Vibrations due to excavation 263parameters. Independent parameters in some way control the blast; the
dependent parameters relate to the ground response.
The main independent parameters are: blasting energy (kgdelay),
W; distance from the blast (m), R; wave propagation velocity in the rock
mass (mls), c; rock bulk density (kg/m3), p; and time (s), t.
The dependent parameters are: maximum ground displacement (m), u;
maximum ground velocity (m/s), v; maximum ground acceleration (m/s2),
a; and frequency (Hz), f.
Dimensional analysis of these parameters results in the following six
dimensionless variables: tclR, W/p?R3, ulr, vlc, aR/c?, ft. The first two are
independent variables; the final four are dependent variables. It is helpful
to graphically present the ground displacement information using the
dimensionless variables.
One of the most important variables is v, the velocity of ground
displacement (we note that this is a vector and should be considered as the
resultant velocity, i.e. v = { v,” + 4 + V?}~”).TO determine v, the maximum
component of velocity, the maximum resultant velocity, or the vector sum
of the maximum components (which may be temporally separated) can be
used. The first of these formulations is, historically, the most used. In Fig.
15.24(a), this velocity is plotted against R/W’/3, which is the inverse cube
root of the dimensionless variable Wlp?R3, assuming that p and c are
sufficiently constant to be neglected. The graph shows the advantage of the
dimensionless approach, because of the coherency of the results from many
different sites and blasting operations.
An alternative approach is to plot the maximum value of v (the
peak particle velocity, PPV) versus different distances from the source
for various vibration inducing operations. In this case, as illustrated in
Fig. 15.24(b), there is a suite of straight lines for the different operations.
Figure 15.24 Blasting characterization using (a) dimensionless and (b) dimensional
methods (from Hendron, 1977).