Critical parameters for the penetration depth in cement-based materials subjected to small caliber non-deformable projectile impact

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Critical parameters for the penetration depth in cement-based materials subjected to small caliber non-deformable projectile impact Fengling Zhang Formal analysis Investigation Writing – Original Draft , Leong Hien Poh Supervision Project administration Writing – Review & Editing , Min-Hong Zhang Supervision; Writing – Review & Editing PII: DOI: Reference:

S0734-743X(19)30770-5 https://doi.org/10.1016/j.ijimpeng.2019.103471 IE 103471

To appear in:

International Journal of Impact Engineering

Received date: Revised date: Accepted date:

11 July 2019 27 November 2019 5 December 2019

Please cite this article as: Fengling Zhang Formal analysis Investigation Writing – Original Draft , Leong Hien Poh Supervision Project administration Writing – Review & Editing , Min-Hong Zhang Supervision; Writing – Review & Editing , Critical parameters for the penetration depth in cement-based materials subjected to small caliber non-deformable projectile impact, International Journal of Impact Engineering (2019), doi: https://doi.org/10.1016/j.ijimpeng.2019.103471

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Highlights 

The influence of identified parameters on penetration depth is investigated.



Experimental matrix of cement-based materials across a wide range of compositions and material properties.



Effective hardness index and elastic modulus are found to have the most influence on penetration depth.

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Critical parameters for the penetration depth in cement-based materials subjected to small caliber non-deformable projectile impact Fengling Zhang, Leong Hien Poh, Min-Hong Zhang Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, 117576, Singapore Abstract It has been recognized that the compressive strength alone cannot accurately describe the penetration depth in cement-based materials subjected to high-velocity non-deformable projectile impact. This paper provides an in-depth investigation with the aim to determine critical effective properties for the penetration depth in cement-based materials across a wide range of compositions and material properties against small caliber non-deformable projectile impact. Compressive strength, elastic modulus, effective hardness index, density, splitting tensile strength, and flexural toughness are considered in the investigation. Cement-based materials investigated include cement pastes, mortars, concretes, ultra-high performance concretes (UHPCs), and engineered cementitious composites (ECCs) with 28-day compressive strengths from 34.2 to 220.2 MPa and elastic moduli from 17.1 to 80.4 GPa. The penetration resistance was evaluated using 300×170×150 mm3 specimens subjected to the impact of conical-nosed projectiles with a diameter of 8.0 mm and a mass of about 7.8 g at velocities of about 400.0 m/s. Within the range of effective properties considered, the effective hardness index and elastic modulus have the most influence on the penetration depth, as these two parameters characterize the overall contributions of constituent components (e.g. aggregate and matrix). It is also found that UHPCs do not exhibit better impact resistance in terms of penetration depth, in comparison to high performance concretes (HPCs) with coarse aggregate. Keywords Projectile impact; penetration depth; hardness; elastic modulus; concrete; UHPC

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Corresponding author. Tel.: +65 6516 4913; Fax: +65 6779 1635. E-mail address: [email protected] (L.H. Poh).

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1. Introduction Concrete has been widely used as a construction material for protective structures that are designed to withstand extreme loadings, such as impact and blast. One broad class of impact loads arises from high-velocity small caliber non-deformable projectiles caused by small arms or blastinduced fragments [1]. The uniaxial unconfined compressive strength of concrete has been universally accepted as a general index in structural analysis, and commonly used as a crucial parameter to be correlated to the concrete resistance against projectile impact, especially penetration depth. For example, the penetration depth of projectiles in concrete is considered to be inversely proportional to the square root of concrete compressive strength in many empirical and semi-empirical formulae proposed for the estimation of penetration depth [2]. With the advancement of concrete technology in recent decades, ultra-high performance concretes (UHPCs) and engineered cementitious composites (ECCs) have increasingly been used in practice. Such concretes may have different compositions compared to conventional concretes, e.g. UHPCs generally do not include coarse aggregate and the maximum aggregate size in UHPCs usually does not exceed 5 mm [3]. The changes in concrete compositions may affect the relationship between the penetration depth in concrete against projectile impact and its compressive strength, since these properties are governed by different parameters. Yankelevsky [4] recently revisited this issue to correlate the concrete penetration resistance to its compressive strength. He concluded that the compressive strength alone cannot be used to describe the concrete penetration resistance, and concrete compositions also play an important role on its resistance against projectile impact. Many studies have indicated the significance of concrete compositions, such as coarse aggregates and fibers, in the resistance of concrete against projectile impact. Zhang et al. [5] studied the impact resistance of concretes with compressive strengths ranging from 45 to 235 MPa. It was found that the penetration depth does not further reduce with increasing the compressive strength beyond a certain level, due to the elimination of coarse aggregate in order to achieve a higher compressive strength. An experimental study by Dancygier et al. [6] showed that the impact resistance of high strength

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concretes (HSCs) with compressive strengths of about 100 MPa, as measured by perforation limit velocity, front and rear face damaged areas, varies considerably due to their differences in mix compositions. Wu et al. [7] studied the effect of coarse aggregate type (corundum and basalt), size (5– 20, 35–45, and 65–75 mm) and volume fraction (30 and 45%) on the impact resistance of concretes with compressive strengths in the range of 102.5–129.2 MPa. It was reported that larger, stronger, and harder coarse aggregate reduces the local impact damage of concretes, including penetration depth, crater diameter, and crater volume. In general, concrete becomes more brittle with increasing compressive strength. Fibers are thus commonly incorporated in high performance concretes (HPCs) and UHPCs to reduce their brittleness. A major role of fibers on the impact resistance of concretes is to reduce the crater damage by arresting the crack propagation through their bridging effect. However, the effect of fibers on the penetration depth is not significant [5, 8]. These findings further confirm that the concrete resistance against projectile impact cannot be solely described by its compressive strength. It is also dependent on the characteristics of underlying material constituents. When a projectile hits a concrete target, the concrete surrounding the projectile nose is subjected to high-intensity triaxial stress states, together with volume changes and local material fracture [4]. The concrete resistance against projectile impact is thus influenced by its shear failure envelope, as well as its equation of state (EOS). However, it can be challenging and costly to determine the shear failure envelope and EOS of concrete. For example, the determination of shear failure envelope requires a triaxial test with a high pressure level (e.g. 1100 MPa reported in Refs. [4, 9]). Similarly, the determination of EOS requires a triaxial test or full-scale detonation/flyer-plate-impact test. It is also noted that these test data are not commonly available in the literature, hence limiting the use of shear failure envelope and EOS in practice. For practical engineering applications, a simple characterization of the overall resistance of cement-based materials against projectile impact is of interest. There is thus a need to identify and determine the suitable effective properties, which can be used to quickly assess the resistance of a cement-based material against projectile impact. Since penetration depth is the most important terminal ballistic factor in the design of impact-resisting

