Research ArticleNumerical Study of Damage Modes and Damage Assessment ofCFST Columns under Blast Loading

Junhao Zhang1 Shiyong Jiang1 Bin Chen2 Chunhai Li3 and Hao Qin3

1Chongqing Key Laboratory of Geomechanics amp Geoenvironmental Protection Logistical Engineering UniversityChongqing 401311 China2Institute of Engineering Mechanics China Earthquake Administration Harbin 150080 China3Beijing Canbao Institute of Architectural Design Beijing 100850 China

Correspondence should be addressed to Shiyong Jiang jiangshy1163com

Received 2 September 2015 Revised 22 November 2015 Accepted 24 November 2015

Academic Editor Sakdirat Kaewunruen

Copyright copy 2016 Junhao Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Columns of frame structures are the key load-bearing components and the exterior columns are susceptible to attack in terroristblasts When subjected to blast loads the columns would suffer a loss of bearing capacity to a certain extent due to the damageimparted which may induce the collapse of them and even cause the progressive collapse of the whole structure In this paperthe high-fidelity physics-based finite element program LS-DYNA was utilized to investigate the dynamic behavior and damagecharacteristics of the widely used concrete-filled steel tube (CFST) columns subjected to blast loads The established numericalmodel was calibrated with test data in open literatures Possible damagemodes of CFST columns under blast loading were analyzedand the damage criterion based on the residual axial load capacity of the columns was adopted to assess the damage degree Aparametric study was conducted to investigate the effects of critical parameters such as blast conditions and column details on thedamage degree of CFST columns Based on the numerical simulation data an empirical equation was proposed to estimate thevariation of columns damage degree with the various parameters

1 Introduction

Concrete-filled steel tube (CFST) columns have been widelyused in engineering structures such as high-rise buildingsarch bridges and factories as they have advantages of highstrength and excellent ductility due to a confinement effectand a changed buckling mode [1 2] With the increase ofterrorist bombings in recent years blast resistance of thestructures has become a consideration in their design process[3] When subjected to blast loads columns may suffer a lossof bearing capacity to a certain extent due to the damageimparted which may induce the collapse of the columns andeven cause the progressive collapse of the whole structureIn addition both concrete and steel of which CFST columnsare composed may respond to blast loads at very high strainrates in the order of 1ndash100 sminus1 or even higher thus makingthe dynamic analysis of the CFST columns different fromthat under static loads and earthquake actions Therefore it

is of realistic significance to study the dynamic behavior anddamage characteristics of CFST columns under blast loading

Fujikura et al experimentally investigated the dynamicresponses of CFST bridge pier column specimens under blastloading According to the magnitude of the support rotationthe damage states of the column specimens were categorizedinto three types that is the plastic deformation onset offracture and postfracture The authors also compared themaximum response of the specimens obtained from thesimplified method based on the equivalent single-degree-of-freedom (SDOF) theory with the test data [4 5] Li et alstudied the dynamic behavior of CFST columns through aseries of field blast experiments They analyzed the effects ofexplosive mass standoff distance axial load ratio concretestrength grade and steel ratio on the displacement and strainresponses of CFST columns which showed global-mode con-trolled responses in the tests [6] Remennikov and Uy carriedout field tests on the CFST specimens and demonstrated the

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 3972791 12 pageshttpdxdoiorg10115520163972791

2 Shock and Vibration

The steel frame

The test pit The pneumatic jack

(a) The steel frame that holds the specimen in place

Steel tubeInfill concrete

LVDTRoller supportGround

Pneumatic jack

Explosive28mm200mm

200

mm

1500

mm

380mm380mm

(b) The test configuration

Figure 1 Test setup (Zhang et al [9])

effects of scaled standoff distance on the mode of responseand failure of the specimens under near-field blast loadingIt was found that CFST members may suffer severe localizeddamage due to the highly localized blast impulse when theexplosive was located quite close to the test members Theauthors also developed a simplified engineering-level modelfor prediction of the mid-span deflection history of theCFST member [7] Ngo et al utilized the coupled Arbi-trary Lagrange Euler (ALE) blast wave-structure interactionalgorithms and numerically investigated the failure patternsdeformation histories and energy absorption characteristicsof CFST members subjected to near-field blast loadingTwo distinct phases of deformation were identified in thestudy of which the local deformation that initially occurredrather than the flexural global deformation that followeddominates the energy absorption history of the columnspecimen [8] Zhang et al carried out blast tests and finiteelement simulations on the axially compressed CFST columnmembers Results indicated that CFST columns showedgood resistance against flexural loads under blast loadingThe energies absorbed by local deformation and flexuraldeformation of the column during the blast loading were alsoinvestigated and it was found that themajority of the energieswere absorbed by global deformation when the mode ofresponse was mainly flexural [9] The authors also investi-gated the dynamic responses and damage characteristics ofthe concrete-filled columns with double-skin tubes to blastloads and the critical parameters that affect the displacementtime histories of the columns were analyzed [10]

The review of these literatures indicates that the mode ofresponse and damage criterion are key issues in understand-ing the dynamic behavior anddamage characteristics ofCFSTcolumns subjected to blast loads as some damage criterionsare only applicable to certain damage mode of the columnsand different conclusionsmay be drawn under varied damagemodes as stated previously The objective of this paper isto study the damage modes and damage assessment ofCFST columns under blast loading The numerical modelis established using the finite element program LS-DYNAand calibrated with correlated experimental studies by otherresearchers Possible damagemodes of the columns subjected

to blast loads are analyzed and the criterion suitable to assessthe degree of the columns damage is adopted accordinglyParameters that may affect the damage degree of the columnsare analyzed in the study they are blast condition columndimension steel ratio and axial load ratio which are thenincorporated into a proposed equation capable of estimatingthe damage degree of CFST columns based on the numericalresults

2 Numerical Model Calibration

The high-fidelity physics-based finite element program LS-DYNA was used in the paper To calibrate the employednumerical models for simulating the dynamic responses ofCFST columns to blast loads one of the blast tests on CFSTcolumns conducted by Zhang et al [9] was simulated anda comparison was made between the test and numericalsimulation results Figure 1 shows the sketch of test setupof column number S4 The dimensions of the column are2500mm (height) times 200mm (width) times 200mm (depth)with the tube thickness of 28mm The yield stress ultimatestress Youngrsquos modulus and elongation of the steel tubeare 3582MPa 4374MPa 2026GPa and 213 respectivelyThe average cubic compressive strength of the infill concreteis 474MPa which is 379MPa if converted to cylindricalcompressive strength During the test the specimen wasfirstly placed on a steel frame which was then placed into thetest pit The specimen was simply supported by four rollers(two at each ends) thus the effective span of it was 2300mmA steel plate was placed between the roller and the column toavoid stress concentrationThe initial axial load (514 kN) wasapplied to the ends of the column through a pneumatic jackprior to blast loading and then 50 kg of emulsion explosive(equivalent to 35 kg of TNT)was ignited in the air at a standoffdistance (center of explosive to the mid of column frontsurface) of 1500mm to generate the blast environment

21 Numerical Model

211 Material Model Considering the large strain and highstrain rate problems involved in analyzing the responses of

Shock and Vibration 3

Stre

ss

0

Yield stress

E

Et

120573 = 0 kinematic hardening

120573 = 1 isotropic hardening

l0 and l are undeformed anddeformed lengths of uniaxialtension specimen

ln(ll0)

Figure 2 Plastic kinematic model for steel modeling

steel tube under blast loading the plastic kinematic modelwhich takes into account the strain hardening and strain rateeffects is adopted for steel simulation The dynamic yieldstress of it is expressed as follows [11]

120590119910

= (1205900

+ 120573119864119875

120576119875

eff) [1 + (120576

119862

)

1119875

] (1)

where 120590119910

is the dynamic yield stress 1205900

is the initial yieldstress 120573 is the hardening parameter (for 120573 equal to 0 and1 resp kinematic and isotropic hardenings are obtained asshown in Figure 2)119864

119875

is the plastic hardeningmodulus119864119875

=

119864119864119905

(119864 minus 119864119905

) 119864 is Youngrsquos modulus and 119864119905

is the tangentmodulus 120576119875eff is the effective plastic strain 120576 is the strain rateand119862 and119875 areCowper-Symonds strain rate parameters [12]Material parameters of the steel tube in the study are listed inTable 1

The infill concrete subjected to blast loading may expe-rience large strains high strain rates and high pressuresBesides the collapse of air void as well as the dilationcaused by shearing cracks plays an important role in thedamage evolution of concrete Thus the Johnson-Holmquist-Cook (JHC) concrete model is used to simulate the concreteand the equivalent stress of it is expressed as a function ofpressure strain rate and damage as follows [13]

120590lowast

= [119860 (1 minus 119863) + 119861119875lowast119873

] (1 + 119862 ln 120576lowast) le 119878MAX (2)

where 120590lowast = 1205901198911015840119888

denotes the normalized equivalent stress(where 120590 and 1198911015840

119888

are the actual equivalent stress and quasi-static uniaxial compressive strength resp) 119860 is the normal-ized cohesive strength 119863 is the accumulated damage 119861 isthe normalized pressure hardening coefficient 119875lowast = 1198751198911015840

119888

is the dimensionless form of pressure 119875 119873 is the pressurehardening exponent 119862 is strain rate coefficient 120576lowast = 120576 120576

0

isthe dimensionless form of strain rate 120576 (where 120576

0

= 10 sminus1 isthe reference strain rate) and 119878MAX is the normalized maxi-mum strength as shown in Figure 3

Nor

mal

ized

equi

vale

nt st

ress120590lowast

Normalized pressure Plowast

120576lowast = 10

120576lowast gt 10

Tlowast(1 minus D)

D = 0 (undamaged)

D = 1 (fractured)

SMAX

Figure 3 JHC model for concrete modeling

The accumulated damage is expressed as

119863 = sum

Δ120576119875

+ Δ120583119875

1198631

(119875lowast

+ 119879lowast

)119863

2

(3)

where Δ120576119875

and Δ120583119875

are the equivalent plastic strain andplastic volumetric strain respectively119863

1

and1198632

are damageconstants and 119879lowast = 1198791198911015840

119888

is the dimensionless tensile hydro-static pressure

The relation between pressure and volumetric strain isdefined as

119875 =

119870119890

120583 0 le 119875 lt 119875119862

119875119862

+ 119870119862

(120583 minus 120583119862

) 119875119862

le 119875 lt 119875119871

1198701

120583 + 1198702

1205832

+ 1198703

1205833

119875 ge 119875119871

(4)

where 119870119890

is the elastic bulk modulus 119870119890

= 119875119862

120583119862

and 119875119862

and 120583119862

are the pressure and volumetric strain when crushingoccurs in concrete120583 is the volumetric strain120583 = (120583minus120583

119871

)(1+

120583119871

) is the corrected volumetric strain and 119875119871

and 120583119871

are thelocking pressure and volumetric strain at the beginning of thefully compacted stage (119875 ge 119875

119871

) 1198701

1198702

and 1198703

are materialconstants of concrete

The reliability of this concrete model in predicting theresponses of concrete structures to blast loads has beendemonstrated by many researchers [14 15] Material parame-ters of the infill concrete in the simulation are listed inTable 2

212 Finite Element Model and Erosion Algorithm TheBelytschko-Tsay shell element is used in the study to modelthe steel tube and the infill concrete is modeled with single-point integration solid elements A mesh size of 25mm isselected for the steel tube and infill concrete through a numer-ical convergence study It is found that further refinementof element size has little effect on the numerical results butincreases the calculation time enormously A perfect bondbetween steel tube and infill concrete is assumed in the

4 Shock and Vibration

Table 1 Material parameters of the steel tube

Parameter Mass density1205881

(kgm3) Poissonrsquos ratio 120592 1205900

(MPa) 119864 (GPa) 119864119905

(MPa) 120573 119862 P Failure strain(FS)

Value 7850 03 358 203 414 0 404 5 02

Table 2 Material parameters of the infill concrete

Parameter Mass density1205882

(kgm3) 119860 119861 119862 119873 1198911015840

119888

(MPa) 119878MAX

Value 2440 079 160 0007 061 379 70

Parameter Shear modulus119866 (GPa)

Maximumtensile pressure119879 (MPa)

Thresholdstrain rateEPS0 (sminus1)

Plastic strainbefore fracture

EFMIN

Crushingpressure119875119862

(MPa)

Crushingvolumetricstrain 119880

119862

Lockingpressure119875119871

(MPa)Value 1486 40 10 001 16 0001 800

ParameterLocking

volumetricstrain 119880

119871

Damageconstant1198631

Damageconstant1198632

Pressureconstant1198701

(GPa)

Pressureconstant1198702

(GPa)

Pressureconstant1198703

(GPa)Value 01 004 10 85 minus171 208

numerical study since no researches have reported a notice-able debond between the twomaterials in blast tests In orderto simulate the physical fracture shear failure and crushingof the concrete under blast loading the erosion algorithm isused to account for concrete failure Considering the strainrate effect on the concrete strength the erosion criterionbased on the principle strain is often used [16] A numberof simulations are carried out with different erosion criteriaand it is found that using principle tensile strain of 001 as theerosion criterion which is also used by Ngo et al [8] leads toreliable predictions of the responses of CFST columns

213 Sequence of Loads Application and Blast LoadModellingIn order to simulate the real stress state of CFST columns thelinearly increasing axial quasi-static loads up to the serviceaxial load level are applied to the top of the column prior toblast loading through the implicit solver To avoid too muchoscillation of the column the time duration for increasingthe loads from zero to full service level is 150ms Then thecomputational algorithm switches from implicit to explicitand the blast loads are applied over the front surface of thecolumn with the axial loads unchanged

Blast loads are generated using the ConWep air blastmodel [17] that is Load Blast Enhanced in LS-DYNA[18] Compared to other techniques that is the ArbitraryLagrangian Eulerian (ALE) methodology this model is morecomputationally efficient to simulate blast loads with a highlevel of accuracy While similar to the model Load Blast italso includes enhancements for treating reflected waves Theloading face of the column is predefined before the generationof blast loads and the time history of blast loads actingon each segment is calculated through ConWep formula asfollows

119875 (119905) = 119875119903

(119905) cos2120579 + 119875119894

(119905) (1 + cos2120579 minus 2 cos 120579) (5)

where 119875(119905) is the reflected overpressure on the definedload segment at moment 119905 119875

119903

(119905) and 119875119894

(119905) are the normal

0 25 50 75 100 125 150 175 200

Time (ms)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

Late

ral d

ispla

cem

ent (

mm

)

Test by Zhang et al [9]Residual displacement in the testNumerical simulation

Figure 4 Comparison of the displacement data from test and thatof numerical simulation

reflected overpressure and incident overpressure at moment119905 respectively and 120579 is the angle of incidence of the blast wave

22 Model Calibration and Discussion Numerical simula-tions of the blast test were carried out and the dynamicresponse and damage mode of column S4 were obtainedSince the recording of LVDT1 at the center of column S4 wasmissing in the test the value of LVDT2 (see Figure 1(b)) at380mm from the center of the column was used to calibratethe numerical model Comparison of the calculated displace-ment time history with test results is shown in Figure 4It is found that the peak displacement of numerical results(509mm) is smaller than that in the test (60mm) while thenumerical residual displacement (354mm) is slightly largerthan the test value (34mm) Several factors as follows may

Shock and Vibration 5

(a) Test result (Zhang et al [9])

Fringe levels

6346eminus02

5289eminus02

4231e

minus02

3173eminus02

2115eminus02

1058e

minus02

0000e

+00

(b) Numerical result

Figure 5 Comparison of the column damage mode in the test andthat from numerical simulation

account for such discrepancies (1) the difference between theactual support condition which is not rigid enough and thoseadopted in the simulation (2) ignorance of the potential lossof axial loads and reduction of flexural resistance consideringthe detachment of the column ends from the loading devicein the test and (3) the limitations of material models indepicting the real-time nonlinear behaviors of steel andconcrete during test Although discrepancies exist betweenthe simulation and test values the largest error with respectto the maximum displacements is within 152 Figure 5shows the comparison of the damage mode of the columnin the test and that from the numerical simulation presentedin effective plastic strain contour and good agreement isobserved in between These results demonstrate that thecalibrated numericalmodel leads to reasonable predictions ofthe dynamic responses and damage modes of CFST columnsto blast loads and can be used for the subsequent study

3 Damage Modes of CFST Column underBlast Loading

31 Column Configuration The above calibrated numericalmodel is utilized herein to simulate dynamic behavior andpossible damagemodes of CFST column under blast loadingThe column is designed based on the specifications providedby Chinese Standard CECS 159 2004 [19] As shown inFigure 6 the dimensions of the column are ℎ (height) times119908 (width)times119889 (depth) = 3700mm times 600mm times 600mm withthe tube thickness of 18mm Parameters of the steel tube andthe infill concrete used in the simulation are the same asthose in Section 2 In order to simulate the real life boundaryconditions for CFST columns a column head and a footingare considered in the numericalmodelThe outer vertical faceof the footing and head are constrained against horizontalmotions and the bottom face of the footing is constrainedagainst vertical motions [20] Horizontal distance from thecharge center to the column front surface that is the standoffdistance is denoted as 119883 And the vertical distance fromthe charge center to the ground that is the height of burstis denoted as 119867

119861

The initial dead weight imposed on the

Table 3 Possible damage modes of the CFST column

119872 (kg) 119867119861

(m) 119885 (mkg13) Damage mode

50 0le021 Localized

022ndash024 Shearge026 Flexural

250 0le025 Localized

030ndash048 Shearge052 Flexural

50 185 le016 Localizedge018 Flexural

column is 35 percent of axial load capacity of the undamagedcolumn which represents the axial load level of a typicalground floor column in a high-rise building

As the blast load parameters are related to both explosivemass and standoff distance the scaled standoff distance isintroduced to consider their combined effects and is definedas [21]

119885 =

119883

11987213

(6)

where 119885 is the scaled standoff distance and 119872 is theequivalent mass of TNT

32 Possible Damage Modes Three damage modes of theCFST column under blast loading have been observedthrough a number of simulations they are flexural damageshear damage and localized damage Table 3 presents damagemodes of the column according to different blast conditionsIt is found that in general explosivewith a small scaled stand-off distance favors a localized damage whilst shear damageand localized damage occur when the explosive is relativelyfar from the columnThis is because the blast loads are highlyintensive when the scaled standoff distance is small and forvery local blast loads acting on the column failure of the infillconcrete and steel tube starts before any considerable overallresponse can occur and the column surfers a localized dam-age However with the increase of scaled standoff distanceblast loads tend to be well-distributed over the surface of thecolumn which is inclined to response globally and undergoshear damage and flexural damage Also the damagemode isaffected by the explosive mass height of burst Typical resultsof these damagemodes are shown with effective plastic straincontours in Figures 7ndash9

Figure 7 shows the flexural damage mode of the CFSTcolumn induced by the detonation of 50 kg of TNT at thescaled standoff distance of 018mkg13 with the height ofburst of 185m In this configuration when the blast loadsacted on the column the mid-part of it responded imme-diately with the increment of lateral deformation Then theareas near the supports of the column began to deform androtate As the global flexural deformation of the columnevolved plastic hinges developed in the mid-part and nearthe supports of the columnwhere the bendingmoments werelarge

6 Shock and Vibration

First-floor column

Second-floor column

Explosive

Second-floor beam

h

HB

X

(a) Explosion scenario

1 1

Section 1-1

Steel tube

Infill concrete

Axial load

Head

Footing

First-floor column

h d t

w

(b) Column details

Figure 6 Sketch of the numerical analysis model

Figure 8 shows the shear damage mode of the columnresulted from 250 kg of TNT detonating on the ground atthe scaled standoff distance of 033mkg13 Due to the largeshear force and the development of shear deformation nearthe supports the infill concrete was sheared off accompaniedwith the rupture of the steel tube around the cross section ofthe column Finally the column failed in brittle shear beforeany ductile flexural hinge developed

As discussed above flexural damage and shear damageof the column are due to the deformation and internal forceof the whole member induced by the blast loads On thecontrary localized damage of the CFST column is dominatedby the deformation and failure of the concrete infill and steeltube in the vicinity of the explosion whilst other parts of thecolumn remain almost elastic and the global deformation ofthe column is small

Figure 9 shows the localized damage mode of the CFSTcolumn caused by the detonation of 50 kg of TNT on theground with the scaled standoff distance of 018mkg13When the impulsive shock front of high intensity metthe column surface the stress waves were generated andpropagated from the tube front surface towards the concreteinfill and the lateral and back surfaces of the tube Then theconcrete close to the explosion was cracked and crushed andthe front side of the tube which lost the internal support ofthe concrete fill was squashed with the bulging of its lateraland back sides As the localized deformation of the columnevolved rupture and local buckling failure of the steel tubetook place yet the global lateral deformation of the columnhad almost not developed at this moment

It should bementioned that these damagemodes are onlytypical ones Sometimes there exists a combination of thesedamage modes

4 Damage Assessment of CFST Columnsunder Blast Loading

41 Damage Criterion As discussed previously the CFSTcolumn subjected to blast loads may undergo flexural dam-age shear damage and localized damage thus the damagecriterion for the column should be chosen carefully andthe appropriate one is expected to be applicable to all thepossible damage modes of the column In this paper thedamage criterion based on the residual axial load capacityis adopted for CFST columns due to the following reasons(1) the structure column is primarily designed to carry theaxial load and the axial load capacity of it reflects bothits global properties and material characteristics (2) thecommonly used deformation-based damage criterions thatis the support rotation lateral deflection and ductility maynot be appropriate for the evaluation of localized damage ofthe column and (3) the residual axial load capacity of thecolumns is an explicit metric of the damage imparted and italso provides information in assessing the collapse possibilityof a blast damaged column

The damage index adopted herein is based on the indexfrom Shi et al [20] and is expressed as

119863119888

= 1 minus

119875residual119875max

(7)

where 119863119888

is the damage degree of CFST columns 119875residual isthe residual axial load capacity of the column after blast loadsand 119875max is the maximum axial load capacity of the columnprior to blast loading Values of 119863

119888

vary between 0 (ieno loss of capacity) and 10 (ie complete loss of capacity)Note that in the paper by Shi et al [20] the maximumaxial load capacity of an undamaged column is calculated

Shock and Vibration 7

Fringe levels

3793eminus02

3161e

minus02

2529eminus02

1897eminus02

1264eminus02

6322eminus03

0000e

+00

(a) CFST column

Fringe levels

3793eminus02

3161e

minus02

2529eminus02

1897eminus02

1264eminus02

6322eminus03

0000e

+00

(b) Infill concrete

Figure 7 Flexural damage mode of CFST column under blast loading

Fringe levels

2000e

minus01

1667eminus01

1333eminus01

1000e

minus01

6667eminus02

3333eminus02

0000e

+00

(a) CFST column

Fringe levels

2392e

minus02

1993eminus02

1594eminus02

1196eminus02

7972e

minus03

3986eminus03

0000e

+00

(b) Infill concrete

Figure 8 Shear damage mode of CFST column under blast loading

8 Shock and Vibration

Fringe levels

2000e

minus01

1667eminus01

1333eminus01

1000e

minus01

6667eminus02

3333eminus02

0000e

+00

(a) CFST column

Fringe levels

2597eminus02

2165eminus02

1732e

minus02

1299eminus02

8658e

minus03

4329eminus03

0000e

+00

(b) Infill concrete

Figure 9 Localized damage mode of CFST column under blast loading

with the provided equation from the standard design codewhich however may lead to the values of119863

119888

below 0 in somecases Therefore both 119875residual and 119875max are determined fromnumerical simulation in this study Here 119875residual119875max is alsotermed as the residual capacity index (RCI) used byWu et al[22] andCrawford et al [23] to assess the damage level of steelreinforced concrete (SRC) columns and reinforced concrete(RC) columns subjected to blast loads

It is noted that if the ratio of the service axial load tomaximum axial load capacity of the column is denoted as 119899then a column whose119863

119888

is greater than (1 minus 119899) is consideredas failed or collapsed since its residual axial load capacity isnot sufficient for the service axial load

42 Steps for Damage Assessment of CFST Columns

Step 1 (derivation of 119875max) During this step the linearlyincreasing axial load is applied on the column head until thecolumn collapses then 119875max is determined as the maximumaxial load that the column can withstand

Step 2 (derivation of 119875residual) Three substeps as follows arerequired to obtain 119875residual (1) before blast loading a linearlyincreasing axial load up to the service axial load is imposedon the column (2) blast loads are applied over the front faceof the column with the service axial load being constant andcalculation is stopped when the damaged column approachesstatic equilibrium (3) a linearly increasing axial load isimposed on the top of the damaged column until it collapses

then 119875residual is determined as the peak of the axial load thatthe damaged column can bear

Step 3 (determination of 119863119888

) Substitute the values of 119875maxand 119875residual into (7) to obtain119863119888

43 Parameters Studied In this section effects of severalkey parameters on the damage degree of CFST columnsare analyzed These parameters include the scaled standoffdistance height of burst explosive mass column depthcolumn width column steel ratio and axial load ratio aslisted in Table 4 in which a contrast case is generated bychanging one of the parameters considered in the benchmarkcase while keeping other parameters unchanged Note thatin each case varied scaled standoff distances are consideredso that the effects aforementioned parameters on the damagedegree of columns within different blast loading regimes canbe assessed

431 Effect of Scaled Standoff Distance 119885 The numericalsimulation results show that 119863

119888

of CFST columns decreaseswith the increasing scaled standoff distance regardless ofother parameters This is because column damage is affectedby the peak overpressure and impulse of the blast wave[21] and both of them drop with the rising scaled standoffdistance which results in a small degree of column damage

432 Effect of Height of Burst119867119861

It is difficult to characterizethe effect of 119867

119861

on the damage degree of the column On

Shock and Vibration 9

Table 4 Parameters used in the numerical parametric study

Parameters 119885 (mkg13) 119867119861

(m) 119872 (kg) 119889 (m) 119908 (m) Steel ratio 120572lowast Axial load ratio 119899Benchmark case 018ndash050 0 50 06 06 013 035Contrast cases 015ndash090 185 250 500 09 12 09 12 016 019 050 065lowast

120572 = 119860119904

119860119888

119860119904

and 119860119888

are the cross-sectional areas of steel tube and infill concrete respectively

07

06

05

04

03

02

01

00

HB = 0mHB = 185m

015 020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

Figure 10 Effects of height of burst on the damage degree

one hand when 119867119861

nears zero the initial blast wave isimmediately reflected and reinforced by the ground On theother the mid-height of the column is expected to surfer themost severe damage due to lack of transverse support Conse-quently as shown in Figure 10 surface burst results in severerdamage to the column than that caused by explosion atcolumnmid-height (119867

119861

= 185m) especially when the stand-off distance is small The effects of119867

119861

on the damage degreeof the column are insignificant at large scaled distancesbecause both the overpressure and impulse on the columnare relatively small in these cases

433 Effect of Explosive Mass119872 Figure 11 shows the effectsof explosive mass on the damage degree of the columnInspections of the figure show that 119863

119888

rises with 119872 for thesame scaled standoff distance indicating that CFST columnis impulse-sensitive since explosive with larger mass hasrelatively more impulse for the column

434 Effects of Column Width 119908 and Depth 119889 Effects ofcolumn depth and width on 119863

119888

are shown in Figure 12Comparedwith the reference column (119908 = 06m 119889 = 06m)columns with larger width and depth tend to have lowerdamage degrees because expanding columnwidth and depthproduces a larger cross section for attenuation of the stresswaves density and contributes to enhancement of the shearresistance as well as flexural strength of the columnHoweverit is found that columns with the same cross section area butdifferent width and depth have varied damage degrees and

07

06

05

04

03

02

01

0002 03 04 05 06 07 08 09 10

Scaled standoff distance Z (mkg13)

M = 50kgM = 250kgM = 500kg

[HB = 0m] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 11 Effects of explosive mass on the damage degree

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

w = 06m d = 06mw = 09m d = 06mw = 12m d = 06m

w = 06m d = 09mw = 06m d = 12m

[HB = 0m] [M = 50kg] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 12 Effects of width and depth on the damage degree

that compared with increasing the column width incrementof the column depth is more effective in reducing the columndamage degree This is because enlarging the column widthsimultaneously results in a rise of blast loads acting on thecolumnwhich balances out the enhancement of columnblastresistance to some extent

10 Shock and Vibration

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

120572 = 013

120572 = 016

120572 = 019

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [n = 035 ]

Dam

age d

egre

eDc

Figure 13 Effects of steel ratio on the damage degree

07

06

05

04

03

02

01

00020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

n = 035

n = 050

n = 065

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [120572 = 013]

Dam

age d

egre

eDc

Figure 14 Effects of axial load ratio on the damage degree

435 Effect of Column Steel Ratio 120572 As shown in Figure 13119863119888

drops with the rising steel ratio This is expected becauseincreasing 120572means a larger steel area and better confinementof infill concrete which will enhance the shear and bendingstrength of the column as well as its resistance to localizeddamage

436 Effect of Column Axial Load Ratio 119899 Effects of axialload ratio on 119863

119888

are shown in Figure 14 Inspection of thefigure reveals that axial load ratio has dual influences on col-umn damage When the scaled standoff is small the columnwith a larger axial load ratio has lower damage degree Thisis because the column under small scaled standoff is likelyto suffer localized damage and shear damage and a higher

axial load will restrain the cracking and crushing of concretewhich enhances the resistance of the column to localizeddamage and shear damage In contrast at a large scaledstandoff distance the column with larger axial load ratio hashigher damage degree The reason is that with the increaseof the scaled standoff distance the column tends to sufferflexural damage which is related to its moment capacity andductility The larger the moment capacity and ductility arethe lower the damage degree is For the CFST column studiedin this section the axial load ratio at the maximum momentcapacity is 022 which is derived by the methods from Choiet al [1] According to the axial load-bending moment (P-M)interactions the moment capacity of the CFST column willdecrease when 119899 rises from 035 to 060 Moreover a risingaxial load will reduce the ductility of the CFST column

