researcharticle analysis of blast wave parameters

Research ArticleAnalysis of Blast Wave Parameters Depending on Air Mesh Size

Hrvoje DraganiT and Damir Varevac

Faculty of Civil Engineering Osijek Josip Juraj Strossmayer University of Osijek Drinska 16a 31000 Osijek Croatia

Correspondence should be addressed to Hrvoje Draganic draganicgfoshr

Received 28 February 2018 Revised 27 May 2018 Accepted 11 June 2018 Published 8 July 2018

Academic Editor Isabelle Sochet

Copyright copy 2018 Hrvoje Draganic and Damir Varevac This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Results of numerical simulations of explosion events greatly depend on the mesh size Since these simulations demand largeamounts of processing time it is necessary to identify an optimal mesh size that will speed up the calculation and give adequateresults To obtain optimal mesh sizes for further large-scale numerical simulations of blast wave interactions with overpasses meshsize convergence tests were conducted for incident and reflected blast waves for close range bursts (up to 5 m) Ansys Autodynhydrocode software was used for blast modelling in axisymmetric environment for incident pressures and in a 3D environmentfor reflected pressures In the axisymmetric environment only the blast wave propagation through the air was considered and in3D environment blast wave interaction and reflection of a rigid surface were considered Analysis showed that numerical resultsgreatly depend on the mesh size and Richardson extrapolation was used for extrapolating optimal mesh size for considered blastscenarios

1 Introduction

Todayrsquos global society faces many challenges that have notbeen present before Not only are military facilities exposedto terrorist threats but also many civilian buildings andstructures are in danger Most of these potential targetscannot be protected since they are in public use and haveto be accessible This paper is part of a wider research ofthe impact of explosions on overpasses that cross over thepublic roads [1 2] The imagined scenario assumes that thevehicle in which explosive is placed is parked underneaththe overpass and then detonated Since it is impossible tocarry out the tests in the 11 scale and handling explosiveis very dangerous and requires special conditions the mostpractical tool is computer simulation In both cases carryingout field tests or computer simulations it is very demandingtask Due to the very nature of the explosion process andmany parameters that affect measured effects even the fieldtests cannot provide accurate and repeatable results On theother hand in the computer simulation some assumptionsand idealizations must be adopted Very important issues inthese simulations are hourglass effect material propertiesfragmentation of material and fireball effect [3] but the

most important task is to determine adequate mesh sizeCoarse mesh may result in useless results but too fine meshmay occupy computer resources for hours and often days incase of complex problems The purpose of this paper is tooffer guidelines for selection of appropriate air mesh sizeTwo scenarios were considered for the purpose of furtherclarifying the influence of air mesh size on simulation resultsand enabling further development of blast loading analysisThe first scenario is ideal free-air explosion where incidentpressures were calculated and the second is specific blastscenario where reflected pressures from the overpass super-structurewere calculated For this latter case the convergencetests were carried out

Several researchers have studied themesh size effect indi-vidually or as a part of broader research on using numericaltools to study blast wave propagation and interaction withstructures Chapman et al [4] conducted a comprehensiveparametric study of model grid size to obtain optimal meshsize as a part of their research on the use of Autodyn 2Dfor simulation of blast wave interaction with structuresTheir results were compared to those from existing simpleexperimental tests and they concluded that Autodyn 2D isa suitable tool for blast wave investigation Luccioni et al [5]

HindawiShock and VibrationVolume 2018 Article ID 3157457 18 pageshttpsdoiorg10115520183157457

2 Shock and Vibration

studied influence of mesh size on blast wave propagation asa part of their research on urban blast They concluded that afiner air mesh (10 cm) gives better results but this can be tooexpensive in the terms of computational time Alternativelya coarser air mesh (50 cm) may be used to obtain qualitativeresults for comparison Shi et al [6] studied the relationshipbetween the scaled distance and blast load parameters ina series of numerical simulations with different mesh sizesand compared the results with those from TM5-1300 [7]They found that the pressure and impulse are less sensitiveto mesh size with an increase of the scaled distance theyalso proposed a method for the adjustment of peak pressuresfor coarse meshes Nam et al [3] determined the maximumelement size to ensure that analytical results are independentof mesh size this eliminates load gradient differences andreduces the gap between explosive and internal energy Dengand Jin [8] conducted a parametric study of free-air blastwave propagation as a part of their research on bridge damageinduced by blast loading Simulation results indicated that a5 cm air mesh size guarantees effective blast loading and reli-able computational results Wilkinson et al [9] in their studyonmodelling close-in detonations in the near field comparednumerical results of overpressure obtained by Autodyn andAir3D Mesh sensitivity analysis was conducted and resultsclearly indicated that mesh dependency of calculated resultsis existent Shin et al [10ndash12] performed numerical 1D 2Dand 3D simulation of close-in detonation of high explosivesin order to validate CFD code for determining incident andreflected overpressure and impulses It was concluded thatmesh refinement studies are needed to establish cell sizes forair blast calculations and that a cell size of R500 should besufficient to predict overpressure histories in the near fieldwhere R is the distance from the centre of the charge tothe monitoring location In addition it was determined thatthe afterburning has a little effect on peak overpressure butcan increase impulse if sufficient oxygen is present Shin etal [12ndash14] as a part of their research on blast parameters ofdetonation of spherical high explosives in free-air performedmesh size analysis on a wide range of scaled distancesAnalysis produced recommendation of new polynomials anddesign charts for detonation parameters of spherical TNTcharges It was concluded that cell size of R500 is sufficientfor calculating pressures in the scaled distance range of 8mkg13 similar to previous research [10]

Referred numerical simulations show that the accuracyof numerical results is strongly dependent on mesh size andblast scenariomdasha mesh size acceptable for one blast scenariomight not be suitable for anotherThis is a clear indicator thata numerical mesh size convergence test needs to be carriedout prior to large-scale numerical simulations

With respect to these results and recommendations forthe purpose of this research it was necessary to determinethe amount of explosive which is likely to be placed underthe overpass Table 1 gives crude estimations of possibleTNT quantities that can be placed in common vehicles andused for explosive deployment under a bridge [21 22] Thefirst three quantities are assumed to be the most probableand may offer some hope of bridge survival detonation of

Table 1 Estimated quantities of explosives for various types ofvehicles

Vehicle type Charge mass [kg]Compact car trunk 115Trunk of a large car 230Closed van 680Closed truck 2270Truck with a trailer 13610Truck with two trailers 27220Note 1 pound = 045 kg

larger TNT quantities would for sure cause imminent bridgecollapse Physical characteristics of vehicles which dictate theshape and confinement of the charge detonation point andconsequent flying debris (fragmentation) are not taken intoconsideration and only transport capacity was used in orderto estimate the amount of explosive

2 Blast Wave Parameters

Explosion is an event of sudden and rapid energy releaseaccompanied by a large pressure and temperature gradienton the wave front It is very important to notice that blastparameters for free-air explosion are much more differentfrom parameters which dictate the influence of explosion onengineering structure in this case the overpass

The blast wave is described by several parameters butthe main one is scaled distance Z which depends on chargeweight W [kg] and charge distance to target R [m] Scaleddistance is calculated by the following expression

119885 = 1198773radic119882 (1)

Use of TNT as a referent explosive for determining Z iswidely accepted The first step in quantifying the blast wavesfrom a source other than TNT is to transform the chargemass into the equivalent mass of TNT In general the TNTequivalent represents the mass of TNT that would resultin an explosion with the same effect as the unit weight ofexplosive under consideration It is defined as the ratio ofthe mass of TNT to the mass of the explosive resulting inthe same magnitude of blast wave (or impulse pressure andenergy) at the same radial distance for each charge whichassumes the scaling laws of Sachs and Hopkins Commonway to make conversion is to multiply the explosive massby the conversion factor determined using one of severalexisting methods (the specific energy based concept pressurebased concept impulse based concept Chapman-Jouguetstate based concept etc)

The primary reason for choosing TNT as the referentexplosive is that most of the available experimental dataregarding the characteristics of blast waves were collectedusing TNT Several methods exist for determining the explo-sive characteristics of different explosives but they do notyield the same values for the TNT equivalent These valuesdepend on the characteristic parameter of the blast wave the

Shock and Vibration 3

Table 2 TNT equivalents

Explosive Specific energy TNT equivalentQ푥 [kJkg] Q푥QTNT

RDX (Cyclonite) 5360 1185Nitro-glycerine (liquid) 6700 1481TNT 4520 1000Semtex 5660 1250C4 6057 1340Note 1 pound = 045 kg

geometry of the load and the distance from the explosivecharge [23] The TNT equivalence of terrorist-manufacturedexplosive material is difficult to define precisely because ofthe variability of its formulation and the quality control of itsmanufacture Table 2 gives the TNT equivalents for the mostcommonly used explosives [24]

Pressure-time history for a blast wave is commonlydescribed by the Friedlander equation [24]

119901 (119905) = 119901푠 [1 minus 1199051199050 ] expminus

1198871199051199050 (2)

where 119901푠 represents the blast wave overpressure b is thewaveform parameter t0 is the positive phase duration andt is considered time Peak overpressure is the maximum blastpressure above normal atmospheric pressure (p0 = 101325kPa) which is dependent on the distance from the deviceIt can be calculated by numerous analytical formulationsdeveloped by researchers [25ndash27] who were able to carry outexperiments on blast wave propagation Differences in resultsexist in peak overpressures for near- and far-field explosionsand they are incorporated in these formulations

As the blast wave travels away from the detonationpoint it undergoes reflection when the forward movingair molecules are brought to rest and further compressedupon meeting an obstacle Combining peak overpressureand dynamic pressure Rankine and Hugoniot derived thefollowing equation for reflected overpressure

119901푟 = 2 sdot 119901푠 [7 sdot 1199010 + 4 sdot 119901푠7 sdot 1199010 + 119901푠 ] (3)

where 1199010 represents the atmospheric pressureFurther important parameters include specific impulse

time of arrival and duration of positive and negative phaseSpecific impulse represents the area beneath the pressure-time curve from arrival time to the end of the positive phaseSpecific impulse is given by the following equation

119894푠 = int푡119860+푡0

푡119860

119901푠 (119905) 119889119905 (4)

where 119905퐴 represents blast wave time of arrival and 1199050 is theduration of the positive phase These specific blast times aswell as other blast parameters can be obtained fromUSArmymanual UFC 3-340-02 [7]

3 Numerical Simulations

Numerical models developed for this investigation werecreated in Ansys Autodyn hydrocode software [28] whichis intended for fluid dynamic analysis Autodyn is a fullythree-dimensional explicit finite difference program whichcan utilize several different numerical techniques (EulerianLagrangian ALE SPH and Shell) to optimize the analysis ofnonlinear dynamic problemsThe structural analysis requiresthe ability to simulate both fluidgas behaviour and structuralresponse

31 Numerical Techniques The Lagrange processor is usedfor modelling solid continua and structures and operateson a structured (I-J-K) numerical mesh of quadrilateral(2D) or brick-type elements (3D) [29] The numerical meshmoves and distorts with the material motion no transportof material occurs from cell to cell The advantage of sucha scheme is that the motion of material is tracked veryaccurately and the material interface and free surfaces areclearly defined The primary disadvantage of the Lagrangeformulation is that for severe material deformations or flowthe numerical mesh will also become highly distorted withattendant loss of accuracy and efficiency or outright failure ofcalculation [30]

The Euler processor is used for modelling fluids gasesand large distortionsThese processors include first-order andsecond-order accuracy schemes A control volume methodis used to solve the equations that govern conservation ofmass momentum and energy Numerical mesh is fixed inspace and material flows through it The advantage of sucha scheme is that large material flows and distortions can beeasily treatedThe disadvantage is that material interfaces andfree surfaces are not naturally calculated and sophisticatedtechniques must be utilized to track material interfacesAdditionally history-dependent material behaviour is moredifficult to track

ALE (Arbitrary Lagrange Euler) is a hybrid processorwherein the numerical mesh moves and distorts accordingto user specification An additional computational step isemployed to move the grid and remap the solution ontoa new grid ALE is an extension of the Lagrange methodand combines the best features of both Lagrange and Eulermethods Due to advantages of both Lagrange and Euleriansolver ALE solver was used for model calculation

Modelling with Ansys using explicit time integration islimited by the Courant-Friedrichs-Levy condition [31] This


condition implies that the time step is limited so that adisturbance (eg stress wave) cannot travel further than thesmallest characteristic element dimension in the mesh in asingle time step Thus the time step criterion for solutionstability is

119889119905cou lt min(119889119909119888 119889119910119888 ) (5)

where dt is the time increment dx and dy are characteristicdimensions of an element and c is the local material soundspeed in an element Based on this condition one canconclude that smaller mesh size implies smaller time stepsand consequently longer calculation time

32 Material Models The numerical models used in thisstudy include three different materials environment explo-sive charge and overpass superstructure Environment wasmodelled as the air which transmits pressure waves pre-sented as an ideal gas and the pressure was related to energyusing following expression

119901 = (120574 minus 1) 120588119890 (6)

where 120588 is air density e is specific internal energy and 120574 is aconstant (ie ratio of specific heats) This expression is oneof the simplest forms of equation of state for gases Gaseousmaterials have no ability to support any kind of stresses andconsequently no strength or failure relations are associatedwith this material

Explosive chargewasmodelled as a spherical TNTchargeSimilar to the air model no strength or failure relations areassociated with explosive material Detonation is a rapid pro-cess that converts explosive material into gaseous productsand it is usually completed at the start of a given simulationTNT explosive was modelled with the Jones-Wilkins-Leeequation of state [32] using following expression

