Blast Resistance of Double-Layered Reinforced Concrete ...

Journal of Advanced Concrete Technology Vol. 9, No. 2, 177-191, June 2011 / Copyright © 2011 Japan Concrete Institute 177

Scientific paper

Blast Resistance of Double-Layered Reinforced Concrete Slabs Composed of Precast Thin Plates Makoto Yamaguchi1, Kiyoshi Murakami2, Koji Takeda3 and Yoshiyuki Mitsui4

Received 20 January 2011, accepted 15 April 2011

Abstract When designing blast-resistant reinforced concrete (RC) structures, reducing spall damage due to reflected tensile stress waves is a major problem. Furthermore, for rapid construction of the blast-resistant structures against sudden terrorist bomb attacks, it is necessary to build it with precast concrete walls and reduce the weight of the precast elements by reducing their size for ease of transportation and construction. In this study, to propose an idea for rapid construction and better blast resistance of blast-resistant RC structures, dou-ble-layered RC slabs composed of precast thin plates, 50 mm thick, were fabricated and utilized for contact detonation tests. The tests were conducted under a condition that the amount of explosives and the dimensions of specimen were constant respectively, and two types of concrete, normal concrete and polyethylene fiber reinforced concrete (PEFRC), were employed as the slab materials. Our results showed that creating an air cavity between the two layers of PEFRC slab was effective in reducing spall damage, while the air space had no advantage in normal RC, under a condition that the thickness of the air space was fixed at 15 mm. Furthermore, the above difference between PEFRC and normal RC slabs was discussed, based on the numerical result on the fracture process of the air-sandwiched normal RC slab.

1. Introduction

When designing important structures such as industrial plants and public facilities, it is necessary to ensure their safety against accidental explosions and terrorist bomb attacks, which happen rarely but can cause serious dam-age.

It is well known that the behaviors of structures under blast loadings are more complicated than those under static loadings. In particular, the fracture modes of rein-forced concrete (RC) slabs subjected to blast loadings are characterized by spalling, due to the tensile stress wave being reflected from the back side of the slab. To protect human lives inside a structure under such conditions, it is necessary to prevent the launch of concrete fragments that accompany spalling. Therefore, reducing spall damage is the most important problem faced by design-ers of blast-resistant RC structures.

The position of the explosives with relation to the RC structures is classified into three locations: 1) a position close to the structure (standoff detonation), 2) a position on the surface of the structure (contact detonation), and 3) a position inside the structure. Among these, contact detonation is regarded as a standard for the other two

cases. Until now, a number of experimental and nu-merical studies have been conducted regarding the evaluation of damage to normal RC slabs subjected to contact detonation (Hader 1985; McVay 1988; Kraus et al. 1994; Nash et al. 1995; Morishita et al. 2000, 2004; Tanaka et al. 2003; Katayama et al. 2007). Furthermore, the following techniques have been proposed for im-proving the blast resistance of RC slabs: one is strengthening with fiber reinforced polymer (FRP) composites (Muszynski et al. 2003; Buchan et al. 2007; Razaqpur et al. 2007; Silva et al. 2007) or steel plates (Lan et al. 2005) on the back surface of the RC slab; the other technique is employing a fiber reinforced concrete as a slab material (Sun et al. 1999; Banthia et al. 2004; Lan et al. 2005; Ngo et al. 2007; Zhou et al. 2008; Coughlin et al. 2010). The authors also conducted the contact detonation tests on polyethylene fiber reinforced concrete (PEFRC) slabs and showed that the PEFRC was more effective in reducing spall damage due to contact detonation as compared with normal concrete (Yama-guchi et al. 2008a, 2011).

For rapid construction of the blast-resistant RC struc-tures against sudden terrorist bomb attacks, it is neces-sary to build it with precast concrete walls and reduce the weight of the precast elements by reducing their thick-ness for ease of transportation and construction. However, it is easily predicted that there will be a decrease in the blast resistance of single RC slabs due to reducing their thickness. Shirai et al. (1997) and Kishi (1999) proposed the multi-layered systems, in which an air cavity or an elastic shock absorber is inserted between two thin RC layers, and showed their good impact resistance to pro-jectile or weight falling impacts, but the blast resistance of these systems to contact detonation has not yet been

1Fellow Researcher, Graduate School of Science and Technology, Kumamoto University, Japan. E-mail: [email protected] 2Professor, Graduate School of Science and Technology, Kumamoto University, Japan. 3Associate Professor, Graduate School of Science and Technology, Kumamoto University, Japan. 4Professor Emeritus, Kumamoto University, Japan.

178 M. Yamaguchi, K. Murakami, K. Takeda and Y. Mitsui / Journal of Advanced Concrete Technology Vol. 9, No. 2, 177-191, 2011

clarified. In this study, to propose an idea for rapid construction

and better blast resistance of blast-resistant RC structures, double-layered RC slabs composed of precast thin plates, 50 mm thick, were manufactured and used for the contact detonation tests. The tests were conducted under a con-dition that the amount of explosives and the dimensions of specimen were constant respectively, and two types of concrete, normal concrete and PEFRC, were employed as the slab materials. The investigation items of this experiment were as follows: 1) influence of internally laid polyethylene fiber mesh reinforcement on the blast resistance, 2) influence of presence of air space between two layers on the blast resistance, 3) influence of shock absorber inserted into the air space on the blast resistance, and 4) influence of thickness of air space and shock absorber on the blast resistance. Furthermore, a nu-merical simulation with the ANSYS AUTODYN code (Birnbaum et al. 1987; Katayama et al. 2007) was con-ducted to reveal the fracture process of the dou-ble-layered normal RC slab with an air cavity to help understanding of the difference between PEFRC and normal RC slabs.

