Combustion, Explosion, and Shock Waves, Vol. 37, No. 5, pp. 607 612, 2001
Attenuation of Blast Overpressures
from Liquid in an Elastic Shell
B. E. Gel fand,1 M. V. Sil nikov,2 UDC 523.593+621.791
A. I. Mikhailin,2 and A. V. Orlov2
Translated from Fizika Goreniya i Vzryva, Vol. 37, No. 5, pp. 128 133, September October, 2001.
Original article submitted July 14, 2000.
Parameters of air blast waves produced by a ground explosion of explosive charges
of mass G = 0.1 1 kg placed in a liquid bounded by an elastic shell were measured
experimentally. Encapsulation of the liquid in the elastic shell leads to an increase in
the compressibility of the medium which transfers the energy of explosion products
to the air and contributes to a significant decrease in air-blast amplitude at a reduced
distance R/G1/3 = 0.63 6.8 m/kg1/3. The efficiency of attenuation of overpressures
by immersing an explosive in a liquid bounded by an elastic shell is comparable to
efficiency of damping blast waves by gas-filled two-phase systems. It is shown that
the main parameter of blast-wave attenuation is the ratio of the mass of the liquid to
the mass of the explosive charge rather than the viscosity and density of the liquid.
INTRODUCTION RDX) charges of mass 0.1 3 kg. Explosion-suppressing
gas-filled shells were made of various porous materials:
The development of methods for suppressing the
mica [1], glass wool and bundles of a metal wire [10],
level of blast loads produced by detonation of high ex-
snow and sand [13], and polyurethane foam [15].
plosive (HE) charges has long been a subject of consid-
The efficiency of protection against high-explosive
erable interest. Such results find various applications
kills by placing HE charges in gas-filled shells can be
in blasting (cutting, welding, and cropping of various
estimated by comparing the amplitudes of blast waves
structures and buildings [1 13]). Recent increase in this
from unconfined charges ("p1 = p1 - p0) with those
interest is motivated by the necessity of safe destruction
from confined charges ("p2 = p2 - p0) away from
of explosive objects placed by terrorists in densely pop-
the explosion source, i.e., at a reduced distance R" =
ulated areas or buildings. Furthermore, in conducting
R/G1/3 > 10 m/kg1/3. Here G is the HE mass, R is
special warfares, a main problem is also the protection
the distance, p0 is the initial pressure, p1 is the blast
against high-explosive and fragment kills during mine
pressure for an air explosion, and p2 is the maximum
clearing [14]. It was found [1 13] that in blasting oper-
blast pressure for explosion of a confined charge. Pala-
ations using the energy of condensed HE charges, im-
marchuk and Postnov [12, 13] found that for aqueous
mersion of explosives in gas-containing multiphase me-
air foams of density 2 d" Ã d" 20 kg/m3, the max-
dia [1 3] or gas-filled shells [4 13] is a very effective
imum degree of attenuation of blast-wave amplitude
means of protection against high-explosive kills. As
Kmax = "p1/"p2 is
the multiphase medium surrounding an HE charge, an
¨max,1 = 20 log ["p1/"p2] = 0.366[Rf/R0] - 0.19 [dB].
aqueous foam of density à = 2 20 kg/m3 was used to
suppress air blast [2 9] and a suspension of gas bub-
Here R0 is the radius of the HE charge and Rf is the
bles in a liquid of density 900 990 kg/m3 was used to
radius of the foamed shell around the charge. The
suppress blast waves in water [3] from HE (TNT and
quantity ¨max,1 did not depend on distance at 8 <
1
R" < 103 m/kg1/3. For gas-filled shells with non-
Semenov Institute of Chemical Physics,
aqueous granular fills, it was found [8 10, 12, 13] that
Russian Academy of Sciences, Moscow 117977.
