Shock Waves (2002) 12: 69 78
Digital Object Identifier (DOI) 10.1007/s00193-002-0136-3
Size of craters produced by explosive charges
on or above the ground surface
R.D. Ambrosini1, B.M. Luccioni1, R. F. Danesi1, J.D. Riera2, M.M. Rocha2
1
Instituto de Estructuras, Universidad Nacional de Tucumán, CONICET, Argentina
2
CPGEC, Univ. Federal de Rio Grande do Sul, Porto Alegre, CNPq, Brasil
Received 19 April 2000 / Accepted 12 December 2001
Published online 11 June 2002 © Springer-Verlag 2002
Abstract. The results of a series of tests performed with different amounts of explosive at short distances
above and below ground level, as well as on the soil surface are briefly described. After an introductory
description of both the main features of the blast wave and the mechanics of crater formation, a brief
review of empirical methods for crater size prediction is presented. Next, the experimental design and
the results obtained are described. The crater dimensions for underground explosions coincide with those
found in the literature. For explosions at ground level the results are qualitatively described by empirical
equations. For explosive charges situated above ground level, the dimensions of the craters are smaller than
those observed in underground and near the surface explosions. Two new single prediction equations for
this case are presented.
Key words: Blast loading, Craters, Soil
1 Introduction rorist attack, from the damage registered. Most research
is related to underground explosions and only a few pa-
pers are concerned with explosions at ground level. Studies
Blasting loads have come into attention in recent years due
about craters produced by explosions above ground level,
to the great number of accidental or intentional events
which would be the case when the explosive charge is sit-
that affected important structures all over the world,
uated in a vehicle, are rarely found in the open technical
clearly indicating that the issue is relevant for purposes of
literature. Some reports are classified information limited
structural design and reliability analysis. In consequence,
to government agencies.
extensive research activities in the field of blast loads have
taken place in the last fewdecades.
Dynamic loads due to explosions result in strain rates
of the order of 10-1 to 103 s-1 which imply short time
2 Blast waves
dynamic behavior of the materials involved, characterized
mainly by a great overstrength and increased stiffness, in
When a condensed high explosive is detonated a blast
comparison with normal, static properties. In the case of
wave is formed. A typical pressure-time profile for a blast
soils, the response and the mechanism of crater forma-
wave in free air is shown in Fig. 1. It is characterized by an
tion are still more complex due to the usual anisotropy
abrupt pressure increase at the shock front, followed by a
and non linear nature of the material, to the variability
quasi exponential decay back to ambient pressure po and
of mechanical properties and the coexistence of the three
a negative phase in which the pressure is less than ambi-
phases: solid, liquid and gaseous. Generally, simplifying
ent. Of particular importance are the following wavefront
assumptions must be made in order to solve specific prob-
parameters:
lems. Until now, most practical problems have been solved
through empirical approaches. Years of industrial and mil-
ps : peak overpressure
itary experience have been condensed in charts or equa-
Ts : duration of the positive phase
tions (Baker et al. 1983; Smith and Hetherington 1994).
is : specific impulse of the wave which is the area beneath
These are useful tools, for example, to establish the weight
the pressure-time curve from the arrival at time ta to
of explosive to yield a perforation of certain dimensions or
the end of the positive phase.
to estimate the type and amount of explosive used in a ter-
The pressure-time history of a blast wave is often de-
Correspondence to: R.D. Ambrosini
(e-mail: dambrosini@herrera.unt.edu.ar) scribed by exponential functions such as Frielander s equa-
70 R.D. Ambrosini et al.: Size of craters produced by explosive charges on or above the ground surface
p(t)
ps
Area is
1st line of
po
sensors
t
Ts
2nd line of
to
sensors
Fig. 1. Blast wave pressure-time history
tion (Smith and Hetherington 1994), which has the form
3rd line of
sensors
t bt
p(t) =ps 1 - exp - (1)
References
Ts Ts
Acceleration transducers
where b is a positive constant called the waveform param-
Pressure transducers
eter that depends on the peak overpressure ps. The most
Data acquisition equipment
widely used approach to blast wave scaling is Hopkinson s
law(Baker et al. 1983) which establishes that similar ex-
A= 2 Series at ground level
plosive waves are produced at identical scaled distances
B = 2 Series at 50 cm over the ground level
when two different charges of the same explosive and with
C = A serie a at 1m over the ground level and serie b at 1m underground
the same geometry are detonated in the same atmosphere.
