> 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-clay-tz-api-api-2007.md).

# Driven Pile Clay TZ (API) \[API, 2014]

API RP 2GEO gives the unit shaft friction of piles in cohesive soils in Section 8.1.3 and the *t-z* curve in Section 8.4.2. The shaft friction equations are those of API RP 2A-WSD \[API, 2007], Section 6.4.2.

The inputs are the **Undrained Shear Strength**, the **Residual to Peak Adhesion Ratio** and the **Displacement at Nominal Unit Skin Friction** of the soil layer.

### Ultimate Side Resistance

$$
\tag{1}
t\_{max} = \alpha s\_u
$$

$$
\tag{2}
\alpha = 0.5\psi^{-0.5} \ (\psi \leq 1.0), \qquad \alpha = 0.5\psi^{-0.25} \ (\psi > 1.0), \qquad \alpha \leq 1.0
$$

$$
\tag{3}
\psi = \frac{s\_u}{p'\_0}
$$

where,

$$t\_{max}$$ = ultimate unit skin friction, the peak of the *t-z* curve\
$$s\_u$$ = undrained shear strength of the soil at the point in question (written $$c$$ in RP 2A-WSD)\
$$p'\_0$$ = effective overburden pressure at the point in question\
$$α$$ = dimensionless friction factor

The effective overburden pressure is computed from the unit weights and thicknesses of the layers above the point and the water table.

### t-z Curve

The curve is a table normalized to the displacement $$z\_{peak}$$ at which the peak skin friction is reached. It follows the sand curve up to the peak, then drops to a residual skin friction $$t\_{res}$$ that is reached at twice that displacement and held beyond:

| $$z/z\_{peak}$$ | 0.00 | 0.16 | 0.31 | 0.57 | 0.80 | 1.00 | 2.00                  | > 2.00                |
| --------------- | ---- | ---- | ---- | ---- | ---- | ---- | --------------------- | --------------------- |
| $$t/t\_{max}$$  | 0.00 | 0.30 | 0.50 | 0.75 | 0.90 | 1.00 | $$t\_{res}/t\_{max}$$ | $$t\_{res}/t\_{max}$$ |

$$z\_{peak}$$ ranges from 0.25 % to 2 % of the pile outer diameter; RP 2GEO recommends 1 % of the diameter in the absence of other data. It is the input **Displacement at Nominal Unit Skin Friction** of the soil layer; when left at 0, OpenBrIM uses 1 % of the pile diameter. With 1 % of the diameter the table is the $$z/D$$ table of RP 2A-WSD \[API, 2007], Figure 6.7.2-1 (0.0016, 0.0031, 0.0057, 0.0080, 0.0100 and 0.0200 $$D$$), which RP 2GEO generalized.

The residual ratio $$t\_{res}/t\_{max}$$ ranges from 0.70 to 0.90 depending on the soil stress-strain behavior, stress history, installation method and load sequence. It is the input **Residual to Peak Adhesion Ratio** of the soil layer, 0.90 by default; a value of 0 is read as 0.90.

{% hint style="info" %}
FB-MultiPier fixes the peak at 1 % of the pile diameter and the residual ratio at 0.90, with no input for either. Leave the displacement at 0 (or enter 1 % of the diameter) and the residual ratio at 0.90 when comparing the two programs; the curves then coincide.
{% endhint %}

***

\[API, 2014] American Petroleum Institute (2014). *Geotechnical and Foundation Design Considerations*, API RP 2GEO, 1st ed. (2011) with Addendum 1 (2014), reaffirmed 2021, Sections 8.1.3 and 8.4.2.

\[API, 2007] American Petroleum Institute (2007). *Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms — Working Stress Design*, API RP 2A-WSD, 21st ed. with errata and supplements, Sections 6.4.2 and 6.7.2.


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