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

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

API RP 2GEO gives the unit end bearing of piles in cohesionless siliceous soils in Section 8.1.4 and the tip load-displacement curve in Section 8.4.3. Both provisions are those of API RP 2A-WSD \[API, 2007], Sections 6.4.3 and 6.7.3.

The model takes the three inputs of the FB-MultiPier *Driven Pile Sand (API)* tip dialog: **Internal Friction Angle**, **Nominal Unit End Bearing** and **Bearing Capacity Factor N\_q**.

### Ultimate End Bearing

$$
\tag{1}
q = N\_q p'*0 \leq q*{nom}
$$

where,

$$q$$ = unit end bearing\
$$p'*0$$ = effective overburden pressure at the pile tip\
$$N\_q$$ = dimensionless bearing capacity factor\
$$q*{nom}$$ = nominal (limiting) unit end bearing entered on the soil layer; 0 = no limit

**Bearing capacity factor.** A **Bearing Capacity Factor N\_q** above 0 is used as entered, which is the RP 2GEO form; the friction angle is then not read. With 0 the factor is read from the design parameter table through the **Internal Friction Angle**, interpolated linearly between the rows and held at the end values outside 20° to 40°. The rows $$N\_q$$ = 12, 20, 40 and 50 belong to soil-pile friction angles of 20°, 25°, 30° and 35°, that is $$φ$$ = 25°, 30°, 35° and 40° with the same $$δ = φ - 5°$$ as the side-resistance model; $$N\_q$$ = 8 at $$φ$$ = 20° is the very loose row of the RP 2A editions before 2007.

**Nominal unit end bearing.** It limits the computed end bearing in both cases. Unlike the nominal unit skin friction of the [side-resistance model](/technical-background/soil-structure-interaction/axial-soil-models/axial-tz-soil-models/driven-pile-sand-tz-api-api-2007.md), which replaces the computed value, it does not set the end bearing by itself; this is also how FB-MultiPier treats the two fields.

Design parameters for cohesionless siliceous soil (very loose and loose sand, loose sand-silt, medium dense and dense silt are marked not applicable in RP 2GEO):

| Soil (relative density)                                     | $$φ$$ (°) | $$N\_q$$ | $$q\_{lim}$$ (ksf) |
| ----------------------------------------------------------- | --------- | -------- | ------------------ |
| Very loose sand (RP 2A editions before 2007, $$N\_q$$ only) | 20        | 8        | –                  |
| Medium dense sand-silt                                      | 25        | 12       | 60                 |
| Medium dense sand, dense sand-silt                          | 30        | 20       | 100                |
| Dense sand, very dense sand-silt                            | 35        | 40       | 200                |
| Very dense sand                                             | 40        | 50       | 250                |

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

### Q-z Curve

A tip displacement of up to 10 % of the pile diameter may be required to mobilize the full end bearing; the recommended curve for both sands and clays is:

| $$z/D$$    | 0.002 | 0.013 | 0.042 | 0.073 | 0.100 |
| ---------- | ----- | ----- | ----- | ----- | ----- |
| $$Q/Q\_p$$ | 0.25  | 0.50  | 0.75  | 0.90  | 1.00  |

where $$Q$$ is the mobilized end bearing and $$Q\_p$$ the total end bearing, $$q$$ times the gross tip area of the pile. The standard has no displacement input for this curve.

***

\[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 8.4.3.

\[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 6.7.3.


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