- Email: [email protected]
Experimental study on scaling the explosion resistance of a one-way square reinforced concrete slab under a close-in blast loading
International Journal of Impact Engineering 49 (2012) 158e164
Contents lists available at SciVerse ScienceDirect
International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng
Experimental study on scaling the explosion resistance of a one-way square reinforced concrete slab under a close-in blast loading Wei Wang, Duo Zhang, Fangyun Lu*, Song-Chuan Wang, Fujing Tang Institute 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
a b s t r a c t
Article history: Received 27 May 2011 Received in revised form 29 March 2012 Accepted 30 March 2012 Available online 14 April 2012
Full-scale experiments involving actual geometries and charges are complicated and costly in terms of both preparation and measurements. Thus, scaled-down experiments are highly desirable. The present work aims to address the scaling of the dynamic response of one-way square reinforced concrete slabs subjected to close-in blast loadings. To achieve this objective, six slabs of two groups were tested under real blast loads. Three slabs with different scale-down factors were investigated using two scaled distances. Two major damage levels were observed, namely, spallation damage from a few cracks, and moderate spallation damage. The test results show that the macrostructure damage and fracture in the experiments are almost similar. However, the local damage in concrete slabs with larger-scale factors is slightly reduced compared with that of slabs with smaller-scale factors. Two empirical equations are proposed based on the results to correct the results when scaling up from the model to the prototype. Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved.
Keywords: Explosion load Dynamic response Reinforced concrete slab Damage mode Scaling
1. Introduction The behaviour analysis and design of hardened structures for protection against short-duration dynamic loadings, such as those induced by air blasts, have been a subject of extensive studies in the last decades. Intensive dynamic loading via detonations should be considered in the structural design and assessment of both military and civilian structures and facilities in such cases. Full-scale blast tests are required to understand the behaviour of slabs under this kind of loading. However, these tests are limited because of security restrictions and the considerable resources required. The present work is intended to address the scaling of the dynamic response of one-way square reinforced concrete (RC) slabs subjected to close-in blast loadings. Considerable research on the behaviour of concrete slabs and panels under blast loads has been conducted in recent years, including experiments on the behaviour of RC [1] and fibrereinforced panels [2] subjected to blast loads. Mosalam [3,4] used divisive analysis to model 2.64 m 2.64 m 0.076 m RC slabs using 0.46 m wide, 0.584 mm thick carbon fibre-reinforced polymer (CFRP) strips on the tension face in the two directions subjected to blast loading. The computational models for both the as-built and
* Corresponding author. Tel.: þ86 13308492212. E-mail address: [email protected] (F. Lu).
retrofitted slabs were verified using experimental results. Lawver [5] performed explosive tests on 9.1 m 9.1 m 0.2 m RC floor slabs, with the charge placed underneath the slab inside a building. Control and CFRP- and glass fibre-reinforced polymer-retrofitted slabs were tested. Both retrofitted slabs were significantly stiffer than the control slab, which had a 380 mm deflection. Ngo [6,7] investigated the blast resistance of ultrahigh-strength concrete panels made of reactive powder concrete. The results showed that the ultrahigh-strength concrete panels performed extremely well, surviving the blast with minor cracks. Luccioni [8] analysed the behaviour of concrete pavement slabs subjected to blast loads produced by the detonation of high explosive charges placed above them. An equation that approximates the relationship of the crater diameter on the pavement with the explosive charge and its height above the pavement was then proposed. Lu and Silva [9,10] studied a procedure that estimates the level of damage produced by different explosive charge weights and standoff distances on RC slabs. Test results showed that the procedure was accurate in predicting the appropriate explosive charge weight and standoff distance that produce a given damage level. McVay [11] characterised the spallation damage on RC slabs under blast loads. Wu [12] estimated the fragment size distribution from concrete spallation due to air blast loads. Ohkubo [13] and Wu [14] evaluated the effectiveness of fibre sheet reinforcement on the explosion resistance of concrete plates. Explosion tests were conducted, and existing formulae were applied to estimate the failure modes
0734-743X/$ e see front matter Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2012.03.010
W. Wang et al. / International Journal of Impact Engineering 49 (2012) 158e164
of concrete plates subjected to contact explosion. Advanced numerical methods such as the mesh-free and finite-element methods have been developed in recent years to simulate the spallation of RC slabs subjected to air blast loads [15e19]. A reliability analysis of the direct shear and flexural failure modes of RC slabs under explosive loadings was also conducted by Hsin [20]. Current design guidelines [21,22] on damage on RC slabs such as TM5 also provide possible combinations of estimated explosive charge weights and standoff distances that can generate certain levels of damage to concrete. Zhou [23] constructed a mesoscale concrete model to simulate the propagation of dynamic failure on a concrete slab under contact detonation. The study demonstrated a practical method of predicting the fragment size distribution using image analysis and numerical simulations. However, the explosion resistance of one-way square RC slabs under a close-in blast loading has not yet been studied. The current methods of analysis for concrete slabs under blast loadings consist of two major approaches, namely, experimental and numerical studies. Although a numerical study is an indirect method of determining the damage on concrete slabs under blast loadings, the use of precision test data to evaluate their accuracy is critically important. Many experimental studies are not feasible because of safety and economic reasons. On the other hand, the preparations and measurements in full-scale development field experiments are complex and expensive. Experiments at reduced scales can identify the critical effects, improve the engineering design, and validate the physics-based models that can be used to predict the structural dynamic response at all scales. A series of experiments using five different two-storey, quarter-scale RC structures was conducted by Woodson and Baylot [24,25] to investigate the response of exterior columns to blast loads. The scaling of the structural response was not included in the study. Neuberger [26,27] addressed the scaling of the dynamic response of clamped circular metal plates subjected to close-range and large spherical blast loadings through in air blast loadings and buried charges. However, few studies have been conducted to estimate the scaling and damage modes of one-way square RC slabs subjected to blast loadings. In the current study, six slabs with three scales, namely, 3:4:5 were tested under close-in blast loadings. The blast loads were generated by the detonation of 0.13 kge0.94 kg TNT explosive charges located at a 0.3 me0.5 m standoff distance above the slabs. The scabbing holes formed on the opposite surface of the specimens were observed and compared. Different damage levels and modes were also studied. The scaling factors that characterise the dynamic response of an RC slab subjected to close-in blast loadings are then presented based on the experimental results. 2. Scaling theory Validation of the physical similarity of a specific phenomenon is crucial for proper scaling. However, the experimental results obtained from the model should be scaled-up correctly to accurately represent the full-scale prototype. The concept of physical similarity, as stated by Barenblatt [28], is a natural generalisation of similarities in geometry. The objective is to obtain identical relationships between quantities that characterise both the prototype (representing the original object) and the model (representing the scaled-down object). The principles of scaling, and the relationships between the parameters of the small-scale model and the full-scale prototype, were stated by Jones [29]. The relevant parameters for the investigated problem are presented in terms of the proportion of the prototype parameter (superscript P) and the corresponding model parameter (superscript M), as follows:
