2018 Scienceline Publication

Journal of Civil Engineering and Urbanism

Volume 8, Issue 2: 17-24; Mar 25, 2018

ISSN-2252-0430

Reduction of Damage of Buried Ammunition Depots

in the Ground by Crumb Rubber Cement against

Explosion Force

Mehdi Mirzaee¹, Mostafa Vaezi², Saeid Mamandi and Omid Abdolrahman



¹Faculty of Engineering, Tarbiat Modares University, Tehran, Iran

²Department of Maritime Engineering, Amir Kabir University, Tehran, Iran

³Faculty of Engineering, Islamic Azad University, Mahabad Branch, Iran

^Corresponding author’s Email: mvaezi7067eng@aut.ac.ir

ABSTRACT: Nowadays, due to the development of missiles with high power of destruction and accuracy as well as

the increase in terrorist attacks, it is better to keep military equipment in the depth of the ground. Using the

underground structures (US) has been interested in shelters and ammunition depots for many years. But these

structures should also be resistant to surface explosions. For this purpose, the structure must be constructed at high

depths or the structure protected by the specific coating. The aim of this study was introduced and evaluates the

performance of a combined coating containing crumb rubber cement (CRC) to prevent the transmission of

compression waves. Hence, to check the effectiveness of this coating by modeling a buried structure in ANSYS LS-

DYNA at a depth of 5 meters from the ground surface and placing crumb rubber cement CRC at a depth of 2 meters

from the ground surface and above the structure, the model was subjected to an explosion equivalent to 100 kilograms

of TNT was analyzed for 25 milliseconds. The results showed that by inserting crumb rubber cement CRC, because of

high elasticity with large deformations of crumb rubber (CR), adding it into concrete can absorb energy and reduce its

transfer to the Layers down, and therefore lead to a reduction in the amount of failure and pressure which applies to

the structure. To investigating the effect of the thickness of the CR layer, the pressure, and failure rate of the structure

was analyzed for 0.1, 0.2, 0.3, 0.4, 0.5 m thickness layers. The results indicated that by increasing the thickness of the

CR from 0.1 m to 0.5 m, the pressure and failure rate is reduced. But the intensity of this decrease of 0.4 meters later

is very low so that it can be ignored. It is concluded that, CR with a thickness of 0.4m with concrete cover can be

considered as a recommended optimal design and an applicable strategy in the construction of buried structures on the

ground against the explosion forces.

Keywords: Ammunition depots, Crumb rubber, Concrete cover, Explosion, TNT

INTRODUCTION

Various structures ranging from coastal structures to

damage caused by land, air, and naval attacks is a

fundamental issue that broadly covers all key infras-

tructures, vital and important military and civilian centers

in the country (Amir et al., 2017 ).

buried concrete depots, as one of the strategic structures,

play a significant role in the military and economic

purposes of a country, which should be given special

attention to their reinforcement. Accordingly, the opti-

mum design of structures such as coastal structures,

concrete structures have been among the main concerns of

many researchers (Pourzangbar et al., 2016, 2017a,

2017b; Pourzangbar, 2012; Yeganeh-Bakhtiary et al.,

2015; Vaezi et al., 2016a, b ).

Passive defense is one of the most effective and

stable defense against threats has always been the focus of

most countries in the world. These structures should also

be resistant to surface explosions. Therefore, it is

important to identify and investigate the parameters that

affect the performance of these structures and increase the

safety of these structures (Feldgun et al., 2011 ). A lot of

research has been carried out on this subject, that in the

below some of them being mentioned. Feldgun et al.

