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

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

API RP 2GEO gives the unit shaft friction of piles in cohesionless siliceous soils in Section 8.1.4 and the *t-z* curve in Section 8.4.2. The shaft friction provisions are those of API RP 2A-WSD \[API, 2007], Section 6.4.3; the *t-z* curve is new in RP 2GEO.

The model takes the four inputs of the FB-MultiPier *Driven Pile Sand (API)* dialog: **Internal Friction Angle**, **Coefficient of Lateral Earth Pressure**, **Nominal Unit Skin Friction** and **Displacement at Nominal Unit Skin Friction**.

### Ultimate Side Resistance

The **Nominal Unit Skin Friction** $$f\_{nom}$$ decides how the peak of the curve is obtained:

$$
\tag{1}
t\_{max} = f\_{nom} \qquad (f\_{nom} > 0)
$$

$$
\tag{2}
t\_{max} = \beta p'*0 \leq f*{lim}, \qquad \beta = K\tan\delta, \qquad \delta = \phi - 5^\circ \qquad (f\_{nom} = 0)
$$

where,

$$t\_{max}$$ = ultimate unit skin friction, the peak of the *t-z* curve\
$$f\_{nom}$$ = nominal unit skin friction entered on the soil layer\
$$β$$ = dimensionless shaft friction factor\
$$p'*0$$ = effective overburden pressure at the point in question\
$$K$$ = coefficient of lateral earth pressure: 0.8 for open-ended pipe piles driven unplugged, 1.0 for full-displacement piles (driven fully plugged or closed ended)\
$$φ$$ = internal friction angle of the soil\
$$δ$$ = friction angle between the soil and the pile wall\
$$f*{lim}$$ = limiting unit skin friction

**Nominal unit skin friction entered (Eq. 1).** The value is the ultimate unit skin friction of the curve itself; the friction angle and $$K$$ are not used. This is how FB-MultiPier treats the field: the entered value replaces the computed friction, it is neither a cap nor a floor on it. With the same nominal unit skin friction and displacement the OpenBrIM and FB-MultiPier curves coincide.

**Nominal unit skin friction left at 0 (Eq. 2).** The skin friction is computed by the standard. RP 2GEO writes it directly with a tabulated shaft friction factor $$β$$; OpenBrIM obtains $$β$$ from the friction angle and $$K$$, so that the inputs remain those of the dialog, and the result lands on the table: $$K$$ = 0.8 with $$φ$$ = 25°, 30°, 35° and 40° gives $$β$$ = 0.29, 0.37, 0.46 and 0.56, and $$K$$ = 1.0 is the 25 % increase the standard allows for full-displacement piles. $$f\_{lim}$$ is read from the same table through the friction angle, interpolated linearly between the rows and held at the end values outside 25° to 40°. FB-MultiPier has no such path: it returns no side resistance when the field is 0.

Design parameters for cohesionless siliceous soil (very loose and loose sand, loose sand-silt, medium dense and dense silt are marked not applicable):

| Soil (relative density)            | $$β$$ | $$φ$$ (°) for $$K$$ = 0.8 | $$f\_{lim}$$ (ksf) |
| ---------------------------------- | ----- | ------------------------- | ------------------ |
| Medium dense sand-silt             | 0.29  | 25                        | 1.4                |
| Medium dense sand, dense sand-silt | 0.37  | 30                        | 1.7                |
| Dense sand, very dense sand-silt   | 0.46  | 35                        | 2.0                |
| Very dense sand                    | 0.56  | 40                        | 2.4                |

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 replaced the bilinear sand curve of RP 2A-WSD \[API, 2007], which was linear to 0.1 in and constant beyond.

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

$$z\_{peak}$$ 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.

{% hint style="info" %}
FB-MultiPier reads a displacement of 0 as "use the earlier bilinear curve", whereas OpenBrIM reads 0 as 1 % of the diameter. Enter the displacement explicitly (0.36 in for a 36 in pile) when comparing the two programs.
{% 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 8.1.4 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 6.4.3 and 6.7.2.


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