Calculator Inputs
Example Data Table
| H (m) | B (m) | φ (deg) | γ (kN/m³) | q (kPa) | Dp (m) | FS Sliding | FS Overturning | qmax (kPa) |
|---|---|---|---|---|---|---|---|---|
| 4.0 | 3.0 | 30 | 18 | 10 | 1.0 | 0.863 | 1.085 | 87.67 |
Formula Used
This tool uses Rankine earth pressure for a level backfill and a simplified gravity-type bulkhead section.
- Ka = tan²(45° − φ/2)
- Soil active force (triangle): Pa,γ = ½·Ka·γ·H²
- Surcharge active force (rectangle): Pa,q = Ka·q·H
- Cohesion correction (optional): Pa,c = −2·c·√Ka·H (clamped so total isn’t negative)
- Hydrostatic force on each side: Pw = ½·γw·hw²
- Overturning moment about toe: sum each force × its lever arm (H/3 for triangles, H/2 for rectangles, h/3 for water).
- Sliding resistance: R = μ·V + Rp·Pp (passive optional and reduced).
- FS sliding: FS = R / Hdrive
- FS overturning: FS = Mresist / Moverturn
- Base eccentricity: x = (Mresist − Moverturn) / V, e = B/2 − x
- Base pressures: qmax/min = (V/B)·(1 ± 6e/B), and check qmin ≥ 0.
How to Use This Calculator
- Choose your units, then enter wall height and base dimensions.
- Provide backfill properties (γ, φ, and optional cohesion).
- Add surcharge and water levels if they apply on site.
- Enter base friction μ and allowable bearing if you want bearing checks.
- Optionally include passive resistance with embedment depth and a reduction factor.
- Press Calculate to view results above the form.
- Use the CSV/PDF buttons to download your latest run.
1) What this bulkhead check covers
This calculator evaluates a gravity-style bulkhead for three core limit states: sliding, overturning, and base bearing. It combines soil, surcharge, and water actions into a single driving set, then compares them against resistance from self-weight, base friction, and optional passive pressure. Results are per meter of wall length for clean scaling.
2) Active pressure data you can sanity-check
With level backfill and Rankine theory, the active coefficient typically falls between about 0.33 (φ≈30°) and 0.22 (φ≈35°). For a 4 m retained height with γ≈18 kN/m³ and φ≈30°, the soil component alone is about 216 kN/m × Ka/2, often landing near 120 kN/m before surcharge and water are added.
3) Surcharge effects are linear with height
Uniform surcharge produces a rectangular lateral pressure of Ka·q across the full height. That means doubling H doubles surcharge force, while soil force scales with H². For quick checks, a 10 kPa surcharge with Ka≈0.33 adds roughly 13 kN/m per meter of wall height, or about 53 kN/m over 4 m.
4) Water levels can dominate the design
Hydrostatic force is ½·γw·h², so it grows rapidly with water depth. One meter of differential water level adds about 4.9 kN/m; three meters adds about 44 kN/m. Because the lever arm is h/3, water can drive overturning even when soil pressures appear modest. Drainage and relief systems often provide the best stability improvement.
5) Passive resistance should be treated cautiously
Passive pressure can materially increase sliding resistance, but field variability and disturbance make it uncertain. The calculator includes a reduction factor (Rp) so you can match conservative practice, commonly 0.3–0.7. Use the embedment depth that is reliably mobilized and avoid relying on passive resistance in front areas that may be excavated later.
6) Reading the factors of safety
Many temporary works adopt FS(sliding) ≥ 1.5 and FS(overturning) ≥ 2.0, while some permanent designs differ by code and load case. If your factors land in the “review” range, first check drainage (water), then geometry (B and Bt), and finally soil parameters. Small increases in base width can significantly reduce eccentricity and peak bearing.
7) Bearing, eccentricity, and the middle-third rule
The base pressure model assumes linear stress distribution. When the resultant stays within the middle third (|e| ≤ B/6), base tension is avoided and qmin remains nonnegative. If qmin drops below zero, consider widening the base, adding heel cover, increasing wall weight, or reducing driving moments through drainage. Always compare qmax to the allowable bearing from the geotechnical report.
8) Practical workflow for site teams
Start with measured geometry and conservative soil parameters from recent logs. Run a dry case (no water) and a wet case (credible water differential) to bracket stability. Save the PDF for daily planning meetings and attach the CSV to design review emails. Re-run whenever excavation depth, surcharge locations, or drainage conditions change.
FAQs
1) Why do my sliding and overturning factors change a lot with water?
Hydrostatic force grows with the square of water depth and acts with an h/3 lever arm. Even moderate differential water levels can add large driving moments compared with soil pressure alone.
2) Should I include cohesion for granular backfill?
Usually no. For drained sands and gravels, set cohesion to zero. Using cohesion can artificially reduce active pressure and may not be mobilized consistently in the field.
3) What does the passive reduction factor represent?
It accounts for uncertainty in mobilizing passive resistance due to disturbance, drainage, and future excavation. Conservative practice often uses 0.3–0.7 depending on site control and code guidance.
4) My qmin is negative. What should I do?
Negative qmin indicates base tension and an eccentric resultant. Increase base width, add heel cover, increase self-weight, or reduce driving forces and moments, typically by improving drainage and lowering water levels.
5) How should I model surcharge near the edge?
This calculator treats surcharge as uniform over the retained height. For localized loads, convert them to an equivalent uniform pressure or use a more detailed lateral pressure method, then compare results for conservatism.
6) Are these checks suitable for sheet pile bulkheads?
Not directly. Sheet piles require embedment and structural analysis using earth pressure diagrams, fixity methods, and bending capacity. Use this tool for gravity-type sections or as a quick screening check only.
7) What results should I keep in a field report?
Record inputs, Ka, net water force, FS sliding, FS overturning, qmax/qmin, and a note on drainage assumptions. Export the PDF for sign-off and the CSV for traceable calculations.