Rankine Active Earth Pressure
Compute Rankine active earth-pressure coefficient Ka and total active thrust Pa from friction angle φ, unit weight γ and height H.
Inputs
Formula
Fundamentals
Compute Rankine active earth-pressure coefficient Ka and total active thrust Pa from friction angle φ, unit weight γ and height H.
This tool computes Rankine Active Earth Pressure from the formula: Ka = (1−sinφ)/(1+sinφ); Pa = ½·Ka·γ·H²
History
Soil and structural mechanics were systematised in the 19th century, supporting modern civil design.
Engineering applications
Used for retaining, foundation and structural member design.
Glossary
| Friction angle φ | Input parameter |
| Soil unit wt. γ | Input parameter |
| Backfill H | Input parameter |
| Active coeff. Ka | Output result |
| Total active Pa | Output result |
How to use
- Fill in Friction angle φ, Soil unit wt. γ, Backfill H in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Active coeff. Ka, Total active Pa in the results area.
Formula · Worked Example · Knowledge
Formula
核心计算关系：Ka = (1−sinφ)/(1+sinφ); Pa = ½·Ka·γ·H²
输入变量：
- Friction angle φ
phi— ° - Soil unit wt. γ
gamma— kN/m³ - Backfill H
H— m
输出结果：
- Active coeff. Ka
Ka - Total active Pa
Pa— kN/m
假设/适用：Earth pressure uses Rankine/Coulomb active assumptions; passive & surcharge handled separately.
Worked Example
根据公式 Ka = (1−sinφ)/(1+sinφ); Pa = ½·Ka·γ·H²，取 Friction angle φ = 30 °；Soil unit wt. γ = 18 kN/m³；Backfill H = 5 m。
代入计算得：Active coeff. Ka = 0.3333；Total active Pa = 75 kN/m。
Key Points
- Earth pressure uses Rankine/Coulomb active assumptions; passive & surcharge handled separately.
- Check both strength and stability (overturning, sliding).
- Support reactions from static equilibrium; continuous structures need force/displacement method.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Friction angle φ (°) | phi | ° | 30 |
| Soil unit wt. γ (kN/m³) | gamma | kN/m³ | 18 |
| Backfill H (m) | H | m | 5 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Active coeff. Ka | Ka | |
| Total active Pa | Pa | kN/m |
Applications
- Simply-supported/cantilever reactions
- Structural equilibrium analysis
- Shear & moment distribution