Improving the resistance of concrete panels to hard projectile impact

Abstract

In this article, the response of nine plain concrete panels to an impact of hard projectiles was examined in an experimental study. The tests were planned with an aim to observe the influence of compressive strength on the performance of concrete under impact loading. Concrete panels with compressive strengths within the range of 26 to 92 MPa subjected to impact by 23 mm hard projectile at velocities within the range of 270 to 348 m/s were studied. Also, using a glass fiber reinforced polymer sheet, as a liner on the rear face of the plain concrete panel, to strengthen the panel was examined. The experimental results indicate that strengthening concrete panel with a rear glass fiber reinforced polymer sheet showed more satisfactory performance under the impact load than increasing compressive strength of concrete. Also, the use of glass fiber reinforced polymer sheets as rear liners in addition to increasing the concrete strength showed superior performance of concrete panels against impact; it is recommended to be used in protective structures.

Keywords

Impact projectile concrete compressive strength glass fiber reinforced polymer sheets

Introduction

In order to prevent perforation and global or even local failure of protective concrete structures (panels, slabs, or walls) resulting from impact loading, impact resistance of concrete with various strengthening methods should be evaluated by performing experiments. There are several techniques introduced as attempts to improve the impact resistance of concrete panels, for example, introducing high and very high strength concrete (e.g. Dancygier et al., 2007; Hanchak et al., 1992), using steel (or other kinds such as polyethylene) fibers in concrete (e.g. Dancygier et al., 2007; Wang et al., 2016), reinforcing the concrete panels with rebar meshes (e.g. Abdel-Kader and Fouda, 2014; Dancygier, 1997; Dancygier and Yankelevsky, 1999; Rajput and Iqbal, 2017), lining with steel plates (e.g. Abdel-Kader and Fouda, 2014; Kojima, 1991; Remennikov and Kong, 2012; Wu et al., 2015a, 2015b) or ballistic fiber reinforced polymer (FRP) sheets on the impacted and/or distal face of the concrete panels (e.g. Abdel-Kader and Fouda, 2017; Barr, 1990), introducing multilayered concrete panels (sometimes having elastic absorbers such as rubber sheets; for example, Gupta and Madhu, 1997; Shirai et al., 1997), or using more than one of these techniques.

In this study, the focus is concentrated on the combination of two techniques: use of high strength concrete and lining with glass fiber reinforced polymer (GFRP) sheet. As will be shown later, the use of high strength concrete technique alone did not give satisfactory performance under the impact load, and the use of GFRP sheets as rear liners in addition to increasing the concrete strength showed superior performance of concrete panels against impact.

Compressive strength of concrete

Concerning high strength concrete, there are several works dealt with the effect of the concrete compressive strength on impact resistance of concrete panels (e.g. Dancygier, 1998; Dancygier et al., 2007; Dancygier and Yankelevsky, 1996; Hanchak et al., 1992; O’Neil et al., 1999; Shirai et al., 1997; Zhang et al., 2005). Hanchak et al. (1992) conducted ballistic perforation experiments on reinforced concrete panels (610 mm × 610 mm × 178 mm) with 48 and 140 MPa concrete compressive strengths, for impact velocities within the range of 300 to 1100 m/s, with 25.4 mm diameter, 0.5 kg mass, and ogive-nosed rods. Their results showed that at impact velocity of 360 m/s, the 48 MPa concrete panel was perforated, whereas the 140 MPa concrete panel was not perforated at impact velocity of 382 m/s (but perforated at impact velocity of 443 m/s with residual velocity of 171 m/s)—a finding that led them to conclude that about threefold increase in compressive strength (from 48 to 140 MPa) resulted in relatively minor improvement of the ballistic perforation performance. Regarding damage, post-test observations of both the (48 and 140 MPa) concrete panels, after impact velocity of 750 m/s, showed that craters on the impacted (front) and distal (rear) faces each had a depth of about one-third the slab thickness while the central one-third region had a nearly circular tunnel. Therefore, it was postulated that penetration resistance in the crater regions is not sensitive to compressive strength.

Shirai et al. (1997) conducted ballistic experiments on reinforced concrete panels (600 mm × 600 mm × 90 mm) to investigate the effect of the concrete strength (normal, 35 MPa; lightweight, 40 MPa; high strength, 57 MPa) on the degree of local damage. The 0.43 kg hard projectile impacted the concrete panels with an average velocity of 170 m/s. From the test results of 35 and 40 MPa concrete panels, scabbing (concrete debris spalled off the rear face of a concrete panel) and/or perforation (a projectile passed completely through a concrete panel) occurred in the two specimens, whereas in the case of the 57 MPa concrete, the panel withstood the projectile and held its damage to the scabbing limit (the radial and circular cracks were appeared but no scabbing occurred on the rear face of a concrete panel; concrete debris did not come off the rear face). This led to the conclusion that concrete strength plays a major role to stop the projectile penetration and scabbing of material.

In an experimental study, Dancygier and Yankelevsky (1996) conducted on the response of normal (~34 MPa) and high strength (~104 MPa) concrete panels (400 mm × 400 mm × 40 mm and 400 mm × 400 mm × 60 mm) to an impact of 0.12 kg conical-nose hard projectile, with impact velocities within the range of 85 to 230 m/s; it was observed that the penetration depth in concrete panel with a high strength was smaller than that in normal concrete panel—a finding that indicates that a higher strength enhances penetration resistance of the concrete panel. Also, it was observed that the scabbing craters of the 104 MPa concrete panels were larger compared to those of the 34 MPa concrete panels. This indicates that high strength panels are characterized by increased brittleness.

Rear face damage assessment of normal (34–39 MPa) and high strength (~112 MPa) concrete panels (400 mm × 400 mm × 50 mm) due to (0.125 kg mass, 25 mm diameter) hard projectile impact at velocities within the range of 100 to 250 m/s was studied experimentally by Dancygier (1998). The scabbing craters at the rear face in the two cases (normal and high strength panels) showed that volumes were similar at similar velocity ratios, with the high strength concrete panels showing a somewhat higher scabbing crater size.

The experimental study (O’Neil et al., 1999) conducted on the impact resistance of normal (35 MPa) and high strength (104 MPa) concrete cylindrical targets (762 mm diameter and 914 mm length) using (0.906 kg mass, 26.9 mm diameter) projectiles at impact velocities within the range of 229 to 754 m/s showed that the penetration depth induced in high strength concrete was ~30% less than that in normal strength concrete. However, damage at the front and rear faces (at impact velocity of about 800 m/s) showed that the amount of visible damage to the high strength concrete panel is about the same as that for the normal strength concrete.

In the experimental study, Zhang et al. (2005) conducted on the impact resistance of (45–235 MPa) concrete panels (300 mm × 170 mm × 150 mm) subjected to impact by (0.015 kg mass, 12.6 mm diameter) ogive-nosed projectile at velocities within the range of 620–700 m/s; an overall reduction in the penetration depth and crater diameter with an increase in the compressive strength of the concrete was observed. However, the trend is not linear. Further increase in the compressive strength (beyond 150 MPa) did not result in further reduction in the penetration depth and crater diameter. Based on their findings and cost consideration, they concluded that high strength concrete with a compressive strength of ~100 MPa appears to be most efficient in concrete structures design against projectile impact.

