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International Journal of Impact Engineering 49 (2012) 158e164

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International Journal of Impact Engineering

journal homepage: www.elsevier .com/locate/ i j impeng

Experimental study on scaling the explosion resistance of a one-way squarereinforced concrete slab under a close-in blast loading

Wei Wang, Duo Zhang, Fangyun Lu*, Song-Chuan Wang, Fujing TangInstitute of Technique Physics, College of Science, National University of Defense Technology, Changsha, Hunan 410073, PR China

a r t i c l e i n f o

Article history:Received 27 May 2011Received in revised form29 March 2012Accepted 30 March 2012Available online 14 April 2012

Keywords:Explosion loadDynamic responseReinforced concrete slabDamage modeScaling

* Corresponding author. Tel.: þ86 13308492212.E-mail address: fangyunlu@126.com (F. Lu).

0734-743X/$ e see front matter Crown Copyright �doi:10.1016/j.ijimpeng.2012.03.010

a b s t r a c t

Full-scale experiments involving actual geometries and charges are complicated and costly in terms ofboth preparation and measurements. Thus, scaled-down experiments are highly desirable. The presentwork aims to address the scaling of the dynamic response of one-way square reinforced concrete slabssubjected to close-in blast loadings. To achieve this objective, six slabs of two groups were tested underreal blast loads. Three slabs with different scale-down factors were investigated using two scaleddistances. Two major damage levels were observed, namely, spallation damage from a few cracks, andmoderate spallation damage. The test results show that the macrostructure damage and fracture in theexperiments are almost similar. However, the local damage in concrete slabs with larger-scale factors isslightly reduced compared with that of slabs with smaller-scale factors. Two empirical equations areproposed based on the results to correct the results when scaling up from the model to the prototype.

Crown Copyright � 2012 Published by Elsevier Ltd. All rights reserved.

1. Introduction

The behaviour analysis and design of hardened structures forprotection against short-duration dynamic loadings, such as thoseinduced by air blasts, have been a subject of extensive studies in thelast decades. Intensive dynamic loading via detonations should beconsidered in the structural design and assessment of both militaryand civilian structures and facilities in such cases. Full-scale blasttests are required to understand the behaviour of slabs under thiskind of loading. However, these tests are limited because of securityrestrictions and the considerable resources required. The presentwork is intended to address the scaling of the dynamic response ofone-way square reinforced concrete (RC) slabs subjected to close-inblast loadings.

Considerable research on the behaviour of concrete slabs andpanels under blast loads has been conducted in recent years,including experiments on the behaviour of RC [1] and fibre-reinforced panels [2] subjected to blast loads. Mosalam [3,4] useddivisive analysis tomodel 2.64m� 2.64m� 0.076mRC slabs using0.46 m wide, 0.584 mm thick carbon fibre-reinforced polymer(CFRP) strips on the tension face in the two directions subjected toblast loading. The computational models for both the as-built and

2012 Published by Elsevier Ltd. All

retrofitted slabs were verified using experimental results. Lawver[5] performed explosive tests on 9.1 m � 9.1 m � 0.2 m RC floorslabs, with the charge placed underneath the slab inside a building.Control and CFRP- and glass fibre-reinforced polymer-retrofittedslabs were tested. Both retrofitted slabs were significantly stifferthan the control slab, which had a 380 mm deflection. Ngo [6,7]investigated the blast resistance of ultrahigh-strength concretepanels made of reactive powder concrete. The results showed thatthe ultrahigh-strength concrete panels performed extremely well,surviving the blast with minor cracks. Luccioni [8] analysed thebehaviour of concrete pavement slabs subjected to blast loadsproduced by the detonation of high explosive charges placed abovethem. An equation that approximates the relationship of the craterdiameter on the pavement with the explosive charge and its heightabove the pavement was then proposed. Lu and Silva [9,10] studieda procedure that estimates the level of damage produced bydifferent explosive charge weights and standoff distances on RCslabs. Test results showed that the procedure was accurate in pre-dicting the appropriate explosive charge weight and standoffdistance that produce a given damage level. McVay [11] charac-terised the spallation damage on RC slabs under blast loads. Wu[12] estimated the fragment size distribution from concrete spall-ation due to air blast loads. Ohkubo [13] and Wu [14] evaluated theeffectiveness of fibre sheet reinforcement on the explosion resis-tance of concrete plates. Explosion tests were conducted, andexisting formulae were applied to estimate the failure modes

