Experimental investigation of blast mitigation and particle–blast interaction during the explosive dispersal of particles and liquids

Abstract

The attenuation of a blast wave from a high-explosive charge surrounded by a layer of inert material is investigated experimentally in a spherical geometry for a wide range of materials. The blast wave pressure is inferred from extracting the blast wave velocity with high-speed video as well as direct measurements with pressure transducers. The mitigant consists of either a packed bed of particles, a particle bed saturated with water, or a homogeneous liquid. The reduction in peak blast wave overpressure is primarily dependent on the mitigant to explosive mass ratio, M/C, with the mitigant material properties playing a secondary role. Relative peak pressure mitigation reduces with distance and for low values of M/C (< 10) can return to unmitigated pressure levels in the mid-to-far field. Solid particles are more effective at mitigating the blast overpressure than liquids, particularly in the near field and at low values of M/C, suggesting that the energy dissipation during compaction, deformation, and fracture of the powders plays an important role. The difference in scaled arrival time of the blast and material fronts increases with M/C and scaled distance, with solid particles giving the largest separation between the blast wave and cloud of particles. Surrounding a high-explosive charge with a layer of particles reduces the positive-phase blast impulse, whereas a liquid layer has no influence on the impulse in the far field. Taking the total impulse due to the blast wave and material impact into account implies that the damage to a nearby structure may actually be augmented for a range of distances. These results should be taken into consideration in the design of explosive mitigant systems.

Full text

Shock Waves
DOI 10.1007/s00193-018-0821-5
ORIGINAL ARTICLE
Experimental investigation of blast mitigation and particle–blast
interaction during the explosive dispersal of particles and liquids
Q. Pontalier1·J. Loiseau2·S. Goroshin1·D. L. Frost1
Received: 24 September 2017 / Revised: 25 March 2018 / Accepted: 29 March 2018
© Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract The attenuation of a blast wave from a high-
explosive charge surrounded by a layer of inert material is
investigated experimentally in a spherical geometry for a
wide range of materials. The blast wave pressure is inferred
from extracting the blast wave velocity with high-speed video
as well as direct measurements with pressure transducers.
The mitigant consists of either a packed bed of particles, a
particle bed saturated with water, or a homogeneous liquid.
The reduction in peak blast wave overpressure is primarily
dependent on the mitigant to explosive mass ratio, M/C, with
the mitigant material properties playing a secondary role.
Relative peak pressure mitigation reduces with distance and
for low values of M/C(<10) can return to unmitigated pres-
sure levels in the mid-to-far field. Solid particles are more
effective at mitigatingthe blast overpressure than liquids, par-
ticularly in the near field and at low values of M/C, suggesting
that the energy dissipation during compaction, deformation,
and fracture of the powders plays an important role. The dif-
ference in scaled arrival time of the blast and material fronts
increases with M/Cand scaled distance, with solid parti-
Communicated by C. Needham.
Electronic supplementary material The online version of this
article (https://doi.org/10.1007/s00193-018- 0821-5) contains
supplementary material, which is available to authorized users.
BD. L. Frost
david.frost@mcgill.ca
Q. Pontalier
quentin.pontalier@mail.mcgill.ca
1McGill University, Macdonald Engineering Building, 817
Sherbrooke Street West, Montreal, QC H3A 0C3, Canada
2Chemistry and Chemical Engineering Department, Royal
Military College, 17 General Crerar Crescent, Kingston,
ON K7K 7B4, Canada
cles giving the largest separation between the blast wave and
cloud of particles. Surrounding a high-explosive charge with
a layer of particles reduces the positive-phase blast impulse,
whereas a liquid layer has no influence on the impulse in the
far field. Taking the total impulse due to the blast wave and
material impact into account implies that the damage to a
nearby structure may actually be augmented for a range of
distances. These results should be taken into consideration
in the design of explosive mitigant systems.
Keywords Blast wave mitigation ·Powder compaction ·
Particle–blast interaction ·Explosive particle dispersal
1 Introduction
Blast waves generated by the detonation of high explosives
are a serious hazard for nearby personnel and structures, and
hence the mitigation of blast waves is an important practical
concern. One common technique for reducing the strength
of a free-field air blast is to surround a high-explosive charge
with a layer of liquid, granular material, and/or porous cellu-
lar material. A variety of blast energy dissipation mechanisms
have been proposed, and the relative importance of the dif-
ferent mechanisms for blast wave mitigation depends on the
particular media used.
The use of a liquid layer for blast attenuation has been
investigated experimentally and numerically. Numerical pre-
dictions of blast mitigation with water surrounding a spher-
ical charge indicate that a reduction in peak overpressure
by up to 80% is possible with a mass of mitigant to explo-
sive ratio M/Cof 10, although the droplet–blast interaction
was not considered in this study [1]. Experimental studies
using water and glycerin in a bulk form have confirmed the
possibility of such a reduction [2,3], with similar mitigation
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Q. Pontalier et al.
observed for the two liquids, ranging from almost 90% in the
mid-field to 80% in the far field for M/C=34 (water)–44
(glycerin) [3]. The blast wave attenuation implies an energy
loss to the mitigant layer, which has been attributed to the
acceleration of the liquid and subsequent fragmentation of
the liquid into fine droplets as well as thermal effects related
to liquid vaporization [1,3]. Several studies have investigated
the mitigation performance using a two-phase medium such
as a liquid droplet mist [3,4] or aqueous foam [5–9] within a
confined area. For mists, the maximum peak blast overpres-
sure attenuation was numerically predicted to be 70% in the
mid-field, with droplet sizes of 27.5µm and a mass load-
ing of 2, defined as the ratio of water to gas mass within a
computational cell [4]. For aqueous foams, reductions in the
peak overpressure, relative to that of a bare high-explosive
charge, were observed experimentally between 90 and 95%,
at scaled distances between 1 and 3 m/kg1/3, respectively
[5]. The attenuation is attributed to the momentum loss in
the complex 3D multiphase structure of these media and is
related to the number of gas cells found within the foams [8].
The high heat capacity of the liquid phase and the compress-
ibility of the gas bubbles also play a significant role in the
mitigation process [10].
The mitigation performance of granular materials has like-
wise been investigated extensively. Sand has been proposed
as a potential candidate [8,11] to mitigate a blast wave. In
small-scale experiments, the attenuation of the peak over-
pressure has been observed to decrease with distance from
a value of 40% in the near field to 5% in the far field with
M/Cbetween 0.1 and 0.2 [8]. Glass, steel, and ceramic [12],
porcelain, plastic, claydite, and polyethylene spheres [13]
have also been studied. In large-scale experiments, perlite
and pumice have been used to reduce the strength of the
blast wave. For example, small pockets of pumice (5.7 cm
thick, m=1.62 kg) placed in the far field reduced the peak
blast overpressure by 66% and the blast impulse by 84% [14].
However, it is not clear, a priori, which properties of the gran-
ular media are most important for mitigation performance.
Material density has been cited as a relevant parameter, sug-
gesting that the transfer of momentum from the explosion to
the particles is an important determinant of blast attenuation
[2]. Porosity of the granular medium is also a significant fac-
tor, resulting in energy dissipation during the shock–medium
interaction leading to compaction of the medium [2,15].
The particle size and thickness of granular layers have also
been cited as potential mitigation parameters [12]. Particle
crushing and rearrangement during void collapse have been
proposed as other contributions to energy dissipation [14].
Compaction mechanisms have been extensively studied by
research groups investigating the response of dry or water-
saturated soils subjected to blast loadings [16–18]. These
studies focus mainly on the shock transmission to buried
structures or underground facilities and the formation of
craters [18]. Finally, the energy dissipation via acceleration of
the mitigant bed has been analyzed in a companion paper as a
function of the mitigant mass to charge mass M/C[19], which
is correlated with the velocity of the explosively dispersed
material according to classical Gurney analysis [20,21].
When a high-explosive charge surrounded by a layer of
inert material is detonated, a shock wave propagates into
the material, radially compacting the material to a degree
which depends on the initial bed porosity, particle compres-
sive strength, and local strength of the shock wave. When the
shock wave reaches the surface of the material layer, a blast
wave is transmitted into the surroundings and an expansion
wave propagates back into the compacted material, causing
it to expand radially outwards [22,23]. The tension induced
within the compacted bed of material causes it to break up
into fragments that have a size on the order of the thickness
of the compacted layer when the expansion wave reaches the
inner surface of the layer [24]. The fragments move radially
outwards, shedding particles in their wake and leading to
the formation of jet-like structures, an example of which is
showninFig.1. Particle jetting is a common feature of high-
explosive particle dispersal; however, jet formation is not
observed for particles with high compressive strength [22].
The explosive dispersal of liquids, in general, also leads to
the formation of droplet jets (see Fig. 1for an example for a
layer of glycerol), although other phenomena, such as cav-
itation within the liquid layer behind the expansion wave,
govern jet formation [25]. The explosive dispersal of liquid-
saturated particle beds leads to the formation of droplet jets
similar to the case of liquid dispersal and is discussed in a
companion paper [26]. Although the mechanism of jet for-
mation is not addressed in the present paper, it is of interest
to determine whether or not the presence of particle/droplet
jets influences the degree of blast wave attenuation.
The present study examines the relative blast wave miti-
gation performance of a layer of either a granular material,
liquid, or a liquid-saturated particle bed surrounding a high-
explosive charge in spherical geometry. A variety of different
mitigant materials are tested, including powders with a range
of particle size, density, and packed bed porosity, covering a
Fig. 1 Jet formation for silicon carbide powder with mass ratio M/C
of 54 (left) and for glycerol with a mass ratio of 5.8 (right)
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Experimental investigation of blast mitigation and particle–blast interaction during the…
wide range of mitigant to charge mass ratios. In some exper-
iments, the blast wave peak overpressure and impulse were
obtained using fast-response pressure transducers located
at various locations from the charge. The peak blast wave
overpressure history very near the charges was determined
with high-speed videography, by measuring the blast wave
velocity with image analysis and then inferring the peak
blast wave overpressure using the Rankine–Hugoniot rela-
tion. The particle–blast interaction is also investigated to
quantify the potential blast pressure recovery as a function
of distance. This paper is structured in the following way:
Sect. 2describes the experimental conditions, and Sect. 3
details the video processing steps used to extract the blast
wave pressure. Section 4presents the experimental results
for the effect of mitigant properties on the attenuation of the
blast wave pressure and impulse and a discussion of the impli-
cations of the results regarding suitable material properties
for blast mitigation is presented in Sect. 5. A complimen-
tary dataset is also attached with the paper as supplementary
material.
2 Experimental overview
The charge casings used in the present study consisted of
thin-walled (1-mm-thick) commercial glass light bulbs with
the filaments removed. Either G40 (nominal dia 12.7 cm)
or G25 (nominal dia 9.5 cm) bulbs were used. A spherical
ball of C-4 (15–82 g) formed by hand was placed in the
middle of the glass sphere with a plastic tube attached to
allow the insertion of an electric detonator into the C-4 prior
to the test. For the dispersal of liquids with a high-explosive
charge, the C-4 was placed within a hollow polyethylene
sphere (m=12.0 g, nominal dia 3.5 cm) to isolate it from
the liquid and provide a means by which the C-4 could be
held rigidly in place at the center of the charge. The PE sphere
was cut in half, filled with C-4, and then reassembled. The
detonator tube was epoxied to the sphere and held in place
with a wooden cross-piece visible at the top of the bulb in
Fig. 2. Flow of detonation products up the tube perturbs the
symmetry of the motion at the top of the charge (see right
photograph in Fig. 1) but has no effect on the lateral motion
of the material or blast. In the case of solid particles, bare
C-4 charges were used. The charge was prepared by filling
the sphere half full of powder, then placing the C-4 ball with
attached tube in the center of the sphere, and then filling the
remainder of the powder such that the C-4 was held in place
by the powder. The charges were supported by a section of
plastic tube attached to the end of a wooden rod, with a height
of burst of 1.5 m.
For some trials, the blast overpressure was recorded with
piezoelectric pressure transducers (PCB 113A24, risetime 
1µs) mounted in lollipop-style gauges (lollipop dia 30 cm) at
Fig. 2 Glass bulb with a central C-4 burster filled with either water
(left) or iron powder (right). The detonator is inserted into the C-4
through the plastic tube visible protruding above the charge. The tube
and C-4 are held in place by the visible wooden cross-piece which is
attached to the bulb
Fig. 3 Photograph of test site with charge, pressure gauge stands, and
high-speed videocameras in the background
various distances from the charge (1.1, 2.0, 4.0m), as shown
in the photograph in Fig. 3. The distance for the farthest
transducer was chosen such that the ground-reflected wave
arrived at the transducer location after the end of the positive
phase of the blast wave signature so that the positive-phase
impulse measurement is not influenced by the reflected wave.
It was not possible to position a gauge stand nearer than about
1 m from the charge as the direct impact of particles with the
gauge obscured the blast pressure signal.
The explosive particle dispersal was recorded with a high-
speed Photron SA5 videocamera recording at 10,000 fr/s.
Prior to a test, a photograph of a checkerboard scale was
taken to establish an absolute length scale. For a resolution of
1024×744 pixels, with a camera-charge distance of 30 m, the
physical size of a pixel ranged from 3.1 to 4.5 mm, depending
on the magnification. (Either a 135 or 180 mm lens was used.)
123

