Engineering Structures 102 (2015) 395–408

Contents lists available at ScienceDirect

Engineering Structures

journal homepage: www.elsevier .com/ locate /engstruct

Investigation of ultra-high performance concrete slab and normalstrength concrete slab under contact explosion

http://dx.doi.org/10.1016/j.engstruct.2015.08.0320141-0296/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: j.li@adelaide.edu.au (J. Li).

Jun Li a,⇑, Chengqing Wu a,b, Hong Hao c

a School of Civil, Environmental and Mining Engineering, The University of Adelaide, North Terrace, SA 5005, Australiab Tianjin Chengjian University & University of Adelaide Joint Research Centre on Disaster Prevention and Mitigation, AustraliacDepartment of Civil Engineering, Curtin University, Kent Street, Bentley, WA 6102, Australia

a r t i c l e i n f o

Article history:Received 27 November 2014Revised 14 August 2015Accepted 20 August 2015Available online 9 September 2015

Keywords:Ultra-high performance concreteContact explosionSPHFinite element

a b s t r a c t

Dynamic performance of concrete structures under blast loading conditions is a topic of importance assuch load generates severe structural damage including flexural damage, shear damage and concretespall damage which may impose threats to the personnel and instruments shielded by the reinforcedconcrete structure. To mitigate blast effects on civil structures, a new kind of concrete material namedUltra-High-Performance-Concrete (UHPC) is now widely studied and applied. UHPC material is knownfor its high compressive and tensile strength, large energy absorption capacity as well as good workabil-ity and anti-abrasion ability. In a previous study, the performance of UHPC slab under blast loads hadbeen investigated through free air explosion tests. The blast resistance capacity of UHPC had beendemonstrated through comparison with normal strength concrete. In the present study, the dynamic per-formance of UHPC slab under contact charge explosion is experimentally studied and compared with nor-mal strength concrete slab under the same loading scenario. Numerical models are established toreproduce both the previous free air explosion tests and the current contact explosion tests. In particular,finite element model is established to simulate the free air explosion test, and coupled smoothed particlehydrodynamics (SPH) method and finite element method is utilized to simulate the contact blast tests.Numerical results are compared with the experimental observations, and the feasibility and accuracyof the numerical model are validated.

� 2015 Elsevier Ltd. All rights reserved.

1. Introduction measurements of the response of the concrete slabs to the blast

In recent decades, with the rising of terrorism threats, increas-ingly more attention is drawn to structural dynamic responseunder blast loading conditions. Structural response under blastloads is a highly complex problem as it involves geometric andmaterial nonlinearity, time dependent structural deformation andloading rate dependent material properties.

Traditional treatments of this problem [1–3] depend mainly onsingle degree of freedom (SDOF) analysis, which is also the pre-ferred method for design analysis as it is relatively straightforwardand easy to use. However, SDOF method based on simplifiedassumptions may not be adequate for reliably modelling a struc-ture with complex geometry under complex loading conditions.

Experimental investigation on this topic can provide intuitionalobservations and useful data of blast induced structural deforma-tion and damage. Schenker et al. [4] conducted full-scale field testson protected and unprotected concrete slabs. Time dependent

waves were successfully recorded and the obtained data had beenused to verify and validate the computer code. Maji et al. [5] con-ducted a full-scale blast test on a structure constructed with fibre-reinforced polymers (FRP) retrofitted masonry walls. It wasobserved that the retrofit was able to withstand the blast load.Smith et al. [6] conducted a series of experiments using smooth-walled tunnels of differing geometry at 1:45 scale and smallpartially-vented cubicles designed to demonstrate that meaningfulresults can be obtained at small scales.

With calibrated material and numerical model, computer basedsimulation could be a powerful supplement to experimental anal-ysis. Different numerical methodologies like finite element method(FEM) and smoothed particle hydrodynamics (SPH) were devel-oped and widely adopted in structural analysis and design. Vastinvestigations utilizing these methods can be found in the previousstudies [7–13]. It has been proved that such computer basednumerical simulations, unlike experimental method which alwaysinvolve safety concern, can provide acceptable predictions of struc-tural response to dynamic loading at a lower cost.

396 J. Li et al. / Engineering Structures 102 (2015) 395–408

Under blast loading conditions, various failure modes includingflexural damage, shear damage and concrete spall damage can beobserved on RC structures. Flexural damage is a desired failuremechanism as it is the most ductile and allows the maximumenergy absorption. However, during blast tests on columns, Craw-ford et al. [14] found, over short loading duration, flexural failurecan only occur if the shear capacity exceeds the bending resistancecapacity. The first failure modes will be diagonal or direct shearfailure if the columns shear capacity is not sufficient enough. Usingreliability analysis technique, Low and Hao [15] developed a modelwhich predicts the most probable failure mechanism between flex-ure and direct shear of a one-way reinforced concrete slab.

Besides flexural and shear damage, concrete spall is another sig-nificant damage mode which is predominant in close-in or contactexplosion scenarios. In such cases, blast impart great amount ofenergy on the structure in the form of stress wave propagation.When the compression stress wave reaches the distal surface ofthe structure component, it will be reflected and then transformedinto tensile stress wave. After superposition of the reflected andincident waves, if the net stress within the concrete materialexceeds its dynamic tensile strength, spall damage happens [16–18]. Without evident structural deformation, spall damage reducesthe cross-sectional area and thus reduces the element load carry-ing capacity. Concrete spall also generates large amount of highspeed flying fragments which impose threats to the personneland equipment inside the structure. In the previous study, Ohtsuet al. [19] experimentally and analytically investigated thedynamic failure of fibre-reinforced concrete (FRC) slabs, and itwas observed that the averaged diameters and the volumes ofthe spall failure remarkably decreased with the increase in theflexural toughness of FRC. Leppänen [20] conducted experimentaland numerical analyses to examine the extent to which the con-crete, at various distances, is affected by the blast wave and frag-ment impacts. The results showed that the damage in theconcrete, from the blast wave and fragment impacts, is localizedin the impact zone. The concrete below this zone, at a depth ofapproximately twice the depth of the maximum penetration, washardly affected at all by the blast wave and fragment impacts. Nashet al. [21] developed a numerical model to predict spall damage toconcrete walls from close-in explosions in air for cased anduncased munitions. The model was used to develop guidelinesfor designing concrete walls to prevent spallation.