Lining of concrete panels by ballistic FRP sheets

Lining (reinforcement or strengthening) of concrete panels by external bonding of FRP materials (laminates, sheets, or plates) has been increasingly used to replace that of steel plates due to their superior properties (Pham and Hao, 2016). The FRP materials have high strength-to-weight ratios, superior corrosion resistance, inherent blending with the structures, easiness of installation, high durability, very low maintenance costs, and faster installation time compared to conventional materials (Buchan and Chen, 2007; Chen and Teng, 2001; Kachlakev et al., 2000; Kim et al., 2009; Pham and Hao, 2016; Razaqpur et al., 2007; Saiidi et al., 2006; Tang and Saadatmanesh, 2005; Yoo et al., 2012).

There are many types of FRP materials available for strengthening concrete structures; however, none of them outperforms the other in all aspects (Pham and Hao, 2016; Tang and Saadatmanesh, 2005). A suitable selection of the FRP material is based on the optimal performance and cost. Generally, GFRP is more economical than carbon fiber reinforced polymer (CFRP) (Buchan and Chen, 2007).

In many studies, the FRP material have been used to improve the resistance of structures against blast loading; however, a limited number of studies concentrated on impact resistance (Abdel-Kader and Fouda, 2017; Pham and Hao, 2016). In an experimental study, Abdel-Kader and Fouda (2017) conducted on normal strength (26 MPa) concrete panels (500 mm × 500 mm × 100 mm) impacted by 23 mm hard projectiles at impact velocities within the range of 270 to 386 m/s, and similar panels strengthened with GFRP sheets at rear faces, the strengthening panels showed superior performance under the impact of hard projectiles. Also, the experimental results (Abdel-Kader and Fouda, 2014, 2017) showed that putting GFRP sheet (or steel plate) only in the front of concrete panel prevented spalling crater, but did not significantly increase its ballistic limit as putting GFRP sheet (or steel plate) in the rear.

The magnitude of damage, resulting from impact of concrete panel by a hard projectile, depends on many factors; some of these variables are related to projectile, such as impact velocity, mass, diameter, and nose shape. The common projectile nose shapes are flat, blunt, spherical, ogive, and conical shapes. A common parameter used to describe ogival nose shapes is the caliber–radius–head (CRH) ratio, which is defined as the ratio of the radius of nose curvature to the projectile diameter. A flat or blunt nose shape is equivalent to a zero CRH. Sharper nose results a higher CRH. A conical nose is equivalent to an infinity CRH; therefore, projectile of conical nose is described in terms of its apex angle. Other variables are related to concrete target, such as target thickness, concrete strength, and reinforcement (Kennedy, 1976). Generally, when projectile strikes concrete panel with certain velocity, one or more of the common damage patterns of impact results may occur (Abdel-Kader and Fouda, 2017; Corbett et al., 1996; Hughes, 1984; Kennedy, 1976; Li et al., 2005); such as penetration, spalling of concrete from the front face, scabbing of concrete from the rear face, perforation, shear failure, or flexural failure, as well as more widespread crack propagation.

With regard to FRP sheets, debonding from concrete substrate is commonly the primary mode of failure for structures, strengthened with FRP, subjected to blast loading (Buchan and Chen, 2007). Other failure modes of panels strengthened with FRP sheets can be classified as FRP rupture, crushing of compressive concrete, concrete cover separation, panel end interfacial debonding, intermediate flexural crack-induced interfacial debonding, or intermediate flexural shear crack-induced interfacial debonding (Teng et al., 2003). Also, almost all failure modes occur in a brittle manner (Min et al., 2011).

In this article, the response of 500 mm × 500 mm × 100 mm plain concrete panels to an impact of 0.175 kg hard projectiles was examined in an experimental study. The tests were planned with an aim to observe the influence of compressive strength of concrete on the performance of concrete under impact loading. Concrete with compressive strengths within the range of 26 to 92 MPa subjected to impact by 0.175 kg, 23 mm hard projectile at velocities within the range of 270 to 348 m/s was studied. Also, using a GFRP sheet, as a liner on the rear face of the plain concrete panel, to strengthen the panel was also examined.

Experiments

In order to evaluate the impact resistance of plain concrete panels of different compressive strengths, comparative impact tests were conducted using four concrete mixtures.

To avoid the effect of specimen’s boundary condition on impact results, the minimum dimension of concrete panels should be greater than 20 times the projectile diameter; furthermore, all the specimens should have the same boundary conditions in order to assure a good comparison between the results (Dancygier, 1998). Therefore, the tested panels were with dimensions of 500 mm × 500 mm × 100 mm. The tested specimen was clamped around the periphery, such that a square of dimensions 400 mm × 400 mm was exposed. The specimens were subjected to an impact of similar hard-steel projectiles, accelerated to varying velocities. The measurements included impact velocity, penetration depth, and crater sizes.

Because of the unsatisfactory results obtained from some tests, as will be shown in the “Experimental results and discussion” section, the subsequent tests were conducted on the remaining concrete panels after strengthening by GFRP sheets at their rear faces. Therefore, the tested specimens were of two types as follows:

Plain concrete specimens: Plain concrete panels without GFRP sheets, having different compressive strengths of concrete within the range of 26 to 92 MPa. The specimens denoted -N at the end; for example, C50-1-N.

Specimens reinforced with rear GFRP sheets: Similar plain concrete panels as type one but having a GFRP sheet lining at their rear faces. The specimens denoted -Y at the end; for example, C50-2-Y.

Setup

The impact tests were conducted in the laboratory setup as described in Figure 1. The projectiles were launched from a 23-mm powder gun that can launch projectiles with velocities within the range of 100 to 970 m/s. The gun was mounted on a rigid mount and the test specimen was mounted on steel frame at a distance of 50 m in front of the gun. The projectile impact velocity was measured with electro-optical velocity measurement device.

Figure 1.

The experimental setup.

Materials

The blunt-nosed hard projectile used in the study was 0.175 kg in mass, 23 mm in diameter, and 64 mm long, as shown in Figure 1. It was made of hard-steel alloy of yield strength of 1726 MPa.

In order to fabricate the concrete panels, four concrete mixtures (designated C25, C50, C75, and C100) were formulated and their mix proportions are given in Table 1. The cement used was type I ordinary Portland cement (OPC) conforming to ASTM C150-89, and the coarse aggregate was crushed dolomite with a maximum nominal size of 10 mm. Concrete mixtures C75 and C100 contained fly ash (superposed) of 65 and 70 kg/m³, respectively. Water to cementitious material (cement and fly ash) ratios, w/cm, were 0.57, 0.34, 0.30 and 0.26 for concrete mixtures C25, C50, C75, and C100, respectively. The concrete was cast in the same way in all specimen types in horizontal forms.

Table 1.

Mix proportions of concrete.

