Method and assumptions

The units, conventions and assumptions on this page hold on every page about piles.

Units and conventions

• SI units: forces in kN, stresses in kPa, lengths in m, unit weights in kN/m³, angles in degrees.
• Depth $z$ is measured down from the ground surface. The pile runs from $z = 0$ to its toe at $z = L$.
• $D$ is the diameter of a circular pile or the side of a square one. Its perimeter is $p = \pi D$ or $4D$, and its toe area $A_p = \pi D^2/4$ or $D^2$.
• The water table is at a depth $z_w$ below the ground surface, negative when water stands above it; $\gamma_w = 9.81$ kN/m³.
• $Q$ is the vertical compressive load on the cap: on the single pile, or on the whole group.
• $p_a = 100$ kPa is the atmospheric pressure, the reference stress in the α table and in Meyerhof’s limit.

Key assumptions

• Shaft and toe reach their ultimate resistance together: $Q_u = Q_s + Q_p$.
• The whole pile, from the ground surface to the toe, carries shaft resistance.
• Pore pressure is hydrostatic below the water table and zero above it, so below it $\sigma'_v = \sigma_v - \gamma_w (z - z_w)$.
• Each stratum is uniform, with one $c_u$ or one $\phi'$. Drained strata carry no cohesion.
• The cap only transfers the load: it bears nothing on the soil, and its weight and the piles’ are not added to $Q$.

Method

The shaft resistance $Q_s$ is added up stratum by stratum: by the α method in an undrained stratum, by the β method in a drained one, where the effective stress stops growing at the critical depth. The toe resistance $Q_p$ comes from the stratum the toe rests on, after Meyerhof. Their sum is the pile’s ultimate capacity, $Q_u = Q_s + Q_p$. A pile on its own is checked on $Q_u$; a group can fail in two ways, as individual piles or as one block, and the weaker governs. Equations has every step, in the order of the calculation report.

References

• Das, B. M., & Sivakugan, N. (2017). Principles of Foundation Engineering, SI edition, 9th ed. Cengage Learning.
• Meyerhof, G. G. (1976). Bearing capacity and settlement of pile foundations. Journal of the Geotechnical Engineering Division, ASCE, 102(GT3), 197–228.