(2011) presented a comprehensive approach to simulating

Conducting passive defense measures in today's

wars to confront enemy invasions and mitigate the

To cite this paper: Mirzaee M, Vaezi M and Mamandi S and Abdolrahman O (2018). Reduction of Damage of Buried Ammunition Depots in the Ground by Crumb Rubber

Cement against Explosion Force. J. Civil Eng. Urban., 8 (2): 17-24. www.ojceu.ir

the distribution of explosive pressure on a flexible or hard

flat barrier in porous soils. Yang and Wang (2006)

investigated the effect of air blast on surface structures

with regard to Shock in the soil. In this research, he also

used the LS-DAYNA finite element software and

modeled the soil into a three-phase mode equation. Lu and

Wang (2006) presented a model for nonlinear dynamical

analysis of explosion and distribution of pressure of it in

the soil. They have modeled by using non-linear analysis

of LS-DYNA software and an appropriate state equation

and behavioral model for materials, soil, explosives, and

structures in an environment. Naghizadeh et al. (2010)

performed numerical modeling of the effect of the surface

explosion on buried structures. They also used a model

similar to the model provided by Lu and Wang for

modeling of geometry. Gholizadeh and Rajabi (2013) in

addition to studied the effects of surface and subsurface

blast on buried structures and their modeling, they have

also predicted strategies for improving the safety of these

structures and their efficiency.

As a result of the explosion, the gas pressure is

formed, which increases with the release of the explosion

source and increases to a maximum positive PSO+

pressure, and then decreases to an ambient pressure

Which this phase is called positive phase. As a result of

the wave propagation, the gases produced by the

explosion are cooled down and pressures are slightly less

than atmospheric pressure. Because of this pressure

difference, it is reversed to the center of the explosion.

The result will be a reduction in pressure or suction which

is called a negative phase. The negative phase suction is

relatively small and gradual so that it is often neglected to

design explosion-resistant structures. The maximum

pressure from the explosion )PSO+( significantly

decreases when it is away from the explosion center

(Corresponding to the third power to the explosion

center), but contrary to that, the loading period (the time

of the load caused by the explosion on the structure)

increases with the increasing distance from the explosion

center (Figure 1) (UFC, 2008 ).

In this study, to prevent the transmission of pressure

waves from the explosion through the soil, and

consequently, to reduce the damage of buried ammunition

depots, a special cover CRC is evaluated. The reason for

using this coating is the high elasticity of the rubber in

absorption and damping the energy of surface explosions.

We will study first the modeling of the LS-DYNA finite

element software, and then introduce the geometric shape

of the model and finally, the results of the research are

discussed.

The TNT element was used to model the explosion

by using the Jones-Wilkins-Lee (JWL) equation. This

model is widely used that in which the pressure caused by

the explosion is defined by (Eq. 1) (Wang et al., 2005 ).



(R

)

(R

)

w



P  A  (1 

)  e

 B  (1 

)  e



(1)

R 



1 0

In which A, B, R1, R2, and w are the material

constants. Parameters of ₀and are the initial density

and the product density of the explosion process

respectively. The initial ratio of the is considered



MATERIAL AND METHODS

 ₀

equal to one. The parameter of Emo is the Primary energy.

The parameters of (Eq. 1) are given in (Table 1) (Wang et

al., 2005 ).

Numerical modeling in LS-DYNA software

In this study, the LS-DYNA software was used to

model, analyze and evaluate the results. This software

uses the finite element method. In this study, the structure

and surrounding soil are modeled in 2-D. In the following,

the equations of the states and the properties of the

materials used to model the soil, structure, air and

explosion phenomenon will be investigated, and then the

geometric of the model with dimensions of modeling is

presented. In the end, the results will be examined.

Explosion

The explosion is characterized by the sudden and

rapid release of sound a large amount of energy,

producing light, heat, sound, and wave at speeds around

the speed of sound (Ngo et al., 2007 ).

When an explosion occurs, the energy is released

suddenly in a very short time (several milliseconds), and

the effect of this energy release is seen in the form of

thermal radiation and the propagation of compressive

waves in space.

