Formula used
This tool uses Rankine earth pressure theory for a level backfill: Ka = (1 − sinφ)/(1 + sinφ), Kp = (1 + sinφ)/(1 − sinφ).
Passive resistance is reduced for safety: Kp′ = Kp / FS.
A simplified cantilever equilibrium is then formed by summing moments about the dredge line: ΣM = 0, which leads to a cubic equation in embedment depth D. The calculator solves this cubic numerically and then applies your embedment increase.
Important: This is a simplified estimate and does not replace project-specific geotechnical design.
How to use this calculator
- Select your units and enter excavation depth H.
- Enter surcharge q and friction angle φ.
- Provide unit weight γ and effective unit weight γ′.
- Choose a passive safety factor and embedment increase percentage.
- Click calculate, then download results as CSV or PDF.
Example data table
| Case | H (m) | q (kN/m²) | φ (°) | γ (kN/m³) | γ′ (kN/m³) | FS | D (with increase) (m) | Mmax (kN·m/m) |
|---|---|---|---|---|---|---|---|---|
| Sample | 4.0 | 10.0 | 32 | 18.0 | 9.0 | 1.50 | 9.19 | 338.5 |
- Level backfill, no wall friction, and simplified cantilever equilibrium.
- Effective unit weight is applied for embedment zone calculations.
- Does not include stratified soils, seismic loading, or staged excavation.
Practical notes for sheet pile embedment planning
1) Why embedment depth controls performance
Embedment provides passive resistance below the dredge line, balancing active pressures above. In many temporary excavations, preliminary embedment often falls near 0.7H to 1.3H, depending on soil strength, water, and surcharge. A small increase in depth can noticeably reduce rotation, lowering bending demand and improving serviceability.
2) Input ranges commonly seen on projects
For granular backfill, friction angle φ frequently ranges from 28° to 38°. Total unit weight γ is often 17–20 kN/m³ (or 105–125 pcf). Typical uniform surcharge values used for planning are 5–20 kN/m² (or 100–400 psf) when adjacent traffic or storage is possible.
3) Earth pressure coefficients you can sanity-check
Using Rankine theory for level backfill, approximate values are: φ=30° → Ka≈0.33, Kp≈3.00; φ=35° → Ka≈0.27, Kp≈3.69; φ=40° → Ka≈0.22, Kp≈4.60. If your input φ is low, expect higher active pressure and deeper embedment.
4) How surcharge changes demand
A uniform surcharge adds a rectangular lateral pressure Ka·q along the retained height. This increases both total thrust and bending moment even when excavation depth remains constant. When the work zone may be loaded later, model the surcharge conservatively and compare results with and without it.
5) Water and effective unit weight
Below the water table, effective or submerged unit weight γ′ better represents soil resistance. A practical estimate is γ′ ≈ γsat − γw, often 8–11 kN/m³ (or 50–70 pcf) for sands. Lower γ′ reduces passive resistance, usually increasing required embedment.
6) Passive safety factor and conservatism
Field conditions, disturbance, and construction tolerances can reduce mobilized passive pressure. This calculator applies Kp′ = Kp/FS. Values near 1.25 may suit controlled conditions, while 1.5–2.0 is common when variability is expected. Increasing FS generally increases embedment and reduces sensitivity to uncertainty.
7) Interpreting moment and section demand
Maximum moment is a key driver for selecting a sheet section. If you provide allowable bending stress, the tool estimates required section modulus from S = M/σallow. For early-stage planning, compare several input cases (low/high φ, with/without surcharge) to understand the controlling scenario.
8) Quality checks before you rely on the result
Confirm backfill slope, staged excavation, and any tiebacks or struts, since they can change behavior. Verify units, especially when switching between metric and imperial. Use the example row as a quick reasonableness check, then document assumptions with the CSV or PDF for review.
FAQs
It represents a simplified cantilever sheet pile estimate for level backfill. It is useful for preliminary sizing, but final design should reflect project staging, support conditions, and verified soil parameters.
Use total unit weight above the dredge line where soil is not submerged. Use effective or submerged unit weight for the embedment zone when groundwater is present, because buoyancy reduces resistance.
The factor reduces passive resistance by lowering Kp to Kp′. Higher values add conservatism, typically increasing embedment and lowering the risk of overestimating passive support under imperfect field conditions.
Designers often add depth to improve stiffness and reduce deflection. The increase is an allowance beyond the theoretical equilibrium depth, supporting constructability and serviceability when tolerances, soil variability, or water effects are uncertain.
Use the value consistent with your material grade, corrosion allowance, and design approach. If you only need embedment, enter a representative stress; if selecting a section, match the value to your structural checks and specifications.
No. The coefficients are based on a level backfill and no wall friction. Sloping ground, surcharges near the edge, and wall-soil interface friction can change pressures and should be handled with a project-specific method.
Differences can come from layered soils, partial saturation, construction sequence, driving disturbance, or support systems. Use this as a planning baseline, then refine with geotechnical inputs, groundwater levels, and an analysis method aligned with the project’s risk profile.