«A Design Guide for Earth Retaining Structures Hugh Brooks Civil & Structural Engineer John P. Nielsen Civil & Geotechnical Engineer Basics of ...»
Basics of Stem Design Here are two very rough rules-of-thumb for assuming stem thickness: If a reinforced concrete stem, try one inch of thickness for each foot of retained height, but not less than eight inches. If a masonry stem, 8" is usually adequate for walls about six feet high, and 12" for walls up to 12 feet.
Higher walls, those with sloping backfills, or when surcharge load are present will require thicker stems.
The controlling design condition for reinforcement occurs at the bottom of the stem (top of footing), where the maximum stem moment occurs. Reinforcing steel must be selected to resist that moment, however, it is not economical to use the same steel design higher up the wall where the moment is less (unless the wall is very low). Usually, after the base of the stem is designed, another design is performed several feet higher, usually at the top of the dowels projecting from the footing. At that point alternate bars can be dropped, or sizes reduced, for economy. The diagram in Figure 7.1 illustrates this concept. If the wall is very high, you may want three or four cut-off levels and perhaps a change in stem thickness, but carefully observe the influence of a battered wall on stem thickness or changes in (concrete to masonry blocks), material. See Figure 7.1.
Figure 7.1. Reinforcing placement in stem
A useful rule to remember is that for a triangular lateral active pressure behind the wall, the moment at the base of the stem diminishes to one-half of that at 0.20H above the base. For example, for a 10 foot retained height the moment is one half its maximum at two feet above the base. In nearly all cases the moment at the top of the dowels is about one-half that at the base of the stem thereby halving the design requirement for continuing lapped reinforcing.
7. DESIGNING THE CANTILEVER WALL STEM Page 49 Basics of Retaining Wall Design Often the stem projects above the retained height to provide a fence barrier, or a wood fence may be added to the top of the stem. In such cases, the wind load on that portion above the earth should be considered in the design, as it contributes to overturning. If the stem is essentially a yard wall and not a retaining wall and with very little earth retention, then remember that the wind can blow from either direction which will require that the wall and footing to be checked for both conditions.
Dowels from Footing into the Stem
(1) Minimum lap for spliced bars, inches, assumes fy = 60 ksi (2) 40 bar diameters for fy = 40 ksi and 48 bar diameters for fy = 60 ksi (48 bar diameters shown) (3) Minimum lap is development length x 1.3, assuming Class B splice. Cannot be reduced for stress level (4) Assumes standard hook and not reduced by ratio As (required) / As (provided) Note: IBC ‘12, 2107.3, deletes for ASD the following development length equation in MSJC ‘11, 184.108.40.206.
(5) “L” = lap length; “H” = hook bar embedment in inches.
Horizontal Temperature / Shrinkage Reinforcing Horizontal reinforcing is necessary to control cracks because of temperature changes and concrete shrinkage. Figure 7.3 shows minimum requirements for both concrete and masonry (CMU).
There may be conditions (climate, aesthetics, and better crack control) where additional reinforcement would be required at designer’s option.
Figure 7.3 Horizontal temperature/shrinkage reinforcement concrete and masonry walls (inches) The ACI requirement for reinforcing in both faces of concrete walls over 10 inches thick is waived for retaining walls in contact with earth per interpretation of ACI – 14.
The easiest way to check stability, sliding, and soil pressure, is to set up a table showing each force and load element, together with the its moment arm measured from the lower front (toe) edge of the footing. An example of such a table is shown on Design Example #1 in Chapter 24.
The tabular format provides an orderly summary of forces, moment arms and moments for easy checking of computations.
Here are a few pointers and guidelines to proportion the footing:
The width of the footing for most conditions will be approximately 2/3 of the retained height.
It is usually most advantageous to have more of the footing width on the heel side of the stem. This will put more soil weight on the heel to improve sliding and overturning resistance.
If there is a property line on the heel side, try to get as much heel width as possible as to provide the additional soil weight. Otherwise, you will have a sliding problem.
If you need a key for sliding resistance, try to keep its depth less than about one-fourth the retained height, but recommend not over about two feet.
If there is a property line on the toe side, the heel of the footing may need to be wider because soil pressures are usually greater at the toe.
Overturning moments, as discussed in Chapter 5, are horizontally applied forces multiplied by the moment arm from the bottom of the footing to the line of action of the force. The primary force causing overturning is the lateral earth pressure against the wall. Derived from a triangular pressure diagram, its point of application is one-third the height above the bottom of the footing.
The height used to compute over-turning is on the virtual plane at the back of the footing (i.e., where this plane intersects the ground surface). Lateral pressure from a surcharge is a uniform load applied to the back of the wall, therefore its point of application is one-half the height and the moment arm is from that point down to the bottom of the footing. See Figure 5.5 which illustrates both conditions. The overturning moment from the lateral earth pressure is acting against the virtual plane at the back of footing as illustrated in Figure 8.1.