2. Experiment

2.1 Experimental method 2.1.1 Materials and mix proportions Table 1 shows the materials used in this experiment. As a normal concrete, ready-mixed concrete with a nominal strength of 30 MPa and a specified slump of 18 cm was employed. For making the PEFRC, binding polyethylene short fiber, 30 mm in length, was used. In order to com-pensate for decrease in slump of fresh PEFRC due to the surface area effects of mixed fibers, ground granulated blast furnace slag and superplasticizer were used. High-early strength Portland cement was also used, in view of the intended application of PEFRC to precast concrete walls. As shock absorbers, chloroprene rubber (HCR), chloroprene sponge (SCR), and expanded poly-styrol (EPS) were used, based on their good shock absorbing capacity against projectile or weight falling impacts (Shirai et al. 1997; Kishi 1999).

The mix proportions of the PEFRC are shown in Table 2. In previous studies (Yamaguchi et al. 2008a, 2011), the authors showed that the flexural toughness, which repre-sents energy absorption capacity of fiber reinforced con-cretes, was an important mechanical characteristic for

Table 1 Materials used.

Normal concrete

Ready-mixed concrete Nominal strength: 30 MPa, Specified slump: 18 cm, Maximum size of coarse aggregate: 20 mm Measured slump: 13.5 cm (in series 1) and 11.5 cm (in series 2) Cement High-early strength Portland cement Fine aggregate

River sand Surface-dried density: 2.63 g/cm3, Water absorption: 2.69%, Maximum size: 2.5 mm, Fineness modulus: 2.58

Coarse aggregate

Crushed stone Surface-dried density: 2.95 g/cm3, Water absorption: 1.27%, Maximum size: 15 mm, Percentage of absolute volume: 56.3%

Admixture Blast furnace slag Density: 2.89 g/cm3, Specific surface area: 6140 cm2/g Supreplasticizer (polycarboxylic acid type)

PEFRC

Short fiber Polyethylene fiber Density: 0.97 g/cm3, Size: 68 μm (diameter) × 30 mm (length), Tensile strength: 1870 MPa, Tensile elastic modulus: 43 GPa, Fracture strain (elongation): 5%

Reinforcing steel bar

Polished steel bar (φ5) 0.2% proof stress: 650 MPa, Tensile strength: 733 MPa, Fracture strain (nominal value): 12.8%

Continuous fiber

Polyethylene fiber mesh sheet Unit weight: 44 g/m2 (fiber: 27 g/m2), Thickness: 0.27 mm, Pitch: 10 mm, Strength: 1.36–1.37 kN/5cm

Shock absorber

Chloroprene rubber (HCR) Density: 1.40 g/cm3, JIS hardness (A): 63.3 Chloroprene sponge (SCR) Density: 0.25 g/cm3, JIS hardness (A): 18.9 Expanded poly-styrol (EPS) Density: 0.028 g/cm3, Flexural strength: 0.34 MPa

Adhesive Polymer cement mortar (in series 1) and Epoxy resin (in series 2)

Table 2 Mix proportions of PEFRC.

Unit weight [kg/m3] Series Vf [%]

W/B [%]

Sg/B [%]

s/a [%] C Sg W S G

Sp/B [%]

Slump [cm]

1 2 4.0 33 50 65 488 488 325 565 341 0.50 12.0

18.5 Notes; Vf: fiber volume fraction, W/B: water-binder ratio, Sg/B: blast furnace slag-binder ratio, s/a: sand percentage, C: cement, Sg:

blast furnace slag, B (= C + Sg): binder, W: water, S: fine aggregate, G: coarse aggregate, Sp: superplasticizer.

M. Yamaguchi, K. Murakami, K. Takeda and Y. Mitsui / Journal of Advanced Concrete Technology Vol. 9, No. 2, 177-191, 2011 179

evaluating the blast resistance of single PEFRC slab. If the flexural toughness of the PEFRC in the upper layer of the double-layered slab is large enough, the damage to the lower layer is expected to be reduced by sacrificial energy absorption of the upper layer. Therefore, the mix proportion of the PEFRC was determined based on the mix proportion for which the flexural toughness was at its peak and the slump was over 10 cm (Yamaguchi et al. 2008b).

For mixing the PEFRC, a forced double axis mixer (55L) was used: first, the cement, blast furnace slag, and aggregates were dry mixed for 15 seconds; secondly, the water and superplasticizer were added and mixed for 90 seconds; finally, the polyethylene short fibers were added and mixed for 3 minutes.

2.1.2 Mechanical characteristics of PEFRC Table 3 shows the material test methods. Three speci-mens were prepared for each test, which were cured in wet conditions for 14 days (for PEFRC) and 28 days (for normal concrete), and then cured in air until testing. The flexural toughness coefficient bσ (JCI 1984; JSCE 2007), which is an important mechanical characteristic against contact detonation (Yamaguchi et al. 2008a, 2011), was calculated using the following equation:

223

bdlT

tb

bb ⋅⋅=

δσ (1)

where Tb: an area under the load – displacement curve until the displacement reached 2.0 mm [N·mm], δtb:

displacement of 2.0 mm, l: span length [mm] and b, d: width and depth of the prism specimen [mm].

The material test results are shown in Table 4. The values of the flexural toughness coefficient of the PEFRC were 9.52 MPa (in series 1) and 8.69 MPa (in series 2): the values of total damage depth (the sum of crater and spall depths) in single, 100-mm thick PEFRC slab by the 200 g explosive charge were estimated to be 55 mm (in series 1) and 59 mm (in series 2), based on previous studies (Yamaguchi et al. 2008a, 2011). As for normal concrete, Morishita et al. (2004) have clarified that the influence of concrete strength on the blast resis-tance of normal RC slab is negligible. Based on their method for estimating damage to normal RC slab, the failure mode of single, 100-mm thick normal RC slab by the 200 g explosive charge was estimated to be ‘breaching’.

2.1.3 Specimen configuration Table 4 and Fig. 1 show a list of thirteen kinds of specimens and how to manufacture the specimens for the contact detonation tests, respectively.