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W. Wang et al. / International Journal of Impact Engineering 49 (2012) 158e164 159

of concrete plates subjected to contact explosion. Advancednumerical methods such as the mesh-free and finite-elementmethods have been developed in recent years to simulate thespallation of RC slabs subjected to air blast loads [15e19]. A reli-ability analysis of the direct shear and flexural failure modes of RCslabs under explosive loadings was also conducted by Hsin [20].Current design guidelines [21,22] on damage on RC slabs such asTM5 also provide possible combinations of estimated explosivecharge weights and standoff distances that can generate certainlevels of damage to concrete. Zhou [23] constructed a mesoscaleconcrete model to simulate the propagation of dynamic failure ona concrete slab under contact detonation. The study demonstrateda practical method of predicting the fragment size distributionusing image analysis and numerical simulations. However, theexplosion resistance of one-way square RC slabs under a close-inblast loading has not yet been studied.

The current methods of analysis for concrete slabs under blastloadings consist of two major approaches, namely, experimentaland numerical studies. Although a numerical study is an indirectmethod of determining the damage on concrete slabs under blastloadings, the use of precision test data to evaluate their accuracy iscritically important. Many experimental studies are not feasiblebecause of safety and economic reasons. On the other hand, thepreparations and measurements in full-scale development fieldexperiments are complex and expensive. Experiments at reducedscales can identify the critical effects, improve the engineeringdesign, and validate the physics-based models that can be used topredict the structural dynamic response at all scales. A series ofexperiments using five different two-storey, quarter-scale RCstructures was conducted by Woodson and Baylot [24,25] toinvestigate the response of exterior columns to blast loads. Thescaling of the structural response was not included in the study.Neuberger [26,27] addressed the scaling of the dynamic response ofclamped circular metal plates subjected to close-range and largespherical blast loadings through in air blast loadings and buriedcharges. However, few studies have been conducted to estimate thescaling and damage modes of one-way square RC slabs subjected toblast loadings.

In the current study, six slabs with three scales, namely, 3:4:5were tested under close-in blast loadings. The blast loads weregenerated by the detonation of 0.13 kge0.94 kg TNT explosivecharges located at a 0.3 me0.5 m standoff distance above theslabs. The scabbing holes formed on the opposite surface of thespecimens were observed and compared. Different damage levelsand modes were also studied. The scaling factors thatcharacterise the dynamic response of an RC slab subjected toclose-in blast loadings are then presented based on the experi-mental results.

2. Scaling theory

Validation of the physical similarity of a specific phenomenon iscrucial for proper scaling. However, the experimental resultsobtained from the model should be scaled-up correctly to accu-rately represent the full-scale prototype. The concept of physicalsimilarity, as stated by Barenblatt [28], is a natural generalisation ofsimilarities in geometry. The objective is to obtain identical rela-tionships between quantities that characterise both the prototype(representing the original object) and the model (representing thescaled-down object). The principles of scaling, and the relation-ships between the parameters of the small-scale model and thefull-scale prototype, were stated by Jones [29]. The relevantparameters for the investigated problem are presented in terms ofthe proportion of the prototype parameter (superscript P) and thecorresponding model parameter (superscript M), as follows:

The linear dimensions are proportional to the scale factor,xPi ¼ xMi $S. The angles are the same, aPi ¼ aMi . The densities of thematerials are the same, rPi ¼ rMi . The stresses of each material arethe same, sPi ¼ sMi . The characteristic times are proportional to thescale factor, sPi ¼ sMi $S. The strains are identical, 3Pi ¼ 3Mi . The loadpressure are the same, and must act at scaled locations, FPi ¼ FMi , atxPi ¼ xMi $S. Deformations at geometrically scaled locations for thecorresponding scaled times are proportional to the scale factor,dPi ¼ dMi $S, at sPi ¼ sMi $S. The angular deformations are the same,uPi ¼ uM

i .Several phenomena may not be scaled according to these

principles. For example, gravitational forces cannot be scaledaccording to the basic principles of geometrically similar scaling.However, high accelerations are involved in this study. Therefore,the gravitational forces are not significant and can be ignored. Thestrain rate in a small-scale model is a magnitude larger than that ina geometrically similar, full-scale prototype. For the case at hand,the material properties are assumed to be approximately scale-independent because the actual scale factor is not very large.Finally, fractures cannot be scaled according to the basic principlesof geometrically similar scaling. However, the scabbing of the slabsis small, and the scale factor is not very large; thus, the similitudecan be assumed as approximately scaled.

When scaling the spherical blast wave phenomena, the mostcommon scaling method used is Hopkinson’s, or the “cube root”scaling law, as shown by Baker [30]. This scaling law states that self-similar blast waves are produced at identical scaled distances whentwo explosive charges of similar geometries, but of differentweights, are detonated in the same atmosphere. For explosions inair, the Hopkinson scaled parameters are as follows [30]:

Z ¼ RE1=3

; s* ¼ sE1=3

; z ¼ IE1=3

(1)

where Z is the scaled distance, s* is the characteristic scaled time ofthe blast wave, z is the scaled impulse, R is the distance from thecentre of the blast source, and E is the source blast energy. This lawimplies that all quantities with the dimensions of pressure andvelocity are unchanged through scaling, i.e., for the same value of Z(note that E can be replaced by the blast source mass W). In thisstudy, Hopkinson’s method was used to calculate the correspond-ing charge weight for the scaled-down model, as follows:

WM ¼ WP

S3(2)

3. Experimental setup

Three similar slabs with different scale-down factors (S ¼ 1.67,1.25, and 1) were tested in the experiments. The dimensions of theslabs are given in Fig. 1 and Table 1; the lengths L are 0.75, 1, and1.25 m, respectively. These specimens were constructed usinga 6 mm diameter bar meshing and spaced at a distance of 75 mmfrom one other in the major bending plane (r ¼ 1.43%), and ata distance of 75mm from one other in the other plane (r¼ 1.43%); ris the reinforcement ratio. Given the material difference, strictlyscaled slabs cannot be achieved in the experiments. The concreteslabs may not have been strictly scaled, particularly with respect tothe reinforcement. However, the concrete and reinforcement barsexhibit the same properties. The reinforcement ratios of the threescaled slabs are almost the same. Therefore, the slabs can beassumed to have been approximately scaled. The concrete has anaverage compressive strength of 39.5 MPa, as measured using threenormal 150 mm � 150 mm � 150 mm concrete cubes; a tensilestrength of 4.2 MPa; and a Young’s modulus of 28.3 GPa. The

Fig. 1. Geometry of the RC slab (L ¼ 750, 1000 and 1250 mm).

W. Wang et al. / International Journal of Impact Engineering 49 (2012) 158e164160

reinforcement has a yield strength of 600 MPa and a Young’smodulus of 200 GPa.

A steel frame was built on the ground (Fig. 2) to ensure that thespecimens are firmly placed. The steel members used for the frameconsisted of 8 mm thick steel angles. The RC slab was clampeddown on each side of the steel angle to prevent uplifting during thetests. Wooden bars of the same width and length as the steel anglewere placed on two sides, between the specimen and the frame, toprovide uniform supporting conditions and prevent direct impactdamage on the specimen edges. The specimens were estimatedusing the fixed supports, although the end restraint in the test wassomewhere between fixed and pinned, and the extent of fixitylikely depends on the magnitude of the imposed blast load and thedamage sustained by the restraints. However, the boundarycondition had minimal effect on the slab damage caused by theinitial stress wave propagation inside the slab.

