Fragblast, Vol. 9, No. 4, December 2005, 205 – 217
Mechanism of loading on plates due to explosive detonation W. L. FOURNEY*, U. LEISTE, R. BONENBERGER and D. J. GOODINGS University of Maryland, College Park, Maryland 20742
This paper investigates the various mechanisms and parameters that are responsible for delivering impulse to a vehicle that is unfortunate enough to detonate a buried mine. Small scale tests are used to examine the effects of air blast or ejected sand in imparting impulse to a plate that is located above the surface of the saturated soil that contains the explosive. Parameters such as confinement, stand off distance, depth of burial of the explosive, density of the soil, and saturation level of the soil are also examined.
Keywords: Buried mines; Vehicle protection; Small scale testing; Air blast; Impulse from explosive detonation
1. Introduction Both the US Navy and the US Army are interested in knowing more about the loading applied to vehicles which are unfortunate enough to detonate a buried mine in the course of performing their normal duties. The Dynamic Effects Laboratory at the University of Maryland has been involved in small scale testing over the past few years to assist the Navy and the Army in understanding the loads that are applied to vehicles when a buried explosive detonates beneath them. At this time the computer codes needed to make such predictions are being developed. The work at the University of Maryland has been in support of the development of these codes. The purpose of our research has been to understand the mechanisms responsible for the applied loads, to develop scaling laws that could be used to determine explosive loads from the detonation of large charges on the vehicles, and at the same time to provide data that could be used by the numerical modelling effort ongoing within both services. The computational effort is aimed at the development, verification, and acceptance of computer codes that can be used to predict stresses and strains in plates due to the detonation of buried mines and hence to design vehicles that can safely withstand the applied loads.
*Corresponding author. Email:
[email protected]
Fragblast ISSN 1385-514X print/ISSN 1744-4977 online Ó 2005 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/13855140500431989
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2. Small scale testing At Maryland the tests being conducted are very small scale. The largest amount of explosive used to date in our testing has been 3.3 g of PETN and RDX (three RP 83 detonators) and the largest size plate of the order of 0.1 square metres in area. The size of the charges used in the field is of the order of tens of kilograms of TNT. Hence an extrapolation from the small scale tests to the field is on the order of a 4000 to 5000 increase in charge size. The test setup used in our model testing at Maryland is shown in figure 1. The sand and water cover (if used) were contained in a 1.5 m 6 1.5 m 6 0.6 m steel tank. The bottom of the tank was covered with coarse gravel and a geotextile mesh placed above the gravel. The area above the mesh was filled to the desired level with uniformly graded medium quartz sand. This sand, referred to as HD-2, has been used in a previous study [1 – 3] on channelling with explosives and the properties of this sand are well known. The plate (20.32 cm 6 20.32 cm 6 0.64 cm) was suspended from the ceiling by four wires which held it at the desired position above the sand surface. The explosive was embedded in the sand at a desired depth of burial and detonated. A high speed video camera was used to photograph the event at 500 frames per second. The position of the plate in the video frames was used to determine the displacement and the velocity of the plate at any given time. Figure 2 is a photograph of three of the charges cemented together. As can be seen from the figure, when three RP-87 charges are connected they are little bigger than 1.27 cm 6 1.27 cm. The total amount of explosive is 207 mg. From the photographs taken by the high speed camera we are able to obtain plate displacement as a function of time. Three to five markers on each plate are used as targets and averaged to calculate the vertical motion of the plate. Assuming that the velocities recorded at the initial times were those at the end of the very short time over which the impulse was applied to the plate, the impulse can be calculated by equating the impulse to the change of linear momentum of the plate. Figure 3 shows a photograph of the physical set up for one of the plate tests. In this case the sand was saturated to the soil surface and was not covered with water.
Figure 1. Test set up used in small scale testing.
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Figure 2. Three RP-87s cemented together to form charge.
Figure 3. Photograph of physical test set-up.
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The standoff distance for the plate to the sand surface was 4.6 cm and the depth of burial (DOB) for the three RP-87s was 1.9 cm (to the centre of gravity of the explosive charge). Figure 4 shows the bottom of the plate at the end of the test, after being tossed into the air by the explosive detonation. The wires remain unbroken so the plate does not strike the sand surface upon return to its original position. As can be seen from figure 4, the sand that impacts the plate sticks quite well to its bottom surface. The plate size seems to be very appropriate for the standoff distance and the DOB utilised in the experiment. That is, the plate size was big enough to capture most of the momentum of the moving sand. This is also evident from viewing the high speed movie taken during the test in that very little sand was seen being ejected around the sides of the plate.