Concrete spall damage occurs in a brittle manner due to the rel-atively low tensile strength of concrete material. In order toimprove the structural tensile resistance and mitigate the effectsof blast loads, externally bonded (EB) or near surface mountedFRP plates are now widely used for retrofitting the existing struc-tures. Muzsynski and Purcell [22] conducted a series of full-scaleexplosion tests on RC walls, retrofitted with FRP on the rear (ten-sile) face. It was observed that the two retrofitted walls had ahigher blast resistance capacity and generally performed betterthan the unretrofitted control wall. Razaqpur et al. [23] experimen-tally verified that overall the FRP retrofitted panels performed bet-ter than the companion control panels without FRP retrofit. Basedon available experimental and numerical investigations, Buchanand Chen [24] summarized blast resistance of FRP compositesand polymer strengthened concrete and masonry structures. Muta-lib and Hao [25] constructed pressure-impulse diagrams for FRPstrengthen RC column to provide correlations between the damagelevels of FRP strengthened RC columns and blast loadings.

Rather than retrofitting the existing structure, in recent dec-ades, increasing attention has been given to the utilization of inno-vative concrete material like ultra-high performance concrete(UHPC) in construction of new structural members. UHPC whichconsists of ultra-fine reactive particles and fibre reinforcement isknown for its high compressive strength which is normally in

excess of 150 MPa. Due to the fibre reinforcement, UHPC is alsocharacterized by their improved tensile strength, durability andimpact as well as blast resistance ability when compared withthe conventional commercial concrete. Utilization of UHPC allowsconstruction of sustainable and economic buildings with extraor-dinary slim design which also satisfies public aesthetic needs.Pioneering applications such as a hybrid (steel and UHPC) pedes-trian bridge in Germany [26], a cable stayed bridge in Korea [27]and a series of pedestrian bridges in New Zealand [28] haveimpressed the world with its great capacity and potentiality.Extensive research was carried out to gain knowledge about theperformance of UHPC structures under blast loading environment.Ngo et al. [29] experimentally investigated blast induced behaviourof UHPC prestressed concrete panels with various thickness andreinforcement detailing. Test results were used to validate afinite-element computer code. Roller et al. [30] adopted UHPC asthe retrofit coating material for reinforced concrete columns, andthe residual loading capacity test demonstrated that UHPC coatingwas an effective measure for protective purpose. Based on shocktube tests on nine UHPC columns, Aoude et al. [31] demonstratedthat the use of UHPC significantly improved the blast performanceof reinforced concrete columns by reducing the maximum andresidual displacements, enhancing damage tolerance, and elimi-nating secondary blast fragments. Astarlioglu and Krauthammer[32] analytically investigated the response of normal-strength(NSC) and UHPC columns to idealized blast loads. They comparedpressure-impulse curves for NSC and UHPC columns and con-cluded that under impulsive loads the UHPC columns can sustainmore than four times the impulse that would cause the NSC col-umns to fail. In more recent studies, Li et al. [33,34] studied UHPCcolumns and slabs under both static and blast loading conditions,the results demonstrated the positive effects of utilizing suchmaterial in protective structural design.

In 2007, a series of free air explosion tests were conducted byWu et al. [35] to investigate the blast resistance of slabs con-structed with both plain ultra-high performance fibre concrete(UHPFC) and reinforced ultra-high performance fibre concrete(RUHPFC). Normal reinforced concrete (NRC) slabs were also testedas control specimens. It was noted the UHPC slabs outperformedthe NRC slab with significantly reduced flexural damage after blast.

In the current study, to investigate the spall damage resistanceof the UHPC, contact explosion tests are carried out. Reinforcednormal strength concrete slab and unreinforced UHPC slab aretested under 1 kg contact charge. Spall damage on these two slabsare recorded and discussed. Besides experimental investigation,numerical simulation is performed to reproduce the contact explo-sion tests and free air explosion tests conducted in 2007. Numeri-cal models are developed for both high explosives and concreteslabs. Finite element analysis is carried out for the free air explo-sion tests in which slabs mainly responded in their global responsemodes, i.e., shear and flexural response modes, in either elastic orplastic range. For contact explosion test simulation, coupled finiteelement and smoothed particle hydrodynamics (SPH) method isadopted, and SPH particles are used to simulate the high explosiveand finite elements are used to simulate the concrete slab. Resultsfrom numerical simulations are compared with the field testresults. The feasibility of the numerical model is verified andvalidated.

2. Experimental program

2.1. Material properties of test specimens

2.1.1. Static strengthUHPC slab used in the current study was constructed by VSL in

their Melbourne laboratory. Material composition of current UHPC

J. Li et al. / Engineering Structures 102 (2015) 395–408 397

is listed in Table 1 [36]. Micro reinforcement high carbon metallicfibres were mixed at a volume dosage of 2%. The fibre length is13 mm and diameter is 0.2 mm and fibre tensile strength is1800 MPa.

An initial heat treatment, consisting of curing in hot water at atemperature of 90 �C for a period not less than 48 h was applied tothe concrete material after setting. Such heat curing acceleratesmaturation of the material and gives it dimensional stabilityimmediately after manufacturing, thereby increasing its durability.Experimental stress strain profiles for the concrete underinvestigation were obtained from the manufacturer for bothuniaxial compression and flexural tension at 28 days. Compressionstress strain curve was obtained from 70 mm diameter cylindertests and flexural tensile stress strain relationship was obtainedfrom standard tensile tests on prisms of square section(100 ⁄ 100 ⁄ 400 mm). Fig. 1 shows the typical representative test-ing data obtained from uniaxial compression and flexural tests.

The compressive strength and tensile strength of UHPC materialare averaged as 175 MPa and 30.2 MPa, respectively. The compres-sive strength and tensile strength of normal strength concrete usedin NRC slab construction are determined as 39.5 MPa and 8.2 MPa,respectively. The Young’s modulus of the NRC and UHPC are28.6 GPa and 41 GPa, respectively. The stress strain curves of UHPCunder uniaxial compression and tension tests are plotted in Fig. 1.

Table 1UHPC mix proportions.