159
The linear dimensions are proportional to the scale factor, aP aM xPi ¼ xM i $S. The angles are the same, i ¼ i . The densities of the . The stresses of each material are materials are the same, rPi ¼ rM i the same, sPi ¼ sM i . The characteristic times are proportional to the P M scale factor, sPi ¼ sM i $S. The strains are identical, 3 i ¼ 3 i . The load pressure are the same, and must act at scaled locations, FiP ¼ FiM , at xPi ¼ xM i $S. Deformations at geometrically scaled locations for the corresponding scaled times are proportional to the scale factor, P M dPi ¼ dM i $S, at si ¼ si $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 scaled according 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. The strain rate in a small-scale model is a magnitude larger than that in a geometrically similar, full-scale prototype. For the case at hand, the material properties are assumed to be approximately scaleindependent because the actual scale factor is not very large. Finally, fractures cannot be scaled according to the basic principles of geometrically similar scaling. However, the scabbing of the slabs is small, and the scale factor is not very large; thus, the similitude can be assumed as approximately scaled. When scaling the spherical blast wave phenomena, the most common scaling method used is Hopkinson’s, or the “cube root” scaling law, as shown by Baker [30]. This scaling law states that selfsimilar blast waves are produced at identical scaled distances when two explosive charges of similar geometries, but of different weights, are detonated in the same atmosphere. For explosions in air, the Hopkinson scaled parameters are as follows [30]:
Z ¼
R ; E1=3
s* ¼
s E1=3
;
z ¼
I E1=3
(1)
where Z is the scaled distance, s* is the characteristic scaled time of the blast wave, z is the scaled impulse, R is the distance from the centre of the blast source, and E is the source blast energy. This law implies that all quantities with the dimensions of pressure and velocity 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 this study, Hopkinson’s method was used to calculate the corresponding 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 the slabs are given in Fig. 1 and Table 1; the lengths L are 0.75, 1, and 1.25 m, respectively. These specimens were constructed using a 6 mm diameter bar meshing and spaced at a distance of 75 mm from one other in the major bending plane (r ¼ 1.43%), and at a distance of 75 mm from one other in the other plane (r ¼ 1.43%); r is the reinforcement ratio. Given the material difference, strictly scaled slabs cannot be achieved in the experiments. The concrete slabs may not have been strictly scaled, particularly with respect to the reinforcement. However, the concrete and reinforcement bars exhibit the same properties. The reinforcement ratios of the three scaled slabs are almost the same. Therefore, the slabs can be assumed to have been approximately scaled. The concrete has an average compressive strength of 39.5 MPa, as measured using three normal 150 mm 150 mm 150 mm concrete cubes; a tensile strength of 4.2 MPa; and a Young’s modulus of 28.3 GPa. The
160
W. Wang et al. / International Journal of Impact Engineering 49 (2012) 158e164
Fig. 1. Geometry of the RC slab (L ¼ 750, 1000 and 1250 mm).
reinforcement has a yield strength of 600 MPa and a Young’s modulus of 200 GPa. A steel frame was built on the ground (Fig. 2) to ensure that the specimens are firmly placed. The steel members used for the frame consisted of 8 mm thick steel angles. The RC slab was clamped down on each side of the steel angle to prevent uplifting during the tests. Wooden bars of the same width and length as the steel angle were placed on two sides, between the specimen and the frame, to provide uniform supporting conditions and prevent direct impact damage on the specimen edges. The specimens were estimated using the fixed supports, although the end restraint in the test was somewhere between fixed and pinned, and the extent of fixity likely depends on the magnitude of the imposed blast load and the damage sustained by the restraints. However, the boundary condition had minimal effect on the slab damage caused by the initial stress wave propagation inside the slab. TNT was used in the explosion tests because it is a standard high explosive deemed chemically safe, making it easier to cast. A detonator was inserted into the top of TNT. The mass of TNT was set at 0.13 kge0.94 kg to determine the effect of scaled distances on the damage on the concrete slabs. The cylindrical charge was suspended above the test specimens by a rope at a specific standoff distance (Fig. 2) and centred over the slab using four string guides. The diameter-to-height ratio of the cylindrical charges was set at approximately 2. All dimensions were scaled when the charge mass was increased. Table 1 summarises the experiment programme. The standoff distances, measured from the centre of the explosive to the top surface of the slab, were set at 300, 400, and 500 mm.
initial state to the formation of a few, barely visible cracks; (2) the threshold for the spallation damage are a few cracks and a hollow sound, to a large bulge in the concrete with a few incidence of spallation on the surface; and (3) moderate spallation damage, from a very shallow spallation, to spallation penetrating about onethird of the plate thickness. In this paper, the damage modes of the slabs were chosen as spallation with the appropriate scaled distance so that the degree of damage can be clearly measured and easily compared. Two pairs of scaled distances were experimentally compared with the spallation damage. The first scaled distance is 0.591 m/kg1/3, and the damage level of the slabs is spallation damage from a few cracks. For the second scaled distance (0.518 m/kg1/3), the damage level of the slabs is moderate spallation damage. Fig. 3 shows a comparison of the damaged slabs with different scale factors (S) at a scaled distance of 0.591 m/kg1/3. The upper face of the slabs [Fig. 3(a)] shows the presence of several small cracks at the centre, which are caused by the high pressure from the explosion, as well as the fixed support. Two evident flexural cracks are formed at the central symmetry line of the slabs, and some annular radial cracks appear on the upper face. The annular
4. Test results The failure modes of slabs under a close-in explosion were characterised by McVay [11] as follows: (1) no damage from the
Table 1 Experimental program. Slab
Scale factor
Dimension (mm)
Explosive mass (kg)
Standoff distance (m)
Scale distance (m/kg1/3)
A B C D E F
1.67 1.67 1.25 1.25 1 1
750 750 30 750 750 30 1000 1000 40 1000 1000 40 1250 1250 50 1250 1250 50
0.13 0.19 0.31 0.46 0.64 0.94
0.3 0.3 0.4 0.4 0.5 0.5
0.591 0.518 0.591 0.518 0.591 0.518 Fig. 2. Test device.