The single plate, composed of a double-layered slab, was of the same size, 600 mm long, 600 mm wide, and 50 mm thick. These dimensions were the same as those in previous studies dealing with the blast resistance of sin-gle slab (Morishita et al. 2000, 2004; Tanaka et al. 2003; Yamaguchi et al. 2008a, 2011). The curing age of the specimens for the contact detonation tests was the same as that in the material tests.

Table 3 Material test methods.

Specimen configuration Number Measurement item Compressive test φ100 × 200 mm cylindrical specimen 3 Compressive stress – strain curve Splitting tensile test φ100 × 200 mm cylindrical specimen 3 Maximum load Flexural test 100 × 100 × 400 mm prism specimen

(span length: 300 mm) 3 Load – displacement curve

(three-point bending) Note; the flexural test was not conducted for normal concrete, because the flexural toughness of normal concrete is negligible due to

its brittle post-peak behavior.

Table 4 Thirteen types of specimens for contact detonation tests and material test results.

Middle layer Series Specimen Type of concrete Type Thickness

Compo-sition

fc [MPa]

E [GPa]

ft [MPa]

fb [MPa]

bσ [MPa]

PE-Mesh PEFRC Mesh reinforcement A 70.6 23.2 7.28 10.2 9.52 NC-Mesh Normal concrete Mesh reinforcement A 41.5 32.1 3.33 – – PE-AIR-15 PEFRC AIR 15 mm B 70.6 23.2 7.28 10.2 9.52

1

NC-AIR-15 Normal concrete AIR 15 mm B 41.5 32.1 3.33 – – PE-HCR-15 PEFRC HCR 15 mm C 59.4 24.3 7.94 9.37 8.69 NC-HCR-15 Normal concrete HCR 15 mm C 35.8 29.3 2.78 – – PE-SCR-15 PEFRC SCR 15 mm C 59.4 24.3 7.94 9.37 8.69 NC-SCR-15 Normal concrete SCR 15 mm C 35.8 29.3 2.78 – – PE-EPS-15 PEFRC EPS 15 mm C 59.4 24.3 7.94 9.37 8.69 NC-EPS-15 Normal concrete EPS 15 mm C 35.8 29.3 2.78 – – PE-AIR-5 PEFRC AIR 5 mm B 59.4 24.3 7.94 9.37 8.69 PE-AIR-30 PEFRC AIR 30 mm B 59.4 24.3 7.94 9.37 8.69

2

PE-HCR-5 PEFRC HCR 5 mm D 59.4 24.3 7.94 9.37 8.69 Notes; fc: compressive strength, E: Young’s modulus, ft: splitting tensile strength, fb: flexural strength, bσ : flexural toughness coef-

ficient. The symbols of ‘Composition’ correspond to those in Fig. 1.


The double-layered slabs used in this experiment were classified into three types: 1) Slabs strengthened with polyethylene fiber mesh

sheets in the bond surface of two layers. Double polyethylene fiber mesh sheets were bonded di-agonally with respect to each other between the bond surfaces of two layers by polymer cement mortar.

2) Slabs with an air space inserted between two layers. We used three different thicknesses of the air space in the air-sandwiched PEFRC slab: 5, 15, and 30 mm. The materials used for making the air space varied between the two experiment series, however, their influence on the size of the crater and spall is con-sidered negligible because the sizes of the crater and spall are ruled by the propagation of the stress waves.

3) Slabs with various shock absorbers inserted into the air space. The thickness of the shock absorber HCR inserted into the middle of the double-layered PEFRC slab varied between 5 and 15 mm.

2.1.4 Test set-up Figure 2 shows the test set-up for the contact detonation. The specimen was supported by two wooden jigs with an inside span of 510 mm, in accordance with previous studies (Morishita et al. 2000, 2004; Tanaka et al. 2003). The explosives (penthrite: 65%, paraffin: 35%, density: 1.30 g/cm3) were installed in the center of the upper surface of the specimen and blasted using an electric detonator. For direct comparison of double-layered and single slabs, both the shape and the amount of explosives were set to the same as those in previous studies dealing with the blast resistance of single slab (Yamaguchi et al. 2008a, 2011): the explosives were cylindrical shaped, with a diameter equal to the height, and the amount of explosives was fixed at 200 g. 2.1.5 Measuring the size of the external damage After the contact detonation tests, the fracture behaviors of the specimens were observed in detail. Before meas-uring the size of the external damage, the concrete frag-ments were removed by hand. Measurement items are shown in Fig. 3. The diameters of the crater, spall, and

Fig. 1 How to manufacture specimens for contact detonation tests.

600 60

0

PEFRC or normal concrete

Polished steel bar φ5@120

50-mm thick single plate

The polyethylene fiber mesh sheets and polymer cement mortar


Series 1: 50-mm wide aluminum plate and polymer cement mortar Series 2: 50-mm wide rectangular lumber and epoxy resin

5, 15, and 30-mm thick air space

50

50

< Composition A >

50

50

< Composition B >

50

50

< Composition C >


50-mm wide rectangular lumber and epoxy resin

15-mm thick shock absorber

50-mm thick single plate 50

50

5-mm thick HCR shock absorber < Composition D > [Unit: mm]

Fig. 2 Test set-up for contact detonation.

Explosives and electric detonator

Rectangular lumber

Plywood Specimen

510 mm


breach were defined as the average value of four meas-urements along the straight lines 1-4, shown in Fig. 3, because the crater, spall and breach might not be sym-metrical. The depth of the damage in the double-layered slabs was evaluated by measuring the maximum damage depth of both layers, since the border between the crater and the spall was not clear in most of the double-layered slabs as will be seen later. 2.2 Results and discussion 2.2.1 Fracture behaviors of the specimens Table 5 shows the fracture behaviors of the specimens after the contact detonation tests.