119901 = 119860(1 minus 1205961198771120594) 119890

minus푅1휒 + 119861(1 minus 1205961198772120594) 119890

minus푅2휒 + 120596120594 (7)

where p is hydrostatic pressure 120594 is specific volume (1120588)and e is specific internal energy and A R1 B R2 and 120596are constants experimentally determined for several commonexplosives [33] The shape of TNT charge in this study isspherical in order to ensure uniform propagation of thepressure waves and thus the clarity of results Materialproperties of TNT and air are given in Table 3

In order to reduce the calculation time and get clearresults rigid material was chosen for the slab This is aspecial feature of Autodyn software which may be used ifthe stresses andor deformations of target object are not ofinterest Insensitivity of the results on the rigid slab meshsize was confirmed by conducting several convergence testsand therefore is eliminated as an influential parameter indetermining the dependency of blast wave parameters onair mesh size Ground surface on which TNT charge wasplaced in 3D simulation before detonation was modelledas rigid boundary in order to provide full reflection ofthe blast wave and also eliminate ground mesh size as

an influential parameter Axisymmetric free-air simulationswere performed using Eulerian solver and 3D simulationswere done using a coupled LagrangianEulerian solver as itallows the combination of the best aspects of Lagrangian andEulerian solvers

33 Parametric Study Modelling process of the impact of theexplosion on overpass structure is divided into two partsFirst 2D FE model of free-air explosion is created Thismodel is composed of circular TNT charge surroundingair and outflow boundary each with its properties (seeTable 3) (free-air axisymmetric model) Radius of the TNTcharge is determined by the specific reference density andchosen weight while radius of the air surrounding may bearbitrary defined (in this case 500 cm in order to shortenthe calculation time) Using axial symmetry only one circlesector may be modelled (Figure 2) and calculated whichgreatly reduces the calculation time The results from thisFE model are used to calculate free-air incident pressuresSecond part is generation of the 3D model by revolving a 2Dsection 360∘ degrees and remapping the incident pressures tothe overpass structure and rigid ground surface in order tocompute reflected pressures (Figure 3)

Since the explosive charge is part of the model it shouldbe investigated whether its own mesh size (different fromair mesh size) affects the results of the simulation It wasconsidered if the refinements of the chargemesh influence thelevel of energy release during detonation time of blast wavearrival or incident pressures especially in 3D simulationsand should be taken into consideration Due to this concernadditional simulations were conducted in order to study anddetermine the influence of charge mesh size Simulationswere conducted by varying air and charge mesh size foreach of the three chosen quantities of explosive Threecharge weights as mentioned earlier 115 kg 230 kg and680 kg of TNT (different line type) three air mesh sizes(different point type) and eight charge mesh sizes wereconsidered Numerical model is axisymmetric as shown inFigure 2 consisting of two separate parts TNT charge andair surrounding Simulation results are shown in Figure 1Figure 1(a) shows normalized pressures while Figure 1(b)shows normalized total blast energy Table 4 shows the valuesused for normalization for each of the three air mesh sizesand three TNT quantities These values were obtained inseparate simulation

Normalization is conducted in regard to the numericalmodel with the same charge and air mesh size ie referentmodels were those with 5 mm 10 mm and 20 mm as bothcharge and air mesh sizes Comparison of normalized totalenergies indicates that differences are minimal for all threeobserved parameters (under 5) with somewhat larger butstill acceptable differences in normalized pressures (under10) Due to minimal differences charge meshes to coincidewith air mesh in every simulation This conclusion also has animpact on accelerating the modelling process because there isno need to mesh separately air and charge part of the model

Free-air axisymmetric numerical simulation of explosionwas performed using twelve different air mesh sizes (Table 5)Here only the TNT in the air environment was modelled


+5

-5093094095096097098099100101102103104105106107

05 1 2 4 8 16 32 64Charge mesh size [mm]

5 mm10 mm20 mm

Nor

mal

ized

tota

l bla

st en

ergy

(a) Normalized total blast energy versus charge mesh size

+10

-10088090092094096098100102104106108110112


Nor

mal

ized

pre

ssur

e

5 mm10 mm20 mm

(b) Normalized pressure versus charge mesh size

Figure 1 Influence of charge mesh size on blast energy and pressures (solid line 115 kg TNT dashed line 230 kg TNT dotted line 680 kgTNT)

TNT chargeW [kg]

r - radius of spherical charge

Air

Outflowboundarycondition

Gauges

R = 500 cm (charge distance to target)

Figure 2 Free-air axisymmetric explosion model

Rigid slabRigid slab

Gauge Point225

225

Gauge Point

Air

TNT chargeW [kg]

Ground surface (rigid)Gauge Point

[cm]450

450

60

500

Edge of numericalmodel


Figure 3 3D explosion model


Table 3 Material properties

(a)

TNTEquation of state JWLdagger

Reference density 163 [gcm3]Parameter A 3738E+08 [kPa]Parameter B 3747E+06 [kPa]Parameter R1 415Parameter R2 090120596 035C-J detonation velocity 6930E+03 [ms]C-J energyunit volume 6000E+06 [kJm3]C-J pressure 2100E+07 [kPa]Initial energy 3681E+06 [mJmg]Note 1 inch = 254 cm 1 pound = 045 kg 1 psi = 689 kPa 1 K = -27215∘C daggerJWL = Jones-Wilkins-Lee

(b)

AirEquation of state Ideal gasReference density 1225E-03 [gcm3]120574 140Reference temperature 28820 [K]Specific heat 71760 [JkgK]Initial energy 2068E+05 [mJmg]Note 1 inch = 254 cm 1 pound = 45359 g 1 psi = 689 kPa 1 K = -27215∘C

Table 4 Pressure and energy values used for normalization

Air mesh size[mm]Charge mesh

size[mm]TNT (kg)

115 230 680Pressure[kPa] Total energy[MJ] Pressure[kPa] Total energy[MJ] Pressure[kPa] Total energy[MJ]

5 5 91715 322 145530 645 284770 191210 10 88728 321 142000 646 278530 191520 20 84162 318 136710 647 271530 1917Note 1 inch = 254 mm 1 pound = 045 kg 1 psi = 689 kPa

and the wave propagation was observed On the edge ofthe air environment an outflow boundary condition wasimplemented to avoid the blast wave reflection and ampli-fication that is to allow free gas outflow from designatedair environment Observed air environment is 5 m radiuswith gauge points placed at equal distances (305 cm) inorder to compare results for different scaled distances airenvironment and gauge position are shown in Figure 2

The 3Dmodel binds the air environment with a rigid slabwhich simulates bridge superstructure and ground level forblast wave reflection and amplification The Eulerian multi-material solver was used for accurate simulation of hot gasexpansion and interaction with structure primarily becausethere are no grid distortions during fluid flow throughcells and it allows large deformations mixing of initiallyseparatematerials and larger time steps Its use requiresmore

computations per cycle finer zoning for similar accuracy andextra cells for potential flow regions

Parametric 3D numerical simulation of a ground explo-sion was performed using nine different air mesh sizes(Table 6) The mesh size of 800 mm was discarded becauseit was too coarse and gave unrealistically small pressuresin comparison to AT-Blast [34] Mesh sizes smaller than313 mm were impractical because of high requirementsfor computer hardware components The ground explosionmodel and gauge scheme are shown in Figure 3 The ideallyrigid concrete slab was placed 5 m above the detonationpoint on the ground which is typical clearing underneath theoverpass In addition using the symmetry only one-quarterof the numerical model presented in Figure 3 was modelledand simulated Additional shortening of calculation time wasachieved by remapping the final solution of axisymmetric


Table 5 Axisymmetric model mesh sizes and number of elements

Mesh size [mm] 039 078 156 313 625 125 25 50 100 200 400 800Number of elements 12821 6410 3205 1598 800 400 200 100 50 25 13 6Note 1 inch = 254 mm

Table 6 3D model mesh sizes and number of elements

Mesh size [mm] 313 625 125 25 50 100 200 400 800Number of elements 829440000 103680000 12960000 1620000 202500 25313 3164 396 49Note 1 inch = 254 mm

analysis for selected charge quantities (115 kg 230 kg and 680kg) as an input (load) to the 3D environment [35]

4 Comparison of Results and Discussion

Numerical simulation results using coarse and fine air meshsizes varied considerably This indicates that mesh size con-vergence tests are needed to obtain the optimal mesh size foran accurate simulation of blast wave propagation Detonationproducts influence blast wave pressures and consequentlyimpulses that is they are within the blast fireball Thepressures depend on the type of explosive as each explosivehas different detonation products The exact influence of thefireball on the pressures could not be determined separatelybecause additional analysis would be needed in which dataare collected outside the fireball radius and compared to thoseobtained within the fireball

41 Incident Pressures Results obtained by free-air axisym-metric numerical simulation were compared with resultsacquired by AT-Blast the software for analytical determina-tion of the referent blast parameters AT-Blast uses equationsfor blast estimation of overpressures at different rangeswhich were developed by Kingery and Bulmash [36] Theseequations are widely accepted as engineering predictionsfor determining free-field pressures and loads on structuresKingery and Bulmash have compiled results of explosive testsin which they detonated charges weighting from less than1 kg to over 400000 kg and used curve-fitting techniquesto represent the data with high-order polynomial equationsAnother reason why AT-Blast was chosen as the referencefor the blast parameter comparison was that the software ispublicly available subjected to ITAR (International Traffic inArms Regulations) controls Unlike AT-Blast ConWep [37]another widely used software for estimating blast propertiesis not available to non-US citizens or organizations thereforeit was not used as an additional control for the numericalresults

It can be seen that decreasing the mesh size allowedmaxi-mum incident pressure to converge to the referent valueWithsmallermesh sizes (from 039 to 125mm)maximum incidentpressures exceeded values obtained by AT-Blast and can beaccounted for by inaccuracies in the experimental pressurereadings (the measuring instruments were influenced by veryhigh pressures and the blastwave duration and time of arrivalwere also very short ie only a fewmilliseconds)The relative

difference in maximum incident pressures measured at thelast gauge point 5 m from detonation point between smallermesh sizes and values generated by AT-Blast can clearlybe seen from Table 7 The closest incident peak pressurewas obtained for the 25 mm mesh size (marked by bold inTable 7) with about 2 maximum difference in relation tothe AT-Blast value Pressure histories for different mesh sizesrelative to AT-Blast pressure values are plotted in Figure 4It can be seen that the rate of pressure amplification fromambient to peak pressure becomes slower and the shape ofthe curve becomes flatter with the increase of the mesh sizeThe calculated incident peak pressure was also smaller withthe larger mesh sizes

If the positive peak incident pressure in relation toscaled distance is considered its value decreases with theincrease of scaled distance This is in accordance with theinitial assumption that with the increase of distance fromdetonation point to structure surface pressures exerted onstructure surfaces are decreasing Figure 5 shows that this isconsistent for all air mesh sizes With smaller air mesh sizepressures became closer to the referent values obtained byAT-Blast

42 Reflected Pressures Results obtained by 3D numericalsimulation were also compared with the results acquired byAT-Blast In terms of absolute values the comparison gave theclosest reflected pressures for 25 mmmesh size in an analysisfor 115 kg and 230 kg of TNT here the minimum differencein relation to AT-Blast values was 857 for 115 kg and 008for 230 kg For 680 kg of TNT closest reflected pressure incomparison to AT-Blast was obtained for 125 mm mesh sizewith difference of 417 (Table 8) Reflected overpressurehistories in relation to AT-Blast reflected overpressure valuesare plotted in Figure 6 Pressure amplification from ambientto peak reflected overpressure has a smaller rate of increaseand the shape of the curve becomes flatter with the increaseof the mesh size as for the incident pressures Pressure-time curve has additional pressure peak after the initialpeak which is caused by blast wave reflection and it can beclearly seen in Figure 6 Calculated reflected overpressure alsobecomes smaller with larger mesh sizes

43 Time of Arrival Mesh size also influenced the blastwave time of arrival Some authors [6] have concluded thatthe arrival time is independent of the mesh size and ifwe consider that the time in blast problems is measured in


Table 7 Comparison of maximum incident pressures in dependency of air mesh size for a gauge point at the range of 5 m

Mesh size

TNT mass115 kg 230 kg 680 kg

Pressure[kPa] Relative error [] Pressure[kPa] Relative error [] Pressure[kPa] Relativeerror []

AT-Blast 127802 ---- 205244 ---- 395410 ----800 mm 54698 5720 88012 5712 192137 5141400 mm 77740 3917 103921 4937 173888 5602200 mm 80467 3704 124939 3913 239468 3944100 mm 104229 1844 172691 1586 315583 201950 mm 121122 523 188842 799 362150 84125 mm 128831 081 204125 055 387796 193125 mm 137132 730 212835 370 405435 254625 mm 142973 1187 218507 646 423193 703313 mm 145485 1384 222499 841 431066 902156 mm 147605 1550 225857 1004 438638 1093078 mm 149513 1699 229079 1161 453793 1477039 mm 149403 1690 229911 1202 456571 1547Note 1 inch = 254 mm 1 pound = 045 kg 1 psi = 689 kPa

Table 8 Comparison of maximum reflected pressures in dependency of air mesh size for a gauge point at the range of 5 m

Mesh size


Pressure[kPa] Relativeerror [] Pressure[kPa] Relative error [] Pressure[kPa] Relative error []

AT-Blast 755390 ---- 1373863 ---- 3069649 ----800 mm 80936 8929 122729 9107 194014 9368400 mm 146437 8061 225222 8361 449597 8535200 mm 244590 6762 417033 6965 877319 7142100 mm 502242 3351 869976 3668 1758410 427250 mm 689083 878 1156610 1581 2408670 215325 mm 820113 857 1372750 008 2939830 423125 mm 887548 1750 1510470 994 3197790 417625 mm 1016160 3452 1544550 1242 3289480 7163125 mm 1012600 3405 1556820 1332 3295300 735Note 1 inch = 254 mm 1 pound = 045 kg 1 psi = 689 kPa

milliseconds differences arising from analyses with differentmesh sizes exist Tendency is that the smaller mesh sizesshorten the time required for the blast wave front to arrive tothe designatedmeasuring point If themesh size is sufficientlysmall it no longer influences the arrival time as can be seenin Figure 7 For larger mesh sizes for which pressure historyis flatter the time of maximum incident pressure is taken asthe time of blast wave arrival

