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Ballistic penetration of a sandbagged redoubt using silica sand and pulverized rubber of various grain sizes

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Title:
Ballistic penetration of a sandbagged redoubt using silica sand and pulverized rubber of various grain sizes
Physical Description:
Book
Language:
English
Creator:
Cole, Robert
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla
Publication Date:

Subjects

Subjects / Keywords:
Projectile
Impact
Granular Systems
Sandbag
Crushing
Dissertations, Academic -- Mechanical Engineering -- Masters -- USF   ( lcsh )
Genre:
non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: The basis of this work is to find how varying the grain size of materials contained in sandbags (sand and crumb rubber) effects the ballistic penetration of the projectiles from both the 7.62x39mm (308-short), and 9mm Luger cartridges. The sandbags were stacked in a pyramidal stacking configuration according to military specifications in order to simulate a section of a sandbag barrier or redoubt as would be seen on the battlefield. The projectiles were fired at the targets, and the velocity and penetration data was recorded. The results concern both military and civilian applications alike. The 7.62x39 round was found to experience more fragmentation as grain size increased, and was also found to have, on average, the least amount of penetration into the largest grains. The 9mm round was found to suffer negligible deformation in all of the various sizes of materials, and when fired at the two types of materials, showed a steady trend of decreasing penetration depth with increasing grain size. The sand had a wearing effect on the projectiles leaving them scared or fragmented and deformed while the rubber kept the rounds in pristine condition.
Thesis:
Thesis (MSME)--University of South Florida, 2010.
Bibliography:
Includes bibliographical references.
System Details:
Mode of access: World Wide Web.
System Details:
System requirements: World Wide Web browser and PDF reader.
Statement of Responsibility:
by Robert Cole.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains X pages.

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University of South Florida Library
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University of South Florida
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All applicable rights reserved by the source institution and holding location.
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usfldc doi - E14-SFE0004764
usfldc handle - e14.4764
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SFS0028056:00001


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ABSTRACT: The basis of this work is to find how varying the grain size of materials contained in sandbags (sand and crumb rubber) effects the ballistic penetration of the projectiles from both the 7.62x39mm (308-short), and 9mm Luger cartridges. The sandbags were stacked in a pyramidal stacking configuration according to military specifications in order to simulate a section of a sandbag barrier or redoubt as would be seen on the battlefield. The projectiles were fired at the targets, and the velocity and penetration data was recorded. The results concern both military and civilian applications alike. The 7.62x39 round was found to experience more fragmentation as grain size increased, and was also found to have, on average, the least amount of penetration into the largest grains. The 9mm round was found to suffer negligible deformation in all of the various sizes of materials, and when fired at the two types of materials, showed a steady trend of decreasing penetration depth with increasing grain size. The sand had a wearing effect on the projectiles leaving them scared or fragmented and deformed while the rubber kept the rounds in pristine condition.
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Ballistic Penet ration of a Sandbagged Redoubt U sing Sil ica Sand and Pulverized Rubber of Various Grain Sizes by Robert Paul Cole A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Department of Mechanical Engineering College of Engineering University of South Florida Major Professor: Stuart Wil k in son, Ph.D Nathan Gallant, Ph.D Rasim Guldiken, Ph.D Date of Approval: October 22, 2010 Key words: Projectile Impact, Granular Systems Sandbag, Cr ushing Copyright 2010, Robert Paul Cole

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Dedication This research is dedicated to all the people who have supported me through the duration of my student life. To my parents, Robert Eugene Cole and Catherine Anne Mckendree, who have given, through strong nourishment, the inspiration to design creatively, I owe my existence. To my friends, who have given me the gift of friendship (even when my responsibilities inhibit my ability to return the favor), I owe greatly. To my fiance Lauren Valdez, who has been with me through the toughest parts of it all, and her parents, Dennis and Bonnie, who put up with me, I owe all my love

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Acknowledgements I would like to acknowledge Dr. Stuart Wilkinson, who helped get this project underway, and who guided me through the entire process.

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i Table of Contents List of Tables ................................ ................................ ................................ ..................... i v List of Figures ................................ ................................ ................................ ...................... v Abstract ................................ ................................ ................................ .............................. i x Chapter 1: Introduction ................................ ................................ ................................ ........ 1 1.1 Ballistics ................................ ................................ ................................ ............. 1 1.1.1 Interior Ballistics ................................ ................................ ................. 2 1.1.2 Exterior Ballistics ................................ ................................ ................ 2 1.1.3 Terminal Ballistics ................................ ................................ .............. 3 1.2 State of the Science ................................ ................................ ............................ 3 1.2.1 Classification of Granular Materials ................................ ................... 4 1.2.2 Limitations of Computer Simulations ................................ ................. 5 Chapter 2: Literature Review ................................ ................................ ............................... 7 2.1 Field Fortification ................................ ................................ .............................. 7 2.2 Experimental Effects ................................ ................................ .......................... 9 2.3 Dynamics and Predictions ................................ ................................ ................ 11 2.3.1 Identifying Properties of Target Material ................................ ......... 12 2.3.1.1 Moisture Conten t ................................ ............................... 13 2.3.1.2 Loose vs. Compacted ................................ ......................... 13 2.3.1.3 Container Effects ................................ ............................... 15 2.3.1.4 Microstructure of Target Sand ................................ ........... 16 2.3.1.5 Frozen Soil ................................ ................................ ......... 16 2.3.2 Influence of Size/Shape ................................ ................................ .... 16 2.3.3 Shock Wave Propagation ................................ ................................ .. 17 2.3.4 Ideal vs. Non Ideal Impact ................................ ................................ 17 2.3.5 Buckling and Phase Transition Effects ................................ ............. 17 2.3.6 Granular Jets ................................ ................................ ..................... 18 2.3.7 Impact Cratering ................................ ................................ ............... 20 2.3.8 Applicability of Rigid Body Dynamics ................................ ............ 20 2.4 Analytical Models ................................ ................................ ............................ 21 2.4.1 Drag and Force on Projectile Penetrating Target .............................. 22 2.4.2 Structure of Granular Systems ................................ .......................... 22 2.5 Simulation Cap abilities ................................ ................................ .................... 23 2.5.1 Particle Algorithms ................................ ................................ ........... 23 2.5.2 Finite Element Analysis ................................ ................................ .... 25 2.6 Bullet Trap Design ................................ ................................ ........................... 25

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ii 2.6.1 Lead Contamination ................................ ................................ .......... 27 Chapter 3: Experimental Setup ................................ ................................ .......................... 29 3.1 Materials ................................ ................................ ................................ .......... 29 3.1.1 Sand ................................ ................................ ................................ ... 31 3.1.2 Rubber ................................ ................................ ............................... 34 3.1.3 Projectiles ................................ ................................ .......................... 37 3.1.4 Firearms ................................ ................................ ............................ 37 3.1.5 Sandbags ................................ ................................ ........................... 39 3.2 Method ................................ ................................ ................................ ............. 39 3.2.1 Sandbag Barrier ................................ ................................ ................ 40 3.2.2 Positioning ................................ ................................ ........................ 41 3.2.3 Measurements ................................ ................................ ................... 43 3.2.3.1 Grain Size ................................ ................................ ........... 43 3.2.3.2 Full Sandbag W eight ................................ .......................... 44 3.2.3.3 Moisture Content ................................ ............................... 44 3.2.3.4 Projectile Mass ................................ ................................ ... 45 3.2.3.5 Projectile Velocity ................................ ............................. 46 3.2.3.6 Penetration Dep th ................................ ............................... 47 3.2.4 Conducting the Tests ................................ ................................ ......... 47 Chapter 4: Results ................................ ................................ ................................ .............. 49 4.1 The 7.62x39 Round ................................ ................................ .......................... 49 4.1.1 The 7.62x39 Round into Sand ................................ .......................... 49 4.1.2 The 7.62x39 Round into Rubber ................................ ....................... 57 4.2 The 9mm Round ................................ ................................ .............................. 63 4.2.1 The 9mm Round into Sand ................................ ............................... 64 4. 2.2 The 9mm Round into Rubber ................................ ........................... 71 4.3 Com parison of Both Rounds ................................ ................................ ............ 77 4.3.1 Sand ................................ ................................ ................................ ... 77 4.3.2 Rubber ................................ ................................ ............................... 82 Chapter 5: Discussion ................................ ................................ ................................ ........ 86 5.1 Effects of Varying Sand Grain Size ................................ ................................ 86 5.1.1 The 7.62x39 Round ................................ ................................ ........... 86 5.1.2 The 9mm Round ................................ ................................ ............... 87 5.2 Effects of Varying Rubber Grain Size ................................ ............................. 89 5.2.1 The 7.62x39 Round ................................ ................................ ........... 89 5.2.2 The 9mm Round ................................ ................................ ............... 90 5.3 Impact Cratering, Granular Jets, and Buck ling/Phase Transition Effects ....... 90 5.4 Tumbling ................................ ................................ ................................ .......... 91 5.5 Influence of Size/Shape ................................ ................................ ................... 92 5.6 Crushing of Sand Grains ................................ ................................ .................. 92 Chapter 6: Conclusions ................................ ................................ ................................ ...... 94 6.1 The 7.62x39 Round ................................ ................................ .......................... 94

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iii 6.1.1 Sand ................................ ................................ ................................ ... 94 6.1.2 Rubber ................................ ................................ ............................... 95 6.2 The 9mm Round ................................ ................................ .............................. 95 6.2.1 Sand ................................ ................................ ................................ ... 96 6.2.2 Rubber ................................ ................................ ............................... 96 6.3 Overall Conclusions ................................ ................................ ......................... 96 Chapter 7: Future Work ................................ ................................ ................................ ..... 99 7.1 Varying Moisture Content ................................ ................................ ............... 99 7.2 Varying Projectile Velocity ................................ ................................ ........... 100 7.3 Computer Based Modeling and Simulation ................................ ................... 100 References ................................ ................................ ................................ ........................ 101 Appendices ................................ ................................ ................................ ....................... 105 Appendix A: Experimental Data ................................ ................................ .......... 10 6 Appendix B: Major Dimension Grain Measurements ................................ ......... 110 Appendix C : Measured Projectile Masses ................................ ........................... 113 Appendix D: ANOVA Results ................................ ................................ ............. 114 Appendix E: T Test Results ................................ ................................ ................. 119 Appendix F: Moisture Meter Calibration ................................ ............................ 120 About the Author ................................ ................................ ................................ ... End Page

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iv List of Tables Table 1 Material Properties ................................ ................................ ................................ 36 Table A Experimental Data ................................ ................................ ............................. 106 Table B Measured Grain Sizes ................................ ................................ ........................ 110 Table C Measured Projectile Masses ................................ ................................ ............... 113 Table D ANOVA Results for 7.62x39 Round into Sand ................................ ................. 114 Table E ANOVA Results for 7.62x39 Round into Rubber ................................ ............. 115 Table F ANOVA Results for 9mm Round into Sand ................................ ...................... 11 6 Table G ANOVA Results for 9mm Round into Rubber ................................ .................. 117 Table H T Test Results ................................ ................................ ................................ .... 119 Table I Moisture Meter Calibration ................................ ................................ ................. 120

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v List of Figures Figure 1 Variation of Roundness and Sphericity of Sand Grains[8] ................................ .. 5 Figure 2 Classification of Sand Grain Roundness [8] ................................ ........................ 5 Figure 3 Cannon Penetration Paths [9] ................................ ................................ ............... 9 Figure 4 Modes of Target Failure for Soli d Targets [1] ................................ ................... 11 Figure 5 Stress Strain Diagram for a Given Sample of Sand [12] ................................ .... 12 Figure 6 Projectile Penetration into Soft Sand [6] ................................ ............................ 14 Figure 7 Projectile Impact with Water [27] ................................ ................................ ...... 19 Figure 8 Simulation of a Cylinder Impacting a Hard Surface [7] ................................ ..... 24 Figure 9 Granular Fill Bullet Trap [37] ................................ ................................ ............ 26 Figure 10 R e Circulating Crumb Rubber Trap [37] ................................ ......................... 26 Figure 11 Stationary Crumb Rubber Trap [37] ................................ ................................ 27 Figure 12 Earth Filled Tire Trap [37] ................................ ................................ ............... 27 Figure 13 Passive Reactive Sand Berm [3] ................................ ................................ ....... 28 Figure 14 Granulate Materials with the 7.62x39 Projec tile ................................ .............. 30 Figure 15 Test Sample of 60/80 Mesh Sand 5x Magnification ................................ ........ 32 F igure 16 Test Sample of 30/65 Mesh Sand 5x Magnification ................................ ........ 32 Figure 17 Test Sample of 20/30 Mesh Sand 5x Magnification ................................ ........ 33 Figure 18 Test Sample of 6/20 Mesh Sand ................................ ................................ ....... 33 Figure 19 Test Sample of 40 Mesh Rubber 5x Magnification ................................ .......... 35 Figure 20 Test Sample of 16/35 Mesh Rubber ................................ ................................ 35

