Page 551 - Rock Mechanics For Underground Mining

TRANSIENT GROUND MOTION

The most generally occurring surface wave is the Rayleigh wave. Particle motion
induced by passage of the wave is backward elliptical, in a vertical plane parallel to the
direction of wave propagation. The motion is equivalent to coupled P and vertically
polarised shear (SV) waves. The nature of the ground motion is illustrated in Figure
17.11b. The intensity of the motion dies out rapidly with depth. The propagation
velocity of the R wave is given by the positive real root of the equation
2
2
2

4C 3 s C − C 2 R C − C R 2 1/2 = C p 2C − C R 2 2 (17.6)
s
p
s
For = 0.25
C R = 0.926 C s = 0.53 C p
A Love wave is generated at the ground surface when a layer of low modulus material
overlies a higher modulus material. This is a relatively common condition, which can
arise when a weathered layer overlies fresh rock, or when backfill has been placed to
produce a level surface. In their refraction at the ground surface, waves are effectively
trapped in the upper soft layer. A Love wave consists of coupled P and horizontally
polarised shear (SH) waves, as illustrated in Figure 17.11c. A particle undergoes flat
elliptical motion, so that the surface displacement corresponds to horizontal shaking.
The propagation speed of the wave is a function of the wavelength of the motion, and
is given by the solution of the equation
2 2
2
G 1 1 C − C L = tan 2 H C L − 1 (17.7)
s1
2
G 2 2 C − C 2 C 2
L s2 s2
where subscripts 1 and 2 refer to the hard and soft media respectively, and H is the
depth of the soft layer.
Equation 17.7 indicates that the C L must lie in the range

C s2 < C L < C s1
Also, for the case H, C L tends to C s1 , indicating that wave propagation is oc-
curring mainly in the hard layer. For H, C L tends to C s2 , indicating wave trans-
mission is occurring mainly in the soft layer.
The generation of surface waves above a blast site is important in that it affects
the range of potential ground disturbance due to transient motion. Body waves are
spherically divergent, so that the amplitude u r (and particle velocity) at some range,
r, is related to r by equation 10.43, i.e.

u r ∝ 1/r
Surface waves are cylindrically divergent in the near-surface rock, so that, from equa-
tion 10.46, u r , (and ˙ u r ) are related to r by

u r ∝ 1/r 1/2

Thus, body waves are subject to attenuation due to geometric spreading at a greater
rate than surface waves. At points remote from an underground blast site, the induced
surface waves are therefore the main source of transient motion.
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