W. Wang et al. / International Journal of Impact Engineering 49 (2012) 158e164
161
Fig. 3. Comparison of the experiment results with different scale factor S (scale distance ¼ 0.591 m/kg1/3).
cracking of specimen “S ¼ 1.67” in Fig. 3(a) is not evident, whereas those in the other two specimens are more evident. This result may be due to the generally greater strength of the small specimen compared with the full-scale one due to the size effect. A tensile spalling crater appears on the back surface of the slab [Fig. 3(b)], which results from the low resistance of concrete to tension. The calculated damaged area on the bottom surface of the slab is calculated using the radius of the spallation area; the results are shown in Fig. 3(b). The radii of the damaged areas are approximately 50, 90, and 120 mm. The slabs suffer from spallation damage from a few cracks. The number of cracks on the upper and bottom faces increases with decreasing scale factor, and the spallation damage on the slab increases. Fig. 4 shows a comparison of the damaged slabs with different scale factors at a scaled distance of 0.518 m/kg1/3. Fig. 4(a) shows the higher number of radial and annular cracking damage on the upper 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 moderate spallation damage, whereas the failure mode of the largest slab is perforation due to the blast load and the shear damage on one of the fixed supports. The damage on the slabs increases with decreasing scale factor. Unlike the other specimens at the same scaled distance (0.518 m/kg1/3), the “S ¼ 1” specimen is perforated, possibly because the larger concrete specimens are weaker due to size effect. Another possible reason is that the slabs were constructed with the same steel bar spaced at the same distance from one other, resulting in a reinforcement ratio that is equivalent to
that of a full-scale specimen, which is slightly lower than that of the small slabs due to the different slab thicknesses. Therefore, the damage on the full-scale specimen is the most serious (Fig. 4). Comparisons of the experimental results at different scale factors are shown in Table 2. The thicknesses h of the slabs are 30, 40, and 50 mm. The central deflections d at the same scaled distance increase with the dimensions at the two scaled distances, and the normalised peak deflection d/h slightly increases with the dimensions at the 0.591 m/kg1/3 scaled distance. However, the normalised peak deflection d/h of the two smaller slabs at the 0.518 m/kg1/3 scaled distance increases, whereas that of the largest slab decreases, because of perforation damage on slab F. The spallation area radius r and the normalised spall radius r/h increase with the dimensions. The scale modelling of the present problem is slightly distorted; thus, the deviation should be taken into account when scaling the results from the model up to the prototype. 5. Discussion This paper addresses the problem of scaling the dynamic response of RC slabs subjected to close-in air blast explosions (unconfined high explosion without fragmentation). The scaling used for the structure is geometrical (replica), whereas that for the explosive charge is based on Hopkinson’s law. While this concept is not new, it has not been previously applied to and validated for the specific case of close-in air blast explosions. Three slabs with different scale-down factors were investigated at two different scaled distances. The experimental results show that the fracture patterns of the specimens are almost similar.
162
W. Wang et al. / International Journal of Impact Engineering 49 (2012) 158e164
Fig. 4. Comparison of the experiment results with different scale factor S (scale distance ¼ 0.518 m/kg1/3).
However, the larger specimens suffer more damage, whereas the smallest specimens suffer the least damage. The larger specimen may be perforated, whereas the smaller specimen may exhibit scabbing without perforation. For instance, at the first scaled distance (0.591 m/kg1/3), the smallest slab suffers the least damage, with no evident annular cracking on specimen “S ¼ 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 scabbing without perforation (Fig. 4). The local damage on the concrete slabs with larger-scale-down factors has been slightly reduced compared with that of the slabs with smaller-scale-down factors. The normalised damage parameters of the slabs slightly increase with the decrease in the scale-down factors. The damage on the larger specimen becomes more serious compared with that on the scaled-down specimen with increasing scaled distance (Fig. 4). The possible reasons for these results are as follows: (1) the larger concrete specimens are Table 2 Comparison of results from tests. Slab
A C E B D F
Dimension (mm)
750 750 30 1000 1000 40 1250 1250 50 750 750 30 1000 1000 40 1250 1250 50
Scale distance (m/kg1/3)
Central deflection d (mm)
d/h
0.591 0.591 0.591 0.518 0.518 0.518
9 15 19 26 35 40
0.3 0.375 0.38 0.87 0.875 0.8
Spall radius r (mm)
r/h
50 90 120 85 120 185
1.67 2.25 2.4 2.83 3 3.7
weaker due to size effect [31]; (2) the larger specimens are less stiff and thus, are more vulnerable to damage because of the structural rigidity of the rebar; and (3) the reinforcements for all the slabs are similarly arranged, leading to a reduction in the reinforcement ratio and resulting in more damage to the large slabs. The smaller-scale specimens show more resistance to close-in air blast explosions than the scaled-up prototype. For instance, the results obtained for the smaller-scale specimens, which show resistance to perforation at the 0.518 m/kg1/3 scaled distance, cannot serve as an indicator of the predicted response of a scaledup prototype, which is perforated when the scaled distance is 0.518 m/kg1/3 (Fig. 4). Thus, when applying the results from the scaled model to the prototype, the test results should be corrected according to the variability of the strain rate and fractures with the blast loading. Based on the data in Table 2, the ratio of the normalised peak deflection d/h and the normalised spall radius r/h are inversely proportional to the slab thickness of the different scaled distances Z and scale-down factors S (Figs. 5 and 6). The following relationship was obtained by fitting the data to correct the effect of the scaledown factors:
d h
¼ 0:0802Z 6:955 1 0:8735e0:0115S
r ¼ 0:3327Z 3:0967 1 þ 6:7318e2:7284S h
(3)
(4)
Equations (3) and (4) and Figs. 5 and 6 show that the similarity is slightly distorted in the current results. For instance, at the first
W. Wang et al. / International Journal of Impact Engineering 49 (2012) 158e164
Fig. 5. Relationship between normalized peak deflection d/h and scaled-down factors.
163
caused by mass detonation using different TNT charges. The scaling used for the structure is geometrical (replica), whereas that for the explosive charge is based on Hopkinson’s law. Three slabs with different scale-down factors were investigated at two different scaled distances. Two major damage modes were observed, namely, spallation damage from a few cracks, and moderate spallation damage. The damage mode changes from flexural, with spall damage on the back surface, to perforation failure damage as the charge weight of the large-scale slab is increased. The experimental results show that the fracture patterns are almost similar. However, the larger specimens suffer more damage, and the smallest specimens suffer the least damage. The larger specimens may be perforated, whereas the smaller specimens may exhibit scabbing without perforation. The local damage on the concrete slabs with larger-scale factors is slightly reduced compared with that of slabs with smaller-scale factors, and the normalised damage parameters of the slabs slightly increase with decreasing scale-down factor. Thus, when applying the results obtained from the scaled model to the prototype, the test results should be corrected according to the variability of the strain rate and fractures with the blast loading. Based on the results, two empirical equations are proposed to correct the results when scaling up from the model to the prototype. Further research on larger slabs under blast loadings should be conducted. Additional research is also needed for RC slabs with different reinforcement ratios to improve their blast resistance. The results of this research will further the development of dynamic material simulation methods and material models.
