CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
NUMERICAL SIMULATION OF ANTI-TANK MINE DETONATIONS
Leo Laine1, Oyvind Ranestad2, Andreas Sandvik1, and Asbjern Snekkevik2
1
ANKER - ZEMER Engineering AS, Grindbakken 1, NO - 0764 Oslo, Norway.
2
Hagglunds Moelv AS, P.O. box 244, NO - 2391 Moelv, Norway.
Abstract. In order to determine the loads on mine-clearing devices generated by detonations of anti-tank
mines, knowledge about the incident impulse and pressure generated in the air are needed. Dependent
factors include the mine's depth of burial and the properties of the soil. Numerical simulations were
performed with a multi-material Euler processor to determine incident impulses and pressure histories from
detonations of fully buried, flushed and surface anti-tank mines for dry porous sand and saturated clay. The
simulations showed that the maximum incident impulse in air, at stand off distance below 1 m, increases
for both flushed and buried mines compared to a surface mine. Additionally, a concentration in the vertical
direction of the maximum impulse was found for the buried mine. For buried mines it was found that the
incident maximum pressure and impulse straight above the mines were significantly affected by the soil
material properties.
INTRODUCTION
Mine clearing vehicles are used in both military
and civilian mine clearing. Hagglunds Moelv AS is a
Norwegian company that produces such vehicles,
designed to withstand heavy anti-tank mines. The
flail system has a rotor in front equipped with chains
and mine clearing tools, Fig. 1, that clear the ground
to a depth of 200 mm and detonate mines
mechanically by hitting them. The stand off distance
from the mine to the rotor is approximately 1 m.
Practical testing indicate that the soil conditions
have large influence on the loads imposed on a mine
clearing vehicle by a detonated mine. The mine's
depth of burial is another parameter that has been
shown to significantly influence the load imposed by
a mine. Experience shows that detonation of buried
mines in water saturated soil gives higher incident
loads than similar detonations in dry sand.
Since the mine clearing equipment is rather complex
and costly, there is a need for numerical calculations
that enable reliable design criteria without extensive
testing. By using the explicit solver AUTODYN™
[1], such detonation scenarios can be investigated
numerically.
FIGURE 1. Armoured Mine Clearing Vehicle (AMCV) built on
a Leopard 1 Main Battle Tank chassis. (Hagglunds Moelv AS)
Transient loads from buried mine detonations
consist of three parts; a shock wave, soil ejecta, and a
blast wind. The main objective in this paper has been
to investigate the influence of soil conditions and the
mine's depth of burial on the pressure histories and
impulses from the incident shock wave in the air
above the mine.
431
Air
MATERIAL MODELLING
The air was modelled by using an ideal gas EOS.
Initial density was 1.3 kg/m3, y=Cp/cv= 1.4, and
internal energy 192.31 kJ/kg which gives an
atmospheric pressure of 100 kPa at 0 °C.
Additionally, a shift pressure was defined to
generate a zero pressure in the air. This means that
"unwanted" initial velocities were avoided.
Dry Sand
Compaction Equation Of State ("EOS") [2] was
utilised to represent the porous sand with initial
density of 1674 kg/m3. The plastic compaction curve
is shown in Fig. 2. The elastic unloading is given by
a density dependent bulk sound speed, Cj(pi).
Explosive
1
• . Plastic compaction curve
— -Asymptotic TMD line
........ Elastic compaction
The mine was represented by a high explosive
charge of type Composition B. The Jones-WilkinsLee EOS was used with the data found in [6].
1
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600 -
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NUMERICAL DESCRIPTIONS
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Numerical and Mesh Description
1
To take account for the large mass transport, a
multi-material Euler processor in AUTODYN™ [1]
was employed to solve the basic continuum
differential equations.
A two-dimensional axis-symmetrical model with
a rectilinear mesh and an element size of 8 mm was
established in an area of 2 m on each side of the
mine. Outside this area the mesh was gradually
coarsened. After a sensitivity study, it was revealed
that the mesh dependency was low for this grid.
1, , .
2200
Density, [kg/m3]
FIGURE 2. The utilised EOS for sand, a piecewise linear
plastic compaction curve with a "solid" asymptote.
Theoretical Maximum Density ("TMD") was set
to 2641 kg/m3, and the solid bulk sound speed was
set to 4631 m/s. A pressure hardening yield surface
was utilised with a density dependent shear modulus,
Gi(pt). Finally, a hydro tensile failure limit with a
small negative pressure value was defined.
The derivation of mechanical properties for sand
is discussed further in [3] and [4].
Material Location and Model Dimensions
The computational domain represents a cylinder
with 4 m radius and 8 m height. The lower half of
the cylinder was filled with soil, whereas the upper
half was filled with air. The mine was represented by
a cylindrical charge with diameter 278 mm and
height 100 mm, i.e. a charge weight of 10.4 kg.
Three different mine positions, shown in Fig. 3, were
analysed for each soil type: The buried mine has 100
mm soil above the charge, the flushed mine has the
top of the charge flushed at ground level, and the
surface mine lies on the ground.
Fully Saturated Clay
Shock EOS [1] was utilised to model the fully
saturated clay with initial density of 1908 kg/m3. A
bilinear relationship between the shock velocity and
particle velocity was defined with c}-\491 m/s,
s,=1.876, c2=1922 m/s, and s2=1.542. The
intersection point was at particle velocity 1273 m/s.
