Chapter No 13 - WEC CIVILIANS

RETAINING WALL INTRODUCTION

1

INTRODUCTION

A retaining wall is a structure built for the purpose of holding back

or retaining or providing one-sided lateral confinement of soil or other

loose material. The loose material being retained pushes against the wall,

tending to overturn and slide it. Retaining walls are used in many design

situations where there are abrupt changes in the ground slope. Perhaps

the most obvious examples to the reader occur along highway or railroad

cuts and fills. Often, retaining walls are used in these locations to reduce

the quantities of cut and fill as well as to reduce the right-of-way width

required if the soils were allowed to assume their natural slopes. Retaining

walls are used in many other locations as well, such as for bridge

abutments, basement walls, and culverts.

2

INTRODUCTION

Several different types of retaining walls will be discussed, but

whichever type is used, there will be three forces involved that must be

brought into equilibrium:

(1) The gravity loads of the concrete wall and any soil on top of the

footing (the so-called developed weight),

(2) The lateral pressure from the soil, and

(3) The bearing resistance of the soil. In addition, the stresses within

the structure have to be within permissible values, and the loads

must be supported in a manner such that undue settlements do

not occur.

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TYPES OF RETAINING WALLS

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Retaining walls are generally classed as being gravity or cantilever types, with several variations possible. These are described in the slides to follow.

The gravity retaining wall, is used for walls of up to about 10 to 12 ft in height. It is usually constructed with plain concrete and depends completely on its own weight for stability against sliding and overturning. It is usually so massive that it is unreinforced. Tensile stresses calculated by the working-stress method are usually kept below Gravity walls may also be constructed with stone or block masonry.

Semi-gravity retaining walls, fall between the gravity and cantilever types. They depend on their own weights plus the weight of some soil behind the wall to provide stability. Semi-gravity walls are used for approximately the same range of heights as the gravity walls and usually have some light reinforcement.

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The cantilever retaining wall or one of its variations is the most

common type of retaining wall. Such walls are generally used for heights

from about 10 to 25 ft. In discussing retaining walls, the vertical wall is

referred to as the stem. The outside part of the footing that is pressed

down into the soil is called the toe, while the part that tends to be lifted is

called the heel. The concrete and its reinforcing are so arranged that part

of the material behind the wall is used along with the concrete weight to

produce the necessary resisting moment against overturning. This resisting

moment is generally referred to as the righting moment.

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When it is necessary to construct retaining walls of greater

heights than approximately 20 to 25 ft, the bending moments at the

junction of the stem and footing become so large that the designer will,

from economic necessity, have to consider other types of walls to handle

the moments. This can be done by introducing vertical cross walls on the

front or back of the stem. If the cross walls are behind the stem (that is,

inside the soil) and not visible, the retaining walls are called counterfort

walls. Should the cross walls be visible (that is, on the toe side), the walls

are called buttress walls. The stems for these walls are continuous

members supported at intervals by the buttresses or counterforts.

Counterforts or buttresses are usually spaced at distances approximately

equal to one-half (or a little more) of the retaining wall heights.

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The counterfort type is more commonly used because it is

normally thought to be more attractive as the cross walls or counterforts

are not visible. Not only are the buttresses visible on the toe side, but their

protrusion on the outside or toe side of the wall will use up valuable space.

Nevertheless, buttresses are somewhat more efficient than counterforts

because they consist of concrete that is put in compression by the

overturning moments, whereas the counterforts are concrete members

used in a tension situation and they need to be tied to the wall with

stirrups. Occasionally, high walls are designed with both buttresses and

counterforts.

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When a retaining wall is placed at a property boundary or next to

an existing building, it may be necessary to use a wall without a toe, or

without a heel. Another type of retaining wall very often encountered is

the bridge abutment. Abutments may very well have wing wall extensions

on the sides to retain the soil in the approach area. The abutment, in

addition to other loads, will have to support the end reactions from the

bridge.

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The use of precast retaining walls is becoming more common. The

walls are built with some type of precast units, and the footings are

probably poured in place. The results are very attractive, and the units are

high-quality concrete members made under “plant controlled” conditions.

Less site preparation is required and the erection of the walls is much

quicker than cast-in-place ones. The precast units can later be

disassembled and the units used again. Other types of precast retaining

walls consist of walls or sheeting actually driven into the ground before

excavation. Also showing promise are the gabions or wire baskets of stone

used in conjunction with geotextile reinforced embankments.