Specimen designation	Cement (OPC) (kg/m³)	Fly ash (superposed) (kg/m³)	Coarse aggregate (crushed dolomite) (kg/m³)	Fine aggregate (sand) (kg/m³)	Water (l/m³)	w/cm^a	Admixture (l/m³)
C25	350	–	1100	760	200	0.57	–
C50	450	–	1100	680	155	0.34	6^b
C75	400	65	1150	640	138	0.30	8^c
C100	420	70	1160	620	127	0.26	12^c

OPC: ordinary Portland cement.

Water to cementitious material (cement and fly ash) ratio.

Rheobuild 850 (superplasticizer produced by MBT).

Glenium C315 (superplasticizer produced by MBT).

The mechanical properties of the concrete for the panels are shown in Table 2. Three specimens were used in the testing of each concrete mixture, and the average of the results obtained was calculated. The average compressive strengths of C25, C50, C75, and C100, which were based on the test results of 150 mm cube strength at 28 days (curing 20 ± 5°C, relative humidity [R.H.] 95%), were 26, 57, 77, and 92 MPa, respectively.

Table 2.

Mechanical proportions of concrete.

Specimen designation	Unit weight28 days (kg/m³)	Compressive strength^a 7 days (MPa)	Average7 days (MPa)	Compressive strength^a 28 days (MPa)	Average28 days f_cu (MPa)	Flexural strength^a 28 days (MPa)	Average28 days (MPa)	Slump (mm)
C25	2415 2402 2405	21.1 19.6 20.3	20	24.9 25.9 27.2	26	4.3 4.8 4.8	4.6	85
C50	2470 2419 2450	43.0 40.6 47.9	44	58.6 54.0 59.6	57	6.7 6.1 6.3	6.4	150
C75	2430 2436 2455	57.6 52.9 55.6	55	75.4 76.9 78.5	77	8.6 8.1 8.0	8.2	125
C100	2438 2451 2442	64.1 65.7 69.0	66	91.7 90.6 94.0	92	8.8 9.1 9.6	9.2	175

Compressive and flexural strengths were the test results of 150 mm cubic and 100 mm x 100 mm x 500 mm beam specimens (curing 20.5°C, R.H. 95%).

In the present experimental study, the lining of concrete panels consisted of GFRP woven roving (twisted in two directions, that is, bidirectional fabric) sheets which are designed to resist the blast loading. The GFRP sheets were supplied in a roll form. According to the manufacturer, the behavior of the GFRP is linear elastic up to failure and the properties of the GFRP were specified by the manufacturer as shown in Table 3. The material used for the bonding of GFRP sheets to the concrete panels was an epoxy resin adhesive with properties, according to the manufacturer, as shown in Table 3. The epoxy resin was applied with a total thickness equal to ~1 mm. The GFRP sheets were adhered 28 days after casting of concrete panels. When the GFRP sheets are used in conjunction with the epoxy laminating resin, the system can provide a dry composite strengthening system.

Table 3.

Properties of the GFRP fibers and the epoxy resin.

GFRP fibers				Epoxy resin
Tensile strength (MPa)	Elastic modulus (GPa)	Ultimate strain (%)	Thickness (mm)	Tensile strength (MPa)	Elastic modulus (GPa)	Ultimate strain (%)	Density (kg/m³)
3000	76	3.0	0.35	90	3.0	8.0	1200

GFRP: glass fiber reinforced polymer.

Experimental results and discussion

The response of concrete panels was indicated through the damage that happened at both of panel faces. There were no measurements of residual velocity; the focus was on the state of perforation according to three levels of response. In the first level, the projectile rebounded or stuck in the specimen (no perforation; NP). The second level refers to the tests in which the projectile perforated the specimen and was found behind it (perforation; P). The third level refers to the tests in which the projectile made severe damage at rear face or full hole through the specimen and was found quite near to the front or back of the specimen (i.e. the projectile has almost zero residual velocity), and it was considered as the perforation limit (PL). Another criterion of the response which was examined was the formation of radial cracks that developed at front face, rear face, and/or through the full depth of the panel.

The magnitude of the impact damage induced in the concrete specimens was evaluated from the mean crater diameter, crater depth, and degree of crack propagation in the specimen. Crater depth was determined by measuring the distance from the impact surface to the deepest point in the crater. The mean spalling (and scabbing, if any) crater diameter was determined by taking the average of measurements in four directions, as shown in Figure 2.

Figure 2.

Evaluation of the mean diameter of the crater area.

Figures 3 to 11 and Tables 4 and 5 show the experimental results (impact velocity, failure state and damage modes) of concrete specimens without (C50-1-N, C75-2-N, C75-3-N and C100-1-N) and with rear GFRP sheets (C25-3-Y, C50-2-Y, C50-3-Y, C75-1-Y, C100-2-Y, C100-3-Y).

Figure 3.

Experimental results of specimens with different concrete strengths.

Figure 4.

Damage of specimen C75-3-N (77 MPa) after impact velocity of 298 m/s.

Figure 5.

Typical front and rear damage of normal and high strength concrete far from PL.

Figure 6.

Experimental results of specimens with rear GFRP sheets.

Figure 7.

Typical front face damage of high strength concrete specimens after projectile impact: (a) without and (b) with a rear GFRP sheet.

Figure 8.

Typical damage of normal and high strength concrete specimens with GFRP sheet.

Figure 9.

Experimental results.

Figure 10.

Predictions of perforation thickness of plain concrete specimen C25.

Figure 11.

Predictions of perforation thickness of plain concrete specimens C25, C50, and C100.

Table 4.

Experimental results of specimens with different concrete strengths.

No.	Specimen	GFRP sheet at the rear	Impact velocity (m/s)	Perforation (P) or not (NP)	Spalling crater		Scabbing crater
No.	Specimen	GFRP sheet at the rear	Impact velocity (m/s)	Perforation (P) or not (NP)	Mean diameter (cm)	Depth (cm)	Mean diameter (cm)	Depth (cm)
Abdel-Kader and Fouda (2014, 2017)	C25-1-N	No	270	PL	12.2	3.5	29.5	6.5
Abdel-Kader and Fouda (2014)	C25-2-N	No	299	P	12	4	25	6
1	C50-1-N	No	337	P	14	3	30	6
2	C75-2-N	No	317	P	12	3	40	7
3	C75-3-N	No	298 (~10% increase)	NP (PL)	11	4	–	–
4	C100-1-N	No	303	P	15	2.5	40	7.5

GFRP: glass fiber reinforced polymer; PL: perforation limit.

Table 5.

Experimental results of specimens with rear GFRP sheets.

No.	Specimen	GFRP sheet at the rear	Impact velocity (m/s)	Perforation (P) or not (NP)	Spalling crater		Scabbing crater
No.	Specimen	GFRP sheet at the rear	Impact velocity (m/s)	Perforation (P) or not (NP)	Mean diameter (cm)	Depth (cm)	Mean diameter (cm)	Depth (cm)
Abdel-Kader and Fouda (2017)	C25-3-Y	Yes	332 (~23% increase)	NP stuck	14	7	–	–
5	C50-2-Y	Yes	338	NP rebound	12	4	–	–
6	C50-3-Y	Yes	348 (~29% increase)	NP stuck	11	4	–	–
7	C75-1-Y	Yes	330	NP rebound	10.5	3.5	–	–
8	C100-2-Y	Yes	334	NP rebound	11	3.5	–	–
9	C100-3-Y	Yes	330	NP rebound	10	3	–	–

GFRP: glass fiber reinforced polymer.

