University of Florida Thesis Or Dissertation Formatting

REFINEMENT OF TEMPORARY MUNITION STORAGE USING SOIL-FILLED WALLS

VINCENT DUPONT

A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE

UNIVERSITY OF FLORIDA

2019

To my family and my friends

ACKNOWLEDGMENTS

I would like to thank my teacher, Dr. Theodor Krauthammer, for sharing is knowledge with my fellow students and me. I would also like to express my gratitude towards my colleagues, now friends that I have met and worked with in my time at the

University of Florida. To my past teachers and mentors, my accomplishments would have never been possible without your advices and guidance. To the Canadian

Department of Defense and the Canadian Military Engineer branch, that made this amazing experience possible for me and many other Canadian officers, thank you.

Finally yet importantly, to my Family, which have and always will be there for me.

TABLE OF CONTENTS

page

ACKNOWLEDGMENTS...... 4

LIST OF TABLES...... 8

LIST OF FIGURES ...... 10

ABSTRACT...... 12

CHAPTER

1 INTRODUCTORY REMARKS ...... 14

1.1 Problem Statement ...... 14 1.2 Objectives ...... 15 1.3 Research Significance ...... 15 1.4 Scope and Organization ...... 15

2 LITERATURE REVIEW AND BACKGROUND INFORMATION ...... 17

2.1 Introduction ...... 17 2.2 Soil-Filled Wall ...... 17 2.3 Blast Event ...... 19 2.3.1 Blast in Open-Air Environment ...... 20 2.3.1.1 Air blast loading case ...... 20 2.3.1.2 Pressure contours ...... 22 2.3.1.3 Sympathetic detonation ...... 22 2.3.2 Blast in Mediums ...... 23 2.3.2.1 Ground shock...... 24 2.3.2.2 Cratering ...... 26 2.3.2.3 Fragments ...... 27 2.4 Previous Experimentations and Research ...... 31 2.4.1 Finite Element Analysis (FEA) and Analytical Modelling ...... 31 2.4.2 Enhancement of Response Prediction Model ...... 32 2.4.3 Technical Report – Operational Munition Storage Optimization – CIPPS 2017 ...... 33 2.5 Existing Directives and Guidelines ...... 34 2.5.1 Current Available Designs ...... 35 2.5.2 Safety Distances ...... 36 2.5.2.1 Pressure effect on the human body ...... 36 2.5.2.2 Fragment effect on the human body ...... 37 2.5.3 Serviceability Limits ...... 37 2.5.3.1 Operational Requirements ...... 38 2.5.3.2 Environment Suitability ...... 38 2.6 Software ...... 39

2.6.1 Conventional Weapon Effects Simulation (ConWep) ...... 39 2.6.2 FRANG ...... 39 2.6.3 SHOCK ...... 40 2.7 Summary ...... 40

3 METHODOLOGY ...... 51

3.1 Introduction ...... 51 3.2 Initial Configuration ...... 51 3.3 Layout Validation ...... 52 3.3.1 Cratering ...... 52 3.3.2 Sympathetic Detonation ...... 53 3.3.2.1 Air blast induced pressure ...... 53 3.3.2.2 Ground shock...... 54 3.4 Load Function ...... 54 3.4.1 Air Blast Load Function ...... 55 3.4.2 Gas Pressure Loading Function ...... 55 3.4.3 Fragment Load Function ...... 56 3.4.4 Ground Shock Effect ...... 56 3.4.5 Combined Effects ...... 57 3.5 Soil-Filled Wall Response ...... 57 3.5.1 Lower Bound Criteria ...... 58 3.5.2 Upper Bound Limit ...... 59 3.6 Safety Distance Calculations ...... 59 3.6.1 Blast Overpressure Safety Distance ...... 59 3.6.2 Fragmentation Safety Distance ...... 60

4 RESULTS AND DISCUSSIONS ...... 61

4.1 Introduction ...... 61 4.2 Initial Dimensions ...... 61 4.2.1 Previous Work ...... 61 4.2.2 Cratering Dimensions ...... 61 4.3 Design Values ...... 62 4.3.1 Structural Characteristics and Geometrical Analysis ...... 62 4.3.2 Sympathetic Detonation ...... 63 4.3.3 Shock Overpressure Loading ...... 64 4.3.4 Gas Pressure Load ...... 65 4.3.5 Fragmentation Load ...... 65 4.3.6 Combined Loading Scenario ...... 66 4.3.7 Ground Shock ...... 66 4.4 Lateral Displacement Analysis ...... 67 4.4.1 Wall Response ...... 67 4.4.1 Roof Response ...... 68 4.5 Pressure-Distance Safety ...... 68 4.6 Construction Guidelines ...... 68

5 CONCLUSION AND RECOMMENDATIONS ...... 80

5.1 Conclusion ...... 80 5.2 Recommendations ...... 82

APPENDIX: CALCULATION WORKSHEETS ...... 84

LIST OF REFERENCES ...... 114

BIOGRAPHICAL SKETCH ...... 116

LIST OF TABLES

Table page

2-1 HESCO Bastion Sizes Chart ...... 41

2-2 TNT Equivalency Factors for Common Explosives ...... 41

2-3 Energy Fluence for Common Explosives ...... 41

2-4 Soils Properties for Ground Shock Calculations ...... 41

2-5 Explosive Constants for Common Explosives ...... 42

2-6 Soil Penetration Constants for Typical Soils ...... 42

2-7 Pressure Induced Damages to Human Body ...... 42

2-8 Soil Properties ...... 42

2-9 Soil Friction Properties ...... 43

4-1 Crater Diameter for Different Soils ...... 70

4-2 Input Parameters for Sympathetic Calculations ...... 70

4-3 Sympathetic Calculations Results ...... 70

4-4 Input Parameters for Shock Pressure Calculations ...... 71

4-5 Output Parameters for Shock Pressure Loading ...... 71

4-6 Input Parameters for Gas Pressure Calculations ...... 71

4-7 Output Parameters for Gas Pressure Loading ...... 71

4-8 Relevant Parameters Regarding Fragment Penetration ...... 72

4-9 Output Parameters for Fragment Loading ...... 72

4-10 Input Parameters for Ground Shock Analysis ...... 72

4-11 Output Displacements from Ground Shock Analysis ...... 72

4-12 Wall Displacements from Dynamic Analysis ...... 73

4-13 Combined Wall Displacement Values ...... 73

4-14 Pressure Values for Given Distance ...... 73

4-15 Distance for Threshold Pressure Values ...... 73

4-16 Linear Weight for Roof Beam Capacity...... 73

LIST OF FIGURES

Figure page

2-1 Mk 84 General Purpose Bomb ...... 43

2-2 Different Stages of HB Construction ...... 43

2-3 Surface Burst Shock Representation ...... 44

2-4 Pressure vs. Time Representation ...... 44

2-5 Pressure vs. Distance representation ...... 44

2-6 Pressure vs. Time idealization ...... 45

2-7 Shock Wave Parameters for Hemispherical TNT Burst ...... 45

2-8 Ground Shock Coupling Factor ...... 46

2-9 Crater Dimensions for Cased and Uncased Explosives ...... 46

2-10 Initial Velocity Graphical Representation ...... 47

2-11 Striking Velocity Graphical Representation ...... 47

2-12 HB after Experimental Testing ...... 48

2-13 HESCO Bastion FE Model ...... 48

2-14 Deformed Shape of HB ...... 48

2-15 LBS System ...... 49

2-16 Experimental Setup Drawing ...... 49

2-17 Numerical Simulation Results ...... 49

2-18 Proposed HB and Munition Layout ...... 50

2-19 Section Cut of Soil Berm ...... 50

4-1 Crater Dimensions in Wet Sandy Clay...... 74

4-2 Different Configurations of Munition Depot ...... 74

4-3 Configuration A with Crater Overlay ...... 75

4-4 Configuration D with Crater Overlay ...... 75

4-5 Sympathetic Detonation – Worst-Case Loading Scenario ...... 75

4-6 Wall Loading Scenario – Configurations A and B ...... 76

4-7 Roof Loading Scenario – Configurations A and B ...... 76

4-8 Wall Loading Scenario – Configurations C and D ...... 77

4-9 Roof Loading Scenario – Configurations C and D ...... 77

4-10 Soil-Filled Wall Layout ...... 78

4-11 Beam Installation ...... 78

4-12 Steel Plate Installation ...... 79

4-13 Roof Installation – Complete Construction ...... 79

Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science

REFINEMENT OF TEMPORARY MUNITION STORAGE USING SOIL-FILLED WALLS

Vincent Dupont

May 2019

Chair: Theodor Krauthammer Major: Civil Engineering

In recent years, modular systems use has been growing. From headquarters to protective works, systems like the Weatherhaven® Modular Tentage System (MTS) and the HESCO® Bastion (HB) have improved the operational flexibility and decreased the logistical burden caused by large-size operations. Although they fulfill many purposes, these commercially available products are not often used as munition storage facilities

(Schilling and Paparone 2005). Due to the lack of technical knowledge and experimentation data, the safety requirements that would go along the use of these systems would most-likely be over-conservative and the resource would end up not being employed in the most efficient manner.

In this present study, we will look into optimizing the use of one of these systems.

This will be done by taking into consideration the combined effects of blast and fragmentation using various software, analytical models and experimentation data.

Using these different elements in a conservative approach, a reliable loading scenario on each structure components will enable us to properly characterize and quantify the response. After having performed a complete analysis, we aim to develop optimized

guidelines for the use of HESCO® Bastion for storage of a given quantity of US Mark 84

General Purpose (GP) bombs.

CHAPTER 1 INTRODUCTORY REMARKS

1.1 Problem Statement

In modern operations, efficiency is key to mission success. Modular storage has been introduced in many military operations and has proven its utility in many ways. It has reduced the logistical workload required to support the different type of operations around the globe. One way of using these modular systems that has been recently looked at is munition storage. Unfortunately, the knowledge surrounding the combined effects of blast and fragments from an engineering perspective as well as the availability technical guidelines regarding the use of these commercially available products is lacking. In the past years, several experimentations and analysis, including those that occurred at the Center for infrastructure Physical Protection and Security (CIPPS), have been conducted to find more about the behavior of these structures under ultra- impulsive. With these research projects, general guidelines for expedient design of munition storage using non-standard materials and configurations have been developed by multiple organizations (Ornai et al. 2018) (U.S. Army Corps of Engineers 2014) U.S.

Explosive Safety Board 2004).

Using the findings of these studies and applying the newly acquired knowledge to a physical configuration that would use commonly found materials and resources would be a step further towards efficiency in deployed operations. In this study, we will take a deeper look at the possibility of using earth-filled walls to serve as protective barriers in munition storage. Using this type of wall and predicting the behavior with different munition configuration and soil fill would enable us to investigate the possibility of employing these configurations in various environments. This will also allow us to find

areas of improvement to further refine the structural response of soil-filled walls subjected to the full spectrum of blast-related effects.