Thus, any distance R from an explosive charge W can be
Fig. 2. Loads and measurement equipment locations
transformed into a characteristic scaled distance Z
R
A cavity is always formed when a confined explosion is
Z = . (2)
1/3
produced in a mass of soil. If the explosion is close to the
W
surface, a crater is formed, a complex interaction taking
The use of Z allows a compact and efficient represen-
place between gravity effects, soil strength and transient
tation of blast wave data for a wide range of situations.
load conditions. The most important variables in defining
In expression (2), W is the charge mass expressed in kilo-
the crater shape and size are the mass W of the explo-
grams of TNT. To quantify blast waves from sources other
sive and the depth of the detonation beneath the air/soil
than TNT, the actual mass of the charge must be con-
interface d. When d <0, the explosive is detonated over
verted into an equivalent TNT mass. This is achieved by
the air/soil interface, d = 0 when the detonation occurs in
multiplying the mass of explosive by a conversion factor
the air/soil interface and d >0 when the explosive is deto-
based on the specific energy, the peak overpressure or the
nated beneath the soil surface. For d >0, the crater mech-
impulse delivered (Baker et al. 1983).
anism is altered by gravitational effects. When the depth
of the detonation increases, larger amounts of subsoil must
be expelled by the explosion. Thus the crater radius and
the depth of the crater increase when d increases, until a
3Crater formation: brief state of the art
certain limit value, from which they rapidly decrease (Bull
and Woodford 1998).
Tests of crater formation are appropriate tools to study
the blast phenomena, the behavior and destructive power Studies concerned with the characteristics of craters
of different explosives and the response of soils and rocks caused by explosions usually resort to dimensional analysis
under this type of load (Persson et al. 1994). The mech- and statistics. The scaling lawestablishes that any linear
anism of crater formation is complex and is related to dimension L of the crater can be expressed as a constant
Ä…
the dynamic physical properties of air, soil and soil-air in- multiplied by W divided by the distance of the charge
terface. Even very carefully performed cratering tests give from the ground, where W represents the equivalent TNT
deviations in the dimensions measured of the order of 10%, mass of explosive and Ä… is a coefficient depending upon if
while differences of as much as 30% to 40% are common gravitational effects can be neglected or not. In the first
(Bull and Woodford 1998). case the cubic root law is applicable (Ä… = 0.33) and in
R.D. Ambrosini et al.: Size of craters produced by explosive charges on or above the ground surface 71
the other cases the functional dependence can be quite numerical and independent research results presented by
complex. Iturrioz et al. (2001) preliminary confirm the formation of
Baker et al. (1991) presents a dimensional study to the same shapes of craters.
model the crater formation phenomenon in the case of
Additionally, Gorodilov and Sukhotin (1996) present
underground explosions. Six parameters are chosen to de- the results of research about the shape and size of craters
fine the problem: the explosive mass W , the depth of the
generated by explosions of underwater surface charges on
explosive charge d, the apparent crater radius R, the soil
sand.
density Á, and two strength parameters to define the soil
The depth of the crater created by an explosion ordi-
properties: one with the dimensions of a stress Ã, related
narily is about one quarter its diameter, but this depends
to soil strength, and the other with the dimensions of a
on the type of soil involved (Kinney and Graham 1985).
force divided by a cubic length (Nm-3) K, that takes
into account gravitational effects.
After a dimensional analysis and many empirical ob-
4 Tests description
servations, the following functional relation may be ob-
tained (Baker et al. 1991)
In order to study blast phenomena and its effects on soils,
7/24
R W
three sets of tests have been performed.
