Pile Axial Capacity Calculator — end bearing, shaft friction and allowable
Piles transmit loads to competent deep strata through two mechanisms: end bearing resistance Qp and shaft friction Qs. This calculator provides the ultimate capacity Qult and allowable capacity Qadm for bored and driven piles in sands and clays, using the classical methods of Meyerhof 1976 and Tomlinson 1994, plus the French LCPC method (Bustamante-Gianeselli 1982) from CPT data. It complies with BS EN 1997-1 (Eurocode 7) for deep foundations and AASHTO LRFD for bridges. It is the essential tool for sizing piles in high-rise buildings, wind turbines, bridges, wharves, transmission towers and any foundation on soft or heterogeneous deposits.
What is it and when is it applied?
A pile resists through the pressure it exerts on the soil at its tip (Qp = qp·Ap) and through the friction between the shaft and the surrounding soil along its length (Qs = Σ qs·As). The total capacity is Qult = Qp + Qs. In dense sands and rocks, Qp dominates (end-bearing pile). In soft clays and fills, Qs dominates (friction pile). It is used when: the surface stratum cannot support the load (soft clays, fills, liquefiable soils); high concentrated loads need to be transmitted; significant seismic or wind horizontal loads exist; or structures with low settlement tolerances are designed.
Applied formulas
Ultimate capacity: Qult = Qp + Qs = qp·Ap + Σ(qs,i · As,i)
End bearing resistance in sands (Meyerhof 1976):
qp = Nq* · σ'v,tip, with Nq* bearing capacity factor for piles (function of φ and L/D)
Nq* ≈ e^(π·tan φ)·tan²(45 + φ/2)·ξ, with ξ = 1 for driven piles, 0.5 for bored piles
qp_max ≈ 15 MPa (practical limit to avoid excessive tip penetration)
Shaft friction in sands: qs = K·σ'v·tan δ, with K = 0.8·K0 driven, 0.5·K0 bored; δ = φ·(0.8-1.0)
End bearing resistance in clays: qp = 9 · Su,tip (bearing capacity factor Nc* = 9 for piles L/D>5)
Shaft friction in clays (α method, Tomlinson 1994):
qs = α · Su, with α = 1 for Su < 25 kPa; α = 0.5 for Su > 100 kPa; interpolate in between
LCPC method from CPT (Bustamante-Gianeselli 1982):
qp = kc · qc_eq (averaged over zone 1.5D above and below the tip); qs = qc/β
kc and β: table by soil type and pile type (typical kc = 0.40-0.55 sands, β = 60-150)
Allowable capacity: Qadm = Qult / FS, with FS = 2.5 static BS EN 1997-1 (Eurocode 7); = 2 with load tests
Calculation example
| Parameter | Value |
|---|---|
| Pile diameter D | 1.0 m |
| Total length L | 25 m |
| Stratum 0-8 m (sandy silt) | Su = 80 kPa (firm clay) |
| Stratum 8-25 m (dense sand) | φ = 36°, γ' = 11 kN/m³ |
| Tip elevation | 25 m (in dense sand) |
| Water table | 8 m |
| Design load | 5,000 kN (per pile) |
| Required FS | 2.5 (BS EN 1997-1 (Eurocode 7) without load test) |
Tip area: Ap = π·D²/4 = π·1²/4 = 0.785 m². Shaft perimeter: p = π·D = 3.142 m. End bearing resistance in dense sand: σ'v at 25 m = 17·8 + 11·17 = 136 + 187 = 323 kPa (net saturated γ below WT). Nq* for φ=36° in bored pile: ξ=0.5, Nq=37.7 → Nq*=37.7·0.5=18.9. qp = 18.9·323 = 6,104 kPa = 6.1 MPa. Check qp_max limit: 6.1 < 15 OK. Qp = 6,104·0.785 = 4,792 kN. Shaft friction in clay (0-8 m), α=0.55 for Su=80 kPa: qs1 = 0.55·80 = 44 kPa. Qs1 = 44·3.142·8 = 1,106 kN. Shaft friction in sand (8-25 m, 17 m length): average σ'v = (17·8 + 11·8.5)/2 + ... better, σ'v at mid-elevation of this section z=16.5 m: σ'v = 17·8 + 11·8.5 = 136 + 93.5 = 229.5 kPa. K=0.5·(1-sin 36°) = 0.5·0.412 = 0.206. δ = 0.8·36° = 28.8°. qs2 = 0.206·229.5·tan 28.8° = 0.206·229.5·0.550 = 26.0 kPa. Qs2 = 26·3.142·17 = 1,388 kN. Total Qs = 1,106 + 1,388 = 2,494 kN. Qult = Qp + Qs = 4,792 + 2,494 = 7,286 kN. Qadm = 7,286/2.5 = 2,914 kN. Design load 5,000 kN > Qadm 2,914 kN → design insufficient. Options: increase L to 30 m (greater tip), increase D to 1.20 m (more tip area and perimeter), or perform an in-situ load test to use FS=2 instead of 2.5.