44 Empirical Equations for Determining the Damage Degreeof CFST Columns The parametric study revealed the signif-icance of parameters affecting the damage degree of CFSTcolumns Through the multivariable regression analysis anempirical equation is proposed in terms of various parame-ters to predict the damage degree and is expressed as follows

119863119888

= [minus1505 ln(11987250

) + 1650 (

119908

06

) minus 3242 (

119889

06

)

minus 131625120572 + 15349119899 + 25011]

sdot 119890[minus648ln(11987250)+533(11990806)minus1091(11988906)minus373minus1230120572+1292119899+2681]119885

(8)

The comparisons of the proposed equation with the ana-lytical results are shown in Figures 15(a)ndash15(f) The scattersdenote the analytical results and the solid lines represent theproposed equation Observation of these figures shows thatthe proposed curves are close to the analytical results formostcases The effects of height of burst on the damage degree ofCFST columns are not reflected by (8) due to the lack of blastdata in the lower height of the column which are limited inthe ConWep model and will be supplemented in the furtherstudies

5 Conclusions

This paper presents a 3D numerical model to investigate thedamage modes and damage assessment of CFST columnsBased on the numerical analysis results the following con-clusions can be drawn

CFST columns under blast loading may undergo theglobal flexural damage and shear damage as well as localizeddamage Flexural damage and shear damage of the columnare mainly attributed to the deformation and internal force ofthe whole member whilst the localized damage is dominatedby the failure of infill concrete and steel tube in the vicinity ofthe explosion

The damage criterion based on the residual axial loadcapacity is adopted for assessing the degree of CFST columnsdamage to blast loadsThrough parametric studies it is foundthat the damage degree of CFST columns decays nearlyexponentially with the increasing scaled standoff distance

Shock and Vibration 11

07

06

05

04

03

02

01

00

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

Dam

age d

egre

eDc

(a)

07

06

05

04

03

02

01

00095090085050 055 060 065 070 075 080

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 500kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

(b)

07

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 12m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

(c)

020

015

010

005

000

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 12m] [120572 = 013] [n = 035]D

amag

e deg

reeD

c

(d)

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 019] [n = 035]

Dam

age d

egre

eDc

(e)

020

025

030

035

015

010

005

000055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 065]

Dam

age d

egre

eDc

(f)

Figure 15 Comparison of analytical results with the proposed curves

12 Shock and Vibration

For the same scaled standoff distance surface burst results inseverer damage to the column than that caused by explosionat columnmid-height and the damage degree increases withthe rising explosive mass and decreases with column depthand width and steel ratio Increasing the axial load enhancesthe resistance of the column against localized damage andshear damage while the effects of axial load on flexuraldamage depend on the axial load-bending moment (P-M)interactions of the column

An equation is derived by fitting the results of parametricstudies to estimate the damage degree of CFST columnsTypical examples confirm that the proposed equation wellrepresents the variation of the column damage degree How-ever future experiments can be conducted for investigatingthe effects of other parameters on the damage degree of CFSTcolumns

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research described in this paper was financially sup-ported by Achievement Transfer Program of Institutionsof Higher Education in Chongqing under Grant noKJZH14220

References

[1] Y-H Choi D A Foutch and J M LaFave ldquoNew approachto AISC P-M interaction curve for square concrete filled tube(CFT) beamndashcolumnsrdquo Engineering Structures vol 28 no 11pp 1586ndash1598 2006

[2] Y-H Choi K S Kim and S-M Choi ldquoSimplified P-M interac-tion curve for square steel tube filled with high-strength con-creterdquoThin-Walled Structures vol 46 no 5 pp 506ndash515 2008

[3] T KrauthammerModern Protective Structures TaylorampFrancisGroup New York NY USA 2008

[4] S C Fujikura M Bruneau and D Lopez-Garcia ldquoExperimen-tal investigation of blast performance of seismically resistantconcrete-filled steel tube bridge piersrdquo Tech Rep MCEER-07-0005 University at Buffalo Buffalo NY USA 2007

[5] S Fujikura M Bruneau and D Lopez-Garcia ldquoExperimentalinvestigation of multihazard resistant bridge piers having con-crete-filled steel tube under blast loadingrdquo Journal of BridgeEngineering vol 13 no 6 pp 586ndash594 2008

[6] G Li H Qu T Yang Y Lu and S Chen ldquoExperimental studyof concrete-filled steel tubular columns under blast loadingrdquoJianzhu Jiegou Xuebao vol 34 no 12 pp 69ndash76 2013 (Chinese)

[7] A M Remennikov and B Uy ldquoExplosive testing andmodellingof square tubular steel columns for near-field detonationsrdquo Jour-nal of Constructional Steel Research vol 101 pp 290ndash303 2014

[8] T Ngo D Mohotti A Remennikov and B Uy ldquoNumericalsimulations of response of tubular steel beams to close-rangeexplosionsrdquo Journal of Constructional Steel Research vol 105 pp151ndash163 2015

[9] F R Zhang C Q Wu H W Wang and Y Zhou ldquoNumericalsimulation of concrete filled steel tube columns against BLASTloadsrdquoThin-Walled Structures vol 92 pp 82ndash92 2015

[10] F Zhang C Wu X Zhao Z Li A Heidarpour and H WangldquoNumerical modeling of concrete-filled double-skin steelsquare tubular columns under blast loadingrdquo Journal of Per-formance of Constructed Facilities vol 29 no 5 Article IDB4015002 2015

[11] Livermore Software Technology Corporation LS-DYNA Theo-retical Manual Livermore Software Technology CorporationLivermore Calif USA 1998

[12] G R Cowper and P S Symonds ldquoStrain-hardening and strain-rate effects in the impact loading of cantilever beamsrdquo TechRep AD144762 Office of Naval Research Arlington Va USA1958

[13] T J Holmquist G R Johnson and W H Cook ldquoA computa-tional constitutive model for concrete subjected to large strainshigh strain rates and high pressuresrdquo in Proceedings of the 14thInternational Symposium on Ballistics Quebec City CanadaSeptember 1993

[14] Q Fang and J Zhang ldquoThree-dimensional modelling of steelfiber reinforced concrete material under intense dynamic load-ingrdquo Construction and Building Materials vol 44 pp 118ndash1322013

[15] Y Li F Lin X L Gu and X Q Lu ldquoNumerical researchof a super-large cooling tower subjected to accidental loadsrdquoNuclear Engineering and Design vol 269 pp 184ndash192 2014

[16] J Li and H Hao ldquoNumerical study of concrete spall damage toblast loadsrdquo International Journal of Impact Engineering vol 68pp 41ndash55 2014

[17] G Randers-Pehrson and K A Bannister ldquoAirblast loadingmodel for DYNA2D and DYNA3Drdquo Tech Rep ARL-TR-1310Army Research Laboratory Adelphi Md USA 1997

[18] Livermore Software Technology Corporation LS-DYNA Key-word Userrsquos Manual (Version 971 R610) Livermore SoftwareTechnology Corporation Livermore Calif USA 2012

[19] CECS ldquoTechnical specification for structures with concrete-filled rectangular steel tube membersrdquo CECS 1592004 ChinaAssociation for Engineering Construction StandardizationBeijing China 2004 (Chinese)

[20] Y Shi H Hao and Z-X Li ldquoNumerical derivation of pressure-impulse diagrams for prediction of RC column damage to blastloadsrdquo International Journal of Impact Engineering vol 35 no11 pp 1213ndash1227 2008

[21] P D Smith and J G Hetherington Blast and Ballistic Loadingof Structures Butterowrth-Heinemenn Oxford UK 1994

[22] K-C Wu B Li and K-C Tsai ldquoThe effects of explosive massratio on residual compressive capacity of contact blast damagedcomposite columnsrdquo Journal of Constructional Steel Researchvol 67 no 4 pp 602ndash612 2011

[23] J E Crawford K B Morrill and J M Magallanes ldquoProtectivedesign for columns against close-in blast effectsrdquo in Proceedingsof the Structures Congress Boston Mass USA April 2014

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Shock and Vibration

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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DistributedSensor Networks

International Journal of

2 Shock and Vibration

The steel frame

The test pit The pneumatic jack

(a) The steel frame that holds the specimen in place

Steel tubeInfill concrete

LVDTRoller supportGround

Pneumatic jack

Explosive28mm200mm

200

mm

1500

mm

380mm380mm

(b) The test configuration

Figure 1 Test setup (Zhang et al [9])

effects of scaled standoff distance on the mode of responseand failure of the specimens under near-field blast loadingIt was found that CFST members may suffer severe localizeddamage due to the highly localized blast impulse when theexplosive was located quite close to the test members Theauthors also developed a simplified engineering-level modelfor prediction of the mid-span deflection history of theCFST member [7] Ngo et al utilized the coupled Arbi-trary Lagrange Euler (ALE) blast wave-structure interactionalgorithms and numerically investigated the failure patternsdeformation histories and energy absorption characteristicsof CFST members subjected to near-field blast loadingTwo distinct phases of deformation were identified in thestudy of which the local deformation that initially occurredrather than the flexural global deformation that followeddominates the energy absorption history of the columnspecimen [8] Zhang et al carried out blast tests and finiteelement simulations on the axially compressed CFST columnmembers Results indicated that CFST columns showedgood resistance against flexural loads under blast loadingThe energies absorbed by local deformation and flexuraldeformation of the column during the blast loading were alsoinvestigated and it was found that themajority of the energieswere absorbed by global deformation when the mode ofresponse was mainly flexural [9] The authors also investi-gated the dynamic responses and damage characteristics ofthe concrete-filled columns with double-skin tubes to blastloads and the critical parameters that affect the displacementtime histories of the columns were analyzed [10]

The review of these literatures indicates that the mode ofresponse and damage criterion are key issues in understand-ing the dynamic behavior anddamage characteristics ofCFSTcolumns subjected to blast loads as some damage criterionsare only applicable to certain damage mode of the columnsand different conclusionsmay be drawn under varied damagemodes as stated previously The objective of this paper isto study the damage modes and damage assessment ofCFST columns under blast loading The numerical modelis established using the finite element program LS-DYNAand calibrated with correlated experimental studies by otherresearchers Possible damagemodes of the columns subjected

to blast loads are analyzed and the criterion suitable to assessthe degree of the columns damage is adopted accordinglyParameters that may affect the damage degree of the columnsare analyzed in the study they are blast condition columndimension steel ratio and axial load ratio which are thenincorporated into a proposed equation capable of estimatingthe damage degree of CFST columns based on the numericalresults

2 Numerical Model Calibration

The high-fidelity physics-based finite element program LS-DYNA was used in the paper To calibrate the employednumerical models for simulating the dynamic responses ofCFST columns to blast loads one of the blast tests on CFSTcolumns conducted by Zhang et al [9] was simulated anda comparison was made between the test and numericalsimulation results Figure 1 shows the sketch of test setupof column number S4 The dimensions of the column are2500mm (height) times 200mm (width) times 200mm (depth)with the tube thickness of 28mm The yield stress ultimatestress Youngrsquos modulus and elongation of the steel tubeare 3582MPa 4374MPa 2026GPa and 213 respectivelyThe average cubic compressive strength of the infill concreteis 474MPa which is 379MPa if converted to cylindricalcompressive strength During the test the specimen wasfirstly placed on a steel frame which was then placed into thetest pit The specimen was simply supported by four rollers(two at each ends) thus the effective span of it was 2300mmA steel plate was placed between the roller and the column toavoid stress concentrationThe initial axial load (514 kN) wasapplied to the ends of the column through a pneumatic jackprior to blast loading and then 50 kg of emulsion explosive(equivalent to 35 kg of TNT)was ignited in the air at a standoffdistance (center of explosive to the mid of column frontsurface) of 1500mm to generate the blast environment

21 Numerical Model

211 Material Model Considering the large strain and highstrain rate problems involved in analyzing the responses of

Shock and Vibration 3

Stre

ss

0

Yield stress

E

Et

120573 = 0 kinematic hardening

120573 = 1 isotropic hardening

l0 and l are undeformed anddeformed lengths of uniaxialtension specimen

ln(ll0)

Figure 2 Plastic kinematic model for steel modeling

steel tube under blast loading the plastic kinematic modelwhich takes into account the strain hardening and strain rateeffects is adopted for steel simulation The dynamic yieldstress of it is expressed as follows [11]

120590119910

= (1205900

+ 120573119864119875

120576119875

eff) [1 + (120576

119862

)

1119875

] (1)

where 120590119910

is the dynamic yield stress 1205900

is the initial yieldstress 120573 is the hardening parameter (for 120573 equal to 0 and1 resp kinematic and isotropic hardenings are obtained asshown in Figure 2)119864

119875

is the plastic hardeningmodulus119864119875

=

119864119864119905

(119864 minus 119864119905

) 119864 is Youngrsquos modulus and 119864119905

is the tangentmodulus 120576119875eff is the effective plastic strain 120576 is the strain rateand119862 and119875 areCowper-Symonds strain rate parameters [12]Material parameters of the steel tube in the study are listed inTable 1

The infill concrete subjected to blast loading may expe-rience large strains high strain rates and high pressuresBesides the collapse of air void as well as the dilationcaused by shearing cracks plays an important role in thedamage evolution of concrete Thus the Johnson-Holmquist-Cook (JHC) concrete model is used to simulate the concreteand the equivalent stress of it is expressed as a function ofpressure strain rate and damage as follows [13]

120590lowast

= [119860 (1 minus 119863) + 119861119875lowast119873

] (1 + 119862 ln 120576lowast) le 119878MAX (2)

where 120590lowast = 1205901198911015840119888

denotes the normalized equivalent stress(where 120590 and 1198911015840

119888

are the actual equivalent stress and quasi-static uniaxial compressive strength resp) 119860 is the normal-ized cohesive strength 119863 is the accumulated damage 119861 isthe normalized pressure hardening coefficient 119875lowast = 1198751198911015840

119888

is the dimensionless form of pressure 119875 119873 is the pressurehardening exponent 119862 is strain rate coefficient 120576lowast = 120576 120576

0

isthe dimensionless form of strain rate 120576 (where 120576

0

= 10 sminus1 isthe reference strain rate) and 119878MAX is the normalized maxi-mum strength as shown in Figure 3

Nor

mal

ized

equi

vale

nt st

ress120590lowast

Normalized pressure Plowast

120576lowast = 10

120576lowast gt 10

Tlowast(1 minus D)

D = 0 (undamaged)

D = 1 (fractured)

SMAX

Figure 3 JHC model for concrete modeling

The accumulated damage is expressed as

119863 = sum

Δ120576119875

+ Δ120583119875

1198631

(119875lowast

+ 119879lowast

)119863

2

(3)

where Δ120576119875

and Δ120583119875

are the equivalent plastic strain andplastic volumetric strain respectively119863

1

and1198632

are damageconstants and 119879lowast = 1198791198911015840

119888

is the dimensionless tensile hydro-static pressure

The relation between pressure and volumetric strain isdefined as

119875 =

119870119890

120583 0 le 119875 lt 119875119862

119875119862

+ 119870119862

(120583 minus 120583119862

) 119875119862

le 119875 lt 119875119871

1198701

120583 + 1198702

1205832

+ 1198703

1205833

119875 ge 119875119871

(4)

where 119870119890

is the elastic bulk modulus 119870119890

= 119875119862

120583119862

and 119875119862

and 120583119862

are the pressure and volumetric strain when crushingoccurs in concrete120583 is the volumetric strain120583 = (120583minus120583

119871

)(1+

120583119871

) is the corrected volumetric strain and 119875119871

and 120583119871

are thelocking pressure and volumetric strain at the beginning of thefully compacted stage (119875 ge 119875

119871

) 1198701

1198702

and 1198703

are materialconstants of concrete

The reliability of this concrete model in predicting theresponses of concrete structures to blast loads has beendemonstrated by many researchers [14 15] Material parame-ters of the infill concrete in the simulation are listed inTable 2

212 Finite Element Model and Erosion Algorithm TheBelytschko-Tsay shell element is used in the study to modelthe steel tube and the infill concrete is modeled with single-point integration solid elements A mesh size of 25mm isselected for the steel tube and infill concrete through a numer-ical convergence study It is found that further refinementof element size has little effect on the numerical results butincreases the calculation time enormously A perfect bondbetween steel tube and infill concrete is assumed in the

4 Shock and Vibration

Table 1 Material parameters of the steel tube

Parameter Mass density1205881

(kgm3) Poissonrsquos ratio 120592 1205900

(MPa) 119864 (GPa) 119864119905

(MPa) 120573 119862 P Failure strain(FS)

Value 7850 03 358 203 414 0 404 5 02

Table 2 Material parameters of the infill concrete

Parameter Mass density1205882

(kgm3) 119860 119861 119862 119873 1198911015840

119888

(MPa) 119878MAX

Value 2440 079 160 0007 061 379 70

Parameter Shear modulus119866 (GPa)

Maximumtensile pressure119879 (MPa)

Thresholdstrain rateEPS0 (sminus1)

Plastic strainbefore fracture

EFMIN

Crushingpressure119875119862

(MPa)

Crushingvolumetricstrain 119880

119862

Lockingpressure119875119871

(MPa)Value 1486 40 10 001 16 0001 800

ParameterLocking

volumetricstrain 119880

119871

Damageconstant1198631

Damageconstant1198632

Pressureconstant1198701

(GPa)

Pressureconstant1198702

(GPa)

Pressureconstant1198703

(GPa)Value 01 004 10 85 minus171 208

numerical study since no researches have reported a notice-able debond between the twomaterials in blast tests In orderto simulate the physical fracture shear failure and crushingof the concrete under blast loading the erosion algorithm isused to account for concrete failure Considering the strainrate effect on the concrete strength the erosion criterionbased on the principle strain is often used [16] A numberof simulations are carried out with different erosion criteriaand it is found that using principle tensile strain of 001 as theerosion criterion which is also used by Ngo et al [8] leads toreliable predictions of the responses of CFST columns

213 Sequence of Loads Application and Blast LoadModellingIn order to simulate the real stress state of CFST columns thelinearly increasing axial quasi-static loads up to the serviceaxial load level are applied to the top of the column prior toblast loading through the implicit solver To avoid too muchoscillation of the column the time duration for increasingthe loads from zero to full service level is 150ms Then thecomputational algorithm switches from implicit to explicitand the blast loads are applied over the front surface of thecolumn with the axial loads unchanged

Blast loads are generated using the ConWep air blastmodel [17] that is Load Blast Enhanced in LS-DYNA[18] Compared to other techniques that is the ArbitraryLagrangian Eulerian (ALE) methodology this model is morecomputationally efficient to simulate blast loads with a highlevel of accuracy While similar to the model Load Blast italso includes enhancements for treating reflected waves Theloading face of the column is predefined before the generationof blast loads and the time history of blast loads actingon each segment is calculated through ConWep formula asfollows

119875 (119905) = 119875119903

(119905) cos2120579 + 119875119894

(119905) (1 + cos2120579 minus 2 cos 120579) (5)

where 119875(119905) is the reflected overpressure on the definedload segment at moment 119905 119875

119903

(119905) and 119875119894

(119905) are the normal

0 25 50 75 100 125 150 175 200

Time (ms)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

Late

ral d

ispla

cem

ent (

mm

)

Test by Zhang et al [9]Residual displacement in the testNumerical simulation

Figure 4 Comparison of the displacement data from test and thatof numerical simulation

reflected overpressure and incident overpressure at moment119905 respectively and 120579 is the angle of incidence of the blast wave

22 Model Calibration and Discussion Numerical simula-tions of the blast test were carried out and the dynamicresponse and damage mode of column S4 were obtainedSince the recording of LVDT1 at the center of column S4 wasmissing in the test the value of LVDT2 (see Figure 1(b)) at380mm from the center of the column was used to calibratethe numerical model Comparison of the calculated displace-ment time history with test results is shown in Figure 4It is found that the peak displacement of numerical results(509mm) is smaller than that in the test (60mm) while thenumerical residual displacement (354mm) is slightly largerthan the test value (34mm) Several factors as follows may

Shock and Vibration 5

(a) Test result (Zhang et al [9])

Fringe levels

6346eminus02

5289eminus02

4231e

minus02

3173eminus02

2115eminus02

1058e

minus02

0000e

+00

(b) Numerical result

Figure 5 Comparison of the column damage mode in the test andthat from numerical simulation

account for such discrepancies (1) the difference between theactual support condition which is not rigid enough and thoseadopted in the simulation (2) ignorance of the potential lossof axial loads and reduction of flexural resistance consideringthe detachment of the column ends from the loading devicein the test and (3) the limitations of material models indepicting the real-time nonlinear behaviors of steel andconcrete during test Although discrepancies exist betweenthe simulation and test values the largest error with respectto the maximum displacements is within 152 Figure 5shows the comparison of the damage mode of the columnin the test and that from the numerical simulation presentedin effective plastic strain contour and good agreement isobserved in between These results demonstrate that thecalibrated numericalmodel leads to reasonable predictions ofthe dynamic responses and damage modes of CFST columnsto blast loads and can be used for the subsequent study

3 Damage Modes of CFST Column underBlast Loading

31 Column Configuration The above calibrated numericalmodel is utilized herein to simulate dynamic behavior andpossible damagemodes of CFST column under blast loadingThe column is designed based on the specifications providedby Chinese Standard CECS 159 2004 [19] As shown inFigure 6 the dimensions of the column are ℎ (height) times119908 (width)times119889 (depth) = 3700mm times 600mm times 600mm withthe tube thickness of 18mm Parameters of the steel tube andthe infill concrete used in the simulation are the same asthose in Section 2 In order to simulate the real life boundaryconditions for CFST columns a column head and a footingare considered in the numericalmodelThe outer vertical faceof the footing and head are constrained against horizontalmotions and the bottom face of the footing is constrainedagainst vertical motions [20] Horizontal distance from thecharge center to the column front surface that is the standoffdistance is denoted as 119883 And the vertical distance fromthe charge center to the ground that is the height of burstis denoted as 119867

119861

The initial dead weight imposed on the

Table 3 Possible damage modes of the CFST column

119872 (kg) 119867119861

(m) 119885 (mkg13) Damage mode

50 0le021 Localized

022ndash024 Shearge026 Flexural

250 0le025 Localized

030ndash048 Shearge052 Flexural

50 185 le016 Localizedge018 Flexural

column is 35 percent of axial load capacity of the undamagedcolumn which represents the axial load level of a typicalground floor column in a high-rise building

As the blast load parameters are related to both explosivemass and standoff distance the scaled standoff distance isintroduced to consider their combined effects and is definedas [21]

119885 =

119883

11987213

(6)

where 119885 is the scaled standoff distance and 119872 is theequivalent mass of TNT

32 Possible Damage Modes Three damage modes of theCFST column under blast loading have been observedthrough a number of simulations they are flexural damageshear damage and localized damage Table 3 presents damagemodes of the column according to different blast conditionsIt is found that in general explosivewith a small scaled stand-off distance favors a localized damage whilst shear damageand localized damage occur when the explosive is relativelyfar from the columnThis is because the blast loads are highlyintensive when the scaled standoff distance is small and forvery local blast loads acting on the column failure of the infillconcrete and steel tube starts before any considerable overallresponse can occur and the column surfers a localized dam-age However with the increase of scaled standoff distanceblast loads tend to be well-distributed over the surface of thecolumn which is inclined to response globally and undergoshear damage and flexural damage Also the damagemode isaffected by the explosive mass height of burst Typical resultsof these damagemodes are shown with effective plastic straincontours in Figures 7ndash9

Figure 7 shows the flexural damage mode of the CFSTcolumn induced by the detonation of 50 kg of TNT at thescaled standoff distance of 018mkg13 with the height ofburst of 185m In this configuration when the blast loadsacted on the column the mid-part of it responded imme-diately with the increment of lateral deformation Then theareas near the supports of the column began to deform androtate As the global flexural deformation of the columnevolved plastic hinges developed in the mid-part and nearthe supports of the columnwhere the bendingmoments werelarge

6 Shock and Vibration

First-floor column

Second-floor column

Explosive

Second-floor beam

h

HB

X

(a) Explosion scenario

1 1

Section 1-1

Steel tube

Infill concrete

Axial load

Head

Footing

First-floor column

h d t

w

(b) Column details

Figure 6 Sketch of the numerical analysis model

Figure 8 shows the shear damage mode of the columnresulted from 250 kg of TNT detonating on the ground atthe scaled standoff distance of 033mkg13 Due to the largeshear force and the development of shear deformation nearthe supports the infill concrete was sheared off accompaniedwith the rupture of the steel tube around the cross section ofthe column Finally the column failed in brittle shear beforeany ductile flexural hinge developed

As discussed above flexural damage and shear damageof the column are due to the deformation and internal forceof the whole member induced by the blast loads On thecontrary localized damage of the CFST column is dominatedby the deformation and failure of the concrete infill and steeltube in the vicinity of the explosion whilst other parts of thecolumn remain almost elastic and the global deformation ofthe column is small

Figure 9 shows the localized damage mode of the CFSTcolumn caused by the detonation of 50 kg of TNT on theground with the scaled standoff distance of 018mkg13When the impulsive shock front of high intensity metthe column surface the stress waves were generated andpropagated from the tube front surface towards the concreteinfill and the lateral and back surfaces of the tube Then theconcrete close to the explosion was cracked and crushed andthe front side of the tube which lost the internal support ofthe concrete fill was squashed with the bulging of its lateraland back sides As the localized deformation of the columnevolved rupture and local buckling failure of the steel tubetook place yet the global lateral deformation of the columnhad almost not developed at this moment

It should bementioned that these damagemodes are onlytypical ones Sometimes there exists a combination of thesedamage modes

4 Damage Assessment of CFST Columnsunder Blast Loading

41 Damage Criterion As discussed previously the CFSTcolumn subjected to blast loads may undergo flexural dam-age shear damage and localized damage thus the damagecriterion for the column should be chosen carefully andthe appropriate one is expected to be applicable to all thepossible damage modes of the column In this paper thedamage criterion based on the residual axial load capacityis adopted for CFST columns due to the following reasons(1) the structure column is primarily designed to carry theaxial load and the axial load capacity of it reflects bothits global properties and material characteristics (2) thecommonly used deformation-based damage criterions thatis the support rotation lateral deflection and ductility maynot be appropriate for the evaluation of localized damage ofthe column and (3) the residual axial load capacity of thecolumns is an explicit metric of the damage imparted and italso provides information in assessing the collapse possibilityof a blast damaged column

The damage index adopted herein is based on the indexfrom Shi et al [20] and is expressed as

119863119888

= 1 minus

119875residual119875max

(7)

where 119863119888

is the damage degree of CFST columns 119875residual isthe residual axial load capacity of the column after blast loadsand 119875max is the maximum axial load capacity of the columnprior to blast loading Values of 119863

119888

vary between 0 (ieno loss of capacity) and 10 (ie complete loss of capacity)Note that in the paper by Shi et al [20] the maximumaxial load capacity of an undamaged column is calculated

Shock and Vibration 7

Fringe levels

3793eminus02

3161e

minus02

2529eminus02

1897eminus02

1264eminus02

6322eminus03

0000e

+00

(a) CFST column

Fringe levels

3793eminus02

3161e

minus02

2529eminus02

1897eminus02

1264eminus02

6322eminus03

0000e

+00

(b) Infill concrete

Figure 7 Flexural damage mode of CFST column under blast loading

Fringe levels

2000e

minus01

1667eminus01

1333eminus01

1000e

minus01

6667eminus02

3333eminus02

0000e

+00

(a) CFST column

Fringe levels

2392e

minus02

1993eminus02

1594eminus02

1196eminus02

7972e

minus03

3986eminus03

0000e

+00

(b) Infill concrete

Figure 8 Shear damage mode of CFST column under blast loading

8 Shock and Vibration

Fringe levels

2000e

minus01

1667eminus01

1333eminus01

1000e

minus01

6667eminus02

3333eminus02

0000e

+00

(a) CFST column

Fringe levels

2597eminus02

2165eminus02

1732e

minus02

1299eminus02

8658e

minus03

4329eminus03

0000e

+00

(b) Infill concrete

Figure 9 Localized damage mode of CFST column under blast loading

with the provided equation from the standard design codewhich however may lead to the values of119863

119888

below 0 in somecases Therefore both 119875residual and 119875max are determined fromnumerical simulation in this study Here 119875residual119875max is alsotermed as the residual capacity index (RCI) used byWu et al[22] andCrawford et al [23] to assess the damage level of steelreinforced concrete (SRC) columns and reinforced concrete(RC) columns subjected to blast loads

It is noted that if the ratio of the service axial load tomaximum axial load capacity of the column is denoted as 119899then a column whose119863

119888

is greater than (1 minus 119899) is consideredas failed or collapsed since its residual axial load capacity isnot sufficient for the service axial load

42 Steps for Damage Assessment of CFST Columns

Step 1 (derivation of 119875max) During this step the linearlyincreasing axial load is applied on the column head until thecolumn collapses then 119875max is determined as the maximumaxial load that the column can withstand

