Foundations · Laterally loaded piles
Laterally loaded pile: p-y analysis (Matlock clay, API sand) calculator
The pile is a beam on non-linear soil springs solved by finite differences with secant-stiffness iteration. Layers use Matlock's soft-clay curve or the API sand curve. Gives head deflection and rotation, the bending-moment and deflection profiles, the maximum moment and its depth, and the p-y curves at four depths.
Standard: API RP 2GEO p-y curves · Matlock (1970) · Reese, Cox & Koop (1974) · finite-difference beam on non-linear springs
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 |
|---|---|---|
| Pile diameter | 0.61 | m |
| Embedded length | 18 | m |
| Section | Steel pipe (wall thickness below) | |
| Steel wall thickness | 12.7 | mm |
| Steel yield / concrete f′c | 350 | MPa |
| Head condition | Free head | |
| Lateral load at the head H | 150 | kN |
| Moment at the head (free head) | 50 | kNm |
| Layers (bottom depth m, 1 Matlock clay / 2 API sand, γ′ kN/m³, su kPa or φ′ °, ε50 or k kN/m³) | 3, 1, 7, 25, 0.02 30, 2, 10, 34, 25000 | |
| Allowable head deflection | 25 | mm |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Bending stiffness EI | 212.7 | MNm² |
| Head deflection | 23.47 | mm |
| Head rotation | 7.529 | mrad |
| Maximum moment | 408.2 | kNm |
| Depth of maximum moment | 3.45 | m |
| Moment capacity (indicative) | 1,098 | kNm |
| First zero-deflection depth | 4.95 | m |
| Toe deflection | 0.000 | mm |
- ✓ Head deflection ≤ allowable — 23.5 mm
- ✓ Maximum moment ≤ capacity — 408 vs 1,098 kNm
- ✓ Pile long enough (toe deflection < 10 % of head)
Method, formulas and assumptions
- Finite differences, 120 segments: EI y'''' + k(y)·y = 0 with secant k = p/y from the p-y curves, iterated to convergence. Head: shear H and moment M (or zero slope); toe: zero moment and shear.
- Matlock soft clay: pu = min[(3 + γ′z/cu + Jz/D)cuD, 9cuD], J = 0.5; p = 0.5pu(y/y50)^⅓, y50 = 2.5ε50D. API sand: p = A pu tanh(kzy / A pu), A = max(0.9, 3 − 0.8z/D).
- Steel pipe Mcap = 0.9·fy·Z (elastic); concrete is a 1 % reinforced estimate only.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.