Constituent Amount

Cement 680 kg/m3

Silica fume 204 kg/m3

Silica flour 204 kg/m3

Sand 974 kg/m3

Steel fibres 156 kg/m3

Superplasticizer 44 l/m3

Water 150 l/m3

Fig. 1. Stress strain relationship of UHPC material.

The steel reinforcement used in the current study has a yieldstrength of 600 MPa and Young’s modulus of 200 GPa.

2.1.2. Strain rate effect and dynamic increase factorIt is commonly acknowledged that under high strain rate load-

ing condition, material properties differ from those under staticcondition [37,38]. The strength enhancement can be representedusing dynamic increase factor (DIF). For normal strength concretewith compressive strength ranging from 20 to 70 MPa, their DIFcan be calculated through equations proposed by Malvar andCrawford [39].

For normal strength concrete compressive strength, the DIFscan be derived from:

DIF ¼ f cf cs

¼_e_es

� �1:026afor _e 6 30 s�1

cs_e_es

� �1=3for _e > 30 s�1

8><>: ð1Þ

where fc is the dynamic compressive strength at _e; fcs is the staticcompressive strength at _es; _e is the strain rate in the range of30 � 10�6 to 300 s�1; _es is the static strain rate 30 � 10�6;logcs = 6.156 a �2; a = 1/(5 + 9fcs/fco); fco = 10 MPa.

For normal strength concrete tensile strength, DIFs can beobtained from:

DIF ¼ f tf ts

¼_e_es

� �dfor _e 6 1 s�1

b _e_es

� �1=3for _e > 1 s�1

8><>: ð2Þ

For steel reinforcement:

DIF ¼ _e10�4

� �a

ð3Þ

where for the yield strength, a = afy = 0.074–0.04fy/60; and for theultimate stress, a = afu = 0.019–0.009fy/60.

Until now, the dynamic strength of UHPC is a topic of limiteddiscussion. Magnusson and Hallgren [40] tested concrete withcompressive strength up to 200 MPa, and they found the load car-rying capacity of steel fibre reinforced concrete was increased inthe dynamic tests due to strain-rate effects. The experimental datasummarised by Malvar and Crawford [41] showed a reducing DIFwith increasing concrete strength. Chen et al. [42] conducteddynamic tensile tests on steel fibre reinforced concrete with vari-ous fibre volume fraction, and the largest DIF observed at a loadingrate of 450 GPa/s is around 1.1. Weidner [43] conducted a series ofdrop hammer tests on both plain concrete and fibre reinforced highstrength concrete, and it was observed that fibre reinforced con-crete specimens did not perform as well as normal strength con-crete specimens when tested dynamically. Fibre reinforcedconcrete specimens tested in tension at elevated temperaturesexhibited a decrease in DIF when compared to room temperature.Millard et al. [44] performed dynamic flexural tensile test on ultra-high strength concrete with different dosages of steel fibre. Theresults show that the strain rate enhancement of flexural strengthfor UHPFRC is reduced as the fibre percentage increases. In fibre-reinforced beams, the fibres resist the lateral spreading of thecracks by bridging across regions of lower strength. Therefore,the beneficial effect of a restraint on lateral crack growth hasalready been partially accounted for by fibre reinforcement, result-ing in higher failure strength under quasistatic loading. Subse-quently, the influence of the higher loading rate on reducinglateral crack development would be lessened.

In the current study, since no data available describing thedynamic behaviour of the UHPC material, a DIF value of 1.0 is usedin the simulation of UHPC under blast loads. This is a rather conser-vative assumption as it underestimates the UHPC strength under

Fig. 3. Contact explosion test.

Fig. 4. Test setup and supporting system.

398 J. Li et al. / Engineering Structures 102 (2015) 395–408

blast loads. This assumption has been adopted in the previousnumerical studies [45,46] and reasonable correlation was noticedbetween numerical results and experimental observation. It isworth pointing out that further study on the dynamic strength ofUHPC material is undergoing through laboratory SHPB tests andthe numerical simulations with the updated DIF values will be con-ducted to validate the assumption made in the current study andfurther improve the modelling accuracy.

2.2. Test setup

In these two contact blast tests, slab dimension is2000 ⁄ 1000 ⁄ 100 mm. the NRC specimen was designed with bothtension and compression reinforcement using a 12 mm diametermesh, with a 10 mm concrete cover. The mesh bars were spacedat 100 mm centres in the major bending plane and 200 mm inthe minor plane. This corresponds to a reinforcement ratio of1.2%. Fig. 2 illustrates the configuration of the NRC slab.

UHPC slab shares the same dimension with the NRC slab butwith no steel reinforcement. The confinement effect from the rein-forcement mesh does not exist in UHPC slab, and the spall damageis solely resisted by the UHPCmaterial. 1 kg explosive charge in theshape of cylinder with ratio of diameter to length 1 is placed on theupper surface of the slab specimens. Due to the predrilled holes inthe slabs for the installation of pressure gauges, the charge is offsetfrom the centre as can be seen in Fig. 3.

Fig. 4 shows the field set up and steel rig supporting system forcontact explosion test. The base steel plates are bolted to the con-crete ground slab to stabilize the testing system, and the slab isplaced on the steel rig with a simply support boundary.

The blast program is summarised in Table 2.

2.3. Test results

Fig. 5 shows the response of NRC slab after 1 kg contact explo-sion. It can be noticed that the slab suffered a 390 mm diameterfailure on the proximal surface as indicated in Fig. 5(a), while thedistal surface of the slab has a larger failure diameter of 710 mmas shown in Fig. 5(b). This is a typical concrete spall and punchingfailure mode. Under contact loading condition, blast pressuredirectly impacts on the proximal surface, and this pressure easilyexceeds the dynamic compressive strength of normal strength con-crete which induces concrete punching failure. Blast load also gen-erates severe stress wave propagation along the slab depthdirection. Upon the interaction between the reflective stress andincident stress, if the resultant stress exceeds the dynamic tensilestrength of the concrete, concrete spall occurs. It is worth notingthat a wedge shape side failure was also observed on the NRC slab

Fig. 2. Dimension and reinforcement of

as shown in Fig. 5(b). It is believed that such failure is caused bythe stress wave propagation within the slab plane. Since the explo-sives offset from the centre to the side, the incident stress wave hasa short distance to travel before it encounters the reflective stresswave from the free edge, only small amount of energy has beendissipated before the wave superposition, and the resultant stressis still larger than the dynamic tensile strength of the concretewhich brings damage to the free edge of the slab.

