Impact resistance of high strength-high ductility concrete

Cement and Concrete Research 98 (2017) 24–35

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Impact resistance of high strength-high ductility concrete Ravi Ranade a, Victor C. Li b,⁎, William F. Heard c, Brett A. Williams c a b c

Institute of Bridge Engineering, Department of Civil, Structural, and Environmental Engineering, University at Buffalo (SUNY), 135 Ketter Hall, Buffalo, NY 14260, USA Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor 2350 Hayward St, Ann Arbor, MI 48109, USA U.S. Army Engineer Research and Development Center (ERDC), 3909 Halls Ferry Rd, Bldg 5028, Vicksburg, MS 39180, USA

a r t i c l e

i n f o

Article history: Received 14 January 2016 5 December 2016 Accepted 27 March 2017 Available online xxxx Keywords: Impact resistance (not listed) High-performance concrete (E) Fiber reinforcement (E) Microcracking (B) Tensile properties (C)

a b s t r a c t The behavior of thin slabs of High Strength-High Ductility Concrete (HSHDC) under multiple, moderate-velocity impacts is investigated via drop-weight impact experiments. HSHDC is a newly developed fiber-reinforced cementitious composite with unique combination of compressive strength (N150 MPa) and tensile ductility (N 3%). The deformation mechanisms, cracking patterns, and impact load resistance of HSHDC slabs are determined and contrasted with the behavior of slabs made of a fiber-reinforced Ultra-high Performance Concrete named Cor-Tuf with compressive strength of about 200 MPa. While the HSHDC slabs exhibit ductile flexural behavior with well-distributed multiple fine cracks, the Cor-Tuf slabs exhibit quasi-brittle flexural and shear failures accompanied by large localized cracks and excessive spalling. Finite element analysis of these slabs' responses reveals that the observed difference in the structural behavior of HSHDC and Cor-Tuf slabs is a direct result of the difference in the tensile ductility of these two materials. © 2017 Elsevier Ltd. All rights reserved.

1. Introduction Impact loads can pose significant threat to our built environment with potentially dangerous consequences. Examples of damaging impact loads include trees, cars, or other objects hurled toward built structures during hurricanes [1,2], large vehicular impacts on bridge piers [3], and terrorism [4]. Mitigating the detrimental effects of impact loads on the structural integrity of our infrastructure, thus making it more resilient, is a major challenge for modern engineers. Structural-scale strategies for enhancing the impact resistance of structures, particularly reinforced concrete (RC) structures, have been demonstrated in the past. These strategies include enhanced reinforcement detailing and enlarged structural dimensions [5–8], barriers around bridge piers to prevent vehicle collisions [9], and external reinforcement of structural elements through fiber-reinforced polymer (FRP) sheets [10,11] and fiber-reinforced concrete (FRC) walls [12]. Although these strategies have proven effective in mitigating the effects of impact loads on RC structures, they do not address the underlying problem of concrete's brittleness and low energy absorption [13]. As a result, severe spalling and scabbing [6] of concrete occurs, which renders these, often costly, structural measures less effective and thus motivates us to seek material-scale solutions to improve the structural resilience under impact loads. Recently, the research focus has shifted toward material-scale solutions employing advanced concrete materials, with greater strength, ⁎ Corresponding author. E-mail address: [email protected] (V.C. Li).

http://dx.doi.org/10.1016/j.cemconres.2017.03.013 0008-8846/© 2017 Elsevier Ltd. All rights reserved.

toughness, and tensile ductility than normal concrete, in the impact resistant design of structural elements. The use of two different categories of advanced concretes, Fiber-Reinforced Ultra-High Performance Concrete (FR-UHPC) [14–27] and Strain Hardening Cementitious Composite (SHCC, also called Engineered Cementitious Composite or ECC) [28,29], has been reported in the literature for enhancing the structural impact resistance compared to normal concrete. While an FR-UHPC is designed for high compressive strength (N150 MPa) and considerably greater toughness compared to normal concrete, an SHCC is designed for high tensile ductility (2–6% tensile strain capacity) that also facilitates significantly greater composite toughness than both concrete and FR-UHPC. Both these classes of advanced concretes have distinct advantages and limitations in the impact resistant design of structures, which are discussed below. A number of studies [14–27] have investigated various aspects of the behavior of FR-UHPC under impact/blast loads load. Due to its extremely high static compressive strength, which is further increased under impact due to rate effects, FR-UHPCs can resist immense compressive stresses at the frontal face (where the impact head contacts the concrete specimen). At the same time, due to greater toughness than concrete, FR-UHPC has significantly greater resistance to cracking. For instance, Nicolaides et al. [25] concluded that FR-UHPC (UHP-CY) slabs perform significantly better than similarly-sized high performance concrete slabs (both containing the same conventional reinforcement) under impact and blast loads as measured by crater diameter, crater volume, and mass loss. Additionally, Mao et al. [26] and Barnett et al. [27] concluded that the blast-resistance of FR-UHPC slabs improves with increasing fiber volume fraction. Post-cracking, some tension-softening FR-

