sliding analysis of a wall on rock should be based on the frictional resistance (tan 9*) of concrete on rock or rock on rock. The values should be obtained from direct shear tests of pre-cut samples of concrete on rock and rock on rock, or direct shear tests on natural rock joints or bedding planes/

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EC 1110-2-510 31 Aug 83

* *

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STRUCTURAL WEDGE

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FIGURE 4-2. SOIL-STRUCTURE SYSTEM

4-8

EC 1110-2-510 4-10b 31 Aug 83

b. Simplified Approach, To shorten the amount of work and still arrive at a satisfactory approximation, a single wedge analysis can be used as described below for the design of a wall. The multiple wedge analysis is described in the section on investigating the sliding stability for existing walls, paragraph 4-12.

4-11. Sliding Analysis for Design.

a. Structural Wedge Analysis. For design purposes a free body of the structural wedge is isolated and the lateral forces from the active - and passive-type wedges, as determined by the method described in Chapter 3, are applied to it. The SRF for the structural wedge (SRFs) can be computed directly from the structural wedge equation in Figure 4-3 (See Appendix E for derivation). If part of the base area of the structural wedge is not in compression, the cohesive shear acting on that part of the base should be neglected and the uplift should be assumed constant.

b. Criteria. The SRFS computed should be equal to or less than those given in Tables 4-1 through 4-3. If the SRFS is greater than the maximum SRF specified for the loading case being analyzed, the base of the wall must be widened, sloped, or a key provided to provide the increased sliding resistance required. If the SRFS is less than the maximum SRF specified, the sliding resistance of the base can be reduced if overturning, settlement, and bearing capacity criteria can still be met.

4-12. Sliding Analysis for Investigation.

a. Structural Wedge Analysis. First, the SRFc can be computed for the structural wedge, as described in paragraph 4-11. If the SRFS is less than or equal to the maximum SRF specified in Tables 4-1 through 4-3, no further analysis is required. If the SRFS is greater than the maximum SRF specified, a multiple wedge analysis, as described below, should be performed to compute the actual SRF for the entire sliding mass, assuming the same SRF for each wedge.

b. Multiple Wedge Analysis.

(1) This method computes the SRF required to bring the sliding mass consisting of the structural wedge and the active- and passive-type wedges into a state of horizontal equilibrium along a given set of slip planes.

(2) The general wedge equation is given in Figure 4-4 (See Appendix F for derivation). This equation is used to compute the sum of the applied forces acting horizontally on each wedge for an assumed SRF. The same SRF is used for each wedge.

4-9

SRFS .

WHERE

SRFg-

PL -

PR =

HL "

< PL~ PR+ HL-HR) COSa-lW+V) SIN a EQ.(4-3)

HR

W

V

U

a

c

tPL~pR + HL~HR) TAN<£ SINa+(W-»-V) TbN<t> COS a - U TAN<£+ CL

STRENGTH REDUCTION FACTOR FOR THE STRUCTURAL WEDGE.

= ABSOLUTE VALUE OF TOTAL HORIZONTAL FORCE FROM ACTIVE-TYPE WEDGES.

= ABSOLUTE VALUE OF TOTAL HORIZONTAL FORCE FROM PASSIVE-TYPE WEDGES.

= ANY HORIZONTAL FORCE ON STRUCTURAL WEDGE ACTING TOWARD THE RIGHT NOT DUE TO THE WEDGES.

* ANY HORIZONTAL FORCE ON STRUCTURAL WEDGE ACTING TOWARD THE LEFT NOT DUE TO THE WEDGES.

« TOTAL WEIGHT OF WATER, SOIL,ROCK OR CONCRETE IN THE STRUCTURAL WEDGE.

* ANY VERTICAL FORCE APPLIED ON THE TOP OF THE STRUCTURAL WEDGE.

= UPLIFT FORCE EXISTING ALONG THE SLIP PLANE OF THE STRUCTURAL WEDGE.

= ANGLE FROM THE HORIZONTAL AT THE LEFT END OF THE SLIP PLANE TO THE SLIP PLANE OF THE STRUCTURAL WEDGE (POSITIVE IS COUNTER-CLOCKWISE, SEE FIGURE 4-5)

= ANGLE OF SHEARING OR INTERNAL FRICTION OF THE STRUCTURAL WEDGE.

* COHESION OR ADHESION, WHICHEVER IS THE SMALLEST, ON THE SLIP PLANE OF THfc STRUCTURAL WEDGE.

= LENGTH ALONG THE SLIP PLANE OF THE STRUCTURAL WEDGE.

FIGURE 4-3. STRUCTURAL WEDGE EQUATION

p,>_(Wj+Vi)pSRFi)TANfr COSaj + SINa J -Uj (SRFj )TAN^i-KHU-HRJ) QsRFj)TAN<ftiSINai-COSqi]+(SRFi)CjLi ^^^^ ''' ' " COSaj- (SRFj)TAN^i SINaj tM*r^

WHERE i = NUMBER OF WEDGE BEING ANALYZED .

(Pi-| -Pj) = SUMMATION OF APPLIED FORCES ACTING HORIZONTALLY ON THE J1*1 WEDGE. (A NEGATIVE VALUE FOR

THIS TERM INDICATES THAT THE APPLIED FORCES ACTING ON THE i^ WEDGE EXCEED THE FORCES

RESISTING SLIDING ALONG THE BASE OF THE WEDGE. A POSITIVE VALUE FOR THE TERM INDICATES

THAT THE APPLIED FORCES ACTING ON THE i* WEDGE ARE LESS THAN THE FORCES RESISTING

SLIDING ALONG THE BASE OF THAT WEDGE.)

= TOTAL WEIGHT OF WATER, SOIL, ROCK OR CONCRETE IN THE ith WEDGE.

= ANY VERTICAL FORCE APPLIED ABOVE TOP OF THE Ith WEDGE .

= ANGLE BETWEEN THE SLIP PLANE SURFACE OF THE i*1 WEDGE AND THE H0RIZ0NTAL(POSmVE IS COUNTER-CLOCKWISE)

= UPLIFT FORCE EXERTED ALONG THE SLIP PLANE SURFACE OF THE i*WEDGE.

= ANY HORIZONTAL FORCE APPLIED ABOVE THE TOP OR BELOW THE BOTTOM OF THE LEFT SIDE ADJACENT WEDGE.

= ANY HORIZONTAL FORCE APPLIED ABOVE THE TOP OR BELOW THE BOTTOM OF THE RIGHT SIDE ADJACENT WEDGE.

= ANGLE OF SHEARING OR INTERNAL FRICTION OF THE i^1 WEDGE.

SRFi = STRENGTH REDUCTION FACTOR FOR SLIDING OF THE Ith WEDGE.

NOTE! ALL WEDGES IN THE SYSTEM MUST HAVE THE SAME SRF. (SEE DERIVATION IN APPENDIX F .)

Cj = COHESION OR ADHESION, WHICHEVER IS THE SMALLEST, ON THE POTENTIAL SLIP SURFACE OF THE ith

WEDGE. (COHESION SHOULD NOT EXCEED THE ADHESION AT THE STRUCTURE-FOUNDATION INTERFACE).

Li = LENGTH ALONG THE SLIP PLANE SURFACE OF THE i*1 WEDGE.

Wj

Vj

ai

"Ri

FIGURE 4-4. GENERAL WEDGE EQUATION

EC 1110-2-510 31 Aug 83 4-12b(3)

(3) The geometry and sign convention of a typical ith wedge and adjacent wedges are shown in Figure 4-5. The distribution of pressures and resultant forces acting on a typical wedge are shown in Figure 4-6.

(4) The critical value of the slip plane angle for the special case of a backfill with an unbroken (uniformly sloping or horizontal) top surface, and a strip surcharge V, can be found by the equations given in paragraph 3-5. For backfill with an irregular top surface, the critical slip plane angle can be approximated by the equations in paragraph 3-5, as described in paragraph 3-9. Thus, an iterative procedure, if needed to find the critical slip plane angle for a wedge more precisely, can be shortened.

(5) An example of a multiple wedge analysis for a typical loading condition is presented in Appendix H.

c. Procedure for a Multiple Wedge Analysis.

(1) Divide the assumed sliding mass into a number of wedges, including a single structural wedge, based on the configuration and discontinuitites of the backfill, wall proportions, and discontinuities of the foundation.

(2) Estimate the SRF for the first trial.

(3) Compute the critical sliding angles for each wedge.

(4) Compute the uplift pressures, if any, along the slip plane. The effects of seepage should be included.

(5) Compute the weight of the wedges, including any water and surcharges.

(6) Compute the summation of the lateral forces for each wedge using the general wedge equation.

(7) Sum the lateral forces for all the wedges.

(8) If the sum of the lateral force is negative, increase the SRF and recompute the sum of the lateral forces. Continue this trial and error process until the sum of the lateral forces is approximately zero for the SRF selected. This will determine the critical SRF for putting the sliding mass in horizontal equilibrium, i.e., where the sum of the applied forces acting horizontally equals the sum of the resisting forces acting horizontally. If the sum of the lateral forces is positive, decrease the SRF and recompute.

4-12

EC 1110-2-510 31 Aug 83

+ x

*- +x

POSITIVE ROTATION OF AXES

+ Yi

NEGATIVE ROTATION OF AXES

+ Yi+| M

+ Yi-|

^i-l

(i-l$t)WEDGE ith WEDGE (STRUCTURAL

/3i + l<

(i +1st) WEDGE

FIGURE 4-5. GEOMETRY OF TYPICAL i* WEDGE AND ADJACENT WEDGES

4-13

EC 1110-2-510 31 Aug 83

TOP OF WEDGE

-TOP OF i + l*t WEDGE

Pi

M > H

FIOUR'E 4-6. PRESSURES AND FORCES ON TYPICAL WEDGE

4-14

EC 1110-2-510 4-13 31 Aug 83

4-13. Basic Concept, Assumptions and Simplifications.

a. Limit Equilibrium. The sliding equilibrium analysis is based on a limit equilibrium approach. The shape of the slip surface is assumed at the start. The forces acting at the ends of the sliding mass have to be known. The necessary shear stress along the presumed slip surface to produce equilibrium is found. Sliding is assumed to occur along the presumed slip surface when the shear stress required for equilibrium exceeds the shear strength of the slip surface.

b. Safety Against Sliding. The design criteria for the sliding equilibrium analysis are expressed in terms of a maximum strength reduction factor (SRF). The inverse of the SRF is the factor of safety against sliding. The SRF, as defined in paragraph 3-3, represents that factor by which the shear strength parameters (TAN 0 and C) are multiplied (reduced) to obtain the shear stress (resistance) needed to bring the sliding mass into a state of horizontal equilibrium along a given set of slip planes. Also, since the in situ strength parameters of rock and soil are never known exactly, one role of the SRF is to compensate for the latitude that exists in assigning single values to such important parameters. Or, in other words, the SRF compensates for the difference between what may be the real shear strength and that assumed for the analysis.

c. Slip Surface, The slip surface can be a combination of planes and curved surfaces, but for simplicity, all slip surfaces are assumed to be planes. These planes form the bases of the wedges. It should be noted that for the analysis to be realistic, the assumed slip planes have to be kinematically possible. In rock the slip planes may be predetermined by discontinuities in the foundation.

d. Two Dimensional Analysis. The sliding equilibrium method presented is a two dimensional analysis. This method should be extended to a three-dimensional analysis if unique three-dimensional geometric features and loads critically affect the sliding stability of a specific structure.

e. Force Equilibrium Only. Only force equilibrium is satisfied. Moment equilibrium is not used. The shearing force acting parellel to the interface of any two wedges is assumed to be negligble. Therefore, the portion of the slip surface at the bottom of each wedge is only loaded by the forces directly above or below it. There is no interaction of vertical effects between the wedges. The resulting wedge forces are assumed horizontal.

f. Displacements. Considerations regarding displacements are excluded from the limit equilibrium approach. The relative regidity of different foundation materials supporting the structure and the concrete

4-15

EC 1110-2-510 31 Aug 83 4-13f

structure itself may influence the results of the sliding stability analysis. Such complex structure-foundation systems may require a more intensive sliding investigation than a limit equilibrium approach. The effects of strain compatibility along the assumed slip surface may be approximated in the limit equilibrium approach by selecting the shear strength parameters from in situ or laboratory tests according to the failure strain selected for the stiffest material.

g. Relationship Between Shearing and Normal Forces. A linear relationship is assumed between the resisting shearing force and the normal force acting on the slip plane beneath each wedge. This relation¬ ship is determined by the Coulomb-Mohr failure criterion.

h. Structural Wedge. The general wedge equation is based on the assumption that shearing forces do not act on the vertical wedge boundaries, hence there can only be one structural wedge since concrete structures transmit significant shearing forces across vertical internal planes. Discontinuities in the slip path beneath the structural wedge should be modeled by assuming an average slip plane along the base of the structural wedge.

i. Interface of Other Wedges with Structural Wedge. The interface between the group of active-type wedges and the structural wedge is assumed to be a vertical plane located at the heel of the structural wedge and extending to the base of the structural wedge. The interface between the group of passive type wedges and the structural wedge is assumed to be a vertical plane located at the toe of the structural wedge and extending to the base of the structural wedge.

4-14. Design Considerations.

a. Effects of Cracks in Foundation. Sliding analyses should consider the effects of cracks on the active side of the structural wedge in the foundation material due to differential settlement, shrinkage or joints in the rock mass. The depth of cracking in cohesive foundation material with a plane ground surface can be estimated with the following equations.

dc = (2 Cd/ r) TAN (450 + 0d/2) (4-5)

where

cd = (SRF) C

^= JAN"1 [(SRF)TAN ^]

4-16

EC 1110-2-510 4-14a 31 Aug 83

The value (dc) in a cohesive foundation should not exceed the embedment of the structural wedge. The depth of cracking in massive strong rock foundations should be assumed to extend to the base of the structural wedge. Shearing resistance along the crack should be ignored and full hydrostatic pressure should be assumed to act at the bottom of the crack. The hydraulic gradient across the base of the structural wedge should reflect the presence of a crack at the heel of the structural wedge.

b. Passive Resistance. When passive resistance is used, special considerations must be made. Rock or soil that may be subjected to high velocity water scouring should not be used unless amply protected. Also, the compressive strength of rock layers must be sufficient to develop the wedge resistance. In some cases wedge resistance should not be assumed without resorting to special treatment such as rock anchors.

Section V. Base Pressures

4-15. Computation of Base Pressures. The base of the retaining wall should be considered as a footing subjected to a horizontal force (F^) and eccentric vertical load (Fy). The intensity of the bearing pressure at the toe and heel, assuming a linear pressure distribution, can be expressed as

q = Fv/B (1 ± 6e/B) (4-6)

where B is the width of the base, Fv is the vertical component of the resultant force acting on the retaining wall, and e is the eccentricity of the vertical component from the center of the base. See Figure 4-1. If the resultant, R, falls outside the middle third of the base, i.e., e is greater than B/6, the pressure distribution below the base will be triangular instead of trapezoidal with maximum pressure equal to the following:

q = 4/3 (Fv/(B - 2e)) (4-7)

4-17

EC 1110-2-510 4-15 31 Aug 83

The base will be in compression over a distance (b) from the toe computed as follows:

b = 3 (B - 2e) (4-8)

4-16. Allowable Base Pressures.

a. Safety Factor. The bearing capacity analysis discussed in Chapter 5 considers both the horizontal and vertical components of the resultant force at the base of the structure. In order to determine the allowable base pressures, a bearing capacity analysis will be necessary for the controlling loading cases as determined by the sliding equilibrium analysis. For each case analyzed the same loadings as determined by the sliding equilibrium analysis should be used. The factor of safety against a bearing failure should be computed by dividing the vertical component of the ultimate bearing capacity by the summation of the vertical forces for the structural wedge.

b. Inadequate Bearing Capacity. If the factor of safety against bearing failure is insufficient, consideration should be given to increasing the width of the base, lowering the base of the wall, or founding the wall on piles.

4-18

DRAFT EC 1110-2-510 31 Aug 83

CHAPTER 5

FOUNDATION ANALYSES

SECTION I. BEARING CAPACITY OF WALL FOUNDATIONS.

5-1. General.

a. EM 1110-2-1903. A discussion of the principles and methods involved in analyzing and evaluating bearing capacities is contained in EM 1110-2-1903, Bearing Capacity of Soils. The manual concludes that Terzaghi's general bearing capacity equation, q = CNC + wz Nq + WbNw, is preferred. However, the manual does not address modifying the general equation for effects of embedment, inclined loads, sloping bases, passive-type wedges with sloping surfaces, overburden pressure, and eccentric loads, all of which are needed for computing the bearing capacity of retaining and flood walls.

b. Shallow Strip Foundations. Only shallow strip foundations will be considered in this manual, i.e., those whose widths are greater than their embedment. Problems related to soil compressibility, local shear, and punching will not be considered in this chapter. However since they are important factors in some bearing capacity failures, due consideration should be given to them in any design.

c. Factor of Safety. The factor of safety is calculated as follows:

FS = Q/ZV (5-1) where

ZV= summation of vertical forces for the structural wedge. Q= vertical component of the ultimate bearing capacity.

5-2. General Bearing Capacity Equation. The general bearing capacity equation is:

Q = B [(Ccd^ctCcgC Nc) + (CqaCqiMquQo Nq) + ^^^^^1 (5-2)

where

Q = vertical component of the ultimate bearing capacity of the foundation.

B = width of the base

Nc, Nq, Ny = bearing capacity factors for a strip load.

5-1

EC 1110-2-510 31 Aug 83 5-2

C = cohesion parameter of the foundation

Qo = effective overburden pressure on the plane passing through the base of the footing.

y = unit weight of the foundation material.

£ = factors as explained in paragraph 5-4 through 5-8.

Figure 5-1 illustrates the meaning of all the terms required to use the information given in paragraphs 5-3 through 5-8. The general bearing capacity equation is taken from Reference 33.

5-3. Bearing Capacity Factors. Bearing capacity factors for a horizontal strip footing under vertical loading are:

Nq=[e(«TAN*)JTAN2^+^ (5_3a)

Nc = (Nq - l)COT<t> (5-3b)

Ny = (Nq - 1) TAN (1.4+) (5-3C)

5-4. Embedment Factors. Embedment factors take into consideration the shearing resistance along the foundation slip plane that exists in the soil above the base of the footing, on the toe side of a wall. These factors can be computed as:

£cd = 1 + 0.2(D/B)TAN(45o + tyl) (5-4a)

fy - £yd = i <♦ = <>) (5-4b)

V = ^yd = 1 +0.1 (D/B)TAN(450 + +72) (+ > 10°) (5.4c)

When <p lies between 0° and 10° a linear interpolation can be made for

{yd between 1 for <)>= 0°, and 1+0.1 (D/B) TAN(450+ +/2) for + = 10°.

5-5. Inclination Factors. Inclination factors account for the effect of load inclination for concentrically loaded foundations. They are computed as follows:

** = ti=V^) (5-5a)

5-2

EC 1110-2-510 31 Aug 83

STRUCTURAL WEDGE

-rrmw wim

B

I. IF PART OF THE BASE OF STRUCTURAL WEDGE IS NOT

IN COMPRESSION, B SHALL BE THE WIDTH OF THE

PART THAT IS IN COMPRESSION.

2. y USED IN THE BEARING CAPACITY EQUATION SHALL

ALWAYS BE THE EFFECTIVE WEIGHT OF THE FOUNDATION

MATERIAL.

FGURE 5-1. ILLUSTRATION OF BEARING CAPACITY TERMS

5-3

EC 1110-2-510 31 Aug 83 5-5

^=(l-f)2 - (5-5b)

Where d is the angle that the line of action of the load makes with the vertical. If <J > f , Cyi should be set equal to zero.

5-6. Base Tilt Factors. These factors are used to take into account the effect of a sloping base. The base tilt factors are computed as:

di =^ = (1 -uTAN*)2 (5-6a)

^ = 1-[^](*=0O) . (5-6b> fe-fc--^*; (*>0°) (5-60 q NcTAN +

where is the angle the slip plane of the structural wedge makes with the horizontal, measured in radians. The sign of will follow the sign conventions given in Chapters 3 and 4.

