> 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-tz-soil-models/driven-pile-mcvay-tz-mcvay-et-al-1989.md).

# Driven Pile (McVay) TZ \[McVay et al., 1989]

$$
\tag{1}
z = \frac{tr}{G\_i}\[ln(\frac{r\_m-\beta}{r-\beta})+\frac{\beta(r\_m-r)}{(r\_m-\beta)(r-\beta)}]
$$

where,

$$t$$ = skin friction (side friction) $$z$$ = vertical displacement (settlement) $$r$$ = pile radius $$G\_i$$ = initial (small-strain) shear modulus of soil $$r\_m$$ = outward radius were the transferred shear stress to soil is negligible $$β$$ = side resistance parameter

The parameter $$β$$ is computed as,

$$
\tag{2}
\beta = \frac{t\_r}{t\_u}
$$

where,

$$t\_u$$ = ultimate side resistance

$$r\_m$$ is assumed to be initially equal to:

$$
\tag{3}
r\_m = \frac{G\_{mid}}{G\_{tip}}L(1-\nu)
$$

where,

$$L$$ = pile length $$ν$$ = Poisson's ratio of soil $$G\_{mid}$$ = shear modulus of soil at mid-depth $$G\_{tip}$$ = shear modulus of soil at the pile tip

***

\[McVay et al., 1989] McVay, M., Townsend, F., Bloomquist, D., O’Brien, M., and Caliendo, J. (1989). Numerical analysis of vertically loaded pile groups. *Foundation Engineering*, pages 675–690


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://docs.openbrim.org/technical-background/soil-structure-interaction/axial-soil-models/axial-tz-soil-models/driven-pile-mcvay-tz-mcvay-et-al-1989.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.