Engineering Failure Analysis 33 (2013) 497–504

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Engineering Failure Analysis

journal homepage: www.elsevier .com/locate /engfai lanal

Experimental study on scaling of RC beams under close-in blastloading

1350-6307/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.engfailanal.2013.06.020

⇑ Corresponding author. Tel.: +86 13975161949.E-mail address: duo.w.zhang@gmail.com (D. Zhang).

Duo Zhang ⇑, ShuJian Yao, Fangyun Lu, XuGuang Chen, Guhui Lin, Wei Wang, Yuliang LinCollege of Science, National University of Defense Technology, Changsha, Hunan 410073, PR China

a r t i c l e i n f o a b s t r a c t

Article history:Received 18 April 2013Received in revised form 13 June 2013Accepted 21 June 2013Available online 5 July 2013

Keywords:Blast loadReinforced concrete beamDamage modesDamage evaluationScaling

Damage effects analysis and assessment of buildings under blast loading is an importantproblem concerned by the area of explosion accident analysis, blast-resistant design,anti-terrorist and military weapon design.

The damage character of RC beam under close-in blast loading is investigated throughexperiments. The damage modes and damage levels of RC beams are studied under differ-ent blast loads. The results show that the spallation area increases with the decrease of thescaled distance. The concrete beams are prone to be damaged in flexure mode with con-crete crushed on the front face, concrete spallation on the back surface and concrete flakeoff on the side surface. The scaling of the dynamic response of reinforced concrete beamssubjected to close-in blast loadings is also studied. The test results showed a similar mac-rostructure damage and fracture in all experiment conditions. But the local damage degreeof RC beams with smaller size has been reduced a little as compared with that of beamswith larger size. Based on the results, empirical equations of the center deflection to heightratio are proposed to correct scaling model considering size effects.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Military assault, terrorist attack and accidental explosion may cause serious damage to buildings and other infrastruc-tures. Important structures, such as government buildings and big bridges are undergoing great risk of attack. In fact, someresearches indicated that terrorist attack and accidental explosion have recently increased worldwide [1–4]. For those rea-son, Damage effects analysis and assessment of buildings under blast loading is very important which concerned by the areaof explosion accident analysis, blast-resistant design, and anti-terrorist and military weapon design [5].

In the anti-explosion research of reinforced concrete (RC) columns, Lan et al. [6] analyzed the damage of a reinforced con-crete column caused by suitcase explosion by using numerical simulation, results show that narrow the stirrup spacing ofrebars can effectively reduce the damage degree of the columns. Bao and Li [7] studied residual strength of reinforced con-crete column after blast load, and proposed a method to describe the residual strength of RC columns based on the ratio ofcenter deflection to column height. Their research indicates that anti-seismic design of RC columns can effectively reduce thedestruction of buildings under blast loading, thereby reducing the probability of progressive collapse. Dakhakhni et al. [8]used a nonlinear multiple DOF model which considered strain rate effect, axialload and bending stiffness of column andother factors to study the impact response and damage process of RC column under blast loading. Based on this model,P–I curves are drowned which is a convenient and efficient method for rapid damage assessment of RC column under blastloading. Shi et al. [9,10] studied the dynamic response and failure mode of reinforced concrete column under blast loading,and fitted an expression of P–I curve by numerical simulation results for the purpose of rapid assessment.

498 D. Zhang et al. / Engineering Failure Analysis 33 (2013) 497–504

Beam members have smaller axial force than column commonly, so lateral loading is the mainly consideration in blast-resistant design of RC beams and the axial force usually can be ignored. Krauthammer [11] proposed a model based on tra-ditional equivalent SDOF method to analyze couple effects of flexural and shear failure of RC beams under blast loading.Krauthammer et al. [12] also analyzed the dynamic response of RC beams under blast loading by finite difference equationwhich is based on Timoshenko beam theory. Ghabossi et al. [13] modeled FOAMHEST test by Finite Element method, thesimulations are in good agreement with the experimental results. Ross [14] obtained an analytical solution of Timoshenkobeam equation which describes the dynamic response of elastic beam under pulse loading. Based on the Timoshenko beamtheory, Fang et al. [15–18] modeled flexural, shear and flexural-shear mixed mode response of RC beams by layered beammethod and finite difference method. Wang et al. [19] studied the scaling of the dynamic response of one-way square RCslabs subjected to close-in blast loadings, and proposed two empirical equations to correct the results when scaling up fromthe model to the prototype.