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vi Figure 21 Test Sample of 3/8 Inch Rubber ................................ ................................ ....... 36 Figure 22 Ammun ition Used During Testing ................................ ................................ ... 37 Figure 23 AR 15 Assault Rifle ................................ ................................ .......................... 38 Figure 24 P226 9mm ................................ ................................ ................................ ......... 38 Figure 25 Sandbags Used in Testing ................................ ................................ ................ 39 Figure 26 How P roperly to Fill Sandbags [42] ................................ ................................ 40 Figure 27 Proper Assembly of a Sandbag Barrier [42] ................................ ..................... 40 Figure 28 Assembly of the Sandbag Barrier ................................ ................................ ..... 41 Figure 29 Setup for 7.62x39 Testing ................................ ................................ ................ 42 Figure 30 Setup for 9mm Testing ................................ ................................ ..................... 43 Figure 31 Analog Soil Moisture Meter ................................ ................................ ............. 45 Figure 32 Competition Electronics ProChrono Digital Chron ograph .............................. 46 Figure 33 Penetration of 60/80 Mesh Sand with Ten 7.62x39 Rounds ............................ 50 Figure 34 Penetration of 30/65 Mesh Sand with Ten 7.62x39 Rounds ............................ 51 Figure 35 Penetration of 20/30 Mesh Sand with Ten 7.62x39 Rounds ............................ 52 Figure 36 Penetration of 6/20 Mesh Sand with Ten 7.62x39 Rounds .............................. 53 Figure 37 Penetration of Each Grade of Sand with Ten 7.62x39 Rounds ........................ 54 Figure 38 Average Penetrati on of the 7.62x39 Round vs. Average Grain Size ............... 55 Figure 39 Post Impact 7.62x39 Bullets, Top to Bottom is Finest to Coarsest .................. 56 Figure 40 Penetration of 40 Mesh Rubber with Ten 7.62x39 Rounds ............................. 58 Figure 41 Penetration of 14/30 Mesh R ubber with Ten 7.62x39 Rounds ........................ 59 Figure 42 Penetration of 3/8 Inch Rubber with Ten 7.62x39 Rounds .............................. 60 Figure 43 Penetration of Each Grade of Rubber with Ten 7.62x39 Rounds .................... 61

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vii Figure 44 Average Penetra tion of 7.62x39 Round vs. Average Grain Size of Rubber .... 62 Figure 45 Post Impact 7.62x39 Bullets, Top to Bottom is Finest to Coarsest .................. 63 Figure 46 Penetration of 60/80 Mesh Sand with Ten 9mm Rounds ................................ 65 Figure 47 Penetration of 30/65 Mesh Sand with Ten 9mm Rounds ................................ 66 Figure 48 Penetration of 23/30 Mesh Sand with Ten 9mm Rounds ................................ 67 Figure 49 Penetration of 6/20 Mesh Sand with Ten 9mm Rounds ................................ ... 68 Figure 50 Penetration of Each Grade of Sand with Ten 9mm Rounds ............................. 69 Figure 51 Average Penetration o f the 9mm Round vs. Average Grain Size .................... 70 Figure 52 Post Impact 9mm Bullets, Top to Bottom is Finest to Coarsest ...................... 71 Figure 53 Penetration of 40 Mesh Rubber with Ten 9mm Rounds ................................ .. 72 Figure 54 Penetration of 14/30 Mesh Rubber with Ten 9mm Rounds ............................. 73 Figure 55 Penetration of 3/8 Inch Rubber with Ten 9mm Rounds ................................ ... 74 Figure 56 Penetration of Each Grade of Rubber with Ten 9mm Rounds ......................... 75 Figure 57 Average Penetration of 9mm Round vs. Average Grain Size of Rubber ......... 76 Figure 58 Post Impact 9mm Bullets, Top to Bottom is Finest to Coarsest ...................... 77 F igure 59 Average Penetration of Both Rounds vs. Average Grain Size ......................... 78 Figure 60 Penetration of Sand vs. Velocity ................................ ................................ ...... 79 Figure 61 Post Impact 7.62x39 Bullets, Top to Bottom is Finest to Coarsest .................. 80 Figure 62 Post Impa ct 9mm Bullets, Top to Bottom is Finest to Coarsest ...................... 81 Figure 63 Average Penetration of Both Rounds vs. Average Grain Size of Rubber ........ 83 Figure 64 Penetration of Rubber vs. Velocity ................................ ................................ .. 85 Figure 65 Average Penetration of 9mm Round vs. Average Grain Size .......................... 88 Figure 66 Effect of Double Sandbag Interface on Penetration ................................ ......... 90

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viii Figure 67 Trauma to Bags ................................ ................................ ................................ 91 Figure 68 White Powder Found in Target Bags Post Impact ................................ ........... 93

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ix Abstract The basis of this work is to find how varying the grain size of materials contained in sandbags (sand and crumb rubber) effects the ballistic penetration of the projectiles from both the 7.62x39 mm (308 short), and 9mm Luger cartridges The sandbags were stacked in a pyramidal stacking configuration according to military specifications in order to simulate a section of a sandbag barrier or redou bt as would be seen on the battlefield The projectiles were fired at the targets, and the velocity and penetration data was recorded. The results concern both military and civilian applications alike. The 7.62x39 round was found to experience more frag mentation as grain size increased, and was also found to have, on average, the least amount of penetration into the largest grains. The 9mm round was found to suffer negligible deformation in all of the various sizes of materials and when fired at the tw o types of material s, showed a steady trend of decreasing penetration depth with increasing grain size. The sand had a wearing effect on the projectiles leaving them scared or fragmented and deformed while the rubber kept the rounds in pristine condition.

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1 Chapter 1: Introduction The initial hypothesis is that the penetration of a projectile into granular matter decreases with increasing grain size. This is reached by taking the extremes of the spectrum into consideration. For instance, if the grains are enlarged to the point that the projectile is, in effect, impacting a solid rock surface, the penetration will be considerably less if there is penetration at all. On the other hand, if the grain size is decreased to the point that the gr anular matter is basically single molecules, there will be no crushing of grains (totally eliminating one mechanism that aids in stopping the projectile), and also creating a less uniform packing order (hence reducing effective density), which acts to redu ce the pressure that stops the bullet, and therefore causes an increase in the penetration depth. With that said, the opposite ends of the spectrum clearly point to a decrease in penetration with an increase in grain size. 1.1 Ballistics T he field of ballisti cs is of high importance with regards to national defense and security. It becomes important to predict the outcome of an impact between any possible projectile and target; whether it is complete destruction of an enemy tank on the battlefield or the comp lete absorption of energy from a handgun bullet by a police proof vest. The problem is there are an infinite number of possible impacts and very little data that can describe materials in these high strain rate conditions [1 ].

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2 In the fiel d of ballistics, there are three main areas of importance: the path of the projectile from rest to the exit of the barrel or tube, known as interior ballistics, the flight of the projectile to the target, or exterior ballistics, and the final stoppage of t he projectile in the target ca lled terminal ballistics [2 ]. 1.1.1 Interior Ballistics Interior Ballistics is a highly complex empirical science which owes its understanding to the an alysis of an incredible bulk of data. There are many factors that such as : projectile mass and materials used mass of propellant, length of barrel, tightness of fit between projectile and barrel, and also the number of twists in the rifl ing of the barrel [2 ]. This multitude of variables, along with the variance of any single componen t due to manufacturing, makes analytical formulation nearly impossible. 1.1.2 Exterior Ballistics The flight of the projectile from barrel to target is stated as exterior ballistics. This is where the projectile is traveling through air at some velocity. Fluid dynamics is applicable to this area of ballistics and it is, for the most part, well understood mathematically and easily modeled on computer. T here are few factors that control a projectile s flight; projectile shape and velocity, relative wind velocity, and gravity dominantly determine the path after launching the projectile. Gravity is considered to remain constant in most cases as it is for this study, and for the medium s in which projectiles travel, typic ally air, the properties are well understood and predictions are possible with great accuracy. The only practical problem confronte d in battlefield

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3 scenarios is the var i ation of wind direction over long distances which concern s snipers and other long distance shooters who deal with these dynamic conditions. 1.1.3 Terminal Ballistics The final deceleration of the projectile as it enters the target is known as terminal ballistics. This is sometimes considered an extension of exterior ballistics with a much denser medium that has far greater structural integrity than air. There are many different targets (ballistic gelatin, Kevlar, steel, etc.) that are either under research curr ently or were recently published [2, 3, 4 and 5 ] detailing the most recent efforts to under stand, and quantify analytically the mechanisms involved such that predict ions can be made for the penetration in some of the most common materials There are many factors determining the path, in time and space, a projectile will take as it travels through a target media ithout good statistical data on a given projectile/target material combination (especially at h igh strain rates) analytical analysis is impossible [1 ] The majority of study is performed through experimental analysis combined wi th advanced modeling techniques. 1.2 State of the Science Currently there are two modes of terminal ballistics research (involving granular matter) trying to reach a connection. There is the experimental approach which concerns itself with idealizing the conditions of the projectile and granular matter by usi ng a very specific projectile shape and orientation of particles (or cylinders in the case of 2 D experiments ) then observing by fast video photography the effects produced by projectile penetration (as in [6 ]) There is also the simulation method which con tains deeply

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4 involved computer code that calculates interactions from one moment to the next, and determines what effects are caused through the duration of penetr ation (as in [7 ]) 1.2.1 Classification of Granular Materials Granular matter comes in many forms from quartz and silica sand to exotic man made silicon carbide powders. In order to classify granulate materials by grain size, two major standards were developed known as the US sieve size and the Tyler Equivalent. The Tyler Equivalent corresponds to the number of openings in the screen per linear inch, while the US sieve size is a number without any physical meaning. The two are very close, and in some cases identical, but vary slightly from each other over the range of interest. Most sand falls between 6 and 80 US sieve size, while finer sand, such as silt, is above 80, and coarser media such as aquarium pebbles is below 6. The range of size for a given sample is determined by what sieve the matter passed through and what sieve it was retained by, or, for example, 60/80 for a sample that passed through a 60 mesh sieve and was retained by an 80 mesh sieve The main issue that comes from granular matter is the complex nature of reactions of the grains Gra ins of sand found in nature are of varying shape and size as shown in F igure s 1 and 2 below. However, due to the current limitations o f modeling and computing power, by and large, the grains are idealized as perfect spheres.

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5 Figure 1 Variation of Roundness and Sphericity of Sand Grains [8 ] Figure 2 Classifica tion of Sand Grain Roundness [8 ] 1.2.2 Limitations of Computer Simulations The number of grains a projectile affects when encountering fine grained sandy media is on the order of 10 8 However, t he number of grains currently feasible for use in computer simulation is on the order of 10 6 which limits both the size of the grains and the control volume cross section that can be used [ 6] With the advancement of computer

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6 science there is an ever improving ability to visualize and study the interactions of grains as projectile penetration occurs. This provides better understanding of the chain of reactions but because the models do not have the ability to consider enough grains, or large enough control volumes there is still disconnect betwee n simulation and reality. Another major problem in defining granular penetration models is the definition of the boundary condi tions, which is one of the most important aspects of the model

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7 Chapter 2: Literature Review Ballistics is a very widely studied topic with a wide range of topic matter. For the following review, there are several areas of interest There is some focus on first hand battlefield knowledge for evidence of what scenarios are possible or probable, but there is also focus placed on the latest modeling and simulation techniques which allows reasonable assum ptions of certain affects that are inherent whe n changing the grain size of the target material. It is evidenced t hrough the timeline of research material that no one cohesive theory defines the projectiles path, however the search for understanding is still underway. 2.1 Field Fortification From the earliest of times there has been interest placed on the effects of a projectile colliding with another object and t he invention of gunpowder has only generated more interest The reasons for fortificatio n are many, but protection from small arms projectile impact is of interest here On the battlefield, or in preparation for battle there is generally minimal time to fortify A s history has shown sandbags supply a tough and easily constructible barrier against most common rounds used in both rifles and pistols. In [9 ] it is tabula ted for the smaller rounds, the penetration depth that is achieved by a 154 grain musket round sh ot into sand at different distances and in 6 to 7 inches (15 18 cm) s said to have achieve d a slightly greater depth of 7.5 to 8.5 inches (19 22 cm)

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8 8 to 14 inches (20 36 cm) The sand used is said to be with a density of 86 lb/ft 3 (1378kg/m 3 ), but no indication is given to the average size of the sand grains There is other target material referred to as is made of clay a nd sand with reference to the penetration of much larger W ith the largest of calibers the penetration is said to have never exceeded 22 feet [9 and 10 ] An interesting illustration ( Figure 3, shown below) depicts the variation in the path of the projectile. Notice the immediate change in direction in the estimated path for one, and the change in orientation of another These larger calibers are out side of the scope of this work, but the fact ors of scaling are of importance when considering the relative size of the projectile to the medium with which it reacts.

