Ground engineering · Sand piles & stone columns
Geosynthetic-encased sand columns (GEC) calculator
Sand or gravel columns wrapped in a geotextile sock for very soft clay under an embankment. Without encasement the column bulges at Kp(σ′r0 + 4cu); the sock adds a confining stress 2T/D. Settlement compatibility in the unit cell (soil settles q/n0 · H/Eoed) gives the column and soil stresses; the ring tension needed to hold the column stress is checked against the geotextile's design strength and stiffness (ring strain).
Standard: Hughes & Withers (1974) bulging · encasement confinement Δσ3 = 2T/D (Murugesan & Rajagopal 2006) · Priebe (1995) basic improvement factor · unit-cell settlement compatibility
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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 |
|---|---|---|
| Column diameter | 0.8 | m |
| Spacing | 2 | m |
| Grid | Triangular | |
| Column fill φ′ | 35 | ° |
| Clay undrained strength cu | 8 | kPa |
| In-situ radial stress σ′r0 at the critical depth | 20 | kPa |
| Embankment load | 70 | kPa |
| Soft clay thickness | 10 | m |
| Clay oedometer modulus | 1.2 | MPa |
| Geotextile ring stiffness J | 2500 | kN/m |
| Geotextile ultimate ring strength | 250 | kN/m |
| Combined reduction factor (creep, damage) | 2 | |
| Allowable ring strain | 4 | % |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Area replacement ratio | 14.5 | % |
| Priebe basic improvement factor n0 | 1.62 | |
| Stress on soil / column | 43.3 / 227.1 | kPa |
| Unencased bulging capacity Kp(σ′r0 + 4cu) | 192 | kPa |
| Extra confinement needed | 9.5 | kPa |
| Ring tension needed / design strength | 3.8 / 125.0 | kN/m |
| Ring strain | 0.15 | % |
| Encased column capacity | 1,345 | kPa |
| Settlement without columns | 583 | mm |
| Settlement with columns (s0/n0) | 361 | mm |
- ✓ Column stress ≤ encased capacity — 17 %
- ✓ Ring tension ≤ design strength
- ✓ Ring strain ≤ allowable — 0.15 %
- ✓ Encasement needed (unencased column would bulge)
Method, formulas and assumptions
- Hughes & Withers bulging: q_ult = Kp(σ′r0 + 4cu); encasement adds Δσ3 = 2T/D, so the sock tension needed is T = (σc/Kp − σ′r0 − 4cu)·D/2.
- Priebe n0 = 1 + a[(5 − a)/(4Kac(1 − a)) − 1], Kac = tan²(45 − φc/2); soil stress σs = q/n0 from settlement compatibility, column stress σc = [q − (1 − a)σs]/a.
- Design ring strength = ultimate/RF (creep, installation damage, chemical); ring strain T/J usually limited to 3–5 %.
- Raithel & Kempfert's analytical model is used for final GEC design.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.