2
Institute of Special Materials, St. Petersburg 194044. ¨max,2 = (3Z - 4) Ä… 2 [dB], irrespective of the thermal
0010-5082/01/3705-0607 $25.00 © 2001 Plenum Publishing Corporation 607
608 Gel fand, Sil nikov, Mikhailin, and Orlov
properties of the fills. Here Z = (V Ã/G)1/3, where à is
the effective density of the granular or porous material,
and V is the volume of the shell, i.e., V Ã is the mass of
the framework of the porous material. As a rule, Ã is
much smaller than the actual density of the framework
material.
The degree of amplitude attenuation Kmax d" 12 15
attained in tests does not agree with the theoretical
value predicted for completion of thermal, phase, and
kinematic exchange processes between the HE explosion
products and the fill of the protective shell [2, 3, 12,
13, 16]. It turns out that the attenuation of blast waves
is determined mainly by the inertia and compressibility
of the fill material. In the studies cited, the compress-
ibility of the fills was ensured by the use of porous gas-
filled materials. The compressibility of these materials
Fig. 1. Equilibrium velocity of sound versus vol-
can be characterized by the velocity of propagation of
ume fraction of gas inclusions in the liquid gas
small pressure perturbations in them or by the equilib-
impermeable shell system [16]: curve 1 refers to wa-
rium velocity of sound D. It is known that D " for
ter in a steel tube with E = 200 GPa, curve 2 to
an incompressible medium and D = cf H" 1450 m/sec
water (cf = 1450 1500 m/sec) for E ", curve 3
to incompressible liquid (cf ") in an incompress-
for water, where cf is the velocity of sound in liquids.
ible shell (E "), and curve 4 to water in an elastic
For an aqueous air foam, D < cg [3], where cg is the
shell with E = 1 GPa.
velocity of sound in the gas that fills the foam cells. In
a suspension of gas bubbles in a liquid, D < cf and even
D < cg [2, 3, 16].
of the shell (tube), and r is the cross-sectional radius of
the shell (tube).
Figure 1 shows curves of D(Ä…) for the practically
BASIC STATEMENTS
interesting water air bubbles system with p = 1 bar
and 2Åšr/t = 10. One can see that for Ä… d" 10-2,
The special features of attenuation of high-
the velocity of sound D depends on the elastic prop-
explosive effects by gas-filled shells revealed in [1 13]
erties of the shell material. When the volume fraction
open up fresh opportunities in developing new types
of gaseous inclusions in the liquid Ä… e" 10-2, or more
of protective devices. This is an urgent problem since
precisely, for Ä… e" "p/Áfc2, the compressibility of the
f
the expeditious use of foamed shells is made difficult by
structure  shell liquid gaseous pores does not depend
sedimentation of foam, and preparation of protective
on the properties of the fill and shell material. Here
shells with other fills involves a number of technical dif-
"p is the amplitude of pressure perturbations. Fig-
ficulties, mentioned partly in [4 10]. We consider the
ure 1 illustrates the main feature of suppression of blast
problem of increasing the compressibility of a continu-
waves from HE charges using gas-filled shells [1 13, 15].
ous liquid (for example, water) by its encapsulation in
In the tests of [1 13, 15], the volume fraction of gaseous
an elastic compressible shell. The solution of this prob-
pores in the liquid was Ä… e" 10-2, and therefore, the
lem is known. As an example, we consider the water
properties of the liquid and shell material had little ef-
air bubbles system in an impermeable flexible shell (for
fect on the compressibility of the medium transmitting
simplicity, a tube) [16]. The velocity of sound in this
the pressure wave. One can see from Fig. 1 that the
system is given by the relation
compressibility of the transmitting medium can be in-
-1
-1 Ä… 1 - Ä… 2Åšr
creased not only by introducing gaseous inclusions into
D2 = Ä…Ág + (1 - Ä…)Áf + + .
p Áfc2 Et
water but also (for Ä… d" 10-2) by encapsulating water
f
in an elastic shell with E < 10 GPa.
