By: Javier Encinas, PE | November 30, 2016

Retaining walls are structures designed to bound soils between two different elevations. A retaining wall is then mainly exposed to lateral pressures from the retained soil plus any other surcharge. Many retaining walls are cantilever-type, but it’s also common to find in practice walls that are laterally restrained at the top, such as in the case of basement walls supported laterally by an elevated floor slab. This article discusses the design of either concrete or masonry top restrained retaining walls. Our software ASDIP RETAIN will be used to support our discussion.

A typical restrained retaining wall is composed of four main components: the Stem, the Toe at the front of the wall, the Heel at the backfill side, and the Shear Key. Frequently the walls are also laterally restrained at the base by the slab on grade, so the shear key is seldom required. The images below show the geometry of a typical top restrained retaining wall.

restrained-retaining-wall-geometry

What lateral earth pressure theory to use?

There are two well-known classical earth pressure theories: Rankine and Coulomb. This subject has been discussed in our previous post Cantilever Retaining Walls: An Overview of the Design Process (Part 1). Since a restrained wall cannot tilt away from the soil to mobilize its shear strength, the active pressure cannot be developed. As a result, a restrained retaining wall should be designed using the At-rest Ko pressure coefficient, instead of the Active Ka commonly used in cantilever walls.

ASDIP RETAIN uses any of the theories described above. In addition, the Equivalent Fluid method may be selected, which assumes the backfill as a fluid of a given density.

What are the typical loads on a restrained retaining wall?

Being the purpose of a retaining wall to maximize the land usage, normally there are surcharge loads on top of the retained mass. These loads may be dead or live, uniformly distributed or concentrated. Driveways, parking lots, equipment, etc, are examples of surcharges in a basement wall. A uniform surcharge will produce a uniform lateral pressure on the wall. A roadway running parallel to the wall may be modeled with a Strip load, and it may be calculated using the Boussinesq approach.

Sometimes the stem extends above the backfill level and this portion of the wall could be exposed to a wind pressure. If the wall is located in a seismic zone, then the seismic effects need to be considered. In this case the Mononobe-Okabe approach is usually followed, which is based on the Coulomb theory previously discussed. The picture below shows schematically the external loads in a typical restrained retaining wall.

restrained-retaining-wall-loads

How do you check the overall stability?

In the post referenced above we discussed the four basic instability modes in a typical retaining wall:

  • Sliding – The backfill and the other applied loads exert a lateral pressure against the wall, so it will tend to slide. If the wall is not laterally restrained at the base, then the sliding mode should be checked for a minimum safety factor of 1.50.
  • Overturning – Since a restrained retaining wall is laterally supported at the top, the overturning mode of failure is therefore prevented.
  • Soil bearing – Usually the bearing pressure under the footing is rectangular or trapezoidal, with the maximum bearing pressure at the end of the toe. The allowable soil bearing pressure should be provided by the soils report, which already includes a safety factor of about 3.0.
  • Global instability – It assumes that a failure surface develops under the wall, causing a massive disturbance and movement of the soil along this surface. This check is a complex analysis that falls in the field of the geotechnical engineering.

The image below shows a restrained retaining wall designed by ASDIP RETAIN with the magnitude and location of the loads that affect the stability analysis, sorted by load combination. The calculated safety factors are also shown for immediate check.

restrained-retaining-wall-stability-check

How do you design the stem?

Since the stem is laterally supported at the top, it can be modeled either as pinned or fixed at base, so it may act as either a pin-pin or a fix-pin beam, and the resulting shears and moments will be completely different. It may be wise to fix the base, so that the stem will be lighter even if the footing gets penalized. The stem must be designed for the maximum positive and negative moments, and the shear must be checked at the critical section located a distance d above the top of the footing.

The picture below shows the different pressures on the stem of a typical retaining wall, sorted by load combination. Note the shear and moment diagrams generated by ASDIP RETAIN for a fix-pin stem, where the shaded area represents the structural capacity of the stem. If the stem is overloaded at any point, the problem can be immediately identified.

restrained-retaining-wall-stem-design

How do you design the footing?

The heel is subjected to the vertical loads acting on the back side of the wall, including the backfill weight and any surcharge. All these loads tend to push the heel down, which acts as a cantilever beam where both the maximum moment and the critical section for shear occur at the face of the stem. The reinforcing steel at the heel should be placed at the top side of the footing.

The toe is another cantilever beam subjected to an upward pressure from the soil reaction. The weight of the fill material on top of the toe should also be considered. In this case, the maximum moment occurs at the front face of the stem, but the shear critical section occurs at a distance d from the stem face. The reinforcing steel at the toe should be placed at the bottom side of the footing.

The picture below shows the construction information of a typical restrained retaining wall. Note that the back vertical rebars have been cut-off in order to optimize the design.

restrained-retaining-wall-reinforcing

Detailed information is available about this structural engineering software by visiting ASDIP RETAIN. You are invited to download a Free 15-Day Software Trial or go ahead and Purchase Your License.

Best regards,

Javier Encinas, PE
ASDIP Structural Software

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