Foundations · Pile settlement
Pile settlement: elastic and t-z calculator
Head settlement of a single pile by the Randolph & Wroth closed form and by a load-transfer (t-z) analysis with elastic-plastic shaft and base springs. The t-z analysis gives the whole load–settlement curve.
Standard: Randolph & Wroth (1978) elastic · simplified t-z / q-z load transfer
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 |
|---|---|---|
| Diameter D | 0.6 | m |
| Length L | 15 | m |
| Pile modulus Ep | 30000 | MPa |
| Soil shear modulus, shaft average | 20 | MPa |
| Soil shear modulus at toe | 30 | MPa |
| Poisson's ratio ν | 0.3 | |
| Ultimate shaft friction fs | 50 | kPa |
| Ultimate base resistance qb | 3000 | kPa |
| Working load P | 800 | kN |
| Settlement limit | 10 | mm |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| ζ = ln(2.5Lρ(1−ν)/r0) | 4.066 | |
| λ = Ep/GL | 1,000 | |
| μL | 1.109 | |
| Head stiffness k | 387,400 | kN/m |
| Elastic settlement (R&W) | 2.07 | mm |
| t-z settlement at P | 3.71 | mm |
| Ultimate shaft / base | 1,414 / 848 | kN |
- ✓ t-z settlement ≤ limit — 3.7 mm
- ✓ P < ultimate capacity
Method, formulas and assumptions
- Pt/(GL r0 wt) = 4/(1−ν) + 2πρ tanh(μL)L/(ζ μL r0)
- t-z: shaft mobilises fs at 1 % D and base qb at 10 % D (linear-plastic); pile compression from the axial force profile
- Simplified load-transfer model for preliminary design. Use measured or published t-z curves for design.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.