5-7. Ground Slope Factors. Ground slope factors are used to correct for a sloping ground surface on the toe side of the wall. The factors are computed as:

4^= ^8= [l -TAN(/J)]2 (5-7a)

4cg = 1 - [T^J (+ = 00) 0? IN RADIANS) ( 5.7b)

Ny = -2SIN/3 (<|> = 0°) (5-7c)

£cg = Sqg--!—^L_ 1 > 0* (5_7d) NCTAN* T

whereJB is the angle the ground surface makes with the horizontal. ># is positive when rotation from the horizontal is clockwise.

5-4

EC 1110-2-510 5-8 31 Aug 83

5-8. Effective Overburden Pressure. q0 is defined as the pressure due to the soil and/or surface loads above the base of the footing, on the toe side of the wall, as follows:

qo = y'D (5-8a)

where is the effective unit weight of the overlying soil, and D is the depth from the soil surface to the base of the structural wedge. For the special case of a sloping surface, compute q0 as:

qo = y'DCOS[ABS(/*)] (5-8b)

5-9. Example. An example problem using the general bearing capacity equation is presented in Appendix G.

SECTION II. SETTLEMENT

5-10. General. A discussion on the various factors involved in the settlement of a structure, on methods for estimating settlements, and on the limitations in the accuracy of conducting settlement analyses from laboratory tests is contained in EM 1110-2-1904, Settlement Analysis. The principles and methods presented are applicable to a large majority of civil works projects. Additional information for unique or special projects can be obtained from various texts on soil mechanics.

SECTION III. DEEP SEATED SLIDING

5-11. General. A deep-seated sliding analysis should be performed to evaluate weak layers which may exist beneath structures. The analysis should be in accordance with procedures outlined in paragraphs 4-12 b & c. The active- and passive-type wedges should be located a sufficient distance apart to allow a rotational slip surface to develop. Generally, a slip plane inscribed in an arc with a radius equal to the height of the active wedge will comply with this requirement. (See Figures 5-2 and 5-3).

5-5

> H- C h-

O 00 I

I

ACTIVE WEDGE VERTICAL FACE AT HEEL

FIGURE 5-2, DEEP SEATED SLIDING ANALYSIS

+

cn I

ACTIVE WEDGE VERTICAL FACE AT TOE

i—* (—*

o > i C ho

OQ I Un

00 H-• UJ o

(FIGURE 5-3. DEEP SEATED SLIDING ANALYSIS

DRAFT ECailO-2-510 31 Aug 83

CHAPTER 6

DESIGN AND CONSTRUCTION DETAILS

6-1. Foundation Preparation. Earth foundations should be properly compacted and should be clean and damp before concrete is placed. Rock foundations should be cleaned and given any other necessary treatment to insure proper bond of concrete to rock. Some rock foundations, primarily shales, require a covering to protect them from deterioration after being exposed and before concrete placement.

6-2. Concrete Mixture Proportions. Consideration should be given to the materials that are economically available for a particular project. EM 1110-2-2000 describes several optional compositions for concrete mixtures; all options which are applicable to the work and which include available materials should be investigated.

6-3. Constructability. The dimensions of the wall should be such that reinforcement and concrete can be properly placed. EM 1110-2-2000 provides guidance for concrete placement. Guide specifications CW 03301 and CW 03305 provide detail requirements for concrete placement. The top thickness of the stem for cantilever concrete walls should be a minimum of 12 inches to facilitate concrete placement. The wall section should be designed for simplicity and maximum re-use of forms. Any construction constraints due to the location of the wall should be included in the design.

6-4. Joints. Walls are designed with joints to allow for expansion, contraction and/or to divide the structure into convenient working units. The locations of all horizontal and vertical joints should be shown on the drawings.

a. Expansion Joints

(1) General. Expansion joints are designed to prevent the crushing and distortion (including displacement, buckling, and warping) of the abutting concrete structural units that might otherwise occur due to the transmission of compressive forces. Compressive forces may be developed by expansion, applied loads or differential movements arising from the configuration of the structure or its settlement. In general, expansion joints are needed to prevent spalling and sometimes to break continuity. In relatively thin reinforced concrete walls such joints should be located where considerable expansion or unequal settlement is anticipated, as at changes in alinement or grade, at abrupt changes in section or at intermediate points when needed. In massive reinforced concrete walls and in gravity walls on rock, expansion joints usually are not provided unless required at abrupt changes in section or at angle monoliths to relieve thrust from expected expansion. Otherwise, adequate

6-1

EC 1110-2-510 31 Aug 83 6-4a(l)

chamfers on each side of each contraction joint usually are sufficient to prevent spalling. Where temperature variations are extreme, modification of these criteria may be required. Reinforcing steel, corner protection angles and other fixed metal embedded in or bonded to the surface of the concrete should not extend through an expansion joint. Where water tightness is needed, waterstops are provided as outlined in paragraph 6-4d.

(2) Joint Filler. The thickness of joint filler necessary to provide stress relief at a joint should be determined from the estimated initial contraction and subsequent expansion from maximum temperature variation. Premoulded expansion joint filler and adequate chamfers should be used.

b. Contraction (Monolith) Joints. These are purposely made planes of weakness designed to regulate cracking that might otherwise occur due to the unavoidable, often unpredictable, contraction of concrete structural units. They also divide the structure into convenient working units and thus serve also as construction joints. Since it is impracticable and uneconomical to provide sufficient reinforcement to prevent cracks entirely, it is desirable to control their location, insofar as is practicable, by vertical contraction joints, across which reinforcement does not extend. No exact rules for the location of such joints can be made. Each job must be studied to determine where the joints should be placed, taking into account the requirements of structural design, the volume of concrete which can be placed economically in a single working unit and the economical use of form units. Typically, contraction joints have been spaced 20 to 30 feet apart. Usually a contraction joint has a plane surface without a key. For cantilever concrete walls vertical joints may be located only in the stem, and the footing may be a continuous placement.

c. Horizontal Construction Joints. These joints are provided to divide a wall into convenient working units, but they should be kept to a minimum. Keys are not permitted in horizontal construction joints as they iterfere with good cleanup of the concrete surface and because a well-bonded flat surface is more dependable to transfer shear.

(1) Gravity Concrete Walls. For this type of wall the horizontal construction joint locations are dictated by the height of each lift of concrete placement. Concrete for gravity walls is usually placed in lifts up to 10 feet high. The top surface of each lift is cleaned and roughened by high pressure water jets before placing the next lift.

(2) Cantilever Concrete Walls. For this type of wall a construction joint between the base and the wall stem should be provided. Additional horizontal joints in the wall stem should be provided by lifts approximately 10 feet high. The surface of each joint should be roughened to obtain as much shear strength across the joint as possible.

6-2

EC 1110-2-510 6-4d 31 Aug 83

d. Joint Details for Flood Walls. For expansion and contraction joint details for flood walls, see paragraph 7-14.

e. Waterstops. Waterstops are provided across joints where water tightness is required. Where appreciable differential movement is possible because of a yielding foundation, non-metallic waterstops, such as rubber or polyvinyl chloride (PVC) waterstops, should be used in accordance with EM 1110-2-2102. For special flood wall waterstop details, see Chapter 7, Section V.

6-5. Backfilling.

a. General. Many types of material can be used for backfill It is advisable to use locally available material when possible.

b. Materials. Clean sands and gravels are the most suitable materials. They are rapid draining, not susceptible to frost action, and remain stable. Silty sands, silts, and coarse grained soils containing some clay are less desirable as they drain slowly, are subject to seasonal volume changes, and m^y lose much of their strength with time. Shrinkage cracks may develop in clay which, when filled with water, can cause full hydrostatic pressures.to act on the wall During winter construction the use of frozen backfill material should not be used under any circumstances. This material mqy appear satisfactory when placed, but it can be adversely affected when it thaws.

c. Drainage. It is necessary to provide a designed drainage system that will prevent the accumlation of water behind the wall regardless of the type of backfill material used. The system should include a gravel pack, perforated pipe or weep holes. Water from a free draining material can be removed by horizontal drains or weepholes.

(1) Horizontal Drains. This type of drain consisting of perforated pipe, surrounded by a filter are preferable. The pipe should be large enough for cleaning and have outlets accessible for cleaning. Collector pipes with 1/4 inch perforations are normally used; however, to minimize clogging due to formation or iron oxides, perforations as large as 3/4- inch may be used in conjunction with additional protective filters.

(2) Weepholes. Weepholes consist of pipe at least 3 inches in diameter extending through the stem of the wall; they constitute a minimum drainage system, Weepholes should be protected against clogging by pockets of gravel in the backfill. They are commonly spaced not more than 10 feet apart vertically and horizontally.

6-3

EC 1110-2-510 31 Aug 83 6-5c(3)

(3) Filter Criteria. Drains must be designed so that seepage water is admitted freely, but movement of backfill particles is prevented. If soil moves into the filter, piping may result or the filter may become clogged and ineffective. A filter properly designed to prevent the infiltration of base materials into the filter material must satisfy stability and permeability criteria as follows:

D15 Filter

Dgs Base < 5

and

D50 Filter

D50 Base < 25

To assure that the filter material is much more permeable than the material being drained, the following condition should be met:

D15 Filter

D15 Base > 5

To prevent clogging of perforated collector pipes or drains, the following requirement must be satisfied:

Circular Openings

D50 Filter

Hole Diameter ■ 1-0

Slotted Openings

D50 Filter

Slot Width > 1-2

The filter materials may satisfy the criteria for stability and permeability but may be too fine to meet the criteria for the circular or slotted pipe openings. If this happens then multilayered or graded filters are required. The filter material must not become segregated or contaminated prior to, during, or after installation. Segregation will result in zones of material too fine te meet the permeability requirements and other zones too coarse to meet the: stability requirements. Contamina¬ tion of the filter material from muddy water, dust, etc during construc¬ tion may clog the voids in the material and prevent proper drainage. In the event that filter or drain materials are contaminated, they should be replaced.

6-4

EC 1110-2-510 6-5d 31 Aug 83

d. Placing and Compacting. The backfill material should be carefully selected. It should be compacted to prevent large settlements due to its own weight. The amount of compaction required depends on the material used and the purpose of the structure. Very strict control of compaction is required when the fill is a cohesive soil, and even when granular fill is used the material should be placed in thin lifts with each lift being compacted before the next lift is placed. However, precautions should be taken to prevent overcompaction which will cause excessive lateral forces to be applied on the structure. If heavy compaction rollers are used within the soil wedge boundary used for computing lateral earth pressures, their effect on the wall should be considered in the design. It is good practice to place impervious soil in the upper lift of the backfill to reduce infiltration of rain water. Backfill should be brought up equally on both sides until the lower-side finished grade is reached.

6-5

OR EC 1110-2-510

31 Aug 83

CHAPTER 7

SPECIAL CONSIDERATIONS FOR FLOOD WALLS

Section I. General

7-1. Introduction. This chapter discusses flood walls. The principal function of a flood wall is to prevent flooding (inundation) of adjacent land. It is subject to hydraulic loading on one side which is resisted by little or no earth loading on the other side. There are two principal types of flood walls, inland and coastal. Inland flood walls typically are installed along a river bank and are subjected to design loadings (pool to freeboard line) for periods of hours or days (long term). Coastal flood walls are primarily subjected to short term loadings (waves from hurricanes along with wind/tide high water surges). The wave loadings are dynamic in nature and only act upon the structure for a few seconds each.

7-2. Background Behind Loading Cases.

a. How Design Water Surface is Determined. The hydraulic data required for flood wall design should be listed in the hydrologic/hydraulic appendix of the pertinent planning document for the project. The flow characteristics noted in historical records and indicated from detailed observation of existing conditions will usually be basic to the design of inland flood walls. Coastal flood walls will frequently require hurricane surge simulation studies and wave setup estimates.

b. Freeboard. The freeboard of a channel is the vertical distance measured from the design water surface to the top of the wall. Freeboard is provided to ensure that the desired degree of protection will not be reduced by unaccounted factors. These might include erratic hydrologic phenomena; future development of urban areas; unforeseen wall settlement; the accumulation of silt, trash and debris; aquatic or other growth in the channels; and variation of resistance or other coefficients from those assumed in design. Local regions where water-surface elevations are difficult to determine may require special considerations. Some examples are locations in or near channel curves, hydraulic jumps, bridge piers, transitions and drop structures, major junctions, local storm inflow structures, and coastal areas. As these regions are subject to wave-action uncertainties in water-surface computations, and possible overtopping of walls, especially for rapid flow, conservative freeboard allowances should be used. The backwater effect at bridge piers may be especially critical if debris accumulation is a problem. The amount of freeboard cannot be fixed by a single, widely applicable formula. It depends in large part on the size and shape of channel, type of channel lining, consequence of damage resulting from over-topping, and velocity and depth of flow. A freeboard allowance of two feet for rectangular sections of channel (with flood walls) is generally considered satisfactory. When large non-breaking waves are incident normal to the stem of the flood

7-1

EC 1110-2-510 31 Aug 83

wall, the amount of freeboard will be determined by the amount of overtopping allowed, remembering that such overtopping can cause significant scour on the protected (toe) side of the wall. This potential for scour can require rigid paving within the area 20 to 30 feet of the wall. It is usually economical to vary concrete wall heights by 0.5 foot increments so that the forms can be reused.

c. Loading Cases. For determining water and soil loads acting on flood walls, see Chapter 3. For the loading cases, see Section I of Chapter 4.

Section II. Seepage Control

7-3. General. The first consideration of a flood wall design should be seepage control requirements. All water-retaining structures are subject to seepage through, under and around. Inadequate control of the seepage, as shown by one example in Figure 7-1, may affect the stability of a flood wall from uplift or loss of support resulting from erosion. Properly controlled seepage, even if quantities of flow remain large, presents little or no hazard. In flood walls, control of through seepage is provided for by waterstops (see Figures 7-2A through 7-2C). Seepage around the wall is controlled by carefully designed and constructed levee wrap-around sections. Provisions to control underseepage vary between projects because flood walls are usually founded on alluvium that consists of layers or lenses of materials with largely varying permeabilities. Flood walls are usually provided with a toe drain, which must be carefully designed, especially when the foundation has a stratum of pervious materials at or near the ground surface. Pervious strata are frequently connected directly to the riverbed and therefore allow rapid transmission of flood heads. Also both natural deposits and constructed fills have stratified permeability properties. The horizontal permeability, Kh, may be many times as great as the vertical permeability, Kv.

7-4. Underseepage Control. Two approximate methods for evaluating underseepage are presented in Chapter 3. They are the line of seepage method and the method of fragments. These methods are appropriate for the analysis of most flood walls, with the method of fragments being preferred. In some instances, where complex problems of geometry, anisotropy, and foundation layering exist, flow nets will have to be constructed for proper analysis. Water pressures obtained form the seepage analysis are used in evaluating the stability of the wall in sliding, overturning and bearing. The uplift pressures and critical exit gradient should be determined. If boils are not a problem, no seepage control measures may be necessary. Where boils are of concern, the underseepage must be controlled. The seepage control measures described in the following paragraphs are all designed to control underseepage by reducing uplift head at the toe and/or to reduce or control the volume of water necessary to control piping.

a. Cutoffs. A cutoff beneath the wall to block seepage through a pervious foundation stratum is the most positive means of eliminating seepage

7-2

EC 1110-2-510 31 Aug 83

EXPLODED VIEW OF FLOW OF WATER AROUND WATERSTOP IN JOINT BETWEEN PROTOTYPE FLOOD WALL MONOLITHS- WATERSTOP BURIED IN INTERIOR OF CONCRETE

PATH OF FLOWING WATER

FIGURE 7-1 FLOW AROUND INTERIOR EMBEDDED WATERSTOP IN THE BASE.

7-3

EC 1110-2-510 31 Aug 83

SEE DETAIL "A

RIYER FACE OF HALL

BOND BREAKER AS REQUIRED (SEE SECTION A-A AND B-B)

/^GROUND SURFACE

TRANSITION-SEE DETAIL-

TYPE "U" WATER STOP

CIRCULAR OPENING OF WATER STOP AT TOP TO BE PLUGGED WITH SOFT RUBBER FOR A MIN¬

IMUM DEPTH OF i INCHES.

7>-r CHAMFER

RIVER FACE OF WALL

TYPE "Y" WATER STOP

DETAIL "A"

CONST JT

STOP

TYPICAL SEtmON

r-^RIVER FACE fT, OF WALL

CONTRACTION JOINTS, BOND BREAKER ;'• x:v'-?1

RIVER FACE OF WALL

jr PREMOULDED EXPANSION JOINT MATERIAL.CMAKE JOiNT lM THICK AT CHANGE OF DIRECTION STEMS)

MWOLITH JOINT TYPE A SECTION A-A MONOLITH JOINT TYPE B

CONTRACTION JOINTS, BOND BREAKER

TYPE MU" WATER STOPS

? PREMOULDED EXPANSION JOINT MATERIAL

JIONOLITH JOINT TYPE A MONOLITH JOINT TYPEy

SECTION B-B

MONOLITH JOINT DETAIL NOTES:

1. DETAILS ARE CONTINUED ON FIGURES 7-2B ft C.

2. EXTREME CARE SHOULD BE EXERCISED IN PLACING TYPEVWATER STOP TO INSURE FIRM CONTACT WITH THE PREPARED SUBGRADE THROUGHOUT ITS ENTIRE CONTACT AREA.

9. TYPE V JOINT USED IN STRAIGHT RUNS OF WALL.

4. TYPE "B" JOINT USED AT JUNCTURES OF WALL WITH GATE WELLS, PUMP STATIONS AND GATE ABUTMENTS, AND IN CHANGE OF DIRECTION MONOLITHS.

FIGURE 7-2A. TYPICAL JOINT AND WATERSTOP DETAILS

7-4

EC 1110-2-510 31 Aug 83

♦<e)

1-6,1-6

TYPE U VyATER STOP

LOW BASE

JL1

X

■VARIES FOR EAOI HEIGHT PER LOW BASE WALL

LOW BASE WALL

RIVER FACE OF WALL

TYPE Y WATER STOI» — '

VARIES -

TYPE "U" WATER STOP-

I

I -6

• 'A'.'

'♦2(3 12'

SKTtPW P-P

I'-6"

*2 /3 12"

r;*.:

PLAN

LOW BASE

*

K

*2(ai2"

;b.- .VD;

: A . I

4

HIGH BASE

/ »-'

^ TYPEV WATERSTOP

SECTION E-E

STOP

S6CTIQN

*4^ 12"

••0 •- • '.* '. TYPE "U" WATERSTOP

86CTI9H F- F

/ARIES

TRANSITIONS AT CHANGES IN WALL HEIGHT

FIGURE 7-2B. TYPICAL JOINT AND WATERSTOP DETAILS (CONT'D)

7^-5

EC 1110-2-510 31 Aug 83

TYPE Y

TYPE "Y" BASE*

TYPE^"

TRANSITION BETWEEN STEM AND BASE

ISOMETRIC SKETCH

TYPE'V

WATER STOP DETAILS

FIGURE 7-2C TYPICAL JOINT AND WATERSTOP DETAILS (CONCLUDED)

7-6

EC 1110-2-510 7-4a 31 Aug 83

problems. A cutoff can consist of an excavated trench backfilled with impervious compacted earth, a slurry trench, an extension of a concrete shear key or a sheet pile wall. A cutoff is usually located at the end of the wall footing on the unprotected (heel) side. A cutoff must penetrate approximately 95 percent or more of the pervious strata before reductions in the quanity of flow can be realized. The decision as to the type and depth of a cutoff should be based on an underseepage analysis using actual site conditions. A steel sheet pile cutoff is not entirely watertight due to leakage at the interlocks but can significantly reduce the possibility of piping of coarse grained material in the foundation. The effectiveness of a steel sheet pile cutoff through a coarse grained stratum in reducing the seepage head (uplift) should generally be assumed to be 25 to 50 percent, if interlock between the | piling is maintained. A steel sheet pile cutoff is less effective in fine grain material than in coarse grain material. Bearing value of a steel sheet pile cutoff should be neglected, as should its effect on uplift for stability purposes if an underseepage analysis has not been performed.

b. Drainage Systems.

