seven craters was 1.07 m/kg1/3. This is consider-
out damaging the underlying frozen ground, as
ably larger than the predicted Ra of 0.71 m/kg1/3
seen in one of the craters (Fig. 4). These reflected
for ice and is out of the range of the scaled crater
waves, traveling upward through the ice, may re-
radius data for ice (Mellor 1986a). If we use the
duce or cancel later shock waves penetrating down-
estimates for the scaled apparent radius of a crater
ward, thus reducing the total effect of the explo-
in snow (Mellor 1965) instead of ice, we get closer
sion.
agreement between the predicted and measured
crater radii. The predicted value would be 0.87
81-mm mortar test results
m/kg1/3 vs. the measured 1.07 m/kg1/3.
The mean apparent radius of the three craters
The size of a crater created by an explosion in-
formed by point-detonating fused projectiles was
1.15 m, resulting in a scaled radius of 1.17 m/kg1/3.
creases as the depth of the explosive charge below
the surface increases up to a certain depth, known
The craters were almost entirely confined to the
as the critical depth. If we assume that the projec-
snow layer on top of the ice. The measured scaled
tile did not explode at the surface but penetrated
radius is higher than the predicted scaled radius
through the snow and a short distance into the ice
of a crater in snow from a surface-placed explosive.
(<0.05 m) before exploding, then the data would
The mean depth of the craters was 0.16 m, giv-
ing a scaled depth of 0.16 m/kg1/3. Because the
be within the maximum range of experimental data
for ice presented by Mellor (1986a). However, there
snow layer was shallow (0.15 m) and the crater
is no field evidence that the projectiles did pen-
was almost entirely confined to this layer, the scaled
etrate into the ice before exploding.
depth may be low because of the reflection of
The seven measured craters had a mean appar-
the shock wave off the ice layer, inhibiting the cra-
ent depth of 0.32 m. This gives a scaled apparent
ter depth development.
depth of 0.25 m/kg1/3, much shallower than the
predicted depth for snow but almost the same as
60-mm mortar test results
the predicted value given by Mellor (1986a) for
Craters formed by the 60-mm mortar projec-
ice. Obviously these comparisons are complicated
tiles had a mean apparent radius of 0.88 m, or a
scaled apparent radius of 1.53 m/kg1/3. The cra-
by several factors. The experimental data used by
Mellor in developing the scaled radius relation-
ters were entirely confined to the snow layer. The
ships were produced by static spherical explosive
measured scaled apparent radius was much higher
than the predicted scaled radius of 0.87 m/kg1/3.
charges placed on the snow or ice surface. The ar-
The measured scaled depth was 0.33 m/kg1/3; this
tillery tests used a cylindrical projectile traveling
at high velocity. The experimental data were for a
is very close to the predicted scaled depth for snow.
single, uniform, semi-infinite-depth medium; we
had a relatively thin, multiple-layered medium with
January 1992
quite different densities and structural properties.
105-mm howitzer firing results
The interaction of the snow and ice layer may
The mean apparent radius of the outer craters
explain the differences in crater size. As the 105-
formed in the snow on the ice sheet of shallow
mm HE projectile penetrates the snow cover and
ponds was 1.72 m. The mean scaled apparent ra-
dius of the six craters was 1.30 m/kg1/3. This is
the point-detonating fuse contacts the ice surface,
the projectile explodes, producing a shock wave.
considerably larger than the predicted Ra of 0.87
m/kg1/3 for snow, even larger than the differences
The shock wave collapses the snow cover as it
propagates downward and outward. Snow is a
noted in the March 1991 test firing. The mean ap-
very good absorber of shock wave energy (John-
parent radius of the six inner craters or holes
son et al. 1991, 1992), so the snow cushions part of
formed in the ice sheet of shallow ponds was 0.68
the explosion. Part of the shock wave propagating
m. The mean scaled apparent radius of these inner
craters is 0.90 m/kg1/3, very close to the predicted
downward will be reflected back off the snowice
scaled apparent radius of 0.94 m/kg1/3 for ice.
interface; this may increase the radius of the crater
formed in the snow layer. Part of the shock wave
The mean depth of the inner craters was 0.68
m, or a scaled depth of 0.52 m/kg1/3. It is difficult
will continue downward through the ice layer,
hitting the icefrozen soil interface. Part of the
to compare this to a predicted depth, since the in-
wave will then be reflected back up. This reflected
ner crater completely pierced the ice sheet and ex-
wave, traveling back upward through the ice, can
tended into the soft pond bottom sediments be-
pop portions of the ice layer out of the crater with-
low the ice.
12
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