Capacity of Single Piles

edafos implements the pile capacity methods presented below.

API Method

American Petroleum Institute (API).

Required Properties

Pile:
  • \(\alpha\) or \(d\): side length or diameter for surface area, \(A_s\) (shaft resistance)
  • \(\alpha\) or \(d\) (\(t\)): side length or diameter (with thickness for open ended) for toe area, \(A_p, A_{pp}\) (toe resistance)
  • pile type: open-ended or closed-ended for \(K\) selection (cohesionless soils)
Soil:
  • type: cohesive/cohesionless classification
  • \(\gamma\): total unit weight for effective stress calculations
  • \(s_u\): undrained shear strength (cohesive soils)
  • \(N_{cor}\): SPT-N corrected to select \(\delta\), \(f_{s.lim}\), \(N_q\), \(q_{s.lim}\) (cohesionless soils)

Note: edafos runs a pre-check to verify that all required properties have been defined prior to running the capacity calculations. Refer to the _pre_check() method for more information.

Cohesive Soils

The revised API method was included in RP-2A (1993) and has been widely used in the offshore industry.

Shaft Resistance

The general equation for shaft resistance is given by:

(1)\[R_s = \sum{f_s A_s}\]

where:

  • \(f_s\): unit shaft resistance (adhesion)
  • \(A_s\): side surface area of pile

and,

(2)\[f_s = \alpha s_u\]

where:

  • \(\alpha\): coefficient as per revised API (1987)
  • \(s_u\): undrained shear strength of soil

The \(\alpha\) factor is calculated based on the conditional in equation (3).

(3)\[\begin{split}\alpha = \begin{cases} 0.5\psi^{-0.5} & \textrm{if} \quad \psi \leq 1.0 \\ 0.5\psi^{-0.25} & \textrm{if} \quad \psi > 1.0 \end{cases} \quad \leq 1.0\end{split}\]

where:

  • \(\psi\): \(s_u/\bar{\sigma'}\) at a depth, \(z\)
  • \(\bar{\sigma'}\): average effective stress (at midpoint)
  • \(s_u\): undrained shear strength of soil

Toe Resistance

The toe resistance is equal to:

(4)\[R_p = q_p A_p\]

where:

  • \(q_p\): unit toe resistance
  • \(A_p\): pile toe cross-sectional area

Important: Toe resistance must always be checked against \(R_p = q_p A_{pp}\) where \(A_{pp}\) is the cross sectional area of soil plug in open end pipe or H-piles at pile toe.

The unit toe resistance, \(q_p\), is given by:

(5)\[q_p = 9 s_u\]

where:

  • \(s_u\): Undrained shear strength at the tip of the pile, usually taken as the average over a distance of two diameters below the tip of the pile.

Cohesionless Soils

Following API RP2A (1987) recommendations.

Shaft Resistance

Shaft resistance is given by the general form in equation (1). Unit shaft resistance for piles in cohesionless soils is calculated by:

(6)\[f_s = K \sigma' \tan{\delta}\]

where:

  • \(K\): coefficient of lateral earth (ratio of horizontal to vertical normal effective stress)
  • \(\bar{\sigma'}\): average effective stress (at midpoint)
  • \(\delta\): friction angle between the soil and the pile wall

Table 7 offers recommended values for the coefficient of lateral earth, \(K\).

Table 7 Values for coefficient of lateral earth, \(K\)
Condition K
unplugged, open-ended pipe piles (tens & comp) 0.8
full-displacement piles 1.0

Table 8 offers guidelines for \(\delta\), the friction angle between the soil and the pile wall as well as limiting, \(f_s\).

Table 8 Guidelines for Side Friction in Siliceous Soil
Soil \(\delta\) , degrees Limiting, \(f_s\)
kips/ft2 | kPa
Very loose to medium, sand to silt 15 1.0 47.8
Loose to dense, sand to silt 20 1.4 67.0
Medium to dense, sand to sand-silt 25 1.7 81.4
Dense to very dense, sand to sand-silt 30 2.0 95.8
Dense to very dense, gravel to sand 35 2.4 114.9

Toe Resistance

Toe resistance is given by the general form in equation (4). Unit toe resistance for piles in cohesionless soils is calculated by:

(7)\[q_p = \sigma' N_q\]

where:

  • \(\sigma'\): effective stress at pile tip (not average)
  • \(N_q\): bearing capacity factor

Table 9 offers guidelines for \(N_q\), bearing capacity factor as well as limiting, \(q_p\).

Table 9 Guidelines for Toe Resistance in Siliceous Soil
Soil \(N_q\) Limiting, \(q_p\)
kips/ft2 | MPa
Very loose to medium, sand to silt 8 40 1.9
Loose to dense, sand to silt 12 60 2.9
Medium to dense, sand to sand-silt 20 100 4.8
Dense to very dense, sand to sand-silt 40 200 9.6
Dense to very dense, gravel to sand 50 250 12.0

In order to interpret Table 8 and Table 9 algorithmically, the correlation in Table 10 is employed in edafos.