= f . (3)
d Ã1/6K1/8d
R
If (scaled radius of the crater) is plotted as a func-
d
7/24 4.1 Site location and soil mechanical properties
tion of W /d, it can be seen that this relation is close
to experimental results and can be approximately simpli-
fied by two straight lines, one with a moderate slope for
The tests were performed in a large flat region, with-
7/24 7/24
W /d > 0.3 and one steeper for W /d < 0.3. For
out rock formations, normally used for agriculture. Two
7/24
W /d < 0.3, the scaled radius of the crater is sensible exploratory drillings and two test pits were used to de-
to small changes in the independent parameter and, due termine the mechanical properties of the soil. The ex-
to this fact, the dependent parameter or the scaled radius ploratory holes were drilled to depths of 2 m and 5 m,
may exhibit great variability. Experimental conditions are respectively, with standard penetration tests (SPT) per-
7/24
better controlled for W /d > 0.3. formed at 1m intervals. The test pits were dug to a depth
It can be deduced that the specific weight Ág is the of 2 m in order to collect undisturbed soil samples for tri-
best measure forKand that Ác2 is the best measure for Ã, axial testing and for a more precise determination of the
where c is the seismic velocity in the soil. If experimental in situ density.
R
results for different types of soils are plotted in a versus
The results of the tests are presented in Tables 1 to 4.
d
7/24
W
The soil profile was quite uniform in the entire 40 × 50 m
graph, it may be clearly seen that there is
Á7/24c1/3g1/8d
testing area, being characterized by
very little variability in the results.
The preceding paragraph refers to underground explo-
1) 0 to 0.70 m Brown clayey silt with organic mat-
sions. There is less information about explosions at ground
ter.
level. Statistical studies of about 200 accidental above-
2) 0.70 to 5.0 m Reddish brown clayey silt of low
ground explosions of relative large magnitude are pre-
plasticity, classification CL, very
sented by Kinney and Graham (1985). The results exhibit
dry.
a variation coefficient of about 30%. From these results,
the following empirical equation for the crater diameter is
proposed
D [m] =0.8W [Kg]1/3 . (4) 4.2 Test series
Additional experimental evidence was obtained during
the surface explosions performed by EMRTC (Energetic The tests were performed in a selected 40 m × 50 m area.
Materials Research Center of the Mineralogical and Tech- A grid with a 10m spacing was used to locate the explo-
nologic Institute of NewMexico). EMRTC conducted ex- sive charges at its nodes, as shown in Fig. 2. Each row
perimental determinations to explore alternative ways of of the grid corresponded to loads of the same magnitude.
controlling the blasting power. In this program, a 3.8 m Charges equivalent to 1, 2, 4, 7 and 10 kg of TNT were
diameter crater was formed by the explosion of 250 kg of located on the five rows. All the charges were spherical.
TNT situated at ground level. In the first two columns indicated as A in Fig. 2, the
In connection with the morphological and structural explosives were situated tangential to the surface. In the
types of the craters, Jones et al. (1997) present an ex- following columns designated as B in Fig. 2, the ex-
tensive study of high explosion and planetary impact plosives were located 0.5 m above ground level. Finally, in
craters and determine three different basic types: (a) bowl- the last two columns indicated as C1 and C2 in Fig. 2, the
shaped, (b) flat-floored with central uplift and (c) flat loads were situated 1 m above ground level (Fig. 3) and
floored with multirings. One of the factors that deter- 1 m underground respectively. The charges above ground
mines the shape is the height of burst. On the other hand, level were located hanging on wood tripods (Fig. 3).
72 R.D. Ambrosini et al.: Size of craters produced by explosive charges on or above the ground surface
Fig. 3. Elevated-charge support system
a
Fig. 4a,b. Blasting tests. a Ground level
explosion; b underground explosion
b
R.D. Ambrosini et al.: Size of craters produced by explosive charges on or above the ground surface 73
D
2000
Dr
1500
1000
"
h
1 2 3
H H H
500
0
0 0.02 0.04 0.06 0.08
-500
-1000
Time [s]
Fig. 6. Definitions of the crater dimensions
Fig. 5. Recorded blast wave pressure-time history
4.3 Explosive description
D3 D2
D1
The explosive used in the tests was Gelamón 80, a NG
based gelatinous explosive theoretically equivalent in mass
a
to 80% TNT. This explosive is similar to Special Gelatine
80 (Formby and Wharton 1996). The weights of explosive
H" D/2
H" D/3
used in each test are indicated in Table 5.
