Ground engineering · Sand piles & stone columns
Sand compaction piles for liquefaction mitigation calculator
Loose sand densified by driving sand compaction piles. At each depth the SPT N gives the relative density and void ratio; the sand pushed in at replacement ratio as reduces the void ratio e1 = e0 − as(1 + e0)·β, giving the improved N. The tool finds the replacement ratio needed to reach the target N in the worst layer, the pile spacing for a square or triangular grid, and the improved profile.
Standard: Japanese SCP densification method (Mizuno et al. 1987; JGS) · Meyerhof Dr–N relation Dr = 21√(N/(0.7 + σ′v/98)) · replacement ratio and spacing
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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 |
|---|---|---|
| Layers: depth (m), SPT N, fines content (%) | 2, 6, 8 4, 8, 10 6, 7, 12 8, 10, 6 10, 12, 5 12, 14, 5 | |
| Groundwater depth | 1.5 | m |
| Unit weight above / below water | 18 | kN/m³ |
| Target SPT N after treatment | 20 | |
| emax | 0.95 | |
| emin | 0.55 | |
| Densification efficiency β (reduce for fines) | 0.9 | |
| Fines content above which SCP is unsuitable | 20 | % |
| Sand pile diameter | 0.7 | m |
| Grid | Triangular |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Governing replacement ratio as | 12.8 | % |
| Pile spacing for d = 0.7 m (triangular) | 1.87 | m |
| z 2 m: N 6 → 20.0 | Dr 51 %, e0 0.746, as needed 12.8 % | |
| z 4 m: N 8 → 23.9 | Dr 55 %, e0 0.732, as needed 10.2 % | |
| z 6 m: N 7 → 22.8 | Dr 48 %, e0 0.759, as needed 11.0 % | |
| z 8 m: N 10 → 32.9 | Dr 54 %, e0 0.734, as needed 6.5 % | |
| z 10 m: N 12 → 38.2 | Dr 56 %, e0 0.726, as needed 4.7 % | |
| z 12 m: N 14 → 42.0 | Dr 58 %, e0 0.719, as needed 3.2 % |
- ✓ Fines ≤ 20 % in every layer (densification effective)
- ✓ Target N reached at every depth
- ✓ Spacing ≥ 1.5 m (constructible) — 1.87 m
Method, formulas and assumptions
- σ′v from the unit weight and groundwater; Dr = 0.21√(N/(0.7 + σ′v/98)) (Meyerhof), e = emax − Dr(emax − emin).
- Densification: e1 = e0 − as(1 + e0)β, with β reduced by fines (× (1 − Fc/50), not below 0.2). The target N fixes e_target and so the required as.
- Spacing: square s = √(Ap/as); triangular s = √(Ap/(as·√3/2)). Confirm by post-treatment SPT/CPT between piles.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.