Q. Pontalier et al.
A wide variety of mitigant materials were tested. Solid par-
ticles included: Chronital S-30 stainless steel shot (Vulkan
Blast Shot), SAE J827 standard S-110 steel shot, pure iron
(FE-114, Atlantic Equipment Engineers), glass (Potters Bal-
lotini impact glass beads, #10 and #13 sizes), brass (BR-102,
Atlantic Equipment Engineers), titanium (TI-109, Atlantic
Equipment Engineers), aluminum (H-95, Valimet Inc.), sil-
icon carbide (30 grit), sand (commercial toy box sand), and
granulated and icing sugar (commercial products). The liq-
uids used included water, glycerol, ethanol, vegetable oil, and
sodium polytungstate, a high-density liquid used for grav-
ity separation. To increase the density of the liquids, several
glycerol trials were carried out with an equal mass of tungsten
carbide powder (1 µm, Geoliquids Inc.) added. In some tri-
als, uniform mixtures of two powders were tested, including
silicon carbide powder mixed with various volume fractions
of steel or glass powder. In a subset of tests, a bed of solid
particles was fully saturated with water. Bulk densities of the
powders were measured experimentally by determining the
mass of a known volume of powder. Depending on how the
powders are tapped, the bulk density can vary. In Table 1,the
average between the untapped and tapped values is reported.
The particle size distributions are monomodal, with the mean
size provided by the manufacturers. In total, blast wave prop-
erties were extracted from 78 trials of 27 different mixtures
spanning a range of mitigant to high-explosive mass ratio
(M/C) from 3.8 to 297.1. A total of 44 trials were conducted
with dry powders, 21 trials with neat liquids, and 13 trials
with water-saturated particles. A summary of all the trials
tested is attached in the supplementary material.
Tabl e 1 Properties of solid particles and liquids tested
Materials Bulk density (g/cm3) Mean size (µm)
Chronital steel (S-30) 4.6±0.17 280
Iron (FE-114) 3.35 ±0.34 220
Steel shot (S-110) 4.46 ±0.33 280
Glass (Potters #13) 1.5±0.08 68
Glass (Potters #10) 1.37 ±0.16 120
Silicon carbide (30 grit) 1.67 ±0.16 600
Aluminum (H-95) 1.50 ±0.09 116
Titanium (TI-109) 1.78 ±0.22 <150
Brass (BR-102) 3.31 ±0.45 <150
Sand 1.67 ±0.09 500 nom.
Granulated sugar 0.92 ±0.07 525
Icing sugar 0.71 ±0.16 20
Wat e r 1 N/ A
Ethanol 0.789 N/A
Glycerol 1.126 N/A
Vegetable oil 0.915 N/A
Sodium polytungstate 2.82 N/A
3 Video analysis procedure
Optical diagnostics are commonly used to visualize shock
waves and blast waves. In laboratory-scale experiments,
shadowgraphy, interferometry, and black-and-white or color
schlieren videography are widely employed, especially in
supersonic–hypersonic facilities but also for small-scale
explosion tests. These techniques have been reviewed by
Kleine et al. [27] and Panigrahi et al. [28]. The background
oriented schlieren (BOS) [29,30] technique is largely applied
to visualizing blast waves in free-field tests [31,32]. This
technique consists of subtracting all the video images con-
taining the blast front from the same, fixed image of an
undistorted background. This method has also proven to
be effective in visualizing underwater shock waves [33]. To
improve the visualization of the blast wave in the field and
diminish the errors associated with the extraction of the blast
wave trajectory, it is also common to place a striped (or zebra)
board behind the charge [34].
In the present paper, two different methods are used to
extract the position of the spherical blast wave as a func-
tion of time and involve the use of several image processing
techniques. If the blast wave peak overpressure is sufficiently
high, it is possible to observe the wave front directly from the
raw video images as a result of the diffraction of the back-
ground light by the density gradient across the blast wave.
Once the location of the wave front has been determined, a
circle may be fitted manually to the most spherical portion of
the blast front. Due to a lack of symmetry of the blast wave
for certain trials, the center of the circle does not necessarily
correspond to the exact location of the charge but is typically
very close. This procedure is repeated for each video image,
maintaining the same center for all the images. If the circle
does not perfectly match the wave front in all directions, the
edge of the circle is placed to precisely coincide with the left
side of the blast wave. The choice of the left side is motivated
by the presence of pressure gauges on the right side that may
slightly perturb the blast wave motion. This method has the
advantage of being relatively fast(i.e., no computational time
is involved), taking into account the sphericity of the blast
front, and also avoiding the addition, or removal, of informa-
tion associated with any image processing technique.
Above a mass ratio of around 50, the blast wave is weak
enough that it is difficult to discern the blast wave front
against the uneven pixel grayscale level of the background in
individual video frames. To enhance the visibility of the blast
front in these cases, it is necessary to perform inter-frame
image processing. The choice of image processing scheme
depends on the brightness, contrast, and pixel intensity of the
particular trial. However, the basic procedure is to compare
consecutive images so that only portions of the image that are
moving (such as a blast wave) are retained. This method dif-
fers slightly from the BOS technique since the video images
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Experimental investigation of blast mitigation and particle–blast interaction during the…
Fig. 4 Different steps of video
processing
are not subtracted from a unique image but rather subtracted
from the previous image. At this point, various routines are
used to enhance the image contrast, apply a thresholding
function, filter the image, and despeckle the image until the
blast wave front is distinctly visible. An overview of the typ-
ical sequence of image processing routines used is shown in
Fig. 4. First, a Matlab Bit-xor transformation is applied to two
consecutive frames. The Bit-xor function compares bits of the
same pixel in the two different images and returns 0 if bits
are equal and 1 otherwise. Pixels which have the same value
(from 0 to 256) are converted to black, and others become
more and less gray. Then, the contrast of the resulting image
is enhanced (imadjust function) and a threshold is set to 4, 5,
or 6 depending on the magnification ratio and the image prop-
erties. As a consequence, only pixels with a value above this
threshold become visible. The next steps consist of remov-
ing the noise from the images. In the first instance, images
are converted to binary, i.e., black and white. Then, several
loops (about 10) of the speckle removal algorithm are used to
remove the smallest noise structures. This algorithm consists
of a small 2D-median filter (3 ×3) which replaces an input
pixel at a specific location by the median value of the input
pixel and its 8 neighbors. If most of the pixels surrounding
the input pixel are black, the output pixel will be black, and
if not, the output pixel will be white. In the end, to eliminate
the largest noise structures, a larger median filter (10 ×10)
is applied. The size of this filter depends also on the image
properties. The ultimate goal of removing the undesirable
pixels is to automatically fit circles to the blast wave front.
Since all of the noisy pixels surrounding the blast front have
been removed, it is then possible to detect the first and last
white pixels on different specific lines that should belong to
the blast front. Then, with at least three points, a circle may be
fitted. One drawback of image processing techniques is that
inevitably some information is either added to or removed
from the image. In particular, the blast front may not be per-
fectly smooth and several “holes” on the blast front may
appear (Fig. 5). The appearance of these holes is primarily
attributed to the non-uniformity of the background (presence
of trees in Fig. 1) and makes it difficult to accurately detect
the blast front. However, in the present study, the circles are
fitted manually since the holes are too numerous on the pro-
cessed images. Several image processing techniques may be
applied to reconstruct the blast wave front by pixel interpo-
lation. The use of a uniform background would also serve
to decrease the numbers of these undesirable image artifacts.
After applying the various image processing techniques, care
must be taken to distinguish the front of the particle cloud,
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Q. Pontalier et al.
Fig. 5 Close-up of blast wave front from a processed image. Due to
non-uniformities in the initial background image, “holes” may appear
in the blast wave front. Under these circumstances, a circle is manually
fitted to the blast wave front
01234567
Time (ms)
0
0.5
1
1.5
2
2.5
Radius (m)
Blast wave radius
3rd order polynomial fit
Fig. 6 Blast wave radius as a function of time for the high-explosive
dispersal of titanium particles saturated with water with M/C=42.69.
Blue crosses refer to the blast radius extracted at a specific instant. The
red line corresponds to a 3rd-order polynomial fit. To obtain the velocity
profile, this fit is differentiated
which may appear as a front similar to a shock wave, from the
blast wave front itself. Once the trajectory of the blast wave
has been unambiguously identified, the procedure for fitting
a circle to the blast wave described previously is applied.
With the image analysis procedure described above, the
spherical blast radius can be determined. Pixel counts are
converted to distance via the pre-trial scale image. Intra-
frame positions and times are used to determine the shock
trajectory, and the shock velocity is extracted by differenti-
ating a polynomial line of best fit to the position–time data
points. Figure 6shows an example of a radius-time history
plotted for a trial in which titanium particles saturated with
water were explosively dispersed.
Several methods can be used to obtain the history of the
blast wave velocity. First, the instantaneous velocity can be
determined at a specific instant based on the change in posi-
tion between two frames:
v(i)=R(i+1)−R(i−1)
t(i+1)−t(i−1)(1)
01234567
Time (ms)
0
100
200
300
400
500
600
Velocity (m/s)
Instantaneous velocity
2nd order polynomial fit
Fig. 7 Velocity profile for titanium particles saturated with water with
M/C=42.69. Solid red line corresponds to a 2nd-order polynomial fit
(derivative of the 3rd-order polynomial fit of the position vs. time curve).
Note that for the last three points of Fig. 6, instantaneous velocities are
not calculable with (1), so not reported. At the right of the dotted-dashed
line, data are not taken into account in the overpressure calculations
where i=image number, R(i)=position of the blast in
the image number i,t(i)=time of the image number i,
v(i)=blast velocity in the image number i.
An example of the velocities calculated in this way is
shown by the blue crosses in Fig. 7. The small changes in
distance of the blast from one video frame to the next leads
to large fluctuations in the velocity due to the lack of precision
in determining the shock front location (discussed at the end
of the section). To obtain a smoother variation in the blast
front velocity, the shock wave trajectory is fit with a 3rd
order polynomial, as shown in Fig. 6. The polynomial is then
differentiated to get the velocity history, which is shown as
the solid red curve in Fig. 7. This fitting function works well
for trials with a mass ratio above 11. However, for mass ratios
below this value, the fit is not accurate enough, especially at
early times. As a result, in the range of mass ratio between
3.7 and 11, a rational mode fit, i.e., a ratio of a linear function
and a second-order polynomial, as shown below in (2),
R(t)=at +b
at2+bt+c(2)
is chosen instead. A comparison between the two fitting func-
tions for a low value of M/Cis shown in Fig. 8. Note that at
later times, the velocity fitting function starts to increase and
diverge from the instantaneous velocity values. This occurs
due to the nature of the fitting function, which reaches a min-
imum and then increases. Hence, at later times, the curve fits
do not follow the velocity data points, which tend to reach a
plateau value. This is a non-physical behavior, and hence the
velocity values to the right of the vertical dashed lines are
discarded.
The Mach number and the pressure ratio across the shock
are then determined from the velocity profile. The Mach num-
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Experimental investigation of blast mitigation and particle–blast interaction during the…
00.511.522.533.544.55
Time (ms)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
Velocity (m/s)
Instantaneous velocity
2nd order polynomial fit
Rational function fit
Fig. 8 Velocity profile for ethanol at M/C=3.76. Solid red line cor-
responds to a 2nd-order polynomial fit. Dashed black line corresponds
to the derivative of the rational fit of the position versus time curve. To
the right of the dotted-dashed lines, the velocity begins to increase and
is not considered reliable
ber Mais calculated assuming the air acts as an ideal gas,
with the speed of sound, c, given by (3), with γtaken to be
constant and equal to 1.405, i.e.,
c=γRT (3)
where c=speed of sound (m/s), γ=1.405 (ratio of
specific heats), R=286.9 J/kg K (specific gas constant),
T=temperature in Kelvins.
The blast wave is assumed to propagate into undisturbed
air, at temperatures ranging from 5 to 25 ◦C, depending on
the trial conditions. Once the speed of sound is determined,
the pressure ratio across the blast can be determined using
the Hugoniot jump relation (4)[35], assuming that the shock
front is relatively thin, and γis constant:
P
P0
=2γ
γ+1M2
a−γ−1
γ+1(4)
When the pressure ratio across the blast is extracted from
the blast trajectory, it is of interest to compare the different
methods of extraction, from raw videos or using the video
analysis procedure to analyze any discrepancies. At an inter-
mediate value of M/C, where both methods can be performed,
the match is relatively accurate as shown in Fig. 9. However,
if the center of the blast wave is not taken to be fixed during
the processing, a more noticeable discrepancy appears. For
the purpose of this study, the center of the circles remains
fixed for all the videos analyzed.
To study the TNT equivalence of bare explosive charges,
Dewey [36] and Kleine et al. [37] have suggested fitting the
blast radius–time curve to the following form:
R(ta)=A+Bcta+Cln(1+cta)+Dln(1+cta)(5)
0 0.5 1 1.5 2 2.5
Radius (m)
0
0.5
1
1.5
2
2.5
3
Ps/P0 raw videos (fixed center)
Ps/P0 processed videos (fixed center)
Ps/P0 processed videos (no fixed center)
Ps/P0 pressure gauge
Fig. 9 Blast peak overpressure as a function of the blast radius for tita-
nium saturated with water at M/C=42.69. The red line corresponds to
the overpressure extracted from raw videos. Black dotted-dashed line
corresponds to the overpressure extracted from the processed video
considering the center of the circle fixed and the blue dashed line con-
sidering the center not fixed. The diamond symbol indicates the value
measured with the pressure transducer
where Ris the blast radius, cthe speed of sound, tathe
time of shock arrival at a given location, and A,B,C,D
are least-squares fit coefficients. Bis often set equal to one
to ensure that the blast velocity at later times approaches
that of the speed of sound. The advantage of such a fit is
its monotonicity. As a consequence, this fit is not associated
with any changes in its trend after a certain time, as men-
tioned earlier for the third-order polynomial. However, this
fit overpredicts the peak overpressure value compared to the
first pressure gauge value and underpredicts the value for the
second gauge. For the first gauge, the third-order polynomial
is closer to the value obtained with the pressure transducer
(Fig. 10). The last pressure gauge is not accessible for com-
parison as it is outside of the camera view. For the purpose of
this study, since the interest is mainly in the near field, blast
trajectories are fitted with the third-order polynomial for all
the trials tested.
The number of parameters that influence the precision of
the pressure measurements from pressure transducers or from
high-speed videography are numerous. Some variation in the
experimental parameters is inevitable, including the center-
ing of the burster charge, the packing fraction of the powder,
presence of voids within the C-4 burster charge, and so on.
Pressure transducers are also subject to spurious signals from
fragment impact as well as baseline drift from thermal effects.
Estimation of the peak overpressure from the video extrac-
tion procedure is also subject to multiple sources of error,
including errors in scaling the distances and errors in deter-
mining the shock front location from a lack of contrast or
a non-uniform background. Furthermore, in the very near
field, the presence of hot reacted gas (fireball) and particles
projected ahead of the blast wave front may modify its prop-
123

