MANUAL OF NATO SAFETY PRINCIPLES FOR THE STORAGE OF MILITARY AMMUNITION AND EXPLOSIVES (May 2010)

AASTP-1

(Edition 1)

Section III - Airblast

2.5.2.1

Introduction

General

Airblast parameters have been thoroughly investigated in the course of data collections carried out for

weapons effects analyses. Open air and open surface detonations have been the subject of complex

experiments and scientific research providing the data basis to determine the relevant airblast loads.

Furthermore, a lot of experimental data and experiences from explosions are available covering the airblast

loads occurring after accidental explosions in ammunition storage facilities. The scientific evaluation of these

data as well will provide the necessary design basis.

Intensity, waveform and interaction of an airblast with persons, structures and equipment items are important

factors in establishing the quantity distances for ammunition and explosives, especially such of hazard division

1.1.

In case standard quantity distance tables are not applied (or cannot be applied), potential explosion sites and

exposed structures must be designed and calculated individually. Under certain circumstances, this procedure

may lead to considerable cost savings in the design of ammunition storage facilities, e.g. in terms of material

and land requirements.

Problem Description

The airblast load due to an explosion may be readily simplified for design purposes. It is characterized by a

relatively flat blast wave, whose peak overpressure and variation with time essentially are functions of distance

and charge, and the dynamic pressure variation with time. It must be noted that deviations from the model

explosion environment will change the airblast parameters.

Assumptions and Definitions

Design and calculation methods for ammunition storage facilities are mainly based on modeling and practice-

oriented assumptions.

In general, the following assumptions are introduced in order to simplify calculation of airblast loads and

reduce input data.

(1)

Charge Shape

The charge is assumed to be hemispherical and placed directly on the ground at sea level.

Note:

Other charge shapes and positions cause asymmetrical propagation of blast and, in part, considerable

deviations of blast parameters.

(-->> Ref [3], [45], [52], [53], [62], [66])

(2)

Reference Explosion

The reference explosion is taken to be the high order detonation of an exposed bare charge of TNT. In case of

explosives other than TNT or different explosion environments, the TNT equivalent mass must be

calculated using a conversion factor.

-II-5-14-

Change 3

AASTP-1

(Edition 1)

Note:

The TNT equivalent factor is not a constant value. Usually, a practicable value is used.

(-->> Table [5-2])

(-->> Ref [1], [3], [4], [55])

(3)

Blast Attenuation by Donor Structure

The attenuation due to the external walls or the earth cover can be taken into account as follows:

Proceeding from the basic assumption that a hemispherical charge explodes on the ground in

the open, an empirical attenuation factor is introduced to extrapolate a fictitious explosives

quantity inside the storage building.

The maximum permissible explosives quantity for the storage building is determined using

empirically developed and up dated regression equations for particular building types.

The airblast loads are determined using empirically developed formulations.

Note:

All methods are based on empirical data.

(-->> Ref [65], [76], [87], [88], [101], [127], [133])

(4)

Terrain and Vegetation

All assumptions relate to flat terrain without obstacles and vegetation.

Rising slops cause an increase of pressure.

Falling slopes cause a decrease of pressure.

A narrow valley with steep sides causes concentrated directional blast.

Significant vegetation, such as wood with a tree top height of more than 3.5 m, consumes

blast energy.

Properties of an Airblast Wave

An airblast wave due to an explosion consists of an incident blast wave and a dynamic blast wave.

(-->> Figure [5-1])

The incident peak overpressure is significantly higher than the dynamic peak overpressure.

For design purposes, the duration of the incident blast wave and the dynamic blast wave may be taken to be

equal although the pressure drops behind the respective shock fronts differ considerably and the dynamic

pressure normally takes longer to decrease to the ambient pressure level. The pressure drop of the incident

blast wave is much steeper.

The negative overpressure phase (suction phase) may be neglected for design purposes.

2.5.2.2

Physical Relations Between Airblast Parameters

The characteristic parameters of a blast wave with a sudden pressure discontinuity at the shock front are as

follows:

Overpressure;

Dynamic pressure

Reflected pressure;

Density;

Shock front velocity;

Particle velocity.

-II-5-15-

Change 3

AASTP-1

(Edition 1)

These parameters are derived using the Rankine-Hugoniot equations. When one of the shock front parameters of the

incident blast wave has been determined as a function of the scaled distance, the other parameters can be calculated

using the Rankine-Hugoniot equations and a simple integration procedure. The Rankine-Hugoniot equations are based

on the principles of conservation of mass, energy and momentum.

(-->> Ref [3], [72])

Restrictions:

The Rankine-Hugoniot equations are only applicable under the condition that the particle

velocity ahead of the shock front is zero ( u_o = 0 ) and that the air behaves like an ideal gas with a specific heat ratio of τ

= 1.4.

It is further assumed that there is one single shock front caused by a surface explosion of a

hemispherical shaped charge.

Rankine-Hugoniot equations

(1)

Shock front velocity U

1/2

6 · P_so

U = a_o ·

1 +

eq [5-01]

7 · P_a

(2)

Particle velocity u

5 · P_so

u =

7 · P_a

(1 + 6 · P_so/ 7 · P_a)^1/2

eq [5-02]

(3)

Air density behind the shock front rho

7 + 6P_so/P_a

Rho =

· rho_,a

7 + P_so/P

eq [5-03]

(4)

Dynamic pressure q_o

q_o = 0.5 · rho · u²

eq [5-04]

P_so2

q_o =

7 · P_a + P_so

eq [5-05]

(5)

Normally reflected pressure P_r

7 · P_a + 4 · P_so

P_r = 2 · P_so ·

7 · P_a + P_so

eq [5-06]

For an ideal gas ( τ = 1.4 ) and high shock front pressure P_so, P_r approaches the limit 8·P_so.

For air, this limit can be exceeded. For low shock front pressures, the reflection factor

approaches the value of 2.

(Detailed formulations: -->> Ref [1], [3], [102])

(6)

Pressure-Time Variations of Incident Airblast and Dynamic Pressure

The time-dependent variation of the incident (side-on) pressure P_s(t), and the dynamic pressure q(t)

may be realistically represented using the modified Friedländer equation:

(-->> Ref [3])

-II-5-16-

Change 3

AASTP-1

(Edition 1)

Ps(t) = Pso · (1 -

) · e^(-β·t/t_o)

0 ≤ t ≤ t_o

eq [5-07]

t_o

q(t) = qo · (1 -

) · e^(-β·t/t_o)

0 ≤ t ≤ t_o

eq [5-08]

(Empirical values for β are given in Table [5-3])

(7)

Positive Impulse

The decisive parameter for the damage caused by airblast is the positive overpressure impulse. It

may be determined by integration of the positive overpressure phase, i.e. it is defined by the total

area below the pressure-time curve.