13

DRAINAGE One of the most important items in designing and constructing

successful retaining walls is the prevention of water accumulation behind the

walls. If water is allowed to build up there, the result can be great lateral

water pressure against the wall and perhaps an even worse situation in cold

climates due to frost action.

The best possible backfill for a retaining wall is a well-drained and

cohesion less soil. Furthermore, this is the condition for which the designer

normally plans and designs. In addition to a granular backfill material, weep

holes of 4 in. or more in diameter (the large sizes are used for easy cleaning)

are placed in the walls approximately 5 to 10 ft on center, horizontally and

vertically. If the backfill consists of a coarse sand, it is desirable to put a few

shovels of pea gravel around the weep holes to try to prevent the sand from

stopping up the holes. 14

DRAINAGE Weep holes have the disadvantages that the water draining

through the wall is somewhat unsightly and also may cause a softening of

the soil in the area of the highest soil pressure (under the footing toe). A

better method includes the use of a 6- or 8-in. perforated pipe in a bed of

gravel running along the base of the wall. Unfortunately, both weep holes

and drainage pipes can become clogged, with the result that increased

water pressure can occur.

The drainage methods described in the preceding paragraphs are

also quite effective for reducing frost action in colder areas. Frost action

can cause very large movements of walls, not just in terms of inches but

perhaps even in terms of a foot or two, and over a period of time can lead

to failures. 15

DRAINAGE

16

FAILURES OF RETAINING WALLS

The number of failures or partial failures of retaining walls is

rather alarming. The truth of the matter is that if large safety factors were

not used, the situation would be even more severe. One reason for the

large number of failures is the fact that designs are so often based on

methods that are suitable only for certain special situations. For instance,

if a wall that has a saturated clay behind it (never a good idea) is designed

by a method that is suitable for a dry granular material, future trouble will

be the result.

17

LATERAL PRESSURES ON RETAINING WALLS

The actual pressures that occur behind retaining walls are quite

difficult to estimate because of the large number of variables present.

These include the kinds of backfill materials and their compactions and

moisture contents, the types of materials beneath the footings, the

presence or absence of surcharge, and other items. As a result, the

detailed estimation of the lateral forces applied to various retaining walls is

clearly a problem in theoretical soil mechanics. For this reason the

discussion to follow is limited to a rather narrow range of cases.

If a retaining wall is constructed against a solid rock face, there

will be no pressure applied to the wall by the rock. But if the wall is built

to retain a body of water, hydrostatic pressure will be applied to the wall.

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At any point the pressure (p) will equal wh, where w is the unit

weight of the water and h is the vertical distance from the surface of the

water to the point in question.

If a wall is built to retain a soil, the soil’s behavior will generally

be somewhere between that of rock and water (but as we will learn, the

pressure caused by some soils is much higher than that caused by water).

The pressure exerted against the wall will increase, as did the water

pressure, with depth but usually not as rapidly. This pressure at any depth

can be estimated with the following expression:

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In this equation, w is the unit weight of the soil, h is the distance

from the surface to the point in question, and C is a constant that is

dependent on the characteristics of the backfill. Unfortunately, the value

of C can vary quite a bit, being perhaps as low as 0.3 or 0.4 for loose

granular soils and perhaps as high as 0.9 or even 1.0 or more for some clay

soils. Charts that are sometimes used for estimating the vertical and

horizontal pressures applied by soil backfills of up to 20-ft heights are

shown in next slide. Several different types of backfill materials are

considered.

Unit weights of soils will vary roughly as follows: 90 to 100 lb/ft³

for soft clays, 100 to 120 lb/ft³ for stiff clays, 110 to 120 lb/ft³ for sands,

and 120 to 130 lb/ft³ for sand and gravel mixes. 20


21


If you carefully study the second chart of last slide, you will

probably be amazed to see how high lateral pressures can be, particularly

for clays and silts. As an illustration, a 1 ft-wide vertical strip is considered

for a 15-ft-high retaining wall backfilled with soil number (4) with an

assumed δ of 10˚ (6 : 1 slope). The total estimated horizontal pressure on

the strip is

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(1) Backfill of coarse-grained soil without admixture of fine particles, very

permeable, as clean sand or gravel.

(2) Backfill of coarse-grained soil of low permeability due to admixture of

particles of silt size.

(3) Backfill of fine silty sand, granular materials with conspicuous clay

content, and residual soil with stones.

(4) Backfill of soft or very soft clay, organic silt, or silty clay.