Figure 1. Diagram of pressure-time wave explosion

Table 1. Parameters related to JWL

Energy/vol

(KJ/m3)

6e6

pressure

(MPa)

2.1e4

Em0

(KJ)

Parameter

Value

(m/s)

6930

3.681e6

Parameter

Value

(MPa)

3.737e5

(MPa)

3.747e3

4.15

0.9 0.35

To cite this paper: Mirzaee M, Vaezi M and Mamandi S and AbdolrahmanO(2018). Reduction of Damage of Buried Ammunition Depots in the Ground by Crumb Rubber Cement

against Explosion Force. J. Civil Eng. Urban., 8 (2): 17-24. www.ojceu.ir

is calibrated based on the explosion loading rate and its

results have been tested and approved by the TM5-855-1

and laboratory results (Leong et al., 2007 ). Also, MO

Granular and Failure model were used to consider the

soil-resistance behavior and the failure model. The

parameters of the equation of state and resistance behavior

are given in Tables 2 and 3.

Soil

The soil used in this study is sandy clay (10% sand)

that surrounds the structured environment. For modeling

the soil against the explosive load it is necessary to

consider its state equation. In this study, based on

Fiserova's research (Fiserova 2005-2006 ), a compaction

state equation for Sandy clay has been used. This equation

Table 2. Parameters of the dense state equation -linear

Density parameter )g/cm³(



Value

1.674

1.740

1.847

1.997

2.144

2.25

2.38

2.485

2.585

2.6713

Pressure parameter (MPa)

Value

4.577

14.98

29.1

59.1

98.1

179.4

290

450.2

650.7

Density parameter )g/cm³(

Value



1.674

1.746

2.086

2.15

2.3

2.57

2.598

2.635

2.641

2.8

Sound speed (m/s)

Value

265.2

852.1

1721.7

1875.5

2264.8

2956

3112

4600

4634

Table 3. Parameters of strength model - MO Granular

Pressure parameter (MPa)

Value



3.4

101.3

184

500

Yield stress (MPa)

Value



_{Y 3}

44.6



Y 2

Y 4

Y 5

Y 6

Y 7

Y 8

Y 9

Y10

4.23

124

226

Density parameter (g/cm3)

Value



1.674

1.74

2.086

2.15

2.3

2.57

2.598

2.635

G₈

2.641

2.8

Shear modulus (MPa)

Value

76.9

869

4030

4900

7770

14.8e3

16.5e3

36.7e3

37.3e3

equation is suitable for explicit dynamic analysis and

provides accurate behavior of materials in high stresses.

The RHT model is an advanced model for plastic material

behavior that is designed for brittle materials by Riddle et

al (1999). This model is especially useful for modeling

concrete with dynamic loading. This model is also

suitable for modeling brittle materials such as rocks and

ceramics. The strength model uses three strength surfaces

(Figure 2) an elastic limit surface, a failure surface and the

remaining strength surface for the crushed material.

Usually, there is a cap on the elastic strength surface.

Wave propagation in the soil

The propagation of the waves caused by the

explosion in the soil in two forms: the volumetric

(pressure) and the surface wave (Riley), which the most

destructive of these is the pressure wave for a buried

structure close to the explosion site. The propagation of

this wave in continuous and free environments can be

calculated by (Eq. 2, Eq. 3) (Lu et al. 2005 ):

n

2.52R

u  160 f (

)

(2)

 .C.u

(3)

Where f_cis the coefficient of connection between the

ground and explosive, w is the explosive mass to Kg, R is

the distance from the explosion to meter, C is the velocity

of the explosion wave in meters per second, P pressure in

soil to kg / m2,



is the density Soil to kg/m3and n is the

soil parameters that can be calculated from TM5-855-1

(Wang et al. 2005 ).

Concrete

For concrete modeling, the P-alpha equation

(Herrmann, 1969 ) and RHT resistance model are used to

describe the deviation results of concrete. The P-alpha

Figure 2. Three strength surfaces for concrete (Lu et al.,

2005)

To cite this paper: Mirzaee M, Vaezi M and Mamandi S and AbdolrahmanO(2018). Reduction of Damage of Buried Ammunition Depots in the Ground by Crumb Rubber Cement

against Explosion Force. J. Civil Eng. Urban., 8 (2): 17-24. www.ojceu.ir

 ^m_fⁱⁿ

Following the hardening phase, additional plastic

straining of the material leads to damage and strength

reduction. Damage is accumulated by (Eq. 4, Eq. 5).

