Small gravityretaining wallsPortland Cement Association tablessimplify design

BY FRANK A. RANDALL, JR.STRUCTURAL ENGINEER

Small gravity retaining walls are re l a t i vely simplestructures that can be built with unskilled labor and

locally available materials. Very little reinforcing steel isneeded because the walls don’t have to resist bendingand shear stresses like those developed in thinner can-t i l e ver walls. Weight of the concrete in a gravity wall pro-vides stability against overturning.

Gravity retaining wall design can be greatly simplifiedt h rough the use of a series of sample designs deve l o p e drecently by the Po rtland Cement Association (PCA). Pre-sented in tabular form, the designs are for wall heights

up to 10 feet, and for walls with ve rtical backs or withnearly ve rtical faces. Walls with ve rtical backs re q u i reless concrete but ones with stepped backs and nearlyve rtical faces are desirable in some cases. If the designerwants maximum surface area at the top of the backfill,walls with stepped backs are pre f e r red. This might be thecase if a parking lot we re to be built on the backfill.

Backfill soil type affects pressures

Four broad types of backfill soil are described in Ta b l e1. A Type 1 soil exerts the smallest ove rt u rning pre s s u reand Type 4 the largest. Gravity walls are n’t feasible whenType 4 backfill soils are used because the lateral or ove r-t u rning pre s s u res are too larg e. The base of the wallwould have to be so wide to resist this pre s s u re that theamount of concrete re q u i red would make the design un-e c o n o m i c a l .

In using this design method it is important to re c o g-n i ze that the four soil-type descriptions in Table 1 arefor backfill soils. Backfill soil can be different from thesoil under the wall and it is not unusual for a “s e l e c t” orhigher quality backfill to be used instead of the nativesoil that is present where the wall is to be built. The PCAdesigns are keyed to specific types of backfill but not tospecific types of soil under the wall. Instead, the designtables tell what pre s s u re a wall exerts on the underlyingsoil and the designer then determines whether that pre s-s u re is safe for the soil at his site. The method for doingthis is described in the example design that follow s. De-s c riptions of bearing soils and allowable bearing pre s-s u res on these soils are given in Tables 2 and 3.

Backfill slope and surcharge

Tables have been developed for two backfill surf a c eslope conditions: a slope of ze ro (level backfill) and as u rface slope of 1 ve rtical to 2 hori zontal (1:2). If the userwants to select a wall for a backfill slope of less than 1:2,he still uses the table for backfill slope of 1:2.

Figure 1. Construction details for a gravity retaining wallwith vertical back.

TABLE 1. TYPES OF BACKFILL SOIL

Type 1. Backfill of coarse-grained, very permeable soil

without admixture of fine particles; examples

are clean sand or gravel.

Type 2. Backfill of coarse-grained soil of low perme-

ability due to admixture of silt-size particles.

Type 3. Backfill of fine silty sand, granular materials with

conspicuous clay content and residual soil with

s t o n e s .

Type 4. Backfill of very soft clay or soft clay, org a n i c

silt, or silty clay.

The lateral pre s s u re on a wall is in-c reased by any load (surc h a rge) placedon top of the backfill. In developing thePCA tables a surc h a rge of 200 poundsper square foot (psf ) was assumed forl e vel backfills and 80 psf for slopingb a c k f i l l s. These are reasonable as-sumptions for most designs.

If the backfill slope is greater than 1:2or if heavier surc h a rges than those as-sumed are expected, the tables can stillbe used for a pre l i m i n a ry design butf u rther modifications would be neces-s a ry.

Lugs provide sliding resistance

Footings for gravity walls illustra t e dwith the tables don’t have level basesbecause more resistance to sliding isneeded than would be provided by al e vel base. To increase the sliding re s i s-t a n c e, shear lugs are placed at the heelof the wall as shown in Fi g u re 1. A shearlug is a deepened section of the footingthat is keyed into the bearing soil. It isplaced at the heel of the footing formaximum effect. The heel side of thelug is formed ve rt i c a l l y. The other sidewill transmit the lateral pre s s u re to the subsoil, butrather than have the lug bear against a ve rtical surf a c eof the soil (which would probably be weakened duri n ge xc a vation), the exc a vation is tapered up to meet the re s tof the footing. If the contractor pre f e r s, he can exc a va t ethe earth in a continuous straight line from one side ofthe footing to the other as shown in Fi g u re 2. This incor-p o rates the shear lug in a triangular base section and ef-f e c t i vely develops sliding re s i s t a n c e.