If a 15-ft-deep lake is assumed to be behind the same wall, the

total horizontal pressure on the strip will be

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For this discussion, a retaining wall supporting a sloping earth fill

is shown below. Part of the earth behind the wall (shown by the hatched

area) tends to slide along a curved surface (represented by the dashed

line) and push against the retaining wall. The tendency of this soil to slide

is resisted by friction along the soil underneath (called internal friction)

and by friction along the vertical face of the retaining wall.

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Internal friction is greater for a cohesive soil than for a non

cohesive one, but the wetter such a soil becomes, the smaller will be its

cohesiveness and thus the flatter the plane of rupture. The flatter the

plane of rupture, the greater is the volume of earth tending to slide and

push against the wall. Once again it can be seen that good drainage is of

the utmost importance. Usually the designer assumes that a cohesion less

granular backfill will be placed behind the walls.

Due to lateral pressure, the usual retaining wall will give or

deflect a little because it is constructed of elastic materials. Furthermore,

unless the wall rests on a rock foundation, it will tilt or lean a small

distance away from the soil due to the compressible nature of the

supporting soils.

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Under the lateral pressures described, the usual retaining wall will

move a little distance and active soil pressure will develop. Among the

many factors that affect the pressure applied to a particular wall are the

kind of backfill material used, the drainage situation, the level of the water

table, the seasonal conditions such as dry or wet or frozen, the presence of

trucks or other equipment on the backfill, and so on.

For these reasons, retaining walls are frequently constructed

with a slight batter, or inclination, toward the backfill so that the

deformations described are not obvious to the passerby.

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For design purposes it is usually satisfactory to assume that the

active pressure varies linearly with the depth of the backfill. In other

words, it is just as though (so far as lateral pressure is concerned) there is a

liquid of some weight behind the wall that can vary from considerably less

than the weight of water to considerably more. The chart shown earlier

shows this large variation in possible lateral pressures. The assumed lateral

pressures are often referred to as equivalent fluid pressures. Values from

30 to 50 pcf are normally assumed but may be much too low for clay and

silt materials.

If the wall moves away from the backfill and against the soil at the

toe, a passive soil pressure will be the result. Passive pressure, which is

also assumed to vary linearly with depth.

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The inclusion or non-inclusion of passive pressure in the design

calculations is a matter of judgment on the designer’s part. For effective

passive pressure to be developed at the toe, the toe concrete must be

placed against undisturbed earth without the use of vertical forms. Even if

this procedure is followed, the designer will probably reduce the height of

the undisturbed soil (h’ in figure) used in the calculations to account for

some disturbance of the earth during construction operations.

As long as the backfills are granular, no cohesive, and dry, the

assumption of an equivalent liquid pressure is fairly satisfactory. Formulas

based on an assumption of dry sand or gravel backfills are not satisfactory

for soft clays or saturated sands. Actually, clays should not be used for

backfills because their shear characteristics change easily and they may

tend to creep against the wall, increasing pressures as time goes by. 28


29


If a linear pressure variation is assumed, the active pressure at

any depth can be determined as

In these expressions, Ca and Cp are the approximate coefficients of

active and passive pressures, respectively. These coefficients can be

calculated by theoretical equations such as those of Rankine or Coulomb.

For a granular material, typical values of Ca and Cp are 0.3 and 3.3. The

Rankine equation (published in 1857) neglects the friction of the soil on

the wall, whereas the Coulomb formula (published in 1776) takes it into

consideration. These two equations were developed for cohesion less soils. 30


For cohesive soils containing clays and/or silts it is necessary to

use empirical values determined from field measurements.

It has been estimated that the cost of constructing retaining walls

varies directly with the square of their heights. Thus as retaining walls

become higher, the accuracy of the computed lateral pressures becomes

more and more important in providing economical designs. Since the

Coulomb equation does take into account friction on the wall, it is thought

to be the more accurate one and is often used for walls of over 20 ft. The

Rankine equation is commonly used for ordinary retaining walls of 20 ft or

less in height. It is interesting to note that the two methods give identical

results if the friction of the soil on the wall is neglected.

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Just revising Soil Mechanics the Rankine expressions for the active

and passive pressure coefficients are given below. In these expressions δ is

the angle the backfill makes with the horizontal, while φ is the angle of

internal friction of the soil. For well-drained sand or gravel backfills, the

angle of internal friction is often taken as the angle of repose of the slope.

One common slope used is 1½ vertically to horizontally.

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Should the backfill be horizontal—that is, should δ be equal to

zero—the expressions become

One trouble with using these expressions is in the determination

of φ. It can be as small as 0˚ to 10˚ for soft clays and as high as 30˚ or 40˚

for some granular materials. As a result, the values of Ca can vary from

perhaps 0.30 for some granular materials up to about 1.0 for some wet

clays.

