Foundations · Pile testing & NDT
Bi-directional (O-cell) test: equivalent top-down capacity calculator
Fits hyperbolas to two points on the upward (shaft) and downward (base) curves and adds them at a common displacement to give the equivalent head capacity.
Standard: ASTM D8169 · hyperbolic curve fitting (Chin–Kondner) · rigid-pile equivalent curve
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 |
|---|---|---|
| Upward: cell load point 1 | 1500 | kN |
| Upward displacement at point 1 | 1.5 | mm |
| Upward: cell load point 2 | 3000 | kN |
| Upward displacement at point 2 | 12 | mm |
| Downward: cell load point 1 | 1500 | kN |
| Downward displacement at point 1 | 10 | mm |
| Downward: cell load point 2 | 3000 | kN |
| Downward displacement at point 2 | 40 | mm |
| Buoyant weight of pile above the cell | 150 | kN |
| Reference settlement for capacity | 25 | mm |
| Design action E* | 2500 | kN |
| φg | 0.75 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Shaft b = Δ(s/Q)/Δs | 0.000 | 1/kN |
| Shaft a | 0.001 | mm/kN |
| Base b | 0.000 | 1/kN |
| Base a | 0.004 | mm/kN |
| Net shaft resistance at sref | 3,091 | kN |
| Base resistance at sref | 2,500 | kN |
| Equivalent head load Qs + Qb | 5,591 | kN |
| Shaft asymptote 1/b − W | 3,350 | kN |
| Base asymptote 1/b | 4,500 | kN |
| Design capacity φg·Qe | 4,193 | kN |
| Check: largest measured displacement | 40.00 | mm |
- ✓ φg·Qe ≥ E*
- ✓ Reference settlement within the measured range
Method, formulas and assumptions
- Shaft b = Δ(s/Q)/Δs = (12/3000-1.5/1500)/(12-1.5) = 2.857e-4 1/kN
- Shaft a = 1.5/1500-2.857e-4*1.5 = 5.714e-4 mm/kN
- Base b = (40/3000-10/1500)/(40-10) = 2.222e-4 1/kN
- Base a = 10/1500-2.222e-4*10 = 0.0044444 mm/kN
- Net shaft resistance at sref = 25/(5.714e-4+2.857e-4*25)-150 = 3090.7 kN
- Base resistance at sref = 25/(0.0044444+2.222e-4*25) = 2500 kN
- Equivalent head load Qs + Qb = 3090.7+2500 = 5590.7 kN
- Shaft asymptote 1/b − W = 1/2.857e-4-150 = 3350 kN
- Base asymptote 1/b = 1/2.222e-4 = 4500 kN
- Design capacity φg·Qe = 0.75*5590.7 = 4193.1 kN
- Check: largest measured displacement = MAX(12,40) = 40 mm
- Elastic shortening of the pile above the cell is ignored (rigid-pile construction); include it for long or slender piles.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.