This tool simplifies the complex calculations needed to assess the active soil pressure on retaining walls and other structures, using established soil mechanics principles such as those formulated by Rankine.
Formula of Active Soil Pressure Calculator
Rankine’s Active Earth Pressure Coefficient (Ka)
- Calculation:
- Ka = (1 – sin(φ)) / (1 + sin(φ))
- Where φ (phi) is the internal angle of friction of the soil.
Active Earth Pressure (Pa)
- Formula:
- Pa = 0.5 * γ * H^2 * Ka
- Where:
- γ (gamma) is the unit weight of the soil.
- H is the height of the retaining wall.
Horizontal Component of Active Earth Pressure (Pah)
- Computation:
- Pah = Pa * cos(δ)
- Where δ (delta) is the wall friction angle.
Vertical Component of Active Earth Pressure (Pav)
- Computation:
- Pav = Pa * sin(δ)
Table for General Terms and Calculations
This table provides a clear overview of key terms related to active soil pressure calculations, along with some standard values or conversion factors to assist users in understanding and applying these calculations without needing to perform complex computations each time.
| Term | Definition | Standard Values/Conversions |
|---|---|---|
| φ (phi) | Internal angle of friction of the soil | Ranges typically between 25° to 40° |
| γ (gamma) | Unit weight of the soil | Commonly around 18 kN/m³ for most soils |
| H | Height of the retaining wall | Measured in meters (m) or feet (ft) |
| Ka | Active earth pressure coefficient | Calculated using φ |
| Pa | Active earth pressure | Calculated as 0.5 * γ * H^2 * Ka |
| δ (delta) | Wall friction angle | Typically assumed to be between 0.5 * φ and 0.67 * φ |
| Pah | Horizontal component of active earth pressure | Calculated as Pa * cos(δ) |
| Pav | Vertical component of active earth pressure | Calculated as Pa * sin(δ) |
Example of Active Soil Pressure Calculator
Scenario:
Consider designing a retaining wall where the height of the wall (H) is 5 meters, the unit weight of the soil (γ) is 18 kN/m³, and the internal angle of friction (φ) is 30 degrees. Assume the wall friction angle (δ) is 15 degrees.
Step-by-Step Calculation:
- Calculate the Active Earth Pressure Coefficient (Ka):
- Ka = (1 – sin(30 degrees)) / (1 + sin(30 degrees)) = (1 – 0.5) / (1 + 0.5) = 0.5 / 1.5 ≈ 0.333
- Calculate the Active Earth Pressure (Pa):
- Pa = 0.5 * 18 kN/m³ * (5 m)^2 * 0.333 ≈ 75 kN/m²
- Determine the Horizontal Component of Active Earth Pressure (Pah):
- Pah = 75 kN/m² * cos(15 degrees) ≈ 72.5 kN/m²
- Determine the Vertical Component of Active Earth Pressure (Pav):
- Pav = 75 kN/m² * sin(15 degrees) ≈ 19.4 kN/m²
Interpretation:
This example calculates that the horizontal component of the active earth pressure exerted on the retaining wall is approximately 72.5 kN/m², while the vertical component is about 19.4 kN/m². These calculations are crucial for designing the wall to withstand the soil’s forces, ensuring its stability and safety.
Most Common FAQs
Active soil pressure represents the minimum pressure exerted by the soil on a structure, crucial for designing stable retaining walls.
The calculator uses standard formulas recognized in geotechnical engineering, ensuring high accuracy as long as input data is correct.