(1) Toe Drains. All flood walls should be provided with a landside toe drain similar to the one shown in Figure 7-3. The toe drain which runs parallel to the wall at the landside edge of the footing provides a positive outlet for underseepage and a check for controlling piping. The toe drain should never be located under the wall footing. A typical toe drain design will consist of a 6-inch to 8-inch diameter pipe perforated on the bottom half and surrounded in all directions with 6 to 10 inches of filter material designed by the filter criteria in paragraph 6-5c(3). The collected water is usually disposed of by gravity outlets into ditches, ponding areas or pump stations. A well designed toe drain system will provide inspection or maintenance access at changes in the toe drain alignment or at intervals not to exceed 500 feet. Discharge pipes should be provided with gate traps that will prevent surface water from entering the toe drain. A seepage analysis should assume tailwater elevation at the elevation of the discharge pipe outlets. For flood walls on bearing piles, the toe drain must protect against "roofing." For an impervious foundation, a toe drain is usually all that is necessary to accommodate the small quantity of seepage. When the foundation contains pervious material, seepage control measures in addition to a toe drain are required.

(2) Trench Drains. When pervious material is near the ground surface, a trench drain may be used to control seepage. A trench drain is an enlarged variation of a toe drain. A trench drain is usually two to four feet * wide. It extends from the ground surface through shallow pervious layers or into a pervious layer underlying a shallow surface blanket. The practical depth for construction of a trench drain will depend on available excavation equipment and site dewatering requirements. The excavation, pipe placement and backfilling of the trench should always be performed in an unwatered construction site. To assure adequate pipe capacity, the collector pipe

7-7

EC 1110-2-510 31 Aug 83

WATER SIDE

GROUND LINE ///0M/

m

LAND SIDE

HEEL i i

}?M/Mf

BASE WIDTH

"TOE DRAIN

-SHEET PILE CUTOFF (OPTIONAL)

SAND 8 GRAVEL

O -1

2-6

6"0 PIPE PERFORATED ON BOTTOM HALF

TOE DRAIN DETAIL

FIGURE 7-3. T-TYPE FLOOD WALL-HORIZONTAL BASE

7-8

EC 1110-2-510 7-4b(2) 31 Aug 83

(perforated on the bottom half) and the outlet pipes should be sized considerably larger than computations indicate to be necessary. Backfill in a trench drain shall conform to filter criteria in paragraph 6-5c(3). A trench drain should be provided with inspection and maintenance access and back flow protection as described for toe drains. The seepage analysis should assume the tailwater elevation equal to the discharge elevation of the trench drain.

c. Relief Wells. Pressure relief wells are used to relieve artesion pressures in pervious layers, usually found at some depth under a surface blanket, which might otherwise cause piping. The depth of penetration is one of the advantages of wells. Another advantage of relief wells is the ease with which they can be constructed after the flood wall has been completed if piezometric pressures indicate the need for additional wells. They are particularly useful in controlling large quantities of seepage in strata of pervious material having direct connections with the river. Because the efficiency of relief wells deteriorates with time, considerable monitoring and maintenance may be required to assure the relief well system provides seepage control for the project life. Design of relief well systems is described in EM 1110-2-1905 and EM 1110-2-1901. The performance of relief wells depends on selection of proper sizes of pipe, gravel filter and well screen, and on careful installation which includes "development" of the well. Relief wells should be pump tested when installed. When the well is pump tested later as part of the evaluation of performance program, the initial pump test results are compared to determine the reduction in well efficiency and to determine when the well needs maintenance and cleaning. A seepage analysis should assume the plane of the line of relief wells as an equal potential surface. The tailwater elevation should be the discharge elevation of the wells. The well spacing is selected to provide the design safety factor at the mid-well pressure head.

d. Riverside Impervious Blankets. Impervious riverside blankets overlying a pervious foundation are effective in reducing the quantity of seepage and to some extent are effective in reducing uplift pressures and gradients landside of the flood wall. They may be constructed over thin natural impervious blankets to improve the effects of the natural blankets or they may be constructed directly on pervious material. In some instances, it may be desirable to remove pervious materials and replace with impervious blanket material. The steepness of the river bank may mean blankets are not feasible to construct. Also, it may not be possible to construct blankets over the portions of the pervious layer under water. A noncontinuous blanket has serious drawbacks inasmuch as only a small area of pervious stratum left exposed to the flood heads may defeat the purpose of the impervious blanket. Riverside impervious blankets need to overlap the riverside base of the flood wall so that potential rupture of the blanket by landward deflection of the flood wall when loaded is minimized. Riverside impervious blankets may be subject to the scouring action of high river stages at the time they would be most needed. To prevent such detrimental action, blankets should be protected immediately after construction. Ordinarily, a well designed and planted

7-9

EC 1110-2-510 31 Aug 83

vegetative cover on straight runs is sufficient. Along outside curves of the river, the blankets should be protected with riprap or other positive protection.

e. Landside Berms. Landside berms can be used to control seepage. They serve to reinforce the natural landside blanket. The design is based on the effective weight of the blanket necessary to resist the uplift head. The berm also extends the seepage path by forcing the seepage exit landward. Proce¬ dures for design are presented in TM 3-424, "Investigation of Underseepage and Its Control" (Reference 35). Landside berms should be constructed of materials more permeable than the natural blanket, otherwise the berm will create a new thin blanket rather than add to the thickness of the natural blanket. All blanketing expected to be used in the construction for the flood wall should be considered in the seepage control design for the wall.

f. Grouting of Open Rock Joints. In cases where rock is high enough that flood walls can be placed directly on the rock, close examination of the rock surface is necessary to determine if open joints are present. Such joints can be detrimental to underseepage control. Open joints should be cleaned out and filled with grout before the concrete base is placed. If the possibility exists for seepage flow through porous or cavernous rock in the foundation, consideration should be given for installing a grout curtain.

7-5. Choice of Seepage Control Measure. Selection of a type of seepage control measure depends first on the critical gradient safety factor that is provided and second on economics if a choice remains after safety considera¬ tions. The need for control is determined by a thorough analysis of the foundation, including permeability studies, and an estimate of the uplift heads and quantities of seepage by use of a proper seepage analysis. Further description and discussion of seepage control measures are included in EM 1110-2-1901.

Section III. Foundation Considerations

7-6. Base Types. The T-wall is the most widely used flood wall type. T-walls are normally constructed with either horizontal or sloped bases. The advantages of each type of base are as follows:

a. Horizontal Base. (Figure 7-3)

(1) The volume of foundation excavation is usually less for a horizontal base and it is simpler to construct.

(2) Bearing values and base pressures for the two base,types are not directly comparable. However, for equal heights, base pressures of the horizontal base generally are smaller because of its reduced earth load and slightly wider base.

7-10

EC 1110-2-510 7.6b 31 Aug 83

b. Sloped Base. (Figure 7-4)

(1) A sloped base may allow shortening or complete elimination of a key, which reduces excavation difficulties. Also, a shorter key will generate less moment in the heel adjacent to the key and will generally allow for a shorter base width to maintain overturning equilibrium.

(2) The deep cover or blanket over the heel of a sloped base lessens the chance of rupturing the cover-as the wall moves under load.

(3) The resultant of applied forces is more nearly normal to a sloped base, thereby reducing the tendency of the structure to slide along that plane.

(4) A full size flood wall test performed by the Ohio River Division (1948-1956) indicated that the sloped base wall moved consistently less than the horizontal base wall of comparable design.

c. Selection, Both base types have their advantages and disadvantages. Final selection will depend upon the specific site condition at the project Under consideration.

7-7. Unsuitable Foundation Material and Overbank Fills, Foundation material found to be unsuitable may be avoided by a change in alignment or may be removed and replaced with suitable earth fill (see Figure 7-5). The wall may also be founded on piles through the unsuitable material. In some cases the removal of unsuitable foundation material involves the removal of or cutting into the existing river bank on which the flood wall is to be placed. In other cases the right-of-way may be so restricted and confining that the flood wall may have to be placed near the top edge of the bank or even riverward of the bank. In those cases overbank fill is permitted, if proper precautionary measures are taken. Careful attention must be paid to the outlining of and removal of unsatisfactory material and to the selection of suitable replace¬ ment material. New material must be obtained, placed and compacted to provide adequate support for the flood wall. Replacement material should undergo the same types of laboratory testing as that which similar existing foundation material is subjected. Placement and compaction techniques should approximate earth dam and levee requirements. Slopes steeper than 1.0V on 1.5H and areas that require hand compaction should be minimized. Slopes on which there is evidence of past instability, or in which fill is a component, should be investigated for stability. All overbank slopes should be investigated for sudden drawdown from top of bank.

7-8. Scour Protection. Occasionally a flood wall is exposed to scouring because of the direction, curvature and velocity of current or waves, characteristics of the soil, topography, etc. Scouring at the wall footing should be considered, and where anticipated, protected with riprap.

7-11

EC 1110-2-510 31 Aug 83

WATER SIDE

GROUND LINE i/WWPt/

BASE WIDTH

SHEET PILE CUTOFF (OPTIONAL)

LAND SIDE

"1 "HW/W

hGURE 7-4. T-TYPE FLOOD WALL-SLOPED BASE

7-12

EC 1110-2-5L0 31 Aug 83

REMOVAL LIMIT

SLOPE NO STEEPER THAN I j TO I EXCEPT WHERE IMPOSSIBLE BE¬ CAUSE OF SPACE RESTRICTIONS

REMOVAL LIMIT

ZONE I UNSUITABLE MATERIAU- POROUS,FILL,CINDERS,BTC, REPLACE WITH SUITABLE MATERIAL '

ZONE

TOP OF SUITABLE MATERIAL'

^ SHEET PILE CUTOFF (OPTIONAL)

ZONE 2 - SUITABLE FOUNDATION MATERIAL

hGURE 7-5. REMOVAL LIMITS OF UNSUITABLE FOUNDATION MATERIAL

7-13

EC 1110-2-510 31 Aug 83

Section IV. Types of Monoliths

7-9. Change-of-Alignment Monoliths. Changes in alignment require special monoliths (see Figure 7-6). Monoliths with less than a 10 degree change (horizontal) do not need to be analyzed as special monoliths. Monoliths of short length or abrupt alignment changes may require very wide bases. A 90- degree corner monolith is an indeterminant structure. Adjacent monoliths should not be considered to provide resistance in the stability analysis.

7-10. Closure and Abutment Monoliths. A number of openings must be provided in many flood walls. The openings provide access for commerce, safety and recreation during periods of low river stages. The number and size of openings depend on local requirements. Each opening must be provided with a moveable closure structure. During flood periods, the closure structure is installed on base and abutment monoliths (this combination is a special monolith). These special monoliths must be designed both for the design water load at high water and traffic loads during low water periods.

7-11. Drainage Structure Monoliths. When topography, foundation conditions and economics permit, it is preferable that structures housing gates and pumps be designed as integral parts of the flood wall. These special monoliths must be designed to minimize differential settlement across a monolith or between adjacent monoliths. For closure gate type requirements and the need for secondary closure gates for drainage outlets, see EM 1110-2-1410.

7-12. Transition Sections Between Flood Walls and Levees.

a. Junctures. A junction between a T-wall and levee is not made directly or abruptly, but with a short transition concrete-capped sheet piling I-wall between the two (see Figures 7-7 and 7-8). One of the primary concepts in the development of this transition is to arrange details so there will be a minimum amount of differential movement of joints of monoliths in the transi¬ tion. The levee end of the transition will usually settle a considerable amount, due primarily to foundation consolidation under the added weight of the levee. The T-wall monolith immediately adjacent to the beginning of the levee adds far less superimposed weight on the foundation. Hence, there is much less settlement at this end of the transition. The I-wall can be satisfactorily adopted as a transition section between levee and T-wall because this type of construction can, and in fact must, be done after completion of the levee. A delay in inserting the i-wall allows for settling of the levee, thus lessening the differential settlement between the levee end of the transition and the T-wall.

b. I-wall. The I-wall portion of the transition is begun where the levee slope (parallel to the protection) becomes 10 feet below top of wall. In cases in which protection is already 10 feet or less near the levee, an I- wall, if used, is merely continued into the levee as shown on Figure 7-7.

7-14

EC 1110-2-510 31 Aug 83

WATER SIDE

LAND SIDE

PLAN

RE-ENTRANT MONOLITHS

1

WATERSIDE

vv

KEYS <<^J- STEM-^

RE-ENTRANT MONOLITH LAND SIDE

PLAN

FIGURE 7-6. RETURN KEYS ON RE-ENTRANT MONOLITH

7-15

hiC 1110-2-510 31 Aug 83

LEVEE

TOP OF EMBANKMENT^

T-WALL

START I-WALL WHERE h BECOMES 10'

EE FIGURE 7-8 FOR SECTION A-A

/ "2

^ A

L GROUND LINE

MAX. ELEVATION OF LOWER END OF PILING

FIRST 1-6 OF CONCRETE CAP CONTINUED TO BOTTOM OF PILE

■7/7/7™

KEY TURNED BACK TO STEM

BOTTOM OF ADJACENT KEY /

LEVEE

ELEVATION

T WALL - I WALL-LEVEE TRANSITION

SHEET PILING ONLY

n I-WALL (CONCRETE CAP AND SHEET PILING)

TOP OF EMB

TOP OF EMBANKMENT

GROUND LINE Jf

-BOTTOM OF CONCRETE

"77777

BOTTOM OF PILING

MAX ELEVATION OF LOWER END OF SHEET PILING; DETERMINED BY STRUCTURAL REQUIREMENTS OR SEEPAGE PROTECTION (SEEP PATH) REQUIREMENTS, WHICHEVER IS LOWER .UP TO POINT "a", THEN LINE abc DETERMINES THIS ELEVATION.

ELEVATION

I WALl-lEVEE TRANSITION

2 VM

hGURE 7-7. FLOOD WALL-LEVEE TRANSITIONS

7-16

EC 1110-2-510 31 Aug 83

1^ HOLES TO BURNED IN FIELD

RIVER FACE OF WALL

-^

TYPE Y WATER STOP TO MAKE SNUG FIT WITH SHEET PILE

WALL STEM OR RETURN KEY

= 2-r CL

JV PREMOULDED EXP

JOINT MATERIAL

CONCRETE CAP TO TERMINATE AT BOTTOM OF ADJACENT WALL KEY

SECTION A-A

NOTE: FOR LOCATION OF SECTION A-A SEE FIGURE 7-7

FIGURE 7-8. TYPICAL DETAIL OF JOINT BETWEEN I-WALL AND T-WALL

7-17

EC 1110-2-510 31 Aug 83

c. Sheet Piling. It should be noted in Figure 7-7 that the sheet piling is continued into the levee beyond the last concrete cap a specified distance.

Section V. Waterstops and Joints

7-13. Waterstops. As shown on Figure 7-2, for yielding foundations a U-shaped (Type "u") waterstop should enclose almost the entire base and a center bulb (Type "y") waterstop, located in the stem, is- joined to the U-shaped waterstop at the bottom of the stem. Experience has shown that a center bulb or dumb-bell waterstop located within the base section is likely to allow excessive seepage. Between monoliths on a foundation requiring a cutoff, the type-'V waterstop in the stem should be extended to tie into the cutoff, and the type-'V waterstop around the base deleted. The earth surface on which a type "u" waterstop is installed must be firm and smooth, with no chips, sags, humps, clods, or loose debris that would prevent intimate contact between the waterstop and soil. See Chapter 6 for general guidance on waterstops.

7-14. Contraction and Expansion Joints. Contraction and expansion joint details are illustrated in Figures 7-2A through 7-2C. Contraction joints (Type "A") should contain a bond-breaker. Expansion joints (Type "B") should contain 1/2-inch preformed expansion joint filler in:

a. All protruding (convex on waterside) monolith bases, and in selected reentrant monolith bases and stems as shown in Figure 7-6.

b. In bases and stems of alternate monolith joints in straight-line runs, if warranted by previous experience with similar foundation conditions.

c. In bases and stems of junctures of walls with gate wells, pump stations, gate abutments and similar structures. Nonflexible material in a protruding angle joint is particularly dangerous.

d. See Chapter 6 for general guidance on joints.

Section VI. Site Considerations

7-15. Adjacent Structures and Rights-of-Way. Flood walls are usually built because only a narrow right-of-way is available. The presence of existing buildings or other structures is usually the reason for a narrow right-of- way. Sewer pipes with open joints, structures with basements and excavations close to the wall may create a hazard to the safety of a flood wall. Also, new structures that are built close to existing flood walls can create the same hazards. Present rights-of-way acquisition policies do not permit legal restrictions to be placed on future construction; however, local interests should be advised in writing of the potential hazards, required design and construction measures, and requested to closely supervise new construction close to the flood wall. Potential hazards can be avoided by proper design

7-18

EC 1110-2-510 7-15 31 Aug 83

and construction measures. One hazard that should be considered is seepage. A basement or other excavation on the landside of the flood wall may result in shortened seepage paths. A basement or excavation on the riverside may also create a safety hazard if it penetrates the impervious blanket or shortens the seepage path. When feasible, the basement or excavation should be backfilled with the same type of material existing in the foundation of the flood wall. If relief wells are selected to control seepage they should be located, if at all possible, between the flood wall toe and the adjacent structure. Discharge elevations may need to be lowered to protect the wall if the basement area is to be protected. The location of relief wells within a basement area is not prohibited, but it leads to problems of construction, maintenance and discharge collection. If the seepage problem is only one of quantity, sump pumping may be used during periods of high water. A second hazard that landside basements and excavations create, is to lessen the resistance to sliding along a foundation failure plane. Potential planes of sliding into basements or excavations should be studied. If backfilling is not possible, other measures include the addition of fill between the stem and the building or strengthening the basement to provide the needed resistance. Riverside excavations which contribute to riverward foundation instability should be backfilled, at least to the extent that stability requirements will be satisfied.

7-16. Architectural and Landscaping Considerations. Aesthetics should be considered in the design of floodwalls, from the standpoint of blending the project with the surroundings. Whenever possible, the wall should appear to be a natural extension of the local topography. The basic design of these structures should be a coordinated effort between the design engineer, the architect, and the landscape architect. While it is seldom feasible to preserve the natural setting intact, design techniques and careful construction methods can be used to protect or even enhance the aesthetic value of the immediate project area. Landscape planting design for project structures should consider the entire area affected by the contemplated construction. Further details may be found in EM 1110-2-39, "Architectural Concrete" and EM 1110-2-301, "Landscape Planting at Floodwalls, Levees and Embankment Dams".

Section VII. Instrumentation

7-17. General. Flood wall instrumentation should be considered so that performance can be monitored, particularly during periods of high water. Specifically, areas with high walls, low embedment ratios, replaced foundation materials, overbank fills, pervious materials in the foundation and changes in direction should be considered for instrumentation. When founding a flood wall on earth, the distance between monoliths with piezometers should not exceed 1000 feet. Properly installed, maintained and observed instrumentation can forewarn of dangerous conditions that may affect the stability of the structure. All instruments should be read soon after construction is complete. Knowing the as-built conditions of the wall is essential to

7-19

EC 1110-2-510 31 Aug 83

accurately determine later behavior. Initial piezometer readings should be repeated until equalization (steady state) occurs. All instrumentation readings should be made by trained survey or flood patrol personnel. Ideally, all instruments will be read frequently during high water stages. During design floods, this procedure may prove nearly impossible because of the need for trained personnel to direct flood fights; but readings should be made at certain, previously selected critical locations during design flood stages. During normal water stages, instruments should be read prior to District periodic inspections so that the inspection party has the necessary evaluation data. It also provides a history of the flood wall reactions over the years during both high and normal water. Information concerning frequency and manner of conducting periodic inspections and evaluations, is contained in ER 1110-2-100.

7-18. Types of Instrumentation. The principal types of flood wall instrumen¬ tation monitor movements, both vertical and horizontal, and hydrostatic pressures in the foundation. The instruments selected should be simple to install and observe, and efficient in performance and functional reliability. The monitoring of the movements provides an indication of possible sliding instability or possible waterstop rupture. The piezometers provide a record of hydrostatic pressures in the foundation which can indicate uplift and possible excessive seepage pressures. Instrumentation systems, installations, and devices, are discussed in detail in EM 1110-2-4300 "Instrumentation of Concrete Structures".

a. Movement Monitoring, All reference points to monitor movements should be tied in to a permanent base line located so that it is unaffected by move¬ ments of the wall. When establishment of a base line is not feasible, the relative movements observed between monoliths can provide valuable data on behavior of the wall. Reference points to monitor the wall movements need to be installed during construction. Noncorrosive metal plugs should be installed in the top surfaces of the stems within 6-inches of each end of each monolith. The reference marks in the plugs of four to six successive monoliths should be placed in a straight line with theodolite or stretched wire. At changes in alignment, the straight line should be continued until it intersects the far side of the next monolith and a reference point for alignment control placed. Each plug's changes in horizontal movement and elevation should be measured to 0.001 feet. Stations to be read with electronic optical reading devices need to be established at locations near the ground surface level on the landside of the stem. Selection of electronic-optical station locations, for the stem should be based on factors such as changes of direction, areas of overbank fill, foundation replacement, high walls, low embedment ratios and junctures of flood walls with drainage structures. The monitoring system selected should be vandal proof. In many cases the monitoring system can be tied into the same baselines, established for the reference markers on top of the wall.

