Retaining Wall Design

Last updated December 18, 2024
By Ian Story

Retaining wall design is a highly inexact science that relies on many assumptions and specifications. Some parts of the process are codified, but many of the decisions to be made are based on engineering judgment, informed by past studies, geotechnical references, and sources outside of the building codes (for example, transportation departments and associations).

Discussion on Forces

Seismic Self Weight

Basics of Retaining Wall Design suggests using ASCE 7-16, equation 15.4-5 (Section 15.4.2) to calculate seismic forces due to self weight. For an importance factor of 1, this gives V = 0.30SDSW.

AASHTO LRFD Bridge Design Specification, Section 11.6.5.1 considers two sources of seismic force: soil lateral pressure (PAE), and wall inertial forces (PIR), where the weight of any soil directly above the heel is included in the weight of the wall for purposes of calculating inertial forces. Research indicates that these two forces tend to act out of phase (i.e., when the seismic component of earth pressure is at a maximum, the inertial force is near a minimum, and vice versa). To account for potential concurrence of phases, the AASHTO specification uses the larger of PAE + 0.5PIR and 0.5PAE + PIR (with 0.5PAE at least equal to the static active soil pressure). AASHTO further calculates PIR as kh(Ww + Ws), where kh is the seismic horizontal acceleration coefficient, Ww is the weight of the wall, and Ws is the weight of soil above the heel.

For typical Seattle sites, the range of kh values appears to be between 0.3 and 0.55, depending on how much sliding is acceptable. Calculating sliding is a challenging task, but the Simplified Newmark Sliding Block Analysis gives a rough ballpark estimate. According to this paper (Jibson), a slope/retaining wall designed for 0.30g is expected to slide a mean distance of around 1 inch in an earthquake with a PGA of 0.45g and a duration of 10 seconds. For reference the equivalent sliding for a wall designed for 0.35g is 0.4 inch and the equivalent sliding for a wall designed for 0.40g is 0.2 inch (all approximate means, with variation).

The WSDOT Geotechnical Design Manual calculates As (ground acceleration) as FPGAPGA, where PGA (peak ground acceleration) is about 0.45G for Seattle (PGA is tabulated for soft rock – Site Class B/C). FPGA is a conversion factor to other site classes, and works out to 1.15 for PGA=0.45 and Site Class D. This gives us a typical As = 0.52 for most Seattle sites. kh is taken as 0.5As where 1 to 2 inches of sliding during an earthquake is acceptable, otherwise kh = As. For slope stability, this gives a typical kh = 0.26 (I commonly see kh = 0.3 used for slope stability analysis). Note: AASHTO uses FPGA = 1.2. Both AASHTO and WSDOT assume kv = 0.

Conclusion: use 0.5kh as the seismic coefficient for self-weight (0.2 is a good value for reduced sliding), but include weight of soil over the toe in self weight. Alternatively, for walls with very large heels, ignore the seismic lateral force from the soil and use 1.0kh as the self-weight seismic coefficient. Use whichever method gives the lower factor of safety.

Cases to Check:

Seismic Loading

How to determine seismic surcharge for soil pressure?

Despite several research papers investigating this topic, the current consensus seems to be that all current pseudostatic methods for calculating seismic loads on retaining walls are overly conservative. But nobody has yet come up with a good approach to reduce them. The basis of most seismic analysis is the Mononobe-Okabe method, which is basically a trial wedge analysis with an additional horizontal gravity component. This procedure breaks down with large accelerations and steep backfill slopes because the predicted failure angle is less than the slope of the backfill, leading to an infinite soil wedge.

I discussed this issue with a local geotechnical engineering firm, and their engineering judgment was to rely on rules of thumb for seismic surcharges rather than using the Mononobe-Okabe method. They typically specify a rectangular pressure distribution of xH psf, where x is a constant (in the ballpark of 8 to 12) and H is the height of retained soil in feet. For backfill slopes of 2H:1V, increase x by 50%. For backfill slopes of 1H:1V, increase x by 100%.

How to handle seismic self weight?

During a seismic event, the inertial mass of the wall and any soil over the heel generate an inertial force that needs to be considered. There isn’t a strong consensus on how to handle this in the literature. Research by Al Atik and Sitar (2010) indicates that the structural inertial response is out of phase with the seismic component of soil loads in most cases. This potentially justifies omitting the inertial loads (or analyzing them as a separate load case from soil seismic loads), but a more conservative approach is to discount inertial loads by 50% to account for some phase overlap. This is the approach that the AASHTO LRFD Bridge Design Specification takes: run 2 load cases, one with seismic loads at 100% and inertial loads at 50%, and one with seismic loads at 50% and inertial loads at 100%.

Digging deeper, a couple additional questions arise:

How to handle soil over the heel? This soil block is typically considered part of the wall’s mass because it moves on the same base as the rest of the wall. Retaining wall design software like Enercalc does not consider this mass, but AASHTO recommends that it be considered part of the inertial weight of the wall. As an interesting wrinkle, however, AASHTO recommends using the soil inertial weight for external stability calcs (overturning and sliding), but not for strength calculations for the stem, on the assumption that the soil mass will be moving in tandem with the wall and will not be applying an inertial load to it.

How to handle the inertial mass of the footing? I haven’t been able to find any good documentation on this. The conservative approach would be to model this the same as the wall mass for external stability calculations (namely sliding, since this mass has a negligible contribution to overturning).

How to Calculate Seismic Inertial Forces

Seismic inertial forces are equal to kh times the weight of the wall elements, where kh is the seismic horizontal acceleration coefficient. The full value of kh is the site-adjusted peak ground acceleration, FpgaPGA, where Fpga is the site-adjusted acceleration factor (1.2 for class D soils in the pacific northwest), and PGA is the peak ground acceleration. For sites in Seattle, PGA is around 0.6 (+- 0.05), which gives a base kh of 0.72. If the wall can tolerate movement during a peak seismic event, the design value can be reduced (based on the Newmark sliding block method). A common reduction value is 50%, which gives kh = 0.36 for many Seattle projects. Rounding up to be conservative, this gives a seismic inertial force equal to 40% of the element’s weight.

Tiered Retaining Wall Surcharges

Horizontal Surcharges

Where the friction force or passive key of an upper wall occurs within the active wedge of a lower wall, the sliding forces of the upper wall need to be applied to the lower wall. The AASHTO LRFD Bridge Design Specification recommends distributing these forces as an inverted triangle over a the height of wall whose active wedge just sees the back of the applied force, and ignoring the load if it occurs outside the active wedge of the whole wall. This approach assumes that some of the horizontal load will be applied to the very top of the lower wall up until the point the footing is moved far enough back, then it suddenly drops to zero. As an approximation this is fine, but I think it can be improved.

This site (GEO5), which is a British geotechnical design package, uses a variant method: the top of the load cuts off at a projected angle (phi) below the front of the lateral load, and extends down to the same point as in the AASHTO method. Within this zone an inverted triangle is used. This is essentially equivalent to assuming the footing sits on cohesionless soil sloped at the limiting friction angle of the soil. The wedge of soil above this can effectively be removed and replaced with an equivalent surface surcharge and the result would be the same. This is equivalent to the Beton Kalender method, without the Ka factor, and using the inverted triangle distribution.

Construction Phase – Overturning

Some sources assert that seismic forces may be neglected for temporary retaining walls. For example:, the WSDOT Bridge Design Manual states that “Any retaining wall that is expected to be in service for more than three years shall be designed for seismic loading.”

Apply all forces that would be present right at the moment of tipping. This includes earth pressures (use active pressure, because overturning requires movement of the wall)

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