H1
H2 H3
b
4.4 Measurement settings
Fig. 7a,b. Crater measurements. a Diameter measurements.
b Depth measurements
The measurement equipment was basically composed of:
5.1 Pressure measurements
a) Acceleration transducers type AS-10TB and AS-5GB,
by Kyowa, to measure soil accelerations. The signals
from the transducers were amplified by a Kyowa signal Pressure-time recordings were obtained from pressure
conditioning system DPM-612B, calibrated for 1000 transducers. Many of them do not exhibit a typical blast
and 2000 mV/g, low-pass filtered at 300 Hz wave characteristic as that represented in Fig. 1. They ap-
b) Differential pressure transducers type 163PC, by Hon- pear to involve superposition of different blast waves and
eywell, to measure overpressures in air. These trans- noise. An example of a recorded blast wave is presented in
Fig. 5. It corresponds to test B7b. Limitations of the mea-
ducers are internally pre-amplified. The calibration
surement system, discussed in the previous section, render
constant for operation with a regulated 8 V power
the recorded pressures useful for descriptive or qualitative
source is around 2 mV/Pa, with peak capability of
purposes only.
1500 Pa. The excessive sensibility for this application
prevented the transducers to be closer than 40 m of
the blast source, due to possible saturation. The trans-
ducer dynamic response had been previously tested up
5.2 Crater size measurements
to 200 Hz, which is recognizably only a fraction of the
acquisition rate.
The following comments apply to the crater size measure-
ment procedure:
All signals have been AD converted by a data acquisi-
tion system consisting of a notebook with a sixteen chan-
(a) The apparent crater diameter D (Fig. 6) was measured
nel PCMCIA Card type DAS 16/330 by Computerboards.
in all cases according to the definition given by Kinney
The acquisition rate was set to 1024 Hz.
and Graham (1985)
(b) 3 measurements of the crater diameter and 3 of the
crater depth were performed, according to Fig. 7.
(c) In general, the craters produced by explosives situated
5 Tests results
at ground level presented a small mound in the center
formed by the loose soil that fell down on the site after
Figure 4 showtwo blasting tests corresponding to a deto- the explosion. This mound was removed to measure
nation at ground level and an underground explosion. height H2 (Fig. 6).
Pressure [Pa]
74 R.D. Ambrosini et al.: Size of craters produced by explosive charges on or above the ground surface
Table 1. Soil properties Drilling S-1
Depth Phreatic Type SPT tests DD H T200 LL % PI % Clas./
HD t/m3
[m] Level of soil t/m3 UCS
Depth [m] N
0.7 (1) 0.5-1.0 6 1.25 1.14 9.6 87 28.1 12.3 CL
1.0 1.5-2.0 12 1.43 1.27 12.7 91 27.9 8.6 CL
2.0 without
3.0 phreatic (2) 19.3 95 31.0 10.4 CL
4.0 water
5.0 End of the drilling
HD: Humid density; DD: Dry density; H: Humidity; T200: Percentage that passes through sieve No200; LL: Liquid limit; PI:
Plastic index; Clas. /UCS: Classification according UCS
Table 2. Soil properties Drilling S-2
Depth Phreatic Type SPT Test HD DD H T200 LL % PI % CLAS.