What the design tables include

The sample designs included in PCA publications aretabulated for three backfill soils (Types 1, 2 and 3), twostyles of wall (either the face or the back is ve rtical), andtwo surface conditions of the backfill (level or 1:2 slope).The different combinations of these va riables are give nin 12 tables. PCA’s Table 4, shown below, is one of thet we l ve and is used in designing walls with ve rtical backsand sloped backfill of Type 3 soil. The column headingscan be further described as follow s.• Wall dimensions listed refer to the dimensions show n

on sketches included with the tables.

• The ove rturning safety factor should be at least 2.0.The lateral force of the backfill soil acts on the wall andtends to rotate it about the toe (counterclockwise inthe figure illustrating Table 4). This rotation must beresisted by the re s t o ring force (weight of the wall plusany ve rtical part of the backfill pre s s u re) which tendsto rotate the wall about the toe in the opposite dire c-

TABLE 2. DESCRIPTION OF BEARING SOILS

Organic Soil. Soil containing significant percentage of partly or wholly decomposed organicmatter. According to the character of the constituents, the term organic clay, organic silt, orpeat is used.

Inorganic Silt. Cohesionless aggregate of grains ranging in size from 0.002 mm to 0.66 mm.Aggregate is nonplastic and consists of grains not distinguishable by the naked eye. Depositsof inorganic silt are described as loose or compact. A lump of the air-dried material has verylittle resistance to crushing.

Sand. Cohesionless aggregate of rock fragments or grains ranging in size from 0.06 mm to 1/4inch. Deposits of sand are described as loose or compact.

Clay. Cohesive soil, plastic within wide range of water content. The consistency of a clay is de-fined by the strength of a fairly undisturbed cylinder whose length is from 1.5 to 2 times its di-ameter, as follows:

C o n s i s t e n c y Field identification Unconfined compres-s i v e

strength, psf

Very soft Easily penetrated a couple of inches Less than 700by fist

S o f t Easily penetrated a couple of inches 700 to 1,199by thumb

S t i f f Penetrated several inches by thumb with 1,200 to 1,999moderate effort

T o u g h Readily indented by thumb but penetrated 2,000 to 3,999only with great effort

Very tough Readily indented by thumbnail 4,000 to 7,999

H a r d Indented with difficulty by thumbnail 8,000 to 16,000

Gravel. Cohesionless aggregate of rounded to angular rock fragments ranging in size from 1⁄4to 8 inches.

Hardpan. Cohesive or cemented material that offers great resistance to hand-excavating tools.

Solid Rock. Sound, unweathered rock without visible voids.

TABLE 3. ALLOWABLE BEARING PRESSURES ON SOILS

Type of soil Maximum pressure, psf

O rganic soil 0

Filled ground or loam 5 0 0

I n o rganic silt—compact 2 , 5 0 0

Sand—silty and compact 3 , 0 0 0

Sand—compact and clean 5 , 0 0 0

Clay—very soft 5 0 0

C l a y — s o f t 1 , 5 0 0

C l a y — s t i f f 2 , 5 0 0

C l a y — t o u g h 3 , 5 0 0

Clay—very tough 4 , 5 0 0

C l a y — h a r d 6 , 0 0 0

G r a v e l 6 , 0 0 0

H a r d p a n 1 2 , 0 0 0

Solid rock 2 0 0 , 0 0 0

Source: Chicago Building Code.Note: Where the bearing materials directly under a foundation over-lie a stratum having lower allowable bearing values, these lower val-ues shall not be exceeded at the level of such stratum. Computation ofthe vertical pressure in the bearing materials at any depth below afoundation shall be made on the assumption that the load is spreaduniformly at an angle of 60 degrees with the horizontal.

tion (clockwise in the figure). A factor of safety of 2.0means that the product of the re s t o ring force and dis-tance to the toe is twice the product of the ove rt u rn i n gl a t e ral force and distance to the toe.