Step 2 (derivation of 119875residual) Three substeps as follows arerequired to obtain 119875residual (1) before blast loading a linearlyincreasing axial load up to the service axial load is imposedon the column (2) blast loads are applied over the front faceof the column with the service axial load being constant andcalculation is stopped when the damaged column approachesstatic equilibrium (3) a linearly increasing axial load isimposed on the top of the damaged column until it collapses

then 119875residual is determined as the peak of the axial load thatthe damaged column can bear

Step 3 (determination of 119863119888

) Substitute the values of 119875maxand 119875residual into (7) to obtain119863119888

43 Parameters Studied In this section effects of severalkey parameters on the damage degree of CFST columnsare analyzed These parameters include the scaled standoffdistance height of burst explosive mass column depthcolumn width column steel ratio and axial load ratio aslisted in Table 4 in which a contrast case is generated bychanging one of the parameters considered in the benchmarkcase while keeping other parameters unchanged Note thatin each case varied scaled standoff distances are consideredso that the effects aforementioned parameters on the damagedegree of columns within different blast loading regimes canbe assessed

431 Effect of Scaled Standoff Distance 119885 The numericalsimulation results show that 119863

119888

of CFST columns decreaseswith the increasing scaled standoff distance regardless ofother parameters This is because column damage is affectedby the peak overpressure and impulse of the blast wave[21] and both of them drop with the rising scaled standoffdistance which results in a small degree of column damage

432 Effect of Height of Burst119867119861

It is difficult to characterizethe effect of 119867

119861

on the damage degree of the column On

Shock and Vibration 9

Table 4 Parameters used in the numerical parametric study

Parameters 119885 (mkg13) 119867119861

(m) 119872 (kg) 119889 (m) 119908 (m) Steel ratio 120572lowast Axial load ratio 119899Benchmark case 018ndash050 0 50 06 06 013 035Contrast cases 015ndash090 185 250 500 09 12 09 12 016 019 050 065lowast

120572 = 119860119904

119860119888

119860119904

and 119860119888

are the cross-sectional areas of steel tube and infill concrete respectively

07

06

05

04

03

02

01

00

HB = 0mHB = 185m

015 020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

Figure 10 Effects of height of burst on the damage degree

one hand when 119867119861

nears zero the initial blast wave isimmediately reflected and reinforced by the ground On theother the mid-height of the column is expected to surfer themost severe damage due to lack of transverse support Conse-quently as shown in Figure 10 surface burst results in severerdamage to the column than that caused by explosion atcolumnmid-height (119867

119861

= 185m) especially when the stand-off distance is small The effects of119867

119861

on the damage degreeof the column are insignificant at large scaled distancesbecause both the overpressure and impulse on the columnare relatively small in these cases

433 Effect of Explosive Mass119872 Figure 11 shows the effectsof explosive mass on the damage degree of the columnInspections of the figure show that 119863

119888

rises with 119872 for thesame scaled standoff distance indicating that CFST columnis impulse-sensitive since explosive with larger mass hasrelatively more impulse for the column

434 Effects of Column Width 119908 and Depth 119889 Effects ofcolumn depth and width on 119863

119888

are shown in Figure 12Comparedwith the reference column (119908 = 06m 119889 = 06m)columns with larger width and depth tend to have lowerdamage degrees because expanding columnwidth and depthproduces a larger cross section for attenuation of the stresswaves density and contributes to enhancement of the shearresistance as well as flexural strength of the columnHoweverit is found that columns with the same cross section area butdifferent width and depth have varied damage degrees and

07

06

05

04

03

02

01

0002 03 04 05 06 07 08 09 10

Scaled standoff distance Z (mkg13)

M = 50kgM = 250kgM = 500kg

[HB = 0m] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 11 Effects of explosive mass on the damage degree

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

w = 06m d = 06mw = 09m d = 06mw = 12m d = 06m

w = 06m d = 09mw = 06m d = 12m

[HB = 0m] [M = 50kg] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 12 Effects of width and depth on the damage degree

that compared with increasing the column width incrementof the column depth is more effective in reducing the columndamage degree This is because enlarging the column widthsimultaneously results in a rise of blast loads acting on thecolumnwhich balances out the enhancement of columnblastresistance to some extent

10 Shock and Vibration

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

120572 = 013

120572 = 016

120572 = 019

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [n = 035 ]

Dam

age d

egre

eDc

Figure 13 Effects of steel ratio on the damage degree

07

06

05

04

03

02

01

00020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

n = 035

n = 050

n = 065

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [120572 = 013]

Dam

age d

egre

eDc

Figure 14 Effects of axial load ratio on the damage degree

435 Effect of Column Steel Ratio 120572 As shown in Figure 13119863119888

drops with the rising steel ratio This is expected becauseincreasing 120572means a larger steel area and better confinementof infill concrete which will enhance the shear and bendingstrength of the column as well as its resistance to localizeddamage

436 Effect of Column Axial Load Ratio 119899 Effects of axialload ratio on 119863

119888

are shown in Figure 14 Inspection of thefigure reveals that axial load ratio has dual influences on col-umn damage When the scaled standoff is small the columnwith a larger axial load ratio has lower damage degree Thisis because the column under small scaled standoff is likelyto suffer localized damage and shear damage and a higher

axial load will restrain the cracking and crushing of concretewhich enhances the resistance of the column to localizeddamage and shear damage In contrast at a large scaledstandoff distance the column with larger axial load ratio hashigher damage degree The reason is that with the increaseof the scaled standoff distance the column tends to sufferflexural damage which is related to its moment capacity andductility The larger the moment capacity and ductility arethe lower the damage degree is For the CFST column studiedin this section the axial load ratio at the maximum momentcapacity is 022 which is derived by the methods from Choiet al [1] According to the axial load-bending moment (P-M)interactions the moment capacity of the CFST column willdecrease when 119899 rises from 035 to 060 Moreover a risingaxial load will reduce the ductility of the CFST column

44 Empirical Equations for Determining the Damage Degreeof CFST Columns The parametric study revealed the signif-icance of parameters affecting the damage degree of CFSTcolumns Through the multivariable regression analysis anempirical equation is proposed in terms of various parame-ters to predict the damage degree and is expressed as follows

119863119888

= [minus1505 ln(11987250

) + 1650 (

119908

06

) minus 3242 (

119889

06

)

minus 131625120572 + 15349119899 + 25011]

sdot 119890[minus648ln(11987250)+533(11990806)minus1091(11988906)minus373minus1230120572+1292119899+2681]119885

(8)

The comparisons of the proposed equation with the ana-lytical results are shown in Figures 15(a)ndash15(f) The scattersdenote the analytical results and the solid lines represent theproposed equation Observation of these figures shows thatthe proposed curves are close to the analytical results formostcases The effects of height of burst on the damage degree ofCFST columns are not reflected by (8) due to the lack of blastdata in the lower height of the column which are limited inthe ConWep model and will be supplemented in the furtherstudies

5 Conclusions

This paper presents a 3D numerical model to investigate thedamage modes and damage assessment of CFST columnsBased on the numerical analysis results the following con-clusions can be drawn

CFST columns under blast loading may undergo theglobal flexural damage and shear damage as well as localizeddamage Flexural damage and shear damage of the columnare mainly attributed to the deformation and internal force ofthe whole member whilst the localized damage is dominatedby the failure of infill concrete and steel tube in the vicinity ofthe explosion

The damage criterion based on the residual axial loadcapacity is adopted for assessing the degree of CFST columnsdamage to blast loadsThrough parametric studies it is foundthat the damage degree of CFST columns decays nearlyexponentially with the increasing scaled standoff distance

Shock and Vibration 11

07

06

05

04

03

02

01

00

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

Dam

age d

egre

eDc

(a)

07

06

05

04

03

02

01

00095090085050 055 060 065 070 075 080

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 500kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

(b)

07

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 12m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

(c)

020

015

010

005

000

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 12m] [120572 = 013] [n = 035]D

amag

e deg

reeD

c

(d)

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 019] [n = 035]

Dam

age d

egre

eDc

(e)

020

025

030

035

015

010

005

000055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 065]

Dam

age d

egre

eDc

(f)

Figure 15 Comparison of analytical results with the proposed curves

12 Shock and Vibration

For the same scaled standoff distance surface burst results inseverer damage to the column than that caused by explosionat columnmid-height and the damage degree increases withthe rising explosive mass and decreases with column depthand width and steel ratio Increasing the axial load enhancesthe resistance of the column against localized damage andshear damage while the effects of axial load on flexuraldamage depend on the axial load-bending moment (P-M)interactions of the column

An equation is derived by fitting the results of parametricstudies to estimate the damage degree of CFST columnsTypical examples confirm that the proposed equation wellrepresents the variation of the column damage degree How-ever future experiments can be conducted for investigatingthe effects of other parameters on the damage degree of CFSTcolumns

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research described in this paper was financially sup-ported by Achievement Transfer Program of Institutionsof Higher Education in Chongqing under Grant noKJZH14220

References

[1] Y-H Choi D A Foutch and J M LaFave ldquoNew approachto AISC P-M interaction curve for square concrete filled tube(CFT) beamndashcolumnsrdquo Engineering Structures vol 28 no 11pp 1586ndash1598 2006

[2] Y-H Choi K S Kim and S-M Choi ldquoSimplified P-M interac-tion curve for square steel tube filled with high-strength con-creterdquoThin-Walled Structures vol 46 no 5 pp 506ndash515 2008

[3] T KrauthammerModern Protective Structures TaylorampFrancisGroup New York NY USA 2008

[4] S C Fujikura M Bruneau and D Lopez-Garcia ldquoExperimen-tal investigation of blast performance of seismically resistantconcrete-filled steel tube bridge piersrdquo Tech Rep MCEER-07-0005 University at Buffalo Buffalo NY USA 2007

[5] S Fujikura M Bruneau and D Lopez-Garcia ldquoExperimentalinvestigation of multihazard resistant bridge piers having con-crete-filled steel tube under blast loadingrdquo Journal of BridgeEngineering vol 13 no 6 pp 586ndash594 2008

[6] G Li H Qu T Yang Y Lu and S Chen ldquoExperimental studyof concrete-filled steel tubular columns under blast loadingrdquoJianzhu Jiegou Xuebao vol 34 no 12 pp 69ndash76 2013 (Chinese)

[7] A M Remennikov and B Uy ldquoExplosive testing andmodellingof square tubular steel columns for near-field detonationsrdquo Jour-nal of Constructional Steel Research vol 101 pp 290ndash303 2014

[8] T Ngo D Mohotti A Remennikov and B Uy ldquoNumericalsimulations of response of tubular steel beams to close-rangeexplosionsrdquo Journal of Constructional Steel Research vol 105 pp151ndash163 2015

[9] F R Zhang C Q Wu H W Wang and Y Zhou ldquoNumericalsimulation of concrete filled steel tube columns against BLASTloadsrdquoThin-Walled Structures vol 92 pp 82ndash92 2015

[10] F Zhang C Wu X Zhao Z Li A Heidarpour and H WangldquoNumerical modeling of concrete-filled double-skin steelsquare tubular columns under blast loadingrdquo Journal of Per-formance of Constructed Facilities vol 29 no 5 Article IDB4015002 2015

[11] Livermore Software Technology Corporation LS-DYNA Theo-retical Manual Livermore Software Technology CorporationLivermore Calif USA 1998

[12] G R Cowper and P S Symonds ldquoStrain-hardening and strain-rate effects in the impact loading of cantilever beamsrdquo TechRep AD144762 Office of Naval Research Arlington Va USA1958

[13] T J Holmquist G R Johnson and W H Cook ldquoA computa-tional constitutive model for concrete subjected to large strainshigh strain rates and high pressuresrdquo in Proceedings of the 14thInternational Symposium on Ballistics Quebec City CanadaSeptember 1993

[14] Q Fang and J Zhang ldquoThree-dimensional modelling of steelfiber reinforced concrete material under intense dynamic load-ingrdquo Construction and Building Materials vol 44 pp 118ndash1322013

[15] Y Li F Lin X L Gu and X Q Lu ldquoNumerical researchof a super-large cooling tower subjected to accidental loadsrdquoNuclear Engineering and Design vol 269 pp 184ndash192 2014

[16] J Li and H Hao ldquoNumerical study of concrete spall damage toblast loadsrdquo International Journal of Impact Engineering vol 68pp 41ndash55 2014

[17] G Randers-Pehrson and K A Bannister ldquoAirblast loadingmodel for DYNA2D and DYNA3Drdquo Tech Rep ARL-TR-1310Army Research Laboratory Adelphi Md USA 1997

[18] Livermore Software Technology Corporation LS-DYNA Key-word Userrsquos Manual (Version 971 R610) Livermore SoftwareTechnology Corporation Livermore Calif USA 2012

[19] CECS ldquoTechnical specification for structures with concrete-filled rectangular steel tube membersrdquo CECS 1592004 ChinaAssociation for Engineering Construction StandardizationBeijing China 2004 (Chinese)

[20] Y Shi H Hao and Z-X Li ldquoNumerical derivation of pressure-impulse diagrams for prediction of RC column damage to blastloadsrdquo International Journal of Impact Engineering vol 35 no11 pp 1213ndash1227 2008

[21] P D Smith and J G Hetherington Blast and Ballistic Loadingof Structures Butterowrth-Heinemenn Oxford UK 1994

[22] K-C Wu B Li and K-C Tsai ldquoThe effects of explosive massratio on residual compressive capacity of contact blast damagedcomposite columnsrdquo Journal of Constructional Steel Researchvol 67 no 4 pp 602ndash612 2011

[23] J E Crawford K B Morrill and J M Magallanes ldquoProtectivedesign for columns against close-in blast effectsrdquo in Proceedingsof the Structures Congress Boston Mass USA April 2014

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Shock and Vibration 3

Stre

ss

0

Yield stress

E

Et

120573 = 0 kinematic hardening

120573 = 1 isotropic hardening

l0 and l are undeformed anddeformed lengths of uniaxialtension specimen

ln(ll0)

Figure 2 Plastic kinematic model for steel modeling

steel tube under blast loading the plastic kinematic modelwhich takes into account the strain hardening and strain rateeffects is adopted for steel simulation The dynamic yieldstress of it is expressed as follows [11]

120590119910

= (1205900

+ 120573119864119875

120576119875

eff) [1 + (120576

119862

)

1119875

] (1)

where 120590119910

is the dynamic yield stress 1205900

is the initial yieldstress 120573 is the hardening parameter (for 120573 equal to 0 and1 resp kinematic and isotropic hardenings are obtained asshown in Figure 2)119864

119875

is the plastic hardeningmodulus119864119875

=

119864119864119905

(119864 minus 119864119905

) 119864 is Youngrsquos modulus and 119864119905

is the tangentmodulus 120576119875eff is the effective plastic strain 120576 is the strain rateand119862 and119875 areCowper-Symonds strain rate parameters [12]Material parameters of the steel tube in the study are listed inTable 1

The infill concrete subjected to blast loading may expe-rience large strains high strain rates and high pressuresBesides the collapse of air void as well as the dilationcaused by shearing cracks plays an important role in thedamage evolution of concrete Thus the Johnson-Holmquist-Cook (JHC) concrete model is used to simulate the concreteand the equivalent stress of it is expressed as a function ofpressure strain rate and damage as follows [13]

120590lowast

= [119860 (1 minus 119863) + 119861119875lowast119873

] (1 + 119862 ln 120576lowast) le 119878MAX (2)

where 120590lowast = 1205901198911015840119888

denotes the normalized equivalent stress(where 120590 and 1198911015840

119888

are the actual equivalent stress and quasi-static uniaxial compressive strength resp) 119860 is the normal-ized cohesive strength 119863 is the accumulated damage 119861 isthe normalized pressure hardening coefficient 119875lowast = 1198751198911015840

119888

is the dimensionless form of pressure 119875 119873 is the pressurehardening exponent 119862 is strain rate coefficient 120576lowast = 120576 120576

0

isthe dimensionless form of strain rate 120576 (where 120576

0

= 10 sminus1 isthe reference strain rate) and 119878MAX is the normalized maxi-mum strength as shown in Figure 3

Nor

mal

ized

equi

vale

nt st

ress120590lowast

Normalized pressure Plowast

120576lowast = 10

120576lowast gt 10

Tlowast(1 minus D)

D = 0 (undamaged)

D = 1 (fractured)

SMAX

Figure 3 JHC model for concrete modeling

The accumulated damage is expressed as

119863 = sum

Δ120576119875

+ Δ120583119875

1198631

(119875lowast

+ 119879lowast

)119863

2

(3)

where Δ120576119875

and Δ120583119875

are the equivalent plastic strain andplastic volumetric strain respectively119863

1

and1198632

are damageconstants and 119879lowast = 1198791198911015840

119888

is the dimensionless tensile hydro-static pressure

The relation between pressure and volumetric strain isdefined as

119875 =

119870119890

120583 0 le 119875 lt 119875119862

119875119862

+ 119870119862

(120583 minus 120583119862

) 119875119862

le 119875 lt 119875119871

1198701

120583 + 1198702

1205832

+ 1198703

1205833

119875 ge 119875119871

(4)

where 119870119890

is the elastic bulk modulus 119870119890

= 119875119862

120583119862

and 119875119862

and 120583119862

are the pressure and volumetric strain when crushingoccurs in concrete120583 is the volumetric strain120583 = (120583minus120583

119871

)(1+

120583119871

) is the corrected volumetric strain and 119875119871

and 120583119871

are thelocking pressure and volumetric strain at the beginning of thefully compacted stage (119875 ge 119875

119871

) 1198701

1198702

and 1198703

are materialconstants of concrete

The reliability of this concrete model in predicting theresponses of concrete structures to blast loads has beendemonstrated by many researchers [14 15] Material parame-ters of the infill concrete in the simulation are listed inTable 2

212 Finite Element Model and Erosion Algorithm TheBelytschko-Tsay shell element is used in the study to modelthe steel tube and the infill concrete is modeled with single-point integration solid elements A mesh size of 25mm isselected for the steel tube and infill concrete through a numer-ical convergence study It is found that further refinementof element size has little effect on the numerical results butincreases the calculation time enormously A perfect bondbetween steel tube and infill concrete is assumed in the

4 Shock and Vibration

Table 1 Material parameters of the steel tube

Parameter Mass density1205881

(kgm3) Poissonrsquos ratio 120592 1205900

(MPa) 119864 (GPa) 119864119905

(MPa) 120573 119862 P Failure strain(FS)

Value 7850 03 358 203 414 0 404 5 02

Table 2 Material parameters of the infill concrete

Parameter Mass density1205882

(kgm3) 119860 119861 119862 119873 1198911015840

119888

(MPa) 119878MAX

Value 2440 079 160 0007 061 379 70

Parameter Shear modulus119866 (GPa)

Maximumtensile pressure119879 (MPa)

Thresholdstrain rateEPS0 (sminus1)

Plastic strainbefore fracture

EFMIN

Crushingpressure119875119862

(MPa)

Crushingvolumetricstrain 119880

119862

Lockingpressure119875119871

(MPa)Value 1486 40 10 001 16 0001 800

ParameterLocking

volumetricstrain 119880

119871

Damageconstant1198631

Damageconstant1198632

Pressureconstant1198701

(GPa)

Pressureconstant1198702

(GPa)

Pressureconstant1198703

(GPa)Value 01 004 10 85 minus171 208

numerical study since no researches have reported a notice-able debond between the twomaterials in blast tests In orderto simulate the physical fracture shear failure and crushingof the concrete under blast loading the erosion algorithm isused to account for concrete failure Considering the strainrate effect on the concrete strength the erosion criterionbased on the principle strain is often used [16] A numberof simulations are carried out with different erosion criteriaand it is found that using principle tensile strain of 001 as theerosion criterion which is also used by Ngo et al [8] leads toreliable predictions of the responses of CFST columns

213 Sequence of Loads Application and Blast LoadModellingIn order to simulate the real stress state of CFST columns thelinearly increasing axial quasi-static loads up to the serviceaxial load level are applied to the top of the column prior toblast loading through the implicit solver To avoid too muchoscillation of the column the time duration for increasingthe loads from zero to full service level is 150ms Then thecomputational algorithm switches from implicit to explicitand the blast loads are applied over the front surface of thecolumn with the axial loads unchanged

Blast loads are generated using the ConWep air blastmodel [17] that is Load Blast Enhanced in LS-DYNA[18] Compared to other techniques that is the ArbitraryLagrangian Eulerian (ALE) methodology this model is morecomputationally efficient to simulate blast loads with a highlevel of accuracy While similar to the model Load Blast italso includes enhancements for treating reflected waves Theloading face of the column is predefined before the generationof blast loads and the time history of blast loads actingon each segment is calculated through ConWep formula asfollows

119875 (119905) = 119875119903

(119905) cos2120579 + 119875119894

(119905) (1 + cos2120579 minus 2 cos 120579) (5)

where 119875(119905) is the reflected overpressure on the definedload segment at moment 119905 119875

119903

(119905) and 119875119894

(119905) are the normal

0 25 50 75 100 125 150 175 200

Time (ms)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

Late

ral d

ispla

cem

ent (

mm

)

Test by Zhang et al [9]Residual displacement in the testNumerical simulation

Figure 4 Comparison of the displacement data from test and thatof numerical simulation

reflected overpressure and incident overpressure at moment119905 respectively and 120579 is the angle of incidence of the blast wave

22 Model Calibration and Discussion Numerical simula-tions of the blast test were carried out and the dynamicresponse and damage mode of column S4 were obtainedSince the recording of LVDT1 at the center of column S4 wasmissing in the test the value of LVDT2 (see Figure 1(b)) at380mm from the center of the column was used to calibratethe numerical model Comparison of the calculated displace-ment time history with test results is shown in Figure 4It is found that the peak displacement of numerical results(509mm) is smaller than that in the test (60mm) while thenumerical residual displacement (354mm) is slightly largerthan the test value (34mm) Several factors as follows may

Shock and Vibration 5

(a) Test result (Zhang et al [9])

Fringe levels

6346eminus02

5289eminus02

4231e

minus02

3173eminus02

2115eminus02

1058e

minus02

0000e

+00

(b) Numerical result

Figure 5 Comparison of the column damage mode in the test andthat from numerical simulation

account for such discrepancies (1) the difference between theactual support condition which is not rigid enough and thoseadopted in the simulation (2) ignorance of the potential lossof axial loads and reduction of flexural resistance consideringthe detachment of the column ends from the loading devicein the test and (3) the limitations of material models indepicting the real-time nonlinear behaviors of steel andconcrete during test Although discrepancies exist betweenthe simulation and test values the largest error with respectto the maximum displacements is within 152 Figure 5shows the comparison of the damage mode of the columnin the test and that from the numerical simulation presentedin effective plastic strain contour and good agreement isobserved in between These results demonstrate that thecalibrated numericalmodel leads to reasonable predictions ofthe dynamic responses and damage modes of CFST columnsto blast loads and can be used for the subsequent study

3 Damage Modes of CFST Column underBlast Loading

31 Column Configuration The above calibrated numericalmodel is utilized herein to simulate dynamic behavior andpossible damagemodes of CFST column under blast loadingThe column is designed based on the specifications providedby Chinese Standard CECS 159 2004 [19] As shown inFigure 6 the dimensions of the column are ℎ (height) times119908 (width)times119889 (depth) = 3700mm times 600mm times 600mm withthe tube thickness of 18mm Parameters of the steel tube andthe infill concrete used in the simulation are the same asthose in Section 2 In order to simulate the real life boundaryconditions for CFST columns a column head and a footingare considered in the numericalmodelThe outer vertical faceof the footing and head are constrained against horizontalmotions and the bottom face of the footing is constrainedagainst vertical motions [20] Horizontal distance from thecharge center to the column front surface that is the standoffdistance is denoted as 119883 And the vertical distance fromthe charge center to the ground that is the height of burstis denoted as 119867

119861

The initial dead weight imposed on the

Table 3 Possible damage modes of the CFST column

119872 (kg) 119867119861

(m) 119885 (mkg13) Damage mode

50 0le021 Localized

022ndash024 Shearge026 Flexural

250 0le025 Localized

030ndash048 Shearge052 Flexural

50 185 le016 Localizedge018 Flexural

column is 35 percent of axial load capacity of the undamagedcolumn which represents the axial load level of a typicalground floor column in a high-rise building

As the blast load parameters are related to both explosivemass and standoff distance the scaled standoff distance isintroduced to consider their combined effects and is definedas [21]

119885 =

119883

11987213

(6)

where 119885 is the scaled standoff distance and 119872 is theequivalent mass of TNT

32 Possible Damage Modes Three damage modes of theCFST column under blast loading have been observedthrough a number of simulations they are flexural damageshear damage and localized damage Table 3 presents damagemodes of the column according to different blast conditionsIt is found that in general explosivewith a small scaled stand-off distance favors a localized damage whilst shear damageand localized damage occur when the explosive is relativelyfar from the columnThis is because the blast loads are highlyintensive when the scaled standoff distance is small and forvery local blast loads acting on the column failure of the infillconcrete and steel tube starts before any considerable overallresponse can occur and the column surfers a localized dam-age However with the increase of scaled standoff distanceblast loads tend to be well-distributed over the surface of thecolumn which is inclined to response globally and undergoshear damage and flexural damage Also the damagemode isaffected by the explosive mass height of burst Typical resultsof these damagemodes are shown with effective plastic straincontours in Figures 7ndash9

Figure 7 shows the flexural damage mode of the CFSTcolumn induced by the detonation of 50 kg of TNT at thescaled standoff distance of 018mkg13 with the height ofburst of 185m In this configuration when the blast loadsacted on the column the mid-part of it responded imme-diately with the increment of lateral deformation Then theareas near the supports of the column began to deform androtate As the global flexural deformation of the columnevolved plastic hinges developed in the mid-part and nearthe supports of the columnwhere the bendingmoments werelarge

6 Shock and Vibration

First-floor column

Second-floor column

Explosive

Second-floor beam

h

HB

X

(a) Explosion scenario

1 1

Section 1-1

Steel tube

Infill concrete

Axial load

Head

Footing

First-floor column

h d t

w

(b) Column details

Figure 6 Sketch of the numerical analysis model

Figure 8 shows the shear damage mode of the columnresulted from 250 kg of TNT detonating on the ground atthe scaled standoff distance of 033mkg13 Due to the largeshear force and the development of shear deformation nearthe supports the infill concrete was sheared off accompaniedwith the rupture of the steel tube around the cross section ofthe column Finally the column failed in brittle shear beforeany ductile flexural hinge developed

As discussed above flexural damage and shear damageof the column are due to the deformation and internal forceof the whole member induced by the blast loads On thecontrary localized damage of the CFST column is dominatedby the deformation and failure of the concrete infill and steeltube in the vicinity of the explosion whilst other parts of thecolumn remain almost elastic and the global deformation ofthe column is small

Figure 9 shows the localized damage mode of the CFSTcolumn caused by the detonation of 50 kg of TNT on theground with the scaled standoff distance of 018mkg13When the impulsive shock front of high intensity metthe column surface the stress waves were generated andpropagated from the tube front surface towards the concreteinfill and the lateral and back surfaces of the tube Then theconcrete close to the explosion was cracked and crushed andthe front side of the tube which lost the internal support ofthe concrete fill was squashed with the bulging of its lateraland back sides As the localized deformation of the columnevolved rupture and local buckling failure of the steel tubetook place yet the global lateral deformation of the columnhad almost not developed at this moment

It should bementioned that these damagemodes are onlytypical ones Sometimes there exists a combination of thesedamage modes

4 Damage Assessment of CFST Columnsunder Blast Loading

41 Damage Criterion As discussed previously the CFSTcolumn subjected to blast loads may undergo flexural dam-age shear damage and localized damage thus the damagecriterion for the column should be chosen carefully andthe appropriate one is expected to be applicable to all thepossible damage modes of the column In this paper thedamage criterion based on the residual axial load capacityis adopted for CFST columns due to the following reasons(1) the structure column is primarily designed to carry theaxial load and the axial load capacity of it reflects bothits global properties and material characteristics (2) thecommonly used deformation-based damage criterions thatis the support rotation lateral deflection and ductility maynot be appropriate for the evaluation of localized damage ofthe column and (3) the residual axial load capacity of thecolumns is an explicit metric of the damage imparted and italso provides information in assessing the collapse possibilityof a blast damaged column

The damage index adopted herein is based on the indexfrom Shi et al [20] and is expressed as

119863119888

= 1 minus

119875residual119875max

(7)

where 119863119888

is the damage degree of CFST columns 119875residual isthe residual axial load capacity of the column after blast loadsand 119875max is the maximum axial load capacity of the columnprior to blast loading Values of 119863

119888

vary between 0 (ieno loss of capacity) and 10 (ie complete loss of capacity)Note that in the paper by Shi et al [20] the maximumaxial load capacity of an undamaged column is calculated

Shock and Vibration 7

Fringe levels

3793eminus02

3161e

minus02

2529eminus02

1897eminus02

1264eminus02

6322eminus03

0000e

+00

(a) CFST column

Fringe levels

3793eminus02

3161e

minus02

2529eminus02

1897eminus02

1264eminus02

6322eminus03

0000e

+00

(b) Infill concrete

Figure 7 Flexural damage mode of CFST column under blast loading

Fringe levels

2000e

minus01

1667eminus01

1333eminus01

1000e

minus01

6667eminus02

3333eminus02

0000e

+00

(a) CFST column

Fringe levels

2392e

minus02

1993eminus02

1594eminus02

1196eminus02

7972e

minus03

3986eminus03

0000e

+00

(b) Infill concrete

Figure 8 Shear damage mode of CFST column under blast loading

8 Shock and Vibration

Fringe levels

2000e

minus01

1667eminus01

1333eminus01

1000e

minus01

6667eminus02

3333eminus02

0000e

+00

(a) CFST column

Fringe levels

2597eminus02

2165eminus02

1732e

minus02

1299eminus02

8658e

minus03

4329eminus03

0000e

+00

(b) Infill concrete

Figure 9 Localized damage mode of CFST column under blast loading

with the provided equation from the standard design codewhich however may lead to the values of119863