3. Verify results from small scale tests When using such small scale tests to predict the results expected when larger sizes of explosive are detonated it is necessary to compare with results obtained from larger tests. This was done with a series of tests conducted for the US Navy at Aberdeen Proving Ground in the summer of 2004. In that series of tests, seven full scale tests were conducted using plates weighing approximately 12,300 kg. The results of that comparison are presented in figure 5. The standoff distances for the plates used in the ARL tests ranged from 40.6 cm to 0 cm. (Test 1 was 40.6 cm and Test 5 was on the surface of the saturated sand.) The size of charge used was either 2.27 or 4.54 kg of TNT. (Test 1 used 4.54 kg and Test 5 used 2.27 kg.) The depth of burial of the explosive ranged from 10.4 to 30.5 cm. (Test 1 was buried 10.4 cm deep and Test 3 was buried 30.5 cm deep.)
Figure 4. Bottom of plate after test is concluded showing sand stuck to plate.
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Figure 5. Comparison of test results from ARL with predictions made from small scale testing at Maryland.
In order to obtain the predicted response of the plates in the field tests, each set of conditions for the field tests was scaled to 203 mg, 609 mg, and 3.3 g of explosive and a predictive curve was developed. This curve was then extrapolated to what would be expected for either 2.27 or 4.54 kg of explosive and that is the number presented in figure 5 for the Maryland data. The impulse expected is plotted along the vertical axis of figure 5 in Newton-seconds. These predictions were provided to ARL prior to them conducting the test series. The lighter coloured bars shown in figure 5 are the results obtained for each of the tests by ARL. The predictions from the small scale tests are quite good considering the size of the extrapolation used in going from the small scale to the field tests. It is our own belief that the predictions are even better than shown as we feel that the plates used in the ARL tests were too small in area and some of the sand thrown up from the detonation was not captured by the plate, whereas in our small scale tests we changed the size of the plate to ensure that most of the sand would hit the plate. Addition information on the comparison between the small scale results and the full scale tests can be found in Fourney et al. [4].
4. Motivation for current paper It is unclear exactly what is applying the loading to the plate when the explosive detonates. Three types of loading immediately come to mind: shock loading, air blast, and loading by the soil that is ejected as the crater is being formed. We will therefore describe some results from additional small scale testing that was conducted to try to better understand the loading on the plate. We did not do any tests that would permit us to distinguish between shock loading and the other two mechanisms. We felt that shock loading should be very small except for the case when the plate is resting on the surface. Whenever the plate is separated from the soil surface with an air gap, the shock that is travelling through the saturated sand will mostly be reflected back into the saturated soil due to the very small impedance of air compared to the impedance of the saturated sand. This has been shown to be true from the results of numerical computations, see, for example, Fourney et al. [5]. We did conduct experiments that would help distinguish between loading by air blast and by soil ejection, and these will be described in the following sections. Before describing those results it is import to point out how changes in explosive size, standoff distance, and depth of burial affect the impulse delivered to the plate from the explosive detonation.
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5. Effects of changes in standoff distance and depth of burial Results from a series of small scale tests at a constant scaled depth of burial and a constant scaled standoff distance for the plate are given in the figure 6, as the charge size is increased. These are the predictive curves developed in support of the full scale testing conducted at ARL and each of the curves is for a given depth of burial and height of target (or standoff distance). Curves labelled 1, 6, 2, and 3 are all for the same standoff distance and only depth of burial varies. Curves labelled 1, 6, 5, and 4 are for the same depth of burial and only standoff distance varies. While standoff distance and explosive charge affect the results greatly, depth of burial is a second order effect. In figure 6, the depth of burial was only changed from 4 to 12 inches for a 4.54 kg charge. In figure 7 results are presented for a much larger variation in depth of burial. In the results given in figure 7, based upon a 4.54 kg charge, the depth of burial investigated would range from 10.2 cm to more than 76.2 cm. There is very little change in impulse—even over this large range of depth of burial. It appears that a maximum impulse would be delivered to the plate at a burial depth of around 40.6 cm for a 4.54 kg charge, but the value is only modestly higher. It is necessary to understand how changes in depth of burial and height of target affect impulse delivered to the plate since in the tests to be described below, these two parameters were changed slightly from test to test.
Figure 6. Impulse delivered to plate as a function of charge size.
Figure 7. Impulse versus depth of burial—small scale testing.