1.2 Objectives

This study will aim at refining the design of an efficient munition storage facility using soil-filled wall while taking into account the entire physical phenomenon surrounding the blast of its internal content. For this study to be considered a success, the fallowing objectives must be met:

• Use materials commonly found in international and domestic operations.

• Mitigate sympathetic detonation of an equivalent amount of munition stored in the adjacent cell.

• Reduce the safety distance to be observed for the fragmentation hazard.

• Reduce the safety distance to be observed for the blast overpressure.

• The solution must be versatile and be employable in various operational environments.

• Provide critical areas of improvement regarding the design and the prediction of the response of the different structural elements.

1.3 Research Significance

This outcome of this research will allow resources that are already employed in many operational theaters to fulfill another critical purpose. In addition, since the safety distance to be observed would be reduced, the footprint of the camp would be smaller.

Ultimately, the extensive logistical burden of force beddown could be significantly reduced and operational flexibility could be increased.

1.4 Scope and Organization

The focus of this study is to validate the fact that an efficient design can be obtained when using soil-filled walls as a temporary munition storage facility. Various

experimental data, software, analytical models as well as conservative assumptions will be used in order to predict the structural response of specific elements of interest.

Ultimately, the findings of this study would have to show improvement regarding the previous available designs for expedient munition storage.

An overview of the history and the soil-filled wall concept as well as the full spectrum of the blast-related phenomenon is presented in the second chapter. This part also includes a summary of the important findings from of the previous studies and research regarding the behavior of soil-filled wall subjected to blast load. The proposed methodology and approach that will be followed to achieve the objectives listed in

Section 1.2 is presented in the third chapter. The specific outcomes and results regarding the proposed munition design are described in the fourth chapter. Finally, a comprehensive summary of the proposed design as well an efficiency statement will conclude this study and will be presented in the fifth chapter. A list of areas of improvements and potential research projects using advance software analysis as well as field experimentations will also be included in this last chapter.

CHAPTER 2 LITERATURE REVIEW AND BACKGROUND INFORMATION

2.1 Introduction

The proper quantification of all the physics involved into blast loading is far different and a lot more complex from the one that pertains to static loading. This has been the primary research subject of many engineers in the recent past, most of them focusing on material behavior upon blast and loading. One of these primary findings is that type of load applied when we have blast loading belongs in the impact loading domain (Krauthammer 2008).

The proposed methodology included in this paper will be a conservative-based solution to a complex problem. A comprehensive study of blast-related first or second order effects will be done to propose a conservative solution as well as areas of improvement to the problem of munition storage in an operation environment.

The munition that will be stored in the cells are US made Mk 84 General Purpose

(GP) manufactured by General Dynamics. These ordonnances are 10-ft long and have a diameter of 18-in at the thickest part. Each contains 945 lbs of Tritonal, which is equivalent to 1195 pounds of TNT. Each pallet contains 2 bombs each, making a single pallet 4-ft deep, 2-ft high and 10-ft long. Each ordonnance weights approximately 2000- lbs and a full pallet weight 4100 lbs. Figure 2-1 shows a single Mk84 GP Bomb.

2.2 Soil-Filled Wall

Decades ago, gabions were first used by engineers and military units to construct hasty structures when needed. With time, the wide use of traditional gabions evolved into sand bag constructions, which were much more convenient. Recently, a new form of gabion has arrived and is taking a larger place in the civil and protective engineering

industry. Civilian and military authorities around the world now commonly use soil-filled walls. Their versatility and ease of construction makes them a great asset in multiple situations. Some organizations use them to prevent flooding or as retaining walls and other use them as protective works. Although they are much alike the traditional gabions, they are quite different into the way that they can be used in a broader operational environment since they do not rely on the availability of large rock boulders.

The idea behind soil-filled walls, or bastion, is quite simple. It mainly consist of three different parts: the container, the liner and the fill. Common commercially available products in the US are manufactured by HESCO® and they have been the industry leader in North America and Eastern Europe for years. Their products are the current standard for most NATO military forces in a variety of uses. These temporary structures can be an important asset in both combat and humanitarian operations around the globe. Recently, they have been considerably used overseas in the Middle-East operations to build camp perimeter and temporary protective structures as well as flood prevention against hurricane Florence in September 2018.

A British entrepreneur called James William Heselden founded the company, whose name stands for Hercules Engineering Solutions Consortium, in 1991. Although they commercialize multiple products with a force protection purpose, they are mostly known for the HESCO Bastions (HB). Their bastions are prefabricated units that come in multiple sizes for diverse applications. The outer container is a welded steel mesh and has interlocking corners. These corners are designed so multiple units can be attached together to create a larger structure. The inside liner of the unit is a resistant polypropylene geotextile fabric. Depending on their dimensions, which are listed in

Table 2-1, they come in packages of 5 to 10 pre-assembled units that can be lifted by hand for ease of construction (HESCO® Group 2016). The units are unfolded, assembled in the proper configuration and then filled with soil or sand to provide the desired protection. The pictures below show the different stages of a protective work construction using HB.

2.3 Blast Event

A blast, commonly known as an explosion, is a chemical reaction characterized by the sudden and violent release of the energy contained in an explosive material transformed into gas and residues. This chemical reaction produces many second order effects. Some are visible to the eye and some are not. Some can be measured and some cannot. We generally classify explosion in two different types: deflagration and detonation. One principal difference is generally observed between both chemical reactions. The reaction speed is much slower in a deflagration than in a detonation.

Therefore, the effect of the energy dissipation in much quicker in a detonation (FEMA

2003). This will be discussed in further details in the coming pages.

This chemical reaction can be initiated by many means. The important factor is the amount of energy that is transferred to the explosive material. This amount of energy, that is specific to all different explosive materials and compounds, is called critical level or energy fluence (Cooper and Kurowski 1996). The energy transfer can be done mechanically, by heat and even by shock. Although both types of reaction can cause some disastrous effects on structures and buildings, detonation will be the subject of a more in-depth analysis in this study.

2.3.1 Blast in Open-Air Environment

When the blast event occurs, the energy released by the chemical reaction rapidly heats the air around the explosive material causing it to expand. This temperature increase causes a high pressure boundary between both the “stable” and the “disturbed” environments. This high pressure front then travels outwards in all directions while trying to reach the natural equilibrium with the surrounding environment.

This is how is created the blast overpressure wave or shock front. This sharp increase in pressure is also called the Von Neuman pressure spike. When the blast wave travels in a free-field environment, its amplitude reduces releasing energy its surrounding environment such as by heating the surrounding air. Overpressure at a given point dissipates quickly as equilibrium is reached without constraints in a matter of milliseconds. When the air molecules reach the point of equilibrium, they still have an inward velocity. This creates a negative pressure phase of much smaller magnitude. A secondary pressure rise phase fallows briefly this negative pressure phase. For design purpose in the blast engineering field, the maximum positive overpressure value, meaning the one that corresponds to the Von Neuman spike, is used as it will have the most impact on the design (Krauthammer 2008).

2.3.1.1 Air blast loading case

The blast overpressure will travel from the origin towards the point of interest at a given speed and magnitude that varies depending on the amount and type of explosive.

At a given distance of the blast event, a structure will be exposed to a remaining peak overpressure that will decay through time. The loading function is done by representing the pressure-time history on a single plot. From this plot, one can take the area under the curve of the positive pressure phase which corresponds to the impulse.

To facilitate the assessment, air blast loading is often represented as a triangular load to measure the structural response. To create that triangular loading function, the same peak pressure and impulse that impacted the structure are maintained. The duration time is then calculated using both previous variables. This way, the duration time of the load is shortened, but this has negligible impact on the predicted response.

This alternate graphical representation is shown in Figure 2-6. For free air explosions, gas pressure is neglected. For internal explosions or the ones occurring in an enclosed structure, the gas pressure also has to be considered.

To find the shock wave parameters due to a blast event, the method that is most commonly used is the scaled distance. To find these parameters, one must first find the direct distance from the point of origin to the target of interest (R). Then, the explosive weight (W) must be converted to its TNT equivalency. The values for TNT equivalency of commonly found explosives are given in Table 2-2.

When these to values are identified. The scaled distance (Z) prescribed in

Equation 2-1 must be found.

푅 푍 = ⁄3 (2-1) √푊

With the calculated scaled distance value, one can use the charts available in the

U.S. Army publication TM 5-855-1 and find the desired parameter(s). These charts enable the person to find the desired pressure, impulse, duration and even shock front velocity. With these parameters, an adequate loading scenario can be created. An example of these chart, the one that pertains for surface TNT explosions, is pictured in

Figure 2-7.

2.3.1.2 Pressure contours

A pressure distribution around the initial detonation points can be defined two different ways. As mentioned before, overpressure decays in all directions. For the first technique, multiple points where the peak overpressure is the same for are considered in different directions. Afterwards, a line is drawn between those points. This technique is used mark the spot where a given pressure value is critical. It can be done for a prescribed level of damage to material or humans and also to prevent sympathetic detonation, which will be explained in the next sub-section.

The other way of using the pressure contour technique is using a given distance as a baseline. This one is done by drawing a line, or a circle, at a given distance from the epicenter of the event. If we have an air blast where no obstructions occur between the central point and the given distance, the pressure contour with both techniques will be identical as the blast pressure travels and decays at the same rate in all directions.

This second technique is more common and will be used in this study.

2.3.1.3 Sympathetic detonation

Sympathetic detonation can easily be compared to a chain reaction. When a detonation occurs, the pressure wave will travel through a medium, either solid or gas, and will reach another explosive material. If the energy contained in the blast wave at the location of the adjacent explosive exceeds the critical energy activation level of the second explosive, we will have detonation. This phenomenon is called sympathetic detonation. This is an important factor that will have to be mitigated during the design of our storage units. In order to do so, the energy fluence, which is the amount of energy required to cause the detonation, will be calculated for a few of the most probable

explosive that could be stored in adjacent cells. This will be done using the fallowing equation (Cooper and Kurowski 1996).

2 E = (푃0 × 푡푑) / (ρ × U) (2-2)

In this equation, E is the energy fluence, Po is peak incident pressure, td refers to the duration time of the triangular load, ρ is the explosive’s density and U is the specific unreacted shock velocity of the explosive. To calculate the specific shock velocity of an explosive one must use the velocity Hugoniot equation, here numbered 2-3. In this equation, co is the bulk sound speed in the explosive material, u is the incident particle velocity and s is a velocity coefficient that varies depending on the material density.

U = 푐표 + (u × s) (2-3)

Then, this value will be compared to the prescribed critical values given in Table

2-3 who are specific for a particular explosive. If the calculated value is greater than the critical energy fluence, detonation will occur.

2.3.2 Blast in Mediums

When a detonation occurs, the released energy will travel in all directions no matter what medium it encounters. It does this in order the re-establish equilibrium.

When a pressure wave changes medium, meaning when there is a change in the density of the material, part of the pressure wave is reflected and another is absorbed by the second medium. A reflected and a transmitted pressure wave are now created.

