Ground engineering · Sand piles & stone columns
Sand compaction piles calculator
Replacement ratio, settlement reduction, composite shear strength, consolidation by radial drainage and sand quantities for sand compaction piles in soft clay.
Standard: Unit-cell replacement · stress concentration · Barron/Hansbo drainage
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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 |
|---|---|---|
| Layout | Triangular | |
| Pile diameter d | 0.7 | m |
| Spacing s | 1.8 | m |
| Soft clay thickness | 10 | m |
| Undrained strength cu | 20 | kPa |
| Coefficient of volume compressibility mv | 1 | m²/MN |
| Applied load Δp (embankment) | 60 | kPa |
| Stress concentration ratio n | 3 | |
| Sand pile φ′ | 30 | ° |
| Sand γ′ (submerged) | 9 | kN/m³ |
| Horizontal coefficient ch | 2 | m²/yr |
| Time after loading | 6 | months |
| Treated plan area | 2000 | m² |
| Sand volume factor (loose → compacted) | 1.3 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Unit-cell area Ae | 2.806 | m² |
| Replacement ratio as | 13.7 | % |
| Stress factor on clay μc | 0.785 | |
| Stress factor on pile μs | 2.354 | |
| Untreated settlement | 600 | mm |
| Treated settlement | 471 | mm |
| Composite shear strength τ (mid-depth) | 32.0 | kPa |
| Equivalent diameter de | 1.89 | m |
| Drain spacing ratio n = de/d | 2.70 | |
| Radial consolidation Uh | 100.0 | % |
| Number of piles | 713 | |
| Sand per pile | 5.00 | m³ |
| Total sand | 3,567 | m³ |
- ✓ Replacement ratio within 10–70 % — 13.7 %
- ✓ Indicative stability 5.14τ / Δp ≥ 1.5 — 2.74
- ✓ Uh ≥ 90 % at the chosen time
Method, formulas and assumptions
- as = Ap/Ae; μc = 1/[1 + (n − 1)as]; μs = n·μc
- Settlement S = μc·mv·Δp·H (settlement-reduction factor β = μc)
- τ = (1 − as)·cu + as·(γ′s·z + μs·Δp)·tan φ′s at z = H/2 (Japanese SCP method, cos²θ term omitted)
- Uh = 1 − exp(−8Th/F), F = ln(de/d) − 0.75 (ideal drain, no smear), Th = ch·t/de²
- Choose n from trials or the literature (typically 2–5); confirm cu gain and settlement with monitoring
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.