ResearchofSteel-ConcreteCompositeBridgeunder...

Research ArticleResearch of Steel-Concrete Composite Bridge underBlasting Loads

Yuan Li and Shuanhai He

School of Highway Changrsquoan University Xirsquoan 710064 China

Correspondence should be addressed to Yuan Li liyuanchdeducn

Received 16 April 2018 Revised 25 June 2018 Accepted 5 August 2018 Published 12 September 2018

Academic Editor Xihong Zhang

Copyright copy 2018 Yuan Li and Shuanhai He is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

is paper presents a study to simulate the performance of steel-plate composite bridge under various blasting loads e multi-Euler domain method based on the fully coupled Lagrange and Euler models is adopted for the structural analysis of explosionprocess with the commercial software Autodyn Due to the difference of material characteristics and space distribution betweenthe concrete and steel part the most adverse position is estimated to be above and below detonation A remarkable differencebetween these two explosive denotations for steel-concrete composite bridge is noted and the failuremode above denotation is thedamage of local concrete deck with the compressionmode near the denotation point showing a standard trigonometric curveefailure mode below denotation includes damage of steel girders and concrete failure near junction

1 Introduction

Blasting incidents are becoming an increasing threat forurban infrastructure in the past years Terrorist attacks andtransport vehicles with explosive and flammable materialscause potential blasting loads structures subjected to Ter-rorism and accidental explosion have become a major threatto the security of international community As crucialthoroughfare for urban traffic system disastrous bridgefailures can bring enormous economic and related loss es-pecially in populated regions Bridge engineers are focusedon bridge antiexplosion and blasting damage assessmentespecially after the incident of 911 However considerationof prominent explosive resistances in both official andnongovernmental design codes for nonmilitary bridges israrely found Steel-concrete composite bridges have beenwidely adopted in urban construction for its advantages likehighly construction speed and cross ability in recent yearsHowever the research of blast on steel-concrete compositebridge is insufficient erefore it is extremely necessary tofigure out the stress and failure mechanism of the steel-concrete composite bridge under blasting load

Many researchers [1ndash3] focused on the structural per-formance of concrete piers or slabs under blasting loads Wu

et al [4] investigated the residual capability of localizedblast-damaged RC columns by LS-DYNA and the commonfailure mode of structures subjected to blast load andsummarized the residual capacity index by a service axialload index Yao et al [5] investigated the damage featuresand dynamic response of RC beams under blasting loadsPan et al [6] investigated three modern types of reinforcedconcrete bridges under various blasting loads includinga slab-on-girder bridge a box-girder bridge and a long-spancable-stayed bridge and discussed the protection perfor-mance of carbon fiber-reinforced polymer on bridgesFujikura and Bruneau [7] studied the blast resistance of steeljacketing bridge piers by experiments Li and Hao [8] an-alyzed steel wire mesh-reinforced concrete slab undercontact explosion

Although the researches about bridge or other con-structions under explosive listed above have obtained someresults and suggestions the research about the performanceof concrete-steel composite bridges under blasting loads isstill very limited In this study a steel-concrete compositebridge is analyzed thoroughly to obtain the damage patternsof bridge and predict propagation rule of explosive waveaccurately To do this a three-dimensional finite elementmodel for concrete-steel composite bridge is established by

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 5748278 9 pageshttpsdoiorg10115520185748278

ANSYS Autodyn Two analysis modules the traditionalpreprocessor and AUTODYN module which is professionalin explosive area are utilized in this study

2 Material Characteristics and Modeling

21 Conservation Equation Explosive process is a high-ratechemical phenomenon in which energy is released rapidlywithin a limited scope which is obviously different fromgeneral structural analysis Carta and Stochino [9] in-vestigated the flexural failure of reinforced concrete beamsunder blasting loads through theoretical models whichindicated that the material constitutive relation and con-servation equation have a decisive effect on the result ofexplosive calculation e materials considered in this studyinclude concrete steel plate ideal air and high-explosiveTNT In order to obtain an accurate and reliable perfor-mance of the steel-concrete composite bridge under blastingloads it is obviously necessary to simulate the behavior ofexplosion in air with an appropriate method Genericallyduring the explosion process (usually in several millisec-onds) the nearby air expands rapidly with high energy andtemperature forming a shock wave which evolves into highpressure on structure timely e spread of shock wave in aircan be described by nonviscous flow deciding by Eulerequation as follows

zq

zt

zf(q)

zx+

zg(q)

zy+

zh(q)

zz 0 (1)

where q is the state vector about time t and f(q) g(q) andh(q) are flux of conservative state variables

q

ρ

ρu

ρω

Q

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

f(q)

ρu

ρu2 + p

ρuv

puω

(Q + p)u

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

g(q)

ρv

ρuv

ρv2 + p

pvω

(Q + p)v

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

h(q)

ρω

ρuω

ρvω

pω2 + p

(Q + p)ω

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2)

where ρ is the density u v and ω are the velocities in the xy and z direction respectively p is the pressure and Q is thetotal energy