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9 Figure 3 Cannon Penetration Paths [9 ] As fo r field fortification in battlefield scenarios, the basic idea is build it big ger than need ed, and i f possible, the barrier should be at least twice the penetration depth of the round being defended against. The reasoning behind this is evident when considering the effects of not one, but multiple shots and the weari ng e ffect it can have on a parapet [9 ] 2.2 Experimental Effects Because penetration knowledge of projectile is imperative for battlefield survival, the effects have been studied by engineers both soldier and civilian alike. There is clearly no better example for a to a projectile than experimental study S ince the beginn ing of research in this area, when it is desired to

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10 know how a target material, such as human flesh, will react to a given round, it is typically easiest to find something similar such as ballistic gelatin or a pig carcass to test against [11 ]. In the same way when someone wants t o know ho w a certain composite react s to projectiles there is need to experiment Generally when penetration is analyzed, a curve fit of the data follows, and for various media and projectiles the coeffi cients vary, but for most cases, of impact with sand, the data has been fit to a second order equation such as Equation (1) f irst proposed by [ 12 ] (1) Equation (1) can also be written as shown below in Equation (2) without linear velocity contribution to acceleration (2) H ere a and b are empirically computed co nstants However, it has been shown that in the case of ballistic sand studies, th ese second order equations do not adequately model the acceleration or easily forecast penetration depth [ 1, 2 11 13 and 14 ] Equation (3) is given by [2 (sand, loose soils, (3) Here, S is the penetration depth, V is the projectile velocity, b and c are empirically determined coefficients and d is a constant In order to predict the depth of penetration, cur rently, the coefficients must be obtained for the given sample. This calls

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11 for testing between the media and the projectile, whi ch will then allow intermediate velocity penetration to be calculated. 2.3 Dynamics and Predictions There are multiple mechanisms for proj ectile penetration as shown below in F igure 4. Figure 4 Modes of Target Failure for Solid Targets [1 ] During penetration of a projectile into a container of sand c ombinations of the d ifferent modes above can be present along with crushing of sand parti cles, and compression of sand particles (see F igure 5 for stress strain analysis of dry quartz sand size 14/40 sieve test sample)

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12 Figure 5 Stress Strain Diagram for a Given Sample of Sand [12 ] The area between the curves represents the work done on the sample and signifies the inelasticity and compressibility of the sand [12 ] It becomes extremely important to characterize the properties of the sand before and after experimentation to fully understand the mechanisms and their effects in the media. There is an infinite number of sand size/moisture combinations that are present in nature and an overall shortfall of experiments to describe suc h variation [ 1 12 15 16 and 17 ] 2.3.1 Identifying Properties of Target Material As previously stated, it is imperative to characterize the properties of the media to fully understand the transient displacement of the projectile in the media. Reference [18 ] has a good review of penetration studies for determining these properties. It is typically easier to identify through direct measurement what properties a specific media has, rather than to theoretically explain the properties of every diff erent media in nature As a result of variation between the properties of the same media at different conditions such as moisture content and void fraction, there is currently little

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13 that can be done for predicting the penetration of any given projectile in a particular media so steps are taken to a void classification of projectile/target material combination and classification of the media alone is promoted. One approach used for determining the elastoplastic properties of granular media is based on the analytic approach and represents the dynamic resistance to shear in the form of a linear fractional function, which depends on a set of parameters having a clear physical meaning of adhesion, the angle of internal friction, and the ultimate resistance to shear [18 ] 2.3.1.1 Moisture Content One important finding in [19 ] is that a penetration into saturated soil is greater than into the same dry sample. It is also demonstrated that shock waves dampen quicker in wet sand than in dry even thou gh the projectile may travel further [19 ]. Several mechanisms are responsible for the decrease in penetrati on depth in dry sand, but slower shock dampening (increased radius of shock wave propagation) and higher friction are thought to be the dominant mechanisms It is said that the penetration is somewhat lubricated by the presence of water in the media [20 ] These findings are also confirmed by [12 ] as well. 2.3.1.2 Loose vs. Compacted There have been studies on the r eaction of soft sand and the effects caused by projectile penetration. One interesting method for testing is introduce d by [ 6] in which the media is carefully de compacted by bubbling gas through it. This allows the dry granular matter (sand) of grain si response to the projectile ; making the granular material more susceptible to displacement by air pressure. One

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14 observ ed phenomenon is the void collapse that occurs behind the projectile and the pressure spike induced granular jet that follows (see F igure 6 below ) Figure 6 Projectile Penetration into Soft Sand [ 6]

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15 The images in Figure 6 were taken with a high speed camera, and the projectile shown is a steel ball of radius 1.25 cm dropped from a height of up to 1.5 m, and the depth of the sand is approximately 25 40 cm. This is a classic example of the effect on soft sand, but clearly the sam e reaction would not occur upon impact with compacted sand. There would be a distinct difference between the media shown and the same media compacted [6, 21 ] 2.3.1.3 Container Effects For the current study it is important to understand the effects the container has on It has been mentioned that the penetration of loosely piled sand is greater than that of sand in a bag by a factor of 4/3 to 2, and the reasoning behind it is some what intuitive. When a projectile enters the sand it first causes a splash. If there is a bag around the sand, this initial splash is attenuated, but as the bullet penetrates the boundary conditions on the sample bag are held within close proximity of t he original positioning, with the a bility to expand slightly. A fter this initial expansion, the sand is forced back inward by the constraining bag. This causes increased pressure on the projectile, as the sand, that would have been pushed away, reverbe ra tes some of its energy back t o the bullet slowing it more quickly Another way effects of the container can be considered is through the density effects and similarly, the effective density. Effective density is used to describe the density of granular matter which is also inversely proportional to the void fraction. The density can play a significant role in determining penetration depth, but is relatively unchanged by compression unless the sides of the sample are contained during loading [22 ]

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16 2.3.1.4 Microstructure of Target Sand There is much interest in understanding the mechanisms that cause a granular bed to orient itse lf especially from the granular materials industry. The common problem confronted is the granules ability to flow as a liquid under certain conditions and not under others [22 ] This can become detrimental to a sorting facility if not handled properly. Currently the beds of grains are coerced to move by sinusoidal oscillations of the holding vessel. This method develops a certain microstructure or packing order in the vessel and is of interest to not only the industry but to the physics community as a whole because of the implications it has with respect to increa sing density and solids fraction of various granular materials [23 ] 2.3.1.5 Frozen Soil There have been test s on frozen soil to see if the pe netration equations given by [12 ] (Equation 1) and also Ross and Hanagud, can provide accurate predictions for penetrat ion depth into frozen soil. I t is indicated that upon selection of the proper mate rial constants, both equations result in fair predictions for impact velocities below 600 m/s [16 ] 2.3.2 Influence of Size/ Shape There are currently scaling issues being confronted by researchers in terminal sand ballistics. In order to successfully model impacts with granular materials the grains of the media have to be idealized as perfect inelastic spheres They must also be made larger, with respect to the pr ojectile, than are normally confronted in practice. This is due to the overall number of grains that can be handled by current computing abilities. This makes translation to real systems slightly harder because the virtual grains are so

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17 dissimilar to the real grains. It is stated in [2 scale linearly with projectile size as several investigations have expected or tried to explain H owever, with p roper inspection of scaling effects it can be shown that there is a con nection between virtual and real systems and possibly an ability to extrapolate the results for other systems [16, and 22 ] 2.3.3 Shock Wave Propagation Shock wave propagation is an important facet of impact engineering because of the energy displ acement that occurs through this mechanism. The shock waves in saturated sandy soil c an be computed using Mie Grneisen provided the Mie Grneisen constants and the dimensional speed of sound can be computed for the target medium. As previously stated, the s hock waves dampen quicker in wet sand than in dry [19 ]. 2.3.4 Ideal vs. Non Ideal Impact Perfect ly perpendicular collisions between projectiles and targets are ideal for maximum penetration, but are not always present in practice S tudies have been performed on various impact orientations to determine the response characteristics of both the target and the projectile [24 and 25 ] Since the adverse penetration effects, such as ricochet, are minimal when the angle of approach is close to 90, the classification of impact for this study is taken to be ideal. 2.3.5 Buckling and Phase Transition Effects The effects of penetration usually entail high pressures and temperatures at the leading edge. For this reason it is important to discuss the paramet ers leading to buckling

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18 and phase transition. In some cases, such as in [5 ] the penetrator can be deformed and even melted and re deposited on the shaft of the projectile. aids in iden tify ing the loading necessary, and determines when the projectile will deform u nder the dynamic loading conditions that occur during penetration [19 ]. [5, and 20 ] (4) It is necessary to obtain accurate transient displacement information in order to determine the acceleration of the projectile which will cause buckling to occur, but in the case of fine, saturated sand and projectile velocities at or below 700 m/s the p rojectile typically suffers little deformation. The effects of wear ca n be seen on the projectile surface after impact 2.3.6 Granular Jets An interesting topic of granular penetration is the phenomenon of granular jet formation. As seen in Figure 6, the granular jet that shoots from the surface just microseconds after impact is very similar to one formed by impact with water (see F igure s 6 and 7) [26 ]

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19 Figure 7 Projectile Impact with Water [27 ] Here, the water gives evidence to the mechanisms that cause jet formation. The solid sphere impacting the surface causes an ejecta sheet and transient axisymmetric crater It can be noticed that there is a void following the projectile that closes causi ng the pressure to spike under the surface resulting in a jet of water projecting through the air in the opposite direction of penetration. This phenomenon is known as void collapse. The same effect occurs in granular media and has certain characteristi cs that pertain to this study. For instance, the Reynolds number is said to reduce to a geometric factor

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20 which is constant for each grain size, and with an increase in grain diameter by a factor of 10 (reduce Re by 100 in formulati on) for frictionless flo w predict s a 10 fold reduction in the height of the jet but experimentation suggests a 100 fold reduction. This has implications on the fluid like nature of sand and gives insight to one of the many possible effects of altering grain size. 2.3.7 Impact Cratering Cratering is under investigation by astrophysicists searching for a better understanding of how crater formation is linked to projectile size and speed. It is essential such that educated assumptions can be made about past and future impacts of celestial bodies. In the current study it is important to understand the mechanisms that cause crater formation and the mechanisms that prevent it from occurring in containment vessels such as sandbags. In sandbags crater formation from a horizontal impa ct is quickly erased by small avalanches or cave ins, and does n o t directly determine penetration depth, but it does have importance when discussing the numerous effects of projectile penetration in granular materials. Impact cratering has two distinct reg ime s of formation defined by the opening dynamics and partial closing. It is noted that the opening dynamics can be modeled by an exponential saturation while the partial closing can be understood throu gh the dynamics of avalanching. T he disturbance in the media is also said to have a well defined propagation velocity [ 2, and 28 ] 2.3.8 Applicability of Rigid Body Dynamics One question a granular medium is in regards to the ability of the grains to act as rigid bodies. It is

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21 clear that the particles themselves do, for the most part respond as rig id bodies, but as noticed by [12 ], there are other, non rigid body, collisions in the granular media that are evidenced by cru shed and broken grains. This facet alone breaks granular impacts from what would be handled th r ough the theories of rigid body dynamics. A nother is the vibrational motion occurring within the medium which according to [30 ] is not corrected by the coefficient of restitution even when friction is factored in [ 4 ] 2.4 Analytical Models Through the history of sand ballistics there have been many attempts to describe quantitatively the response of a granular medium This is typically done by integrating the acceleration equation of the projectile to find the transient displacement as a function of impact velocity which can lead to extraneous data points such as when velocity approaches zero. Also, the analytical models cannot take a ll variables into account that are found in impacts with granular materials such as moisture content, grain size variation, grain shape variation, etc. [ 1, 5 28 and 31 ] N early all models published have empirically derived constants that entail ed experi mental observations on the media. Studie s pe rformed on other materials have determined the pressure needed to accelerate the projectile from its initial velocity to stop in the given time. This method does not take into account the mechanisms involved, i t merely uses the average value for pressure resisting penetration ( P ) equated with the initial kin etic energy (see Equation 5) [32 ]. (5) Another factor that differs from source to source is the effe ct of gravity. For the most simplified studies pitting a steel ball dropped from a specific height v ersu s a bed of

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22 granules under the acceleration of gravity g ravity must be factored in, but with regard to this study, there is a negligible effect of gravity because the projectile travels ho rizontally through the medium [ 6]. Not only does t his eliminate the gravity term in the equation, but also the hydrostatic pressure effects of penetrating deeper into the media. These are present for the case of horizontal penetra tion path, but are relatively constant as depth stays constant. 2.4.1 Drag and Force on Projectile Penetrating Target As stated previously there have been efforts to determine forces on a projectile by estimating the average pressure created upon impa ct [32 ], and other studies that have tried to explain the mechanisms which cause the pressure and forces, but currently there is no cohesive theory that describes penetration into granular media [5, and 33 ] In [ 22 ] (2008) h owever, becau se the physics of such events must account for both fluid and solid like behavior during impact, the understanding remains limited. No comprehensive continuum theory exists for even the relatively low impact velocity of a rock dropped into beach sand fro m an outreached hand 2.4.2 Structure of Granular Systems Another aspect of granular penetration science is in the understanding of how the granulate is arranged. It is impossible to quantify the variation of structure in mathematical terms outside of the statistical realm. The individual grains of the sand are inherently individual in shape, and size which prevents the analytical solution for the structure of the bed. That can be optimized by very specific sorting and regulation of shape of grains, but it takes from the practicality of real world application. If the grains must be meticulously selected so the model will produce good results, then there is still

