Geotechnical Engineering

DHARM

664 GEOTECHNICAL ENGINEERING

bearing. If this does not happen, the pile is said to meet ‘refusal’. The shape of the wave de-
pends upon the rigidity of the pile. If the maximum stress produced exceeds the strength of the
pile, the pile will get damaged due to ‘over driving’.

To obtain a solution for the wave equation, it is necessary to know the approximate
values of length, cross-section, elastic properties and weight of the pile and the pile hammer
characteristics, and to assign suitable values for spring constants and soil damping. By ana-
lysing changing conditions for successive small increments of time, the effects of the travelling
force wave are simulated. This requires numerical integration, which is conveniently handled
by a computer. Generally, the analysis is used for diagnosing causes of unusual driving behav-
iour or as a guide for more efficient choice of equipment or pile.

Approximate methods—dynamic pile driving formulae

Approximate methods of dynamic analysis or the socalled ‘dynamic pile-driving formulae’,
have been used for more than a century to predict pile capacity. These are developed from
work-energy theory and are simpler to apply than the wave equation. Hence, these formulae
are still useful in predicting pile capacity from simple observations of driving resistance.

The basic assumption underlying the pile formulae is that the kinetic energy delivered
by the pile hammer is transferred to the pile and the soil and, accomplishes useful work by
forcing the pile into the soil against its dynamic resistance.

Thus, the basic work-energy equation is as follows:

Wh × H × η = Qup × s + Energy losses ...(Eq. 16.18)

where Wh = weight of pile hammer,

H = height of fall of hammer,
η = efficiency of hammer,
Qup = ultimate capacity of the pile, and
s = penetration (set) of the pile per blow.
This relationship is solved for Qup, assumed to be equal to the capacity of the pile under
sustained loading.

Energy losses include those due to elastic compression of the pile, soil, pile cap and
cushion and by heat generation. Variations in the several pile formulae result from the differ-
ent methods to account for the energy losses, which is also the major uncertainty in this ap-
proach.

The assumption of work-energy theory does not properly consider the effect of impact
on a long member such as a pile; however, some of the formulae which consider the losses in an
empirical manner, have shown reliability for predicting the pile capacity in cohesionless soil.

Engineering News formula, Danish formula and Hiley’s formula are the more commonly
used pile formulae.

Engineering news formula

The ‘Engineering News’ formula (Wellington, 1886) was derived from observations of driving
of timber piles in sand with a drop hammer. The general form of this equation is as follows:

Qup =

WH

sC

h

()+

...(Eq. 16.19)