NRC slab in contact explosion test.

Table 2Blast program.

Slab no. Description Rebar ratio Standoff distance (m) Scaled distance (m/kg1/3) Explosive charge (kg)

NRC RC slab 1.2% Contact explosion – 1.0UHPC Unreinforced UHPC – Contact explosion – 1.0

Table 3Contact explosion induced damage.

Slab no. Damage diameters (mm)

dtop dbottom

NRC 390 710UHPC 350 380

J. Li et al. / Engineering Structures 102 (2015) 395–408 399

Fig. 6 shows the response of UHPC after 1 kg contact explosion.Similar damage mode as seen on the NRC slab is observed. How-ever, after detailed measurement, the UHPC slab is found to havesmaller damage diameter on both the top and bottom surface,i.e. 350 mm and 380 mm, respectively, and there is small differ-ence between the upper and bottom damage area diameter. Theseobservations could be explained by the two factors. Firstly, thesteel fibre composites in UHPC slab can effectively prevent con-crete cracking and even bridge over the concrete cracks to mitigatethe bottom surface spall damage. Secondly, UHPC has ultra-highcompressive strength and significant material ductility as shownin Fig. 1 which means it can absorb large amount of blast energy,thus reduce the concrete punching failure on the upper surface.It is worth noting that the UHPC slab in this contact explosion testdoes not have any steel reinforcement, and the spall damage can befurther confined if reinforcement mesh is included.

Table 3 summarises the spall damage diameters of both slabs.

3. Numerical simulation

In this section, to demonstrate the UHPC behaviour under vari-ous blast loads and verify the proposed numerical model, free airexplosion tests conducted in 2007 by Wu et al. [35] as well asthe current contact explosion tests are numerically investigated.The material properties (both the UHPC and NRC), specimendimensions and testing systems in the free air explosion tests are

(a) Top surface

Fig. 5. NRC response to contact explosion (a) to

(a) Top surface

Fig. 6. UHPC response to contact explosion (a) t

identical with contact explosion tests discussed above. In total fourslabs as summarised in Table 4 are numerically studied.

3.1. Material model

Numerical investigations in the present study are performedusing LS-DYNA, which is especially developed for nonlineardynamic simulations. In LS-DYNA, various material models suchas Pseudo Tensor (MAT_16), Brittle Damage (MAT_96), JohnsonHolmquist Concrete (MAT_111) and Concrete Damage Rel3(MAT_72_REL3) can be used for concrete modelling under dynamicloading condition.

In the present study, Concrete_Damage_Rel3 is used for mod-elling normal strength concrete. Concrete_Damage_Rel3 is aplasticity-based model, and it uses three shear failure surfaceswhich change shape, depending on the confinement pressure.The damage and strain rate effect is included in this model. Themajor advantage of this model is that it is based on a single user

(b) Bottom surface

p face of slab and (b) bottom face of slab.

(b) Bottom surface

op face of slab and (b) bottom face of slab.

Table 4Slabs and blast scenarios considered in numerical simulation.

Slab no. Description Rebar ratio (%) Standoff distance (m) Scaled distance (m/kg1/3) Explosive charge (kg)

NRC-2007 RC slab 1.2 1.5 0.75 8.2UHPC-2007 Reinforced UHPC 1.2 1 0.37 20.1NRC RC slab 1.2 Contact explosion – 1.0UHPC Unreinforced UHPC – Contact explosion – 1.0

400 J. Li et al. / Engineering Structures 102 (2015) 395–408

input parameter, i.e., the unconfined compressive strength. Theremaining model parameters are automatically generated using abuilt-in algorithm and can also be modified by users.

The above mentioned material model is suitable for modellingthe brittle behaviour of plain concrete. They cannot well modelthe damage softening behaviour in post-yield stage of UHPC. More-over, these models involve too many parameters to be determinedby simple material tests. In the present study, the material proper-ties provided by the UHPC company are limited to the uniaxialcompression and flexural tension stress–strain relationships.

To make use of most of the available test data, hydrodynamicmaterial model ‘‘Elastic–Plastic Hydrodynamics Model” is adoptedto describe the dynamic behaviour of UHPC. This model can besimplified as a bilinear elastic–plastic stress strain relationshipsuitable for most engineering materials including those with pres-sure dependent yield behaviours such as concrete. As shownin Fig. 7. The yield strength ry is a function of the effective plasticstrain �eP.

ry ¼ r0 þ Eh�eP ð4Þwhere r0 is the initial yield strength, Eh represents the plastic hard-ening modulus defined in terms of Young’s modulus, E, and the tan-gent modulus Et, as

Eh ¼ Et � EE� Et

ð5Þ

Using the data from uniaxial compression tests the relationshipbetween the effective stress and the effective plastic strain �eP, asshown in Fig. 8 can be determined. Interpolation from the datacurve can be conducted, and in this case the parameter Eh is nolonger required for input during calculations.

Effective stress is defined in terms of the deviatoric stresstensor sij = rij � dijrkk /3 as

�r ¼ 32SijSij

� �12

ð6Þ

Fig. 7. Uniaxial bilinear elastic–plastic stress–strain model.

and the effective plastic strain can be defined as

�eP ¼Z t

0

23_epij _e

pij

� �12

dt ð7Þ

where t denotes time, _epij is the plastic strain rate.Table 5 lists the tabulated input of effective stress–effective

plastic strain data for UHPC.The shock response of UHPC was considered using the Mie–

Gruneisen equation of state. With cubic shock velocity-particlevelocity, the Gruneisen equation of state defines pressure for com-pressed material as:

p ¼ q0C2l 1þ 1� c0

2

� �l� a

2l2

� 1� ðS1 � 1Þl� S2

l2

lþ1 � S3l3

ðlþ1Þ2h i2 þ ðc0 þ alÞE ð8Þ

and for expanded material as:

p ¼ q0C2lþ ðc0 þ alÞE ð9Þ

where C is bulk sound velocity termed as the intercept of the Us–Up

curve, S1, S2 and S3 are the coefficients of the slope of the Us–Up

curve; c0 is the Gruneisen gamma; a is the first order volume cor-rection to c0; and l = q/q0�1.