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UHPCs also exhibit deflection-hardening (not necessarily strainhardening) that lends them high flexural energy absorption capacity. In spite of these advantages, the above studies [14–27] highlight the following limitations of tension-softening FR-UHPC performance under impact loads (strain-hardening FR-UHPCs may not possess these limitations): (1) extreme brittleness of the matrix causes severe spalling and scabbing at the free distal (back) face where the incident compressive stress wave reflects as a tensile stress wave, (2) damage is often localized along the yield lines of a slab or mid-section of the beam with little multiple cracking, (3) overall performance is largely proportional to compressive strength and fiber content often requiring a large volume fraction of fibers, greater than or equal to 3%, and (4) strain incompatibility between tension-softening FR-UHPC and steel in conventionally reinforced specimens prevents complete utilization of the main reinforcement capacity. These limitations of tension-softening FR-UHPC's behavior under impact load primarily stem from low tensile ductility of the material. In contrast to tension-softening FR-UHPC, an SHCC (or ECC) possesses significant tensile ductility with strain-hardening behavior after the first crack [30], which improves the impact performance of SHCC specimens at the distal face. The use of SHCC overcomes the above limitations of tension-softening FR-UHPC under impact (or dynamic) loads [28,29,31]. However, due to significantly lower compressive strength (less than half) than FR-UHPC [32], SHCC specimens may sometimes crush and fail at the frontal face. Additionally, SHCC specimens exhibit larger deformations than FR-UHPC specimens in the elastic stage due to significantly lower elastic modulus. Even at small inelastic deformation in a deflection-hardening FR-UHPC specimen, the corresponding permanent deformation (to absorb the same impact energy) in a similarly-sized SHCC specimen is greater, which reduces the resilience of the structural element. Thus, while a tension-softening FR-UHPC enhances impact performance mainly by the virtue of its high strength (both compression and tension) and toughness, SHCC enhances impact performance due to its tensile ductility; therefore, a combination of high compressive strength and tensile ductility in one material is expected to maximize the material's impact resistance. A new fiber-reinforced cementitious composite, named High Strength-High Ductility Concrete (HSHDC) [33,34], has been recently developed at the University of Michigan in collaboration with the U.S. Army Engineer Research and Development Center (ERDC). Under quasi-static loads, HSHDC exhibits a unique combination of ultra-high compressive strength (N150 MPa) and ultra-high tensile ductility (N3% under direct tension). The tensile rate effects study on HSHDC indicates that it maintains high tensile ductility of about 3% at strain rates of up to 10/s [35,36]. This paper investigates the impact resistance of HSHDC in comparison with Cor-Tuf, a tension-softening but deflection-hardening FRUHPC. The hypothesis of this study is that the combination of high compressive strength and tensile ductility of HSHDC should translate into better impact resistance than Cor-Tuf (a future study will evaluate and compare the impact resistances of HSHDC and SHCC to determine the influence of compressive strength on the impact resistance of these materials). Although this hypothesis may sound intuitive based on our understanding of flexural behavior (under impact loads) as a combination of compression and tension, there has been no study on very-high/ ultra-high strength concretes that supports this hypothesis and quantifies the benefit of using a high performance material that is strong and ductile (HSHDC) over another high performance concrete that is strong and tough (Cor-Tuf). In order to test the above hypothesis, an experimental investigation aimed at evaluating the impact resistance of HSHDC through dropweight impact tests on thin slabs and comparison with Cor-Tuf is reported in this paper. The mechanical properties of HSHDC and Cor-Tuf are discussed in a separate section below. The major difference in mechanical behavior is that while HSHDC shows significant strainhardening under direct tension, Cor-Tuf softens in tension beyond a

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tensile strain of about 0.15%. Furthermore, the average uniaxial compressive strength of the HSHDC is 166 MPa [33] and that of the CorTuf is 201 MPa [36]. This experimental investigation is supplemented by a 3D non-linear rate-dependent finite element (FE) model of the drop-weight experiments to gain insights into the failure modes, crack patterns, and stress-strain profiles. The details of these research tasks are given in the following sections. 2. Research significance This research, for the first time, investigates the impact behavior of thin slabs made with HSHDC which is a newly invented fiberreinforced cementitious composite with a unique combination of compressive strength (≈166 MPa) and tensile ductility (≈3.4%). For comparison, similarly sized Cor-Tuf slabs are used as control. Cor-Tuf has an average compressive strength of 201 MPa and contains hooked steel fibers at a volume fraction of 3.26% for enhancing the composite toughness. Most of the past studies on impact behavior of FR-UHPC or SHCC/ECC have compared one of these high-performance concretes with normal concrete. This study directly compares two highperformance concretes and investigates the influence of the material's tensile ductility on the structural performance under impact load. The 3D rate-dependent finite-element analysis presented in this study provides crucial insights into the structural response of the slabs, which will aid in implementing the integrated structures and materials design methodology for efficient tailoring of materials for structural resilience against impact loads. 3. Experimental investigation 3.1. Material compositions The mix proportions for the two materials, HSHDC and Cor-Tuf, investigated in this study are given in Table 1, and the properties of fibers used in these two composites are given in Table 2. The HSHDC matrix, similar to that of the Cor-Tuf, is designed for achieving very high compressive strength. The variety of particle sizes of the ingredients facilitates dense particle packing. The addition of silica fume enhances the production of calcium silicate hydrates and other strength-giving products through pozzolanic reaction in addition to densifying aggregate/cement paste and fiber/matrix interfaces. The water-to-cementitious material ratio (w/cm) is limited to 0.15 to reduce the porosity. While the HSHDC contains ultra-high molecular weight polyethylene fibers (henceforth referred to as “PE fibers”), Cor-Tuf contains hooked steel fibers. The average viscosity and yield stress of the HSHDC matrix are 6.0 Pa-s and 186.2 Pa, respectively, whereas those properties of the Cor-Tuf matrix are 5.5 Pa-s and 170 Pa, respectively. Slump of both mixtures (with fibers) is about 190 mm, measured using the standard procedure in ASTM C143. Further details about the ingredient selection, mixing procedures, and rheological characterization of HSHDC and Cor-Tuf are presented in Ranade et al. [33] and O′Neil [37], respectively. The volume fraction of the steel fibers in the FR-UHPC (3.26%) is significantly greater than that of the PE fibers in HSHDC (2%). The rheology of the FR-UHPC has been optimized to homogenously disperse the relatively high volume fraction (3.26%) of fibers using appropriate dosage of high range water-reducing admixture. In spite of the lower volume fraction of fibers in HSHDC, the micromechanics-based design of HSHDC ensures efficient utilization of the high aspect ratio and superior mechanical properties of the PE fibers (compared to the steel fibers) to achieve composite tensile ductility, as detailed in Ranade et al. [34]. Cor-Tuf has been developed by the researchers at the US Army Corps of Engineers over the last two decades [16,37–40]. Although there are other FR-UHPCs [41,42] that possess greater tensile strain capacity than Cor-tuf, the reasons for choosing Cor-tuf for this research are the following. The impact resistance of Cor-tuf has been well established in not only small-scale laboratory experiments but also in large-scale

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R. Ranade et al. / Cement and Concrete Research 98 (2017) 24–35

Table 1 Mix proportions of HSHDC and Cor-Tuf. Constituent

Class H cement Silica fume Silica flour Silica sand Tap water HRWRAa PE fiberb Hooked steel fiberb a b

Particle size (μm)

30–80 0.1–1 5–100 100–600 – – – –

HSHDC

Cor-Tuf

Weight relative to cement

Weight per unit volume, kg/m3

Weight relative to cement

Weight per unit volume, kg/m3

1 0.389 0.277 0.700 0.208 w/cm = 0.15 0.0176 0.0214 –

907 353 251 635 189 16 19 –

1 0.389 0.277 0.967 0.208 w/cm = 0.15 0.0151 – 0.313

817 318 226 791 170 12 – 256

Total HRWRA content. Properties of fibers are given in Table 2.

impact and blast load tests and field studies. Additionally, the authors of this paper are well-versed with the material and mixing procedure of Cor-tuf which is essential for consistently producing such specialized materials. At the same time, Cor-tuf is representative of a number of tension-softening FR-UHPCs as surveyed by Russell and Graybeal [43]. Cor-tuf, therefore, serves as a good baseline to compare the impact resistance of HSHDC.