This phenomenon will occur even if one of the medium is air. The angle at which the pressure wave hits the medium and well as the materials density will determine the amplitude of the reflected pressure, which is usually greater than the peak incident value. Since we know that pressure waves travel in all directions, considering reflected

pressure is important in enclosed medium such as ground or, in our case, munition storage facilities. At the worst case, we can have multiple positive overpressure values at the same time and location resulting in an unexpectedly high pressure peak for a short duration (Krauthammer 2008). This could cause severe damage to resources if unaccounted. Reflected pressures must then be used to create reliable loading scenarios when considering internal explosions such as the one in this study.

2.3.2.1 Ground shock

After the explosion occurs near or on the ground level, multiple pressure waves a created. First, a pressure wave will travel along the surface, compressing the ground to form an air-induced ground shock wave. Almost simultaneously, a pressure wave will also travel through the soil. This direct-induced ground pressure wave also travel in all directions, bouncing on bedrock and on the surface creating a maze of colliding waves.

As the pressure travels in the ground, it loses energy to the profit of the soils which undergoes compaction and possibly plastic deformation fallowing that energy transfer.

As the pressure reaches the point of interest, it will exert a reduced pressure on the target. At close range, this pressure will reach the point of interest after the one that travelled by air, since the blast wave propagation speed depends on the material size and density (Krauthammer 2008).

To find a given value for a pressure wave travelling through a solid medium, the technique is more complicated than for a free-air blast even though the pressure-time distribution has roughly the same shape. The fallowing method is also prescribed in the

U.S. Army TM 8-855-1. To find the value of the peak incident pressure, Equation 2-4 must be used.

푃0 = 푓 × 휌푐 × 160 × 휆−푛 (2-4)

In this equation, λ is the scaled depth of burst. It fallows an equivalent logic that the scaled distance but for underground wave propagation, meaning that λ equals to

R/W1/3 (see Sub-Section 2.3.1.1). The second variable, f, is the coupling factor. This also depends on the general type of medium that the pressure wave will propagate through. This value can be found using the graph shown in Figure 2-8. This factor is a function of the λ value initially found.

The next variable, ρc, is the acoustic impedance of the medium. This factor accounts for the resistance to wave propagation for a given medium. The last factor, n, is the attenuation coefficient. Both of these factors depend on the type of medium.

Values of these variables for commonly found soils can be found in Table 2-4.

Since calculations regarding blast engineering are often done using the conservation of the energy principle. Equation 2-5 enable us to find the particle velocity and ultimately the kinetic energy propagated by the blast wave in a given medium.

푉0 = 푃0 / 휌푐 (2-5)

The one thing that is missing to create a reliable loading function from a ground shock is the impulse. This value can be found using Equation 2-6. In this equation, ρ0 is the mass density of the soil.

−푛+1 3 퐼0 = 푓 × 휌0 × 1.1 × 휆 / √푊 (2-6)

The time of arrival for the ground shock to reach a given distance of interest can be found using Equation 2-7. From this arrival time, the pressure will rise at its peak fallowing Equation 2-8. The duration time can be computed using the specific impulse and pressure.

푡푎 = 푅 / 푐 (2-7)

푡푟 = 0.1 × 푡푎 (2-8)

A proper loading function can now be created using the steps previously stated for an underground or a surface structure exposed to ground shock.

2.3.2.2 Cratering

When a surface explosion occurs, a massive disturbance of the soil underneath and beside the explosive will occur. Since the energy release is so intense, some of the soil will be sent flying in the air while a portion will undergo plastic deformation and another will simply compact. The initial radius of the hole created by the soil that went flying, or the ejecta, is called the true radius. When the ejecta falls back on the ground a smaller size crater will be noticeable. This one has a radius called the apparent radius

(Krauthammer 2008). In this case, we are concerned that the true radius of the crater could excavate the soil underneath the storage unit walls. By excavating the soil, a structural instability of our wall will be induced by the explosion. Also, pressure would be able to create uplifting of the structure, reducing the friction with the ground and easing the lateral movement of the walls.

For the sake of this study, the parameter of importance is the true radius that would be created by the explosion. As the ejecta will be contained, it will not pose a significant threat. The depth of the crater is irrelevant for the outcome of this study.

To find the diameter of the crater, knowing that the explosive will be near the surface of the ground, Figure 2-10 can be used when we have detonation of ordonnances containing a specific amount of high explosive (HE). This figure enables the user to find the crater parameters as a function of the containment characteristics of the explosive (cased of uncased), the soil type and the scaled depth of burst.

2.3.2.3 Fragments

Fragments and debris are considered as any object being projected in the air by cause of the explosion. In a conventional munition environment, debris are less of a concern even if they have more mass since their travelling speed in much slower than fragments. Fragments, however, are a treat that is to be consider when we have detonation of high explosive (HE). Most of the fragments will come from the casing of the ordonnance. When we have a high-order reaction, the casing cannot contain the amount of energy being release and will shatter in random size pieces. The size, amount and mean mass of the fragments varies between every ordonnance since they are based on manufacturing techniques and materials. Experimental studies can show us the tendency for a given ordonnance, but the exact values are almost impossible to predict.

Fragments coming from the casing of the explosive will have an initial velocity and mass. This velocity will decay as the fragments travel through the air. Depending on the location of the structure, the fragments could have enough energy remaining to perforate the membrane and penetrate into the filling. As they penetrate, they will cause displacements and compaction in the filling while transferring their kinetic energy into the sand. Given the density of the soil and the pertinent data for the fragments, it is possible to use the fallowing method to compute the pertinent parameters regarding the fragments and create a loading function that will represent the reality.

When fragments hit a structure, they will inevitably transfer energy upon impact.

In order to assess the amount of energy being transferred, the principle of the conservation of energy should be applied. The total kinetic energy contained into the fragments can be obtained with their mass and their impact velocity. The fragments will

impact the structure at a given time and transfer their entire kinetic energy to the structure. In a conservative approach, these values can be used to create a loading function that pertains only to the fragments. This loading function will have a triangle shape, where the maximum peak will begin at the time of impact and will decay in a linear fashion until the fragments have reached the maximum depth and have stopped moving. In a real environment, the fragments will dissipate a lot of their energy by deformation, friction and heat release to the wall.

An approach presented by Gurney in the 1940’s enables us to find the total number of fragments coming from a single bomb given the physical properties of the explosive device. Gurney’s equation to find the total number of fragments, Nm, is as follows:

푊푐 √푚/푀 푁푚 = ( ⁄2 × 푀) × −푒 (2-9)

In this equation, Wc is the total weight of the casing expressed in ounces. m is a critical mass, meaning that the value of Nm will return a the number of fragments with a mass greater the value of m. To account for all the fragments coming from the casing, the chosen value for m has to be 0. M is a mass factor calculated by using Equation 2-

10. For the Mk84 GP Bomb, the value of M is 0.204 oz (U.S. Department of the Army

1986).

2 2 5/3 2/3 푡푐 푀 = 퐵푥 × 푡푐 × 푑 × (1 + ⁄ ) (2-10) 푖 푑푖

In this last equation, Bx is an explosive specific characteristic found using Table

2-5. The two other variables, tc and di, correspond to the average casing thickness and the average inside diameter of the casing respectively.

One can now further the search for the critical parameters by finding both the initial and the striking velocity of the fragments. For the initial velocity, Vi, the value of G in Table 2-5 is used. In this equation, W is the total weight of the explosive in TNT equivalent and Wc is the total weight of the casing. For the Mk84 GP Bomb, the initial velocity of the fragment is 7760 fps (U.S. Department of the Army 1986).

−2 푊 푊 푉푖 = 퐺 × √[( ⁄ ) / (1 + ⁄ ) ] (2-11) 푊푐 2 × 푊푐

The striking velocity, Vs, is found using Equation 2-12. Wf is the design fragment weight. For the Mk 84 GP Bomb, this value is 2.25 oz (U.S. Department of the Army

1986) .Rf is the range between the initial location of the fragment and the point of interest.

푅푓 −0.004 × ⁄3 √푊푓 푉푠 = 푉푖 × 푒 (2-12)

Both velocities can also be found using Figures 2-10 and 2-11. These charts require the user to know the same parameters but ease the burden of calculating the exponential function.

The remaining parameter that needs to be computed is the depth of penetration

(Dp). TM 5-855-1 contains specific charts regarding the depth of penetration in steel and concrete. For this study, since we know that a material fill will be used in the HB, the following equation will be used.

3 2 퐷푝 = 1.975 × √푊푓 × 퐾푝 × log10(1 + 4.65 × 푉푠 ) (2-13)

In this equation, the newly introduced parameter, Kp, is a soil penetration constant. Typical values of this constant for given soil can be found in Table 2-6.

Using the values previously found, we can find the total kinetic energy of one fragment at impact by using the kinetic energy, Ek, equation found below.

1 2 퐸푘 = ⁄2 × 푀푓 × 푉푠 (2-14)

Assuming that the energy dissipates in a linear fashion as the fragment penetrates the soil and that we have a conservative system, one can find the initial striking force of the fragment by dividing the total kinetic energy by the penetration depth given by the procedure described earlier. The remaining important factor, the duration time, is found following the assumption that the velocity of the fragment also decays in a linear fashion. With the initial striking velocity and penetration depth, it is possible to use Equation 2-15 and find the time it will take the fragment to stop moving.

1 퐷푃 푡푑 = ⁄ × ⁄ 2 (2-15) 2 푉푠

Using the value of the peak striking force and the load duration time, one can now create a triangular loading function for one fragment. It is also possible to find the impulse delivered by one fragment by calculating the area under the recently created loading function.

Now that we have the loading function for one fragment, we have to account for the total amount of fragments by using Gurney’s initial parameter. One assumption that can be made is that all the fragments will hit the wall at the same time and will cause the same loading than previously found. As we used the mean fragment mass and striking velocity, this is a safe assumption to make.

2.4 Previous Experimentations and Research

2.4.1 Finite Element Analysis (FEA) and Analytical Modelling

In 2009, Dr. Kevin Scherbatiuk conducted a study in order to numerically predict the response of soil-filled walls to blast loading. He also aimed at proposing and validating an analytical model that would enable us to determine the planar behavior or a structure with given loading conditions. In order to do so, a series of experiments were conducted and the results were compared with two analytical models as well as a finite element analysis (FEA) performed using LS-Dyna, a commercially available software.

Figure 2-12 shows the response of a HB construction to far-field blast loading.

Using LS-Dyna, Dr. Scherbatiuk was able to model a series of HB construction subjected to a blast load. He modeled different wall configurations using a 37.5mm mesh size for all the different walls. The steel wiring was also modeled as connecting as pins at each node of the mesh, which is a more than reasonable representation of reality given the mesh size. The influence of the geotextile was neglected in this FE model since it has too little impact on the resistance function of the structure. Downward vertical acceleration was used to simulate gravity and different values for friction coefficient were used to properly model the interaction between the soil and the structure.

By looking at Figures 2-12 and 2-14, we can see that the dominant mode of deformation of the structure is rotation. Corner shear and compression was also observed at the location of the rotation. Small to negligible lateral displacements occurred during the simulation. These results were similar to the one observed during the physical experimentations. This type of behavior from the HB was used to define both analytical models.

