> For the complete documentation index, see [llms.txt](https://docs.openbrim.org/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.openbrim.org/technical-background/soil-structure-interaction/axial-soil-models/axial-qz-soil-models/driven-pile-clay-qz-skempton-skempton-1951.md).

# Driven Pile Clay QZ (Skempton) \[Skempton, 1951]

For piles tipped in clay the unit end bearing is related to the tip displacement through the bearing capacity factor of \[Skempton, 1951] and the strain at 50 % of the maximum stress:

$$
\tag{1}
q = \frac{N\_cc\_u}{2}\Bigl(\frac{z}{2D\varepsilon\_{50}}\Bigr)^{n} \leq N\_cc\_u
$$

where,

$$q$$ = unit end bearing resistance\
$$c\_u$$ = undrained shear strength of the soil at the tip\
$$N\_c$$ = bearing capacity factor, 9.0 for deep foundations\
$$D$$ = pile diameter\
$$ε\_{50}$$ = strain at 50 % of the maximum stress\
$$z$$ = vertical displacement of the pile tip\
$$n$$ = exponent, 0.5 for clays

Half of the ultimate resistance is mobilized at a tip displacement of 2\*\*$$Dε\_{50}$$\*\*, and the full resistance $$N\_cc\_u$$ at 4 times that displacement for $$n$$ = 0.5.

{% hint style="info" %}
The Building Research Congress paper is not yet on file (only unofficial re-hosted copies exist online), so the relationship is implemented as it is reported in the secondary literature. It will be checked against \[Skempton, 1951] once the original is obtained.
{% endhint %}

***

\[Skempton, 1951] Skempton, A. W. (1951). The bearing capacity of clays. In *Proc. Building Research Congress*, London, Vol. 1, 180–189. (Paper not on file.)


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