3D distribution was applied to best-fit the observed distribution. This upper limit for 3D distribution is physically justified by the lack of freedom for fibers in the thickness dimension of these planar specimens (dogbones and coupons). Further details about the influence of orientation distribution on the bridging stress-crack opening relation and other micromechanical parameters of HSHDC are given in Ranade et al. [34,36]. In this study, it is assumed that the orientation distribution of the PE fibers in the drop-weight impact slab specimens is similar to the distribution observed in coupon specimens which are significantly (about 2.5 times) wider than the dogbone specimens. The direct tension tests on HSHDC coupons with constant cross-sectional area do not satisfactorily capture the material behavior due to stress-concentrations and premature failure outside the gauge region within the grips [36]. Instead, the direct tension response of HSHDC dogbones was used in conjunction with the orientation distribution observations in dogbones and coupons to analytically compute the ultimate tensile strength and ductility of HSHDC coupons. These material properties computed for coupons, further modified by incorporating the rate effects (explained below), were used in the finite element model [44] of the drop-weight impact tests to simulate the behavior of HSHDC. As mentioned above, the direct tension response of HSHDC shown in Fig. 1 is determined at quasi-static strain rate of 10−4/s. However, the strain rates imposed on the material during moderate velocity impacts range from 0.1–10/s. Therefore, rate effects on HSHDC's tensile response were determined by Ranade et al. [35] at both macro- and micro-length scales. The main conclusions of that study (relevant for this paper) were that the tensile strain capacity of HSHDC decreases to 2.9% at strain rate of 0.1/s but plateaus beyond that for strain rates up to 10/s. The ultimate tensile strength of HSHDC and matrix cracking strength increase by about 42% and 53%, respectively. The relative insensitivity of the frictional bond between the PE fiber and the cementitious matrix, coupled with increase in the strength and modulus of the PE fiber at higher strain rates explain the aforementioned rate effects on the material's behavior [35]. These rate effects on the tensile response of HSHDC are incorporated in the material model used for the finite element analysis of HSHDC slabs (discussed below); while the rate effects on the compressive response of HSHDC are assumed to be similar to the rate effects on ultra-high performance concretes of similar compressive strengths reported in previous studies [44]. The direct tension response of an average Cor-Tuf dogbone specimen is shown and compared with the response of an identical HSHDC specimen in Fig. 1(a). Unlike HSHDC, Cor-Tuf exhibits a strainsoftening response under direct tension. The average tensile strain capacity of eight Cor-Tuf dogbone specimens is 0.12% with high CV of

3.2. Mechanical properties of materials As reported in Ranade et al. [33], the average of compressive strengths of eight 51 mm cube specimens of HSHDC at quasi-static loading rate is 166 MPa with coefficient of variation (CV) of 6.1%. Full stressstrain curves of these cube specimens are given in Ranade et al. [33]. Furthermore, the average compressive strength of six 76 mm cube specimens of HSHDC is 159 MPa with CV of 4.4%. In comparison, the average compressive strength of six 51 mm cube specimens of Cor-Tuf is 201 MPa with CV of 3.7% [36]. Similar compressive strength of Cor-Tuf has been reported by other researchers [39,40] using the 51 mm cube specimens and larger sized cubes (76 mm cubes) and cylinder specimens (100 mm × 200 mm and 150 mm × 300 mm cylinders). Complete mechanical characterization of HSHDC under direct uniaxial tension at quasi-static displacement rate (0.5 mm/min) is presented in Ranade et al. [33]. The dogbone-shaped specimen geometry, direct tension test setup, and the stress-strain curve of an average HSHDC (and Cor-Tuf) dogbone specimen is shown in Fig. 1. Full details about the specimen preparation, curing, and test procedures are presented in Ranade et al. [33]. The results show that the average tensile strain capacity of eight dogbone specimens of HSHDC is 3.4% with CV of 11%, and the average ultimate tensile strength is 14.5 MPa with CV of 6%. HSHDC achieves such a high tensile ductility through the process of multiple micro-cracking which is made possible by the favorable fiber/matrix micromechanical interaction [34]. A major factor that significantly influences the behavior of HSHDC under direct tension is the orientation distribution of the PE fibers. Ranade et al. [34,36] observed the orientation distribution of PE fibers in the aforementioned dogbone specimens and thin coupon specimens (300 mm long, 76 mm wide, and 12.7 mm thick) of HSHDC using fluorescence microscopy. It was determined that the observed fiber orientation distribution in planar specimens can be analytically expressed as a linear combination (weighted sum, where weights are determined through statistical best-fit) of theoretical 2D [p(ϕ) = 2/π] and 3D [p(ϕ) = sin(ϕ) / {cos(0°) − cos(ϕ1)}] random distributions of fibers where ϕ1 is the upper limit of the inclination angle up to which the Table 2 Properties of PE and Hooked Steel Fibers. Fiber type

Length (mm)

Diameter (μm)

Tensile strength (MPa)

Elastic modulus (GPa)

Volume fraction

PE Hooked steel

12.7 30

28 550

3000 1300

100 210

2% (HSHDC) 3.26% (Cor-Tuf)

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Fig. 1. Direct tension response of HSHDC and Cor-Tuf dogbone specimens made using the same mold, conditions of casting, and loaded under displacement control at the rate of 0.5 mm/min. (a) Stress-strain response (b) Direct tension test setup used for both materials (c) Dogbone specimen geometry used for both materials in the direct tension tests (all dimensions in mm) [33,36]. * Average LVDT Displacement is the average of the displacements recorded by the two LVDTs over the gauge length shown in Fig. 1(b). Tensile strain is computed by dividing the average displacement by the gauge length of 980 mm.

27%, and their average ultimate tensile strength is 11.2 MPa with CV of 9%. Due to the longer hooked steel fiber used in Cor-Tuf, direct tension tests were also performed on larger size Cor-Tuf dogbone specimens (with cross-sectional area of 76 mm × 76 mm in the gauge region) by Ranade [36]. The average tensile strain capacity and the average ultimate tensile strength reduced to 0.09% and 7.6 MPa, respectively, due to more 3D distribution of steel fibers in the large dogbones. Instead of forming multiple micro-cracks, Cor-Tuf only one or two macro-cracks and the subsequent displacement is caused only by the opening of a single crack. As a result, the concept of “tensile strain” is not meaningful in the tension-softening regions of the stress-strain curve.