119888

below 0 in somecases Therefore both 119875residual and 119875max are determined fromnumerical simulation in this study Here 119875residual119875max is alsotermed as the residual capacity index (RCI) used byWu et al[22] andCrawford et al [23] to assess the damage level of steelreinforced concrete (SRC) columns and reinforced concrete(RC) columns subjected to blast loads

It is noted that if the ratio of the service axial load tomaximum axial load capacity of the column is denoted as 119899then a column whose119863

119888

is greater than (1 minus 119899) is consideredas failed or collapsed since its residual axial load capacity isnot sufficient for the service axial load

42 Steps for Damage Assessment of CFST Columns

Step 1 (derivation of 119875max) During this step the linearlyincreasing axial load is applied on the column head until thecolumn collapses then 119875max is determined as the maximumaxial load that the column can withstand

Step 2 (derivation of 119875residual) Three substeps as follows arerequired to obtain 119875residual (1) before blast loading a linearlyincreasing axial load up to the service axial load is imposedon the column (2) blast loads are applied over the front faceof the column with the service axial load being constant andcalculation is stopped when the damaged column approachesstatic equilibrium (3) a linearly increasing axial load isimposed on the top of the damaged column until it collapses

then 119875residual is determined as the peak of the axial load thatthe damaged column can bear

Step 3 (determination of 119863119888

) Substitute the values of 119875maxand 119875residual into (7) to obtain119863119888

43 Parameters Studied In this section effects of severalkey parameters on the damage degree of CFST columnsare analyzed These parameters include the scaled standoffdistance height of burst explosive mass column depthcolumn width column steel ratio and axial load ratio aslisted in Table 4 in which a contrast case is generated bychanging one of the parameters considered in the benchmarkcase while keeping other parameters unchanged Note thatin each case varied scaled standoff distances are consideredso that the effects aforementioned parameters on the damagedegree of columns within different blast loading regimes canbe assessed

431 Effect of Scaled Standoff Distance 119885 The numericalsimulation results show that 119863

119888

of CFST columns decreaseswith the increasing scaled standoff distance regardless ofother parameters This is because column damage is affectedby the peak overpressure and impulse of the blast wave[21] and both of them drop with the rising scaled standoffdistance which results in a small degree of column damage

432 Effect of Height of Burst119867119861

It is difficult to characterizethe effect of 119867

119861

on the damage degree of the column On

Shock and Vibration 9

Table 4 Parameters used in the numerical parametric study

Parameters 119885 (mkg13) 119867119861

(m) 119872 (kg) 119889 (m) 119908 (m) Steel ratio 120572lowast Axial load ratio 119899Benchmark case 018ndash050 0 50 06 06 013 035Contrast cases 015ndash090 185 250 500 09 12 09 12 016 019 050 065lowast

120572 = 119860119904

119860119888

119860119904

and 119860119888

are the cross-sectional areas of steel tube and infill concrete respectively

07

06

05

04

03

02

01

00

HB = 0mHB = 185m

015 020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

Figure 10 Effects of height of burst on the damage degree

one hand when 119867119861

nears zero the initial blast wave isimmediately reflected and reinforced by the ground On theother the mid-height of the column is expected to surfer themost severe damage due to lack of transverse support Conse-quently as shown in Figure 10 surface burst results in severerdamage to the column than that caused by explosion atcolumnmid-height (119867

119861

= 185m) especially when the stand-off distance is small The effects of119867

119861

on the damage degreeof the column are insignificant at large scaled distancesbecause both the overpressure and impulse on the columnare relatively small in these cases

433 Effect of Explosive Mass119872 Figure 11 shows the effectsof explosive mass on the damage degree of the columnInspections of the figure show that 119863

119888

rises with 119872 for thesame scaled standoff distance indicating that CFST columnis impulse-sensitive since explosive with larger mass hasrelatively more impulse for the column

434 Effects of Column Width 119908 and Depth 119889 Effects ofcolumn depth and width on 119863

119888

are shown in Figure 12Comparedwith the reference column (119908 = 06m 119889 = 06m)columns with larger width and depth tend to have lowerdamage degrees because expanding columnwidth and depthproduces a larger cross section for attenuation of the stresswaves density and contributes to enhancement of the shearresistance as well as flexural strength of the columnHoweverit is found that columns with the same cross section area butdifferent width and depth have varied damage degrees and

07

06

05

04

03

02

01

0002 03 04 05 06 07 08 09 10

Scaled standoff distance Z (mkg13)

M = 50kgM = 250kgM = 500kg

[HB = 0m] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 11 Effects of explosive mass on the damage degree

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

w = 06m d = 06mw = 09m d = 06mw = 12m d = 06m

w = 06m d = 09mw = 06m d = 12m

[HB = 0m] [M = 50kg] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 12 Effects of width and depth on the damage degree

that compared with increasing the column width incrementof the column depth is more effective in reducing the columndamage degree This is because enlarging the column widthsimultaneously results in a rise of blast loads acting on thecolumnwhich balances out the enhancement of columnblastresistance to some extent

10 Shock and Vibration

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

120572 = 013

120572 = 016

120572 = 019

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [n = 035 ]

Dam

age d

egre

eDc

Figure 13 Effects of steel ratio on the damage degree

07

06

05

04

03

02

01

00020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

n = 035

n = 050

n = 065

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [120572 = 013]

Dam

age d

egre

eDc

Figure 14 Effects of axial load ratio on the damage degree

435 Effect of Column Steel Ratio 120572 As shown in Figure 13119863119888

drops with the rising steel ratio This is expected becauseincreasing 120572means a larger steel area and better confinementof infill concrete which will enhance the shear and bendingstrength of the column as well as its resistance to localizeddamage

436 Effect of Column Axial Load Ratio 119899 Effects of axialload ratio on 119863

119888

are shown in Figure 14 Inspection of thefigure reveals that axial load ratio has dual influences on col-umn damage When the scaled standoff is small the columnwith a larger axial load ratio has lower damage degree Thisis because the column under small scaled standoff is likelyto suffer localized damage and shear damage and a higher

axial load will restrain the cracking and crushing of concretewhich enhances the resistance of the column to localizeddamage and shear damage In contrast at a large scaledstandoff distance the column with larger axial load ratio hashigher damage degree The reason is that with the increaseof the scaled standoff distance the column tends to sufferflexural damage which is related to its moment capacity andductility The larger the moment capacity and ductility arethe lower the damage degree is For the CFST column studiedin this section the axial load ratio at the maximum momentcapacity is 022 which is derived by the methods from Choiet al [1] According to the axial load-bending moment (P-M)interactions the moment capacity of the CFST column willdecrease when 119899 rises from 035 to 060 Moreover a risingaxial load will reduce the ductility of the CFST column

44 Empirical Equations for Determining the Damage Degreeof CFST Columns The parametric study revealed the signif-icance of parameters affecting the damage degree of CFSTcolumns Through the multivariable regression analysis anempirical equation is proposed in terms of various parame-ters to predict the damage degree and is expressed as follows

119863119888

= [minus1505 ln(11987250

) + 1650 (

119908

06

) minus 3242 (

119889

06

)

minus 131625120572 + 15349119899 + 25011]

sdot 119890[minus648ln(11987250)+533(11990806)minus1091(11988906)minus373minus1230120572+1292119899+2681]119885

(8)

The comparisons of the proposed equation with the ana-lytical results are shown in Figures 15(a)ndash15(f) The scattersdenote the analytical results and the solid lines represent theproposed equation Observation of these figures shows thatthe proposed curves are close to the analytical results formostcases The effects of height of burst on the damage degree ofCFST columns are not reflected by (8) due to the lack of blastdata in the lower height of the column which are limited inthe ConWep model and will be supplemented in the furtherstudies

5 Conclusions

This paper presents a 3D numerical model to investigate thedamage modes and damage assessment of CFST columnsBased on the numerical analysis results the following con-clusions can be drawn

CFST columns under blast loading may undergo theglobal flexural damage and shear damage as well as localizeddamage Flexural damage and shear damage of the columnare mainly attributed to the deformation and internal force ofthe whole member whilst the localized damage is dominatedby the failure of infill concrete and steel tube in the vicinity ofthe explosion

The damage criterion based on the residual axial loadcapacity is adopted for assessing the degree of CFST columnsdamage to blast loadsThrough parametric studies it is foundthat the damage degree of CFST columns decays nearlyexponentially with the increasing scaled standoff distance

Shock and Vibration 11

07

06

05

04

03

02

01

00

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

Dam

age d

egre

eDc

(a)

07

06

05

04

03

02

01

00095090085050 055 060 065 070 075 080

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 500kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

(b)

07

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 12m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

(c)

020

015

010

005

000

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 12m] [120572 = 013] [n = 035]D

amag

e deg

reeD

c

(d)

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 019] [n = 035]

Dam

age d

egre

eDc

(e)

020

025

030

035

015

010

005

000055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 065]

Dam

age d

egre

eDc

(f)

Figure 15 Comparison of analytical results with the proposed curves

12 Shock and Vibration

For the same scaled standoff distance surface burst results inseverer damage to the column than that caused by explosionat columnmid-height and the damage degree increases withthe rising explosive mass and decreases with column depthand width and steel ratio Increasing the axial load enhancesthe resistance of the column against localized damage andshear damage while the effects of axial load on flexuraldamage depend on the axial load-bending moment (P-M)interactions of the column

An equation is derived by fitting the results of parametricstudies to estimate the damage degree of CFST columnsTypical examples confirm that the proposed equation wellrepresents the variation of the column damage degree How-ever future experiments can be conducted for investigatingthe effects of other parameters on the damage degree of CFSTcolumns

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research described in this paper was financially sup-ported by Achievement Transfer Program of Institutionsof Higher Education in Chongqing under Grant noKJZH14220

References

[1] Y-H Choi D A Foutch and J M LaFave ldquoNew approachto AISC P-M interaction curve for square concrete filled tube(CFT) beamndashcolumnsrdquo Engineering Structures vol 28 no 11pp 1586ndash1598 2006

[2] Y-H Choi K S Kim and S-M Choi ldquoSimplified P-M interac-tion curve for square steel tube filled with high-strength con-creterdquoThin-Walled Structures vol 46 no 5 pp 506ndash515 2008

[3] T KrauthammerModern Protective Structures TaylorampFrancisGroup New York NY USA 2008

[4] S C Fujikura M Bruneau and D Lopez-Garcia ldquoExperimen-tal investigation of blast performance of seismically resistantconcrete-filled steel tube bridge piersrdquo Tech Rep MCEER-07-0005 University at Buffalo Buffalo NY USA 2007

[5] S Fujikura M Bruneau and D Lopez-Garcia ldquoExperimentalinvestigation of multihazard resistant bridge piers having con-crete-filled steel tube under blast loadingrdquo Journal of BridgeEngineering vol 13 no 6 pp 586ndash594 2008

[6] G Li H Qu T Yang Y Lu and S Chen ldquoExperimental studyof concrete-filled steel tubular columns under blast loadingrdquoJianzhu Jiegou Xuebao vol 34 no 12 pp 69ndash76 2013 (Chinese)

[7] A M Remennikov and B Uy ldquoExplosive testing andmodellingof square tubular steel columns for near-field detonationsrdquo Jour-nal of Constructional Steel Research vol 101 pp 290ndash303 2014

[8] T Ngo D Mohotti A Remennikov and B Uy ldquoNumericalsimulations of response of tubular steel beams to close-rangeexplosionsrdquo Journal of Constructional Steel Research vol 105 pp151ndash163 2015

[9] F R Zhang C Q Wu H W Wang and Y Zhou ldquoNumericalsimulation of concrete filled steel tube columns against BLASTloadsrdquoThin-Walled Structures vol 92 pp 82ndash92 2015

[10] F Zhang C Wu X Zhao Z Li A Heidarpour and H WangldquoNumerical modeling of concrete-filled double-skin steelsquare tubular columns under blast loadingrdquo Journal of Per-formance of Constructed Facilities vol 29 no 5 Article IDB4015002 2015

[11] Livermore Software Technology Corporation LS-DYNA Theo-retical Manual Livermore Software Technology CorporationLivermore Calif USA 1998

[12] G R Cowper and P S Symonds ldquoStrain-hardening and strain-rate effects in the impact loading of cantilever beamsrdquo TechRep AD144762 Office of Naval Research Arlington Va USA1958

[13] T J Holmquist G R Johnson and W H Cook ldquoA computa-tional constitutive model for concrete subjected to large strainshigh strain rates and high pressuresrdquo in Proceedings of the 14thInternational Symposium on Ballistics Quebec City CanadaSeptember 1993

[14] Q Fang and J Zhang ldquoThree-dimensional modelling of steelfiber reinforced concrete material under intense dynamic load-ingrdquo Construction and Building Materials vol 44 pp 118ndash1322013

[15] Y Li F Lin X L Gu and X Q Lu ldquoNumerical researchof a super-large cooling tower subjected to accidental loadsrdquoNuclear Engineering and Design vol 269 pp 184ndash192 2014

[16] J Li and H Hao ldquoNumerical study of concrete spall damage toblast loadsrdquo International Journal of Impact Engineering vol 68pp 41ndash55 2014

[17] G Randers-Pehrson and K A Bannister ldquoAirblast loadingmodel for DYNA2D and DYNA3Drdquo Tech Rep ARL-TR-1310Army Research Laboratory Adelphi Md USA 1997

[18] Livermore Software Technology Corporation LS-DYNA Key-word Userrsquos Manual (Version 971 R610) Livermore SoftwareTechnology Corporation Livermore Calif USA 2012

[19] CECS ldquoTechnical specification for structures with concrete-filled rectangular steel tube membersrdquo CECS 1592004 ChinaAssociation for Engineering Construction StandardizationBeijing China 2004 (Chinese)

[20] Y Shi H Hao and Z-X Li ldquoNumerical derivation of pressure-impulse diagrams for prediction of RC column damage to blastloadsrdquo International Journal of Impact Engineering vol 35 no11 pp 1213ndash1227 2008

[21] P D Smith and J G Hetherington Blast and Ballistic Loadingof Structures Butterowrth-Heinemenn Oxford UK 1994

[22] K-C Wu B Li and K-C Tsai ldquoThe effects of explosive massratio on residual compressive capacity of contact blast damagedcomposite columnsrdquo Journal of Constructional Steel Researchvol 67 no 4 pp 602ndash612 2011

[23] J E Crawford K B Morrill and J M Magallanes ldquoProtectivedesign for columns against close-in blast effectsrdquo in Proceedingsof the Structures Congress Boston Mass USA April 2014

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4 Shock and Vibration

Table 1 Material parameters of the steel tube

Parameter Mass density1205881

(kgm3) Poissonrsquos ratio 120592 1205900

(MPa) 119864 (GPa) 119864119905

(MPa) 120573 119862 P Failure strain(FS)

Value 7850 03 358 203 414 0 404 5 02

Table 2 Material parameters of the infill concrete

Parameter Mass density1205882

(kgm3) 119860 119861 119862 119873 1198911015840

119888

(MPa) 119878MAX

Value 2440 079 160 0007 061 379 70

Parameter Shear modulus119866 (GPa)

Maximumtensile pressure119879 (MPa)

Thresholdstrain rateEPS0 (sminus1)

Plastic strainbefore fracture

EFMIN

Crushingpressure119875119862

(MPa)

Crushingvolumetricstrain 119880

119862

Lockingpressure119875119871

(MPa)Value 1486 40 10 001 16 0001 800

ParameterLocking

volumetricstrain 119880

119871

Damageconstant1198631

Damageconstant1198632

Pressureconstant1198701

(GPa)

Pressureconstant1198702

(GPa)

Pressureconstant1198703

(GPa)Value 01 004 10 85 minus171 208

numerical study since no researches have reported a notice-able debond between the twomaterials in blast tests In orderto simulate the physical fracture shear failure and crushingof the concrete under blast loading the erosion algorithm isused to account for concrete failure Considering the strainrate effect on the concrete strength the erosion criterionbased on the principle strain is often used [16] A numberof simulations are carried out with different erosion criteriaand it is found that using principle tensile strain of 001 as theerosion criterion which is also used by Ngo et al [8] leads toreliable predictions of the responses of CFST columns

213 Sequence of Loads Application and Blast LoadModellingIn order to simulate the real stress state of CFST columns thelinearly increasing axial quasi-static loads up to the serviceaxial load level are applied to the top of the column prior toblast loading through the implicit solver To avoid too muchoscillation of the column the time duration for increasingthe loads from zero to full service level is 150ms Then thecomputational algorithm switches from implicit to explicitand the blast loads are applied over the front surface of thecolumn with the axial loads unchanged

Blast loads are generated using the ConWep air blastmodel [17] that is Load Blast Enhanced in LS-DYNA[18] Compared to other techniques that is the ArbitraryLagrangian Eulerian (ALE) methodology this model is morecomputationally efficient to simulate blast loads with a highlevel of accuracy While similar to the model Load Blast italso includes enhancements for treating reflected waves Theloading face of the column is predefined before the generationof blast loads and the time history of blast loads actingon each segment is calculated through ConWep formula asfollows

119875 (119905) = 119875119903

(119905) cos2120579 + 119875119894

(119905) (1 + cos2120579 minus 2 cos 120579) (5)

where 119875(119905) is the reflected overpressure on the definedload segment at moment 119905 119875

119903

(119905) and 119875119894

(119905) are the normal

0 25 50 75 100 125 150 175 200

Time (ms)

0

minus10

minus20

minus30

minus40

minus50

minus60

minus70

Late

ral d

ispla

cem

ent (

mm

)

Test by Zhang et al [9]Residual displacement in the testNumerical simulation

Figure 4 Comparison of the displacement data from test and thatof numerical simulation

reflected overpressure and incident overpressure at moment119905 respectively and 120579 is the angle of incidence of the blast wave

22 Model Calibration and Discussion Numerical simula-tions of the blast test were carried out and the dynamicresponse and damage mode of column S4 were obtainedSince the recording of LVDT1 at the center of column S4 wasmissing in the test the value of LVDT2 (see Figure 1(b)) at380mm from the center of the column was used to calibratethe numerical model Comparison of the calculated displace-ment time history with test results is shown in Figure 4It is found that the peak displacement of numerical results(509mm) is smaller than that in the test (60mm) while thenumerical residual displacement (354mm) is slightly largerthan the test value (34mm) Several factors as follows may

Shock and Vibration 5

(a) Test result (Zhang et al [9])

Fringe levels

6346eminus02

5289eminus02

4231e

minus02

3173eminus02

2115eminus02

1058e

minus02

0000e

+00

(b) Numerical result

Figure 5 Comparison of the column damage mode in the test andthat from numerical simulation

account for such discrepancies (1) the difference between theactual support condition which is not rigid enough and thoseadopted in the simulation (2) ignorance of the potential lossof axial loads and reduction of flexural resistance consideringthe detachment of the column ends from the loading devicein the test and (3) the limitations of material models indepicting the real-time nonlinear behaviors of steel andconcrete during test Although discrepancies exist betweenthe simulation and test values the largest error with respectto the maximum displacements is within 152 Figure 5shows the comparison of the damage mode of the columnin the test and that from the numerical simulation presentedin effective plastic strain contour and good agreement isobserved in between These results demonstrate that thecalibrated numericalmodel leads to reasonable predictions ofthe dynamic responses and damage modes of CFST columnsto blast loads and can be used for the subsequent study

3 Damage Modes of CFST Column underBlast Loading

31 Column Configuration The above calibrated numericalmodel is utilized herein to simulate dynamic behavior andpossible damagemodes of CFST column under blast loadingThe column is designed based on the specifications providedby Chinese Standard CECS 159 2004 [19] As shown inFigure 6 the dimensions of the column are ℎ (height) times119908 (width)times119889 (depth) = 3700mm times 600mm times 600mm withthe tube thickness of 18mm Parameters of the steel tube andthe infill concrete used in the simulation are the same asthose in Section 2 In order to simulate the real life boundaryconditions for CFST columns a column head and a footingare considered in the numericalmodelThe outer vertical faceof the footing and head are constrained against horizontalmotions and the bottom face of the footing is constrainedagainst vertical motions [20] Horizontal distance from thecharge center to the column front surface that is the standoffdistance is denoted as 119883 And the vertical distance fromthe charge center to the ground that is the height of burstis denoted as 119867

119861

The initial dead weight imposed on the

Table 3 Possible damage modes of the CFST column

119872 (kg) 119867119861

(m) 119885 (mkg13) Damage mode

50 0le021 Localized

022ndash024 Shearge026 Flexural

250 0le025 Localized

030ndash048 Shearge052 Flexural

50 185 le016 Localizedge018 Flexural

column is 35 percent of axial load capacity of the undamagedcolumn which represents the axial load level of a typicalground floor column in a high-rise building

As the blast load parameters are related to both explosivemass and standoff distance the scaled standoff distance isintroduced to consider their combined effects and is definedas [21]

119885 =

119883

11987213

(6)

where 119885 is the scaled standoff distance and 119872 is theequivalent mass of TNT

32 Possible Damage Modes Three damage modes of theCFST column under blast loading have been observedthrough a number of simulations they are flexural damageshear damage and localized damage Table 3 presents damagemodes of the column according to different blast conditionsIt is found that in general explosivewith a small scaled stand-off distance favors a localized damage whilst shear damageand localized damage occur when the explosive is relativelyfar from the columnThis is because the blast loads are highlyintensive when the scaled standoff distance is small and forvery local blast loads acting on the column failure of the infillconcrete and steel tube starts before any considerable overallresponse can occur and the column surfers a localized dam-age However with the increase of scaled standoff distanceblast loads tend to be well-distributed over the surface of thecolumn which is inclined to response globally and undergoshear damage and flexural damage Also the damagemode isaffected by the explosive mass height of burst Typical resultsof these damagemodes are shown with effective plastic straincontours in Figures 7ndash9

Figure 7 shows the flexural damage mode of the CFSTcolumn induced by the detonation of 50 kg of TNT at thescaled standoff distance of 018mkg13 with the height ofburst of 185m In this configuration when the blast loadsacted on the column the mid-part of it responded imme-diately with the increment of lateral deformation Then theareas near the supports of the column began to deform androtate As the global flexural deformation of the columnevolved plastic hinges developed in the mid-part and nearthe supports of the columnwhere the bendingmoments werelarge

6 Shock and Vibration

First-floor column

Second-floor column

Explosive

Second-floor beam

h

HB

X

(a) Explosion scenario

1 1

Section 1-1

Steel tube

Infill concrete

Axial load

Head

Footing

First-floor column

h d t

w

(b) Column details

Figure 6 Sketch of the numerical analysis model

Figure 8 shows the shear damage mode of the columnresulted from 250 kg of TNT detonating on the ground atthe scaled standoff distance of 033mkg13 Due to the largeshear force and the development of shear deformation nearthe supports the infill concrete was sheared off accompaniedwith the rupture of the steel tube around the cross section ofthe column Finally the column failed in brittle shear beforeany ductile flexural hinge developed

As discussed above flexural damage and shear damageof the column are due to the deformation and internal forceof the whole member induced by the blast loads On thecontrary localized damage of the CFST column is dominatedby the deformation and failure of the concrete infill and steeltube in the vicinity of the explosion whilst other parts of thecolumn remain almost elastic and the global deformation ofthe column is small

Figure 9 shows the localized damage mode of the CFSTcolumn caused by the detonation of 50 kg of TNT on theground with the scaled standoff distance of 018mkg13When the impulsive shock front of high intensity metthe column surface the stress waves were generated andpropagated from the tube front surface towards the concreteinfill and the lateral and back surfaces of the tube Then theconcrete close to the explosion was cracked and crushed andthe front side of the tube which lost the internal support ofthe concrete fill was squashed with the bulging of its lateraland back sides As the localized deformation of the columnevolved rupture and local buckling failure of the steel tubetook place yet the global lateral deformation of the columnhad almost not developed at this moment

It should bementioned that these damagemodes are onlytypical ones Sometimes there exists a combination of thesedamage modes

4 Damage Assessment of CFST Columnsunder Blast Loading

41 Damage Criterion As discussed previously the CFSTcolumn subjected to blast loads may undergo flexural dam-age shear damage and localized damage thus the damagecriterion for the column should be chosen carefully andthe appropriate one is expected to be applicable to all thepossible damage modes of the column In this paper thedamage criterion based on the residual axial load capacityis adopted for CFST columns due to the following reasons(1) the structure column is primarily designed to carry theaxial load and the axial load capacity of it reflects bothits global properties and material characteristics (2) thecommonly used deformation-based damage criterions thatis the support rotation lateral deflection and ductility maynot be appropriate for the evaluation of localized damage ofthe column and (3) the residual axial load capacity of thecolumns is an explicit metric of the damage imparted and italso provides information in assessing the collapse possibilityof a blast damaged column

The damage index adopted herein is based on the indexfrom Shi et al [20] and is expressed as

119863119888

= 1 minus

119875residual119875max

(7)

where 119863119888

is the damage degree of CFST columns 119875residual isthe residual axial load capacity of the column after blast loadsand 119875max is the maximum axial load capacity of the columnprior to blast loading Values of 119863

119888

vary between 0 (ieno loss of capacity) and 10 (ie complete loss of capacity)Note that in the paper by Shi et al [20] the maximumaxial load capacity of an undamaged column is calculated

Shock and Vibration 7

Fringe levels

3793eminus02

3161e

minus02

2529eminus02

1897eminus02

1264eminus02

6322eminus03

0000e

+00

(a) CFST column

Fringe levels

3793eminus02

3161e

minus02

2529eminus02

1897eminus02

1264eminus02

6322eminus03

0000e

+00

(b) Infill concrete

Figure 7 Flexural damage mode of CFST column under blast loading

Fringe levels

2000e

minus01

1667eminus01

1333eminus01

1000e

minus01

6667eminus02

3333eminus02

0000e

+00

(a) CFST column

Fringe levels

2392e

minus02

1993eminus02

1594eminus02

1196eminus02

7972e

minus03

3986eminus03

0000e

+00

(b) Infill concrete

Figure 8 Shear damage mode of CFST column under blast loading

8 Shock and Vibration

Fringe levels

2000e

minus01

1667eminus01

1333eminus01

1000e

minus01

6667eminus02

3333eminus02

0000e

+00

(a) CFST column

Fringe levels

2597eminus02

2165eminus02

1732e

minus02

1299eminus02

8658e

minus03

4329eminus03

0000e

+00

(b) Infill concrete

Figure 9 Localized damage mode of CFST column under blast loading

with the provided equation from the standard design codewhich however may lead to the values of119863

119888

below 0 in somecases Therefore both 119875residual and 119875max are determined fromnumerical simulation in this study Here 119875residual119875max is alsotermed as the residual capacity index (RCI) used byWu et al[22] andCrawford et al [23] to assess the damage level of steelreinforced concrete (SRC) columns and reinforced concrete(RC) columns subjected to blast loads

It is noted that if the ratio of the service axial load tomaximum axial load capacity of the column is denoted as 119899then a column whose119863

119888

is greater than (1 minus 119899) is consideredas failed or collapsed since its residual axial load capacity isnot sufficient for the service axial load

42 Steps for Damage Assessment of CFST Columns

Step 1 (derivation of 119875max) During this step the linearlyincreasing axial load is applied on the column head until thecolumn collapses then 119875max is determined as the maximumaxial load that the column can withstand

Step 2 (derivation of 119875residual) Three substeps as follows arerequired to obtain 119875residual (1) before blast loading a linearlyincreasing axial load up to the service axial load is imposedon the column (2) blast loads are applied over the front faceof the column with the service axial load being constant andcalculation is stopped when the damaged column approachesstatic equilibrium (3) a linearly increasing axial load isimposed on the top of the damaged column until it collapses

then 119875residual is determined as the peak of the axial load thatthe damaged column can bear

Step 3 (determination of 119863119888

) Substitute the values of 119875maxand 119875residual into (7) to obtain119863119888

43 Parameters Studied In this section effects of severalkey parameters on the damage degree of CFST columnsare analyzed These parameters include the scaled standoffdistance height of burst explosive mass column depthcolumn width column steel ratio and axial load ratio aslisted in Table 4 in which a contrast case is generated bychanging one of the parameters considered in the benchmarkcase while keeping other parameters unchanged Note thatin each case varied scaled standoff distances are consideredso that the effects aforementioned parameters on the damagedegree of columns within different blast loading regimes canbe assessed

431 Effect of Scaled Standoff Distance 119885 The numericalsimulation results show that 119863

119888

of CFST columns decreaseswith the increasing scaled standoff distance regardless ofother parameters This is because column damage is affectedby the peak overpressure and impulse of the blast wave[21] and both of them drop with the rising scaled standoffdistance which results in a small degree of column damage

432 Effect of Height of Burst119867119861

It is difficult to characterizethe effect of 119867

119861

on the damage degree of the column On

Shock and Vibration 9

Table 4 Parameters used in the numerical parametric study

Parameters 119885 (mkg13) 119867119861

(m) 119872 (kg) 119889 (m) 119908 (m) Steel ratio 120572lowast Axial load ratio 119899Benchmark case 018ndash050 0 50 06 06 013 035Contrast cases 015ndash090 185 250 500 09 12 09 12 016 019 050 065lowast