If a difference of plusmn15 was considered all arrival timeswere within this range Results presented in Figure 7 showthat the numerical analysis provided earlier arrival times incomparison to AT-Blast Similar to incident pressures therewas a tendency for smaller mesh sizes to shorten the arrival

time if the mesh size was sufficiently small it no longer hadan influence on the arrival time

5 Result Convergence

Individual application of numerical methods differs in thelevel of accuracy with which a numerical model can reflectthe physical phenomena An analysis with the help ofcomplex numerical models is particularly applicable if thereis no closed analytical solution and if the experiments areimpossible or insufficient In all such cases the questionarises about the ability of such analysis to correctly predictthe results of the physical process in question The first


039 mm078 mm156 mm313 mm625 mm125 mm25 mm

50 mm100 mm200 mm400 mm800 mmAT-Blast

05 10 15 20 25 30 35 40 45 5000Time [ms]

0200400600800

1000120014001600

Inci

dent

pea

k pr

essure

[kPa

]

(a) 115 kg TNT (compact car trunk)

039 mm078 mm156 mm313 mm625 mm125 mm25 mm


0250500750

1000125015001750200022502500

Inci

dent

pea

k pr

essure

[kPa

]

05 10 15 20 25 30 35 40 45 5000Time [ms]

(b) 230 kg TNT (trunk of a large car)

10 20 30 40 5000Time [ms]

0500

100015002000250030003500400045005000

Inci

dent

pea

k pr

essure

[kPa

]

039 mm078 mm156 mm313 mm625 mm125 mm25 mm


(c) 680 kg TNT (closed van)

Figure 4 Pressure-time histories for analysed TNT quantities

recommended procedure within the verification process isthe mesh refinement study Its main objective is to evaluatethe error of discretization and to check if the applied mesh issufficiently refined

51 Richardson Extrapolation The mesh refinement study isconducted based on a comparison of the results for at leasttwo but usually three meshes [29] The Richardson extrap-olation serves as a higher-order estimate of the evaluatedquantity A quantity f calculated for a mesh characterizedby parameter (mesh size) h can be expressed using Taylorrsquostheorem In practice the Richardson extrapolation is gener-alized for any also noninteger p-th order approximations andthe mesh refinement ratio r and is considered as p + 1 orderapproximation The exact solution of extrapolation can bedescribed as an asymptotic solution for a mesh with element

dimension h approaching zero Estimate of the asymptoticsolution is given by

119891ℎ=0 cong 1198911 + 1198911 minus 1198912119903푝 minus 1 (8)

where 119891ℎ=0 denotes asymptotic solution for h approaching 0(extrapolated value) 1198911 and 1198912 second-order approximationsof 119891ℎ=0 r is refinement ratio and p is order of convergenceRefinement ratio r can be set as arbitrary when usingunstructured meshes or as a constant if regular meshes areconsidered There is no recommendation about refinementratio selection In this study refinement ratio is set as a con-stant value of 2 whichmeans that the finer meshes consideredare generated by dividing node spacing in all directions intohalves Order of convergence p can be calculated no matterwhat refinement ratio is selected constant or arbitrary For


039 mm078 mm156 mm313 mm625 mm125 mm25 mm


03 04 05 06 07 08 09 10 1102Scaled distance [mkg13]

0

2000

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sitiv

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a]


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03 04 05 06 07 08 0902Scaled distance [mkg13]

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]


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02 03 04 0501 06Scaled distance [mkg13]

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ent p

eak

pres

sure

[kPa

]


Figure 5 Variation of positive incident peak pressure with scaled distance


Secondary pressure peak

800 mm400 mm200 mm100 mm50 mm

25 mm125 mm625 mm3125 mmAT-Blast

0

2000

4000

6000

8000

10000

12000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]


Secondarypressure peak

800 mm400 mm200 mm100 mm50 mm


02000400060008000

1000012000140001600018000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



0

5000

10000

15000

20000

25000

30000

35000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]

800 mm400 mm200 mm100 mm50 mm



Figure 6 Reflected pressure-time histories

Incident wave

800 mm 400 mm 200 mm 100 mm 50 mm 25 mm 125 mm 625 mm 3125 mm 156 mm 078 mm 039 mm

115 kg 252 240 258 250 239 234 228 224 222 221 220 220230 kg 217 200 214 206 201 194 190 187 185 183 182 182680 kg 173 177 172 168 160 152 148 144 143 142 140 140

1214161820222426

Arr

ival

tim

e [m

s]

AT-Blast

AT-Blast

AT-Blast

(a) Reflected wave

AT-Blast

AT-Blast

AT-Blast

Reflected wave

800 mm 100 mm200 mm400 mm 50 mm 25 mm 125 mm 3125 mm625 mm115 kg 216 282 278 254 241 231 225 225 224230 kg 183 244 234 211 199 191 186 185 187680 kg 135 176 192 161 153 147 143 143 143

Arr

ival

tim

e [m

s]

28262422201816141210

30

(b) Incident wave

Figure 7 Blast wave time of arrival for different air mesh sizes


Table 9 Extrapolated pressure values (119891ext) and GCI for axisymmetric simulation

TNT mass 119891ext [kPa] Min [kPa] Max [kPa] GCI r p115 kg 149396 149395 149411 001 200 411230 kg 230202 229547 230275 016 200 195680 kg 457198 455787 457355 017 200 244Note 1 pound = 045 kg 1 psi = 689 kPa

Table 10 Extrapolated overpressure values (119891표ext) and GCI for 3D simulation

TNT mass 119891표ext [kPa] Min [kPa] Max [kPa] GCI r p115 kg 1012499 1012473 1012727 001 200 516230 kg 1563723 1548191 1565449 055 200 147680 kg 3295694 3294807 3295793 001 200 397Note 1 pound = 045 kg 1 psi = 689 kPa

structured meshes order of convergence can be calculatedusing (9) and for unstructured meshes using (10)

119901 = log ((1198913 minus 1198912) (1198912 minus 1198911))log 119903 (9)

119901 = 1003816100381610038161003816ln 100381610038161003816100381611989132 minus 119891211003816100381610038161003816 + 119902 (119901)1003816100381610038161003816log 11990321

119902 (119901) = ln(119903푝21 minus 119904119894119892119899 (11989132 minus 11989121)119903푝32 minus 119904119894119892119899 (11989132 minus 11989121))(10)

where 119891푖푗 = 119891푖 minus 119891푗 and 119903푖푗 = ℎ푖ℎ푗 If constant refinementratio is implemented in equation for calculating order ofconvergence for unstructured meshes (implemented in (10))equal value as for equation for structured mesh should beobtained All parameters used in extrapolation and obtainedresults are listed in Tables 9 and 10

Given in a percentagemanner the grid convergence index(GCI) can be considered as a relative error bound showinghow the solution calculated for the finest mesh is far from theasymptotic value It predicts how much the solution wouldchange with further refinement of the mesh The smaller thevalue of the GCI the better This indicates that the computedsolution is within the asymptotic range The safety factors119865푠 are arbitrarily set based on the accumulated experienceon computation fluid dynamics (CFD) calculations [38ndash40] The safety factor represents 95 confidence for theestimated error bound This assumption can be expressedas the following statement There is 95 confidence that theconverged solution is within the range [f 1(1 minus GCI12100)f 1(1 + GCI12100)] The GCI is defined as

119866119862119868 = 119865푠 |120576|119903푝 minus 1100 (11)

where 119865푠 is a safety factor The recommended CFD values ofthe safety factor 119865푠 are119865푠 = 30 when two meshes are considered119865푠 = 125 for three and more meshes

Quantity 120576 defines relative difference between subsequentsolutions

120576 = 1198911 minus 11989121198911 (12)

Due to lack of experimental investigation and reliance onAT-Blast values Richardson extrapolation was introduced todetermine convergence of the simulations Pressure values(119891푖푗) were obtained through numerical simulations usingdifferent mesh sizes with a constant refinement ratio (r)of 2 With known solutions order of convergence (p) wasdetermined using (9) based on three subsequent pressurevalues Extrapolated pressures (119891ext and 119891표ext) were calcu-lated using pressures from two subsequent meshes (119891푖 and119891푖+1) order of convergence (p) and refinement ratio (r)Table 9 lists the pressure extrapolated values for axisymmetricsimulations and Table 10 for 3D simulations together withestimated error bounds GCI refrainment ratio and orderof convergence Extrapolated values were obtained by usingthree smallest airmesh sizes 156mm 078mm and 039mmfor axisymmetric and 125 mm 625 mm and 313 mm for3D simulations respectively following the previously statedcalculation procedure given by [41]

With the reduction of the mesh size pressures convergeto a value dependent on the charge mass as can be seenin Figure 8 This fact should be taken with caution becausesmaller mesh sizes substantially prolong calculation time anddemand large quantities of computational memory Meshsizes which produce pressure difference in comparison toextrapolated pressure less than 10 are considered sufficientlyaccurate for engineering use The analysis was based onclose-in and intermediate scaled distances from 0 mkg13

to 1 mkg13 that coincide with the previously mentionedbridge superstructure distance from the road surface If lowerbound is considered appropriate incident pressure values areobtained for 125 mm air mesh size for 115 kg 230 kg and 680kg of TNT respectively

Gauge point of interest was located in the lower planeof bridge superstructure at a distance of 5 m from groundplane which is equivalent to scaled distances for each TNT


+ 10 (upper bound)

- 10 (lower bound)

115 kgAT-BlastRichardsonrsquos extrapolation for 115 kg TNT p=149396 kPa

Acceptable mesh size

0

300

600

900

1200

1500

1800

Inci

dent

overpre

ssur

e [kP

a]

25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

500

1000

1500

2000

2500

3000

Inci

dent

overpre

ssur

e [kP

a]

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

1000

2000

3000

4000

5000

6000

Inci

dent

overpre

ssur

e [kP

a]

Figure 8 Determination of acceptable air mesh size for incident overpressures

quantity 103 mkg1and3 for 115 kg 082 mkg1

and3 for 230 kgand 057 mkg1

and3 for 680 kg Using Richardson extrapolationand accepting 10 upper and lower bound it was possibleto obtain acceptable air mesh sizes for reflected pressures(Figure 9) Analysis resulted in air mesh sizes of 125 mmfor 115 kg TNT and 25 mm for 230 kg and 680 kg TNTbeing adequate for pressure-structure interaction analysis Ifit is considered that it is practically impossible to determineabsolutely accurate blast pressures using experimental mea-surements or numerical simulation according to this analysis

AT-Blast could provide an adequate approximation of blastwave pressures for both incident and reflected pressures AT-Blast calculated pressures are very close or are within thevalue of lower bound (10) of extrapolated pressures clearlydepicted in Figures 8 and 9 which is yet another argumentfor using AT-Blast for quick assessment of blast pressures

52 Empirical and Analytical Expressions Empirical andanalytical expressions are given in literature for estimatingblast overpressure Some of the expressions are based on the


+ 10 (upper bound)

- 10 (lower bound)

115 kgAT-BlastRich ext for 115 kg TNT p=1012498 kPa


0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

100

mm

400

mm

200

mm

800

mm

125

mm

313

mm

625

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

800

mm

200

mm

400

mm

100

mm

625

mm

125

mm

313

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

5000

10000

15000

20000

25000

30000

35000

40000

Refle

cted

overpre

ssur

e [kP

a]

25 m

m

50 m

m

400

mm

200

mm

800

mm

100

mm

625

mm

125

mm

313

mm

Mesh size

Figure 9 Determination of acceptable air mesh size for reflected overpressures

analysis of experimentally acquired pressure data while otherare product of purely mathematical algorithms Expressionsare given for calculating overpressures generated from spher-ical or hemispherical airbursts Based on the parametersused for numerical simulations (stand of distance of 5 mand charge weight of 115 kg 230 kg and 640 kg) calcu-lation of analytical and empirical expressions for incidentoverpressure estimation by different authors was conductedCalculated results were used for numerical and AT-Blast

overpressure evaluation The list of analytical expressions wasgiven by Ullah et al (2017) [42] Table 11 gives some perspec-tive on calculated values and differences of expressions withAT-Blast and FEM simulations Based on the results given inTable 11 calculations provide a wide variety of overpressurevalues with differences ranging from 01 to 166

If results from Table 11 are analysed it can be seen that forsome equations calculated overpressure is higher than fromAT-Blast and in other cases overpressure is lower than from


Table 11 Comparison of analytical expressions with AT-Blast and FEM overpressures [kPa]

TNT massW 115 kg 230 kg 640 kgRange R 5 mScaled distance Z 1028 0816 0580FEM 128831 204125 387796Richardson extrapolation 149396 230202 457198AT-Blast 127802 205244 395410

