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6.17 Pile driving formulas

An alternative method for determining the collapse load of driven piles in situ is to correlate it with the energy required to drive the pile into the soil. Several equations have been proposed for this and are implemented in pile driving equipment software to verify whether a pile has reached the required ultimate geotechnical strength Qf when driven at the pre-determined depth (or determine the penetration depth where the required Qf is reached).

One of the earliest equations is the Engineering News (EN) Record formula, which was derived in 1888 by AM Wellington, editor of the Engineering News Record, to measure the capacity of light-weight timber piles on the basis of work-energy theory (Lawton et al. 1986):

(6.85) {Q_{f,test}} = \dfrac{{{n_1}{W_R}h}}{{{s_p} + {C_1}}}

where WR is the weight of the hammer; h is the height of fall; sp is the pile penetration depth per blow, taken as the average value obtained from the last few driving blows; C1 is a constant, equal to C1 = 25 mm for drop hammers and C1 =2 .5 mm for steam hammers; n1 is a constant depending on the hammer efficiency, provided in Table 6.11.

Table 6.11. Typical values for the n1 factor (Budhu 2011).
Hammer type n1
Drop hammer 0.75-1.0
Single-acting hammer 0.75-0.85
Double-acting hammer 0.85
Diesel hammer 0.85-1.0

The EN formula has been modified several times over the years, to account for developments in driving technology. A more recent version of Eq. 6.85 is (Michigan State Highway Department 1965):

(6.86) {Q_{f,test}} = \left( {\dfrac{{{E_{EN}}{W_R}h}}{{{s_p} + C}}} \right) \times \left( {\dfrac{{{W_R} + n_{EN}^2{W_p}}}{{{W_R} + {W_p}}}} \right)

where EEN is the efficiency of the hammer, from Table 6.12; C = 2.54 mm (s and h in mm too); Wp is the weight of the pile; nEN is the coefficient of restitution between the hammer and the pile tip, provided in Table 6.13.

Table 6.12. Typical values for the EEN factor (Michigan State Highway Department 1965).
Hammer type EEN
Single and double-acting hammer 0.70-0.85
Diesel hammer 0.80-0.90
Drop hammer 0.70-0.90
Table 6.13. Typical values for the nEN factor (Michigan State Highway Department 1965).
nEN
Cast-iron hammer and concrete piles (without cap) 0.40-0.50
Wood cushion on steel piles 0.30-0.40
Wooden piles 0.25-0.30

 

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Fundamentals of foundation engineering and their applications Copyright © 2025 by University of Newcastle & G. Kouretzis is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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