In specimen PE-Mesh, a delamination of the bond surface between the PEFRC layers was observed. On the back surface of the lower layer, a small bulge and spall occurred, but the launch of the PEFRC fragments was prevented. Multiple fine cracks propagated in a radial pattern from the spall, and a straight macro-crack parallel to the wooden jigs was also observed on the back side of the lower layer.

In specimen NC-Mesh, no breach occurred in the bond layer because of the polyethylene fiber mesh reinforce-ment, but the bond layer was largely twisted under the detonation point and breach occurred in both of the normal RC layers. On the back side of the lower layer, a very large spall occurred and macro-cracks propagated in a radial pattern from the spall. Furthermore, cracks penetrating from the top to the bottom were observed in both of the normal RC layers.

In specimen PE-AIR-15, no breach occurred in the upper layer, because the PEFRC fragments at the back surface of the upper layer were prevented from being launched by contact with the upper surface of the lower layer. On the back surface of the lower layer, cross-shaped cracking similar to static flexural cracking was observed without the spall which is typical of con-tact detonation. Furthermore, fine internal cracks parallel to the back surface were observed in the lower layer.

In specimen NC-AIR-15, which had the same struc-ture as specimen PE-AIR-15, a large breach occurred in both of the normal RC layers. The local failure, which

occurred in the lower layer, was in the shape of a trun-cated cone, which is characteristic of punching shear failure. The cracks in this specimen were larger than those in specimen NC-Mesh, and cracking parallel to the side surfaces of the slab was also observed.

As for specimens PE-HCR-15, PE-SCR-15 and PE-EPS-15, a PEFRC bulge created in the back surface of the upper layer compressed the shock absorber below it in all of the three specimens, however, the damage to the shock absorbers was different according to their hardness: shock absorbers SCR and EPS (with low hardness) were completely squashed under the detona-tion point, and the PEFRC bulge made contact with the upper surface of the lower layer; shock absorber HCR (with high hardness) prevented the PEFRC bulge from contacting the upper surface of the lower layer. Cross-shaped cracking was detected on the back surface of the lower layer in all of the three specimens, but there was no great difference in them among the three speci-mens.

The fracture behaviors of specimens NC-HCR-15, NC-SCR-15 and NC-EPS-15 were similar to that of specimen NC-AIR-15 in spite of the variety of shock absorbers, except for the spall diameter in specimen NC-HCR-15, which was slightly larger than those in the others. In specimen NC-EPS-15, the EPS shock absorber was completely squashed under the detonation point.

In specimen PE-AIR-5, a PEFRC bulge which formed in the back surface of the upper layer was in contact with the upper surface of the lower layer. This was also ob-served in specimen PE-AIR-15. However, the local fail-ure in the upper layer of specimen PE-AIR-5 was smaller than that in specimen PE-AIR-15, and the cracking on the back surface of the lower layer in the former became larger than that in the latter. In specimen PE-AIR-30, on the other hand, a breach occurred in the upper layer be-cause of the launch of the PEFRC fragments created in the back surface of the upper layer, and very fine radial cracks were observed on the back surface of the lower layer.

In specimen PE-HCR-5, large cross-shaped cracks were observed, and a small bulge and spall occurred on the back surface of the lower layer. Furthermore, the internal cracks in the lower layer propagated more ex-tensively than those in specimen PE-HCR-15.

2.2.2 Evaluating the size of the external damage Table 6 shows the size of the external damage measured. (1) Influence of internally layered polyethylene fiber mesh reinforcement on external damage Figure 4 shows the influence of the internally laid poly-ethylene fiber mesh reinforcement on the external dam-age. In Figs. 4 and 5, the damage depth of the single slab (Yamaguchi et al. 2008a, 2011) is expressed by the crater depth (Cd) and spall depth (Sd).

For normal RC, the damage in the mid-reinforced slab is almost as large as that in the single, 100-mm thick slab,

Fig. 3 Measuring size of external damage.

Crater or spall

1

2 3 4

Du

C

Dl

S

Du

C

Dl

S

Crater

Spall

CraterSpall

Note: C: crater diameter, S: spall diameter, Du: damage depth of upper layer, Dl: damage depth of lower layer.


PE-Mesh NC-Mesh PE-AIR-15 NC-AIR-15 Detonation side

Section

Back side

PE-HCR-15 NC-HCR-15 PE-SCR-15 NC-SCR-15 Detonation Side

Section

Back side

PE-EPS-15 NC-EPS-15 PE-AIR-5 PE-AIR-30 PE-HCR-5 Detonation Side

Section

Back side

Note; each specimen had been supported at both the left and right sides.

Table 5 Fracture behaviors of specimens.


and the total damage depth (the sum of damage depths in both layers for the double-layered slabs) reached 100 mm in both specimens. In PEFRC, on the other hand, the total damage depth in the mid-reinforced slab was slightly smaller than that in the single slab. This may be because the flexural toughness coefficient of the PEFRC used in the former was slightly larger than that in the latter or because a delamination of the bond surface had occurred in the former.

More investigations are needed to develop a stronger means of joining the layers, however, it may be difficult to improve the blast resistance of both the PEFRC and the normal RC slabs using layered polyethylene fiber mesh reinforcement because the propagation of the stress wave into the lower layer cannot be prevented by this method.

(2) Influence of the presence of air space between two layers on the external damage Figure 5 shows the influence of the presence of air space between the two layers on the external damage.

In the PEFRC, the spall damage in the lower layer was remarkably reduced by inserting an air space, because the propagation of the stress wave into the lower layer was prevented by the air cavity. For the normal RC, however, the size of the external damage in the air-sandwiched slab was as large as that in the single, 100-mm thick slab, and the total damage depth reached 100 mm in both specimens.

From these results, it was shown that the effect of an air space inserted between two layers depended on the kind of concrete used: making an air space 15 mm thick in the middle of the double-layered PEFRC slab was effective in reducing spall damage, however the air space had no advantage in the normal RC. The fracture mechanism of the air-sandwiched slab subjected to con-tact detonation will be analytically investigated in the next chapter.

