Rankine Earth Pressure Theory
Rankine's theory assumes a cohesionless soil, a frictionless wall, and a vertical soil-wall interface. It evaluates the lateral earth pressures applied by the soil mass onto the retaining wall.
The total force per unit length of the wall is calculated as:
Frequently Asked Questions
Using Rankine's theory, the active earth pressure coefficient Ka is calculated from the angle of internal friction. Then the total active force is 0.5 * Ka * Unit Weight * Height^2.
A retaining wall resists: active earth pressure (soil pushing horizontally against the wall, calculated using Rankine or Coulomb theory); hydrostatic pressure (if drainage is poor, water pressure can exceed soil pressure); surcharge loads from vehicles or structures on retained soil; and seismic forces in earthquake zones. Poor drainage is the leading cause of retaining wall failure.
The Rankine active earth pressure coefficient: Ka = tan²(45° − φ/2), where φ is the soil internal friction angle. For typical granular fill (φ=30°): Ka = tan²(30°) = 0.333. The active earth pressure at depth h is pa = Ka × γ × h, where γ is soil unit weight (typically 18–20 kN/m³). At 3m depth with these values: pa = 0.333 × 19 × 3 = 19 kPa.
Minimum factors of safety for retaining wall stability: Overturning — FS ≥ 1.5 (permanent loads), FS ≥ 1.2 (with seismic); Sliding — FS ≥ 1.5; Bearing capacity of foundation — FS ≥ 2.0 to 3.0; Global slope stability — FS ≥ 1.3–1.5. These values are specified in Eurocode 7 (EC7), AASHTO, and local geotechnical standards. Higher factors apply for critical structures.
Water buildup behind a retaining wall dramatically increases lateral pressure. A fully saturated soil exerts both active earth pressure AND hydrostatic pressure (from water column). The combined pressure can be 2–3× higher than drained conditions, easily exceeding design capacity. Always provide: weep holes at 1.5–2m spacing, granular backfill, and a drainage blanket or perforated pipe at the wall base.
Gravity walls (mass concrete or stone) — suitable up to 1.0–1.5m; rely on self-weight; no reinforcement needed. Cantilever walls (reinforced concrete L or T shape) — economical for 1.5–6m; engineered design required. MSE walls (mechanically stabilised earth) — cost-effective for heights over 3m with geogrid reinforcement. Gabion walls — flexible, permeable, good for moderate heights and aesthetic applications.