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23 d isconnect between the mode l and the real system reaction; p roving the analytical approach still only provides estimates, which can also be achieved through Equation 1 provided the constants are chosen appropriately (a method that can very easily give upper and lower bounds for penetration depth). 2.5 Simulation Capabilities Beyond the experimental and analytical method s, is the simulation method As stated previously, currently the number of grains that can be modeled is on the order of 10 6 The number of grains in a cubic foot of sand is on the order of 10 9 This does not allow for the simulation of even a standard round penetrating beach sand. There are studies performed with quasi 2 D simulation and experimentation. These simulations involve a cylind er dropped into a container with either smaller cylinders or spherical grains. In some cases the spherical grains are limited to a depth of eight grains such that the overall number is kept near 10 6 [ 6]. Other simulations are used to determine ballistic characteristics of composite materials [32 ] This type of analysis is beneficial because, once the model accurately predicts effects for a given sample and is compared with test data, the model can be adjusted to test a multitude of combinations without excessive experimentation. 2.5 .1 Particle Algorithms Particle algorithms are used to simulate various materials from solid homogeneous materials such as steel and aluminum to granular matter such as sand. The capabilitie s of this modeling technique are still limited by the number of particles used. In [7 ] a generalized particle a lgorithm (GPA) for high velocity impacts and other dynamics problems is presented. T opics are also discussed such as nodal connectivity

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24 (fixed and variable), which is determin ed by the level of distortion such that computation time is minimized without hindering results. Variable nodal connectivity allows for nodes to share different neighbors throughout the computation, while fixed nodal connectivity can be used through small deformations to facilitate faster computation time. Artificial viscosity is discussed in two forms: nodal viscosity and bond viscosity. It is stated that nodal viscosity is equivalent to that used in finite element and finite difference surface is discussed and modeled using this t echnique as shown in Figure 8 [7 ]. Figure 8 Simulation of a Cyli nder Impacting a Hard Surface [7 ] The nodes are easily seen along with possible fracture sites. This type of model can be used to represent the projectile (as shown) or the granular media. The difference lies in the nodes ability to move freely when the nodal connectivity is negated. Here it becomes imperative to accurately depict the boundary conditions.

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25 2.5 .2 Finite Element Analysis Finite element analysis is not amenable to this study aside from the ability to model the projectile. It would not be reasonable to model every grain as an individual elements for two reasons: 1) the shape of the elements would not represent the shape of the grains without having either spherical elements or multiple elements per grain, and 2) the boundar y conditions between nodes would require extra computations as elements move throughout the simulation which would exponential ly increase computation time [23, and 34 ]. 2.6 Bullet Trap Design There has been much consideration for the design of bullet traps at firing ranges because of the need for tough containment. A bullet trap can capture tens of thousands of rounds in a typical lifespan The basic idea for bulle t trap design is to capture the projectiles without endangering the shooter. Traps come in many forms (as shown in Figures 9 12), and vary in size and capacity. The traps shown vary in capacity from 10,000 (Figure 12) to 100,000 rounds (Figure 10). It is important to note that all traps shown utilize either tires or granulated tire material which is of low cost and is readily available [ 35, 36, 37, and 38 ]

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26 Figure 9 Granular Fill Bullet Trap [37 ] Figure 10 Re Circulating Crumb Rubber Trap [ 37 ]

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27 Figure 11 Stationary Crumb Rubber Trap [ 37 ] Figure 12 Earth Filled Tire Trap [ 37 ] 2.6.1 Lead Contamination Recently there has been much concern over the heavy metals leaching from firing ranges (180 million pounds) was made into bullets and much of this makes it into the

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28 environment at firing ranges. A s a result measures are being taken in new bullet trap design to contain spent rounds for recycling. S and has been recently studied a possible low maintenanc e alternative to higher priced traps (see Figure 13 below) [3, and 39 ] Agents can be added to the sand to capture heavy metals before they leach from the firing range with as great as 90% effectiveness. Figure 13 Passive Reactive Sand Berm [3]

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29 Chapter 3: Experimental Setup The present study was designed to assist the military by determining the optimum grain size of sand or crumb rubber to use in sandbagged fortifications. To this end, military style sandbags were used, and filled and stacked to military specifications. Bullet caliber and manufacture similar to that used by the Tal iban in Afghanistan was used [40 ]. There are many variables in determining ballistic penetration in granular systems from the shape and size of the penetrator to the grain size of the matter. Many characteristics are taken to be relatively constant for the purposes of this study such as th e grain roundness compaction of the bed, and the angle of approach for the projectile. The reason is to clearly define a reasonable scope without sacrificing the realistic nature of the scenario. 3.1 Materials Materials for this study were purchased from local wholesale producers of silica sand and crumb rubber. The need for multiple sizes of the same sand proved difficult, but eventually lead to Florida Silica Sand Company with a location in Plant City, Florid a, who produces four grades of silica sand and many other granular products and stones. The crumb rubber was purchased directly from an industrial recycler of used tires named Global Tire Recycling located in Wildwood, Florida. The granulate ma terials ca n be seen in Figure 14 ( below ) compared to the size of the 7.62x39 round. The sandbags used to hold the granulate materials were purchased from esandbags.com.

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30 Figure 14 Granulate Materials with the 7.62x39 Projectile

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31 3.1.1 Sand The sand, as stated before, is silica sand which has been screened through different sieves of varying sizes. A statistical analysis has been performed on the test sand to determine the mean major dimension of each grade in order to compare the findings w ith the respective mesh sizes given by the producer. The mean major dimension sizes (on a 97% confidence interval) are: 0.355 0.039 0.813 0.045 1.178 0.104 and 2.19 0.21 mm for the 60/80, 30/65, 20/30 and 6/20 meshes respectively. The mesh op enings are given as 0.177, 0.250, 0.210, 0.5 95, 0.841 and 3.36 mm square, for the 80, 60, 65, 30, 20 and 6 meshes respectively [41 ]. As previously stated, granulate s are categorized by their ability to pass through one screen and be retained by another. Samples are shown below in Figure s 15 18 The effective density was measured to be approximately 1421, 1520, 1630, and 1658 [kg/m 3 ] for 60/80, 30/65, 20/30, and 6/20 mesh sands respectively

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32 Figure 15 Test Sample of 60/80 Mesh Sand 5x Magnification Figure 16 Test Sample of 30/65 Mesh Sand 5x Magnification

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33 Figure 17 Test Sample of 20/30 Mesh Sand 5x Magnification Figure 18 Test Sample of 6/20 Mesh Sand

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34 3.1.2 Rubber The rubber is made from recycled tires. The producer gives what appears to be the average size. A statistical analysis has been performed on the test rubber to determine the mean major dimension of each grade in order to compare the findings with the resp ective sizes given by the producer. The mean major dimension sizes from the samples taken (on a 97% confidence interval) are: 0.305 0.070 2.58 0.30 and 14.90 1.38 mm for the 40 and 14/30 meshes, and 3/8 inch sizes respectively. The mesh openings are given as 0.420, 0.595, and 1.19 mm for the 40, 30 and 14 meshes respectively [41 ]. As previously stated, a granulate is categorized by its ability to pass through one screen and get re tained by another except in the case of the 40 mesh rubber that has no lower bound. Sampl es are shown below in Figures 19 21 The effective density was measured to be approximately 398, 478, and 409 [kg/m 3 ] for 40 mesh, 13/40 mesh, and 3/8 inch rubbers r espectively

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35 Figure 19 Test Sample of 40 Mesh Rubber 5x Magnification Figure 20 Test Sample of 16/35 Mesh Rubber

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36 Figure 21 Test Sample of 3/8 Inch Rubber Table 1 (below) shows all of the various media and the measured material properties. Table 1 Material Properties

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37 3.1.3 Projectiles In order to maintain the realistic nature of the experiments the projectiles used are some of the most widely available and common types o f ammunition on the market. The rounds tested are the 123 grain full metal jacket (FMJ) Silver Bear 7.62x39, and the 115 grain FMJ Brown Bear 9mm (see Figure 22 ). The se rounds were used because as stated in [40 ], Taliban forces were found dead after a fi refight with 7.62x3 9 ammunition in their herefore, the ammunition chosen for testing was Russian Also, t used rounds for handguns, and therefore was chosen to show the effects of a much slower projectile. The ammunition was purchased through www.cheaperthandirt.com, an online dealer. Figure 22 Ammunition Used During Testing 3.1.4 Firearms The firearms used during testing are the AR 15 assault rifle, and the P226 9mm by Rock River Arms and Sig Sauer respectively. The AR 15 (which normally fires the .223 caliber) has a conversion kit that chambers the rifle to shoot the 7.62x39 round

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38 normall y found in the AK 47 and SKS assault rifles a long with several others (see Figures 23 and 24 below). Figure 23 AR 15 Assault Rifle Figure 24 P226 9mm

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39 3.1.5 Sandbags and made from polypropylene mesh. The bags are 1600 hour UV rated standard military issue sandbags. The sandbags were found through amazon.com, and purchased from www.esandbags.com, an online dealer (See Figure 25 ). Figure 25 Sandbags U sed in Testing 3.2 Method In order to study the effects of varying grain size, it is important to maintain consistency from test to test. The granular matter used was purchased locally and bagged on site in standard military issue sandbags. The sandbags are used to contain the granular matter in a real world battlefield type situation. There are some parameters that are uncontroll able, such as moisture content, but this was measured.

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40 3.2 .1 Sandbag Barrier The sandbags were stacked and filled in accordance with the US Army Corps of Engineers handbook [42 ]. S andbags were filled with target material and placed in a pyramidal stacking order as shown in Figure s 26 27 and 28 This form of barrier is easily constructed and is tough enough to handle multiple rounds without failure. The pyramid starts with a layer of five bags by five bags, then a layer four bags by four bags, then three by three, two by two, and topped by a single b ag The stack was positioned such that the long side of the b ag fa ced the oncoming projectiles. Figure 26 How Properly to Fill Sandbags [42 ] Figure 27 Proper A ssembly of a Sandbag Barrier [42 ]

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41 Figure 28 Assembly of the Sandbag Barrier As mentioned before there are differences in the reaction of contained sand and loose sand. There is also a difference between interior bags and the top row which is unconstrained on the top and sides; for this reason, the target bag is an interior bag, not on the top and no t on the bottom. The target bag was positioned in the center of the stack, or, the third layer, center bag of the three exposed that face the oncoming projectiles. For the purposes of maintaining consistency, the target bag is replaced after each shot. This required un stacking the top bag, the two by two layer and removing the target bag (or bags) from the third layer. 3.2 .2 Positioning For the positioning of the barrier with respect to the firing platform there must be enough room between the two to f acilitate use of the chronograph or velocity measurement apparatus. For the use of the rifle and the 7.62x39 round, the shooting platform was positioned about 40 ft up range from the sandbagged redoubt with the chronograph placed about 10 ft in front of t he barrier as shown in Figure 29

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42 Figure 29 Setup for 7.62x39 Testing For the use of the pistol, the shooting platform was positioned about 9 ft from the barrier with the chronograph in the center as shown in Figure 30 The target layer of sandbags was aligned with the line of shot, such that th e tops and bottoms of the bags we re not penetrated by the most deeply penetrating rounds

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43 Figure 30 Setup for 9mm Testing 3.2 .3 Measurements Well taken measurements are the most important aspect of any testing. Therefore, t he measurements were taken with extreme care and consistency There were several measurements taken: average grain size, weight of full sandbag, moisture content of the granular media, projectile weight, projectile velocity, and penetration depth. 3.2 .3.1 Grain Size G rain size w as measured by the Leitz Optical Microscope and software at the Nanotechnology Education and Research Center at the Universit y of South Florida Tampa Campus, and by a Mitutoyo micrometer for the larger grain sizes. The average size of grains is found through a statistical analysis of the largest length measured from

