Retaining Wall Stability Calculator (Overturning, Sliding & Bearing)

How it works

Ka = tan²(45° − φ/2) · soil thrust Pa = ½·Ka·γ·H² at H/3 · surcharge thrust Pq = Ka·q·H at H/2 · FS overturning = ΣMresisting / ΣMoverturning (≥ 2.0) · FS sliding = μ·ΣW / (Pa + Pq) (≥ 1.5) · x̄ = (Mr − Mo)/ΣW, e = B/2 − x̄ · qmax,min = ΣW/B × (1 ± 6e/B) when e ≤ B/6, otherwise qmax = 2ΣW/(3x̄).

A cantilever retaining wall must not tip over, slide or overload the soil under its toe. The backfill pushes on a vertical plane through the heel with Rankine active pressure, and the weights of the stem, the base slab and the soil standing on the heel hold the wall in place. Overturning is checked about the toe, sliding against base friction, and bearing with the trapezoidal pressure from the eccentric resultant. Passive resistance in front of the toe and the surcharge on the heel are ignored, which is conservative; the safety factors (2.0 overturning, 1.5 sliding) are the usual values in standard foundation-engineering texts and many building codes. A keyed base or a wider heel improves sliding.

Worked example

A 4 m wall with a 2.8 m base (0.6 m toe, 0.3 m stem, 0.4 m slab) retains soil at 18 kN/m³ and φ = 30° with a 10 kPa surcharge. Ka = 0.333, so Pa = ½ × 0.333 × 18 × 4² = 48.0 kN/m and Pq = 0.333 × 10 × 4 = 13.3 kN/m, giving an overturning moment of 64.0 + 26.7 = 90.67 kN·m/m. The stem (25.92 kN/m), slab (26.88 kN/m) and 1.9 m of soil over the heel (123.12 kN/m) give ΣW = 175.92 kN/m and a resisting moment of 284.84 kN·m/m: FS overturning = 3.14 and FS sliding = 0.55 × 175.92/61.33 = 1.58. The resultant sits 0.296 m off centre, inside B/6, so the toe pressure is 102.7 kPa and the heel pressure 22.9 kPa — under the 150 kPa allowable.

Sources: FHWA — Soils and Foundations Reference Manual Vol. II, Chapter 9 (retaining structures) · Retaining wall — design for stability

Frequently asked questions