Foundations · Pile settlement
Piled raft: load sharing and load–settlement (Randolph / Poulos) calculator
Raft stiffness from a rigid plate on an elastic half-space, pile-group stiffness from Randolph & Wroth with a group exponent, the raft–pile interaction factor, then the share of load carried by the raft and a tri-linear load–settlement curve that switches to raft-only stiffness once the piles reach capacity (Poulos–Davis–Randolph).
Standard: Randolph (1994) piled raft · Poulos (2001) PDR method · Randolph & Wroth (1978) · AS 2159
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 |
|---|---|---|
| Raft width B | 20 | m |
| Raft length L | 30 | m |
| Total design load (service) | 60000 | kN |
| Soil Young's modulus Es | 30 | MPa |
| Poisson's ratio ν | 0.3 | |
| Soil homogeneity ρ (G at L/2 ÷ G at L) | 0.75 | |
| Number of piles | 24 | |
| Pile diameter | 0.6 | m |
| Pile length | 18 | m |
| Pile modulus Ep | 30 | GPa |
| Group settlement exponent ω (Rs = n^ω) | 0.5 | |
| Ultimate geotechnical capacity per pile | 2600 | kN |
| Raft ultimate bearing pressure | 400 | kPa |
| Allowable settlement | 50 | mm |
| Required overall factor of safety | 2 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Single-pile stiffness k1 | 199.2 | MN/m |
| Pile-group stiffness Kp = k1 n^(1−ω) | 975.7 | MN/m |
| Raft stiffness Kr | 911.2 | MN/m |
| Raft–pile interaction αrp | 0.487 | |
| Piled-raft stiffness Kpr | 1,283.9 | MN/m |
| Raft share of load (elastic) X | 46.8 | % |
| Load at which piles reach capacity P1 | 117.2 | MN |
| Settlement at design load | 46.7 | mm |
| Raft share at design load | 46.8 | % |
| Average pile load | 1,331 | kN |
| Ultimate capacity (piles + raft) | 302.4 | MN |
| Overall factor of safety | 5.04 |
- ✓ Settlement ≤ allowable — 46.7 mm
- ✓ Overall FS ≥ 2 — 5.04
- ✓ Piles not fully mobilised at design load (stiff response) — elastic
Method, formulas and assumptions
- k1 (Randolph & Wroth): P/(w G r0) = [4/(1 − ν) + 2πρ tanh(μL)L/(μL ζ r0)] / [1 + 4 tanh(μL)L/(πλ(1 − ν)μL r0)]
- Kp = k1·n^(1 − ω) (group settlement ratio Rs = n^ω); Kr = E·d/(1 − ν²) with d = √(4BL/π) (rigid circular plate)
- αrp = 1 − ln(rc/r0)/ζ with rc = √(BL/nπ); X = Kr(1 − αrp)/(Kp + Kr(1 − 2αrp)); Kpr = (Kp + Kr(1 − 2αrp))/(1 − αrp² Kr/Kp)
- PDR curve: s = P/Kpr up to P1 = n·Qu/(1 − X), then (P − P1)/Kr is added; ultimate = n·Qu + qult·B·L (block failure to be checked separately).
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.