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44 up to 100 different grains (see Appendix B ) The sample was taken from each of four sizes of sand and from the three sizes of crumb rubber. 3.2 .3.2 Full Sandbag Weight The weight of each filled sandbag was measured by scale and filled to the same weight of 40 and 13.5 pounds for the sand and rubber respectively As shown in Figure 26 above, 40 lb is the recommended weight to fill sandbags with sand [42 ] The density wa s measured to be approximately 1421, 1520, 1630, and 1658 [kg/m 3 ] for 60/80 mesh 30/65 mesh 20/30 mesh and 6/20 mesh sand respectively and approximately 409, 478, 398 [kg/m 3 ] for 40 mesh, 14/30 mesh, and 3/8 inch crumb rubber respectively Although the density varies slightly, the sandbags were filled to the same weight, not volume For the rubber, a bag was initially filled until the volume approximately matched that of the sand, and then measured to be 13.5 pounds. 3.2 .3.3 Moisture Cont ent Moisture c ontent was measured by a standard analog soil moisture meter (see Figure 31 below) The meter has a scale from zero to ten. When the dry sand is measured there is no change in the needle position from its position when exposed to air, but w hen the meter is place in water it reads a value of ten. The measurements are relatively constant throughout testing There is a bias in the meter that was tested by heating the sand to eliminate trace water in the sample while measuring the mass before and after with an Ohaus triple beam balance. The mass decreased less than 0.1% during this process. The moisture meter maintained a non zero value (as shown in Appendix F ). From this, it can be concluded that the moisture level during testing was approximately zero. B e cause th e granulate materials were stored in a barn, they were subjected to slight

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45 fluctuations of air moisture with the changing F lorida humidity. Howeve r, the media was kept away from rain and morning dew which allowed it to remain as dry as possible without dehumidification or air conditioning. Records of temperature and relative humidity were taken as well (as shown in Appendix A) Figure 31 Analog Soil Moisture Meter 3.2 .3.4 Projectile Mass Projectile mass i s given by the manufacturer in units of grains and confirmed by measurement with Mettler AE 260 Data Range digital scale Since some projectiles experience wear and deformation upon impact, and also because the projectiles cannot be removed from the cartridges and then reassembled without the proper equipment, the average mass of the ten projectiles fired into 40 mesh rubbe r was taken to be the average mass of the projectiles for all shots. The average mass measured was 7.999 0.022 and 7.463 0.023 grams (123.45 and 115.17 grains) for the 7.62x39 and 9mm respectively (see Appendix C for measurements) The manufacturers give the masses as 123 and 115 grains (7.97 and 7.45 grams) for the 7.62x39 and 9mm respectively.

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46 3.2 .3.5 Projectile Velocity Projectile velocity is recorded by a ProChrono Digital C hronograph by Competition Electronics (see Figure 32 sh own below) This chronograph is ca pab le of measuring velocities in the r ange of 25 to 7,000 [ft/s] (7.6 to 2134 [m/s]) with an accuracy of 1%. It stores up to 891 velocity measurements in a non volatile memory and can determine average velocity, standard deviation high velocity, low velocity and extreme spread for a series of rounds The chronograph used in these experiments utilizes light sensors that detect the passing bullet from one sensor to the next. The main limitation of this apparatus is the l ighting conditions necessary to detect projectiles (no early morning or evening tests were successful ). The chronograph was protected by two full sandbags placed in front of it. Figure 32 Competition Electronics ProChrono Digita l Chronograph

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47 3.2 .3.6 Penetration Depth Penetration depth was carefully measured by tape measure from the entry point on the sandbag to the farthest point on the projectile from the entry point at its final resting position This means that the actual penetration is measured, not the relative penetration with respe of sight This does not take into a ccount any curved paths however, o nly straight line penetration f r o m entry to r esting point. The position of each round was first approximately located using a n inductance type metal detector then by probing the gran ular matter with a fine wire to better determine the position. Finally the layers of granulate we re carefully removed by brushing and scooping it away until the projec tile wa s exposed such that the measurement could be made. Orientation and condition of the bullet was noted along with the number of bags penetrated in the shot (see Appendix A) 3.2.4 Conducting the Tests In order to acquire a sample of data that is larg e enough to base conclusions upon yet small enough to perform with in a reasonable time frame the number of tests chosen to perform is ten. With the number of tests at ten per type of round and media, having two different rounds, four different sandy media, and the weight of each sandbag at 40 pounds, the amount of sand required to be moved in and out of th e stack was over 3200 pounds. This entailed moving three times that amount in order to un stack and re stack the barrier. Each test of sandy media required moving three bags such that the top of the target bag was exposed, finding the bullet, laying another target bag in place without causing unevenness of the target bag, and re stacking the barrier. The time taken t o find a particular round varied with its positioning inside the bag.

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48 Each firearm was carefully handled and kept in a safe position with the safety on between all tests. The rifle was loaded with one bullet at a time without the use of a magazine. The pistol was loaded with a magazine and was directed away from the target area during the search for each bu llet. The de cocker was also utiliz ed between each shot to ensure the gun could not be unintentionally discharged.

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49 Chapter 4: Results After successfully firing and r ecovering ten shots from each firearm into each media the velocity, penetration depth, moisture levels and any necessary notes were recorded. The following chapter shows the product of the tests. The sand and rubber were tested against both the 7.62x39 and 9mm rounds. The penetration of each material/round combination is shown below along with comparison of the individual round and all four sands used in this experiment. 4.1 The 7.62x39 Round The 7.62x39 round was tested for penetration in the four sizes of sand and the three sizes of rubber. 4.1.1 The 7.62x39 Round into Sand The penetration of the 7.62x39 round in the various sandy media, as measur ed, is shown below in Figures 33 36 The compilation of all 7.62x39 tests into sand is shown in Figur e 3 7 Performing a one way Analysis of Variance (ANOVA) test on the 7.62x39 penetration into sand data gives a probability of 98.9% that penetration does depend on grain size (see Appendix D for more statistical data).

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50 Figure 33 Penetration of 60/80 Mesh Sand with Ten 7.62x39 Round s 0 5 10 15 20 25 30 35 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 60/80 mesh

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51 Figure 34 Penetration of 30/65 Mesh Sand with Ten 7.62x39 Round s 0 5 10 15 20 25 30 35 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 30/65 mesh

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52 Figure 35 Penetration of 20/30 Mesh Sand with Ten 7.62x39 Round s 0 5 10 15 20 25 30 35 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 20/30 mesh

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53 Figure 36 Penetration of 6/20 Mesh Sand with Ten 7.62x39 Round s 0 5 10 15 20 25 30 35 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 6/20 mesh

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54 Figure 37 Penetration of Each Grade of Sand with Ten 7.62x39 Round s There is clearly a fair amount of experimental scatter. In order to better depict any possible trends in the data, the following, Figure 38 shows average penetration of the 7.62x39 round plotted against the average grain size of each material. 0 5 10 15 20 25 30 35 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 60/80 mesh 30/65 mesh 20/30 mesh 6/20 mesh

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55 Figure 38 Average Penetration of the 7.62x39 Round vs. Average Grain Size This shows a very slight trend down from left to right illustrating decreasing penetration depth with increasing grain size but this apparent trend might not be statistically significant due to the low R 2 value The error bars rep resent the 97% 0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 2.5 Penetration Depth [cm] Grain Size [mm] 60/80 mesh 30/65 mesh 20/30 mesh 6/20 mesh Trendline R 2 =0.4575

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56 confidence interval on which the mean penetration is expected to exist. The collected rounds are shown below in Figure 39 The rounds are ordered by the media used to stop them vertically with increasing grain size from top row to bottom r ow Figure 39 Post Impact 7.62x39 Bullets, Top to Bottom is Finest to Coarsest

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57 4.1.2 The 7.62x39 Round into Rubber The penetration of the 7.62x39 round in the various rubbery media, as measu red, is shown below in Figures 40 42 The compilation of all 7.62x39 tests i nto rubber is shown in Figure 43 Performing a one way ANOVA test on the 7.62x39 penetration into rubber data gives a probability of 99.99% that penetration does depend on grain size.

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58 Figure 40 Penetration of 40 Mesh Rubber with Ten 7.62x39 Round s 0 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 40 mesh

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59 Figure 41 Penetration of 14/30 Mesh Rubber with Ten 7.62x39 Round s 0 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 14/30 mesh

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60 Figure 42 Penetration of 3/8 Inch Rubber with Ten 7.6 2x39 Round s 0 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 3/8 inch

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61 Figure 43 Penetration of Each Grade of Rubber with Ten 7.62x39 Round s There is a noticeable fact that shows through the 14/30 data. The penetration is either near 60 or 70 cm, but not really within the 60 70 cm rang e. This will be addressed in Chapter 5. 0 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 40 mesh 14/30 mesh 3/8 inch

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62 Figure 4 4 shows average penetration of the 7.62x39 round plotted against the average grain size of each rubbery material. Figure 44 Average Penetration of 7.62x39 Round vs. Average Grain Size of Rubber 0 10 20 30 40 50 60 70 80 90 100 0 5 10 15 Penetration Depth [cm] Grain Size [mm] 40 mesh 14/30 mesh 3/8 inch Trendline R 2 =0.6677

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63 The error bars represent the 97% confidence interval on which the mean penetration is expected to exist. Here, the R 2 value of the trend line to the data is still too low to make assertions about the penetration being linearly or otherwise dependent on grain size. The collected rounds are shown below in Figure 4 5 The rounds are ordered by the media used to stop them vertically with increasing grain size from top row to bottom row. Figure 45 Post Impact 7.62x39 Bullets, Top to Bottom is Finest to Coarsest 4.2 The 9mm Round The 9mm round was tested for penetration in the four sizes of sand and the three sizes of rubber.

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64 4.2.1 The 9mm Round into Sand The penetration of the 9mm round in the various sandy media, as measured, is shown below in Figures 46 4 9 The compilation of all 9mm test s into sand is shown in Figure 50 Performing a one way ANOVA test on the 9mm penetration into sand data gives a probability of nearly 100% that penetration does depend on grain size.

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65 Figure 46 Penetration of 60/80 Mesh Sand with Ten 9mm Round s 0 5 10 15 20 25 30 35 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 60/80 mesh

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66 Figure 47 Penetration of 30/65 Mesh Sand with Ten 9mm Round s 0 5 10 15 20 25 30 35 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 30/65 mesh

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67 Figure 48 Penetration of 23/30 Mesh Sand with Ten 9mm Round s 0 5 10 15 20 25 30 35 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 20/30 mesh

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68 Figure 49 Penetration of 6/20 Mesh Sand with Ten 9mm Round s 0 5 10 15 20 25 30 35 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 6/20 mesh

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69 Figure 50 Penetration of Each Grade of Sand with Ten 9mm Round s There is, again, clearly a fair amount of experimental scatter. In order to better depict any possible trends in the data, the following Figure 51 shows average penetration of the 9mm round plotted against the average grain size of each material. 0 5 10 15 20 25 30 35 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 60/80 mesh 30/65 mesh 20/30 mesh 6/20 mesh

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70 Figure 51 Average Penetration of the 9mm Round vs. Average Grain Size Here, the trend is very clear: the larger th e grain size the less penetr ation (down from left to right), and with the R 2 value close to 1, there is a good fit of the data to the linear trend line. The error bars represent the 97% confidence interval on which the 0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 2.5 Penetration Depth [cm] Grain Size [mm] 60/80 mesh 30/65 mesh 20/30 mesh 6/20 mesh Trendline R 2 =0.9911

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71 mean penetration is expected to exis t. The collected rou nds are shown below in Figure 52 The rounds are ordered by the media used to stop them vertically with increasing grain size from top row to bottom row. Figure 52 Post Impact 9mm Bullets, Top to Bottom is Finest to Coarsest It can be noticed that some bullets appear untouched on the sides while others show significant wear. Thi s is because every bullet has both, a relatively untouched side and a side with wear. Th is will be discussed more in Chapter 5. 4.2.2 The 9mm Round into Rubber The penetration of the 9mm round in the various rubbery media, as measur ed, is shown below in Figures 53 55 The compilation of all 7.62x39 tests i nto rubber is shown

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72 in Figure 56 P erforming a one way ANOVA test on the 9mm penetration into sand data gives a probability of 99 .9 9 % that penetration does depend on grain size Figure 53 Penetration of 40 Mesh Rubber with Ten 9mm Round s 0 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 40 mesh

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73 Figure 54 Penetration of 14/30 Mesh Rubber with Ten 9mm Round s 0 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 14/30 mesh

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74 Figure 55 Penetration of 3/8 Inch Rubber with Ten 9mm Round s 0 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 3/8 inch

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75 Figure 56 Penetration of Each Grade of Rubber with Ten 9mm R ound s Figure 57 below, shows average penetration of the 9mm round plotted against the average grain size of each material 0 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 9 10 Penetration Depth [cm] 40 mesh 14/30 mesh 3/8 inch

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76 Figure 57 Average Penetration of 9mm Round vs. Average Grain Size of Rubber Here, the trend is very clear: the larger the grain size the less penetr ation (down from left to right), and with the R 2 value close to 1, there is a good fit of the data to the 0 10 20 30 40 50 60 70 80 90 100 0 2 4 6 8 10 12 14 16 Penetration Depth [cm] Grain Size [mm] 40 mesh 14/30 mesh 3/8 inch Trendline R 2 =0.9849

