Pile Capacity (α and β Methods)
Ultimate axial capacity of a single straight-shaft pile in clay (α method) or sand (β method). Sums skin friction and end-bearing contributions, with allowable capacity by factor of safety. For homogeneous-soil idealization; layered soils require summing per-layer skin friction.
Defaults: 1-ft diameter pile, 40 ft long, in stiff clay (cu = 1500 psf, α = 0.55) — typical building foundation pile. Switch soil type to "sand" for the β method.
α method (clay) — Tomlinson chart
The α factor is read from a Tomlinson-type chart vs cu. Approximate fit: α = 1.0 for cu < 500 psf, declining to α = 0.4 for cu > 5000 psf. The reduction reflects how stiff clay has lower adhesion to the pile face per unit shear strength than soft clay does — partly because of remolding around the pile during driving.
Total stress (α) is appropriate for short-term load, before the pile-soil interface drains. For long-term sustained loads, the β method (effective stress) gives more reliable predictions.
β method (sand and effective stress)
β = K tan δ where K is the lateral earth pressure ratio on the pile shaft and δ is the pile-soil interface friction angle. Typical β ranges:
- Driven pile in loose sand: β = 0.20 to 0.30
- Driven pile in dense sand: β = 0.30 to 0.50
- Drilled shaft (bored pile): β = 0.15 to 0.25 (lower K because no driving compaction)
- Open-end pipe pile or H-pile: use lower β; soil plugging is uncertain
Critical depth concept: skin friction in sand reaches a maximum value at Lc/B ≈ 10–20 below ground, then plateaus. Above that depth, σ'v increases linearly. Below, it's roughly constant. This calculator uses average σ'v across the embedment length, which over-predicts for very long piles.
End bearing in sand — Nq matters
For sand, qp = σ'v(tip) × Nq. Nq is highly sensitive to φ — at φ = 30°, Nq ≈ 30; at φ = 40°, Nq ≈ 200. This calculator uses the Berezantsev/Meyerhof correlation:
Nq = exp(π tan φ) × tan²(45 + φ/2) (same as Vesić bearing-capacity factor, conservative)
For piles bearing on dense sand or gravel, end bearing dominates; for piles in clay, skin friction dominates (typically > 80%).
FS values
- FS = 3.0: standard for design with full geotechnical investigation and CPT/SPT data.
- FS = 2.0: pile design verified by full-scale load test (ASTM D1143).
- FS = 2.5: dynamic load test verification (PDA, CAPWAP).
What this doesn't do
- Group effects (efficiency, settlement of pile group)
- Lateral capacity (use COM624 or LPILE for that)
- Negative skin friction from consolidating fill — adds load, doesn't help
- Driveability or wave-equation analysis (GRLWEAP)
Reference: Tomlinson, M.J. (1957). "The Adhesion of Piles Driven in Clay Soils." Proc. 4th ICSMFE, London. AASHTO LRFD Bridge Design Specifications, §10.7. FHWA NHI-05-042 (2006). Design and Construction of Driven Pile Foundations.