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6. Mechanism tests 6.1. Air blast We were first interested in determining how much impulse would be delivered to a plate from air blast alone. To investigate this we conducted a test with three RP-80s (609 mg of explosive) cemented together in a pancake charge. The charge was placed on a steel plate which was lying on the surface of the sand bed, and the test plate was placed 1.9 cm above the top of the charge. The charge was actually placed so that its centre of gravity was 0.4 cm above the steel plate. The test was conducted as described above and the impulse delivered to the test plate (based on the initial velocity of the plate) was 3.2 N-sec. This impulse is quite low compared to our base line tests which employed the same charge and the same standoff distance, but used a different burial depth of 0.5 cm. For this condition the impulse measured was 8.5 N-sec (actually the average of three repeat tests). We then repeated the test with a circular cylinder surrounding the steel plate and the charge, as shown in figure 8. The cylinder was 30.5 cm in diameter and 20.3 cm tall. It therefore was buried in the sand with the bottom below the steel plate and was situated such that the test plate sat on top of the cylinder at the proper standoff distance. The impulse measured in that test was 16.2 N-sec. Figure 9 shows the results of the two air blast tests compared to the base line case. The results indicate that air blast alone could only count for about one third of the impulse delivered to a plate from a detonating explosive. If the air blast is confined, then the impulse applied to the plate would be approximately twice as large as the impulse delivered to the plate from saturated sand.
6.2. Confinement A second series of tests was conducted to determine how the confinement might affect the impulse delivered to a plate when the charge is buried in saturated soil. Three tests were conducted: one with the charge confined with the same cylinder used in the above
Figure 8. Test for air blast with confinement.
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test but with the explosive buried at 0.5 cm below the sand surface, a second with a steel plate beneath the charge which was buried again at 0.5 cm, and a third with the cylindrical confinement and the steel plate beneath the charge which again was buried at a depth of 0.5 cm. All plates were positioned with the same standoff distance as before (1.9 cm). A drawing of the test set up for the test with both the cylinder and the plate is shown in figure 10. Again, the result for the base line case was an impulse delivered to the plate of 8.5 N-sec. For the test with only the cylinder the impulse measured was 9.1 N-sec. For the test with only the steel plate the measured impulse was 10.6 N-sec. For the test with both the steel plate and the cylinder the impulse measured was 10.6 N-sec. Figure 11 compares the impulse measured in the base line case, the case with only the cylinder, the case with only the steel plate, and the case with both the cylinder and the steel plate. It appears that the cylinder (confinement) adds very little when sand is striking the test plate. The buried plate increases the impulse delivered by about 20%, and the steel plate and the cylinder increases the impulse delivered by the same 20%. Hence it appears, unlike with the air blast alone, that confinement of the sand is of very little use in increasing the impulse delivered to a plate due to explosive detonation.
Figure 9. Comparison of impulse on plate from air blast.
Figure 10. Set up for test that used both the cylinder and the plate.
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6.3. Saturation Another series of tests was conducted to determine how the saturation of the sand affects impulse delivered to the plate. A test was conducted in a mix of dry soil composed of 50% sand and 50% (crumbled) clay. In this test the standoff distance was reduced to 1.7 cm and the depth of burial was also reduced to 0.3 cm. Again the charge used was three RP-80s. The impulse measured for the dry soil was 2.49 N-sec. Recall that reducing the standoff distance would increase the impulse significantly while the reduced depth of burial should have very little effect on the impulse measured. A second test was conducted with the charge in water only. For this test the standoff distance was also 1.7 cm and the depth of burial (in the water) was also 0.3 cm. In this test the impulse measured was 9.43 N-sec. Figure 12 compares these results to the base line case. Recall that the base line case had a large standoff distance and depth of burial. It appears that the impulse resulting from the detonation of a charge in dry soil is quite small compared to that for saturated sand. It also appears that water alone results in an impulse slightly larger than for saturated sand. In fact, it appears that saturation of the soil is very important for increasing the impulse delivered to a plate from an explosive. Figure 13 shows the results from a series of tests that used the 50:50 mixture of clay and sand as the soil and for which the water
Figure 11. Impulse from sand, cylinder, plate, and both plate and cylinder.
Figure 12. Impulse from dry soil, base line in saturated sand, and water only.
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content was increased from zero percent saturation to 100% saturation. In these tests, the charge was again three RP-80s with a depth of burial of 0.6 cm and a standoff distance of 1.7 cm. It is quite apparent that the saturation of the soil has a pronounced affect on the impulse delivered.
6.4. Density In addition to saturation, other aspects of the soil bed are expected to influence impulse from a buried charge: soil density, and soil strength characteristics are two in particular. For a given soil, the range in soil densities is small. This is particularly the case in granular soils, and especially when they are uniformly graded as HD-2 is. Soil strength characteristics, which are a function of both soil density and soil type, are expected to have a greater influence. To explore that thesis, five soil mixes were created, ranging from 100% sand, to 15% sand and 85% clay. All soils were saturated and the densities of these mixes ranged from 1.82 g/cm3 to 2.00 g/cm3. Figure 14 shows the results of that series of tests, plotting soil density as the abscissa. That figure indicates that there was very little effect on impulse over this range of soil densities. It is also evident that soil type had little identifiable influence on impulse. This is emphasised by the observation that impulse from an explosive buried in the 15% sand:85% clay mix was equal to the impulse from an explosive buried in the 85% sand:15% clay mix. Therefore, in these saturated soil tests, both soil density—explored over a typical range of soil densities—and soil type, appear to be second order effects, and much less important to the resulting impulse than soil saturation. In order to explore the effect of density further, we conducted additional tests using the densest particulate material that we could think of, namely lead shot. Lead has a specific gravity roughly four times that of soil solids, and its frictional strength as a particulate mass would be expected to be somewhat less than for sand, since the coefficient of friction for lead equals 0.43 and the coefficient of friction for rough quartz equals 0.51 [6]. In this test we used lead shot of the type utilised in loading shotgun shells. We made a test bed of saturated lead shot and conducted a test with all other test
Figure 13. Impulse as a function of percent saturation. 50:50 clay:sand mix.