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structures and crater damage can be effectively controlled by the incorporation of fibers, this study will focus only on the penetration depth. The objective of this study is to determine the critical effective properties governing the penetration depth in cement-based materials across a wide range of not only compositions but also material properties, when subjected to impact of small caliber non-deformable projectiles. Based on information from literature review that will be discussed in Section 1.1, a series of effective properties is identified for investigation, including (1) compressive strength, (2) elastic modulus, (3) effective hardness index, (4) density, (5) tensile strength, and (6) flexural toughness. Considering the difficulty of determining the direct tensile strength of cement-based materials, the splitting tensile strength will be used instead of the direct tensile strength. The cement-based materials with a wide range of compositions including cement pastes, mortars, concretes, ECCs, and UHPCs were investigated in this study. The water to cementitious materials ratio (w/cm) ranged from 0.17 to 0.60. Effects of fine aggregate type (siliceous and bauxite sand) and maximum aggregate size (10 and 20 mm) were also investigated. Experimental results of these cement-based materials were analysed and compared. The resistance of cement-based materials against non-deformable projectile impact was evaluated by a gas gun system with impact velocities of approximate 400 m/s. The projectiles were fabricated from ASSAB XW42 steel and hardened to 6062 HRC with a diameter of 8 mm and a mass of about 7.8 g. 1.1. Literature review on effect of parameters of cement-based materials on penetration depth Over the years, research work have been conducted to enhance the understanding of the resistance of cement-based materials against projectile impact. The impact response of a cement-based material not only depends on its properties, but also depends on the properties of projectiles, e.g. projectile geometry, mass, and velocity. The literature review focuses mainly on the influence of various parameters of cement-based materials on the penetration depth subjected to non-deformable projectile impact. The influence of the properties of projectiles can be found in Refs. [10-12]. As there is no standard test method for the impact resistance of cement-based materials, the projectiles and target 5

geometries in the literature vary significantly. Hence, experimental details are included in the literature review to better understand the influence of various parameters on the penetration depth. 1.1.1. Compressive strength The penetration depth in cement-based materials subjected to projectile impact is related to their compressive strength, and it in general reduces with the increase in compressive strength [5-8, 13-18]. Dancygier and Yankelevsky [14] compared the penetration depths in normal strength concretes (NSCs) and HSCs. The NSC and HSC targets (400×400×60 mm3) were subjected to conical nose projectile (25 mm in diameter, 120 g in mass, and velocities from 85 to 230 m/s) impact. The penetration depths in the HSCs with compressive strengths of 95-110 MPa are 10-20% less than those in the NSCs with compressive strengths of 34-35 MPa. O’Neil et al. [15] compared the penetration depths in NSC, HSC, and UHPC targets (Ø762×914 mm3) impacted by ogive nose projectiles with a diameter of 26.9 mm, a mass of 906 g, and velocities of 229-754 m/s. The penetration depth in the UHPC with a compressive strength of 159 MPa is about 30% lower than those in the HSCs with compressive strengths of 90-104 MPa, and around 50% lower than those in the NSC with a compressive strength of 35 MPa. Zhang et al. [5] investigated the penetration depths in concretes (300×170×150 mm3) with compressive strengths from 45 to 235 MPa when subjected to impact by ogive-nosed projectiles (12.6 mm in diameter, 15 g in mass, 2.5 in caliber-radius-head, and velocities ranging between around 620 and 700 m/s). In general, the penetration depth reduces with an increase in the compressive strength of concretes. However, beyond a threshold value, the further increase in the compressive strength does not result in a reduction of the penetration depth. This is explained by the removal of coarse aggregate in concrete to achieve a higher compressive strength due to the improvement in the underlying material homogeneity. The presence of coarse aggregate appears to be beneficial to reduce the penetration depth. The influence of coarse aggregate will be discussed further in Section 1.1.4. Although the effect of compressive strength on the penetration depth has been extensively studied, it should be noted that some of the experimental studies in the literature cover narrow ranges in terms of compressive strengths and compositions. Accordingly, the conclusions in these studies may not be 6

applicable beyond the ranges of the compressive strengths and compositions considered. Besides the compressive strength, limited information on other properties of cement-based materials is available in these experimental studies. Moreover, the compressive strength may be determined by different specimen shapes and sizes in these studies, which makes the comparison of results from different studies difficult. In summary, there is a lack of information in the literature on the effect of compressive strength, other material properties and compositions on the penetration depth across a wide range of cement-based materials including NSCs, HSCs, HPCs, UHPCs, and ECCs. 1.1.2. Elastic modulus In earlier works, the elastic modulus was considered to have a secondary influence on penetration depth, as the elastic moduli of concretes in general vary within a narrow range [2, 10]. The influence of elastic modulus was thus not considered in almost all empirical formulae for the estimation of penetration depth [2]. This is probably valid for conventional concretes. However, with the introduction of newly developed cement-based materials, such as UHPCs and ECCs, the elastic modulus can vary over a wide range, and may thus have a non-negligible influence on the penetration depth. Recently, an experimental study by Wang et al. [18] showed that the penetration depth reduces with an increase in the elastic modulus of cement-based materials. Their study included three HSCs with coarse aggregate, one high strength mortar (HSM), and two ECCs without coarse aggregate. Therewith, the HSCs have much higher elastic moduli than the HSMs and ECCs. However, the experimental data in Wang et al. [18] are limited. Hence, the effect of elastic modulus needs further investigation. 1.1.3. Hardness The experimental study by Wang et al. [18] on the resistance of cement-based materials (600×600×400 mm3) subject to ogive-nosed projectile (28 mm in diameter, 249 g in mass, 3 in calibre-radius-head, and velocities of 400 and 600 m/s ) impact showed that the penetration depth decreases with an increase in the effective hardness index, which is defined as the weighted hardness of mortar matrix and embedded coarse aggregate based on their relative proportions along the 7