Here Ä… is the volume fraction of the gas bubbles in the
liquid, Ág is the gas density, Áf is the liquid density, p is
the pressure, E is the modulus of elasticity of the shell
(tube wall) material, Åš is a coefficient that takes into
EXPERIMENTAL TECHNIQUE
account the fixing conditions of the shell (Åš = 1 - 0.5µ
for a tube with one end fixed, Åš = 1 - µ2 for a tube The efficiency of decreasing the high-explosive ef-
with both ends fixed; µ is Poisson s ratio), t is the wall fect by placing HE charges in a liquid bounded by an
Attenuation of Blast Overpressures from Liquid in an Elastic Shell 609
elastic shell was studied in a number of field experi-
ments. The experimental technique was described pre-
viously [17, 18]. In the present tests, air-blast param-
eters were measured in ground explosions of spherical
TNT charges of mass 0.1 and 1 kg. To prevent attenua-
tion of blast waves due to energy losses in the interaction
with ground (formation of a cavity and partial transfer
of energy by the wave into ground), HE charges were
placed on a 1.2 × 1.2 m steel slab. The thickness of the
slab was varied from 30 to 60 mm. All explosions were
performed in an exposed area.
Air-blast parameters were measured by six stream-
lined piezoelectric transducers placed at a distance from
the charge (R) along two perpendicular directions. For
explosion of TNT charges of mass 0.1 kg, the transduc-
ers were located at a height of 0.1 m above the ground
at distances R = 0.8, 1.1, and 1.5 m from the charge.
For explosion of TNT charges of mass 1 kg, the trans-
ducers were at a height of 1 m above the ground at dis-
tances R = 1.5, 2.25, 2.72, and 3.7 m from the charge to
exclude the effect of reflected waves. In the Hopkinson
Sadovskii reduced variables R" = R/(2G)1/3, we have
1.36 < R" < 6.8 m/kg1/3 and 0.63 < R" < 3.2 m/kg1/3
Fig. 2. Air blast wave amplitude versus reduced dis-
tance: curves 1 and 2 refer to the calculation results
for ground explosions of charges of mass 0.1 and 1 kg, re-
from [19] and [2, 3], respectively; the points refer to
spectively. The measured amplitudes of pressure waves
the measurement results for an unconfined charge;
from unconfined charges agree with empirical values
the shaded region refers to charges in elastic liquid
predicted by Sadovskii s formulas [19] with an accuracy
explosion suppressors.
of not less than Ä…10%. These formulas were also used
for further comparison with parameters of waves from
confined charges. No special degassing measures were taken when fill-
The charges were encapsulated in an elastic double- ing the shells with liquids. The working liquids were an
walled cylindrical shell filled with a liquid. The inner aqueous solution of calcium chloride and glycerin. A so-
shell was 0.15 m in diameter and 0.15 m high and its lution of calcium chloride was used to change the den-
volume was H"2.6 liters. Between the inner and outer sity of the liquids. Glycerin served as a sample highly
shells there was a layer 0.04 m thick. The total volume viscous liquid. A number of tests was performed using
of the fill was H"5.2 liters. sand as a fill.
Explosion suppressors for TNT charges of mass
0.1 kg were located in a shell made of a polyethylene
sheet of thickness t = 2 mm with a maximum axial
EXPERIMENTAL RESULTS
elongation of H"400%. The mass of the shell was 0.6 kg.
A number of tests were performed with TNT charges
Figure 2 gives a general idea of how the parame-
of mass 1 kg in a rubber shell (t = 2 mm) containing
ters of blast waves change when HE charges are placed
50 kg of water. The maximum axial elongation of the
in a gas-filled shell or immersed in a liquid in an elastic
rubber was H"400%. The elasticity of the rubber shell
shell. Curve 1 and the points are, respectively, the cal-
was reduced by coating its external surface with a so-
culation of [19] and experimental results for unconfined
lidifying polyurethane foam layer. Table 1 summarizes
charges. Curve 2 refer to the data of [2, 3] for explosion
main data on the explosion suppressors used (Nos. 1 6):
of TNT in an aqueous air foam with à H" 10 kg/m3.
