Geotechnical Engineering

DHARM

838 GEOTECHNICAL ENGINEERING

The distance between the two geophones, D 8 , is then measured. It can be proved from
the theory of wave propagation that the wave length in this particular case is four times the
distance Dg. The velocity, Cs, of the propagating shear wave can be obtained from Vs = f.λ,
where f is the frequency of vibration (cps) which is the same as that of the oscillator. This may
be got from vibration record or by means of a tacheometer.
Alternatively, the output from the geophones may be connected to the two vertical am-
plifiers of a double beam oscilloscope. The distance between the two geophones is so adjusted
that the two traces on the oscilloscope screen are 180° out of phase. The distance between the
geophones in then equal to half the wave length (λ) of the vibration. The shear wave velocity
may be calculated as before.

The modulus of elasticity (E) and the shear modulus (G) may be calculated from the

following equations:

E = 2ρCs^2 (1 + υ) ...(Eq. 20.71 (a))

G = ρCs^2 ...(Eq. 20.71 (b))

where ρ is the density of the soil and v, the Poisson’s ratio of soil.

The following values may be used for the Poisson’s ratio:

clay : 0.50

sand : 0.30 to 0.35

Rock : 0.15 to 0.25

As a general rule, υ may be assumed as 0.3 for cohesionless soils and 0.4 for cohesive

soils.

The test is carried out with the frequency of the oscillator set to the operating frequency

of the actual machine. The ratio of the dynamic force to static weight of concrete test block and

the oscillator taken together should be kept the same as that in the actual machine foundation.

Aliter

The shear modulus can also be obtained from the experimentally determined value of coeffi-

cient of elastic uniform compression as follows:

E = 2G(1 + υ) ...(Eq. 20.72)

and Cu =

α

υ

E

()BL

.

1

1

−^2 ...(Eq. 20.73)

where α is a constant which depends on the aspect ratio L

B

F

HG

I

KJ

, L and B being the length and

breadth of the rectangular block used in the test. Table 20.3 gives the values of α for various

values of

L

B

, according to Barkan (19.62).