The current analysis methods for RC beams under blast loading consist of two major approaches, experimental andnumerical studies. Many experimental studies are not feasible because the preparations and measurements in full-scaledevelopment field experiments are complex and expensive. In the field of explosion, the factor of safety should also be underconsideration. Experiments at reduced scales can identify the critical effects, improve the engineering design, and validatethe physics-based models that can be used to predict the structural dynamic response at all scales. However, few studieshave been conducted to estimate the damage levels and validate the scaling law of RC beams subjected to blast loadings.

In the current study, some experiments are carried on for the following three purposes. First is to obtain the images ofdifferent damage degree and the corresponding scale distance (Z = R/x1/3). Second is to test if scaling law (or geometricalsimilitude law) of blast experiment is still available.

2. Design of RC beams and blast loading

2.1. Design and manufacture

There are 3 sets of specimen, and their dimensional ratio is 3:4:5. The dimensions are 850 mm � 75 mm � 75 mm,1100 mm � 100 mm � 100 mm and 1350 mm � 125 mm � 125 mm. The tensile, compressive and hoop reinforcement barused in the tests are all U6-HPB235. The number and dimension of beams are listed in Table 1, the numbering law of thespecimens is that the first number represent the different dimensions and the second number experiment condition. Thedistribution of reinforcing bars in the RC beams is shown in Fig. 1 and a photo of the reinforcing bars and beam specimensis given in Fig. 2.

Uniaxial compressive strength of concrete is contrived to be 40 MPa. When the RC beams are constructed, three concretecubes (150 mm � 150 mm � 150 mm) are poured at the same time for measurement of the concrete’s real strength.

2.2. Material strength test

The yield strength and ultimate strength of reinforcement steel U6HPB235 are 395 MPa and 501 MPa which are obtainedthrough WAW-E600C tests in Hunan University. The uniaxial compressive strength f 0c of concrete tubes is tested according toGB/T50081-2002, and the average f 0c is 40.45 MPa.

Table 1Experimental program.

Beam Dimension (mm) TNT mass (kg) Standoff distance (m) Scale distance (m/kg1/3)

B1-1 75 � 75 � 850 0.22 0.3 0.50B1-2 0.32 0.3 0.44B2-1 100 � 100 � 1100 0.36 0.4 0.57B2-2 0.45 0.4 0.50B2-3 0.51 0.4 0.44B2-4 0.75 0.4 0.40B3-1 125 � 125 � 1350 0.99 0.5 0.50B3-2 1.46 0.5 0.44

Fig. 1. Distribution of reinforcing bars in RC beams.

Fig. 2. Reinforcing bars and beam specimens.

D. Zhang et al. / Engineering Failure Analysis 33 (2013) 497–504 499

2.3. Experimental setup

The test program is summarized in Table 1, TNT explosive is used in the tests for it is a standard high explosive which ischemically safe and easy to cast. TNT mass is set at 0.22–1.46 kg to examine the influence of the explosive mass to the dam-age degree of RC beams. TNT is compressed to a caky cylinder suspended over the center of RC beam as shown in Fig. 3 and

TNT Air pressure guage

Displacement needle

Momentum cylinders

Standoff

Fig. 3. Picture of the test setup.

Fig. 4. The illustration of test setup.

Fig. 5. Sketch maximum deflection measurement by steel needles.

0

10

20

30

40

50

0 20 40 60 80 100

Deflection (mm)

Fig. 6. Numerical simulation results of maximum deflection and residual deflection obtained by equivalent SDOF method.

500 D. Zhang et al. / Engineering Failure Analysis 33 (2013) 497–504

the TNT is ignited by an electronic detonator which is inserted at the top of it. The standoff distance was measured from theunderside of the TNT charge to the top surface of beam, and a distance of 0.3–0.5 m is selected in the current study.