3.4. Experimental setups and procedures The drop-weight impact test setup used in this study is shown in Fig. 3. It consists of a cylindrical impact head mounted under a loading tray, the total weight of which can be adjusted by adding or removing steel plates as required. The loading tray is connected to two pillow blocks which in turn slide smoothly on two vertical precision-ground, hardened steel guide-shafts (25 mm dia). These guide-shafts are mounted on the sturdy structural frame of the test setup. The drop-

3.3. Drop-weight impact specimens Thin slabs of dimensions 300 mm × 300 mm × 25 mm (thickness) as shown in Fig. 2 were used in this experimental study to compare the impact resistances of HSHDC and Cor-Tuf. The specimens were made of either HSHDC or Cor-Tuf with no additional reinforcement. During casting, both the materials were poured at the center of their respective molds and moderate vibration was applied using a vibration table to facilitate the material flow toward the corners of the slab molds. All the specimens were demolded after two days of casting and subjected to the heat-accelerated curing procedure (detailed in Ranade et al. [33]), which entails seven days of curing in water at room temperature followed by five days of curing in water at 90 °C and three days of curing in air at 90 °C.

Fig. 2. Drop-weight impact specimen dimensions.

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Fig. 3. Drop-weight impact test setup (a) Full Setup (b) Instrumentation (zoomed view of the dashed circle) (c) Specimen Holder.

weight assembly, consisting of the impact head, the loading tray, and the pillow blocks, can be raised to a desired height by a hoisting rope. After hoisting to the desired height, the drop-weight assembly is connected to the overhead beam of the structural frame via an active electromagnet. At this point, the hoisting rope is disengaged as the loading assembly is held in place by the electromagnet. Switching off the electromagnet releases the drop-weight assembly for impact onto the specimen kept on a steel specimen holder, which sits on an extremely heavy steel base. The instrumentation used in the drop-weight tests is shown in Fig. 3(b). It consists of three parallel dynamic load cells, L1-3 in Fig. 3(b), each with a maximum capacity of 44.5 kN (10,000 lbf) and arranged such that their centers are equidistant from the center of the impact head. In order to ensure that all the load cells are engaged simultaneously at the moment of impact, the mounting screw that connects the impact head to the loading tray is pre-tensioned to apply precompression on all the load cells. In addition, the impact region on the specimen is sanded to ensure smooth and level contact with the impact head. The acceleration-time history of the drop-weight assembly is recorded by two accelerometers (A1 and A2) with a range of 1500 g. These accelerometers are mounted on the opposite sides of the loading tray and their readings are averaged, which eliminates any sidewobbling/vibration effects of the drop-weight assembly on the acceleration time-history. All the aforementioned sensors are connected to a high frequency data acquisition system with maximum sampling frequency of 1 MHz. As there are five sensors in all, each sensor can be sampled at a maximum frequency of 200 kHz. With this arrangement, the maximum recordable impact force and average acceleration of the impact head are 133.5 kN (30,000 lbf) and 1500 g, respectively, at 200 kHz per channel. The experimental details of this drop-weight impact study, comparing the performance of HSHDC and Cor-Tuf slabs with varying kinetic energies of impact head and varying head diameter, are given in

Table 3. A constant weight of 16.04 kg was dropped repeatedly on both HSHDC and Cor-Tuf slabs using a cylindrical steel head of 75 mm diameter from three different heights of 0.35 m, 0.70 m, and 1.40 m. The calculation of the impact velocity (used to compute kinetic energy) is detailed in the next paragraph. The impacts are repeated for either 20 times or until slab failure, whichever occurs first. Almost zero rebound of the impact head, either due to flexural failure of the slab or due to head penetration in the slab, is deemed as ‘slab failure’. In addition to the above set of impacts with the 75 mm head, drop-weight impacts with a 50 mm cylindrical head were used to qualitatively determine the influence of head size on the failure modes of HSHDC and Cor-Tuf slabs. The footprint of three required load cells is larger than the 50 mm head's cap area, and therefore, no instrumentation was used for the impacts with the 50 mm head. Two slabs each of HSHDC and Cor-Tuf were used in all the impact cases investigated in this study. The impact velocity is calculated from the vertical position of the drop-weight assembly at different times. A 30 fps (frames per second) video of the drop, obtained with a high-quality digital camera, provides the position of the drop weight assembly at time intervals of 1/30 s. If the dynamic frictional force between the drop-weight assembly and the guide-shafts is assumed constant, the impact velocity can be determined using position-time observations as inputs in the Newtonian equations of motion. The computed impact velocities corresponding to various drop-heights are shown in Table 3. 4. Results of experiments and discussion 4.1. Single impact In this section, the response of an HSHDC slab under a single impact is described; multiple-impact responses of HSHDC slabs and comparison with Cor-Tuf slabs are discussed in the next section. The first impact on the HSHDC slab specimen H4.60-1 (naming scheme is given

R. Ranade et al. / Cement and Concrete Research 98 (2017) 24–35

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Table 3 Experimental parameters of the drop-weight impact tests. Specimens Instrumented impacts 2 × (HSHDC & Cor-Tuf)a 2 × (HSHDC & Cor-Tuf) 2 × (HSHDC & Cor-Tuf) Non-instrumented impacts 2 × (HSHDC & Cor-Tuf) a

Head diameter

Drop weight

Drop height

Impact velocity

75 mm

16.04 kg

0.35 m 0.70 m 1.40 m

2.30 m/s 3.25 m/s 4.60 m/s

50 mm

16.11 kg

0.70 m

3.25 m/s

Multiple impacts 20 or head penetration without rebound – whichever occurs first

Specimen naming example for the instrumented impacts: H4.60-1: H for HSHDC; 4.60 for impact velocity (m/s); 1 for specimen number (out of 2 of this kind).

in the footnote of Table 3) is taken as an example to describe the singleimpact response. The contact force-time history and the displacementtime history for this impact are shown in Fig. 4. In this figure, the black continuous curves represent experimental observations and the blue curves are computed using FE analysis described in the next section. The displacement-time history is derived by twice-integrating the observed acceleration-time history (reported in Ranade [36]) with respect to time. The time history of a single drop-weight impact can be described in three stages: initial impulse and contact of the impact head with the HSHDC slab, depression of the slab and impact head to maximum displacement, and rebound until the contact between the impact head and the HSHDC slab is lost. These three stages of the drop-weight impact, S1-S3, are discussed below. Stage S1 comprises of the initial impulse (spike in contact force) reaching the peak contact force (PCF) value of about 110 kN at 0.04 ms (Fig. 4). During this stage, the impact head comes in contact with the HSHDC slab, and the PCF is theoretically equal to the rate of change of momentum of the drop-weight assembly due to the impact. As a result, the PCF is not only dependent on the elastic stiffness and inertia of the slab but also on the surface textures of the slab and the impact head. For instance, if the contact surfaces (particularly that of the slab) are rough, the transfer of momentum from the impact head to the slab will be slowed down by the crushing of the surface asperities, causing a decrease in the PCF. The observed PCF is also dependent on the sampling frequency of the data acquisition (DAQ) system, which in this case is limited to 200 kHz. Higher sampling frequency may result in higher observed PCF.