Authors 115 kg 230 kg 640 kg AT-Blast FEM

Sadovskyi (1952) 112085 206343 523609 -123 05 324 -130 11 350Brode (1955) 71640 133280 353040 -439 -351 -107 -444 -347 -90Naumyenko and Petrovskyi (1956) 89498 183390 527790 -300 -106 335 -305 -102 361Adushkin and Korotkov (1961) 4643 -7401 -67898 -964 -1036 -1172 -964 -1036 -1175Henrych and Major (1979) 73489 108154 202294 -425 -473 -488 -430 -470 -478Held (1983) 189186 300314 594123 480 463 503 468 471 532Kinney and Graham (1985) 94971 155123 304487 -257 -244 -230 -263 -240 -215Mills (1987) 162744 322164 892013 273 570 1256 263 578 1300Hopkins-Brown and Bailey (1998) 84974 145984 273452 -335 -289 -308 -340 -285 -295Gelfand and Silnikov (2004) 88673 142376 271482 -306 -306 -313 -312 -303 -300Bajic (2007) 179963 335567 863899 408 635 1185 397 644 1228NDEDSC 98110 179636 453084 -232 -125 146 -238 -120 168UFC-3-340-02 80000 200000 320000 -374 -26 -191 -379 -20 -175Newmark and Hansen (1961) 90612 164706 413865 -291 -198 47 -297 -193 67Wu and Hao (2005) 95323 173086 421617 -254 -157 66 -260 -152 87Ahmad et al (2012) 228405 423275 1052411 787 1062 1662 773 1074 1714Siddiqui and Ahmad (2007) 96442 149941 287667 -245 -269 -272 -251 -265 -258Ahmad et al (2012a) 147335 285818 760302 153 393 923 144 400 961Swisdak (1994) 127639 204812 382712 -01 -02 -32 -09 03 -13UFC-3-340-02 120000 220000 410000 -61 72 37 -69 78 57Note 1 ft = 03048 m 1 pound = 045 kg 1 psi = 689 kPa

Table 12 Kingery blast coefficients

Z [mkg13] A1 B1 C1 D1 E1 F1 G102 - 29 7211 -2107 -0323 0112 0069 0000 000029 - 238 7594 -3052 0410 0026 -0013 0000 0000238 - 1985 6054 -1407 0000 0000 0000 0000 0000

AT-BlastThe same can be said for FEM results Exact value ofoverpressures (p푠) for analysed charge quantities is obtainedby Swisdakrsquos equation (see (13)) but that is because it is basedon the Kingery-Bulmash equation and parameters and AT-Blast internal equations are exactly those defined by Kingery-Bulmash

119901푠 = exp (1198601 + 1198611 times (ln (119885)) + 1198621 times (ln (119885))2 + 1198631times (ln (119885))3 + 1198641 times (ln (119885))4 + 1198651 times (ln (119885))5 times 1198661times (ln (119885))6) times 10minus3

(13)

where Z is the scaled distance and A1 B1 C1 D1 E1 F1and G1 are simplified Kingery air blast coefficients given inTable 12

Due to large discrepancy between overpressures calcu-lated using different expressions and AT-Blast (and numer-ical) results it is hard to evaluate overall performance ofAT-Blast Expressions are mathematical equations obtainedthrough correlation with experimental data andmost of theseapproaches are limited by extent of overall experimental datasetThe tendency of empirical or analytical expressions is thatthe range of the charge (scaled distance) is decreasing so is theaccuracy reduced This is due to uncertainties in measuredexperimental data in near field and contact explosions


Table 13 Incident pressure comparison

Author TNT[kg] R[m] Z[mkg03]

Free-field Pressure [MPa] Relative error []M E FEM ATB

125 mm ME MFEM MATB[15] 1302 500 213 026 017 027 025 3462 576 501[16] 805 200 100 173 130 175 136 2486 109 2123

[17] 2739 550 182 026 NA 025 035 NA 380 3540950 315 012 015 010 2324 1587

[18] 800 500 250 020 NA 023 017 NA 1265 1423Note 1 kg = 0453592 kg 1 ft = 03048 m 1 psi = 689 kPa M measured E estimated FEM finite element model ATB AT-Blast NA not available

Table 14 Reflected pressure comparison


Reflected Pressure [MPa] Relative error []M E FEM ATB

25 mm ME MFEM MATB

[19] 100 150 150 190 NA 162 253 NA 1494 33111750 058 2901 2136 2972 2636 243

[20] 390 585 372 024 019 026 016 2000 911 3125[15] 1302 150 064 1692 1702 1392 2419 059 1775 4296

[17] 1837 310 117 420 332 413 520 2092 177 23772739 103 553 494 572 755 1068 354 3656

[18]

500

500

292 060 055 077 035 826 2847 40682000 184 141 136 142 136 398 091 3983000 161 179 248 155 204 3870 1348 14414000 146 556 273 286 274 5086 4856 5079

Note 1 kg = 0453592 kg 1 ft = 03048 m 1 psi = 689 kPa M measured E estimated FEM finite element model ATB AT-Blast

6 Validation of Numerical Models

Validation of numerical models was conducted based oncomparison of numerical simulation results and experi-mental measurements Purpose of this comparison is toestablish the degree of error of parametrically determinedacceptable air mesh size in obtaining field measured blastpressures Results are compared not only with measuredbut also with estimated pressures given in research listedin Tables 13 and 14 Researchers estimated pressures usingCONWEP andor analytical calculation Incident pressuresweremeasured using free-field pressure gauges positioned onsomedistance fromexplosive chargewhile reflected pressuresweremeasured by pressure gauges positioned in such away toreduce influence ofmaterial deformation and deterioration topressure values Sensors were placed on a rigid containmentstructure that provided planed support and boundary condi-tions for test specimens during experiment In experimentaltesting performed by [15 20] sensors were positioned on thesurface of tested specimen and they were not able to measurepressures in all tests From eight sensors positioned by [20]just three to four were able to successfully measure blastpressures the rest of the data was corrupted due to sensormalfunctioning Table 13 provides comparison of measuredand simulated incident pressures while Table 14 gives com-parison of reflected pressures Pressures were additionally

estimated by AT-Blast in order to validate the software as atool for quick pressure and impulse assessment

In Table 13 it can be seen that the numerical resultsoverestimate measured incident pressures from 1 to 25From Table 14 it is impossible to draw general conclusionabout reflected pressure variations nevertheless pressuresare within acceptable error margin from which it can be con-cluded that numerical models provide sufficiently accurateresults If compared to estimated values by authors and AT-Blast numerical results provide smaller errors in previouslystated range Estimated values are generally larger thanthose measured which provides pressure overestimation andaccounts for all possible measurement errors This pressureoverestimation can lead to conservative structural design butfrom the aspect of human life protection in structures ofhigher importance this is acceptable

7 Conclusion

No recommendations exist for mesh size selection in blastload numerical simulations since the size of the finite elementstrongly depends on the blast scenario For this reason themesh size convergence tests were carried out for groundexplosion scenarios Tests comprised axisymmetric and 3Dblast numerical simulations in which different air mesh


sizes were used to compare the results with AT-Blast andextrapolated values A 10 difference of blast parameters inrelation to extrapolated values was considered sufficientlyaccurate for engineering use and based on this assumptionair mesh size recommendations were made for two differentblast scenarios

In both cases (free-air and reflected scenario) coarsemesh led to stretching of the pressure-time profile withouta distinct arrival time of the blast front If the rate of initialpressure rise is not very steep (close to 90∘) but rathergradual it is clear sign that the mesh size is too coarseAnother indication of inadequacy of mesh size is lack ofclear secondary pressure peak (see Figure 6) Finer meshshortened the time required for blast wave front to arrive tothe structure and if the mesh size was sufficiently small itno longer influenced the arrival time In the general case offree-air explosion the largest mesh size which is adequate tocapture all the blast parameters is 125 mm For the specificblast scenario (detonation of the charge beneath the bridgestructure) the largest adequate mesh sizes are 125 mm for115 kg of TNT and 25 mm for 230 and 680 kg of TNT

Results supported the initial presumption that withthe increase of distance between the detonation point andstructure pressures are decreasing but the sensitivity onthe mesh size and scattering of the results are greater forsmaller scaled distances The pressure values for larger scaleddistances were less sensitive to air mesh size

It should be emphasized that this research was carriedout for ideal conditions (spherical shape of charge rigidbridge deck and rigid ground) Further research should aimto investigate pressure variations in less ideal cases boxlikecharges nonrigid concrete slab compressible ground andexplosive confined in car trunk (with offset from groundlevel)

Data Availability

Authors state that themajority of data acquired from researchand input parameters needed for numerical simulations(repeatability of simulations) is listed in tables implementedin the submitted article If additional data is requestedauthors will be more than glad to share it with interestedresearchers Authors think that publicly available data con-tributes to research better quality it is an opportunity fordiscussion and exchange of new ideas among researchers

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research presented in this paper is a part of the researchproject ldquoBehaviour of Medium and Short Length BridgesSubjected to Blast Loadrdquo supported by the Faculty of CivilEngineering Osijek and support for this research is gratefullyacknowledged

References

[1] H Draganic Overpasses Subjected to Blast Load Faculty ofCivil Engineering Osijek Josip Juraj Strossmayer University ofOsijek Osijek 2014

[2] H Draganic and D Varevac ldquoNumerical simulation of effect ofexplosive action on overpassesrdquo Gradjevinar vol 69 no 6 pp437ndash451 2017

[3] J W Nam J J Kim S B Kim N H Yi and K J Byun ldquoAstudy onmesh size dependency of finite element blast structuralanalysis induced by non-uniform pressure distribution fromhigh explosive blast waverdquo KSCE Journal of Civil Engineeringvol 12 no 4 pp 259ndash265 2008

[4] T C Chapman T A Rose and P D Smith ldquoBlast wave simu-lation using AUTODYN2D a parametric studyrdquo InternationalJournal of Impact Engineering vol 16 no 5-6 pp 777ndash787 1995

[5] B Luccioni D Ambrosini and R Danesi ldquoBlast load assess-ment using hydrocodesrdquo Engineering Structures vol 28 no 12pp 1736ndash1744 2006

[6] Y Shi Z Li and H Hao ldquoMesh size effect in numericalsimulation of blast wave propagation and interaction withstructuresrdquo Transactions of Tianjin University vol 14 no 6 pp396ndash402 2008

[7] UFC Structures to Resist The Effects of Accidental Explosions2008

[8] R-B Deng and X-L Jin ldquoNumerical Simulation of BridgeDamage under Blast LoadsrdquoWSES Transactions on Computersvol 8 p 10 2009

[9] WWilkinson D Cormie J Shin andAWhittaker ldquoModellingclose-in detonations in the near-fieldrdquo in Proceedings of the15th International Symposium on Interaction of the Effects ofMunitions with Structures Potsdam Germany 2013

[10] J Shin A SWhittaker D Cormie andWWilkinson ldquoNumer-ical modeling of close-in detonations of high explosivesrdquoEngineering Structures vol 81 pp 88ndash97 2014

[11] J Shin A Whittaker D Cormie and A Aref Verificationand validation of a CFD code for modeling detonations of highexplosives 2015

[12] J Shin Air-blast effects on civil structures State University ofNew York Buffalo 2014

[13] J Shin A S Whittaker and D Cormie ldquoIncident and Nor-mally Reflected Overpressure and Impulse for Detonations ofSpherical High Explosives in Free Airrdquo Journal of StructuralEngineering (United States) vol 141 no 12 2015

[14] J Shin A Whittaker and D Cormie ldquoEstimating incident andreflected airblast parameters updated design chartsrdquo in Pro-ceedings of the 16th international symposium for the interactionof the effects of munitions with structures (ISIEMS 16) 2015

[15] N Yi J J Kim T Han Y Cho and J H Lee ldquoBlast-resistantcharacteristics of ultra-high strength concrete and reactivepowder concreterdquoConstruction and Building Materials vol 28no 1 pp 694ndash707 2012

[16] C Q Wu L Huang and D J Oehlers ldquoBlast testing ofaluminum foam-protected reinforced concrete slabsrdquo Journal ofPerformance of Constructed Facilities vol 25 no 5 pp 464ndash4742011

[17] AGhaniRazaqpurATolba andEContestabile ldquoBlast loadingresponse of reinforced concrete panels reinforced with exter-nally bonded GFRP laminatesrdquoComposites Part B Engineeringvol 38 no 5-6 pp 535ndash546 2007


[18] T S Lok and J R Xiao ldquoSteel-fibre-reinforced concrete panelsexposed to air blast loadingrdquo Proceedings of the Institution ofCivil Engineers Structures and Buildings vol 134 no 4 pp 319ndash331 1999

[19] J Li C Wu and H Hao ldquoResidual loading capacity ofultra-high performance concrete columns after blast loadsrdquoInternational Journal of Protective Structures vol 6 no 4 pp649ndash669 2015

[20] L Chen Q Fang J Fan Y Zhang H Hao and J LiuldquoResponses of masonry infill walls retrofitted with CFRP steelwire mesh and laminated bars to blast loadingsrdquo Advances inStructural Engineering vol 17 no 6 pp 817ndash836 2014

[21] A H Hameed ldquoDynamic Behaviour Of Reinforced ConcreteStructures Subjected To External Explosion A Thesisrdquo JumadaElawal vol 1428 2007

[22] J S Humphreys ldquoPlastic deformation of impulsively loadedstraight clamped beamsrdquo Journal of Applied Mechanics vol 32no 1 pp 7ndash10 1964

[23] A Freidenberg A Aviram L K Stewart D Whisler HKim and G A Hegemier ldquoDemonstration of tailored impactto achieve blast-like loadingrdquo International Journal of ImpactEngineering vol 71 pp 97ndash105 2014

[24] G C Mays and P D Smith ldquoBlast effects on buildings Designof buildings to optimize resistance to blast loadingrdquo T Telford1995

[25] N Newmark and R Hansen Design of blast resistant structuresShock and vibration Handbook vol 3 1961 Design of blastresistant structures Shock and vibration Handbook

[26] J Drake L Twisdale R Frank et al ldquoProtective ConstructionDesign Manual Resistance of Structural Elements (SectionIX)rdquo Report ESL-TR-87-57 Air Force Engineering and ServicesCenter Tyndall Air Force Base 1989

[27] P D Smith J G Hetherington and P Smith Blast and ballisticloading of structures Butterworth-Heinemann Oxford 1994

