Model wall resistance with Coulomb passive equations. Test batter, soil friction, surcharge, and depth quickly. See clean results, export files, and review design notes.
| Case | φ (deg) | δ (deg) | β (deg) | θ (deg) | γ (kN/m³) | H (m) | q (kPa) | Kp | Total thrust (kN/m) |
|---|---|---|---|---|---|---|---|---|---|
| Case A | 30 | 10 | 0 | 0 | 18 | 4 | 0 | 4.1433 | 596.635 |
| Case B | 34 | 16 | 8 | 0 | 18 | 5 | 12 | 10.0910 | 2,875.921 |
| Case C | 38 | 12 | 5 | 6 | 19 | 6 | 20 | 6.9481 | 3,210.030 |
The calculator uses the Coulomb passive earth pressure coefficient:
Kp = cos²(φ + θ) / [cos²θ × cos(δ − θ) × (1 − √((sin(φ + δ) × sin(φ + β)) / (cos(δ − θ) × cos(β − θ))))²]
Then it computes passive wall-face stress at depth z as:
σp(z) = Kp × (γz + q)
Soil thrust from self weight is:
Psoil = 0.5 × Kp × γ × H²
Surcharge thrust is:
Pq = Kp × q × H
Total wall-face thrust is:
Ptotal = Psoil + Pq
The code also estimates the horizontal component using cos(δ − θ). Use the reduced thrust only when your design method accepts a safety factor in that form.
Passive earth pressure is the resistance developed when a wall moves into soil. Designers use it for embedded walls, toe checks, shear keys, and sliding resistance studies. The coefficient links geometry and soil strength to pressure. A better coefficient gives better first-pass design numbers.
Soil friction angle usually has a strong effect. A higher φ often raises passive resistance. Wall friction also changes the answer. Backfill slope and wall batter modify the wedge geometry. Unit weight, wall height, and surcharge then scale the final thrust and depth stress values.
Kp is dimensionless. It is the main coefficient. The stress at depth z shows the estimated wall-face pressure at one point. The base stress gives the largest value in a linear distribution. Soil thrust is the triangular part. Surcharge thrust is the rectangular part. Their sum is the total wall-face thrust.
The plot shows how stress builds with depth. That makes it easier to compare a no-surcharge case with a loaded backfill case. It also helps you see when a large coefficient creates steep pressure growth. Quick visual checks can catch odd input combinations before design review.
Coulomb passive pressure is useful for screening and teaching. Still, engineers should be careful with high wall friction, steep slopes, layered soils, groundwater, and special construction stages. Those cases may need more refined methods, project criteria, and local code checks before final design.
Kp is the passive earth pressure coefficient. It converts vertical stress into passive wall pressure for the selected geometry and friction conditions.
Wall friction changes the force direction and the wedge equilibrium. Even modest δ values can raise or destabilize the calculated passive resistance.
Certain angle combinations make the square-root or denominator invalid. That usually means the chosen geometry is outside the stable range of this closed-form equation.
Yes. A uniform surcharge adds a rectangular pressure block. The calculator includes it in depth stress and total thrust outputs.
No. Add hydrostatic and seepage effects separately. Water can control the design and should not be ignored in retaining wall work.
Use it for calculation support and early checks. Final design should follow project criteria, geotechnical reports, drainage assumptions, and code requirements.
Some workflows apply a factor of safety to passive resistance. This field helps compare nominal resistance with a reduced design value.
Use a consistent set. This page assumes angles in degrees, length in meters, unit weight in kN/m³, and stress or surcharge in kPa.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.