Geoscience Reference
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where
r
stands for the distance measured from the wave source along the wave path and
t
is the elapsed time. Note that this equation stands for wave propagation in the positive
directionof
r
.Accordingly,thesoilvelocity,compressionalstrain,andthecompressional
stress,
σ
,inthe
r
direction are derived as
U
Velocity
=
∂
u
/∂
t
=
(2)
U
/
Normal strain
=−
∂
u
/∂
r
=
Vp
(3)
E
Vp
U
=
E
Vp
×
σ
=
E
×
(
normal strain
)
=
velocity
(4)
Thus, the velocity history in Figure15.8 also implies that the stress history is reasonably
represented by one cycle of loading (Figure15.9), and, moreover, the unloading in the
second half of the cycle is less significant than the first half. Hence, the present study
supposesthattheintensityofstressincrementsduringfirstcompressionandthefollowing
extension have the ratio of 100:75 (Figure15.9). The magnitude of stress is determined
by an empirical formula on
73
R
−
1
.
25
maximum velocity
:
PPV
=
1
.
√
W
(5)
in which
PPV
designates the maximum soil velocity (m/s),
R
the distance from the
point of blasting, and
W
the weight of the employed explosive (kgf). For experimen-
tal reproduction of stress-strain history caused by blasting, the maximum velocity given
by Eq. (5) was converted to strain by Eq. (3), firstly, and the strain was further converted
to stress history by using such an experimental data as the monotonic undrained triaxial
compression in Figure15.11.
With these points in mind, two sequences of blasting around the point of interest are
discussed. The first and the second sequence employ order of blasting which starts from
one end towards the other. By ignoring blasting at far distances, the P wave propagation
from two consecutive blastings is found to induce principal stress in similar directions;
UndrndTraxl.qpc
100
Consolidated under
100 kPa
80
50 kPa
60
40
Undrained triaxial compression
on loose Toyoura sand (Dr
=50%)
20
0
0
0.002
0.004
0.006
Axial strain (in decimal)
0.008
0.01
Strain
ε
PPV
a
Fig. 15.11. Monotonic undrained loading oftriaxial compressional stress