References
Fig. 6. Relationship between normalized spall radius r/h and scaled-down factors.
scaled distance (0.591 m/kg1/3), the smallest slab suffers the least damage, with no evident annular cracking in specimen “S ¼ 1.67” [Fig. 3(a)]. However, the “S ¼ 1” specimen is perforated at the 0.518 m/kg1/3 scaled distance, whereas the other smaller specimen exhibits scabbing without perforation (Fig. 4). Thus, the damage on the largest specimen is the most serious, with the normalised peak deflection d/h and normalised spall radius r/h slightly decreasing with the increase in the scale-down factor S (Figs. 5 and 6). The relationship is derived only from data for scale-down factors less than 2 and damage level due to spallation; thus, it must be used with caution for scale-down factors larger than 2. The above formula (3) and (4) has been used to calculate the peak deflection and spall radius of the slab in Section 4. More importantly, the equation can only be used to correct the scaling on the test slabs and would be inappropriate for more general usage. 6. Conclusions This paper addresses the problem of scaling the dynamic response of one-way square RC slabs to close-in blast loadings
[1] Mays GC, Hetherington JG, Rose TA. Response to blast loading of concrete wall panels with openings. ASCE J Struct Eng 1999;125(12):1448e50. [2] Lok TS, Xiao JR. Steel-fibre-reinforced concrete panels exposed to air blast loading. Proc Inst Civil Eng Struct Build 1999;134:319e31. [3] Mosalam KM, Mosallam AS. Nonlinear transient analysis of reinforced concrete slabs subjected to blast loading and retrofitted with CFRP composites. Compos Part B-Eng 2001;32:623e36. [4] Mosallam A, Haroun M, Mosalam KM. Repair and rehabilitation of reinforced and unreinforced concrete slabs with polymer composites. In: Forde MC, editor. Proceedings of the structural faults þ Repair-2001. London, UK. Edinburgh UK: Engineering Technics Press; 2001, July 4e6. 2001. A keynote paper, CD-ROM. [5] Lawver D, Daddazio R, Jin Oh G, Lee CKB, Pifko AB, Stanley M. Simulating the response of composite reinforced floor slabs subjected to blast loading. ASME Int Mech Eng Cong Wash DC; 2003:15e22. [6] Ngo T, Mendis P, Krauthammer T. Behavior of ultrahigh-strength prestressed concrete panels subjected to blast loading. J Struct Eng-ASCE 2007;133: 1582e90. [7] Ngo T. Behaviour of high strength concrete subject to impulsive loading. Ph.D. thesis, Univ. of Melbourne, Australia. 2005. [8] Luccioni BM, Luege M. Concrete pavement slab under blast loads. Int J Impact Eng 2006;32:1248e66. [9] Lu B, Silva PF. Improving the blast resistance capacity of RC slabs with innovative composite materials. Compos Part B-Eng 2007;38:523e34. [10] Silva PF, Lu B. Blast resistance capacity of reinforced concrete slabs. J Struct Eng-ASCE 2009;135:708e16. [11] Mcvay MK. Spall damage of concrete structures. Technical Report SL 88e22. US Army Corps of Engineers Waterways Experiment Station; 1998. [12] Wu C, Nurwidayati R, Oehlers DJ. Fragmentation from spallation of RC slabs due to airblast loads. Int J Impact Eng 2009;36:1371e6. [13] Ohkubo K, Beppu M, Ohno T, Satoh K. Experimental study on the effectiveness of fiber sheet reinforcement on the explosive-resistant performance of concrete plates. Int J Impact Eng 2008;35:1702e8. [14] Wu C, Oehlers DJ, Rebentrost M, Burman N, Whittaker AS. Blast testing of ultrahigh performance fiber concrete slabs and FRP retrofitted RC slabs. Eng Struct 2009;31:2060e9. [15] Nash PT, Vallabhan CVG, Knight TC. Spall damage to concrete walls from close in cased and uncased explosions in air. ACI Struct J 1995;92(6):680e8. [16] Rabczuk T, Eibl J, Stempniewski L. Numerical analysis of high speed concrete fragmentation using a meshfree Lagrangian method. Eng Fract Mech 2004; 71(4e6):547e56.
164
W. Wang et al. / International Journal of Impact Engineering 49 (2012) 158e164
[17] Rabczuk T, Eibl J. Simulation of high velocity concrete fragmentation using SPH/MLSPH. Int J Numer Meth Eng 2003;56(10):1421e44. [18] Xu K, Lu Y. Numerical simulation study of spallation in reinforced concrete plates subjected to blast loading. Comput Struct 2006;84:431e8. [19] Zhou XQ, Hao H, Deeks AJ. Modeling dynamic damage of concrete slab under blast loading. In: Hao H, Lok TS, Lu GX, editors. Proceeding of the 6th Asia-Pacific conference on shock and impact loads on structures, December, Perth, WA, Australia; 2005. p. 703e10. ISBN: 981-05-3550-3. [20] Low HY, Hao H. Reliability analysis of direct shear and flexural failure modes of RC slabs under explosive loading. Eng Struct 2002;24:189e98. [21] TM5-1300. Structures to resist the effect of accidental explosions. US Department of the Army, Navy and Air Force Technical Manual; 1990. [22] TM5-855. Design and analysis of hardened structures to conventional weapons effects. Department of Defense, UFC 3-340-01, USA; 2002. [23] Zhou XQ, Hao H. Mesoscale modelling and analysis of damage and fragmentation of concrete slab under contact detonation. Int J Impact Eng 2009;36: 1315e26.
[24] Woodson SC, Baylot JT. Structural collapse: quarter-scale model experiments. Technical Report SL-99e8. US Army Corps of Engineers Engineer Research and Development Center; 1999. [25] Woodson SC, Baylot JT. Quarter-scale building/column experiments. In: Mohamed E, editor. Proceeding of advanced technology in structural engineering, Philadelphia, PA, USA; 2000. pp. 1e8. [26] Neuberger A, Peles S, Rittel D. Scaling the response of circular plates subjected to large and close-range spherical explosions. Part I: air-blast loading. Int J Impact Eng 2007;34:859e73. [27] Neuberger A, Peles S, Rittel D. Scaling the response of circular plates subjected to large and close-range spherical explosions. Part II: buried charges. Int J Impact Eng 2007;34:874e82. [28] Barenblatt GI. Scaling. Cambridge: Cambridge University Press; 2003. pp.37e51. [29] Jones N. Structural impact. Cambridge: Cambridge University Press; 1989. pp.489e519. [30] Baker W. Explosions in air. Austin: University of Texas Press; 1973. pp. 54e77. [31] Bazant ZP. Size effect in blunt fracture: concrete, rock. Metal J Eng Mech 1984; 110(4).