Where D1 and D2 are damage constants,

is the

minimum strain to reach failure,  _pland p* is the

p_spall p^*( f_tf_c)

pressure normalized by f_c, and

where f_t



D  

(4)

(5)

failure

and f_care tensile and compressive strength, respectively.



Tables 4 and 5 shows the parameters used for the P-Alpha

equation and the RHT resistance model Respectively:

failure

spall

min



 D (p  p

)

 

Table 4. Parameters of the state equation- P-Alpha

Porous dens

(g/cm3)

Ref. dens

(g/cm3)

2.75

Porous sound speed

Init. Com. pr.

Sol. Com. Pr.

(KPa)

Parameter

(m/s)

(KPa)

Value

2.314

2.92e3

23.3e3

6e6

B1,B2

Parameter

Value

MPa

904e4

35.27e3

39.58e3

1.22

Table 5. Parameters of strength model - RHT

Shear modul.

ft/fc

fs/fc

Parameter

(Mpa)

16.7e3

(Mpa)

0.1

1.6

Value

0.18

Gelas/Gplas

Parameter

Value

Brit. To Duc. Trans.

0.0105

Elas. Stre./ft

0.7

0.61

0.68

Parameter

Elas. Stre./fc

Com. Stre. Exp

Tens. Stre. Exp.

Value

0.53

1.6

0.61

0.032

0.036



Parameter

f ,min

Value

0.04

0.01

state equations for ideal gases, which has been used in

many applications that include gas movement. This

equation is defined as (Eq. 7).

Reinforcement steel bar

The steel 1006, with a linear equation and the

Johnson-Cook resistance model, were used with regard to

the failure due to the strain of the plastic (Autodyn help,

2005 ). The Johnson-Cook model is a rate dependent,

elastic-plastic model. The model defines the yield stress Y

by (Eq. 6) (Autodyn help, 2005 ).

P  ( 1).e

Where

(7)





and

Are adiabatic exponent,

density and special air temperature. The parameters of

(Eq.7) are given in Table 7.

(6)

Y  [Y  B. ][1  C log  ][1  T

]

Table 6. Linear Equation and Johnson-Cook Resistance

Model

 _p

Where Y₀is the initial yield strength,

is the

Shear

yield

Yield

Stre.

Hard. Hard.

Stra.Rat.

Cons.

^*_p

Cons

Exp.

effective plastic strain,

is the normalized effective

Parameter

(Mpa)

plastic strain rate, B,C,n, m are material constants. T_His

homologous temperature, T_H (T T_room) (T_meltT_room

Value

81.7e3

350

275

0.36

0.022

)

Ref. Stra.

Rat.

Ultimate Plastic Strain

Parameter

with T_meltbeing the melting temperature and T_roomthe

ambient temperature. The parameters of the linear

equation and the reinforcing resistance model are given in

(Table 6).

Value

0.2

Table 7. Parameters of the ideal gas state equation



Atmosphere

Ref. Dens.

(g/cm³)

Ref. Temp.

Parameter

Value

Ideal gas state equation was used to model the air

around the model. This equation is one of the simplest

(K)

1.4

1.225e-3

288.2

To cite this paper: Mirzaee M, Vaezi M and Mamandi S and AbdolrahmanO(2018). Reduction of Damage of Buried Ammunition Depots in the Ground by Crumb Rubber Cement

against Explosion Force. J. Civil Eng. Urban., 8 (2): 17-24. www.ojceu.ir

transmit air pressure and the transmission element was

used around the soil environment.

