Rankine Earth Pressure Calculator (Retaining Wall Thrust)
Active and passive earth pressure coefficients and the horizontal thrust on a retaining wall per metre, from the soil's friction angle, unit weight and the wall height.
Results
The dashed line marks the value you entered.
What this tool does
Rankine's theory treats the soil behind a smooth, vertical wall with a level surface as being on the point of failing: the pressure then grows in a straight line with depth, which makes the resultant thrust ½·Ka·γ·H² act at one third of the height above the base. For a friction angle of 30° the active coefficient is exactly 1/3 and the passive one is 3. It is for dry, cohesionless soil only — water behind the wall, a surcharge, clay cohesion or a sloping fill all change the answer — and a wall that cannot move is loaded closer to the at-rest value, about 1 − sin φ.
Formula
Ka = tan²(45° − φ/2) · Kp = tan²(45° + φ/2) · P = ½ Ka γ H² per metre, acting at H/3 above the base
Variables
| Symbol | Meaning | Unit |
|---|---|---|
ph | Soil friction angle φ | ° |
ga | Unit weight of the soil | kN/m³ |
h | Height | m |
PA | Active thrust per metre of wall | kN/m |
KA | Active coefficient Ka | — |
KP | Passive coefficient Kp | — |
ZA | Height of the thrust above the base | m |
SA | Active pressure at the base | kPa |
PP | Passive thrust per metre of wall (same height) | kN/m |
Worked example
- Soil friction angle φ30 °
- Unit weight of the soil18 kN/m³
- Height3 m
- Active thrust per metre of wall27.0 kN/m
- Active coefficient Ka0.333
- Passive coefficient Kp3.000
- Height of the thrust above the base1.00 m
- Active pressure at the base18.0 kPa
- Passive thrust per metre of wall (same height)243.0 kN/m
Limitations
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.