120572 = 119860119904

119860119888

119860119904

and 119860119888

are the cross-sectional areas of steel tube and infill concrete respectively

07

06

05

04

03

02

01

00

HB = 0mHB = 185m

015 020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

Figure 10 Effects of height of burst on the damage degree

one hand when 119867119861

nears zero the initial blast wave isimmediately reflected and reinforced by the ground On theother the mid-height of the column is expected to surfer themost severe damage due to lack of transverse support Conse-quently as shown in Figure 10 surface burst results in severerdamage to the column than that caused by explosion atcolumnmid-height (119867

119861

= 185m) especially when the stand-off distance is small The effects of119867

119861

on the damage degreeof the column are insignificant at large scaled distancesbecause both the overpressure and impulse on the columnare relatively small in these cases

433 Effect of Explosive Mass119872 Figure 11 shows the effectsof explosive mass on the damage degree of the columnInspections of the figure show that 119863

119888

rises with 119872 for thesame scaled standoff distance indicating that CFST columnis impulse-sensitive since explosive with larger mass hasrelatively more impulse for the column

434 Effects of Column Width 119908 and Depth 119889 Effects ofcolumn depth and width on 119863

119888

are shown in Figure 12Comparedwith the reference column (119908 = 06m 119889 = 06m)columns with larger width and depth tend to have lowerdamage degrees because expanding columnwidth and depthproduces a larger cross section for attenuation of the stresswaves density and contributes to enhancement of the shearresistance as well as flexural strength of the columnHoweverit is found that columns with the same cross section area butdifferent width and depth have varied damage degrees and

07

06

05

04

03

02

01

0002 03 04 05 06 07 08 09 10

Scaled standoff distance Z (mkg13)

M = 50kgM = 250kgM = 500kg

[HB = 0m] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 11 Effects of explosive mass on the damage degree

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

w = 06m d = 06mw = 09m d = 06mw = 12m d = 06m

w = 06m d = 09mw = 06m d = 12m

[HB = 0m] [M = 50kg] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 12 Effects of width and depth on the damage degree

that compared with increasing the column width incrementof the column depth is more effective in reducing the columndamage degree This is because enlarging the column widthsimultaneously results in a rise of blast loads acting on thecolumnwhich balances out the enhancement of columnblastresistance to some extent

10 Shock and Vibration

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

120572 = 013

120572 = 016

120572 = 019

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [n = 035 ]

Dam

age d

egre

eDc

Figure 13 Effects of steel ratio on the damage degree

07

06

05

04

03

02

01

00020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

n = 035

n = 050

n = 065

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [120572 = 013]

Dam

age d

egre

eDc

Figure 14 Effects of axial load ratio on the damage degree

435 Effect of Column Steel Ratio 120572 As shown in Figure 13119863119888

drops with the rising steel ratio This is expected becauseincreasing 120572means a larger steel area and better confinementof infill concrete which will enhance the shear and bendingstrength of the column as well as its resistance to localizeddamage

436 Effect of Column Axial Load Ratio 119899 Effects of axialload ratio on 119863

119888

are shown in Figure 14 Inspection of thefigure reveals that axial load ratio has dual influences on col-umn damage When the scaled standoff is small the columnwith a larger axial load ratio has lower damage degree Thisis because the column under small scaled standoff is likelyto suffer localized damage and shear damage and a higher

axial load will restrain the cracking and crushing of concretewhich enhances the resistance of the column to localizeddamage and shear damage In contrast at a large scaledstandoff distance the column with larger axial load ratio hashigher damage degree The reason is that with the increaseof the scaled standoff distance the column tends to sufferflexural damage which is related to its moment capacity andductility The larger the moment capacity and ductility arethe lower the damage degree is For the CFST column studiedin this section the axial load ratio at the maximum momentcapacity is 022 which is derived by the methods from Choiet al [1] According to the axial load-bending moment (P-M)interactions the moment capacity of the CFST column willdecrease when 119899 rises from 035 to 060 Moreover a risingaxial load will reduce the ductility of the CFST column

44 Empirical Equations for Determining the Damage Degreeof CFST Columns The parametric study revealed the signif-icance of parameters affecting the damage degree of CFSTcolumns Through the multivariable regression analysis anempirical equation is proposed in terms of various parame-ters to predict the damage degree and is expressed as follows

119863119888

= [minus1505 ln(11987250

) + 1650 (

119908

06

) minus 3242 (

119889

06

)

minus 131625120572 + 15349119899 + 25011]

sdot 119890[minus648ln(11987250)+533(11990806)minus1091(11988906)minus373minus1230120572+1292119899+2681]119885

(8)

The comparisons of the proposed equation with the ana-lytical results are shown in Figures 15(a)ndash15(f) The scattersdenote the analytical results and the solid lines represent theproposed equation Observation of these figures shows thatthe proposed curves are close to the analytical results formostcases The effects of height of burst on the damage degree ofCFST columns are not reflected by (8) due to the lack of blastdata in the lower height of the column which are limited inthe ConWep model and will be supplemented in the furtherstudies

5 Conclusions

This paper presents a 3D numerical model to investigate thedamage modes and damage assessment of CFST columnsBased on the numerical analysis results the following con-clusions can be drawn

CFST columns under blast loading may undergo theglobal flexural damage and shear damage as well as localizeddamage Flexural damage and shear damage of the columnare mainly attributed to the deformation and internal force ofthe whole member whilst the localized damage is dominatedby the failure of infill concrete and steel tube in the vicinity ofthe explosion

The damage criterion based on the residual axial loadcapacity is adopted for assessing the degree of CFST columnsdamage to blast loadsThrough parametric studies it is foundthat the damage degree of CFST columns decays nearlyexponentially with the increasing scaled standoff distance

Shock and Vibration 11

07

06

05

04

03

02

01

00

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

Dam

age d

egre

eDc

(a)

07

06

05

04

03

02

01

00095090085050 055 060 065 070 075 080

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 500kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

(b)

07

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 12m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

(c)

020

015

010

005

000

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 12m] [120572 = 013] [n = 035]D

amag

e deg

reeD

c

(d)

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 019] [n = 035]

Dam

age d

egre

eDc

(e)

020

025

030

035

015

010

005

000055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 065]

Dam

age d

egre

eDc

(f)

Figure 15 Comparison of analytical results with the proposed curves

12 Shock and Vibration

For the same scaled standoff distance surface burst results inseverer damage to the column than that caused by explosionat columnmid-height and the damage degree increases withthe rising explosive mass and decreases with column depthand width and steel ratio Increasing the axial load enhancesthe resistance of the column against localized damage andshear damage while the effects of axial load on flexuraldamage depend on the axial load-bending moment (P-M)interactions of the column

An equation is derived by fitting the results of parametricstudies to estimate the damage degree of CFST columnsTypical examples confirm that the proposed equation wellrepresents the variation of the column damage degree How-ever future experiments can be conducted for investigatingthe effects of other parameters on the damage degree of CFSTcolumns

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research described in this paper was financially sup-ported by Achievement Transfer Program of Institutionsof Higher Education in Chongqing under Grant noKJZH14220

References

[1] Y-H Choi D A Foutch and J M LaFave ldquoNew approachto AISC P-M interaction curve for square concrete filled tube(CFT) beamndashcolumnsrdquo Engineering Structures vol 28 no 11pp 1586ndash1598 2006

[2] Y-H Choi K S Kim and S-M Choi ldquoSimplified P-M interac-tion curve for square steel tube filled with high-strength con-creterdquoThin-Walled Structures vol 46 no 5 pp 506ndash515 2008

[3] T KrauthammerModern Protective Structures TaylorampFrancisGroup New York NY USA 2008

[4] S C Fujikura M Bruneau and D Lopez-Garcia ldquoExperimen-tal investigation of blast performance of seismically resistantconcrete-filled steel tube bridge piersrdquo Tech Rep MCEER-07-0005 University at Buffalo Buffalo NY USA 2007

[5] S Fujikura M Bruneau and D Lopez-Garcia ldquoExperimentalinvestigation of multihazard resistant bridge piers having con-crete-filled steel tube under blast loadingrdquo Journal of BridgeEngineering vol 13 no 6 pp 586ndash594 2008

[6] G Li H Qu T Yang Y Lu and S Chen ldquoExperimental studyof concrete-filled steel tubular columns under blast loadingrdquoJianzhu Jiegou Xuebao vol 34 no 12 pp 69ndash76 2013 (Chinese)

[7] A M Remennikov and B Uy ldquoExplosive testing andmodellingof square tubular steel columns for near-field detonationsrdquo Jour-nal of Constructional Steel Research vol 101 pp 290ndash303 2014

[8] T Ngo D Mohotti A Remennikov and B Uy ldquoNumericalsimulations of response of tubular steel beams to close-rangeexplosionsrdquo Journal of Constructional Steel Research vol 105 pp151ndash163 2015

[9] F R Zhang C Q Wu H W Wang and Y Zhou ldquoNumericalsimulation of concrete filled steel tube columns against BLASTloadsrdquoThin-Walled Structures vol 92 pp 82ndash92 2015

[10] F Zhang C Wu X Zhao Z Li A Heidarpour and H WangldquoNumerical modeling of concrete-filled double-skin steelsquare tubular columns under blast loadingrdquo Journal of Per-formance of Constructed Facilities vol 29 no 5 Article IDB4015002 2015

[11] Livermore Software Technology Corporation LS-DYNA Theo-retical Manual Livermore Software Technology CorporationLivermore Calif USA 1998

[12] G R Cowper and P S Symonds ldquoStrain-hardening and strain-rate effects in the impact loading of cantilever beamsrdquo TechRep AD144762 Office of Naval Research Arlington Va USA1958

[13] T J Holmquist G R Johnson and W H Cook ldquoA computa-tional constitutive model for concrete subjected to large strainshigh strain rates and high pressuresrdquo in Proceedings of the 14thInternational Symposium on Ballistics Quebec City CanadaSeptember 1993

[14] Q Fang and J Zhang ldquoThree-dimensional modelling of steelfiber reinforced concrete material under intense dynamic load-ingrdquo Construction and Building Materials vol 44 pp 118ndash1322013

[15] Y Li F Lin X L Gu and X Q Lu ldquoNumerical researchof a super-large cooling tower subjected to accidental loadsrdquoNuclear Engineering and Design vol 269 pp 184ndash192 2014

[16] J Li and H Hao ldquoNumerical study of concrete spall damage toblast loadsrdquo International Journal of Impact Engineering vol 68pp 41ndash55 2014

[17] G Randers-Pehrson and K A Bannister ldquoAirblast loadingmodel for DYNA2D and DYNA3Drdquo Tech Rep ARL-TR-1310Army Research Laboratory Adelphi Md USA 1997

[18] Livermore Software Technology Corporation LS-DYNA Key-word Userrsquos Manual (Version 971 R610) Livermore SoftwareTechnology Corporation Livermore Calif USA 2012

[19] CECS ldquoTechnical specification for structures with concrete-filled rectangular steel tube membersrdquo CECS 1592004 ChinaAssociation for Engineering Construction StandardizationBeijing China 2004 (Chinese)

[20] Y Shi H Hao and Z-X Li ldquoNumerical derivation of pressure-impulse diagrams for prediction of RC column damage to blastloadsrdquo International Journal of Impact Engineering vol 35 no11 pp 1213ndash1227 2008

[21] P D Smith and J G Hetherington Blast and Ballistic Loadingof Structures Butterowrth-Heinemenn Oxford UK 1994

[22] K-C Wu B Li and K-C Tsai ldquoThe effects of explosive massratio on residual compressive capacity of contact blast damagedcomposite columnsrdquo Journal of Constructional Steel Researchvol 67 no 4 pp 602ndash612 2011

[23] J E Crawford K B Morrill and J M Magallanes ldquoProtectivedesign for columns against close-in blast effectsrdquo in Proceedingsof the Structures Congress Boston Mass USA April 2014

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Shock and Vibration

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International Journal of

Shock and Vibration 5

(a) Test result (Zhang et al [9])

Fringe levels

6346eminus02

5289eminus02

4231e

minus02

3173eminus02

2115eminus02

1058e

minus02

0000e

+00

(b) Numerical result

Figure 5 Comparison of the column damage mode in the test andthat from numerical simulation

account for such discrepancies (1) the difference between theactual support condition which is not rigid enough and thoseadopted in the simulation (2) ignorance of the potential lossof axial loads and reduction of flexural resistance consideringthe detachment of the column ends from the loading devicein the test and (3) the limitations of material models indepicting the real-time nonlinear behaviors of steel andconcrete during test Although discrepancies exist betweenthe simulation and test values the largest error with respectto the maximum displacements is within 152 Figure 5shows the comparison of the damage mode of the columnin the test and that from the numerical simulation presentedin effective plastic strain contour and good agreement isobserved in between These results demonstrate that thecalibrated numericalmodel leads to reasonable predictions ofthe dynamic responses and damage modes of CFST columnsto blast loads and can be used for the subsequent study

3 Damage Modes of CFST Column underBlast Loading

31 Column Configuration The above calibrated numericalmodel is utilized herein to simulate dynamic behavior andpossible damagemodes of CFST column under blast loadingThe column is designed based on the specifications providedby Chinese Standard CECS 159 2004 [19] As shown inFigure 6 the dimensions of the column are ℎ (height) times119908 (width)times119889 (depth) = 3700mm times 600mm times 600mm withthe tube thickness of 18mm Parameters of the steel tube andthe infill concrete used in the simulation are the same asthose in Section 2 In order to simulate the real life boundaryconditions for CFST columns a column head and a footingare considered in the numericalmodelThe outer vertical faceof the footing and head are constrained against horizontalmotions and the bottom face of the footing is constrainedagainst vertical motions [20] Horizontal distance from thecharge center to the column front surface that is the standoffdistance is denoted as 119883 And the vertical distance fromthe charge center to the ground that is the height of burstis denoted as 119867

119861

The initial dead weight imposed on the

Table 3 Possible damage modes of the CFST column

119872 (kg) 119867119861

(m) 119885 (mkg13) Damage mode

50 0le021 Localized

022ndash024 Shearge026 Flexural

250 0le025 Localized

030ndash048 Shearge052 Flexural

50 185 le016 Localizedge018 Flexural

column is 35 percent of axial load capacity of the undamagedcolumn which represents the axial load level of a typicalground floor column in a high-rise building

As the blast load parameters are related to both explosivemass and standoff distance the scaled standoff distance isintroduced to consider their combined effects and is definedas [21]

119885 =

119883

11987213

(6)

where 119885 is the scaled standoff distance and 119872 is theequivalent mass of TNT

32 Possible Damage Modes Three damage modes of theCFST column under blast loading have been observedthrough a number of simulations they are flexural damageshear damage and localized damage Table 3 presents damagemodes of the column according to different blast conditionsIt is found that in general explosivewith a small scaled stand-off distance favors a localized damage whilst shear damageand localized damage occur when the explosive is relativelyfar from the columnThis is because the blast loads are highlyintensive when the scaled standoff distance is small and forvery local blast loads acting on the column failure of the infillconcrete and steel tube starts before any considerable overallresponse can occur and the column surfers a localized dam-age However with the increase of scaled standoff distanceblast loads tend to be well-distributed over the surface of thecolumn which is inclined to response globally and undergoshear damage and flexural damage Also the damagemode isaffected by the explosive mass height of burst Typical resultsof these damagemodes are shown with effective plastic straincontours in Figures 7ndash9

Figure 7 shows the flexural damage mode of the CFSTcolumn induced by the detonation of 50 kg of TNT at thescaled standoff distance of 018mkg13 with the height ofburst of 185m In this configuration when the blast loadsacted on the column the mid-part of it responded imme-diately with the increment of lateral deformation Then theareas near the supports of the column began to deform androtate As the global flexural deformation of the columnevolved plastic hinges developed in the mid-part and nearthe supports of the columnwhere the bendingmoments werelarge

6 Shock and Vibration

First-floor column

Second-floor column

Explosive

Second-floor beam

h

HB

X

(a) Explosion scenario

1 1

Section 1-1

Steel tube

Infill concrete

Axial load

Head

Footing

First-floor column

h d t

w

(b) Column details

Figure 6 Sketch of the numerical analysis model

Figure 8 shows the shear damage mode of the columnresulted from 250 kg of TNT detonating on the ground atthe scaled standoff distance of 033mkg13 Due to the largeshear force and the development of shear deformation nearthe supports the infill concrete was sheared off accompaniedwith the rupture of the steel tube around the cross section ofthe column Finally the column failed in brittle shear beforeany ductile flexural hinge developed

As discussed above flexural damage and shear damageof the column are due to the deformation and internal forceof the whole member induced by the blast loads On thecontrary localized damage of the CFST column is dominatedby the deformation and failure of the concrete infill and steeltube in the vicinity of the explosion whilst other parts of thecolumn remain almost elastic and the global deformation ofthe column is small

Figure 9 shows the localized damage mode of the CFSTcolumn caused by the detonation of 50 kg of TNT on theground with the scaled standoff distance of 018mkg13When the impulsive shock front of high intensity metthe column surface the stress waves were generated andpropagated from the tube front surface towards the concreteinfill and the lateral and back surfaces of the tube Then theconcrete close to the explosion was cracked and crushed andthe front side of the tube which lost the internal support ofthe concrete fill was squashed with the bulging of its lateraland back sides As the localized deformation of the columnevolved rupture and local buckling failure of the steel tubetook place yet the global lateral deformation of the columnhad almost not developed at this moment

It should bementioned that these damagemodes are onlytypical ones Sometimes there exists a combination of thesedamage modes

4 Damage Assessment of CFST Columnsunder Blast Loading

41 Damage Criterion As discussed previously the CFSTcolumn subjected to blast loads may undergo flexural dam-age shear damage and localized damage thus the damagecriterion for the column should be chosen carefully andthe appropriate one is expected to be applicable to all thepossible damage modes of the column In this paper thedamage criterion based on the residual axial load capacityis adopted for CFST columns due to the following reasons(1) the structure column is primarily designed to carry theaxial load and the axial load capacity of it reflects bothits global properties and material characteristics (2) thecommonly used deformation-based damage criterions thatis the support rotation lateral deflection and ductility maynot be appropriate for the evaluation of localized damage ofthe column and (3) the residual axial load capacity of thecolumns is an explicit metric of the damage imparted and italso provides information in assessing the collapse possibilityof a blast damaged column

The damage index adopted herein is based on the indexfrom Shi et al [20] and is expressed as

119863119888

= 1 minus

119875residual119875max

(7)

where 119863119888

is the damage degree of CFST columns 119875residual isthe residual axial load capacity of the column after blast loadsand 119875max is the maximum axial load capacity of the columnprior to blast loading Values of 119863

119888

vary between 0 (ieno loss of capacity) and 10 (ie complete loss of capacity)Note that in the paper by Shi et al [20] the maximumaxial load capacity of an undamaged column is calculated

Shock and Vibration 7

Fringe levels

3793eminus02

3161e

minus02

2529eminus02

1897eminus02

1264eminus02

6322eminus03

0000e

+00

(a) CFST column

Fringe levels

3793eminus02

3161e

minus02

2529eminus02

1897eminus02

1264eminus02

6322eminus03

0000e

+00

(b) Infill concrete

Figure 7 Flexural damage mode of CFST column under blast loading

Fringe levels

2000e

minus01

1667eminus01

1333eminus01

1000e

minus01

6667eminus02

3333eminus02

0000e

+00

(a) CFST column

Fringe levels

2392e

minus02

1993eminus02

1594eminus02

1196eminus02

7972e

minus03

3986eminus03

0000e

+00

(b) Infill concrete

Figure 8 Shear damage mode of CFST column under blast loading

8 Shock and Vibration

Fringe levels

2000e

minus01

1667eminus01

1333eminus01

1000e

minus01

6667eminus02

3333eminus02

0000e

+00

(a) CFST column

Fringe levels

2597eminus02

2165eminus02

1732e

minus02

1299eminus02

8658e

minus03

4329eminus03

0000e

+00

(b) Infill concrete

Figure 9 Localized damage mode of CFST column under blast loading

with the provided equation from the standard design codewhich however may lead to the values of119863

119888

below 0 in somecases Therefore both 119875residual and 119875max are determined fromnumerical simulation in this study Here 119875residual119875max is alsotermed as the residual capacity index (RCI) used byWu et al[22] andCrawford et al [23] to assess the damage level of steelreinforced concrete (SRC) columns and reinforced concrete(RC) columns subjected to blast loads

It is noted that if the ratio of the service axial load tomaximum axial load capacity of the column is denoted as 119899then a column whose119863

119888

is greater than (1 minus 119899) is consideredas failed or collapsed since its residual axial load capacity isnot sufficient for the service axial load

42 Steps for Damage Assessment of CFST Columns

Step 1 (derivation of 119875max) During this step the linearlyincreasing axial load is applied on the column head until thecolumn collapses then 119875max is determined as the maximumaxial load that the column can withstand

Step 2 (derivation of 119875residual) Three substeps as follows arerequired to obtain 119875residual (1) before blast loading a linearlyincreasing axial load up to the service axial load is imposedon the column (2) blast loads are applied over the front faceof the column with the service axial load being constant andcalculation is stopped when the damaged column approachesstatic equilibrium (3) a linearly increasing axial load isimposed on the top of the damaged column until it collapses

then 119875residual is determined as the peak of the axial load thatthe damaged column can bear

Step 3 (determination of 119863119888

) Substitute the values of 119875maxand 119875residual into (7) to obtain119863119888

43 Parameters Studied In this section effects of severalkey parameters on the damage degree of CFST columnsare analyzed These parameters include the scaled standoffdistance height of burst explosive mass column depthcolumn width column steel ratio and axial load ratio aslisted in Table 4 in which a contrast case is generated bychanging one of the parameters considered in the benchmarkcase while keeping other parameters unchanged Note thatin each case varied scaled standoff distances are consideredso that the effects aforementioned parameters on the damagedegree of columns within different blast loading regimes canbe assessed

431 Effect of Scaled Standoff Distance 119885 The numericalsimulation results show that 119863

119888

of CFST columns decreaseswith the increasing scaled standoff distance regardless ofother parameters This is because column damage is affectedby the peak overpressure and impulse of the blast wave[21] and both of them drop with the rising scaled standoffdistance which results in a small degree of column damage

432 Effect of Height of Burst119867119861

It is difficult to characterizethe effect of 119867

119861

on the damage degree of the column On

Shock and Vibration 9

Table 4 Parameters used in the numerical parametric study

Parameters 119885 (mkg13) 119867119861

(m) 119872 (kg) 119889 (m) 119908 (m) Steel ratio 120572lowast Axial load ratio 119899Benchmark case 018ndash050 0 50 06 06 013 035Contrast cases 015ndash090 185 250 500 09 12 09 12 016 019 050 065lowast

120572 = 119860119904

119860119888

119860119904

and 119860119888

are the cross-sectional areas of steel tube and infill concrete respectively

07

06

05

04

03

02

01

00

HB = 0mHB = 185m

015 020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

Figure 10 Effects of height of burst on the damage degree

one hand when 119867119861

nears zero the initial blast wave isimmediately reflected and reinforced by the ground On theother the mid-height of the column is expected to surfer themost severe damage due to lack of transverse support Conse-quently as shown in Figure 10 surface burst results in severerdamage to the column than that caused by explosion atcolumnmid-height (119867

119861

= 185m) especially when the stand-off distance is small The effects of119867

119861

on the damage degreeof the column are insignificant at large scaled distancesbecause both the overpressure and impulse on the columnare relatively small in these cases

433 Effect of Explosive Mass119872 Figure 11 shows the effectsof explosive mass on the damage degree of the columnInspections of the figure show that 119863

119888

rises with 119872 for thesame scaled standoff distance indicating that CFST columnis impulse-sensitive since explosive with larger mass hasrelatively more impulse for the column

434 Effects of Column Width 119908 and Depth 119889 Effects ofcolumn depth and width on 119863

119888

are shown in Figure 12Comparedwith the reference column (119908 = 06m 119889 = 06m)columns with larger width and depth tend to have lowerdamage degrees because expanding columnwidth and depthproduces a larger cross section for attenuation of the stresswaves density and contributes to enhancement of the shearresistance as well as flexural strength of the columnHoweverit is found that columns with the same cross section area butdifferent width and depth have varied damage degrees and

07

06

05

04

03

02

01

0002 03 04 05 06 07 08 09 10

Scaled standoff distance Z (mkg13)

M = 50kgM = 250kgM = 500kg

[HB = 0m] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 11 Effects of explosive mass on the damage degree

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

w = 06m d = 06mw = 09m d = 06mw = 12m d = 06m

w = 06m d = 09mw = 06m d = 12m

[HB = 0m] [M = 50kg] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 12 Effects of width and depth on the damage degree

that compared with increasing the column width incrementof the column depth is more effective in reducing the columndamage degree This is because enlarging the column widthsimultaneously results in a rise of blast loads acting on thecolumnwhich balances out the enhancement of columnblastresistance to some extent

10 Shock and Vibration

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

120572 = 013

120572 = 016

120572 = 019

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [n = 035 ]

Dam

age d

egre

eDc

Figure 13 Effects of steel ratio on the damage degree

07

06

05

04

03

02

01

00020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

n = 035

n = 050

n = 065

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [120572 = 013]

Dam

age d

egre

eDc

Figure 14 Effects of axial load ratio on the damage degree

435 Effect of Column Steel Ratio 120572 As shown in Figure 13119863119888

drops with the rising steel ratio This is expected becauseincreasing 120572means a larger steel area and better confinementof infill concrete which will enhance the shear and bendingstrength of the column as well as its resistance to localizeddamage

436 Effect of Column Axial Load Ratio 119899 Effects of axialload ratio on 119863

119888

are shown in Figure 14 Inspection of thefigure reveals that axial load ratio has dual influences on col-umn damage When the scaled standoff is small the columnwith a larger axial load ratio has lower damage degree Thisis because the column under small scaled standoff is likelyto suffer localized damage and shear damage and a higher

axial load will restrain the cracking and crushing of concretewhich enhances the resistance of the column to localizeddamage and shear damage In contrast at a large scaledstandoff distance the column with larger axial load ratio hashigher damage degree The reason is that with the increaseof the scaled standoff distance the column tends to sufferflexural damage which is related to its moment capacity andductility The larger the moment capacity and ductility arethe lower the damage degree is For the CFST column studiedin this section the axial load ratio at the maximum momentcapacity is 022 which is derived by the methods from Choiet al [1] According to the axial load-bending moment (P-M)interactions the moment capacity of the CFST column willdecrease when 119899 rises from 035 to 060 Moreover a risingaxial load will reduce the ductility of the CFST column

44 Empirical Equations for Determining the Damage Degreeof CFST Columns The parametric study revealed the signif-icance of parameters affecting the damage degree of CFSTcolumns Through the multivariable regression analysis anempirical equation is proposed in terms of various parame-ters to predict the damage degree and is expressed as follows

119863119888

= [minus1505 ln(11987250

) + 1650 (

119908

06

) minus 3242 (

119889

06

)

minus 131625120572 + 15349119899 + 25011]

sdot 119890[minus648ln(11987250)+533(11990806)minus1091(11988906)minus373minus1230120572+1292119899+2681]119885

(8)

The comparisons of the proposed equation with the ana-lytical results are shown in Figures 15(a)ndash15(f) The scattersdenote the analytical results and the solid lines represent theproposed equation Observation of these figures shows thatthe proposed curves are close to the analytical results formostcases The effects of height of burst on the damage degree ofCFST columns are not reflected by (8) due to the lack of blastdata in the lower height of the column which are limited inthe ConWep model and will be supplemented in the furtherstudies

5 Conclusions

This paper presents a 3D numerical model to investigate thedamage modes and damage assessment of CFST columnsBased on the numerical analysis results the following con-clusions can be drawn

CFST columns under blast loading may undergo theglobal flexural damage and shear damage as well as localizeddamage Flexural damage and shear damage of the columnare mainly attributed to the deformation and internal force ofthe whole member whilst the localized damage is dominatedby the failure of infill concrete and steel tube in the vicinity ofthe explosion

The damage criterion based on the residual axial loadcapacity is adopted for assessing the degree of CFST columnsdamage to blast loadsThrough parametric studies it is foundthat the damage degree of CFST columns decays nearlyexponentially with the increasing scaled standoff distance

Shock and Vibration 11

07

06

05

04

03

02

01

00

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

Dam

age d

egre

eDc

(a)

07

06

05

04

03

02

01

00095090085050 055 060 065 070 075 080

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 500kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

(b)

07

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 12m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

(c)

020

015

010

005

000

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 12m] [120572 = 013] [n = 035]D

amag

e deg

reeD

c

(d)

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 019] [n = 035]

Dam

age d

egre

eDc

(e)

020

025

030

035

015

010

005

000055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 065]

Dam

age d

egre

eDc

(f)

Figure 15 Comparison of analytical results with the proposed curves

12 Shock and Vibration

For the same scaled standoff distance surface burst results inseverer damage to the column than that caused by explosionat columnmid-height and the damage degree increases withthe rising explosive mass and decreases with column depthand width and steel ratio Increasing the axial load enhancesthe resistance of the column against localized damage andshear damage while the effects of axial load on flexuraldamage depend on the axial load-bending moment (P-M)interactions of the column

