Ground engineering · Ground improvement
Footing on sand columns: bearing and settlement calculator
Pad footing on a group of sand (or stone) columns in soft clay. The improved block gets a composite friction angle tanφcomp = a·μc·tanφc and cohesion (1 − a)cu (Barksdale & Bachus, with stress concentration ratio n), giving its bearing capacity by Terzaghi with the allowable pressure; the single-column bulging capacity is also checked. Settlement of the treated zone is the untreated settlement divided by Priebe's factor.
Standard: Barksdale & Bachus (1983) composite strength (stress concentration) · Terzaghi bearing on the improved block · Priebe (1995) improvement factor with load share
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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 |
|---|---|---|
| Footing width (square) | 2.4 | m |
| Founding depth | 0.8 | m |
| Column load on the footing (service) | 900 | kN |
| Sand column diameter | 0.6 | m |
| Columns under the footing | 4 | |
| Column φ′ | 38 | ° |
| Clay cu | 25 | kPa |
| Unit weight | 17 | kN/m³ |
| Stress concentration ratio n | 3 | |
| Column length (treated depth) | 6 | m |
| Clay mv | 0.25 | m²/MN |
| Required factor of safety | 2.5 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Area replacement ratio a | 19.6 | % |
| Composite φ′ / c | 18.3° / 20.1 kPa | |
| Bearing factors Nc / Nq / Nγ | 13.3 / 5.4 / 4.2 | |
| Ultimate bearing (square footing) | 491 | kPa |
| Allowable bearing qu/FS | 196 | kPa |
| Applied pressure | 156 | kPa |
| Column stress (μc·q) / bulging capacity | 337 / 506 | kPa |
| Priebe improvement factor n0 | 2.04 | |
| Settlement untreated / treated | 164 / 81 | mm |
- ✓ Applied pressure ≤ allowable — 80 %
- ✓ Column stress ≤ bulging capacity / 1.5
- ✓ Treated depth ≥ 2B (stress bulb)
Method, formulas and assumptions
- Barksdale & Bachus: μc = n/(1 + (n − 1)a); tanφcomp = a·μc·tanφc; ccomp = (1 − a)cu.
- Terzaghi square footing: qu = 1.3cNc + γDNq + 0.4γBNγ on the composite parameters.
- Column bulging: Kp(σ′r0 + 4cu) with σ′r0 ≈ γ·2d at the bulging depth (Hughes & Withers).
- Settlement: untreated mv·q·0.7Lc (average stress factor) divided by Priebe's n0.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.