Pile axial capacity
The static axial capacity of a single vertical pile through a layered soil profile: side resistance summed over the layers plus toe resistance, for driven piles by the methods of FHWA GEC 12 (2016) and for drilled shafts by FHWA GEC 10 (2018), checked against the largest compression and tension of the ASCE 7-22 combinations with the engineer's factors of safety (ASD) or resistance factors (LRFD). Each layer is split at the groundwater level and the pile head and evaluated at its mid-depth, as the GEC illustrative examples do: thinner layers follow a varying profile more closely.
Inputs of the pile capacity check #
- Pile: driven pile or drilled shaft; round (closed-end pipe, precast round, shaft), square (precast) or an entered perimeter and toe area (H-pile or open pipe: whether the box or the steel area applies is the engineer's call, GEC 12 7.10.7); the embedded length, the depth of the head below grade (no side resistance above it: cap, scour, excavation), the groundwater depth.
- Soil layers (top down from grade, to below the tip): clay (total unit weight, undrained strength su; an α per layer when the engineer reads it from the Tomlinson curves) or sand (φ', N60 for drilled shafts; β and Nt for driven piles, from local experience or the ranges of GEC 12 Table 7-9 after Fellenius 2014).
- Driven piles: α in clay by API RP 2A (Randolph and Murphy 1985: α = 0.5ψ^-0.5 for ψ = su/σ'v ≤ 1, 0.5ψ^-0.25 above, ≤ 1) or entered; an optional limit on the toe resistance in sand (the β-method itself has none).
- Drilled shafts: the test the su comes from (CIUC as entered; UU and UC converted by GEC 10 Eqs. 10-17, 10-16), the exponent m of Eq. 10-11 (0.6 clean quartzitic sand, 0.8 silty sand), the neglected top of the shaft in clay (5 ft is common practice, GEC 10 10.3.5.2).
- Factors: ASD factors of safety for compression and uplift; LRFD resistance factors for side resistance in clay and sand, toe and uplift (GEC 10 values prefilled; the AASHTO driven-pile values are in the hints, to confirm against the code text); the uplift side resistance as a part of the compression value; the pile weight against uplift (buoyant below the water table; 0.6 of it in ASD, 0.9 in LRFD, as the dead-load factors of the uplift combinations).
- Loads: per load type, unfactored, compression positive and tension negative.
Auto-design varies the embedded length in 1-ft steps within the soil profile (and the width when unlocked); the soil, coefficients, loads and factors are the engineer's. See Auto-design.
Checks performed #
| Check | Basis |
|---|---|
| Compression ≤ Rn / FS or φsc Rs,clay + φss Rs,sand + φp Rp | Rn = Σ fs·perimeter·thickness + qp·At |
| Driven, clay | fs = α su; toe 9 su (GEC 12 α-method) |
| Driven, sand | fs = β σ'v (GEC 12 Eq. 7-19); toe Nt σ'p (Eq. 7-20) |
| Shaft, clay | fs = α su(CIUC), α = 0.30 + 0.17/(su/pa) (GEC 10 Eq. 10-18); base N*c su, N*c of Table 10-2 (9 at 2,000 psf and up), Eq. 10-20 when the depth is less than 3B |
| Shaft, sand | β = (1 − sin φ')(σ'p/σ'v)^sin φ' tan φ' ≤ Kp tan φ', σ'p/pa = 0.47 N60^m, β at its 7.5-ft value above that depth (Eqs. 10-8 to 10-13); base 0.60 N60 tsf ≤ 30 tsf (Eq. 10-14) |
| Tension ≤ ratio × Rs / FS + 0.6 W (ASD) or φup ratio × Rs + 0.9 W (LRFD) | only when a combination gives tension |
The drawings show the pile in the soil profile (layers, groundwater, head and tip) and the unit and cumulative side resistance along the pile.
Limitations #
- A single vertical pile: group effects and block failure, downdrag (negative skin friction), settlement and the pile's structural capacity are not checked; drivability (wave equation), set-up and relaxation are not covered.
- Nordlund's method and the Tomlinson α curves are chart based: enter α (and β) per layer when using them.
- Rock sockets, cased zones (casing reduction factors) and open-end plugging are not modelled; enter equivalent values.
- Layers are evaluated at mid-depth; split thick layers where the stress or strength changes much.
- The resistance factors prefilled are GEC 10's for drilled shafts; for driven piles enter the agency's factors.
Verification examples #
Verification status: 12 values compared in 5 examples (3 published, 2 hand calculations from the cited equations): 12 within tolerance, 0 recorded deviations. Code basis: the provisions it uses were read in the target edition.
Published worked examples (backend/tests/test_verify_pile_capacity.py):
| Source | What it checks | Published | ILX Calcs |
|---|---|---|---|
| FHWA GEC 10 (2018) Illustrative Example 10-1: 5-ft shaft, silty sand 0 to 15 ft and 15 to 33 ft, water at 15 ft | side resistance of layers 1 and 2 | 197.2, 635.6 kips | ≈ 196.6, 631 kips (hand-checked; the example's layer 2 line uses 1.08 for its β of 0.98) |
| Example 10-2: stiff clay 33 to 60 ft, UU su = 2,000 psf | su(CIUC), side resistance | 2,571 psf, 479.7 kips | ≈ 2,571 psf, 479.8 kips |
| Example 10-3 | base qBN, RBN | 23.1 ksf, 453.6 kips | ≈ 23.14 ksf, 454.3 kips |
Hand calculations cover the driven-pile α (API RP 2A) and β / Nt methods, the toe in clay, the uplift resistance and the LRFD sum. The GEC 12 design examples print DRIVEN program output rather than hand calculations, so no driven-pile example is reproduced.