• Sliding friction values are checked to ensure that thewall doesn’t move in a hori zontal direction as a re s u l tof lateral pre s s u re caused by the backfill. Two va l u e sa re listed. H’/V’ is the total hori zontal force on the walldivided by the total ve rtical force on the bottom of thefooting. The maximum recommended value for thisfactor depends on the type of subsoil. For coarse-

g rained soil without silt it shouldn’t exceed 0.37, forc o a r s e - g rained soil with silt it shouldn’t exceed 0.30and for silty soils it shouldn’t exceed 0.23. These va l u e sa re based upon providing a factor of safety of 1.5against sliding and using assumed values for coeffi-cient of friction between the concrete and soil.The other column under the heading of sliding fri c-

tion, labeled shear stre s s, gives the hori zontal force onthe wall per lineal foot of wall divided by the footingwidth. This value is used when the wall is built on clay;the value should be no greater than half of the uncon-fined compre s s i ve strength for the clay subsoil. Ty p i c a lranges for unconfined compre s s i ve strengths of claysoils are given in Table 2.• Soil pre s s u re is the ve rtical pre s s u re under the footing

caused by the weight of the wall. It va ries uniform l yb e t ween the toe and the heel of the footing and shouldnot exceed the allowable bearing pre s s u res for the soilon which the footing is built. Allowable bearing pre s-s u res for different types of soil are given in Table 3.

• The volume of concrete in cubic yards per lineal footof wall is the last item listed in the table and is self ex-p l a n a t o ry.A general pro c e d u re for using the tables is given in the

b ox and an example problem is work e d .

Construction details

Decisions concerning seve ral construction details areneeded before working drawings are pre p a red. Thedepth below grade to the bottom of the footing is deter-mined by the depth of exc a vation necessary to reach soilwith suitable bearing capacity. The bottom of the footingdoes not necessarily have to be below the frost line sincethe consequences of frost heave are not as seve re as theywould be for a building.

Weep holes or backdrains are essential to pre vent ex-c e s s i ve hyd rostatic pre s s u res from building up. A gra d e dfilter at the back of the weep hole is needed to keep back-fill soil from washing out.

Keys are needed in the top of the footing and re b a rd owels should be placed at the heel of the wall. Use No.4 bars, 4 feet long and spaced 2 feet apart on centers. If

Figure 3. A stepped instead of an inclined face makesplacement of concrete easier and avoids problems withform flotation.

TABLE 4. GRAVITY RETAINING WALLS WITH SLOPED BACKFILL OF TYPE 3 SOIL

Sliding friction S o i lWall dimensions O v e r t u r n i n g S h e a r p r e s s u r e , Volume of

safety factor H ’ / V ’ s t r e s s , p s f c o n c r e t e ,h a b c p s f

T o e , H e e l y d3/ f t

9 ’ 1 1 ” 1 9 . 5 ” 6 ’ 6 ” 2 4 ” 2 . 5 0 . 1 8 3 1 0 2 3 0 0 1 1 0 0 1 . 8 19 ’ 0 ” 1 8 ” 6 ’ 0 ” 2 4 ” 2 . 5 0 . 1 7 2 8 0 2 1 0 0 1 1 0 0 1 . 5 58 ’ 1 ” 1 6 . 5 ” 5 ’ 6 ” 2 4 ” 2 . 6 0 . 1 7 2 5 0 1 9 5 0 1 0 0 0 1 . 3 17 ’ 2 ” 1 5 ” 5 ’ 0 ” 2 4 ” 2 . 6 0 . 1 6 2 2 0 1 8 0 0 9 0 0 1 . 0 96 ’ 3 ” 1 3 . 5 ” 4 ’ 6 ” 2 4 ” 2 . 6 0 . 1 5 1 9 0 1 6 0 0 8 0 0 0 . 8 95 ’ 4 ” 1 2 ” 4 ’ 0 ” 2 4 ” 2 . 7 0 . 1 5 1 7 0 1 5 0 0 7 0 0 0 . 7 14 ’ 5 ” 1 0 . 5 ” 3 ’ 6 ” 2 4 ” 2 . 7 0 . 1 4 1 4 0 1 4 0 0 6 0 0 0 . 5 53 ’ 6 ” 9 ” 3 ’ 0 ” 2 4 ” 2 . 7 0 . 1 3 1 1 0 1 2 0 0 5 0 0 0 . 4 1

Reprinted with permission of the Portland Cement Association

h o ri zontal construction joints are needed at any leve la b ove the top of the footing, dowels and keys are need-ed there also.