An equation is derived by fitting the results of parametricstudies to estimate the damage degree of CFST columnsTypical examples confirm that the proposed equation wellrepresents the variation of the column damage degree How-ever future experiments can be conducted for investigatingthe effects of other parameters on the damage degree of CFSTcolumns

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research described in this paper was financially sup-ported by Achievement Transfer Program of Institutionsof Higher Education in Chongqing under Grant noKJZH14220

References

[1] Y-H Choi D A Foutch and J M LaFave ldquoNew approachto AISC P-M interaction curve for square concrete filled tube(CFT) beamndashcolumnsrdquo Engineering Structures vol 28 no 11pp 1586ndash1598 2006

[2] Y-H Choi K S Kim and S-M Choi ldquoSimplified P-M interac-tion curve for square steel tube filled with high-strength con-creterdquoThin-Walled Structures vol 46 no 5 pp 506ndash515 2008

[3] T KrauthammerModern Protective Structures TaylorampFrancisGroup New York NY USA 2008

[4] S C Fujikura M Bruneau and D Lopez-Garcia ldquoExperimen-tal investigation of blast performance of seismically resistantconcrete-filled steel tube bridge piersrdquo Tech Rep MCEER-07-0005 University at Buffalo Buffalo NY USA 2007

[5] S Fujikura M Bruneau and D Lopez-Garcia ldquoExperimentalinvestigation of multihazard resistant bridge piers having con-crete-filled steel tube under blast loadingrdquo Journal of BridgeEngineering vol 13 no 6 pp 586ndash594 2008

[6] G Li H Qu T Yang Y Lu and S Chen ldquoExperimental studyof concrete-filled steel tubular columns under blast loadingrdquoJianzhu Jiegou Xuebao vol 34 no 12 pp 69ndash76 2013 (Chinese)

[7] A M Remennikov and B Uy ldquoExplosive testing andmodellingof square tubular steel columns for near-field detonationsrdquo Jour-nal of Constructional Steel Research vol 101 pp 290ndash303 2014

[8] T Ngo D Mohotti A Remennikov and B Uy ldquoNumericalsimulations of response of tubular steel beams to close-rangeexplosionsrdquo Journal of Constructional Steel Research vol 105 pp151ndash163 2015

[9] F R Zhang C Q Wu H W Wang and Y Zhou ldquoNumericalsimulation of concrete filled steel tube columns against BLASTloadsrdquoThin-Walled Structures vol 92 pp 82ndash92 2015

[10] F Zhang C Wu X Zhao Z Li A Heidarpour and H WangldquoNumerical modeling of concrete-filled double-skin steelsquare tubular columns under blast loadingrdquo Journal of Per-formance of Constructed Facilities vol 29 no 5 Article IDB4015002 2015

[11] Livermore Software Technology Corporation LS-DYNA Theo-retical Manual Livermore Software Technology CorporationLivermore Calif USA 1998

[12] G R Cowper and P S Symonds ldquoStrain-hardening and strain-rate effects in the impact loading of cantilever beamsrdquo TechRep AD144762 Office of Naval Research Arlington Va USA1958

[13] T J Holmquist G R Johnson and W H Cook ldquoA computa-tional constitutive model for concrete subjected to large strainshigh strain rates and high pressuresrdquo in Proceedings of the 14thInternational Symposium on Ballistics Quebec City CanadaSeptember 1993

[14] Q Fang and J Zhang ldquoThree-dimensional modelling of steelfiber reinforced concrete material under intense dynamic load-ingrdquo Construction and Building Materials vol 44 pp 118ndash1322013

[15] Y Li F Lin X L Gu and X Q Lu ldquoNumerical researchof a super-large cooling tower subjected to accidental loadsrdquoNuclear Engineering and Design vol 269 pp 184ndash192 2014

[16] J Li and H Hao ldquoNumerical study of concrete spall damage toblast loadsrdquo International Journal of Impact Engineering vol 68pp 41ndash55 2014

[17] G Randers-Pehrson and K A Bannister ldquoAirblast loadingmodel for DYNA2D and DYNA3Drdquo Tech Rep ARL-TR-1310Army Research Laboratory Adelphi Md USA 1997

[18] Livermore Software Technology Corporation LS-DYNA Key-word Userrsquos Manual (Version 971 R610) Livermore SoftwareTechnology Corporation Livermore Calif USA 2012

[19] CECS ldquoTechnical specification for structures with concrete-filled rectangular steel tube membersrdquo CECS 1592004 ChinaAssociation for Engineering Construction StandardizationBeijing China 2004 (Chinese)

[20] Y Shi H Hao and Z-X Li ldquoNumerical derivation of pressure-impulse diagrams for prediction of RC column damage to blastloadsrdquo International Journal of Impact Engineering vol 35 no11 pp 1213ndash1227 2008

[21] P D Smith and J G Hetherington Blast and Ballistic Loadingof Structures Butterowrth-Heinemenn Oxford UK 1994

[22] K-C Wu B Li and K-C Tsai ldquoThe effects of explosive massratio on residual compressive capacity of contact blast damagedcomposite columnsrdquo Journal of Constructional Steel Researchvol 67 no 4 pp 602ndash612 2011

[23] J E Crawford K B Morrill and J M Magallanes ldquoProtectivedesign for columns against close-in blast effectsrdquo in Proceedingsof the Structures Congress Boston Mass USA April 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Shock and Vibration

First-floor column

Second-floor column

Explosive

Second-floor beam

h

HB

X

(a) Explosion scenario

1 1

Section 1-1

Steel tube

Infill concrete

Axial load

Head

Footing

First-floor column

h d t

w

(b) Column details

Figure 6 Sketch of the numerical analysis model

Figure 8 shows the shear damage mode of the columnresulted from 250 kg of TNT detonating on the ground atthe scaled standoff distance of 033mkg13 Due to the largeshear force and the development of shear deformation nearthe supports the infill concrete was sheared off accompaniedwith the rupture of the steel tube around the cross section ofthe column Finally the column failed in brittle shear beforeany ductile flexural hinge developed

As discussed above flexural damage and shear damageof the column are due to the deformation and internal forceof the whole member induced by the blast loads On thecontrary localized damage of the CFST column is dominatedby the deformation and failure of the concrete infill and steeltube in the vicinity of the explosion whilst other parts of thecolumn remain almost elastic and the global deformation ofthe column is small

Figure 9 shows the localized damage mode of the CFSTcolumn caused by the detonation of 50 kg of TNT on theground with the scaled standoff distance of 018mkg13When the impulsive shock front of high intensity metthe column surface the stress waves were generated andpropagated from the tube front surface towards the concreteinfill and the lateral and back surfaces of the tube Then theconcrete close to the explosion was cracked and crushed andthe front side of the tube which lost the internal support ofthe concrete fill was squashed with the bulging of its lateraland back sides As the localized deformation of the columnevolved rupture and local buckling failure of the steel tubetook place yet the global lateral deformation of the columnhad almost not developed at this moment

It should bementioned that these damagemodes are onlytypical ones Sometimes there exists a combination of thesedamage modes

4 Damage Assessment of CFST Columnsunder Blast Loading

41 Damage Criterion As discussed previously the CFSTcolumn subjected to blast loads may undergo flexural dam-age shear damage and localized damage thus the damagecriterion for the column should be chosen carefully andthe appropriate one is expected to be applicable to all thepossible damage modes of the column In this paper thedamage criterion based on the residual axial load capacityis adopted for CFST columns due to the following reasons(1) the structure column is primarily designed to carry theaxial load and the axial load capacity of it reflects bothits global properties and material characteristics (2) thecommonly used deformation-based damage criterions thatis the support rotation lateral deflection and ductility maynot be appropriate for the evaluation of localized damage ofthe column and (3) the residual axial load capacity of thecolumns is an explicit metric of the damage imparted and italso provides information in assessing the collapse possibilityof a blast damaged column

The damage index adopted herein is based on the indexfrom Shi et al [20] and is expressed as

119863119888

= 1 minus

119875residual119875max

(7)

where 119863119888

is the damage degree of CFST columns 119875residual isthe residual axial load capacity of the column after blast loadsand 119875max is the maximum axial load capacity of the columnprior to blast loading Values of 119863

119888

vary between 0 (ieno loss of capacity) and 10 (ie complete loss of capacity)Note that in the paper by Shi et al [20] the maximumaxial load capacity of an undamaged column is calculated

Shock and Vibration 7

Fringe levels

3793eminus02

3161e

minus02

2529eminus02

1897eminus02

1264eminus02

6322eminus03

0000e

+00

(a) CFST column

Fringe levels

3793eminus02

3161e

minus02

2529eminus02

1897eminus02

1264eminus02

6322eminus03

0000e

+00

(b) Infill concrete

Figure 7 Flexural damage mode of CFST column under blast loading

Fringe levels

2000e

minus01

1667eminus01

1333eminus01

1000e

minus01

6667eminus02

3333eminus02

0000e

+00

(a) CFST column

Fringe levels

2392e

minus02

1993eminus02

1594eminus02

1196eminus02

7972e

minus03

3986eminus03

0000e

+00

(b) Infill concrete

Figure 8 Shear damage mode of CFST column under blast loading

8 Shock and Vibration

Fringe levels

2000e

minus01

1667eminus01

1333eminus01

1000e

minus01

6667eminus02

3333eminus02

0000e

+00

(a) CFST column

Fringe levels

2597eminus02

2165eminus02

1732e

minus02

1299eminus02

8658e

minus03

4329eminus03

0000e

+00

(b) Infill concrete

Figure 9 Localized damage mode of CFST column under blast loading

with the provided equation from the standard design codewhich however may lead to the values of119863

119888

below 0 in somecases Therefore both 119875residual and 119875max are determined fromnumerical simulation in this study Here 119875residual119875max is alsotermed as the residual capacity index (RCI) used byWu et al[22] andCrawford et al [23] to assess the damage level of steelreinforced concrete (SRC) columns and reinforced concrete(RC) columns subjected to blast loads

It is noted that if the ratio of the service axial load tomaximum axial load capacity of the column is denoted as 119899then a column whose119863

119888

is greater than (1 minus 119899) is consideredas failed or collapsed since its residual axial load capacity isnot sufficient for the service axial load

42 Steps for Damage Assessment of CFST Columns

Step 1 (derivation of 119875max) During this step the linearlyincreasing axial load is applied on the column head until thecolumn collapses then 119875max is determined as the maximumaxial load that the column can withstand

Step 2 (derivation of 119875residual) Three substeps as follows arerequired to obtain 119875residual (1) before blast loading a linearlyincreasing axial load up to the service axial load is imposedon the column (2) blast loads are applied over the front faceof the column with the service axial load being constant andcalculation is stopped when the damaged column approachesstatic equilibrium (3) a linearly increasing axial load isimposed on the top of the damaged column until it collapses

then 119875residual is determined as the peak of the axial load thatthe damaged column can bear

Step 3 (determination of 119863119888

) Substitute the values of 119875maxand 119875residual into (7) to obtain119863119888

43 Parameters Studied In this section effects of severalkey parameters on the damage degree of CFST columnsare analyzed These parameters include the scaled standoffdistance height of burst explosive mass column depthcolumn width column steel ratio and axial load ratio aslisted in Table 4 in which a contrast case is generated bychanging one of the parameters considered in the benchmarkcase while keeping other parameters unchanged Note thatin each case varied scaled standoff distances are consideredso that the effects aforementioned parameters on the damagedegree of columns within different blast loading regimes canbe assessed

431 Effect of Scaled Standoff Distance 119885 The numericalsimulation results show that 119863

119888

of CFST columns decreaseswith the increasing scaled standoff distance regardless ofother parameters This is because column damage is affectedby the peak overpressure and impulse of the blast wave[21] and both of them drop with the rising scaled standoffdistance which results in a small degree of column damage

432 Effect of Height of Burst119867119861

It is difficult to characterizethe effect of 119867

119861

on the damage degree of the column On

Shock and Vibration 9

Table 4 Parameters used in the numerical parametric study

Parameters 119885 (mkg13) 119867119861

(m) 119872 (kg) 119889 (m) 119908 (m) Steel ratio 120572lowast Axial load ratio 119899Benchmark case 018ndash050 0 50 06 06 013 035Contrast cases 015ndash090 185 250 500 09 12 09 12 016 019 050 065lowast

120572 = 119860119904

119860119888

119860119904

and 119860119888

are the cross-sectional areas of steel tube and infill concrete respectively

07

06

05

04

03

02

01

00

HB = 0mHB = 185m

015 020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

Figure 10 Effects of height of burst on the damage degree

one hand when 119867119861

nears zero the initial blast wave isimmediately reflected and reinforced by the ground On theother the mid-height of the column is expected to surfer themost severe damage due to lack of transverse support Conse-quently as shown in Figure 10 surface burst results in severerdamage to the column than that caused by explosion atcolumnmid-height (119867

119861

= 185m) especially when the stand-off distance is small The effects of119867

119861

on the damage degreeof the column are insignificant at large scaled distancesbecause both the overpressure and impulse on the columnare relatively small in these cases

433 Effect of Explosive Mass119872 Figure 11 shows the effectsof explosive mass on the damage degree of the columnInspections of the figure show that 119863

119888

rises with 119872 for thesame scaled standoff distance indicating that CFST columnis impulse-sensitive since explosive with larger mass hasrelatively more impulse for the column

434 Effects of Column Width 119908 and Depth 119889 Effects ofcolumn depth and width on 119863

119888

are shown in Figure 12Comparedwith the reference column (119908 = 06m 119889 = 06m)columns with larger width and depth tend to have lowerdamage degrees because expanding columnwidth and depthproduces a larger cross section for attenuation of the stresswaves density and contributes to enhancement of the shearresistance as well as flexural strength of the columnHoweverit is found that columns with the same cross section area butdifferent width and depth have varied damage degrees and

07

06

05

04

03

02

01

0002 03 04 05 06 07 08 09 10

Scaled standoff distance Z (mkg13)

M = 50kgM = 250kgM = 500kg

[HB = 0m] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 11 Effects of explosive mass on the damage degree

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

w = 06m d = 06mw = 09m d = 06mw = 12m d = 06m

w = 06m d = 09mw = 06m d = 12m

[HB = 0m] [M = 50kg] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 12 Effects of width and depth on the damage degree

that compared with increasing the column width incrementof the column depth is more effective in reducing the columndamage degree This is because enlarging the column widthsimultaneously results in a rise of blast loads acting on thecolumnwhich balances out the enhancement of columnblastresistance to some extent

10 Shock and Vibration

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

120572 = 013

120572 = 016

120572 = 019

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [n = 035 ]

Dam

age d

egre

eDc

Figure 13 Effects of steel ratio on the damage degree

07

06

05

04

03

02

01

00020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

n = 035

n = 050

n = 065

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [120572 = 013]

Dam

age d

egre

eDc

Figure 14 Effects of axial load ratio on the damage degree

435 Effect of Column Steel Ratio 120572 As shown in Figure 13119863119888

drops with the rising steel ratio This is expected becauseincreasing 120572means a larger steel area and better confinementof infill concrete which will enhance the shear and bendingstrength of the column as well as its resistance to localizeddamage

436 Effect of Column Axial Load Ratio 119899 Effects of axialload ratio on 119863

119888

are shown in Figure 14 Inspection of thefigure reveals that axial load ratio has dual influences on col-umn damage When the scaled standoff is small the columnwith a larger axial load ratio has lower damage degree Thisis because the column under small scaled standoff is likelyto suffer localized damage and shear damage and a higher

axial load will restrain the cracking and crushing of concretewhich enhances the resistance of the column to localizeddamage and shear damage In contrast at a large scaledstandoff distance the column with larger axial load ratio hashigher damage degree The reason is that with the increaseof the scaled standoff distance the column tends to sufferflexural damage which is related to its moment capacity andductility The larger the moment capacity and ductility arethe lower the damage degree is For the CFST column studiedin this section the axial load ratio at the maximum momentcapacity is 022 which is derived by the methods from Choiet al [1] According to the axial load-bending moment (P-M)interactions the moment capacity of the CFST column willdecrease when 119899 rises from 035 to 060 Moreover a risingaxial load will reduce the ductility of the CFST column

44 Empirical Equations for Determining the Damage Degreeof CFST Columns The parametric study revealed the signif-icance of parameters affecting the damage degree of CFSTcolumns Through the multivariable regression analysis anempirical equation is proposed in terms of various parame-ters to predict the damage degree and is expressed as follows

119863119888

= [minus1505 ln(11987250

) + 1650 (

119908

06

) minus 3242 (

119889

06

)

minus 131625120572 + 15349119899 + 25011]

sdot 119890[minus648ln(11987250)+533(11990806)minus1091(11988906)minus373minus1230120572+1292119899+2681]119885

(8)

The comparisons of the proposed equation with the ana-lytical results are shown in Figures 15(a)ndash15(f) The scattersdenote the analytical results and the solid lines represent theproposed equation Observation of these figures shows thatthe proposed curves are close to the analytical results formostcases The effects of height of burst on the damage degree ofCFST columns are not reflected by (8) due to the lack of blastdata in the lower height of the column which are limited inthe ConWep model and will be supplemented in the furtherstudies

5 Conclusions

This paper presents a 3D numerical model to investigate thedamage modes and damage assessment of CFST columnsBased on the numerical analysis results the following con-clusions can be drawn

CFST columns under blast loading may undergo theglobal flexural damage and shear damage as well as localizeddamage Flexural damage and shear damage of the columnare mainly attributed to the deformation and internal force ofthe whole member whilst the localized damage is dominatedby the failure of infill concrete and steel tube in the vicinity ofthe explosion

The damage criterion based on the residual axial loadcapacity is adopted for assessing the degree of CFST columnsdamage to blast loadsThrough parametric studies it is foundthat the damage degree of CFST columns decays nearlyexponentially with the increasing scaled standoff distance

Shock and Vibration 11

07

06

05

04

03

02

01

00

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

Dam

age d

egre

eDc

(a)

07

06

05

04

03

02

01

00095090085050 055 060 065 070 075 080

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 500kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

(b)

07

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 12m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

(c)

020

015

010

005

000

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 12m] [120572 = 013] [n = 035]D

amag

e deg

reeD

c

(d)

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 019] [n = 035]

Dam

age d

egre

eDc

(e)

020

025

030

035

015

010

005

000055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 065]

Dam

age d

egre

eDc

(f)

Figure 15 Comparison of analytical results with the proposed curves

12 Shock and Vibration

For the same scaled standoff distance surface burst results inseverer damage to the column than that caused by explosionat columnmid-height and the damage degree increases withthe rising explosive mass and decreases with column depthand width and steel ratio Increasing the axial load enhancesthe resistance of the column against localized damage andshear damage while the effects of axial load on flexuraldamage depend on the axial load-bending moment (P-M)interactions of the column

An equation is derived by fitting the results of parametricstudies to estimate the damage degree of CFST columnsTypical examples confirm that the proposed equation wellrepresents the variation of the column damage degree How-ever future experiments can be conducted for investigatingthe effects of other parameters on the damage degree of CFSTcolumns

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research described in this paper was financially sup-ported by Achievement Transfer Program of Institutionsof Higher Education in Chongqing under Grant noKJZH14220

References

[1] Y-H Choi D A Foutch and J M LaFave ldquoNew approachto AISC P-M interaction curve for square concrete filled tube(CFT) beamndashcolumnsrdquo Engineering Structures vol 28 no 11pp 1586ndash1598 2006

[2] Y-H Choi K S Kim and S-M Choi ldquoSimplified P-M interac-tion curve for square steel tube filled with high-strength con-creterdquoThin-Walled Structures vol 46 no 5 pp 506ndash515 2008

[3] T KrauthammerModern Protective Structures TaylorampFrancisGroup New York NY USA 2008

[4] S C Fujikura M Bruneau and D Lopez-Garcia ldquoExperimen-tal investigation of blast performance of seismically resistantconcrete-filled steel tube bridge piersrdquo Tech Rep MCEER-07-0005 University at Buffalo Buffalo NY USA 2007

[5] S Fujikura M Bruneau and D Lopez-Garcia ldquoExperimentalinvestigation of multihazard resistant bridge piers having con-crete-filled steel tube under blast loadingrdquo Journal of BridgeEngineering vol 13 no 6 pp 586ndash594 2008

[6] G Li H Qu T Yang Y Lu and S Chen ldquoExperimental studyof concrete-filled steel tubular columns under blast loadingrdquoJianzhu Jiegou Xuebao vol 34 no 12 pp 69ndash76 2013 (Chinese)

[7] A M Remennikov and B Uy ldquoExplosive testing andmodellingof square tubular steel columns for near-field detonationsrdquo Jour-nal of Constructional Steel Research vol 101 pp 290ndash303 2014

[8] T Ngo D Mohotti A Remennikov and B Uy ldquoNumericalsimulations of response of tubular steel beams to close-rangeexplosionsrdquo Journal of Constructional Steel Research vol 105 pp151ndash163 2015

[9] F R Zhang C Q Wu H W Wang and Y Zhou ldquoNumericalsimulation of concrete filled steel tube columns against BLASTloadsrdquoThin-Walled Structures vol 92 pp 82ndash92 2015

[10] F Zhang C Wu X Zhao Z Li A Heidarpour and H WangldquoNumerical modeling of concrete-filled double-skin steelsquare tubular columns under blast loadingrdquo Journal of Per-formance of Constructed Facilities vol 29 no 5 Article IDB4015002 2015

[11] Livermore Software Technology Corporation LS-DYNA Theo-retical Manual Livermore Software Technology CorporationLivermore Calif USA 1998

[12] G R Cowper and P S Symonds ldquoStrain-hardening and strain-rate effects in the impact loading of cantilever beamsrdquo TechRep AD144762 Office of Naval Research Arlington Va USA1958

[13] T J Holmquist G R Johnson and W H Cook ldquoA computa-tional constitutive model for concrete subjected to large strainshigh strain rates and high pressuresrdquo in Proceedings of the 14thInternational Symposium on Ballistics Quebec City CanadaSeptember 1993

[14] Q Fang and J Zhang ldquoThree-dimensional modelling of steelfiber reinforced concrete material under intense dynamic load-ingrdquo Construction and Building Materials vol 44 pp 118ndash1322013

[15] Y Li F Lin X L Gu and X Q Lu ldquoNumerical researchof a super-large cooling tower subjected to accidental loadsrdquoNuclear Engineering and Design vol 269 pp 184ndash192 2014

[16] J Li and H Hao ldquoNumerical study of concrete spall damage toblast loadsrdquo International Journal of Impact Engineering vol 68pp 41ndash55 2014

[17] G Randers-Pehrson and K A Bannister ldquoAirblast loadingmodel for DYNA2D and DYNA3Drdquo Tech Rep ARL-TR-1310Army Research Laboratory Adelphi Md USA 1997

[18] Livermore Software Technology Corporation LS-DYNA Key-word Userrsquos Manual (Version 971 R610) Livermore SoftwareTechnology Corporation Livermore Calif USA 2012

[19] CECS ldquoTechnical specification for structures with concrete-filled rectangular steel tube membersrdquo CECS 1592004 ChinaAssociation for Engineering Construction StandardizationBeijing China 2004 (Chinese)

[20] Y Shi H Hao and Z-X Li ldquoNumerical derivation of pressure-impulse diagrams for prediction of RC column damage to blastloadsrdquo International Journal of Impact Engineering vol 35 no11 pp 1213ndash1227 2008

[21] P D Smith and J G Hetherington Blast and Ballistic Loadingof Structures Butterowrth-Heinemenn Oxford UK 1994

[22] K-C Wu B Li and K-C Tsai ldquoThe effects of explosive massratio on residual compressive capacity of contact blast damagedcomposite columnsrdquo Journal of Constructional Steel Researchvol 67 no 4 pp 602ndash612 2011

[23] J E Crawford K B Morrill and J M Magallanes ldquoProtectivedesign for columns against close-in blast effectsrdquo in Proceedingsof the Structures Congress Boston Mass USA April 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 7

Fringe levels

3793eminus02

3161e

minus02

2529eminus02

1897eminus02

1264eminus02

6322eminus03

0000e

+00

(a) CFST column

Fringe levels

3793eminus02

3161e

minus02

2529eminus02

1897eminus02

1264eminus02

6322eminus03

0000e

+00

(b) Infill concrete

Figure 7 Flexural damage mode of CFST column under blast loading

Fringe levels

2000e

minus01

1667eminus01

1333eminus01

1000e

minus01

6667eminus02

3333eminus02

0000e

+00

(a) CFST column

Fringe levels

2392e

minus02

1993eminus02

1594eminus02

1196eminus02

7972e

minus03

3986eminus03

0000e

+00

(b) Infill concrete

Figure 8 Shear damage mode of CFST column under blast loading

8 Shock and Vibration

Fringe levels

2000e

minus01

1667eminus01

1333eminus01

1000e

minus01

6667eminus02

3333eminus02

0000e

+00

(a) CFST column

Fringe levels

2597eminus02

2165eminus02

1732e

minus02

1299eminus02

8658e

minus03

4329eminus03

0000e

+00

(b) Infill concrete

Figure 9 Localized damage mode of CFST column under blast loading

with the provided equation from the standard design codewhich however may lead to the values of119863

119888

below 0 in somecases Therefore both 119875residual and 119875max are determined fromnumerical simulation in this study Here 119875residual119875max is alsotermed as the residual capacity index (RCI) used byWu et al[22] andCrawford et al [23] to assess the damage level of steelreinforced concrete (SRC) columns and reinforced concrete(RC) columns subjected to blast loads

It is noted that if the ratio of the service axial load tomaximum axial load capacity of the column is denoted as 119899then a column whose119863

119888

is greater than (1 minus 119899) is consideredas failed or collapsed since its residual axial load capacity isnot sufficient for the service axial load

42 Steps for Damage Assessment of CFST Columns

Step 1 (derivation of 119875max) During this step the linearlyincreasing axial load is applied on the column head until thecolumn collapses then 119875max is determined as the maximumaxial load that the column can withstand

Step 2 (derivation of 119875residual) Three substeps as follows arerequired to obtain 119875residual (1) before blast loading a linearlyincreasing axial load up to the service axial load is imposedon the column (2) blast loads are applied over the front faceof the column with the service axial load being constant andcalculation is stopped when the damaged column approachesstatic equilibrium (3) a linearly increasing axial load isimposed on the top of the damaged column until it collapses

then 119875residual is determined as the peak of the axial load thatthe damaged column can bear

Step 3 (determination of 119863119888

) Substitute the values of 119875maxand 119875residual into (7) to obtain119863119888

43 Parameters Studied In this section effects of severalkey parameters on the damage degree of CFST columnsare analyzed These parameters include the scaled standoffdistance height of burst explosive mass column depthcolumn width column steel ratio and axial load ratio aslisted in Table 4 in which a contrast case is generated bychanging one of the parameters considered in the benchmarkcase while keeping other parameters unchanged Note thatin each case varied scaled standoff distances are consideredso that the effects aforementioned parameters on the damagedegree of columns within different blast loading regimes canbe assessed

431 Effect of Scaled Standoff Distance 119885 The numericalsimulation results show that 119863

119888

of CFST columns decreaseswith the increasing scaled standoff distance regardless ofother parameters This is because column damage is affectedby the peak overpressure and impulse of the blast wave[21] and both of them drop with the rising scaled standoffdistance which results in a small degree of column damage

432 Effect of Height of Burst119867119861

It is difficult to characterizethe effect of 119867

119861

on the damage degree of the column On

Shock and Vibration 9

Table 4 Parameters used in the numerical parametric study

Parameters 119885 (mkg13) 119867119861

(m) 119872 (kg) 119889 (m) 119908 (m) Steel ratio 120572lowast Axial load ratio 119899Benchmark case 018ndash050 0 50 06 06 013 035Contrast cases 015ndash090 185 250 500 09 12 09 12 016 019 050 065lowast

120572 = 119860119904

119860119888

119860119904

and 119860119888

are the cross-sectional areas of steel tube and infill concrete respectively

07

06

05

04

03

02

01

00

HB = 0mHB = 185m

015 020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

Figure 10 Effects of height of burst on the damage degree

one hand when 119867119861

nears zero the initial blast wave isimmediately reflected and reinforced by the ground On theother the mid-height of the column is expected to surfer themost severe damage due to lack of transverse support Conse-quently as shown in Figure 10 surface burst results in severerdamage to the column than that caused by explosion atcolumnmid-height (119867

119861

= 185m) especially when the stand-off distance is small The effects of119867

119861

on the damage degreeof the column are insignificant at large scaled distancesbecause both the overpressure and impulse on the columnare relatively small in these cases

433 Effect of Explosive Mass119872 Figure 11 shows the effectsof explosive mass on the damage degree of the columnInspections of the figure show that 119863

119888

rises with 119872 for thesame scaled standoff distance indicating that CFST columnis impulse-sensitive since explosive with larger mass hasrelatively more impulse for the column

434 Effects of Column Width 119908 and Depth 119889 Effects ofcolumn depth and width on 119863

119888

are shown in Figure 12Comparedwith the reference column (119908 = 06m 119889 = 06m)columns with larger width and depth tend to have lowerdamage degrees because expanding columnwidth and depthproduces a larger cross section for attenuation of the stresswaves density and contributes to enhancement of the shearresistance as well as flexural strength of the columnHoweverit is found that columns with the same cross section area butdifferent width and depth have varied damage degrees and

07

06

05

04

03

02

01

0002 03 04 05 06 07 08 09 10

Scaled standoff distance Z (mkg13)

M = 50kgM = 250kgM = 500kg

[HB = 0m] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 11 Effects of explosive mass on the damage degree