Fig. 4. Contact force and displacement time histories of the first impact on specimen H4.60-1.

After this initial transfer of momentum in stage S1, the drop-weight assembly continues to depress the slab due to its remaining momentum; however, the slab and the impact head oscillate at different frequencies during the first half of stage S2. These oscillations are reflected in the contact force-time history in Fig. 4 up to about 0.8 ms. After the slab is sufficiently deformed (with some plastic deformation), the slab and the drop-weight assembly move together to the bottommost position (maximum displacement), which marks the end of stage S2. During stage S3, the drop-weight assembly rebounds from the maximum displacement position due to the residual elasticity of the HSHDC slab. The impact assembly is accelerated upwards by the slab until it completely loses contact with the slab, at which point the contact force reduces to zero. 4.2. Multiple impacts The impact load bearing capacities (measured using the PCF) of HSHDC slabs are compared to those of Cor-Tuf slabs under multiple impacts in Fig. 5. As shown in Table 3, these instrumented multiple impacts were performed with the 75 mm impact head at three different impact velocities (2.30 m/s, 3.25 m/s, and 4.60 m/s). In all the graphs of Fig. 5, the data points for HSHDC specimens are represented by circles connected with continuous gray lines, and the data points for FR-UHPC specimens are represented by triangles connected with dashed red lines. For both materials, filled shapes (circles or triangles) represent specimen #1 and unfilled shapes represent the data points for specimen #2 (2 specimens are tested for each material at a given impact velocity). As observed in Fig. 5a for the lowest velocity impact at 2.30 m/s, the peak contact force (PCF) for the specimens of both the materials remains almost constant with increasing number of impacts. The energy imparted in these impacts is insufficient in deforming the slabs to produce any significant inelastic tensile strains at the distal face. This is confirmed by the visual observations of the back faces of these slabs, which show only a few cracks at the end of 20 impacts in the specimens of both the materials. It should be noted that although Cor-Tuf is strainsoftening under direct tension, it exhibits deflection-hardening under flexure up to small inelastic displacements. Thus, minor flexural damage caused by the lowest velocity impacts does not reduce the impact load bearing capacity of the slabs of either material. Increasing the impact velocities to 3.25 m/s (Fig. 5b) and 4.60 m/s (Fig. 5c) increases the kinetic energy of the drop-weight assembly to 2 and 4 times, respectively, that of the impact at 2.30 m/s. Unlike the impacts at 2.30 m/s, these higher velocity impacts on HSHDC and Cor-Tuf slabs produce significant inelastic tensile strains, which accumulate with increasing number of impacts. As soon as the deflectionhardening capacity of the Cor-Tuf slab is exceeded, it starts to lose its impact load bearing capacity as observed by the drops in PCF in Fig. 5b and c. The drop in PCF of Cor-Tuf slabs occurs more rapidly at 4.60 m/s compared to 3.25 m/s. In contrast, PCF in HSHDC slabs remains almost constant for all the impact velocities investigated in this study. While the Cor-Tuf slabs fail (definition of ‘failure’ is given in Section 3.2) under flexure before 20 impacts at these higher velocities (except slab #C3.25–1, which, although did not fail, has significantly reduced PCF), HSHDC slabs maintain their integrity and continue to rebound the drop-weight assembly during all the 20 impacts. The damage tolerance

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Fig. 5. Comparison of multiple-impact performance of HSHDC (H) and Cor-Tuf (C) slabs.

of HSHDC, which is significantly higher than Cor-Tuf under tension, allows the HSHDC slabs to absorb more impact energy while maintaining structural integrity. The significantly improved response of HSHDC from 6 impacts onwards compared to Cor-Tuf shows the greater residual energy absorbing ability of HSHDC compared to Cor-Tuf. If we extend the results of

