Foundations · Pile settlement
Pile group settlement & cap load distribution (interaction factors) calculator
Each pile's head stiffness from Randolph & Wroth and the interaction factor α = ln(rm/s)/ln(rm/r0) between every pair. A rigid cap settles uniformly (pile loads from the inverse of the interaction matrix); a flexible cap shares the load equally and settles unevenly. Also the conventional rigid-cap statics with moments, and the group settlement ratio compared with Fleming's n^ω.
Standard: Randolph (1994) interaction factors · Poulos & Davis (1980) · Fleming et al. (2009) · 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 |
|---|---|---|
| Pile coordinates x, y (m) | 0, 0 2.4, 0 4.8, 0 0, 2.4 2.4, 2.4 4.8, 2.4 | |
| Pile diameter | 0.6 | m |
| Pile length | 20 | m |
| Pile modulus | 30 | GPa |
| Soil modulus (average) | 40 | MPa |
| Poisson's ratio | 0.3 | |
| Homogeneity ρ | 0.75 | |
| Vertical load on the cap | 6000 | kN |
| Moment about the x axis | 400 | kNm |
| Moment about the y axis | 600 | kNm |
| Design geotechnical capacity per pile φg·Rug | 1600 | kN |
| Allowable settlement | 25 | mm |
| Allowable differential settlement (flexible cap) | 5 | mm |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Single-pile stiffness k1 | 260.0 | MN/m |
| Influence radius rm | 26.3 | m |
| Rigid cap settlement | 12.75 | mm |
| Group settlement ratio Rs (interaction) | 3.32 | |
| Rs by Fleming n^0.5 | 2.45 | |
| Rigid cap: max / min pile load (axial only) | 1,188 / 624 | kN |
| Rigid cap + moments: max pile load | 1,306 | kN |
| Conventional statics: max / min | 1,118 / 882 | kN |
| Flexible cap: max / min settlement | 13.54 / 12.55 | mm |
| Flexible cap differential settlement | 0.99 | mm |
- ✓ Max pile load (rigid cap + moments) ≤ φg·Rug — 1,306 kN
- ✓ Conventional statics max ≤ φg·Rug — 1,118 kN
- ✓ Rigid cap settlement ≤ allowable — 12.8 mm
- ✓ Flexible cap differential ≤ allowable — 0.99 mm
- ✓ No pile in tension under axial load
Method, formulas and assumptions
- k1 by Randolph & Wroth (1978); interaction α(s) = ln(rm/s)/ln(rm/r0), rm = 2.5ρL(1 − ν), α = 0 beyond rm.
- Rigid cap: equal settlement w; loads P = k1·w·A⁻¹·1, w = P/(k1 Σ(A⁻¹·1)). Flexible cap: equal loads P/n, settlement wi = Σj αij Pj / k1.
- Conventional statics: Pi = P/n + My xi/Σx² + Mx yi/Σy² (rigid cap, equal pile stiffness).
- Elastic superposition of α over-predicts interaction in large groups (intervening piles stiffen the soil); Fleming's Rs = n^ω (ω ≈ 0.4–0.6) is given as a check.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.