7-20

EC 1110-2-bIO 7-18b 31 Aug 83

b. Foundation Piezometers. Design, installation and observations of piezometers are described in EM 1110-2-1908, Part I. The simplest, most reliable method of measuring pore water pressures is the open tube piezometer. For impervious soils, the Casagrande type of piezometer with 24- inch long porous stone is recommended. In order to measure the piezometric pressure at the porous tip, the boring for installation of the Casagrande type piezometer must be effectively sealed against migration of seepage along the piezometer riser. For semi-pervious to pervious soils, a driven well-point type of piezometer is recommended. Where possible, the well-point should be driven into undersized, pre-bored holes. More piezometers can be added if foundation conditions warrant.

Section VIII. O&M Manual Requirements

7-19. General. A general coverage of the requirements of local cooperation is made in EM 1120-2-109 "Federal Participation in Major Drainage Improve¬ ments". As written, the regulations are general in nature and obviously cannot give detailed instructions for the maintenance and operation of a specific project; so it is necessary for the District Office having jurisdiction over the specific project to issue an adequate Operation and Maintenance Manual for the guidance of local interests.

Section IX. Review of Existing Flood Walls

7-20. Inspection. Flood walls should be inspected during the scheduled periodic inspections, after major periods of high water, and when special events warrant an inspection (building or excavating near the wall, etc.). A determination of areas which may be weak or critical from the standpoint of leakage and stability should be made. Criteria for this determination are described below. Areas deficient in any of the criteria will be considered weak or critical, depending on the degree of deficiency.

a. Horizontal Movement. Areas in which movement of a straight section of monoliths or differential movement between any two monoliths is greater than expected will be considered critical.

b. Joint Opening or Spreading. Joints referred to in this paragraph are those having a waterstop embedded in the interior of the section. Using the results of the full size flood wall test performed by the Ohio River Divison, (ORD) in 1955, expected spreading of joints at 90 degree re-entrant corner monoliths (concave on riverside) will be 42 percent of the expected movement of the straight run walls. Not only may joints at corner monoliths become critical upon application of load, but joints below ground which are open should be considered critical. Any joint can become open through loss of joint filler or through unequal settlement between adjacent monoliths or structures such as levees, pump houses, gate wells and gate abutments. Some joints below ground may need to be excavated to determine the adequacy of

7-21

EC 1110-2-510 31 Aug 83

joint filler. If the expected joint opening is greater than the allowable, the area should be considered critical.

c. Head Cover. Any areas in which the earth cover over the waterward end of the heel is less than 5 feet will be considered critical. In addition, walls over 20 feet above ground having cover less than 0.1H + 3* (H= height of stem) should be considered critical.

d. Foreign Material in Joints. The presence of inflexible foreign material, such as grout and pieces of aggregate in expansion joints is dangerous from two standpoints. Grout, particularly if located within the fold of the waterstop, destroys the flexibility of the waterstop and, upon the occurrence of differential movements, allows the waterstop to be torn. Grout and pieces of aggregate anywhere in the joint prevent the joint from fulfilling its expansion function. This condition becomes particularly dangerous at protruding angle locations; i.e. where the wall appears convex when viewed from the river. Here, the wall may be tilted waterward by a wedging action upon expansion of adjacent monoliths in hot weather, and overstress in the stem at its base occurs. The same tilting can occur at re¬ entrant monoliths (Figure 7-6), but there the tilting is landward and the reinforcing is more nearly adequate to resist the stress. For angle monoliths protruding toward the river, the landside temperature steel can be quickly overstressed.

e. Waterstops. Joints with torn or parted waterstops should be considered critical. Torn waterstops may not be noticed during an inspection, particularly if the joint has not spread open. If sufficient differential movement has occurred it should be assumed that the waterstop is torn. The amount of tearing to be allowed should be based on factors causing piping; however, this is very difficult to predict. In the above cases, if a total differential movement (transverse and longitudinal combined) of 1/2 inch or more has occurred, the waterstop should be considered torn unless shown otherwise.

f. Foundation Voids. All unequal settlements should be viewed with suspicion"^ In particular, unequal settlements adjacent to structures such as pump houses and gate wells should be the subject of rigid examination. Usually, one or two monoliths, or a portion of one monolith, is constructed on compacted fill in these areas. Initial unequal settlement may cause the first monolith to bridge or wedge between the second monolith and the other structure. Further consolidation of the fill then leaves a dangerous void or voids under this base. Only undergound examination will reveal the presence of these voids.

g. Stabilty Analyses. Original seepage assumptions or patterns should be reviewed for realistic representation of actual foundation conditions. Particular attention should be paid to foundations having pervious strata which connect directly with the river. Where indicated, new seepage should be

7-22

EC 1110-2-510 7-20g 31 Aug 83

computed and stability analyses recomputed. In addition to a recomputation of uplift, the shear strengths used in the original analyses should be re¬ evaluated on the basis of a study of types of soil and their drainage and consolidation characteristics. In cases where there is a lack of sufficient foundation information in suspected weak areas, new soil samples should be obtained as close to the existing wall as is feasible. In areas where heel cover is less than 5 feet and additional cover is not feasible nor planned, full flood head should be assumed to act down to the bottom of the base or key if one is used. Areas found with questionable stability should be closely observed during high floods.

h. Basements and Other Excavations. The seepage aspects and the foundation stability of walls which have had basements excavated on either side of and adjacent to the wall since the original design and construction were completed should be investigated.

i. Seepage Conditions Landside of Floodwalls. These areas should be investigated thoroughly and contol or relief provided if needed.

7-21. Repair Measures (emergency and permanent).

a. General. The following repair measures are suggested only. Their use is not mandatory if more feasible or economical measures can be devised for the individual problems involved.

b. Additional Landside Cover. The most obvious and straight-forward method of reducing anticipated horizontal movement is the addition of landside cover or fill to the wall (see Figure 7-9). At locations where additional landside fill is not feasible nor possible due to highways, railroads and other structures, measures such as those described in paragraph 7-21d below to reduce seepage pressure will have to be employed to decrease landward movement.

c. Additional Waterside Cover. In areas where earth cover over the waterward end of the heel is deficient, the recommended remedy is the addition of cover.

d. Supplemental Waterstops. The supplemental waterstop scheme shown in Figures 7-10A and B is a means of correcting for torn waterstops, open joints and possible earth cracking over the key because of thin heel cover or excessive movements. The sheet piling shown in the scheme is necessary to provide additional cut-off to compensate for loss of part or all of the normal seep path between earth and the waterside face of the key. The pile cap should be placed at the bottom of the key to limit excessive leakage of water around the upstream and downstream ends of the pile curtain as the wall moves landward under load. Another possible method of repair is to seal the opening below the existing waterstop in the base by injecting cement grout. The

7-23

EC 1110-2-510 31 Aug 83

SAND,OR SAND AND GRAVEL

PATH OF POSSIBLE LEAKAGE IN SPREAD JOINTS

NOTE: THE AREA AND DEPTH OF MATERIAL SHALL BE SUFFICIENT TO PREVENT LOSS OF FOUNDATION MATERIAL AS DETERMINED BY OBSERVATION OF THE OUTFLOW.

FIGURE 7-9. EMERGENCY MEASURES TO CONTROL PIPING

7-24

EC 1110-2-510 31 Aug 83

CONCRETE PILE CAP-

TYPE U HATER STOP "

-^ -^

2h

/

S* — HiTER SIDE ©F tf\^ / EXISTIN© KEY *C#

' ^^îHIET PILIliS-

TYPE-U" j M | WATER STOPJ !! j4v

TYPE "Y- WATER STOP

5>- ÊMISTHI© RIVER I FACE OF WALL

tiCTiew i-> HCT»tW A-A

vAme«

i-r

^JfARift «»*« J—\c r ^- EMMMMil JOWT-

sto*

, '-f

TTT

1—i

ttlVlR met EMISTMM • I WALL,TOP •?■*•• f

- MmM OF EXISTMt KCY

'#§1^

4î«"T»«iMiMirr PILt LIFT HOLE OR MOLE MRNIO IN FIELD

SAMOOLAST Oil OUSM HAMMER EKISTIIti SURFACE

EXIStlNfi IMTEff STOP * . A CXPAKtlOU JOIMT .

SECTKHi C-C

SECTION A-A a B-B

NOTE;

FOR SECTION D-D, SEE FIOUiE 7-IOS.

FIGURE 7-IOA. PERMANENT WATERSTOP REPAIR MEASURES

7-25

EC 1110-2-510 31 Aug 83

ALL CIRCULAR OPENINGS AT WATER STOP EXTREMITIES ARE TO SE PLUOOED WITH SOFT RUMER FOR A M IN DEPTH OF 2 INCHES —

I CHAMFER-

TYPE"Y"WATER STOP-

^

. —FILL WITH BITUMINOUS CEMENT

-TOP OF EXISTING WALL

| DOWEL SOLTS

AST OR BUSH HAMMER EXIST SURFACE

DRIVER FACE OF EXISTIM

SECTION AT TOP OF WALL SEE DETAIL "A" FOR CONNECTION OF TYPEMU"WITH TYPE V WATER STOP

TYPE MU"WATER STOP

Ip"*^ SHEET PILING

TYPICAL SECTION AT JOINTS

TOP OF SHEET PILE

TYPE Y RUBBER WATER STOP

EXISTING RIVER FACE OF WALL

X JOINT^ i

W-EXISTING 'l EXPANSION 'l JOINT /

CONTINUOUS WELD

PETAiL V

PUAH AT TOP y WALl

•4^12

I DOWEL BOLTS Q 12

TOP OF BASE SLAB

SANDBLAST OR BUSH HAMMER EXIST SURFACE

TOP OF BASE SLA»-^

.-. I.BMl^^i^SANOOLASf 0*i / .* -■■-*.. '* BUSH HAMMER % ;A'^V|IoiA. EXIST SURMC^7

EXIST EXPANSION JOINT

EXIST WALL BASE^-) '-i

SECTION D-D

NOTES: (FOR DETAIL V)

I. } X ZjRUm* STRIPS ARE FOR USE ONLY AT CMAMGCS Ml D4RCCTION WNCRC TVPCMU* STOP MUST BE CMT ON A BIAS A«B RE¬ JOINED. ON STRAIOMT RUNS THESE STMFS MSB NOT ME USES.

2. BULM OF TYPEVSTOF ARE SNAWCB DOWN TO WEB TO PROVIOC A FLAT SUR¬

FACE FOR BOLTING TO INSIOE OF TYPE'V STOP.

3. ALL RUBSER SURFACES IN CONTACT

WITH EACH OTHER ARE COATED WITH RUMER CEMENT

NOTES:

1. FOR DET/NLS OF TYPE"YM • TYPEV RWOSER

WATER STOPS, SEE FIGURE 7-EC.

2. ALL STEEL IN BLISTERS 2" CLEAR .

3. FOR SECTttM C-C, SEE FIGURE 7-IOA.

4. FOR SECTION D-D LOCATION, SEE

FIGURE 7- IOA.

FIGURE 7-I0B. PERMANENT WATERSTOP REFttlR MEASURES (CONCLUDED)

7-26

EC 1110-2-510 7-21d 31 Aug 83

opening above the waterstop in the base could be sealed with an elastic sealant such as polysulphide elastomer.

e. Other Problem Areas. Foreign incompressible material in the joints should be removed by the most expedient method. Riverside excavations near the heel should be back-filled with impervious material if it is suspected that dangerous seepage conditions may occur during high water.

f. Emergency Repair Measures. Where differential movement has torn the waterstop above ground, water may squirt through the joint. This presents no serious structural problem and, depending on the size of the resulting stream, presents only a psychological problem. A weighted strip of canvas or plywood dropped over the waterside of the wall may serve to reduce the flow. Exces¬ sive movement or tipping of the wall may indicate potential sliding failure. On the ORD test wall (1955) the full size wall tended to tip waterward under loads up to 10 feet. Thereafter, all stems tipped or deflected landward. At present, the only known repair treatment is to load bulk sand and gravel landward of the stem. Although the fill has the disadvantage of creating an overturning force on the wall, the fill will provide considerable passive resistance to landward movement of the floodwall through its actions on potential failure surfaces in the foundations under and landward of the base. Boils and leaks may result from almost any combination of horizontal movement, opening of joints, shallow heel cover and torn waterstops below ground. The most feasible solution appears to be to ring the boil area with sand bags or to cover it with large amounts of sand and gravel to a height and width sufficient to stop or appreciably slow water flow. In either case, sufficient hydrostatic back pressure must be built up to reduce the velocity of flow, thus reducing the scouring and piping action of water. Failure to detect and stop boils promptly could lead to complete failure of a section of wall.

g. Overtopping Scour Control. For coastal walls or other walls where scour has removed landside cover, consideration should be given to placing concrete slabs over the restored cover within a distance of 20 feet from the wall stem.

7-27

DRAFT EC 1110-2-510 31 Aug 83

CHAPTER 8

GRAVITY CONCRETE WALLS

8-1. General. Factors favoring concrete gravity type retaining walls are shallow depth of overburden, a competent foundation, and an adequate source of fine and coarse aggregate for the required volume of concrete. See Chapter 2, Section I for additional comments on gravity walls.

8-2. Foundation Investigation. The requirements for the foundation investigation are discussed in Chapter 2, Section V.

8-3. Materials. Relatively low concrete compressive strengths (2,000 to 2,500 psi) will usually meet the requirements for the gravity type wall. Where more durability is desirablet as at the outer surface, the exterior concrete can be of higher strength than the interior mass. The age the design strength is to be obtained should be decided by the designer depending on the loading conditions anticipated. Materials and mixture proportioning should follow guide specification CW 03305 and EM 1110-2-2000.

8-4. Design.

a. Magnitude and Distribution of Forces.

(1) Dead!oad. The unit weight of concrete is usually assumed to be 150 pounds per cubic foot. Other dead loads considered should be super¬ imposed backfill and the weights of any equipment or other structures supported by the wall.

(2) External Water Pressure. The pressure exerted by water above ground and water in the ground should be determined as described in Section II of Chapter 3.

(3) Internal Water Pressure (Uplift). The uplift on a lift (horizontal construction joint) within the body of a concrete gravity wall for long term water levels should be taken as 50 percent of the value obtained by assuming a straight line variation between the full hydrostatic pressures acting on each side the wall. Uplift pressures on the base of the wall should be determined by the methods described in Section II of Chapter 3.

(4) Lateral Earth Pressures. Lateral earth pressures should be determined by the methods presented in Section I of Chapter 3.

(5) Wind and Earthquake Forces. These supplemental forces should be determined by the methods presented in Section III of Chapter 3.

8-1

EC 1110-2-510 31 Aug 83

b. Load Cases. The load cases should be those described in Section I of Chapter 4.

c. External Stability. Sliding and overturning stability should be determined by the methods and criteria discussed in Chapter 4.

d. Internal Stability. The resultant of all forces acting on any horizontal section should fall within the kern or sufficiently close to the kern of the section to keep the tensile stresses low. See EM 1110-1- 2101 for allowable concrete stresses.

e. Foundation Analyses. Foundation analyses should be performed in accordance with the methods described in Chapter 5.

8-2

DRAFT EC 1110-2-510 31 Aug 83

CHAPTER 9

CANTILEVER REINFORCED CONCRETE WALLS

9-1. GENERAL. The cantilever reinforced concrete wall is a special type of a gravity wall in which part of the stabilizing weight is supplied by the weight of the backfill resting on the base slab. The structural members are designed for stress due to bending and shear. See Chapter 2, Section I, for additional general corments on cantilever concrete walls.


9-3. Materials. Concrete materials and mixture proportioning should follow guide specification CW 03301 and EM 1110-2-2000. Typically, a concrete compressive strength of 3,000 psi is used for retaining walls. The age the specified strength is to be obtained should be decided by the designer depending on the loading conditions anticipated. Steel reinforcement bars should follow the specifications in the ACI Building Code,3^ with the exception that for hydraulic structures the grade of steel will be limited to ASTM Grade 60 without special approval.

9-4. Reinforcement Cover. For hydraulic structures the minimum reinforcement cover should comply with EM 1110-2-2103. For non-hydraulic structures the minimum reinforcement cover should comply with the ACI Building Code34 requirements.

9-5. Load Cases. The load cases should be those described in Section I of Chapter 4. The magnitude and distribution of the loads should be determined as described in Chapter 3.

9-6. Structural Stability. Sliding and overturning stability should be determined by the methods and criteria discussed in Chapter 4.

9-7. Reinforced Concrete Design.

a. General. Reinforced concrete walls should be designed with the strength design method in accordance with the current ACI Building Code, 34, except as herein specified. Notations used are the same as those in the ACI Building Code, except those defined herein. (See Appendix J for a complete list of notation used in Chapter 9.) WES Technical Report SL-80-43bf contains design aids consistent with the information presented in this chapter.

9-1

EC 1110-2-510 31 Aug 83

b. Hydraulic Structures - Strength and Serviceability.

(1) Required Strength. Reinforced concrete hydraulic structures should be designed to have strengths at all sections at least equal to those calculated for the factored loads and forces in the following combinations that are applicable;

¥

U =1.50+1.9 (Hw + Hp + Fw + Fp + Fy + S|J (9-1)

U = 0.9D + 1.9 (Hw + Hp + Fw + Fp + Fu) (9-2)

U « 0.9D + 1.9W (9-3)

U = 0.75D.5D + 1.9(HW + Hp + Fw ♦ Fp + Fu + SL + W + FQ)] (9-4)

U = 0.75C1.5D + 1.9(HW + Hp + Fw + Fp + Fu + Si + E)] (9-5)

U » 0.75[1.5(D 4- T) + 1.9(HW ♦ Hp ♦ Fw + Fp + Fy + SL)] (9-6)

where the ACI definition of D is modified as

D = dead load of the concret members only, and the additional symbols are defined as

Hw = earth mass or related internal moments and forces. Hp = lateral earth pressure or related internal moments and forces. Fw » water mass or related moments and forces. Fp = lateral water pressure or related internal moments and forces. Fy = vertical uplift pressure or related internal moments and

forces. SL = surcharge loads. Fp = additional pressure due to wave action.

(2) Design Strength of Reinforcement. The design should be based on yield strengths of reinforcement of 40,000 psi and 48,000 psi for ASTM Grade 40 and Grade 60 steels, respectively, except for calculating development lengths. The development length for Grade 40 and Grade 60 steels should be based on yield strengths of 40,000 psi and 60,000 psi, respectively. Reinforcement with a yield strength in excess of Grade 60 shall not be used unless a detailed investigation of ductility and serviceability requirements is conducted in consultation with and approved by HQ USAGE (DAEN-ECE-D).

9-2

EC 1110-2-510 9-7b(3) 31 Aug 83

(3) Maximum Tension Reinforcement. For flexural members, and for members subject to combined flexure and compressive axial load when the design axial load strength ^Pn is less than the smaller of O.lOf'cAg or <f> Pfo, the ratio of tension reinforcement provided generally should not exceed 0.25/^ . Reinforcement ratios greater than 0.25/ob but less than 0.50/ob , may be used if excessive deflections are not predicted when using the method specified in the ACI Building Code34 or 0ther methods that predict deformations in substantial agreement with the results of comprehensive tests. Reinforcement ratios in excess of 0.50/ob should not be used unless a detailed investigation of serviceability requirements, including computation of deflections, is conducted in consultation with and approved by HQ USACE (DAEN-ECE-D)

(4) Minimum Reinforcement of Flexural Members. At any section of a flexural member where reinforcement is required by analysis, the minimum reinforcement requirements specified in the ACI Building Code34 should apply, except that fy should be in accordance with paragraph 9-6.b(2).

(5) Control of Deflections and Cracking Cracking and deflections due to service loads need not be investigated if the limits on design strength specified in paragraph 9-7b(2)., and a reinforcement ratio of 0.25/Ob are not exceeded. Where these limitations are exceeded, extensive investigation of deformation and cracking due to service loads should be made in consultation with higher authority.

