Ground engineering · Sand piles & stone columns
Rigid inclusions (CMC) with a load transfer platform calculator
Grid of rigid inclusions under an embankment or slab with a granular load-transfer platform. Arching by the Marston formula of BS 8006: load on each inclusion head, efficiency, residual stress on the soft soil and its settlement, inclusion stress against a fraction of f′c and the geotechnical capacity. Checks the platform height for full arching.
Standard: BS 8006-1 Marston arching (Cc) · ASIRI (2012) recommendations · AS 3600 plain concrete
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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 |
|---|---|---|
| Grid spacing (square) | 2 | m |
| Inclusion diameter | 0.4 | m |
| Head / cap width (0 = none) | 1 | m |
| Fill + LTP height above heads | 2.5 | m |
| Fill unit weight | 20 | kN/m³ |
| Traffic / uniform surcharge | 20 | kPa |
| Inclusion support | End-bearing (Cc = 1.95H/a − 0.18) | |
| Soft layer thickness | 8 | m |
| Soft layer oedometer modulus | 2.5 | MPa |
| Inclusion concrete f′c | 15 | MPa |
| Allowed fraction of f′c | 0.3 | |
| Geotechnical capacity per inclusion φg·Rug | 400 | kN |
| Allowable soft-soil settlement between heads | 50 | mm |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Equivalent head width a | 1.000 | m |
| Vertical stress at head level σ′v | 70.0 | kPa |
| Arching coefficient Cc | 4.695 | |
| p′c / σ′v = (Cc a / H)² | 3.53 | |
| Load on each inclusion | 246.9 | kN |
| Efficiency (share to inclusions) | 88.2 | % |
| Stress on soil between heads | 11.0 | kPa |
| Soft-soil settlement (upper bound) | 35.3 | mm |
| Inclusion axial stress | 1.96 | MPa |
| Height for full arching 1.4(s − a) | 1.40 | m |
| Area replacement ratio | 3.14 | % |
- ✓ Fill height ≥ 1.4(s − a) (Marston valid, full arching) — 2.50 vs 1.40 m
- ✓ Inclusion stress ≤ 0.3 f′c — 1.96 MPa
- ✓ Inclusion load ≤ φg·Rug — 247 kN
- ✓ Soft-soil settlement ≤ allowable — 35.3 mm
Method, formulas and assumptions
- BS 8006 (Marston): p′c/σ′v = (Cc·a/H)², Cc = 1.95H/a − 0.18 for end-bearing and 1.5H/a − 0.07 for friction inclusions; a = cap width or the square of equal area to the inclusion.
- Load per inclusion = p′c·a² ≤ σ′v·s²; residual stress on soil = (σ′v s² − P)/(s² − a²); settlement = σsoil·Hs/Eoed (no reduction for negative skin friction: an upper bound).
- Platform height ≥ 1.4(s − a) gives full arching (BS 8006); ASIRI recommends checking the inclusion stress (here ≤ 0.3 f′c for unreinforced inclusions) and the geotechnical capacity including negative skin friction.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.