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

January 19, 2021

A retaining wall is a structure exposed to lateral pressures from the retained soil plus any other surcharges and external loads. All overall stability failure modes must be thoroughly checked, but cantilever walls may be particularly sensitive to overturning problems. This article discusses the process to calculate the overturning safety factor in either concrete or masonry cantilever retaining walls. Our software ASDIP RETAIN will be used to support the discussion.

A typical 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. The left image below shows the geometry of a typical cantilever retaining wall.

In addition to the retained backfill, retaining walls may be subject to surcharge loads at the top of the retained mass. The position of the water table should also be considered in the design. The stem may also have concentrated loads at the top. When the stem extends above the backfill, the retaining wall may be exposed to wind load. When retaining walls are located in seismic zones the seismic effects are considered by utilizing the Mononobe-Okabe approach.

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 water table pressure is triangular. The seismic pressure diagram is trapezoidal, with the higher pressure at the top. The wind pressure is uniform. The right picture above shows schematically the lateral pressure diagrams on a typical retaining wall.

## How do you calculate the overturning safety factor?

The horizontal pressures on the backfill side will push the wall outward, which will tend to overturn around the end of the toe, as shown at the right image. The overturning moment is the sum of the horizontal forces times the distance to the footing base.

This overturning moment must be resisted by an opposite moment produced by the sum of the vertical forces times the distance to the toe end, including the wall selfweight and the weight of the backfill over the heel and toe.

The factor of safety against overturning is defined as the resisting moment divided by the overturning moment, and the minimum value should be 1.50.

As an example, the picture below shows the ASDIP RETAIN overturning 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 1.5 for the load combination shown.

## Takeaway

The design of cantilever retaining walls includes the calculation of the overturning safety factor and other stability checks. These calculations may be cumbersome and time-consuming, particularly when multiple types of loads are involved. ASDIP RETAIN includes the design of cantilever retaining walls, with multiple options to optimize the design in less time.

For a more in-depth discussion of the loads and overall stability modes in a cantilever retaining wall please read the post Cantilever Retaining Walls: Overview of the Design Process. For an overview of the user interface, you may be interested also in the post How to Design Cantilever Retaining Walls Using ASDIP RETAIN.  For our collection of blog posts about retaining walls please visit Structural Retaining Wall Design.

Best regards,

Javier Encinas, PE
ASDIP Structural Software

• debasis mallick says:

I prefer using line diagram analysis for fixing length of toe and heel from outer surface of wall the error thus caused is nominal (2.5-1.8) t/m^3. Two simple equations with two unknowns get formed and are needed to be solved for various load combinations. The largest of both with appropriate thickness required from design considerations are inserted to cross check which finalises the work.

Thank you to much sir, it’s very valuable increment in my knowledge.I hop you will continuously propagation these valuable awareness about constructional engineering.

• M S A Mihraj says:

Tall cantilever retaining wall stability issue overturning / sliding are critical.
Additional base pressure if ground supported & shear also critical leads to uneconomical design.
Better consider counter fort retaining wall or reinforced earth -suppose to be most cost effective options than vertical cantilever design.

• Javier Encinas, PE says:

Cantilever retaining walls are cost effective up to about 15 feet (3 m) high. In some cases it’s the only option if there are existing structures on top of the backfill, where neither counter fort nor reinforced earth are possible. Counter fort walls do help to reduce the bending on the stem, but the stability requirements remain. A well designed cantilever wall may be more cost effective than a similar counter fort wall due to the additional forming, material, and labor. What type of wall to use will depend on the particular circumstances of each project.

• Farid says:

Should one use 60% of the resisting as load combination 7 of the AISC code.

• Javier Encinas, PE says:

Did you mean combination 7 of ASCE-7? No, per IBC 1807 those combinations do not apply.