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

w = 06m d = 06mw = 09m d = 06mw = 12m d = 06m

w = 06m d = 09mw = 06m d = 12m

[HB = 0m] [M = 50kg] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 12 Effects of width and depth on the damage degree

that compared with increasing the column width incrementof the column depth is more effective in reducing the columndamage degree This is because enlarging the column widthsimultaneously results in a rise of blast loads acting on thecolumnwhich balances out the enhancement of columnblastresistance to some extent

10 Shock and Vibration

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

120572 = 013

120572 = 016

120572 = 019

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [n = 035 ]

Dam

age d

egre

eDc

Figure 13 Effects of steel ratio on the damage degree

07

06

05

04

03

02

01

00020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

n = 035

n = 050

n = 065

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [120572 = 013]

Dam

age d

egre

eDc

Figure 14 Effects of axial load ratio on the damage degree

435 Effect of Column Steel Ratio 120572 As shown in Figure 13119863119888

drops with the rising steel ratio This is expected becauseincreasing 120572means a larger steel area and better confinementof infill concrete which will enhance the shear and bendingstrength of the column as well as its resistance to localizeddamage

436 Effect of Column Axial Load Ratio 119899 Effects of axialload ratio on 119863

119888

are shown in Figure 14 Inspection of thefigure reveals that axial load ratio has dual influences on col-umn damage When the scaled standoff is small the columnwith a larger axial load ratio has lower damage degree Thisis because the column under small scaled standoff is likelyto suffer localized damage and shear damage and a higher

axial load will restrain the cracking and crushing of concretewhich enhances the resistance of the column to localizeddamage and shear damage In contrast at a large scaledstandoff distance the column with larger axial load ratio hashigher damage degree The reason is that with the increaseof the scaled standoff distance the column tends to sufferflexural damage which is related to its moment capacity andductility The larger the moment capacity and ductility arethe lower the damage degree is For the CFST column studiedin this section the axial load ratio at the maximum momentcapacity is 022 which is derived by the methods from Choiet al [1] According to the axial load-bending moment (P-M)interactions the moment capacity of the CFST column willdecrease when 119899 rises from 035 to 060 Moreover a risingaxial load will reduce the ductility of the CFST column

44 Empirical Equations for Determining the Damage Degreeof CFST Columns The parametric study revealed the signif-icance of parameters affecting the damage degree of CFSTcolumns Through the multivariable regression analysis anempirical equation is proposed in terms of various parame-ters to predict the damage degree and is expressed as follows

119863119888

= [minus1505 ln(11987250

) + 1650 (

119908

06

) minus 3242 (

119889

06

)

minus 131625120572 + 15349119899 + 25011]

sdot 119890[minus648ln(11987250)+533(11990806)minus1091(11988906)minus373minus1230120572+1292119899+2681]119885

(8)

The comparisons of the proposed equation with the ana-lytical results are shown in Figures 15(a)ndash15(f) The scattersdenote the analytical results and the solid lines represent theproposed equation Observation of these figures shows thatthe proposed curves are close to the analytical results formostcases The effects of height of burst on the damage degree ofCFST columns are not reflected by (8) due to the lack of blastdata in the lower height of the column which are limited inthe ConWep model and will be supplemented in the furtherstudies

5 Conclusions

This paper presents a 3D numerical model to investigate thedamage modes and damage assessment of CFST columnsBased on the numerical analysis results the following con-clusions can be drawn

CFST columns under blast loading may undergo theglobal flexural damage and shear damage as well as localizeddamage Flexural damage and shear damage of the columnare mainly attributed to the deformation and internal force ofthe whole member whilst the localized damage is dominatedby the failure of infill concrete and steel tube in the vicinity ofthe explosion

The damage criterion based on the residual axial loadcapacity is adopted for assessing the degree of CFST columnsdamage to blast loadsThrough parametric studies it is foundthat the damage degree of CFST columns decays nearlyexponentially with the increasing scaled standoff distance

Shock and Vibration 11

07

06

05

04

03

02

01

00

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

Dam

age d

egre

eDc

(a)

07

06

05

04

03

02

01

00095090085050 055 060 065 070 075 080

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 500kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

(b)

07

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 12m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

(c)

020

015

010

005

000

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 12m] [120572 = 013] [n = 035]D

amag

e deg

reeD

c

(d)

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 019] [n = 035]

Dam

age d

egre

eDc

(e)

020

025

030

035

015

010

005

000055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 065]

Dam

age d

egre

eDc

(f)

Figure 15 Comparison of analytical results with the proposed curves

12 Shock and Vibration

For the same scaled standoff distance surface burst results inseverer damage to the column than that caused by explosionat columnmid-height and the damage degree increases withthe rising explosive mass and decreases with column depthand width and steel ratio Increasing the axial load enhancesthe resistance of the column against localized damage andshear damage while the effects of axial load on flexuraldamage depend on the axial load-bending moment (P-M)interactions of the column

An equation is derived by fitting the results of parametricstudies to estimate the damage degree of CFST columnsTypical examples confirm that the proposed equation wellrepresents the variation of the column damage degree How-ever future experiments can be conducted for investigatingthe effects of other parameters on the damage degree of CFSTcolumns

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research described in this paper was financially sup-ported by Achievement Transfer Program of Institutionsof Higher Education in Chongqing under Grant noKJZH14220

References

[1] Y-H Choi D A Foutch and J M LaFave ldquoNew approachto AISC P-M interaction curve for square concrete filled tube(CFT) beamndashcolumnsrdquo Engineering Structures vol 28 no 11pp 1586ndash1598 2006

[2] Y-H Choi K S Kim and S-M Choi ldquoSimplified P-M interac-tion curve for square steel tube filled with high-strength con-creterdquoThin-Walled Structures vol 46 no 5 pp 506ndash515 2008

[3] T KrauthammerModern Protective Structures TaylorampFrancisGroup New York NY USA 2008

[4] S C Fujikura M Bruneau and D Lopez-Garcia ldquoExperimen-tal investigation of blast performance of seismically resistantconcrete-filled steel tube bridge piersrdquo Tech Rep MCEER-07-0005 University at Buffalo Buffalo NY USA 2007

[5] S Fujikura M Bruneau and D Lopez-Garcia ldquoExperimentalinvestigation of multihazard resistant bridge piers having con-crete-filled steel tube under blast loadingrdquo Journal of BridgeEngineering vol 13 no 6 pp 586ndash594 2008

[6] G Li H Qu T Yang Y Lu and S Chen ldquoExperimental studyof concrete-filled steel tubular columns under blast loadingrdquoJianzhu Jiegou Xuebao vol 34 no 12 pp 69ndash76 2013 (Chinese)

[7] A M Remennikov and B Uy ldquoExplosive testing andmodellingof square tubular steel columns for near-field detonationsrdquo Jour-nal of Constructional Steel Research vol 101 pp 290ndash303 2014

[8] T Ngo D Mohotti A Remennikov and B Uy ldquoNumericalsimulations of response of tubular steel beams to close-rangeexplosionsrdquo Journal of Constructional Steel Research vol 105 pp151ndash163 2015

[9] F R Zhang C Q Wu H W Wang and Y Zhou ldquoNumericalsimulation of concrete filled steel tube columns against BLASTloadsrdquoThin-Walled Structures vol 92 pp 82ndash92 2015

[10] F Zhang C Wu X Zhao Z Li A Heidarpour and H WangldquoNumerical modeling of concrete-filled double-skin steelsquare tubular columns under blast loadingrdquo Journal of Per-formance of Constructed Facilities vol 29 no 5 Article IDB4015002 2015

[11] Livermore Software Technology Corporation LS-DYNA Theo-retical Manual Livermore Software Technology CorporationLivermore Calif USA 1998

[12] G R Cowper and P S Symonds ldquoStrain-hardening and strain-rate effects in the impact loading of cantilever beamsrdquo TechRep AD144762 Office of Naval Research Arlington Va USA1958

[13] T J Holmquist G R Johnson and W H Cook ldquoA computa-tional constitutive model for concrete subjected to large strainshigh strain rates and high pressuresrdquo in Proceedings of the 14thInternational Symposium on Ballistics Quebec City CanadaSeptember 1993

[14] Q Fang and J Zhang ldquoThree-dimensional modelling of steelfiber reinforced concrete material under intense dynamic load-ingrdquo Construction and Building Materials vol 44 pp 118ndash1322013

[15] Y Li F Lin X L Gu and X Q Lu ldquoNumerical researchof a super-large cooling tower subjected to accidental loadsrdquoNuclear Engineering and Design vol 269 pp 184ndash192 2014

[16] J Li and H Hao ldquoNumerical study of concrete spall damage toblast loadsrdquo International Journal of Impact Engineering vol 68pp 41ndash55 2014

[17] G Randers-Pehrson and K A Bannister ldquoAirblast loadingmodel for DYNA2D and DYNA3Drdquo Tech Rep ARL-TR-1310Army Research Laboratory Adelphi Md USA 1997

[18] Livermore Software Technology Corporation LS-DYNA Key-word Userrsquos Manual (Version 971 R610) Livermore SoftwareTechnology Corporation Livermore Calif USA 2012

[19] CECS ldquoTechnical specification for structures with concrete-filled rectangular steel tube membersrdquo CECS 1592004 ChinaAssociation for Engineering Construction StandardizationBeijing China 2004 (Chinese)

[20] Y Shi H Hao and Z-X Li ldquoNumerical derivation of pressure-impulse diagrams for prediction of RC column damage to blastloadsrdquo International Journal of Impact Engineering vol 35 no11 pp 1213ndash1227 2008

[21] P D Smith and J G Hetherington Blast and Ballistic Loadingof Structures Butterowrth-Heinemenn Oxford UK 1994

[22] K-C Wu B Li and K-C Tsai ldquoThe effects of explosive massratio on residual compressive capacity of contact blast damagedcomposite columnsrdquo Journal of Constructional Steel Researchvol 67 no 4 pp 602ndash612 2011

[23] J E Crawford K B Morrill and J M Magallanes ldquoProtectivedesign for columns against close-in blast effectsrdquo in Proceedingsof the Structures Congress Boston Mass USA April 2014

International Journal of

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Active and Passive Electronic Components

Control Scienceand Engineering

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

8 Shock and Vibration

Fringe levels

2000e

minus01

1667eminus01

1333eminus01

1000e

minus01

6667eminus02

3333eminus02

0000e

+00

(a) CFST column

Fringe levels

2597eminus02

2165eminus02

1732e

minus02

1299eminus02

8658e

minus03

4329eminus03

0000e

+00

(b) Infill concrete

Figure 9 Localized damage mode of CFST column under blast loading

with the provided equation from the standard design codewhich however may lead to the values of119863

119888

below 0 in somecases Therefore both 119875residual and 119875max are determined fromnumerical simulation in this study Here 119875residual119875max is alsotermed as the residual capacity index (RCI) used byWu et al[22] andCrawford et al [23] to assess the damage level of steelreinforced concrete (SRC) columns and reinforced concrete(RC) columns subjected to blast loads

It is noted that if the ratio of the service axial load tomaximum axial load capacity of the column is denoted as 119899then a column whose119863

119888

is greater than (1 minus 119899) is consideredas failed or collapsed since its residual axial load capacity isnot sufficient for the service axial load

42 Steps for Damage Assessment of CFST Columns

Step 1 (derivation of 119875max) During this step the linearlyincreasing axial load is applied on the column head until thecolumn collapses then 119875max is determined as the maximumaxial load that the column can withstand

Step 2 (derivation of 119875residual) Three substeps as follows arerequired to obtain 119875residual (1) before blast loading a linearlyincreasing axial load up to the service axial load is imposedon the column (2) blast loads are applied over the front faceof the column with the service axial load being constant andcalculation is stopped when the damaged column approachesstatic equilibrium (3) a linearly increasing axial load isimposed on the top of the damaged column until it collapses

then 119875residual is determined as the peak of the axial load thatthe damaged column can bear

Step 3 (determination of 119863119888

) Substitute the values of 119875maxand 119875residual into (7) to obtain119863119888

43 Parameters Studied In this section effects of severalkey parameters on the damage degree of CFST columnsare analyzed These parameters include the scaled standoffdistance height of burst explosive mass column depthcolumn width column steel ratio and axial load ratio aslisted in Table 4 in which a contrast case is generated bychanging one of the parameters considered in the benchmarkcase while keeping other parameters unchanged Note thatin each case varied scaled standoff distances are consideredso that the effects aforementioned parameters on the damagedegree of columns within different blast loading regimes canbe assessed

431 Effect of Scaled Standoff Distance 119885 The numericalsimulation results show that 119863

119888

of CFST columns decreaseswith the increasing scaled standoff distance regardless ofother parameters This is because column damage is affectedby the peak overpressure and impulse of the blast wave[21] and both of them drop with the rising scaled standoffdistance which results in a small degree of column damage

432 Effect of Height of Burst119867119861

It is difficult to characterizethe effect of 119867

119861

on the damage degree of the column On

Shock and Vibration 9

Table 4 Parameters used in the numerical parametric study

Parameters 119885 (mkg13) 119867119861

(m) 119872 (kg) 119889 (m) 119908 (m) Steel ratio 120572lowast Axial load ratio 119899Benchmark case 018ndash050 0 50 06 06 013 035Contrast cases 015ndash090 185 250 500 09 12 09 12 016 019 050 065lowast

120572 = 119860119904

119860119888

119860119904

and 119860119888

are the cross-sectional areas of steel tube and infill concrete respectively

07

06

05

04

03

02

01

00

HB = 0mHB = 185m

015 020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

Figure 10 Effects of height of burst on the damage degree

one hand when 119867119861

nears zero the initial blast wave isimmediately reflected and reinforced by the ground On theother the mid-height of the column is expected to surfer themost severe damage due to lack of transverse support Conse-quently as shown in Figure 10 surface burst results in severerdamage to the column than that caused by explosion atcolumnmid-height (119867

119861

= 185m) especially when the stand-off distance is small The effects of119867

119861

on the damage degreeof the column are insignificant at large scaled distancesbecause both the overpressure and impulse on the columnare relatively small in these cases

433 Effect of Explosive Mass119872 Figure 11 shows the effectsof explosive mass on the damage degree of the columnInspections of the figure show that 119863

119888

rises with 119872 for thesame scaled standoff distance indicating that CFST columnis impulse-sensitive since explosive with larger mass hasrelatively more impulse for the column

434 Effects of Column Width 119908 and Depth 119889 Effects ofcolumn depth and width on 119863

119888

are shown in Figure 12Comparedwith the reference column (119908 = 06m 119889 = 06m)columns with larger width and depth tend to have lowerdamage degrees because expanding columnwidth and depthproduces a larger cross section for attenuation of the stresswaves density and contributes to enhancement of the shearresistance as well as flexural strength of the columnHoweverit is found that columns with the same cross section area butdifferent width and depth have varied damage degrees and

07

06

05

04

03

02

01

0002 03 04 05 06 07 08 09 10

Scaled standoff distance Z (mkg13)

M = 50kgM = 250kgM = 500kg

[HB = 0m] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 11 Effects of explosive mass on the damage degree

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

w = 06m d = 06mw = 09m d = 06mw = 12m d = 06m

w = 06m d = 09mw = 06m d = 12m

[HB = 0m] [M = 50kg] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 12 Effects of width and depth on the damage degree

that compared with increasing the column width incrementof the column depth is more effective in reducing the columndamage degree This is because enlarging the column widthsimultaneously results in a rise of blast loads acting on thecolumnwhich balances out the enhancement of columnblastresistance to some extent

10 Shock and Vibration

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

120572 = 013

120572 = 016

120572 = 019

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [n = 035 ]

Dam

age d

egre

eDc

Figure 13 Effects of steel ratio on the damage degree

07

06

05

04

03

02

01

00020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

n = 035

n = 050

n = 065

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [120572 = 013]

Dam

age d

egre

eDc

Figure 14 Effects of axial load ratio on the damage degree

435 Effect of Column Steel Ratio 120572 As shown in Figure 13119863119888

drops with the rising steel ratio This is expected becauseincreasing 120572means a larger steel area and better confinementof infill concrete which will enhance the shear and bendingstrength of the column as well as its resistance to localizeddamage

436 Effect of Column Axial Load Ratio 119899 Effects of axialload ratio on 119863

119888

are shown in Figure 14 Inspection of thefigure reveals that axial load ratio has dual influences on col-umn damage When the scaled standoff is small the columnwith a larger axial load ratio has lower damage degree Thisis because the column under small scaled standoff is likelyto suffer localized damage and shear damage and a higher

axial load will restrain the cracking and crushing of concretewhich enhances the resistance of the column to localizeddamage and shear damage In contrast at a large scaledstandoff distance the column with larger axial load ratio hashigher damage degree The reason is that with the increaseof the scaled standoff distance the column tends to sufferflexural damage which is related to its moment capacity andductility The larger the moment capacity and ductility arethe lower the damage degree is For the CFST column studiedin this section the axial load ratio at the maximum momentcapacity is 022 which is derived by the methods from Choiet al [1] According to the axial load-bending moment (P-M)interactions the moment capacity of the CFST column willdecrease when 119899 rises from 035 to 060 Moreover a risingaxial load will reduce the ductility of the CFST column

44 Empirical Equations for Determining the Damage Degreeof CFST Columns The parametric study revealed the signif-icance of parameters affecting the damage degree of CFSTcolumns Through the multivariable regression analysis anempirical equation is proposed in terms of various parame-ters to predict the damage degree and is expressed as follows

119863119888

= [minus1505 ln(11987250

) + 1650 (

119908

06

) minus 3242 (

119889

06

)

minus 131625120572 + 15349119899 + 25011]

sdot 119890[minus648ln(11987250)+533(11990806)minus1091(11988906)minus373minus1230120572+1292119899+2681]119885

(8)

The comparisons of the proposed equation with the ana-lytical results are shown in Figures 15(a)ndash15(f) The scattersdenote the analytical results and the solid lines represent theproposed equation Observation of these figures shows thatthe proposed curves are close to the analytical results formostcases The effects of height of burst on the damage degree ofCFST columns are not reflected by (8) due to the lack of blastdata in the lower height of the column which are limited inthe ConWep model and will be supplemented in the furtherstudies

5 Conclusions

This paper presents a 3D numerical model to investigate thedamage modes and damage assessment of CFST columnsBased on the numerical analysis results the following con-clusions can be drawn

CFST columns under blast loading may undergo theglobal flexural damage and shear damage as well as localizeddamage Flexural damage and shear damage of the columnare mainly attributed to the deformation and internal force ofthe whole member whilst the localized damage is dominatedby the failure of infill concrete and steel tube in the vicinity ofthe explosion

The damage criterion based on the residual axial loadcapacity is adopted for assessing the degree of CFST columnsdamage to blast loadsThrough parametric studies it is foundthat the damage degree of CFST columns decays nearlyexponentially with the increasing scaled standoff distance

Shock and Vibration 11

07

06

05

04

03

02

01

00

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

Dam

age d

egre

eDc

(a)

07

06

05

04

03

02

01

00095090085050 055 060 065 070 075 080

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 500kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

(b)

07

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 12m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

(c)

020

015

010

005

000

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 12m] [120572 = 013] [n = 035]D

amag

e deg

reeD

c

(d)

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 019] [n = 035]

Dam

age d

egre

eDc

(e)

020

025

030

035

015

010

005

000055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 065]

Dam

age d

egre

eDc

(f)

Figure 15 Comparison of analytical results with the proposed curves

12 Shock and Vibration

For the same scaled standoff distance surface burst results inseverer damage to the column than that caused by explosionat columnmid-height and the damage degree increases withthe rising explosive mass and decreases with column depthand width and steel ratio Increasing the axial load enhancesthe resistance of the column against localized damage andshear damage while the effects of axial load on flexuraldamage depend on the axial load-bending moment (P-M)interactions of the column

An equation is derived by fitting the results of parametricstudies to estimate the damage degree of CFST columnsTypical examples confirm that the proposed equation wellrepresents the variation of the column damage degree How-ever future experiments can be conducted for investigatingthe effects of other parameters on the damage degree of CFSTcolumns

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research described in this paper was financially sup-ported by Achievement Transfer Program of Institutionsof Higher Education in Chongqing under Grant noKJZH14220

References

[1] Y-H Choi D A Foutch and J M LaFave ldquoNew approachto AISC P-M interaction curve for square concrete filled tube(CFT) beamndashcolumnsrdquo Engineering Structures vol 28 no 11pp 1586ndash1598 2006

[2] Y-H Choi K S Kim and S-M Choi ldquoSimplified P-M interac-tion curve for square steel tube filled with high-strength con-creterdquoThin-Walled Structures vol 46 no 5 pp 506ndash515 2008

[3] T KrauthammerModern Protective Structures TaylorampFrancisGroup New York NY USA 2008

[4] S C Fujikura M Bruneau and D Lopez-Garcia ldquoExperimen-tal investigation of blast performance of seismically resistantconcrete-filled steel tube bridge piersrdquo Tech Rep MCEER-07-0005 University at Buffalo Buffalo NY USA 2007

[5] S Fujikura M Bruneau and D Lopez-Garcia ldquoExperimentalinvestigation of multihazard resistant bridge piers having con-crete-filled steel tube under blast loadingrdquo Journal of BridgeEngineering vol 13 no 6 pp 586ndash594 2008

[6] G Li H Qu T Yang Y Lu and S Chen ldquoExperimental studyof concrete-filled steel tubular columns under blast loadingrdquoJianzhu Jiegou Xuebao vol 34 no 12 pp 69ndash76 2013 (Chinese)

[7] A M Remennikov and B Uy ldquoExplosive testing andmodellingof square tubular steel columns for near-field detonationsrdquo Jour-nal of Constructional Steel Research vol 101 pp 290ndash303 2014

[8] T Ngo D Mohotti A Remennikov and B Uy ldquoNumericalsimulations of response of tubular steel beams to close-rangeexplosionsrdquo Journal of Constructional Steel Research vol 105 pp151ndash163 2015

[9] F R Zhang C Q Wu H W Wang and Y Zhou ldquoNumericalsimulation of concrete filled steel tube columns against BLASTloadsrdquoThin-Walled Structures vol 92 pp 82ndash92 2015

[10] F Zhang C Wu X Zhao Z Li A Heidarpour and H WangldquoNumerical modeling of concrete-filled double-skin steelsquare tubular columns under blast loadingrdquo Journal of Per-formance of Constructed Facilities vol 29 no 5 Article IDB4015002 2015

[11] Livermore Software Technology Corporation LS-DYNA Theo-retical Manual Livermore Software Technology CorporationLivermore Calif USA 1998

[12] G R Cowper and P S Symonds ldquoStrain-hardening and strain-rate effects in the impact loading of cantilever beamsrdquo TechRep AD144762 Office of Naval Research Arlington Va USA1958

[13] T J Holmquist G R Johnson and W H Cook ldquoA computa-tional constitutive model for concrete subjected to large strainshigh strain rates and high pressuresrdquo in Proceedings of the 14thInternational Symposium on Ballistics Quebec City CanadaSeptember 1993

[14] Q Fang and J Zhang ldquoThree-dimensional modelling of steelfiber reinforced concrete material under intense dynamic load-ingrdquo Construction and Building Materials vol 44 pp 118ndash1322013

[15] Y Li F Lin X L Gu and X Q Lu ldquoNumerical researchof a super-large cooling tower subjected to accidental loadsrdquoNuclear Engineering and Design vol 269 pp 184ndash192 2014

[16] J Li and H Hao ldquoNumerical study of concrete spall damage toblast loadsrdquo International Journal of Impact Engineering vol 68pp 41ndash55 2014

[17] G Randers-Pehrson and K A Bannister ldquoAirblast loadingmodel for DYNA2D and DYNA3Drdquo Tech Rep ARL-TR-1310Army Research Laboratory Adelphi Md USA 1997

[18] Livermore Software Technology Corporation LS-DYNA Key-word Userrsquos Manual (Version 971 R610) Livermore SoftwareTechnology Corporation Livermore Calif USA 2012

[19] CECS ldquoTechnical specification for structures with concrete-filled rectangular steel tube membersrdquo CECS 1592004 ChinaAssociation for Engineering Construction StandardizationBeijing China 2004 (Chinese)

[20] Y Shi H Hao and Z-X Li ldquoNumerical derivation of pressure-impulse diagrams for prediction of RC column damage to blastloadsrdquo International Journal of Impact Engineering vol 35 no11 pp 1213ndash1227 2008

[21] P D Smith and J G Hetherington Blast and Ballistic Loadingof Structures Butterowrth-Heinemenn Oxford UK 1994

[22] K-C Wu B Li and K-C Tsai ldquoThe effects of explosive massratio on residual compressive capacity of contact blast damagedcomposite columnsrdquo Journal of Constructional Steel Researchvol 67 no 4 pp 602ndash612 2011

[23] J E Crawford K B Morrill and J M Magallanes ldquoProtectivedesign for columns against close-in blast effectsrdquo in Proceedingsof the Structures Congress Boston Mass USA April 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 9

Table 4 Parameters used in the numerical parametric study

Parameters 119885 (mkg13) 119867119861

(m) 119872 (kg) 119889 (m) 119908 (m) Steel ratio 120572lowast Axial load ratio 119899Benchmark case 018ndash050 0 50 06 06 013 035Contrast cases 015ndash090 185 250 500 09 12 09 12 016 019 050 065lowast

120572 = 119860119904

119860119888

119860119904

and 119860119888

are the cross-sectional areas of steel tube and infill concrete respectively

07

06

05

04

03

02

01

00

HB = 0mHB = 185m

015 020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

Figure 10 Effects of height of burst on the damage degree

one hand when 119867119861

nears zero the initial blast wave isimmediately reflected and reinforced by the ground On theother the mid-height of the column is expected to surfer themost severe damage due to lack of transverse support Conse-quently as shown in Figure 10 surface burst results in severerdamage to the column than that caused by explosion atcolumnmid-height (119867

119861

= 185m) especially when the stand-off distance is small The effects of119867

119861

on the damage degreeof the column are insignificant at large scaled distancesbecause both the overpressure and impulse on the columnare relatively small in these cases

433 Effect of Explosive Mass119872 Figure 11 shows the effectsof explosive mass on the damage degree of the columnInspections of the figure show that 119863

119888

rises with 119872 for thesame scaled standoff distance indicating that CFST columnis impulse-sensitive since explosive with larger mass hasrelatively more impulse for the column

434 Effects of Column Width 119908 and Depth 119889 Effects ofcolumn depth and width on 119863

119888

are shown in Figure 12Comparedwith the reference column (119908 = 06m 119889 = 06m)columns with larger width and depth tend to have lowerdamage degrees because expanding columnwidth and depthproduces a larger cross section for attenuation of the stresswaves density and contributes to enhancement of the shearresistance as well as flexural strength of the columnHoweverit is found that columns with the same cross section area butdifferent width and depth have varied damage degrees and

07

06

05

04

03

02

01

0002 03 04 05 06 07 08 09 10

Scaled standoff distance Z (mkg13)

M = 50kgM = 250kgM = 500kg

[HB = 0m] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 11 Effects of explosive mass on the damage degree

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

w = 06m d = 06mw = 09m d = 06mw = 12m d = 06m

w = 06m d = 09mw = 06m d = 12m

[HB = 0m] [M = 50kg] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

Figure 12 Effects of width and depth on the damage degree

that compared with increasing the column width incrementof the column depth is more effective in reducing the columndamage degree This is because enlarging the column widthsimultaneously results in a rise of blast loads acting on thecolumnwhich balances out the enhancement of columnblastresistance to some extent

10 Shock and Vibration

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

120572 = 013

120572 = 016

120572 = 019

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [n = 035 ]

Dam

age d

egre

eDc

Figure 13 Effects of steel ratio on the damage degree

07

06

05

04

03

02

01

00020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

n = 035

n = 050

n = 065

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [120572 = 013]

Dam

age d

egre

eDc

Figure 14 Effects of axial load ratio on the damage degree

435 Effect of Column Steel Ratio 120572 As shown in Figure 13119863119888

drops with the rising steel ratio This is expected becauseincreasing 120572means a larger steel area and better confinementof infill concrete which will enhance the shear and bendingstrength of the column as well as its resistance to localizeddamage

436 Effect of Column Axial Load Ratio 119899 Effects of axialload ratio on 119863

119888

are shown in Figure 14 Inspection of thefigure reveals that axial load ratio has dual influences on col-umn damage When the scaled standoff is small the columnwith a larger axial load ratio has lower damage degree Thisis because the column under small scaled standoff is likelyto suffer localized damage and shear damage and a higher

axial load will restrain the cracking and crushing of concretewhich enhances the resistance of the column to localizeddamage and shear damage In contrast at a large scaledstandoff distance the column with larger axial load ratio hashigher damage degree The reason is that with the increaseof the scaled standoff distance the column tends to sufferflexural damage which is related to its moment capacity andductility The larger the moment capacity and ductility arethe lower the damage degree is For the CFST column studiedin this section the axial load ratio at the maximum momentcapacity is 022 which is derived by the methods from Choiet al [1] According to the axial load-bending moment (P-M)interactions the moment capacity of the CFST column willdecrease when 119899 rises from 035 to 060 Moreover a risingaxial load will reduce the ductility of the CFST column

44 Empirical Equations for Determining the Damage Degreeof CFST Columns The parametric study revealed the signif-icance of parameters affecting the damage degree of CFSTcolumns Through the multivariable regression analysis anempirical equation is proposed in terms of various parame-ters to predict the damage degree and is expressed as follows

