Model sloping backfills and rough wall interfaces easily. Get coefficient, pressure, and resultant force outputs. Built for practical retaining wall checks and fast comparison.
| φ | δ | β | θ | H | γ | q | Water depth | Ka | Total thrust | Resultant height |
|---|---|---|---|---|---|---|---|---|---|---|
| 34° | 20° | 8° | 5° | 6 m | 18 kN/m³ | 12 kPa | 2.5 m | 0.32170 | 186.238 kN/m | 1.854 m |
The calculator uses the generalized Coulomb active earth pressure coefficient for a rough wall, sloping backfill, and battered wall face.
Ka = cos²(φ − θ) / [cos²θ × cos(δ + θ) × (1 + √(sin(δ + φ) × sin(φ − β) / (cos(δ + θ) × cos(β − θ))))²]
Where φ is soil friction angle, δ is wall friction angle, β is backfill slope from horizontal, and θ is wall batter from vertical.
Soil pressure at depth z is taken as σh = Ka × γ × z × cosβ.
Soil thrust per meter wall length is Pa,soil = 0.5 × Ka × γ × H² × cosβ.
Surcharge thrust per meter wall length is Pa,q = Ka × q × H × cosβ.
Hydrostatic water thrust is handled separately as Pw = 0.5 × γw × hw², where hw is submerged height behind the wall.
The resultant location above the base is found from the sum of moments divided by the total thrust.
Choose degrees or radians first. Keep every angle in that same unit.
Enter φ, δ, β, and θ carefully. Use the sign convention shown in each label.
Enter wall height, soil unit weight, surcharge, and wall length. Leave water depth blank for dry conditions.
Press Calculate. The result panel appears above the form. Review Ka, thrust, pressure, and resultant height.
Use the CSV button for spreadsheet work. Use the PDF button for a quick report copy.
Check that β stays below φ for this active case. If the geometry is invalid, revise the input values.
Coulomb active earth pressure matters in retaining wall design. It predicts how soil pushes when the wall moves slightly outward. The coefficient links soil weight to lateral pressure. Engineers use it for walls, basements, bridge abutments, and shoring systems.
This calculator handles sloping backfills and wall friction. That makes it more flexible than a simple Rankine check. You can enter soil friction, wall friction, wall batter, surcharge, and water depth. The tool then returns the active pressure coefficient, base pressure, total thrust, and resultant height.
Coulomb theory assumes a planar failure wedge. It also assumes drained granular backfill and a wall that can mobilize active conditions. The pressure usually varies linearly with depth for soil weight. Surcharge adds a uniform lateral component. Water pressure is added separately when water stands behind the wall.
The coefficient becomes sensitive when the backfill slope approaches the soil friction angle. It also changes when wall friction rises. A rough wall often lowers the active thrust compared with a smooth wall. Batter can also shift the result. Because of that, consistent angle definitions are important.
Use the calculator early in design studies. It helps compare options quickly. You can test flatter backfills, drainage improvements, or lower surcharge conditions. That supports safer and more economical wall sizing. It also helps with hand-check verification during reviews.
The reported thrust is per meter length by default. Enter a larger wall length when you need a total project force. The resultant location helps with overturning checks. Base pressure helps with facing, stem, and tieback evaluation. Export tools also make documentation easier for reports and field discussions.
Good engineering judgement still matters. Verify soil parameters from site data. Check whether cohesion, seismic loading, compaction effects, traffic loads, and groundwater fluctuations require a different method. For unusual geometry, confirm the result with detailed geotechnical design procedures and project standards before final construction decisions.
Clear drainage is especially important. Water can dominate the lateral load even when the soil coefficient is moderate. A drained backfill with filters and outlets often improves performance. Always align assumptions with wall movement, backfill compaction, and the governing design code used on the project during design checks.
Ka is the active earth pressure coefficient. It converts vertical soil stress into lateral stress when the wall moves enough to reach the active condition.
Use Coulomb theory when wall friction, wall batter, or backfill slope matters. It is more general than a basic smooth-wall approach.
θ is the wall face inclination measured from vertical. Enter the value that matches your design convention and drawing geometry.
The active Coulomb expression needs a valid failure wedge. When the backfill slope approaches or exceeds soil friction, the square-root term becomes nonphysical.
Yes. Uniform surcharge is converted to a constant lateral pressure using Ka. That load is added to the triangular soil pressure.
Water pressure is added separately as hydrostatic pressure below the entered water depth. It does not change Ka in this simplified drained-soil workflow.
Yes. The main thrust and moment values are first calculated per meter of wall. Enter wall length to get total project force and moment.
No. It is a practical calculation tool. Final design should still consider project code rules, drainage, compaction, seismic effects, and site investigation data.
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.