Geotechnical Engineering

DHARM

ELEMENTS OF SOIL DYNAMICS AND MACHINE FOUNDATIONS 833

defined in a similar manner (IS: 2810-1979 “Glossary of Terms relating to Soil Dynamics (First
Revision)”).
All these coefficients are used for the evaluation of the spring stiffness of soil in various
modes of vibration. These coefficients are functions of soil-type and of size and shape of the
foundation; however, they are often assumed to be functions of soil type only for the sake of
convenience.
The spring constant (k) for the various modes of vibration are related to these coeffi-
cients as follows:

(i) For Vertical Vibrations kz = Cu.Af ...(Eq. 20.64 (a))

(ii) For horizontal (sliding) kτ = Cτ.Af ...(Eq. 20.64 (b))

vibrations

(iii) For pitching or rocking kφ = Cφ.Ix (or y) ...(Eq. 20.64 (c))

vibrations

(iv) For torsional vibrations kψ = Cψ.Iz ...(Eq. 20.64 (d))

Here Af is the area of horizontal contact surface between the foundation and the soil,

and I is the second moment of contact area about the corresponding axis passing through the

centroid of the base.

Damping is a measure of energy dissipation in the system. Being a physical property of

the system, it can be evaluated only by experiments. The Damping Ratio, D, may be determine

either from a ‘free vibration test’ or a ‘forced vibration test’.

The dynamic shear modulus (G) and Poisson’s (v) may be determined from a field vibra-

tion test of a cement concrete block as explained in the I.S. code or practice -IS: 5249-1977

“Method of Test for determination of insitu dynamic properties of soil (First Revision)”.

Each of these tests/methods for the determination of the soil parameters will now be

considered sequentially.

Repeated Plate Bearing Test (for the determination of Cu and hence kz)

In a typical plate bearing test, load is applied on to a rigid plate and the vertical deformation is

measured by dial gauges. Typical test data are put in the form of a plot between the applied

stress on the soil through the plate and the corresponding vertical deformation of the soil

below the plate, as shown in Fig. 20.19.

Stress

B

O Vertical deformation

Fig. 20.19 Typical plot from the results of a plate bearing test