Design Procedures for a Cantilever Retaining Wall

A typical cantilever retaining wall is illustrated by the insert sketch in Fig. 8.21. This rigid-type wall can be constructed with or without a base shear key (see Fig. 8.20) depending on an analysis for resistance to sliding, as discussed later.

The specifications of the owner will govern the selection and use of backfill materials behind retaining walls. In most cases, clean backfill materials having an internal friction angle of at least 34° are assumed in the design of retaining walls, subject to the fol­lowing considerations:

1. With a proper drainage system and with backfilling controlled so that no compaction-induced lateral loads are applied to the wall, the above-noted or better material may be used in construction. A minimum lateral earth pressure of 30 (lb/ft[10] [11])/ft (4.7 kN/m[12]) (equivalent fluid weight) for level backfills, or 40 (lb/ft2)/ft (6.3 kN/m3) for 2:1 sloped fills, should be assumed.

2. Backfill is assumed as on-site inorganic material; however, if it is of a lower class designation, the wall must be designed for an equivalent fluid weight lateral pressure suitable for that class. Therefore, should the designer select a backfill material of lower classification, it will be necessary to clearly specify the backfill material by a supple­mental project special provision and to use an appropriate equivalent fluid weight lateral pressure for design.

The design aids provided in Figs. 8.22 and 8.23 may be used for preliminary dimen­sions in the design of a cantilever cast-in-place retaining wall. On the basis of the Rankine theory of earth pressure, final design may proceed with the following steps:

NOTES:

Class I backfill (see Fig. 8.41)

Class D concrete

Coef. of friction (soil to soil = 0.67, soil to concrete = 0.42)

FIGURE 8.22 Aid for preliminary design of cast-in-place concrete retaining walls showing wall and footing dimensions. (From Bridge Design Manual, Section 5, Colorado Department of Transportation, Denver, Colo., with permission)

width b is approximately one-third to one-half of B. The ratio of footing width to overall height should be in the range from 0.4 to 0.8 for T-shaped walls as shown by the design aids in Figs. 8.22 and 8.23. In these preliminaries, wide-base L-shaped walls (footing width to height ratios larger than 0.8) are used for low wall heights (less than 10 ft or 3 m), and the factor of safety with respect to overturning is relaxed from a minimum of 2.0 to 1.5 when considering the case of D + E + RI.

4. Draw a vertical line from the back face of the footing to the top of the fill. This line serves as the boundary of the free body to which the earth pressure is applied. The applied active earth pressure can be estimated by Rankine theory, and the direction assumed parallel to the backfill surface. Compute the resultant P of the applied earth pressure and associated loads. Resolve P into horizontal and vertical components Ph and Pv, and apply at one-third the total height Ht of the imaginary boundary from the bottom of the footing. (See Fig. 8.21.)

5. Take a free body of the stem and compute the loads applied at the top of the stem as well as loads along the stem (height H), and find the moment and shear enve­lope to meet all the design cases at several points along the height. The working stress design method and the concept of shear friction can be used to calculate the shear strength at the joint between footing and stem.

Wall height at stem (ft)

NOTES:

Class I backfill (see Fig. 8.41)

Class D concrete

Coef. of friction (soil to soil = 0.67, soil to concrete = 0.42)

FIGURE 8.23 Aid for preliminary design of cast-in-place concrete retaining walls showing toe pressure and steel and concrete quantities. (From Bridge Design Manual,

Section 5, Colorado Department of Transportation, Denver, Colo., with permission)

6. Calculate the weight W, which is the sum of the weight of concrete and the weight of soil bounded by the back of the concrete wall and the vertical line defined by step 4 above. Find the distance from the extremity of the toe to the line of action of W, which is the stabilizing moment arm a.

7. Calculate the overturning moment Mo applied to the wall free body with respect to the tip of the toe as:

(8.5)

Calculate the resisting moment Mr with respect to the tip of the toe as:

M = Wa + P B

r v

The safety factor SF against overturning is

Mr

SF (overturning) =——-

M

o

Wa + P B

Ph H, /3

h t

The required safety factor (overturning) should be equal to or greater than 2.0 unless otherwise accepted and documented by the engineer (see step 3).

8. Compute the eccentricity e of the applied load with respect to the center of the footing based on the net moment:

The resultant should be within the middle third of the footing width; i. e., the absolute value of e should be less than or equal to B/6 to avoid tensile action at the heel.

