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Retaining Wall Stability

Rankine active pressure gives K_a = tan²(45 − φ/2) — for a typical φ = 30° soil that is exactly 1/3. The thrust acts at H/3 up from the base, and the two classic checks are whether the wall tips over its toe and whether it simply slides.

Retained height H (m)

Soil unit weight γ (kN/m³)

Friction angle φ (°)

Wall weight (kN/m)

Base width B (m)

Surcharge (kPa)

Base friction coefficient

Active coefficient Ka

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Active thrust Pa

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Overturning moment

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Resisting moment

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FS overturning (need 2.0)

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FS sliding (need 1.5)

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Active (Rankine) pressure assumes the wall can rotate slightly away from the soil; a restrained wall sees higher at-rest pressure. Bearing pressure, global slope stability, drainage and hydrostatic pressure behind an unfree-draining wall are all separate checks — and water is what fails most retaining walls.

PRELIMINARY SIZING ONLY — not a code-compliant design check. These are first-pass equations; they omit member stability, local buckling, shear and combined-stress interaction, connections, second-order effects and jurisdiction-specific factors. Codes vary by country and edition. Structural design must be performed and sealed by a qualified engineer.