(6) Distribution of Flexural Reinforcement. The spacing of flexural tension reinforcement shall not generally exceed 18 inches for Grade 40 steel, or 12 inches for Grade 60 steel.

c. Hydraulic Structures - Reinforced Concrete Design.

(1) Design Assumptions.

(a) Strain. The assumed maximum useable strain at the extreme concrete compression fiber should be equal to 0.003. The design strain, S^ at the extreme concrete compression fiber should be limited to 0.5 Em for hydraulic structures.

(b) Balanced Conditions. Balanced conditions exist at a cross section when the tension reinforcement reaches the strain corresponding to its specified yield strength, fy, just as the concrete in compression reaches its design strain, £^#

(c) Concrete Stress. A concrete stress of O.SSfc1 should be assumed uniformly distributed over an equivalent compression zone bounded by the edges of the section and a straight line lying parallel to the neutral axis at a distance a = Smz from the extreme compression fiber. The factor ^ should be taken as 0.55 for values of f'c up to 4,000 psi. For values of f'c greater than 4,000 psi, J5>m should be 0.50.

9-3

EC 1110-2-510 31 Aug 83

(d) Eccentricity Ratio. The eccentricity ratio e' is defined as:

e, Mu/Pu + d - h/2

dT*— d (9-7)

where e = eccentricity of axial load measured from the centroid of the tension reinforcement and Pu is positive for compression and negative for tension.

(2) Tension Reinforcement Only - Compressive Axial Load. (See Figure 9-1).

(a) Maximum Design Axial Load. The design axial load strength of compression members should not be taken greater than:

*Pn(max) " 0.7*[0.85f^(A - pbd) + f pbd] (9-8)

or

♦Pn(niax) = O-W-85^ " Pbd) + '^^pbd] (9-8a)

(b) Compression or Tension Control, The eccentricity ratio, e'/d, for the balanced condition is:

em 2km

2

d 2km-

pf M y

(9-9)

where

6 E e . m s m ^ Esem + f (9-10)

9-4

EC 1110-2-510 31 Aug 83

AXIAL COMPRESSION AND FLEXURE-SINGLE REINFORCEMENT

Pu^Pn

^ 21

0.85 fc

pbd

f::-?Jr

^cu — ^m

F E 0

II TsAsf^Ji ^

a = kud

fsu= £suEs

€.uS|j

FREE BODY DIAGRAM STRAIN

Pu = O.esf'cbkyd - Asfsu Mu - Put'sO.SSf'cbkudtd- \ kud)

BALANCED CONDITION

d "€m+€ fTITCy

^-~ 0.85fc /am ± €m

km^ =^[€^-y] Solve Pu and Mu simultaneously for e'm with fsu = fyand kg = km

TENSION CONTROL (e' >e,m) Pu r

Solve Py and Mu simultaneously for ku with fsu = fy

€cu "^m

Pu

COMPRESSION CONTROL (e' < e'm and c < d )

c ^ m d "(€m+€su)

fsu= €suEs=^f!D(ySm-ku)

Solve Pu ond Mu simultaneously

for kuwith fsu = E?i€m ()9m-ku) ku

0.85 f'c

y?

_i | t »- O

V

Asfsu. €Su<€y

FIGURfe 9-1. AXIAL COMPRESSION AND FLEXURE -SINGLE REINFORCEMENT

9-5

EC 1110-2-510 31 Aug 83

If e'/d is equal to or less than em(7d> the strength of the section is controlled by compression. If e'/d, is greater than em

,/c|> the strength of the section is controlled by tension. Sections controlled by tension should be designed so:

♦Pn-#[0.85f£ku-pfy3bd (9.11)

and

♦ Mn = « C0.85f;ku - pf JCfl - (1 - ^)]bd2 (9-12)

where

s.v/f-'^^f-tS1- 1) (9-13)

Sections controlled by compression should be designed so:

♦ Pn -♦CO.SSf^ - pfsu3b(l (9-14)

and

*Mn - * [0.85f;ku - pfsu][fl - (1 - JLNbd2 (9-15)

9-6

EC 1110-2-510 9-7c(2)(b) 31 Aug 83

where

m E^y - "„) _ (9.15a)

su ku - y

and Ku is determined from the following equation by direct or iterative methods:

k 3 + 2f^ - Ik 2 + r^fy^k - Vsy6' . 0 (9-16) ku + Z[d Uku l0.42Sf'd,Ku 0.425f;d u

(3) Tension and Compression Reinforcement - Compressive Axial Load. (See Figure 9-2).

(a) Maximum Design Axial Load. The design axial load strength ^Pn of compression members should not be taken greater than:

♦Pn(max)= 0.7 ♦( 0.85f«[Ag - (P + P^bd] .

+ fy(p •+ p'Jbd} (9.17)

or

♦^(max)58 0.7*{0.85f;CAg-(p + P,)bd]

+ Es£jp.* P'ibd} (9-17a)

1

9-7

EC 1110-2-510 31 Aug 83

AXIAL COMPRESSION AND FLEXURE-DOUBLE REINFORCEMENT

b PuS$pn A'sfsu^ xa=$mc

T it As=pbd

T"

P5 L

'n ^STIU^ .a

yA ;3—T «

As= pbd ^

T<Asfy

su^fy/Es

€su^fy/Es a= ku d

FREE BODY DIAGRAM STRAIN

Pu = 0.85fbbkud + A,sfsu-Asfsu Mu = Pue'=0.85fcbkud(d- -^-J+A'sfsuW-d')

BALANCED CONDITIONS

knr0"?^". :m

• su = f _ /3md'

gm~| + €j

kmd €m

.E

p /"Asf'su jn—- .O-SSfc/ €m

Sdwe Pyand Mu simultontousiy for e^ with ky = km, fsu=fy ond fsu = Eg C'sy

A?

As I Asfy L^ -su

TENSION CONTROL (e'>em)

ku-ffrndfr /Sm-ku ;**

Solve Py and My simultaneously for kywith fsu = fy and

f'su = Es ^su

/ ku-fim<itJ v 'SP^^ A'sf su

€cu<em

COMPRESSION CONTROL («'< e'm ond csd)

Q em+esu ku ^ - \0.85fc / u. - r^^ "^—f fsuzi^lULt^./Smi')

ku a

Solve Pu and Mu simultaneously for ku with

fsu - Es €m Q3m.klJ j Qrid

ku ^

f'Su=ILfi!L(ku-^ml,)

A'sf' su

Ol

m

•■'•../

As-^

Asfsu L^ :su

FIGURE 9-2. AXIAL COMPRESSION AND FLEXURE -DOUBLE REINFORCEMENT

9-8

EC 1110-2-510 9-7c(3)(b) 31 Aug 83

(b) Compression or Tension Control. The eccentricity ratio, e'/d, for the balanced condition is:

e- "m *m Q.AZSf'

r= p vr*— (9-1^ 2lc_ - -^ r + su £lfm 0.425f^ 0.425^

If e /d is equal to or less than e'm/d, the strength of the section is controlled by compression. If e /d is greater than e'm/d, the strength of the section is controlled by tension. Km is given by equation (9-10) and:

x. . *ku " gm d") c , , % fSu ' U -k T E5

CV <

fv (9-19) Tf^T Vy i Ty

where ky = km

Sections controlled by tension should be designed so:

♦P^ - ♦C0.85f^ku + p'f^ - pfy3bd (9-20)

and

♦"„ 3 *&'***& + P'^u - ^T ' <! " Id^bd2 (9-21)

9-9

EC 1110-2-510 31 Aug 83 9-7c(3)(b)

where

f. . (ku ' &m ^ r f

fsu " (BB - ku) Vy i Ty (9-22)


Sections controlled by compression should be designed so:

*Pn =*[0.85fMcu ♦ p'f^ - pfsu]bd (9-24)

and

♦Mn = ^0.85f'ku + p'f;u - pfsu]cf - (1 - ^)]bd2 (9-25)

where

9-10

EC 1110-2-510 9-7c(3)(b) 31 Aug 83

E e (B - k ) f = s mVPm "__>.* (9-26)

f;« s Esem[kuk" gm(' )] i fy (9-27)


C

P (1 £-)Jku 0#425f. LP (j-)(j- c

+ £•- 1) ^Pff1)] - 0 (9-28)

(c) Other Considerations. Compression reinforcement is usually not considered effective when designing retaining walls. Walls designed as doubly reinforced must be reinforced laterally in accordance with the ACI Building Code 34.

(4) Flexural and Tension Capacity. (See Figure 9-3)

(a) Tension Reinforcement in Both Faces. For e'/d greater than zero, reinforcement must be provided in both faces when the eccentricity ratio e'/d is in the following range:

^-id^fi0 (9"29)

9-11

EC 1110-2-510 31 Aug 83

AXIAL TENSION AND FLEXURE

DOUBLE TENSION REINFORCEMENT (d-ê'rO)

?! / I

L-£*»"{£

As= pbd Âs

FfrEE BQPY PIA<?RAM

Pu = Asfy + A'sf 'su Pue's Asfsu (d-d1)

^~€y-Es

STRAIN

SINGLE TENSION REINFORCEMENT

b

o.esf'ci tm i 1-

€y "(C+d) Q a C = kud

iÔ , At s 0 or

^;

€cu— ^m

•u"*r u FREE BODY DIAGRAM

kud Pu = Asfy-0.85fcbkud Pue' =0.85 f'c bkud (d ^- )

TENSION AND COMPRESSION REINFORCEMENT (e'<0. c^d')

bj ■ A',' "Asf SU

T

^

Asn ^'U €cu < €m

€su =€y

FREE BODY DIAGRAM

Pu = Asfy- 0.85 fcbkud - A'sf'su

Pue'=0.85f£bkud(d- -^ ) - A'sf'su(d-d')

STRAIN

ku-/3m d/d fsU-Es€y(K"-^^)

v Pm- ku '

hGURE 9-3. AXIAL TENSION AND FLEXURE

9-12

EC 1110-2-510 9-7c(4)(a) 31 Aug 83

The design axial load should not be greater than:

♦Pn(max) " 0.8* (p "t p'Jf bd (9-30)

The section should be designed so:

♦pna*(pfy + P,^u)bd (9-31)

and

h x 6*^2 ♦ Mn^(pfy + p'f;u)[(l -^.f-W (9-32)

where

».+f)

P — - P V 'T'T'

9-13

(9-33)

and Ku is determined from the following equation:

,d' n d' e\ e' k . 'T^'T-^yT (9.34)

u e 1 #1 d e

EC 1110-2-510 31 Aug 83 9-7c(4)(a)

Sections subject to a tension load with an eccentricity ratio e'/d less than zero should be designed using equations (9-20), (9-21), (9-22) and (9-23).

(b) Tension Reinforcement in One Face. For sections with tension reinforcement in one face the eccentricity ratio e'/d must be less than zero. These sections should be designed using equations (9-11) and (9-12) where Ku is given by:

=1-V/d l)2+i \0.425fcj/

/d|- (e'/d - 1) (9-35)

(5) Pure Flexural Capacity. The capacity of members in bending, without axial thrust, with reinforcement in one face only may be calculated as follows:

*Mn = + efyi i efy V

bdz (9-36)

Equation (9-35) is valid when;

e ;< em =; 0.85 fc' kmj

fv I

where K^ is determined by equation (9-10). Ifp is greater than/^, the reinforcement stress is less than fy and is given by:

9-14

EC 1110-2-510 9-7c(5) 31 Aug 83

f ._ e

and

+Mn = ihfJi - -S^l bd2i (9.37)

d. Non-Hydraulic Structures - Strength and Serviceability, The strength and serviceability requirements for non-hydraulic structures should be in accordance with the current ACI Building Code 34.

e. Non-Hydraulic Structures - Reinforced Concrete Design. Limits on strain, reinforcement and concrete stress should be in accordance with the current ACI Building Code 34. Equations (9-7) through (9-34) should be used to design sections by substituting £c for £m and /3 for An'

f. Shear Strength. The shear strength Vc provided by concrete should be computed in accordance with the ACI Building Code 34 requirements. For cantilever retaining walls the maximum factored shear force should be computed at a distance d from the base of the stem for stem design, at a distance d from the stem for toe design, at the face of the stem for heel design, and at the base of the key for key design. Where an L-shaped wall without a toe is used the shear force should be computed at the base of the stem for stem design.

9-8. Foundation Analyses. Foundation analyses should be performed in accordance with the methods described in Chapter 5.

9-15

DRAFT EC 1110-2-510 31 Aug 83

CHAPTER 10

CANTILEVER SHEET PILE WALLS

10-1. General. Cantilever sheet pile walls may be composed of steel, aluminum or concrete sheet piling. When the driven sheet piles are capped by a concrete wall, it is called an "I-wall". I-walls are normally used only for flood walls, rarely for retaining walls.

10-2. Materials. Wood sheet piles are seldom used today, though they were popular prior to about 1960. Precast concrete is increasing in its use, and is available throughout the continental United States. Aluminum sheet piles are rarely used except for low bulkheads exposed to sea water. Steel is the most common material used for sheet piling. Steel Z-sections are particularly suited to cantilever and anchored sheet pile wall construction, in,that they develop a maximum resistance to bending per unit of weight and the interlock is located where the longitudinal shear is zero. Also, the section modulus of an individual pile is the same as an equal length of interlocked pile wall. Aluminum and steel sheet piling should not be used in highly corrosive foundation areas. Aluminum sheet piling in contact with some wet clays may be subject to high rates of corrosion. For information concerning corrosion exposure refer to the U. S. Army Engineers Construction Engineering Research Laboratory (CERL).

10-3. I-walls.

a. General. I-walls (Figure 2-2) have the disadvantage of more stem deflection under water loads than other type walls of the same height. To limit stem deflections the concrete cap and steel sheet piling should act as one stiff member. This requires that the piling be embedded into the concrete a sufficient distance that bonding of steel and concrete make the two elements act as one. As an added feature for the assurance of an integrated wall the horizontal reinforcing steel for the concrete cap should be welded to the piling wherever the two are contiguous. Deflection of the (Type 1) I-wall can be reduced by a small toe on the landside (Type 2, see Figure 2-2). A five-foot landside toe decreases stem deflection up to 40 percent. The addition of a batter pile (Type 3) provides much resistance to deflection.

b. Transitions. The I-wall is ideal as a transition section between a levee and a T-wall, because its construction after completion of the levee and T-wall reduces the influences of differential movement. Most of the settlement under the T-wall will be completed by the time the I-wall is constructed. Stability of I-Type walls depends on the lateral earth pressures developed by the depth of embedment. If the embedment requirement for foundation stability of the I-wall is not as great as the required seepage control depth for the adjoining T-wall, the embedment of

10-1

EC 1110-2-510 31 Aug 83 10-3b

the I-wall piling should be increased to at least the same elevation as the bottom of the T-wall. When a key is used in the T-wall, "return" keys should be provided between the T-wall key and the I-wall. Details for the design of junctures between levee, I-wall and T-wall are illustrated in Figure 7-7.

c. Seepage Forces. Seepage forces resulting from the water pressure acting on the wall, must be considered. These forces affect the magnitude and distribution of lateral earth pressures as well as the net water load acting on the wall. Such forces depend on uplift pressures in underlaying strata, on permeability of the piling and on depth of cracking, if any, which may occur along the riverside face of the wall. The permeability of driven sheet piling, and its ability to retard or prevent water seepage has not been definitely determined. Tests have been inconclusive and differences of opinion exist. Therefore, sheet pile flood walls, including I-walls, should be checked for both of the following conditions:

(1) Sheet piling assumed to have the same permeability as the surrounding soil (pervious condition).

(2) Sheet piling assumed completely impervious.

The water surface on the landside may be arrived at by the line of seepage method, the method of fragments, or by constructing a flow net for both condition "1" and "2". Separate hand computations or computer runs should be made for each of the two assumptions and the "worst" condition used for selecting the length and size of piling. Normally the pervious condition (1) is the most critical.

10-4. Design.

a. Introduction. The design procedure for cantilever sheet pile walls outlined in this chapter differs from the generalized procedures for the design of T-walls discussed previously in this manual. This chapter assumes a sheet pile wall with or without a concrete cap (Type 1, Figure 2-2). It does not consider I-wall types 2 or 3, which are actually preferred for those rare instances of broad reaches of I-type flood walls (over 75 feet in length).

b. Analysis. Hand computations should be performed as outlined in EM 1110-2-2906 "Design of Pile Structures and Foundations". Solutions performed by the computer program CSHTWAL ("Design/Analysis of Anchored or Cantilevered Sheet Pile Walls by Classical Methods") are preferred. Detailed documentation of the program may be obtained from Reference 38.

10-2

EC 1110-2-510 10-4c 31 Aug 83

c. Stresses. A base stress of 20,000 psi may be used for design of steel sheet pile walls. For concrete sheet pile, the American Concrete Institute - Building Code Requirements for Reinforced Concrete (Reference 34) may be used regardless of exposure conditions.


10-3

DRAFT EC 1110-2-510 31 Aug 83

CHAPTER 11

ANCHORED SHEET PILE WALLS

11-1. General. An anchored sheet pile wall resists lateral forces by the use of tie-back anchors in addition to the passive resistance of the soil and the bending resistance of the piling. Anchored sheet pile walls are generally used for retaining walls or bulkheads. One type is used for flood walls; it consists of an I-wall with batter piles connecting to the middle of the concrete upper section. It can be built without dewatering the site; but does not lend itself to a rigorous analysis (Fig. 2-2).

11-2. Materials. Refer to Chapter 10, (Cantilever Sheet Pile Walls).

11-3. Design:

a. General. As for the cantilevered sheet pile walls discussed in the previous chapter (Chapter 10), the design procedures for anchored sheet pile walls differs from the generalized procedures for the design of T-walls discussed previously in chapters 2 through 5 of the Manual.

b. Analysis. Hand computations should be performed as outlined in EM 1110-2-2906 "Design of Pile Structures and Foundations". Solutions performed by the computer program CSHTWAL ("Design/Analysis of Anchored or Cantilevered Sheet Pile Walls by Classical Methods") are preferred. Detailed documentation of the program may be obtained from Reference 38.

c. Stress and Foundations Investigation. These items are the same as discussed in Chapter 10, (Cantilever Sheet Pile Walls).

11-1

DRAFT APPENDIX A

REFERENCES

EC 1110-2-510 31 Aug 83

1. ER 1110-1-803, Constructibility

2. ER 1110-2-100, Periodic Inspection & Continuing Evaluation of Completed Civil Works Structures

3. ER 1110-2-1806, Earthquake Design and Analysis for Corps of Engineers Projects

4. EM 1110-1-1801, Geological Investigations

5. EM 1110-1-2101, Working Stresses for Structural Design

6. EM 1110-2-39, Architectural Concrete

7. EM 1110-2-301, Landscape Planting at Floodwalls, Levees & Embankment Dams

8. EM 1110-2-1410, Interior Drainage of Leveed Urban Areas: Hydrology

9. EM 1110-2-1803, Subsurface Investigations - Soils

10. EM 1110-2-1901, Soil Mechanics Design - Seepage Control

11. EM 1110-2-1902, Stability of Earth and Rock-Fill Dams

12. EM 1110-2-1903, Bearing Capacity of Soils

13. EM 1110-2-1904, Soil Mechanics Design - Settlement Analysis

14. EM 1110-2-1905, Design of Finite Relief Well Systems

15. EM 1110-2-1906, Laboratory Soils Testing

16. EM 1110-2-1907, Soil Sampling

17. EM 1110-2-1908, Instrumentation of Earth and Rock-Fill Dams (Ground-Water & Pore Pressure Observations) (Part 1)

18. EM 1110-2-2000, Standard Practice for Concrete

19. EM 1110-2-2102, Waterstops and Other Joint Materials

A-l

EC 1110-2-510 31 Aug 83

20. EM 1110-2-2103, Details of Reinforcement - Hydraulic Structures

21. EM 1110-2-2906, Design of Pile Structures and Foundations

22. EM 1110-2-4300, Instrumentation for Concrete Structures

23. EM 1120-2-109, Federal Participation in Major Drainage Improvements

24. CW 03150, Expansion, Contraction and Construction Joints in Concrete

25. CW 03301, Cast-in-Place Structural Concrete

26. CW 03305, Mass Concrete

27. Rock Testing Handbook, "Standard and Recommended Methods." Available from: U.S. Army Engineer Waterways Experiment Station, P. 0. Box 631, Vicksburg, MS 39180.