In the present tests, the projectile impact velocities were within the range of 270–348 m/s. This range, unfortunately, was not enough to determine the perforation limit of specimens with rear GFRP sheets.

Effect of compressive strength

A number of nine high strength concrete panels were prepared for testing under impact to study the effect of compressive strength. These panels were divided into three groups with nominal compressive strengths of 57, 77, and 92 MPa, and denoted C50, C75, and C100, respectively. Table 4 and Figure 3 show the experimental results of four specimens (C50-1-N, C75-2-N, C75-3-N, and C100-1-N) in addition to the experimental results of two normal strength (26 MPa) concrete specimens (C25-1-N, C25-2-N). It should be mentioned that the experimental results of these two specimens have been published before (Abdel-Kader and Fouda, 2014, 2017). The test results of specimen C25-1-N showed a rebound of the projectile, with very small velocity, at an impact velocity of 270 m/s despite the creation of complete hole through the specimen; this impact velocity was considered as the perforation limit (PL) of this 100 mm thick concrete specimen. At impact velocity of 299 m/s, the projectile perforated the specimen C25-2-N with less damage (less energy dissipation); crater sizes were decreased with increase of the impact velocities far from the perforation limit.

At the beginning of the experiments, a projectile was shouted on the specimen C50-1-N with an impact velocity of 337 m/s. The projectile perforated the specimen and divided it into major parts apart with wide cracks. The second projectile was shouted on the specimen C75-2-N with a smaller impact velocity of 317 m/s. Once more, as in the case of the specimen C50-1-N, the projectile perforated the specimen and divided it into major parts apart with wide cracks. The third shout was on the specimen C75-3-N with further reduction in impact velocity (298 m/s). In this case, the projectile rebounded and could not perforate the specimen. However, like the above two specimens (C50-1-N and C75-2-N), the specimen C75-3-N was divided into five major parts apart as shown in Figure 4. The fourth projectile was shouted on the specimen C100-1-N with an impact velocity of 303 m/s. Again, the projectile perforated the specimen and divided it into major parts apart with wide cracks.

From test results of specimens C75-2-N and C75-3-N (see Table 4), the impact velocity of 298 m/s was considered as the perforation limit (PL) of specimen (C75) with concrete strength of 77 MPa. It should be mentioned here that the perforation limit was taken as the highest velocity not giving perforation, and not by taking average of the highest velocity not giving perforation and the lowest velocity giving complete perforation of the target. Also, the test results present in Table 4 show that the specimen (C100) with higher concrete strength of 92 MPa has no more increase in the ballistic resistance than that of specimen C75 (77 MPa); this is because the projectile perforated the specimen C100-1 at an impact velocity of 303 m/s, which is quite near to the perforation limit of specimen C75 (298 m/s) (see Figure 3). From Table 4, it appears that in regard to impact velocities, the closer (303 m/s) to the perforation limit (298 m/s) of the specimen, the more damage occurrence in the specimen.

From the test results shown in Table 4, it is evident that the ballistic resistance of concrete specimens (C75 and C100) with high strengths (77 and 92 MPa) is about 10% higher than the ballistic resistance of similar specimen (C25) but with normal strength (26 MPa). This means that there was a minor improvement of the ballistic perforation performance when increasing the compressive strength more than threefold. Therefore, it was concluded that there was no need to continue shouting on the rest of specimens.

With regard to crater sizes, it was observed that scabbing (at the rear face) craters of the high strength concrete panels were larger and more severe compared to the craters of the normal strength concrete panels; this is obviously because of the relatively high brittleness. However, the high strength concrete panels had spalling (at front face) craters that were equal in size or to some extent larger than those of the normal strength concrete panels. It was noticed that, at the front face for all specimens, the spalling diameter were within the range of 11 to 15 cm (see Table 4 and Figure 3). This means that the spalling crater is not influenced significantly by the impact velocity or the compressive strength of concrete (the volume of spalling remained almost constant in the considered range of velocity and concrete strength). Typical failure modes of normal and high strength concrete panels are shown in Figure 5; high strength concrete panel experienced the brittle cracking, whereas normal strength concrete failed in a little bit ductile manner.

With regard to radial cracking, for all specimens with high strength, wide cracks were observed, and these cracks extended through the depth of the specimen to the rear face and the specimens split into major parts. These findings indicate that high strength concrete specimens are characterized by increased brittleness.

Effect of lining by rear GFRP sheets

It was shown in the above section that increasing the compressive strength of concrete more than threefold has small gain (~10%) in the ballistic resistance of the panel against impact. Therefore, it was decided to improve the ballistic resistance of the remaining five specimens (C50-2-Y, C50-3-Y, C75-1-Y, C100-2-Y, and C100-3-Y) of high strength concrete by lining with rear GFRP sheets. The test results (impact velocity, failure state, and damage modes) of these five specimens, in addition to the test results of a normal strength (26 MPa) concrete specimen (C25-3-Y), are presented in Table 5 and Figure 6. It should be mentioned that the experimental results of specimen C25-3-Y have been published before (Abdel-Kader and Fouda, 2017). The experimental results of specimen C25-3-Y showed that, at an impact velocity of 332 m/s, the projectile was blocked inside the specimen at the rear face and did not perforate the specimen. Also, there was an obvious bulging of the GFRP sheet of mean outer diameter about 40 cm (see Abdel-Kader and Fouda, 2017).

As shown in Table 5 and Figure 6, optimistic test results were obtained. In all the specimens, the projectile could not perforate, the specimens were able to withstand the projectile with impact velocities up to 348 m/s, and the projectile either rebounded as in the case of the four specimens C50-2-Y, C75-1-Y, C100-2-Y, and C100-3-Y, or stuck as in the case of specimen C50-3-Y.

The influence of the rear GFRP sheet is clearly visible; an increase of ~17% more than the perforation limit (298 m/s) of high strength concrete specimen without lining was recorded, which is also considered ~29% increase more than the perforation limit (270 m/s) of normal strength concrete specimen without GFRP sheet C25-1-N. It is worth mentioning that the experiment showed that the high strength concrete specimens with GFRP sheets could withstand projectiles at higher impact velocity, more than the present velocity of 348 m/s. However, as mentioned above, in the present tests, the projectile impact velocities were within the range of 270 to 348 m/s and this range was not enough to determine the perforation limit of specimens with rear GFRP sheets.

No major damage was observed on the concrete specimens or the GFRP sheet. With regard to radial cracking, no wide cracks were observed at the front face of all high strength concrete specimens; only limited hairline radial cracks (or none) were observed (see Figure 6). At the rear face of all high strength concrete specimens, there was no debonding of the rear GFRP sheet outside the scabbing zones. However, due to the reflection of pressure waves, a scabbing scatters occurred in some specimens, which was blocked by the rear GFRP sheet and accordingly a little bugling of the rear GFRP sheet occurred.