9. The toe pressure q can be evaluated and checked by the following equation:

The toe pressure must be equal to or less than the allowable bearing capacity based on the soils report. Toe pressure is most effectively reduced by increasing the toe dimension.

10. The footing, both toe and heel, can be designed by working strength design. Soil reactions act upward and superimposed loads act downward. The heel design loads should include the portion of the vertical component Pv of earth pressure that is applied to the heel. For the toe design loads and stability, the weight of the overburden should not be used if this soil could potentially be displaced at some time during the life of the wall.

11. Check the factor of safety against sliding without using a shear key. The coef­ficient of friction between soil and concrete is approximately tan (/3ф), where ф is the internal friction angle of the soil in radians. Neglect the passive soil resistance in front of the toe. The sliding resistance SR can be evaluated as:

SR = (W + Pv) tan (|ф) (8.10)

The SF (sliding), which is SR/Ph, should be equal to or greater than 1.5. If SF (sliding) is less than 1.5, then either the width of the footing should be increased or a shear key should be installed at the bottom of the footing.

If a shear key is the choice, the depth of the inert block dc is computed by the sum of the key depth KD and the assumed effective wedge depth, which is approximately half the distance between the toe and the front face of the shear key (b/2). Using the inert block concept, knowing the equivalent fluid weight (yp) of passive soil pressure, and neglecting the top 1 ft (300 mm) of the toe overburden T, the toe passive resistance P is

p

Pp = 0.57p[(To + T + dc — 1)2 — (To + T — 1)2] (8.11)

Total sliding resistance F from friction is the sum of the horizontal component of the resistance from toe to shear key and the resistance from shear key to heel. Therefore:

where ф = internal friction angle of base soil

R1 = soil upward reaction between toe and key, lb/ft (kN/m) R2 = soil upward reaction between key and heel, lb/ft (kN/m)

Sliding resistance is

SR = F + Pp (8.13)

The SF (sliding), which is SR/Ph, should be equal to or greater than 1.5.

12. Repeat steps 3 through 11 as appropriate until all design requirements are satisfied.

Figure 8.24 represents typical values for equivalent fluid pressures of soils. These values are suggested for use in the absence of a more detailed determination.

Structural backfill class designation	Type of soil (compaction conforms with AASHTO 90-95% T180)	Typical values for equivalent fluid unit weight of soils, lb/ft3abc (kN/m3)
Condition	Level backfill	2:1 (H: V) backfill
Class Id: borrowed,	Loose sand or gravel	(Active)	40	50 (6.3/7.9)
selected, coarse-		(At rest)	55	65 (8.6/10)
grained soils	Medium dense sand or	(Active)	35	45 (5.5/7.1)
	gravel	(At rest)	50	60 (6.3/9.4)
	Dense6 sand or gravel,	(Active)	30	40 (4.7/6.3)
	95% T180	(At rest)	45	55 (7.1/8.6)
Class IIAf: on-site,	Compacted, clayed,	(Active)	40	50 (6.3/7.9)
inorganic, coarse-	sand gravel	(At rest)	60	70 (9.4/11)
grained soils, low	Compacted, clayed,	(Active)	45	55 (7.1/8.6)
percentage of fines	silty gravel	(At rest)	70	80 (11/13)
Class IIB: on-	Compacted, silty/sandy	Site-specific material, use with
site, inorganic	gravelly, low/medium	special attention;	see geotech-
LL < 50%	plasticity lean clay	nical engineer. Soils report on
		workmanship of compaction,
		drainage design, and waterstop
		membrane is required.
Class IIC: on-	Fat clay, elastic silt that	Not recommended
site, inorganic	can become saturated
LL > 50%
a At rest, pressure should be used for earth that does not deflect or move.
b Active pressure state is defined by movement at the top of wall of 1/240 of the wall height.
c The effect of additional earth pressure that may be induced by compaction or water should
be added to that of earth pressure.
d Class I: 30 percent or more retained on no. 4 sieve and 80 percent or more retained on no.
200 sieve.
6 Dense: No less than 95 percent density per AASHTO T180.
f Class IIA: 50 percent or more retained on no. 200 sieve.

FIGURE 8.24 Typical values for equivalent fluid pressure for soils. (From Bridge Design Manual, Section 5, Colorado Department of Transportation, Denver, Colo., with permission)