Contents lists available at SciVerse ScienceDirect
International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng
Experimental study on scaling the explosion resistance of a one-way square reinforced concrete slab under a close-in blast loading Wei Wang, Duo Zhang, Fangyun Lu*, Song-Chuan Wang, Fujing Tang Institute 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
a b s t r a c t
Article history: Received 27 May 2011 Received in revised form 29 March 2012 Accepted 30 March 2012 Available online 14 April 2012
Full-scale experiments involving actual geometries and charges are complicated and costly in terms of both preparation and measurements. Thus, scaled-down experiments are highly desirable. The present work aims to address the scaling of the dynamic response of one-way square reinforced concrete slabs subjected to close-in blast loadings. To achieve this objective, six slabs of two groups were tested under real blast loads. Three slabs with different scale-down factors were investigated using two scaled distances. Two major damage levels were observed, namely, spallation damage from a few cracks, and moderate spallation damage. The test results show that the macrostructure damage and fracture in the experiments are almost similar. However, the local damage in concrete slabs with larger-scale factors is slightly reduced compared with that of slabs with smaller-scale factors. Two empirical equations are proposed based on the results to correct the results when scaling up from the model to the prototype. Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved.
Keywords: Explosion load Dynamic response Reinforced concrete slab Damage mode Scaling
1. Introduction The behaviour analysis and design of hardened structures for protection against short-duration dynamic loadings, such as those induced by air blasts, have been a subject of extensive studies in the last decades. Intensive dynamic loading via detonations should be considered in the structural design and assessment of both military and civilian structures and facilities in such cases. Full-scale blast tests are required to understand the behaviour of slabs under this kind of loading. However, these tests are limited because of security restrictions and the considerable resources required. The present work is intended to address the scaling of the dynamic response of one-way square reinforced concrete (RC) slabs subjected to close-in blast loadings. Considerable research on the behaviour of concrete slabs and panels under blast loads has been conducted in recent years, including experiments on the behaviour of RC [1] and fibrereinforced panels [2] subjected to blast loads. Mosalam [3,4] used divisive analysis to model 2.64 m 2.64 m 0.076 m RC slabs using 0.46 m wide, 0.584 mm thick carbon fibre-reinforced polymer (CFRP) strips on the tension face in the two directions subjected to blast loading. The computational models for both the as-built and
* Corresponding author. Tel.: þ86 13308492212. E-mail address: [email protected] (F. Lu).
retrofitted slabs were verified using experimental results. Lawver [5] performed explosive tests on 9.1 m 9.1 m 0.2 m RC floor slabs, with the charge placed underneath the slab inside a building. Control and CFRP- and glass fibre-reinforced polymer-retrofitted slabs were tested. Both retrofitted slabs were significantly stiffer than the control slab, which had a 380 mm deflection. Ngo [6,7] investigated the blast resistance of ultrahigh-strength concrete panels made of reactive powder concrete. The results showed that the ultrahigh-strength concrete panels performed extremely well, surviving the blast with minor cracks. Luccioni [8] analysed the behaviour of concrete pavement slabs subjected to blast loads produced by the detonation of high explosive charges placed above them. An equation that approximates the relationship of the crater diameter on the pavement with the explosive charge and its height above the pavement was then proposed. Lu and Silva [9,10] studied a procedure that estimates the level of damage produced by different explosive charge weights and standoff distances on RC slabs. Test results showed that the procedure was accurate in predicting the appropriate explosive charge weight and standoff distance that produce a given damage level. McVay [11] characterised the spallation damage on RC slabs under blast loads. Wu [12] estimated the fragment size distribution from concrete spallation due to air blast loads. Ohkubo [13] and Wu [14] evaluated the effectiveness of fibre sheet reinforcement on the explosion resistance of concrete plates. Explosion tests were conducted, and existing formulae were applied to estimate the failure modes
0734-743X/$ e see front matter Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2012.03.010
W. Wang et al. / International Journal of Impact Engineering 49 (2012) 158e164
of concrete plates subjected to contact explosion. Advanced numerical methods such as the mesh-free and finite-element methods have been developed in recent years to simulate the spallation of RC slabs subjected to air blast loads [15e19]. A reliability analysis of the direct shear and flexural failure modes of RC slabs under explosive loadings was also conducted by Hsin [20]. Current design guidelines [21,22] on damage on RC slabs such as TM5 also provide possible combinations of estimated explosive charge weights and standoff distances that can generate certain levels of damage to concrete. Zhou [23] constructed a mesoscale concrete model to simulate the propagation of dynamic failure on a concrete slab under contact detonation. The study demonstrated a practical method of predicting the fragment size distribution using image analysis and numerical simulations. However, the explosion resistance of one-way square RC slabs under a close-in blast loading has not yet been studied. The current methods of analysis for concrete slabs under blast loadings consist of two major approaches, namely, experimental and numerical studies. Although a numerical study is an indirect method of determining the damage on concrete slabs under blast loadings, the use of precision test data to evaluate their accuracy is critically important. Many experimental studies are not feasible because of safety and economic reasons. On the other hand, the preparations and measurements in full-scale development field experiments are complex and expensive. Experiments at reduced scales can identify the critical effects, improve the engineering design, and validate the physics-based models that can be used to predict the structural dynamic response at all scales. A series of experiments using five different two-storey, quarter-scale RC structures was conducted by Woodson and Baylot [24,25] to investigate the response of exterior columns to blast loads. The scaling of the structural response was not included in the study. Neuberger [26,27] addressed the scaling of the dynamic response of clamped circular metal plates subjected to close-range and large spherical blast loadings through in air blast loadings and buried charges. However, few studies have been conducted to estimate the scaling and damage modes of one-way square RC slabs subjected to blast loadings. In the current study, six slabs with three scales, namely, 3:4:5 were tested under close-in blast loadings. The blast loads were generated by the detonation of 0.13 kge0.94 kg TNT explosive charges located at a 0.3 me0.5 m standoff distance above the slabs. The scabbing holes formed on the opposite surface of the specimens were observed and compared. Different damage levels and modes were also studied. The scaling factors that characterise the dynamic response of an RC slab subjected to close-in blast loadings are then presented based on the experimental results. 2. Scaling theory Validation of the physical similarity of a specific phenomenon is crucial for proper scaling. However, the experimental results obtained from the model should be scaled-up correctly to accurately represent the full-scale prototype. The concept of physical similarity, as stated by Barenblatt [28], is a natural generalisation of similarities in geometry. The objective is to obtain identical relationships between quantities that characterise both the prototype (representing the original object) and the model (representing the scaled-down object). The principles of scaling, and the relationships between the parameters of the small-scale model and the full-scale prototype, were stated by Jones [29]. The relevant parameters for the investigated problem are presented in terms of the proportion of the prototype parameter (superscript P) and the corresponding model parameter (superscript M), as follows:
159
The linear dimensions are proportional to the scale factor, aP aM xPi ¼ xM i $S. The angles are the same, i ¼ i . The densities of the . The stresses of each material are materials are the same, rPi ¼ rM i the same, sPi ¼ sM i . The characteristic times are proportional to the P M scale factor, sPi ¼ sM i $S. The strains are identical, 3 i ¼ 3 i . The load pressure are the same, and must act at scaled locations, FiP ¼ FiM , at xPi ¼ xM i $S. Deformations at geometrically scaled locations for the corresponding scaled times are proportional to the scale factor, P M dPi ¼ dM i $S, at si ¼ si $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 scaled according 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. The strain rate in a small-scale model is a magnitude larger than that in a geometrically similar, full-scale prototype. For the case at hand, the material properties are assumed to be approximately scaleindependent because the actual scale factor is not very large. Finally, fractures cannot be scaled according to the basic principles of geometrically similar scaling. However, the scabbing of the slabs is small, and the scale factor is not very large; thus, the similitude can be assumed as approximately scaled. When scaling the spherical blast wave phenomena, the most common scaling method used is Hopkinson’s, or the “cube root” scaling law, as shown by Baker [30]. This scaling law states that selfsimilar blast waves are produced at identical scaled distances when two explosive charges of similar geometries, but of different weights, are detonated in the same atmosphere. For explosions in air, the Hopkinson scaled parameters are as follows [30]:
Z ¼
R ; E1=3
s* ¼
s E1=3
;
z ¼
I E1=3
(1)
where Z is the scaled distance, s* is the characteristic scaled time of the blast wave, z is the scaled impulse, R is the distance from the centre of the blast source, and E is the source blast energy. This law implies that all quantities with the dimensions of pressure and velocity 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 this study, Hopkinson’s method was used to calculate the corresponding 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 the slabs are given in Fig. 1 and Table 1; the lengths L are 0.75, 1, and 1.25 m, respectively. These specimens were constructed using a 6 mm diameter bar meshing and spaced at a distance of 75 mm from one other in the major bending plane (r ¼ 1.43%), and at a distance of 75 mm from one other in the other plane (r ¼ 1.43%); r is the reinforcement ratio. Given the material difference, strictly scaled slabs cannot be achieved in the experiments. The concrete slabs may not have been strictly scaled, particularly with respect to the reinforcement. However, the concrete and reinforcement bars exhibit the same properties. The reinforcement ratios of the three scaled slabs are almost the same. Therefore, the slabs can be assumed to have been approximately scaled. The concrete has an average compressive strength of 39.5 MPa, as measured using three normal 150 mm 150 mm 150 mm concrete cubes; a tensile strength of 4.2 MPa; and a Young’s modulus of 28.3 GPa. The
160
W. Wang et al. / International Journal of Impact Engineering 49 (2012) 158e164
Fig. 1. Geometry of the RC slab (L ¼ 750, 1000 and 1250 mm).
reinforcement has a yield strength of 600 MPa and a Young’s modulus of 200 GPa. A steel frame was built on the ground (Fig. 2) to ensure that the specimens are firmly placed. The steel members used for the frame consisted of 8 mm thick steel angles. The RC slab was clamped down on each side of the steel angle to prevent uplifting during the tests. Wooden bars of the same width and length as the steel angle were placed on two sides, between the specimen and the frame, to provide uniform supporting conditions and prevent direct impact damage on the specimen edges. The specimens were estimated using the fixed supports, although the end restraint in the test was somewhere between fixed and pinned, and the extent of fixity likely depends on the magnitude of the imposed blast load and the damage sustained by the restraints. However, the boundary condition had minimal effect on the slab damage caused by the initial stress wave propagation inside the slab. TNT was used in the explosion tests because it is a standard high explosive deemed chemically safe, making it easier to cast. A detonator was inserted into the top of TNT. The mass of TNT was set at 0.13 kge0.94 kg to determine the effect of scaled distances on the damage on the concrete slabs. The cylindrical charge was suspended above the test specimens by a rope at a specific standoff distance (Fig. 2) and centred over the slab using four string guides. The diameter-to-height ratio of the cylindrical charges was set at approximately 2. All dimensions were scaled when the charge mass was increased. Table 1 summarises the experiment programme. The standoff distances, measured from the centre of the explosive to the top surface of the slab, were set at 300, 400, and 500 mm.
initial state to the formation of a few, barely visible cracks; (2) the threshold for the spallation damage are a few cracks and a hollow sound, to a large bulge in the concrete with a few incidence of spallation on the surface; and (3) moderate spallation damage, from a very shallow spallation, to spallation penetrating about onethird of the plate thickness. In this paper, the damage modes of the slabs were chosen as spallation with the appropriate scaled distance so that the degree of damage can be clearly measured and easily compared. Two pairs of scaled distances were experimentally compared with the spallation damage. The first scaled distance is 0.591 m/kg1/3, and the damage level of the slabs is spallation damage from a few cracks. For the second scaled distance (0.518 m/kg1/3), the damage level of the slabs is moderate spallation damage. Fig. 3 shows a comparison of the damaged slabs with different scale factors (S) at a scaled distance of 0.591 m/kg1/3. The upper face of the slabs [Fig. 3(a)] shows the presence of several small cracks at the centre, which are caused by the high pressure from the explosion, as well as the fixed support. Two evident flexural cracks are formed at the central symmetry line of the slabs, and some annular radial cracks appear on the upper face. The annular
4. Test results The failure modes of slabs under a close-in explosion were characterised by McVay [11] as follows: (1) no damage from the
Table 1 Experimental program. Slab
Scale factor
Dimension (mm)
Explosive mass (kg)
Standoff distance (m)
Scale distance (m/kg1/3)
A B C D E F
1.67 1.67 1.25 1.25 1 1
750 750 30 750 750 30 1000 1000 40 1000 1000 40 1250 1250 50 1250 1250 50
0.13 0.19 0.31 0.46 0.64 0.94
0.3 0.3 0.4 0.4 0.5 0.5
0.591 0.518 0.591 0.518 0.591 0.518 Fig. 2. Test device.