In order to achieve the solution an ideal state equation isintroduced by Zhou et al [10] as follows

p (cminus 1)ρe (3)

where e is the internal energy value of which is set to2068times108 to ensure that the structure is at a standard at-mosphere pressure at the beginning of the analysis c is theadiabatic exponent of ideal air and ρ is the material densityMaterial parameters of air are shown in Table 1

22 Materials Constitutive With an explosion taking placenearby bridges accept a dynamic transient shock waveerefore the damage of concrete occurs in a flash Toanalyze and simulate the destruction of concrete under thesudden impact during explosion the concrete failure modelof RiedelndashHiermaierndashoma is considered for concreteconstitutive properties which include elastic limit surfacefailure surface and residual strength surface e consti-tutive model of RHT is shown in Figure 1

e equation is as follows

σlowasteq(p θ ε) YlowastTXC(p)R3(θ)Frate(_ε) (4)

where YlowastTXC(p) is the compressing meridian Frate(_ε) is theaugmentation factor of strain rate and R3(θ) is the cornerfunction Researchers have shown that there are some de-fects in the original RHTmodel in spite of wide applicationon explosion analysis Tu and Lu [11] modified the residualstrength surface and tensionmeridian Nystrom and Gylltoft[12] introduced the bilinear principal tensile stress failurecriterion in the RHT model Leppanen [13] modified thetensile stress-strain relationship and tensile strength strainrate of the RHT model In this study the principal stresstensile failure was considered instead of original tensilefailure model of RHT value of which was set at 50e3 Cracksoftening option was set and the value of fracture energy was100 In explosive analysis the RHT constitutive relation isusually used with the p-alpha state equation together ep-alpha state equation is shown as follows

P(ρ E) A1μ + A2μ2

+ A3μ3

+ B0 + B1μ( 1113857ρ0e

μ ρρ0

1113888 1113889minus 1

(5)

where A1 A2 A3 B0 and B1 are calculation parametersρ0 is the initial density and e is the internal energy eparameters are mostly obtained through experiments In thisresearch Adobe 18-RHT is used in this analysis for itsadaptability and widespread applicability from the literatureMaterial constitutive of steel is much more simple thanconcrete Bearing steel 27YS is used in explosive analysisValues of the parameters and other failure mechanism ofthese two constitutive relations are found in the literature[14]

2 Advances in Civil Engineering

JonesndashWilkinsndashLee (JWL) state equation is used tomodel to explosive material and ambient air which canindicate the interaction between explosive pressure and airenergy clearly e air range surfaces adopt the flow-outboundary condition e JWL equation is as follows

P A 1minusω

R1V1113888 1113889e

minusR1V+ B 1minus

ωR2V

1113888 1113889eminusR2V

+ωE0

V (6)

where p is the pressure during explosion V is the volumeratio of detonation products to initial explosive E0 is theinternal energy of unit volume and A B R1 R2 and ωare material parameters values of which are shown inTable 2

23 Finite Element Modeling Figure 2 shows the crosssection of a 40m single span steel-concrete composite bridgewhose deck width is 1250 cm ere are two I-shaped steelgirders placed 670 cm apart in the bridge Concrete bridgedecks are adopted for its high pressure resistance and drivingcomfort Shear studs are adopted for the connection betweenI-shaped steel girders and concrete deck which is consideredas ideal connection in this study e concrete deck is fullyrestrained with the steel girders e height of the box girderis 220 cm while top plate width of I-shaped is 90 cm andbottom width is 110 cm Transverse beams are set at every 8meters in longitudinal directions to enhance the structuralintegrity In this study the concrete and steel girders aremodeled with 8-node solid Lagrange elements and 4-nodeshell elements Because of the complex nonlinearity of themacroscopic concrete the improved RiedelndashHiermaierndashoma (RHT) concrete failure model and the porousequation of state (EOS) model are utilized to consider thelarge-scale heterogeneity and porosity Due to the

complexity of structure the three-dimensional finite ele-ment model was first established by using preprocessormodule of traditional ANSYS predisposition Explosionexecution was completed in the analysis module ofAUTODYN through ldquoK filerdquo e accuracy of the analysis ishighly affected by the cell size especially for nonlinearitymulti-Euler analysiseoretically a smaller mesh size of thefinite element model will obtain more precise structuralperformance under blasting loads However it is infeasibleto model components with unreasonable small mesh sizePan et al [6 15] pointed out that a 10 cmmesh size can havean adequate assurance rate to ensure a reliable pressure-timehistory and dynamic structural response e range of air isalso a key factor for computational efficiency and it isimpossible to simulate an infinite space of air A moreeconomical approach is used to define the air flow interfaceFlow-out boundary in this study is introduced for the airrsquosfree edge Explosive analysis begins with a standard atmo-sphere which is achieved by defining the initial energy of airFigure 3 shows the AUTODYN analysis model