TNT was used in the explosion tests because it is a standard highexplosive deemed chemically safe, making it easier to cast. Adetonator was inserted into the top of TNT. The mass of TNT was setat 0.13 kge0.94 kg to determine the effect of scaled distances on thedamage on the concrete slabs. The cylindrical charge wassuspended above the test specimens by a rope at a specificstandoff distance (Fig. 2) and centred over the slab using fourstring guides. The diameter-to-height ratio of the cylindricalcharges was set at approximately 2. All dimensions were scaledwhen the charge mass was increased. Table 1 summarises theexperiment programme. The standoff distances, measured from thecentre of the explosive to the top surface of the slab, were set at300, 400, and 500 mm.

4. Test results

The failure modes of slabs under a close-in explosion werecharacterised by McVay [11] as follows: (1) no damage from the

Table 1Experimental program.

Slab Scalefactor

Dimension (mm) Explosivemass (kg)

Standoffdistance (m)

Scale distance(m/kg1/3)

A 1.67 750 � 750 � 30 0.13 0.3 0.591B 1.67 750 � 750 � 30 0.19 0.3 0.518C 1.25 1000 � 1000 � 40 0.31 0.4 0.591D 1.25 1000 � 1000 � 40 0.46 0.4 0.518E 1 1250 � 1250 � 50 0.64 0.5 0.591F 1 1250 � 1250 � 50 0.94 0.5 0.518

initial state to the formation of a few, barely visible cracks; (2) thethreshold for the spallation damage are a few cracks and a hollowsound, to a large bulge in the concrete with a few incidence ofspallation on the surface; and (3) moderate spallation damage,from a very shallow spallation, to spallation penetrating about one-third of the plate thickness. In this paper, the damage modes of theslabs were chosen as spallation with the appropriate scaleddistance so that the degree of damage can be clearly measured andeasily compared.

Two pairs of scaled distances were experimentally comparedwith the spallation damage. The first scaled distance is 0.591m/kg1/3,and the damage level of the slabs is spallation damage from a fewcracks. For the second scaled distance (0.518 m/kg1/3), the damagelevel of the slabs is moderate spallation damage.

Fig. 3 shows a comparison of the damaged slabs with differentscale factors (S) at a scaled distance of 0.591m/kg1/3. The upper faceof the slabs [Fig. 3(a)] shows the presence of several small cracks atthe centre, which are caused by the high pressure from theexplosion, as well as the fixed support. Two evident flexural cracksare formed at the central symmetry line of the slabs, and someannular radial cracks appear on the upper face. The annular

Fig. 2. Test device.

Fig. 3. Comparison of the experiment results with different scale factor S (scale distance ¼ 0.591 m/kg1/3).

W. Wang et al. / International Journal of Impact Engineering 49 (2012) 158e164 161

cracking of specimen “S ¼ 1.67” in Fig. 3(a) is not evident, whereasthose in the other two specimens are more evident. This result maybe due to the generally greater strength of the small specimencompared with the full-scale one due to the size effect. A tensilespalling crater appears on the back surface of the slab [Fig. 3(b)],which results from the low resistance of concrete to tension. Thecalculated damaged area on the bottom surface of the slab iscalculated using the radius of the spallation area; the results areshown in Fig. 3(b). The radii of the damaged areas are approxi-mately 50, 90, and 120mm. The slabs suffer from spallation damagefrom a few cracks. The number of cracks on the upper and bottomfaces increases with decreasing scale factor, and the spallationdamage on the slab increases.