The shock velocity–particle velocity relationship is non-linearand is given by:

Us ¼ C þ S1Up þ S2UP

Us

� �UP þ S3

UP

Us

� �2

UP ð10Þ

It is well recognized that for most materials, the second-orderand higher terms are negligible, the parameters S2 and S3 are thentaken as zeros. Shock velocity Us varies linearly with respect tothe particle velocity Up as

Us ¼ C þ S1 � Up ð11ÞMacroscopically, concrete is an isotropic material. For isotropic

elastic bodies, the bulk sound velocity Cwas determined as

C ¼ffiffiffiffiffiffiffiffiffiK=q

pð12Þ

In which K is the UHPC bulk modulus equals to 2E9ð1�2cÞ, c is Pois-

son’s ratio.

Fig. 8. Effective stress and effective plastic strain interpolated from tabulated input.

Table 5Effective stress–effective plastic strain data for describing UHPC hardening and softening.

Effective plastic strain Effective stress (MPa) Effective plastic strain Effective stress (MPa)

Point 1 0 165 Point 9 0.005 150Point 2 0.0005 170 Point 10 0.0055 149Point 3 0.001 175 Point 11 0.006 148Point 4 0.002 170 Point 12 0.0065 147Point 5 0.00275 165 Point 13 0.007 146Point 6 0.003 162 Point 14 0.00725 145Point 7 0.0035 160 Point 15 0.0075 143Point 8 0.004 155 Point 16 0.008 140

J. Li et al. / Engineering Structures 102 (2015) 395–408 401

In summary, in the present study, the non-linear stress soften-ing behaviour of UHPC is modelled by the tabulated stress–straincurve of the elastic–plastic hydrodynamic material model in LS-DYNA. The tensile stress failure is determined by the tensile cut-off value which equals to 30 MPa according to the tensile stressof UHPC. The shock response of UHPC is modelled using the Mie–Gruneisen equation of state.

The parameter in the EOS used in the present study is given inTable 6. After substituting Young’s modulus (41 GPa), materialdensity (2650 kg/m3), Poisson’s ratio (0.15) into Eq. (12), bulksound velocity can be estimated as 2100 m/s. Due to the lack ofdynamic tests data, the slope of the Us–Up curve S1 and Gruneisengamma c0 are sourced from previous numerical simulations onsteel fibre reinforced concrete [47]. It should be noted thatalthough the following numerical results demonstrate the feasibil-ity of adoption of this material model and the correspondingparameters, further dynamic material tests are deemed necessaryto verify the assumptions.

Steel reinforcement in the current study is simulated by MAT_Piecewise_Linear_Plasticity (MAT_24). This model allows the defi-nition of arbitrary stress versus strain curve and arbitrary strainrate curve. Also, failure based on a plastic strain or the minimumtime step size can be defined.

Crack and concrete spall can be simulated in LS-DYNA througheither the tied node with failure definition or the element erosionalgorithm. The first method requires duplicated nodes to bedefined and tied together in selected regions. Using the erosionalgorithm, concrete finite element model is created in conventionalmanner, and when the element response such as the principlestress or strain exceeds the defined value, such element will beautomatically eroded and erased from the finite element model.

When choosing the erosion criterion for NRC and UHPC in thecurrent study, the primary concern is to avoid massive deletionof the elements and maintain the mass conservation. Ideally ero-sion should not be used to delete elements. This, however, is notpossible when modelling large deformation in the post-failureregion such as concrete spall damage. Therefore, to avoid erodingelements prematurely, large strain is usually chosen as the erosioncriterion (Note this strain is not necessarily the material fracturestrain).

For NRC material, typical concrete strain at peak tensile stressunder static loading is around 0.00025 (which is one tenth of thepeak compressive strain). Considering the softening phase, theconcrete fracture strain may be assumed as 5 � 0.00025 =0.00125. Taken into the consideration of other effects like strain

Table 6Parameter for the equation of state describing the UHPC.

EOS C0 2100 m/sS1 1.4c0 2

rate effect (DIF up to 7 under tension) and confinement effect fromthe reinforcement, this value can be even higher than 0.2. ForUHPC material, according to the flexural stress strain curve asshown in Fig. 1, UHPC has peak tensile strain around 0.002, andthis value is about 8 times higher than NSC material. However,under dynamic tensile loading condition, UHPC is significantly lessrate sensitive (DIF slightly larger than 1). This means underdynamic loading condition, the fracture strain for both UHPC andNRC are more or less the same. Therefore, an erosion criterionwhich is the same as the NRC is adopted for UHPC. Furthermore,considering that FE models for UHPC and NRC slabs have the samemesh density, uniform erosion criterion can give sound compar-ison on the crack propagation of the two materials.

After large amount of trials, a principal strain equal to 0.4 ischosen as the erosion criterion. If the criterion is set higher, ele-ment distortion due to large element deformation under blastloading happens; if the criterion is set lower, premature erosionand element deletion occur which violate the mass conservationand the results are no longer reliable. Table 7 summaries the mate-rial property used in the current study.

3.2. Numerical model

Finite element model of the slab under free air explosion ismodelled in ANSYS-LS-DYNA and shown in Fig. 9(a). The bound-ary condition of the test slab is shown in Fig. 9(b). In the majorbending plane, nodes within 0.1 m width towards the ends ofslab are selected and their vertical direction degree of freedomis constrained. Two different sizes of element are used in themodel. The element size close to the slab centre is 8 mm whileelement size close to the boundary is 40 mm. Convergence testshows that further decrease of the central element size canslightly increase the simulation accuracy; however at the costof enormous computational time and effort. The relatively largerelement size close to the boundary can effectively reduce thestress concentration and avoid early erosion of the boundaryelements.

3.3. Free air explosion tests simulation

The blast load modelling in the free air explosion is through the⁄Load_Blast function in LS-DYNA. The utilization of this functionavoids the detailed modelling of the explosive charge and shock

Table 7Material properties.

