--------------------- | ------- | ----------- | --------------------------------------------------------------------------------- | | Pile diameter | d | in / mm | Cross-section width of the pile | | Embedment length | L | ft / m | Total length below ground surface to pile tip | | Pile type | -- | -- | Driven displacement, bored/CFA, or drilled shaft | | Layer thickness | t_i | ft / m | Thickness of each soil layer | | Undrained shear strength | cu | psf / kPa | For cohesive layers (clay, silt) | | Friction angle | phi | degrees | For cohesionless layers (sand, gravel) | | Unit weight | gamma | pcf / kN/m3 | Total unit weight of each soil layer | | Water table depth | z_w | ft / m | Depth to groundwater below surface | | Number of piles | n_piles | -- | Total number of piles in the group | | Pile spacing | s | ft / m | Center-to-center spacing between piles | | Factor of safety | FS | -- | Applied to ultimate capacity (typical 2.0-3.0) | | Steel grade | Fy | ksi / MPa | Yield strength (AISC: 36, 50, 65 ksi; EN: S235-S460) | | Corrosion allowance | ca | in / mm | Sacrificial thickness per service life (typical 0.0625 in for steel piles) | | Lateral load | H | kips / kN | Applied lateral load at pile head | | Eccentricity | e | in / mm | Height of lateral load above ground surface | | Pile head fixity | -- | -- | Free-head (no moment restraint) or fixed-head (cap provides rotational restraint) |

Design methodology

Alpha Method for Cohesive Soils (API RP2A)

Skin friction in clay is computed as:

fs = alpha x cu

where alpha is an empirical adhesion factor that decreases with increasing undrained shear strength:

• cu <= 500 psf (24 kPa): alpha = 1.00
• 500 < cu <= 1000 psf (24-48 kPa): alpha = 1.00 - 0.0015 x (cu - 500)
• cu > 1000 psf (48 kPa): alpha = 0.50

End bearing capacity in cohesive soils:

qb = Nc x cu = 9 x cu   (for L/d > 4)

where Nc is the bearing capacity factor for deep foundations. For L/d < 4, Nc is reduced per Skempton's deep foundation factors.

Beta Method for Cohesionless Soils (FHWA)

Skin friction in sand and gravel:

fs = beta x sigma'_v

where:
  beta = K x tan(delta)
  K = lateral earth pressure coefficient
    Driven displacement piles: K = 1.0-1.5
    Driven H-piles: K = 0.8-1.2
    Bored/CFA piles: K = 0.6-0.8
  delta = pile-soil interface friction angle = 0.8 x phi (steel)
  sigma'_v = effective vertical stress at the layer midpoint

Typical beta values:

End Bearing in Cohesionless Soils (Meyerhof)

End bearing capacity for piles in sand:

qb = Nq x sigma'_v  (limited to qb,max)

where:
  Nq = bearing capacity factor from Meyerhof (1976)
    Nq increases with friction angle: Nq(30 deg) = 18, Nq(35 deg) = 33, Nq(40 deg) = 64
  qb,max = 15 MPa (150 tsf) for driven piles
  qb,max = 10 MPa (100 tsf) for bored piles

The limiting values prevent over-prediction of end bearing at high effective stresses.

Total Ultimate Capacity

The total pile capacity is the sum of shaft friction and end bearing:

Qu = Qs + Qb

where:
  Qs = sum(fs_i x As_i) for each soil layer i
  Qb = qb x Ab

  As_i = pi x d x t_i  (shaft area per layer)
  Ab = pi x d^2 / 4  (base area, closed-end or plugged)

Allowable capacity: Qa = Qu / FS, where FS is typically 2.0-3.0 depending on the level of site investigation and field verification testing.

Pile Group Efficiency (Converse-Labarre)

For pile groups, the efficiency factor eta_g accounts for stress zone overlap:

eta_g = 1 - (theta/90) x [(n-1)m + (m-1)n] / (m x n)

where:
  theta = arctan(d/s)  (in degrees)
  d = pile diameter
  s = center-to-center spacing
  m, n = number of rows and columns

Total group capacity: Qg = eta_g x n_piles x Qu (where Qu is the single pile capacity).

