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European Journal of Scientific Research

ISSN 1450-216X Vol.46 No.4 (2010), pp.554-562 EuroJournals Publishing, Inc. 2010

http://www.eurojournals.com/ejsr.htm

Analytical and Numerical Study on Explosion into/on

Cohesion less Soils

Hamed Niroumand

Department of Geotechnical Engineering, Faculty of Civil Engineering

University Technology Malaysia

E-mail:[email protected]

Khairul Anuar KassimDeputy Dean, Faculty of Civil Engineering, University Technology Malaysia

Abstract

The article reviews the analytical and numerical studies of explosion into/on

cohesion less soils during the last forty years. Various numerical methods for estimating of

behavior of soils during explosion have been developed. This paper discusses differenttheories and numerical studies on explosion into/on cohesion less soils by previous

researchers. Analyses were beginning from E. B. Polyak and E. N. Sher (1978), A. T.

Rodionov and A. G. Terent'ev (1985) until the most recent analysis such as H. Niroumand(2009) are reviewed. This analysis was pioneered by Absil et al (1997), Dorn et al. (1999),

Williams et al. (2000), Laine, L., et al. (2001), Niekerk (2001), Wang (2001), Cheng et al.

(2002), Fairlie et al. (2002), Gupta (2002), Jacko et al. (2002), Persson et al. (2003),Rhijnsburger (2003), Fierov et al (2004), S.O. Olofsson(2007) and H. Niroumand(2009)

will also be discussed. The results include most recent theories and numerical studies thataccompanied by experimental results.

Keywords: Explosion, Numerical Analysis, JWL, Cohesion less Soil, Analytical, Euler,

Lagrange

IntroductionThe last years, some researchers have been tries to research explosion and different loads in order tosafety the design underground structures and design of different vehicles used in military. Simulation

of the performance of soil subjected to close-in explosion of explosives materials a challenge for

different reasons. Its important to study the interaction between the explosion and soil responsebecause different structures affected by soil deformation subject to detonations. In recent years it

implemented the Eulerian mesh and multi-material option which has extended its modeling capacity

and enabled a comprehensive technique to become feasible. The simulation and numerical analysis isvery important in this research. The numerical simulations allow the approach to a reasonable

configuration; minimize the number of the experimental cases, saving considerable amounts of cost

and time. Finite element method (FEM) studies are widely used in defense related engineeringanalyses, such as high velocity impact and penetration. Protection of army vehicles and personnel

against landmine threats is an important issue in the area of defense research. Responses of the vehicle

being subjected to various explosions loading can be iteratively modeled using codes and appropriate

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Analytical and Numerical Study on Explosion into/on Cohesion less Soils 555

numerical techniques. This approach reduces the cost of expensive experimental tests. Researchers use

numerical simulation to research various tasks with different focus such as (a) injury of occupants, (b)

design of vehicle components and (c) attenuation material.Numerical analysis and simulations dealing with explosion are summarized in Table1. The

table focuses on parameters depend to blast loading. Analytical and Numerical analyses of the effect of

sand conditions and the depth of buried explosive undertaken by Laine et al.(2001) presented the

following conclusions: A buried explosive gives a much lower maximum pressure acting over a long

duration than the flush and surface-laid explosive. In contrast, the incident impulse of a buriedexplosive was the highest at distances above the ground less than 1m. Blast loading caused by a buried

explosive is concentrated in the vertical direction more than a surface explosive that is more spatiallyspread. Thus, it can be stated that the effect of soil condition has a great in flounce on the pressure and

impulse during explosion. Although, these numerical simulations were not validated by experimental

data and details on soil were not presented.A methodology for simulating soil explosion is presented by Fairlie et al (2002). Firstly, two

approaches in AUTODYN-2D were investigated for modeling high explosive:

(1) Multi-material Euler solver employing Jones-Wilkins-Lee, (JWL) equation of state (EOS)for detonation products,

(2) Single material Euler solver employing ideal gas equation of state for detonation products.

It was observed that prediction of the aim momentum is consistent. Therefore, further modelingand analysis used the ideal gas equation of state approach for detonation products. He used in theexperiments conducted by Bergeron et al (2000) was modeled in AUTODYN-3D. The Lagrangian grid

was filled using the cohesion less soil model derived by Laine et al (2001).By comparing the numerical

results with experimental data, it was concluded that the impulse from a mine buried in dry cohesionless soil was over estimated by 24% respectively by the numerical model. Therefore, varying sand

parameters, namely moisture content and initial density amplifies the impulse generated by the mine.

Numerical results obtained by Wang (2001) were compared with field results performed byBergeron et al (2000). Comparison shows that the numerical predictions of positive phase duration and

the displacement of ejecta front over estimated experiments by 36% and 10% respectively. The

findings are on the same plane in the case of a surface explosion as well. Both field investigation and

numerical analyses play significant roles in this research. The analysis helped minimize the number ofthe experimental tests required, which are usually very costly, and also help to interpret the test results.