Q. Pontalier et al.
Fig. 10 Comparison of peak overpressures between the 3rd-order
polynomial and the fit by Dewey and Kleine for titanium particles sat-
urated with water at M/C=42.69 from processed videos (the centers
of the circles are fixed). At 1.1 m, the peak overpressure value for the
third-order polynomial is closer to the value obtained with the pressure
gauge as compared to the other fit. The fit by Dewey and Kleine enables
to access a more extensive range but underpredicts the pressure gauge
measurement at 2.0 m. The camera view does not include the last gauge,
and hence the comparison at 4.0 m is impossible
agation rate. Due to the higher temperature compared to the
ambient air, the speed of sound c, the Mach number Ma, and
value of γwill be modified and hence the assumption of a
constant value of γin (4) is no longer valid.
A rough estimation may be obtained for the error associ-
ated with the extraction of the blast front position. This error
is one or two pixels, but is averaged by the fitting process of
the radius-time curve, and a value of one pixel is retained.
Depending on the distance from the charge and M/C,the
corresponding error in velocity is estimated to range from a
maximum of 40 m/s for blast fronts far from the explosion
center and for high M/C, to a maximum of 100 m/s in the
near field and for low M/C. In percentage, the error linked
to the estimation of the velocity and the Mach number cor-
responds to about 10%, and will be multiplied by 2 (20%)
when converted to peak pressure due to the square exponent
of the Mach number in (4).
Due to the difficulty in precisely calculating the error mar-
gins for the reasons noted above, and for clarity, the error bars
have been removed on all the following plots to facilitate
a more direct comparison between the results. The repro-
ducibility of the method is analyzed in the following sections
and also illustrated in the supplementary material by compar-
ing trials at similar M/C. The degree of scatter in the results
for trials with the same materials with similar M/Cvalues
is illustrated by comparing curves (e) and (f) for glass from
Fig. 12 (although the particle size differs in these two trials)
and curves (h) and (j) for water in Fig. 17. Discrepancies
between the peak pressures inferred from the high-speed
videography and values measured directly by the pressure
transducer located at a distance of 1.1 m from the charge cen-
ter are analyzed in Table 2. Depending on the charge mass
used (28 or 75 g), the corresponding scaled distance is either
Z=2.34 m/kg1/3or Z=3.25 m/kg1/3. The comparison
for dry powders is limited to two types of material, includ-
ing S-110 steel shot, Ballotini impact glass beads (both #10
and #13 sizes). The errors calculated range from zero to a
maximum discrepancy of 12.5%. Note that the conversion of
the peak pressure into peak overpressure and the use of the
logarithmic scale in Figs. 12 and 17 and the figures presented
in the supplementary material exaggerate these errors.
4 Results
In this section, the experimental results are presented in the
following way. Section 4.1 presents the typical blast pres-
sure histories recorded with pressure transducers. Section
4.2 details the results relative to peak overpressures for both
granular mitigants and liquids or liquid/powder mixtures. In
Sect. 4.3, a comparison is made between the arrival times of
blast waves with that of particles. Finally, in Sect. 4.4, a com-
parison of positive-phase impulses is given for both types of
material.
4.1 Blast overpressure profile
In addition to the estimation of peak blast overpressure
using image analysis of the blast wave trajectories, overpres-
sure measurements were obtained with piezoelectric pressure
transducers in selected trials. (All the values are reported in
the supplementary material.) The pressure gauge data were
limited to measurements at either three or five specific loca-
tions and were placed relatively far from the charge so that
the pressure field very near the charge was not obtained. In
the near field, the glancing impact of high-velocity particles
with the transducer can introduce spurious spikes on the pres-
sure signals. Pressure gauges were triggered as soon as the
blast passed the first gauge. Figure 11 illustrates the typi-
cal overpressure measurements obtained with the gauges at
three different locations for the dispersal of glass particles
saturated with water, with M/C=62.3, recorded with a
time resolution of 0.2 or 5 µs. (Oscilloscope time resolu-
tion for each trial is reported in the supplementary material.)
For aesthetics, the high-frequency noise in the signals due
to impact of the particles with the gauge or gauge stand
has been smoothed with a Savitzki–Golay filter with a first-
order polynomial and a frame size of 21, on the curves of
Fig. 11. Nevertheless, the peak blast overpressures have been
determined using the raw pressure data. As any spurious
high-frequency noise fluctuations make a negligible contri-
bution to the blast impulse, the blast impulses have been
calculated using the trapezoid method of integration using
the raw data. Note that for each curve, the second pressure
123

