Calculator inputs
Use wall batter as the angle from vertical. Use backfill slope as the angle from horizontal.
Formula used
Kp = cos²(φ + θ) / [ cos²θ × cos(δ − θ) × (1 − √( sin(δ + φ) × sin(φ + β) / ( cos(δ − θ) × cos(β − θ) ) ))² ]
Psoil = 0.5 × γ × H² × Kp
Psurcharge = q × H × Kp
Pcohesion = 2 × c × H × √Kp
Ptotal = Psoil + Psurcharge + Pcohesion
This page combines the Coulomb passive coefficient with soil weight, uniform surcharge, and an optional cohesion term.
Top pressure uses surcharge and cohesion. Base pressure adds the depth-dependent soil pressure.
For critical design, verify whether a curved passive failure method is more appropriate.
How to use this calculator
- Enter wall height and soil unit weight.
- Enter the soil friction angle and wall friction angle.
- Add backfill slope and wall batter if they exist.
- Enter uniform surcharge and cohesion when needed.
- Click the calculate button to generate Kp and thrust.
- Review the graph, pressure values, and resultant location.
- Download the result as CSV or PDF for reporting.
- Check warnings before using values for final design decisions.
Example data table
| Case | H (m) | φ (°) | δ (°) | β (°) | q (kPa) | c (kPa) | Kp | Total thrust (kN/m) | Base pressure (kPa) |
|---|---|---|---|---|---|---|---|---|---|
| Level backfill, smooth wall | 4.00 | 30.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.0000 | 432.000 | 216.000 |
| Surcharge and wall friction | 5.00 | 32.00 | 8.00 | 4.00 | 12.00 | 0.00 | 4.9884 | 1,484.039 | 533.755 |
| Cohesive backfill review | 6.00 | 35.00 | 10.00 | 2.00 | 15.00 | 8.00 | 5.8102 | 2,845.987 | 822.942 |
Frequently asked questions
1. What does this calculator estimate?
It estimates Coulomb passive earth pressure coefficient, pressure distribution, component thrusts, total thrust, and the resultant location above the wall base.
2. When should passive pressure be checked?
Check passive pressure when a wall, toe, key, or embedded element mobilizes resistance by moving into soil.
3. What angle is wall batter here?
Wall batter is entered as the wall face angle measured from vertical. Zero means a vertical wall face.
4. Does the calculator include surcharge?
Yes. A uniform surcharge is converted into an added rectangular passive pressure block using the same passive coefficient.
5. How is cohesion handled?
Cohesion is added as a constant passive contribution using 2c√Kp. Verify whether long-term design should reduce or ignore cohesion.
6. Is Coulomb always safe for passive design?
No. Passive resistance may be overestimated when wall friction is high because real passive failure surfaces are often curved.
7. Why might the calculator reject my inputs?
Some angle combinations make the coefficient undefined. Reduce slope, wall friction, or wall batter until the square-root and denominator remain valid.
8. What units should I use?
Use meters for height, kN/m³ for unit weight, kPa for surcharge and cohesion, and degrees for all angles.