2 1 2 Rock dynamics and time-dependent aspects
bonded to bars Steel SPeclmen Steel
input rod ouput rod(a) Hopkinson bar (a) Piezoelectric transducersFigure 13.3 The Hopkinson bar and piezoelectric transducer methods for dynamic
properties. (a) Hopkinson bar. (b) Piezoelectric transducers.
way in which the energy is absorbed during the creation of the dynamic
complete stress-strain curve can be studied. Alternatively, piezoelectric
transducers can be used: these can be calibrated to directly indicate the
elastic constants for the pre-peak portion of the stress-strain curve. The
transducers are widely used, and apparatus is commercially available for
its implementation.
Since the wave propagation velocities are a function of the elastic rock
properties, it follows that the P- and S-wave velocities and associated
factors such as attentuation can be used to estimate the rock properties on
a literally global scale. A shear wave can only travel through a material that
can sustain a shear stress: consequently, shear waves do not travel through
liquids. During the early recording of seismic waves generated by
earthquakes at long distances from the foci, it was found that at certain
points on the Earth's surface there would be an absence of early shear wave
arrivals-normally the faster P-wave arrives first, followed by the slower
S-wave, followed by the surface waves and a complex mixture of reflected
and refracted waves. From the absence of the early shear wave arrivals, it
was realized that the Earth has a liquid core.
On a smaller scale, the manifold ways in which dynamic waves can be
generated and recorded provides great potential for ground exploration
techniques. Through the installation of a suitable array of geophones, and
by measuring the wave transit times and hence estimating velocities, there
is a powerful indicator method of establishing inhomogeneity, anisotropy
and, indeed, continuity and linear elasticity-i.e. all the CHILE versus
DIANE factors. Moreover, with the increasing sophistication of such
techniques, e.g. the recent developments in tomography, there is the
opportunity to use non-destructive testing to provide a three-dimensional
mechanical characterization of a rock mass. This is one of the most exciting
developments in rock characterization methods.
Another ramification of the existence of stress waves is the importance
of waves being reflected at a free face. In Fig. 13.4(a), we show the general
circumstances when a stress wave encounters an interface between two
continua with different elastic properties. In the general case, part of the
wave will be refracted as it passes into the second medium and part of the