| Scenario | State | H (m) | φ (°) | q (kPa) | Water depth from top (m) | K | P (kN/m) | y above base (m) |
|---|---|---|---|---|---|---|---|---|
| Granular, dry backfill | active | 4.00 | 32.0 | 10.0 | 4.00 | 0.3073 | 56.54 | 1.48 |
| Water table mid-height | active | 6.00 | 30.0 | 15.0 | 3.00 | 0.3333 | 173.43 | 1.99 |
| At-rest, moderate surcharge | at rest | 5.00 | 28.0 | 20.0 | 5.00 | 0.5305 | 169.11 | 1.93 |
This tool estimates lateral earth pressure using standard coefficients and integrates the pressure diagram to find total thrust and its line of action.
- Effective vertical stress at depth z: dry zone uses σ′v = γ z; below water uses submerged unit weight γ′ = γ_sat − γ_w.
- Earth pressure coefficient: Active Ka = tan²(45° − φ/2), Passive Kp = tan²(45° + φ/2), At-rest K0 ≈ 1 − sinφ.
- Sloping backfill option (Active): Ka = cosβ · (cosβ − √(cos²β − cos²φ)) / (cosβ + √(cos²β − cos²φ)) (requires β ≤ φ).
- Surcharge adds a uniform lateral component: pq = K · q.
- Cohesion (approx.): Active reduces pressure by 2c√K; Passive increases by 2c√K. At-rest cohesion is omitted by default.
- Hydrostatic water pressure below the water table: pw = γw(z − zwt).
- Resultant thrust: P = ∫ p(z) dz, and moment about base: M = ∫ p(z) · y(z) dz. Line of action is y = M / P.
- Select your unit system and the earth pressure state.
- Enter the wall height, friction angle, and unit weights.
- Add surcharge, cohesion, and water table depth if present.
- Turn on the tension crack cap for cohesive active cases.
- Click Calculate to view results above the form.
- Download CSV or PDF to attach with submittals.
After calculating, you can export the last result set:
- CSV is ideal for spreadsheets and logs.
- PDF provides a clean, printable summary page.
1) Why earth pressure drives wall sizing
Lateral earth pressure is often the controlling action for small and mid-height retaining walls. For granular backfill with φ around 30° to 34°, the active coefficient commonly falls near 0.28 to 0.33, meaning only about one third of vertical stress becomes lateral demand at the wall face.
2) Understanding active, at-rest, and passive states
Active pressure applies when the wall can move slightly outward; at-rest applies when movement is restrained; passive develops when the wall pushes into soil. For φ = 30°, typical K values are about Ka ≈ 0.33, K0 ≈ 0.50, and Kp ≈ 3.00, showing how strongly the selected state affects thrust.
3) Unit weight and height change forces quickly
Soil unit weight is usually 17 to 20 kN/m³ for common fills, and the pressure diagram grows with depth. Because the soil component is roughly proportional to H², increasing wall height from 4 m to 6 m can raise thrust by about (6/4)² ≈ 2.25 times, even before adding surcharge.
4) Surcharge loads add a uniform lateral block
Uniform surcharge, such as traffic or storage, adds a constant lateral component of K·q along the wall. For Ka = 0.33 and q = 15 kPa, surcharge contributes about 5 kPa everywhere, increasing total thrust by roughly 5·H kN/m per meter of wall length.
5) Water table and hydrostatic pressure
Water is often more critical than soil. Hydrostatic pressure rises linearly with depth at γw ≈ 9.81 kN/m³. If the water table is 3 m below the top of a 6 m wall, the water component alone reaches about 29 kPa at the base, adding significant overturning moment.
6) Cohesion and tension crack handling
Cohesive soils can reduce active pressure in theory, but real backfills may crack and lose tensile capacity. The calculator’s tension crack cap prevents negative pressures. This is a practical way to avoid unconservative “suction” results when c is entered for short-term or partially drained conditions.
7) Resultant thrust and line of action
Design checks use the resultant thrust P and its application point y above the base. A triangular soil-only diagram places y near H/3. When surcharge adds a rectangular block or water adds another triangle, y often shifts upward or downward, changing the overturning moment and base reaction demand.
8) Using outputs for field and design decisions
Use the reported pressures to compare drainage options, backfill selection, and surcharge control. Export the CSV for takeoff logs and the PDF for submittals. For critical walls, confirm assumptions with a geotechnical report, consider wall friction, seismic loading, and layered soils, then document final design inputs.
FAQs
1) Which earth pressure state should I select?
Use active for walls that can rotate or translate slightly, at-rest for restrained walls, and passive for resistance in front of the wall. When unsure, consult design criteria or a geotechnical engineer.
2) What water table value should I enter?
Enter the depth from the backfill surface to the groundwater level. If the wall is drained and backfill stays dry, set it equal to wall height. If seepage is expected, enter the realistic highest groundwater elevation.
3) Why does the thrust change so much with height?
Soil pressure increases with depth, so the overall thrust scales roughly with the square of wall height for soil-only conditions. A small increase in height can create a much larger increase in total lateral force and moment.
4) Can I rely on cohesion to reduce the active pressure?
Be careful. Cohesion may be short-term and can be lost due to cracking, wetting, or disturbance. The tool can include cohesion, but many designs conservatively use c = 0 for backfill behind retaining walls.
5) What does the “tension crack cap” do?
It prevents negative lateral pressures in cohesive active cases by setting any computed negative value to zero. This aligns with the practical assumption that soil cannot sustain tension at the wall interface.
6) Are the pressure results total or effective?
Displayed pressures are total lateral pressures at the wall: effective earth pressure plus hydrostatic water pressure below the water table. This approach is useful for structural demand and drainage comparisons.
7) Does the calculator include seismic or wall friction effects?
No. It focuses on common static conditions using standard coefficients, surcharge, cohesion, and water table effects. For seismic zones, special wall systems, or layered soils, apply project standards and a full geotechnical analysis.