This calculator aids engineers by automating the computation of earth pressure necessary for the design of retaining walls. Whether for small residential projects or major public infrastructure, understanding the forces exerted by soil is essential for stability and safety.
Formula of Active Earth Pressure Calculator
Rankine's Earth Pressure Theory
The formula for Rankine active earth pressure for a retaining wall is:
sigma_a = (1 / 2) * gamma * H^2 * K_a
where:
sigma_a= active earth pressuregamma= unit weight of the soilH= height of the retaining wallK_a= Rankine active earth pressure coefficient
The Rankine active earth pressure coefficient (K_a) is calculated as:
K_a = tan^2(45 degrees - (phi / 2))
where:
phi= angle of internal friction of the soil
Coulomb's Earth Pressure Theory
The Coulomb formula for active earth pressure is:
sigma_a = (1 / 2) * gamma * H^2 * K_a
The Coulomb active earth pressure coefficient (K_a) is derived as follows:
K_a = [cos^2(alpha) * (cos(phi) - sqrt(cos^2(phi) - cos^2(beta - alpha)))] / [cos(beta) * cos(alpha + delta) * (1 + sqrt(sin(beta + delta) * sin(phi + alpha) / (cos(beta - alpha) * cos(alpha + delta))))]
where:
alpha= angle of wall frictionbeta= inclination angle of the backfill surfacedelta= angle of soil-wall friction
Table for General Terms and Calculations
This table includes essential terms related to earth pressure calculations, along with some common conversions that can be use without needing to perform calculations each time.
| Term | Definition | Common Values/Conversions |
|---|---|---|
| Sigma_a (σa) | Active earth pressure | Calculated as per formulas provided |
| Gamma (γ) | Unit weight of the soil | Typically 18 kN/m³ (for average soil) |
| H | Height of the retaining wall | Variable, as required by the design |
| Ka | Active earth pressure coefficient | Calculated as per Rankine or Coulomb theory |
| Phi (φ) | Angle of internal friction of the soil | Typically ranges from 25° to 40° |
| Alpha (α) | Angle of wall friction | Typically about 2/3 of φ |
| Beta (β) | Inclination angle of the backfill surface | Dependent on the site conditions |
| Delta (δ) | Angle of soil-wall friction | Typically assumed as 2/3 of φ for estimates |
Example of Active Earth Pressure Calculator
Scenario:
A civil engineer needs to calculate the active earth pressure on a retaining wall that is 5 meters high, with a soil unit weight (γ) of 20 kN/m³ and an angle of internal friction (φ) of 30 degrees. The wall has no friction with the soil (α = 0°).
Calculation using Rankine's Theory:
- Determine Ka: Ka = tan^2(45° - (φ / 2)) = tan^2(45° - (30° / 2)) = tan^2(30°) Ka ≈ 0.333
- Calculate Sigma_a (σa): σa = (1 / 2) * γ * H^2 * Ka = (1 / 2) * 20 kN/m³ * (5 m)^2 * 0.333 σa ≈ 83.25 kN/m²
Interpretation:
The active earth pressure on the retaining wall is approximately 83.25 kN/m². This indicates the lateral pressure exerted by the soil against the structure, which must be considered in the wall's design to ensure stability and safety.
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Most Common FAQs
Active earth pressure refers to the force exerted by soil on a retaining structure when it moves away from the structure, while passive earth pressure is the resistance of soil to being pushed by the structure.
The calculator is designed to provide results within the standard error margins acceptable in civil engineering, based on the inputs of soil properties and structural dimensions.