3 Bridge Performance and Result Discussion

Terrorist attacks and accidental explosion are always un-predictable for which reason it is necessary to make a largenumber of detonation scenarios In this study consideringthe particularity of composite structure detonation loca-tions are the key factor of damage mode 100 kg weight ofTNT equivalent is considered for a car bomb Above-deckand below-deck detonation are simulated in this studyBecause of the instantaneity and tremendousness of ex-plosion energy the effect of gravity and other live load areneglected during such short period

31 Above-Deck Detonation Dynamite is located in themiddle of the bridge 80 centimeters above the deck Figure 4shows the wave propagation of a 100 kg weight TNT byusing the three-dimensional multi-Euler domain methode blasting wave has spread to whole lateral of the bridgesystem within only 60 millisecondse section at the top ofthe explosive shows the flow-out circumstance

In order to illustrate the transmission rules of blastpressure on structure clearly gauges in the air were definedto record the high blast pressure and impulse at differentlocations during calculation as shown in Figure 5 Figure 6shows the pressure history of Gauge 28 where the curve issimilar to a triangle e peak reaches 1546E6 kPa with thetime corresponding to the peak value is only 1512Eminus 1millisecond Generally the area of this triangle can be uti-lized to describe the degree of explosion Figure 7 shows thevelocity history of Gauge 28 where the air impacts downrapidly towards the bridge deck in a very short time and thenis reflected An opposite velocity can be got in the diagramMoments later velocity curve vibrates around the zero line

rough the calculation results of monitoring points theoverall trends are that a smaller the pressure will be obtainedwith a greater distance Figure 8 shows the pressure-timehistory of some gauges Meanwhile Gauge 16 seams have

Table 1 Material parameters of air

ρ (g middot cmminus3) e (J middot kgminus1) c

1225Eminus 3 2068times108 14

Deviatoric stressσeq Tens meridian

Comp meridian

Residual strengthYfric

Pressure pHardening surface

Ypre

Initial elasticElastic limit Ycl

Fail surfaceYfail

Figure 1 e RHT constitutive model used for concrete

Advances in Civil Engineering 3

a larger pressure peak than Gauge 17 and it is due to thenegative pressure phenomenon which occurs in a smalldistance from detonation

Figure 9 summarizes the ultimate damage states in thecase of above-deck detonation It can be seen clearly that dueto the full connement eect and the highly reectedpressure a 46mtimes 46m damage area was generated shyesurface of the deck is predominantly damaged by directcrushing of RC elements and at the same time there is nodamage observed in the I-shaped steel girder Figures 10 and11 present stress distribution It can be seen that the bluearea in the middle of the bridge reects the quitting ofconcrete under blasting loads

32Below-DeckDetonation Another situation for the urbanbridge is carried out Overpass bridges can suer a below-deck detonation because of heavy volume of trac belowthem In this section explosive detonation is arranged rightdown the composite bridge Figure 12 presents a below-deckexplosion process explosive wave forms within a rectanglespace between the I-shaped steel girders in the process oftransmission

Figure 13 shows the structure deformation underblasting loads A large local deformation occurs in the steelgirder value of which reaches 158mm Because of the

transverse beam the max deformation is not in the midspanFigure 14 shows the stress distribution on damage stateStructural failure occurs mainly in two positions the rstone is the local failure of steel girder itself and the other is thejuncture position of steel girder and concrete deck

In a similar way Gauges are dened to gure out thestress characteristics and damage mechanism on struc-ture Gauges 113 114 and 50 to 54 are arranged on thelongitudinal direction and Gauges 54 75 and 96 arearranged on the transverse direction which is shown inFigure 15 Figure 16 shows velocity-time history of Gaugeson z direction shye curve of 53 is even higher than Gauge54 on local scale It is because that the transverse beamright near the point limits the local deformation Othercurves of Gauge points decreased with distance Figure 17shows velocity-time history of Gauge points of the hor-izontal setting shye velocity of Gauge 75 presents someirregularity because of the I-shaped steel beam and thelocal reection eect of the explosion wave shye pressure-time history of Gauges 113 and 114 (horizontal near thedetonation point) illustrates the same phenomenon shyeirpressure curves cannot be simply concluded as typicaltriangle and there are two peaks which are shown inFigures 18 and 19 Apparently both failure characteristicsand blasting loads below the detonation are very dierentfrom those above the detonation

Table 2 Material parameters of JWL equation state

Parameter R1 Parameter R2 Parameter A (MPa) Parameter B (MPa) Parameter ω Density ρ (g middot cmminus3) V E (J middot kgminus1)415 090 3738E5 3747E3 035 163 100 70E6

Concrete deck

I shape steel girder

2222

018

240 100 100570 240

1250

Transverse beam

110

60

Figure 2 shye cross section (unit cm)

xy

z

Material locationFlow outVoidMAT-ELAS1-1MAT-ELAS2-2AIRTNT-2lt1gt

Figure 3 Analysis module in AUTODYN


x

y

2m times 10

5mtimes

4

Material location

Void

MAT-ELAS1-1

MAT-ELAS2-2

AIR

TNT-2lt1gt1 2 3 4 5 6 7 8 9 10 11

12 13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33

34 35 36 37 38 39 40 41 42 43 44

45 46 47 48 49 50 51 52 53 54 55

Figure 5 Dened gauges in case of above-deck detonation

xyz

(a)

xyz

(b)

xyz

(c)