The first analytical model was an energy-based approach resting on the simple rotation of the structure along an axis located the bottom corner of the wall on the opposite side of the blast. This model did not account for lateral sliding of the wall or the influence of ground shock. The pressure was assumed uniformly applied on the structure. Damping was neglected, which is a conservative approach in the case.

The second analytical model is a little more conservative and was proven to be a little more accurate. This models also only accounts for the rotation as the main response mode of the structure, but takes deformation of the base into account. This gives us a more representative approach to both reality and the outcome of the FEA model. The base shear is taken into account in this scenario, which is why the results are closer with this model than the previous one.

At the end of the experiment, It was determined that the FEA showed the best correlation with the experimental results with most results landing in a 5% difference.

The first analytical model, named Rigid-Body Rotation, was proven to undermine the actual displacement of the structure. The second analytical model was found to be a much better alternative to conduct pre-emptive calculations to predict the mode of response of a blast-loaded HB.

2.4.2 Enhancement of Response Prediction Model

In 2015, an international cooperation between the United Kingdom (UK) and

Germany led to another series of field experimentations and a report entitled

Enhancement of Hesco-Bastion Wall Models to Better Predict Magnitudes of Response

Under Far-Field Loading Conditions surfaced in 2017. This research was directed by H.

Dirlewanger and aimed at better simulating the HB behavior when loaded from far-field conditions. Using a Large Blast Simulator (LBS), which mimics blast-loading using

pressurized gas bottles, they were re-create multiple loading scenarios for different configurations of HB and other type of walls. Then, they compared the experimental results to those obtained using LS-DYNA to perform the FEA.

Upon completion of testing, they realized that the behavior varied significantly even with similar configuration and loading conditions. They later found out that two unaccounted for variables had a greater than expected influence on the wall’s response.

The presence of water in the fill would greatly diminish the shear resistance of the wall.

Therefore, the shear simulation near the assigned rotation axis underestimated the real- time shear slipping that occurred fallowing the field experimentation. To properly account for these variables, they changed some of the material properties. The second variable was that the density of the fill was not uniform. The soil at the top was not as compacted that the one at the bottom. By creating a different material model they found out that the wall would fail at a much lower impulse than previously thought but that the wall’s dominant mode of response was still the same.

2.4.3 Technical Report – Operational Munition Storage Optimization – CIPPS 2017

During the spring 2017 semester, the students of the Applied Protective

Structures Class had to complete a similar study as part as their final class project.

Their work will be used as a benchmark for this research.

In their study, the students also used HB and stored Mk 84 GP bombs inside the austere munition depot. To quantify the response of the structure, they took the peak incident pressure that the wall would feel and applied it to the entire wall. This approach will be refined in this report since the equivalent uniformly distributed load corresponding to the reflected pressure will be used to predict the structural response.

They assumed a lateral displacement of the HB fallowed by a complete overturning of

the structure. Since experimental testing have shown that the HB will crumble and not lift, this failure mechanism be refined in this study and described in Section 3-5. They were effectively able to store 32 ordonnances inside the structure. With this amount of ordonnance, they reduced the danger radius due to pressure from 400 m to 300 m when considering a simultaneous detonation of all the explosives contained in the cell.

Although reduced, the danger radius stayed the same due to the fragmentation hazard, since this treat could not be reduced under 400 m, even considering many HB configurations. Therefore, a complete mitigation of the fragmentation hazard is required to reduce the danger radius around the storage cell.

This research aims to refine the process and findings fallowing the submittal of the project as many items were unaccounted for by the student group. Calculations and assumptions taken by the students will be modified to reflect the new orientation of this project. Supplementary first and second order effects of a blast event, such as gas pressure, cratering and ground shock, will be considered in this design. Additional mitigation measures will be implemented in order to reduce the fragmentation hazard, which is something that could not be done using the previous design. Figure 2-18 shows the proposed design from this study.

2.5 Existing Directives and Guidelines

Written guidelines and regulations are to be followed when explosives are involved for both domestic and expeditionary operations. Storage of explosives ordonnances is one of the domains that is controlled in many ways by the civilian and military authorities. Safety distances, maximum net explosive quantity (NEQ) and many more topics are included in different publications. The U.S. Army Corp of Engineers and the U.S. Department of the Army and other governmental agencies keep the regulations

that relate to munition storage in publications, most of which have been used as references in this current project. Although many elements are stated in those works, many do not pertain to the present project. Here are a few of the regulations that will have to be taken into considerations in order to re-think the design of the munition depot:

• DOD 6055-09-M, Ammunition and Explosives Safety Standards: General Explosives Safety Information and Requirements.

• UFC 3-340-02, Structures to Resist the Effects of Accidental Explosions.

• UFC 4-420-01, Ammunition and Explosives Storage Magazines.

2.5.1 Current Available Designs

Expeditionary storage of munitions is regulated differently than in-country storage. The chosen design highly depends on how permanent the installation needs to be. The layout and construction of the magazine will also vary in function of the available resources as well as the ordonnances to be stored. The most basic arrangement that can be currently done, according to NATO guidelines, is the use of a massive soil berm on three sides of the munition storage (NATO Standardization Office

2010). This rudimentary arrangement, shown in Figure 2-18, requires a decent amount of material, but for which procurement can be easily done. Other than heavy equipment, which is normally integral to the deployed units, no other building materials are necessary making this layout an easy solution for deployed units. The distance D in the fallowing graph represents the distance between the ammunition stacks and the Q represents the NEW, in kg of TNT, of the biggest amount of explosives.

On the other specter of available designs, structures made of reinforced concrete

(RC) are favored when it comes to a more permanent storage solution. The U.S.

Department of Defense Explosives Safety Board (DDESB), in partnership with the U.S.

Army Corps of Engineers and the National Institute of Building Sciences, developed a series of engineering drawings and design guidelines for standard barricades. The drawings cover most existing barricades that are applicable for different configurations.

These are available for permanent or non-permanent storage of a small amount of munitions (U.S. Army Corps of Engineers 2011). A few in-between storage options, such as ARAMCO walls, can be also used in different circumstances. These last storage solutions require an extensive amount of resources and cannot be easily implemented in an operational theater where the logistical aspect becomes too much of a burden.

2.5.2 Safety Distances

STANAG 4440 provides various Quantity-Distance (QD) limits that are applicable to different installations throughout NATO operations. Depending on the design of the magazine, the type and the amount of explosives, the safety distances varies. The safety distance is important because it will dictate how much of a footprint the magazine needs in order to be implemented and operate in a safe area. Two distinct elements are to be accounted for in predicting the safety distance: the blast overpressure and the fragments. Currently, the minimum safety distance is 400 m, or 1315 ft, according to the

NATO standards (NATO Standardization Office 2015) and 381 m, or 1250 ft, according to the US DoD (U.S. Army Corps of Engineers 2015).

2.5.2.1 Pressure effect on the human body

The most important reason why maintaining a safety distance is critical is to mitigate the negative effects on the human body. Blast pressure, as well as fragments, can cause serious injuries and even death to humans if exposed to a certain threshold.

UFC 3-340-02 includes guidelines and pressure-impulse diagrams that related the expected damage to the body exposed to specific loading scenarios pressure.

Ultimately, one should design for pressures lower than 2.3 psi according to the

Department of Defense. For fragments, exposure should be avoided. In order to keep the conservative approach, a critical pressure value of 2 psi will be used for this project.

Table 2-7 includes the different peak pressure values that correspond to significant injuries that a human would suffer if exposed. For fragments, the design standard is to ensure that the trajectory of a conservatively chosen fragment will not

2.5.2.2 Fragment effect on the human body

For fragments, the design standard is to ensure that the trajectory of a conservatively chosen fragment will not travel at a distance exceeding the safety distance. This approach could be used to account for the fill being projected by the loading of the roof. Recommendations regarding this matter are included in Chapter 5 of this study.

2.5.3 Serviceability Limits

To properly operate in an austere environment, the final design will have to include some mitigation measures. This will enable it to suit multiple operational theater environments. Resisting the elements is critical in order to allow soldiers to use the structure without constrains. Water management will be a major issue that will need to be addressed. The use of proper soil as a subgrade, fill and roof will also be a matter of interest. More details regarding construction guidelines and requirements are discussed at the end of the fourth chapter.

2.5.3.1 Operational Requirements

The proposed design will have to allow maneuverability of personnel and equipment. Inside the depot, enough clearing has to be available to allow free movement of a forklift and a ground guide. Since the Mk 84 Bomb is not the only ordonnance used on a regular basis by the armed forces, sympathetic detonation calculations should be performed for other explosives potentially stored in adjacent cells using the same configuration.

2.5.3.2 Environment Suitability

Few environmental concerns have to be taken into account in the design of the structure, rain being the main issue. The subgrade soil, or foundation, of the structure must be able to sustain the weight of the depot construction. This subgrade must not significantly deform. The fill to be used must allow drainage of the rainwater. In order to let the mater flow on the roof of the structure, it is recommended that silt and clay-free small rocks or gravel are to be used to fill the roof. All other remaining fill should be chosen wisely and clay content should be reduced to a minimum. This meaning that the using an earthy, clay or organic filled soil should be avoided. To account for those different type of soils, calculations will be performed using different values for density, porosity and friction coefficients for both wet and dry conditions. Doing this will enable the deployed units to use more than one fill material for their magazine design. Medium sand, fine gravel as well as coarse gravel fallowing specifications will be used in the calculations to validate the proposed design. The wet density was calculated by adding the unit weight of water per cubic centimeter as per the porosity percentage to account for a 100% saturated soil. To obtain the friction coefficient, the tangent of the critical angle of repose was done.

2.6 Software

2.6.1 Conventional Weapon Effects Simulation (ConWep)

ConWep (Hyde 1992) is a software that enables the user to obtain specific parameters regarding a blast event. Primarily, it is meant to be used by engineers in the validation or design or hardened facilities. Using a large munition database included in the software, one can choose an existing ordonnance of interest or can also create his own. This software performs precise calculations fallowing the equations and the charts enclosed in the U.S. Department of the Army TM 5-855-1 publication.

Using this platform, one can obtain the critical parameters for air blast, ground shock, fragment or projectile penetration as well as cratering. All the particulars, such as but not limited to the distance from target or the soil type, are considered into these calculations. More specifically, ConWep will be used to obtain data regarding the cratering, ground shock, fragment penetration as well as pressure counter in this study.

This valuable data can then be used to create a specific loading function. By performing a dynamic analysis, the designer can validate if the selected design will meet the chosen criteria’s.

2.6.2 FRANG

FRANG is a software developed by the Naval Civil Engineering Laboratory

(NCEL) in 1989. Since then, the organization has been renamed the Engineering and

Expeditionary Warfare Center (EXWC). Its purpose is to calculate the specific parameters linked to the gas pressure generated by an internal explosion. Using the explosive weight, the total volume and the venting area the program will calculate the peak gas pressure and impulse due to the confinement. This program can also account for frangible panels such as door or windows.

In this study, FRANG will be used to create the loading function coming from the gas pressure due to the internal detonation of the ordonnances stored inside the cell.