General impulse equation:

i_s =

P_s(t) · dt

P_so · t_o

s =

· ( 1 -

1 - e-β

)

eq [5-09]

q_o· t_o

1 -

· (1 -

) -

· e-β

Iq =

β²

eq [5-10]

Scaling Laws

(1)

General

The conversion of airblast parameters, distances and explosive charge masses from parameters of a

known explosion environment may be accomplished using scaling laws.

(2)

Cube-Root Law

Theoretically, the relation between distance, pressure, and explosive charge mass may be expressed

by a cube-root law. Full scale tests have shown that this proportionality between distance and charge

mass applies to quantities up to the megaton range.

(3)

Scaling

Distance - Charge Mass

1/3

R_x

Q_x

eq [5-11]

R_o

Q_o

1/3

Q_x

R_x = R_o ·

Q_o

eq [5-12]

-II-5-17-

Change 3

AASTP-1

(Edition 1)

Dynamic impulse:

Time - Charge Mass:

1/3

R_x

Q_x

t_x = t_o ·

= t_o ·

R_o

Q_o

eq [5-13]

Impulse - Charge Mass:

1/3

R_x

Q_x

I_x = I_o ·

= I_o ·

R_o

eq [5-14]

Airblast parameters measure for different charge masses and at different atmospheric conditions

may be converted to standard conditions applying the Hopkinson-Cranz cube-root law and the Sachs

scaling laws. The latter is only applicable to ideal gases, i.e. it is not suited for air and high shock

front pressures.

Scale Factors …

… for Pressure P

P_a

eq [5-15]

S_P =

P_a,s

… for distance R

eq [5-16]

… for time t

eq [5-17]

… for impulse I

eq [5-18]

--> Index X_a,_s …. standard conditions at sea level

-II-5-18-

Change 3

AASTP-1

(Edition 1)

(4)

TNT equivalent

For determining the characteristic airblast parameters, it is advisable to convert the actual charge

mass to the equivalent TNT charge mass in order to make use of the various existing design

diagrams which are usually related to TNT. For design purposes, the values given in Table [5-2]

may be used.

The majority of measurements of airblast parameters so far has been carried out using pure TNT charges. For

calculations related to other explosives with or without confinement and different explosion

environments, it is advisable to use the respective TNT equivalents for these conditions. These

equivalents are individually determined with respect to pressure and impulse by means of tests or

defined using the specific detonation energy of the explosive.

E^d

exp

QTNT,e = Ň

Ň · Q

exp

E^d

TNT

eq [5-19]

Q_{TNT,e (kg)}

equivalent TNT charge mass

Q_exp (kg)

actual explosive charge mass

E^dTNT (J/kg)

specific detonation energy of TNT

E^dexp (J/kg)

specific detonation energy of the actual explosive

2.5.2.3

Determination of Characteristic Airblast Parameters for Surface Detonations

Hemispherical

Explosive Charges in the Open

Characteristic Airblast Parameters

Peak side-on overpressure

P_so

MPa

Dynamic overpressure

q_o

MPa

reflected overpressure

MPa

Scaled positive side-on impulse

i_s

MPa-ms/(kg)^1/3

Scaled positive reflected impulse

i_r

MPa-ms/(kg)^1/3

Positive airblast duration

t_o

Arrival time

t_a

Shock front velocity

m/s

Particle velocity behind shock front

m/s

Note:

The scaled parameters must be multiplied by the cube root of the TNT equivalent mass.

Design Fundamentals

(1)

Design Diagrams

For design and damage assessment purposes, the characteristic airblast parameters may be

determined from Figure

[5-2a] and

[5-2b] taking into account the assumptions previously

established. The diagrams are based on numerous tests and apply to charge masses from 1 kg up to

400 000 kg.

(-->> Ref [5])

-II-5-19-

Change 3

AASTP-1

(Edition 1)

The curves shown in Figure [5-2a] and [5-2b] may be programmed as polynomial equations on a

personal computer. The respective data are summarized in Table [5-5].

(additional information: -->> Ref [3])

(2)

Common Formulas

The formulations described in Table [5-5] are not suited to be used with pocket calculators.

Therefore, the following formulas are recommended for quick calculations

with

acceptable

accuracy.

(-->> Ref [133 revised]) …

Explosive

TNT, TNT - equivalent

Type of detonation

surface detonation

Place of detonation

in the open

Scaled distance

z = R / (Q)^1/3 (m / (kg)^1/3)

Charge mass

(kg)

Distance

(m)

Peak Side-On Overpressure P_so (MPa)

Range

Function

0.50 ≤ Z < 0.75

P_so = 1.313137 . Z^(-1.910441)

0.75 ≤ Z < 3.50

P_so = 1.330026 . Z^(-2.218832)

3.50 ≤ Z < 8.50

P_so = 0.724571 . Z^(-1.726565)

P_so = 0.293592 . Z^(-1.295654)

8.50 ≤ Z < 30.00

Scaled Side-on Impulse i_s (MPa-ms/(kg^1/3))

Range

Function

0.50 ≤ Z < 1.0

i_s =

41.2564 · Z⁵ + 144.608 · Z⁴

- 198.8880 · Z³ + 134.238 · Z²

44.3554 · Z + 5.8956

1.0 ≤ Z ≤ 30.0

i_s =

- 0.254674 · Z^(-0.918606)

Positive Pressure Duration T_o (ms)

Linear pressure waveform:

2 · I_s

T_o =

P_so

eq [5-20]

Is = is · NEQ^(1/3)

eq [5-21]

Exponential Pressure Waveform:

-->> Figure [5-2a], [5-2b]

Pressure Drop Constant β

The pressure drop constant β is determined by iteration of the following equation:

P_so · t_o

β²

I_s

β - (1 - e(-β))

eq [5-22]

-II-5-20-

Change 3

AASTP-1

(Edition 1)

2.5.2.4

Determination of Characteristic Airblast Loads due to an Explosion Event in an Ammunition

Storage Facility

Earth-Covered Aboveground Storage Buildings

(1)

General

Blast pressure and impulse are attenuated by the encasement of the potential explosion site. The

degree of pressure and impulse reduction depends on the mass of the covering or shielding material

(e.g. ammunition confinement, building encasement, earth cover) as well as the loading density. The

attenuation effect may be observed mainly in the near field close to the explosion site, whereas in

the far field the values approach and partly even exceed those for an open surface detonation of a

hemispherical shaped charge. At these large distances, however, the pressure values are already on a

comparatively low level. The attenuation effect is of particular importance for the prevention of

sympathetic detonation between ammunition storage buildings.

