Foundation Engineering / Pile capacity in clay — the α-method

Adhesion, not cohesion

Why the pile never gets the strength the laboratory measured.

Lesson review: expert verification remains open

This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.

Corrections checked in this pass

Aligned the adhesion-curve marker with the actual stress-ratio axis.

Checks needed for project use

A geotechnical reviewer must confirm drainage and stress basis, bearing-factor formulation, correlations and settlement influence factors. Partial factors and project-specific ground conditions are outside these teaching checks.
Select adhesion method for soil, installation, effective stress and loading history; the curve is an empirical comparison.

These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.

Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.

Read the lesson register and outstanding review notes

Why this matters

The α-method relates shaft resistance to undrained shear strength through an empirical adhesion factor. Selecting α requires a method appropriate to the pile installation and clay, supported by local evidence where available.

By the end of this lesson you should be able to

Explain what happens to clay around a pile during installation
Apply α layer by layer rather than as an average
Compute base resistance with the deep bearing factor

Shaft resistance in clay — the α-method

Q_s = \sum \alpha \, s_u \, \pi D \, \Delta L

What it calculates: Undrained shaft resistance, summed over the layers a pile passes through

$\alpha$: Adhesion factor — the fraction of s_u the interface actually delivers (—)
s_u: Undrained shear strength of the layer (kPa)
D: Shaft diameter (m)
$\Delta L$: Thickness of the layer along the shaft (m)

This assumes

Undrained conditions — appropriate to the short term, which usually governs in clay
α from a correlation fitted to load tests, with substantial scatter

In plain terms: A total-stress method: it never mentions effective stress or the water table, because in the undrained case s_u already contains them. That is its convenience and its limitation.

What α represents. Installation changes the stress state and condition of the clay beside the shaft. The empirical factor accounts for those effects within the calibration of a particular method; it is not universally below one.

The illustrative strength-ratio correlation decreases as s_u/σ′v increases. Do not infer clay sensitivity directly from overconsolidation ratio or transfer a driven-pile correlation to bored piles without checking its applicability. Time-dependent setup or relaxation also needs site-specific evidence.

Worked example

A bored pile through two clays

Given

Bored pile, D = 0.6 m, embedded 18 m
0–8 m: soft clay, s_u = 40 kPa. 8–18 m: firm clay, s_u = 90 kPa
γ = 19 kN/m³, water table at ground level, so γ′ = 9.19 kN/m³
α from the strength ratio s_u/σ′v in each layer

Find

The shaft and base resistances, and the split

Practice

A 0.6 m bored pile passes through 10 m of firm clay with s_u = 90 kPa and α = 0.576. What shaft resistance does that layer contribute, in kN?