projectile trajectory. More details on the definition of effective hardness index can be found in Wang et al. [18]. Due to limited experimental data in Wang et al. [18], the influence of effective hardness index also needs to be further studied to understand the role of hardness on the resistance of cementbased materials. 1.1.4. Constituent materials The resistance of cement-based materials to projectile penetration also depends on their constituent components, including coarse aggregate, fine aggregate, and fibers [4-6, 13]. The influence of these constituent components on the penetration depth will be discussed in this section. (1) Coarse and fine aggregates The experimental study by Zhang et al. [5] indicated that the incorporation of granite coarse aggregate appears to be beneficial to the impact resistance in terms of a reduction in penetration depth. Coarse aggregate may act as barriers to the projectile penetration and crack propagation. Based on the mass loss of projectiles after striking against cement-based material targets, Wang et al. [18] reported that the coarse aggregate can provide additional friction to the projectile penetration, thus reduce the penetration depth. Another experimental study of Zhang et al. [8] further confirmed that the higher strength aggregate with larger sizes can decrease the penetration depth, as long as the workability of concrete is satisfactory and the maximum aggregate size meets the requirements of structural applications. A similar experimental result was also reported by Wu et al. [16] with basalt coarse aggregate. The influence of coarse aggregate type (corundum and basalt), size (5-20, 35-45, and 65-75 mm), and volume fraction (30 and 45%) on the penetration depth was also studied by Wu et al. [7]. The beneficial effect of aggregate is not limited only to those of larger sizes. In the experimental study of Wang et al. [18], the presence of fine aggregate (less than 0.25 mm) was shown to reduce the penetration depth to some extent. Dancygier et al. [6] reported that the addition of fine aggregate increases the perforation resistance in terms of perforation limit velocity.

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The significance of aggregate on reducing the penetration depth is generally accepted [4-8, 18]. However, it is not clear which material properties of cement-based materials can reflect the contribution of aggregate. Coarse and fine aggregates may affect the density [19, 20], compressive strength [21, 22], elastic modulus [21, 23], effective hardness index [18], tensile strength [23, 24], and flexural toughness [25, 26] of cement-based materials. The influence of these parameters on the penetration depth needs further investigations to better understand the contribution of aggregate to the resistance of cement-based materials against projectile impact. (2) Fibers Plain concretes are brittle materials with low tensile strength and toughness. Fibers are commonly added to overcome these limitations, especially for HPCs and UHPCs. The influence of fibers, including steel (ST) fibers [5, 6, 8, 13, 16, 27-35], polypropylene (PP) fiber [8, 28, 29, 35, 36], polyethylene (PE) fibers [8, 27], polyvinyl alcohol (PVA) fibers [35, 37], Kevlar fibers [29], on the penetration depth under projectile impact has been studied extensively. There is a consensus that the incorporation of fibers does not have significant influence on the penetration depth [5, 6, 8, 13, 16, 18, 30-34, 36, 38], although a small amount of fibers (e.g. 0.5% steel fiber by volume) can effectively reduce the crater diameter (e.g. 20-40%) due to the bridging effect of fibers [8]. It should be noted that the compositions of cement-based materials in these studies do not vary significantly (e.g. type and size of coarse aggregate, type of fine aggregate, and other ingredients). For cement-based materials made of a wide range of compositions, the effect of fibers on the penetration depth has not been well studied. 1.1.5. Tensile strength and toughness The incorporation of fibers increases the tensile strength to a certain extent and enhances the toughness of cement-based materials substantially due to their bridging effects [32, 39, 40]. Although the presence of aggregate has an influence on the splitting tensile strength and flexural toughness [2326], the effect of fibers is much more pronounced. It has been reported by Le et al. [39] that the incorporation of 1% steel fibers by volume increases the splitting tensile strength of concrete with a 9

w/cm of 0.26 by more than 80%. The effect of tensile strength and toughness on the penetration depth is thus similar to that of fibers, as discussed in Section 1.1.4 [1, 18]. Similar to the influence of fibers, the tensile strength and toughness do not substantially affect the penetration depth in concretes. The influence of tensile strength and toughness on the penetration depth in cement-based materials across a wide range of constituent materials, however, is still not immediately clear from literature. 1.2. Research significance The penetration depth in cement-based materials subjected to projectile impact cannot be solely characterized by their compressive strength. A better comprehension of critical effective properties for the penetration resistance of cement-based materials is becoming increasingly crucial in the design of impact-resisting structures. This study attempts to identify and determine the effective properties having the most influential effect on the penetration depth in cement-based materials when impacted by high-velocity small caliber non-deformable projectiles, across a wide range of compositions and material properties. The experimental results of this study will provide basic information on the resistance of cement-based materials to projectile penetration, give fundamental insights into the quick assessment of penetration depth and selection of materials for the design of protective structures, towards more effective and economical impact-resisting structures. 2. Experimental details 2.1. Materials ASTM Type I ordinary Portland cement (also complying with EN CEM I 52.5N) and tap water were used for all cement-based materials. Undensified silica fume1 that satisfies ASTM C1240 [41] was used for cement-based materials with low w/cm. Class F fly ash satisfying ASTM C618 [42] was used for a PVA fiber reinforced ECC (ECC-PVA). Siliceous sand (main composition: SiO2) with a specific gravity of 2.63 was used as fine aggregate in mortars and concretes. Bauxite sand (main composition: Al2O3) with a specific gravity of 3.20 was used in some mortar mixtures for comparison.

