# Cantilever Retaining Wall Bearing Pressure Calculation

September 21, 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, including the bearing capacity of the supporting soil. This article discusses the cantilever retaining wall calculation of the soil bearing pressures. Our software ASDIP RETAIN will be used to support the discussion.

## What are the typical loads on a retaining wall?

In addition to the retained backfill, retaining walls may be subject to surcharge loads at the top of retained mass. A surcharge may be a strip load. The stem may also have concentrated loads at the top. When the stem extends above 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 Mononobe-Okabe approach.

Each applied load has a particular effect on the wall. As an example, 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 image below shows schematically the typical loading diagrams.

## Retaining wall calculation of soil bearing pressure

The horizontal pressures on the backfill side will produce an overturning moment with respect to the base of the footing. This overturning moment OTM will be resisted by an opposite resisting moment RM produced by the vertical forces Rv, including the wall selfweight and the weight of the backfill over the heel. The eccentricity e is defined as the location of the vertical resultant with respect to the center of the footing.

When the eccentric resultant falls within the kern = L / 6 (within the middle third of the footing), the entire footing is under compression and the bearing diagram is a trapeze, as shown in the example above. In this case the maximum bearing pressure is Rv / L + 6 * Rv * e / L2.

When the eccentric resultant falls outside the kern (out of the middle third of the footing), the footing is under partial bearing and the diagram is a triangle. In this case the maximum bearing pressure is Rv / (0.75 * L – 1.5 * e).

When the maximum bearing pressure exceeds the allowable limit, a disturbance in the supporting soil mass may produce a differential settlement of the structure, as shown below.

As an example, the picture below shows the ASDIP RETAIN bearing calculations for a cantilever retaining wall. Note that the controlling load combination is based on service loads, since the wall stability is being checked. In this case the eccentricity is small and the resultant falls within the middle third of the footing, therefore the bearing diagram is a trapeze with the maximum value at the end of the toe. The maximum calculated bearing pressure is well below the allowable limit.

## Takeaway

Bearing over-pressure is one of the stability failure modes that needs to be checked as part of the design of a cantilever retaining wall. ASDIP RETAIN calculates the bearing pressure for any resultant eccentricity, and finds the controlling service load combination.

For a more in-depth discussion of the theories and overall stability modes please read the blog post Cantilever Retaining Walls: Overview of the Design Process. For our collection of blog posts about retaining walls please visit Structural Retaining Wall Design.

Best regards,

Javier Encinas, PE
ASDIP Structural Software

• John UGWUAGBO says:

Hi
That’s a nice one but just thought of two things
1.on surfaces that are not paved rain water increases the load on retaining wall since you didn’t account for it I thought you could have mentioned an assumption of presence of weep holes
2 Even if Passive pressure is present.It does not mobilize early enough to help.I thought you would have mentioned that it is safer to ignore it
Thanks

• Javier Encinas, PE says:

1.- ASDIP Retain does consider the hydrostatic pressure due to high water table, in case that there are no weep holes.
2.- Passive pressure affects the sliding resistance of the wall. Please note that this post is about bearing.

• Hayrettin says:

I read the post. I must say that well done…… I just want to add one point, i never designed in past tapered stem at front face. Although that will change small amount on reisisting moment , u may consider..thnks.

• Javier Encinas, PE says:

Thank you for your comment. ASDIP Retain considers tapered stems at either side.

• Hayrettin says:

Dear JAVIER, i just want to remind the importance of horizontal rebar and the rebar mesh at front face of stem. In past, i faced (at hot climates , i.e. Middle East) vertical live cracks at stem, i mean during the day time the cracks expanding and during night closing..I checked the temperature stresses (considering the temp diffrence at soil side and front face) and found substantial amounts which typical 0,002A dist. rebar is not enough… I preferred modul length 6 m for C.J and provided expansion joint at every 12 m and i provided horizontal rebar as per temp and shrinkage calculation… good luck..

• Javier Encinas, PE says:

Thank you for your comment. I agree on the importance of the temperature and shrinkage steel.

• Iyaye Praise says:

What is RM and OTM in the video

• Javier Encinas, PE says:

RM = Resisting moment.
OTM = Overturning moment.