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77 linear trend line. The error bars represent the 97% confidence interval on which the mean penetration is expected to exist. The collected roun ds are shown below in Figure 58 The rounds are ordered by the media used to stop them vertically with increasing grain size from top row to bottom row. Figure 58 Post Impact 9mm Bullets, Top to Bottom is Finest to Coarsest 4.3 Comparison of Both Rounds The effects of varying velocity and size/shape of the round can be noticed best, when both rounds are plott ed together. The following give s comparison with respe ct to grain size, velocities and the penetration achieved, both by average and by the individual shots. 4.3.1 Sand It is clear that the 9mm rounds did not suffer the deformation and fragmentation that was apparent in the 7.62x39 rounds. This limits the conclusions that can be reached about the relationship of velocity, but the facts are still conclusive as will be discussed in

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78 Chapters 5 and 6. Below in F igure 59 the average penetration of both rounds is plotted against the average gr ain sizes of the target material. Figure 59 Average Penetration of Both Rounds vs. Average Grain Size 0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 2.5 Penetration Depth [cm] Grain Size [mm] 60/80 7.62x39 30/65 7.62x39 20/30 7.62x39 6/20 7.62x39 68/80 9mm 30/65 9mm 20/30 9mm 6/20 9mm

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79 There is overlap of the two rounds in the case of the 30/65 mesh sand but it can be noticed that on average, the 9mm round pe netrated further or just as far as the (much f aster) 7.62x39 round. Figure 60 (shown below) shows the relationship between velocity and penetration depth of the two rounds. Figure 60 Penetration of Sand vs. Velocity 0 5 10 15 20 25 30 0 200 400 600 800 Penetration Depth [cm] Velocity [m/s] 60/80 mesh 7.62x39 30/65 mesh 7.62x39 20/30 mesh 7.62x39 6/20 mesh 7.62x39 60/80 mesh 9mm 30/65 mesh 9mm 20/30 mesh 9mm 6/20 mesh 9mm

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80 The graph s hows a noticeable difference between the scatter of the 9mm rounds (on the left) and the 7.62x39 rounds (on the right), and it is, again, clear that on average, the penetration of the 9mm rounds is greater than that of the much faster 7.62x39 rounds. Th ere are reasons for this apparent trend that may not allow for conclusions to be reached with regard to velocity dependent penetration. The collected rounds are shown again in Figures 61 and 62 Figure 61 Post Impact 7.62x39 Bullets, Top to Bottom is Finest to Coarsest

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81 Figure 62 Post Impact 9mm Bullets, Top to Bottom is Finest to Coarsest There is no apparent fragmentation or deformation in the case of the 9mm as is present in t he 7.62x39 rounds that were collected T Tests were performed between all grain sizes of sand for both the 7.62x39 and 9mm rounds in order to determine if there is a significant difference of penetration between grain sizes (See Appendix E). It is shown that, in many instances, grains of different sizes allow significantly different penetration depths.

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82 4.3.2 Rubber The rubber shows trends that are not present in the case of the sand. There is greater average penetration into the rubber with the 7.62x39 round which does not hold true wi th the sand. Below in Figure 63 the average penetration of both rounds is plotted against the average grain sizes of the target material. T Tests were performed between all grain sizes of rubber for both the 7.62x39 and 9mm rounds in order to determine if there is a significant difference of penetration between grain sizes. It is shown that, in many instances, grains of different sizes allow significantly different penetration depths.

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83 Figure 63 Average Penetration of Both Rounds vs. Average Grain Size of Rubber 0 10 20 30 40 50 60 70 80 90 100 0 5 10 15 20 Penetration Depth [cm] Grain Size [mm] 40 mesh 7.62x39 14/30 mesh 7.62x39 3/8 inch 7.62x39 40 mesh 9mm 14/30 mesh 9mm 3/8 inch 9mm

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84 In this case it is easy to see that the faster 7.62x39 round penetrated significantly deeper into the media than its 9mm counterpart. This could be due to the l ack of deformation in both rounds or a totally different phenomenon related to the shear pressure as a function of velocity. This will be discussed further in Chapters 5 and 6. There appears to be a greater dependence on the velocity for penetration into rubbe r as can be noticed in Figure 64 (shown below). Here, the projectile penetration is plotted versus projectile velocity.

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85 Figure 64 Penetration of Rubber vs. Velocity There is clearly greater penetration in all rubbery medi a with the 7.62x39 round than there is with the 9mm round. This could be due to the shape/size of the two rounds, or the effect of velocity. It can be noticed that the 7.62x39 round travels at nearly twice the velocity of the 9mm round, but does not nece ssarily achieve twice the penetration. 10 20 30 40 50 60 70 80 0 200 400 600 800 Penetration Depth [cm] Velocity [m/s] 40 mesh 7.62x39 14/30 mesh 7.62x39 3/8 inch 7.62x39 40 mesh 9mm 14/30 mesh 9mm 3/8 inch 9mm

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86 Chapter 5: Discussion There are several noticeable trends invol ving the penetration of the 9mm round, however the 7.62x39 round does not follow the same trends. In sand and rubber, the 9mm consistently shows reduction in penetration with increasing grain size, but the same is not necessarily true with the 7.62x39 round. One facet of the data that is consistent between the two rounds and media (sand and rubber) is that the largest of the gra in sizes experiences the lowest average penetration. Another noticeable trend is the tendency of the 9mm round to penetrate deeper in sand on average (regardless of grain size) than the 7.62x39 round. This is independent of deformation in the finest sand (60/80 mesh) because in several shots, the 7.62x39 round had negligible deformation, and still penetrated less 5.1 Effects of Varying Sand Grain Size Understanding the overall effects of varying grain size is a complicated problem. In order to tackle this problem, the two rounds should be looked at independently. 5.1.1 The 7.62x39 Round The effects of varying grain size of sand on the 7.62x39 round is of great importance because this particular round is used both with and against US military forces. The overall effect that is first noticed, when looking at the projectiles after impact, is that the round fragments more when fired at coarser sand. When the data is examined it becomes apparent that the round also manages to penetrate less in the coarser sand. This

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87 phenomenon could be understood through the effects of taking this to the extremes on both ends of the spectrum. For instance, if the grains are enlarged to the point that the projectile is, in effect, impacting a solid rock surface, the penet ration wil l be considerably less if there i s penetration at all. On the other hand, if the grain size is decreased to the point that the granular matter is basically single molecules, there will be no crushing of grains (totally eliminating one mechanism that aids in stopping the projectile), and also creating a less uniform packing order (hence reducing effective density), which acts to reduce the pressure that stops the bullet, and therefore causes an increase in the penetration depth. With that said, t he opposite ends of the spectrum clearly point to a decrease in penetration with an increase in grain size. The problem found in the data is that for the samples tested, an intermediate grain size showed the highest penetration, not the finest but rather the second finest. 5.1.1 The 9mm Round The results are more conclusive with the 9mm round than with the 7.62x39 round which could be due to many reasons. There is said to exist for a given granular material, a critical velocity, above and below this velocity, projectiles will experience less p enetration. Since the 9mm is far slower than its counterpart, this could be a sign that the critical velocity lies somewhere between, or even at a slower velocity than the 9mm travels One thing that is noticeable that relates directly to this study is t he effect that varying the grain size has on the penetration of the 9mm round. For every increase in grain size there is a direct decrease in the average penetration into the respective media (see Figure 65 below ).

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88 Figure 65 Average Penetration of 9mm Round vs. Average Grain Size This graph shows (for the grain sizes, and over the range of sizes, tested) a nearly linear relationship between the grain size and average penetration depth. 0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 2.5 Penetration Depth [cm] Grain Size [mm] 60/80 mesh 30/65 mesh 20/30 mesh 6/20 mesh Trendline R 2 =0.9911

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89 5.2 Effects of Varying Rubber Grain Size Varying grain size in rubber has similar effects to those found in sand. The reaction of the 7.62x39 was to penetrate deeper into an intermediate grain size. The largest grain sizes had the smallest penetrations of all tested. However, unlike sand, the rubber was penetrated deeper by the 7.62x39 round than the slower 9mm round In the 3/8 inch rubber the bullets tended to get deflected and travel up or down into adjacent bags. This proved difficult to test the penetration, as many tes ts were not measurable. 5.2.1 The 7.62x39 Round One interesting note on the reaction of the 7.62x39 round was its ability to, on occasion, break into the third bag. As previously stated, the 14/30 mesh rubber and 7.62x39 combination produced consistent re sults with penetration either at around 60 cm or around 70 cm, but not really in between (as depicted in Figure 66 below) This was noticed during testing as well. Many shots into the 40 and 14/30 mesh rubbers ended with the bullet resting at the very end of the second sandbag which is around 60 cm. W ith the 14/30 mesh on occasion the bullet would penetrate the third bag, except, instead of stopping just past 60 cm, the bullet would penetrate much deeper. This gives a clue to the effects of using the woven polypropylene sandbag as a method for containing crumb rubber.

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90 Figure 66 Effect of Double Sandba g Interface on Penetration 5.2.2 The 9mm Round The 9mm round proved to give the most consistent results in terms of average penetration. There is a clear trend across the range of granulated rubber tested that points to larger chunks as being the most efficient at stopping the 9mm bullets. 5.3 Impact Cratering, Granular Jets, and Buckling/Phase Transition Effects No granular jets were filmed during this experimentation, and due to the design of the redoubt, the oncoming bullets left no clear craters, however impact did cause an impression in the side of each sandbag which proved to have more prominence in the coars er sand, namely the 6/20 mesh. In some cases, the bag suffered what was deemed

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91 Figure 67 is a picture of a bag that showed this effect. Figure 67 Trauma to Bags The presence of the trauma was not present in the bags that contained the finer sands, the rubber materials and was not present with the use of the 9mm round. As for Buckling and phase transition, the effects on the projectiles is shown in the drastically fra gmented 7.62x39 ro unds in the preceding Figures 39 and 61 The 9mm round did not suffer extreme deformation, but did show signs of wear on one side. 5.4 Tumbling It was recorded that the position of the round at its final resting point in the bag was ofte n sideways or backwards. In the case of the 9mm and in some of the least damaged 7.62x39 rounds, it was noticed that one side had greater wear. This could be due to the worn side being on the leading edge after initial penetration during the period from straight entry to sideways or backwards resting position. The position of the bullet

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92 as it passed through multiple bags in the case of the rubber, can be noted upon as being sideways in many cases. The bullets would often leave a large hole as they trav eled from one bag to another. It seems this is due to the orientation of the projectiles as they passed through the bags. 5.5 Influence of Size/Shape The effects of varying size and shape were not noticeable because the projectiles that differed in shape also differed in velocity In the case of the sand it seemed that the velocity played a far greater role than the shape and size because the 7.62x39 projectiles are 7.62 mm in diameter and the 9mm projectiles are 9 mm in diameter, also the 7.62x39 project iles are more conically shaped than the round ended 9mm rounds. Together, the size and shape of the 7.62x39 seem better for penetration, yet the penetration was noticeably less in most cases. Again, it is hard to base conclusions upon this because of the variance in velocity, but it can be said that the change in shape did not have as much effect as the change in velocity. It appears that increasing velocity causes the sand to shear thickening is referred to, for fluids, as being dilatant. 5.6 Crushing of Sand Grains There was a noticeable amount of white powder present in the bags near the path of the bullet after each shot (shown in Figure 68 below). This was more prevalent in the larger sizes of sand, and since the 7.62x39 rounds were tested first and suffered greater wear and fragmentation in the larger sizes of sand, it was originally thought that this white powder could be lead dust. Aft er tests began with the 9mm, it was noticed that the white powder was still present. With the condition of the 9mm rounds being whole and

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93 still fully jacketed, the assumption of lead powder being a possible answer was proved not probable. Instead, it is thought to be a sign of the crushing of grains that occurs in sand impacts. Figure 68 White Powder Found in Target Bags Post Impact This white powder lead from the entry point to the bullet, and actually served as an indicator t o the path the projectiles traveled through the media.

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94 Chapter 6: Conclusions The most conclusive effects of varying grain size are found with the use of the 9mm caliber. There are other mechanisms such as fragmentation and deformation that directly impact penetration performance in the case of the 7.62x39 into sand and these effects change with gr ain size, but for this reason the 7.62x39 proved to have unintended results and therefore unintended conclusions. 6.1 The 7.62x39 Round The 7 .62x39 round travels at approximately 700 m/s when fired through the AR 15, and has the potential fo r causing great damage to anything downrange For that reason it is important to find out how to best stop it, and what characteristics should be consider ed when constructing a redoubt to do so 6.1 .1 Sand It is important to consider all aspects when using sand to stop projectiles. One point of entry for the project ile. It was found that with larger grains of sand, the hourglass effect was attenuated by the larger grains. As the grains size became closer to the size of the hole the projectile entered the bag through, they did not move as freely through the hole, and therefore more sand sta yed in the pile overall However, in some tests with the larger grains the trauma to the bag caused larger openings for the sand to escape.