1

Elkem Microsilica Grade 940U, Norway

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Sieved quartz sand (main composition: SiO2) with particle sizes less than 0.25 mm was used in the ECC-PVA mixture. Crushed granites with maximum aggregate sizes of either 10 mm or 20 mm and a specific gravity of 2.65 were used as coarse aggregate in concretes. To avoid any possible effect from the fine dust on the surface of 20-mm granite aggregates as reported in Ref. [18], these granite aggregates were washed before use. The particle size distributions of the siliceous sand, bauxite sand, 10-mm granite aggregate, and 20-mm granite aggregate are shown in Fig. 1. Bauxite sand was sieved and re-combined to minimize the differences in the particle size distributions between bauxite and siliceous sand. The properties of straight brass-coated steel fibers2, PE fibers3, and PVA fibers4 used in this study are given in Table 1. A polycarboxylate-based superplasticizer 5 with a specific gravity of 1.1 was used in the cement-based materials with silica fume/fly ash, whereas a naphthalene-based superplasticizer 6 with a specific gravity of 1.2 was used in the cement-based materials without silica fume/fly ash for workability purposes. 100

Passing (%)

80

Siliceous sand Bauxite sand 10-mm granite aggregate 20-mm granite aggregate

60 40 20 0 0.01

0.1

1

10

100

Sieve size (mm)

Fig. 1. Particle size distributions of siliceous sand, bauxite sand, 10-mm granite aggregate, and 20-mm granite aggregate

2

Dramix@, Bekaert, Belgium Pte., Ltd., Belgium SPECTRA fiber 900, Honeywell, Japan 4 Kuralon REC-15, Kuraray Co., Ltd., Japan 5 ADVA 181N, GCP Applied Technologies, Singapore 6 DARACEM 100, GCP Applied Technologies, Singapore 3

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Table 1. Properties of steel, PE, and PVA fibers

Steel (ST) fiber

Length Diameter (mm) (µm) 13 160

Elastic modulus (GPa) 200

Tensile strength (MPa) 2500

Density (kg/m3) 7800

Polyethylene (PE) fiber

12

39

66

2610

970

Polyvinyl alcohol (PVA) fiber

12

40

41

1612

1300

Fiber type

2.2. Mix proportions and specimen preparations Mix proportions of cement-based materials are given in Table 2. To achieve a wide range of compositions, cement pastes, mortars, concretes, ECCs, and UHPCs were investigated with w/cms ranging from 0.17 to 0.60. All cement pastes, mortars, and concretes were reinforced with 0.5% steel fibers by volume to prevent the splitting of specimens after impact test, which enables the measurement of penetration depth in tested specimens. Compared to conventional concrete, ECCs show enhanced shatter resistance with reduced spalling, scabbing, fragmentation, and damaged zone against projectile impact [27]. Two ECCs with different fibers were included for comparison: the first being a typical ECC with high volume fly ash and 2% PVA fibers by volume developed by Wang and Li [43] to attain high tensile strain capacity; the other being a hybrid-fiber reinforced ECC (0.5% steel fibers and 1.5% PE fibers by volume) developed by Maalej et al. [27] to achieve a desired balance between strain capacity and ultimate strength for impact resistance. The behavior of UHPCs subjected to high-velocity projectile impact is not well understood and the relevant information is limited. Thus, four UHPCs with 28-day Ø100×200-mm cylinder compressive strengths exceeding 150 MPa were also included in this study. One was fabricated in laboratory with a maximum aggregate size of 4.75 mm and cured under ambient temperature, whereas the other three were commercially-available proprietary products from various sources. Cement-based materials without coarse aggregate, e.g. cement pastes, mortars, ECCs, and UHPCs, were mixed using a Hobart mixer while cement-based materials with coarse aggregate, e.g. concretes, were mixed using a pan mixer at an ambient temperature of about 30°C. To prevent fiber balling, the

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steel, PE, and PVA fibers were added manually at the final step. The PE and PVA fibers were broken loose using compressed air before adding to the ECCs. The flowabilities of cement pastes, mortars, ECCs, and UHPCs were determined according to BS EN 1015-3 [44], whereas the flowabilities of concretes were determined according to BS EN 12350-3 [45]. The target flowabilities (Table 2) were chosen to ensure consolidations. No segregation of steel fibers was observed for all cement-based materials. After casting, all specimens were left in the casting room and covered by plastic sheets to prevent moisture loss. All specimens were deomolded after 24 hours and cured in a fog room for another 6 days, followed by exposure in the laboratory air until testing at specified ages.

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Table 2. Mix proportions of cement-based materials including cement pastes, mortars, concretes, ECCs, and UHPCs Coarse aggregate Mix proportions (kg/m3) Fine Mix ID w/cm aggregate Maximum Type Cement SF FA Water C.A. F.A. type size (mm) ST FRCP-0.35 0.35 ---1327 133 -511 --39 Cement FRCP-0.28 0.28 ---1479 148 -455 --39 pastes FRCP-0.17 0.17 ---1803 180 -337 --39 FRM-0.60 0.60 Siliceous --549 --330 -1288 39 FRM-0.28 0.28 Siliceous --751 75 -231 -1288 39 FRM-0.17 0.17 Siliceous --901 90 -168 -1288 39 Mortars FRM-0.60B 0.60 Bauxite --549 --330 -1567 39 FRM-0.28B 0.28 Bauxite --751 75 -231 -1567 39 FRM-0.17B 0.17 Bauxite --901 90 -168 -1567 39 FRC-0.60 0.60 Siliceous Granite 10 359 --216 946 810 39 FRC-0.50 0.50 Siliceous Granite 10 410 --205 946 760 39 Concretes FRC-0.35 0.35 Siliceous Granite 10 480 --168 946 776 39 FRC-0.28 0.28 Siliceous Granite 10 450 45 -139 946 772 39 FRC-0.28-20 0.28 Siliceous Granite 20 433 43 -133 1006 743 39 ECC-ST+PE 0.25 ---1478 148 -414 --39 ECCs ECC-PVA 0.25 Siliceous --587 -704 323 -469 -UHPC 0.17 Siliceous --987 175 -197 -987 156 Proprietary-1 -----------UHPCs Proprietary-2 -----------Proprietary-3 ------------