W. Wang et al. / International Journal of Impact Engineering 49 (2012) 158e164
161
Fig. 3. Comparison of the experiment results with different scale factor S (scale distance ¼ 0.591 m/kg1/3).
cracking of specimen “S ¼ 1.67” in Fig. 3(a) is not evident, whereas those in the other two specimens are more evident. This result may be due to the generally greater strength of the small specimen compared with the full-scale one due to the size effect. A tensile spalling crater appears on the back surface of the slab [Fig. 3(b)], which results from the low resistance of concrete to tension. The calculated damaged area on the bottom surface of the slab is calculated using the radius of the spallation area; the results are shown in Fig. 3(b). The radii of the damaged areas are approximately 50, 90, and 120 mm. The slabs suffer from spallation damage from a few cracks. The number of cracks on the upper and bottom faces increases with decreasing scale factor, and the spallation damage on the slab increases. Fig. 4 shows a comparison of the damaged slabs with different scale factors at a scaled distance of 0.518 m/kg1/3. Fig. 4(a) shows the higher number of radial and annular cracking damage on the upper 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 moderate spallation damage, whereas the failure mode of the largest slab is perforation due to the blast load and the shear damage on one of the fixed supports. The damage on the slabs increases with decreasing scale factor. Unlike the other specimens at the same scaled distance (0.518 m/kg1/3), the “S ¼ 1” specimen is perforated, possibly because the larger concrete specimens are weaker due to size effect. Another possible reason is that the slabs were constructed with the same steel bar spaced at the same distance from one other, resulting in a reinforcement ratio that is equivalent to
that of a full-scale specimen, which is slightly lower than that of the small slabs due to the different slab thicknesses. Therefore, the damage on the full-scale specimen is the most serious (Fig. 4). Comparisons of the experimental results at different scale factors are shown in Table 2. The thicknesses h of the slabs are 30, 40, and 50 mm. The central deflections d at the same scaled distance increase with the dimensions at the two scaled distances, and the normalised peak deflection d/h slightly increases with the dimensions at the 0.591 m/kg1/3 scaled distance. However, the normalised peak deflection d/h of the two smaller slabs at the 0.518 m/kg1/3 scaled distance increases, whereas that of the largest slab decreases, because of perforation damage on slab F. The spallation area radius r and the normalised spall radius r/h increase with the dimensions. The scale modelling of the present problem is slightly distorted; thus, the deviation should be taken into account when scaling the results from the model up to the prototype. 5. Discussion This paper addresses the problem of scaling the dynamic response of RC slabs subjected to close-in air blast explosions (unconfined high explosion without fragmentation). The scaling used for the structure is geometrical (replica), whereas that for the explosive charge is based on Hopkinson’s law. While this concept is not new, it has not been previously applied to and validated for the specific case of close-in air blast explosions. Three slabs with different scale-down factors were investigated at two different scaled distances. The experimental results show that the fracture patterns of the specimens are almost similar.
162
W. Wang et al. / International Journal of Impact Engineering 49 (2012) 158e164
Fig. 4. Comparison of the experiment results with different scale factor S (scale distance ¼ 0.518 m/kg1/3).
However, the larger specimens suffer more damage, whereas the smallest specimens suffer the least damage. The larger specimen may be perforated, whereas the smaller specimen may exhibit scabbing without perforation. For instance, at the first scaled distance (0.591 m/kg1/3), the smallest slab suffers the least damage, with no evident annular cracking on specimen “S ¼ 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 scabbing without perforation (Fig. 4). The local damage on the concrete slabs with larger-scale-down factors has been slightly reduced compared with that of the slabs with smaller-scale-down factors. The normalised damage parameters of the slabs slightly increase with the decrease in the scale-down factors. The damage on the larger specimen becomes more serious compared with that on the scaled-down specimen with increasing scaled distance (Fig. 4). The possible reasons for these results are as follows: (1) the larger concrete specimens are Table 2 Comparison of results from tests. Slab
A C E B D F
Dimension (mm)
750 750 30 1000 1000 40 1250 1250 50 750 750 30 1000 1000 40 1250 1250 50
Scale distance (m/kg1/3)
Central deflection d (mm)
d/h
0.591 0.591 0.591 0.518 0.518 0.518
9 15 19 26 35 40
0.3 0.375 0.38 0.87 0.875 0.8
Spall radius r (mm)
r/h
50 90 120 85 120 185
1.67 2.25 2.4 2.83 3 3.7
weaker due to size effect [31]; (2) the larger specimens are less stiff and thus, are more vulnerable to damage because of the structural rigidity of the rebar; and (3) the reinforcements for all the slabs are similarly arranged, leading to a reduction in the reinforcement ratio and resulting in more damage to the large slabs. The smaller-scale specimens show more resistance to close-in air blast explosions than the scaled-up prototype. For instance, the results obtained for the smaller-scale specimens, which show resistance to perforation at the 0.518 m/kg1/3 scaled distance, cannot serve as an indicator of the predicted response of a scaledup prototype, which is perforated when the scaled distance is 0.518 m/kg1/3 (Fig. 4). Thus, when applying the results from the scaled model to the prototype, the test results should be corrected according to the variability of the strain rate and fractures with the blast loading. Based on the data in Table 2, the ratio of the normalised peak deflection d/h and the normalised spall radius r/h are inversely proportional to the slab thickness of the different scaled distances Z and scale-down factors S (Figs. 5 and 6). The following relationship was obtained by fitting the data to correct the effect of the scaledown factors:
d h
¼ 0:0802Z 6:955 1 0:8735e0:0115S
r ¼ 0:3327Z 3:0967 1 þ 6:7318e2:7284S h
(3)
(4)
Equations (3) and (4) and Figs. 5 and 6 show that the similarity is slightly distorted in the current results. For instance, at the first
W. Wang et al. / International Journal of Impact Engineering 49 (2012) 158e164
Fig. 5. Relationship between normalized peak deflection d/h and scaled-down factors.
163
caused by mass detonation using different TNT charges. The scaling used for the structure is geometrical (replica), whereas that for the explosive charge is based on Hopkinson’s law. Three slabs with different scale-down factors were investigated at two different scaled distances. Two major damage modes were observed, namely, spallation damage from a few cracks, and moderate spallation damage. The damage mode changes from flexural, with spall damage on the back surface, to perforation failure damage as the charge weight of the large-scale slab is increased. The experimental results show that the fracture patterns are almost similar. However, the larger specimens suffer more damage, and the smallest specimens suffer the least damage. The larger specimens may be perforated, whereas the smaller specimens may exhibit scabbing without perforation. The local damage on the concrete slabs with larger-scale factors is slightly reduced compared with that of slabs with smaller-scale factors, and the normalised damage parameters of the slabs slightly increase with decreasing scale-down factor. Thus, when applying the results obtained from the scaled model to the prototype, the test results should be corrected according to the variability of the strain rate and fractures with the blast loading. Based on the results, two empirical equations are proposed to correct the results when scaling up from the model to the prototype. Further research on larger slabs under blast loadings should be conducted. Additional research is also needed for RC slabs with different reinforcement ratios to improve their blast resistance. The results of this research will further the development of dynamic material simulation methods and material models.