Figure 4 Blast wave spread of above-deck explosive TNT at dierent times (a) 085 milliseconds (b) 17 milliseconds and (c) 599milliseconds

Gauge 28

05 10 1500Time (ms)

50 times 105

10 times 106

15 times 106

Pres

sure

(kPa

)

Figure 6 Pressure history of Gauge 28

Gauge 28

1 2 3 4 5 60Time (ms)

ndash800

ndash600

ndash400

ndash200

0

Z-ve

loci

ty (m

s)

Figure 7 Velocity history of Gauge 28


33 Discussion of Failure Characteristics Generally thefailure characteristics of composite beam under blastingloads are dramatically inuenced by detonation locationsWhen blast happens above the deck the concrete of bridge

deck is subjected to the impact load directly Failure char-acteristics of concrete deck are similar to general failuremode and a symmetrical area of destruction is formed asshown in Figures 9 and 11 Meanwhile the I steel girder bear

Gauge 12Gauge 13Gauge 14


0

500

1000

1500

Pres

sure

(kPa

)

1 2 3 4 5 60Time (ms)

Figure 8 Pressure-time history of Gauges

Damage [All]1000e + 00

9000e ndash 01

8000e ndash 01

7000e ndash 01

6000e ndash 01

5000e ndash 01

4000e ndash 01

3000e ndash 01

2000e ndash 01

1000e ndash 01

0000e + 00

46 times 46m

xyz

Figure 9 Damage of the bridge

x

yz

Mis stress (kPa)1086e + 039771e + 028685e + 027599e + 026513e + 025428e + 024343e + 023257e + 022171e + 021086e + 020000e + 00

Figure 10 Stress distribution of I-shaped beam


x

y

z


Figure 11 Stress distribution of concrete deck

Material status

Void

Hydro

Elastic

Plastic

Bulk failxy

z

Figure 12 Blast wave spread of above-deck explosive TNT at dierent times

Displacement Y (mm)1502e + 021379e + 021256e + 021132e + 021009e + 028059e + 017626e + 016390e + 015160e + 013928e + 012695e + 011462e + 012291e + 00ndash1004e + 01

ndash158e + 02mm

ndash2237e + 01ndash3469e + 01ndash4702e + 01ndash5935e + 01ndash7168e + 01ndash8401e + 01ndash9634e + 01ndash1087e + 02ndash1210e + 02ndash1333e + 02ndash1456e + 02ndash1560e + 02

x

y

z

Figure 13 Deformation suering from explosive load


bending moments in the instant of the explosion Whenexplosive happens below the deck the overpressure char-acteristic of the structure is more complex Shock wavereections are produced in local space shye overpressuretime curve near the blast point showed multiple peaks andthe I-shaped girder deformed considerably

4 Conclusions

shyis paper presents the blast analysis results of concrete-steelcomposite bridge by an accurate simulation of explosionprocess shye conclusions are as follows

In the case of a steel-concrete composite bridge a 100 kgTNT above-deck explosion right on the midspan of thebridge is identied as the most critical case shye force ofexplosion lead to a 46times 46m damage area signicantlyshyepressure history curve of the point right below the explosivecan be described as a typical triangle because of the hol-lowness above the bridge deck It means that a simple tri-angle time load can be utilized in explosive analysis insteadof complex simulation of the whole blasting systemArranging the detonation point at the center it can be shownthat a smaller pressure peak will be obtained with a fartherdistance shyere is not a remarkable disruption on steelI-shaped beam

For below-deck detonation of composite bridge the blastpropagation is more complex than that of the above-deckdetonation Blasting loads lead to more deformations andstresses for steel girder shye damage pattern mainly occurs


0

2

4

6

Z-ve

loci

ty (m

s)

1 2 3 4 5 60Time (ms)

Figure 17 Velocity-time history of Gauges

xyz

Figure 14 Stress distribution of damage state

I girder

I girder

Detonation point

2m times 6

5mtimes

2

50 51 52 53 54

75

96

113 114

Figure 15 Dened gauges in case of down-deck detonation


Gauge 53Gauge 54

0

2

4

6

8

Z-ve

loci

ty (m

s)

1 2 3 4 5 60Time (ms)


Gauge 113

1 2 3 4 5 60Time (ms)

0

500

1000

1500

2000

2500

Pres

sure

(kPa

)

Figure 18 Velocity-time history of Gauge 113


on two positions steel girder near the blasting detonationand the conjunction with concrete deck and steel girder shyeblast wave is also dierent from an ordinary open areacausing a reection in the narrow part between the two steelgirders shye pressure-time history curve is not a simpletriangle which means a simplied time load cannot beutilized to replace the actual explosive process shye trans-verse beam plays an important role in displacement limi-tation but the overall destruction of the structure still lays onthe local steel yield strength and the joint failure

