Library / Civil / CIV-46
Civil
Height of the active resultant above the wall base
Height above the base at which the total active thrust acts: the soil-weight force Pγ acts at H/3 and the surcharge force Pq at H/2, so the resultant is their force-weighted average.
- Ref
- CIV-46
- Rev
- v1
- Field
- Civil
- Result
- y [m]
The resultant acts where the moments of the two pressure diagrams balance. The triangular soil force Pγ acts at H/3 above the base and the rectangular surcharge force Pq acts at H/2, so the resultant height is the force-weighted average, y = (PγH/3 + PqH/2)/(Pγ + Pq). It lies between H/3 and H/2, closer to H/2 as the surcharge share grows.
Height above the base at which the total active thrust acts: the soil-weight force Pγ acts at H/3 and the surcharge force Pq at H/2, so the resultant is their force-weighted average. Both forces are per metre of wall. Include any water or other pressure component with its own force and arm.
Calculator
- Total force, Pγ + Pq120,000 N/m
- Overturning moment about the base270,000 N·m/m
- Resultant height as a fraction of H0.375
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The thrust of 120 kN/m acts 2.25 m above the base, 0.375 of the wall height; with no surcharge it would be H/3.
- The overturning moment is 270 kN·m per metre of wall.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| H Wall height | 0.5 to 15 m | 0.1875 | 5.625 | 5.438 | +10% | +10 % |
| P_γ Soil-weight force | 0 to 500,000 N/m | 2.057 | 3 | 0.9434 | +10% | −0.775 % |
| Pq Surcharge force | 0 to 500,000 N/m | 2 | 2.847 | 0.8475 | +10% | +0.813 % |
Sweep of Surcharge force
| Surcharge force (N/m) | Resultant height (m) |
|---|---|
| 0 | 2 |
| 62,500 | 2.41 |
| 125,000 | 2.581 |
| 187,500 | 2.676 |
| 250,000 | 2.735 |
| 312,500 | 2.776 |
| 375,000 | 2.806 |
| 437,500 | 2.829 |
| 500,000 | 2.847 |
Sweep one variable
Variables and how each one contributes
Resultant height
What the equation gives you. Everything else feeds it.
Wall height
The wall height, in m. Raises the resultant height in direct proportion. Raising it by 10 % (to 6.6) moves the result by +10 %, from 2.25 to 2.475 m.
Soil-weight force
The soil-weight force per metre of wall, in N/m. A larger share of triangular pressure lowers the resultant toward H/3. Raising it by 10 % (to 99,000) moves the result by −0.775 %, from 2.25 to 2.233 m.
Surcharge force
The surcharge force per metre of wall, in N/m. A larger share of rectangular pressure raises the resultant toward H/2. Raising it by 10 % (to 33,000) moves the result by +0.813 %, from 2.25 to 2.268 m.
Worked example with the values above
- Moments about the base: Pγ H/3 + Pq H/2 = 180,000 + 90,000 = 270,000 N·m/m.
- Total force: Pγ + Pq = 120,000 N/m.
- y = 270,000 / 120,000 = 2.25 m.
Assumptions and limits
- A vertical smooth wall, level drained cohesionless backfill, and enough wall movement to mobilise the active or passive state.
- Effective stresses for soil strength, with water pressure computed separately.
Common mistakes
- Using total instead of effective stress below the water table.
- Using the active coefficient where the wall cannot move, when at-rest pressure applies.
- Entering the friction angle in degrees where the page needs radians.
Statistics and uncertainty
Earth pressure is among the most uncertain quantities in structural design. The effective friction angle is rarely known to better than ±2° to 3°, which alone changes Ka by 10 % to 15 %, and the wall movement needed to reach the active state is rarely checked. Treat the numbers as estimates with generous margins.
Where it is used
- Designing retaining walls, basement walls and sheet piles.
- Finding overturning moments and sliding forces on walls.
Maths you need
- Effective stress: total stress minus pore water pressure
- Friction angle: the angle whose tangent is the shear to normal stress ratio at failure
- Active and passive states: minimum and maximum lateral stress at limiting equilibrium