Experimental investigation of blast mitigation and particle–blast interaction during the…
Tabl e 2 Comparison between peak pressures obtained with the video analysis and pressure gauge measurements at 1.1 m from the explosion center
Materials C(g) M(g) M/CScaled distance Z(m/kg1/3 )P
P0(videos) P
P0(pressure gauges) Difference (%)
Steel 110 75 1600 21.3 2.34 1.52 1.36 11.8
Steel 110 75 4130 55.1 2.34 1.30 1.28 1.6
Steel 110 28 4192 149.7 3.25 1.11 1.10 0.01
Glass dry #13 75 488 6.5 2.34 1.71 1.62 5.6
Glass dry #13 28 1312 46.9 3.25 1.20 1.19 0.8
Glass dry #13 28 1294 46.2 3.25 1.12 1.10 1.8
Glass dry #10 75 1328 17.7 2.34 1.40 1.43 2.1
Glass dry #10 28 1328 47.4 3.25 1.06 1.11 4.5
Glass dry #10 28 1332 47.6 3.25 1.14 1.12 1.8
Water 28 902 32.2 3.25 1.40 1.43 2.1
Water 28 374 13.35 3.25 1.48 1.48 0.0
Glass wet #13 75 676 9.0 2.34 1.94 1.83 6.0
Glass wet #13 75 1744 23.25 2.34 1.76 1.69 4.1
Glass wet #13 28 1744 62.3 3.25 1.21 1.25 3.2
Glass wet #13 28 1788 63.9 3.25 1.27 1.23 3.3
Glass wet #10 28 1830 65.4 3.25 1.26 1.25 0.08
Glass wet #10 75 1748 23.3 2.34 1.80 1.79 0.01
Titanium wet 75 3202 42.7 2.34 1.39 1.38 0.07
Titanium wet 75 3182 42.4 2.34 1.33 1.52 12.5
05101520
-0.1
0
0.1
0.2
0.3
1.1 m
2.0 m
4.0 m
Peak overpressures
Fig. 11 Blast overpressure as a function of time captured with pressure
gauges for glass (Ballotini #13 impact) beads saturated with water at
M/C=62.3
spike due to the arrival of the ground-reflected wave occurs
after the completion of the primary positive phase of the sig-
nal. These signals were used to determine the positive-phase
impulse of the blast wave at various locations.
4.2 Peak overpressure
The peak overpressures derived from videography results are
plotted as a function of scaled distance, Z, defined as,
Z=R
W1/3(6)
where Z=scaled distance (m/kg1/3), R=dimensional
distance (m), W=(charge mass in equivalent TNT)=
mass of explosive,(kg)×ε(effectiveness factor)for all tri-
100101
10-1
100
101
a)
c)
b)
g)
f)
l)
j)
h)
i)
k)
d)
e)
Kinney and Graham
a) Granulated sugar M/C = 3.93
b) Glass dry #13 M/C = 6.50
c) H95 Al M/C = 6.72
d) H95 Al M/C = 17.09
e) Glass dry #10 M/C = 17.20
f) Glass dry #13 M/C = 17.70
g) Sand M/C = 19.2
h) SiC M/C = 54.01
i) Sand M/C = 54.89
j) Steel 110 M/C = 55
k) SiC/Glass #10 (50/50) M/C = 56.1
l) Chronital steel M/C = 57.116
Fig. 12 Blast wave peak overpressure as a function of scaled distance,
Z, for dry powders obtained by videography
123

Q. Pontalier et al.
als in subsequent sections. Following Kinney and Graham
[38], the equivalent TNT charge mass, W, is equal to the
mass of C-4 multiplied by an relative effectiveness factor,
ε. In the present study, for peak overpressures, a value of
ε=1.39 is taken for C-4 which is a bit above the common
value of 1.37 [39] but still in the range of accepted values
(1.16–1.47 depending on the distance from the charge [40]).
A value of 1.39 was chosen to fit with previous experimental
data in the region of interest 0.5m/kg
1/3<Z<12 m/kg1/3.
The normalized peak overpressure is defined by Ps
P0, with
Ps=Ps−P0, with Psrepresenting the value of the blast
peak pressure and P0=1 atm. The scaled distance is a useful
engineering parameter to compare strengths of blast waves
generated by high explosives of different masses and com-
position. The classical blast scaling law [38] asserts that, for
given atmospheric conditions, two explosions should give
identical blast waves at a given scaled distance Z.
4.2.1 Granular mitigants
Figure 12 shows the peak overpressure as a function of scaled
distance in a log–log plot for different dry granular mitigants
and mass ratios ranging from 3.9 to 57.1. The solid red line
corresponds to the peak overpressure of a bare C-4 charge
based on the Kinney and Graham database [38]. This curve
is based upon the assumption that the blast propagates in
undisturbed atmospheric air (modeled as an ideal gas), out-
side of the detonation products. The peak overpressures for
the eight different materials, and a mixture of silicon carbide
and glass particles are shown. The curves extracted from
the videos are spread over a range of scaled distances from
Z=0.5m/kg
1/3to Z=4.0m/kg
1/3. In some cases, the sat-
uration of the camera sensor by the fireball radiation obscures
the visibility of the blast wave front at early times. As a result,
the curves do not start at the same Zvalues. Also, depending
on M/C, the blast wave emerges from the cloud of fragments
at different times and hence may be first visible at differ-
ent Zvalues. In particular, with increasing M/C, the blast
wave front is visible much closer to the charge compared to
low M/Cvalues. This phenomenon is explored more fully in
Sect. 4.3.
At scaled distances less than one, the peak overpressure is
reduced by about one order of magnitude with the pressure
reduction increasing with increasing M/C, regardless of the
mitigant material, as expected. Also, for all the materials
studied, it is interesting to note that the decay rates of the
mitigated overpressure curves do not follow the decay of a
bare charge in air. In particular, in the near field, the blast
overpressure from a mitigated charge decays significantly
more slowly than for a representative bare high-explosive
charge described by the Kinney and Graham curve. However,
after Z=2m/kg
1/3, the mitigated overpressure decay rate
of certain materials approaches the decay rate of the baseline
100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
a)
c)
b)
g)
f)
l)
j)
h)
i)
k)
e)
d)
a) Granulated sugar M/C = 3.93
b) Glass dry #13 M/C = 6.50
c) H95 Al M/C = 6.72
d) H95 Al M/C = 17.09
e) Glass dry #10 M/C = 17.20
f) Glass dry #13 M/C = 17.70
g) Sand M/C = 19.2
h) SiC M/C = 54.01
i) Sand M/C = 54.89
j) Steel 110 M/C = 55
k) SiC/Glass #10 (50/50) M/C = 56.1
l) Chronital steel M/C = 57.116
Fig. 13 Ratio of the mitigated blast wave peak overpressure over the
peak overpressure of a blast wave for a bare HE charge in air (Kinney
and Graham database) as a function of the scaled distance, Z, for dry
powders
bare charge in air. Furthermore, for the smallest M/Cvalue
tested, the normalized overpressure recovers to almost the
same value as that of an unmitigated charge in the far field.
To facilitate the comparison between the peak overpres-
sure of the mitigated charges with a bare charge, the ratio of
the mitigated overpressure to that of the baseline case for a
bare charge from Kinney and Graham is shown in Fig. 13
for all reported trials with dry powders. The greatest degree
of mitigation occurs at small scaled distances, and the pres-
sure mitigation decreases monotonically with distance from
the charge. For clarity, the ends of several curves have been
omitted (not represented on the graphs), when the artefact
of the velocity fitting procedure described earlier produced
errors in the velocity (and hence blast pressure). However,
the pressure attenuation continues to decrease in the far field
as shown in Fig. 16.
Adding more material mass for a given high-explosive
mass increases the mitigation effect in the near field (Fig. 13),
with mitigated pressures normalized with the baseline case
ranging from a low value (i.e., greatest pressure mitigation)
of 2.6% at Z=0.7m/kg
1/3for a mixture of SiC and glass
with M/C=56, to a high value of 91% at Z=4.5m/kg
1/3
for glass dry #13 with M/C=6.5.
To illustrate the dependence of pressure mitigation on M/C
in the near field to mid-field, two values of scaled distance
were arbitrarily chosen (Z=0.8 and 1.5 m/kg1/3) and then at
these values of Z, the corresponding mitigated overpressure
123

Experimental investigation of blast mitigation and particle–blast interaction during the…
ΔPs/P0
M/C
100101102103
0
1
2
3
4
5Brass
SiC/Glass #10 (50%,50%)
Chronital steel
Granulated sugar
Iron
Glass #10
Glass #13
Sand
Icing sugar
Aluminum
SiC
SiC/Steel 110 (50%,50%)
SiC/Steel 110 (80%,20%)
SiC/Steel 110 (33%,67%)
Steel 110
Power fit
Z = 0.8 m.kg−1/3
Fig. 14 Blast wave peak overpressure as a function of M/Cat Z=
0.8m/kg
1/3in the case of solid powders. Data points for granulated
sugar (M/C=3.93) and SiC ( M/C=54.01) have been extrapolated
from Fig. 12. The data point for brass at M/C=46.85 is obscured by
other data points and thus is not visible
values were extracted from Fig. 12. Figure 14 shows the
results for the mitigated overpressure as a function of M/C
for Z=0.8m/kg
1/3clustered within a broad band. (Data
for Z=1.5m/kg
1/3are omitted for clarity but are reported
in the supplementary material.) At each scaled distance, the
overpressures are reduced with increasing M/C. The decay
rates are a weak function of M/Cand can be represented by
the following power law fits:
Ps
P0
=α×M
C−β
(7)
where
(α, β) =(10.14,0.651)for Z=0.8m/kg
1/3
(α, β) =(5.64,0.611)for Z=1.5m/kg
1/3
The reproducibility of the results using the videography
method can be analyzed by comparing the results for trials
for a specific material at similar M/Cvalues, e.g., Chroni-
tal steel (M/C≈57), glass #10 and #13 ( M/C≈47)
or iron (M/C≈41). A maximum discrepancy of 14% in
terms of peak pressure is observed for glass #13. The M/C
ratio appears to be the primary factor in reducing the over-
pressure for a given Zvalue, and the solid particle material
properties play a secondary role. To quantify the influence
of different types of materials at a specific M/Cvalue on
the overpressure reduction, each set of materials possess-
101102
0
1
2
3
4
5
a)
b)
c)
e)
d)
f)
g)
a) Chronital steel
b) Steel 110
c) Aluminum
d) SiC
e) Granulated sugar
f) Glass #13
g) Glass #10
Fig. 15 Comparison between blast wave peak overpressureof different
solid powders as a function of M/Cat Z=0.8m/kg
1/3
ing at least three data points has been fitted with similar
power laws in Fig. 15. The results for the different mate-
rials fall within a broad band, but there seem to be some
systematic differences in the mitigation performance. Care
must be taken in comparing the differences, since the data
from the various materials span different ranges of mass
ratio M/C. With the above caution in mind, the peak over-
pressure mitigation efficiency of the powders can be sorted
from the least efficient to the most efficient, respectively:
Chronital steel (α, β) =(4.67,0.388), S-110 steel (α, β) =
(13.96,0.668), H-95 aluminum (α, β) =(11.14,0.655),
SiC (30 grit) (α, β) =(10.48,0.692), granulated sugar
(α, β) =(17.71,0.864), glass #13 (α, β) =(11.68,0.749),
and glass #10 (α, β) =(8.91,0.729). The coefficients of
the power laws indicate that the inclusion of data at very
low M/Cvalues makes the fits steeper. However, the power
laws can be still considered as weak (β<1). A maxi-
mum discrepancy of approximately 50% is obtained between
Chronital steel and glass #10 at M/C=60. The discrep-
ancy between glass #10 and glass #13 is around 15% at
M/C=20. Trials from Fig. 14, not shown in Fig. 15,
such as icing sugar and sand, have peak overpressure val-
ues comprised between the aluminum and the glass curves.
Conversely, iron and brass have peak overpressure values
closer to the two curves for steel. The addition of silicon
carbide to S-110 steel powders appears to slightly reduce
the peak overpressure compared to pure steel powders. The
comparison at Z=1.5m/kg
1/3, given in the supplemen-
tary materials, indicates that the discrepancy between glass
123