28. International Society for Rock Mechanics, Commission on Standardization of Laboratory and Field Tests, "Suggested Methods for Determining Shear Strengths," Document No. 1, February 1974. Available from: Printing and Publishing Office, National Academy of Sciences, 2101 Constitution Avenue, N.W., Washington, DC 20418.

29. Casagrande, Leo, "Comments on Conventional Design of Retaining Structures," Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 99 No. SM2, February 1973, pp 181-197. Available from: ASCE Publication Fulfillment, 345 East 47th Street, New York, NY 10017.

30. Matsuo, Minoru and Kenmochi, Satoru and Yagi, Hideki, "Experimental Study on Earth Pressure of Retaining Wall by Field Tests", Soils and Foundations, Vol. 18, No. 3, September 1978, pp 27-41. Available from: Japanese Society of Soil Mechanics and Foundation Engineering, Suga-yama Building-4F, Kanda Awaji-cho 2-23 Chiyoda-ku, Tokyo 101, Japan.

31. Harr, M. E., Mechanics of Particulate Media, McGraw-Hill, New York, 1977. Available from: McGraw-Hill International Book Company, 1221 Avenue of the Americas, New York, NY 10020.

32. Shore Protection Manual, U.S. Army Coastal Engineering Research Center, Vol. 1 of 3, 1977. Available from: Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402.

33. Mosher, Reed L. and Pace, Michael E., "User's Guide: Computer Program for Bearing Capacity Analyses of Shallow Foundations (CBEAR)" Instruction Report K-82-7, June 1982, U.S. Army Engineer Waterways Experiment Station, P. 0. Box 631, Vicksburg, MS 39180.

A-2

EC 1110-2-510 31 Aug 83

34. "Building Code Requirements for Reinforced Concrete", ACI 318, American Concrete Institute, P. 0. Box 19150, Redford Station, Detroit, MI 48219.

35. Waterways Experiment Station, "Investigation of Underseepage and Its Control," Technical Memorandum 3-424, October 1956, U.S. Army Engineer Waterways Experiment Station, P. 0. Box 631, Vicksburg, MS 39180.

36. Liu, Tony C. and Gleason, Scott, "Strength Design of Reinforced Concrete Hydraulic Structures," Technical Report SL-80-4, December 1981, U. S. Amy Engineer Waterways Experiment Station, P. 0. Box 631, Vicksburg, MS 39180.

37. Westergaard, H.M., "Water Pessures on Dams During Earthquakes", Transaction, ASCE, vol. 98, 1933, pp. 418-433. Available from: ASCE Publication Fulfillment, 345 East 47th Street, New York, NY 10017.

38. Dawkins, William P., "User's Guide: Computer Program for Design and Analysis of Sheet Pile Walls by Classical Methods (CSHTOAL)," Instruction Report K-81-2, February 1981, U. S. Army Engineer Waterways Experiment Station, P.O. Box 631 Vicksburg, MS 39180.

A-3

APPENUMX B "EC1110-2-510

PERIV/ATJONI OF EQUATION F<yR dc - SE£ PAG£ S-i.

THE. I4OV:I-ZOK\TAU pt- E^LOM; AT "Ti-iti. boTroK Op A COUEStOhj

CRACK.j WITH A DEPTI-I ^C BELOW TWE Top SOP-FA^s^ w

~1&V& o THE £<pU4TtoM FCH THE HtfirmiTAL PfiKSCU&EL

AT AN"f l-rt/MT ON TMEi SLIP PLANE. 3F A VV/epa£ IS 'SlVEM

-^w ^ -y^v v t+tb^i4> ~fc*icc) &*!aOrtcc+Unfierce

W K! cH ■ ( S OE fc!Ve.D IN Pt Q . C -1 OF-' A PPfc'KS D t >. C.

0 = )fdc $t&)ijMpQ*t;<f''

( +(sRf!)fiM<l)t!lf1<X_

(SIKF)C

&/r} ordjd (?r f c^r^j <p- Ct^-cc

USING ftcapBR ~<'$n ZonvF-MTioN fcK Ahi Acrivt Type, '/kc^i:

Jc \J - (sRf^fartjrtAJflGc] (SUP)

yF/ -i-(s^F)'(A-f,'4> ^^[(sRr-Tfef^^V- ^n^ ^ ^j

B-l

APPE.NP1Y C EC 1110-2-510 31 Aug 83

?OATIOM Dg.8lVATIQM OF EQTTATION TO PF-'T^Ktl IME. TT4E CRITICAL

'/ALU'ts. OF QC Foiz. A WEDOE SUP PL^^ê.

^s4

«.

^^(tft^^-toV)^)

THE UNIT PRESSURE.S -^y AMD -j^ ARE ASSUKED TO t>£ Ti-iE

KA'ÔK AMU MlNCK. pKlMCtV'AL isrrpESCE^ ACTIMG AT A^V PÎMT

^f1 THE. swp PLAK\& (SEfc FIGURE Aeove), -f^ /s Vt)^ To -WE

Wrr'GHT OF hUTE-RlAL JW lUE Vvle-PÊ^PiP-W-CTbY AB6V6 Ti4£- PatKfn

AMD AM^j V^TlCftL-fKESSUPE AT THE- PDlMT PU-E. To EvreRUW-

FdfcCEs AcriyJ6 0M~faE.Wfc-.D6e., WHEN -^ i«, ^nc»)M T^B VALUE

ftF -f:ri MAj tie PB.Te«niHE.D FROtA HOUR'^ -IP-C LS op tm&i

F<5K An^ VALUE, OF CC, -^ /JMO 7^- AKE.J-TW6. sjRzss NO«MAI_TO

Tf-ie. Sup PLAÊ AND THE sue^R STRESS ALOM(5 THE SL\p PLAWEÂT

""Hê. -SAME PoiMT. A MOHfl. ZlfiCLE. DERIVATION F^K -^ fS

SNoWM »H F\GURE. C-l .

C-l

EC 1110-2-510 31 Aug 83

fN= d!k(l-MM2d$+jfyl.(l-6o<.2<x)

(&i%)(-^°o-^u

~~K

<VJ

j i OhLZoC = 2 &*£'(£ ' ',- C&4, 2.CC - £ ^-fC^

-fi = = t,, 1 + -fcvrlbtcuOtf J c

FfGU^E C-1.

C-2

EC 1110-2-510 31 Aug 83

WEIGHT OF WHPSI: •= Y ( C4^Jc)

Z(^f]OC--t23L^lP)

STfi\P SURCHARGE. ~ V

A'JG, VHHTICAL PKECSUKE. ON SLIP H..AWE « ~fv(M(>',

//.'

-fvfim) -- z r -ft- dc

TOTAL HORIZONTAL PaRce on "SLIP pLAfie - ft

PH = "ft f'**) [" ttf^l <£ -1/M^^ -]- ^yj GTCMdC-ftArf^ -^t "^

y/rir su ;

Stsn or CM (JC-J' -/vri ^ Stys '^oc

PM =

p^ =

. Ctf-Jc}

C-3

EC 1110-2-510 31 Aug 83

TAKIH^ THE PlKST DfcfclUATlVft OF ft ^ WiTrt RBSPECT TO ^

A ML/ 5eTT\MG \T SÛ/Û TA Zef<i6 A <?UAPÂT!C tLq>'JATi-*>M

IS OBTAIUFLP. THE. VAKSA6LH l»4 "Tm^ eÛATiOK 15 '>»irt-CXlj.

AML "D-IL-: F^'JATJOM M/i'j >ii-- W*.:TTri\ As v-'ou^'/)'-":■ I

-4-- "Z- -

yfr+dc)

tartoC.

7™* 4 Vi^dc) *(4SJh =s O

TNJS QonF-F-tctEMT /H FgouT OF tostL cC Mfty He r.AU.cv

CI, AtJU THC ENTiKZL . Thl'.KV T&l'M Cfi:.LB.O C^ #

TH&U :

^/Ki. <sC = c/ ±l/£?~+4ci

CC , -^ (siM^ ■+4Ci.

!M OKPCK. PO^. TMt£ S16N1 OaMV/EWTlON To ASKtH Uirm TWE

"Tv. r Or THIS MAHUM. S THE EQUATIONS • FW? AH ACTIVE Type

W&J76H AMP A PfjSSWE TyPE WeP6E. SHflULO fcE w^rm-fj

oc = Â-WT'^- . G/- y^v-^d AcTVt' tyfji Wetet:

L _, /- C, 4- ]fc^-h4-Cz\ ffisstm ^fPZ Wxv*z

a-A-

EC 1110-2-510 31 Aug 83

|T SHOULD ©^ NOTEP THAT FOR A LtMrr&t? E<?iJiLiBRiUtA

T(fr. ^NAL-YS]S ., THE VALUES Wt^ AMD C> T^ itT.

IJCKU IN) COg.pp1C)KWTS ^1 At)C? C^. SHOU'JD Bf:

(C f. v') tavt 43 AM t) (SR P ) C K£v P?' ■'T1 y e.Ly #

IT SHOULD ALSO BE NOTES? THAT O/C IS AuAjAys 7E;fc'0;

EXCEPT r-:oR ACTIVE. TfplE WE-PQgS )M COHESWE MATTRiAU.

Dg-Rw/A-îon OF E-<?iJATiOM Vn - SEE Â^n c-!!.

THE E<?uATiONi$ FCJR C, AMP C-a. A^-t NOT VALID UM&M

TWL. VAUJli OP V (STRIP ûRCWAKGti-; 1^ Too L-AV.<r,E-#

V\lHGN V 1^ |£<?UA-U TG OR GIK.&ATEP- TMAM A C'EIOTJiM

HAVIMU^ VAuue Viî TI-IE VALUE op ^ Swiouu;

bG SH-T IN ACCORDANT IS" WITH FARAGÂPW 3-5 b.

Tun VALUE OK- Vt-i 1^ FoaND SW SL-TTIH^ TÊI

DE-HÎAIMATOR OF C0FFlCimT«> '-( AnDC^ E<p J AL¬

TO ZL-K,-; AMI? SOL^.TI^ F^^ V# Twis VALJB I^VM,

O = (^F)^^ + y^ê)

fl

C-5

APPF..ND1X D EC 1110-2-510

31 Aug 83

DET&RKitviATioN OF LIME OF ACTIOM FOR MOisizOtlTAL Fo^m (SEE FtG'JR.E: 3-7 )

LlM^ OF ACTlOfNi - PwH

_ mJc)cir._,

= \Nci. I !.:'.

THE. MoRl-Z-ONiTAL F<5gCE;Dui TO TWE VOEISHT ©F MATEfc.'AL lM TUCi.

PAKALLB.L 0<5P.M1 ABCE-; ACTS ALOM^ A LiNfc AT DISTAMCG

'&-*<: AlkJVti Fd»MT P As. SH<5WM IN) TMe RaofcE A^V£. TU£ "2.

l-Iof?iZOKTAL. FoRQ.e -j DU£ TO THE WfcKSWT OF MATERIAL. IN

TftiAM^Li: CDt~. i'^ AssoM.Rf To ACT QW ALOK^ A Uue. AT

PlOTAMCE -A™^. AfeovE. Pot^-r D. Twe ToTAvL HopiZOMTAL

F^RCE DLJ& TO TW£ TOTAL W&iaHT <DF THE. Wtf.i--9£ •?;

P.. /<y(^-J'<) ( l< ]*> A cotJS-rAirr

fi-iE HOHEHT op-Tmo ^ORCE- ABOUT fo/frrp IS

D-l

EC 1110-2-510 31 Aug fi3

eAB<e(j^) + g^c^), M WM

'-,'? - ^r _; /<-,

'>.*■, JC- /nLP-' KV

( 3 M?) « Mwi^

/k'y (-Ji-Jcfdc 4

K^ ( >U.Vc)J

2. (~ta>rLtf~iZL4^F>j & (fafi-cC-1Znf) •= MWM

G (-fco^oC — ~kix^~$r>~j WM

THE DISTANCE. FRai^ PoiNT D To THS U!NE. JF A^-TWM

/WH ■=i

rwt^

VwH " ^- jey^W)

V-2-

EC 1110-2-510 31 Aug 83

LINE, OF AC

tjk s fc TION • - Pv

- V .^.

iL* 1 ^*- f

)

^ f

^^-—-J 1

■—

6 \

\ x i / k Jl

0

R i

t

FROM TUB G&oM&TRy Of- W£ &&)}/£. FMUPE *. 7 c y

X-

//,« ^ , -rf. G-Yfru^-ltn,?, /

D-2

EC 1110-2-510 APPENDIX E 31 Aug 83

MEL D E p WAT ION OF " TRU CTO RA L VÊPG E. EQ UAT 0 Nj

CUVEN : Geuir-tfAL. NAIEDGE. £c?UA'TlOKi 1 i-t^. 4-4}

-I- (.skF^,Ci. L.;^ ~ [câu - (SR5.)-fo/n t^S^vi^

Se-T PjL-l - Pu AMD f-o » Pi Awp CoLVt F^ ^KF5 FoR TWE

GTRUCTUÂL lAJfJÊ

4-(SR|^)CL

jj- C Pu-Pf? P ML-NRXIM^^ - (m)j)ttilj)<!d40C+ U "Ulfi -CLJC^fi) ■=

~ ( PL - PR T- ML- ft*} G^d oC -P flAi W)QM CC

E-

APPENDrx F EC 1110-2-510

31 Aug 83

DRAFT j^ER'VATIONl GENERAL 'AJEDfrE. EQUATION

G\,.JeM: FREEl BOPM DiAQRAK OF ArH ,/JE£?6£. See Pic 4-4 FOR pepw/TioM opTems.

/

4n

/

-1——*+* J-GC

'■^\

^

WQlTIL BQUIUBRIUM S^UATIO^JS NoKMAL /MV fAMLELL To $L)P PUWt.

4 £., (> (- ^) - ^ OJ r- ^^ TA = fW/ +V/.y- s^^ 4 QlLt-Hi^c**. **. 4 (fe-TPA.) CVACCJ.

F-l

EC 1110-2-510 31 Aug 83

ACCORPJWG To MoHR- CouL-OMB FAluuRt- ££nEPj.jrl}

VJ/are. THE EQUAT/O^ FOP Tn'e STZBNGW IR£VUCT/OH FACTOX SRF^ t

WH&RS. FSU. ■= FACTOR OF SApery,

Sut-STiTurg E-xptessioNS FoR 71 Aw Hj. !firo "'*& BPufinohi FoK ZkFM.

SOLVE Fof- ( fe-i - t.j

F-2.

DRAFT EC 1110-2-510

31 Aug 83

APPENDIX G

CANTILEVER WALL DESIGN EXAMPLE

Analysis

Strength Reduction Factor

Bearing Capacity

Strength Design

Working Stress Design Comparison

Earthquake Analysis

Page

G-2 thru G-7

G-7

G-8 thru G-20

G-21

G-22 thru G-26

G-l

tEC 1110-2-510 31 Aug 83

Der-i-vi WALL. FOR. C'OW-^^U S»QV^M Sv.-...Tri^Ta UAVEL A FACTOR OF >-^-.:r^ AtSAUvf^L'L^'v^ e.v>^"".»r^5"i;F^ SRF EQUAL To VS. ——--^

2.0 Ttf/CK /HfB&VloUS

J^-^c

^ lg.0 (vTSUHArfe) ,

<f>g

77777:

(3)

EL.I02J51

*-# ^tO'

BL.IZST.O C i

ST

1: i

T

1 5

; ^RsA^ ^

S'i.iP fLA*/^ -

FouNV&moN

r** t

±=35° ; ^2=^

FouftCATlONl XsKruKATBP^ O.I20KCJ Y&icrtUfiW • 0.057$ KCP

^=20" /Os= 3.60 ATSA

?A.^ w*

<*&) = f*>?{C'-Vtf + 4£*) ) WML C, = 2{SRF)tt1}J>~ C-KWO

«-5 2.. 46' L 2-

<^|) .'S NniATivE. W'ilCh' A6f:»L£S Wft-i THE S/^w CoNWrtnoN OFTUE

G-2.

EC 1110-2-510 31 Aug 83

THE. CRITICAL VALUE OF <X(I) my &£■ CALctju\T&.D As

p WilL &B. ASSUHBV Z<?UAL To Zg^ . £(.•:,«£/$& TW£ EFFECT ^F &

iS StftLL CcHpkf-'W To THL EFFECT Cf- THe.~TOTkL M/E/^WT^p TWr:

Wec<SE.

T^F. CtrnCAL VAU;?. OF <*&) ff/0/ BE CAiOOLAT&P As

C2 = (sFF)tiu4> [l ~ £*p)Mfc)] " 0 « /.<W

CALCULATE- UPLIFTS £y ^/A/£ cy- SmtPASZ MnAQP (stte PftRAQMrM 3-ll)

■Oft = ^fcife)/* .r'*^yft«^V./f, /.47 ^

.Q£

PC 1110-2-510 31 Aug 83

CALCULKTE. UJ&I^HT oy \AJ£Î:-.SJAMO SufecÂKGES

'AL I.BO' ^V ^

Ypr

/

WEPG£L 0)

Wiô* &xo. 12.)(}a.<X>'x!*.**'= zi.ss-*

Vd)as 2*0*U5X MM* = 4;!5%T

WEPCJE. (2-)

/.s'x^.sV o./s ~ SJ.CG x 7,75' = B^.ri

It.ox'-z.s* e.is ~ (o.lg X ^.ô' - iv'.Tii"

f7.tJ ^,i^ 0,120 s ;o.<23 y/5.zb"= /45.5,o

v^ ft If . Xfc.2f ' = " ''-^ /'/Hfi./iii/K.K.D^

Ha) = ,'?.'::?I^T -4-»'..-5 -f 3t>40g n.49-Y(p^,fr! rê y

$-4-

EC 1110-2-510 31 Aug 83

V%) = y^L (o.'^^.IS) (2.5) = Q.4g^T

_£ALCUL^T£. LATERAL FbfiCES (fcefG.fi. Ta FlG.3-/ AM PAMGMftf 3-6.)

PvO") =-^5lf;<iX 4.15 = -2./5 X /2,45's ~-6.77 j

oxb &#) -&$. f-ytw-b Sen df^.)

Pwa') = -<3,75iw.3y>c 0,SO a - 3.24 * ;Vt3 s - £-.2^

?v(i)= -o.mwx 5.2/ = -4,/5 x: f/Jt" = -?,'3

G-5

EC 1110-2-510 31 Aug 83

WfePQE (4) OCfr) =r 3$./?'

(SRF

SCF

J^i C tffr) - $RF)w!4 Svrt 'Xft)

Co* #(4) - (SHtyitft ZW *(4)

^ 1.0 49&1

= -a. 5?; 4'.'

fW4) Pue*) = -o,-zi\±n QA5-=-o.m 4,%Y,= "OTA

\.04W\%o.$t+M= 2.54x l-^S" = 3J& Pel (4.) -

3.55"

B.S5-

/(<?) = -fag = MY ( eu.l©».0/

OvERTuRWMgr STABILITY

WfeJ=3a.4o^ Jl.4^ = 441.22 Lfo)=r-6.6<? )< 10.2(3 = -6e. ^4

—\l.tfX 1.31 SB -!36.7^ — 3.22/ /.£/= - S.^O

g.'TSy |.|<f = 5.55

/F 7.44= /.56 PT 3.<?6

PT

IS SAT15F!£t>.

^-6

EC 1110-2-510 31 Aug 83

CAICULATTE. SRFW RE(?a\R6.P PQR STRUCTURAL \A)£t7^e^'<St:fe))■

FOR SUPiKJ^ E<pmU5RtOh To SXiST^ (fe/e 7^ F/G. 4-3)

fru-PA + Mu-MR)&J^ - (W&-) 4V®) s^^ oCCs) SRF5 =

PL = Pco4&)s 14.^ + 3^2= 17.^/ ^r

FR = ffc - 2.^3 ^ PT

WL = O ; l-lpj-r^ ) 0C3=O; W(3)rr33.4^^r

KSF L(3>=/3

PT

SRF5 « ^ 17.^1-2,^X0 - 33.40(0 (IT. «* / - £■ «?8)(p) 4 ^8.4d(ol3<>y?7)Q) -G.tffasW?) ioMli)

CALCULATE &BARtu(* Cfyp^ciry (set QiAPTBF Z)

SfMCg S>4, j 'S'yZ W/LU BE T/Vf**»J As ZEK^,

^fi - o.0575x2..5 = ^*/4

F5 3/. 7/ = .3. c?^

^-7

EC 1110-2-510 31 Aug 83

DFTERMmg LftTfLRAt. f^&SSU^. DigrR^T'OM OM gACVT ^ WALL..