[28] ANSYS ldquoANSYS AUTODYN User manualrdquo in ANSYS Release140 pp 1ndash464 Canonsburg PA USA 2010

[29] L Kwasniewski ldquoApplication of grid convergence index in FEcomputationrdquo Bulletin of the Polish Academy of SciencesmdashTech-nical Sciences vol 61 no 1 pp 123ndash128 2013

[30] N K Bimbaum J Tancreto and K Hager ldquoCalculation of blastloading in the high performance magazine with AUTODYN-3Drdquo DTIC Document 1994

[31] R Courant K Friedrichs and H Lewy ldquoUber die partiellendifferenzengleichungen der mathematischen physikrdquo Mathe-matische Annalen vol 100 no 1 pp 32ndash74 1928

[32] G Baudin and R Serradeill ldquoReview of Jones-Wilkins-Leeequation of staterdquo in Proceedings of the EPJ Web of Conferencesvol 10 00021 2010

[33] E L Lee H C Hornig and JW Kury ldquoAdiabatic Expansion OfHighExplosiveDetonationProductsrdquo TechRepUCRLndash50422California Univ Livermore Lawrence Radiation Lab 1968

[34] ARA AT-Blast in Applied Research Associates Inc Vicks-burg Mississippi USA 2013

[35] ANSYS ldquoRemapping Tutorial Revision 43rdquo in AutodynExplicite Software for Nonlinear Dynamics pp 1ndash32 Canons-burg PA USA 2005

[36] G K Schleyer M J Lowak M A Polcyn and G S LangdonldquoExperimental investigation of blast wall panels under shockpressure loadingrdquo International Journal of Impact Engineeringvol 34 no 6 pp 1095ndash1118 2007

[37] J-A Calgaro M Tschumi and H Gulvanessian DesignersrsquoGuide to Eurocode 1 Actions on Bridges 2010

[38] I Celik and O Karatekin ldquoNumerical experiments on appli-cation of richardson extrapolation with nonuniform gridsrdquoJournal of Fluids Engineering vol 119 no 3 pp 584ndash590 1997

[39] J Slater Examining spatial (grid) convergence Public tutorialon CFD verification and validation vol MS 86 NASA GlennResearch Centre 2006

[40] L E Schwer ldquoIs your mesh refined enough Estimating dis-cretization error using GCIrdquo in LS-DYNA Forum GermanyBamberg 2008

[41] I B Celik ldquoProcedure for estimation and reporting of uncer-tainty due to discretization in CFD applicationsrdquo Journal ofFluids Engineering vol 130 no 7 pp 0780011ndash0780014 2008

[42] A Ullah F Ahmad H-W Jang S-W Kim and J-W HongldquoReview of analytical and empirical estimations for incidentblast pressurerdquoKSCE Journal of Civil Engineering pp 2211ndash22252017

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studied influence of mesh size on blast wave propagation asa part of their research on urban blast They concluded that afiner air mesh (10 cm) gives better results but this can be tooexpensive in the terms of computational time Alternativelya coarser air mesh (50 cm) may be used to obtain qualitativeresults for comparison Shi et al [6] studied the relationshipbetween the scaled distance and blast load parameters ina series of numerical simulations with different mesh sizesand compared the results with those from TM5-1300 [7]They found that the pressure and impulse are less sensitiveto mesh size with an increase of the scaled distance theyalso proposed a method for the adjustment of peak pressuresfor coarse meshes Nam et al [3] determined the maximumelement size to ensure that analytical results are independentof mesh size this eliminates load gradient differences andreduces the gap between explosive and internal energy Dengand Jin [8] conducted a parametric study of free-air blastwave propagation as a part of their research on bridge damageinduced by blast loading Simulation results indicated that a5 cm air mesh size guarantees effective blast loading and reli-able computational results Wilkinson et al [9] in their studyonmodelling close-in detonations in the near field comparednumerical results of overpressure obtained by Autodyn andAir3D Mesh sensitivity analysis was conducted and resultsclearly indicated that mesh dependency of calculated resultsis existent Shin et al [10ndash12] performed numerical 1D 2Dand 3D simulation of close-in detonation of high explosivesin order to validate CFD code for determining incident andreflected overpressure and impulses It was concluded thatmesh refinement studies are needed to establish cell sizes forair blast calculations and that a cell size of R500 should besufficient to predict overpressure histories in the near fieldwhere R is the distance from the centre of the charge tothe monitoring location In addition it was determined thatthe afterburning has a little effect on peak overpressure butcan increase impulse if sufficient oxygen is present Shin etal [12ndash14] as a part of their research on blast parameters ofdetonation of spherical high explosives in free-air performedmesh size analysis on a wide range of scaled distancesAnalysis produced recommendation of new polynomials anddesign charts for detonation parameters of spherical TNTcharges It was concluded that cell size of R500 is sufficientfor calculating pressures in the scaled distance range of 8mkg13 similar to previous research [10]

Referred numerical simulations show that the accuracyof numerical results is strongly dependent on mesh size andblast scenariomdasha mesh size acceptable for one blast scenariomight not be suitable for anotherThis is a clear indicator thata numerical mesh size convergence test needs to be carriedout prior to large-scale numerical simulations

With respect to these results and recommendations forthe purpose of this research it was necessary to determinethe amount of explosive which is likely to be placed underthe overpass Table 1 gives crude estimations of possibleTNT quantities that can be placed in common vehicles andused for explosive deployment under a bridge [21 22] Thefirst three quantities are assumed to be the most probableand may offer some hope of bridge survival detonation of

Table 1 Estimated quantities of explosives for various types ofvehicles

Vehicle type Charge mass [kg]Compact car trunk 115Trunk of a large car 230Closed van 680Closed truck 2270Truck with a trailer 13610Truck with two trailers 27220Note 1 pound = 045 kg

larger TNT quantities would for sure cause imminent bridgecollapse Physical characteristics of vehicles which dictate theshape and confinement of the charge detonation point andconsequent flying debris (fragmentation) are not taken intoconsideration and only transport capacity was used in orderto estimate the amount of explosive

2 Blast Wave Parameters

Explosion is an event of sudden and rapid energy releaseaccompanied by a large pressure and temperature gradienton the wave front It is very important to notice that blastparameters for free-air explosion are much more differentfrom parameters which dictate the influence of explosion onengineering structure in this case the overpass

The blast wave is described by several parameters butthe main one is scaled distance Z which depends on chargeweight W [kg] and charge distance to target R [m] Scaleddistance is calculated by the following expression

119885 = 1198773radic119882 (1)

Use of TNT as a referent explosive for determining Z iswidely accepted The first step in quantifying the blast wavesfrom a source other than TNT is to transform the chargemass into the equivalent mass of TNT In general the TNTequivalent represents the mass of TNT that would resultin an explosion with the same effect as the unit weight ofexplosive under consideration It is defined as the ratio ofthe mass of TNT to the mass of the explosive resulting inthe same magnitude of blast wave (or impulse pressure andenergy) at the same radial distance for each charge whichassumes the scaling laws of Sachs and Hopkins Commonway to make conversion is to multiply the explosive massby the conversion factor determined using one of severalexisting methods (the specific energy based concept pressurebased concept impulse based concept Chapman-Jouguetstate based concept etc)

The primary reason for choosing TNT as the referentexplosive is that most of the available experimental dataregarding the characteristics of blast waves were collectedusing TNT Several methods exist for determining the explo-sive characteristics of different explosives but they do notyield the same values for the TNT equivalent These valuesdepend on the characteristic parameter of the blast wave the







119901 (119905) = 119901푠 [1 minus 1199051199050 ] expminus

1198871199051199050 (2)






119894푠 = int푡119860+푡0

푡119860

119901푠 (119905) 119889119905 (4)










119889119905cou lt min(119889119909119888 119889119910119888 ) (5)



119901 = (120574 minus 1) 120588119890 (6)



119901 = 119860(1 minus 1205961198771120594) 119890

minus푅1휒 + 119861(1 minus 1205961198772120594) 119890

minus푅2휒 + 120596120594 (7)









+5

-5093094095096097098099100101102103104105106107


5 mm10 mm20 mm

Nor

mal

ized

tota

l bla

st en

ergy


+10

-10088090092094096098100102104106108110112


Nor

mal

ized

pre

ssur

e

5 mm10 mm20 mm



TNT chargeW [kg]


Air


Gauges




Gauge Point225

225

Gauge Point

Air

TNT chargeW [kg]


[cm]450

450

60

500






(a)



(b)




size[mm]TNT (kg)























Mesh size





Mesh size










039 mm078 mm156 mm313 mm625 mm125 mm25 mm


05 10 15 20 25 30 35 40 45 5000Time [ms]

0200400600800

1000120014001600

Inci

dent

pea

k pr

essure

[kPa

]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm


0250500750

1000125015001750200022502500

Inci

dent

pea

k pr

essure

[kPa

]

05 10 15 20 25 30 35 40 45 5000Time [ms]


10 20 30 40 5000Time [ms]

0500

100015002000250030003500400045005000

Inci

dent

pea

k pr

essure

[kPa

]

039 mm078 mm156 mm313 mm625 mm125 mm25 mm










039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

2000

4000

6000

8000

10000

12000

14000Po

sitiv

e pea

k in

cide

nt pre

ssur

e [kP

a]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Posi

tive i

ncid

ent p

eak

pres

sure

[kPa

]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

5000

10000

15000

20000

25000

30000

35000

40000

45000

Posi

tive i

ncid

ent p

eak

pres

sure

[kPa

]





800 mm400 mm200 mm100 mm50 mm


0

2000

4000

6000

8000

10000

12000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



800 mm400 mm200 mm100 mm50 mm


02000400060008000

1000012000140001600018000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



0

5000

10000

15000

20000

25000

30000

35000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]

800 mm400 mm200 mm100 mm50 mm




Incident wave


115 kg 252 240 258 250 239 234 228 224 222 221 220 220230 kg 217 200 214 206 201 194 190 187 185 183 182 182680 kg 173 177 172 168 160 152 148 144 143 142 140 140

1214161820222426

Arr

ival

tim

e [m

s]

AT-Blast

AT-Blast

AT-Blast

(a) Reflected wave

AT-Blast

AT-Blast

AT-Blast

Reflected wave


Arr

ival

tim

e [m

s]

28262422201816141210

30

(b) Incident wave









119901 = 1003816100381610038161003816ln 100381610038161003816100381611989132 minus 119891211003816100381610038161003816 + 119902 (119901)1003816100381610038161003816log 11990321




119866119862119868 = 119865푠 |120576|119903푝 minus 1100 (11)



120576 = 1198911 minus 11989121198911 (12)






+ 10 (upper bound)

- 10 (lower bound)



0

300

600

900

1200

1500

1800

Inci

dent

overpre

ssur

e [kP

a]

25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

500

1000

1500

2000

2500

3000

Inci

dent

overpre

ssur

e [kP

a]

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

1000

2000

3000

4000

5000

6000

Inci

dent

overpre

ssur

e [kP

a]








+ 10 (upper bound)

- 10 (lower bound)



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

100

mm

400

mm

200

mm

800

mm

125

mm

313

mm

625

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

800

mm

200

mm

400

mm

100

mm

625

mm

125

mm

313

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

5000

10000

15000

20000

25000

30000

35000

40000

Refle

cted

overpre

ssur

e [kP

a]

25 m

m

50 m

m

400

mm

200

mm

800

mm

100

mm

625

mm

125

mm

313

mm

Mesh size











Z [mkg13] A1 B1 C1 D1 E1 F1 G102 - 29 7211 -2107 -0323 0112 0069 0000 000029 - 238 7594 -3052 0410 0026 -0013 0000 0000238 - 1985 6054 -1407 0000 0000 0000 0000 0000



(13)







125 mm ME MFEM MATB[15] 1302 500 213 026 017 027 025 3462 576 501[16] 805 200 100 173 130 175 136 2486 109 2123

[17] 2739 550 182 026 NA 025 035 NA 380 3540950 315 012 015 010 2324 1587





25 mm ME MFEM MATB

[19] 100 150 150 190 NA 162 253 NA 1494 33111750 058 2901 2136 2972 2636 243

[20] 390 585 372 024 019 026 016 2000 911 3125[15] 1302 150 064 1692 1702 1392 2419 059 1775 4296

[17] 1837 310 117 420 332 413 520 2092 177 23772739 103 553 494 572 755 1068 354 3656

[18]

500

500

292 060 055 077 035 826 2847 40682000 184 141 136 142 136 398 091 3983000 161 179 248 155 204 3870 1348 14414000 146 556 273 286 274 5086 4856 5079






7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








119901 (119905) = 119901푠 [1 minus 1199051199050 ] expminus

1198871199051199050 (2)






119894푠 = int푡119860+푡0

푡119860

119901푠 (119905) 119889119905 (4)










119889119905cou lt min(119889119909119888 119889119910119888 ) (5)



119901 = (120574 minus 1) 120588119890 (6)



119901 = 119860(1 minus 1205961198771120594) 119890

minus푅1휒 + 119861(1 minus 1205961198772120594) 119890

minus푅2휒 + 120596120594 (7)









+5

-5093094095096097098099100101102103104105106107


5 mm10 mm20 mm

Nor

mal

ized

tota

l bla

st en

ergy


+10

-10088090092094096098100102104106108110112


Nor

mal

ized

pre

ssur

e

5 mm10 mm20 mm



TNT chargeW [kg]


Air


Gauges




Gauge Point225

225

Gauge Point

Air

TNT chargeW [kg]


[cm]450

450

60

500






(a)



(b)




size[mm]TNT (kg)























Mesh size





Mesh size










039 mm078 mm156 mm313 mm625 mm125 mm25 mm


05 10 15 20 25 30 35 40 45 5000Time [ms]