From Table 5 and Figure 6, it can be seen that, at the front face of all high strength concrete specimens, the spalling diameters were within the range of 10 to 12 cm and the penetration depths were within the range of 3 to 4 cm, that is, small difference in the results. The spalling crater size appeared unaffected by the concrete strength within the present range of 57 to 92 MPa and the narrow range of impact velocity (330–348 m/s). However, it is obvious that the penetration depth and crater diameter in high strength concrete specimens are smaller than in those with normal strength concrete.

A comparison between the failure modes in high strength concrete specimens without and with rear GFRP sheets confirms the benefit of the existence of GFRP sheets, which act as barriers to resist the reflected tension waves and to prevent crack propagation not only at the rear face but also through the specimens up to the front face. Typical front face damage of two high strength concrete panels, one without and the other with a rear GFRP sheet, is shown in Figure 7. The rear GFRP sheet helps (besides concrete tensile strength) in resisting the transverse tensile stresses that cause radial cracks. It appears that the radial cracks that propagate from the impact center start first near the rear face of specimen and, therefore, the existence of the GFRP sheet at rear (not at front) face of specimen prevents the propagation of these radial cracks. It should be mentioned here that lining a concrete panel with a steel plate or a GFRP sheet at the front face only did not prevent the propagation of these radial cracks (see Abdel-Kader and Fouda, 2014, 2017). It is evident that the addition of a GFRP sheet to the rear face of a concrete panel suffered a lower level of damage and can minimize or completely prevent scabbing damage. Furthermore, its use at the rear face of concrete panel, where reflected tension waves are expected to develop and generate scabbing, intends to improve the panel response against projectile impact.

Typical failure modes of normal and high strength concrete panels with rear GFRP sheets are shown in Figure 8. At impact velocity of 332 m/s, in the case of normal strength concrete, there was an obvious bulging of the GFRP sheet of mean outer diameter about 40 cm due to the blocking of concrete scabbing scatters, whereas less damage was observed in the case of high strength concrete at almost similar impact velocity (334 m/s); no visible cracks were observed at the front face and no bulging of the rear GFRP sheet. At the front face, the spalling crater diameters were 14 and 11 cm in normal and high strength cases, respectively.

From above it can be seen that the high strength concrete panels with rear GFRP sheets performed better as protective barriers compared with the two other cases: normal strength concrete panels with GFRP sheets and high strength concrete panels without GFRP sheets.

Finally, the experimental results can be summarized for all specimens, as shown in Figure 9. The impact velocities against the existence of GFRP sheets (-Y means specimen with a rear GFRP sheet, and -N means without) are shown; the cases where the specimen stopped the projectile (no perforation; NP) are drawn as red bars, the yellow bars are drawn for perforation limit (PL), and the green bars are drawn for perforation (P) cases.

As shown in Figure 9, it is evident that there is a considerable improvement of the specimen performance against perforation due to the existence of GFRP sheets at the rear face; as mentioned before, there was an increase of about 29% in the perforation limit, from 270 m/s for normal strength concrete specimen without GFRP sheet to 348 m/s for high strength concrete specimen with rear GFRP sheet.

Last note is that the impact resistance of high strength concrete panels is significantly dependent upon the existence of enough reinforcement at the rear face, such as GFRP sheet. High strength concrete panels perform better than panels of normal strength concrete when there is enough reinforcement at the rear face.

Assessment of test results with the commonly used formulae

Many of the available protective design guidelines recommend the use of empirical approaches for the assessment of penetration, scabbing, and perforation. If the objective of engineering design of perforation-resistant barriers is the estimation of perforation and scabbing thicknesses rather than predicting the detailed geometry of failure, a number of empirical formulae have been developed to facilitate this objective (Kennedy, 1976; Li et al., 2005; Wen and Xian, 2015; Yankelevsky, 2017). Among these empirical formulae are the following (the notation used for repeatedly mentioned symbols in the formulae is given in Table 6).

Table 6.

Parameters used for the formulae.

Parameter	Symbol	Value and units
Projectile diameter	d	0.023 m
Projectile mass	M	0.175 kg
Projectile cross-sectional area	A	4.155 × 10⁻⁴ m²
Projectile impact velocity	V_o	270 and 300 m/s
Projectile nose shape factor (N = 0.72 for flat-nosed bodies, 0.84 for blunt-nosed bodies, 1.00 for average bullet nose “spherical end,” and 1.14 for very sharp nose); N_h = 1.12 for blunt nose in Hughes	N, N, N_h*	1.00, 1.12
Caliber density of the projectile	D = M/d³	14,383 kg/m³
Target thickness	H_o, h_o	100 mm
Target thickness to projectile diameter ratio	χ = H_o/d	4.35
Penetration depth	x	m
Perforation thickness	e	m
Scabbing thickness	h_s	m
Concrete cube compressive strength	f_cu	26, 57, and 92 MPa
Concrete cylinder compressive strength	f_c = 0.8 f_cu	20.8, 45.6, and 73.6 MPa
Concrete density	ρ_c	2400 kg/m³
Coefficient which is a function of the concrete strength	k	3.39 × 10⁻⁴
Aggregate characteristic size	a	10 mm
Concrete penetrability factor	K	180/(f_c)^0.5
Concrete nature coefficient (K_p = 0.00426 for normal reinforced concrete)	K_p	0.00426

The modified Petry formula

The modified Petry formula (Amirikian, 1950; Chen et al., 2008) was one of the most common formulae used in the United States to predict the penetration depth x in an infinite concrete target. The modified Petry II formula in SI units is given by

\frac{x}{d} = k \frac{M}{d^{3}} \log_{10} (1 + \frac{V_{o}^{2}}{19, 974}) (SI units)

(1)

It is suggested that k = 0.0795 K_P, where K_P is the concrete penetrability which is a function of the concrete strength and the degree of reinforcement or is a function of the concrete strength only (Amirikian, 1950; Kennedy, 1976) and be taken as 6.36 × 10⁻⁴ for massive plain concrete, 3.39 × 10⁻⁴ for normal reinforced concrete, and 2.26 × 10⁻⁴ for specially reinforced concrete in which the front and rear face steel are laced together with special ties. No value was given for high strength concrete.