NRC andNRC-2007

UHPC andUHPC-2007

Steel

Young’s modulus 28.3 GPa 45 GPa 200 GPaCompressive strength 39.5 MPa 175 MPa –Tensile strength 8.2 MPa 30 MPa 600 MPaErosion principle strain 0.4 0.4 0.2

Fig. 9. Finite element model of slab.

402 J. Li et al. / Engineering Structures 102 (2015) 395–408

wave propagation in air, thus it can save the computational effort.The disadvantage of this function is that it cannot model the shockwave and structure interaction. The reliability of this function insimulating blast loads on structures has been proven and it is verycommonly used in numerical simulations of structural responsesto blast loads.

In this section, free air explosion on two slabs, i.e. NRC-2007and UHPC-2007 are simulated. The numerical results are thencompared with the experimental results. Fig. 10 shows theresponse of NRC-2007 with the plastic strain contour. It can beobserved that the slab deforms in the plastic region, and noscabbing or spall damage happens. The plastic strain of concreteis used as the damage indicator in this material model(Concrete_Damage), and it can be noticed that at the time of30 ms when the plastic strain distribution becomes stable, andthe contour shows the concrete cracks concentrate at the slab

1ms

8 ms

20 ms

Fig. 10. NRC-2007 s

mid-span and the crack lengths decrease towards the slab bound-ary. This damage observation is close to the field test results asshown in Fig. 11.

The time history curves of the mid-span displacement andvelocity are plotted in Fig. 12. In the experiment, the LVDT usedfor the displacement recording debonded from the slab after thefirst peak, thus the comparison of the entire history curve is notavailable here. However, it is noticed that, during the test, the peakdisplacement in the first vibration period is captured as 38 mm.The numerical simulation gives a value of around 36 mm and theprediction accuracy is high. The slight underestimation can beattributed to the explosive charge shape effect. Explosive used inthe test is cylindrical shaped, however in LS-DYNA, Load_Blastfunction is based on spherical TNT explosion in free air. The chargeshape caused the blast wave to be directional, bringing about ahigher pressure magnitude in the test than predicted by the

ms

ms

ms

5

10

30

lab simulation.

Fig. 11. NRC-2007 field observation [35].

-0.04

-0.03

-0.02

-0.01

0

0 0.01 0.02 0.03 0.04 0.05 0.06

Dis

plac

emen

t (m

)

Time (ms)

Midspan displacement

-12

-8

-4

0

4

0 0.01 0.02 0.03 0.04 0.05 0.06

Vel

ocity

(m/s

)

Time (ms)

Midspan velocity

Fig. 12. Time history curves of midspan response.

3 ms ms 20

Fig. 13. UHPC-2007 slab response simulation.

Fig. 14. UHPC-2007 field observation [35].

J. Li et al. / Engineering Structures 102 (2015) 395–408 403

numerical method [48]. The permanent displacement given by thenumerical simulation is about 20 mm, and the slab exhibits a plas-tic deformation.

Fig. 15. concrete crush

Fig. 13 shows the simulation of UHPC-2007 under severe freeair explosion with a scaled distance of 0.37 m/kg1/3. Slab flexuraldamage at mid-span can be clearly noticed. In the plastic hingeregion, concrete elements are eroded. Cracks on the upper surfaceand opening on the bottom side are observed. Comparing with thefield observations as shown in Fig. 14, the numerical model wellreproduces the slab damage mode. Again, due to the LVDT debond-ing from the slab, the time history curves cannot be compared.

Comparison of the plastic hinge in the mid span is shown inFig. 15, and it can be noted that the numerical model utilizingthe Mat_Elastic_Plastic_Hydrodynamics can well simulate the con-crete crushing and cracking. It is believed that further decreasingthe element size could give even better crack simulation, however,the computational effect would increase enormously.

The ultra-high strength concrete was observed to be an effec-tive material which resists a large blast at a small scale distance.

and bottom crack.

Fig. 16. Coupled FE model and SPH particles.

404 J. Li et al. / Engineering Structures 102 (2015) 395–408

3.4. Contact explosion tests simulation

Contact explosion simulation is through the coupled finiteelement method and smoothed particle hydrodynamics method.The SPH method was originally developed by Lucy [49] and Gin-gold and Monaghan [50]. Instead of finite elements, this method

1 ms

8 ms

15 ms

Fig. 17. Explosio

uses discrete particles, interacting with each other via an interpo-lation function. Since this method is Lagrangian and mesh free, it iswell suited to analyse large deformation events involving failureand fragmentation [51], and the utilization of using such methodsimulating the high explosive explosions are also found in litera-ture [52,53]. In the present study, in order to simulate interaction

ms

ms 10

20ms

5

n expansion.

0.1 ms ms

0.3 ms ms

1 ms ms

7 ms ms

15 ms ms

3

10

20

0.2

0.5

Fig. 18. Slab NRC top surface response.

J. Li et al. / Engineering Structures 102 (2015) 395–408 405

of explosion wave with the slab, and capture large deformation ofthe explosive, the high explosive material is simulated throughSPH particles and test slab is modelled with finite elements asshown in the free air tests. MAT_High_Explosive is adopted to

simulate the high explosive material, Mat_Concrete_Damage_Rel3and Mat_Elastic_Plastic_Hydrodynamics are used to simulate theNRC slab and UHPC slab respectively, and the MAT_Piecewise_Linear_Plasticity is used to model the steel reinforcement.

Fig. 19. Slab NRC bottom response.

0.1 ms ms

10 ms ms

3

20

Fig. 20. Slab UHPC top surface response.

406 J. Li et al. / Engineering Structures 102 (2015) 395–408

In total, 12500 SPH particles are generated in cylinder shape tomodel the explosive. The SPH particles and test slab model areshown in Fig. 16.

Contact between the SPH particles and test slab is modelledthrough the LS-DYNA built-in algorithm ⁄CONTACT_NODES_TO_SURFACE, and default value is used in the contact setup.

Fig. 17 shows the explosion phenomenon modelled in the pre-sent study. The explosive expansion and corresponding blast wave-front pressure can be clearly observed in the figure.

Fig. 18 shows the top surface response of the target slab NRC.The punching and spall failure quickly expands with time. Thedamage extends quickly in the first 10 ms, and remains stableafterwards. No global deformation can be observed which indicatesthe slab response under contact explosion is highly localized.