119863119888

= [minus1505 ln(11987250

) + 1650 (

119908

06

) minus 3242 (

119889

06

)

minus 131625120572 + 15349119899 + 25011]

sdot 119890[minus648ln(11987250)+533(11990806)minus1091(11988906)minus373minus1230120572+1292119899+2681]119885

(8)

The comparisons of the proposed equation with the ana-lytical results are shown in Figures 15(a)ndash15(f) The scattersdenote the analytical results and the solid lines represent theproposed equation Observation of these figures shows thatthe proposed curves are close to the analytical results formostcases The effects of height of burst on the damage degree ofCFST columns are not reflected by (8) due to the lack of blastdata in the lower height of the column which are limited inthe ConWep model and will be supplemented in the furtherstudies

5 Conclusions

This paper presents a 3D numerical model to investigate thedamage modes and damage assessment of CFST columnsBased on the numerical analysis results the following con-clusions can be drawn

CFST columns under blast loading may undergo theglobal flexural damage and shear damage as well as localizeddamage Flexural damage and shear damage of the columnare mainly attributed to the deformation and internal force ofthe whole member whilst the localized damage is dominatedby the failure of infill concrete and steel tube in the vicinity ofthe explosion

The damage criterion based on the residual axial loadcapacity is adopted for assessing the degree of CFST columnsdamage to blast loadsThrough parametric studies it is foundthat the damage degree of CFST columns decays nearlyexponentially with the increasing scaled standoff distance

Shock and Vibration 11

07

06

05

04

03

02

01

00

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

Dam

age d

egre

eDc

(a)

07

06

05

04

03

02

01

00095090085050 055 060 065 070 075 080

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 500kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

(b)

07

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 12m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

(c)

020

015

010

005

000

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 12m] [120572 = 013] [n = 035]D

amag

e deg

reeD

c

(d)

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 019] [n = 035]

Dam

age d

egre

eDc

(e)

020

025

030

035

015

010

005

000055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 065]

Dam

age d

egre

eDc

(f)

Figure 15 Comparison of analytical results with the proposed curves

12 Shock and Vibration

For the same scaled standoff distance surface burst results inseverer damage to the column than that caused by explosionat columnmid-height and the damage degree increases withthe rising explosive mass and decreases with column depthand width and steel ratio Increasing the axial load enhancesthe resistance of the column against localized damage andshear damage while the effects of axial load on flexuraldamage depend on the axial load-bending moment (P-M)interactions of the column

An equation is derived by fitting the results of parametricstudies to estimate the damage degree of CFST columnsTypical examples confirm that the proposed equation wellrepresents the variation of the column damage degree How-ever future experiments can be conducted for investigatingthe effects of other parameters on the damage degree of CFSTcolumns

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research described in this paper was financially sup-ported by Achievement Transfer Program of Institutionsof Higher Education in Chongqing under Grant noKJZH14220

References

[1] Y-H Choi D A Foutch and J M LaFave ldquoNew approachto AISC P-M interaction curve for square concrete filled tube(CFT) beamndashcolumnsrdquo Engineering Structures vol 28 no 11pp 1586ndash1598 2006

[2] Y-H Choi K S Kim and S-M Choi ldquoSimplified P-M interac-tion curve for square steel tube filled with high-strength con-creterdquoThin-Walled Structures vol 46 no 5 pp 506ndash515 2008

[3] T KrauthammerModern Protective Structures TaylorampFrancisGroup New York NY USA 2008

[4] S C Fujikura M Bruneau and D Lopez-Garcia ldquoExperimen-tal investigation of blast performance of seismically resistantconcrete-filled steel tube bridge piersrdquo Tech Rep MCEER-07-0005 University at Buffalo Buffalo NY USA 2007

[5] S Fujikura M Bruneau and D Lopez-Garcia ldquoExperimentalinvestigation of multihazard resistant bridge piers having con-crete-filled steel tube under blast loadingrdquo Journal of BridgeEngineering vol 13 no 6 pp 586ndash594 2008

[6] G Li H Qu T Yang Y Lu and S Chen ldquoExperimental studyof concrete-filled steel tubular columns under blast loadingrdquoJianzhu Jiegou Xuebao vol 34 no 12 pp 69ndash76 2013 (Chinese)

[7] A M Remennikov and B Uy ldquoExplosive testing andmodellingof square tubular steel columns for near-field detonationsrdquo Jour-nal of Constructional Steel Research vol 101 pp 290ndash303 2014

[8] T Ngo D Mohotti A Remennikov and B Uy ldquoNumericalsimulations of response of tubular steel beams to close-rangeexplosionsrdquo Journal of Constructional Steel Research vol 105 pp151ndash163 2015

[9] F R Zhang C Q Wu H W Wang and Y Zhou ldquoNumericalsimulation of concrete filled steel tube columns against BLASTloadsrdquoThin-Walled Structures vol 92 pp 82ndash92 2015

[10] F Zhang C Wu X Zhao Z Li A Heidarpour and H WangldquoNumerical modeling of concrete-filled double-skin steelsquare tubular columns under blast loadingrdquo Journal of Per-formance of Constructed Facilities vol 29 no 5 Article IDB4015002 2015

[11] Livermore Software Technology Corporation LS-DYNA Theo-retical Manual Livermore Software Technology CorporationLivermore Calif USA 1998

[12] G R Cowper and P S Symonds ldquoStrain-hardening and strain-rate effects in the impact loading of cantilever beamsrdquo TechRep AD144762 Office of Naval Research Arlington Va USA1958

[13] T J Holmquist G R Johnson and W H Cook ldquoA computa-tional constitutive model for concrete subjected to large strainshigh strain rates and high pressuresrdquo in Proceedings of the 14thInternational Symposium on Ballistics Quebec City CanadaSeptember 1993

[14] Q Fang and J Zhang ldquoThree-dimensional modelling of steelfiber reinforced concrete material under intense dynamic load-ingrdquo Construction and Building Materials vol 44 pp 118ndash1322013

[15] Y Li F Lin X L Gu and X Q Lu ldquoNumerical researchof a super-large cooling tower subjected to accidental loadsrdquoNuclear Engineering and Design vol 269 pp 184ndash192 2014

[16] J Li and H Hao ldquoNumerical study of concrete spall damage toblast loadsrdquo International Journal of Impact Engineering vol 68pp 41ndash55 2014

[17] G Randers-Pehrson and K A Bannister ldquoAirblast loadingmodel for DYNA2D and DYNA3Drdquo Tech Rep ARL-TR-1310Army Research Laboratory Adelphi Md USA 1997

[18] Livermore Software Technology Corporation LS-DYNA Key-word Userrsquos Manual (Version 971 R610) Livermore SoftwareTechnology Corporation Livermore Calif USA 2012

[19] CECS ldquoTechnical specification for structures with concrete-filled rectangular steel tube membersrdquo CECS 1592004 ChinaAssociation for Engineering Construction StandardizationBeijing China 2004 (Chinese)

[20] Y Shi H Hao and Z-X Li ldquoNumerical derivation of pressure-impulse diagrams for prediction of RC column damage to blastloadsrdquo International Journal of Impact Engineering vol 35 no11 pp 1213ndash1227 2008

[21] P D Smith and J G Hetherington Blast and Ballistic Loadingof Structures Butterowrth-Heinemenn Oxford UK 1994

[22] K-C Wu B Li and K-C Tsai ldquoThe effects of explosive massratio on residual compressive capacity of contact blast damagedcomposite columnsrdquo Journal of Constructional Steel Researchvol 67 no 4 pp 602ndash612 2011

[23] J E Crawford K B Morrill and J M Magallanes ldquoProtectivedesign for columns against close-in blast effectsrdquo in Proceedingsof the Structures Congress Boston Mass USA April 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Shock and Vibration

07

06

05

04

03

02

01

00015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

120572 = 013

120572 = 016

120572 = 019

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [n = 035 ]

Dam

age d

egre

eDc

Figure 13 Effects of steel ratio on the damage degree

07

06

05

04

03

02

01

00020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

n = 035

n = 050

n = 065

[HB = 0m] [M = 50kg] [w = 06m] [d = 06m] [120572 = 013]

Dam

age d

egre

eDc

Figure 14 Effects of axial load ratio on the damage degree

435 Effect of Column Steel Ratio 120572 As shown in Figure 13119863119888

drops with the rising steel ratio This is expected becauseincreasing 120572means a larger steel area and better confinementof infill concrete which will enhance the shear and bendingstrength of the column as well as its resistance to localizeddamage

436 Effect of Column Axial Load Ratio 119899 Effects of axialload ratio on 119863

119888

are shown in Figure 14 Inspection of thefigure reveals that axial load ratio has dual influences on col-umn damage When the scaled standoff is small the columnwith a larger axial load ratio has lower damage degree Thisis because the column under small scaled standoff is likelyto suffer localized damage and shear damage and a higher

axial load will restrain the cracking and crushing of concretewhich enhances the resistance of the column to localizeddamage and shear damage In contrast at a large scaledstandoff distance the column with larger axial load ratio hashigher damage degree The reason is that with the increaseof the scaled standoff distance the column tends to sufferflexural damage which is related to its moment capacity andductility The larger the moment capacity and ductility arethe lower the damage degree is For the CFST column studiedin this section the axial load ratio at the maximum momentcapacity is 022 which is derived by the methods from Choiet al [1] According to the axial load-bending moment (P-M)interactions the moment capacity of the CFST column willdecrease when 119899 rises from 035 to 060 Moreover a risingaxial load will reduce the ductility of the CFST column

44 Empirical Equations for Determining the Damage Degreeof CFST Columns The parametric study revealed the signif-icance of parameters affecting the damage degree of CFSTcolumns Through the multivariable regression analysis anempirical equation is proposed in terms of various parame-ters to predict the damage degree and is expressed as follows

119863119888

= [minus1505 ln(11987250

) + 1650 (

119908

06

) minus 3242 (

119889

06

)

minus 131625120572 + 15349119899 + 25011]

sdot 119890[minus648ln(11987250)+533(11990806)minus1091(11988906)minus373minus1230120572+1292119899+2681]119885

(8)

The comparisons of the proposed equation with the ana-lytical results are shown in Figures 15(a)ndash15(f) The scattersdenote the analytical results and the solid lines represent theproposed equation Observation of these figures shows thatthe proposed curves are close to the analytical results formostcases The effects of height of burst on the damage degree ofCFST columns are not reflected by (8) due to the lack of blastdata in the lower height of the column which are limited inthe ConWep model and will be supplemented in the furtherstudies

5 Conclusions

This paper presents a 3D numerical model to investigate thedamage modes and damage assessment of CFST columnsBased on the numerical analysis results the following con-clusions can be drawn

CFST columns under blast loading may undergo theglobal flexural damage and shear damage as well as localizeddamage Flexural damage and shear damage of the columnare mainly attributed to the deformation and internal force ofthe whole member whilst the localized damage is dominatedby the failure of infill concrete and steel tube in the vicinity ofthe explosion

The damage criterion based on the residual axial loadcapacity is adopted for assessing the degree of CFST columnsdamage to blast loadsThrough parametric studies it is foundthat the damage degree of CFST columns decays nearlyexponentially with the increasing scaled standoff distance

Shock and Vibration 11

07

06

05

04

03

02

01

00

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

Dam

age d

egre

eDc

(a)

07

06

05

04

03

02

01

00095090085050 055 060 065 070 075 080

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 500kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

(b)

07

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 12m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

(c)

020

015

010

005

000

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 12m] [120572 = 013] [n = 035]D

amag

e deg

reeD

c

(d)

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 019] [n = 035]

Dam

age d

egre

eDc

(e)

020

025

030

035

015

010

005

000055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 065]

Dam

age d

egre

eDc

(f)

Figure 15 Comparison of analytical results with the proposed curves

12 Shock and Vibration

For the same scaled standoff distance surface burst results inseverer damage to the column than that caused by explosionat columnmid-height and the damage degree increases withthe rising explosive mass and decreases with column depthand width and steel ratio Increasing the axial load enhancesthe resistance of the column against localized damage andshear damage while the effects of axial load on flexuraldamage depend on the axial load-bending moment (P-M)interactions of the column

An equation is derived by fitting the results of parametricstudies to estimate the damage degree of CFST columnsTypical examples confirm that the proposed equation wellrepresents the variation of the column damage degree How-ever future experiments can be conducted for investigatingthe effects of other parameters on the damage degree of CFSTcolumns

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research described in this paper was financially sup-ported by Achievement Transfer Program of Institutionsof Higher Education in Chongqing under Grant noKJZH14220

References

[1] Y-H Choi D A Foutch and J M LaFave ldquoNew approachto AISC P-M interaction curve for square concrete filled tube(CFT) beamndashcolumnsrdquo Engineering Structures vol 28 no 11pp 1586ndash1598 2006

[2] Y-H Choi K S Kim and S-M Choi ldquoSimplified P-M interac-tion curve for square steel tube filled with high-strength con-creterdquoThin-Walled Structures vol 46 no 5 pp 506ndash515 2008

[3] T KrauthammerModern Protective Structures TaylorampFrancisGroup New York NY USA 2008

[4] S C Fujikura M Bruneau and D Lopez-Garcia ldquoExperimen-tal investigation of blast performance of seismically resistantconcrete-filled steel tube bridge piersrdquo Tech Rep MCEER-07-0005 University at Buffalo Buffalo NY USA 2007

[5] S Fujikura M Bruneau and D Lopez-Garcia ldquoExperimentalinvestigation of multihazard resistant bridge piers having con-crete-filled steel tube under blast loadingrdquo Journal of BridgeEngineering vol 13 no 6 pp 586ndash594 2008

[6] G Li H Qu T Yang Y Lu and S Chen ldquoExperimental studyof concrete-filled steel tubular columns under blast loadingrdquoJianzhu Jiegou Xuebao vol 34 no 12 pp 69ndash76 2013 (Chinese)

[7] A M Remennikov and B Uy ldquoExplosive testing andmodellingof square tubular steel columns for near-field detonationsrdquo Jour-nal of Constructional Steel Research vol 101 pp 290ndash303 2014

[8] T Ngo D Mohotti A Remennikov and B Uy ldquoNumericalsimulations of response of tubular steel beams to close-rangeexplosionsrdquo Journal of Constructional Steel Research vol 105 pp151ndash163 2015

[9] F R Zhang C Q Wu H W Wang and Y Zhou ldquoNumericalsimulation of concrete filled steel tube columns against BLASTloadsrdquoThin-Walled Structures vol 92 pp 82ndash92 2015

[10] F Zhang C Wu X Zhao Z Li A Heidarpour and H WangldquoNumerical modeling of concrete-filled double-skin steelsquare tubular columns under blast loadingrdquo Journal of Per-formance of Constructed Facilities vol 29 no 5 Article IDB4015002 2015

[11] Livermore Software Technology Corporation LS-DYNA Theo-retical Manual Livermore Software Technology CorporationLivermore Calif USA 1998

[12] G R Cowper and P S Symonds ldquoStrain-hardening and strain-rate effects in the impact loading of cantilever beamsrdquo TechRep AD144762 Office of Naval Research Arlington Va USA1958

[13] T J Holmquist G R Johnson and W H Cook ldquoA computa-tional constitutive model for concrete subjected to large strainshigh strain rates and high pressuresrdquo in Proceedings of the 14thInternational Symposium on Ballistics Quebec City CanadaSeptember 1993

[14] Q Fang and J Zhang ldquoThree-dimensional modelling of steelfiber reinforced concrete material under intense dynamic load-ingrdquo Construction and Building Materials vol 44 pp 118ndash1322013

[15] Y Li F Lin X L Gu and X Q Lu ldquoNumerical researchof a super-large cooling tower subjected to accidental loadsrdquoNuclear Engineering and Design vol 269 pp 184ndash192 2014

[16] J Li and H Hao ldquoNumerical study of concrete spall damage toblast loadsrdquo International Journal of Impact Engineering vol 68pp 41ndash55 2014

[17] G Randers-Pehrson and K A Bannister ldquoAirblast loadingmodel for DYNA2D and DYNA3Drdquo Tech Rep ARL-TR-1310Army Research Laboratory Adelphi Md USA 1997

[18] Livermore Software Technology Corporation LS-DYNA Key-word Userrsquos Manual (Version 971 R610) Livermore SoftwareTechnology Corporation Livermore Calif USA 2012

[19] CECS ldquoTechnical specification for structures with concrete-filled rectangular steel tube membersrdquo CECS 1592004 ChinaAssociation for Engineering Construction StandardizationBeijing China 2004 (Chinese)

[20] Y Shi H Hao and Z-X Li ldquoNumerical derivation of pressure-impulse diagrams for prediction of RC column damage to blastloadsrdquo International Journal of Impact Engineering vol 35 no11 pp 1213ndash1227 2008

[21] P D Smith and J G Hetherington Blast and Ballistic Loadingof Structures Butterowrth-Heinemenn Oxford UK 1994

[22] K-C Wu B Li and K-C Tsai ldquoThe effects of explosive massratio on residual compressive capacity of contact blast damagedcomposite columnsrdquo Journal of Constructional Steel Researchvol 67 no 4 pp 602ndash612 2011

[23] J E Crawford K B Morrill and J M Magallanes ldquoProtectivedesign for columns against close-in blast effectsrdquo in Proceedingsof the Structures Congress Boston Mass USA April 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 11

07

06

05

04

03

02

01

00

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035]

055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

Dam

age d

egre

eDc

(a)

07

06

05

04

03

02

01

00095090085050 055 060 065 070 075 080

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 500kg] [w = 06m] [d = 06m] [120572 = 013] [n = 035 ]

Dam

age d

egre

eDc

(b)

07

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 12m] [d = 06m] [120572 = 013] [n = 035]

Dam

age d

egre

eDc

(c)

020

015

010

005

000

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 12m] [120572 = 013] [n = 035]D

amag

e deg

reeD

c

(d)

06

05

04

03

02

01

00

Analytical resultsProposed equation

015 020 025 030 035 040 045

Scaled standoff distance Z (mkg13)

[M = 50kg] [w = 06m] [d = 06m] [120572 = 019] [n = 035]

Dam

age d

egre

eDc

(e)

020

025

030

035

015

010

005

000055020 025 030 035 040 045 050

Scaled standoff distance Z (mkg13)

Analytical resultsProposed equation

[M = 50kg] [w = 06m] [d = 06m] [120572 = 013] [n = 065]

Dam

age d

egre

eDc

(f)

Figure 15 Comparison of analytical results with the proposed curves

12 Shock and Vibration

For the same scaled standoff distance surface burst results inseverer damage to the column than that caused by explosionat columnmid-height and the damage degree increases withthe rising explosive mass and decreases with column depthand width and steel ratio Increasing the axial load enhancesthe resistance of the column against localized damage andshear damage while the effects of axial load on flexuraldamage depend on the axial load-bending moment (P-M)interactions of the column

An equation is derived by fitting the results of parametricstudies to estimate the damage degree of CFST columnsTypical examples confirm that the proposed equation wellrepresents the variation of the column damage degree How-ever future experiments can be conducted for investigatingthe effects of other parameters on the damage degree of CFSTcolumns

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research described in this paper was financially sup-ported by Achievement Transfer Program of Institutionsof Higher Education in Chongqing under Grant noKJZH14220

References

[1] Y-H Choi D A Foutch and J M LaFave ldquoNew approachto AISC P-M interaction curve for square concrete filled tube(CFT) beamndashcolumnsrdquo Engineering Structures vol 28 no 11pp 1586ndash1598 2006

[2] Y-H Choi K S Kim and S-M Choi ldquoSimplified P-M interac-tion curve for square steel tube filled with high-strength con-creterdquoThin-Walled Structures vol 46 no 5 pp 506ndash515 2008

[3] T KrauthammerModern Protective Structures TaylorampFrancisGroup New York NY USA 2008

[4] S C Fujikura M Bruneau and D Lopez-Garcia ldquoExperimen-tal investigation of blast performance of seismically resistantconcrete-filled steel tube bridge piersrdquo Tech Rep MCEER-07-0005 University at Buffalo Buffalo NY USA 2007

[5] S Fujikura M Bruneau and D Lopez-Garcia ldquoExperimentalinvestigation of multihazard resistant bridge piers having con-crete-filled steel tube under blast loadingrdquo Journal of BridgeEngineering vol 13 no 6 pp 586ndash594 2008

[6] G Li H Qu T Yang Y Lu and S Chen ldquoExperimental studyof concrete-filled steel tubular columns under blast loadingrdquoJianzhu Jiegou Xuebao vol 34 no 12 pp 69ndash76 2013 (Chinese)

[7] A M Remennikov and B Uy ldquoExplosive testing andmodellingof square tubular steel columns for near-field detonationsrdquo Jour-nal of Constructional Steel Research vol 101 pp 290ndash303 2014

[8] T Ngo D Mohotti A Remennikov and B Uy ldquoNumericalsimulations of response of tubular steel beams to close-rangeexplosionsrdquo Journal of Constructional Steel Research vol 105 pp151ndash163 2015

[9] F R Zhang C Q Wu H W Wang and Y Zhou ldquoNumericalsimulation of concrete filled steel tube columns against BLASTloadsrdquoThin-Walled Structures vol 92 pp 82ndash92 2015

[10] F Zhang C Wu X Zhao Z Li A Heidarpour and H WangldquoNumerical modeling of concrete-filled double-skin steelsquare tubular columns under blast loadingrdquo Journal of Per-formance of Constructed Facilities vol 29 no 5 Article IDB4015002 2015

[11] Livermore Software Technology Corporation LS-DYNA Theo-retical Manual Livermore Software Technology CorporationLivermore Calif USA 1998

[12] G R Cowper and P S Symonds ldquoStrain-hardening and strain-rate effects in the impact loading of cantilever beamsrdquo TechRep AD144762 Office of Naval Research Arlington Va USA1958

[13] T J Holmquist G R Johnson and W H Cook ldquoA computa-tional constitutive model for concrete subjected to large strainshigh strain rates and high pressuresrdquo in Proceedings of the 14thInternational Symposium on Ballistics Quebec City CanadaSeptember 1993

[14] Q Fang and J Zhang ldquoThree-dimensional modelling of steelfiber reinforced concrete material under intense dynamic load-ingrdquo Construction and Building Materials vol 44 pp 118ndash1322013

[15] Y Li F Lin X L Gu and X Q Lu ldquoNumerical researchof a super-large cooling tower subjected to accidental loadsrdquoNuclear Engineering and Design vol 269 pp 184ndash192 2014

[16] J Li and H Hao ldquoNumerical study of concrete spall damage toblast loadsrdquo International Journal of Impact Engineering vol 68pp 41ndash55 2014

[17] G Randers-Pehrson and K A Bannister ldquoAirblast loadingmodel for DYNA2D and DYNA3Drdquo Tech Rep ARL-TR-1310Army Research Laboratory Adelphi Md USA 1997

[18] Livermore Software Technology Corporation LS-DYNA Key-word Userrsquos Manual (Version 971 R610) Livermore SoftwareTechnology Corporation Livermore Calif USA 2012

[19] CECS ldquoTechnical specification for structures with concrete-filled rectangular steel tube membersrdquo CECS 1592004 ChinaAssociation for Engineering Construction StandardizationBeijing China 2004 (Chinese)

[20] Y Shi H Hao and Z-X Li ldquoNumerical derivation of pressure-impulse diagrams for prediction of RC column damage to blastloadsrdquo International Journal of Impact Engineering vol 35 no11 pp 1213ndash1227 2008

[21] P D Smith and J G Hetherington Blast and Ballistic Loadingof Structures Butterowrth-Heinemenn Oxford UK 1994

[22] K-C Wu B Li and K-C Tsai ldquoThe effects of explosive massratio on residual compressive capacity of contact blast damagedcomposite columnsrdquo Journal of Constructional Steel Researchvol 67 no 4 pp 602ndash612 2011

[23] J E Crawford K B Morrill and J M Magallanes ldquoProtectivedesign for columns against close-in blast effectsrdquo in Proceedingsof the Structures Congress Boston Mass USA April 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Shock and Vibration

For the same scaled standoff distance surface burst results inseverer damage to the column than that caused by explosionat columnmid-height and the damage degree increases withthe rising explosive mass and decreases with column depthand width and steel ratio Increasing the axial load enhancesthe resistance of the column against localized damage andshear damage while the effects of axial load on flexuraldamage depend on the axial load-bending moment (P-M)interactions of the column

An equation is derived by fitting the results of parametricstudies to estimate the damage degree of CFST columnsTypical examples confirm that the proposed equation wellrepresents the variation of the column damage degree How-ever future experiments can be conducted for investigatingthe effects of other parameters on the damage degree of CFSTcolumns

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research described in this paper was financially sup-ported by Achievement Transfer Program of Institutionsof Higher Education in Chongqing under Grant noKJZH14220

References

[1] Y-H Choi D A Foutch and J M LaFave ldquoNew approachto AISC P-M interaction curve for square concrete filled tube(CFT) beamndashcolumnsrdquo Engineering Structures vol 28 no 11pp 1586ndash1598 2006

[2] Y-H Choi K S Kim and S-M Choi ldquoSimplified P-M interac-tion curve for square steel tube filled with high-strength con-creterdquoThin-Walled Structures vol 46 no 5 pp 506ndash515 2008

[3] T KrauthammerModern Protective Structures TaylorampFrancisGroup New York NY USA 2008

[4] S C Fujikura M Bruneau and D Lopez-Garcia ldquoExperimen-tal investigation of blast performance of seismically resistantconcrete-filled steel tube bridge piersrdquo Tech Rep MCEER-07-0005 University at Buffalo Buffalo NY USA 2007

[5] S Fujikura M Bruneau and D Lopez-Garcia ldquoExperimentalinvestigation of multihazard resistant bridge piers having con-crete-filled steel tube under blast loadingrdquo Journal of BridgeEngineering vol 13 no 6 pp 586ndash594 2008

[6] G Li H Qu T Yang Y Lu and S Chen ldquoExperimental studyof concrete-filled steel tubular columns under blast loadingrdquoJianzhu Jiegou Xuebao vol 34 no 12 pp 69ndash76 2013 (Chinese)

[7] A M Remennikov and B Uy ldquoExplosive testing andmodellingof square tubular steel columns for near-field detonationsrdquo Jour-nal of Constructional Steel Research vol 101 pp 290ndash303 2014

[8] T Ngo D Mohotti A Remennikov and B Uy ldquoNumericalsimulations of response of tubular steel beams to close-rangeexplosionsrdquo Journal of Constructional Steel Research vol 105 pp151ndash163 2015

[9] F R Zhang C Q Wu H W Wang and Y Zhou ldquoNumericalsimulation of concrete filled steel tube columns against BLASTloadsrdquoThin-Walled Structures vol 92 pp 82ndash92 2015

[10] F Zhang C Wu X Zhao Z Li A Heidarpour and H WangldquoNumerical modeling of concrete-filled double-skin steelsquare tubular columns under blast loadingrdquo Journal of Per-formance of Constructed Facilities vol 29 no 5 Article IDB4015002 2015

[11] Livermore Software Technology Corporation LS-DYNA Theo-retical Manual Livermore Software Technology CorporationLivermore Calif USA 1998

[12] G R Cowper and P S Symonds ldquoStrain-hardening and strain-rate effects in the impact loading of cantilever beamsrdquo TechRep AD144762 Office of Naval Research Arlington Va USA1958

[13] T J Holmquist G R Johnson and W H Cook ldquoA computa-tional constitutive model for concrete subjected to large strainshigh strain rates and high pressuresrdquo in Proceedings of the 14thInternational Symposium on Ballistics Quebec City CanadaSeptember 1993

[14] Q Fang and J Zhang ldquoThree-dimensional modelling of steelfiber reinforced concrete material under intense dynamic load-ingrdquo Construction and Building Materials vol 44 pp 118ndash1322013

[15] Y Li F Lin X L Gu and X Q Lu ldquoNumerical researchof a super-large cooling tower subjected to accidental loadsrdquoNuclear Engineering and Design vol 269 pp 184ndash192 2014

[16] J Li and H Hao ldquoNumerical study of concrete spall damage toblast loadsrdquo International Journal of Impact Engineering vol 68pp 41ndash55 2014

[17] G Randers-Pehrson and K A Bannister ldquoAirblast loadingmodel for DYNA2D and DYNA3Drdquo Tech Rep ARL-TR-1310Army Research Laboratory Adelphi Md USA 1997

[18] Livermore Software Technology Corporation LS-DYNA Key-word Userrsquos Manual (Version 971 R610) Livermore SoftwareTechnology Corporation Livermore Calif USA 2012

[19] CECS ldquoTechnical specification for structures with concrete-filled rectangular steel tube membersrdquo CECS 1592004 ChinaAssociation for Engineering Construction StandardizationBeijing China 2004 (Chinese)

[20] Y Shi H Hao and Z-X Li ldquoNumerical derivation of pressure-impulse diagrams for prediction of RC column damage to blastloadsrdquo International Journal of Impact Engineering vol 35 no11 pp 1213ndash1227 2008

[21] P D Smith and J G Hetherington Blast and Ballistic Loadingof Structures Butterowrth-Heinemenn Oxford UK 1994

[22] K-C Wu B Li and K-C Tsai ldquoThe effects of explosive massratio on residual compressive capacity of contact blast damagedcomposite columnsrdquo Journal of Constructional Steel Researchvol 67 no 4 pp 602ndash612 2011

[23] J E Crawford K B Morrill and J M Magallanes ldquoProtectivedesign for columns against close-in blast effectsrdquo in Proceedingsof the Structures Congress Boston Mass USA April 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of