Once the values of Ca and Cp are determined, the total horizontal

pressures, Ha and Hp, can be calculated as being equal to the areas of the

respective triangular pressure diagrams. 33


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For instance, with reference made to last figure, the value of the

active pressure is

In addition to these lateral pressures applied to the retaining wall,

it is considered necessary to add the effect of frost action at the top of the

stem.

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FOOTING SOIL PRESSURES

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Because of lateral forces, the resultant of the horizontal and

vertical forces R intersects the soil underneath the footing as an eccentric

load, causing greater pressure at the toe. This toe pressure should be less

than the permissible value qa of the particular soil. It is also desirable to

keep the resultant force within the kern or the middle third of the footing

base.

If the resultant force intersects the soil within the middle third of

the footing, the soil pressure at any point can be calculated with the

formula to follow exactly as the stresses are determined in an

eccentrically loaded column.

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In this expression, Rv is the vertical component of R or the total

vertical load, e is the eccentricity of the load from the center of the

footing, A is the area of a 1-ft-wide strip of soil of a length equal to the

width of the footing base, and I is the moment of inertia of the same area

about its centroid. This expression is correct only if Rv falls within the kern.

This expression can be reduced to the following expression, in

which L is the width of the footing from heel to toe.

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If the resultant force falls outside of the middle third of the

footing, the preceding expressions are not applicable because they

indicate a tensile stress on one side of the footing a stress the soil cannot

supply. Such a situation should not be permitted in a retaining wall and is

not considered further.

The soil pressures computed in this manner are only rough

estimates of the real values and thus should not be valued too highly. The

true pressures are appreciably affected by quite a few items other than

the retaining wall weight. Included are drainage conditions, temperature,

settlement, pore water, and so on.

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DESIGN OF SEMIGRAVITY RETAINING WALLS As previously mentioned, semi-gravity retaining walls are

designed to resist earth pressure by means of their own weight plus some

developed soil weight. Because they are normally constructed with plain

concrete, stone, or perhaps some other type of masonry, their design is

based on the assumption that only very little tension or none at all can be

permitted in the structure. If the resultant of the earth pressure and the

wall weight (including any developed soil weight) falls within the middle

third of the wall base, tensile stresses will probably be negligible.

A wall size is assumed, safety factors against sliding and

overturning are calculated, the point where the resultant force strikes the

base is determined, and the soil pressures are calculated. It is normally

felt that safety factors against sliding should be at least 1.5 for cohesion

less backfills and 2.0 for cohesive ones. 40

DESIGN OF SEMIGRAVITY RETAINING WALLS Safety factors of 2.0 for overturning are normally specified. A

suitable wall is probably obtained after two or three trial sizes. Example

13.1 illustrates the calculations that need to be made for each trial.

Figure 13.8(a) shows a set of approximate dimensions that are

often used for sizing semi-gravity walls. Dimensions may be assumed to

be approximately equal to the values given and the safety factors against

overturning and sliding computed. If the values are not suitable, the

dimensions are adjusted and the safety factors are recalculated, and so

on. Semi-gravity walls are normally trapezoidal in shape, as shown in

Figure 13.8(a), but sometimes they may have broken backs, as illustrated

in Figure 13.8(b).

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DESIGN OF SEMIGRAVITY RETAINING WALLS

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EFFECT OF SURCHARGE

Should there be earth or other loads on the surface of the

backfill, the horizontal pressure applied to the wall will be

increased. If the surcharge is uniform over the sliding area behind

the wall, the resulting pressure is assumed to equal the pressure

that would be caused by an increased backfill height having the

same total weight as the surcharge. It is usually easy to handle this

situation by adding a uniform pressure to the triangular soil

pressure for a wall without surcharge, as shown in the figure.

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EFFECT OF SURCHARGE

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EFFECT OF SURCHARGE

If the surcharge does not cover the area entirely behind

the wall, some rather complex soil theories are available to consider

the resulting horizontal pressures developed. As a consequence, the

designer usually uses a rule of thumb to cover the case, a procedure

that works reasonably well. He or she may assume, that surcharge

cannot affect the pressure above the intersection of a 45˚ line from

the edge of the surcharge to the wall. The lateral pressure is

increased, as by a full surcharge, below the intersection point. This

is shown in the right side of the figure.

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EFFECT OF SURCHARGE

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Chapter No 13 - WEC CIVILIANS

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