# Shaft Resistance of Piles

Courses > Foundation Analysis and Design > Bearing Capacity of Piles (Deep Foundations) > Shaft Resistance of Piles

## Introduction on Shaft Resistance of Piles :

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 of Shaft Resistance of Piles:

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:

$q_{sL}=K \sigma '_{v0}tan\delta$

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

### Undrained Saturated Clays (Short-term clays):

alpha method:

$q_{sL}=\alpha S_u$

obtain α using the following equation from Kulhawy

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

where Pa = atmospheric pressure; Su = undrained shear strength

lambda method:

$q_{sL}=\lambda(q+2S_u)$

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):

$q_{sL}=f_s$

$q_{sL}=\rho q_c$

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

$\rho = 0.11(10)^{-1.3tan\phi}$

or

$\rho = \frac{3}{I_{rr}}$

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:

$q_{sL}=0.02p_aN_{60}$
Low displacement piles:

$q_{sL}=0.01p_aN_{60}$
For driven piles in sand, Briaud suggested that:

$q_{sL}=0.224p_a(N_{60})^{0.29}$

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