It is even clearer to observe the spall damage from the bottomsurface as shown in Fig. 19, comparing with the experimentalobservations of NRC on the bottom side, the numerical model givesexcellent predictions on the structural damage. Concrete spall,

0.1 ms ms

10 ms ms 20

3

Fig. 21. Slab UHPC bottom surface response.

Table 8Spall damage dimension comparison.

Slab Damage diameters (mm)

Experimentaltop

Experimentalbottom

Numericaltop

Numericalbottom

NRC 390 710 360 700UHPC 350 380 310 330

J. Li et al. / Engineering Structures 102 (2015) 395–408 407

punching and tearing of the steel reinforcement are all well simu-lated with high fidelity.

Fig. 20 shows the ultra-high performance concrete slab UHPCunder 1 kg contact explosion. Similar to the NRC slab, the concretecrush and spall is highly localized and the structure restores stabil-ity in a short period of time. Due to the high compressive strength,the concrete crush on the proximal face facing the explosive is sig-nificantly confined comparing with the NRC slab.

On the distal face of the UHPC slab, concrete spall failure whichis induced by the severe tensile wave propagation is again seenclearly as shown in Fig. 21. However, with the contribution fromthe steel fibre, the spall area is not as significant as seen on theNRC slab. It is worth noting that in this UHPC slab, no steel rein-forcement is placed, and according to the previous study [9,17],with the inclusion of the steel reinforcement, the spall damagecan be further mitigated.

In the contact explosion tests, the minimum global flexuralbehaviour was expected on the test slabs, thus no LVDT wasinstalled on the slab for the deflection time history recording.Due to the lack of quantitative data of the test slab, only the failuremode and failure dimension are compared between the test slabsand numerical results, and the comparison are summarised inTable 8. It is noticed that the numerical method gives good predic-tion of the spall damage diameter. Again the superior blast resis-tance capacity of UHPC slab is demonstrated.

4. Concluding remarks

Two contact explosion tests on normal concrete slab and ultra-high performance concrete slab are conducted. From the experi-mental results, it is noticed that due to the contribution from theultra-high compressive strength and steel fibre reinforcement,UHPC has significantly reduced concrete punching and spall dam-age as compared with the NRC slab. Rational numerical models forUHPC and NRC under blast loads are developed. Free air explosiontests conducted in a previous study and the current contact explo-sion tests are reproduced in hydro-code LS-DYNA using the pro-posed numerical models. Finite Element method is used for freeair explosion simulation while the coupled SPH and Finite Elementmethod is utilized for the contact explosion simulation. From theresults comparison of the damage mode and spall damage area,it is concluded that the proposed numerical model and methodol-ogy can well reproduce the structural response of normal strengthconcrete slab and UHPC slab under various blast loading condi-tions. The numerical results again demonstrated the superior blastresistance capacity of UHPC material.

Acknowledgements

The research presented in this paper jointly supported by theARC Discovery Grant DP140103025, the National Natural ScienceFoundation of China under Grant 51278326, and the NationalKey Technology R&D Program of the Ministry of Science and Tech-nology of China (2012BAJ07B05) is gratefully acknowledged.

References

[1] American Society of Civil Engineers. Design of blast resistant buildings inpetrochemical facilities; 1997.

[2] UFC. Structures to resist the effects of accidental explosions. Department ofDefense, Unified Facilities Criteria 3-340-02, Washington, DC.

[3] Biggs JM. Introduction to structural dynamics. New York: McGraw-Hill; 1964.[4] Schenker A, Anteby I, Gal E, Kivity Y, Nizri E, Sadot O, Michaelis R, Levintant O,

Ben-Dor G. Full-scale field tests of concrete slabs subjected to blast loads. Int JImpact Eng 2008;35:184–98.

408 J. Li et al. / Engineering Structures 102 (2015) 395–408

[5] Maji AK, Brown JP, Urgessa GS. Full-scale testing and analysis for blast-resistant design. J Aeros Eng 2008;21:217–25.

[6] Smith P, Mays G, Rose T, Teo K, Roberts B. Small scale models of complexgeometry for blast overpressure assessment. Int J Impact Eng 1992;12:345–60.

[7] Zhou X, Hao H. Mesoscale modelling and analysis of damage andfragmentation of concrete slab under contact detonation. Int J Impact Eng2009;36:1315–26.

[8] Xu K, Lu Y. Numerical simulation study of spallation in reinforced concreteplates subjected to blast loading. Comput Struct 2006;84:431–8.

[9] Li J, Hao H. Numerical study of concrete spall damage to blast loads. Int JImpact Eng 2014;68:41–55.

[10] Li J, Hao H. Influence of brittle shear damage on accuracy of the two-stepmethod in prediction of structural response to blast loads. Int J Impact Eng2013;54:217–31.

[11] Li J, Hao H. Numerical study of structural progressive collapse usingsubstructure technique. Eng Struct 2013;52:101–13.

[12] Wang Z, Lu Y, Hao H, Chong K. A full coupled numerical analysis approach forburied structures subjected to subsurface blast. Comput Struct2005;83:339–56.

[13] Xu J-X. Analysis of structural response under blast loads using the coupledSPH–FEM approach. J Zhejiang Univ Sci A 2008;9:1184–92.

[14] Crawford JE, Malvar LJ, Morrill KB. Reinforced concrete column retrofitmethods for seismic and blast protection. In: Proc of society of Americanmilitary engineering symposium on compressive force protection; 2001.

[15] Low HY, Hao H. Reliability analysis of direct shear and flexural failure modes ofRC slabs under explosive loading. Eng Struct 2002;24:189–98.

[16] Grady D. The spall strength of condensed matter. J Mech Phys Solids1988;36:353–84.