(2)

Attenuation Effect

Attenuation by Donor Buildings

The degree of attenuation by donor buildings must be expected to differ for the main directions of

blast (frontward, sideward and rearward) (Ref [133 (revised)], [65]). With standard earth-covered

ammunition storage buildings, the highest pressure attenuation occurs in rearward direction. Since

the front faces are usually uncovered, the near-field pressure acting in frontward direction is

normally higher than that of an open surface detonation while it is considerably lower in the far

field.

Test evaluation (Ref [65], [87], [88], [133]) have shown that for scaled distances in excess of Z ≈ 10

to 15 m/kg^^1/3 the blast pressure in sideward direction is usually higher than that in frontward

direction. In practice, this phenomenon has no considerable effect since the pressure level at these

distances is already below ≈ 0.01 MPa. The blast wave acting in rearward direction shows a

different behavior from that acting in side-ward direction. Its pressure values approach those of the

front wave; pressure equalization, however, happens at a considerably slower rate. The above

observations may be transferred to the impulse behavior.

Attenuation by Acceptor Buildings

The earth covers of ammunition storage buildings considerably reduce the airblast loads acting upon

the external parts of the structures (soil berm shielding effect). The soil pressure loading at the soil-

structure interface is significantly smaller than the loading due to a blast wave impacting directly.

Peak overpressure and reflection factors are reduced whereas the loading duration increases. Thus,

the probability of spalling at the inside surface of the walls is reduced, and the peaks of the

dynamically relevant motion parameters are flattened.

Figure [5-2g] (-->> Ref [59]) shows a comparison of the airblast wave peak overpressure normally

reflected at an external wall with the normally reflected peak pressures of various soil types at the

soil-structure interface.

(3)

Type of Construction

The individual construction of earth-covered ammunition storage buildings corresponding to an

established standard type does not significantly influence the donor-specific attenuation effect. The

decisive parameter with respect to blast attenuation in the near field is the mass to be moved which

usually consists of approximately 80-90% earth cover material.

The essential factors at to acceptor-specific attenuation are the geometry and the material of the

earth cover. Earth covers of low-density materials, such as loose sand or a loose gravel-sand

mixture, are most effective in reducing airblast loads.

-II-5-21-

Change 3

AASTP-1

(Edition 1)

(-->> Figure [5-2g])

(4)

Formulations for Characteristic Airblast Parameters

Test evaluations provided the following formulas for calculating the characteristic airblast

parameters taking into account the attenuation effect of a standard earth cover.

(-->> Ref [133] / Figure [5-2c] and [5-2e])

Side-On Peak Overpressure P_so (MPa)

eq [5-23]

Airblast

Function

Direction

Front

P_so = 0.435 ·

z(1-541)

Side

P_so = 0.301188 · z^(1.364270)

Rear

P_so = 0.300052 · z^(1.513182)

Scaled Side-On Impulse i_s(MPa-ms/ (kg^1/3))

eq [5-24]

Airblast

Function

Direction

Front

i_s = 0.263627 · z^(-1-027171)

Side

i_s = 0.191082 · z^(-0.922905)

Rear

i_s= 0.120419 · z^(-0.888696)

Calculation of the Remaining Parameters -->> eq [7-13], [-714]

Detached Uncovered Ammunition Storage Buildings

(1)

General

After an explosion event in a detached uncovered ammunition storage building as well, airblast,

peak overpressure and impulse will be considerably attenuated as compared with a free field

detonation. The attenuation, however, is not as high as with earth-covered ammunition storage

buildings since the masses to be moved are significantly smaller.

Ammunition Storage Structures Protected by Earth Mounds or Barricades - Magazines, Ammunition Stacks

(1)

General

Tests have demonstrated that earth mounds or barricades have no significant blast attenuation effect.

A load reducing effect due to interference with the airblast may only be observed in the near field

(scaled distance Z ≈ 1 m/kg^1/3). This effect, however, cannot exactly be quantified and thus should

be disregarded in the calculations. There are graphical prediction methods for estimating the blast

loads behind barricades. (-->> Ref [211])

(2)

Characteristic Airblast Parameters

For the assessment of exposed buildings in the vicinity, airblast loads similar to those of a free field

detonation should be assumed.

-II-5-22-

Change 3

AASTP-1

(Edition 1)

2.5.2.5

Airblast Loading of Exposed Sites (ES)

General / Load Model

The interaction between airblast loads and complex structures is a complicated process the treatment of which

requires a high standard of knowledge and experience. Buildings for the storage and handling of ammunition

usually are simple structures. Typical features are:

Flat or arched roof;

Closed Regular, clear contours, usually box-like shape;

construction; openings, such as windows, hatches and doors, constitute less than 5% of the total

area;

Approximately uniform strength, i.e. resistance, of all structural elements.

For practical purposes (explosions at a large distance from the structure), it may be assumed that the airblast

strikes the structure as a planar wave front and that the time-dependent pressure level is thus evenly distributed

over each surface of the structure.

In the case of a close-in detonation, this approach would be to conservative since the varying pressure levels of

the blast wave strike the various regions of the structure at different times.

In principle, the structural elements exposed to an airblast should be individually designed with respect to the

incident blast loading acting directly upon them.

Sometimes, it may be required to demonstrate the stability of a structure as a whole. In such cases, it

must be taken into consideration that - similar as with a close-in detonation - the blast acts on the

various structural elements at different times and with varying intensity.

The blast loading of a structure depends on the following characteristics:

Load parameters: -

- Pressure-time variation

-->> Reflected pressure

-->> Side-On pressure

-->> Dynamic pressure

- Positive impulse

Structure parameters

- Dimensions

- Shape

- Design

- Material strength

Orientation with respect to airblast

Determination of Relevant Load Waveforms

(Figure [5-4], [5-5] and [5-6])

(1)

General

A fully developed and largely undisturbed airblast wave is most exactly expressed by an exponential

function (Friedländer function).

(-->> Ref [3])

Triangular or bilinear blast waveforms used so far in order to simplify calculations usually provide

results which are conservative.

