Cantilever retaining wall stability: overturning, sliding and bearing

A cantilever retaining wall has two separate jobs. As a rigid body it must not tip, slide or overload the soil under it. As a set of concrete members, the stem, toe and heel must carry the bending and shear that the soil puts into them. The IBC treats these differently. Stability is checked with unfactored loads and a safety factor. Member strength is designed with factored loads under ACI 318-19. This article covers the first job: the stability checks of IBC 2021 §1807.2, with a complete worked example.

What the IBC requires

IBC 2021 §1807.2.1 requires retaining walls to be designed for stability against overturning, sliding, excessive foundation pressure and water uplift. §1807.2.2 sends the designer to §1610 for the lateral soil loads. §1807.2.3 sets the safety factor:

• Overturning and sliding: a minimum safety factor of 1.5 in each case.
• Loads: the load combinations of §1605 do not apply to this check. The design uses 1.0 times the nominal loads (0.7 times the nominal earthquake load), and the variable loads are investigated with one or more of them set to zero.
• Sliding definition: the safety factor is the available soil resistance at the base of the wall foundation divided by the net lateral force applied to the wall foundation.
• Seismic exception: where earthquake loads are included, the minimum safety factor for sliding and overturning is 1.1.

Bearing has no 1.5 factor in §1807.2.3. The maximum soil pressure is compared directly to the allowable bearing pressure, which already carries the geotechnical engineer's safety factor. Where no report exists, IBC §1806.2 and Table 1806.2 give presumptive allowable bearing pressures, lateral bearing values and friction coefficients by soil class (use the values in the referenced table).

Lateral earth pressure

For a wall free to rotate at the top, the backfill is in the active state. The Rankine coefficient for a level backfill is:

The pressure is triangular, so the resultant per foot of wall and its location are:

For a cantilever wall with a heel, the usual practice is to apply the Rankine pressure on a vertical plane through the back of the heel (the "virtual back"), with H measured from the bottom of the footing to the top of the backfill. The soil sitting on the heel then counts as part of the wall's weight.

Coulomb theory adds wall friction δ and applies the pressure on the actual back of the wall. For φ = 30°, δ = 20°, a vertical back and level backfill, Coulomb gives K_a = 0.297, with the force inclined at δ; its horizontal component corresponds to 0.297 · cos 20° = 0.279. Coulomb is the natural choice for gravity walls and for the stem itself. For the stability of a cantilever wall with a long heel, the Rankine virtual-back approach is the standard one. Whichever theory you use, use it consistently: the virtual back goes with the soil on the heel counted as weight.

At-rest pressure applies when the wall cannot rotate enough to mobilize the active state: K₀ = 1 − sin φ = 0.5 for φ = 30° (Jaky). IBC §1610.1 permits retaining walls free to move and rotate at the top to be designed for active pressure; walls restrained at the top, such as basement walls, are designed for at-rest pressure. Table 1610.1 gives presumptive lateral soil loads by soil type for use without a geotechnical report (use the values in the referenced table).

Water. The pressures above assume a drained backfill. If drainage cannot be relied on, add hydrostatic pressure and use the buoyant unit weight below the water table. The water term often exceeds the soil term.

Surcharge. A uniform surcharge q on the backfill adds a rectangular pressure K_a · q over the full height, with resultant K_a · q · H at H/2. Because §1807.2.3 requires variable loads to be investigated with one or more set to zero, a live-load surcharge is included as a lateral force but its vertical weight on the heel is not counted as resistance to overturning or sliding.

Seismic. IBC §1803.5.12 requires the geotechnical investigation for structures in Seismic Design Category D, E or F to address dynamic seismic lateral earth pressures on retaining walls supporting more than 6 ft of backfill. That pressure enters the stability check at 0.7 times its nominal value, with the 1.1 minimum safety factor.

The three checks

Take moments about the toe, the point the wall would rotate about.

ΣM_R is the resisting moment of the wall and soil weights. ΣM_O is the overturning moment of the lateral forces. ΣW is the total vertical load on the base, μ the base friction coefficient, P_p the passive resistance in front of the toe, and ΣP_h the total horizontal driving force.

For bearing, locate the resultant and find its eccentricity from the center of the footing:

• Resultant within the kern (e ≤ B/6): the whole base is in compression and the pressure is trapezoidal: q = (ΣW/B)(1 ± 6e/B). The plus sign gives the toe pressure.
• Resultant outside the kern (e > B/6): soil cannot take tension, so the heel lifts off. The pressure is triangular over a contact length of 3x̄, and q_max = 2ΣW / (3x̄).

The code does not require the resultant to stay within the middle third. It is standard practice for walls on soil because full contact limits rotation and the uneven settlement that tilts a wall forward. A resultant outside the kern also raises the toe pressure quickly: q_max is 2ΣW/B at e = B/6 and climbs without limit as x̄ shrinks.

Friction and passive resistance

The friction coefficient μ is a geotechnical input, and it moves the sliding check more than anything else. For concrete cast against granular soil, values between tan(⅔φ) and tan φ are common. For φ = 30° that range is 0.364 to 0.577. Use the value in the geotechnical report.