Q. Pontalier et al.
100101
10-2
10-1
100
Kinney and Graham
Glass dry #13 (M/C = 6.5)
Glass dry #10 (M/C = 17.7)
Glass dry #13 (M/C = 19.28)
Steel 110 (M/C = 21.33)
Glass dry #13 (M/C = 46.21)
Glass dry #13 (M/C = 46.85)
Glass dry #10 (M/C = 47.42)
Glass dry #10 (M/C = 47.57)
Sand (M/C = 51.8)
Sand (M/C = 53.57)
Steel 110 (M/C = 55.06)
Steel 110 (M/C = 62.7)
Aluminum (M/C = 120.29)
Sand (M/C = 128.78)
Steel 110 (M/C = 149.7)
Fig. 16 Blast wave peak overpressure as a function of scaled distance,
Z, for dry powders obtained from pressure gauges
#10 and Chronital steel reduces slightly to 40% but that
the discrepancy between the two glass powders increases to
25%.
Peak overpressures obtained with pressure gauges in the
mid-to-far field are shown in Fig. 16. As expected, the peak
overpressure decreases with M/Cas a weak power law and
the mitigation of the peak overpressure continues to decrease
with distance. The comparison between glass powders and
steel indicates that glass particles continue to outperform
steel at reducing the peak blast overpressure. Indeed, S-
110 steel has peak overpressure values comparable to that
of glass even with mass ratios about three times higher
(M/C=149.7 compared with M/C≈47). At M/C≈20,
S-110 steel appears to have lower peak overpressure values
than glass #10 but is subject to high uncertainties when com-
paring with the videography results (11.8%). In the same
fashion, sand outperforms aluminum with comparable peak
overpressure values for M/C, respectively, at 52 and 120. On
the other hand, the effect of particle size for glass powders is
not clear given the discrepancy (almost 50% between glass
#13 at M/C≈47 and Z=3.24 m/kg1/3), but glass #13
performs better than glass #10 in the far field, contrary to the
behavior in the near field at M/C=17–19.
4.2.2 Liquids and powders saturated with water
In the same manner as in Fig. 12,Fig.17 presents the decay
of peak blast overpressure as a function of scaled distance
for mitigants consisting of pure liquids or powders fully sat-
100101
10-1
100
101
102
b)
a)
c)
e)
g)
j)
h)
i)
k)
m)
d)
f)
l)
Kinney and Graham
a) Ethanol M/C = 3.76
b) Vegetable oil M/C = 4.25
c) Water M/C = 4.69
d) Ethanol M/C = 10.37
e) Glycerol w/tungsten carb M/C = 10.7
f) Vegetable oil M/C = 11.41
g) Vegetable oil M/C = 30.57
h) Water M/C = 32.21
i) Glycerol w/tungsten carb M/C = 32.21
j) Water M/C = 33.57
k) SiC/Steel 110 (10/90) wet M/C = 148
l) SiC/Steel 110 (20/80) wet M/C = 159
m) Steel 110 wet M/C = 168
Fig. 17 Blast wave peak overpressure as a function of the scaled dis-
tance, Z, in the case of liquids/powders saturated with water
urated with water. Figure 18 presents the normalized results
for the liquid and saturated particle trials. The reduction in
peak overpressures with liquids and powders saturated with
water surrounding the charge follows the same trend as for
solid powders with large pressure reductions at small scaled
distances and with the pressures approaching more closely
to that of a bare charge for Z>2m/kg
1/3, except for the
case of the largest values of M/C. As for solid powder, the
attenuation can be quantified in the far field from the pressure
gauge data (Fig. 21). From Fig. 18, the case of S-110 steel
shot saturated with water, with M/C=168, generates the
highest attenuation with a value of 2% at a scaled distance
of Z=0.7m/kg
1/3. On the other hand, for all the materials
with M/C<35 (except for curve h)) the peak blast over-
pressure recovers to a value similar to that of an unmitigated
charge for scaled distances of Z>2m/kg
1/3.
A similar analysis is presented for the liquid experiments,
where the peak overpressure is plotted as a function of
M/Cfor two values of scaled distance. These results fol-
low a similar power law decay as with the solid powders,
but with different coefficients for (7): (α, β) =(26.37,0.85)
for Z=0.8m/kg
1/3and (α, β) =(10.88,0.699)for
Z=1.5m/kg
1/3. As for solid powders, the reduction in
peak overpressure for Z=0.8m/kg
1/3as a function of M/C
is shown in Fig. 19. (The graph for Z=1.5m/kg
1/3is given
in the supplementary material.) Here, the reproducibility of
the videography method is given for glycerol (M/C≈6),
water (M/C≈30), titanium wet (M/C≈40), and glass
wet (M/C≈60). A maximum discrepancy of 13% in terms
of peak pressure is observed for water.
123

Experimental investigation of blast mitigation and particle–blast interaction during the…
10-1 100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1b)
a)
c)
e)
g)
j)
h)
i)
k)
m)
d)
f)
l)
a) Ethanol M/C = 3.76
b) Vegetable oil M/C = 4.25
c) Water M/C = 4.69
d) Ethanol M/C = 10.37
e) Glycerol w/tungsten carb M/C = 10.7
f) Vegetable oil M/C = 11.41
g) Vegetable oil M/C = 30.57
h) Water M/C = 32.21
i) Glycerol w/tungsten carb M/C = 32.21
j) Water M/C = 33.57
k) SiC/Steel 110 (10/90) wet M/C = 148
l) SiC/Steel 110 (20/80) wet M/C = 159
m) Steel 110 wet M/C = 168
Fig. 18 Normalized blast wave peak overpressure versus scaled dis-
tance for liquids and powders saturated with water
ΔPs/P0
M
/
C
100101102103
0
1
2
3
4
5
6
7
8
9Ethanol
Glass #10 wet
Glass #13 wet
Glycerol
Glycerol w/tungsten carbide
Steel 110 wet
SiC/Steel 110 (10%,90%) wet
SiC/Steel 110 (20%,80%) wet
Sodium polytungstate
Titanium wet
Vegetable oil
Water
Power fit
Z = 0.8 m.kg−1/3
Fig. 19 Blast wave peak overpressure as a function of M/Cat Z=
0.8m/kg
1/3in the case of liquids/powders saturated with water. Data
points for several trials are not visible because they are obscured by
other data points (e.g., glycerol w/tungsten M/C=32.21 is behind the
water data point and similarly glycerol M/C=40.75 is obscured by
the sodium polytungstate data)
Blast mitigation performances can be compared on a per
material basis in Fig. 20. In comparison with dry pow-
ders, the results for liquids and saturated particles as a
function of M/Cfall within a much tighter band, indicat-
100101102
0
1
2
3
4
5
6
7
8
9
a)
b)c)
e)
d)
a) Glycerol
b) Vegetable oil
c) Ethanol
d) Glass #13 wet
e) Water
Fig. 20 Comparison between blast wave peak overpressure as a func-
tion of M/Cat Z=0.8m/kg
1/3in the case of liquids or powders
saturated with water
ing that the material properties play a relatively minor role
in this case. Nevertheless, water (α, β) =(28.94,0.93)
appears to produce the largest peak overpressure attenuation,
whereas glycerol (α, β) =(40.42,1.00)and vegetable oil
(α, β) =(32.51,0.90)produce the least. Ethanol (α, β) =
(28.57,0.88)and glass #13 wet (α, β) =(35.75,0.98)
fall in between with similar performances. The discrepancy
between the best mitigant (water) and the worst mitigants
(vegetable oil, glycerol) falls between 15 and 20%, depend-
ing on the mass ratio. At Z=0.8m/kg
1/3, this discrepancy
appears to increase slightly to 23–27%. The addition of tung-
sten carbide powder to glycerol slightly reduces the blast
attenuation shown in Fig. 19 for low M/C, but the mixture
has a similar mitigation performance with the other liquids at
M/C≈32. Moreover, all the powders saturated with water
have relatively similar mitigation performances. Neverthe-
less, contrary to solid powders, the effect of particle size is
not clear. Indeed, at M/C=23, glass #10 has a lower peak
overpressure but a higher peak overpressure at M/C≈63
compared to glass #13. Peak overpressures values for sodium
polytungstate fall between the peak overpressure values for
glycerol and water.
As for Fig. 16,Fig.21 presents the peak overpressure
for liquids or powders saturated with water in the mid-to-far
field obtained with pressure gauges. The peak overpressure
mitigation, as for solid powders, decreases in the far field and
scales as a weak power law of M/C. At similar M/Cvalues,
glass wet #13 attenuates the peak overpressure slightly better
in the far field compared to glass wet #10. At low M/Cvalues,
123