[17] McVay MK. Spall damage of concrete structures. DTIC Document 1988.[18] Foglar M, Hajek R, Kovar M, Štoller J. Blast performance of RC panels with

waste steel fibers. Constr Build Mater 2015;94:536–46.[19] Ohtsu M, Uddin FA, Tong W, Murakami K. Dynamics of spall failure in fiber

reinforced concrete due to blasting. Constr Build Mater 2007;21:511–8.[20] Leppänen J. Experiments and numerical analyses of blast and fragment

impacts on concrete. Int J Impact Eng 2005;31:843–60.[21] Nash PT, Vallabhan C, Knight TC. Spall damage to concrete walls from close-in

cased and uncased? Explosions in air. ACI Struct J 1995;92.[22] Muszynski LC, Purcell MR. Composite reinforcement to strengthen existing

concrete structures against air blast. J Compos Construct 2003;7:93–7.[23] Ghani Razaqpur A, Tolba A, Contestabile E. Blast loading response of reinforced

concrete panels reinforced with externally bonded GFRP laminates. Compos BEng 2007;38:535–46.

[24] Buchan PA, Chen JF. Blast resistance of FRP composites and polymerstrengthened concrete and masonry structures – a state-of-the-art review.Compos B Eng 2007;38:509–22.

[25] Mutalib AA, Hao H. Development of P–I diagrams for FRP strengthened RCcolumns. Int J Impact Eng 2011;38:290–304.

[26] Fehling E, Bunje K, Schmidt M. Gärtnerplatz – Bridge over River Fulda inKassel: Multispan Hybrid UHPC-Steel Bridge. In: Designing and building withUHPFRC. John Wiley & Sons, Inc.; 2013. pp. 0–136.

[27] Chin W, Kim Y, Cho J-R, Park J. Dynamic characteristics evaluation ofinnovative UHPC pedestrian cable stayed bridge. Engineering 2012;4(12):869–76.

[28] Rebentrost M, Wight G. Perspective on UHPCs from a specialist constructioncompany. In: Designing and building with UHPFRC. John Wiley & Sons, Inc.;2013. pp. 189–208.

[29] Ngo T, Mendis P, Krauthammer T. Behavior of ultrahigh-strength prestressedconcrete panels subjected to blast loading. J Struct Eng 2007;133:1582–90.

[30] Roller C, Mayrhofer C, Riedel W, Thoma K. Residual load capacity of exposedand hardened concrete columns under explosion loads. Eng Struct2013;55:66–72.

[31] Aoude H, Dagenais FP, Burrell RP, Saatcioglu M. Behavior of ultra-highperformance fiber reinforced concrete columns under blast loading. Int JImpact Eng 2015;80:185–202.

[32] Astarlioglu S, Krauthammer T. Response of normal-strength and ultra-high-performance fiber-reinforced concrete columns to idealized blast loads. EngStruct 2014;61:1–12.

[33] Li J, Wu C, Hao H, Su Y. Investigation of ultra-high performance concrete understatic and blast loads. Int J Protect Struct 2015;6:217–35.

[34] Li J, Wu C, Hao H. An experimental and numerical study of reinforced ultra-high performance concrete slabs under blast loads. Mater Des 2015;82:64–76.

[35] Wu C, Oehlers DJ, Rebentrost M, Leach J, Whittaker AS. Blast testing of ultra-high performance fibre and FRP-retrofitted concrete slabs. Eng Struct2009;31:2060–9.

[36] Ngo TD. Behaviour of high strength concrete subject to impulsive loading2005.

[37] Hao Y, Hao H, Li Z-X. Numerical analysis of lateral inertial confinement effectson impact test of concrete compressive material properties. Int J Protect Struct2010;1:145–68.

[38] Hao Y, Hao H, Zhang XH. Numerical analysis of concrete material properties athigh strain rate under direct tension. Int J Impact Eng 2012;39:51–62.

[39] Malvar LJ, Crawford JE. Dynamic increase factors for concrete. DTIC Document1998.

[40] Magnusson J, Hallgren M. Reinforced high strength concrete beams subjectedto air blast loading. In: Structures under shock and impact VIII. Wit Press;2004. pp. 53–62.

[41] Malvar L, Crawford J, Morrill K. K and C concrete material model, release III –automated generation of material model input. Karagozian and case structuralengineers. Technical report 2000 TR-99-24.3; 2000.

[42] Chen R, Liu Y, Guo X, Xia K, Lu F. Dynamic tensile properties of steel fiberreinforced concrete. Dynamic Behavior of Materials, vol. 1. Springer; 2011. p.37–42.

[43] Weidner AM. Dynamic properties of concrete and fiber reinforced concrete atroom and elevated temperatures, Department of Civil and EnvironmentalEngineering. University of Utah; 2013.

[44] Millard S, Molyneaux T, Barnett S, Gao X. Dynamic enhancement of blast-resistant ultra high performance fibre-reinforced concrete under flexural andshear loading. Int J Impact Eng 2010;37:405–13.

[45] Wang Z, Wu J, Wang J. Experimental and numerical analysis on effect of fibreaspect ratio on mechanical properties of SRFC. Constr Build Mater2010;24:559–65.

[46] Thiagarajan G, Kadambi AV, Robert S, Johnson CF. Experimental and finiteelement analysis of doubly reinforced concrete slabs subjected to blast loads.Int J Impact Eng 2015;75:162–73.

[47] Teng T-L, Chu Y-A, Chang F-A, Shen B-C, Cheng D-S. Development andvalidation of numerical model of steel fiber reinforced concrete for high-velocity impact. Comput Mater Sci 2008;42:90–9.

[48] Anderson J, Katselis G, Caputo C. Analysis of a generic warhead part I:experimental and computational assessment of free field overpressure. DTICDocument 2002.

[49] Lucy LB. A numerical approach to the testing of the fission hypothesis. Astron J1977;82:1013–24.

[50] Gingold RA, Monaghan JJ. Smoothed particle hydrodynamics: theory andapplication to non-spherical stars. Mon Not R Astron Soc 1977;181:375–89.

[51] Rabczuk T, Eibl J. Simulation of high velocity concrete fragmentation usingSPH/MLSPH. Int J Numer Meth Eng 2003;56:1421–44.

[52] Liu MB, Liu GR, Zong Z, Lam KY. Computer simulation of high explosiveexplosion using smoothed particle hydrodynamics methodology. ComputFluids 2003;32:305–22.

[53] Liu MB, Liu GR, Lam KY, Zong Z. Meshfree particle simulation of the detonationprocess for high explosives in shaped charge unlined cavity configurations.Shock Waves 2003;12:509–20.