Result: Qult = 7,286 kN · Qadm = 2,914 kN · Design load 5,000 kN → requires redesign (increase D or L)
Interpretation of results
The 66 % end bearing / 34 % shaft friction distribution confirms this is an end-bearing pile on dense sand. This configuration is sensitive to the quality of excavation base cleaning: if mud or debris remains, the tip does not mobilise and half the capacity is lost. Concreting with tremie as soon as excavation is finished, or base grouting, is recommended to ensure tip-soil contact. To increase margin without changing geometry, consider a static load test which allows FS=2 (Qadm = 3,643 kN) but still insufficient for 5,000 kN.
Reference standards
- BS EN 1997-1 (Eurocode 7) — Geotechnical design, specific section on piles and FS = 2.5 without test
- Manual of Contract Documents for Highway Works (MCHW) Vol. N°3 — Deep foundations for bridges
- AASHTO LRFD Bridge Design — Section 10 on driven and bored piles
- Meyerhof, G.G. (1976). Bearing capacity and settlement of pile foundations
- Tomlinson, M.J. (1994). Pile design and construction practice, 4th ed.
- Bustamante, M. & Gianeselli, L. (1982). Pile bearing capacity prediction from CPT (LCPC)
- FHWA-NHI-16-009 — Design and construction of driven pile foundations
- FHWA-NHI-10-016 — Drilled shafts — construction procedures and LRFD design methods
Frequently asked questions
Driven or bored, which do I choose?
Driven (steel profile, precast or prestressed concrete): more economical, better tip quality control, no slurry generation. Limitations: noise and vibration (not suitable in dense urban areas), maximum lengths 20-30 m. Bored (bored pile, caisson): adaptable to obstructions, allows L up to 60+ m, good lateral capacity. Disadvantages: requires bentonite slurry or casing in unstable soils, base cleaning is critical, more expensive.
When do I perform a load test?
Projects with more than 50 piles or unit loads > 3,000 kN benefit from a static load test (PDA or static load test) to validate the calculated capacity. It reduces FS from 2.5 to 2 according to BS EN 1997-1 (Eurocode 7), which equates to 25 % more allowable capacity. In large projects (towers, long bridges) the cost of the test (US$ 15-30 thousand) is widely offset by savings in pile quantity/length.
What is the group effect in piles?
When piles are installed in a group spaced less than 3·D apart, the total capacity is less than the sum of individual capacities. An efficiency factor η = 0.7-0.9 is applied according to the Converse-Labarre 1941 method. In soft clays the group effect is more critical (η = 0.6-0.8); in dense sands it is smaller (η = 0.85-1.0). Recommended spacing: 3·D centre to centre.
How do I evaluate lateral capacity?
Lateral (horizontal) capacity: Broms 1964 method for short and long piles in sands and clays, or the p-y method by Matlock-Reese (software LPILE, ALLPILE). Capacity depends on fixity moment, head rotation, soil stiffness and pile stiffness. Typical horizontal loads: seismic (building inertia), wind, lateral embankment thrust. Designed for a head deflection < 2.5 cm under service load.