Civil Engineering Reference
In-Depth Information
and use the greatest, termed the Peak Particle
Velocity (PPV), to assess damage potential. The
difference between the particle velocity of a stress
wave, and the velocity of propagation of the wave
can be explained as follows. As the wave passes
through the ground, each particle of the rock and
soil undergoes an elliptical motion, and it is the
velocity of this oscillating motion (possibly up to
0.5 m/s) that is measured in assessing blast dam-
age. In contrast, the velocity of propagation of
the wave is in the range 300-6000 m/s, and this
has no direct bearing on damage.
Ground motion can be described as a sinus-
oidal wave in which the variation of the particle
velocity
v
with time
t
is given by (Figure 11.17):
If the particle velocity
v
has been measured,
then the displacement
δ
can be found by integ-
ration, and the acceleration
a
by differentiation
as follows:
v
ω
ωv (
m
/
s
2
)
δ
=
and
a
=
or
ωv
9.81
(
g
/
ms
2
)
a
=
(11.15)
The most reliable relationship between blast
geometrics and ground vibration is that relating
particle velocity to
scaled distance
. The scaled dis-
tance is defined by the function
R/
√
W
, where
R
(m) is the radial distance from the point of
detonation, and
W
(kg) is the mass of explosive
detonated per delay. Field tests have established
that the maximum particle velocity,
V
(mm/s)
is related to the scaled distance by following
attenuation relationship (Oriard, 1971):
v
=
A
sin
(ωt)
(11.12)
where
A
is the amplitude of the wave, and
ω
is the
angular velocity. The magnitude of the angular
velocity given by
k
R
β
2
π
1
T
V
=
√
W
(11.16)
ω
=
2
πf
=
(11.13)
where
k
and
β
are constants that have to be
determined by measurements on each particular
blasting site. Equation (11.16) plots as a straight
line on log-log paper, where the value of
k
is given
by the PPV intercept at a scaled distance of unity,
and the constant
β
is given by the slope of the line.
An example of such a plot is given in Figure 11.18.
In order to obtain data from the preparation of
a plot, such as that in Figure 11.19, it is necessary
to make vibration measurements with a suitable
monitoring instrument. Table 11.5 shows typ-
ical specifications for a seismograph suitable for
measuring blast vibrations, as well as vibrations
produced by a wide range of construction equip-
ment such as pile drivers. Of importance for
monitoring non-blasting applications is the useful
frequency range of the equipment; for the Instan-
tel DS677, this range is 2-250 Hz, which means
that vibrations with frequencies outside this
range will not be detected. Some of the features
of instruments currently available (2003) are
measurement of both ground vibration—velocity,
where
f
is of the frequency (vibrations per
second, or Hertz) and
T
is the period (time for one
complete cycle). The wavelength
L
of the vibra-
tion is the distance from crest to crest of one full
cycle and is related to the period
T
and the velocity
of propagation
V
by
L
=
VT
(11.14)
Period,
T
Crest
A
2
3
4
Time
Trough
Figure 11.17
Sinusoidal wave motion for typical
ground vibrations.