0200400600800

1000120014001600

Inci

dent

pea

k pr

essure

[kPa

]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm


0250500750

1000125015001750200022502500

Inci

dent

pea

k pr

essure

[kPa

]

05 10 15 20 25 30 35 40 45 5000Time [ms]


10 20 30 40 5000Time [ms]

0500

100015002000250030003500400045005000

Inci

dent

pea

k pr

essure

[kPa

]

039 mm078 mm156 mm313 mm625 mm125 mm25 mm










039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

2000

4000

6000

8000

10000

12000

14000Po

sitiv

e pea

k in

cide

nt pre

ssur

e [kP

a]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Posi

tive i

ncid

ent p

eak

pres

sure

[kPa

]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

5000

10000

15000

20000

25000

30000

35000

40000

45000

Posi

tive i

ncid

ent p

eak

pres

sure

[kPa

]





800 mm400 mm200 mm100 mm50 mm


0

2000

4000

6000

8000

10000

12000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



800 mm400 mm200 mm100 mm50 mm


02000400060008000

1000012000140001600018000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



0

5000

10000

15000

20000

25000

30000

35000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]

800 mm400 mm200 mm100 mm50 mm




Incident wave


115 kg 252 240 258 250 239 234 228 224 222 221 220 220230 kg 217 200 214 206 201 194 190 187 185 183 182 182680 kg 173 177 172 168 160 152 148 144 143 142 140 140

1214161820222426

Arr

ival

tim

e [m

s]

AT-Blast

AT-Blast

AT-Blast

(a) Reflected wave

AT-Blast

AT-Blast

AT-Blast

Reflected wave


Arr

ival

tim

e [m

s]

28262422201816141210

30

(b) Incident wave









119901 = 1003816100381610038161003816ln 100381610038161003816100381611989132 minus 119891211003816100381610038161003816 + 119902 (119901)1003816100381610038161003816log 11990321




119866119862119868 = 119865푠 |120576|119903푝 minus 1100 (11)



120576 = 1198911 minus 11989121198911 (12)






+ 10 (upper bound)

- 10 (lower bound)



0

300

600

900

1200

1500

1800

Inci

dent

overpre

ssur

e [kP

a]

25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

500

1000

1500

2000

2500

3000

Inci

dent

overpre

ssur

e [kP

a]

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

1000

2000

3000

4000

5000

6000

Inci

dent

overpre

ssur

e [kP

a]








+ 10 (upper bound)

- 10 (lower bound)



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

100

mm

400

mm

200

mm

800

mm

125

mm

313

mm

625

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

800

mm

200

mm

400

mm

100

mm

625

mm

125

mm

313

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

5000

10000

15000

20000

25000

30000

35000

40000

Refle

cted

overpre

ssur

e [kP

a]

25 m

m

50 m

m

400

mm

200

mm

800

mm

100

mm

625

mm

125

mm

313

mm

Mesh size











Z [mkg13] A1 B1 C1 D1 E1 F1 G102 - 29 7211 -2107 -0323 0112 0069 0000 000029 - 238 7594 -3052 0410 0026 -0013 0000 0000238 - 1985 6054 -1407 0000 0000 0000 0000 0000



(13)







125 mm ME MFEM MATB[15] 1302 500 213 026 017 027 025 3462 576 501[16] 805 200 100 173 130 175 136 2486 109 2123

[17] 2739 550 182 026 NA 025 035 NA 380 3540950 315 012 015 010 2324 1587





25 mm ME MFEM MATB

[19] 100 150 150 190 NA 162 253 NA 1494 33111750 058 2901 2136 2972 2636 243

[20] 390 585 372 024 019 026 016 2000 911 3125[15] 1302 150 064 1692 1702 1392 2419 059 1775 4296

[17] 1837 310 117 420 332 413 520 2092 177 23772739 103 553 494 572 755 1068 354 3656

[18]

500

500

292 060 055 077 035 826 2847 40682000 184 141 136 142 136 398 091 3983000 161 179 248 155 204 3870 1348 14414000 146 556 273 286 274 5086 4856 5079






7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




119889119905cou lt min(119889119909119888 119889119910119888 ) (5)



119901 = (120574 minus 1) 120588119890 (6)



119901 = 119860(1 minus 1205961198771120594) 119890

minus푅1휒 + 119861(1 minus 1205961198772120594) 119890

minus푅2휒 + 120596120594 (7)









+5

-5093094095096097098099100101102103104105106107


5 mm10 mm20 mm

Nor

mal

ized

tota

l bla

st en

ergy


+10

-10088090092094096098100102104106108110112


Nor

mal

ized

pre

ssur

e

5 mm10 mm20 mm



TNT chargeW [kg]


Air


Gauges




Gauge Point225

225

Gauge Point

Air

TNT chargeW [kg]


[cm]450

450

60

500






(a)



(b)




size[mm]TNT (kg)























Mesh size





Mesh size










039 mm078 mm156 mm313 mm625 mm125 mm25 mm


05 10 15 20 25 30 35 40 45 5000Time [ms]

0200400600800

1000120014001600

Inci

dent

pea

k pr

essure

[kPa

]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm


0250500750

1000125015001750200022502500

Inci

dent

pea

k pr

essure

[kPa

]

05 10 15 20 25 30 35 40 45 5000Time [ms]


10 20 30 40 5000Time [ms]

0500

100015002000250030003500400045005000

Inci

dent

pea

k pr

essure

[kPa

]

039 mm078 mm156 mm313 mm625 mm125 mm25 mm










039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

2000

4000

6000

8000

10000

12000

14000Po

sitiv

e pea

k in

cide

nt pre

ssur

e [kP

a]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Posi

tive i

ncid

ent p

eak

pres

sure

[kPa

]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

5000

10000

15000

20000

25000

30000

35000

40000

45000

Posi

tive i

ncid

ent p

eak

pres

sure

[kPa

]





800 mm400 mm200 mm100 mm50 mm


0

2000

4000

6000

8000

10000

12000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



800 mm400 mm200 mm100 mm50 mm


02000400060008000

1000012000140001600018000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



0

5000

10000

15000

20000

25000

30000

35000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]

800 mm400 mm200 mm100 mm50 mm




Incident wave


115 kg 252 240 258 250 239 234 228 224 222 221 220 220230 kg 217 200 214 206 201 194 190 187 185 183 182 182680 kg 173 177 172 168 160 152 148 144 143 142 140 140

1214161820222426

Arr

ival

tim

e [m

s]

AT-Blast

AT-Blast

AT-Blast

(a) Reflected wave

AT-Blast

AT-Blast

AT-Blast

Reflected wave


Arr

ival

tim

e [m

s]

28262422201816141210

30

(b) Incident wave









119901 = 1003816100381610038161003816ln 100381610038161003816100381611989132 minus 119891211003816100381610038161003816 + 119902 (119901)1003816100381610038161003816log 11990321




119866119862119868 = 119865푠 |120576|119903푝 minus 1100 (11)



120576 = 1198911 minus 11989121198911 (12)






+ 10 (upper bound)

- 10 (lower bound)



0

300

600

900

1200

1500

1800

Inci

dent

overpre

ssur

e [kP

a]

25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

500

1000

1500

2000

2500

3000

Inci

dent

overpre

ssur

e [kP

a]

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

1000

2000

3000

4000

5000

6000

Inci

dent

overpre

ssur

e [kP

a]








+ 10 (upper bound)

- 10 (lower bound)



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

100

mm

400

mm

200

mm

800

mm

125

mm

313

mm

625

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

800

mm

200

mm

400

mm

100

mm

625

mm

125

mm

313

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

5000

10000

15000

20000

25000

30000

35000

40000

Refle

cted

overpre

ssur

e [kP

a]

25 m

m

50 m

m

400

mm

200

mm

800

mm

100

mm

625

mm

125

mm

313

mm

Mesh size











Z [mkg13] A1 B1 C1 D1 E1 F1 G102 - 29 7211 -2107 -0323 0112 0069 0000 000029 - 238 7594 -3052 0410 0026 -0013 0000 0000238 - 1985 6054 -1407 0000 0000 0000 0000 0000



(13)







125 mm ME MFEM MATB[15] 1302 500 213 026 017 027 025 3462 576 501[16] 805 200 100 173 130 175 136 2486 109 2123

[17] 2739 550 182 026 NA 025 035 NA 380 3540950 315 012 015 010 2324 1587





25 mm ME MFEM MATB

[19] 100 150 150 190 NA 162 253 NA 1494 33111750 058 2901 2136 2972 2636 243

[20] 390 585 372 024 019 026 016 2000 911 3125[15] 1302 150 064 1692 1702 1392 2419 059 1775 4296

[17] 1837 310 117 420 332 413 520 2092 177 23772739 103 553 494 572 755 1068 354 3656

[18]

500

500

292 060 055 077 035 826 2847 40682000 184 141 136 142 136 398 091 3983000 161 179 248 155 204 3870 1348 14414000 146 556 273 286 274 5086 4856 5079






7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



+5

-5093094095096097098099100101102103104105106107


5 mm10 mm20 mm

Nor

mal

ized

tota

l bla

st en

ergy


+10

-10088090092094096098100102104106108110112


Nor

mal

ized

pre

ssur

e

5 mm10 mm20 mm



TNT chargeW [kg]


Air


Gauges




Gauge Point225

225

Gauge Point

Air

TNT chargeW [kg]


[cm]450

450

60

500






(a)



(b)




size[mm]TNT (kg)























Mesh size





Mesh size










039 mm078 mm156 mm313 mm625 mm125 mm25 mm


05 10 15 20 25 30 35 40 45 5000Time [ms]

0200400600800

1000120014001600

Inci

dent

pea

k pr

essure

[kPa

]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm


0250500750

1000125015001750200022502500

Inci

dent

pea

k pr

essure

[kPa

]

05 10 15 20 25 30 35 40 45 5000Time [ms]


10 20 30 40 5000Time [ms]

0500

100015002000250030003500400045005000

Inci

dent

pea

k pr

essure

[kPa

]

039 mm078 mm156 mm313 mm625 mm125 mm25 mm










039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

2000

4000

6000

8000

10000

12000

14000Po

sitiv

e pea

k in

cide

nt pre

ssur

e [kP

a]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Posi

tive i

ncid

ent p

eak

pres

sure

[kPa

]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

5000

10000

15000

20000

25000

30000

35000

40000

45000

Posi

tive i

ncid

ent p

eak

pres

sure

[kPa

]





800 mm400 mm200 mm100 mm50 mm


0

2000

4000

6000

8000

10000

12000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



800 mm400 mm200 mm100 mm50 mm


02000400060008000

1000012000140001600018000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



0

5000

10000

15000

20000

25000

30000

35000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]

800 mm400 mm200 mm100 mm50 mm




Incident wave


115 kg 252 240 258 250 239 234 228 224 222 221 220 220230 kg 217 200 214 206 201 194 190 187 185 183 182 182680 kg 173 177 172 168 160 152 148 144 143 142 140 140

1214161820222426

Arr

ival

tim

e [m

s]

AT-Blast

AT-Blast

AT-Blast

(a) Reflected wave

AT-Blast

AT-Blast

AT-Blast

Reflected wave


Arr

ival

tim

e [m

s]

28262422201816141210

30

(b) Incident wave









119901 = 1003816100381610038161003816ln 100381610038161003816100381611989132 minus 119891211003816100381610038161003816 + 119902 (119901)1003816100381610038161003816log 11990321




119866119862119868 = 119865푠 |120576|119903푝 minus 1100 (11)



120576 = 1198911 minus 11989121198911 (12)






+ 10 (upper bound)

- 10 (lower bound)



0

300

600

900

1200

1500

1800

Inci

dent

overpre

ssur

e [kP

a]

25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

500

1000

1500

2000

2500

3000

Inci

dent

overpre

ssur

e [kP

a]

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

1000

2000

3000

4000

5000

6000

Inci

dent

overpre

ssur

e [kP

a]








+ 10 (upper bound)

- 10 (lower bound)



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

100

mm

400

mm

200

mm

800

mm

125

mm

313

mm

625

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

800

mm

200

mm

400

mm

100

mm

625

mm

125

mm

313

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

5000

10000

15000

20000

25000

30000

35000

40000

Refle

cted

overpre

ssur

e [kP

a]

25 m

m

50 m

m

400

mm

200

mm

800

mm

100

mm

625

mm

125

mm

313

mm

Mesh size











Z [mkg13] A1 B1 C1 D1 E1 F1 G102 - 29 7211 -2107 -0323 0112 0069 0000 000029 - 238 7594 -3052 0410 0026 -0013 0000 0000238 - 1985 6054 -1407 0000 0000 0000 0000 0000



(13)







125 mm ME MFEM MATB[15] 1302 500 213 026 017 027 025 3462 576 501[16] 805 200 100 173 130 175 136 2486 109 2123

[17] 2739 550 182 026 NA 025 035 NA 380 3540950 315 012 015 010 2324 1587





25 mm ME MFEM MATB

[19] 100 150 150 190 NA 162 253 NA 1494 33111750 058 2901 2136 2972 2636 243

[20] 390 585 372 024 019 026 016 2000 911 3125[15] 1302 150 064 1692 1702 1392 2419 059 1775 4296

[17] 1837 310 117 420 332 413 520 2092 177 23772739 103 553 494 572 755 1068 354 3656

[18]

500

500

292 060 055 077 035 826 2847 40682000 184 141 136 142 136 398 091 3983000 161 179 248 155 204 3870 1348 14414000 146 556 273 286 274 5086 4856 5079






7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




(a)



(b)




size[mm]TNT (kg)























Mesh size





Mesh size










039 mm078 mm156 mm313 mm625 mm125 mm25 mm


05 10 15 20 25 30 35 40 45 5000Time [ms]