2.6.3 SHOCK

SHOCK, which was also developed by EXWC in 1990, is a computer program that calculates the important parameters regarding the overpressure from an internal explosion. Unlike ConWep, this software accounts for the reflected pressure from all the adjacent structural elements, making the output more relevant in the case of an internal explosion.

To obtain these parameters, the program creates a grid of over 1000 points on the blast surface and then performs calculations. This method, which follow the step presented in the UFC 3-340-02, enables the reader to obtain the pressure relevant to a portion of or the entire blast surface. This software will be used in this study to obtain the shock wave parameters using the internal dimensions of our storage units.

2.7 Summary

Even though blast loading is considered abnormal, there are still many ways available to represent the entire phenomenon and predict the structural response.

Taking into account all elements surrounding an explosion and turning it into a usable loading scenario can seem complex, but can be done with a conservative approach.

The approach taken in this study will be discussed in more details in the following chapter.

Table 2-1. HESCO Bastion Sizes Chart (HESCO® Group 2016) Unit Number Volume (ft3) Height (ft, in) Width (ft, in) Depth (ft, in) 1 55.125 4’ 6’’ 3’ 6’’ 3’ 6’’ 2 8 2’ 2’ 2’ 3 34.328 3’ 3’’ 3’ 3’’ 3’ 3’’ 4 Cell size is multiple layers of another available size. 5 Cell size is multiple layers of another available size. 6 22 5’ 6’’ 2’ 2’ 7 355.25 7’ 3’’ 7’ 7’ 8 72 4’ 6’’ 4’ 4’ 9 20.313 3’ 3’’ 2’ 6’’ 2’ 6’’ 10 181.25 7’ 3’’ 5’ 5’ 11 4 4’ 1’ 1’ 12 85.75 7’ 3’ 6’’ 3’ 6’’ 19 110.25 9’ 3’ 6’’ 3’ 6’’

Table 2-2. TNT Equivalency Factors for Common Explosives (Krauthammer, 2008) Explosive TNT Equivalency Factor ANFO 0.82 Comp A-3 1.09 Comp B 1.11 Comp C-4 1.36 PETN 1.27 Tritonal 1.07

Table 2-3. Energy Fluence for Common Explosives (Cooper and Kurowski 1996) Explosive Critical Energy Fluence (cal/cm3) TNT 1.09 Comp B 1.11 Pentolite 1.27

Table 2-4. Soils Properties for Ground Shock Calculations (Krauthammer 2008) Soil Type Seismic Velocity Acoustic Impedance Att. Coefficient “c” (ft/s) “ρc” (psi*s/ft) “n” Loose Sands and Gravel 600 12 3 - 3.25 Dry Sands 1000 22 2.75 Dense Sands 1600 44 2.5 Wet Sandy Clay 1800 48 2.5 Saturated Sandy Clay 5000 130 2.25 - 2.5 Heavy Saturated Clay >5000 150 - 180 1.5

Table 2-5. Explosive Constants for Common Explosives (U.S. Department of the Army 1986) Explosive Bx G (Oz1/2 / in7/6) (103 fps) TNT 0.3 7.6 Comp A-3 0.22 Not Available Comp B 0.22 8.8 Comp C-4 Not Available 8.3 Pentolite 0.25 8.1 Tritonal 0.3 7.6

Table 2-6. Soil Penetration Constants for Typical Soils (U.S. Department of the Army 1986) Soil Type Kp (in / oz1/3) Limestone 0.775 Sandy Soil 5.29 Soil with Vegetation 6.95 Clay Soil 10.6

Table 2-7. Pressure Induced Damages to Human Body (U.S. Department of the Army 2008) Severity Short-term Maximum Long-term Maximum Effective Pressure (psi) Effective Pressure (psi) Eardrum Rupture Threshold 5 2 50 percent 15 5 Lung Damage Threshold 30-40 10-15 50 percent 80 and above 30 and above Lethality Threshold 100-120 30-40 50 percent 130-180 45-60 Near 100 percent 200-250 65-85

Table 2-8. Soil Properties (Obrzurd and Truty 2018) Dry Unit Weight Porosity Wet Unit Weight Modulus Soil Type (lbf/ft3) (%) (lbf/ft3) (ksi) Medium Sand 105 39 130 20 Fine Gravel 110 34 131.5 22 Coarse Gravel 120 28 138 18

Table 2-9. Soil Friction Properties (Obrzurd and Truty 2018) Soil Type Angle of Repose (°) Friction Coefficient Medium Sand 35 0.7 Fine Gravel 45 1 Coarse Gravel 30 0.57

Figure 2-1. Mk 84 General Purpose Bomb

Figure 2-2. Different Stages of HB Construction. A) Staked packages, B) Deployment of units, C) Fill by an excavator and D) Final Construction (HESCO® Group 2016)

Figure 2-3. Surface Burst Shock Representation (U.S. Department of the Army 1986)

Figure 2-4. Pressure vs. Time Representation (U.S. Department of the Army 1986)

Figure 2-5. Pressure vs. Distance representation (U.S. Department of the Army 1986)

Figure 2-6. Pressure vs. Time idealization (U.S. Department of the Army 1986)

Figure 2-7. Shock Wave Parameters for Hemispherical TNT Burst (U.S. Department of the Army 1986)

Figure 2-8. Ground Shock Coupling Factor (U.S. Department of the Army 1986)

Figure 2-9. Crater Dimensions for Cased and Uncased Explosives (U.S. Department of the Army 1986)

Figure 2-10. Initial Velocity Graphical Representation (U.S. Department of the Army 1986)

Figure 2-11. Striking Velocity Graphical Representation (U.S. Department of the Army 1986)

Figure 2-12. HB after Experimental Testing (Scherbatiuk 2009)

Figure 2-13. HESCO Bastion FE Model (Scherbatiuk 2009)

Figure 2-14. Deformed Shape of HB (Scherbatiuk 2009)

Figure 2-15. LBS System (Dirlewanger et al. 2017)

Figure 2-16. Experimental Setup Drawing (Dirlewanger et al. 2017)

Figure 2-17. Numerical Simulation Results. A) Original Fill Model and B) Revised Fill Model (Dirlewanger et al. 2017)

Figure 2-18. Proposed HB and Munition Layout (CIPPS 2016)

Figure 2-19. Section Cut of Soil Berm (Ornai et al. 2018)

CHAPTER 3 METHODOLOGY

3.1 Introduction

In this coming section, the guidelines and steps that will be taken to design an optimized storage facility using soil-filled walls will be presented. Although some experimentations on the soil-filled walls behavior under blast loading have been done in the past, there are no exact mathematical solutions enabling us to predict the exact behavior of the structure. Even if such a solution existed, there would be too many uncontrollable variables that would come in play who would greatly affect the outcome of the structural response. Therefore, a conservative approach to the design of the munition storage must be followed throughout all stages of this design.

3.2 Initial Configuration

The general shape of the storage facility will not be changed from the one stated in the different publications. The “U” shape will still be used in this design. Instead of using soil berms, who require lots of soil and occupy a large area, the structure will be designed using HESCO Barriers. This way, the storage solution should be more practical and economical. This will enable the different military organizations to save precious time, money and resources while being deployed on operations worldwide.

The inside shape will be re-arranged to prevent shrapnel from escaping the storage unit. A middle wall will be added to the HB layout. Although this structure will not be accounted for in the structural analysis, it will play a critical role in the fragment hazard mitigation as well as a support for the roofing system.

Multiple barrier configurations will be considered to find the most suitable structure. By changing the number of units, we can change the height and the width of

our structure, therefore the mass, while conserving the prescribed shape. This will be done in order to meet our validation design criteria’s such as the maximum displacement and fragment penetration. The suggested shape must allow freedom of maneuver inside the storage facility but must also be conservative in order to occupy the smallest footprint possible.

Different amount of ordonnances will be considered into the design while keeping in mind that storing too little explosive would be a waste of time and storing a lot would require a tremendous amount of resources to contain the destructive potential of such an explosive weight. The amount of explosive that can be stored in a single cell will be evaluated by using the total amount of explosive and detonating it at the same time.

Both the effects of the blast pressure and the fragmentation will be used to predict the behavior of the structure.

3.3 Layout Validation

The different layout options, regarding the thickness of HB to use, will then be compared in order to select the most efficient configuration of HESCOs as a function of the amount of explosive. Many criteria’s will have to be met for the design to be deemed acceptable.

3.3.1 Cratering

Using ConWep, it is possible to find the shape and dimensions of the crater that will be created after the explosion. Given the charge weight and the type of soil as inputs, the software will perform the proper calculations and give back the cratering depth and true radius. With this information, we can assure that the chosen charge weight will not cause cratering under the closest unit of HESCO. Different types of soil will be considered to find a reasonable distance at which the wall must be located from

the stack of explosives. The obtained value will be assessed in order to confirm that units can maneuver efficiently in-and-out of the depot.

As mentioned previously, if the crater reaches underneath the structure, a void will be created. An important part of the foundation will then be missing, causing an inevitable instability of our structure. The newly created void will also allow overpressure to penetrate and exert an uplifting force on our structure. An uplifting force is to be avoided in our case since it will reduce the friction between the ground surface and the bottom of our structure also potentially allowing our structure to further displace horizontally. The behavior of an HESCO wall under a strong uplifting force being unknown to us, it would be non-conservative to not set our boundaries to avoid cratering to occur. Therefore, the HB has to be located outside of the predicted crater caused by the explosion of the munition stored inside the magazine.

3.3.2 Sympathetic Detonation

Sympathetic detonation of the secondary explosives stored in adjacent cells must be prevented to avoid a destructive chain reaction. In order to do so, the critical energy fluence, which is the amount of energy required to cause the detonation, will be calculated for a few of the most probable explosive that could be stored in adjacent cells. Calculations will be done using the fallowing the procedure described in Sub-

Section 2.3.1.3. The obtained value will then be compared to the values previously presented in Table 2-3.

3.3.2.1 Air blast induced pressure

Overpressure reaching the adjacent stack of explosives could cause detonation.

The first thing that will be done is to find the distance at which the adjacent stack of explosive will be stored for the different configurations. Then, we can use different

software’s and formulas to find the overpressure at this distance. Even though the magazine will have a roof, the structure will not be pressure-tight and will leak at the top of the wall located between both magazines. The shortest path for the blast to travel to the adjacent cell will be a straight line to the top of the wall, then across and down towards the munition stack.

By entering the amount of explosive as an input in the air blast calculation tool of

ConWep, we can find what will be the blast overpressure at the distance of interest. Our design will meet the overpressure criteria of the sympathetic detonation validation only when the value will be under the critical energy fluence value found in Table 2-3.

3.3.2.2 Ground shock

Upon detonation, a pressure wave will also travel through the soil to reach the stack of munition stored in the adjacent cell. Using ConWep, we can find the value of the peak ground pressure as it reaches the stack of explosives stored in the adjacent cell. By using different explosive weight, type of soil and distances as inputs, we can obtain various values of pressure that can then be compared to the critical pressure values to confirm that sympathetic detonation will not occur. The outcome of these calculations will enable us to confirm that our chosen explosive weight and configuration will not cause detonation and will finalize the verifications pertaining to the sympathetic design criteria.

