Coulomb Earth Pressure Calculator
Estimate the active earth pressure behind a vertical retaining wall using Coulomb's theory, which — unlike the smoother Rankine method — credits the friction that develops between the wall stem and the soil. Enter the soil friction angle, an optional wall-friction angle, the soil unit weight and the wall height to get the active coefficient Ka, the horizontal thrust per metre of wall, and the point where that thrust acts.
Enter Values
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the soil (internal) friction angle φ in degrees — typically 28–36° for a compacted granular backfill.
- Optionally set the wall friction angle δ (default 20°, often ⅓φ–⅔φ), the soil unit weight γ (default 18 kN/m³) and the wall height H in metres.
- Read Ka, the active thrust Pa in kN per metre run, and the H/3 lever arm; use these in an overturning and sliding check.
How it works
The Coulomb active coefficient for a vertical wall back and level backfill is Ka = cos²φ / [cosδ·(1 + √(sin(φ+δ)·sinφ / cosδ))²]. The total active thrust per metre run is Pa = ½·Ka·γ·H², and because pressure grows linearly with depth the resultant acts at one-third of the height above the base (H/3). Adding wall friction δ reduces Ka compared with a frictionless wall, giving a smaller — but still design-relevant — horizontal force.
Worked example
Worked example. For φ = 30°, δ = 20°, γ = 18 kN/m³ and H = 4 m: cos²30° = 0.75, the root term = 0.6384, so the bracket (1+0.6384)² = 2.6845 and the denominator cos20°×2.6845 = 2.5230. Ka = 0.75 / 2.5230 = 0.2973. The active thrust Pa = 0.5 × 0.2973 × 18 × 4² = 42.81 kN/m, acting 1.333 m above the base.
Common mistakes
- Using this vertical-back / level-backfill form when the backfill slopes or the wall face is battered — those cases need the full Coulomb equation and give a larger coefficient.
- Ignoring surcharge, groundwater or cohesion; a water table alone can more than double the horizontal force on the wall.
- Taking an over-optimistic wall-friction angle δ — assuming full δ = φ can unsafely under-predict the thrust, so keep δ conservative and compare against Rankine.
Frequently asked questions
How is Coulomb different from Rankine earth pressure?
Rankine assumes a frictionless (smooth) wall and gives a purely horizontal thrust, while Coulomb accounts for wall friction δ, which lowers the active coefficient and inclines the resultant. For a vertical wall with level backfill and δ = 0 the two methods agree; as δ increases, Coulomb predicts a smaller active force. Design for the more conservative of the two.
Where does the active thrust act?
For a triangular (linearly increasing) pressure distribution the resultant of the active thrust acts at one-third of the wall height above the base, i.e. H/3. Surcharge or water pressure change the shape of the distribution and therefore shift the point of application, so this H/3 value applies only to the simple soil-only case.
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