RC beam is nearly clamped at the steel frame support as shown in Fig. 3, and the Fig. 4 is an explanation about it. Thedeflection of the bottom of the RC beam under blast loading is measured by a cluster of steel needles which are stabbedin a barrel filled with fine sand. The needles perforate an aluminum plate cover perpendicularly, so that they can move onlyalong longitudinal direction. Before detonation, the upper ends of the needles are in a plain which is parallel to and with asmall distance from the bottom of the RC beam. After detonation, beam bends and the bottom of the beam with touch theneedles and make them more deeply into the sand. The displacement of the needle is deemed to be the maximum deflectionof the beam at the touch point on the bottom surface, and the maximum deflection of the beam can be easily got through aconversion formula of similar triangles (as shown in Fig. 5).The numerical simulation results of maximum deflection andresidual deflection obtained by equivalent SDOF method is shown in Fig. 6.

3. Experimental results and analysis

3.1. Damage analysis of RC beams under blast loading of different charge (scaled distance)

In order to test the blast resistance performance of RC beam under blast loading of different scaled distance, TNT charge ishanged above the center of the beam, and the standoff distance is 400 mm. The scaled distance is changed by changing thecharge weight. The test results are shown in Table 2.

The test results of RC beams with same size and configuration (B2-1, B2-2, B2-3 and B2-4) under different scaled distanceblast loading are shown in Figs. 7–10.

It is showed that RC beam bent under transverse impulsive loading firstly. With the increasing of deflection, tensile frac-ture at the back face and compressive fracture at front face occurred. When the scaled distance is small enough, spallation atthe back surface of the beam occurred which is because the compressive stress wave in the concrete reflected tensile wave atthe free surface (back surface), and the reflected tensile wave interacts with the tail of the compressive stress wave, when thetensile stress produced by the tensile wave is larger than the ultimate tensile strength of the concrete, spallation produced.Spall zone area is also growing with the increase of the loading dose. At the same time, damage mode of the RC beam istranslating from overall bending fracture (as shown in Fig. 7) to plastic hinge and spallation damage (as shown in Figs. 8and 9). At last, severe exfoliation and spalling are occurred at the front and back of the beam, and concrete crack area per-forate through the height of beam (as shown in Fig. 10 below).

Table 2The test results of reinforced concrete beams.

Beam Scaleddistance(m/kg1/3)

Centraldeflectiond (mm)

Deflectionthicknessratio d/h

Spalllengthd (mm)

d/h Phenomenon description

B2-1 0.57 9 0.09 0 0 Slight damage. No obvious residual displacement, three obvious bendingcracks appear on the back of beam, one of them is cracked to 3/4 height ofthe beam. Lateral shedding region is about 12 cm long. As shown in Fig. 7

B2-2 0.50 25 0.25 70 0.7 Moderate damage. Obvious bending failure, the width of compressionfracture area at the front face is about 8 cm. Tensile crack and spallationappeared at the bottom, and is about 7 cm length. Both the crack area of thefront and back face has not caused a throughout damage. As shown in Fig. 8

B2-3 0.44 35 0.35 120 1.2 Heavy damage. Severe exfoliation and spalling are occurred at the front andback of the beam, and concrete crack area perforate through the height ofbeam. Front compressional fragmented area is about 10 cm width, backspallation area is about 12 cm width. As shown in Fig. 9

B2-4 0.40 40 0.40 150 1.5 Severe damage, layer-crack collapse phenomena is observed which is muchheavier than heavy damage. Front compressional fragmented area is about12 cm width, back spallation area length is about 15 m width. As shown inFig. 10

ecafediS)b(noitcurtsedllarevoehT)a(

ecafkcaB)d(ecaftnorF)c(

Fig. 7. Reinforced concrete beam B2-1 damage effect (Z = 0.57 m/kg1/3).

ecafediS)b(noitcurtsedllarevoehT)a(

ecafkcaB)d(ecaftnorF)c(

Fig. 8. Reinforced concrete beam B2-2 damage effect (Z = 0.50 m/kg1/3).

D. Zhang et al. / Engineering Failure Analysis 33 (2013) 497–504 501

3.2. Failure analysis of different sizes of RC beams

In order to study the damage similarity of reinforced concrete beam of different dimensions under blast loading, and toobtain identical relationships between the prototype (representing the original object) and the model (representing thescaled-down object). The principles of scaling, and the relationships between the parameters of the small-scale modeland the full-scale prototype, which is called ‘‘replica’’ law, were stated by Baker [20]. In other words, the geometrical param-eters for the prototype (superscript P) and the model (superscript M) satisfy the following relationship:

rPe

rMe¼ hP

hM ¼bP

bM ¼LP

LM ¼dP

dM ¼ S ð1Þ

(b) Sideface(a) Theoveralldestruction

(d) Backface(c) Frontface

Fig. 9. Reinforced concrete beam B2-3 damage effect (Z = 0.44 m/kg1/3).

