| H (m) | Bt (m) | Bh (m) | γ (kN/m³) | φ (deg) | q (kPa) | Hw (m) | FS Sliding | FS Overturning | qmax (kPa) |
|---|---|---|---|---|---|---|---|---|---|
| 4.0 | 1.0 | 2.0 | 18 | 30 | 10 | 0 | ≈ 1.6 | ≈ 2.3 | ≈ 165 |
| 5.0 | 1.2 | 2.6 | 19 | 32 | 15 | 1.5 | ≈ 1.4 | ≈ 2.0 | ≈ 210 |
- Rankine active coefficient (level backfill):
Ka = tan²(45° − φ/2) - Rankine (sloping backfill):
Ka = cosβ·(cosβ − √(cos²β − cos²φ)) / (cosβ + √(cos²β − cos²φ)) - Active soil force:
Pa = 0.5·γ·Ka·H² - Surcharge force:
Pa,q = q·Ka·H - Cohesion reduction (drained approximation):
Pa,c = 2·c·√Ka·H(total horizontal is not allowed below zero) - Water pressure:
Pw = 0.5·γw·Hw² - Overturning FS:
FSot = Mr / Mo - Sliding FS:
FSsl = ( (W − U)·tanφb + cb·B ) / Ptotal - Bearing:
qavg = (W − U)/B,e = B/2 − xR,qmax/min = qavg·(1 ± 6e/B)
- Enter wall geometry: retained height, toe/heel widths, and thicknesses.
- Enter backfill parameters: unit weight, friction angle, and slope.
- Add surcharge if traffic, storage, or slabs load the backfill.
- Include water heights if drainage is uncertain; add under-base head for uplift.
- Set base interface values from geotechnical recommendations (φb and cb).
- Click Calculate Stability, then review sliding, overturning, and bearing checks.
- Export the report using the CSV or PDF buttons in the result panel.
Key stability outputs to review
Use the calculated Ka, total horizontal force, and driving moment to confirm load realism. Typical minimum targets are FS sliding ≥ 1.50 and FS overturning ≥ 2.00 for service conditions. If water is present, hydrostatic force increases with Hw², so even 1.0 m of water adds about 4.9 kN/m pressure at the base. The calculator reports forces per meter length, so multiply by wall length for total load. For preliminary sizing, keep q in the 5–20 kPa range and verify with project load combinations.
Geometry changes that improve safety
Increasing base width B raises resisting moment and reduces bearing stress. A 0.3 m increase in heel width often boosts Mr more than the same increase at the toe because soil weight acts farther from the toe. Thickening the base (Tb) increases W and friction resistance, but verify constructability and settlement limits. A modest toe increase can help reduce eccentricity toward the heel, improving bearing distribution. When adjusting dimensions, recheck qmax and qmin to avoid uplift or tension at the base.
Soil inputs and sensible ranges
Backfill unit weight commonly ranges from 17–20 kN/m³, while φ for clean granular backfill is often 30–38°. Cohesion should be set to 0 for long‑term drained design unless a justified value is provided. For sloping backfill, keep β below φ to remain within Rankine assumptions used here.
Water management and uplift effects
Behind‑wall water height Hw adds lateral force and can control overturning. Under‑base head Hu reduces effective vertical load through uplift Uw = 0.5·γw·Hu·B, lowering both friction and bearing capacity margin. Provide drainage, filters, and outlets so Hw and Hu remain near zero in design scenarios.
Reporting and decision thresholds
Export CSV or PDF for submittals and internal reviews, then document the input basis: soil report date, assumed surcharge, and groundwater conditions. Watch eccentricity: |e| should remain within B/6 to avoid tension at the base. If qmax exceeds allowable qa, widen the base, reduce surcharge, or improve founding conditions.
1) What wall types does this calculator fit best?
It is suited to gravity and cantilever retaining walls where loads can be approximated per meter length, using Rankine active pressure assumptions and simplified self‑weight geometry.
2) Why does the calculator show “EXCEEDS” for eccentricity?
When |e| is greater than B/6, the resultant leaves the middle third, implying possible base tension. Increase base width, shift weight toward the toe, or reduce lateral loads.
3) Should I include cohesion for backfill?
Usually no for long‑term drained design. Cohesion can reduce calculated active force, but it may not persist with cracking, wetting, or disturbance. Use a geotechnically justified value.
4) How do water inputs affect safety factors?
Hw adds hydrostatic lateral force that grows with the square of water depth. Hu creates uplift that reduces effective vertical load, lowering frictional sliding resistance and increasing bearing pressures.
5) What if sliding FS is low but overturning is acceptable?
Increase base width, improve base friction (φb), add a shear key, lower groundwater, or reduce surcharge. Sliding is often controlled by effective vertical load and interface properties.
6) Are the output thresholds always the same?
No. Target factors depend on codes, risk level, load combinations, and site variability. Use the shown checks as a screening tool and confirm final criteria with project requirements.