Based on the penetration depth calculated from the above formula, Amirikian (1950) suggested that the perforation thickness e could be obtained from

\frac{e}{d} = 2 \frac{x}{d}

(2)

and scabbing thickness h_s could be obtained from

\frac{h_{s}}{d} = 2.2 \frac{x}{d}

(3)

The modified Ballistic Research Laboratory formula

The Ballistic Research Laboratory (BRL) formula (Bangash, 1989; Gwaltney, 1968) was developed in 1968 to calculate the penetration depth x in concrete struck by a rigid projectile. The modified BRL formula in SI units is given by

\frac{x}{d} = \frac{1.33 \times 10^{- 3}}{\sqrt{f_{c}}} (\frac{M}{d^{3}}) d^{0.2} V_{o}^{1.33} (SI units)

(4)

Based on the above penetration depth, the perforation limit e is given by Chelapati et al. (1972) as

\frac{e}{d} = 1.3 \frac{x}{d}

(5)

and the modified BRL formula for scabbing thickness h_s is (Linderman et al., 1974)

\frac{h_{s}}{d} = 2 \frac{x}{d}

(6)

The US Army Corps of Engineers formula

Depending on statistical fitting of experimental data, the US Army Corps of Engineers (ACE, 1946; Chelapati et al., 1972) developed the following formulae in 1946 to determine the penetration depth x

(\frac{x}{d}) = \frac{3.5 \times 10^{- 4}}{\sqrt{f_{c}}} (\frac{M}{d^{3}}) d^{0.215} V_{o}^{1.5} + 0.5 (SI units)

(7)

Based on the penetration depth given above, the formulae for perforation thickness e and scabbing thickness h_s are given by

\frac{e}{d} = 1.32 + 1.24 \frac{x}{d} for 1.35 < \frac{x}{d} < 13.5 or 3 < \frac{e}{d} < 18

(8)

\frac{h_{s}}{d} = 2.12 + 1.36 \frac{x}{d} for 0.65 < \frac{x}{d} \leq 11.75 or 3 < \frac{h_{s}}{d} < 18

(9)

The above perforation and scabbing formulae are based on regression analyses of data from ballistic tests on 37, 75, 76.2, and 155 mm steel cylindrical missiles. Additional data for 0.5 caliber bullets were obtained in 1944, and the above formulae were modified to

\frac{e}{d} = 1.23 + 1.07 \frac{x}{d}

(10)

\frac{h_{s}}{d} = 2.28 + 1.13 \frac{x}{d}

(11)

for the same range of validation parameters. However, equations (10) and (11) differ only slightly from equations (8) and (9). Because large projectile diameters were used to formulate equations (8) and (9), they are more appropriate for missile impacts relevant to nuclear facilities.

The modified formula of the National Defense Research Committee

This formula (Kennedy, 1966; National Defense Research Committee (NDRC), 1946) was put forward in 1946 by the US NDRC based on the ACE formulae. The NDRC study was stopped without completely defining the factor K (which is a concrete penetrability factor, similar to K_P introduced in the modified Petry formula). Kennedy (1966) defined the factor K in terms of f_c $(K = 180 / \sqrt{f_{c}})$ by fitting this relationship to the experimental data available for the larger missile diameters.

The modified NDRC formula in SI units is given by

G = 3.8 \times 10^{- 5} \frac{N^{*} M}{d \sqrt{f_{c}}} {(\frac{V_{o}}{d})}^{1.8} (SI units)

(12)

where

G = {(\frac{x}{2 d})}^{2} for \frac{x}{d} \leq 2 \to \frac{x}{d} = 2 G^{0.5} for G \geq 1

(13a)

G = \frac{x}{d} - 1 for \frac{x}{d} > 2 \to \frac{x}{d} = G + 1 for G < 1

(13b)

Perforation e and scabbing limits h_s can be predicted by extending the ACE formulae to thin targets, that is

\frac{e}{d} = 1.32 + 1.24 \frac{x}{d} for 1.35 < \frac{x}{d} < 13.5 or 3 < \frac{e}{d} < 18

(14)

\frac{h_{s}}{d} = 2.12 + 1.36 \frac{x}{d} for 0.65 < \frac{x}{d} \leq 11.75 or 3 < \frac{h_{s}}{d} < 18

(15)

Kar formula

Kar (1978; Bangash, 1989) revised the NDRC in order to account for the type of missile material in terms of Young’s modulus

G = 3.8 \times 10^{- 5} {(\frac{E}{E_{s}})}^{1.8} \frac{N^{*} M}{d \sqrt{f_{c}}} {(\frac{V_{o}}{d})}^{1.8} (SI units)

(16)

where

\frac{x}{d} = 2 G^{0.5} for G \geq 1

(17a)

and

\frac{x}{d} = G + 1 for G < 1

(17b)

where E and E_s are the Young’s moduli of the projectile and steel, respectively.

The perforation and scabbing limits account for both the size of aggregates a and the Young’s modulus of the projectile. The perforation limit is given by

\frac{e - a}{d} = 1.32 + 1.24 \frac{x}{d} for 1.35 < \frac{x}{d} < 13.5

(18)

The scabbing limit is given by

\frac{h_{s} - a}{d} b = 2.12 + 1.36 \frac{x}{d} for 0.65 < \frac{x}{d} \leq 11.75

(19)

where a is half of the aggregate size in concrete and b = (E_s/E)^0.2. If the material of the projectile is steel, the penetration depth prediction formula is identical to the modified NDRC formula.

Chang formula

Considering a flat ended steel cylinder impacting a reinforced concrete panel, Chang (1981) suggested a perforation limit e

\frac{e}{d} = {(\frac{61}{V_{o}})}^{0.25} {(\frac{M V_{o}^{2}}{d^{3} f_{c}})}^{0.5} (SI units)

(20)

and scabbing limits h_s

\frac{h_{s}}{d} = 1.84 {(\frac{61}{V_{o}})}^{0.13} {(\frac{M V_{o}^{2}}{d^{3} f_{c}})}^{0.4} (SI units)

(21)

These formulae were proposed based on a range of the test data in the limits 16.0 ⩽ V_o ⩽ 311.8 m/s, 0.11 ⩽ M ⩽ 342.9 kg, 50.8 ⩽ d ⩽ 304.8 mm, and 22.8 ⩽ f_c ⩽ 45.5 MPa. Actually, Chang (1981) was the first researcher to use dimensionally homogeneous equations in the presentation of empirical formulae (Li et al., 2005).

Haldar–Hamieh formula

Haldar and Hamieh (1984) suggested the use of a dimensionless impact factor I_a defined by

I_{a} = \frac{M N^{*} V_{o}^{2}}{d^{3} f_{c}}

(22)

to predict the penetration depth, that is

\frac{x}{d} = - 0.0308 + 0.2251 I_{a} for 0.3 \leq I_{a} \leq 4.0

(23a)

\frac{x}{d} = 0.6740 + 0.0567 I_{a} for 4.0 < I_{a} \leq 21.0

(23b)

and

\frac{x}{d} = 1.1875 + 0.0299 I_{a} for 21.0 \leq I_{a} \leq 455.0

(23c)

Based on the above formulae for penetration depth, it was suggested that the perforation limit could be calculated using the NDRC formula. The scabbing limit is determined by the NDRC formula if I_a is less than 21; if I_a exceeds this value, the following formula should be used

\frac{h_{s}}{d} = 3.3437 + 0.0342 I_{a} for 21 \leq I_{a} \leq 385

(24)

Hughes formula

Hughes (1984) suggested the following formulation for the penetration depth

\frac{x}{d} = 0.19 \frac{N_{h} I_{h}}{S}

(25)

where the projectile nose shape factor N_h, which depends on CRH, is 1.0, 1.12, 1.26, and 1.39 for flat, blunt, spherical, and very sharp noses, respectively. These values of projectile nose shape coefficient were obtained by fitting the above equation to the predictions of the NDRC penetration formula for a given nose shape over its whole range of applicability. I_h is a non-dimensional impact factor defined by