3.4 Load Function

Defining a proper loading function for our wall is critical to be able to predict displacements and behavior of the HB. The load function, in this scenario, will be a combination of the effects of the shock overpressure, the gas pressure and the energy transferred by the fragments upon impact. The effect of the ground shock will be

assessed afterwards as it will affect the structure differently than the three previous blast-related elements.

3.4.1 Air Blast Load Function

The different air blast-induced parameters will be computed using SHOCK. With this software, it is possible to obtain the parameters required to create an equivalent uniformly distributed load (UDL) on a wall exposed to a blast in an internal explosion such as in this study case. By providing the proper inputs, we will get the values of the peak reflected overpressure and the specific impulse for each structural element of interest. The time of arrival of the peak pressure wave will be found using ConWep since this software have more integrated outputs. All the impulse will be deemed as occurring in the first positive portion of the blast loading. With these, we can then create a triangular load function with known start and end times. The distance dictated by the cratering criteria will determine the initial separation between the stack of explosive and the wall.

3.4.2 Gas Pressure Loading Function

When we have the detonation of the explosive, the gas that is released from the chemical reaction will be confined to the volume of the munition storage. This confinement effect will cause an increase of pressure due to the gas being trapped inside the depot.

Using FRANG, we will be able to find the values of the peak equivalent gas pressure as well as the equivalent impulse. With those values, one can create a triangular loading function and apply it at any given point of the structure. The assumption that the peak pressure due to the gas will occur at the same time as the one due to the shock will be made.

3.4.3 Fragment Load Function

As mentioned in Sub-Section 2.3.2.3.2, the approach that will be taken to create the fragment loading function will be based on multiple sources leading to a calculation involving the conservation of the energy in the system. Gurney’s approach will be used to find the number of fragments coming from a single Mk 84 using it’s physical properties and explosive content.

Using this approach while assuming an equal lateral distribution of the fragment upon explosion, we can find the total number of fragments that will hit the sidewall and the roof, therefore creating a loading function that could simulate a uniform loading by fragments. Even though the fragments will hit on an angle, their force vectors will be assumed lateral as an added safety factor.

3.4.4 Ground Shock Effect

Once the detonation occurs a shockwave will propagate through the soil and reach the target of interest. The direct distance between the center of the wall and the centroid of the stack of explosives will be used to find compute the scaled ground distance. Different type of soils will be used to obtain different ground shock parameters. The worst-case scenario will be used to create the combined loading function and ultimately compute the structural response for each of the elements.

The effect of ground shock will be assessed as a base excitation of the structure.

The structural properties will remain unchanged for this assessment. Using the outputs from ConWep, we will be able to find the maximum acceleration of the center of mass caused by the ground motion after analysis. By using the structural properties of the wall as well as the outputs of ConWep regarding the peak acceleration, one can find the maximum displacement of the structure.

The wall will be assessed as a lumped mass concentrated at its centroid wall. The particular mass and moment if inertia will depend on the specific configuration.. The soils modulus of elasticity that will be used will be 20000psi which corresponds to a medium-compacted mix of sand and gravel containing a minimum amount of silts. The modulus will be modified using an area ratio method to include the effect of the steel and membrane. The specific stiffness will be taken as being the one pertaining to a pinned-pinned beam to account for the proper support condition. The stiffness will be calculated using Equation 3-1 below. (Budynas and Nisbett 2011)

48 × 퐸 × 퐼 퐾 = ⁄퐿3 (3-1)

The mass of the liner and the steel mesh will be neglected to maintain the conservative approach

3.4.5 Combined Effects

To impose a realistic loading scenario on the HB, all three of the recently created triangular loading functions at their respective time of arrival will be considered. The response of each structural element to their specific loading function will be computed using the procedure specified in the following section. As mentioned, the effect of ground shock will be assessed separately. The effects of both the triangular loads and the base excitation due to the ground shock will be added and then compared to out boundary limits to confirm the conformity of our design to our displacement criteria.

3.5 Soil-Filled Wall Response

To find the response vectors of the HB, a dynamic analysis will be performed.

The mass of the soil will be lumped into a single point mass therefore enabling a single degree of freedom (SDOF) approach. The Newmark-Beta method will be used to find

the displacement, velocity and acceleration at given times for the HB. To resist these loads, the friction of the wall with the foundation, the support conditions as well as the inertial effects of the mass will be considered. The wall will be modeled as a double-pin supported beam. The large mass of soil present on each side of the exposed span will refrain the supports from moving significantly. The connection of the span portion of the beam will not be connected in any particular way other than the regular HB construction method therefore not creating a fixed connection on either side.

3.5.1 Lower Bound Criteria

Once the SDOF analysis is performed, one can find the final displacement of the wall. As shown by the previous studies in Section 2.4, uniform lateral displacement is not the first mode of response for HB under blast loading. Therefore, a comprehensive approach towards the calculated value of the lateral displacement is critical to define the acceptance criteria. As found in previously conducted far-field blast loading experiments

(Dirlewanger et al. 2017), a HB cell will deform and crumble before significantly moving laterally. In fact, a hinge forms on the lower opposite corner of the blast surface. This was found to be the primary mode of response in both FEA analysis and field experimentations. From these results, it was also found that crumbling of the structure will most likely occur when the center of mass crosses the rotation axis, meaning that the displacement of the structure at the location of its center of mass will be half of the blast surface depth which is the direction that is normal to the plane being loaded. This last will serve as the lower bound for the displacement analysis of our structure. If the obtained value of our displacement is smaller than this value, our design will be considered has having too much mass and not being optimal.

3.5.2 Upper Bound Limit

The ultimate goal is that we do not want the HB to touch the adjacent explosive and potentially cause the detonation of the explosives that could be stored in those cells. Since the behavior of the HB is unknown under close-range explosions such as our case, it is possible that horizontal translation coupled with crumbling occurs as a primary structural response. To cope with this unknown factor, the maximum allowed displacement for our structure will be the distance between the initial location of the back of the wall and the first stack of explosives. This distance will be dictated by the cratering criteria. Displacement greater than this value will result in either the total weight or the stiffness of the structural element being too small, meaning that the cross- sectional dimensions of our structural elements must be reviewed.

3.6 Safety Distance Calculations

Determining the final safety distance is done in order to prove that the new design will provide a more efficient way of storing Mk 84 bombs in an austere environment.

3.6.1 Blast Overpressure Safety Distance

The determination of the safety distance for blast overpressure will be done using the values of the UFC 3-340-02 regarding the damage to the human body. To establish the specific safety distance, values of the peak overpressure for specific distances, as described in Section 2.5.2.1, will be compared to the values of Table 2-7. In a conservative approach, the pressure values associated with long-term exposure are to be used. Therefore, a threshold of 2 psi will be the upper limit at which the pressure value will be deemed safe for humans. ConWep will be used to find the value of the peak overpressure at a given distance from the munition depot.

3.6.2 Fragmentation Safety Distance

As mentioned before, the safety distance for the fragments cannot be reduced to an acceptable value with only the U-shape design. The only option that is left is to catch all the fragments with the structure itself. To achieve this goal, a roof and a front wall will be added to the magazine. As mentioned, the penetration depth of the fragments will be calculated using ConWep. Since the density of the material could vary depending on the type of fill being used, different materials will be used as inputs. In order to make the fragmentation mitigation method effective, the fragments must not perforate the full depth of the structural element. The penetration depth will be calculated for all surfaces exposed to the blast, since the speed at which the fragments will hit the wall will vary for each sides and the roof. This way, the blast overpressure will be the driving factor for the safety distance to be respected in order to ensure the safety of the personnel.

CHAPTER 4 RESULTS AND DISCUSSIONS

4.1 Introduction

This chapter contains the results to calculations and discussions regarding the conformity to the multiple acceptance criteria. This chapter also includes details regarding the measures to include in the design to implement the proposed expedient munition storage solution in various environments.

4.2 Initial Dimensions

4.2.1 Previous Work

The technical paper that was produced by CIPPS in 2016 was used as a stepping stone for this design. They established that a HB configuration with a depth of

20 ft and a height of 14.5 ft would suffice to prevent the adjacent stack of explosive to be hit by the wall using 32 Mk 84 bombs. This means that their design would have met our upper boundary condition for acceptance regarding the displacement. The fact that they did not model the wall the same way as it is done in this study enables us to look at smaller configurations for the wall while using the same quantity of explosives.

4.2.2 Cratering Dimensions

ConWep was used to compute the crater caused by the detonation of a single

Mk 84 bomb at ground level. Different types of soil were used as inputs to find a range of values for the crater diameter. The bigger crater occurred while using wet sandy clay as a base soil. Although the storage facility should not be built on such soil, taking this into account for the cratering radii stays within the conservative approach of this design.

Figure 4-1 shows the output of ConWep using one surface laid Mk 84 detonating using wet sandy clay. Table 4-1 contains the outputs for all the potential types of soils.

With these previous values, one can see that the maximum diameter for the crater is 34.6 ft. For safety precaution, a value a 20 ft will be chosen as a standoff between the explosive ordonnances and the external walls of the storage unit. This distance value will be used to create the loading function. This distance also allows enough room inside the storage unit for maneuverability of the Light Capability Rough

Terrain Forklift (LCRTF), which has a width of 78 inches and a length of 225 inches including the forks. This forklift, a military variant of the JCB’s 900-Serie, has a 14 ft turning radius (JCB inc. 2014). This dimension will be also taken into consideration when designing the access to the storage facility.

4.3 Design Values

4.3.1 Structural Characteristics and Geometrical Analysis

Four different configurations will be evaluated for their potential use. The first ones will both be using 32 units of Mk 84 bombs. This configuration will then be housing a total of 30240 lbs of Tritonal or, in TNT equivalency, 38240 lbs. Configuration A will have a blast-surface depth of 15 ft and a height of 14.5 ft. Configuration B will see the depth reduced by 5 ft. The two other configurations that will be analyzed will see a reduced quantity of explosives. 24 ordonnances will be stored in the depot for

Configurations C and D. These two last configurations will then contain 22680 lbs of

Tritonal or 28680 lbs of TNT. The first of the two, Configuration C, will have a blast- surface depth of 15-ft. The last configuration will have this value reduced to 10-ft.

Top views of all four of these configurations are presented in Figure 4-2. All four of these configurations will include a 5 ft wide middle wall that will serve as a support to reduce the span of the roof beams. This middle beam will be taken into account when finding the gas pressure values, but will not provide any additional protection or safety

to the design. These configurations also have a 15 ft long overhang to from that middle wall on each side to prevent the fragments from exiting by the entrance of the depot. All units for the walls are Mil 10. Dimensions for this specific unit can be found in Table 2-1.

When applying the crater radii of 17.5 ft to these configurations, we can visually confirm that the crater will not interfere with the side wall which is our primary structural element of interest in this study. Figures 4-3 and 4-4 show a top view of Configuration A and D with an overlay of the potential cratering dimension caused by the detonation of each of the explosives inside. When drawn, a 20 ft standoff distance was used between the wall and the edge of the explosives stored inside.

