Calculator
Example Data Table
| Mode | φ (°) | δ (°) | β (°) | θ (°) | H (m) | γ (kN/m³) | q (kPa) | K | Total force (kN/m) |
|---|---|---|---|---|---|---|---|---|---|
| Active | 30.00 | 10.00 | 0.00 | 0.00 | 6.00 | 18.00 | 0.00 | 0.30847 | 99.943 |
| Active | 34.00 | 12.00 | 5.00 | 3.00 | 7.00 | 19.00 | 12.00 | 0.29755 | 163.506 |
| Passive | 32.00 | 15.00 | 0.00 | 0.00 | 5.00 | 18.00 | 8.00 | 5.54085 | 1,468.326 |
Formula Used
Active: Ka = cos²(φ − θ) / [cos²θ × cos(δ + θ) × (1 + √Ra)²]
Ra = [sin(φ + δ) × sin(φ − β)] / [cos(δ + θ) × cos(β − θ)]
Passive: Kp = cos²(φ + θ) / [cos²θ × cos(δ − θ) × (1 − √Rp)²]
Rp = [sin(φ + δ) × sin(φ + β)] / [cos(δ − θ) × cos(β − θ)]
Lateral pressure at depth z is taken as p(z) = K(γz + q).
Soil force = 0.5 × K × γ × H².
Surcharge force = K × q × H.
Total resultant height is taken from the combined triangle and rectangle pressure blocks.
How to Use This Calculator
- Enter the soil friction angle, wall friction angle, and backfill slope angle.
- Enter wall inclination from vertical. Use zero for a vertical wall.
- Add soil unit weight, retained height, and any uniform surcharge.
- Select active, passive, or both states.
- Press the calculate button to show the result block above the form.
- Review the coefficient, pressures, total force, and resultant location.
- Export the visible results to CSV or PDF when needed.
Coulomb Earth Pressure Coefficient Guide
Why this coefficient matters
Coulomb earth pressure coefficients help engineers estimate lateral soil action on retaining structures. The method is useful when wall friction, wall batter, and sloping backfill must be included. That makes it more flexible than very simple earth pressure assumptions. A practical coefficient improves checks for sliding, overturning, structural design, and foundation demand.
What the calculator evaluates
This calculator estimates active pressure, passive resistance, or both. It accepts soil friction angle, wall friction angle, backfill slope, and wall inclination. It also includes retained height, soil unit weight, and a uniform surcharge. The result set shows the coefficient, equivalent fluid value, top pressure, base pressure, total force, and resultant height above the base.
How the inputs affect the answer
Higher soil friction usually reduces active pressure and increases passive resistance. Added surcharge increases lateral demand at every depth. A sloping backfill can raise the active coefficient. Wall friction changes the interaction between soil and structure. Wall inclination also matters because the geometry changes the assumed wedge and the force balance.
How to interpret the outputs
Use the coefficient with care. The coefficient is only part of retaining wall design. You still need drainage review, groundwater review, load combinations, and structural checks. The equivalent fluid value helps when preparing a quick design load. The resultant height helps when calculating moments and comparing design alternatives.
Common design workflow
Start with realistic soil parameters from testing or approved geotechnical reports. Enter the wall geometry exactly as shown on the section drawing. Then review the active case for retained fill loading. Review the passive case separately if the design is allowed to rely on soil resistance. Compare the force level and line of action before moving into structural design.
Good engineering practice
Keep angle conventions consistent across your design sheets. Confirm whether the project uses active, passive, or at-rest assumptions. Passive resistance should be applied carefully and often with code limits. Field conditions, compaction, water, layered soils, and cohesion can change behavior. This tool is best for fast preliminary checks and disciplined design comparisons.
Use the results carefully
Closed-form equations are efficient, but they still depend on reasonable assumptions. Real walls may face drainage issues, compaction loads, seismic demand, traffic loads, and construction tolerances. Always confirm project standards and local codes. The calculator is strong for organized preliminary work, option screening, and clear documentation during design development.
FAQs
1. What does the Coulomb coefficient represent?
It represents the ratio used to convert vertical soil stress into lateral earth pressure. It helps estimate active pressure or passive resistance for retaining wall calculations.
2. When should I choose active pressure?
Choose active pressure when the wall can move slightly away from the backfill. That small movement allows the soil to mobilize a lower lateral stress state.
3. When is passive resistance appropriate?
Choose passive resistance when the wall or footing pushes into soil. Engineers usually apply it carefully because construction disturbance can reduce the available resistance.
4. What angle should I enter for wall inclination?
Enter the wall back face inclination from vertical. Use zero for a vertical wall. Positive values should match your design convention consistently.
5. Does surcharge change only the bottom pressure?
No. A uniform surcharge adds a constant rectangular pressure block over the full height. It increases top pressure, bottom pressure, and the total resultant force.
6. Can I use this tool for cohesive soil?
This page focuses on frictional Coulomb coefficients and surcharge effects. Cohesion, water pressure, and layered soil behavior need additional engineering treatment outside this simplified setup.
7. Why do some angle combinations fail?
Some combinations create invalid geometry for the selected closed-form expression. That can make the square-root term or denominator nonphysical, so the calculator warns you.
8. Is this enough for final retaining wall design?
No. Use it for preliminary design, checking, and comparison. Final design should also include drainage, structural capacity, settlement, sliding, overturning, bearing, and code review.