Fig. 4 shows a comparison of the damaged slabs with differentscale factors at a scaled distance of 0.518 m/kg1/3. Fig. 4(a) showsthe higher number of radial and annular cracking damage on theupper side of the slabs compared with that in the slabs in Fig. 3(a).Similarly, spallation has occurred on the bottom surface of the slab[Fig. 4(b)]. The radii of the spall damage area are approximately 85,120, and 185 mm. The two smaller slabs suffer from moderatespallation damage, whereas the failure mode of the largest slab isperforation due to the blast load and the shear damage on one ofthe fixed supports. The damage on the slabs increases withdecreasing scale factor. Unlike the other specimens at the samescaled distance (0.518 m/kg1/3), the “S ¼ 1” specimen is perforated,possibly because the larger concrete specimens are weaker due tosize effect. Another possible reason is that the slabs were con-structed with the same steel bar spaced at the same distance fromone other, resulting in a reinforcement ratio that is equivalent to

that of a full-scale specimen, which is slightly lower than that of thesmall slabs due to the different slab thicknesses. Therefore, thedamage on the full-scale specimen is the most serious (Fig. 4).

Comparisons of the experimental results at different scalefactors are shown in Table 2. The thicknesses h of the slabs are 30,40, and 50 mm. The central deflections d at the same scaleddistance increase with the dimensions at the two scaled distances,and the normalised peak deflection d/h slightly increases with thedimensions at the 0.591 m/kg1/3 scaled distance. However, thenormalised peak deflection d/h of the two smaller slabs at the0.518 m/kg1/3 scaled distance increases, whereas that of the largestslab decreases, because of perforation damage on slab F. Thespallation area radius r and the normalised spall radius r/h increasewith the dimensions. The scale modelling of the present problem isslightly distorted; thus, the deviation should be taken into accountwhen scaling the results from the model up to the prototype.

5. Discussion

This paper addresses the problem of scaling the dynamicresponse of RC slabs subjected to close-in air blast explosions(unconfined high explosion without fragmentation). The scalingused for the structure is geometrical (replica), whereas that for theexplosive charge is based on Hopkinson’s law. While this concept isnot new, it has not been previously applied to and validated for thespecific case of close-in air blast explosions.

Three slabs with different scale-down factors were investigatedat two different scaled distances. The experimental results showthat the fracture patterns of the specimens are almost similar.

Fig. 4. Comparison of the experiment results with different scale factor S (scale distance ¼ 0.518 m/kg1/3).

W. Wang et al. / International Journal of Impact Engineering 49 (2012) 158e164162

However, the larger specimens suffer more damage, whereas thesmallest specimens suffer the least damage. The larger specimenmay be perforated, whereas the smaller specimen may exhibitscabbing without perforation. For instance, at the first scaleddistance (0.591 m/kg1/3), the smallest slab suffers the least damage,with no evident annular cracking on specimen “S¼ 1.67” [Fig. 3(a)].However, the “S ¼ 1” specimen is perforated at the 0.518 m/kg1/3

scaled distance. The other smaller specimen exhibits scabbingwithout perforation (Fig. 4).

The local damage on the concrete slabs with larger-scale-downfactors has been slightly reduced compared with that of theslabs with smaller-scale-down factors. The normalised damageparameters of the slabs slightly increase with the decrease in thescale-down factors. The damage on the larger specimen becomesmore serious compared with that on the scaled-down specimenwith increasing scaled distance (Fig. 4). The possible reasons forthese results are as follows: (1) the larger concrete specimens are

Table 2Comparison of results from tests.

Slab Dimension (mm) Scaledistance(m/kg1/3)

Centraldeflectiond (mm)

d / h Spall radiusr (mm)

r / h

A 750 � 750 � 30 0.591 9 0.3 50 1.67C 1000 � 1000 � 40 0.591 15 0.375 90 2.25E 1250 � 1250 � 50 0.591 19 0.38 120 2.4B 750 � 750 � 30 0.518 26 0.87 85 2.83D 1000 � 1000 � 40 0.518 35 0.875 120 3F 1250 � 1250 � 50 0.518 40 0.8 185 3.7

weaker due to size effect [31]; (2) the larger specimens are less stiffand thus, are more vulnerable to damage because of the structuralrigidity of the rebar; and (3) the reinforcements for all the slabs aresimilarly arranged, leading to a reduction in the reinforcement ratioand resulting in more damage to the large slabs.