I_{h} = \frac{M V_{o}^{2}}{d^{3} f_{t}}

(26)

Hughes (1984) employed the tensile strength of the concrete f_t instead of its compressive strength f_c as used by Haldar and Hamieh (1984), which seems inappropriate because the penetration resistance is dominated by the compressive strength of the concrete target (Li et al., 2005). However, the ratio between the tensile strength and the compression strength of concrete is normally a constant, and therefore, either using f_t or using f_c for the impact factor only causes a difference of constant (Li et al., 2005). Hughes (1984) also accounted for the influence of the strain rate on the tensile strength of concrete by introducing a dynamic increase factor S so that the tensile strength f_t was replaced by Sf_t. Dynamic increase factor S was obtained through an empirical calibration with penetration results

S = 1.0 + 12.3 \ln (1.0 + 0.03 I_{h})

(27)

The perforation and scabbing limits are predicted by

\frac{e}{d} = 3.6 \frac{x}{d} for \frac{x}{d} < 0.7

(28a)

\frac{e}{d} = 1.58 \frac{x}{d} + 1.4 for \frac{x}{d} \geq 0.7

(28b)

and

\frac{h_{s}}{d} = 5.0 \frac{x}{d} for \frac{x}{d} < 0.7

(29a)

\frac{h_{s}}{d} = 1.74 \frac{x}{d} + 2.3 for \frac{x}{d} \geq 0.7

(29b)

The formulae were verified in the range of available test data for I_h < 3500. However, they are conservative when I_h < 40 and H_o/d < 3.5.

Criepi formula

The formula of Central Research Institute of Electric Power Industry (Criepi) (Kojima, 1991) for the penetration depth in SI unit is given by

\frac{x}{d} = \frac{0.0265 N^{*} M d^{0.2} V_{o}^{2} (114 - 6.83 \times 10^{- 4} f_{c}^{2 / 3})}{f_{c}^{2 / 3}} [\frac{0.2 (d + 0.25)}{H_{o} (d + 1.25 H_{o})}] (SI units)

(30)

The perforation and scabbing limits, which are determined by non-dimensional numbers and therefore independent of a particular unit system, are given by

\frac{e}{d} = 0.90 {(\frac{61}{V_{o}})}^{0.25} {(\frac{M V_{o}^{2}}{d^{3} f_{c}})}^{0.5} (SI units)

(31)

and

\frac{h_{s}}{d} = 1.75 {(\frac{61}{V_{o}})}^{0.13} {(\frac{M V_{o}^{2}}{d^{3} f_{c}})}^{0.4} (SI units)

(32)

The above two equations are modified from Chang’s formulae for perforation and scabbing limits.

AEC–EDF perforation formula

Based on a series of drop-weight and air gun tests to develop reliable predictions on ballistic performance of reinforced concrete slabs under missile impact, the French Atomic Energy Commission (AEC) and the French Electrical Power Company, Electricite de France (EDF) (Sokolovsky et al., 1977) suggested a perforation limit formula

\frac{e}{d} = 0.82 \frac{M^{0.5} V_{o}^{0.75}}{ρ_{c}^{0.125} f_{c}^{0.375} d^{1.5}} (SI units)

(33)

where ρ_c is the density of the concrete. The ballistic limit (perforation velocity) V_p (m/s) is given by

V_{p} = 1.3 ρ_{c}^{1 / 6} f_{c}^{0.5} {(\frac{d H_{o}^{2}}{M})}^{2 / 3} (SI units)

(34)

The influence of the reinforcement ratio was analyzed and compared with an empirical formula modified by the United Kingdom Atomic Energy Authority (UKAEA; Fullard et al., 1991). Fullard et al. (1991) extended equation (34) to non-circular missile cross-section and reinforced concrete, that is

V_{p} = 1.3 ρ_{c}^{1 / 6} f_{c}^{0.5} {(\frac{p H_{o}^{2}}{π M})}^{2 / 3} {(r + 0.3)}^{0.5} (SI units)

(35)

where H_o is the thickness of the target, p is the perimeter of the missile cross-section, and r is the average percentage of reinforcement (% each way, each face [EWEF]). Equation (35) is valid for 20 < V_o < 200 (m/s).

The UKAEA formula

Based on extensive studies conducted for the protection of nuclear power plant structures in the United Kingdom, Barr (1990) suggested the following further modification to the NDRC formula, directed mainly toward the lower impact velocities more relevant to the nuclear industry

G = 3.8 \times 10^{- 5} \frac{N^{*} M}{d \sqrt{f_{c}}} {(\frac{V_{o}}{d})}^{1.8} (SI units)

(36)

which is the same as equation (12). The dependence of the penetration depth on the G-function in equation (36) is

\frac{x}{d} = 0.275 - {[0.0756 - G]}^{0.5} for G \leq 0.0726

(37a)

\frac{x}{d} = {[4 G - 0.242]}^{0.5} for 0.0726 \leq G \leq 1.0605

(37b)

\frac{x}{d} = G + 0.9395 for G \geq 1.0605

(37c)

The parameter ranges of this formula for which the accuracy of the penetration prediction has been assessed are 25 < V_o < 300 m/s, 2244 MPa, and 5000 < M/d³ < 200,000 kg/m³. Within these ranges, the accuracy of the prediction of the normalized depth of penetration x/d is ±20% for x/d > 0.75 and +100% to −50% for x/d < 0.75.

For the scabbing limit, Barr (1990) proposed (Wicks and Fullard, 1992)

\frac{h_{s}}{d} = 5.3 G^{0.33}

(38)

The perforation velocity in SI units is further modified according to the AEC–EDF perforation (ballistic limit) formula (equation (34)) and Fullard (1991) (equation (35)) to

V_{p} = V_{a} for V_{a} \leq 70 m / s

(39a)

and

V_{p} = V_{a} [1 + {(\frac{V_{a}}{500})}^{2}] for V_{a} > 70 m / s

(39b)

where

V_{a} = 1.3 ρ_{c}^{1 / 6} f_{c}^{0.5} {(\frac{p H_{o}^{2}}{π M})}^{2 / 3} {(r + 0.3)}^{0.5} [1.2 - 0.6 (\frac{C_{r}}{H_{o}})] (SI units)

(40)

The perforation formulae given by equations (39) and (40) are only applicable for flat-nose projectiles. Hemispherical nosed projectiles with a diameter approximately equal to the target thickness showed that such projectiles required up to 30% higher velocities to perforate a reinforced concrete target than a flat-faced projectile having the same mass and diameter. Thus, Barr (1990) suggested using the above formulae for a flat nose to give conservative estimates for the perforation behavior of non-flat-nosed projectiles.