(3) Influence of shock absorber inserted into the air space on the external damage Figure 6 shows the influence of a shock absorber in-serted into the 15-mm thick air space on the external damage. In this figure, experimental data on the dou-ble-layered slab with a 15-mm thick air space are also shown for comparison.

In all of the four PEFRC specimens, the total damage depth was determined by the damage depth of the upper layer, because the local failure in the lower layer was prevented completely. The total damage depth of the specimens with EPS and AIR reached nearly 50 mm, which was the thickness of the upper layer, and the

Table 6 Size of external damage measured.

Specimen T [mm]

C [mm]

S [mm]

Du [mm]

Dl [mm]

PE-Mesh 100 127 54 35 19 NC-Mesh 100 164 378 50 50 PE-AIR-15 100 131 0 49 0 NC-AIR-15 100 180 306 50 50 PE-HCR-15 100 134 0 38 0 NC-HCR-15 100 192 408 50 50 PE-SCR-15 100 138 0 43 0 NC-SCR-15 100 195 329 50 50 PE-EPS-15 100 139 0 50 0 NC-EPS-15 100 186 320 50 50 PE-AIR-5 100 139 0 35 0 PE-AIR-30 100 133 0 50 0 PE-HCR-5 100 141 47 40 19 Note; T: total slab thickness (except for thickness of air space

or shock absorber).

Fig. 4 Influence of internally laid polyethylene fiber mesh reinforcement on external damage.

0102030405060708090100

050

100150200250300350400450500

σB [MPa]

E [GPa]

σt [MPa]

σb [MPa]

bσ [MPa]

* 54.6 22.5 7.65 8.79 8.12 ** 41.6 31.9 3.48 – –

C a

nd S

[mm

]

Du a

nd D

l (C

d and

Sd)

[mm

]

Singleslab*

Mid- reinforcement

Single slab**

Mid- reinforcement

C S Du (Cd) Dl (Sd)

(a) PEFRC (b) Normal RC

Note; material properties of concretes used for the single slabs are as follows (Yamaguchi et al. 2008a, 2011):

The testing methods are the same as shown in Table 3.

Fig. 5 Influence of presence of 15-mm thick air space between two layers on external damage.

0102030405060708090100

050

100150200250300350400450500

C a

nd S

[mm

]

Du a

nd D

l (C

d and

Sd)

[mm

]

Singleslab

Air- sandwich

Single slab

Air- sandwich

Dl=0

(a) PEFRC (b) Normal RC Note; the concretes used for the single slabs were the

same as those in Fig. 4.

C S Du (Cd) Dl (Sd)


damage to the specimen with HCR was the smallest of the four specimens. This may be because the PEFRC bulge which formed on the back surface of the upper layer tends to be more easily buried in the least resistant shock absorber below it.

In the normal RC, the values of spall diameter in the specimens with shock absorbers were larger than that in the specimen with the air space; that tendency was most noticeable in the specimen with HCR. However, the total damage depth reached 100 mm in all of the four speci-mens.

From these results, in both double-layered PEFRC and normal RC slabs, we conclude that the addition of a shock absorber in the air space shows no advantage in reducing spall damage.

(4) Influence of thickness of air space and shock absorber on the external damage Figure 7 shows the influence of the thickness of the air space and the HCR shock absorber on the external dam-age of the double-layered PEFRC slab.

For the air-sandwiched PEFRC slab, the damage depth of the upper layer tended to increase as the air gap be-came thicker, because the launch of the PEFRC frag-ments occurred in the back surface of the upper layer. On the other hand, the cracking on the back surface of the lower layer became smaller with a thicker air gap, as shown in Table 5. Therefore, increasing the thickness of the air space may be effective in improving the blast resistance of the air-sandwiched PEFRC slab, because the upper layer behaves as an effective sacrificial ele-ment.

The damage depth of the upper layer of the dou-ble-layered PEFRC slab with the HCR shock absorber stayed almost constant in spite of the change in the thickness of the HCR shock absorber, because the launch of the PEFRC fragments in the back surface of the upper layer was hindered by the shock absorber HCR below. In the lower layer, a small spall occurred with the 5-mm thick shock absorber, while the 15-mm one prevented the spall. Therefore, the blast resistance of the dou-ble-layered PEFRC slab may be raised by increasing the thickness of the shock absorber. However, the shock absorber has no advantage over the air space in reducing spall damage, as stated above.

3. Numerical simulation

Based on the above test results, it is important to clarify the fracture mechanism of the double-layered slab with an air space. In this chapter, a numerical simulation was conducted to reveal the fracture process of the air-sandwiched normal RC slab to help understanding of the difference between normal RC and PEFRC slabs. For the numerical simulation, a multiple solver type hydro-code, ANSYS AUTODYN, was used (Birnbaum et al. 1987; Katayama et al. 2007).

3.1 Analytical method 3.1.1 Analytical system A two-dimensional axisymmetric model was used in the numerical simulation, as shown in Fig. 8. In problems where the explosives behave as a gas after the detonation, the Eulerian solver that is suitable for modeling the flu-idity of the explosive products should be properly adapted to the explosive parameters. However, in this problem, the element with few bulks (steel bars) and the explosive products may interact after the breaching of the RC slab. Since the thickness of the steel element is smaller than the mesh size of the Eulerian element modeling the explosive products, the Lagran-gian-Eulerian interactive solver cannot give an accurate

Fig. 6 Influence of shock absorber inserted into 15-mm thick air space on external damage.

Fig. 7 Influence of thickness of air space and HCR shock absorber on external damage.