Fibers PE --------------14.4 ------

PVA ---------------26 -----

SP 1.7 4.0 16.6 0 4.3 12.7 0 3.6 15.9 0 2.0 8.0 10.0 8.0 7.2 5.8 21.0 ----

Flow 190mm 185mm 180mm 200mm 155mm 150mm 195mm 160mm 160mm 4s 5s 5s 5s 6s 160mm 190mm 150mm ----

Note: 1 w/cm – water to cementitious materials ratio, SF – silica fume, FA – fly ash, C.A. – coarse aggregate, F.A. – fine aggregate, ST – steel fiber, PE – polyethylene fiber, PVA – polyvinyl alcohol fiber, SP – superplasticizer, FRCP – steel fiber reinforced cement paste, FRM – steel fiber reinforced mortar, FRC – steel fiber reinforced concrete, ECC – engineered cementitious composite, UHPC – ultra-high performance concrete. 2 Due to excessive bleeding and segregation of steel fibers, cement pastes with w/cms of 0.50 and 0.60 are not successfully fabricated. The concrete with a w/cm of 0.17 is abandoned because of unsatisfied workability and consolidation.

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2.3. Test methods 2.3.1. Material characterization of cement-based materials Table 3 summarizes the test methods and specimen information used in this study. The identified effective properties of cement-based materials were determined according to relevant standards (Table 3). Rockwell hardness is widely used in material characterization and quality control of materials due to its non-destructive nature, rapid measurement, and ease of application (no special requirements required for specimens) [46]. The Rockwell hardness of a material is determined by measuring the depth of indentation under a total test force compared to that obtained under a preliminary test force. Recently it has been applied to cement-based materials [18]. In this study, Rockwell hardness was determined from the side casting surfaces of 100 mm3 cubes. A 1/16-inch (1.6-mm) diameter ball indenter with a preliminary test force of 3 kgf (29 N) and a total test force of 15 kgf (147 N) was adopted to obtain a reasonable range of hardness for all cement-based materials according to the recommendation in Ref. [46] and an earlier study by Wang et al. [18]. In the present study, Rockwell hardness is classified as the Rockwell superficial hardness with a scale symbol of HR15T according to ASTM E18 [47]. For each cement-based material mix design, a total of at least 100 indentation readings were taken on three 100 mm3 cubes. For the hardness test in this study, a cement-based material is considered as a two-phase composite: one phase comprising of cement paste/mortar (cement paste with fine aggregate), with coarse aggregate constituting the second phase. Here, cement paste/mortar are classified collectively as one single phase since the constituent components of them (e.g. hardened paste or/and fine aggregate) are generally smaller than the projectile size used. This is partially motivated by the fact that it can be challenging to determine the hardness of fine aggregate, given its small size. More specifically, concrete is assumed to be a two-phase composite with coarse aggregates evenly embedded in mortar matrix, while cement paste, mortar, ECC, and UHPC are assumed to be single phase materials due to the absence of coarse aggregate. The interfacial transition zone (ITZ) between coarse aggregate and mortar matrix is not considered for simplicity. 15

Table 3. Test methods and specimen information in material characterization and high-velocity impact test Properties

Test methods

Density Compressive strength

Specimens Size (mm3)

Number1

ASTM C39 [48]

100 200

At least 3

ASTM C39 [48]

100 200

At least 3

Wang et al. [18]

100 200

At least 3

Elastic modulus

ASTM C469 [49]

100 200

At least 3

Poisson’s ratio

ASTM C469 [49]

100 200

At least 3

Compressive stress-strain behavior

Rockwell hardness Splitting tensile strength Flexural toughness and load-deflection behavior High-velocity impact test

Wang et al. [18], ASTM E18 [47] ASTM C496 [50]

100 100 100 100 200

At least 3

Testing ages After demold 28 days, date of impact test2 28 days 28 days, date of impact test2 28 days 28 days, date of impact test2

At least 3

28 days

ASTM C1609 [51]

100 100 400

At least 3

28 days

Zhang et al. [5]

300 170 150

3-73

Date of impact test2

Note: 1 The number of specimens at each specified testing age. A new specimen is used for each testing. 2

At around 91 days after casting.

3

At least 3 specimens for each cement paste and mortar mixture, at least 5 specimens for each concrete

mixture with 10-mm coarse aggregate, at least 7 specimens for each concrete mixture with 20-mm coarse aggregate, at least 4 specimens for each ECC and UHPC mixture.

It should be pointed out that the Rockwell hardness test, which is done on the surface of 100 mm3 cubes, generally gives an indentation depth of less than 1 mm [18, 52]. For concrete, the measured hardness value is thus mainly a characterization of the mortar matrix near the surface, instead of the concrete composite. This motivates the definition of an effective hardness index in our earlier work [18] as an overall characterization of the concrete resistance against high-velocity non-deformable projectile impact. When subjected to a projectile impact, the penetration of the projectile in a concrete target is dependent on the relative fractions of its constituent components (e.g. coarse aggregate and mortar matrix) along the projectile trajectory. The effective hardness index (

) of concrete is thus

defined as the weighted hardness of coarse aggregate and mortar matrix, based on their relative fractions along the projectile trajectory, which will be discussed in the next paragraph. However, as mentioned in the preceding paragraph, cement paste, mortar, ECC, and UHPC are considered as single

16

phase materials due to the absence of coarse aggregate. The measured hardness values of these materials from the surface of 100 mm3 cubes are thus regarded as their “effective” hardness indices. For concrete, its coarse aggregate and mortar matrix are idealized as cubic volumes along the projectile trajectory, as illustrated in Fig. 2. The one-dimensional (1D) equivalent length of coarse aggregate and mortar matrix along the projectile trajectory is defined as respectively, where

and

matrix cubes, respectively,

√

and

√

,

are the 1D equivalent lengths of idealized coarse aggregate and mortar and

are the volume fractions of coarse aggregate and mortar matrix

in concrete, respectively. The relative fractions of coarse aggregate and mortar matrix along the projectile trajectory are calculated as