Crumb rubber (CR)

For CR modeling, rubber element with mechanical

properties of NBR rubber was used with state equation

and hyperelastic resistance model (Autodyn help, 2005,

Pornprasit et al., 2016 ). This equation is suitable for

modeling materials with high strain range. There are

several models in the hyperelastic resistivity model for

solving the problem. In this study, we used the Ogden

model. The Ogden model is suitable for materials with a

range of strain energy potentials of over 700% (Autodyn

help, 2005 ). Due to the high rubber capability in energy

absorption, this model is suitable. The strain energy

potential of the Ogden model is defined as Eq. (8):

(Autodyn help, 2005 ):

Geometric of the model

For modeling of concrete structures, soil, explosives,

and air were used from Lagrangian, ALE and Eulerian,

respectively. The model used consists of three parts:

structure, soil, air. The explosive is equivalent to 100

kilograms of TNT. Figure

3 shows a graphical

representation of the modeling geometry in the software.

₁

₁

 

₂

(₁ ₂ ₃ 3)

₂



(₁ ₂ ₃ 3)

₂

(8)

₃

₃

(₁ ₂ ₃ 3)

(J 1)²



(J 1)⁴



(J 1)⁶

d₁

d₂

d₃

Where

strain energy potential

and J are

_p



Figure 3. Modeling geometry in the software

deviatoric principal stretches of the left–Cauch -Green

tensor and determinant of the elastic deformation gradient

Sensitivity analysis

To test the sensitivity of the results to the size of

_p _p

d _p

are material constants. In

respectively.

and

(Tables 8 and 9), the parameters used for the Hyperelastic

state equation and Hyperelastic-Ogden 3rd Order strength

model are expressed.

mesh, the pressure output at a depth of 3 meters from the

soil surface was compared for different sizes of the mesh

(Figure 4). As shown in Figure 4, with a reduction in the

size of the elements from 0.5 m to 0. 1 m, significant

changes are made to the results. On the other hand, by

reducing the size of the elements from 0.125 meters later,

the output pressure is very small and can be ignored. So

the mesh size of 0.125 m was chosen as the optimal mesh.

Table 8. Parameters of Hyperelastic state equation

Ref. Dens.

Parameter

(g/cm³)

Value

Table 9. Parameters of Hyperelastic-Ogden 3rd Order

element size=0.1(m)

element size=0.125(m)

element size=0.25(m)

element size=0.5 (m)

3.5

strength model

Mu1

Alpha1

Mu2

Alpha2

Parameter

(Kpa)

(1/Kpa)

(Kpa)

Value

1.18

4.82e-6

1.3

618.03

2.5

(1/Kpa)

Mu3

(Kpa)

-9.81

Alpha3

(1/Kpa)

Parameter

Value

1.5

-2

Boundary condition of the model

0.5

In this study, the flow-out and transmission elements

were used to create a semi-infinite environment and to

prevent the return of the explosive pressure waves. These

elements provide the pass of flow and materials from the

boundaries of the model. The flow out element was used

at the boundaries of the space around the model to

-0.5

Time (ms)

Figure 4. Variations of Pressure vs. time for different

sizes of elements

To cite this paper: Mirzaee M, Vaezi M and Mamandi S and AbdolrahmanO(2018). Reduction of Damage of Buried Ammunition Depots in the Ground by Crumb Rubber Cement

against Explosion Force. J. Civil Eng. Urban., 8 (2): 17-24. www.ojceu.ir

RESULTS AND DISCUSSION

Distribution of wave explosion in the soil

To investigate the propagation of the wave explosion

in the soil and the pressure at different depths, gauges

were placed at depths of one meter at a distance. Figure 5

shows the pressure against time at depths of 1 and 2

meters from the soil surface for 25 milliseconds of

analysis.

Figure 5 showed that the intensity of the pressure

caused by the explosion has been reduced by increasing

the distance from the soil surface (the explosion site).

Figure 6. Graphical pattern of failure in model A: in the

absence of concrete cushions and rubber substrates; B: in

the presence of concrete cushions and no substratum; C:

in the presence of rubber substrates and concrete cushions

Figure 5. Pressure diagrams in soil A: At a depth of 1

meter from the ground B: At a depth of 2 meters from the

ground

Also, to investigate the effect of the protective

layer CRC pressure and failure at a depth of 3 m below

the protective layer were measured at gauge No. 3 at

different times. The pressure and failure variations

diagram at a depth of 3 meters and above the structure are

showen in Figures 7 and 8 for different states of the CR

substrate.