Data Availability

shye data used in the manuscript can be replicated throughcalculation method as described in the manuscript shye datasupporting the conclusions of the study can be obtained inthe manuscript

Conflicts of Interest

shye authors declare that they have no conicts of interestregarding the publication of this paper

Acknowledgments

shye authors would like to acknowledge the nancial supportprovided by the Fundamental Research Funds for theCentral Universities of China under Grant nos310821161012 and 300102218214 shye help of engineers andtechnicians in the Key Laboratory of Bridge Detection Re-inforcement Technology Ministry of Communications ofChangrsquoan University is highly appreciated shyese supportsare gratefully acknowledged

References

[1] Y S Tai T L Chu H T Hu and J Y Wu ldquoDynamic re-sponse of a reinforced concrete slab subjected to air blastloadrdquo eoretical and Applied Fracture Mechanics vol 56no 3 pp 140ndash147 2011

[2] C F Zhao and J Y Chen ldquoDamage mechanism and mode ofsquare reinforced concrete slab subjected to blast loadingrdquoeoretical and Applied Fracture Mechanics vol 63-64pp 54ndash62 2013

[3] S J Yao D Zhang F Y Lu W Wang and X G ChenldquoDamage features and dynamic response of RC beams underblastrdquo Engineering Failure Analysis vol 62 pp 103ndash111 2016

[4] K C Wu B Li and K C Tsai ldquoResidual axial compressioncapacity of localized blast-damaged RC columnsrdquo In-ternational Journal of Impact Engineering vol 38 no 1pp 29ndash40 2011

[5] S J Yao D Z Zhang X G Chen F Y Lu and W WangldquoExperimental and numerical study on the dynamic responseof RC slabs under blast loadingrdquo Engineering Failure Analysisvol 66 pp 120ndash129 2016

[6] Y X Pan C E Ventura and M M S Cheung ldquoPerformanceof highway bridges subjected to blast loadsrdquo EngineeringStructures vol 151 pp 788ndash801 2017

[7] S Fujikura and M Bruneau ldquoExperimental investigation ofseismically resistant bridge piers under blast loadingrdquo Journalof Bridge Engineering vol 16 no 1 pp 63ndash71 2011

[8] J Li andH Hao ldquoNumerical study of concrete spall damage toblast loadsrdquo International Journal of Impact Engineeringvol 68 pp 41ndash55 2014

[9] G Carta and F Stochino ldquoshyeoretical models to predict theexural failure of reinforced concrete beams under blastloadsrdquo Engineering Structures vol 49 pp 306ndash315 2013

[10] X Q Zhou V A Kuznetsov H Hao and J Waschl ldquoNu-merical prediction of concrete slab response to blast loadingrdquoInternational Journal of Impact Engineering vol 35 no 10pp 1186ndash1200 2008

[11] Z G Tu and Y Lu ldquoModications of RHTmaterial model forimproved numerical simulation of dynamic response ofconcreterdquo International Journal of Impact Engineering vol 37no 10 pp 1072ndash1082 2010

[12] U Nystrom and K Gylltoft ldquoComparative numerical studiesof projectile impacts on plain and steel-bre reinforcedconcreterdquo International Journal of Impact Engineering vol 38no 2-3 pp 95ndash105 2011

[13] J Leppanen ldquoConcrete subjected to projectile and fragmentimpacts modelling of crack softening and strain rate de-pendency in tensionrdquo International Journal of Impact Engi-neering vol 32 no 11 pp 1828ndash1841 2006

[14] C Sauer A Heine and W Riedel ldquoDeveloping a validatedhydrocode model for adobe under impact loadingrdquo In-ternational Journal of Impact Engineering vol 104 pp 164ndash176 2017

[15] Y X Pan B Y B Chan and M M S Cheung ldquoBlast loadingeects on an RC slab-on-girder bridge superstructure usingthe multi-Euler domain methodrdquo Journal of Bridge Engi-neering vol 18 no 11 pp 1152ndash1163 2013

Gauge 114

1 2 3 4 5 60Time (ms)

0

500

1000

1500

Pres

sure

(kPa

)



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Submit your manuscripts atwwwhindawicom

ANSYS Autodyn Two analysis modules the traditionalpreprocessor and AUTODYN module which is professionalin explosive area are utilized in this study