For structural elements with span directions perpendicular to the shock front of a blast wave, a step-

by-step analyses of the time-dependent blast loading would be required. This procedure is simplified

-II-5-23-

Change 3

AASTP-1

(Edition 1)

by the use of an equivalent load model which represents the instantaneous element loading by a

time-dependent evenly distributed loading producing the same stresses (inter-sectional forces) in the

element. Details on this subject are given in Ref [3] for instance.

The above mentioned analyses will be applied to reinforced concrete structures provided upper and

lower reinforcements extend across the entire span.

Basic equations

(1)

Symbols

(-->> List of Symbols)

Building height H_s or 0.5 · building width, whichever is the smaller value

L_w,x/L Ratio between blast wave length and span of the structural element under consideration

X Position index

Centre of element strip; relevant shock front position

(2)

Airblast Duration and Blast Wave Length

2 · I_s,x

t_of,x

eq [5-27]

P_so,x

L_w,x = U_,x · t_o,x

(approximate value)

eq [5-28]

(3)

Equivalent Load Factors and Blast Wave Position Factor

The equivalent load factors and the blast wave position factor may be derived from Figure [5-3] or

determined using the following polynomial functions ….

L_w,_x / L

C_x

0.0048 · C⁵ - 0.0584 · C⁴ + 0.2817 · C³ - 0.6963 · C² +

0.9551 · C + 0.2433

eq [5-29]

D/L

0.0098 · C⁵ - 0.1203 · C⁴ + 0.5682 · C³ - 1.3207 C² +

1.6217 · C - 0.0774

eq [5-30]

L · D/L

eq [5-31]

(4)

Determination of Characteristic Airblast Parameters

Pos

P_so,_x

Is,x

P_{r x}

I_r,x

t_a,x

t_o,x

U_,x

L_w,x

(x)

MPa

MPa-ms

MPa

MPa-ms

m/s

-II-5-24-

Change 3

AASTP-1

(Edition 1)

. . . Determination of required airblast parameters from Figure [5-2a] through [5-2f]:

P_so,2 ; I_s,2 ; U_,2 ; t_o,2

. . . Determination of L_w,2 using eq [5-28]

. . . Determination of C_E and D/L or D as functions of L_w,2/ L using Figure [5-3] or eq [5-29] through

[5-31]

. . . Determination of dynamic pressure qo,2 as a function of C_E · P_so,2 using Figure [5-2b] or eq [5-4]

and [5-5]

. . . Determination of drag coefficient C_d related to q_o,2 using Table [5-4]

. . . Calculation of peak overpressure and total impulse:

P_o = C_E · P_so,2 + C_D · q_o,2

s = 0.5 · Po · t2,eff

- Pressure waveform for t = 0 at front edge of structure:

0 ≤ t ≤ t_d

P_s(t) = P_o ·

t_d

· t_d

t_d ≤ t ≤ t_2,eff

P_s(t) = P_o ·

1 -

t_2,eff- t

Direction of Span of Relevant Element is Parallel to the Shock Front;

Considering a Loaded Element Strip

(-->> Figure [5-5])

Assumption: Uniform time-dependent pressure loading of an element strip

2 · I_s

t_of,s =

P_so,s

t_d =

U_,s

- Procedure:

. . . Determination of airblast parameters . . .

P_so,s ; I_s,s ; U_,s ; t_o,s

at position s, i.e. at the center of the element strip using Figure [5-2a] through [5-2f]

-II-5-27-

Change 3

AASTP-1

(Edition 1)

. . . Determination of dynamic pressure qo,s using Figure [5-2b] or eq [5-4] and [5-5]

. . . Determination of drag coefficient C_D related to q_o,s using Table [5-4]

. . . Determination of peak overpressure P_o:

0.5 · t_d

P_o = (P_so,s + C_D · q_o,s) ·

1 -

t_of,s

. . . Determination of total impulse I_s:

I_s = 0.5 · P_o · (0.5 · t_d + t_of,s)

Pressure waveform for t = o at front edge of element strip

0 ≤ t ≤ t_d = L_s/U_,s

P_s(t) = P_o

t_d

t - t_d

P_s(t) = (P_o ·

1 -

t_d ≤ t ≤ 0.5 · t_d + t_of,s

t_of,s - 0,5 · t_d

Rear Wall

As soon as the shock front passes the rear edge of the roof or the side walls, the blast wave expands

and produces secondary waves which propagate across the rear wall and will partly be reflected by the

ground.

An equivalent uniform time-dependent pressure load is calculated for the rear wall as well.

2 · I_s,3

t_of,3=

P_so,3

t_d

U_,2

t_3,eff = [ 2· H_s / (U_,2 + U_,3) ] + t_of,3

(rough)

t_3,eff = (t_a,3 - t_a,2) + t_of,3

(exact)

L_w,3 = U_,3 · t_of,3

(rough)

Procedure:

... Determination of required airblast parameters from Figure [5-2a] through [5-2f] ...

P_so,3 ; I_s,3 ; U_,3 ; U_,2 ; t_o,3

. . . Determination of factors C_E and D/L or D as functions of the ratio L_w,3 / H_s using eq [5-28] or

Figure [5-3]

. . . Determination of t_d

-II-5-28-

Change 3

AASTP-1

(Edition 1)

. . . Determination of dynamic pressure q_o,3 as a function of C_E · P_so,3 using Figure [5-26] or eq [5-4]

. . . Determination of drag coefficient C_D as a function of q_o,3 using Table [5-4]

. . . Determination of peak overpressure and total impulse at position -3- . . .

Peak overpressure: P_o = C_E · P_so,3 + C_D · q_o,3

Total impulse : I_s = 0.5 · P_o · (t_3,eff)

- Pressure variation for t = 0 at rear edge of structure:

0 ≤ t ≤ t_d

P_s(t) = P_o ·

t_d

t - t_d

t_d ≤ t ≤ t_3,eff

P_s(t) = (P_o ·

1 -

t_2,eff - t_d

2.5.2.6

References

Essential references -->> Section VIII

Ref

[1], [3], [4], [5], [17], [45], [52], [53], [54], [62], [65], [72], [73], [76], [77], [78], [81], [82], [83],

[84], [85], [86], [87], [88], [101], [102], [128], [133]

-II-5-29-

Change 3

AASTP-1

(Edition 1)

Section IV - Projections

- Fragments, Debris, Lobbed Ammunition -

2.5.3.1

Introduction

General

An explosion of an ammunition storage site produces the following four types of projections:

Ammunition fragments

Debris from earth cover

Structural debris

Crater ejecta

The following discussion attempts to set forth principles and guidelines which may be useful for the proper

design of shelters and layout of safe ammunition and explosives storage areas when standard quantity distance

tables cannot be applied. Effective administrative safety provisions and, in particular, structural measures

against fragment and debris hazards may permit the reduction of quantity distances, thereby lowering the costs

for the construction and maintenance of ammunition storage facilities to a considerable extent.