As shown in Figures 7 and 8, the presence of a

single concrete cover only has a very small effect on the

results. While modeling of CR has achieved significant

changes in the number of results. On the other hand, the

amount of pressure and damage decreases with the

increase in the thickness of the CR layer. Also, according

to the results, it can be seen that the reduction of pressure

Impact of crumb rubber cement (CRC) on results

In order to investigate the effect of CRC on the

results, by modeling concrete cover and CR at a depth of 2

m from the ground surface and by comparing the results

of pressure at a depth of 3 m (under the sub-layer of CR in

the presence and absence of these layers effect these

layers were examined. Figure 6 illustrated the graphic

failure of the structure in the presence and absence of CR

and concrete cover.

To cite this paper: Mirzaee M, Vaezi M and Mamandi S and AbdolrahmanO(2018). Reduction of Damage of Buried Ammunition Depots in the Ground by Crumb Rubber Cement

against Explosion Force. J. Civil Eng. Urban., 8 (2): 17-24. www.ojceu.ir

and damage is a slight decrease after 0.4 m thickness.

Therefore, the thickness of 0.4 m can be determined as

optimal thickness.

CONCLUSION

In this study, the effect of crumb rubber cement (CRC)

on reducing the amount of failure and pressure caused by

the explosion phenomenon was investigated. Therefore,

the geometric model of the structure and its surrounding

soil, as well as the explosion phenomenon, was analyzed

in the LS-DYNA finite element software. The results

showed that despite the CR and with an increase in the

thickness of the CR layer, the amount of the failure and

pressure applied to the structure caused by the explosion

wave is greatly reduced. But this reduction is very small

and can be ignored after 0.4 meters in thickness.

Therefore, 0.4 m thickness of the CR was selected as the

optimum thickness of the CR layer to control the failure

and pressure.

In order to check the accuracy of maximum

explosion pressure, using the (Eq. 2, Eq. 3) and also the

parameters of Table 10 (TM5-855-1, 1984), the maximum

value of the pressure from the results of the software is

compared with the experimental results as follows.

As can be seen in table 10, the maximum value of

the pressure from the experimental relation is

conservative, which can be due to the linearity of the

equation.

Without concrete cover and rubber crumb"

4.5

With concrete cover and without rubber crumb

with concrete cover and rubber crumb=0.1(m)

with concrete cover and rubber crumb=0.2(m)

3.5

with concrete cover and rubber crumb=0.3(m)

According to the results of this research, it can be

seen that the reason for the high performance of the crumb

rubber in absorption and damping of energy is its high

elasticity. Therefore, high- elasticity polymeric materials

can be used to absorb more energy.

with concrete cover and rubber crumb=0.4(m)

2.5

with concrete cover and rubber crumb=0.5(m)

1.5

0.5

DECLARATIONS

-0.5

Time (ms)

Authors’ contribution

Figure 7. Pressure changes vs. time in different modes of

All authors contributed equally to this work.

existence and absence of (CR) and concrete cover at a depth of 3

meters

Competing interests

The authors declare that they have no competing

interests.

Without concrete cover and crumb rubber

With concrete cover and without crumb rubber

with concrete cover and crumb rubber=0.1(m)

with concrete cover and crumb rubber=0.2(m)

with concrete cover and crumb rubber=0.3(m)

with concrete cover and crumb rubber=0.4(m)

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0.35

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To cite this paper: Mirzaee M, Vaezi M and Mamandi S and AbdolrahmanO(2018). Reduction of Damage of Buried Ammunition Depots in the Ground by Crumb Rubber Cement

against Explosion Force. J. Civil Eng. Urban., 8 (2): 17-24. www.ojceu.ir

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To cite this paper: Mirzaee M, Vaezi M and Mamandi S and AbdolrahmanO(2018). Reduction of Damage of Buried Ammunition Depots in the Ground by Crumb Rubber Cement

against Explosion Force. J. Civil Eng. Urban., 8 (2): 17-24. www.ojceu.ir