Foundations · Pile settlement
Pile load–settlement curve: Fleming hyperbolic (CEMSET) calculator
Predicts the full load–settlement curve of a single pile from its ultimate shaft and base capacities. Shaft load follows Ps = Us·Δ/(Ms·Ds + Δ) with the flexibility factor Ms; base load follows Δb = 0.6·Ub·Pb/[Db·Eb(Ub − Pb)]; elastic shortening of the shaft and any free length is added. Reports the settlement at the working load and at 1.5 × working load, the share carried by the base and the load at 10 % of the diameter.
Standard: Fleming (1992) hyperbolic shaft and base functions (CEMSET) · elastic shortening with Ke = 0.5 · interpretation of maintained load tests
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 |
|---|---|---|
| Ultimate shaft capacity Us | 2500 | kN |
| Ultimate base capacity Ub | 1800 | kN |
| Shaft diameter Ds | 0.75 | m |
| Base diameter Db | 0.75 | m |
| Shaft flexibility factor Ms | 0.002 | |
| Soil modulus below the base (at 25 % of Ub) | 60 | MPa |
| Embedded length | 20 | m |
| Free (unsupported) length | 0 | m |
| Pile modulus | 30 | GPa |
| Working load | 2000 | kN |
| Allowable settlement at the working load | 15 | mm |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Settlement at the working load | 5.3 | mm |
| Shaft / base load at the working load | 1,765 / 235 | kN |
| Settlement at 1.5 × working load | 18.7 | mm |
| Load at 10 % of the base diameter | 3,815 | kN |
| Factor of safety on the ultimate (Us + Ub) | 2.15 |
- ✓ Working-load settlement ≤ allowable — 5.3 mm
- ✓ Overall FS ≥ 2.0
Method, formulas and assumptions
- Shaft: Δs = Ms·Ds·Ps/(Us − Ps), i.e. Ps = Us·Δ/(Ms·Ds + Δ); Ms ≈ 0.001–0.002 stiff clay, 0.002–0.004 sand.
- Base: Δb = 0.6·Ub·Pb/[Db·Eb(Ub − Pb)] with Eb the secant modulus at 25 % of the base capacity.
- Shortening = (Pb + Ke·Ps)·L/(A·Ep) + P·Lo/(A·Ep), Ke = 0.5 for uniform friction.
- Fit Ms and Eb to a maintained load test (CEMSET back-analysis) before relying on predictions.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.