Geotechnical Engineering

DHARM

ELEMENTS OF SOIL DYNAMICS AND MACHINE FOUNDATIONS 829

The primary source of dynamic loading of soil is machinery of different kinds, which
cause dynamic forces and vibrations of the foundations for the machinery.

20.3.1Characteristics of Soil Under Dynamic Loading

Vibrations caused by dynamic loading impart energy to the soil particles. The soil grains slip
into and fill up corresponding void spaces (densification of soil), pore water tends to escape, the
modulus of elasticity tends to change, and so does its bearing capacity. The shock tends to
reduce the internal friction and adhesion considerably. Loose granular soils may be densified
by vibration, while it will have relatively smaller effect on cohesive soils. Saturated fine sand
or silt may undergo a phenomenon of ‘liquefaction’ as they tend to become ‘quick’ under the
action of dynamic forces under certain conditions.

Thus it may be understood that the engineering properties and behaviour of a soil will
be significantly affected by the application of dynamic loading.

20.3.2Natural Frequency of Foundation-Soil system

It has been stated earlier that the frequency of a system undergoing free vibration damping is
known as the natural frequency of the system. However, when this idea is to be applied to a
machine foundation-soil system, it should be realized that, unlike in the case of the Mass-
spring-dashpot model in which the spring was assumed to be weightless, the soil which is
analogous to the spring has weight. Thus, the response curve of a machine foundation-soil
system does not match exactly the response curve of the Mass-spring-Dashpot model. (A re-
sponse curve is merely the plot between the frequency versus amplitude of motion). This is
because of the interaction of flexibility, inertia, and damping present in the system (Whitman-
1966).

The natural frequency of the system is once again defined as

ωn =

k

M

and fn =

ω

ππ

n k

2 M

1

2

=

where M = Mf + Ms ...(Eq. 20.60)

Here Mf = Mass of the machine and foundation,

and Ms = Mass of the soil participating in the vibration.

The definition of resonant frequency of the system has to be based on the equation for fn,
taking cognisance of Eq. 20.60. While Mf is easily evaluated, determination of an appropriate
value for Ms in this equation is a ticklish problem, and involves some degree of empiricism.

20.3.3 Tolerance Limits

Tolerance limits for amplitudes are generally specified by the manufacturers of machinery.
The permissible amplitude of a machine foundation is governed by the relative importance of
the machine and the sensitivity of the neighbouring structure to vibration.

When the permissible amplitudes are not given by the manufacturer, the values sug-
gested by Richart (1970) may be adopted for preliminary design (Fig. 20.18). The envelope
described by the shaded line in this figure indicates the limit for “safety”; it need not be a limit