Problem Description

The assessment of fragment and debris hazard is for the most part based on probabilistic approaches. The

reason for this is the fact that fragmentation and debris forming is a random process occurring under physical

environmental conditions which are not exactly definable.

Proposed Solution

Ballistic and distribution parameters form the basis for the damage assessment of projections, i.e. for

establishing their hazard characteristics and hazard potentials. Ballistic parameters are initial velocity,

horizontal and vertical angles of departure as well as mass whereas distribution is determined with respect to

number and mass of projections.

The vulnerability of the respective target is related to the damaging effect of the projections in order to

determine the hazard level.

2.5.3.2

Fragments

General

An explosion event in an ammunition storage building involves a hazard from emitted fragments generated by

detonating ammunition items in the Potential Explosion Site (PES).

Fragment generation essentially takes place in two phases:

During the explosion

After the explosion event due to detonation of ammunition items being ejected from the

potential explosion site or impacting on a hard surface

With cylindrical ammunition items, most of the fragments are projected in radial direction while only

a few heavy fragments are emitted from the nose and base at a low velocity. For worst case

considerations, it is assumed that the ammunition item detonates with its longitudinal axis parallel to

the respective structural component.

-II-5-30-

Change 3

AASTP-1

(Edition 1)

The emission of direct fragments from a potential explosion site depends on the properties of the respective

structural components as well as on the time relation between fragment movement, airblast propagation, and

build-up of chamber pressure.

The decisive parameters are …

Loading density;

Arrangements of stored ammunition;

Ammunition type.

For aboveground storage of ammunition, the following hazard levels are distinguished depending on the type

of storage.

Open storage

Full fragment hazard

Ammunition storage building without earth cover

Reduced fragment hazard.

High fragment absorption by structural components.

The velocity of impeded fragments is reduced by approx. 85% (energy absorption ≈ 95%).

Locations of high fragment hazard are the front area and the doors of the ammunition storage

building.

Earth-covered ammunition storage building

Little to no fragment hazard.

Due to the inert behavior of the structure and earth cover mass, the high velocity fragments are almost

completely absorbed.

Fragment Mass Distribution

(1)

Constant

M_A = B_x · t_c5/6 · d_i1/3 · ( 1 + t_c/d_i)

(kg)^1/2

eq [5-36]

B_x (kg^1/2) / ( m^7/6)

explosive constant in accordance with Table [5-6]

t_c (m)

casing thickness

d_i (m)

inner casing diameter

(2)

Number of Fragments

Fragment mass distribution is represented in the form of the cumulative distribution of the number

of fragments N_f,individually heavier than a defined mass M_f, as a function of M_f. Such a function

may be derived directly from the results obtained by testing or determined analytically using the

Mott distribution:

eq [5-37]

Formulation according to Ref [2], [3], [4]

eq [ 5-38]

-II-5-31-

Change 3

AASTP-1

(Edition 1)

Total number of fragments:

N_t = M_c / (2 . M_A2)

eq [5-39]

Mass of nominal fragment for design purpose:

M_d = M_A2 . I_n2(1 - C_L)

for … 0.9500 ≤ C_L≤ 0.9999

for … 0.9999 ≤ C_L≤ 1.0000

Number of fragments individually heavier than M_f :

Detonating stacks of ammunition tend to produce mass distributions with a relatively higher

percentage of heavy fragments than single items detonating individually.

For practical purposes, the number of heavy fragments is the most important parameter, since they

are the most effective fragments with regard to ballistics and energy content.

A distribution of the form given above (Mott distribution), but with its main emphasis on the heavier

portion of the fragment spectrum, is useful for representing test results and defining hazard levels.

Fragment Ballistics

If the mass distribution, angles of departure and initial velocities of fragments at the point of origin are

known, trajectories, impact parameters and distribution density of the fragments can be determined.

Gravity and atmospheric drag are essential parameters affecting the trajectory, which should be taken

into account, at any rate, in order to find a safe and economical solution.

(1)

Ballistic Properties

Preformed and irregular fragments may be assumed to be geometrically similar.

Fragment mass M_f and presented area A_f are proportional and related by the shape factor k . . .

M_f = k · A_f ^3/2

eq [5-40]

This shape factor or ballistic density is determined empirically from ballistic tests and depends on

the type of ammunition.

(-->> Table [5-7])

(2)

Initial Velocity

Besides field measurements during fragmentation trials, the initial velocity of a fragment may be

estimated from the . . .

. . . Gurney formula :

-II-5-32-

Change 3

AASTP-1

(Edition 1)

V_o = G / ((M_c/_Mex) + (n/ (n+2)))^1/2

eq [5-41]

G = √(2·E)

Gurney velocity, a constant for a given explosive Values:

-->> Table [5-6]

Geometrical constant:

-->> Table [5-8]

The basis for the equation above is an analysis of the behavior of a cylindrical or spherical casing

subjected to an internal gas pressure. For projectiles, the formula may only be applied to fragments

emitted radial from the casing.

Note:

The Gurney formula is not mass-dependent and applies primarily to fragments of up to 150

g, approximately. For heavier fragments, the formula gives a conservative result, since lower initial

velocities are to be expected. The Gurney formula is adapted to different types of ammunition. Thus,

there are different Gurney constants and geometrical constants. The literature referenced below

contains details and additional formulations for the determination of initial velocities.

Ref [164 et al] -->> additional formulations:

. . Modified Gurney formula

. . Lukanow-Molitz formula

. . Swedish formula

. . Allison-Schriempf formula

. . Gabeaud formula

(3)

Angle of Departure

Fragments from individual items of ammunition normally depart radial from the casing. Depending

upon the type of ammunition, the area fragment distribution varies along the projectile axis.

For details and modeling procedures refer to the literature reference in Section VIII.

- e.g. Ref [171], [173], [174]

(4)

Trajectory

For design purposes in the far-field range (with regard to the explosion site) the influence of gravity

is essential. When designing shelters, or if the near field is concerned, the effect of gravity is

negligible and straight trajectories may be assumed.

Non-linear fragment trajectories are very important for safety-related analyses of ammunition.

(5)

Trajectory Calculation

Fragment trajectories are usually calculated with computers using numerical formulations since

closed solutions are impossible due to the complex parameters such as wind, atmospheric drag etc.

influencing the trajectory.