P0). ,4.;, ^a- Ts^s " (to«i»*««»ws-'; P(i)s 3.22 X l'£| = 3.^0 f

pgi7.tf[^T Ko. $>&> 17.91 = m * y

= 24 av"-J?-y= 24-7.35= Afi.fS

Kf-P M 3r24)2'

''L 3 C?.4),t'

^ 1?X>7.«| (-3*16.15 -24) ... Ts" (24)^'

L5205 r*r

^L. J£4.erv ] 1—

/ i v

/ 1 ~\ao

Hi* ^4f^ i

> J V

/ "QD

fvrtJffcr /l.Wi ,» -...„ —^ *

1 4 / KSF" k"

1 / /.3^/p . ftUOLf i ^i

I.SZosKse

G-8

EC 1110-2-510 31 Aug 83

FACTORED LOADS (see. PARAGRAPH 1-1'£)

EL, 12.4.0%

\<1tir=$.te%T

. 1-

6-?

EC 1110-2-510 31 Aug 83

MOHEKT AWC SUEAft fttAafiAKgFgR. FA<:TOR.£P LflADfi.

5TF.H

EL. /24.0

/f*n"-K

grt F''-A<r

BL.l'r.j Ztfr-K

FL.IIO.SO I Ijx

t:j:Z3 ts*

I

L i- "wx"

nS"7T/g"r-

&L. 125,0

ELin...b

(5-/C5

EC 1110-2-510 31 Aug 83

MotAKUT AMP SHEAR f lAQRAHS FOR FACTPRtip LJQAPS

MKEL

__ BACK FACE. *> <}F STEM

G-l(

fC 1110-2-510 31 Aug 83

Mot-Mrirr AMP SH£AR DiA&teAHSFog. FACTOFLEP LOADS

4 Vu

4>MH

(j-II.

EC 1110-2-510 31 Aug 83

STEM - REiMFQftCEb COKICRLTE DESI^KI

"fc* '*>** y -r^= 40 ^ ^MAjjas O. lOlZ (^jl'KAUUC îHT'JK.Jl^ i - ..5.a

P •= > ; -^- /-yî AT LL. IOCS'

pHw = 190. ?r' = 1281,72 ) K; = 2544.13

(ALTn'MA-E ^// i #/o 6A/?5 OH&'CTRS. As - 2.*3$)

IM-VC

AT FL. )'05.£S

4MH« 1-5 vrf-^ HaMBMT P/A6PAH)= ::DO ) MM * 10.45.47"

«47/'Ol w

•? ■= /<;.S6.(5T iî-i^fgy^faftf 3= G.O0&&I5

*£ As-» .rv.j.L^>'.'. y 12x23.53 - l.%7cr

AT EL. iog.flp

4 MM =.• 75FTf^t.-. noHENT p.A^. ^0'N-^ M^ ^ j O00 .g-K

»=ll%^«3oV;-|^}-'j.«27.d7j cl=Z2*7j J.^re tin

As = UC?'^

7452.4

^-/3

EC 1110-2-510 31 Aug 83

iU-i< AT EL. 112.OO

<Mf.. » ■33PT"K(pR-ahA M«5KM-.TP(M^=S£?';,M"^ MM = 4-40''

ba "a", ^ .-* 3d- f-l^) 12 = 24.?3"; c/= 1^,^^ «.4fiS-^^i/a= 43 77.M-

7 46TK14 44^

— T.

* - 4.^) - p-o^y^Cmtj AT K..liS.30

T = ^0d23t»; A^ - 0.55, '-^r

< i, - •<

^MM = jflFT"K^H3«Mowr.»\rx>«^,)e \70IW~^ HM = liM^'"'

b =\t*} 4i « -So"- (^),2= 22^"; d^n.'s] lAW-Ubd^z 4847, C5-

l33.2>3

■kJ (( - «l^?Xl2)f,7.^ - o.oooM As = o./^ !*fr

PLQ-T '^A^FaR, "STE^

«.!?'

et.ttc.oG i<f.¥-

/a.?<?

£i../(D7.67 /

/ /.S?'"1-

EL. Ufe, oo

£L, j(?2,5r

2,74 w*-

T«JE PLOT SHOWS THAT *!Q6AR5@i?rt ARE ADE^JATE FORFLEVURE AT EL,|O7.67; !; '■, •■• * $ BMsGn" ARE.AL'E<?UATE Fbf: r-E-i<MRLi.ATBi..//O.Sioi

11 " ' ^ ll ^6 BMS&UL" ARG AtEipvAi-E fee P-E-.'.-jm- ArrGL. 1)3,00'

r-»-/-4

EC 1110-2-510 31 Aug 83

TFEttmATlONl OF *ngA,fc5

IN ACC0S1PANCE W»Trt ACT 313-77^ 12.1) ) DETf^KiyjE Rf.^ r- HVTIHS.OH

OF *;\ t-AVf-. AB^VE ^-L,;:'.'.^V.

$Ht< (ÊL 107-47- -JtE M0Mb'-rt>IA$li.) = 8'' - 76'?'''" j Mw = I062>.tf7

b--12'\ ^=22,21- x e = Las

) ) 'X2'2.'Z4 = O.tfWi-lf

i". * 4^,-?5 -\R48g.i5)^ 4(SM.n) s i7. t^*' 2-

Acr ?2,M.5 : s^.,:/'. v !2v',4.r^ '^TT , c(-22.2.4*

ACT a.it.4- $ ^ :: 12,2.2 :

YT^~ \J~3AT3

USE: 24,'6/TEI-J-SION

TEKMIMATE. *!! BAK-5(S EL. IO<J.^7

lEKHIKJATjOH Or ^[Q bAW£.

|H Acco^pAlice. \/\)irw ACI 318-77' KtH) DETV* K'ut: ELXTLMSIO^

GpÔ^^.- : A^^vf-i 5'L. (IO.?-:'.

6H^4^T^&/6,N-K) MM^VOS"'"*;!;,-'' i-^73rf

e^ /.17 i'c. X2°.l3

= a.aosi I

— •=! a •P- //<7x3.Nir'^ /.7X 3 x 5r7gr33 1^005// "r (oto*sn)'*(n)bo.r$)t

lsTART*-g1rAP:S At EL 110^^ "-LKHÂTE *\Q BfÔ ATI" L.l^.^"

<3-/F

EC 1110-2-510 31 Aug 83

TEfcKUnATloM OF^S BARS (LAP VhTW ^ feAftQ

tfj ACcoftp^ncE. WJ^H ACI 318-77 j/2./6; DETEKHIME. LAP Fo^*2 To

*<£> &ARS ^ ABO'JE. E.L. li'i.O.

^tfu= 20PT^- 24<0!%K HM*: Z^^.^?"7^ U 12^ cZa ;f.4<5'

€ = - ^I ^— =^^3 37SS 12x17.4

,s " U.a»3^35;TS (o,oott<ft5)7tiV)(l1.4)z-

fs2- 1502.87 fs 4 ^!4-?.53=o<, ■£*= !7.GI **'< 4?

USE CLAs-i 6 bfLicE.^is = l.VjU.

K Y3CO O /

AmrnARSLy -START #Q> eAfe'Q AT *.Lt\il.ooTi:MmTi=. *€ BARS AT fcL.11a.67

C^^JK, SK-HA/2. Fr.-j'W.iJiTseF A^X i^j/.sj,

A'| EL, 1Q"7.C ? .>£> ■

AT EL./IO.STO

^*//* (%)^Vc*(%)fe?5y2VidOoX'3L,l2*73)» I5,442L&

AT EL. H3.0O y ^

^-^

EC 1110-2-510 31 Aug 83

AT t 3F VcfeT^L WALL. I2.£IMF.

^Mu* VlO.^'.-F'l-Z.OZ^J-. )30.50=: .'5^3 ; 4 = 0^ MM = 1740

^ = 12"; ^^ao^^gs") ©.445-fc'kJa« ^(W.? ■K= l-VfiT 1740, » 0.o<?5-?45 1 ' V' 7SWr x - 4o(i- ^f^:y/#?^ ; ^^ - ' ^ "' (ALTERNATE ^ 10 4 #7 eAf?£at-.l 0?CTP,0

AT i.5o FROH\ FACE pp STEM

e = 4<J(/-

1)73.^3 0td62>tt 2)(ll)(4S)'

-^ o.tfo4fl4> As« 1.21 ,Jn

AT 3.50 FftoKj FACE "T- ST6-N\

9562.5

e« C&73-33 ;A/Z

4o(|.££|^!5)^)(25) - ^ ^.^235S-; As * 0.7/ '^T

AT 5.SO Fgort FACE: OF STEM

,/n-lt ^ MH = 2^ "K(Ff?.0M MOMBIT t'l^t ,)= -^' ^ Mi4 = 2.?3t'i3

K 0*015IS*?

N-K

-^0.= |-\ I- 273.*3

e= _.

'AL f' aT

= 3,000425' As- 0.90''Tr i *•.*_... FAce OP Sirr^

l-s

- 4. 0<3 ' 4_._Li ^

6-/7

kc 1110-2-510 31 Aug 83

TEFWlHKTltiN ^tO BARS

#]& tAkS ARE KiCT Ô'D FOR. FL&XURF. AT A ?o\^T 4:00 FKOlATv4Vr. K/.CL

;^: Gu-H. H) ACÔVI AU,:E. WITH ACI 316*77; 12.11; DE-.T-tfMlnfc.

ACZ. il.lt.5": o(*25H^ ;zJb~T2.-/<!/i7 = |5'.f41'

A cr 12, ii.4. îz.z.z:

1.^ = O.X>t>Z3?>

'.l>7X* V , J.7x3*S7S.93 _.. ^^

4sL~ 8^.23-fs +fâs".05 *0 -4^= '£,45^'

i^J = g>>^4/ |.27y 4qa<a^ _ 37

"TSP #?£ FACTORis \. 4

= 25*

T^KH'.VJATE, *|0 E>A^S 6-1" FOSH BACfiL fACIc. OF STGK,!« ttE-P^L,

TfeV.KlHATE.4 lo BARS (l.4j^fS"s 57>')4'^'Vpg>n B^CK FACE OF ST&H/KJ To&t

Toe- feBINPORCE-P GPKJCftETfc t^'SI^

AT FAee OF STEM

+ MM = 77.06^ #47Z.'N~* M^1=;o^7»47,w"K,

^îz^cl-as" ; 0,425f^J2- 9562.S

1 I 99-<l.2.S

ALTEPIHATE ÎO 4.-*6 BtfcS on C^CTK-S, )

J

(S-/.g

EC 1110-2-510 31 Aug 83

AT ^X> rgon ^FCS. OF STE^

P>NP T&RMNATIM P^/MT fag.*io BARS

Xf-fi't*^ V j. /.7x3X4^33-3 ^^

Ê a /fs Yo'<*xl>&X'+aid*^\« 7.75-^ ^ Z5 " « ^tf.

T^-RÎMATE ÎO BARS 4'-|*lFf?oM FACE CF STEM

CHECK SHEAR, U* S-T^K AT OVSTA^CU d Ae^yg. gLt\o^.so

Vc* 2.\[3MO /I^X24.<?/= 3^743 >V«

CU^CK. SUBAR \^ VJI-gL AT FACE- ^^ STCM

Cu&c2^ SHE-AR IM Toe. AT g.ag' FPOH PACE, dr- -JSTEM

b=l2.,')d=25rt j 4>VN='ZXK ; VN« ZS.?**

\|<i = ^\|3aGO XI^X25- = 32£63L6;>W/

f

^Wf

EC 1110-2-510 31 Aug 83

RE-lUFORCCVtertT SutAttARvf

« a 5 W

£L.I2S.O

4*CL. C-#-l

EL 118.67

£1.117.00 _

EL. 113.23

&-■!/<>>$-

H-.W.67

*.!&&%

4ti*<&n!iZyr

#<&@/2"?

&L.ioo,6~r ~(*<

*

Ufcu

I- -I t ^-s'L

/^♦tto^ti" 5#7 W

Jf *IFST*UMZ STP. ACX HOOK

I'-JI"

G-zo

! EC 1110-2-510 j 31 Aug 83

IttVESTlGATlOU OF STRESSES N STEH AT E.L. 102,5 ^ {JSMC, Vjot^C'.U^ STTRES-S

P&Sl^M AMD TKE-' KEltÔRCE-HBUT PSTERHiMgP S'( OTREKI^TK PE^lij! ^

b - 12" } 4 « 30" 3 <,{ = aS1' ) 6=: T^Hr- = AOdff S33

-f — ' ^ r' gM

Tu? * }OXO,6&-14w$*s G.oi4233

•** \[$*6i43}£f+iiMM -0.0*4233 <* 0,ZSOlS0

-is J- ?i?JL?!J£i -=0.293284

" ^ t.'Xto-o.44 xl'Z- _ ^/?4 < )t()SK5/

"^ * e.35oi^^fg3'^4xii(25y"

TKE \MM.OT\-IATIOW b^ '^RVÎWG ST«£55 PCS/^N JOF Tffg SECTiOM r)f!AWUP t'i STmniiTh wLS'..j!.) iMpICATg^ THAT VÂLLS CfeOKjh^W

i^/ trrHtK.. Me;TW«t WILL, fcu -^f'tf'Ar-Afc'L^.

^-2/

EC 1110-2-510 31 Aug 83

CHECK WALL FOR EARTMQUAKE CONDIT/ON _, MINIMUM FACTO A:

OF SAFBTY ASAlrfST SLWJNG EQUAL To till j SRFEQoALTa /?.?.

KEFFH TO FiGufiE ON F/ide. G-j, (SEE. fifiRAGMfH 3-15.)

Kh =• o.tO

CALCULATE CRlTtCAL VALUIZ. Op OC^y.

C, = zCs^ta^-f, - 2. (at9)(0.700202)^ I.ZC0374

L.^-: —^ C __ _ — a.55Q>bfY o.Kojoozo*)

CALCULATE cizintAL ^AL.U£. OF <*&) 2

0C& = - 4S'- *«-'t««<-""7n = -54.47'

c AL-cut A -re. UpuF-ro : (t/tm. IF TeepAr, t MmuoD)

J.DtL ~ ^'%-\ - 4.^' Son CL (4) l l

LEN6TN OF S£BPA<$£ PATH = m+3.*<l Hl + ^Zi* 37.13

MA - a j M0 * Oo- JMp^o^zs^ o.4w «SF

//.. - (to.zo - M-.zyx/S) s>.ot>zs- - o.53oyKl'F y ^ \ 37./3 / JX. h -. (12.56 - 32..27X/0)A o^Zi? - 0.22 SO

u '" K 37.13 J

TJlzj- (y>.4z<>VA6l$$o<r) x g^/ ../.4^ ^T-

Ub; = 1£<1121±£L±1££» ,%M •= 0-S3%T, JT^ lo.z'(FMM TVL)

"Oc-O - O.Z.'ZSG yc 4tz& ~ 0,49/FF

MSF

G-ZZ

EC 1110-2-510 31 Aug 83

tlfi . ZULATE We id NT OP Weu$£$ AHP SufidHAFTjC-S

I4JZ' W' ISO M't-o' Ac

w&tHi& ft):

Wn - ^ o.n* i4. ft. / .7, ^ = /^, g 3 /FT"

l^j-r; -. ^ y^.AJSx 6.zi! x lo.oo— O. IC* fyT

V rr z.'xo,//£)C i4.JZ = 3,25 ^r

WGOGB (z) :

V = (2 x<J.//5^ /,21) + &(<>. 12)(?.& ttsyi.*t) 4 (ojzSjO.Zl/to) ^4.7t %r

WEP4E (3')'. (tee FA4f£ 3G)

W = S2.40%T j X - 11.41 (FmToe) y = /o.97'(AMCBLmo)

W= V%(O.IZO')(3.45)(^S) ^ O.SZ^FT

<i-25

EC 1110-2-510 31 Aug 83

CALCULATE LATBRAL pop PES

WG.P<$E 0) I (5KF)tA.n4C*4%+&nfr'n _ O.<l(6,'fej(0.S2t4)-0,'WO _

— fepp') fa-r-J' - — 0.572.5

PWM = -0,4854* J*.*? ■= - 2./7 X%/2^ -14.50

fys-H-, -<<>,4854x OJC - - 0,0? X5J3= - OA5

Pv - - 0. 4254 * 3. z5 ~ - 1,52 x/£#43^ -/?.£/

Pu - -O.SIZB * 2.51 = -- /.4f X5;^3 - - 2.67

(B.Q. ) A/A = - o.l(f6.m<i.t&W5}-= -2.02 X /7.ff- -3^3^)

Y- - /3f-53^ /A 4^'

— (SRF)(tivn<t)) c*j. 0fy-.(sxF)2ow/fi s^iecfr, - - 0.3<84&

/V = ~o.n47* 0,17 -:=■ -O.ZJO xo,^^ - o.n

ty' ^ -0,7141* 4.7% •* '-2t<nx\,ZG= -3,41

fa * -0.3W5* 1,4% •* " 0.5*7 X\.20= - 0.<>2

(e. $,'/ A!t= - 0,/ (o,z744.78) rs-o.Sl XI4A0~ -nAT

_ -9.33 g 4^'

EC 1110-2-510 31 Aug 83

VJBDGE (?) - (£.?.) F/L ~-O.IO (32.40) - -3.<d4%T ) YzJtHl

WeMb (4):

(SRFJIMU^ CM^ + Smcfo __6.1 fasAiXoStf?) + QMS ^ /^y^^ <U4.cr.+ - (^RFyis^4> s** d&j " o. lo77 ^fl(0,s{AXo.9U%)

- (i5RF)tA^4> _ _ CSICZ

.«,,,',> "?4Zd

(SRfS)c ^ 0. ?74S'

pw _ /.3711X ®.52 - O.nZx 0.13 - -0.60

fa - - 0.$?a6x 0,44 —- f'te * 0.^3= - #. 2Z

fcL = o,g74srx 4,2^ - 3.7$ x t.zs = 4.6>6

(F.Q.) \4L = - 0.10 y a.S% = - 0.05* 'U7- - Q-Q?

P(4) = 4./4^r 4.^ TT 4*7& _ / n* FT

QVeKTuRtJins STA 6 jury

W&) = 2>$.4o x 11.41 = 44LZ2

^6)= ~ ^.^^ X ^'2^3 « - 67.67

-/3.34X /^46 = - /3<7.54 — 1.10 / 4,44 =- «7,32

-3.^4 X /^,77- - 42.11

4/4 x /.£<? ^ 4.^7 , ^-

e= "^ -Z?*1* 3>/2'>-^ =3-*e' (1$% OF PA SB fN CaMpPKSS/OhJ)

EC 1110-2-510 31 Aug 83

L3 =r 3 *&,#$ ■= |7.64',

CALCULATE SRFS R&V'P £*£ STAucrdAfiLWfS'<r£('i/Jm5£3)

/fe •=• 4,14 ^r j ^-o

ft. - Pp FHL. = /^/4 ^r

y o&f+yt&M+Q&yM64)(fi - r^M>&.364>A *« r/^4;

6-2^

nmrr EC "10-2-510 UKArl jl^M

APPENDIX H

CAMTILEVEt WAU IMVB8TIGATI0H CXAHPLE

An«lyi» Pay«

Strength Reduction Factor R-2 thru R-9

EarthqiMkn Analysis 8-10 thru H-15

H-l

EC 1110-2-510 31 Aug 83

/Nvksf/<SAT£ EXISTING WALL^gbR^cVNPiTiQM SHOWN ftBLOEK

To PETmM l N> B. FA eToft 0£ SAFETY A<5AiN5T SLrPw<;, (see. pAJp}<3&Aph/ 4-it.a..)

/7.Q0'

piANKeTj Y=4//5rK°F 'i.s' #MIM

ZTZ^

(3)

^z:

EL. 166.01

. I

f iiil

LA

« *:

*, v

^ "^ri;—W^

FoohJDA~nam

SLjL

bACKFIi-L*. Ys*T**r*0 & 0,12.5 ^ YHOJST ~ O.KO*'1*

<P = 554 C a<3

FOU.« CAT .10*11. . Y.S.^TM^^^M9rF>-!^^.^f^MM^^-^'Q^75 KCP

f=^ C. * <3.60 >fap

|5T T<2'AL ASSOKE sRFst

CfiTiCAu VAuue. ^) rAAv &£ CALCULATTEt? A« i C"5*2 0lM4MPfi 3-F.)