University of Manchester Institute of Science and Technology formula

In 1985, United Kingdom Nuclear Electric (UKNE) initiated a major research program on the behavior of concrete structures against the local impact effect of hard missile by establishing the R3 Concrete Impact Working Party (Reid and Wen, 2001). A collection of empirical formulae were proposed to predict critical kinetic energies of missiles for identified local impact effects on reinforced concrete slabs (Reid and Wen, 2001). The proposed empirical formulae for penetration depth x is given by (Li et al., 2006)

\frac{x}{d} = (\frac{2}{π}) \frac{N^{*}}{0.72} \frac{M V_{o}^{2}}{σ_{t} d^{3}}

(41)

where the nose shape factor N*, which depends on CRH, is 0.72, 0.84, 1.0, and 1.13 for flat, hemispherical, blunt, and sharp noses, respectively. The parametric ranges are 50 < d < 600 mm, 35 < M < 2500 kg, 0 < x/d < 2.5, and 3 < V_o < 66.2 m/s

σ_{t} (Pa) = 4.2 f_{c} (Pa) + 135.0 \times 10^{6} + [0.014 f_{c} (Pa) + 0.45 \times 10^{6}] V_{o} (m / s)

(42)

This equation can be used for rate-dependent characteristic strength of concrete.

The critical kinetic energies of the missile causing perforation E_p and scabbing E_s for H_o/d < 5 are given as follows.

The critical kinetic energy for perforation E_p is

\frac{E_{p}}{η σ_{t} d^{3}} = - 0.01 (\frac{H_{o}}{d}) + 0.02 {(\frac{H_{o}}{d})}^{3} for 1 \leq \frac{H_{o}}{d} < 5

(43)

η = \frac{3}{8} (\frac{d}{C_{r}}) r_{t} + 0.5 if (\frac{d}{C_{r}} < \sqrt{\frac{d}{d_{r}}})

(44a)

η = \frac{3}{8} \sqrt{\frac{d}{d_{r}}} r_{t} + 0.5 if (\frac{d}{C_{r}} \geq \sqrt{\frac{d}{d_{r}}})

(44b)

where d is the diameter of the projectile, d_r is the diameter of the reinforcing steel bar, C_r is the rebar spacing, and r_t is the total bending reinforcement (r_t = 4r, with r being % EWEF, defined as $r = π d_{r}^{2} / 4 H_{o} C_{r}$ , where H_o is the thickness of the concrete target).

The critical kinetic energy for scabbing E_s is

\frac{E_{s}}{η σ_{t} d^{3}} \frac{N^{*}}{0.72} = - 0.005441 (\frac{H_{o}}{d}) + 0.01386 {(\frac{H_{o}}{d})}^{3}

(45)

where the nose shape factor is considered same as in penetration formula.

The perforation and scabbing models are applicable for 22 < d < 600 mm, 1 < M < 2622 kg, 0 < V_o < 427 m/s, 19.9 < f_c < 78.5 MPa, 0 < r < 4% EWEF, and 50.8 < H_o < 640 mm.

Li et al. (2006) further modified the University of Manchester Institute of Science and Technology (MIST) formulae in terms of critical energies required for scabbing and perforation of the concrete targets for flat-nose hard missile impact. According to them, the critical impact energy for perforation E_cp is

\frac{E_{c p}}{f_{c} d^{3}} = \frac{π}{4} \frac{σ_{t}}{f_{c}} [\frac{H_{o}}{d} - 3.0] for \frac{H_{o}}{d} > 1

(46)

The critical impact energy for scabbing E_cs is

\frac{E_{c s}}{f_{c} d^{3}} = \frac{1}{2} \frac{σ_{t}}{f_{c}} [- 0.005441 \frac{H_{o}}{d} + 0.01386 {(\frac{H_{o}}{d})}^{3}] for \frac{H_{o}}{d} \leq 5

(47)

Most of the above empirical formulae do not explicitly include the reinforcement ratio. The formulae predict the impact resistance of targets that are normally reinforced (reinforcement ratio within the range 0.3%–1.5%). Reinforcement ratios within this range have little or no effect on the target perforation resistance (Abdel-Kader and Fouda, 2014; Dancygier, 1997; Li et al., 2005). The application range of the empirical formulae (which were mainly developed by data fitting of test results) depends on the tests performed. The notation used for repeatedly mentioned symbols in the above formulae, their values, and corresponding units in SI system is given in Table 6.

Using the above formulae, the perforation thickness e for specimens of nominal compressive strengths of 26, 57, and 92 MPa (denoted C25, C50, and C100) at given velocities (270 and 300 m/s) was calculated and shown in Figures 10 and 11.

In Figure 10, the perforation thicknesses estimated by all formulae for specimen C25 at impact velocity of 270 m/s are shown. Most of the formulae agreed well with the experiment (in experiment, the perforation thickness was 100 mm for the impact velocity of 270 m/s). The closest predicted perforation thicknesses to the experiment were coming from modified BRL (equation (5)), Criepi (equation (31)), and Kar (equation (18)) formulae. Hughes and modified Petry formulae (equations (28) and (2)) gave more conservative results (higher predicted perforation thicknesses were obtained compared with the experiment).

When increasing the impact velocity from 270 to 300 m/s, all the estimated perforation thicknesses increase but with different percentages (Figure 10).

Figure 11 shows the perforation thicknesses estimated by all formulae for specimens C25, C50, and C100 at impact velocity of 270 and 300 m/s. It can be seen from Figure 11 that when increasing the compressive strength more than twice (from 26 to 57 MPa), all the estimated perforation thicknesses decrease (with different percentages), except for modified Petry formula (equation (2)). This is because the concrete penetrability K_P was kept constant (3.39 × 10⁻⁴) as for normal reinforced concrete since no value was given for high strength concrete. The closest predicted perforation thickness to the experiment was coming from Kar (equation (18)) formula, which reflects what was observed in the experiment of plain concrete specimens without lining that increasing the compressive strength of concrete more than threefold has small gain (~10%) in the ballistic resistance of the panel against impact. Modified NDRC (equation (14)) and modified MIST (equation (46)) also gave good results (Figure 11).

Regarding concrete specimens lining with GFRP sheets, the above empirical formulae are not suitable to predict their perforation limit. This is because the formulae were calibrated from empirical results of only plain or reinforced specimens.

In the open literature, to the best knowledge of the authors, there is no empirical formula to predict the perforation limit for concrete specimens lining with GFRP sheets. Therefore, a numerical analysis is needed, which will be a topic for a future work.

Conclusion

In this article, a series of experiments, which is similar except for concrete compressive strength, was conducted to observe the influence of compressive strength of concrete on the performance of concrete under impact loading. Also, strengthening the panels by GFRP sheets was examined. The main conclusions that can be derived from the present study indicate the following:

More than 17% increase was observed when using GFRP sheet as a rear liner of the high strength concrete panels, and more than 29% increase was observed when increasing the compressive strength from 26 to 57 MPa and using a GFRP sheet as a rear liner.

In case of concrete panels without GFRP, the observed relatively minor improvement of the ballistic perforation when increasing the concrete compressive strength more than once (from 26 to 92 MPa) may attribute to the relative decrease in tensile strength and/or residual fracture strength with increasing the compressive strength.

The use of GFRP sheets as rear liners in addition to increasing the concrete strength showed superior performance of concrete panels against impact; however, further studies are still needed, particularly to determine the most efficient level of high strength of concrete in design against impact, to be used in protective structures.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors of this paper gratefully acknowledge the support of the Egyptian Ministry of Defense for generous financial support of this study.

ORCID iD

Mohamed Abdel-Kader

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