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parameters identical to the soil tests. The results of that test compared to the soil samples (plotted in figure 14) and pure water are all shown in figure 15, with density plotted on the abscissa. Even accounting for differences in particulate media strength characteristics, the trend is evident: as density increases the impulse delivered to the plate decreases. Furthermore, pure water, with the smallest density and zero shear strength, transmitted the greatest impulse. As a final trial, we also tested the lead shot in a dry condition. The impulse delivered to the plate in that case was nearly the same as it was in the saturated condition: 6.05 N-sec versus 6.23 N-sec. This contradicts the trend indicated by data in figure 13.
Figure 14. Impulse as a function of density.
Figure 15. Impulse as a function of density using different media.
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This is considered to indicate the effect of real soil strength properties, including the generation of transient water pressures within the particulate mass during the explosive event, and emphasizes that impulse from explosives buried in soil can only be determined reliably using real soil as the particulate mass.
7. Conclusions An examination of the collection of small scale tests presented above indicates that at most, the air blast accounts for only one third of the impulse delivered to the plate from an explosive detonation. If the air blast is confined, then the impulse delivered is quite large—even compared with that delivered by a sand – air blast combination. It also appears that a hard bottom (plate beneath the explosive) will increase the amount of impulse delivered to the plate, but only by about 20%. Furthermore, it appears that confining the saturated sand being ejected adds little to the impulse delivered to the plate. Of the three ways of loading a plate—shock, air blast, and ejected soil, ejected soil is by far the largest contributor. Shock (at least for charges buried in the soil) is extremely small, air blast contributes about one third of the impulse, and soil ejected upward accounts for two thirds of the impulse. While density of the soil (over the typical range of soil density) and even soil type appear to have very little effect on the impulse delivered to a plate, saturation of the soil is very important. As saturation is increased from 0 to 100% the impulse increases by a factor of nearly four. When the effects of particulate material density were examined outside the typical range of soil density, density does appear to have an effect on impulse: particulate beds with greater density transmitted less impulse. In addition, it appears that water alone could be a good medium for delivering impulse from an explosive detonation.
Acknowledgements The work reported herein was performed in cooperation with the Indian Head Division of Naval Surface Warfare and was supported by PEO Littoral and Mine Warfare, Ms Kimberly Munch and Lt-Col. Phillip Salinas (PMS495). The work reported herein was performed in cooperation with the Indian Head Division of NSWC. The authors would like to acknowledge the very professional help of Steven Spencer, Markus Mueller, and Sebastian Gedak, undergraduate students who set up and performed many of the tests described in the paper. We would also like to acknowledge the technical interaction and good advice from Leslie Taylor from NSWC Indian Head Division, Bill Szymczak from NRL, and Reed Skaggs from the Army Research Laboratory.
References [1] Taylor, L.C., Skaggs, R.R. and Gault, W., 2005, Vertical impulse measurements of mines buried in saturate sand. ISEE 31st Annual Conference on Explosives and Blasting Techniques, Orlando, FL, February. [2] Fourney, W.L., Taylor, L. and Robeson, D., 1999, Underwater cratering and channeling with explosives. International Journal for Blasting and Fragmentation (FRAGBLAST), 3, 65 – 183.
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[3] Fourney, W.L., Goodings, D.J., Bonenberger, R.J. and Leiste, U., 2002, Visualization of cratering in an underwater environment. International Journal of Blasting and Fragmentation (FRAGBLAST), 6, 1 – 20. [4] Fourney, W.L., Goodings, D., Bonenberger, R.J. and Leiste, U., 2001, Cratering and channeling in an underwater environment. BAI’s Tenth High-Tech Seminar on Blasting Technology, Nashville, Tenn., July 22 – 26. [5] Fourney, W.L., Bonenberger, R., Goodings, D. and Leiste, U., 2004, Impulse delivered to a plate from explosive detonation. ISEE 30th Annual Conference on Explosives and Blasting Techniques, New Orleans, LA, February. [6] Lambe, T.W. and Whitman, R.V., Soil Mechanics (New York: John Wiley and Sons).