To minimize random cracking which would mar thea p p e a rance of the wall, ve rtical control joints can be pro-vided at about a 15-foot spacing. Gro oves used to formthe control joints can be filled with a joint sealant so thatg roundwater doesn’t stain the wall face.

If walls are built with sloping faces, upw a rd hyd ro s t a t-ic pre s s u re of the fresh concrete may cause flotation ofthe forms unless they are securely anchored to the base.An alternate method of building the non-ve rtical face isto create steps with ve rtical form s. The stepped wall, ass h own in Fi g u re 3 on page 981, makes placement of con-c rete easier and avoids problems with form flotation. Di-mensions for the steps can be chosen to keep the we i g h tof the wall, the safety factor against ove rt u rning or slid-ing and the bearing pre s s u re the same as for a wall witha sloping face.

Engineer may have to prepare and refine the design

Because allowable bearing pre s s u res on soils va ryf rom one building code jurisdiction to another, the typi-cal designs should be adapted to local conditions andshould conform with any legal re q u i re m e n t s. The sam-ple designs are intended to be helpful in the pre p a ra t i o nof complete plans. If the wall construction is contro l l e dby a gove rning body, working drawings may have to bep re p a red and approved by a qualified engineer or arc h i-t e c t .

Editor’s note:The sample designs described are found in two separatepublications: “Small Concrete Gravity Retaining Walls” (IS222), and “More Design Tables for Small Concrete GravityRetaining Walls” (Comments on Concrete No. 20). Singlecopies of both are available free of charge while the supplylasts. Request them from the Building Design and Construc-tion Department, Portland Cement Association, 5420 OldOrchard Road, Skokie, Illinois 60077.

To illustrate the use of the PCA design tables, assume that

a gravity retaining wall is to be built for the conditions illus-

trated in the sketch above. Steps in the precess are as follows:

1. Enter the appropriate table. In this case it is Table 4 (the

only PCA sample design table illustrated in this article) be-

cause the backfill is most like Type 3 in Table 1. If in doubt

about which of two types to use, choose the higher number.

Note also that the backfill is sloped, but less than 1:2, that the

s u rc h a rge is less than 80 psf and that a vertical back is ac-

c e p t a b l e .

2. Choose height (H) value. In the example use 7’-2”, the

value next higher than the 6’-8” needed.

3. Examine sliding friction. Since the bearing soil is a stiff

c l a y, use the shear stress value of 220 psf. This is compare d

with the allowable shear stress in the bearing soil which is

half of the unconfined compressive strength. From Table 2,

for stiff clay, 1200 psf is a conservative estimate of the uncon-

fined compressive strength and 0.5x1200=600 psf which is

g reater than 220 psf. Sliding friction is acceptable. If the bear-

ing soil were not a clay, the H’/V’ value would be used for

the sliding friction check as described in the article.

4. Examine the soil bearing pressure. The maximum

p re s s u re shown in the table is 1800 psf and from Table 3, the

allowable pre s s u re is 2500 psf. Bearing pre s s u re is accept-

a b l e .

Note: If, in either steps 3 or 4, values in the tables exceed the al-lowable values, several options would be available to the designer:change to a backfill having a lower type number, modify the bearingsoil to increase its bearing capacity or use a wider and thicker foot-i n g .

5. Determine the volume of concrete required. The table

shows that 1.09 cubic yards of concrete will be needed per

lineal foot of 7’-2”-high wall but since the height actually

needed is only 6’-8”, this value can be adjusted as follows:

1.09x6.67/7.17=1.01 cubic yards per lineal foot of wall. The

height can be reduced to 6’-8”, leaving the a, b and c dimen-

sions in Table 4 the same.

6. Determine the construction details and prepare work-ing drawings. This re q u i res decisions to be made about plac-

ing the footing at the re q u i red depth, stepping the face, pro-

viding weep holes, specifying concrete properties and

similar details. These are discussed in more detail in the dis-

cussion of the PCA design tables.

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