For this purpose, efficient programs considering the essential parameters affecting the trajectory are

available.

(-->> ref [201], [203])

Trajectory Calculation Procedures and References :

Subject Matter

References

(1)

Exterior Ballistics of Fragments

[164]

C_D Values for Irregular Fragments

(2)

Mass and Shape Distribution

[163]

Laws for Irregular Fragments

[4]

(3)

SIACCI Method

[165]

-II-5-33-

Change 3

AASTP-1

(Edition 1)

(4)

Primary and Secondary Fragments

[211], [4]

(5)

Fragmentation

[211], [1]

(6)

Fragment Protection

[3]

(6)

Trajectory Velocity

For the practically relevant range, the fragment velocity as a function of distance can be estimated from the

exponential function below, assuming a constant drag coefficient and disregarding gravity.

The C_D-value can be obtained from Figure [5-7] or Table [5-9] :

V_(R)= V_o. e^(-R/L)

eq [5-42]

2 · (k² · M_f)^(1/3)

L =

eq [5-43]

(C_D · rho)

(7)

Impact Velocity

The impact velocity varies between the near-field limits (low-angles of departure) according to eq

[5-44] and the far-field limits (long fragment distance) according to eq [5-45], with the latter

physically representing the terminal velocity in free fall.

- Conservative formulas for the estimation:

. . . near field:

V_i = V_o · e^(-(Re/L))

(m/s)

eq [5-44]

. . . far field:

(m/s)

eq [5-45]

- According to Ref [1], [3] . . .

V_i = V_o · e^(-(0.004·Re·/M_f(1/3))

(m/s)

eq [5-46]

(8)

Impact Angle

The fragment impact angle depends upon the departure parameters and other external conditions

(wind, air density, fragment parameters etc.).

For design purposes, normal impact, i.e. a_i = 90^o, is to be assumed.

(9)

Impact Energy/Impact Impulse

Impact energy and impact impulse, respectively, are decisive parameters for the assessment of

fragment hazard levels.

The fragment mass M_f and the impact velocity V_i are essential parameters.

M_f · V_i2

Impact energy: E_kin = E_i =

(J)

eq [5-47]

Impact impulse: I_i

= M_f . V_i

(Ns)

eq [5-48]

-II-5-34-

Change 3

AASTP-1

(Edition 1)

(10)

Fragment Number Density

The probability of fragments striking a target (ES) at a given position is determined by the area

density of flux of fragments, through the target area projected on a plane normal to the fragment

trajectory at impact. When gravity effects are considered, numerical calculation techniques must be

utilized even if simplifying assumptions have to be made regarding atmospheric drag and the mass

distribution of the fragments. If gravity is ignored, however, the fragment flux with respect to

distance follows an inverse-square law.

Assuming:

The Mott fragment mass distribution;

Fragment masses greater than the defined mass M_f ;

A target area normal to the fragment trajectory at a distance R.

The area density q_f of fragments is given by:

Q_o

q_f =

e^{(-(2Mf/Mo)1/2)}

(Number / m²)

eq [5-49]

R²

Determination of Q_o on the basis of the individual fragment distribution curves for ammunition or

according to

-->> Ref [1], [3], [4]

In this approximation, consideration of the influence of gravity refers to its effect on impact velocity

but not to the terminal phase of the trajectory.

The effective value of Q_o

, Q_o,eff depends upon the prevailing storage conditions. The effective

value for fragments from a stack of ammunition is estimated by multiplying the value for a single

ammunition item by the effective number of items N_E.

Q_o,eff

= Q_o · N_E

eq [5-50]

For a stack in the open, N_E is derived from:

N_E = 0.9 · N_s + 0.1 · N_T

eq [5-51]

For a stack in an earth-covered magazine N_E is:

N_E = 0.7 · N_s + 0.1 · N_T

eq [5-52]

Where

N_E

Effective number of items of ammunition

N_s

Number of items of ammunition on the side of the stack facing the

potential target

N_T

Number of items of ammunition in the top layer of the stack.

Hazard Potential

(1)

Probability of Impact

The probability of impact P_f of an individual fragment or a fragment flux is calculated using the

area density q_f .

The impact process is assumed to be uniformly random in the vicinity of the target point, so that

fragment impact is equally probable on all equal area elements in the vicinity of the point. The

-II-5-35-

Change 3

AASTP-1

(Edition 1)

probability of impact P_f of one or more fragments of a mass Mf or greater on a given target area is

thus given by:

P_f = 1 - e^(-qf·AT)

eq [5-53]

q_f

(Number/m²)

with eq [5-49]

A_T (m²)

target area

For a standing man, e.g., facing the explosion:

. . . A_T ≈ 0.56 m²

(2)

Hazard Criteria / Hazard Levels

Fragment hazard levels for a given target are determined using the essential parameters below:

Fragment density at the target or hit probability of the individual fragment or the fragment

flux;

Impact energy - kinetic energy - of the individual fragment:

E_kin = E_i = (M_f · V_i2) / 2

(Nm)

eq [5-54]

Impact impulse of the individual fragment:

I_i

= M_f · V_i

(Ns)

eq [5-55]

Vulnerability / destructibility criteria of the target in question.

(3)

Injury Criteria / Casualty Criteria

A variety of functions of impact velocity and fragment mass have been proposed as injury criteria.

NATO-wide, a lethal fragment is defined as a fragment with a kinetic energy exceeding the critical

value of 79 Joules. This limit applies to fragment masses ranging from a few grams to several

kilograms. In most cases, severe injuries will be caused.

Further details -->> Section VII

Fragment Calculation Procedure

(1)

Calculation of the initial fragment velocity

using the . . .

GURNEY-Constant

Table [5-6]

GURNEY-Formula

eq [5-41]

with n = 2 for cylindrical projectiles

(2)

Calculation of the number of fragments

. . . per unit solid angle based on the number of fragments Q_o or Q_o,eff emitted from an item of

ammunition or ammunition stack in the direction of interest. This is usually the direction

perpendicular to the ammunition axes.

-II-5-36-

Change 3

AASTP-1

(Edition 1)

(3)

Determination of the average fragment mass M_o

using . . .

Available data bases;

The average mass M_o of an individual item of ammunition, obtained by fitting a Mott

distribution to data from a single item, emphasizing the heavier fragments within the mass spectrum.

In order to account for the greater ballistic and energetic effectiveness of fragments from stacks of

ammunition, a shape factor k = 4.74 g/cm³ will be assumed.