this study, it seems likely that at higher velocity impacts, while CorTuf may fail only in 1–2 impacts, HSHDC slabs will take significantly greater energy to fail due to their damage tolerance and saturate multiple-cracking ability. The visual appearance of damaged Cor-Tuf and HSHDC slabs after about 20 impacts with 75 mm head at 3.25 m/s is shown in Figs. 6 and 7, respectively. At its distal face (experiencing tension), the Cor-Tuf slab exhibits mainly four large flexural cracks emanating from the center of the slab. Due to the structural support conditions (Fig. 3c), the maximum principal tensile strain occurs normal to the sections joining the center to the third of the slab edges of these two-way symmetric slabs (shown through FE analysis in the next section). The Cor-Tuf slab (Fig. 6) is unable to distribute the damage due to the material's tension-softening behavior, and therefore, the entire tensile strain localizes at these sections. Large chunks of the matrix randomly break away from the specimen during the impacts and cracking process. The flexural damage concentration is so intensive that the flexural cracks reach the frontal (compression) face of the Cor-Tuf slabs and cause visible cracks (Fig. 6a). Thus, the Cor-Tuf slabs exhibit quasi-brittle flexural failure, which involves concentrated damage along the yield lines of the slab with almost no diffusion of damage caused by the tension softening behavior of the material (the sensitivity of the failure mode of Cor-Tuf slabs toward the size of the impact head, as discussed below, is also caused by such material behavior). In contrast with Cor-Tuf, the HSHDC slab (Fig. 7), due to its tensionhardening behavior, spreads the tensile strain into multiple fine cracks propagating radially outward in numerous directions from the center of the slab. A relatively large crack (relative to the other fine cracks in HSHDC) always occurs at the center of the HSHDC slab as the bending moment and resulting tensile stress are the largest at the point of impact. Due to the relatively uniform distribution of flexural damage in HSHDC slabs, there is no significant visible damage on the compression face (Fig. 7a). Additionally, almost no spalling is observed during the impacts on HSHDC slabs. Unlike Cor-Tuf, the HSHDC slabs exhibit ductile flexural behavior without failure up to 20 impacts with welldistributed multiple fine radial cracks for all impact load levels investigated in this study. The damage patterns in HSHDC and Cor-Tuf slabs caused by the impacts with 75 mm head (discussed above) at 3.25 m/s are visually compared to that caused by the impacts with 50 mm head (noninstrumented) at the same velocity (the total weight of the dropweight assembly is approximately the same). Comparing the frontal faces of the two Cor-Tuf slabs impacted by 50 mm and 75 mm heads, a punching-shear hole is visible in Fig. 8a (50 mm head), which is absent in Fig. 6a (75 mm head). The effect of the punching is also visible on the distal face of the Cor-Tuf slab in Fig. 8b. This brittle punching-shear failure of the Cor-Tuf slab by the 50 mm head occurs at the 15th impact, which is 5 impacts less than that needed for the flexural failure of the Cor-Tuf slab by the 75 mm head. In contrast, the punching-shear effect is not observed in the HSHDC slab on any face (Fig. 9), and the ductile flexural behavior (without failure) is maintained even with the smaller 50 mm head. The ductile behavior of HSHDC in tension also improves its shear behavior, similar to that observed in other strain hardening materials, such as SHCC [45]. Thus, while the failure mode of the Cor-Tuf slabs changes from flexure to punching-shear on reducing the size of the impact head, no such effect is observed in HSHDC slabs due to the material's tensile ductility. The factors that can significantly influence the impact performance of HSHDC (or any other FRC) are fiber dispersion and orientation, which in turn are influenced by mix processing, specimen/structural dimensions, and casting procedure [36]. The viscosity of the matrix must be specifically tuned for a given fiber/matrix combination and mixer's torque to achieve homogenous fiber distribution throughout the fresh mixture [46]. A planar specimen/structural configuration such as that in the HSHDC slabs of this study likely results in a 2D orientation distribution of the fibers as they are limited by the small thickness of the slab.

R. Ranade et al. / Cement and Concrete Research 98 (2017) 24–35

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Fig. 6. Damage condition of the Cor-Tuf slab C3.25-1 after impact #19 with 75 mm head (the slab disintegrates into 4 pieces after the next impact).

A 3D orientation distribution (e.g. in a beam or a column) results in a lower bridging capacity and therefore lower tensile stress capacity than the 2D distribution [47]. The casting procedure can also influence the fiber dispersion and orientation. For example, casting in layers likely result in a preferred 2D orientation distribution of fibers and fewer fibers in the interlayer zone compared to the layers. As mentioned above, the fiber dispersion and orientation distribution can be observed through fluorescence microscopy and digital image analysis [48]. These observations can be used to modify the micromechanics-based scalelinking analysis to predict the tensile and impact properties of HSHDC [34]. Such detailed analysis is underway and it will be included in a separate article. Another important factor to be considered in future research, particularly for blast resistance, is the influence of temperature on the behavior of HSHDC. The PE fibers in HSHDC have melting point of about 150 °C, which can be exceeded near a blast site. Previous research [49, 50] on the influence of high temperature on the mechanical properties of SHCCs suggests that the melting of the polymer fibers significantly diminishes their tensile performance. In spite of this deterioration, a positive effect is that the molten fibers leave interconnected paths within the cementitious matrix, which allow water and other gases to escape freely without causing spalling of concrete. Thus, considerable residual compressive strength is maintained. An ongoing study will determine whether similar phenomenon is observed in HSHDC and its implications on the impact and blast resistance of HSHDC structural elements.

5. Finite element analysis and comparison with experimental results The FE analysis was used in this study to gain insights into the experimentally determined structural response of the HSHDC and Cor-Tuf slab specimens presented in the last section. A detailed literature review of the past FE analysis of fiber-reinforced concretes along with the modeling approaches, challenges, and results are presented in Ranade [36]. The development and verification of a phenomenological plasticity-based material model for HSHDC and Cor-Tuf, and its use in the 3D rate-dependent, non-linear FE modeling of thin slabs subjected to drop-weight impact loads in the software LS-Dyna is presented in Ranade et al. [44]. These material and FE models are used to investigate the behavior of the slabs of both the materials for the load cases of this study, and the results of the FE analysis are discussed below. In the following, the global forces and displacements are first used to verify the FE model with the experimental results; then, the stresses and strains generated within the specimens are queried from the FE model output, which are otherwise difficult to determine through experiments. 5.1. Forces and displacements In Fig. 4, the force-time history computed from the FE analysis for the impact on an HSHDC slab with drop-weight of 16.04 kg and impact velocity of 4.60 m/s is compared to the experimentally determined force-time history of the corresponding drop-weight impact. The

Fig. 7. Damage condition of the HSHDC slab H3.25-1 after impact #20 with 75 mm head (back face of HSHDC is painted white to make the multiple fine cracks visible).

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R. Ranade et al. / Cement and Concrete Research 98 (2017) 24–35

Fig. 8. Damage condition of the Cor-Tuf slab #1 after impact #15 with 50 mm head at 3.25 m/s.

computed curve (marked FEM) in Fig. 4 seems to have sharper contrast, with stronger peaks and valleys of the contact force with time, compared to the experimental curve. As mentioned in Section 3.2, the sampling frequency of the data acquisition system used in the drop-weight experiments is limited to 200 kHz per sensor, which limits the signal contrast. This particularly causes a large difference between the experimentally determined PCF and that computed from the FE analysis. In addition to sampling limitation, the influence of the surface texture of the slab (as discussed in Section 4.1) in slightly slowing down the drop-weight assembly, before the impact head starts compressing the bulk of the material, may also result in smaller PCF compared to the computed PCF. The FE analysis assumes perfectly flat slab surface. In spite of this discrepancy between the two curves in terms of signal contrast, the computationally determined response shows a good overall agreement with the experimental force-time history, as the area under the force-time curve (impulse or change of momentum) is approximately the same for both the curves. Although the computationally determined PCFs are significantly higher than the experimentally observed PCFs, the maximum computed displacements closely match the maximum displacements derived from the observed acceleration-time histories. The PCFs and maximum head displacements are computed and compared with the corresponding experimental impacts in Table 4. Almost all the experimentally determined maximum displacements are greater than those determined by the FE analysis except the 3.25 m/s velocity impact on Cor-Tuf slab. This may be due to the crushing of small asperities on the surface of