(a) The overall destruction

(c) Front face

(b) Side face

(d) Backface

Fig. 10. Reinforced concrete beam B2-4 damage effect (Z = 0.40 m/kg1/3).

502 D. Zhang et al. / Engineering Failure Analysis 33 (2013) 497–504

According to the ‘‘replica’’ law, strain and stress should be the same in the prototype and model beam. re is the radius ofthe explosive sphere, h is the height of the beam, b is the width of the beam, l is the length of the beam, d is the standoffdistance of explosive. Two sets of experiment have carried out so as to expecting damage degrees of the test results are mod-erate and heavy damage respectively.

There are 3 specimens in each set, which geometrical size satisfy formula (1) and is 3:4:5 as shown in Table 1. The largestbeam is designated as prototype model, so the scale factor S of the largest beam is 1, and the other two scale factor S are 5/3and 4/3.

The results of experiments to test the ‘‘replica’’ law are shown in Figs. 11 and 12. Exfoliation and spalling of various ex-tents are observed at the back of the beams, compressional fracture occurs at the front of the beam. In a word, the damagemodes and deformation are geometrical similar approximately, but the damage extent is much severe with the bigger size(smaller S), as shown in Fig. 13.

(a) The overall destruction

The specimen from top to bottom are B1-1, B2-2 and

B3-1

(b) Side face

The specimen from top to bottom are B1-1, B2-2 and

B3-1

Fig. 11. The destruction effect comparison of RC beam with different size (Z = 0.50 m/kg1/3).

(a) The overall destruction

The specimen from top to bottom are B1-2, B2-3 and

B3-2

(b) Side face

The specimen from top to bottom are B1-2, B2-3and

B3-2

Fig. 12. The destruction effect comparison of RC beam with different size (Z = 0.44 m/kg1/3).

Fig. 13. The relationship between RC beam deflection thickness ratio d/h and scale factor S.

D. Zhang et al. / Engineering Failure Analysis 33 (2013) 497–504 503

Through the test data in Table 2, we can find that the deflection thickness ratio d/h is related to scaled distance Z and scalefactor S.

In order to consider the size effects on ‘‘replica’’ law (geometrical similar law). The relationship between deflection thick-ness ratio d/h and scaled distance Z and scale factor S is fitted as shown in formula (2) and Fig. 13.

dh¼ 0:075Z�2:39ð1� 0:127e0:89SÞ ð2Þ

where e is the natural const.Formula (2) is based on test results, When the cross section shape of beams is rectangle and the scale factor S is within the

range of our experiments, the formula (2) we proposed in this paper is suitable. Also we should pay attention to is, whether itis suitable for a great scale factor S or other cross-section shape beams (with different cross section, like cylinder) need fur-ther study, but in engineering applications, most of RC structures employ the rectangle section shape beams.

4. Summary

Through experimental study, the blast resistant performance and the damage morphological feature and failure modes ofreinforced concrete beam is analyzed in detail. And the damage levels and damage modes of reinforced concrete beam underclose-in explosion is obtained.

504 D. Zhang et al. / Engineering Failure Analysis 33 (2013) 497–504

Studies have shown: The reinforced concrete beam bending quickly under the impact of explosive blast wave, tensilefracture at the back face and compressive fracture at front face is observed. At the same time, spallation at the back surfaceof the beam occurred because of reflected tensile wave produced at the free surface (back surface). With the increase ofexplosive mass, damage mode of the RC beam is translating from overall bending fracture to plastic hinge and spallationdamage, and severe exfoliation and spalling.

The similar law of blasting of the RC beam under explosive loading were also studied in the current research, the resultsshow that: With a same scale distance, the damage modes and deformation of specimens in different dimensions are geo-metrical similar approximately, the only different is that the deflection thickness ratio d/h is little bigger and the damagedegree is little severer with a bigger beam size (smaller S). At the same time, a formula on explosion deformation similarlaw is established using the method of curve fitting which considered the shrinkage ratio and the scale distance correction.

Acknowledgements

Supported by the National Natural Science Foundation of China (Grant No. 11202236) and the Research Project of Na-tional University of Defense Technology (Grant No. JC110218).

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