Miscellaneous piling problems 435When designing shallow foundations for machinery, vibrations which might cause damage
or nuisance to the surroundings can be absorbed or attenuated by increasing the mass of
the foundation block. There are old ‘rules-of-thumb’which require the ratio of the mass of the
foundation to the mass of the machine to be in the range of 1:1 to 4:1 depending on the type
of machine. The resulting required mass of the foundation may be excessive for loose or weak
soils leading to excessive settlement, even under static loading conditions, and necessitating
the provision of a piled foundation. Also, it may be necessary to employ piles on sites where
the water table is at a depth of less than one-half of the width of the block below the underside
of the base or even within a depth of twice the width of the block. This is because water trans-
mits amplitudes of vibration almost undamped over long distances which might result in
damaging effects over a wide area surrounding the installation. Similarly, piles may be desir-
able if a rigid stratum of rock or strongly cemented soil exists within a depth of times the
block width. Such a stratum reflects energy waves and magnifies their amplitude of vibration.
Generally, the effect of providing a piled foundation to a reciprocating or rotating machine
is to increase the natural frequency of the installation in the vertical, rocking, pitching, and
also possibly longitudinal, modes. This is because of the behaviour of the mass of soil
enclosed by the pile group acting with the pile cap and the piles themselves. The soil mass
may be relatively small where the piles act in end bearing, or large in the case of friction
piles. The natural frequency may be decreased in the lateral and yawing modes of vibration
because of the low resistance of piles to lateral loads at shallow depths.
To ensure that the ratio of the frequency of the disturbing moment or disturbing force
applied by the machinery to the natural frequency of the machine–foundation–soil system
is either greater or less than the required value, it is necessary to calculate the natural
frequency of the system. This is a complex matter, particularly for piled foundations, and is
beyond the scope of the present book. The reader is referred to the publications of
Barkan(9.1), Hsieh(9.2), Whitman and Richart(9.3), and Richart et al.(9.4)for general guidance.
Irish and Walker(9.5)have established design curves relating the natural frequency of piles
of various types to their effective length, both for the vertical and the rocking modes of
vibration. The American Concrete Institute(9.6)presents various design criteria and methods
of analysis, design and construction as currently applied to dynamic equipment foundations.
9.1.2 Pile design for static machinery loading
Piles and pile groups carrying static loads from machinery should be designed by the
methods described in Chapters 4 and 5. Particular attention should be paid to the avoidance
of excessive differential settlement of the pile cap; the differential movement should
not exceed 8 mm. The centre of gravity of the machine combined with the pile cap and
supporting piles should be located as nearly as possible on a vertical line through the
centroid of the pile group, and the eccentricity of the combined masses should not be greater
than 5% of the length of the side of the pile group. If possible the centre of gravity of the
machine and soil mass should be below the top of the pile cap.
9.1.3 Pile design for dynamic loading from machinery
Generally, it can be stated that the effect of applying dynamic loads to piles in fine-grained soils
is to reduce their shaft friction and end-bearing value, i.e. to reduce their ultimate carrying
capacity, and the effect in coarse-grained soils is to reduce their shaft friction but to increase
their end-bearing resistance at the expense of increased settlement under working load.