OpenSpecEngineering

Estimates the axial compression capacity of a single driven or bored pile in one uniform soil: the friction along its shaft plus the bearing at its tip. Use the α method for clay and the β method for sand [1], [3], [4]. Use it to size a pile’s diameter and length before a detailed design or a load test.

Equations

Q_ult = f_s·A_s + q_p·A_p
A_s = π·D·L     A_p = π·D²/4

Clay:   f_s = α·c_u
Clay:   q_p = 9·c_u

Sand:   f(z) = β·γ′·z
Sand:   q_p = N_q·γ′·L

D is the pile diameter and L its embedded length. In clay, c_u is the undrained shear strength and α the adhesion factor, the share of c_u that the shaft mobilizes. α is near 1 for soft clay and falls to about 0.5 or less for stiff clay [1]. In sand, γ′ is the effective unit weight (submerged below the water table), so γ′·z is the effective vertical stress at depth z. β = K·tan δ combines the lateral earth pressure coefficient and the pile–soil friction angle, and N_q is the end-bearing factor. f_s in sand is the average of f(z) over the shaft.

Choosing a sand description fills in β, N_q and the limiting values from API RP 2A [2], [5]. Unit friction then stops growing at f_lim, and the result shows the depth where that happens. End bearing stops at q_lim. With custom β and N_q, no limits are applied, so long piles in sand come out too strong.

Limits and common mistakes

• The soil is one uniform layer. For layered ground, add the shaft friction of each layer by hand.
• The API sand values are for open-ended pipe piles driven unplugged into silica sand. Other piles and soils need their own values.
• The capacity is geotechnical only. Check the pile itself as a column, and the group effect for closely spaced piles.
• A factor of safety of 2 to 3 is usual; use the lower end only with load tests.

Worked example

A 600 mm pipe pile is driven 25 m into dense sand below the water table, where γ′ is 9.5 kN/m³. What load can it carry with a factor of safety of 3?

1. Choose Soil / Method Cohesionless soil — β / Nq method.
2. Enter Pile Diameter 0.6 m, Embedded Length 25 m and Effective Unit Weight 9.5.
3. Choose Sand Description Dense sand, or very dense sand-silt.
4. Enter Factor of Safety 3 and press Solve. The Solution shows: Shaft resistance Qs: 2,536.28 kN
   End bearing Qp: 2,686.06 kN
   Ultimate capacity Qult: 5,222.34 kN
   Allowable capacity Qult / FS: 1,740.78 kN
   Depth where shaft friction reaches f_lim: 21.968 m

Check by hand. Friction reaches 96 kPa at z = 96 / (0.46 × 9.5) = 21.97 m. Above that it averages 48 kPa, so the shaft carries π × 0.6 × (48 × 21.97 + 96 × 3.03) = 2,536 kN. The tip gets 40 × 9.5 × 25 = 9,500 kPa, below the 10,000 kPa limit, on 0.2827 m²: 2,686 kN.