Once verified by the field tests, it can be used as a design tool for the consequent improvement of the

system under research. Modeling of landmine explosion is highly complicated, involving an explosioncausing shock wave propagation in soil and air and then interaction with a structure. A simulation

modeling tool needs to incorporate adequately these challenging factors. Ls-Dyna3d software appeared

to be a suitable code currently available for its research. Since a number of assumptions and numericapproximation techniques are employed in Ls - Dyna, verification is important for each problem. Wang

in his report described a benchmark case applying Dyna to simulate an explosion in soil and air. The

simulation is compared with results from a well-defined landmine-explosion field. The agreement was

reasonably good. This work had provided a base for further modeling and analysis of a system

involving a structure, such as an army vehicle, subject to a landmine explosion.

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Williams et al (2000) investigated the floor deflection of a vehicle using a simple empirical

impulse model for cohesion less soil. This was obtained to generate an initial velocity boundary

condition, in spite of their using finite element method software, LS-DYNA-3D. The only variablesand parameter of the model was density (2170kg.m).No other soil properties were incorporated in the

model to predict pressure loading and momentum transfer. This setting resulted in a plate deformation

of 578mm, while experimental results presented a deformation of 287mm. This obvious discrepancy

was due to the fact that energy absorption mechanism of sand was not implemented into the empirical

model used.Another notable effort, Gupta is an algorithm derived from the empirical-based code CONWEP

and implemented into the finite element method software LS-DYNA, in order to generate explosionoverpressure loading on a panel. When results of simulations that focused on the response of a plate are

not in good agreement with field data ,i.e. the value of deformation, it has been concluded that further

study of the plate model needs to be carried out or simple scale-up of the explosive material is done.T. Rodionov and A. G. Terent'ev (1985), One of the simple mathematical models in the theory

of the deformation of continuous media in an blast is the solid-liquid model. This does not describe the

dynamics of the soil and so enables us to determine only approximate characteristics of the crater. Thismodel has now been used to study a wide range of problems in determining a crater in a continuous

medium with various tensile characteristic and various positions of the explosive. Authors considered

below within the framework of the solid- liquid model boundary-value problems in determining acrater in the blasts of point explosives and uniformly distributed explosives on the surface and deepwithin an isotropic cohesion less soils with angular and curvilinear free boundaries.

E. B. Polyak and E. N. Sher (1978), The basic idea proposed in i of the solid-liquid model of an

explosion in the ground consists in that in regions close to the blast the tensile forces are small incomparison with the pressure and the inertial loading, and the medium here can be assumed to be ideal.

High velocities and displacements (liquid zone) were characteristic for that zone. These areas were

separated by a transition layer. As a first approximation, it is assumed that it layer is infinitely thin andis a sealed boundary for the moving ideal medium. If the compressibility of the soil is neglected, then

for the incompressible ideal medium in the liquid zone of the blast a pulsed formulation is applicable,

in which the action of the blast is described in terms of the pressure pulse exerted on the medium by

the blast products.

Figure 3: The Craters Profiles by E. B. Polyak and E. N. Sher (1978),

It can be seen from Figure2 that this theory enables the experimental shapes of the craters

obtained in soils by the blast of a surface cord charge to be described satisfactorily.

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558 Hamed Niroumand and Khairul Anuar Kassim

S.O. Olofsson(2007) modeled impact of explosive load that it considede in the design of civil

defense structures. Blast occurring below soil level generates a ground shock wave that effects buried

structures in the proximity of the blast point. The program code FLAC suggested an opportunity tomodel the propagation of soil shock waves as well as interaction soil-structures. These researchers

present the procedure setup of a numerical model against field test for a buried explosion. Explosion

effected from a conventional bomb were estimated by using CONWEP that it is a field data compiled

by the U.S. Army (US Army, 1986).

Figure 4: Location of Experimental Points Relative to the Center of Explosive by S.O. Olofsson(2007)

Figure 5: Model Dimensions and Boundary Conditions by S.O. Olofsson(2007)

Fierov et al (2004), investigated an approach that mirrors this requirement was presented in

its research. The blast of an antitank mine is modeled and analyzed by using the non-linear dynamics

analysis code program, AUTODYN. The initial simulation setup included of a hemispherical chargelaid on a perfectly reflective plane. Two equations of state for explosive materials were investigated,

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with the first one being the commonly obtained to empirical equation of state, Jones-Wilkins-Lee

(JWL). The second research applied the ideal gas equation of state, often advanced for simplification in

complicated models. The mesh sensitivity research was carried out. Two parameters of explosionwaves, namely maximum pressure and specific impulse, are evaluated and compared with accessible

experimental data used from CONWEP. Consequently, a blast of a mine laid on cohesion less soil was

modeled using JWL EOS and explosion parameters were compared with the last model.