[m] level of soil [t/m3] [t/m3] /UCS
Depth [m] N
0.70 without (1) 0.5 1.0 9 1.33 1.22 9.2 88 28.1 10.7 CL
phreatic
water
1.0 (2) 1.5 2.0 11 1.52 1.35 12.6 93 25.9 7.0 CL
2.0 End of the drilling
HD: Humid density; DD: Dry density; H: Humidity; T200: Percentage that passes through sieve No200; LL: Liquid limit; PI:
Plastic index; Clas./UCS: Classification according UCS
Table 3. Soil properties Trial pit C-1
Depth Phreatic Type Fric. (o) Coh HD DD H T200 LL % PI % Clas./
[m] level of soil [MPa] [t/m3] [t/m3] UCS
0.7 without (1)
1.0 phreatic (2) 24 0.036 1.47 1.32 11.7 CL
2.0 water 1.61 1.45 11.2 CL
Fric.: Angle of internal friction; Coh.: Cohesion; HD: Humid density; DD: Dry density; H: Humidity; T200: Percentage that
passes through sieve No200; LL: Liquid limit; PI: Plastic index; Clas./UCS: Classification according UCS
Table 4. Soil properties Trial pit C-2
Depth Phreatic Type Fric. (o) Coh HD DD H T200 LL % PI % Clas./
[m] level of soil [MPa] [t/m3] [t/m3] UCS
0.7 without (1)
1.0 phreatic (2) 1.46 1.33 10.2 CL
2.0 water 25 0.026 1.64 1.43 14.7 CL-ML
Fric.: Angle of internal friction; Coh.: Cohesion; HD: Humid density; DD: Dry density; H: Humidity; T200: Percentage that
passes through sieve No200; LL: Liquid limit; PI: Plastic index; Clas./UCS: Classification according UCS
R.D. Ambrosini et al.: Size of craters produced by explosive charges on or above the ground surface 75
a
Fig. 8a,b. Craters obtained in two tests.
a Superficial explosion crater; b under-
ground explosion crater
b
(d) The shape of most of the craters was flat-floored with idea about the completeness of the detonations for small
central uplift. charges.
In Fig. 9 the results shown in Table 9 are presented
As illustration, the craters due to surface and underground
graphically in conjunction with the experimental results
explosions are shown in Fig. 8
presented by Baker et al. (1991) for alluvium soils. It can
The mean dimensions of the craters are indicated in
be seen in Fig. 9 that there is excellent agreement between
Tables 6 to 9 for explosions at ground level, over the
the present results and the corresponding to Baker et al.
ground and underground, respectively.
(1991) although the types of soils involved are different.
Moreover, for this case, the exponent Ä… =7/24 is the most
appropriate.
6 Results analysis
6.1 Underground explosions 6.2 Explosions at ground level
Due to the great number of published test results con- In Fig. 10, the results corresponding to charges at ground
cerning underground explosions, these results are useful level (Table 6) are presented in conjunction with straight
in order to verify that the mechanics of the process of lines defined by equation 4 Ä… 30%. It can be seen that
the explosions were properly developed and to give an most of the values are between the mean and the -30%
76 R.D. Ambrosini et al.: Size of craters produced by explosive charges on or above the ground surface
Table 5. Mass of Gelamon 80 and theoretical equivalent TNT Table 7. Dimensions of the craters produced by explosions
mass located at 0.5 m above ground level
Test Mass of Equivalent TNT
Test Mean Central D/H2 h
Gelamon 80 (kg) mass (kg)
diameter (cm) depth (cm) ratio
A1a 1.25 1
B1a 43 5 8.6
A1b 1.25 1
B1b 34 4.5 7.6
A2a 2.5 2
B2a 48 6.5 7.4
A2b 2.5 2
B2b 62 6.5 9.5
A4a 5.0 4
B4a 46 6.5 7.1
A4b 5.0 4
B4b 55 6 9.2
A7a 8.75 7
B7a 69 10.5 6.6
A7b 8.75 7
B7b 75 7 10.7
A10a 12.5 10
B10a 72 9.5 7.6
A10b 12.5 10
B10b 75 8 9.4
B1a 1.25 1
B1b 1.25 1
Table 8. Dimensions of the craters produced by explosions
B2a 2.5 2
located at 1.0 m above ground level (a)
B2b 2.5 2
B4a 5.0 4
Test Mean Central D/H2
B4b 5.0 4
diameter (cm) depth (cm) ratio
B7a 8.75 7
C1a 34 4 8.5
B7b 8.75 7
C2a 52 4 13
B10a 12.5 10
C4a 43.5 4 10.9
B10b 12.5 10
C1a 1.25 1
Table 9. Dimensions of the craters produced by underground
C1b 1.25 1
explosions (b)
C2a 2.5 2
C2b 2.5 2 Test Mean Central D/H2
C4a 5.0 4 diameter (cm) depth (cm) ratio
C4b 5.0 4 C1b(92) 215 40 5.4
C7a 8.75 7 C2b(90) 268 49 5.5
C7b 8.75 7 C4b(87) 304 83 3.7
C10a 12.5 10 C7b(96) 347 107 3.2
C10b 12.5 10 C10b(98) 393 127 3.1
100
Table 6. Dimensions of the craters produced by explosions at
ground level
Test Mean Central D/H2
10
diameter (cm) depth (cm) ratio
A1a 62 11 5.6
A1b 54 10.5 5.1
A2a 78 12.5 6.2 1
A2 70 12 5.8
A4a 95 17 5.6
A4b 73 21 3.5
0.1
A7a 158 21 7.5
0.1 1 10 100
A7b 138 22 6.3
A10a 148 22 6.7
W(7/24)/d [kg(7/24)/m]
A10b 164 31.5 5.2
Baker et al 1991 Serie Cb
Fig. 9. Crater dimensions for underground explosions
(D/2)/d
R.D. Ambrosini et al.: Size of craters produced by explosive charges on or above the ground surface 77
7
12
6 D/H = 5,05 abs(d) + 5,7817
2
10
Serie A
5
Eq. (4) Inf.