0102030405060708090100

050

100150200250300350400450500

0102030405060708090100

050

100150200250300350400450500

C a

nd S

[mm

]

Du a

nd D

l [m

m]

HCR SCR EPS AIR (a) PEFRC

Dl=0Dl=0

Dl=0 Dl=0

C a

nd S

[mm

]

Du a

nd D

l [m

m]

HCR SCR EPS AIR (b) Normal RC

C S Du (Cd) Dl (Sd)

050

100150200250300350400450500

0102030405060708090100

C a

nd S

[mm

]

Du a

nd D

l [m

m]

5 mm 15 mm 30 mm 5 mm 15 mm (a) AIR (b) HCR

Dl=0

Dl=0 Dl=0 Dl=0

C S Du (Cd) Dl (Sd)


solution in this case. Therefore, in this calculation, the concrete and the explosives were modeled by the La-grangian element, and shell elements were applied to the steel bars and the aluminum plate, in accordance with the previous study of Katayama et al. (2007). The polymer cement mortar of the bonding layer was ignored.

Although the target RC slab was square in the ex-periment, it was assumed to be a circular plate which was inscribed to the actual RC slab. The reinforcement was also modeled by a thin circular plate with an equivalent mass. The bending moment was ignored for the shell element modeling of the reinforcement, i.e., it was as-sumed to be a membrane. The wooden jig which sup-ported the RC slab was assumed to be stiff and was modeled by the boundary condition.

3.1.2 Material models (1) Explosives We applied the Jones-Wilkins-Lee (JWL) equation of state to the explosives (Lee et al. 1968) and used a pro-grammed ‘on-time burning’ model, assuming ideal sta-tionary detonation. The equation of state (EOS) is de-fined as follows:

1 2

1 2

1 exp 1 exp refR Rp A B e

R R⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎛ ⎞

= − − + − − +⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠

ωη ωη ωηρη η

(2)

where p: pressure, η: ρ/ρref, ρ: density, ρref: reference density, e: internal energy, and A, B, R1, R2, and ω are the material parameters of the explosives. The detonation properties and the JWL parameters for many explosives have been compiled by Dobratz et al. (1985). However, since the explosives used in this experiment were not ordinary ones, we calculated their properties and pa-rameters by the revised Kihara-Hikita EOS (Tanaka

2003). The material parameters for the explosives used are shown in Table 7. The constitutive model of the explosive was ignored and assumed to be hydrodynamic. (2) Concrete Koshika et al. (1992) analytically clarified that -6.0 MPa was suitable for the spall strength (negative threshold hydrostatic pressure when spall occurs) of concrete sub-jected to steel projectile impact (impact velocity: 400 m/s). However, in case of the contact detonation (deto-nation velocity: 6278 m/s), the absolute value of spall strength was expected to be larger than -6.0 MPa, be-cause of the strain rate effect on concrete strength. Therefore, in this calculation, the spall strength of the concrete was assumed to be -7.0 MPa. In the previous report of the Japan Nuclear Energy Safety Organization, it was confirmed that the numerical result with the con-crete spall strength of -7.0 MPa showed a good agree-

Fig. 8 Two-dimensional axisymmetric model used in numerical simulation.

300 mm 28.9 mm

45 mm

50 mm 50

mm

50

mm

15 m

m

57.8

mm

Stiff boundary

Aluminum plate (20 × 6)

Reinforcements t = 0.643 mm

Concrete (120 × 20)

Explosives (120 × 46)

270 mm

Note; the numbers in parentheses mean the numerical mesh divisions.

Table 7 Material parameters for explosives.

Equation of state JWL Reference density (ρref) [g/cm3] 1.3189 JWL parameter (A) [GPa] 578.4123 JWL parameter (B) [GPa] 10.1342 JWL parameter (R1) [–] 5.711761 JWL parameter (R2) [–] 1.425701 JWL parameter (ω) [–] 0.279831 Detonation velocity (Vdet) [m/s] 6278 Internal energy per unit volume (E0) [GJ/m3] 5.8409 C-J pressure (PC-J) [GPa] 12.774 Constitutive law (Hydro) Erosion strain (Geometrical strain) [%] 500

Note; ‘Erosion’ is a technique wherein Lagrangian elements are transformed into free mass points not connected to the original element (Katayama 2007).


ment with the experimental result on normal RC slab subjected to contact detonation. The EOS adapted to the concrete was the linear equation in which pressure (p) is proportional to density (ρ):

μKp = , 1/ −≡ refρρμ (3)

where K: bulk modulus, μ: compressibility, ρ: density, and ρref: reference density. K and the shear modulus (G) were calculated using Eqs. (4) and (5) with Young’s modulus (E) and Poisson’s ratio (v):

)21(3 vEK−

= (4)

)1(2 vEG+

= (5)

where v was assumed to be 0.2. As the constitutive law for concrete, the

Drucker-Prager criterion was adopted (Chen 1982). This model assumes that the yield stress (Y) is proportional to the pressure (p), as shown in Fig. 9. In this calculation, it was assumed that Y did not exceed the maximum value (Ymax). The Drucker-Prager equation is expressed by Eq. (6) using the slope (a) and vertical intercept (b) of the straight line:

),min( max baPYY += (6)

The static tensile strength (ft) was calculated using Eq. (7) with a static compressive strength (fc) (JSCE 1996):

3/223.0 ct ff ×= (7)

The strain rate (ε ) was assumed to be in the order of 104 (unit: 1/s), and the dynamic compressive strength (fc

d) and dynamic tensile strength (ftd) proposed by Ya-

maguchi et al. (1989a, 1989b) were introduced into the Drucker-Prager equation as follows:

cd

c ff ])(log02583.0log05076.0021.1[ 2εε ⋅+⋅−=

(8)

td

t ff ])(log04379.0log02987.08267.0[ 2εε ⋅+⋅+=

(9)

where the unit of ε in Eqs. (8) and (9) was 1/μs. The relationship between the cohesion (c) and friction

angle (φ) is defined as follows:

)sin1/(cos2 φφ −= cf dc (10a)

)sin1/(cos2 φφ += cf dt (10b)

The following equations are derived using the rela-tionship of d

td

c ffn /≡ :

2/dtfnc = (11a)