Figure 6: Material Location for Explosion in Various Deployments in Dry Sand by Fierov et al (2004)

H. Niroumand(2009), simulated the dispersion behavior of sand subjected to explosion on thesurface of a sand layer. The simulation was conducted using AUTODYN. Explosion effects from an

explosive were achieved by using the code program Conventional Weapon Effects Backfill

(CONWEB), which is based on field data compiled by the U.S.army (US Army, 1986). Three differentgoverning equations were used for air, sand and explosive. Ideal gas equation was used to equate the

movement of air and the dry sand was based on compaction effort. For the explosion, the JWL (Jones-

Wilkins-Lee) equation was used. Author presented the effect of explosion on the crater depth, craterdiameter and overpressure exerted on sand and the surrounding air. The results had shown that crater

depth and diameter increase with time during explosion. The experimental data on crater depth

however were initially lower than the numerical simulation but increased more than the numerical

simulation after 30ms. The overpressure showed a reducing trend with time. The numerical simulationbased on AUTODYN predicted higher crater depth and overpressure at the initial stage but showed a

good agreement with the experimental data with time.

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Figure 7: Material Position During Explosion in 1.36ms by H.Niroumand(2009)

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Table 1: Analytical and Numerical Studies on Explosion into/on Cohesion less Soils

E. B. Polyak and E. N.

Sher (1978)

Mathematical model - Solid Liquid model Rigid surface

A. T. Rodionov and A. G.

Terent'ev (1985)

Mathematical model - Solid Liquid model Rigid surface

Absil et al (1997) AUTODYN 2 475gr Composition B -

Dorn et al. (1999) FLUENT and LS-DYNA - - -

Williams et al. (2000) LS-DYNA - 7.5kg C4 Cohesion less soilLaine, L., et al. (2001) AUTODYN 8 10.4 kg Composition B Cohesion less soil

Niekerk (2001) MSC. Dytran - 800gr Pentolite -

Wang (2001) LS-DYNA - 100gr C4 Cohesion less soil

Cheng et al. (2002) AUTODYN and MSC.

Dytran

10 5 kg TNT Rigid surface

Fairlie et al. (2002) AUTODYN 25 1 kg C4 Cohesion less soil

Gupta (2002) LS-DYNA - 907.2gr Pentolite -

Jacko et al. (2002) AUTODYN - 500gr TNT -

Persson et al. (2003) AUTODYN - 0.125/0.5/1/4 kg PETN -

Rhijnsburger (2003) LS-DYNA - 10kg TNT Rigid surface

Fierov et al (2004) AUTODYN - 100gr TNT Cohesion less soil

S.O.Olofsson(2007) FLAC - - -

H. Niroumand(2009) AUTODYN 10 100gr TNT Cohesion less soil

ConclusionSome of last researchers were reported dealing with numerical / simulation analysis of the limiting

different numerical methods and code programs in explosion into/on cohesion less soils. Theinvestigation shows that sand properties and depth of buried explosive significantly influence

explosion output. So, it is important to investigate the sand properties along with the blast parameters.Some of the research work reported did not include the cell size, detail of modeling. There for, it is

need to more research for prediction of behavior of cohesion less soils by new methods in numericalanalysis during explosion.

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mine detonations in the vicinity of vehicles.In 15th International symposiumon the Military

Aspects of Blast and Shock(DRDB, Defence Research Establishment Suffield, Banff, Canada,

September1997).

[2] Bergeron, D.M., and Tremblay, J.E. Canadian research to characterize mine blast output. In 16 thInternational Symposium on the Military Aspects of Blast and Shock (Oxford, UK, September

2000), pp.501511,

[3] Bergeron, D.M., et al. Numerical and experimental study of in-soil explosions from a multiphase perspective. In 8thInternationalSymposiumon Interaction of the Effects of Munitionswith Structures (McLean, USA, April1997), pp.1134,

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[7] Fierov,D., etal.. Numerical simulations as a reliable alternative for landmine explosionstudies: The AUTODYN approach. Journal of Impact Engineering.

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[8] Gupta, A.D. Modeling and analysis of transient response in a multilayered composite panel dueto explosive blast. In 20thInternationalSymposiumonBallistics (Orlando, USA,

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[10] Niekerk,B. Land mine protection dealing with the uncertainties. In 10 th European AFV AttackAnd Survivability Symposium (Shrivenham, UK, May 2001).

[11] Niroumand, H., Simulation Comparison of Dispersion Behavior of Dry Sand Subjected toExplosion, International Journal of Geomechanic, ASCE, under review

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