4 8
Eq. (4) Mean
3
6
Eq. (4) Sup.
2
EMRTC
4
1
0
2
0 2 4 6 8
0
W1/3 [kg of TNT]1/3
0 0.5 1 1.5
Fig. 10. Crater dimensions for explosions at ground level
abs(d) (m)
10
Fig. 12. Crater diameter/depth ratio for explosions above
ground level
6.4 Relation diameter/depth
1
The statistical values of the diameter/depth ratios for the
craters showed in Tables 6 to 9 are presented in Table 10.
Underground explosions (d >0) approximate the relation
D/H2 = 4 (Kinney and Graham 1985). The results for
0.1
explosions on or above ground level are plotted in Fig. 12
as a function of the charge height d. It can be seen that
110 100
a linear function provides an excellent description. The
expression obtained is
W1/3/abs(d)[kg1/3/m]
D/H2 =5.78+5.05|d| . (6)
Serie B Serie Ca Serie A Linear approx.
Fig. 11. Crater dimensions for explosions above ground level
This expression can be useful in order to determine the
height of the burst d from the diameter of the crater D
and the depth of the crater H2 at the centre of the crater.
line. This could be attributed to the fact that the charges
Obviously, the validity of Eq. (6) is restricted to heights of
were tangential to the surface and were not strictly on the
the bursts lower than 1.0 m, but the height of the charges
ground surface. However, due to the small radius of the
from terrorist attacks with vehicle bombs is of that order.
charges (0.05 m to 0.14 m for charges of 1 and 10 kg of
TNT respectively) the results are appropriate. The result
by EMRTC mentioned in Sect. 3 is also plotted in Fig. 10.
7 Conclusions
" The crater dimensions for underground explosions co-
6.3 Explosions above ground level
incide with those found in the literature. For the soil de-
scribed in this paper (Tables 1 to 4) a relation can be
found between the apparent crater diameter D, the mass
In Fig. 11, the results from series B and Ca are presented
of the explosive W7/24 and the height of the charge d, as
(Tables 7 and 8). Moreover, the results corresponding to
suggested by Baker et al. (1991).
tangential explosions (Table 6) are incorporated consider-
" The crater dimensions for explosions at ground level
ing the radius of the explosive as the height of the charges
qualitatively conform to Eq. (4) of Kinney and Graham
over the ground.
(1985).
The dimensions of the crater for d < 0 (explosions
" In the case of explosives located at a height above
above ground level) can be approximated by the following
ground level, the craters were significantly smaller than
relationship:
those produced by explosions at ground level or under-
ground. This result is of practical interest, because the
1/3
D/2 W
data found in the open literature about this topic is scarce,
log =1.241 log - 0.818 . (5)
|d| |d|
and also because this is generally the case, when the ex-
plosive is being transported in trucks or cars.