4.3.2 Sympathetic Detonation

Calculations were performed to confirm that these explosive weights and configurations would not cause detonation of potential secondary explosives that could be stored in adjacent cells. For these calculations, the ground shock and the shock overpressure were both considered as potential initiators of sympathetic detonation.

The blast parameters needed to perform the calculations were acquired with the

ConWep with regards to the ones pertaining to the ground shock and with SHOCK for the ones related to the shock overpressure. Table 4-2 contains these outputs of these analysis. It is important to mention that the straight distance was used for the ground shock and the distance going above the wall in a straight line then across the wall and then downwards directly to the stack was used for the shock overpressure. It was also confirmed that none of the loading scenarios would overlap. This means that both physical phenomenon’s do not occur at the same time for a given geometry.

Calculations were performed using the method presented in Sub-Section 2.3.1.3.

The worst scenario was found to be with Configuration B. Figure 4-5 is a graphical representation of the worst-case loading scenario for the adjacent stack of munition.

The outcome of these calculations showed explosives stored in adjacent cells would not detonate. Therefore, our criteria regarding sympathetic detonation is met since a chain reaction would not occur. Although the Pentolite, mostly used in detonators, did not detonate, it should not be stored with secondary explosives according to current explosive safety regulations for expedient storage solutions.

Calculations performed for the design criteria are presented in Annex A. Table 4-3 shows the results of the calculations that were performed for three commonly found explosives.

4.3.3 Shock Overpressure Loading

Using SHOCK, the pressure values for the side wall and the roof were computed for the different configurations. The total amount of explosives and the span length being different, the important values regarding the shock pressures will vary. Table 4-4 shows the parameters that were used to create the loading functions for the shock, gas and fragmentation. Table 4-5 contains the output values of the various SHOCK software runs that were used to create the triangular loading function.

Using these parameters, one can create a triangular loading function for the side wall and the roof given a specific configuration. Graphical representations of the loading scenarios due to the shock overpressure and combined effects for each configuration are presented in Sub-Section 4.3.6.

4.3.4 Gas Pressure Load

The containment caused by the addition of a roof to the structure will cause the gas pressure to exert pressure on each structural element. Using the procedure mentioned in Sub-Section 3.4.2 and the geometry elements stated in Table 4-6, one can find the loading parameters regarding the gas pressure loading for the side wall and the roof. Table 4-7 contains the output parameters from FRANG that will be used to create the gas pressure triangular loading scenario.

Using these parameters, one can create a triangular loading function for the side wall and the roof given a specific configuration. Graphical representations of the loading scenarios due to the gas pressure and combined effects for each configuration are presented in Sub-Section 4.3.6.

4.3.5 Fragmentation Load

The first parameter that is to be found is the fragments penetration depth given a distance and barrier type. For the side wall, only the soil was considered as a resistance to penetration. For the roof, a 0.25 in thick mild steel plate was added to the barrier as a first layer. Table 4-8 contains the relevant parameters regarding the penetration depth calculations that were done using ConWep. Two different types of soil, which are a sandy soil and a soil with vegetation, were considered during this analysis. For this part of the analysis, the penetration on a given element will not be depending on the configuration as only one bomb is considered, and the distance is the same for all four configurations. From these outputs, we can apply the procedure described in Sub-

Section 2.3.2.3.2. Using Gurney’s Method, it was found that a single ordonnance would produce a total of 79326 fragments. With a geometrical analysis, it was found that 10% of the fragments would hit the side wall. For the roof, this value goes up to 18.7%. This

was calculated assuming unchanged structural element properties as well as an equal lateral distribution of the fragments. The outcome of these calculations is presented in

Table 4-9. As to the different soil types, it was found that using sandy soil, which causes a shallower penetration depth, provoked a greater value to the pressure as the striking force is inversely proportional to the depth of penetration. Calculations regarding the loading scenario due to fragments are available in the Annex B of the Appendix.

Using these parameters, one can create a triangular loading function for the side wall and the roof given a specific configuration. Graphical representations of the loading scenarios due to the fragment pressure and combined effects for each configuration are presented in Sub-Section 4.3.6.

4.3.6 Combined Loading Scenario

With these three previous elements combined, four different loading scenarios can be created. A specific loading scenario will be applied to the structural elements for a given configuration. For Configurations A and B, the loading scenario will be the same for both the roof and the side walls, but the mass and moment of inertia will change when the dynamic analysis will be performed. The same goes for Configurations C and

D. Figures 4-6 through 4-9 are graphical representations of the different loading scenarios for the structural elements of interest.

4.3.7 Ground Shock

Ground Shock will be assessed differently than the rest of the second order effects of the blast. The shockwave that will travel through the ground will cause base excitation underneath the wall. Peak ground acceleration and the specific structural properties will be used to compute the maximum displacement of the wall.

Table 4-10 contains the important parameters that will be used to find the ground shock induced motion of the side wall. A complete assessment of the structural properties used for each configuration is presented in the Annex C of the Appendix. The evaluation will be done only regarding the side wall as the roof does not have a point of contact with the ground.

Using these values, the specific displacement of the centroid of the wall for each configuration was found by performing a non-linear analysis. These values are compiled in Table 4-11. Annex D of the Appendix contains the calculations leading to these displacement values.

4.4 Lateral Displacement Analysis

4.4.1 Wall Response

In addition to the displacement caused by the ground shock, we now have to account for the shock, gas and fragments effects on the structural elements of interest.

To do this, the same structural properties than for the ground shock analysis were used.

When applying the loads parameters mentioned in Tables 4-5, 4-7 and 4-9, the displacements values for in Table 4-12 were found. The calculations that lead to these numbers can be found in the Annex E of the Appendix for Configurations A and B and in the Annex F of the Appendix for configurations C and D.

As described before, these recently obtained values are to be added to the ones obtained by analyzing the effect of the ground shock on the structure. These combined values are included in Table 4-13. Their acceptance will be discussed further in Chapter

4.4.1 Roof Response

The motion of the roof was assessed following the same procedure than the wall, but the calculated displacement values were of thousands of feet for both loading scenarios. Even by doubling the weight of the wall, the displacement still exceeded a thousand feet while maintaining a positive velocity after 1000 ms while the wall reached its maximal displacement after roughly 40 ms for each of the four configurations. Motion vectors for the roof can be found in the Annex E of the Appendix for Configurations A and B and in the Annex F of the Appendix for Configurations C and D.

This leads us to think that the way the loading function was created is too conservative and the assumptions regarding the response of the roof need to be reviewed. Suggested improvements regarding these two-aspects are included in the final remarks of Chapter 5.

4.5 Pressure-Distance Safety

To find the distance at which the pressure is deemed safe for humans for both configurations ConWep will be used. The analysis was performed for all configurations.

Table 4-14 contains the results of the pressure at a given distance and Table 4-15 contains the specific distances for 2 and 2.3 psi which correspond to our chosen threshold and to the threshold according to the U.S. Army.

4.6 Construction Guidelines

To properly construct this munition depot, many elements have to be taken into account. In addition to maintaining the dimensions previously mentioned throughout this study, one should ensure the following:

• The ground capacity should be suitable for construction of this depot. Ground preparation and drainage works are to be done prior to ensure that the subsurface doesn’t come unstable.

• Clean sand or small gravel should be used in the soil-filled wall. The response of the structure will vary depending on many factors, water content and density being two of them. Silts and clays should be sieved out from the fill when access to clean filling material is limited.

• The roof should be sloped between 2 and 4 % going towards the back of the depot. This will allow drainage of the roof, therefore keeping the structural response as close as predicted before. Wet soil will also add weight to the roof, making the design less efficient. An example of proper roof grading, as well as construction steps, is shown in Figures 4-10 through 4-13. In the proposed design, bearing plates are used underneath the beams to create the slope.

• Choosing the proper roofing materials should be not underestimated. The sheeting size, such as pictured in Figure 4-11 will dictate the beam spacing. The sheet should be supported on both ends and at mid-span. Table 4-16 contains a brief summary of the applied linear UDL as a function of the beam spacing and the fill depth.

Table 4-1. Crater Diameter for Different Soils Soil Type Crater Depth (ft) Crater Diameter (ft) Dry Sand 6.8 22.8 Dry Sandy Clay 8 25.1 Wet Sand 9 28.5 Wet Sandy Clay 11.7 34.6

Table 4-2. Input Parameters for Sympathetic Calculations Parameter Shock Overpressure Ground Shock Configuration A Peak Pressure (P0) 234.9 psi 116.1 psi Impulse (I0) 796.3 psi*ms 4468 psi*ms Time of Arrival (ta) 9.65 ms 38.89 ms

Duration Time (td) 6.78 ms 76.97 ms End Time (tf) 16.43 ms 115.86 ms Configuration B Peak Pressure (P0) 271.5 psi 139.7 psi Impulse (I0) 743.7 psi*ms 4994 psi*ms Time of Arrival (ta) 8.5 ms 36.11 ms Duration Time (td) 5.48 ms 71.5 ms End Time (tf) 13.98 ms 107.61 ms Configuration C Peak Pressure (P0) 192.3 psi 91.32 psi Impulse (I0) 734.1 psi*ms 3516 psi*ms Time of Arrival (ta) 9.65 ms 38.89 ms Duration Time (td) 7.64 ms 77 ms End Time (tf) 17.29 ms 115.89 ms Configuration D Peak Pressure (P0) 223.3 psi 109.9 psi Impulse (I0) 741.8 psi*ms 3929 psi*ms Time of Arrival (ta) 8.5 ms 36.11 ms Duration Time (td) 6.64 ms 71.5 ms End Time (tf) 15.14 ms 107.61 ms

Table 4-3. Sympathetic Calculations Results Explosive Max Calculated Value Critical Value (cal/cm2) (cal/cm2) TNT Shock Overpressure 0.061 32 Ground Shock 0.378 32 Pentolite Shock Overpressure 0.073 2 Ground Shock 0.567 2 Composition B Shock Overpressure 0.057 44 Ground Shock 0.316 44

Table 4-4. Input Parameters for Shock Pressure Calculations Parameter Configurations A and B Configurations C and D (ft) (ft) Distance (Centroid – Wall) 27.5 27.5 Distance (Centroid – roof) 13.5 13.5 Wall Height 14.5 14.5 Span (Wall and Roof) 55 45

Table 4-5. Output Parameters for Shock Pressure Loading Parameter Configurations A and B Configurations C and D Side Wall Peak Pressure (P0) 8211.4 psi 7710.2 psi Impulse (I0) 32550.1 psi*ms 26269.8 psi*ms Time of Arrival (ta) 4.003 ms 4.003 ms Duration Time (td) 7.928 ms 6.814 ms Total Time (tf) 11.931 ms 10.817 ms Roof Peak Pressure (P0) 7762.5 psi 7706.2 psi Impulse (I0) 17924.6 psi*ms 15744.2 psi*ms Time of Arrival (ta) 1.186 ms 1.186 ms Duration Time (td) 4.618 ms 4.086 ms Total Time (tf) 5.804 ms 5.272 ms