Q. Pontalier et al.
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Kinney and Graham
Water (M/C = 4.56)
Glass wet #13 (M/C = 9.01)
Water (M/C = 13.35)
Glass wet #13 (M/C = 23.25)
Glass wet #10 (M/C = 23.3)
Water (M/C = 32.21)
Titanium wet (M/C = 42.42)
Titanium wet (M/C = 42.69)
Glycerol (M/C = 45.8)
Glass wet #13 (M/C = 62.28)
Glass wet #13 (M/C = 63.85)
Glass wet #10 (M/C = 65.35)
Water (M/C = 83.83)
Fig. 21 Blast wave peak overpressure as a function of scaled distance,
Z, for liquids or powders saturated with water obtained with pressure
gauges
water and glass wet have similar peak overpressure values,
but the wetted powders have higher mitigation performances
at high M/Cvalues.
To facilitate the comparison of the peak blast overpres-
sure attenuation performance of solid particles versus liquids
(or particles saturated with water) for a given M/Cratio, the
power law fits to the data shown in Figs. 14 and 19 are nor-
malized by the value of the baseline bare charge in air and
plotted in Fig. 22. In the near field, for Z=0.8m/kg
1/3,
for M/Cvalues greater than about 30, the blast overpres-
sure is highly attenuated, with values less than 10% of the
value for a bare charge for both granular mitigants and liq-
uids or water-saturated powder beds. Moreover, in the same
region, for small M/Cvalues, powders are about twice as
effective at mitigating blast overpressure. As M/Cincreases,
the differences are reduced and all materials exhibit a similar
mitigation performance.
4.3 Arrival time
To visualize the relative position between the leading edge of
the particles or particle jets (the method of extraction of jet
trajectories is discussed in another publication [19]) and the
blast wave for each trial, it is convenient to plot the arrival
time of each front as a function of distance, determined from
video footage, on the same graph, in the manner of Brode
[41]. Similar to the scaling of distance, the arrival time may
100101102
0
0.2
0.4
0.6
0.8
1
1.2
d)
b)
c)
a)
a) Z = 0.8 m/kg1/3 (solid powders)
b) Z = 1.5 m/kg1/3 (solid powders)
c) Z = 0.8 m/kg1/3 (liquids/wet powders)
d) Z = 1.5 m/kg1/3 (liquids/wet powders)
Fig. 22 Effective peak blast overpressure mitigation as a function of
M/Cfor solid powders and liquids/powders saturated with water in the
near field to mid-field, at two different scaled distances
be scaled as follows:
ts=ta
W1/3(8)
where ts=scaled blast arrival time (ms/kg1/3), ta=actual
blast arrival time (ms), W=charge mass in equivalent TNT
(defined previously).
Figure 23 shows the blast wave and material arrival times,
as a function of Z, for three arbitrary materials at different
M/Cvalues for granular mitigants. Similarly, Fig. 24 shows
the arrival times for liquids/powders saturated with water,
determined using the same spherical fitting technique. Time
zero corresponds to the time of detonation of the burster
charge, and the material location is determined by finding
the maximal spatial extent of the particles or particle jets at
a given time. These graphs indicate that the trajectories of
blast waves for a mitigated charge are retarded compared to
an ideal blast wave for a bare high-explosive charge. For the
relatively light aluminum particles, with a low value of M/C,
the particles follow closely behind the blast wave. However,
for steel particles with a large value of M/C, the jets lag
behind the blast front at a considerable distance. For the case
of liquids or powders saturated with water, the liquid droplets
follow more closely behind the blast wave than for solid par-
ticles. For the case of glass powder saturated with water, it is
difficult to distinguish between the glass particles and water
droplets, although in this case the jets rapidly decelerate some
distance from the charge, possibly due to breakup and vapor-
123

Experimental investigation of blast mitigation and particle–blast interaction during the…
0 0.5 1 1.5 2 2.5 3 3.5 4
0
5
10
15
Kinney and Graham
Al M/C = 6.72
Glass #10 M/C = 17.7
Steel 110 M/C = 55.1
Fig. 23 Scaled time of arrival as a function of the scaled distance for
granular powders. Solid lines: blast wave, dashed lines: jets
0 0.5 1 1.5 2 2.5 3 3.5 4
0
5
10
15
Kinney and Graham
Glass #13 wet M/C = 9.01
Glass #10 wet M/C = 23.3
Sodium polytungstate M/C = 40
Fig. 24 Scaled time of arrival as a function of the scaled distance for
liquids. Solid lines: blast wave, dashed lines: jets
ization of the droplets. Furthermore, the jets may overtake
the blast front for the lowest M/Cvalues, as seen in Fig. 24
for Z<3m/kg
1/3.
The effect of M/Con the separation between the blast
wave and the leading edge of the particle cloud is illustrated
in Fig. 25, which shows a single photographic frame from
Fig. 25 Single photographic frames (on the left) from three different
experiments at the same scaled time (see 8)of2.2 ms/kg1/3as a function
of M/C. The pictures on the right show the same image, subtracted from
a consecutive image, to enhance the visibility of the blast wave. No pixel
noise filters are applied to the images, so scattered black pixels are still
visible in the background. The top image is for the dispersal of S-110
steel shot (M/C=55.1), the middle image the dispersal of dry #10
glass beads (M/C=17.7), and the bottom image the dispersal of a bed
of #10 glass beads saturated with water (M/C=23.3). In each case
the high-explosive mass is 75g. All of the photographs are at the same
scale. (The circular lollipop gauge mount, visible on the right, has a
diameter of 30 cm.) Note that the jets can overtake the blast at the top of
the charge due to the jetting of detonation products up the tube housing
the detonator. Moreover, the jets can also penetrate the blast front on
the sides in the near field and for low M/Cvalues (see Fig. 26)
three different experiments, taken at the same scaled time of
2.2 ms/kg1/3. For each experiment, the original photograph
is shown on the left and a processed image is shown on the
right. The original image is subtracted from a consecutive
image to highlight the parts of the image that are moving,
including the blast wave and particle fronts, such that the
distance between the blast wave and particle front is readily
visible. Contrary to the previous video processing technique,
no pixel noise filter was applied, and hence scattered black
pixels are still evident in the background. The upper two
photographs show the dispersal of dry powders (S-110 steel
at the top, with M/C=55.1 and #10 glass powders in the
middle, with M/C=17.7). As the mass ratio decreases,
the distance between the particle front and the blast wave
123

Q. Pontalier et al.
0 20 40 60 80 100 120 140 160 180
0
5
10
15
20
25
c)
b)
a)
d)
e)
f)
a) Solid powders Z = 0.8 m/kg 1/3
b) Solid powders Z = 1.5 m/kg 1/3
c) Solid powders Z = 2.33 m/kg 1/3
d) Liquids/wet powders Z = 0.8 m/kg 1/3
e) Liquids/wet powders Z = 1.5 m/kg 1/3
f) Liquids/wet powders Z = 2.33 m/kg 1/3
Fig. 26 Separation between blast waves and jets (difference in scaled
arrival time) as a function of M/Cfor solid powders and liquids/powders
saturated with water at Z=0.8m/kg
1/3,Z=1.5m/kg
1/3and Z=
2.33 m/kg1/3. The negative separation for the lowest M/Cvalues shows
the possibility that the jets to overtake the blast front
decreases, as expected. The picture on the bottom shows the
dispersal of a wetted bed of #10 glass powder. Even though
the M/Cvalue (23.3) is higher than for the dry powder, the
material jets (a mixture of liquid and powder) for the slurry
case follow more closely behind the blast wave than for the
dry powder. This indicates that with dry powder beds, there
is greater energy dissipation during particle dispersal and the
material velocity is less.
To make a more quantitative comparison of the distance
between the material front and the blast wave for liquid and
granular mitigants, it is convenient to plot the difference of
the scaled arrival time between the materials and the blast
wave as a function of M/Cin Fig. 26 according to:
ts=tsjets −tsblast (9)
To obtain such a plot, the scaled arrival times of both the
blast wave and material front have been extracted from the
fitted time versus distance trajectory plots. At each Zvalue,
the difference between the scaled times was extracted for 31
trials for granular mitigants and 24 trials for liquids/powders
saturated with water. For clarity, all the data points are not
represented on the graph. For each scaled distance, a linear
function was fitted to the data points, with the error bars rep-
resenting the maximum data point divergence for the whole
curves. Solid powders show the largest scatter in the results
due to the difficulty in extracting an unambiguous value for
the particle front, particularly far from the charge center when
the particle density is low and for non-jetting powders (e.g.,
steel). In the case of liquids or powders saturated with water,
the scatter is mainly attributed to the differences between liq-
uids and powders saturated with water, the latter sustaining
the coherence of the jets close to the blast front over longer
distances and less subject to drag.
It is clear that the difference in scaled time between the
material and blast fronts increases with M/Cand Z. More-
over, at given M/Cand Zvalues, solid powders lead to the
highest separation between the blast wave and the cloud of
fragments. This discrepancy between liquids and solid pow-
ders continues to increase with increasing Zand M/C.Even
if jets particles/droplets can overtake the blast on top of the
charge due to burster/jetting effects (see Fig. 25), generally
jets lag behind the blast front on the sides. However, for very
low M/Cvalues, jets may cross the blast front on the sides.
This effect is indicated in Fig. 26 by the negative tsvalues.
4.4 Positive-phase impulse
The positive-phase blast impulse is an important parameter
when assessing the potential for structural damage due to
blast waves. The positive-phase impulse I+is defined as
the area under the curve of the first positive section of the
overpressure curve, i.e.,
I+=tf
ta
P
P0
dt(10)
with tf=ta+td,tabeing the time of arrival of the blast wave,
and tdbeing the duration time of positive overpressure. For
the convenience of comparing results from experiments with
different high-explosive masses, it is of interest to define a
scaled impulse as follows:
I+
s=I+
W1/3(11)
where I+=positive-phase blast wave impulse (bar ·ms),
I+
s=scaled positive-phase blast wave impulse (bar ·
ms/kg1/3), W=charge mass in equivalent TNT (defined
previously) with a relative effectiveness factor ε=1.15 in
the definition of W, which was determined empirically by
Bogosian et al. [40], and differs from the relative effective-
ness factor for pressure. The impulse data are obtained for
all trials by integrating the blast overpressure-time history
obtained with the side-on piezoelectric pressure transducers.
The trapezian method of integration has been used with a
minimum of 140 points associated with the positive overpres-
sure phase. The time resolution of the pressure measurements
was between 0.2 and 5 µs (depending on the trial—see sup-
plementary material). Another method for determining blast
123