This expression can be useful in order to determine the " Two new single prediction equations for the dimen-
mass of the explosive W from the diameter of the crater sions of the crater produced by explosions over the ground
D and the height of the burst d. are presented in Eqs. (5) and (6). The first expression can
D[m]
D/H
2
(D/2)/abs(d)
78 R.D. Ambrosini et al.: Size of craters produced by explosive charges on or above the ground surface
Table 10. Statistical values of the relations diameter/depth for the craters by explosions above ground level
D/H2 ratio Underground Ground level 0.5 m 1.0 m
explosions explosions explosions explosions
Mean 4.18 5.75 8.37 10.8
Standard deviation 1.18 1.07 1.31 2.25
Coefficient of variation (%) 28.3 18.6 15.6 20.8
be useful in order to determine the mass of the explosive Bull JW, Woodford CH (1998). Camouflets and their effects on
runway supports. Computer and Structures 69/6: 695 706
W from the diameter of the crater D and the height of the
Formby SA, Wharton RK (1996) Blast characteristics and
burst d. The second equation can be useful to determine
TNT equivalence values for some commercial explosives
the height of the burst d from the diameter of the crater D
detonated at ground level. Journal of Hazardous Materi-
and the depth of the crater H2 at the centre of the crater.
als 50: 183 198
Gorodilov LV, Sukhotin AP (1996) Experimental investigation
Acknowledgements. The authors wishes to thank the collab-
of craters generated by explosions of underwater surface
oration of Eng. Ruiz Martinez, the owner of the test field
charges on sand. Combustion, Explosion, and Shock Waves,
and Eng. Orlando, the explosives expert. Moreover, the finan-
Vol. 32, No 3, 344 346
cial support of the CONICET (Argentina) and CNPq (Brazil)
Iturrioz I, Riera JD (2001) Numerical Study of the Effect of
is gratefully acknowledged. Special acknowledgements are ex-
Explosives On a Plane Surface, XII Congress on Numerical
tended to the reviewers of the first version of the paper, since
Methods and their Applications, ENIEF 2001, Córdoba,
their useful suggestions lead to many improvements of the final
Argentina, In Spanish
version.
Jones GHS, Roddy DJ, Henny RW, Slater JE (1997) Defence
Research Establishment Suffield Explosion Craters and
Planetary Impact Craters: Morphological and Structural
Deformation Analogues, 15th International Symposium on
References
Military Aspect of Blast and Shock, Alberta, Canada
Kinney GF, Graham KJ (1985) Explosive shocks in air. 2nd
Baker WE, Cox PA, Westine PS, Kulesz JJ, Strehlow RA
Edition, Springer Verlag, Berlin
(1983) Explosion hazards and evaluation. Elsevier, Ams-
Persson PA, Holmberg R., Lee J (1994) Rock blasting and
terdam
explosives engineering, CRC Press, USA
Baker WE, Westine PS, Dodge FT (1991) Similarity methods
Smith PD, Hetherington JG (1994) Blast and Ballistic Loading
in engineering dynamics. Elsevier, Amsterdam
of Structures, Butterworth-Heinemann Ltd, Great Britain
Wyszukiwarka
Podobne podstrony:
Analysis of Post Detonation Products of Different Explosive ChargesAssessment of cytotoxicity exerted by leaf extractsSOME DEEPER ASPECTS OF MASONIC SYMBOLISM by A E WaiteYifeng, Tjosvold Effects of warm heartedness and reward distribution on10 Rules of Anal Sex by Jack MorinOccultations of PPM stars by Mars 1950 2050Occultations of PPM stars by Venus 1950 2050Occultations of PPM stars by Uranus 1950 2050Legacy Of Brutality Tab by MisfitsInduction of two cytochrome P450 genes, Cyp6a2 and Cyp6a8 of Drosophila melanogaster by caffeineOccultations of PPM stars by Neptun 1950 2050Practical Analysis Techniques of Polymer Fillers by Fourier Transform Infrared Spectroscopy (FTIR)Calculation of Dust Lifting by a Transient Shock WaveThe Lessons of Asgard ed by Stephen A McNallen (1985)Identification of 32 bit x86 CPUs based on reset signature[42]Oxidative breakage of cellular DNA by plant polyphenols A putative mechanism for anticancer proconsolation of philosophy Notes by Llewellyn JohnsOccultations of PPM stars by Saturn 1950 2050więcej podobnych podstron