the slabs, as discussed in Section 4.1. These asperities are of the order of 100 μm, which is consistent with the difference between the experimental and computed maximum displacements. Overall, the error in displacement estimation is b 13% for all the load cases investigated in this study. 5.2. Stresses and strains The hydrostatic pressure, p = −(σ1 + σ2 + σ3) / 3, at the centroidal sections (a section containing the centroid of the slab that is parallel to one of the four lateral sides of the slabs) of HSHDC and Cor-Tuf slabs is plotted in Fig. 10 for three particular points on the force-time and displacement-time histories. The first point corresponds to the peak contact force (F = PCF); the second point signifies the point where the impact head reaches its bottommost position (δ = δmax); and the third point corresponds to the point where the impact head loses contact with the slab specimen during rebound (i.e. F = 0 on the forcetime history). At F = PCF in Fig. 10, the conical shape of the pressure contours at the slab sections of both the materials resemble that of a classical beam under flexure loads with compressive stresses (green, yellow, and red) at the top and tensile stresses (dark blue) at the bottom. As the slabs bend, higher compressive stresses are visible (as more intense red color on top) in the HSHDC slab section due to its greater tensile resistance than the Cor-Tuf slab. The neutral axis (light blue contour) is high, near the top, in both the slabs indicating inelastic deformation

Fig. 9. Damage condition of the HSHDC slab #1 after impact #20 with 50 mm head at 3.25 m/s.

R. Ranade et al. / Cement and Concrete Research 98 (2017) 24–35 Table 4 Comparison of FE analysis with experimental results of the first impact. Material

HSHDC

Cor-Tuf

a

Impact velocity (m/s)

2.30 3.25 4.60 2.30 3.25 4.60

Peak contact force (kN)

Maximum displacement (mm)

FEA

Exp.

Errora

FEA

Exp.

Errora

100 121 146 107 134 141

57 77 103 64 87 105

75.4% 57.1% 41.7% 67.2% 54.0% 34.3%

1.04 1.64 2.59 1.05 1.82 3.31

1.15 1.66 2.78 1.10 1.62 3.49

−9.6% −1.2% −6.8% −4.5% 12.3% −5.2%

Error (%) = (FEA − Exp) / Exp × 100.

during the downward motion of the impact head. At δ = δmax, low compressive stress (cyan and green) contours are visible at the distal face of the slabs, as the maximum tensile stress (dark blue) contour moves upward in both HSHDC and Cor-Tuf slabs. Overall, the hydrostatic pressure profiles at the centroidal sections of the slabs are similar to that of a beam undergoing flexural vibrations, and the stresses generated in the HSHDC slab are higher than that in the Cor-Tuf slab due to superior tensile performance of the HSHDC material. The computed maximum principal (tensile) strain distribution at the distal face of the slabs at maximum head displacement (δ = δmax) is shown in Fig. 11. The tensile strains increase with increasing head displacement. Due to the flexural mode of deformation and the boundary conditions, largest strains occur at the center of both HSHDC and CorTuf slabs fanning out toward the thirds of the slab edges. However, the strain pattern is highly diffused in HSHDC slab as compared to Cor-Tuf slab. As pointed out in Section 4.2, the tensile ductility of HSHDC allows the material to spread the damage evenly, which is not possible in Cor-Tuf due to its tensile softening behavior. As a result, while the maximum principal strain remains under 1% in HSHDC slab at all points, they are as high as 3% in the Cor-Tuf slab. The tensile strain capacity of the Cor-Tuf is an order of magnitude lower than 3% (Fig. 1), which physically results in severe spalling at the distal face. In the experimentally observed failure crack pattern in the Cor-Tuf slabs (Fig. 6), the major crack seems to follow one (weaker) of the two crack branches (seen in the computed strain distribution) in each quadrant of the slab. Thus, the positive influence of the material's tensile

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ductility on the diffusion of the maximum principal strain at the distal face of the slab is clearly noticeable in the computed strain distributions. The minimum principal (compressive) stress distribution at the frontal face of the slabs is shown in Fig. 12. Fan-shaped compressive stress contours appear at the frontal face of the slabs, similar to the tensile stress contours at the distal face. As discussed above, the compressive stress is higher at the frontal face of the HSHDC slab than the CorTuf slab due to the greater tensile resistance of the former material in the inelastic stage. The diffusion of tensile strain at the distal face also assists in spreading the compressive stress more evenly at the frontal face of the HSHDC slab compared to the Cor-Tuf slab. This becomes particularly critical in the rebound stage, as tensile stress appears over a larger area at the frontal face of the Cor-Tuf slab compared to HSHDC causing spalling of the material there, which is visible in the experimental observations (Fig. 6). Thus, in spite of its higher compressive strength than HSHDC, the Cor-Tuf slab under dynamic loads cracks significantly at the compressive face due to lack of tensile ductility. 6. Conclusions and future work The structural resilience of HSHDC slabs, in comparison with Cor-Tuf slabs, under drop-weight impact loads is demonstrated in this paper. The influence of impact loads on the slabs of both materials is investigated experimentally, using drop-weight tests, as well as through FE analysis using LS-Dyna. The following conclusions can be drawn from the investigations reported in this paper. • Under multiple drop-weight impacts, while HSHDC slabs maintain their impact load-bearing capacity (as measured by the PCF) up to 20 impacts and structural integrity, Cor-Tuf slabs gradually lose their capacity and fail before the 20th impact. Increasing the impact velocity causes more rapid reduction of PCF of Cor-Tuf slabs with the number of impacts, whereas, it has negligible effect on the behavior of HSHDC slabs, which exhibit almost no reduction in PCF with the number of impacts at all velocities investigated in this study. • Reduction in the size of the impact head causes premature punching shear failure in Cor-Tuf slabs. This catastrophic mode of failure is not observed in HSHDC slabs. While the Cor-Tuf slabs exhibit quasibrittle flexural and shear failures accompanied by large localized

Fig. 10. Computed hydrostatic pressure distributions at the centroidal sections of HSHDC and Cor-Tuf slabs.