Note: For driven piles in sand, eta_g is typically > 1.0 (densification effect); for bored piles in clay, eta_g is typically < 1.0 (overlapping shear zones). Minimum pile spacing of 2.5d is recommended.

Elastic Settlement

Single pile settlement under working load:

delta = (Q x I) / (d x Es)

where:
  Q = applied working load
  I = influence factor (typically 0.5-1.0 depending on L/d and pile compressibility)
  d = pile diameter
  Es = representative soil elastic modulus

For pile groups, the settlement is amplified by the group settlement ratio Rs = sqrt(n_piles) to Rs = n_piles^0.5 to 1.0, depending on spacing and soil type.

Steel Pile Structural Capacity (AISC 360-22)

Steel piles (H-piles and pipe piles) must satisfy structural strength requirements per AISC 360-22. The nominal section properties are reduced by the corrosion allowance: effective area A_eff = A - (corrosion loss), effective section modulus S_eff computed on the reduced section.

Axial compression (Chapter E):

phi_c x Pn >= Pu

where:
  Pn = Fcr x Ag  (flexural buckling limit state)
  Fcr = 0.658^(Fy/Fe) x Fy  for Fe >= 0.44 Fy (inelastic buckling)
  Fcr = 0.877 x Fe           for Fe < 0.44 Fy (elastic buckling)
  Fe = pi^2 x E / (KL/r)^2
  K = effective length factor (typically 0.7-1.0 for piles with lateral soil restraint)
  L = unbraced length (use embedment length with soil lateral support)
  phi_c = 0.90

For fully embedded piles, lateral soil restraint permits K <= 1.0 even for free-head conditions because the soil provides continuous lateral bracing along the embedment length.

Flexure (Chapter F):

phi_b x Mn >= Mu

where:
  Mn = Mp = Fy x Z  for compact sections
  Mn = Fy x S       for noncompact sections
  phi_b = 0.90

Lateral loads produce bending moments that vary with depth. Peak moment typically occurs at 5-10 pile diameters below the ground surface for free-head piles in sand.

Combined axial and flexure (Chapter H):

For Pu/phiPn >= 0.2:  Pu/phiPn + (8/9)(Mux/phiMnx + Muy/phiMny) <= 1.0
For Pu/phiPn < 0.2:   Pu/(2 x phiPn) + (Mux/phiMnx + Muy/phiMny) <= 1.0

Corrosion allowance per AISC 360-22 B3.14: For steel piles in undisturbed natural soil, corrosion is typically negligible. For piles exposed to disturbed fill, fluctuating groundwater, or aggressive pH, deduct 0.0625 in (1.6 mm) from the exposed perimeter. In marine environments, a 0.125 in (3.2 mm) corrosion allowance over the design life is common.

Lateral Pile Capacity — Broms Method

The Broms method (1964) provides closed-form solutions for ultimate lateral load capacity of single piles. The method distinguishes between short (rigid) and long (flexible) piles, and between cohesive and cohesionless soils.

Pile classification:

Short pile:  L < 2T  (rigid, fails by soil yielding)
Long pile:   L > 4T  (flexible, fails by plastic hinging)

where T = (EI / nh)^0.2  (characteristic length for sand)
      T = (EI / k)^0.25   (characteristic length for clay)
      nh = coefficient of horizontal subgrade reaction (sand)
      k = subgrade reaction modulus (clay)

Ultimate lateral capacity in cohesive soils:

For short piles (free-head):

Hu = 9 x cu x d x (L - 1.5d)

For long piles (free-head), the pile forms a plastic hinge:

Hu = (2 x Mp) / (e + 1.5d + f/2)

where:
  f = Hu / (9 x cu x d)  (depth to point of zero shear, solved iteratively)
  Mp = plastic moment capacity of the pile section

For fixed-head piles, the ultimate lateral capacity is approximately double that of free-head piles due to rotational restraint at the cap.

Ultimate lateral capacity in cohesionless soils:

For short piles (free-head):

Hu = (0.5 x gamma x d x L^3 x Kp) / (e + L)

where:
  Kp = tan^2(45 + phi/2) = passive earth pressure coefficient

For long piles (free-head), plastic hinge governs:

Hu = Mp / (e + 0.54 x sqrt(Hu / (gamma x d x Kp)))

Solve iteratively.