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95 A fairly noticeable conclusion is that the finer sand tends to leave the bullet less deformed and in one piece and therefore if the goal is to mitigate heavy metals from leaching into groundwater at outdoor shooting ranges that utilize sand as a bullet trap, fine grained sand should be used rather than coarse sand. In using sand as a barrier for stopping bullets it can be sta ted that very coarse sand (>2 mm grains) prevents penetration better than fine sand in the case of a single shot. However, m ultiple shots could have a wearing effect on the sand m aking it inherently smaller with every shot. 6. 1.2 Rubber In shooting the 7.62x39 round into sandbags filled with rubber, the thickness and ord er of the sandbags can affect the overall penetration, because, as stated in Chapter 5, the bag can be a tough ba rrier to break through, even when the projectile has the potential for penetrating much further. If the sandbag was not used to contain the rubber, greater penetration would have occurred, and therefore, the boundary conditions are of great importance whe n modeling impact of solid projectiles on crumb rubber targets especially in terms of the flexibility and toughness of the container. 6.2 The 9mm Round The 9mm round used in experimentation traveled at a velocity of approximately 360 m/s, and proved to hav e different reactions to both targets than the 7.62x39 round. The data on the 9mm shots contains trends that are hard to ignore, and are actually desirable when making generalizations about the effects of varying the grain size of the media on penetration depth. With every increase of grain size, a decrease in penetration is observed. The 9mm round stayed in tact in all experiments. Tumbling of the round was observed in all media.

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96 6.2.1 Sand Under impact with the sand, the 9mm round showed slight wearing of one side, and with every increase of grain size, the round, showed slightly larger indentations on the tip. Decreasing penetration depth was shown to correlate with increasing the grain si ze of the sand. This was not the case with the 7.62x39 round, but also differed in the lack of deformation. 6.2.2 Rubber The 9mm round showed similar results in rubber as were observed in sand. The penetration decrease d wi th every increase in grain size; however, the number of different rubber grain sizes tested is lower than that used in the sand experiments. 6.3 Overall Conclusions Projectile penetration into granular med ia is significantly dependent on the grain size of the media The 9mm penetration data shows a strong linear relationship between grain size and penetration depth (decreasing penetration with increasing grain size) in both materials Sand is better than rubber for stopping bullets in the shortest distance Pistol and rifle penetration in sand are nearly equal The 7.62x39 projectile travels at a velocity approximately 93% greater than that of the 9 mm 7.62x39 projectile penetration in rubber is approximately 33% greater than that of the 9mm Fine sand causes less deformation and fragment ation of the projectiles than coarse

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97 Fine sand is better for preventing unwanted heavy metal leachate into groundwater at outdoor firing ranges that utilize sand as a bullet trap Coarse sand allows the least amount of penetration for either round Coarse ru bber allows the least amount of penetration for either round Rubber causes little to no deformation or wear on the projectiles making it better suited for firing ranges that recycle spent ammunition Pound for pound, sand is better for stopping 7.62x39 roun d s (coarse sand being the absolute best) Pound for pound, rubber is better for stopping 9mm round s (coarse rubber being the absolute best) The bag suffers more trauma when coarse sand is used rather than fine sand The best media to use in a given situatio n depends on the characteristics that are most important to the user. If the least possible penetration is of greatest importance, coarse sand is the best choice. If keeping the rounds intact, therefore preventing environmental contamination is of import ance, fine sand or rubber is best. Whenever possible, firing range operators should implement recycled tire material in their bullet traps for this reason. For military applications, it is necessary to utilize a fire retardant with crumb rubber to preven t the barrier from igniting and releasing noxious gases. Rubber can be used in military applications under certain circumstances, but it is necessary to compensate for the increase in penetration when compared with sand. One fact noted previously is that wet sand is less effective at preventi ng penetration than dry sand [12 19, and 20 ]. It is reasonable to question whether this

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98 would be the case for rubber as well, or that rubber might show a reverse trend and get better with increasing moisture levels. Also, it is possible that rubber might shed water better than sand and preserve itself as a lighter, more easily movable barrier. In conclusion, it appears that the initial hypothesis of decreasing penetration depth with increasing grain size is fairly accurate when considering a la rge difference of grain sizes

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99 Chapter 7: Future Work In order to better understand the phenomenon recorded in the present study, the effects of several variables need to be studied further. It is understood that moisture content directly reduces, in certain cases, the penetration of a projectile into sandy media. However, the questions remain of what the significance of moisture content is with varying grain size and how varying projectile velocity effects penetration as well. 7.1 Varying Moisture Content Does moisture have less of an effect on coarse san d than it does on fine sand? If so, how much of an effect does it have? This can be answered through a series of similar tests in which water is introduced in varying amounts, or added liberally to the point of total saturation. The problem lies in appr opriately defining what moisture levels can and should be tested, because as this work deals with relatively only one moisture content (dry), an experiment of varying moisture content would clearly eclipse this work in scope. Many tests need to be perform ed on all various sizes for each level of moisture, and therefore the number of tests is multiplied by each degree of moisture tested. It might be appropriate to test fully saturated sand and at least one intermediate moisture level, as might exist on the battlefield. This might entail just leaving a sprinkler on the sand overnight to simulate a rainstorm and letting it dry for a day or two. In this case, the sand will have time to allow excess water to escape, while still maintaining a significant moist ure level.

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100 7.2 Varying Projectile Velocity It is clear, in the present study, that projectile velocity plays a significant role in penetration depth into sandy media. It becomes easy to speculate, that a slower 7.62 mm projectile might achieve more penetr ation than the ones tested Further testing of the same projectile at different velocities might give insight of the critical velocity at which the projectile achieves the greatest penetration. It is necessary to have ample data of penetration at many di fferent velocities such that conclusions can be reached with respect to velocity dependent penetration in the various media. It is, again, clear that the breadth of testing necessary to fully classify any given impact of a projectile and granular material is very large. The number of tests needed to determine the effects of all variables involved becomes exponentially greater than those of the present work. However, if there is enough data at discrete levels of velocity and moisture, then trends can be fo rmed and functions can be attained involving velocity, moisture and grain size. This would be a great improvement over the simplified penetration equations that are merely quadratic functions of velocity with coefficients dependent on grain size and moist ure content that must be determined for every different combination. 7.3 Computer Based Modeling and Simulation There are possibilities of modeling the granulate materials as solid viscoelastic continuum instead of modeling the individual grains, but in or der to do so, more study is necessary in determining the plastoelastic properties of various grain sizes at various moisture levels especially at high strain rates.

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101 References 1. J. Zukas / Impact Dynamics: Theory and Experiment / US Army Armament Research and Development Command Ballistic Research Laboratory Technical Report (1980) ARBRL TR 02271 2. G. Stone / Projectile Penetration into Representative Targets / Sandia National Laboratories Sandia Report (1994) SAND94 1490 3. B. Jones / Reducing Lead Contamination and Exposure on Military Firing Ranges Through the Practical Application of Ballistic Containment Systems Fourth Edition / Marine Corps Logistics Base Multi Commodity Maintenance Cen ter Engineering Department (1999) 20001020 093 4. W. Stronge / Rigid Body Collisions With Friction / Proceedings: Mathematical and Physical Systems 431 (1990) 169 181 5. T. Jiang et al. / Time Dependent Penetration Model for High Velocity Impact & Penetration: Phase Transition Studies / AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 46 (2005) 2356 6. D. Lohse et al. / Impact on Soft Sand: Void Collapse and Jet Formation / Physical Review Letters 93 (2004) 198003 7. G. Johnson et al. / A Generalized Particle Algorithm for High Velocity Impact Computations / Computational Mechanics 25 (2000) 245 256 8. Jensona, Collection Studio / World Atlas of Sands / Sand Collection Forums (2010) http://www.sand atlas.com/en/shape of sand grains/ 9. D. Mahan / An Elementary Course of Military Engineering Part I. Comprising Field Fortification, Military Mining and Siege Operations (1870) 10. N. Drummond et al. / Biting the Bullet / Military Surplus Collectors Forums (2009) 1 22 11. H. Beyer / Observations on the Effects Produced by the 6 mm Rifle and Projectile An Experimental Study / Journal of Boston Society of Medical Sciences (1898) 117 136

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102 12. W. Allen et al. / Dynamics of a Projectile Penet rating Sand / Journal of Applied Physics 28 (1957) 370 376 13. M. Uddin et al. / Improving Ballistic Performance of Polyurethane Foam by Nanoparticle Reinforcement /Journal of Nanotechnology (2009) 794740 14. L. Kyziol / Shooting Resistance of Non Metallic Materials / Polish Maritime Research 14 (2007) 68 72 15. M. Hou et al. / Dynamics of a Projectile Penetrating in Granular Systems / Physical Review E (2005) 062301 16. P. Richmond / Influence of Nose Shape and L/D Ratio on Projectile Penetration in Frozen Soil / US Army Corps of Engineers Cold Regions Research and Engineering Laboratory Special Report (1980) 80 17 17. P. Westine / Prediction of Transient Displacement, Velocity, and Force on Projectiles Penetrating Cohesive Soil s / Journal of Terramechanics 12 (1975) 149 170 18. V. Bazhenov et al. / Method for Identifying Elastoplastic Properties of Ground Media by Penetration of Impactors / Mechanics of Solids 43 (2008) 678 674 19. A. Kharab et al. / Penetration of Cylindrical Project iles into Saturated Sandy Media / Experimental Mechanics 49 (2009) 605 612 20. A. Savvateev et al. / High Speed Penetration into Sand / International journal of Impact Engineering 26 (2001) 675 681 21. M. Hou et al. / Projectile Impact and Penetration in Loose G ranular Bed / Science and Technology of Advanced Materials 6 (2005) 855 859 22. D. Goldman et al. / Scaling and Dynamics of Sphere and Disk Impact into Granular Media / Physical Review 77 (2008) 021308 23. A. Rosato et al. / Microstructure Evolution in Compacted Granular Beds / Powder Technology 109 (2000) 255 261 24. D. Longcope, Jr. / Oblique Penetration Modeling and Correlation with Field Tests into a Soil Target / Sandia National Laboratories Sandia Report (1996) SAND96 2239 25. W. Goldsmith / Review, Non Ideal Pro jectile Impact on Targets / International Journal of Impact Engineering 22 (1999) 95 395 26. S. Thoroddsen et al. / Granular Jets / Physics of Fluids 13 (2001) 4 6

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103 27. Popular Mechanics / The Anatomy of a splash: High speed photo gallery (2010) http://www.popularmechanics.com/cm/popularmechanics/images/splash_physics 28. J. Boudet et al. / Dynamics of Impact Cratering in Shallow Sand Layers / Physical Review Lett ers 96 (2006) 158001 29. H. Katsuragi et al. / Unified Force Law for Granular Impact Cratering / Nature Physics 3 (2007) 420 423 30. D. Stoianovici et al. / A Critical Study of the Applicability of Rigid Body Collision Theory / ASME Journal of Applied Mechanics 63 (1996) 307 316 31. G. Zhu et al. / Penetration of Laminated Kevlar by Projectiles II Analytical Model / International Journal of Solids Structures 29 (1992) 421 436 32. R. Woodward et al. / Resistance to Penetration and Compression of Fibre Reinforced Composi te Materials / Composites Engineering 4 (1994) 0961 9526 33. M. Ciamarra et al. / Dynamics of Drag and Force Distributions for Projectile Impact in a Granular Medium / Physical Review Letters 92 (2004) 194301 34. H. Mahfuz et al. / Investigation of High Velocity Impact on Integral Armor Using Finite Element Method / International Journal of Impact Engineering 24 (2000) 203 217 35. TRW Systems Integration Group / Bullet Trap Feasibility Assessment / US Army Environmental Center Defense Evaluation Support Activity (19 96) 0605 117 36. TRW Systems Integration Group / Bullet Trap Feasibility Assessment and Implementation Plan / US Army Environmental Center Defense Evaluation Support Activity (1996) SFIM AEC ET CR96195 37. / US Army Environmental Center (1997) 0605 118 38. J. Hlzle / Soft Recovery of Large Calibre Flying Processors/ International Symposium of Ballistics 19 (2001) 373 378 39. S. Larson et al. / Amended Ballistic Sand Studies to Provide Low Maintenance Lead Containment at Active Small Arms Firing Range Systems / US Army Corps of Engineers Engineer Research and Development Center (2007) ERDC TR 07 14 40. International Herald Tribune / Taliban Fighting With US Ammo (2009) http://www.military.com/news/article/taliban fighting with us ammo.html

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104 41. AZoM.com / Particle Size US Series and Tyler Mesh Size Equivalents (2002) http://www.azom.com/details.asp?ArticleID=1417 42. US Army Corps of Engineers / How to Fill Sandbags (2010) http://www.mvs.usace.army.mil/conops/emergency/sandbag.html 43. E. Fahrenthold / Shock Physics Simulation using a Hybrid Particle Element Method / Shock Compression of Condensed Matter (2005) 48 3 486

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105 Appendi ces

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106 A ppendix A: Experimental Data Table A Experimental Data

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107 Appendix A: (C ontinued) Table A (C ontinued)