(4)

Determination of the mass M_f of the lightest hazardous fragment

Reaching a specified distance R using a parameter for the critical kinetic energy of a hazardous

fragment.

Formulation 1:

The terminal energy of a fragment of mass M_f in free fall is less than the

critical energy.

E_cr

M_f = 2 ·

(kg)

eq [5-56]

V_i2

V_i = V_o · e^{(-R / L)}

(m/s)

2 · k^(2/3)

L =

· M_f(1/3)

(m)

C_D · rho

Formulation 2:

The terminal energy of a fragment of mass M_f in free fall is greater than

the critical energy.

3/4

(kg)

eq [5-57]

2 · E_cr

M_f

g · L₁

Notes:

- Whichever gives the smaller value of M_f will be used.

- For E_cr = 79 Joules and k = 4.74 g/cm∧3 the transition occurs at Mf = 0.1 kg, approximately.

(5)

Calculation of the area fragment density

For fragments heavier than M_f and distance R in accordance with eq [5-49].

Alternatively, the distance R at which the critical density q_cr

(1/56 m²) for hazardous fragments is

exceeded will be determined iterative using eq [5-49], [5-56] and [5-57].

Note:

The result is the larger of the two values of R so obtained.

(6)

Determination of the injury probability

The determination of the injury probability p at distance R from eq [5-53].

For small values of qf , the following approximation applies:

p ≈ q · A_T

eq [5-58]

-II-5-37-

Change 3

AASTP-1

(Edition 1)

Notes:

The procedure above can be adapted for use with an injury criterion other than impact

energy.

Ballistic terminal parameters from other calculations may of course be introduced.

(7)

Stacks Effects

There are strong indications that the fragmentation characteristics of stacks of ammunition differ

significantly from those of a single detonating item.

Detonating stacks emit a higher number of larger or heavier fragments.

This effect is influenced by the charge-to-metal (casing) ratio. Ammunition with small values of this

ratio (e.g. artillery projectiles) generally produce fragments of greater individual mass.

The initial fragment velocities for stacks of ammunition have been observed to be almost

twice as high as for fragments from single items of ammunition.

In the case of mass detonations, only the items of ammunition on the sides and top of a

rectangular stack appear to contribute to the far-field area density of hazardous fragments.

2.5.3.3

Debris and Crater Ejecta

Structural Debris

(1)

General

An accidental explosion in an ammunition storage facility produces an impulsive peak overpressure leading to

the shattering of or heavy damage to the structure. The resulting structural debris generally come

from walls, foundation, bottom slab, ceiling, piers, screens, and fixtures.

The subsequent 'quasi-static' internal pressure ruptures the building and vents through newly

created or existing openings. Shattered structural components and other objects located on or within

the building are accelerated by the releasing overpressure and projected from the explosion site.

Main debris distribution is approximately normal to or at an acute angle to the original building

walls or main axes.

These debris constitute a substantial hazard to objects and personnel in the vicinity.

The size of the structural debris depends upon the . . .

. . . Construction of the building,

. . . Material of the building and the strength of the material,

. . . Type of ammunition,

. . . Loading density.

Small structural debris are to be expected in the case of . . .

. . . Increasing loading density,

. . . Brittle material,

. . . Low-strength material,

. . . Thin-walled structural component,

. . . A small percentage of reinforcement,

. . . Pre-damaging due to fragment impact.

Larger structural debris are to be expected in case of . . .

-II-5-38-

Change 3

AASTP-1

(Edition 1)

. . . A solid, heavy construction,

. . . Strong reinforcement,

. . . Tough material,

. . . Low loading density,

. . . A blast effect alone.

(2)

Debris Mass Density

Detached Ammunition Storage Building

The debris/fragment departure from a detached ammunition storage building depends on several

parameters, i.e . . .

. . . Loading density,

. . . Type of ammunition/casing factor,

. . . Geometry and strength of the building,

. . . Direction of debris departure with regard to the building.

In Ref [76] the debris mass density is given by the following equation . . .

(-0.29)

rho_,deb = 0.36 · M_a · ^(0.58) · e^{(-0..047·R·Q} ⁾

(kg / m²)

eq [5-59]

all masses are in tons (to) = 1,000 kg

R (m)

distance from the building center

f₁

-->> Figure [5-8]

V_i (m³)

internal volume of building

Q (to)

NEQ_TNT (to)

M_a . . . Total mass of ejecta

Ma = Mo + Mg + Mm

(to)

M_g . . . Mass of building

Mg = f1 . Vi

(to)

M_o . . . Ejected earth mass of apparent crater

Mo ≈ 100 · NEQTNT

(to)

M_m

… mass of ejected ammunition components in (to)

Estimates:

M_m ≈ 0.0

mines and high explosive

M_m ≈ 0.25 · V_i

cased ammunition

Earth-Covered Ammunition Storage Building

In addition to the parameters decisive for the debris projection from detached ammunition storage

buildings, in this case also the type, geometry and mass of the earth cover are of importance

(-->> Ref [75]) …

rho_,deb = 0.036 · M_a · e^(-0.015·R) )

(kg / m²)

eq [5-60]

-II-5-39-

Change 3

AASTP-1

(Edition 1)

all masses are in tons (to) = 1,000 kg

R (m)

distance from the building center

f₁

-->> fig/[5-8]

V_i (m³)

internal volume of building

M_a . . . Total mass of ejecta

Ma = Mo + Mg + Mm

(to)

M_g . . . Mass of building

Mg = f1 · Vi

(to)

M_o . . . Ejected earth mass of apparent crater and earth cover (standard) empirical

hypothesis:

mass of standard earth cover ≈ 4 to 5 · M_g

Mo ≈ 100 · NEQTNT + 4 · Mg

(to)

M_m . . . mass of ejected ammunition components (to)

Estimates:

M_m ≈ 0.00

mines and high explosive

M_m ≈ 0.25 · V_i

cased ammunition

(3)

Ballistics

Because of the high complexity of the event, it is very difficult to reliably determine the ballistic

parameters of structural debris or crater ejecta resulting from an accidental explosion. There are not

as many fundamental and other basic data available as is the case for fragments.

The departure parameters - velocity, angle, and mass - may vary substantially with the explosion

environment. The engineer de-signing potentially exposed sites must, under these conditions,

normally rely on threshold functions.

Velocity of Departure

The velocity of departure is dependent upon the loading density, the type of explosive, the structural

strength, and the point of departure of the debris.

The full scale tests described, e.g., in Ref [86], [106], where fragments and debris have been

thoroughly recorded and evaluated, confirm the above statements. Normally, fragments are

accelerated more effectively than building debris or crater ejecta because of the higher loading

density.