2 Material Characteristics and Modeling

21 Conservation Equation Explosive process is a high-ratechemical phenomenon in which energy is released rapidlywithin a limited scope which is obviously different fromgeneral structural analysis Carta and Stochino [9] in-vestigated the flexural failure of reinforced concrete beamsunder blasting loads through theoretical models whichindicated that the material constitutive relation and con-servation equation have a decisive effect on the result ofexplosive calculation e materials considered in this studyinclude concrete steel plate ideal air and high-explosiveTNT In order to obtain an accurate and reliable perfor-mance of the steel-concrete composite bridge under blastingloads it is obviously necessary to simulate the behavior ofexplosion in air with an appropriate method Genericallyduring the explosion process (usually in several millisec-onds) the nearby air expands rapidly with high energy andtemperature forming a shock wave which evolves into highpressure on structure timely e spread of shock wave in aircan be described by nonviscous flow deciding by Eulerequation as follows

zq

zt

zf(q)

zx+

zg(q)

zy+

zh(q)

zz 0 (1)

where q is the state vector about time t and f(q) g(q) andh(q) are flux of conservative state variables

q

ρ

ρu

ρω

Q

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

f(q)

ρu

ρu2 + p

ρuv

puω

(Q + p)u

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

g(q)

ρv

ρuv

ρv2 + p

pvω

(Q + p)v

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

h(q)

ρω

ρuω

ρvω

pω2 + p

(Q + p)ω

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(2)

where ρ is the density u v and ω are the velocities in the xy and z direction respectively p is the pressure and Q is thetotal energy

In order to achieve the solution an ideal state equation isintroduced by Zhou et al [10] as follows

p (cminus 1)ρe (3)

where e is the internal energy value of which is set to2068times108 to ensure that the structure is at a standard at-mosphere pressure at the beginning of the analysis c is theadiabatic exponent of ideal air and ρ is the material densityMaterial parameters of air are shown in Table 1

22 Materials Constitutive With an explosion taking placenearby bridges accept a dynamic transient shock waveerefore the damage of concrete occurs in a flash Toanalyze and simulate the destruction of concrete under thesudden impact during explosion the concrete failure modelof RiedelndashHiermaierndashoma is considered for concreteconstitutive properties which include elastic limit surfacefailure surface and residual strength surface e consti-tutive model of RHT is shown in Figure 1

e equation is as follows

σlowasteq(p θ ε) YlowastTXC(p)R3(θ)Frate(_ε) (4)

where YlowastTXC(p) is the compressing meridian Frate(_ε) is theaugmentation factor of strain rate and R3(θ) is the cornerfunction Researchers have shown that there are some de-fects in the original RHTmodel in spite of wide applicationon explosion analysis Tu and Lu [11] modified the residualstrength surface and tensionmeridian Nystrom and Gylltoft[12] introduced the bilinear principal tensile stress failurecriterion in the RHT model Leppanen [13] modified thetensile stress-strain relationship and tensile strength strainrate of the RHT model In this study the principal stresstensile failure was considered instead of original tensilefailure model of RHT value of which was set at 50e3 Cracksoftening option was set and the value of fracture energy was100 In explosive analysis the RHT constitutive relation isusually used with the p-alpha state equation together ep-alpha state equation is shown as follows

P(ρ E) A1μ + A2μ2

+ A3μ3

+ B0 + B1μ( 1113857ρ0e

μ ρρ0

1113888 1113889minus 1

(5)

where A1 A2 A3 B0 and B1 are calculation parametersρ0 is the initial density and e is the internal energy eparameters are mostly obtained through experiments In thisresearch Adobe 18-RHT is used in this analysis for itsadaptability and widespread applicability from the literatureMaterial constitutive of steel is much more simple thanconcrete Bearing steel 27YS is used in explosive analysisValues of the parameters and other failure mechanism ofthese two constitutive relations are found in the literature[14]



P A 1minusω

R1V1113888 1113889e

minusR1V+ B 1minus

ωR2V

1113888 1113889eminusR2V

+ωE0

V (6)











1225Eminus 3 2068times108 14


Comp meridian



Ypre


Fail surfaceYfail











Concrete deck


2222

018

240 100 100570 240

1250

Transverse beam

110

60


xy

z




x

y

2m times 10

5mtimes

4

Material location

Void

MAT-ELAS1-1

MAT-ELAS2-2

AIR

TNT-2lt1gt1 2 3 4 5 6 7 8 9 10 11

12 13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33

34 35 36 37 38 39 40 41 42 43 44

45 46 47 48 49 50 51 52 53 54 55


xyz

(a)

xyz

(b)

xyz

(c)


Gauge 28

05 10 1500Time (ms)

50 times 105

10 times 106

15 times 106

Pres

sure

(kPa

)


Gauge 28

1 2 3 4 5 60Time (ms)

ndash800

ndash600

ndash400

ndash200

0

Z-ve

loci

ty (m

s)







0

500

1000

1500

Pres

sure

(kPa

)

1 2 3 4 5 60Time (ms)



9000e ndash 01

8000e ndash 01

7000e ndash 01

6000e ndash 01

5000e ndash 01

4000e ndash 01

3000e ndash 01

2000e ndash 01

1000e ndash 01

0000e + 00

46 times 46m

xyz


x

yz




x

y

z



Material status

Void

Hydro

Elastic

Plastic

Bulk failxy

z



ndash158e + 02mm


x

y

z




4 Conclusions





0

2

4

6

Z-ve

loci

ty (m

s)