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108 A ppendix A: (C ontinued) Table A (C ontinued)

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109 Appendix A: ( C ontinued) Table A (C ontinued)

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110 A ppendix B: Major Dimension Grain Measurements T able B Measured Grain Sizes Sand Rubber # 60/80 30/65 20/30 6|20 40 mesh 14 30 3/8" 1 0.148 0.575 0.708 1.39 0 0.019 1.09 9.14 2 0.172 0.596 0.822 1.55 0 0.03 0 1.4 0 9.41 3 0.204 0.64 0 0.837 1.55 0 0.043 1.55 9.64 4 0.206 0.679 0.914 1.585 0.044 1.69 9.74 5 0.214 0.69 0 0.961 1.715 0.05 0 1.92 10.74 6 0.216 0.695 0.968 1.72 0 0.069 2 .00 10.99 7 0.217 0.724 0.997 1.785 0.07 0 2.05 11.16 8 0.225 0.73 0 1.03 0 1.8 00 0.076 2.06 13.08 9 0.231 0.735 1.047 1.92 0 0.081 2.1 0 13.15 10 0.232 0.764 1.051 1.995 0.103 2.11 13.2 0 11 0.233 0.772 1.077 2.015 0.108 2.39 14.13 12 0.236 0.776 1.098 2.03 0 0.113 2.4 0 14.58 13 0.237 0.788 1.107 2.09 0 0.115 2.41 15.14 14 0.245 0.796 1.124 2.09 0 0.118 2.42 15.16 15 0.252 0.802 1.132 2.125 0.119 2.43 15.21 16 0.255 0.804 1.148 2.145 0.13 0 2.54 15.34 17 0.258 0.835 1.15 0 2.205 0.135 2.55 15.72 18 0.258 0.861 1.157 2.28 0 0.141 2.65 16.05 19 0.261 0.865 1.173 2.29 0 0.145 2.82 16.15 20 0.264 0.869 1.173 2.305 0.152 2.84 16.2 0 21 0.279 0.885 1.22 0 2.34 0 0.155 2.86 16.35 22 0.281 0.905 1.259 2.39 0 0.157 3.02 16.45 23 0.286 0.923 1.269 2.415 0.16 0 3.03 16.55 24 0.286 0.94 0 1.307 2.44 0 0.162 3.09 16.73 25 0.288 0.947 1.34 0 2.45 0 0.177 3.16 16.96 26 0.288 0.949 1.554 2.52 0 0.186 3.38 17.55 27 0.293 0.952 1.565 2.67 0 0.186 3.5 0 17.89 28 0.295 0.953 1.706 2.915 0.191 3.59 19.78 29 0.296 0.965 1.727 3.07 0 0.192 4.15 21.65 30 0.302 0.966 1.731 3.975 0.194 4.3 0 23.22 31 0.302 0.202 32 0.309 0.203 33 0.309 0.205 34 0.311 0.208 35 0.313 0.215

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111 Appendix B: (C ontinued) Table B (C ontinued) Sand Rubber # 60/80 30/65 20/30 6|20 40 mesh 14 30 3/8" 36 0.314 0.223 37 0.314 0.225 38 0.318 0.226 39 0.32 0 0.228 40 0.32 0 0.228 41 0.32 0 0.229 42 0.322 0.232 43 0.323 0.238 44 0.324 0.261 45 0.325 0.27 0 46 0.336 0.273 47 0.338 0.281 48 0.338 0.282 49 0.341 0.283 50 0.349 0.284 51 0.352 0.303 52 0.353 0.31 0 53 0.354 0.315 54 0.358 0.319 55 0.359 0.321 56 0.366 0.326 57 0.372 0.327 58 0.373 0.327 59 0.381 0.327 60 0.382 0.33 0 61 0.382 0.335 62 0.382 0.337 63 0.385 0.338 64 0.39 0 0.343 65 0.39 0 0.368 66 0.394 0.37 0 67 0.395 0.373 68 0.395 0.389 69 0.396 0.394 70 0.398 0.395

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112 Appendix B: ( C ontinued) Table B ( C ontinued) Sand Rubber # 60/80 30/65 20/30 6|20 40 mesh 14 30 3/8" 71 0.399 0.395 72 0.406 0.398 73 0.408 0.4 00 74 0.408 0.4 00 75 0.412 0.4 00 76 0.413 0.403 77 0.414 0.412 78 0.418 0.413 79 0.42 0 0.417 80 0.42 0 0.424 81 0.428 0.425 82 0.429 0.428 83 0.431 0.433 84 0.432 0.436 85 0.435 0.45 0 86 0.438 0.451 87 0.448 0.461 88 0.451 0.464 89 0.451 0.484 90 0.458 0.493 91 0.479 0.502 92 0.486 0.53 0 93 0.513 0.565 94 0.515 0.595 95 0.519 0.615 96 0.537 0.643 97 0.554 0.668 98 0.566 0.757 99 0.634 0.823 100 0.68 0 0.97 0 Average 0.3546 0.8127 1.1784 2.1923 0.3051 2.583 14.902 Standard Deviation 0.09736 0.114549 0.26118 0.52131 0.17603 0.75472 3.4700

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113 A ppendix C : Measured Projectile Masses Table C Measured Projectile Masses Mass [g] # 7.62x39 9mm 1 8.007 7.513 2 8.053 7.462 3 7.998 7.457 4 8.012 7.403 5 8.008 7.417 6 7.981 7.49 0 7 8.023 7.449 8 7.935 7.492 9 8.01 0 7.468 10 7.967 7.476 Average 7.9994 7.4627 Std Dev 0.03227 0.03368 Mass [ Grains ] 123.45 115.17

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1 14 A ppendix D : ANOVA Results Table D ANOVA Results for 7.62x39 Round into Sand Source of Sum of d.f. Mean F Variation Squares Squares between 79.39 3 26.46 4.317 error 220.7 36 6.131 total 300.1 39 The probability of this result, assuming the null hypothesis, is 0.011 Group A: 60/80 Mesh; Number of items= 10 13.0 18.2 18.8 19.0 19.6 20.0 20.2 21.0 22.4 22.5 Mean = 19.470 95% confidence interval for Mean: 17.88 thru 21.06 Standard Deviation = 2. 69 High = 22.50 Low = 13.00 Median = 19.80 Average Absolute Deviation from Median = 1.75 Group B: 30/65 Mesh; Number of items= 10 18.0 18.0 19.0 19.7 20.0 20.2 21.0 22.3 24.8 27.0 Mean = 21.000 95% confidence interval for Mean: 19.41 thru 22.59 St andard Deviation = 2.93 High = 27.00 Low = 18.00 Median = 20.10 Average Absolute Deviation from Median = 2.06 Group C: 20/30 Mesh; Number of items= 10 16.0 16.1 16.3 17.0 17.3 17.4 18.2 18.5 18.7 21.5 Mean = 17.700 95% confidence interval for Mean: 16.11 thru 19.29 Standard Deviation = 1.65 High = 21.50 Low = 16.00 Median = 17.35 Average Absolute Deviation from Median = 1.16

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115 Appendix D : (C ontinued) Table D (C ontinued) Group D: 6/20 Mesh; Number of items= 10 15.1 15.4 16.1 16.1 16.5 17.2 17.2 18.6 21.0 22.5 Mean = 17.570 95% confidence interval for Mean: 15.98 thru 19.16 Standard Deviation = 2.44 High = 22.50 Low = 15.10 Median = 16.85 Average Absolute Deviation from Median = 1.73 Table E ANOVA Results for 7.62x39 Round into Rubber Sour ce of Sum of d.f. Mean F Variation Squares Squares between 612.4 2 306.2 17.10 error 483.5 27 17.91 total 1096. 29 The probability of this result, assuming the null hypothesis, is less than .0001 Group A: 40 Mesh; Number of items= 10 58.0 59.5 60.0 60.0 60.5 61.0 61.0 61.5 63.0 67.0 Mean = 61.150 95% confidence interval for Mean: 58.40 thru 63.90 Standard Deviation = 2.44 High = 67.00 Low = 58.00 Median = 60.75 Average Absolute Deviation from Median = 1.55 Group B: 14/30 Mesh; Number of items= 10 58.0 60.0 61.0 61.0 69.0 69.5 70.0 70.0 71.0 72.0 Mean = 66.150 95% confidence interval for Mean: 63.40 thru 68.90 Standard Devi ation = 5.42 High = 72.00 Low = 58.00 Median = 69.25 Average Absolute Deviation from Median = 4.35

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116 Appendix D : (C ontinued) Table E (C ontinued) Group C: 3/8 Inch; Number of items= 10 48.0 52.0 52.5 53.5 53.5 54.5 56.0 59.0 59.0 63.0 Mean = 55.100 95 % confidence interval for Mean: 52.35 thru 57.85 Standard Deviation = 4.29 High = 63.00 Low = 48.00 Median = 54.00 Average Absolute Deviation from Median = 3.20 Table F ANOVA Results for 9mm Round into Sand Source of Sum of d.f. Mean F Variation Squares Squares between 72.96 3 24.32 10.29 error 85.06 36 2.363 total 158.0 39 The probability of this result, assuming the null hypothesis, is 0.000 Group A: 60/80 Mesh; Number of items= 10 21.5 21.5 21.5 22.0 22.0 22.5 22.5 22.5 23.0 23.5 Mean = 22.2 95% confidence interval for Mean: 21.26 thru 23.24 Standard Deviation = 0.677 Hi = 23.5 Low = 21.5 Median = 22.2 Average Absolute Deviation from Median = 0.550 Group B: 30/65 Mesh; Number of items= 10 18.5 19.9 20.0 20.5 20.5 20.5 20.5 21.5 23.0 25.0 Mean = 21.0 95% confidence interval for Mean: 20 .00 thru 21.98 Standard Deviation = 1.82 Hi = 25.0 Low = 18.5 Median = 20.5 Average Absolute Deviation from Median = 1.11

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117 Appendix D : (C ontinued) Table F (Continued) Group C: 20/30 Mesh; Number of items= 10 18.5 18.5 19.0 19.0 19.0 20.5 21.0 21.5 22 .5 25.0 Mean = 20.4 95% confidence interval for Mean: 19.46 thru 21.44 Standard Deviation = 2.11 Hi = 25.0 Low = 18.5 Median = 19.8 Average Absolute Deviation from Median = 1.65 Group D: 6/20 Mesh; Number of items= 10 17.0 17.5 17.5 17.5 18.5 18. 5 19.0 19.5 20.0 20.0 Mean = 18.5 95% confidence interval for Mean: 17.51 thru 19.49 Standard Deviation = 1.11 Hi = 20.0 Low = 17.0 Median = 18.5 Average Absolut e Deviation from Median = 0.900 Table G ANOVA Results for 9mm Round into Rubber Source of Sum of d.f. Mean F Variation Squares Squares between 1341. 2 670.7 84.65 error 213.9 27 7.923 total 1555. 29 The probability of this result, assuming the null hypothesis, is less than .0001 Group A: 40 Mesh; Number of items= 10 50.0 50.0 51.0 52.0 52.0 52.5 52.5 53.0 54.5 55.0 Mean = 52.250 95% confidence interval for Mean: 50.42 thru 54.08 Standard Deviati on = 1.67 High = 55.00 Low = 50.00 Median = 52.25 Average Absolute Deviation from Median = 1.25

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118 Appendix D : (C ontinued) Table G (Continued) Group B: 14/30 Mesh; Number of items= 10 46.0 46.5 47.0 47.5 47.5 48.0 48.5 48.5 49.0 50.5 Mean = 47.900 95% confidence interval for Mean: 46.07 thru 49.73 Standard Deviation = 1.31 High = 50.50 Low = 46.00 Median = 47.75 Average Absolute Deviation from Median = 1.00 Group C: 3/8 Inch; Number of items= 10 30.0 30.5 33.0 35.0 35.5 36.5 39.5 41.0 41.0 42.0 Mean = 36.400 95% confidence interval for Mean: 34.57 thru 38.23 Standard Deviation = 4.39 High = 42.00 Low = 30.00 Median = 36.00 Average Absolu te Deviation from Median = 3.60

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119 A ppendix E: T Test Results Table H T Test Results

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120 A ppendix F : Moisture Meter Calibration Table I Moisture Meter Calibration

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About the Author Robert Paul Cole is a mechanical engineering student at the University of South Florida in the College of Engineering. His educational interests include: mechanics, heat transfer, and so Robert has lived and worked in Florida for m ost of his life. He graduated from Pasco High School (just north of USF) and after meeting the entrance requireme nts began work in the College of Engineering. After his first semester he then transferred to Dodge City Community College in Ford County, Kansas, where he played college football and continued to take as many engineering courses as possible (Dodge City C ommunity College did not have an engineering school) until 2006 when he transferred back to USF to the College of Engineering. He has fulfilled all coursework requirements for both the B.S. and M.S. in Mechanical Engineer ing, and anticipates becoming a pr ofessional enginee r by 201 4