References
Fig. 6. Relationship between normalized spall radius r/h and scaled-down factors.
scaled distance (0.591 m/kg1/3), the smallest slab suffers the least damage, with no evident annular cracking in specimen “S ¼ 1.67” [Fig. 3(a)]. However, the “S ¼ 1” specimen is perforated at the 0.518 m/kg1/3 scaled distance, whereas the other smaller specimen exhibits scabbing without perforation (Fig. 4). Thus, the damage on the largest specimen is the most serious, with the normalised peak deflection d/h and normalised spall radius r/h slightly decreasing with the increase in the scale-down factor S (Figs. 5 and 6). The relationship is derived only from data for scale-down factors less than 2 and damage level due to spallation; thus, it must be used with caution for scale-down factors larger than 2. The above formula (3) and (4) has been used to calculate the peak deflection and spall radius of the slab in Section 4. More importantly, the equation can only be used to correct the scaling on the test slabs and would be inappropriate for more general usage. 6. Conclusions This paper addresses the problem of scaling the dynamic response of one-way square RC slabs to close-in blast loadings
[1] Mays GC, Hetherington JG, Rose TA. Response to blast loading of concrete wall panels with openings. ASCE J Struct Eng 1999;125(12):1448e50. [2] Lok TS, Xiao JR. Steel-fibre-reinforced concrete panels exposed to air blast loading. Proc Inst Civil Eng Struct Build 1999;134:319e31. [3] Mosalam KM, Mosallam AS. Nonlinear transient analysis of reinforced concrete slabs subjected to blast loading and retrofitted with CFRP composites. Compos Part B-Eng 2001;32:623e36. [4] Mosallam A, Haroun M, Mosalam KM. Repair and rehabilitation of reinforced and unreinforced concrete slabs with polymer composites. In: Forde MC, editor. Proceedings of the structural faults þ Repair-2001. London, UK. Edinburgh UK: Engineering Technics Press; 2001, July 4e6. 2001. A keynote paper, CD-ROM. [5] Lawver D, Daddazio R, Jin Oh G, Lee CKB, Pifko AB, Stanley M. Simulating the response of composite reinforced floor slabs subjected to blast loading. ASME Int Mech Eng Cong Wash DC; 2003:15e22. [6] Ngo T, Mendis P, Krauthammer T. Behavior of ultrahigh-strength prestressed concrete panels subjected to blast loading. J Struct Eng-ASCE 2007;133: 1582e90. [7] Ngo T. Behaviour of high strength concrete subject to impulsive loading. Ph.D. thesis, Univ. of Melbourne, Australia. 2005. [8] Luccioni BM, Luege M. Concrete pavement slab under blast loads. Int J Impact Eng 2006;32:1248e66. [9] Lu B, Silva PF. Improving the blast resistance capacity of RC slabs with innovative composite materials. Compos Part B-Eng 2007;38:523e34. [10] Silva PF, Lu B. Blast resistance capacity of reinforced concrete slabs. J Struct Eng-ASCE 2009;135:708e16. [11] Mcvay MK. Spall damage of concrete structures. Technical Report SL 88e22. US Army Corps of Engineers Waterways Experiment Station; 1998. [12] Wu C, Nurwidayati R, Oehlers DJ. Fragmentation from spallation of RC slabs due to airblast loads. Int J Impact Eng 2009;36:1371e6. [13] Ohkubo K, Beppu M, Ohno T, Satoh K. Experimental study on the effectiveness of fiber sheet reinforcement on the explosive-resistant performance of concrete plates. Int J Impact Eng 2008;35:1702e8. [14] Wu C, Oehlers DJ, Rebentrost M, Burman N, Whittaker AS. Blast testing of ultrahigh performance fiber concrete slabs and FRP retrofitted RC slabs. Eng Struct 2009;31:2060e9. [15] Nash PT, Vallabhan CVG, Knight TC. Spall damage to concrete walls from close in cased and uncased explosions in air. ACI Struct J 1995;92(6):680e8. [16] Rabczuk T, Eibl J, Stempniewski L. Numerical analysis of high speed concrete fragmentation using a meshfree Lagrangian method. Eng Fract Mech 2004; 71(4e6):547e56.
164
W. Wang et al. / International Journal of Impact Engineering 49 (2012) 158e164
[17] Rabczuk T, Eibl J. Simulation of high velocity concrete fragmentation using SPH/MLSPH. Int J Numer Meth Eng 2003;56(10):1421e44. [18] Xu K, Lu Y. Numerical simulation study of spallation in reinforced concrete plates subjected to blast loading. Comput Struct 2006;84:431e8. [19] Zhou XQ, Hao H, Deeks AJ. Modeling dynamic damage of concrete slab under blast loading. In: Hao H, Lok TS, Lu GX, editors. Proceeding of the 6th Asia-Pacific conference on shock and impact loads on structures, December, Perth, WA, Australia; 2005. p. 703e10. ISBN: 981-05-3550-3. [20] Low HY, Hao H. Reliability analysis of direct shear and flexural failure modes of RC slabs under explosive loading. Eng Struct 2002;24:189e98. [21] TM5-1300. Structures to resist the effect of accidental explosions. US Department of the Army, Navy and Air Force Technical Manual; 1990. [22] TM5-855. Design and analysis of hardened structures to conventional weapons effects. Department of Defense, UFC 3-340-01, USA; 2002. [23] Zhou XQ, Hao H. Mesoscale modelling and analysis of damage and fragmentation of concrete slab under contact detonation. Int J Impact Eng 2009;36: 1315e26.
[24] Woodson SC, Baylot JT. Structural collapse: quarter-scale model experiments. Technical Report SL-99e8. US Army Corps of Engineers Engineer Research and Development Center; 1999. [25] Woodson SC, Baylot JT. Quarter-scale building/column experiments. In: Mohamed E, editor. Proceeding of advanced technology in structural engineering, Philadelphia, PA, USA; 2000. pp. 1e8. [26] Neuberger A, Peles S, Rittel D. Scaling the response of circular plates subjected to large and close-range spherical explosions. Part I: air-blast loading. Int J Impact Eng 2007;34:859e73. [27] Neuberger A, Peles S, Rittel D. Scaling the response of circular plates subjected to large and close-range spherical explosions. Part II: buried charges. Int J Impact Eng 2007;34:874e82. [28] Barenblatt GI. Scaling. Cambridge: Cambridge University Press; 2003. pp.37e51. [29] Jones N. Structural impact. Cambridge: Cambridge University Press; 1989. pp.489e519. [30] Baker W. Explosions in air. Austin: University of Texas Press; 1973. pp. 54e77. [31] Bazant ZP. Size effect in blunt fracture: concrete, rock. Metal J Eng Mech 1984; 110(4).