⁄(

) and

⁄(

) , respectively. The effective

hardness index of concrete is defined as Eq. (1). As fibers do not have significant effect on the penetration depth [5, 8, 16], fibers are not accounted for in the determination of effective hardness index [18]. (1) where

and

are the hardness values of coarse aggregate determined from natural rock (93.7 ±

3.3 HR15T for granite) and mortar matrix determined from the side casting surface of concrete specimens.

Projectile trajectory

Mortar matrix

lm

Coarse aggregate

lca

Fig. 2. Schematic diagram of idealized coarse aggregate and mortar matrix cubes for determining the effective hardness index of concrete 2.3.2. Impact tests of cement-based materials A gas gun facility with a 12.7-mm bore (Fig. 3(a)) was used for impact tests. As shown in Fig. 3(b), conical-nosed projectiles with a head of 60°C, a diameter of 8 mm, and a mass of around 7.8 g were used, which were fabricated from ASSAB XW-42 grade steel and hardened to 60-62 HRC to 17

ensure negligible deformation of the projectiles (Table 4). The ASSAB XW-42 is a high-carbon, highchromium steel alloyed with molybdenum and vanadium. The projectiles used in this study are equivalent to NATO 7.62×39 mm Armor-Piercing Incendiary (API-BZ) that covers most of the loads caused by small caliber arms and fragments generated by an explosion [53-55]. A specially designed sabot (polypropylene plastic, mass of about 1.72 g) was fixed onto the projectile for proper fitting into the barrel diameter. The projectiles were propelled by compressed helium gas at a pressure of about 35 bar to achieve impact velocities of about 400 m/s. To ensure consistency, a new projectile was used for each impact test. Table 4. Physical and mechanical properties of ASSAB XW-42 grade steel Material XW-42

Density Elastic Poisson’s Ultimate strength Yield strength Rockwell 3 (kg/m ) modulus (GPa) ratio (MPa) (MPa) hardness (HRC) 7700 210 0.30 2950-3100 2150-2200 60-62

High-velocity projectile impact tests were conducted using specimens with a dimension of 300×170×150 mm3 (thickness of 150 mm) at around 91 days after casting to minimize the effect of testing ages. The target dimension was selected following some preliminary studies to ensure that no rear face damage (e.g. scabbing and perforation) occurs in all target specimens considered in this study. The targets used can thus be regarded as semi-infinite targets. A target dimension of 300×170×150 mm3 was also utilized in Refs. [5, 8, 27, 37]. Before each impact test, the front and rear faces of each specimen were whitewashed for better visualization. Thereafter, 10-mm grids were drawn on these faces. As illustrated in Fig. 3(a) and Fig. 4, each specimen was placed in a steel containment jip with a 10-mm steel plate backing, and aligned such that upon impact, the projectile trajectory is perpendicular to the center of impact face of each specimen. Steel plates were placed against the two side faces of each specimen to fill the gap between containment jip and specimen (Fig. 4), to restrain the specimen movement in the transverse direction during impact. The projectile impact velocity was measured using a pair of laser sensors placed sequentially in the projectile trajectory direction just before it struck against the specimen (Fig. 3(a)). Impact velocity was determined as

18

⁄

, where

is the distance between the two laser sensors (100 mm in this study),

is the

time interval between the spikes of the sensors as recorded by an oscilloscope.

(a)

Specimen chamber Gas gun system 150 mm

Firing pin

Gas chamber

100 mm

Barrel Projectile with sabot

(b)

Laser

Target

Helium gas cylinder

10-mm-thick steel plate

Steel containment jig

Steel bar Steel bar Steel block for support

24.3 mm

17.4 mm

18 mm

15 mm

60

Ø 8.0 mm

Ø 12.6 mm Sabots

Projectiles

Projectiles and sabots

Fig. 3. (a) Schematic set up of impact test, and (b) details of ASSAB XW42 grade steel projectile and corresponding sabot Due to the small projectile size, the extent of damage in concrete targets caused by the impact can thus be dependent on the constituent components which the projectile struck against. Therefore, 5-7 specimens were tested for each concrete mixture to account for the variability in experimental results (Table 3). The average values and standard deviations for each set of experimental tests were reported. It is highlighted that each target specimen was impacted by only one projectile to ensure consistency in test conditions. The practical limitation of having a projectile diameter that is smaller than the maximum aggregate size was also presented in other studies [5, 7, 32, 53, 54, 56-60]. Local impact damage induced in the specimens was evaluated through the penetration depth, equivalent crater diameter, and crater volume according to our earlier work [18]. The penetration depth was determined by measuring the distance from the impact face to the deepest point in the target. The equivalent crater diameter was defined as the diameter of an equivalent circle having the same area as the crater on the

19

impact face, which was determined by counting the number of 10-mm grids. The crater volume was determined by the volume of sand (maximum size of 0.25 mm) required to fill the crater in the target.

10-mm steel plate

Side face of target

Steel containment jip

Target

10-mm steel plate

10-mm steel plate Impact or front face of target

Fig. 4. Target specimen set up in steel containment jip One granite cylinder (Ø75×130 mm3) cored from the same source as coarse aggregate was also used to investigate the resistance of the granite specimen against projectile impact. Due to the constraints in obtaining a larger granite specimen, the granite specimen used is smaller than the cement-based materials. The granite cylinder was placed at the center of mold (300×170×150 mm3) with its surrounding filled with UHPC, as shown in Fig. 5. This procedure was also adopted by Li et al. [61]. Based on preliminary studies, the damage induced by projectile impact was confined to a localized area within the cross-sectional area of granite cylinder. The penetration depth obtained can thus be considered to be similar to that from a large granite specimen [61].