Passive resistance in front of the toe uses K_p = (1 + sin φ) / (1 − sin φ) = 3.0 for φ = 30°. Passive pressure needs far more movement to develop than active pressure, and the soil providing it is the soil most likely to be disturbed. Common practice:

• Neglect the top foot of soil in front of the toe, or the depth subject to frost, desiccation or future excavation, whichever is greater.
• Ignore passive entirely where a utility trench, pavement removal or erosion could take away the soil in front of the toe.
• Some designers reduce the remaining passive force by a mobilization factor. That is an engineering convention, not a code value; follow the geotechnical report.
• Do not count passive resistance in the overturning check. It is a sliding resistance.

Where sliding still falls short, a shear key below the footing moves the sliding surface deeper and adds passive resistance in front of the key. Widening the heel adds weight, and therefore friction, at the cost of more excavation.

Worked example: 10 ft retained height

Given, per foot of wall:

• Total height from bottom of footing to top of level backfill H = 12.0 ft; soil in front of the toe 2.0 ft deep (to the bottom of the footing), so the retained height is 10.0 ft.
• Footing 8.0 ft wide by 1.25 ft thick: toe 2.5 ft, stem 1.0 ft thick, heel 4.5 ft. Stem height above the footing 10.75 ft.
• Backfill γ = 120 pcf, φ = 30°, drained, no surcharge. Concrete 150 pcf.
• Base friction coefficient μ = 0.45 and allowable bearing pressure 2,500 psf, both taken from the geotechnical report.
• Soil over the toe is ignored as a resisting weight (it can be removed).

Lateral force and overturning moment

Vertical forces and resisting moment about the toe

Overturning

Sliding, friction only

Friction alone does not do it. Count passive resistance in front of the toe, neglecting the top 1.0 ft of the 2.0 ft of soil:

How sensitive is this to μ? With μ = tan(⅔ · 30°) = 0.364, the same wall gives 1.13 on friction alone and 1.31 with the discounted passive. With μ = tan 30° = 0.577 it gives 1.79 on friction alone. Halving the discounted passive force as a mobilization allowance gives (4,012.9 + 270) / 2,880 = 1.49. Sliding is the check that governs this wall, and it is governed by geotechnical inputs.

Bearing

What a surcharge does to the same wall

As a sensitivity check only, not part of the passing design above: add a 250 psf live-load surcharge on the backfill. The lateral surcharge force is (1/3) × 250 × 12.0 = 1,000 lb/ft at 6.0 ft, so ΣM_O rises to 17,520 ft-lb/ft. With the vertical surcharge on the heel ignored as resistance, FS_OT = 44,216.25 / 17,520 = 2.52, still comfortable. Sliding drops to (4,012.9 + 540) / 3,880 = 1.17, which fails. A wall that carries a parking area or a driveway at the top almost always needs a key or a longer heel, and sliding is where that shows up first.

For contrast with the kern case: had the resultant landed at x̄ = 2.0 ft with the same 8,917.5 lb/ft, e = 2.0 ft > B/6, the contact length would be 3 × 2.0 = 6.0 ft and q_max = 2 × 8,917.5 / (3 × 2.0) = 2,973 psf. Moving the resultant 1.67 ft toward the toe more than doubles the toe pressure and exceeds the allowable.

Stem and footing strength: a separate design

Once the wall is stable, the stem, toe and heel are designed as reinforced concrete members under ACI 318-19, which this article does not cover in depth. ACI 318-19 Chapter 13 directs the stem of a cantilever retaining wall to one-way slab design under Chapter 7, and the toe and heel are designed as cantilevers from the face of the stem. Those checks use factored loads. ASCE 7-22 §2.3 (strength design) and §2.4 (allowable stress design) include the lateral earth pressure H with a factor of 1.6 in strength design (1.0 in ASD) where it adds to the primary load effect, and 0.9 (0.6 in ASD) where it is permanent and resists it. The factored combinations do not replace the §1807.2.3 stability check, and the 1.5 safety factor is not applied on top of factored loads.

How StructuralClaw handles it

The StructuralClaw retaining wall module runs the IBC 2021 §1807.2 stability checks on nominal loads and keeps them apart from the factored stem, heel and toe design, so the 1.5 safety factor and the load factors never stack. Active, at-rest and passive pressures are separate soil cases, and the passive mobilization factor and the depth of soil to neglect at the toe are explicit inputs rather than buried assumptions. The module is part of the StructuralClaw desktop program, which is coming soon.

• International Code Council, 2021 International Building Code, §1806.2 and Table 1806.2 (presumptive load-bearing values), §1807.2 (retaining walls), §1610 (soil lateral loads), §1803.5.12 (seismic lateral earth pressure).
• ASCE/SEI 7-22, Minimum Design Loads and Associated Criteria for Buildings and Other Structures, §2.3 and §2.4 (load combinations including H).
• ACI 318-19, Building Code Requirements for Structural Concrete, Chapter 13 (foundations) and Chapter 7 (one-way slabs).