Engineering Rock Mechanics

Stress waves 21 1

Particle

motion

r Particie A\\\\

II I I1 motion I

propagation

Direction of

Direction of

wave propagation

(a) Longitudinal (b) Transverse

title

tion

(c) Rayleigh (d) Love

Figure 13.2 Longitudinal, transverse, Rayleigh and Love waves.

particle motion is parallel to the direction of wave propagation, as illus-
trated in Fig. 13.2(c); with Love waves the particle motion is perpendicular
to the direction of wave propagation, as illustrated in Fig. 13.2(d).
Love waves are found to occur under certain conditions in a stratified
solid, depending on the relative shear wave velocities in the different
strata.
It is instructive to consider the numerical value of the longitudinal and
shear wave velocities and their ratios for an example rock. Taking p = 25
kN/m3, E = 20 GPa and v = 0.35, the various relations presented above give
vp = 1133 m s-', vs = 544 m s-', vS/V~ = 0.48, = 894 m s-*, VSB~ = 544
m s-l and vmdvp~~ = 0.61. In a site investigation, and with the assumption
of a CHILE material, we might use the P-and S-wave velocities, together
with a density assumption, to estimate the in situ values of E and v.
In the laboratory the dynamic properties of rock can be studied
with the Hopkinson bar, or by directly inputting P- and S-waves via
piezoelectric transducers. These two tests are illustrated in Fig. 13.3. In the
Hopkinson bar, a single controlled P-wave pulse passes along the first
steel bar, through a cylindrical rock specimen, and into the second steel
bar. Using strain gauges installed on both the steel bars, the amplitude of
the wave can be studied both before and after it passes through the
rock specimen. By steadily increasing the amplitude of the pulse, the