Shaft Resistance of Piles

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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:

Q_{ult}=Q_{tip,ult}+Q_{sL}=q_{tip-ult}A_b+sum q_{si}A_{si}

where Q tip,ult  = tip resistance; QsL = skin resistance; qtip-ult  = bearing stress; Ab = area of pile tip; qsi  = skin friction of ith layer; Asi = skin area in contact with ith layer;


Concepts and Formulas


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.

Granular Soils and Drained Clays (Long-term clays):

K-δ Method:

q_{sL}=K sigma '_{v0}tandelta

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.

â–º 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


â–º 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


Undrained Saturated Clays (Short-term clays):

alpha method:

q_{sL}=alpha S_u

obtain α using the following equation from Kulhawy

alpha = 0.21+0.26frac{P_a}{S_u}leq1

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):


ho q_c

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

ho = 0.11(10)^{-1.3tanphi}


ho = frac{3}{I_{rr}}

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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