Experimental investigation of blast mitigation and particle–blast interaction during the…
100101
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Kinney and Graham
Glass dry #13 (M/C = 6.5)
Glass dry #10 (M/C = 17.7)
Glass dry #13 (M/C = 19.28)
Steel 110 (M/C = 21.33)
Glass dry #13 (M/C = 46.21)
Glass dry #13 (M/C = 46.85)
Glass dry #10 (M/C = 47.42)
Glass dry #10 (M/C = 47.57)
Sand (M/C = 51.8)
Sand (M/C = 53.57)
Steel 110 (M/C = 55.06)
Steel 110 (M/C = 62.7)
Aluminum (M/C = 120.29)
Sand (M/C = 128.78)
Steel 110 (M/C = 149.7)
Fig. 27 Scaled positive-phase blast wave impulse as a function of
scaled distance Zfor the case of solid powders
impulse using optical data to characterize the density gra-
dients within the flow field has been reviewed by Biss and
McNesby [42]. This method is not practical in the present
situation due to the presence of a non-uniform background
and the presence of compacted fragments that perturb the
local pixel intensity. In this data set, due to the high density
of particles in the near field, pressure gauges are located rel-
atively far from the charge center corresponding to a scaled
distance between Z=1.98 m/kg1/3to Z=12.57 m/kg1/3.
4.4.1 Impulses for dry powder mitigants
Figure 27 presents the scaled impulse results for five different
types of powders. In all cases, the blast impulse falls below
the values for a bare charge from Kinney and Graham, by
up to a factor of 5. The spread in the results is the result of
variations in the M/Cvalue. Reproducibility of the results can
be obtained by comparing glass #10 and #13 at M/C≈47.
The maximum discrepancy is found to be 21% for glass #13
at Z=6.29 m/kg1/3.
At high M/Cvalues, aluminum and sand have lower
impulse values compared to steel even if their mass ratios
are lower (120.29 and 128.78, respectively, compared to
149.7) suggesting that steel particles attenuate less. How-
ever, at an M/Cvalue around 50, the impulses between sand
and steel are relatively similar for Zjust above 2 m/kg1/3,
but a discrepancy appears for higher Zand steel impulses
are more reduced. This discrepancy is attributed to the noisy
overpressure-time signal for the sand trial. Also, at M/C=
101102
10-1
a)
b)
c)
Steel 110
Glass dry #13
Glass dry #10
a) Z = 3.46 m/kg1/3
b) Z = 6.29 m/kg1/3
c) Z = 12.57 m/kg1/3
Fig. 28 Scaled impulse as a function of M/Cat three different scaled
distances Zfor solid powders. Green-edged dots are extrapolated from
Fig. 27
21.3, steel generates similar impulses as glass at M/C≈47.
Particle size seems also to affect the impulses. Contrary
to peak overpressures in the near field, glass #13 particles
appear to attenuate the impulses more at M/C≈47. Also,
glass #13 M/C=6.5 appears to have similar impulses
(or even lower for Z>8m/kg
1/3) compared to glass #10
M/C=17.7. Figure 28 shows the average dependence of
scaled impulses with M/Cfor 3 different Zvalues for M/C
between 17.7 and 149.7. The data can be fit once again with
power law fits (straight lines in logarithmic scale) according
to (7) with the following coefficients:
(α, β) =(1.356,0.517)for Z=3.46 m/kg1/3
(α, β) =(0.807,0.506)for Z=6.29 m/kg1/3
(α, β) =(0.463,0.535)for Z=12.57 m/kg1/3
For comparison, several data points for steel and glass #10
have been extrapolated from Fig. 27 and added to Fig. 28.
Steel particles appear to have lower positive-phase impulses
compared to glass, especially for M/C<63. Conversely,
on average, glass #13 has lower impulses compared to glass
#10.
4.4.2 Impulse for liquid and water-saturated powder
mitigants
In a similar manner, the scaled impulses for liquids and
liquid-saturated powders are plotted as a function of Zand
M/C(for given Zvalues) in Figs. 29 and 30, respectively.
In the far field, most of the positive-phase impulses are
123

Q. Pontalier et al.
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Kinney and Graham
Water (M/C = 4.56)
Glass wet #13 (M/C = 9.01)
Water (M/C = 13.35)
Glass wet #13 (M/C = 23.25)
Glass wet #10 (M/C = 23.3)
Water (M/C = 32.21)
Titanium wet (M/C = 42.42)
Titanium wet (M/C = 42.69)
Glycerol (M/C = 45.8)
Glass wet #13 (M/C = 62.28)
Glass wet #13 (M/C = 63.85)
Glass wet #10 (M/C = 65.35)
Water (M/C = 83.83)
Fig. 29 Scaled positive-phase impulse as a function of scaled distance
Zfor a high explosive surrounded by a liquid or powder saturated with
water
found to be above the Kinney and Graham curve except for
Z<3m/kg
1/3. The reproducibility is given by titanium wet
with a maximum discrepancy of 6.5% at Z=2.49 m/kg1/3.
In contrast with powders, liquid mitigants have virtually no
influence on the decay of the scaled positive-phase impulse
with distance, in comparison with a bare HE charge. Fur-
thermore, from Fig. 30, the scaled impulse does not depend
on M/C. No clear trend can be extracted on a material basis
except that on average, powders saturated with water appear
to have lower impulses than liquids. Also, contrary to solid
powders, glass #10 wet has slightly lower impulses compared
to glass #13 wet.
Similarly to Fig. 22,Fig.31 shows the comparison of
the average attenuation of the blast positive-phase impulse
for solid particles versus liquids (or particles saturated with
water) for M/Cbetween 15 and 160, in the far field. Note that
the normalized impulse values for liquids/particles saturated
with water are higher than unity since impulse values are
above the Kinney and Graham curve in Fig. 29. On average,
for each type of material, the normalized impulse increases
more slowly with scaled distance, though not linearly. For
solid powders, a discrepancy between Z=6.29 m/kg1/3and
Z=12.57 m/kg1/3is visible for low M/Cbut disappears
at high M/C.AtM/C=15, solid powders have impulse
values of 72.7, 75.9, 77.6% at, respectively, Z=3.46, 6.29,
and 12.57 m/kg1/3, normalized to those for liquids/powders
saturated with powders. At M/C=160, the percentages
drop to 21.4, 22.9, and 21.8%.
101102
10-1
100
a)
b)
c)
Water
Glass wet #13
Glass wet #10
a) Z = 3.46 m/kg 1/3
b) Z = 6.29 m/kg 1/3
c) Z = 12.57 m/kg 1/3
Fig. 30 Scaled impulse as a function of M/Cat three different fixed
scaled distances Zfor liquids or powders saturated with water
101102
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
a)
b)
c)
d)
e)
f)
a) Z = 3.46 m/kg1/3 (solid powders)
b) Z = 6.29 m/kg1/3 (solid powders)
c) Z = 12.57 m/kg1/3 (solid powders)
d) Z = 3.46 m/kg1/3 (liquids/wet powders)
e) Z = 6.29 m/kg1/3 (liquids/wet powders)
f) Z = 12.57 m/kg1/3 (liquids/wet powders)
Fig. 31 Effective blast wave impulse mitigation as a function of M/C
for solid powders and liquids/powders saturated with water in the far
field, at three different scaled distances
5 Discussion
Figures 12,13,17, and 18 demonstrate that the peak blast
overpressure from a high-explosive charge may be reduced
by more than one order of magnitude by surrounding the
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Experimental investigation of blast mitigation and particle–blast interaction during the…
charge with a layer of mitigating material, provided that the
mass of mitigant is sufficiently large, relative to the high-
explosive mass. The mitigation is most effective in the near
field for solid powders, particularly for scaled distances of
Z<2m/kg
1/3. The attenuation of the peak overpressure
is primarily dependent on the M/Cratio, for a given scaled
distance as shown in Figs. 14 and 19. Since the mitigant
mass, or mass ratio, is the key parameter controlling the
effectiveness of blast mitigation, it is likely that the transfer
of momentum and heat (investigated numerically in another
publication [43]) from the detonation products to the particles
is the primary mechanism for reducing the blast overpres-
sure in the near field. Increasing the inert mass surrounding
a high-explosive charge will increase the amount of thermal
energy extracted from the expanding detonation products.
For the case of liquids, which are relatively incompressible,
there will be little compaction work done on the liquid as
the shock propagates through it, and little evaporation over
this short timescale. Hence, the transfer of momentum and
heat to the liquid will again be primarily responsible for the
mitigation of the peak blast overpressure in the near field.
For the case of solid powders, the compaction of the
porous bed and deformation of the particles also contribute to
mitigating the blast overpressure. The relative importance of
compaction compared with the transfer of heat and momen-
tum can be determined by comparing the average decay of
peak blast overpressure as a function of M/Cfor liquids
and solids powders in the near field (Z=0.8m/kg
1/3)
(see Fig. 22). The absolute value compared to unity for
liquids/wet powders (dashed line c) reflects the degree of
mitigation due to the heat and momentum transfer, and the
difference between this curve and the curve for solid powders
(solid line a) is a measure of the additional pressure reduc-
tion due to compaction effects. The reduction in pressure due
to compaction at low M/Cvalues is less significant than the
reduction due to the transfer of heat and momentum, but it is
still important. For M/Cvalues above 100, the pressure reduc-
tion is dominated by the transfer of heat and momentum and
the contribution of compaction is negligible. This result is
expected as compaction losses will be most important near
the high-explosive charge due to decay of the shock pres-
sure with distance inside the particle bed. With the increase
in inert mass around the charge, the compaction losses do
not significantly increase, and hence become relatively less
important to the overall energy transfer.
In a recent publication, Milne [44] used hydrocode cal-
culations to develop an empirical correlation for the particle
velocity obtained during the explosive dispersal and showed
that the velocity deficit, in comparison with the conventional
Gurney velocity, is largely due to losses during the pow-
der compaction stage. A similar argument likely explains
the pressure mitigation effect of powders. Liquids, in con-
trast with powders, have negligible initial porosity, and hence
energy dissipation due to pore collapse does not play a role
during shock propagation through the liquid. For powders
saturated with water, the interstitial liquid between the parti-
cles is capable of supporting stress, and hence preventing the
formation of force chains and limiting particle interaction
driven by deformation and compaction. Other phenomena
play a role during the explosive dispersal of liquids, including
cavitation behind the inward-propagating expansion wave
generated when the shock wave reaches the liquid surface.
Re-compaction of the bubbly liquid generated by cavitation
by the expanding explosive products, and breakup of the liq-
uid into droplets and subsequent droplet evaporation will also
occur, as discussed in a recent publication on the dynamics
of liquid dispersal [25]. It is likely that the energy consumed
by these processes is eventually returned to the flow field
through particle drag and expansion of the vapor produced,
leading to the lack of impulse deficit observed experimentally
in the far field.
As a secondary effect, at a specific M/Cvalue, the material
properties appear to influence the peak overpressure reduc-
tion. In particular, particles that form jets when explosively
dispersed show a higher peak overpressure attenuation in the
near field compared to particles that are less prone to form
jets (i.e., Chronital steel, S-100 steel). A difference of up to
50% in peak overpressure values can be observed (Fig. 15), at
given M/Cvalues, between the heavier steel (Chronital steel,
the worst mitigant) and the glass powder with the largest
particle size (glass #10, the best mitigant). The higher heat
capacity of the glass particles [43] and the ability of these par-
ticles to deform, crush or fracture more easily is a possible
explanation for this difference of mitigation. All materials
that are easily deformed, crushed, or fractured (e.g., glass
#13, granulated sugar, icing sugar) show mitigation perfor-
mances closer to the glass #10 powder. Conversely, heavy
metal particles, such as S-110 steel, iron, and brass, have peak
overpressure values closer to that of Chronital steel. Ductile
metals, such as aluminum, as well as hard, but brittle pow-
ders like silicon carbide and sand exhibit intermediate values.
When homogeneously mixed with silicon carbide, S-110
steel exhibits a higher mitigation performance, suggesting
that compaction and fracturing of the brittle component still
occurs in a powder mixture. In the case of liquids or powders
saturated with water, differences are less with a maximum
discrepancy of 20% between water, the best mitigant and
glycerol the worst mitigant (Fig. 20). Ethanol and vegetable
oil have intermediate peak overpressure values. Factors that
may contribute to the difference in the mitigation perfor-
mances include the heat absorption and the heat required
to vaporize the liquids. Indeed, ethanol has a lower latent
enthalpy of vaporization on a mass basis [45] and specific
heat [46](Hvap =846kJ/kg, cp=2.3−2.72 kJ/(kg K),
at temperatures between 0 and 40 ◦C) compared to water
[Hvap =2257 kJ/kg, cp=4.19 kJ/(kg-K)]. On the other
123

