Geotechnical Engineering

DHARM

ELEMENTS OF SOIL DYNAMICS AND MACHINE FOUNDATIONS 839

Table 20.3 Value of α for rectangular foundations (Barkan 1962)

Aspect ratio L/B Value of α

1 1.06

1.5 1.07

2 1.09

3 1.13

5 1.22

10 1.41

The coefficient of elastic uniform compression may also be obtained as follows based on
the provisions given in IS:5249-1977.

The vibration pick-up is fixed on top of the block and the amplitudes are obtained by
means of an oscillograph for different frequencies of excitation. The frequency corresponding
to the peak amplitude is determined. This is the resonant frequency, fn. Then Cu is got from
the equation

Cu =

4 π^22 fM

A

n

b

...(Eq. 20.74)

where M is the mass of the test block plus mounted mechanical equipment,

fn is the resonant frequency in cps, and
Ab is the contact area of the test block with soil.
Having determined one of the soil constants, say Cu, from an insitu test on soil, the
other dynamic soil constants may be evaluated approximately from the following relations
suggested by Barkan.

(i) Coefficient of elastic uniform shear,

Cτ = 0.5Cu ...(Eq. 20.75 (a))

(ii) Coefficient of elastic nonuniform compression

Cφ = 2Cu ...(Eq. 20.75 (b))

(iii) Coefficient of elastic nonuniform shear

Cψ = 0.75Cu ...(Eq. 20.75 (c))

Determination of Damping Ratio, D

(a) Free Vibration test. Free vibrations are induced in the block is some suitable way,
such as hitting the block on top with a hammer. The decay curve is obtained on a vibration
recorder connected to a vibration pick-up fixed to the concrete block.

The damping ratio is obtained from the formula

D =

1

2

1

π 2

log

z

z

...(Eq. 20.76)

where z 1 and z 2 are peak amplitudes at two successive peaks of the decay curve (Fig. 20.12 (c))
(This is valid for small values of D only).