1 2 3 4 5 60Time (ms)


xyz


I girder

I girder

Detonation point

2m times 6

5mtimes

2

50 51 52 53 54

75

96

113 114



Gauge 53Gauge 54

0

2

4

6

8

Z-ve

loci

ty (m

s)

1 2 3 4 5 60Time (ms)


Gauge 113

1 2 3 4 5 60Time (ms)

0

500

1000

1500

2000

2500

Pres

sure

(kPa

)




Data Availability




Acknowledgments


References
















Gauge 114

1 2 3 4 5 60Time (ms)

0

500

1000

1500

Pres

sure

(kPa

)





RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



P A 1minusω

R1V1113888 1113889e

minusR1V+ B 1minus

ωR2V

1113888 1113889eminusR2V

+ωE0

V (6)











1225Eminus 3 2068times108 14


Comp meridian



Ypre


Fail surfaceYfail











Concrete deck


2222

018

240 100 100570 240

1250

Transverse beam

110

60


xy

z




x

y

2m times 10

5mtimes

4

Material location

Void

MAT-ELAS1-1

MAT-ELAS2-2

AIR

TNT-2lt1gt1 2 3 4 5 6 7 8 9 10 11

12 13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33

34 35 36 37 38 39 40 41 42 43 44

45 46 47 48 49 50 51 52 53 54 55


xyz

(a)

xyz

(b)

xyz

(c)


Gauge 28

05 10 1500Time (ms)

50 times 105

10 times 106

15 times 106

Pres

sure

(kPa

)


Gauge 28

1 2 3 4 5 60Time (ms)

ndash800

ndash600

ndash400

ndash200

0

Z-ve

loci

ty (m

s)







0

500

1000

1500

Pres

sure

(kPa

)

1 2 3 4 5 60Time (ms)



9000e ndash 01

8000e ndash 01

7000e ndash 01

6000e ndash 01

5000e ndash 01

4000e ndash 01

3000e ndash 01

2000e ndash 01

1000e ndash 01

0000e + 00

46 times 46m

xyz


x

yz




x

y

z



Material status

Void

Hydro

Elastic

Plastic

Bulk failxy

z



ndash158e + 02mm


x

y

z




4 Conclusions





0

2

4

6

Z-ve

loci

ty (m

s)

1 2 3 4 5 60Time (ms)


xyz


I girder

I girder

Detonation point

2m times 6

5mtimes

2

50 51 52 53 54

75

96

113 114



Gauge 53Gauge 54

0

2

4

6

8

Z-ve

loci

ty (m

s)

1 2 3 4 5 60Time (ms)


Gauge 113

1 2 3 4 5 60Time (ms)

0

500

1000

1500

2000

2500

Pres

sure

(kPa

)




Data Availability




Acknowledgments


References
















Gauge 114

1 2 3 4 5 60Time (ms)

0

500

1000

1500

Pres

sure

(kPa

)





RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










Concrete deck


2222

018

240 100 100570 240

1250

Transverse beam

110

60


xy

z




x

y

2m times 10

5mtimes

4

Material location

Void

MAT-ELAS1-1

MAT-ELAS2-2

AIR

TNT-2lt1gt1 2 3 4 5 6 7 8 9 10 11

12 13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33

34 35 36 37 38 39 40 41 42 43 44

45 46 47 48 49 50 51 52 53 54 55


xyz

(a)

xyz

(b)

xyz

(c)


Gauge 28

05 10 1500Time (ms)

50 times 105

10 times 106

15 times 106

Pres

sure

(kPa

)


Gauge 28

1 2 3 4 5 60Time (ms)

ndash800

ndash600

ndash400

ndash200

0

Z-ve

loci

ty (m

s)







0

500

1000

1500

Pres

sure

(kPa

)

1 2 3 4 5 60Time (ms)



9000e ndash 01

8000e ndash 01

7000e ndash 01

6000e ndash 01

5000e ndash 01

4000e ndash 01

3000e ndash 01

2000e ndash 01

1000e ndash 01

0000e + 00

46 times 46m

xyz


x

yz




x

y

z



Material status

Void

Hydro

Elastic

Plastic

Bulk failxy

z



ndash158e + 02mm


x

y

z




4 Conclusions





0

2

4

6

Z-ve

loci

ty (m

s)

1 2 3 4 5 60Time (ms)


xyz


I girder

I girder

Detonation point

2m times 6

5mtimes

2

50 51 52 53 54

75

96

113 114



Gauge 53Gauge 54

0

2

4

6

8

Z-ve

loci

ty (m

s)

1 2 3 4 5 60Time (ms)


Gauge 113

1 2 3 4 5 60Time (ms)

0

500

1000

1500

2000

2500

Pres

sure

(kPa

)




Data Availability




Acknowledgments


References
















Gauge 114

1 2 3 4 5 60Time (ms)

0

500

1000

1500

Pres

sure

(kPa

)





RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


x

y

2m times 10

5mtimes

4

Material location

Void

MAT-ELAS1-1

MAT-ELAS2-2

AIR

TNT-2lt1gt1 2 3 4 5 6 7 8 9 10 11

12 13 14 15 16 17 18 19 20 21 22

23 24 25 26 27 28 29 30 31 32 33

34 35 36 37 38 39 40 41 42 43 44

45 46 47 48 49 50 51 52 53 54 55


xyz

(a)

xyz

(b)

xyz

(c)


Gauge 28

05 10 1500Time (ms)

50 times 105

10 times 106

15 times 106

Pres

sure

(kPa

)


Gauge 28

1 2 3 4 5 60Time (ms)

ndash800

ndash600

ndash400

ndash200

0

Z-ve

loci

ty (m

s)







0

500

1000

1500

Pres

sure

(kPa

)

1 2 3 4 5 60Time (ms)



9000e ndash 01

8000e ndash 01

7000e ndash 01

6000e ndash 01

5000e ndash 01

4000e ndash 01

3000e ndash 01

2000e ndash 01

1000e ndash 01

0000e + 00

46 times 46m

xyz


x

yz




x

y

z



Material status

Void

Hydro

Elastic

Plastic

Bulk failxy

z



ndash158e + 02mm


x

y

z




4 Conclusions





0

2

4

6

Z-ve

loci

ty (m

s)

1 2 3 4 5 60Time (ms)


xyz


I girder

I girder

Detonation point

2m times 6

5mtimes

2

50 51 52 53 54

75

96

113 114



Gauge 53Gauge 54

0

2

4

6

8

Z-ve

loci

ty (m

s)

1 2 3 4 5 60Time (ms)


Gauge 113

1 2 3 4 5 60Time (ms)

0

500

1000

1500

2000

2500

Pres

sure

(kPa

)




Data Availability




Acknowledgments


References
















Gauge 114

1 2 3 4 5 60Time (ms)

0

500

1000

1500

Pres

sure

(kPa

)





RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






0

500

1000

1500

Pres

sure

(kPa

)

1 2 3 4 5 60Time (ms)



9000e ndash 01

8000e ndash 01

7000e ndash 01

6000e ndash 01

5000e ndash 01

4000e ndash 01

3000e ndash 01

2000e ndash 01

1000e ndash 01

0000e + 00

46 times 46m

xyz


x

yz




x

y

z



Material status

Void

Hydro

Elastic

Plastic

Bulk failxy

z



ndash158e + 02mm


x

y

z




4 Conclusions





0

2

4

6

Z-ve

loci

ty (m

s)

1 2 3 4 5 60Time (ms)


xyz


I girder

I girder

Detonation point

2m times 6

5mtimes

2

50 51 52 53 54

75

96

113 114



Gauge 53Gauge 54

0

2

4

6

8

Z-ve

loci

ty (m

s)

1 2 3 4 5 60Time (ms)


Gauge 113

1 2 3 4 5 60Time (ms)

0

500

1000

1500

2000

2500

Pres

sure

(kPa

)




Data Availability




Acknowledgments


References
















Gauge 114

1 2 3 4 5 60Time (ms)

0

500

1000

1500

Pres

sure

(kPa

)





RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


x

y

z



Material status

Void

Hydro

Elastic

Plastic

Bulk failxy

z



ndash158e + 02mm


x

y

z




4 Conclusions





0

2

4

6

Z-ve

loci

ty (m

s)

1 2 3 4 5 60Time (ms)


xyz


I girder

I girder

Detonation point

2m times 6

5mtimes

2

50 51 52 53 54

75

96

113 114



Gauge 53Gauge 54

0

2

4

6

8

Z-ve

loci

ty (m

s)

1 2 3 4 5 60Time (ms)


Gauge 113

1 2 3 4 5 60Time (ms)

0

500

1000

1500

2000

2500

Pres

sure

(kPa

)




Data Availability




Acknowledgments


References
















Gauge 114

1 2 3 4 5 60Time (ms)

0

500

1000

1500

Pres

sure

(kPa

)





RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



4 Conclusions





0

2

4

6

Z-ve

loci

ty (m

s)

1 2 3 4 5 60Time (ms)


xyz


I girder

I girder

Detonation point

2m times 6

5mtimes

2

50 51 52 53 54

75

96

113 114



Gauge 53Gauge 54

0

2

4

6

8

Z-ve

loci

ty (m

s)

1 2 3 4 5 60Time (ms)


Gauge 113

1 2 3 4 5 60Time (ms)

0

500

1000

1500

2000

2500

Pres

sure

(kPa

)




Data Availability




Acknowledgments


References
















Gauge 114

1 2 3 4 5 60Time (ms)

0

500

1000

1500

Pres

sure

(kPa

)





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
















Gauge 114

1 2 3 4 5 60Time (ms)

0

500

1000

1500

Pres

sure

(kPa

)





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


ResearchofSteel-ConcreteCompositeBridgeunder...

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