Table 4-6. Input Parameters for Gas Pressure Calculations Parameter Configurations A and B Configurations C and D Explosive Weight 19 120 lbs TNT 14 140 lbs TNT Total Volume 23 443.75 ft3 19 181.25 ft3 Vented Area 342.5 ft2 322.5 ft2 Time Step 0.01 ms 0.01 ms

Table 4-7. Output Parameters for Gas Pressure Loading Parameter Configurations A and B Configurations C and D Side Wall Peak Pressure (P0) 2111.58 psi 1950.4 psi Impulse (I0) 24 909.76 psi*ms 20 194.14 psi*ms Time of Arrival (ta) 4.003 ms 4.003 ms Duration Time (td) 23.593 ms 20.708 ms Total Time (tf) 27.596 ms 24.711 ms Roof Peak Pressure (P0) 2111.58 psi 1950.4 psi Impulse (I0) 24 909.76 psi*ms 20 194.14 psi*ms Time of Arrival (ta) 1.186 ms 1.186 ms Duration Time (td) 23.593 ms 20.708 ms Total Time (tf) 24.779 ms 21.894 ms

Table 4-8. Relevant Parameters Regarding Fragment Penetration Parameter Sandy Soil Soil with Vegetation Side Wall Range to Target 20 ft 20 ft Initial Fragment Velocity 7760 fps 7760 fps Fragment Striking Velocity 7300 fps 7300 fps Penetration Depth 32.8 in 43.09 in Roof Range to Target 11.5 ft 11.5 ft Initial Fragment Velocity 7760 fps 7760 fps Fragment Striking Velocity 7492 fps 7492 fps Penetration Depth 30.15 in 39.6 in

Table 4-9. Output Parameters for Fragment Loading Parameter Configurations A and B Configurations C and D Side Wall Peak Pressure (P0) 23506.734 psi 21547.839 psi Impulse (I0) 2200.402 psi*ms 2017.035 psi*ms Time of Arrival (ta) 2.656 ms 2.656 ms Duration Time (td) 0.187 ms 0.187 ms Total Time (tf) 2.843 ms 2.843 ms Roof Peak Pressure (P0) 27339.453 psi 25061.166 psi Impulse (I0) 2260.742 psi*ms 2072.347 psi*ms Time of Arrival (ta) 1.498 ms 1.498 ms Duration Time (td) 0.165 ms 0.165 ms Total Time (tf) 1.663 ms 1.663 ms

Table 4-10. Input Parameters for Ground Shock Analysis Parameter Configuration Configuration Configuration Configuration A B C D Wall Mass (kip*ms2/in) 3253301.331 2168867.554 2661791.998 1774527.999 Stiffness (lbf/in) 3692042.074 1093938.392 6740888.889 1997300.412 Frequency (rad/ms) 0.0337 0.0225 0.0503 0.0335 Peak Acceleration (g’s) 194.7 253.3 153.2 198.6

Table 4-11. Output Displacements from Ground Shock Analysis Parameter Configuration Configuration Configuration Configuration A B C D Peak Displacement (ft) 5.52 16.158 1.946 5.677

Table 4-12. Wall Displacements from Dynamic Analysis Parameter Configuration Configuration Configuration Configuration A B C D Peak Displacement (in) 52.991 72.014 28.198 46.119

Table 4-13. Combined Wall Displacement Values Parameter Configuration Configuration Configuration Configuration A B C D Peak Displacement (ft) 9.936 22.159 4.296 9.52

Table 4-14. Pressure Values for Given Distance Distance Configurations A and B Configurations C and D (ft) (psi) (psi) 100 39.9 33.97 200 13.82 11.75 300 7.36 6.34 400 4.83 4.19 500 3.53 3.09 600 2.77 2.43 700 2.26 1.99 800 1.91 1.69 900 1.65 1.57

Table 4-15. Distance for Threshold Pressure Values Pressure Configurations A and B Configurations C and D (psi) (ft) (ft) 2 772 698 2.3 692 627

Table 4-16. Linear Weight for Roof Beam Capacity Beam Spacing 4-ft Deep Fill 6-ft Deep Fill (ft) (lbf/ft) (lbf/ft) 3 1175 1745 4 1565 2325 5 1955 2905 6 2345 3485 8 3125 4645

Figure 4-1. Crater Dimensions in Wet Sandy Clay

Figure 4-2. Different Configurations of Munition Depot. A) Configuration A, B) Configuration B, C) Configuration C and D) Configuration D

Figure 4-3. Configuration A with Crater Overlay

Figure 4-4. Configuration D with Crater Overlay

Figure 4-5. Sympathetic Detonation – Worst-Case Loading Scenario

Figure 4-6. Wall Loading Scenario – Configurations A and B

Figure 4-7. Roof Loading Scenario – Configurations A and B

Figure 4-8. Wall Loading Scenario – Configurations C and D

Figure 4-9. Roof Loading Scenario – Configurations C and D

Figure 4-10. Soil-Filled Wall Layout

Figure 4-11. Beam Installation

Figure 4-12. Steel Plate Installation

Figure 4-13. Roof Installation – Complete Construction

CHAPTER 5 CONCLUSION AND RECOMMENDATIONS

5.1 Conclusion

The overall objectives of this study were to provide a refined expedient solution for temporary munition storage. This solutions had to be deployable in diverse operational environments and had to be constructible by already imbedded resources of the deployed organization. For the proposition to be deemed acceptable, the safety radius due to pressure as well as the fragments had to be reduced and sympathetic detonation of munition stored in adjacent cells had to be mitigated. In this study, four different configurations of munition depot were evaluated regarding their suitability for storage of a given quantity of Mk 84 GP Bomb. Aside these hard criteria’s, reasonable and conservative assumptions had to be made throughout the conduct of this study. At the end, the proposed solution had to also include areas of improvement to further refine the prediction models of soil-filled wall under blast loading conditions.

Cratering and Sympathetic detonation were first evaluated for all for configurations in order to create a suitable geometry for the rest of the calculations.

Afterwards, the combined effects of the fragments, shock overpressure, gas pressure and ground shock were assessed to find parameters regarding the displacement of the wall. Although all configuration met the sympathetic detonation and the cratering criteria, not all were met by the four configurations once it came to the second part of the analysis. Only Configurations A and D met the displacement criteria. The combined displacement of the ground motion and the dynamic analysis for these two configurations landed in between our displacement boundaries. Both configurations had combined displacements of 9.936 ft and 9.52 ft for Configurations A and D respectively.

With regards to the roof’s behavior fallowing the dynamic analysis, the calculated displacement was much greater than expected. It was assessed that both the assumptions and the analysis method were too conservative and led to a massive displacement value for both configurations. Changes regarding the loading function as well as the side wall and the roof have to be made. These proposed changes as well as other specific areas of improvement are explained in a more in-depth fashion in the

Sub-Section 5.2 below. None the less, Configurations A and D were then evaluated as to their potential of reducing the danger radius due to the pressure.

Upon performing the pressure-distance calculations, we were able to reduce the safety standoff using these configurations since the fragmentation hazard is now completely mitigated. For configuration A, this standoff distance was reduced to a rounded value of 775 ft or 240 m for the 2 psi threshold. For the official threshold value of 2.3 psi, the safety distance was reduced to 695 ft or 215 m. For Configuration D, this distance was reduced to a rounded value of 700 ft or 220 m for the 2 psi threshold. For the official threshold value of 2.3 psi, the safety distance was reduced to 630 ft or 195 m. This reduction enables a smaller footprint for a force beddown, which is not to be neglected on large scale operations.

There was no analysis performed regarding the cost efficiency of the proposed design solutions since no previous solutions included both steel and soil in the design.

In addition, giving a specific cost per volume for a steel section would be trivial as it depends on the local economic situation where the munition storage would be implemented.

5.2 Recommendations

Although this study was done using a rigorous conservative approach, many assumptions were made and areas of improvement were identified. To refine the findings of this study, the following elements should be considered.

• Since the behavior of soil-filled wall under close-range blast loading is unknown, field experiments should be conducted to refine the expected structural response before and passed the crumbling point.

• Direct shear was not evaluated in this study. Experiments should be done to better predict if the connections at the mid span of the wall would sustain the load and enable a structural response that resembles the one suspected in this study. To avoid this situation, the units could be staggered for every layer normal to the blast-surface.

• The modulus of elasticity used was roughly estimated. As per the experimental testing, we know that the wall will behave in a non-linear fashion. Deriving two different modulus for both elastic and inelastic regions for the wall would enable a better prediction of the structural response.

• For every applied load, the wall was assessed as intact regarding its structural properties. Other than by the damping in the wall, energy loss was not accounted for .A modified approach should be done to refine the behavior of the wall once it crumbled.

• Modelling the response of the blast-loaded roof as a lumped-mass being resisted by its own weight needs to be refined. Using such method, the displacements found were humongous and unrealistic. This comes back to the concept of deformation of the section and energy dissipation, but in another axis this time.

• The amplitude of the load due to the fragment should be reduced. The fragments dissipate a lot of their kinetic energy during penetration by friction, heat transfer and compaction of the soil. Only a slight portion of this energy transfers to the wall and induces motion in the axis of interest. Experimental testing on small scale models should be performed to find reduction factors based on both the fragments and the barrier properties. These factors could then be applied on the calculated kinetic energy of the fragments at impact to create a loading scenario that better resemble the real physical phenomenon.

• As a particular element responds to the applied load, the internal volume of the structure, the distance as well as the venting area all increase. This may affect the fragments striking velocity if they do not strike the element first. The shock and gas would also be affected. Their peak amplitude would remain the same,

but the decay would be accelerated. It is recommended that the loading function should be modified to include these varying factors.

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[18] U.S. Army Corps of Engineers. (2008). “UFC 3-340-02 Structures to Resist the Effects of Accidental Explosions.” U.S. Department of Defense, Washington, DC, USA.

[19] U.S. Army Corps of Engineers. (2015). “UFC 4-420-01 Ammunition and Explosives Storage Magazines.” U.S. Department of Defense, Washington, DC, USA.

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BIOGRAPHICAL SKETCH

Vincent Dupont is a Canadian military engineer currently studying at the

University of Florida on an international program subsidized by the Canadian

Government. He was born and raised in St-Jean-sur-Richelieu, QC. He joined the

Canadian Forces in 2006 as part of the Regular Officer Training Program (ROTP).

Having acquired a Bachelor’s Degree in Civil Engineering from the Royal Military

College of Canada (RMCC) in 2011, he afterwards served in multiple military units as an officer in the engineer branch.

He first completed a graduate diploma in International Engineering Project

Management at the École de Technologie Supérieure (ÉTS) in Montréal, QC while employed as a property manager for the Canadian Forces Garrison Longue-Pointe.

After this employment, he was selected to attend the graduate program of Structural

Engineering at the University of Florida. This present study is the culmination of his work and knowledge acquired while stationed in Gainesville, FL.

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