Table 10 SPT-N corrected Correlations
Density \(N_{cor}\) (bpf) \(\phi\) (deg)
Very loose 0 - 4 < 28
Loose 5 - 10 28 - 30
Medium dense 11 - 30 30 - 36
Dense 31 - 50 36 - 41
Very Dense over 50 > 41

In which case Table 8, Table 9 and Table 10 can be consolidated as in Table 11.

Table 11 Guidelines for Shaft and Toe Resistance in Siliceous Soil with SPT-N values
Soil \(N_{cor}\) (bpf) \(\delta\) (deg) \(f_{s.lim}\) (ksf) \(N_q\) \(q_{p.lim}\) (ksf)
Very loose to medium, sand to silt 0 - 4 15 1.0 8 40
Loose to dense, sand to silt 5 - 10 20 1.4 12 60
Medium to dense, sand to sand-silt 11 - 30 25 1.7 20 100
Dense to very dense, sand to sand-silt 31 - 50 30 2.0 40 200
Dense to very dense, gravel to sand over 50 35 2.4 50 250

Olson 90 Method

The Olson 90 method is for cohesionless soils only. It was created from a database of 31 load tests on steel pipe piles.

Required Properties

Pile:
  • \(\alpha\) or \(d\): side length or diameter for surface area, \(A_s\) (shaft resistance)
  • \(\alpha\) or \(d\) (\(t\)): side length or diameter (with thickness for open ended) for toe area, \(A_p, A_{pp}\) (toe resistance)
  • pile type: open-ended or closed-ended for \(K\) selection (cohesionless soils)
Soil:
  • type: cohesive/cohesionless classification
  • \(\gamma\): total unit weight for effective stress calculations
  • \(s_u\): undrained shear strength (cohesive soils)
  • desc, \(N_{cor}\): soil description and SPT-N corrected to select \(\delta\), \(f_{s.lim}\), \(N_q\), \(q_{s.lim}\) (cohesionless soils)

Note: edafos runs a pre-check to verify that all required properties have been defined prior to running the capacity calculations. Refer to the _pre_check() method for more information.

Cohesionless Soils

Olson 90 is similar to the Revised API method with two main differences. First, the coefficient of lateral earth, \(K\), is calculated rather than taken from Table 7. In Olson 90, \(K\) is:

(8)\[\begin{split}K = \begin{cases} 0.16 + 0.015 \, N_{cor} & \textrm{non-displacement piles}\\ 0.70 + 0.015 \, N_{cor} & \textrm{full displacement piles} \end{cases}\end{split}\]

where:

  • \(N_{cor}\): SPT-N values corrected for overburden pressure

Next, Olson 90 provides revised guidelines for shaft and tow resistances which are offered in Table 12.

Table 12 Olson 90 guidelines for Shaft and Toe Resistance
Soil \(N_{cor}\) (bpf) \(\delta\) (deg) \(f_{s.lim}\) (ksf) \(N_q\) \(q_{p.lim}\) (ksf)
Gravel 0 - 4 [20] [1.4] [12] [60]
5 - 10 [25] [1.7] [20] [100]
11 - 30 [30] [2.0] [40] [200]
over 30 [35] [2.4] [60] [250]
Sand / Gravel 0 - 4 [20] [1.4] [12] [60]
5 - 10 [25] [1.7] [20] [100]
11 - 30 [30] [2.0] [40] [200]
over 30 [35] [2.4] [60] [250]
Sand 0 - 4 [20] [1.0] [50] [40]
5 - 10 30 1.1 120 120
11 - 30 35 1.9 120 190
31 - 50 40 2.6 120 190
51 - 100 40 3.7 130 200
over 100 40 3.8 220 530
Sand / Silt 0 - 4 10 [1.0] [10] [10]
5 - 10 10 [1.0] [20] [40]
11 - 30 15 [1.4] 50 110
31 - 50 20 2.0 100 160
51 - 100 [30] [2.0] [100] [200]
101 - 200 [34] [20] [100] [200]
over 200 40 20 [100] [200]
Silt 0 - 4 [10] [1.0] [10] [40]
5 - 10 15 [1.0] [10] [40]
11 - 30 20 [1.4] [10] [40]
31 - 50 20 [1.4] [12] [60]
over 50 [25] [1.4] [12] [60]

Note:

  • Must not interpolate. In using values in Table 12, use the line corresponding to N = 4 for any layer with N less than or equal to 4, the line corresponding to 10 for N = 5 - 10, and so on.
  • Number in brackets were extrapolated, no supporting data.