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Fig. 11. Comparison of computed maximum principal (tensile) strain distribution at the distal face of HSHDC and Cor-Tuf slabs at maximum head displacement.

cracks and excessive spalling, the HSHDC slabs exhibit ductile flexural behavior (without failure until 20 impacts) with well-distributed multiple fine radial cracks with almost no spalling, regardless of the impact head diameter. • The drop-weight experiments and the structural response of HSHDC and Cor-Tuf slabs were satisfactorily simulated in LS-Dyna. In particular, the response parameters involving time-integration, such as displacement and area under the force-time curve (impulse), showed good agreement with the experimental results. Although there is a large discrepancy in the predicted PCFs as compared to experimentally determined PCFs of the slabs, it may be attributed to the experimental limitation of sampling frequency; additional experiments with higher sampling frequency are required to confirm this hypothesis. • The FE analysis revealed that the tensile strain is evenly diffused at the back faces of the HSHDC slabs (due to flexural deformation) even under the most energetic impact investigated in this study, which supports the experimental observation of multiple fine cracks. In

contrast, the FE analysis of the Cor-Tuf slab exhibits strain concentrations at the back face, which are consistent with the experimental observation of large (mm sized) cracks and early failure. The FE analysis shows that the ductile structural response of the HSHDC slab is a direct result of the material's tensile ductility, whereas a lack thereof causes a quasi-brittle behavior as observed in the Cor-Tuf slabs. Overall, the experimental observations and the finite element analysis presented in this study support the hypothesis that the combination of high compressive strength and tensile ductility of HSHDC translate into better impact resistance than Cor-Tuf. Although this paper will serve as a benchmark for HSHDC properties under impact (and potentially blast) loads in future work on larger structures, there is substantial need for further research to make HSHDC a viable material for protective structures. The tensile properties of HSHDC are dependent on the orientation distribution and dispersion homogeneity of the PE fibers, which further depends on the shape and

Fig. 12. Comparison of computed minimum principal (compressive) stress distribution at the frontal face of HSHDC and Cor-Tuf slabs at maximum head displacement.

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dimensions of the specimen mold. Although the change in fiber distribution can be incorporated in the finite element model by appropriately varying the material properties, tension (and compression) specimens sawed out from the slabs (instead of directly cast dogbones) should be used in the future for more accurate determination of material properties. Impacts and blasts caused by weapons generate 2–3 orders of magnitude greater strain rates in the material. Material characterizations at multiple length scales using Kolsky bar and shock tube are underway to understand the material performance at such high strain rates. Similar to Cor-tuf and other FR-UHPCs, HSHDC members with and without conventional steel reinforcement will be tested in the future to meet given structural performance criteria such as penetration depth, crater diameter, perforation, mass loss, frangibility, and energy absorption. Acknowledgements This research at the University of Michigan was supported by a research contract (W912HZ-08-C-0056) from the U.S. Army ERDC, Vicksburg, MS. Helpful discussions with T. Rushing, T. Slawson, B. Williams, and J. Davis of ERDC are gratefully acknowledged. The authors also acknowledge the material suppliers Honeywell, Lafarge-Holcim, Bekaert, US Silica, Elkem, and WR Grace, for providing materials for this research. Permission to publish was granted by the Director, Geotechnical and Structures Laboratory at ERDC. References [1] C.D. Eamon, P. Fitzpatrick, D.D. Truax, Observations of structural damage caused by hurricane Katrina on the Mississippi Gulf Coast, J. Perform. Constr. Facil. 21 (2007) 117–127. [2] J. Padgett, R. DesRoches, B. Nielson, M. Yashinsky, O. Kwon, N. Burdette, E. Tavera, Bridge damage and repair costs from hurricane Katrina, J. Bridg. Eng. 13 (2008) 6–14. [3] S. El-Tawil, E. Severino, P. Fonseca, Vehicle collision with bridge Piers, J. Bridg. Eng. 10 (2005) 345–353. [4] E. Eskew, S. Jang, Impacts and Analysis for Buildings Under Terrorist Attacks, University of Connecticut, 2012 (CEE Articles) http://digitalcommons.uconn.edu/cee_articles/1. [5] AASHTO, LRFD Bridge Design Specifications, American Association of State Highway and Transportation Officials, Washington, DC, 1998. [6] R.P. Kennedy, A review of procedures for the analysis and design of concrete structures to resist missile impact effects, Nucl. Eng. Des. 37 (1976) 183–203. [7] A. Hummeltenberg, B. Beckmann, T. Weber, M. Curbach, Investigation of concrete slabs under impact load, Appl. Mech. Mater. 82 (2011) 398–403. [8] M.E. Mohamed, E.M. Eltehawy, I.M. Kamal, A.A. Aggour, Experimental analysis of reinforced concrete panels penetration resistanceProceedings of the 13th International Conference on Aerospace Sciences and Aviation Technology 2009, pp. 26–28 (ASAT-13). [9] H. Ross Jr., D. Sicking, R.A. Zimmer, J.D. Michie, Recommended Procedures for the Safety Performance Evaluation of Highway Features, Transportation Research Board, Washington DC, 1993. [10] ACI Committee 440, Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures(ACI Technical Documents ACI440.2R-02) 2002. [11] J. Kasan, K. Harries, R. Miller, R. Brinkman, Limits of application of externally bonded CFRP repairs for impact-damaged prestressed concrete girders, J. Compos. Constr. 18 (2014), A4013013. [12] P. Sukontasukkul, S. Jamnam, M. Sappakittipakorn, N. Banthia, Preliminary study on bullet resistance of double-layer concrete panel made of rubberized and steel fiber reinforced concrete, Mater. Struct. 47 (2014) 117–125. [13] S. Mindess, N. Banthia, C. Yan, The fracture toughness of concrete under impact loading, Cem. Concr. Res. 17 (1987) 231–241. [14] S. Mindess, L. Zhang, Impact resistance of fibre-reinforced concrete, Proc. Inst. Civ. Eng. Struct. Build. 162 (2009) 69–76. [15] A.E. Naaman, V.S. Gopalaratnam, Impact properties of steel fibre reinforced concrete in bending, Int. J. Cem. Compos. Light. Concr. 5 (1983) 225–233. [16] E.F. O'Neil, B.D. Neeley, J.D. Cargile, Tensile properties of very-high-strength concrete for penetration-resistant structures, Shock. Vib. 6 (1999) 237–245. [17] V. Bindiganavile, N. Banthia, Polymer and steel fiber-reinforced cementitious composites under impact loading—part 1: bond-slip response, ACI Mater. J. 98 (2001) 10–16. [18] V. Bindiganavile, N. Banthia, Polymer and steel fiber-reinforced cementitious composites under impact loading—part 2: flexural toughness, ACI Mater. J. 98 (2001) 17–24. [19] V. Bindiganavile, N. Banthia, B. Aarup, Impact response of ultra-high-strength fiberreinforced cement composite, ACI Mater. J. 99 (2002) 543–548.

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