A deep foundation is a type of foundation which transfers building loads to the earth farther down from the surface than a shallow foundation does, to a subsurface layer or a range of depths.

A pile is typically a vertical structural element of a deep foundation, driven or drilled deep into the ground at the building site.

Ultimate bearing capacity of piles is the sum of its skin resistance and tip resistance:

where Q_{ tip,ult} = tip resistance; Q_{sL} = skin resistance; q_{tip-ult} = bearing stress; A_{b} = area of pile tip; q_{si} = skin friction of i^{th }layer; A_{si} = skin area in contact with i^{th} layer;

There are numerous methods that have been used over the years to estimate shaft resistance. A few of these methods are illustrated in this section.

**K-δ Method:**

K and δ are usually estimated based on the type of pile and the characteristics of the soil.

Here are some methods to estimate these two parameters.

► Estimate K:

1- Stas and Kulhawy method:

Foundation type and methd of installation | Ratio of horizontal soil stress coefficient to in-situ value, K/K0 |
---|---|

Jetted pile | 1/2 to 2/3 |

Drilled shaft, cast-in-place | 2/3 to 1 |

Driven pile, small displacement | 3/4 to 5/4 |

Driven pile, large displacement | 1 to 2 |

2- Sowers method:

Foundation type | Ratio of horizontal soil stress coefficient to in-situ value, K/K0 | |
---|---|---|

Loose sand (Dr < 30%) | Dense sand (Dr > 70%) | |

Jetted piles | 0.5 to 0.75 | 0.5 to 1.0 |

Drilled piles | 0.75 to 1.5 | 1 to 2 |

Driven piles | 2 to 3 | 3 to 4 |

► Estimate δ

1- Stas and Kulhawy method:

Interface materials | Ratio of interface angle of friction to soil angle of friction δ/φ | Typical field analogy |

sand/rough concrete | 1.0 | cast-in-place |

sand/smooth concrete | 0.8 to 1.0 | precast |

sand/rough steel | 0.7 to 0.9 | corrugated |

sand/smooth steel | 0.5 to 0.7 | coated |

sand/timber | 0.8 to 0.9 | pressure-treated |

**alpha method:**

obtain α using the following equation from Kulhawy

where Pa = atmospheric pressure; Su = undrained shear strength

**lambda method: **

where q is the mean effective vertical stress over the embedded pile length and λ is obtained from the figure below (from Kulhawy). According to Kulhawy, the values of λ shown in the figure below are valid only for steel pipe piles. Limited research has shown that λ for drilled shafts (typically less than 20 ft deep) is on the order of about 1/3 to 2/3 of the values shown in the figure below.

**Direct Estimates from In Situ Tests:**

From the CPT test, pile shaft resistance can be determined from either the sleeve friction (fs) or the tip resistance (qc):

where ρ is the friction ratio. For driven piles, the value of rho can be estimated from either of the following equations:

or

Values of ρ for drilled shafts are 1/3 to 1/2 the values shown in the two equations above.

Meyerhof recommended the following equations for shaft resistance in high and low

displacement piles:

High displacement piles:

Low displacement piles:

For driven piles in sand, Briaud suggested that:

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