~(£KF7t&j\4> *"

ti-2.

EC 1110-2-510 31 Aug 83

CRITICAL VALUE. QF ^fe) MA^_6E. CALCOLATED AS:.

■2.

<%}= r45a~ ^(^Ft^l^))"]^ g^./^

CALCULI T6: MT£* pftg$S0(t&S fH MeTtiOD Of fRAOMEHTS ;

ASOOHZ BerrtW OF AfOlFt&R iS ATgLJSMfafafftwPHZ-n)

(j)® -L-ar =.-£?■*L..A4f

X<$ = ot<?f + 0.6?+af4'?=. i,<ft

At) = A 04Z5 F/2.T ..... '6(oi79+o.*l')l m Q, 2,077 KSF

■Lm (-44 J

1% = ^ (Q.4Z(440.&267)3.f?az: ).S1 %T

1% * ^ (ot5267+0.-3fi77)t7 - 7.01 ^FT

13(4) * Ufa ^77)4,04 - 0*61 %T

H-3

EC 1110-2-510 31 Aug 83 ."

CALCULATE. WEi&tT OF WZVOBS AM SuRCÂês '.

i v' #&*■>•

TST

Wep6B0) :

Ws -HCQ » /t M. ooe*. % bi * jo, a*. = o.yffcr

TO ) ^ 2'ic o.itSz \%.06 4.l5%r

v<£> = (o.]isxi.mz)Fy/6îwsytji>ti+aj&feoi)(}o)_ =5.31 ^T

W£) + \/&7 = ff.3/ + 0.30 - 5.41 %T

MtBPGZ (3) I W) = 35.^3 ^r

^4-

EC 1110-2-510 31 Aug 83

CALCULf{Tl _LA7eAAL . FbAC&S '

(0 O.6073 +0.W*(6 'inf) *T

0.61*1- 4a2M&(o.7nfj =-3M Pr

% 44^.242^ 0.'ttU+0.<ltiQ-4.VlUp.GL)i0.4O(4.o$ fO * 0.7$&l - 0.1426(0,C/21 ) = t.ll'FT

p ■ *9.oa(o-&*Cxi - o) - (io<fxo.i4&)+ (0.4*1-7') _ fay %T

2ND Ik/A-L __j££Urt£ ...SjgfL^o.ro

Czrac*'^.VALUC *F_.<fyymyfiiCALSUUfi(L;AS:

„ _ £/_* 2:v-0.7fi_0.70.- oA%

.Q/^Tf^.Ak-yAL'je... 0F &&) HAy && CAUiuLKftc As;

_ ._^> *..- Us^ .Mik^^i] = ^ 52./g*

C«rr/ML I/^LOE op.aCft) Mty && CALCULATE As;

■ ^g [4sa- W&fr***? « 37.^5'

/¥-£■

EC 1110-2-530 31 Aug 83

CALCULATS. WATRR. PRESSURE?. By HETHOO OF FRAGMENTS;

^- ^55 = /2-4<;'; J>#=vrm =^^ /c^ /7-^'

F/?oM PA$E //-3

X^c - 6.5Z&7 ; //-^ - 0.4^t4

JJLAÔ ) M^D = 0.3077

/lit s ^

TJ6) ^ &(oMriOz.**) ~ Z^SPFT

'11^= ^(^,42/4^.W>./r'U (.fofa

TJ(i/~ I/* (o,~ 2Q>74 0,W77) 17 - 7.0? ^T

CALCULATE VJBIGUT OF WGLOOES AND SuucmPGES I

WMO) - &Co.n)(l7.35)(l?.t7)= 20.71 %T

Ws-nG).^J4^)(7A3) 0O.<»± 0./1 %T

VfO= t'CojlS) (17.35) = 3.7?

V^)= ^ (<m)0,<*4)(t,S) = 0.27^r

V(J9 = ^lSyi,9^l)+i(^{9î9,5y/.f^f(0.l2i)ff.fîo)^ 5.!$%-'

'^7 4V(s.,)« SA2^Fr

W&tc (3); W& = 3gt^3 ^'•7'

EC 1110-2-510 31 Aug 83

vJei*5£(4>:

A%) - Vz {0J2)(M2)(Z.$)* 0.4$ fa

CALCULATE LATEEAL FORCES :

/?/7 = 24.2(r*(o>41*0.51&L-o.96ti)- 6AfM _ ./3f93 Vrr o. 5762. 4 ^ 4f fA 24 27?

6, g.4£ (o.t5StOM36-0.7t%)'' 0'l5S(L5Q)+aJ&J7) =.-3.0S%r fc' 6.t,/3& + o.2.B5(o.79%)

p ^ 4<ri(6.lS5*0.'n%46.to2£)-O.zSS(o.63) +O.4tf4.o7) Jfa 1(4) » o.7F^ - o.issca.tisc^ ! ■" '

P(i) =. 38.03 fo.gg5^] -o)~ (0.Z5S*7.O9)+ (0&t\i)_ /Ff0§fT I -o

l^- *P* P(D +P© +P<D+P^- M!^ >

GKAPHICAU pETg-RnmATtoN roP. EQ^^n&R^uM

.(it /.//^t

E(&0ILI16WUM FblMT

Q. SRF = O.feS

I FS« S<?P 1.47

tf.60 ^ ^.7<?

5Rt=

>/-7

EC 1110-2-510 31 Aug 83

3gp. TRI/M- (^KF =O.G8>) TO CWECIC QMPMCAL SOLUTIOM POP- SRP.

(SRF)rfeu^= 0.4T6 j (SRF')t2^4^j^)- <?. 2475j (S(i.F)C= 0.44S

C^) ; <%) ArtD CC4 MA^ 66 CALCULATH-D By Tue SAME KE.THOD A *

USED U "T|2.\ALS I AM17 2.. TH^SS VALUCS- AE-E. *

flC(j) = -se.340

CALCULATE. WATEI<. PaessuRes e-y METWOP OF FRAQH^TS:

FROM PASg I'j Uc= 0.5ZC7 Mfi= 0.42-14 Ajp~0,d077 f

"0(0 = i4 Co.^z/4.X/2,?sr)= 2.64'^"r

Ufe')^ li(o.4U4+o.92GJ)@.l7)ys 1.50 "^T"

IT©)-a ^(o.5^7 +0.3(577)('l7) = 7.^7 4T

U^ = yz(. o.-itri) (4.60 ■= ^^^ ^T

CALCULATE. WIEIGUT OF VOecês AN^ Sop-cÂRqEs,:

WM*) « ^(0.1^67.77)07.?^)= 2'.zf

Vfs-Mtf)-^^-305)^'5^ C'**) - d.l7

V(0= O.llS (Zô) 07.V7') = 4.o7 25.47 ^r = W^ + Vfc)

Vyi^- 'A(O.IZ.)6.1*)(Z-B) - o.2f^

V^. aji5(2)(i'*k#oj$(ww.s)(i.%)+0je5(/.%)Qd) ^ F./S" ^T

Wfa^vro- 5.47 ^r

WE.P6E (4) N , . yK/

*SP

EC 1110-2-510 31 Aug 83

CALCULATS LATtSAU FORCES I

^ * o\«.o4 +0.476 (O.T97^ ; * I*'4* n

g.47 (MMS* O.g'63~ O.'n'£)-6,2#ts(t$O)+0M'6{3.\t) __ - .,% !&) = 0.€/63 + 0.£475(o.7?75-) ~"

p 0.48ro.2475^0.7g7r40.6/g3)~^.2475(6.g2>tft^g^&) V ^J * 0.7*7.<r- o,t47S(o.6l63) " '^

p 3 8.03 rp.^fSxf-o) - 0.147S(7.o7) +0,408 (17) _ ^

"S-P » ?,> f ^4^)+P^«-O.OS^T =^0

cwecic? GRAPHICAL, ^LUTJON OM PAcie H~7

SR.F s o.&«

Ps- —I— « 1,47

/V-?

EC 1110-2-510

31 Aug 83

iNvzsTiGArre. WALL Fail EAffiJQUAKt. CoNOmoN, MIMMUH FACTOK

OF SAtFETy MfiMSr SuVlNQ EtpUALTo l.tl , SRF^a.9.

RepflK Tn FlGUfiS 0t4 PAOIB IH^ Kh = o.lo

1ST TI^AL : ASSUMB SPF = o. lo

CA-LCULATE CRITSCAL \J'ALUS. FopcC^y'.

C-j = 2 Co. 7)Co.?6) = l,2.& r - <s' ?(o' 7o)Ef- ** ffo 7oy°' ^B' 0'za - O $545-

2-~ A9(0.7O>)_ ""

CALOOLATB. CftmcA't VAtm Fop <%$;;

CCQ=.-4S = - 54. o7

CALCULATE CxtT/CALi/ALim FOZ #&)*.

&#) = 45 — 1__ £ s 3SA3 »

CALcoLftrre WAT£R fftztsufle Am UPLIFTS By Mertioe t*p

FRAGmMTS ; ( SeE fA$e 2h? FoR F£.£ssupj£ CAUlOlATMHO)

JA3^ -Zt44~ UM, lee* ZW7~3'0<?

uo? ^ Yz (o.42i4) )un * 2.4g ^r \J(£) = ,/z(ot42i4-POA2i7)3.of = 1.4C %T

Ufr) = '^(o.Sza moWjn =■ 7.01 ^FT

Ufa) - /^ (0.3077) 4.ZL - 0.U %r

H-io

EC 1110-2-510 31 Aug 83

CALCULATB. H/ztft/T OF tA/£VGE5> Avp SomtiAR&Es

14. IZ l.tl' . /.s' 1.0 . ^^ 1'± ^ ») * 5.0

We-ods. (i) ; WH = lA(o.n)(i4,IZ)(l<t,u)'- M3%r

WI-H » ^ (at609)(C.vC)(io.oo) s o,iQ%r

V =- 2(0,115) (14.11) zz 3.25^-

WB-DGS. (£) : y = '/z(o.iz)(l.zi)(2.5) = ^2.7 #r

]/ ^ (o.m)@yw)i'M%^itoti)(kiQfaiis^ 4.7$ %r

Wzv6£&) :

IV = (l£)(6'lz)(SA5)(l,5) = 0.5 t%T

ti'tl

EC 1110-2-510 31 Aug 83

CALCULATE. LATEP-AL FORGES ;

fcQ-HiJ)) « 0&'2*+0./&3.ts)[0.f(ai0)(!i.ttg$-0.s4Aol-o.'l(o.'X))(t.4$) __ _ //,2f% 0.5z?4- o.cf(o.70)(-oM7^ " ~

n , 0,52 £oACo.3&4)(Q,t6ll)+OM^O^(o.%^<lUji.OT(o.<p)(4^) W-HM= a, 90f7- AfCe-MX*****)

fa-tiL®* ±£lf^

(B,Q) HLQ) --O.IO (/6.23 iO,l<* 43X5)^-2*02^

(E.Q.) Mtb)^ -a.fQ (0.Z7+4.72)= -O./S^FT

(B, $,) UL(3)=-0,/O(3%A'4^ -3,20 %T

(Z$) HL (A-) =-O,l0 (0.52) = -Q.oS ^r

2.P= -lll2f-Z.2& 4173144.07-2,61- 0.fr-3.&-0.05=3#P>'O

H-tZ

EC 1110-2-510 31 Aug 83

ZND TKiAL : ASSUHE 5RP ^o.zo

CALCULATE CfimcftL VALUH FOA cq,)'.

C, = 2, (o,l6)(o,7d) * 1*12.

£ _ oXfoMfr- o.'6(0.7o/o.26)}-O.ZO __ ^ssol 0.^(0,70)

OC0?^ ^T'UZ-^f+^2^^ ^S4.74-0

CALCULATE dAmcfit VAWB Fop &&)*

Z ==

CALCULATB CRITICAL VALUE. FOR 00(401

CALCULATE UptiFrs :

/** * ~o!Wl * /*-27; ^c * "S^fjy ^ 3'/3,

d

cp * !7; S-PZ - 6f&de>l

U(0 - '4 (0.42/4)(IZ.Z/) "=• 2.57%-

U60» JA(ol42j440.52^7)(B./3)^ I^S7PT

Ufc)^ >£( 0.5267 ±0.3*77)07)-= V'tfftT

U(4) , ^ (o.3o77)(4.l7) - 0'i+%T

CALCULATE wctdnrOF mttGEs ANP SURMARG&S:

WM= !£(o,n)(/&.*3)0m) = 11.36 %T. ^ - '/t(o.A>$<7<**)('0) - 0,12 I/FT

yy _ z(a.ii$)0(>Ti-5) = 5.75^7-

EC 1110-2-510 31 Aug 83

Wzostt z: W - '/2(o,lz)0.M)(2.$)^ 0.18 %T

V = (QM)(^O.tE)4{^(o,l0.nn^'^^0.1^.^1^ £17%T

WEP4E 4; tf* (&.)(0.te)(3.T5)(t.5l - 0.50 %T

CfiLCuLATe. Lfne-PAL FaPCBS ; P0)-l-lLO) = (23.e7)C4*(A™fa&44)-0.8/s41-0M7$(k.S7)m- /2.Sf%r

0.5744 — 0>f(O.70X-O<7/$6)

p a fiis- ($• M)[&*(&Z&4)(o.Go)- QtUl-M(o.v64)f.ft) td,%(@&)($.J3)

P(Z-)-HL&)~ -z-tf^r

p z%.63[4Mo.3&4)Q)l-QMzte4Y?.oi)4oMt>yf7) i(S)-H(&) - j

P6v)-/4e)= n.n%r

P, n ,-i os6Lo-*(*-MX(Lto)iL0.^^oA(0.*M)(drt+o.ifo)fi.rr) T/yl 1 "* /"T L f 4L I ^ i ■ iT*. ■ II ■ -■ ■ ii-.r.- ■■ - -i-T. , vv ■ r.ii.ii- i IV-n. ■ Ti- 'i. •-. v. .LUBIVI ■|--r;lli

?£)-&&)= 3.S7%r

HLO) = -o.io(13.27') = -^.33^: tit£)=-o.i6(5.z€)* - o.S3%r * ~~ J * * % 9 J 11 "'III-•-'•'• ■ 'I'

H-14

EC 1110-2-510 31 Aug 83

\fs -I2.S1-2.21417.1743.57-2.33-0.53-3.20-0.05 « -0.77l%r

GPAfhilCAL DBTBRMlfJATMN OF SAP FoR BfUlLlBRPJHI

J$7 TfrAL

a) °

43.26 KT \j~

ftfCHLlfiRiuM If SUF-o.ZIS

~0.77%T

ZNp TfiiAL

SRF

F5 * ~5PF g /'g3 >/.;/

H-15

DRAFT EC 1110-2-510 31 Aug 83

APPENDIX I

NOTATION

Chapters 3, 4, and 5

Symbol Term

B Base width of wall or width of base in compression. C Cohesion on slip plane of wedge. Cd Developed cohesion on slip plane of wedge. Cf: Hydrodynamic factor. D Depth of material in front of wall to base of structural

wedge.

HL Horizontal force, acting to the right, applied to wedge. HR Horizontal force, acting to the left, applied to wedge. Hy Height of Py force above bottom of wedge. Hs Average of highest 1/3 of all waves or depth of saturation

in wedge. Hi Average of highest 1 percent of all waves.

Hb Height of wave which breaks in water depth d^. L Length along slip plan of wedge. N Force normal to slip plane of wedge. Nc, Nq, N Bearing capacity factors for strip load. P Lateral (horizontal) force produced by wedge.

PL Absolete value of total horizontal force from acti ve-type-wedges.

PR Absolete value of total horizontal force from passi ve-type-wedges.

(Pi-l-P-j) Summation of applied forces acting horizontally on ith

wedge. Pv Part of lateral wedge force due to surcharge. P^M Part of lateral wedge force due to moist weight of

material.

P^IS Part of lateral wedge force due to difference in weight between saturated and moist material.

Py Part of lateral wedge force due to uplift on slip plan. PCL Part of lateral wedge force due to cohesive resistance

along slip plane. PE Hydrodynamic force given by Westergaard1s equation. Q Vertical component of ultimate bearing capacity.

SRF Strength reduction factor. SRFS Strength reduction factor for structural wedge. T Force tangential to slip plane of wedge. U Uplift force normal to slip plane of wedge.

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EC 1110-2-510 31 Aug 83

Symbol Term

V Vertical force applied to wedge.

2 Summation of vertical forces for structural wedge. VM Maximum value of V for which equations 3-8 and 3-9 are

valid. W Total weight of material in wedge, y Height of P force above bottom of wedge. dc Depth of tension crack in cohesive backfill.

dfo Depth of water at breaking wave occurrence. e Eccentricity of resultant at base of structual wedge. hj Head loss through fragment of flow region. h Total head differential across wall or height of wedge, q Foundation pressure at base of structural wedge.

q0 Effective overburden pressure. u Uplift pressure on slip plane of wedge. " Angle between slip plane of wedge and horizontal.

S Angle between top of wedge and horizontal. Y Unit weight of material. Y1 Effective unit weight of material. ♦ Angle of internal friction on slip plane of wedge. $4 Developed angle of internal friction on slip plane of

wedge.

<J>j Form factor for fragment of flow region, a Stress normal to slip plane, x Applied shear stress on slip plane of wedge. Tp Shear strength of wedge material.

S Bearing capacity factor.

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DRAFT APPENDIX J

NOTATION

Chapter 9

Symbol Term

EC 1110-2-510 31 Aug 83

a Depth of equivalent rectangular stress block. Ag Gross area of section, sq. in. Ag Area of tension reinforcement, sq. in. IV s Area of compression reinforcement, sq. in. b Width of compression face of member, in.

c Distance from extreme compression fiber to neutral axis, in. d Distance from extreme compression fiber to centroid of

tension reinforcement, in. d1 Distance from extreme compression fiber to centroid of

compression reinforcement, in. D Dead load of the concrete members only. e1 Eccentricity of axial load measured from the centroid of

the tension reinforcement.

e'm Eccentricity of the nominal axial load strength, at balanced strain conditions for hydraulic structures, measured from the centroid of the tension reinforcement.

E Load effects of earthquake, or related internal moments and forces.

Eo Modulus of elasticity of reinforcement, psi. f*c Specified compressive strength of concrete, psi.

Calculated stress at < compression controls.

fsu Calculated stress at centroid of tension reinforcement when

f'sy Calculated stress at centroid of compression reinforcement. fy Specified yield strength of reinforcement, psi. Fp Additional pressure due to wave action or related internal

moments and forces. Fp Lateral water pressure or related internal moments and

forces. Fu Vertical uplift pressure or related internal moments and

forces.

Fw Water mass or related internal moments and forces. h Total depth of section, in. Hp Lateral earth pressure or related internal moments and

forces. Hw Earth mass or related internal moments and forces. km Ratio of stress block depth (a) to the effective depth (d),

at balanced strain conditions for hydraulic structures.

ku Ratio of stress block depth (a) to the effective depth (d).

J-l

EC 1110-2-510 31 Aug 83

Symbol Term

L Live loads or related internal moments and forces. Mn Internal moment due to nominal axial load, Pn. My Internal moment due to factored axial load, Py. Pb Axial load at given eccentricity at the balanced strain

condition.

Pn Nominal axial load strength at given eccentricity. Pu Factored axial load at given eccentricity. SL Surcharge pressure or related internal moments and forces. T Cumulative effects of temperature, creep, shrinkage, and

differential settlement. U Required strength to resist factored loads or related

internal moments and forces.

W Wind load or related internal moments and forces. ^ A coefficient which accounts for the difference between the

distribution of actual compression stresses and the assumed rectangular distribution of stresses,

e^ Design strain at the extreme concrete compression fiber =

e¥ \ Strain at the centroid of the tension reinforcement < fy/ES.

# \ Strength reduction factor.

p * Ratio of tension reinforcement, As/bd. * Pb Reinforcement ratio producing balanced strain conditions. %, Reinforcement ratio corresponding to balanced strain

conditions for hydraulic structures. p1 Ratio of compression reinforcement, A's/bd.

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