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, 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.