# Cantilever Retaining Walls: How to Calculate the Sliding Safety Factor

September 10, 2019

Retaining walls are structures designed to bound soils between two different elevations, therefore they are mainly exposed to lateral pressures from the retained soil plus any other surcharge. Cantilever walls may be sensitive to sliding problems, particularly if founded on poor soils. This article discusses how to calculate the sliding safety factor in cantilever retaining walls. Our software ASDIP RETAIN will be used to support the discussion.

## What are the pressures acting on a retaining wall?

In addition to the retained backfill, retaining walls may be subject to surcharge loads at the top of retained mass, or a high water table. When the stem extends above backfill the retaining wall may be exposed to wind load. If the retaining wall is located in a seismic zone the seismic pressures should also be considered. The image below shows schematically the pressure diagrams on a typical retaining wall.

Each applied load has a particular effect on the wall. The backfill exerts a triangular lateral pressure calculated per the corresponding earth pressure theory. The surcharge produces a uniform rectangular pressure on the wall. The seismic pressure is trapezoidal, with the higher pressure at the top. The action of these loads produces a bearing pressure under the footing, and a passive pressure at the front of the wall.

For a more in-depth discussion of the soil lateral pressure theories and overall stability modes please see the post Cantilever Retaining Walls: Overview of the Design Process.

## How do you calculate the sliding safety factor?

The horizontal pressures on the backfill side will push the wall outward, which will tend to slide on its footing. The driving force from the applied loads must be resisted by an opposite friction force at the interface of the footing base and the underlying soil, produced by the bearing pressure against the base. In addition, the passive pressure against the front face of the wall and footing may be considered as well.

When the friction plus passive forces are not high enough to counteract the pushing force, a shear key can be designed under the wall footing. This structural element will bear laterally against the soil, increasing the sliding resistance. The position of the key along the footing is not very important, but many engineers prefer to place it just under the stem, so that the wall rebars can be extended down into the key.

Per 2015 IBC 1807.2.1, "Where a keyway is extended below the wall base with the intent to engage passive pressure and enhance sliding stability, lateral soil pressures on both sides of the keyway shall be considered in the sliding analysis". This provision was removed in the 2018 IBC, without further explanation. It seems that the intent of the code is to go back to the design philosophy prior to the 2009 IBC, where this provision requiring the active pressure diagram to be extended down to the bottom of the key didn't exist.

The factor of safety against sliding is defined as the resisting forces (friction + passive) divided by the driving lateral force, and the minimum value should be 1.50. Where seismic loads are included, the minimum safety factor should be 1.10.

As an example, the image below shows the ASDIP RETAIN sliding calculations. Note that the load combinations are based on service loads, since the wall stability is being checked. In this example the safety factor is greater than 1.50 for the load combination shown.

## Takeaway

ASDIP RETAIN includes the design of cantilever retaining walls, with multiple options to optimize the design easily. The sliding failure mode should be checked as part of the design, considering the correct pressure diagrams at both sides of the wall.

Detailed information is available about this structural engineering software by visiting ASDIP RETAIN. For a design example see the post Cantilever Retaining Wall Design Example Using ASDIP RETAIN. For our collection of blog posts about retaining walls please visit Structural Retaining Wall Design.