Shock Hugoniot Data [5] for water and water
saturated Tuff were used to establish the US-UP
relationship. The Gruneisen coefficient was set to
0.1, and a non pressure hardening yield surface was
used as a strength model. A small negative pressure
value was also defined as a hydro tensile failure
limit.
Boundary Conditions
Outflow [1] boundary was used for the air. The
all equal [1] option was utilised in the air which
allows all materials to flow out through the
boundaries. Transmit [1] boundary condition was
used for the soil material.
432
Surface Mine on Sand
Flushed Mine in Sand
Buried Mine in Sand
Surface Mine on Clay
Flushed Mine in Clay
Buried Mine in Clay
111111
F: I?lasfee4mmv
* S: S«itt;« mm
B: Swied sfciue
FIGURE 3. The location of buried, flushed, surface mine,
coordinate system, and target points.
0,4
0,6
0.8
1
Stand Off to Target, X [m]
1,2
FIGURE 5. Maximum values of the incident pressure plotted
against Stand Off to Target distance.
RESULTS
Crater sizes and particle velocities of the
generated ground shock in the soil showed
reasonable agreement with [7]. The incident pressure
histories in the air recorded at stand off distance 1 m
straight above the charge from different mine
detonations in clay are shown in Fig. 4. The buried
mine has significantly lower maximum pressure, but
much longer duration than the two other mines.
A-- Surface Mine on Sand
o-- Flushed Mine in Sand
*•- Buried Mine in Sand
A- Surface Mine on Clay
*- Flushed Mine in Clay
*- Buried Mine in Clay
•••••-- Surface Mine on Clay (Max 14.7 MPa)
—— Flushed Mine in Clay (Max 16.4 MPa)
14 •
——Buried Mine in Clay (Max 2 MPa)
0.8
1
.
1,2
1,4
Stand Off to Target, X [m]
FIGURE 6. Maximum values of the incident impulse plotted
against Stand Off to Target distance.
Angular Results
b
/| Flushed m
Figure 7 and Fig. 8 show the maximum values
for pressures and impulses plotted against the angle,
a. All the pressures decreases with an increasing
angle, but the results show that surface mine
pressures increase at the angle greater than 45
degrees. This increase in pressure is also reflected in
the impulse results in Fig. 8. By observing the areas
below the impulse curves, it can be seen that surface
mines generate a larger and more evenly distributed
impulse, and that burial focuses the impulse straight
above the mine. It can be concluded that surface
mines generate a larger total impulse in the air, but
buried mines generate the largest maximum impulse
straight above the mine. The reduced total impulse
reflects the increased coupling factor to the soil for
the buried mine.
3 /[»iriedmineL
2-
V/
^
f£L__
0,5
[ms]
FIGURE 4. Pressure histories recorded at stand off distance of 1
m above the ground for different detonations.
Vertical Results
Figure 5 shows maximum incident pressure as a
function of the stand off distance above the mine.
The values for the buried mine lies at a lower level
than the two other mines. The burial of the mine
influences the incident impulse in a different way
than the pressures, Fig. 6. The impulse values for
buried mines are highest for stand off distances
below 1 m. The impulse values were recorded 15 ms
after detonation.
433
impulse for surface mines. On buried mines
however, the effect of soil material was shown to be
significant.
The incident impulse measured 1 m in the
vertical direction shows that the impulse is more
focused straight above the mine for the buried mines.
The higher impulses obtained for buried mines
suggest that these may be more dangerous for
structures. However, several other factors are
expected to influence structural loads, such as
reflected pressure, shock wave velocity and soil
ejecta.
Further numerical investigations and experiments
are planned in order to study structural behaviour
under mine explosions for structures with both large
and
small
exposed
cross-sections.
These
investigations are expected to reveal how the
structural response is influenced by soil properties
and mine burial.
-- Surface Mine on Sand
-- Flushed Mine in Sand
-• Buried Mine in Sand
- Surface Mine on Clay
- Flushed Mine in Clay
-Buried Mine in Clay
FIGURE 7. Maximum values of the incident pressure plotted
against the angle, a.
-Surface Mine on Sand
- Flushed Mine in Sand
-- Buried Mine in Sand
- Surface Mine on Clay
-Flushed Mine in Clay
-Buried Mine in Clay
REFERENCES
1.
2.
FIGURE 8. Maximum values of the incident impulse plotted
against the angle, a.
3.
Sand vs. Clay
Maximum pressure and impulse values for sand
and clay, one meter above the ground, are compared
in Table 1. The overall results show clearly that mine
detonations in fully saturated clay in flushed and
buried mine scenarios result in higher values than the
same mines detonated in sand.
4.
5.
6.
TABLE 1. Comparison between incident pressures and impulses
in sand and clay at stand off distance of 1 m above the ground.
Location
Surface
Flushed
Buried
7.
(Pclav"Psand)/Psand
0,9%
6,0%
30,7%
-8,7%
10,6%
25,5%
CONCLUSION
Incident pressures and impulses were calculated
for a mine with different kind of burial both for sand
and fully saturated clay. The soil material was shown
to have little effect on incident max pressure and
434
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