Foundations · Pile settlement
Pile group settlement: equivalent raft and settlement ratio calculator
Group of friction piles replaced by an equivalent raft at two-thirds of the embedded length, its plan size spread at 1 in 4 from the outer piles. The vertical stress below the raft spreads 2 : 1 into each compressible layer and the consolidation settlement is Σ mv·Δσ·h; pile shortening above the raft is added. The result is compared with the settlement-ratio estimate s_group = s_single·n^ω.
Standard: Tomlinson (equivalent raft at 2L/3, 1:4 spread) · 2:1 stress distribution · mv consolidation per layer · Fleming et al. settlement ratio Rs = n^ω
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 |
|---|---|---|
| Piles in x | 4 | |
| Piles in y | 3 | |
| Pile spacing | 2 | m |
| Pile diameter | 0.6 | m |
| Pile length | 18 | m |
| Total working load on the group | 9000 | kN |
| Pile modulus | 30000 | MPa |
| Layers below the raft level: thickness (m), mv (m²/MN) | 4, 0.08 5, 0.06 6, 0.04 6, 0.03 | |
| Single-pile settlement at the average pile load | 6 | mm |
| Settlement ratio exponent ω (0.33–0.5) | 0.5 | |
| Allowable group settlement | 50 | mm |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Group plan size (outer piles) | 6.60 × 4.60 | m |
| Equivalent raft depth 2L/3 | 12.00 | m |
| Raft size after 1 : 4 spread | 10.60 × 12.60 | m |
| Raft pressure | 67.4 | kPa |
| Layer 1 (4 m, mv 0.08): Δσ at mid-depth | 48.9 kPa → 15.7 mm | |
| Layer 2 (5 m, mv 0.06): Δσ at mid-depth | 27.6 kPa → 8.3 mm | |
| Layer 3 (6 m, mv 0.04): Δσ at mid-depth | 16.2 kPa → 3.9 mm | |
| Layer 4 (6 m, mv 0.03): Δσ at mid-depth | 10.3 kPa → 1.9 mm | |
| Consolidation settlement below the raft | 29.7 | mm |
| Pile shortening above the raft | 0.8 | mm |
| Group settlement (equivalent raft) | 30.5 | mm |
| Settlement ratio estimate s1·n^ω | 20.8 | mm |
- ✓ Group settlement ≤ allowable — 30.5 mm
- ✓ Spacing ≥ 2.5D
Method, formulas and assumptions
- Tomlinson: the load is applied at 2L/3 on a raft spread at 1H : 4V from the group outline (friction piles); for end-bearing piles put the raft at the toe.
- Δσ at layer mid-depth = Q/[(B + z)(L + z)] (2 : 1); settlement = mv·Δσ·h per layer.
- Pile shortening ≈ 0.75 × average pile load × 2L/3 /(A·Ep).
- Settlement ratio: s_group = s_single·n^ω (ω ≈ 0.5 clay, 0.33 sand; Fleming et al. 2009). Use the larger estimate.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.