)1/(2cos += nnφ (11b)

)1/(1sin +−= nnφ (11c)

The failure surface in the Drucker-Prager model is defined as the following expression using coefficients α and κ:

021 =−+ κα JI (12)

where I1 and 2J are the first and second invariants of stress, respectively. By adapting a condition that the failure surface of the Drucker-Prager model is inserted into Mohr-Coulomb’s law, the following expressions are derived:

)sin3(3sin2

φφα

−=

(13a)

)sin3(3cos6

φφκ

−=

c

(13b)

From Eqs. (13), the slope (a) and vertical intercept (b) in the Drucker-Prager model are:

α33=a , κ3=b (14)

Equation (14) can be rewritten using n and fcd:

2)1(3

+−

=nna

, d

cfn

b2

3+

= (15)

The slope (a) and vertical intercept (b) were calculated by substituting fc

d, ftd and n in Eq. (15). The material

parameters used for the concrete are shown in Table 8.

(3) Steel In cases where steel is subjected to a strong shock force, an EOS which depends on density and internal energy should be properly adapted. In this calculation, however, the linear EOS was adapted to the steel, because the steel

Yield stress #1

Yield stress

Yield stress #2Ymax

a

b

Pressure #1 Pressure #2 Pressure

Spall strength

Fig. 9 Relationship between pressure and yield stress in Drucker-Prager model.


reinforcements were modeled by shell elements in which the status of both the density and the internal energy was not taken into account. E = 205.9 GPa and v = 0.3 were assumed, and the bulk modulus and shear modulus were calculated by the same method as adapted to concrete.

The Johnson-Cook constitutive model was applied to the steel (Johnson and Cook 1983). In this model, the yield stress (Y) is estimated by the function of equivalent plastic strain (εp), dimensionless equivalent plastic strain rate ( 0

* /εεε p= , 0.10 =ε (1/s)) and homologous tem-perature (T*):

)1)(ln1)(( ** mnp TCBAY −++= εε (16)

where A, B, n, C, m are the material parameters, and T* is defined by:

roommelt

room

TTTTT−−

=* (17)

where Troom is the room temperature, and Tmelt is the melting temperature.

The material parameters used for the steel are shown in Table 9. Among the parameters of the Johnson-Cook model, A was determined by the measurement of 0.2% proof stress, and the other parameters were determined based on the values of 1006 carbon steels standardized by the American Iron and Steel Institute. However, the thermal term is neglected for the shell solvers, because no volume change, consequently no temperature changes of the elements are calculated in the solvers.

As the fracture strain in the calculation, not the nomi-nal value (12.8%) but the true value (12.6%) was adopted. The tensile strength calculated by the Johnson-Cook equation with these parameters was 778.1 MPa, which was close to the measured value of 733 MPa.

(4) Aluminum For aluminum, the Mie-Grüneisen form of the shock Hugoniot EOS (McQueen et al. 1970) and the John-son-Cook constitutive model (Johnson and Cook 1983) were applied. The material parameters were determined by the value for 2024Al (Johnson and Cook 1983), how-ever, the details were left out because it is not a principal object of this calculation. 3.2 Results and discussion Figure 10 shows the comparison of the damage of the air-sandwiched normal RC slab between the experiment and the calculation at 0.5 ms.

The numerical result seems to evaluate the spall di-ameter in the lower layer a little larger than the experi-ment, but the overall results of the damage to the RC slab in the calculation show a fairly good agreement with the experiment. It should be noted that all of the red-colored parts of concrete in Fig. 10 (a) are not necessarily crushed, because the concrete is expected to retain its strength in the direction of no cracking.

The distribution of equivalent plastic strain is also

shown in Fig. 10 (b). Parts with over 1.5% of strain exist within the concrete, however they are distributed within

Table 8 Material parameters for concrete.

Equation of state Liner Reference density (ρref) [g/cm3] 2.4 Bulk modulus (K) [GPa] 17.833 Constitutive law Drucker-PragerShear modulus (G) [GPa] 13.375 Pressure #1 (P1) [MPa] -14.71 Pressure #2 (P2) [MPa] 22.38 Yield stress #1 (Y1) [MPa] 0 Yield stress #2 (Y2) [MPa] 150 Failure criterion (Hydro) Spall strength (Pmin) [MPa] -7.0 Erosion strain (Geometrical strain) [%] 100

Table 9 Material parameters for steel.

Equation of state Liner Reference density (ρref) [g/cm3] 7.9 Bulk modulus (K) [GPa] 171.6 Constitutive law Johnson-CookShear modulus (G) [GPa] 79.21 Basic yield stress (A) [MPa] 650 Hardening constant (B) [MPa] 275 Hardening exponent (n) [–] 0.36 Strain rate constant (C) [–] 0.022 Thermal softening exponent (m) [–] 1.0 Fracture criterion Plastic strainFracture strain, (εp

max) [%] 12.6 Erosion strain (Plastic strain) [%] 12.1

Elastic Plastic Failure (a) Material status at 0.50 ms

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 (%)

(b) Distribution of equivalent plastic strain at 0.50 ms

(c) Experimental result

Fig. 10 Comparison of damage to air-sandwiched normal RC slab between the experiment and the calculation.


a limited area. Therefore, the damage to both layers may be ruled by the spall failure mode rather than the com-pressive failure mode.

Figure 11 shows the temporal changes in the material status (0.02–0.20 ms). In the figure, the concrete frag-ments launched from the back side of the upper layer due to the spall failure act as an impact load on the upper surface of the lower layer, and then cause spall failure accompanied by breaching to the lower layer. Therefore, it was clarified that the damage in the lower layer was not due to the detonative loading directly but to the impact of the concrete fragments from the back surface of the up-per layer.

