Rankine Active Pressure

ENGINEERING – GEOTECHNICAL ENGINEERING CALCULATOR Rankine Active Pressure A precise tool.
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What is the Rankine Active Pressure & How does it work?
The Rankine theory provides a simple way to estimate the lateral earth pressure that a retaining wall must resist when the soil behind it is allowed to expand (active condition). It assumes a homogeneous, isotropic soil mass, a vertical wall, and that the wall moves enough to mobilize the active state without any wall friction. In the active state the horizontal stress at any depth (z) is given by (sigma_a = K_a gamma z), where (gamma) is the unit weight of the soil and (K_a) is the active earth‑pressure coefficient. The coefficient depends only on the soil’s internal friction angle (phi) and is derived from limit equilibrium of a soil element. The coefficient (K_a) is calculated using the classic Rankine expression. Once (K_a) is known, the pressure distribution is linear with depth, reaching its maximum at the base of the wall. This linear distribution is the basis for designing the size and reinforcement of retaining structures.
K_a = tan^2left(45^{circ} – frac{phi}{2}right)
K_a = active earth‑pressure coefficient
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Parameters
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Frequently Asked Questions
What is the Rankine Active Pressure formula?
The formula for Rankine Active Pressure is Οƒ_a = K_a * Ξ³ * z, where Οƒ_a is the horizontal stress, K_a is the active earth pressure coefficient, Ξ³ is the unit weight of soil, and z is the depth.
When would you use the Rankine theory?
Rankine theory is used to estimate lateral earth pressure on retaining walls when the soil behind the wall is allowed to expand (active condition) without any wall friction.
What does K_a represent in the formula?
K_a represents the active earth pressure coefficient, which depends on the angle of internal friction of the soil and the cohesion of the soil.
How do you determine the unit weight (Ξ³) of soil?
The unit weight of soil is typically determined by multiplying the bulk density of the soil by its water content. It can also be estimated using standard soil tables or laboratory tests.
What factors affect the value of K_a?
K_a is influenced by the angle of internal friction (Ο†) and cohesion (c) of the soil. Generally, higher Ο† and lower c values result in a smaller K_a.
Can Rankine theory be used for cohesive soils?
Rankine theory is typically applied to cohesionless soils. For cohesive soils, other theories like Coulomb’s theory might provide more accurate results.
How does the depth (z) affect the active pressure?
The active pressure increases linearly with depth according to the formula Οƒ_a = K_a * Ξ³ * z. Thus, deeper pressures are greater than shallower ones.

Results are for informational purposes only and do not constitute professional advice.