Foundations · Pile capacity
Neutral plane, drag force and downdrag settlement (unified method) calculator
Single pile through settling ground. The load curve (dead load plus accumulated negative friction from the top) and the resistance curve (toe resistance plus positive shaft friction from the bottom) intersect at the neutral plane. The drag force is the load gained above it, the maximum pile load is checked against the structural capacity (live load is not added to drag), and the pile settles as much as the ground does at the neutral plane plus elastic shortening.
Standard: Fellenius unified design method (2004, 2020) · AS 2159 Cl 4.4 negative friction · settlement at the neutral plane
Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| Shaft resistance: bottom depth (m), unit shaft resistance (kPa) | 6, 15 14, 30 24, 60 | |
| Diameter | 0.5 | m |
| Length | 24 | m |
| Dead load | 900 | kN |
| Live load | 300 | kN |
| Toe resistance mobilised | 600 | kN |
| Ground settlement at the surface (long term) | 120 | mm |
| Depth where ground settlement becomes zero | 18 | m |
| Pile modulus | 30000 | MPa |
| Structural design capacity φNs | 3500 | kN |
| Allowable pile settlement | 30 | mm |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Neutral plane depth | 14.66 | m |
| Drag force | 580 | kN |
| Maximum pile load (at the neutral plane) | 1,480 | kN |
| Ground settlement at the neutral plane | 22.3 | mm |
| Elastic shortening | 4.5 | mm |
| Pile head settlement | 26.8 | mm |
| Dead + live load (no drag) for geotechnical check | 1,200 | kN |
- ✓ Dead load + drag force ≤ structural capacity — 42 %
- ✓ Pile settlement ≤ allowable — 26.8 mm
- ✓ Neutral plane within the pile
Method, formulas and assumptions
- Load curve Q(z) = Qd + ∫₀ᶻ fs·πD dz (all shaft friction above the neutral plane is negative); resistance curve R(z) = Rt + ∫ᶻᴸ fs·πD dz; the intersection is the neutral plane (Fellenius).
- The structural check uses dead load + drag force; live load and drag force are not combined because transient load reverses the negative friction.
- The pile settles with the ground at the neutral plane (plus elastic shortening): if that settlement is too large, lengthen or improve the toe so the neutral plane moves down.
- Here ground settlement is linear from S0 at the surface to zero at zs; use a consolidation analysis for the real profile.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.