Table 10 shows the analogical fracture process of the double-layered PEFRC slab with a 15-mm thick air gap (specimen PE-AIR-15), as well as the fracture process of specimen NC-AIR-15 based on the numerical result. In the upper layer of the PEFRC slab, the PEFRC near the back surface is not broken into pieces by the tensile stress wave, because of the bridging effects of polyethylene short fibers. Simultaneously, the PEFRC fragments bulged from the back surface of the upper layer may be decelerated by the polyethylene short fibers bridging at the spall face of the upper layer. Therefore, the fragments, which are thrust from the back surface of the upper layer of the normal RC slab, are prevented from being launched by their contact with the upper surface of the

lower layer in the PEFRC slab. Moreover, in the lower layer of the PEFRC slab, very fine internal cracks par-allel to the back surface are observed, which are expected to form the spall face in the normal RC slab, but the crack

Table 10 Difference in fracture process between air-sandwiched normal RC and PEFRC slabs.

Normal RC (by the numerical result) PEFRC (by analogy with the numerical result) Upper layer The concrete near the back surface of the upper layer is

broken into pieces by the tensile stress wave due to contact detonation, and the fine concrete fragments are lunched from the back surface.

The PEFRC near the back surface of the upper layer is not broken into pieces by the tensile stress wave, be-cause of the bridging effects of polyethylene short fibers (a). Furthermore, the PEFRC fragments bulged from the back surface may be decelerated by the poly-ethylene short fibers bridging at the spall face.

Lower layer The concrete fragments, launched from the back sur-face of the upper layer, act as an impact load on the upper surface of the lower layer. And then, on the back side of the lower layer, spall damage accompanied by breaching is created by the tensile stress wave due to the impact of the upper layer fragments.

The PEFRC fragments of the upper layer act as an impact load on the upper surface of the lower layer. However, no spall occurs on the back surface of the lower layer. This may be because of the deceleration of the upper layer fragments and of the bridging of polyethylene short fibers at the spall cracking face in the lower layer (b). As a result, the spall damage is prevented completely, and the failure mode of the lower layer changes from ‘local failure’ to ‘flexural failure’ (c) (Zhang et al. 2007).

Section Upper layer

Lower layer a. PEFRC fragments

b. Spall cracking

Upper layer

Lower layer

c. Flexural cracking

0.02 ms

0.04 ms

0.06 ms

0.08 ms

0.10 ms

0.15 ms

0.20 ms

Elastic Plastic Failure

Fig. 11 Temporal change in material status.


opening is prevented by the polyethylene short fibers bridging at the spall cracking face, and cross-shaped cracking similar to static flexural cracking is observed on the back surface.

Based on the above discussion, the better blast resis-tance of the air-sandwiched PEFRC slab may be ex-plained qualitatively, considering the interaction between the following two factors: 1) the decline in impact force of the upper layer fragments on the lower layer, by means of the deceleration of the fragments, and 2) the change in failure mode of the lower layer from ‘local failure’ to ‘flexural failure’ (Zhang et al. 2007). Both factors are due to the bridging effects of the polyethylene short fibers.

4. Conclusions

In this study, to propose an idea for rapid construction and better blast resistance of blast-resistant RC structures, the contact detonation tests were conducted on dou-ble-layered RC slabs composed of precast thin plates, 50 mm thick, made of either normal concrete or PEFRC. Furthermore, a numerical simulation was conducted to reveal the fracture process of the double-layered normal RC slab with an air cavity to help understanding of the difference between PEFRC and normal RC slabs. As a result, the following conclusions were reached: (1) It is difficult to improve the blast resistance of dou-

ble-layered PEFRC and normal RC slabs by internal polyethylene fiber mesh reinforcement sheets.

(2) Creating an air cavity in the middle of the dou-ble-layered PEFRC slab is an effective way of re-ducing the spall damage, while the air space has no advantage in the normal RC, under a condition that the thickness of the air space is fixed at 15 mm. Furthermore, the damage in the lower layer of the air-sandwiched PEFRC slab tends to diminish as the thickness of the air gap increases.

(3) In both the double-layered PEFRC and normal RC slabs, shock absorbers (chloroprene rubber, chloro-prene sponge, and expanded poly-styrol) inserted into the air space had no advantage in reducing spall damage.

(4) On the analogy of the numerical result on the air-sandwiched normal RC slab, the better blast re-sistance of the air-sandwiched PEFRC slab may be explained qualitatively, by the high toughness of both layers due to the bridging effects of the poly-ethylene short fibers.

We are assuming the double-layered slabs with an air cavity to be applied to a sandwich wall system, in which the structural frames are inserted between two thin PEFRC plates, composing important structures such as industrial plants and public facilities. However, the con-clusions of this study cannot directly be applied in the practice of building constructions, because the blast resistance of the double-layered slab may be influenced by other factors such as dimensions of slab, amount of explosives, mix proportion of fiber reinforced concrete,

and way of attaching the panels to the frames. Further, more investigations are needed to clarify the fracture mechanism of the double-layered PEFRC slabs subjected to contact detonation.

Acknowledgements This study was supported by the Global COE Program on Pulsed Power Science (Base leader: Professor Hidenori Akiyama) of the Faculty of Engineering, Kumamoto University. The contact detonation tests were carried out in the Shockwave and Condensed Matter Research Center of Kumamoto Univ. The authors greatly appreci-ate the help of Professor Shigeru Itoh, Assistant Profes-sor Kenichi Matsuyama, Assistant Susumu Akimaru, technical officials Sadao Kai and Shigeru Tanaka, part-time technical staff Hironori Maehara, and all the staffs of the Itoh Laboratory and the Building Materials Laboratory of Kumamoto Univ. The authors would also like to thank Toyobo Co., Ltd., Ariake Concrete Co., Ltd., Fuji-Con Chemical Co., Ltd., BASF Pozzolith Co., Ltd. and Itochu Techno-Solutions Co., Ltd. for their coopera-tion in conducting the experiments and the numerical simulation. References Banthia, N., Bindiganavile, V. and Mindess, S., (2004).

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