Q. Pontalier et al.
hand, glycerol is denser than the two previous liquids and
possesses a higher heat of vaporization (Hvap =974 kJ/kg)
compared to ethanol but has a slightly higher cp[cp=
2.43 kJ/(kg-K)]. Similar arguments could explain differ-
ences in the peak overpressure mitigation in the near field
for vegetable oil and sodium polytungstate. Conversely, the
addition of particles in liquids (e.g., glycerol with tungsten
carbide) or the addition of water to a powder bed may affect
the vaporization of the liquids, hence reducing the mitigation
performance in the near field. To explore the importance of
different liquid properties on blast attenuation more fully,
detailed hydrocode calculations are needed, in which the
heat transfer to the liquid, liquid fragmentation into droplets
and vaporization effects are all considered. Blast attenua-
tion during particle dispersal is explored computationally in
a companion paper [47], and while heat transfer effects are
considered, liquid fragmentation is not modeled in this work.
The rate of decay of the peak overpressure in the near
field (Z<2m/kg
1/3) for powder and liquid mitigants is
less than for an unmitigated high-explosive charge (see Figs.
12,17). It is likely that the motion of particles influences
the blast wave propagation, even if the particle front does
not follow closely behind the blast front. It is hypothesized
that the particle front is effectively acting as a porous pis-
ton, which generates pressure disturbances. Each particle,
or group of particles in close proximity, will drive a bow
shock ahead of it (if particle velocities are higher than the
local speed of sound), which collectively perturb the local
flow field. These perturbations are all the more important in
the near field where the local particle density is high. These
pressure disturbances propagate upstream in the hot, post-
shocked air, augmenting the pressure and impulse behind
the blast wave. As the blast wave expands radially, it slows
down, and ultimately the disturbances are able to catch the
blast wave and influence the peak overpressure. In the far
field (Z>2m/kg
1/3), the blast front and front of the cloud
of particles are well separated. In this zone, the particle den-
sity becomes quite low due to the radial expansion of the
particle front, and the particle influence on the blast wave
propagation becomes insignificant. Hence, in the far field,
the rate of decay of the peak overpressure becomes closer to
that of an unmitigated blast wave (Figs. 12,17) but mitiga-
tion performances continue to decrease in the far field (Figs.
16,21). In the present experiments, combustion in the dis-
persed material cloud was only observed in a few cases (e.g.,
for icing sugar and ethanol). However, the combustion was
only initiated after the blast propagation and hence had no
influence on the blast wave motion.
Jets of solid particles and liquid droplets exhibit some-
what different dynamics. For a given M/C, solid particle jets
initially have a lower velocity than liquid jets due to losses
during compaction of the particle bed. However, jets of liq-
uid droplets are subject to fragmentation, which increases the
droplet surface area and causes the liquid jets to decelerate
more rapidly than solid particle jets [25]. Particles accelerate
at early times when they are still within the detonation prod-
ucts and hence are not visible by videography. As soon as the
particles leave the detonation products, they begin to deceler-
ate due to drag with the surrounding gas and the momentum
of the particles will be converted back to momentum of
the gas. Hence, even in the far field, pressure disturbances
still influence the pressure field behind the blast front and
contribute to the blast impulse. Furthermore, all momentum
losses by evaporation of the liquid behind the blast front will
be converted back into momentum of the gas. As a result,
for liquids, the blast momentum is totally recovered behind
the leading shock front independently of M/Cand the pres-
sure impulse is essentially the same as an unmitigated charge
(Fig. 30). For solid powders, a part of the total blast momen-
tum is permanently lost during the compaction and implies a
reduction in blast impulse (Fig. 27). By increasing the mass
ratio, impulses are reduced similarly to peak overpressures
and follow the same decay as a function of M/C(Figs. 28,
31). As noted earlier, the rate of decay is higher at low M/C
due to the loss of momentum by compaction but diminishes
at high M/Cwhen compaction losses become less signifi-
cant compared to the transfer of heat and momentum to the
particles.
The investigation of the effect of material properties on
the peak blast overpressure and positive-phase impulse atten-
uation is more complex in the far field. Indeed, the blast
attenuation in the far field is a consequence of two factors: (i)
the energy/momentum loss during the shock propagation in
the initial material layer, and (ii) the blast energy/momentum
recovery through the motion of the particles mentioned in the
previous paragraph. The latter effect depends mainly on the
ability of the particles to give their energy back to the flow by
drag, which depends on the shape, velocity, size, and density
of the dispersed particles. In particular, the largest glass par-
ticles (glass #10) attenuate the peak blast overpressure more
in the near field than the far field (Fig. 15) but appear to miti-
gate both the peak overpressure and the impulse less in the far
field (Figs. 16,27). This phenomenon indicates that the blast
overpressure recovers faster for the glass #10 particles. This
phenomenon is counterintuitive since smaller particles are
more subject to drag and should be able to give their energy
back to the flow more quickly. Hence, the blast pressure
should be higher in the far field for the smallest particles. It is
hypothesized that during the compaction of the initial particle
bed, the glass #10 particles fracture into smaller fragments
than that for the glass #13 powder. In addition, steel particles
are found to be better at reducing the blast pressure in the far
field, contrary to the near field. This effect can be attributed to
the higher particle size of the steel shot, compared to the glass
particles (see Table 1), which decreases the overpressure
recovery as mentioned earlier. The non-jetting behavior of
123

Experimental investigation of blast mitigation and particle–blast interaction during the…
the steel particles may also diminish the energy/momentum
recovery process compared to jetting powders, although this
appears to be a secondary effect since the blast mitigation for
steel particles (non-jetting) is on the same order as for iron
particles (jetting), which have a similar density. In the case of
liquids or solid powders, the comparison between materials
in the far field is difficult due to the lack of statistics. Nev-
ertheless, powders saturated with water show, on average,
slightly better impulse attenuations than liquids, suggesting
that residual compaction can occur during the propagation of
the initial shock through wetted powders.
It is found that solid powders are more effective than liq-
uids at mitigating peak blast overpressures and impulses.
However, in practical situations, the loading on a structure
consists of not only the impulse due to the interaction of
the blast wave and subsequent air flow, but also the impulse
from the impact of the particles [48]. Hence, in many cases
the reduction in blast impulse may be overwhelmed by
the particle impulse [49]. Furthermore, to obtain a signif-
icant reduction in the peak overpressure in the far field, a
large amount of inert material is required relative to the
high-explosive mass. For example, to obtain an order of mag-
nitude reduction in blast overpressure at a scaled distance of
Z=2m/kg
1/3requires a mass ratio of 50.
6 Conclusions
The mitigation of a blast wave created by the detonation of
a high explosive was investigated experimentally. Various
types of mitigants including a wide range of solid particles,
liquids, and particles saturated with water have been tested.
The peak blast wave overpressure was inferred from the anal-
ysis of the blast wave motion from the high-speed video
records, and the positive-phase blast impulse was determined
from side-on pressure transducers at several distances from
the charge. The primary results of this study are as follows:
1. Solid powders, liquids, or powders saturated with a liq-
uid can be used as blast wave mitigants. However, solid
powders outperform liquids with respect to mitigating
the blast wave peak overpressure, especially in the near
field and at low ratios of the mass of mitigant to the
high-explosive charge. The difference in mitigation per-
formance is likely due to the energy loss during the
compaction and deformation of solid powders at early
times.
2. The comparison between mitigation efficiencies of solid
powders and liquids suggests that mitigation is mainly
due to the transfer of heat and momentum. However,
at low M/C, shock-induced compaction of the particle
bed and particle deformation of the particles is a signifi-
cant contributing factor for the blast mitigation for solid
powders. At high M/C, the relative contribution of defor-
mation/compaction compared to the transfer of heat and
momentum becomes negligible.
3. The decay of the blast peak overpressure for both granular
solid and liquid mitigants as a function of M/Cfollows a
weak power law function. The decay of blast impulse as
a function of M/Cfor the solid powders also exhibits a
power law decay. However, in the case of the liquids or
liquid-saturated powders, blast impulses in the far field
are essentially the same or slightly higher as that of an
unmitigated charge with the same high-explosive mass
and does not depend on the mass ratio.
4. The degree of blast mitigation in the near field with either
powders or liquids/wet powders surrounding a charge is
primarily dependent on M/C. The material properties play
a secondary role in the mitigation process. In the case of
solid particles, jetting powders (all the powders tested
except steel) show higher mitigation performances than
non-jetting powders (steel), by up to 50%. Glass parti-
cles show the best peak blast overpressure and impulse
attenuation. Factors that likely contribute to the good per-
formance of glass particles include its high heat capacity,
and the tendency of the powder to deform and frac-
ture. Other easily crushable, brittle, or ductile powders
(e.g., sugar, silicon carbide, sand, aluminum) are found
to attenuate the blast more than dense metallic powders
(iron, brass, S-110 steel, and Chronital steel). In the case
of liquids, the difference in mitigation performance is
small (up to 20%). Water appears to attenuate the blast the
most in the near field possibly due to its higher heat capac-
ity and heat of vaporization. Water-saturated powders
attenuate the blast slightly more in the far field compared
to liquids, indicating that residual compaction may occur
during the propagation of the shock through the initial
bed.
5. It is hypothesized that the slower rate of decay of the
peak blast overpressure in the near field for a mitigated
charge versus an equivalent bare charge is due to pres-
sure support induced by the motion of the mitigant which
effectively acts as a porous piston. The local pressure
disturbances from the particle–flow interaction eventu-
ally catch up to the leading shock front and perturb the
peak overpressure. This particle–blast interaction, which
depends principally on the properties of the dispersed
materials (e.g., shape, particle/droplet size, density), gen-
erates a complex blast mitigation dependence on material
properties in the far field. In a companion paper, the
details of the particle–blast wave interaction are explored
more fully with hydrocode calculations [47].
In future work, a more precise quantification of the influ-
ence of material properties on the blast attenuation could
be achieved by improving the accuracy of the videography
123

Q. Pontalier et al.
method. The inclusion of a uniform background behind the
charge and increasing the spatial resolution of the high-speed
videography could significantly improve the analysis. Also,
the use of small mass of mitigant to charge ratio would high-
light the discrepancy. The assessment of damage to nearby
structures due to the combined blast-particle impulse is a
natural extension of the present work. Finally, the effect of
particles embedded within a high explosive, in comparison
with stratified explosive-particle systems, is of interest.
Acknowledgements The authors thank Rick Guilbeault at the Cana-
dian Explosive Research Laboratory for assistance with the experiments
and A. Longbottom of Fluid Gravity Engineering for discussions and
the Defense Threat Reduction Agency for financial support. The authors
also acknowledge the assistance of Yann Grégoire for the processing
of the images in Fig. 25. The authors would also like to thank the three
anonymous reviewers for their many constructive comments.
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