Engineering Rock Mechanics

Time-dependency 2 1 3

c;, c;

Interface

at x = 0

c, = vp

c2 = \'\

Incident wave

Snell's law aoolie? to reflection and

Incident P-wave -1

P

/I -1

Incident S-wave pi = sin-i(-sinp,) c;

(xy polarisation) c;

Incident'S-wave

(z polarisation)

Generated

wave

F r

e e

wave reflected f a

as tensile wave C e

(a) Refraction and reflection at an interface (b) Reflection at a free face

Figure 13.4 The behaviour of longitudinal stress waves at material interfaces.
(a) Refraction and reflection at an interface. (b) Reflection at a free face.

wave will be reflected back into the first medium. This has implications for
the measurements of such waves and the mechanisms of wave propaga-
tion and rock failure during blasting.
However, the phenomenon of paramount importance is illustrated in
Fig. 13.4(b)-i.e. a compressive longitudinal stress wave is reflected as a
tensile longitudinal stress wave at a 'free face'. Such free faces occur
regularly in rock masses, in the form of discontinuites, but the one that
has greatest significance is formed by the rock-air interface. In fact,
Fig. 13.4(b) is a special case of Fig. 13.4(a) where almost all the energy is
reflected, with little being refracted into the air. The concept of the 'free
face' is critical in the design of all blasting rounds, and forms the basis of
the specialized pre-splitting and smooth-wall blasting techniques (see
Chapter 15).
In the next section, we consider the broad spectrum of material behav-
iour occurring over the wide range of strain rates likely to be encountered
in engineering.

13.3 Time-dependency

We noted that no time component is incorporated in elasticity theory: it is
assumed that the stresses and strains develop instantaneously on loading
or unloading. However, we noted in Chapter 6 when discussing the
complete stress-strain curve, that the exact form of the curve will depend
on the strain rate at which it is determined. It is commonly observed at rock
engineering sites, that the rock continues to deform after a stress change
occurs-e.g. convergence of well bores and tunnels. So, it is evident that,