Depending upon the structure of the building and the loading density, more or less massive

structural debris nevertheless can achieve velocities of departure of up to V_o = 1,000 m/s.

Since their mass is generally greater than that of fragments, they must be considered to have a higher

energetic effectiveness in the far field.

Angle of Departure

Generally, structural debris will depart at an angle normal to the structure surface. Vertical and

horizontal angles of departure vary from approximately ±10^o to ±20^o. Depending upon the loading

-II-5-40-

Change 3

AASTP-1

(Edition 1)

density and the structural design of the building at intersections and junctions of components, angles

of departure of up to approximately 30^o from the normal may occur due to angular moments at the

time of departure.

(-->> Ref [155], [157], [200], [211])

(4)

Hazard / Damage Predictions

The hazard level with respect to personnel or material depends upon the local situation and the

predominant type of load. Debris impact density and impact energy constitute essential hazard

parameters.

Detailed Hazard Data -->> Section VII

Inside inhabited buildings situated at the required quantity distance to the explosion site, the hazard

to persons is mainly due to secondary debris formed in the close vicinity by the air-blast. The limit

pressure currently specified for inhabited buildings is approximately 5 kPa.

(-->> Section VII).

This overpressure causes minor structural damage such as glass breakage, cracks in plaster, and

damage to the exterior wall lining.

Debris from Earth Covers and Crater Ejecta

(1)

General

Soil and rock material being ejected from the explosion crater is defined as "crater ejecta". In the

case of accidental explosions involving only individual ammunition components or small quantities

of explosives, the load case "crater ejecta" generally constitutes a minor potential hazard as

compared to the other effects such as airblast, fragments, structural debris and shock.

In the case of surface bursts of larger quantities of explosives, however, a substantial debris hazard

has to be assumed, and the load case "crater ejecta" has to be taken into account in the safety-related

assessment of ammunition facilities and their surroundings.

The cover material of earth-covered ammunition storage facilities produces additional ejecta. With

standard installations, this covering material should consist of fine-grain particles with a relatively

small mass. Projection distance and impact energy of this material are generally less than that of

structural debris.

(2)

Mass Density

In Ref [31], the mass density of the crater ejecta for an open surface burst is given by the following

mean relationship. .

rho_,ej = 27 · NEQ_TNT1.4 · R^(-3.6)

(kg / m²)

eq [5-61]

NEQ (kg) ; R (m)

(3)

Ballistics

The ballistic performance of crater ejecta is similar to that of structural debris.

Formulations for ballistic parameters of crater ejecta have been examined and developed.

-->> Ref [31], [32], [33], [76], [77].

-II-5-41-

Change 3

AASTP-1

(Edition 1)

Ejecta Range

In the case of explosions on the surface of or inside cohesive soil, the total mass of ejecta is to be

found within the following range . . .

R_ej ≈ 30 · R_a

eq [5-62]

The maximum projection distances of crater ejecta are determined by an NEQ^0.4 - law and depend

upon the type of soil . . .

. . . for rock

R_ej,max = 30 m/kg ^0.4

. . . for soil

R_ej,max = 12 m/kg ^0.4

(4)

Hazard Area (estimated)

Explosions on the surface of or inside cohesive soil or rock lead to longer ejecta distances.

The data from Table [5-10] may be used as estimates for these cases.

(5)

Hazard Criteria

The hazard from ejecta (crater, earth cover) is due to their kinetic energy (impact force) upon impact

and due to their penetration or punching capability. This primarily affects weaker structural

components such as roofs, ceilings and large walls of relatively low thickness.

Whereas less solid ejecta material (gravel, sand, clayey sand, clay, etc.) crumbles upon impact or is

subjected to heavy deformations, solid, practically undeformable material (e.g. rock, broken stone,

gravel) has a hazardous penetration and punching capability.

Penetration by "Undeformable" Ejecta

"Quasi-undeformable" ejecta transfer high, short shock impulses to the target material exposing it

to risk of punching or perforation.

The penetration capability of high-strength rock (basalt, granite) as compared to soft rock (friable

standstone, slate) may be assumed to be 7 to 1 .

Figure [5-9] shows the penetration of mild steel plate by hard rock ejecta.

Figure [5-10] shows estimates of the perforation threshold of non reinforced concrete slabs for the

impact of hard rock ejecta.

The diagrams are based on the conservative assumption of an impact of "undeformable" ejecta in a

realistic velocity range.

Hazard thresholds for persons and material -->> Section VII

(6)

Load Assumptions for Structural Component Design

Undeformable Crater Ejecta

The design of structural components assuming dynamic loads can be facilitated in the case of solid

ejecta using the "impulse formulation".

(-->> Ref [7 (2.3 and 5.5)], [3])

Shock Impulse:

I = M_ej · V_i

(Ns) eq [5-63]

-II-5-42-

Change 3

AASTP-1

(Edition 1)

I²

yel

Maximum Deformation:

y_m =

(m) eq [5-64]

2 · M_str · R_m

Deformable Crater Ejecta

Moist, cohesive ejecta is deformed upon impact and acts as solid ejecta with a lower peak impulse,

but a longer effective duration.

Building damages are caused less due to punching than to local bending failures.

A simplified structural component design assuming a dynamic load can be carried out with the

following formulations . . .

V_f

1_d

≈

1.12 · (M_ej / rho) ^1/3

(m)

V_m

(V_i + V_f) / 2

(m/s)

Mean shock impulse:

I_m = M_ej· V_m

(Ns)

Deformation assumption (empirical) : x_pl = 2/3 · 1_d

(m)

Shock period:

x_pl

2 · l_d

t_d=

V_m

2 · v_m

Load:

. . . Peak load for triangular load history:

2 · l_dm

F_max=

(N)

t_d

. . . Peak load for constant load history:

I_m

F_d=

(N)

t_d

Figure [5-10] shows estimates for the maximum shock loads of long distance ejecta.

(-->> Ref [1])

Dynamic Strength Increase

The short-time loading of protective structures - ammunition storage magazines, aircraft shelters,

etc. - involves an increase in strength of the loaded material as a function of loading rate.

For the load cases described, the "Dynamic Increase Factor" (DIF) should be selected from the

values given in Table [5-11] and Ref [1], [4] respectively.

-II-5-43-

Change 3

MANUAL OF NATO SAFETY PRINCIPLES FOR THE STORAGE OF MILITARY AMMUNITION AND EXPLOSIVES (May 2010) - page 10