DHARMELEMENTS OF SOIL DYNAMICS AND MACHINE FOUNDATIONS 873
SUMMARY OF MAIN POINTS
- ‘Soil Dynamics’ is defined as that part of Soil Mechanics which deals with the behaviour of soil
under dynamic loading. This has application is a wide variety of fields of Civil engineering activ-
ity; one important field of application is the design of machine foundations. - There are six modes of vibration for a block or body-three translational and three rotational. Of
these, Vertical vibrations are of most common occurrence in machine foundations, in addition to
lateral vibrations or sliding in some horizontal machines. - ‘Free Vibration’ is vibration which occurs under the influence of forces inherent in the system
itself, while ‘forced vibration’ requires the continuous use of an external force or exciting force,
which may be continuous periodic force as in reciprocating machinery or an impulse as in impact
machinery. Of course, an external force is required to initiate even free vibrations. - The frequency with which a system undergoes free vibration is known as its ‘natural frequency’,
which will have different values in different modes of vibration for any system. - The particular operating frequency, equal to the natural frequency of a system, at which the
amplitude of motion of the system becomes excessively large is known as the ‘resonant frequency’.
Obviously, resonant conditions must be avoided. - ‘Damping’ in a physical system is resistance to motion-this may be viscous damping, friction
damping, internal damping, interfacial damping, or radiation damping. A system is said to be
negatively damped if it draws energy from some source during vibration. - Free and forced vibration may occur without and with damping, the latter being more common
in practical situations. The ratio of dynamic amplitude to static displacement is called ‘magnifi-
cation factor’. - The limiting value of the damping coefficient for the motion to be periodic is called the ‘coeffi-
cient of critical damping’. - In forced vibration with damping, the exciting force may be applied by an electromagnetic vibra-
tor which produces constant force-amplitude, or by an oscillator with rotating unbalanced masses
producing an exciting force proportional to the square of the frequency. - The ‘Coefficient of elastic uniform compression’ is defined as the constant of proportionality
between the compressive stress and the elastic part of the settlement of soil; it is different from
the coefficient of subgrade reaction which is similarly defined but the total settlement of the soil
being the criterion.
The ‘repeated plate bearing test’ is used for the determination of the coefficient of elastic uni-
form compression; the value of latter has been found to be inversely related to the size of the
plate.
The dynamic soil parameters such as ‘shear modulus’ or modulus of elasticity’ may be obtained
from a standard block vibration test in which the shear wave velocity is measured. - Block-type machine foundations are commonly used for reciprocating machines as also for im-
pact machines. - The important design criteria for the design of a machine foundation are:
(i) The foundation should be capable of withstanding the superimposed loads-static and dy-
namic-without the risk of shear failure and without harmful settlement.
(ii) Resonant conditions must be avoided with a margin of safety.
(iii) Amplitude of vibration should be within permissible limits prescribed by the manufacturers
or by the appropriate authority.