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.
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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.
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.
Javier Encinas, PE
ASDIP Structural Software