Wooden mold (300 170 150 mm3)

Granite core (Ø75 130 mm3)

UHPC

Fig. 5. Granite specimen preparation for impact test

20

3. Results and discussion 3.1. General description of experimental results 3.1.1. Characterization of cement-based materials and granite The identified effective properties of cement-based materials, including density, compressive strength, elastic modulus, effective hardness index, splitting tensile strength, and flexural toughness, are summarized in Table 5. The effective properties of granite which were determined from Ø75×130 mm3 cylinders cored from the same source as coarse aggregate are also included in Table 5 for comparison. Experimental details for the determination of granite effective properties can be found in Ref. [39]. 35 Cement paste Mortar Concrete

(a) 80

30

(b)

Cement paste Mortar Concrete

25

Load (kN)

Compressive stress (MPa)

100

60 40

20 15 10

20 0 0

5 5000

10000

15000

20000

25000

Strain (με)

0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Deflection (mm)

Fig. 6. Mechanical behavior of the cement paste, mortar, and concrete with compressive strengths of about 90 MPa under quasi-static loadings, (a) stress-strain behavior under uniaxial compression, and (b) load-deflection behavior under four-point bending From Table 5, it can be seen that the compressive strengths of cement-based materials at 28 days range from 34.2 to 220.2 MPa while the compressive strength of granite is 238.5 MPa. Furthermore, a wide range of other effective properties is also obtained, e.g. the elastic moduli from 17.1 to 80.4 GPa and effective hardness indices from 34.8 to 79.4 at 28 days. It is also noted that although the compressive strengths of the cement paste (FRCP-0.28), mortar (FRM-0.28), and concrete (FRC-0.35) are comparable at about 90 MPa, their stress-strain and load-deflection behaviors (Fig. 6), as well as other properties (Table 5), differ considerably. This indicates that the influence of constituent materials should be considered in the description of a specific cement-based material. 21

3.1.2. Resistance of cement-based materials and granite to projectile impact Table 6 summarizes the experimental results of the high-velocity impact tests of cement-based materials and granite targets, in terms of the penetration depth. The results of the equivalent crater diameter and crater volume are provided in Appendix A. Since this study focuses only on the penetration depth, the analyses and discussions will only involve the relevant results pertaining to penetration depth, for a clear and concise presentation. The influence of different effective properties on the equivalent crater diameter and crater volume will be presented in a future work. Representative photos of the post-test projectiles are shown in Appendix B. It can be seen that there are negligible deformation and damage for all projectiles, and thus can be regarded as non-deformable projectiles. Representative photos depicting the extent of damage on the front faces of the cement-based material and granite targets after impact are provided in Appendix C. Rear face damage, such as scabbing and perforation, was not observed for all specimens in the post-test examinations. With the addition of fibers (e.g. steel, PE, and PVA), all specimens stayed intact as a single piece after impact tests. This indicates the importance of incorporating fibers for the prevention of severe property losses and life injuries caused by the ejection of fragments from cement-based materials. The impact velocities of the projectiles varied from 380 to 435 m/s. The slightly different impact velocities may affect the penetration depth to some extent. Zhang et al. [5] reported that the penetration depth increases almost linearly with impact velocities ranging from about 250 to 650 m/s. This phenomenon was also observed by Maalej et al. [27] and Feng et al. [62]. The penetration depths are thus normalized with respect to the corresponding impact velocities in the present study. The average normalized penetration depths will be used for the following discussion, and this methodology was also adopted in Refs. [1, 5, 7, 8, 53, 55, 57, 59, 60, 63, 64]. As shown in Table 6, the normalized penetration depth in cement pastes decreases as the w/cm reduces from 0.35 to 0.28 and 0.17 and the compressive strength increases from 72.4 MPa to 93.8 MPa and 136.0 MPa. This demonstrates clearly that an enhanced cement paste contributes to the reduction of penetration depth. For a given compressive strength of about 90 MPa, the normalized

22

penetration depth in the mortar and concrete is about 35% and 50% less than that in the cement paste, respectively. This indicates that the presence of fine and coarse aggregates helps to decrease the penetration depth, an observation that is further supported by the much smaller penetration depth in the granite specimen. The beneficial effect of aggregate in reducing the penetration depth was also reported in our earlier work [18], where the impact resistance of cement-based materials with maximum aggregate sizes of either 10 mm or 20 mm (same as those in this study) was experimentally investigated using 28-mm-diameter, 249-g-mass non-deformable projectiles. The beneficial effect of aggregate is further demonstrated by the experimental results of the UHPCs. In spite of having much higher compressive strengths (>150 MPa), the normalized penetration depths in UHPCs (without coarse aggregate) are generally higher than those in HPCs with coarse aggregate. To achieve higher compressive strengths of above 150 MPa, coarse aggregate is usually removed in UHPCs to improve the underlying material homogeneity. The elimination of coarse aggregate increases the compressive strength, but does not result in a corresponding reduction of the penetration depth, which is consistent with those reported in Refs. [5, 8, 18]. To sum up, these observations imply that both the presence of aggregate and the improvement of cement paste matrix can benefit the impact resistance of cementbased materials in terms of a reduction in the penetration depth. The incorporation of aggregate seems more effective than the enhancement of cement paste matrix to reduce the penetration depth. It is also noted that for the same w/cm ratios, the normalized penetration depths in mortars with bauxite sand are about 10-24% lower than those with siliceous sand (Fig. 7). This indicates that bauxite sand appears to be more effective in decreasing the penetration depth. One possible reason is that the bauxite sand is stronger and harder compared to siliceous sand, and the use of bauxite sand enhances the mechanical properties of mortars. Detailed discussion on the effect of bauxite sand on the mechanical properties and impact resistance of mortars will be presented in a future work. The effect of aggregate size and volume fraction will be discussed in Section 3.3.

23

Normalized penetration depth (x10-3 mm/(m/s))

80 Mortars-siliceous sand Mortars-bauxite sand

-13.1%

70 60 50 40

-24.2%

-10.3%

30 20 10 0

0.60

0.28

0.17

w/cm

Fig. 7. Comparison of the normalized penetration depth in mortars with siliceous sand and bauxite sand As illustrated in Fig. 8, the mass losses of projectiles after striking against mortars and concretes are significantly higher than those after striking against cement pastes. It is also observed that in comparison to these targets with siliceous sand, the projectile mass losses are much higher for those with bauxite sand after impact tests. These observations imply that the presence of aggregate, particularly stronger and harder aggregate, can provide additional friction to the projectile during the penetration process. The projectile penetration depth in targets is reduced since a portion of kinetic energy is lost due to the abrasion to the projectile caused by the presence of aggregate. In addition, the aggregate can act as barriers to crack propagation and thus further decrease the penetration depth [5, 18].

