Calculate the Rankine active earth pressure on a smooth vertical wall backfilled with cohesionless soil. K_a = tan²(45°−φ/2). Optional uniform surcharge q. Returns the base pressure p₀, the total force P, and the resultant height.
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Key facts
Category
Math & Numbers
Input types
number
Output type
json
Sample coverage
4
API ready
Yes
Overview
Calculate the Rankine active earth pressure on a smooth vertical retaining wall backfilled with cohesionless soil. This calculator computes the active earth pressure coefficient (Ka), base pressure, total lateral force, and the height of the resultant force, with optional support for uniform surcharge loads.
When to use
Designing smooth, vertical retaining walls backfilled with dry, cohesionless soil.
Estimating lateral earth pressures and resultant force locations for preliminary geotechnical design.
Evaluating the impact of uniform surcharge loads on the lateral pressure distribution of a retaining structure.
How it works
1Input the soil friction angle (φ) in degrees, the wall height (H) in meters, and the soil unit weight (γ) in kN/m³.
2Optionally enter a uniform surcharge load (q) in kPa acting on the backfill surface.
3The tool calculates the active earth pressure coefficient (Ka) using the formula Ka = tan²(45° − φ/2).
4It computes the base pressure, total lateral force, and the height of the resultant force above the wall base.
Use cases
Geotechnical engineers sizing gravity or cantilever retaining walls in granular soils.
Civil engineering students verifying homework calculations for lateral earth pressure distributions.
Structural designers calculating lateral load inputs for retaining wall stability checks against sliding and overturning.
Examples
1. Standard Retaining Wall with Cohesionless Backfill
Geotechnical Engineer
Background
Designing a 5-meter-high concrete retaining wall backfilled with clean sand.
Problem
Determine the lateral active earth pressure coefficient, total force per meter, and the resultant force location to perform stability checks.
How to use
Enter 30 for the friction angle, 5 for the wall height, and 18 for the soil unit weight. Leave the surcharge field blank.
Outcome
The tool calculates a Ka of 0.3333, a base pressure of 30.00 kPa, a total lateral force of 75.00 kN/m, and a resultant height of 1.67 meters above the base.
2. Retaining Wall with Surface Surcharge
Structural Designer
Background
A 5-meter retaining wall has a roadway nearby, imposing a uniform surcharge load of 10 kPa on the backfill surface.
Problem
Calculate the combined lateral force from both the soil and the surcharge, along with the new resultant height.
How to use
Enter 30 for the friction angle, 5 for the wall height, 18 for the soil unit weight, and 10 for the surcharge.
Outcome
FAQ
What is Rankine's active earth pressure theory?
It is a method that assumes a plastic equilibrium state in a soil mass behind a smooth, vertical retaining wall to calculate lateral earth pressure.
Can this calculator handle cohesive soils?
No, this calculator is designed specifically for cohesionless (granular) soils where cohesion (c) is zero.
How does a surcharge load affect the resultant height?
A uniform surcharge adds a rectangular pressure distribution, which shifts the resultant force height upward compared to soil pressure alone.
What units should I use for the inputs?
Use degrees for the friction angle, meters for wall height, kN/m³ for soil unit weight, and kPa for surcharge.
Does this tool account for wall friction or sloping backfills?
No, Rankine's basic theory assumes a smooth vertical wall and a horizontal backfill surface.
The tool outputs a total lateral force of 91.67 kN/m (75.00 kN/m from soil and 16.67 kN/m from surcharge) and a resultant height of 1.82 meters above the base.