Single pile — bearing capacity

What this page computes

The page determines the axial compressive bearing capacity of a single pile, as the sum of two contributions that are computed separately:

\(Q_u = Q_s + Q_p\)

where \(Q_s\) is the shaft friction, accumulated layer by layer over the pile length, and \(Q_p\) is the base resistance. The allowable capacity follows from a global factor of safety, \(Q_{adm} = Q_u / FS\).

The two components do not mobilise at the same displacement

This is the observation that changes how the result should be read. Shaft friction mobilises almost fully within a few millimetres of movement, whereas base resistance needs 5–10% of the diameter — for a 600 mm pile, that is 30 to 60 mm of settlement.

The practical consequence: two piles with the same ultimate capacity can behave completely differently in service. A floating pile, which takes its capacity from the shaft, is stiff from small displacements onward. An end-bearing pile only reaches the computed capacity after a settlement that may be unacceptable to the structure. That is why the page reports the fraction of the capacity carried by the shaft explicitly and flags the extreme cases.

The sum \(Q_s + Q_p\) is an ultimate capacity, not a state reached simultaneously.

Sand: the vertical stress is capped

The unit shaft friction in cohesionless soil is written

\(f_s = K \cdot \sigma'_v \cdot \tan\delta\)

The term most often got wrong is \(\sigma'_v\). The vertical effective stress entering this relationship does not grow without bound with depth. Measurements show that beyond a critical depth, on the order of 15–20 diameters, the unit friction levels off — usually attributed to arching between particles, which sheds stress away from the shaft.

Without this cap, a 30 m pile in sand comes out appreciably stronger than it really is, and the error grows with length. The page applies the cap but keeps it as a parameter, not a constant: the literature gives values between 15 and 20, and some codes do not apply it at all. Enter 0 to disable it and see how much it is worth in your case.

\(K\) belongs to the installation method, not to the soil

The lateral pressure coefficient \(K\) is the second parameter worth attention, because it depends on how the pile is installed, not only on the ground:

• bored pile — the soil relaxes during drilling, so \(K \approx K_0 = 1 - \sin\varphi\);
• driven pile — the soil is displaced laterally, and \(K\) can reach \(1.4 \cdot K_0\) or more.

There is no "correct" value independent of installation. The ratio \(\delta/\varphi\) between pile–soil friction and the internal friction of the soil is usually taken around 0.67, higher for cast-in-place concrete, whose surface is rough, than for steel.

Clay: the base works with \(9c_u\), not with \(N_q\)

Under undrained conditions the base resistance follows Skempton:

\(q_p = 9 \cdot c_u\)

Not the sand bearing-capacity factors. Confusing the two is the classic mistake for piles in clay and produces absurdly large values, because \(N_q\) grows exponentially with \(\varphi\), and for a clay improperly treated as a frictional material the result loses any connection to reality.

On the shaft in clay the friction is taken as \(f_s = \alpha \cdot c_u\), with \(\alpha\) between 0.4 and 1.0, decreasing as \(c_u\) increases: stiff clays mobilise a smaller fraction of their cohesion at the pile interface.

What the calculation does not cover

A single pile under axial compression is treated. Outside the scope:

• group effects — closely spaced piles overlap their stress bulbs, and the group capacity is not the sum of the individual capacities;
• negative skin friction, where a settling layer hangs off the pile instead of supporting it;
• lateral loading and moments at the pile head;
• uplift, where the base does not work and the friction differs from its compressive value.

The formulas are the standard ones (Das, Principles of Foundation Engineering, chapters 11–12), but — unlike earth pressure, shallow-foundation bearing capacity and Boussinesq, each of which has an external benchmark on this platform — they have not been checked against a published worked example. The internal tests cover the structure of the calculation and its behaviour as parameters vary, not a reference value. Read the result as preliminary sizing.