Geotechnical Engineering

DHARM

832 GEOTECHNICAL ENGINEERING

Shear or S-Wave

This wave induces the motion of the soil particles in a direction perpendicular to the direction

of propagation of the wave. The velocity of the wave, Cs, may be expressed as

Cs =

G

ρ ...(Eq. 20.62)

where G = shear modulus of the soil.

Rayleigh or R-Wave

This wave is propagated at or near the surface and induces motion of the soil particle in the

shape of a vertical ellipse.

The velocity, CR, of this wave may be taken as almost equal to Cs for all practical pur-

poses.

Compression Bar Wave

This wave is propagated in thin bars or columns of soil materials which induces motion of the

soil particle in the direction of propagation of the wave (bar axis). The velocity of this wave, Cb,

is expressed as

Cb =

E

ρ ...(Eq. 20.63)

P-Waves, S-Waves, and R-Waves are used in field tests, and S-Waves and compression

bar waves are used in laboratory tests for the evaluation of the soil parameters under dynamic

conditions.

20.3.6Determination of Soil Parameters
As already indicated in sub-section 20.3.4, the soil parameters needed in the analysis of ma-
chine foundation by the Mass-spring-dashpot model are the spring constant, k, and the damp-
ing ratio, D, while those needed in the analysis by the elastic half-space approach are shear
modulus G, and Poisson’s ratio, v, of the soil:
The spring constant can be obtained from the coefficient of elastic uniform compression,
Cu, which, in turn, may be determined by ‘repeated plate bearing test’.
The coefficient of elastic uniform compression, Cu, is defined as the constant of propor-
tionality between the compressive stress or external uniform pressure on soil and the elastic
part of the settlement (It has been observed that, within a certain range of loading, there is a
linear relationship between the elastic settlement, Se, and the external uniform pressure pz).
This is different from the coefficient (or modulus) of subgrade reaction, which is taken as the
constant of proportionality between the total settlement and the external pressure on soil. It is
obvious that Cu is always greater than this since the ‘elastic’ part of deformation is always
smaller than the total settlement. The dimensions for these coefficients are ‘FL–3 and the units
are kg/cm^3 (MKS) or kN/m^3 (SI).
The corresponding coefficients for horizontal translation (lateral or longitudinal), rota-
tion about X- or Y-axis (pitching or rocking), and rotation about Z-axis or vertical axis (yawing
or torsion) are respectively called ‘coefficient of elastic uniform shear (Cτ), ‘coefficient of elastic
non-uniform compression (Cφ), and ‘coefficient elastic non-uniform shear (Cψ). They are also