Rankine Earth Pressure Calculator
A 6 m wall retaining dry sand (φ = 30°, γ = 18 kN/m³) carries an active thrust of 108 kN/m, acting 2 m above the base.
108 kN/m
- Coefficient Ka
- 0.3333333333
- Pressure at the top
- 0 kPa
- Pressure at the base
- 36 kPa
- Line of action above the base
- 2 m
Step-by-step solution
- Ka = tan²(45° − φ/2) = 0.3333333333
- σ(z) = K(γz + q) − 2c√K → top 0 kPa, base 36 kPa
- P = area of the pressure diagram = 108 kN per metre run
Rankine Earth Pressure Formula
σa = Ka(γz + q) − 2c√Ka, σp = Kp(γz + q) + 2c√Kp
Ka = tan²(45° − φ/2), Kp = tan²(45° + φ/2)
Worked Example
A 6 m smooth vertical wall retaining dry sand with φ = 30° and γ = 18 kN/m³:
- Ka = tan²(45° − φ/2) = 0.3333333333
- σ(z) = K(γz + q) − 2c√K → top 0 kPa, base 36 kPa
- P = area of the pressure diagram = 108 kN per metre run
Pressure at the top: 0 kPa · Pressure at the base: 36 kPa · Line of action above the base: 2 m
GATE tip
For a submerged backfill split the diagram: Ka γ′ z for the soil plus the full water pressure γw z, since water has K = 1.
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Frequently asked questions
What is the depth of tension crack?
In a cohesive soil the active pressure is negative to z₀ = 2c/(γ√Ka); the crack is ignored when computing thrust.
How does a surcharge act?
A uniform surcharge q adds a constant Ka q over the whole height, a rectangle in the pressure diagram.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Rankine Earth Pressure Calculator. Retrieved October 29, 2026, from https://scientificconverters.com/calculators/rankine-earth-pressure-calculator/
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Scientific Converters, "Rankine Earth Pressure Calculator," scientificconverters.com. Accessed: Oct. 29, 2026. [Online]. Available: https://scientificconverters.com/calculators/rankine-earth-pressure-calculator/