0200400600800

1000120014001600

Inci

dent

pea

k pr

essure

[kPa

]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm


0250500750

1000125015001750200022502500

Inci

dent

pea

k pr

essure

[kPa

]

05 10 15 20 25 30 35 40 45 5000Time [ms]


10 20 30 40 5000Time [ms]

0500

100015002000250030003500400045005000

Inci

dent

pea

k pr

essure

[kPa

]

039 mm078 mm156 mm313 mm625 mm125 mm25 mm










039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

2000

4000

6000

8000

10000

12000

14000Po

sitiv

e pea

k in

cide

nt pre

ssur

e [kP

a]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Posi

tive i

ncid

ent p

eak

pres

sure

[kPa

]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

5000

10000

15000

20000

25000

30000

35000

40000

45000

Posi

tive i

ncid

ent p

eak

pres

sure

[kPa

]





800 mm400 mm200 mm100 mm50 mm


0

2000

4000

6000

8000

10000

12000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



800 mm400 mm200 mm100 mm50 mm


02000400060008000

1000012000140001600018000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



0

5000

10000

15000

20000

25000

30000

35000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]

800 mm400 mm200 mm100 mm50 mm




Incident wave


115 kg 252 240 258 250 239 234 228 224 222 221 220 220230 kg 217 200 214 206 201 194 190 187 185 183 182 182680 kg 173 177 172 168 160 152 148 144 143 142 140 140

1214161820222426

Arr

ival

tim

e [m

s]

AT-Blast

AT-Blast

AT-Blast

(a) Reflected wave

AT-Blast

AT-Blast

AT-Blast

Reflected wave


Arr

ival

tim

e [m

s]

28262422201816141210

30

(b) Incident wave









119901 = 1003816100381610038161003816ln 100381610038161003816100381611989132 minus 119891211003816100381610038161003816 + 119902 (119901)1003816100381610038161003816log 11990321




119866119862119868 = 119865푠 |120576|119903푝 minus 1100 (11)



120576 = 1198911 minus 11989121198911 (12)






+ 10 (upper bound)

- 10 (lower bound)



0

300

600

900

1200

1500

1800

Inci

dent

overpre

ssur

e [kP

a]

25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

500

1000

1500

2000

2500

3000

Inci

dent

overpre

ssur

e [kP

a]

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

1000

2000

3000

4000

5000

6000

Inci

dent

overpre

ssur

e [kP

a]








+ 10 (upper bound)

- 10 (lower bound)



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

100

mm

400

mm

200

mm

800

mm

125

mm

313

mm

625

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

800

mm

200

mm

400

mm

100

mm

625

mm

125

mm

313

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

5000

10000

15000

20000

25000

30000

35000

40000

Refle

cted

overpre

ssur

e [kP

a]

25 m

m

50 m

m

400

mm

200

mm

800

mm

100

mm

625

mm

125

mm

313

mm

Mesh size











Z [mkg13] A1 B1 C1 D1 E1 F1 G102 - 29 7211 -2107 -0323 0112 0069 0000 000029 - 238 7594 -3052 0410 0026 -0013 0000 0000238 - 1985 6054 -1407 0000 0000 0000 0000 0000



(13)







125 mm ME MFEM MATB[15] 1302 500 213 026 017 027 025 3462 576 501[16] 805 200 100 173 130 175 136 2486 109 2123

[17] 2739 550 182 026 NA 025 035 NA 380 3540950 315 012 015 010 2324 1587





25 mm ME MFEM MATB

[19] 100 150 150 190 NA 162 253 NA 1494 33111750 058 2901 2136 2972 2636 243

[20] 390 585 372 024 019 026 016 2000 911 3125[15] 1302 150 064 1692 1702 1392 2419 059 1775 4296

[17] 1837 310 117 420 332 413 520 2092 177 23772739 103 553 494 572 755 1068 354 3656

[18]

500

500

292 060 055 077 035 826 2847 40682000 184 141 136 142 136 398 091 3983000 161 179 248 155 204 3870 1348 14414000 146 556 273 286 274 5086 4856 5079






7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


















Mesh size





Mesh size










039 mm078 mm156 mm313 mm625 mm125 mm25 mm


05 10 15 20 25 30 35 40 45 5000Time [ms]

0200400600800

1000120014001600

Inci

dent

pea

k pr

essure

[kPa

]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm


0250500750

1000125015001750200022502500

Inci

dent

pea

k pr

essure

[kPa

]

05 10 15 20 25 30 35 40 45 5000Time [ms]


10 20 30 40 5000Time [ms]

0500

100015002000250030003500400045005000

Inci

dent

pea

k pr

essure

[kPa

]

039 mm078 mm156 mm313 mm625 mm125 mm25 mm










039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

2000

4000

6000

8000

10000

12000

14000Po

sitiv

e pea

k in

cide

nt pre

ssur

e [kP

a]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Posi

tive i

ncid

ent p

eak

pres

sure

[kPa

]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

5000

10000

15000

20000

25000

30000

35000

40000

45000

Posi

tive i

ncid

ent p

eak

pres

sure

[kPa

]





800 mm400 mm200 mm100 mm50 mm


0

2000

4000

6000

8000

10000

12000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



800 mm400 mm200 mm100 mm50 mm


02000400060008000

1000012000140001600018000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



0

5000

10000

15000

20000

25000

30000

35000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]

800 mm400 mm200 mm100 mm50 mm




Incident wave


115 kg 252 240 258 250 239 234 228 224 222 221 220 220230 kg 217 200 214 206 201 194 190 187 185 183 182 182680 kg 173 177 172 168 160 152 148 144 143 142 140 140

1214161820222426

Arr

ival

tim

e [m

s]

AT-Blast

AT-Blast

AT-Blast

(a) Reflected wave

AT-Blast

AT-Blast

AT-Blast

Reflected wave


Arr

ival

tim

e [m

s]

28262422201816141210

30

(b) Incident wave









119901 = 1003816100381610038161003816ln 100381610038161003816100381611989132 minus 119891211003816100381610038161003816 + 119902 (119901)1003816100381610038161003816log 11990321




119866119862119868 = 119865푠 |120576|119903푝 minus 1100 (11)



120576 = 1198911 minus 11989121198911 (12)






+ 10 (upper bound)

- 10 (lower bound)



0

300

600

900

1200

1500

1800

Inci

dent

overpre

ssur

e [kP

a]

25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

500

1000

1500

2000

2500

3000

Inci

dent

overpre

ssur

e [kP

a]

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

1000

2000

3000

4000

5000

6000

Inci

dent

overpre

ssur

e [kP

a]








+ 10 (upper bound)

- 10 (lower bound)



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

100

mm

400

mm

200

mm

800

mm

125

mm

313

mm

625

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

800

mm

200

mm

400

mm

100

mm

625

mm

125

mm

313

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

5000

10000

15000

20000

25000

30000

35000

40000

Refle

cted

overpre

ssur

e [kP

a]

25 m

m

50 m

m

400

mm

200

mm

800

mm

100

mm

625

mm

125

mm

313

mm

Mesh size











Z [mkg13] A1 B1 C1 D1 E1 F1 G102 - 29 7211 -2107 -0323 0112 0069 0000 000029 - 238 7594 -3052 0410 0026 -0013 0000 0000238 - 1985 6054 -1407 0000 0000 0000 0000 0000



(13)







125 mm ME MFEM MATB[15] 1302 500 213 026 017 027 025 3462 576 501[16] 805 200 100 173 130 175 136 2486 109 2123

[17] 2739 550 182 026 NA 025 035 NA 380 3540950 315 012 015 010 2324 1587





25 mm ME MFEM MATB

[19] 100 150 150 190 NA 162 253 NA 1494 33111750 058 2901 2136 2972 2636 243

[20] 390 585 372 024 019 026 016 2000 911 3125[15] 1302 150 064 1692 1702 1392 2419 059 1775 4296

[17] 1837 310 117 420 332 413 520 2092 177 23772739 103 553 494 572 755 1068 354 3656

[18]

500

500

292 060 055 077 035 826 2847 40682000 184 141 136 142 136 398 091 3983000 161 179 248 155 204 3870 1348 14414000 146 556 273 286 274 5086 4856 5079






7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



039 mm078 mm156 mm313 mm625 mm125 mm25 mm


05 10 15 20 25 30 35 40 45 5000Time [ms]

0200400600800

1000120014001600

Inci

dent

pea

k pr

essure

[kPa

]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm


0250500750

1000125015001750200022502500

Inci

dent

pea

k pr

essure

[kPa

]

05 10 15 20 25 30 35 40 45 5000Time [ms]


10 20 30 40 5000Time [ms]

0500

100015002000250030003500400045005000

Inci

dent

pea

k pr

essure

[kPa

]

039 mm078 mm156 mm313 mm625 mm125 mm25 mm










039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

2000

4000

6000

8000

10000

12000

14000Po

sitiv

e pea

k in

cide

nt pre

ssur

e [kP

a]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Posi

tive i

ncid

ent p

eak

pres

sure

[kPa

]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

5000

10000

15000

20000

25000

30000

35000

40000

45000

Posi

tive i

ncid

ent p

eak

pres

sure

[kPa

]





800 mm400 mm200 mm100 mm50 mm


0

2000

4000

6000

8000

10000

12000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



800 mm400 mm200 mm100 mm50 mm


02000400060008000

1000012000140001600018000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



0

5000

10000

15000

20000

25000

30000

35000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]

800 mm400 mm200 mm100 mm50 mm




Incident wave


115 kg 252 240 258 250 239 234 228 224 222 221 220 220230 kg 217 200 214 206 201 194 190 187 185 183 182 182680 kg 173 177 172 168 160 152 148 144 143 142 140 140

1214161820222426

Arr

ival

tim

e [m

s]

AT-Blast

AT-Blast

AT-Blast

(a) Reflected wave

AT-Blast

AT-Blast

AT-Blast

Reflected wave


Arr

ival

tim

e [m

s]

28262422201816141210

30

(b) Incident wave









119901 = 1003816100381610038161003816ln 100381610038161003816100381611989132 minus 119891211003816100381610038161003816 + 119902 (119901)1003816100381610038161003816log 11990321




119866119862119868 = 119865푠 |120576|119903푝 minus 1100 (11)



120576 = 1198911 minus 11989121198911 (12)






+ 10 (upper bound)

- 10 (lower bound)



0

300

600

900

1200

1500

1800

Inci

dent

overpre

ssur

e [kP

a]

25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

500

1000

1500

2000

2500

3000

Inci

dent

overpre

ssur

e [kP

a]

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

1000

2000

3000

4000

5000

6000

Inci

dent

overpre

ssur

e [kP

a]








+ 10 (upper bound)

- 10 (lower bound)



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

100

mm

400

mm

200

mm

800

mm

125

mm

313

mm

625

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

800

mm

200

mm

400

mm

100

mm

625

mm

125

mm

313

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

5000

10000

15000

20000

25000

30000

35000

40000

Refle

cted

overpre

ssur

e [kP

a]

25 m

m

50 m

m

400

mm

200

mm

800

mm

100

mm

625

mm

125

mm

313

mm

Mesh size











Z [mkg13] A1 B1 C1 D1 E1 F1 G102 - 29 7211 -2107 -0323 0112 0069 0000 000029 - 238 7594 -3052 0410 0026 -0013 0000 0000238 - 1985 6054 -1407 0000 0000 0000 0000 0000



(13)







125 mm ME MFEM MATB[15] 1302 500 213 026 017 027 025 3462 576 501[16] 805 200 100 173 130 175 136 2486 109 2123

[17] 2739 550 182 026 NA 025 035 NA 380 3540950 315 012 015 010 2324 1587





25 mm ME MFEM MATB

[19] 100 150 150 190 NA 162 253 NA 1494 33111750 058 2901 2136 2972 2636 243

[20] 390 585 372 024 019 026 016 2000 911 3125[15] 1302 150 064 1692 1702 1392 2419 059 1775 4296

[17] 1837 310 117 420 332 413 520 2092 177 23772739 103 553 494 572 755 1068 354 3656

[18]

500

500

292 060 055 077 035 826 2847 40682000 184 141 136 142 136 398 091 3983000 161 179 248 155 204 3870 1348 14414000 146 556 273 286 274 5086 4856 5079






7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

2000

4000

6000

8000

10000

12000

14000Po

sitiv

e pea

k in

cide

nt pre

ssur

e [kP

a]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Posi

tive i

ncid

ent p

eak

pres

sure

[kPa

]


039 mm078 mm156 mm313 mm625 mm125 mm25 mm



0

5000

10000

15000

20000

25000

30000

35000

40000

45000

Posi

tive i

ncid

ent p

eak

pres

sure

[kPa

]





800 mm400 mm200 mm100 mm50 mm


0

2000

4000

6000

8000

10000

12000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



800 mm400 mm200 mm100 mm50 mm


02000400060008000

1000012000140001600018000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



0

5000

10000

15000

20000

25000

30000

35000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]

800 mm400 mm200 mm100 mm50 mm




Incident wave


115 kg 252 240 258 250 239 234 228 224 222 221 220 220230 kg 217 200 214 206 201 194 190 187 185 183 182 182680 kg 173 177 172 168 160 152 148 144 143 142 140 140

1214161820222426

Arr

ival

tim

e [m

s]

AT-Blast

AT-Blast

AT-Blast

(a) Reflected wave

AT-Blast

AT-Blast

AT-Blast

Reflected wave


Arr

ival

tim

e [m

s]

28262422201816141210

30

(b) Incident wave









119901 = 1003816100381610038161003816ln 100381610038161003816100381611989132 minus 119891211003816100381610038161003816 + 119902 (119901)1003816100381610038161003816log 11990321




119866119862119868 = 119865푠 |120576|119903푝 minus 1100 (11)



