Ground engineering · Consolidation & preloading
Wick drains with preload: time–settlement (Hansbo) calculator
Prefabricated vertical drains in a soft clay under a preload with surcharge. Equivalent drain diameter, influence zone, Hansbo's μ with smear and well resistance, combined radial and vertical consolidation (Carrillo), the settlement under the design load and the preload, and whether the preload removes all design-load primary settlement in the time available.
Standard: Hansbo (1981) smear & well resistance · Barron (1948) · Terzaghi · Carrillo (1942) combined flow
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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 |
|---|---|---|
| Clay thickness | 10 | m |
| Drainage | Two-way (top and bottom) | |
| Vertical coefficient of consolidation cv | 1.5 | m²/yr |
| ch / cv | 2 | |
| Drain pattern | Triangular | |
| Drain spacing | 1.2 | m |
| Drain band width | 100 | mm |
| Drain band thickness | 4 | mm |
| Smear ratio ds/dw | 2.5 | |
| Permeability ratio kh/ks | 2 | |
| Drain discharge capacity qw | 100 | m³/yr |
| Compression index Cc | 0.9 | |
| Initial void ratio e0 | 2 | |
| Initial σ′v at mid-layer | 40 | kPa |
| Design (permanent) load Δσ | 50 | kPa |
| Preload incl. surcharge Δσ | 75 | kPa |
| Time available for preloading | 9 | months |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Equivalent drain diameter dw | 66.2 | mm |
| Influence diameter De | 1.260 | m |
| n = De/dw | 19.0 | |
| μ (smear + well resistance) | 3.14 | |
| Final settlement under design load | 1,057 | mm |
| Final settlement under preload | 1,376 | mm |
| Degree needed to remove design settlement | 76.8 | % |
| Combined U at 9 months | 97.9 | % |
| Settlement at 9 months | 1,348 | mm |
| Time to reach the required degree | 3.50 | months |
| Without drains: Uv at 9 months | 23.9 | % |
- ✓ Preload removes all design-load primary settlement in the time available — 97.9 % vs 76.8 %
- ✓ Preload greater than the design load
Method, formulas and assumptions
- Hansbo: Uh = 1 − exp(−8Th/μ), Th = ch t/De², μ = ln(n/s) + (kh/ks) ln s − 0.75 + (2/3)π l² kh/qw (well resistance averaged over the drain length l).
- dw = 2(a + b)/π; De = 1.05S (triangular) or 1.128S (square). Uv from Terzaghi (Sivakugan & Vigneswaran approximation); combined U = 1 − (1 − Uh)(1 − Uv) (Carrillo).
- Primary settlement s = Cc H/(1 + e0) · log[(σ′0 + Δσ)/σ′0]; required degree under the preload = s(design)/s(preload).
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.