the material of the shell and fill, the velocity of sound
The shaded region corresponds to the above-described
in the fill cf, the absolute density of the liquid fill Áf,
tests on HE charges immersed in a liquid in elastic shells
the acoustic resistance of the fill (Ác)f, the parameter
and to the data of [17, 18]. One can see that the ef-
(M/G)1/3 (M is the mass of the fill and G is the mass
ficiency of blast attenuation by the foam is compara-
of the HE charge), the parameter ¨max,2, and the de-
ble to the efficiency of blast attenuation by a liquid in
gree of attenuation of the blast-wave amplitude K.
an elastic shell. Figure 3 illustrates in detail the effect
610 Gel fand, Sil nikov, Mikhailin, and Orlov
TABLE 1
Shell cf , Áf , (Ác)f ,
Fill (M/G)1/3 ¨, dB K K-1
No.
material m/sec kg/m3 106 kg/(m2 · sec)
Solution
1 Polyethylene 1450 1290 1.87 4.02 8.1 Ä… 2 2.05 3.25 0.31 0.48
of calcium
chloride
2 Polyethylene Glycerin 1920 1260 2.42 3.95 7.8 Ä… 2 1.96 3.1 0.32 0.51
3 Polyethylene Water 1450 1000 1.45 3.72 7.1 Ä… 2 1.81 2.87 0.35 0.55
4 Polyethylene Sand  1810  4.53 9.6 Ä… 2 2.27 3.79 0.26 0.42
5 Rubber Water 1450 1000 1.45 3.68 7.0 Ä… 2 1.79 2.83 0.35 0.56
Rubber
6 Water 1450 1000 1.45 3.72 7.1 Ä… 2 1.81 2.87 0.35 0.55
+ polyurethane foam
Fig. 3. Air blast amplitude versus distance for vari-
ous explosions of 0.1 kg of TNT (the numbers at the
curves correspond to the explosion suppressors listed
in Table 1).
Fig. 4. Degree of attenuation of air blast waves ver-
sus distance in ground explosion of 0.1 kg of TNT
of different explosion suppressors on the dependence of
(the numbers at the curves correspond to explosion
the amplitudes of blast waves on the distance (expo-
suppressors listed in Table 1).
nential approximation is used). One can see that the
efficiency of all liquid explosion suppressors is almost
the same (within the measurement error of Ä…10%). It
HE in a liquid, the quantity K does not decrease with
was found that sand ensures the minimum degree of
attenuation of blast waves. Glycerin is less compress- distance within the range R" d" 3.1 m/kg1/3. Table 1
ible than water (velocities of sound D are 1920 m/sec compares our experimental data with calculated values
and 1450 m/sec, respectively), which compensates for of ¨max,2 for gas-filled shells. One can see that the cal-
the effect of higher density. Figure 4 shows the degree culated values of K agree well (with allowance for the
of attenuation of blast-wave amplitude versus the dis- stated spread of measurement results) with experimen-
-1 -1
tance Ke = "p2/"p1 = Ke (R"). For explosion of tal values of Ke.
Attenuation of Blast Overpressures from Liquid in an Elastic Shell 611
ing liquids in elastic confinements is comparable in effi-
ciency to the blast attenuation using gas-filled shells or
aqueous foams. The ratio of the HE mass to the total
mass of the liquid and the elastic shell is the determin-
ing parameter in the attenuation of blast loads. The
energy losses due to the kinetic acceleration of the liq-
uid, facilitated by the elastic properties of the container,
appear to have a dominant role in the suppression of air
waves. The heat removed from the explosion products
and expended in heating and possible evaporation of the
liquid contribute little to attenuation of blast waves.
To obtain a comprehensive idea of the attenuation
of blast overpressures from an HE in a liquid-filled elas-
tic confinement, one need to measure the static-pressure
pulse and duration of the positive compression phase.
For further improvement of protective means, it is nec-
essary to construct  pressure pulse diagrams and de-
scribe the transformation of the blast-wave profile in
the coordinates  pressure time at any distance from
the HE charge compared to the standard diagrams for
the unconfined charge.
Fig. 5. Air blast wave amplitude versus distance for
ground explosion of 1 kg of TNT: curves 1 and 2
refer to tests with explosion suppressor Nos. 5 and
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