120576 = 1198911 minus 11989121198911 (12)






+ 10 (upper bound)

- 10 (lower bound)



0

300

600

900

1200

1500

1800

Inci

dent

overpre

ssur

e [kP

a]

25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

500

1000

1500

2000

2500

3000

Inci

dent

overpre

ssur

e [kP

a]

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

1000

2000

3000

4000

5000

6000

Inci

dent

overpre

ssur

e [kP

a]








+ 10 (upper bound)

- 10 (lower bound)



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

100

mm

400

mm

200

mm

800

mm

125

mm

313

mm

625

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

800

mm

200

mm

400

mm

100

mm

625

mm

125

mm

313

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

5000

10000

15000

20000

25000

30000

35000

40000

Refle

cted

overpre

ssur

e [kP

a]

25 m

m

50 m

m

400

mm

200

mm

800

mm

100

mm

625

mm

125

mm

313

mm

Mesh size











Z [mkg13] A1 B1 C1 D1 E1 F1 G102 - 29 7211 -2107 -0323 0112 0069 0000 000029 - 238 7594 -3052 0410 0026 -0013 0000 0000238 - 1985 6054 -1407 0000 0000 0000 0000 0000



(13)







125 mm ME MFEM MATB[15] 1302 500 213 026 017 027 025 3462 576 501[16] 805 200 100 173 130 175 136 2486 109 2123

[17] 2739 550 182 026 NA 025 035 NA 380 3540950 315 012 015 010 2324 1587





25 mm ME MFEM MATB

[19] 100 150 150 190 NA 162 253 NA 1494 33111750 058 2901 2136 2972 2636 243

[20] 390 585 372 024 019 026 016 2000 911 3125[15] 1302 150 064 1692 1702 1392 2419 059 1775 4296

[17] 1837 310 117 420 332 413 520 2092 177 23772739 103 553 494 572 755 1068 354 3656

[18]

500

500

292 060 055 077 035 826 2847 40682000 184 141 136 142 136 398 091 3983000 161 179 248 155 204 3870 1348 14414000 146 556 273 286 274 5086 4856 5079






7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




800 mm400 mm200 mm100 mm50 mm


0

2000

4000

6000

8000

10000

12000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



800 mm400 mm200 mm100 mm50 mm


02000400060008000

1000012000140001600018000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]



0

5000

10000

15000

20000

25000

30000

35000

Refle

cted

overpre

ssur

e [kP

a]

05 10 15 20 25 30 35 40 45 5000Time [ms]

800 mm400 mm200 mm100 mm50 mm




Incident wave


115 kg 252 240 258 250 239 234 228 224 222 221 220 220230 kg 217 200 214 206 201 194 190 187 185 183 182 182680 kg 173 177 172 168 160 152 148 144 143 142 140 140

1214161820222426

Arr

ival

tim

e [m

s]

AT-Blast

AT-Blast

AT-Blast

(a) Reflected wave

AT-Blast

AT-Blast

AT-Blast

Reflected wave


Arr

ival

tim

e [m

s]

28262422201816141210

30

(b) Incident wave









119901 = 1003816100381610038161003816ln 100381610038161003816100381611989132 minus 119891211003816100381610038161003816 + 119902 (119901)1003816100381610038161003816log 11990321




119866119862119868 = 119865푠 |120576|119903푝 minus 1100 (11)



120576 = 1198911 minus 11989121198911 (12)






+ 10 (upper bound)

- 10 (lower bound)



0

300

600

900

1200

1500

1800

Inci

dent

overpre

ssur

e [kP

a]

25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

500

1000

1500

2000

2500

3000

Inci

dent

overpre

ssur

e [kP

a]

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

1000

2000

3000

4000

5000

6000

Inci

dent

overpre

ssur

e [kP

a]








+ 10 (upper bound)

- 10 (lower bound)



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

100

mm

400

mm

200

mm

800

mm

125

mm

313

mm

625

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

800

mm

200

mm

400

mm

100

mm

625

mm

125

mm

313

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

5000

10000

15000

20000

25000

30000

35000

40000

Refle

cted

overpre

ssur

e [kP

a]

25 m

m

50 m

m

400

mm

200

mm

800

mm

100

mm

625

mm

125

mm

313

mm

Mesh size











Z [mkg13] A1 B1 C1 D1 E1 F1 G102 - 29 7211 -2107 -0323 0112 0069 0000 000029 - 238 7594 -3052 0410 0026 -0013 0000 0000238 - 1985 6054 -1407 0000 0000 0000 0000 0000



(13)







125 mm ME MFEM MATB[15] 1302 500 213 026 017 027 025 3462 576 501[16] 805 200 100 173 130 175 136 2486 109 2123

[17] 2739 550 182 026 NA 025 035 NA 380 3540950 315 012 015 010 2324 1587





25 mm ME MFEM MATB

[19] 100 150 150 190 NA 162 253 NA 1494 33111750 058 2901 2136 2972 2636 243

[20] 390 585 372 024 019 026 016 2000 911 3125[15] 1302 150 064 1692 1702 1392 2419 059 1775 4296

[17] 1837 310 117 420 332 413 520 2092 177 23772739 103 553 494 572 755 1068 354 3656

[18]

500

500

292 060 055 077 035 826 2847 40682000 184 141 136 142 136 398 091 3983000 161 179 248 155 204 3870 1348 14414000 146 556 273 286 274 5086 4856 5079






7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









119901 = 1003816100381610038161003816ln 100381610038161003816100381611989132 minus 119891211003816100381610038161003816 + 119902 (119901)1003816100381610038161003816log 11990321




119866119862119868 = 119865푠 |120576|119903푝 minus 1100 (11)



120576 = 1198911 minus 11989121198911 (12)






+ 10 (upper bound)

- 10 (lower bound)



0

300

600

900

1200

1500

1800

Inci

dent

overpre

ssur

e [kP

a]

25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

500

1000

1500

2000

2500

3000

Inci

dent

overpre

ssur

e [kP

a]

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

1000

2000

3000

4000

5000

6000

Inci

dent

overpre

ssur

e [kP

a]








+ 10 (upper bound)

- 10 (lower bound)



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

100

mm

400

mm

200

mm

800

mm

125

mm

313

mm

625

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

800

mm

200

mm

400

mm

100

mm

625

mm

125

mm

313

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

5000

10000

15000

20000

25000

30000

35000

40000

Refle

cted

overpre

ssur

e [kP

a]

25 m

m

50 m

m

400

mm

200

mm

800

mm

100

mm

625

mm

125

mm

313

mm

Mesh size











Z [mkg13] A1 B1 C1 D1 E1 F1 G102 - 29 7211 -2107 -0323 0112 0069 0000 000029 - 238 7594 -3052 0410 0026 -0013 0000 0000238 - 1985 6054 -1407 0000 0000 0000 0000 0000



(13)







125 mm ME MFEM MATB[15] 1302 500 213 026 017 027 025 3462 576 501[16] 805 200 100 173 130 175 136 2486 109 2123

[17] 2739 550 182 026 NA 025 035 NA 380 3540950 315 012 015 010 2324 1587





25 mm ME MFEM MATB

[19] 100 150 150 190 NA 162 253 NA 1494 33111750 058 2901 2136 2972 2636 243

[20] 390 585 372 024 019 026 016 2000 911 3125[15] 1302 150 064 1692 1702 1392 2419 059 1775 4296

[17] 1837 310 117 420 332 413 520 2092 177 23772739 103 553 494 572 755 1068 354 3656

[18]

500

500

292 060 055 077 035 826 2847 40682000 184 141 136 142 136 398 091 3983000 161 179 248 155 204 3870 1348 14414000 146 556 273 286 274 5086 4856 5079






7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



+ 10 (upper bound)

- 10 (lower bound)



0

300

600

900

1200

1500

1800

Inci

dent

overpre

ssur

e [kP

a]

25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

500

1000

1500

2000

2500

3000

Inci

dent

overpre

ssur

e [kP

a]

+ 10 (upper bound)

- 10 (lower bound)



25 m

m

50 m

m

100

mm

200

mm

400

mm

800

mm

039

mm

078

mm

156

mm

313

mm

625

mm

125

mm

Mesh size

0

1000

2000

3000

4000

5000

6000

Inci

dent

overpre

ssur

e [kP

a]








+ 10 (upper bound)

- 10 (lower bound)



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

100

mm

400

mm

200

mm

800

mm

125

mm

313

mm

625

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

800

mm

200

mm

400

mm

100

mm

625

mm

125

mm

313

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

5000

10000

15000

20000

25000

30000

35000

40000

Refle

cted

overpre

ssur

e [kP

a]

25 m

m

50 m

m

400

mm

200

mm

800

mm

100

mm

625

mm

125

mm

313

mm

Mesh size











Z [mkg13] A1 B1 C1 D1 E1 F1 G102 - 29 7211 -2107 -0323 0112 0069 0000 000029 - 238 7594 -3052 0410 0026 -0013 0000 0000238 - 1985 6054 -1407 0000 0000 0000 0000 0000



(13)







125 mm ME MFEM MATB[15] 1302 500 213 026 017 027 025 3462 576 501[16] 805 200 100 173 130 175 136 2486 109 2123

[17] 2739 550 182 026 NA 025 035 NA 380 3540950 315 012 015 010 2324 1587





25 mm ME MFEM MATB

[19] 100 150 150 190 NA 162 253 NA 1494 33111750 058 2901 2136 2972 2636 243

[20] 390 585 372 024 019 026 016 2000 911 3125[15] 1302 150 064 1692 1702 1392 2419 059 1775 4296

[17] 1837 310 117 420 332 413 520 2092 177 23772739 103 553 494 572 755 1068 354 3656

[18]

500

500

292 060 055 077 035 826 2847 40682000 184 141 136 142 136 398 091 3983000 161 179 248 155 204 3870 1348 14414000 146 556 273 286 274 5086 4856 5079






7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



+ 10 (upper bound)

- 10 (lower bound)



0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

100

mm

400

mm

200

mm

800

mm

125

mm

313

mm

625

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Refle

cted

overpre

ssur

e [kP

a]

50 m

m

25 m

m

800

mm

200

mm

400

mm

100

mm

625

mm

125

mm

313

mm

Mesh size

+ 10 (upper bound)

- 10 (lower bound)



0

5000

10000

15000

20000

25000

30000

35000

40000

Refle

cted

overpre

ssur

e [kP

a]

25 m

m

50 m

m

400

mm

200

mm

800

mm

100

mm

625

mm

125

mm

313

mm

Mesh size











Z [mkg13] A1 B1 C1 D1 E1 F1 G102 - 29 7211 -2107 -0323 0112 0069 0000 000029 - 238 7594 -3052 0410 0026 -0013 0000 0000238 - 1985 6054 -1407 0000 0000 0000 0000 0000



(13)







125 mm ME MFEM MATB[15] 1302 500 213 026 017 027 025 3462 576 501[16] 805 200 100 173 130 175 136 2486 109 2123

[17] 2739 550 182 026 NA 025 035 NA 380 3540950 315 012 015 010 2324 1587





25 mm ME MFEM MATB

[19] 100 150 150 190 NA 162 253 NA 1494 33111750 058 2901 2136 2972 2636 243

[20] 390 585 372 024 019 026 016 2000 911 3125[15] 1302 150 064 1692 1702 1392 2419 059 1775 4296

[17] 1837 310 117 420 332 413 520 2092 177 23772739 103 553 494 572 755 1068 354 3656

[18]

500

500

292 060 055 077 035 826 2847 40682000 184 141 136 142 136 398 091 3983000 161 179 248 155 204 3870 1348 14414000 146 556 273 286 274 5086 4856 5079






7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








Z [mkg13] A1 B1 C1 D1 E1 F1 G102 - 29 7211 -2107 -0323 0112 0069 0000 000029 - 238 7594 -3052 0410 0026 -0013 0000 0000238 - 1985 6054 -1407 0000 0000 0000 0000 0000



(13)







125 mm ME MFEM MATB[15] 1302 500 213 026 017 027 025 3462 576 501[16] 805 200 100 173 130 175 136 2486 109 2123

[17] 2739 550 182 026 NA 025 035 NA 380 3540950 315 012 015 010 2324 1587





25 mm ME MFEM MATB

[19] 100 150 150 190 NA 162 253 NA 1494 33111750 058 2901 2136 2972 2636 243

[20] 390 585 372 024 019 026 016 2000 911 3125[15] 1302 150 064 1692 1702 1392 2419 059 1775 4296

[17] 1837 310 117 420 332 413 520 2092 177 23772739 103 553 494 572 755 1068 354 3656

[18]

500

500

292 060 055 077 035 826 2847 40682000 184 141 136 142 136 398 091 3983000 161 179 248 155 204 3870 1348 14414000 146 556 273 286 274 5086 4856 5079






7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






125 mm ME MFEM MATB[15] 1302 500 213 026 017 027 025 3462 576 501[16] 805 200 100 173 130 175 136 2486 109 2123

[17] 2739 550 182 026 NA 025 035 NA 380 3540950 315 012 015 010 2324 1587





25 mm ME MFEM MATB

[19] 100 150 150 190 NA 162 253 NA 1494 33111750 058 2901 2136 2972 2636 243

[20] 390 585 372 024 019 026 016 2000 911 3125[15] 1302 150 064 1692 1702 1392 2419 059 1775 4296

[17] 1837 310 117 420 332 413 520 2092 177 23772739 103 553 494 572 755 1068 354 3656

[18]

500

500

292 060 055 077 035 826 2847 40682000 184 141 136 142 136 398 091 3983000 161 179 248 155 204 3870 1348 14414000 146 556 273 286 274 5086 4856 5079






7 Conclusion







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







Data Availability




Acknowledgments


References














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


researcharticle analysis of blast wave parameters

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