Lateral deflection at working load (elastic range):

y = (H x e^3)/(3 x EI) + (H x e^2 x L)/(2 x EI)   for a free-head pile

where E is the elastic modulus of steel (29,000 ksi / 200,000 MPa) and I is the moment of inertia of the pile cross-section. Lateral deflection under service load is typically limited to 0.25-0.5 inches (6-12 mm) depending on structure tolerance.

p-multiplier for group lateral effects: For piles in a group subjected to lateral load, the Broms single-pile capacity is reduced by p-multipliers: leading row = 0.8, middle rows = 0.4, trailing rows = 0.3 (per AASHTO LRFD recommendations for 3d spacing).

Common pitfalls

• Over-reliance on empirical correlations: The Alpha and Beta methods are empirical. Always calibrate against site-specific load test data when available.
• Ignoring negative skin friction: Fills placed after pile installation, groundwater lowering, or liquefiable layers can cause downdrag that adds axial load rather than providing resistance.
• Bored pile base condition: Bored piles in wet conditions may have soft bottom conditions (sediment accumulation at the base). A factor of safety of 3.0 is commonly applied to end bearing for slurry-constructed shafts.
• Pile group block failure: For closely spaced piles in clay, the entire block may fail as a unit. Check block capacity as Qu_block = (block perimeter x average cu x L) + (block base area x Nc x cu) when spacing is less than 3d.
• Setup and relaxation: Driven piles in clay gain capacity over time (setup) as excess pore pressures dissipate; driven piles in dense saturated silt may lose capacity (relaxation) as negative pore pressures dissipate. Time-dependent effects should be assessed with restrike testing.
• Corrosion underestimation: Steel H-piles and pipe piles in disturbed fill, fluctuating groundwater, or low-pH soils lose section over time. Always apply AISC 360-22 Section B3.14 corrosion allowance. For marine piles, steel jackets, or piles near industrial fill, a thicker allowance may be required — consult the geotechnical report for site-specific corrosion potential.
• Ignoring P-delta effects on slender piles: Partially exposed piles (pile bents, trestle piers above ground) are susceptible to second-order P-delta moments under combined axial and lateral load. AISC 360-22 Chapter C requires consideration of second-order effects when the second-order moment exceeds 5% of the first-order moment.
• Using free-head Broms equations for piles with cap restraint: A pile cap providing rotational restraint increases lateral capacity by a factor of approximately 2 compared to free-head conditions. Neglecting this fixity under-predicts capacity and may result in unnecessarily conservative pile counts.

Frequently Asked Questions

How is pile axial capacity calculated using the Alpha method? The Alpha method (API RP2A) computes total pile capacity as Qu = Qb + Qs, where Qb is end bearing and Qs is shaft friction. For cohesive soils, skin friction fs = alpha x cu, where alpha decreases with increasing undrained shear strength: alpha = 1.0 for cu <= 500 psf, alpha decreases linearly to 0.5 for cu >= 1000 psf. End bearing qb = Nc x cu = 9 x cu for piles with L/d > 4. The Alpha method is widely used for driven piles in saturated clay where pore pressure dissipation and setup effects are expected.

What is the difference between driven and bored pile capacity? Driven piles (displacement piles) densify granular soils and generate higher shaft friction due to increased lateral earth pressure (K = 1.0-1.5 for sand). They also experience pore pressure buildup and subsequent setup in clay. Bored piles (non-displacement, drilled shafts) relieve in-situ stress and have lower shaft friction (K = 0.6-0.8 for sand) but can achieve higher end bearing in rock. Driven pile capacity in sand is typically 30-60% higher than bored piles of the same diameter due to compaction effects. Bored piles require careful base cleaning to mobilize end bearing.

How does pile group efficiency affect total capacity? Pile group efficiency eta_g accounts for overlapping stress zones in closely spaced piles. For piles in sand, efficiency is typically > 1.0 (group capacity exceeds sum of individual capacities) due to densification between piles during driving. For piles in clay, efficiency is typically < 1.0 due to overlapping shear zones. The Converse-Labarre formula computes eta_g based on pile diameter, spacing, and group geometry. Minimum center-to-center spacing of 2.5d to 3.0d is standard practice.

