blows per unit penetration distance to develop this resistance, using a hammer of given rated
energy or weight and height of drop. The driving stress is assumed to be the ultimate driving
resistance divided by the cross-sectional area of the pile, and this must not exceed the safe
working stress on the pile material. As already stated in Section 1.4, the dynamic resistance
is not necessarily equal to the static load-bearing capacity. However, if soil mechanics
calculations as described in Chapter 4 have been made to determine the required size and
penetration depth necessary to develop the ultimate bearing capacity, then either a simple
dynamic pile driving formula or, preferably, stress-wave theories can be used to check that
a hammer of a given weight and drop (or rated energy) will not overstress the pile in driving
it to the required penetration depth. If at any stage of penetration the stresses are excessive
a heavier hammer must be used, but if greater hammer weights and lesser drops still cause
overstressing then other measures, such as drilling below the pile toe or using an insert
pile having a smaller diameter, must be adopted.
It is important to note that in many instances the soil resistance to driving will be higher
than the value of ultimate bearing capacity as calculated for the purpose of determining the
allowable pile load. This is because calculations for ultimate bearing capacity are normally
based on average soil parameters. Where soil strength data are scanty it is necessary to
assume conservative parameters. However, when considering resistance to driving, the
possible presence of soil layers stronger than the assumed average must be taken into
account. Hence, when assessing driving stresses it is advisable to make a separate calcula-
tion of ultimate bearing capacity based on soil strength values higher than the average. Also,
in cases where negative skin friction is added to the working load, the soil strata within
which the drag-down is developed will provide resistance to driving at the installation stage.
Methods of recording hammer blows and measurements of temporary compression and set
as described in Section 11.3.1 are useful as a means of site control of driving operations, but
they are not helpful for determining stresses caused in the pile body by hammer impact.
A widely used method of calculating driving stresses is based on the stress-wave theory
developed by Smith(7.2). The pile is divided into a number of elements in the form of rigid
masses. Each mass is represented by a weight joined to the adjacent element by a spring as
shown in the case of modelling a pile carrying an axial compression load in Figure 4.29. The
hammer, helmet, and packing are also represented by separate masses joined to each other and to
the pile by springs. Shaft friction is represented by springs and dashpots attached to the sides of
the masses (Figure 4.29) which can exert upward or downward forces on them. The end-bearing
spring can act only in compression. The resistance of the ground at toe is assumed to act as a
resisting force to the downward motion of the pile when struck by the hammer. Friction on the
pile shaft acts as a damping force to the stress wave as determined from the side springs and
dashpots. For each blow of the hammer and each element in the hammer–pile system,
calculations are made to determine the displacement of the element, the spring compression of
the element, the force exerted by the spring, the accelerating force and the velocity of the ele-
ment in a given interval of time. This time interval is selected in relation to the velocity of the
stress wave and a computer is used to calculate the successive action of the weights and springs
as the stress wave progresses from the head to the toe of the pile. The output of the computer
is the compressive or tensile force in the pile at any required point between the head and toe.
The input to the computer comprises the following data:
(1) Length of pile
(2) Material of pile380 Structural design of piles and pile groups