Wind pressure on the stem projecting above the soil or on a fence sitting atop a wall can also cause overturning. Wind pressures are computed in accordance with the applicable building code, and generally range from 12 to 30 psf.
Seismic, if applicable, will also contribute to overturning. That was discussed in Chapter 6.
If there is significant depth of soil or ponded water above the toe of the footing, this lateral force could be viewed by some as being deductible from the heel-side active force for computing overturning and sliding. Our recommendation is to disregard this concept because it may not remain in place during the design life of the wall. Only consider the depth of soil on toe side below the top of the footing when computing passive resistance.
Resisting Moments By convention, resisting forces are all vertical loads applied to the footing. These forces include the stem weight, footing weight, the weight of the soil over the toe and heel, and a surcharge if applicable and any axial load applied to the top of the wall. The total resisting moment is the summation of these loads multiplied by the moment arm of each measured from the front bottom edge of the footing. See Figure 8.2.
The generally accepted factor of safety against overturning is 1.5, although some agencies require more. When seismic is included, a factor of 1.1 is permitted by IBC ‘12.
To determine overturning and resisting moments, eccentricities and soil pressures, you should tabulate these values as illustrated on Design Example #1, Chapter 24.
Vertical Component of Active Pressure From a Sloped Backfill If the backfill is sloped, there is a vertical component of the lateral pressure, which is assumed to act on a vertical plane at the back of the footing. This vertical component can act to resist overturning because when the wall starts to rotate there will be a frictional resistance along that plane. See Figure 8.3.
Figure 8.3 Vertical Component of Active Pressure
There is, however, controversy over whether to use this vertical component for soil pressure calculations because its use can significantly reduce soil bearing pressure and may not be justifiable if there is a large heel dimension. Similarly, it may not be justified to add vertical force to increase friction for sliding resistance. Most texts recommend using the vertical component only to resist overturning – not to reduce sliding or soil bearing. However, this judgment is left to the engineer.
Determining Soil Bearing Pressure The allowable soil bearing value, q all, is within the purview of the geotechnical engineer, and usually varies from 1000 psf for poorer soil (or without a substantiating soil investigation), to 4000 psf for dense soil.
After you have assumed a footing width, taking into account property lines or other conditions that may restrict the heel or toe distances, you can determine the applied soil pressure by determining the eccentricity of the total vertical force load with respect to the centerline of the footing. This is done as follows: first determine how far from the edge of the toe the resultant vertical force acts. This is simply the total overturning moment minus the resisting moment, divided by the total vertical force.
The method of reinforced concrete design known as the Strength Design (SD) Method should be used to design retaining wall footings. Strength Design requires the soil pressure to be factored to compute shears and moments. See the Design Examples for procedures. Footing design based upon Strength Design requires factoring the upward soil pressure attributable to lateral earth pressure by 1.6, and pressure attributable to the weight of earth or other dead loads be factored by
1.2. Because these two components apply to footing factoring it may be reasonable to simplify by factoring the ASD soil pressure by their average: [(1.6 + 1.2) /2] = 1.4).
Embedment of Stem Reinforcing Steel into Footing
For an adequate moment connection from the stem into the footing it is customary to extend the stem reinforcing into the footing a depth sufficient to form a 90 bar hooked toward the toe (or heel if the distance is insufficient). In practice, the footing bars are placed first and extend as dowels up into the stem to lap with continuing stem reinforcing. See Figure 9.1.
Embedment depth can be reduced by the stress level in the reinforcing depending upon the application of ACI 318-11,12.5.3 (d) which states that excess reinforcement can be credited except where “...anchorage or development is not specifically required...” Required dimensions and radii of hooked bars are shown on Figure 9.1. Embedment requirements plus the three inches of protective concrete cover determine the minimum total depth of the footing.
Piles, Piers, and Caissons Returning wall support options perform essentially the same function: to penetrate soil to a depth sufficient to achieve greater load bearing capacity than would be provided by a spread footing.
This is achieved either by end bearing or frictional resistance along the lateral area of the shaft, or both.
PILES accomplish this by being driven (steel, concrete, or timber) to either bear on hard strata or develop sufficient skin-friction through the depth of penetration. Concrete piles are usually the choice for retaining walls and abutments, and are either driven precast concrete, or cast-in-place in drilled bores.
CAISSONS is a term often used interchangeably with piers. Caissons are usually large diameter piers, but can have narrow shafts with a flared (bell) bottom for greater bearing area. Neither type is often used for retaining walls.
PIERS is a term used to describe a relatively short cast-in-place concrete shaft foundation. Some codes define a pier (as opposed to a pile or caisson) as having a depth-to-diameter ratio less than twelve. A pier’s supporting capacity is achieved by a combination of lateral surface friction and end bearing but some codes do not allow both combined. If a masonry retaining wall has spaced pilasters, the pilasters can be cantilevered up from an embedded pier (see Pilaster Masonry Wall,