The smaller-scale specimens show more resistance to close-inair blast explosions than the scaled-up prototype. For instance,the results obtained for the smaller-scale specimens, which showresistance to perforation at the 0.518 m/kg1/3 scaled distance,cannot serve as an indicator of the predicted response of a scaled-up prototype, which is perforated when the scaled distance is0.518 m/kg1/3 (Fig. 4). Thus, when applying the results from thescaled model to the prototype, the test results should be correctedaccording to the variability of the strain rate and fractures with theblast loading.

Based on the data in Table 2, the ratio of the normalised peakdeflection d/h and the normalised spall radius r/h are inverselyproportional to the slab thickness of the different scaled distances Zand scale-down factors S (Figs. 5 and 6). The following relationshipwas obtained by fitting the data to correct the effect of the scale-down factors:

d

h¼ 0:0802Z�6:955

�1� 0:8735e0:0115S

�(3)

rh

¼ 0:3327Z�3:0967�1þ 6:7318e�2:7284S

�(4)

Equations (3) and (4) and Figs. 5 and 6 show that the similarity isslightly distorted in the current results. For instance, at the first

Fig. 5. Relationship between normalized peak deflection d/h and scaled-down factors.

Fig. 6. Relationship between normalized spall radius r/h and scaled-down factors.

W. Wang et al. / International Journal of Impact Engineering 49 (2012) 158e164 163

scaled distance (0.591 m/kg1/3), the smallest slab suffers the leastdamage, with no evident annular cracking in specimen “S ¼ 1.67”[Fig. 3(a)]. However, the “S ¼ 1” specimen is perforated at the0.518 m/kg1/3 scaled distance, whereas the other smaller specimenexhibits scabbing without perforation (Fig. 4). Thus, the damage onthe largest specimen is the most serious, with the normalised peakdeflection d/h and normalised spall radius r/h slightly decreasingwith the increase in the scale-down factor S (Figs. 5 and 6).

The relationship is derived only from data for scale-downfactors less than 2 and damage level due to spallation; thus, itmust be used with caution for scale-down factors larger than 2.The above formula (3) and (4) has been used to calculate thepeak deflection and spall radius of the slab in Section 4. Moreimportantly, the equation can only be used to correct the scalingon the test slabs and would be inappropriate for more generalusage.

6. Conclusions

This paper addresses the problem of scaling the dynamicresponse of one-way square RC slabs to close-in blast loadings

caused by mass detonation using different TNT charges. The scalingused for the structure is geometrical (replica), whereas that for theexplosive charge is based on Hopkinson’s law.

Three slabs with different scale-down factors were investigatedat two different scaled distances. Two major damage modes wereobserved, namely, spallation damage from a few cracks, andmoderate spallation damage. The damage mode changes fromflexural, with spall damage on the back surface, to perforationfailure damage as the charge weight of the large-scale slab isincreased.

The experimental results show that the fracture patterns arealmost similar. However, the larger specimens suffer moredamage, and the smallest specimens suffer the least damage.The larger specimens may be perforated, whereas the smallerspecimens may exhibit scabbing without perforation. The localdamage on the concrete slabs with larger-scale factors is slightlyreduced compared with that of slabs with smaller-scale factors,and the normalised damage parameters of the slabs slightlyincrease with decreasing scale-down factor. Thus, whenapplying the results obtained from the scaled model to theprototype, the test results should be corrected according to thevariability of the strain rate and fractures with the blast loading.Based on the results, two empirical equations are proposed tocorrect the results when scaling up from the model to theprototype.

Further research on larger slabs under blast loadings should beconducted. Additional research is also needed for RC slabs withdifferent reinforcement ratios to improve their blast resistance. Theresults of this research will further the development of dynamicmaterial simulation methods and material models.

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