What is negative skin friction and when does it occur? Negative skin friction (downdrag) occurs when the surrounding soil settles more than the pile, dragging the pile downward. Common causes include placement of fill on compressible soil after pile installation, groundwater lowering causing consolidation of soft clay layers, and liquefaction-induced settlement. Downdrag adds axial load to the pile rather than providing resistance and can reduce net geotechnical capacity by 20-50%. It must be separated from the live load contribution when checking structural strength per AASHTO and FHWA guidelines.

How are pile capacities verified in the field? Field verification methods include: (1) Static load test (ASTM D1143) — the most reliable method, applying incremental loads up to 200-300% of design load. (2) High-strain dynamic testing (PDA, ASTM D4945) — uses pile driving analyzer with wave equation analysis (CAPWAP) during driving or restrike. (3) Statnamic testing — applies a controlled impulsive load with extended duration to mobilize static response. (4) Osterberg cell (O-cell) testing — a hydraulic jack embedded in the pile separates shaft and end bearing components. Design capacities should be verified by at least one static load test per site.

How is the structural strength of a steel pile checked per AISC 360-22? Steel pile structural strength is verified using AISC 360-22 Chapters E, F, and H. Axial compression uses the flexural buckling limit state with Pn = Fcr x Ag, where Fcr depends on the slenderness parameter KL/r. The effective length factor K is typically 1.0 or less for fully embedded piles due to lateral soil restraint. Flexural strength checks phi_b x Mn >= Mu with phi_b = 0.90. Combined axial-flexural interaction uses the bilinear AISC interaction equation (Chapter H1). A corrosion allowance (typically 0.0625 in) is deducted from the section per AISC 360-22 B3.14 before computing structural capacity.

How does the Broms method estimate lateral pile capacity? The Broms method (1964) provides closed-form equations for ultimate lateral pile capacity by distinguishing between short (rigid) and long (flexible) piles. In cohesive soils, short pile capacity is Hu = 9 x cu x d x (L - 1.5d) for free-head conditions; long piles form a plastic hinge governed by the moment capacity Mp. In cohesionless soils, the passive wedge resistance is Hu = (0.5 x gamma x d x L^3 x Kp) / (e + L) for short piles. Fixed-head piles have approximately double the free-head capacity. The method also distinguishes between failure modes: soil yield (short piles) versus structural yield (plastic hinging in long piles).

Related calculators

• Pile capacity reference → — Detailed pile capacity calculation with worked examples
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• Combined footing → — Combined and strap footing design
• Anchor embedment → — Concrete anchor embedment depth design
• Base plate anchors → — Steel column base plate and anchor bolt design
• Load combinations → — ASCE 7-16 factored load combinations
• Unit converter →
• All tools directory →
• All reference tables →

Code references

• AISC 360-22 Chapter E — Design of members for compression (steel pile axial capacity)
• AISC 360-22 Chapter F — Design of members for flexure (lateral load bending)
• AISC 360-22 Chapter H — Design of members for combined forces and torsion
• AISC 360-22 Section B3.14 — Corrosion allowance for steel piles in natural soil and disturbed fill
• API RP2A — Recommended practice for planning, designing, and constructing fixed offshore platforms (Alpha method)
• Broms, B.B. (1964) — Lateral resistance of piles in cohesive soils. ASCE Journal of Soil Mechanics, 90(SM2), 27-63
• Broms, B.B. (1964) — Lateral resistance of piles in cohesionless soils. ASCE Journal of Soil Mechanics, 90(SM3), 123-156
• FHWA-NHI-10-016 — Drilled shafts: construction procedures and LRFD design methods
• FHWA-NHI-10-017 — Design and construction of driven pile foundations
• AASHTO LRFD Bridge Design Specifications, Section 10 — Foundations (pile design provisions)
• IBC Section 1810 — Deep foundations
• AS 2159 — Piling design and installation (Australian Standard)
• EN 1997-1 Section 7 — Pile foundations (Eurocode 7)

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