Projectile mass loss (%)

1.0 0.9

Bauxite sand

0.8 0.7 0.6 0.5 0.4 Cement pastes Mortars Concretes UHPCs Granite

0.3 0.2 0.1 0.0 30

60

90

120

150

180

210

240

Compressive strength (MPa)

Fig. 8. Mass loss of projectiles after striking cement-based materials and granite specimens

24

3.2. Influence of identified effective properties on the penetration depth The influence of each identified effective property of cement-based materials on the normalized penetration depth is shown in Fig. 9. The compressive strength, elastic modulus, and effective hardness index at the date of impact tests were used. Due to the lack of experimental data for other effective properties at the date of impact tests, the density utilized was obtained after demolding, while those of splitting tensile strength and flexural toughness were determined at 28 days. It is noted that the identified effective properties may not be independent of one another. For example, the American Concrete Institute (ACI) Committee 318 [65] has recommended a relationship between compressive strength, elastic modulus, and density as is the elastic modulus of concrete (MPa),

for NSCs, where

is the density of concrete (kg/m3), and

is the

compressive strength of concrete (MPa). The ACI 318 model is applicable for NSCs with compressive strengths less than 42 MPa and densities between 1442 and 2563 kg/m3. In addition, it should be pointed out that the penetration depth is dependent on the combined effect of several different properties of cement-based materials, as indicated in Ref. [4]. However, the corresponding analyses are generally complicated since these properties may not be independent of one another. For ease of application in engineering practice, it is thus desirable to have a quick estimate of the penetration depth, for given projectile and target characteristics. While the identified effective properties may not be independent as mentioned above, it is highlighted that only the effect of each effective property is investigated respectively in this study.

25

Table 5. Material characterization of cement pastes, mortars, concretes, ECCs, UHPCs, and granite

Mix ID

w/cm

FRCP-0.35 Cement pastes

Mortars

Concretes

0.35

Fine aggregate type

Coarse aggregate Type

Max size

--

--

--

FRCP-0.28

0.28

--

--

--

FRCP-0.17

0.17

--

--

--

FRM-0.60

0.60

Siliceous

--

--

FRM-0.28

0.28

Siliceous

--

--

FRM-0.17

0.17

Siliceous

--

--

FRM-0.60B

0.60

Bauxite

--

--

FRM-0.28B

0.28

Bauxite

--

--

FRM-0.17B

0.17

Bauxite

--

--

FRC-0.60

0.60

Siliceous

Granite

10mm

FRC-0.50

0.50

Siliceous

Granite

10mm

FRC-0.35

0.35

Siliceous

Granite

10mm

FRC-0.28

0.28

Siliceous

Granite

10mm

FRC-0.28-20

0.28

Siliceous

Granite

20mm

ECC-ST+PE

0.25

--

--

--

ECC-PVA

0.25

Siliceous

--

--

UHPC

0.17

Siliceous

--

--

Proprietary-1

--

--

--

--

Proprietary-2

--

--

--

--

Proprietary-3

--

--

--

--

Granite3

--

--

--

--

ECCs

UHPCs

Granites

Density after demold (kg/m3) 2035 (2)1 2133 (1) 2341 (1) 2136 (3) 2232 (3) 2430 (5) 2467 (3) 2679 (3) 2778 (6) 2342 (3) 2389 (3) 2415 (2) 2449 (3) 2446 (4) 2027 (5) 1866 (3) 2492 (6) 2654 (34) 2567 (10) 2926 (7) 26502

Compressive strength (MPa) 28 days

Age of impact test

70.9 (5.4) 90.4 (5.3) 137.1 (5.4) 34.2 (0.4) 88.0 (2.7) 142.8 (4.6) 40.3 (0.3) 120.1 (0.5) 189.7 (3.4) 40.9 (1.6) 57.4 (0.9) 87.7 (2.0) 122.0 (1.9) 113.1 (1.9) 76.6 (2.8) 37.9 (2.3) 156.3 (2.0) -168.1 (10.1) 220.2 (4.1) 238.5 (12.2)

72.4 (4.6) 93.8 (5.7) 136.0 (2.3) 37.9 (0.2) 93.4 (1.4) 146.9 (1.4) 45.0 (0.3) 120.0 (2.4) 190.9 (3.4) 43.8 (1.3) 61.1 (0.2) 93.5 (2.8) 118.1 (3.4) 114.6 (3.6) 78.8 (3.8) 42.0 (1.2) 161.0 (7.6) 202.3 (8.5) 175.6 (13.9) 229.4 (4.1) --

Elastic modulus (GPa) 28 days 17.1 (0.5) 22.2 (0.6) 34.6 (0.9) 21.1 (0.6) 36.2 (0.2) 48.8 (0.5) 29.6 (0.9) 56.5 (2.1) 76.4 (1.7) 29.0 (1.1) 32.7 (0.2) 40.5 (0.8) 44.5 (1.1) 46.0 (0.7) 20.0 (0.4) 18.9 (0.4) 47.7 (0.4) -47.3 (1.4) 80.4 (0.6) 65.0 (7.2)

Note: 1 Experimental results are presented as average of at least three specimens with standard deviation in parentheses. 2 Experimental results are presented as average of two specimens. 3 Experimental results of granite are determined from Ø75×130-mm cylinders.

26

Age of impact test 18.7 (0.9) 22.9 (0.9) 36.0 (0.4) 21.5 (0.7) 36.7 (0.4) 49.5 (0.7) 30.1 (0.5) 56.8 (1.2) 77.7 (2.1) 29.4 (0.8) 33.9 (0.2) 41.4 (0.6) 46.7 (0.2) 48.2 (0.5) 20.7 (1.0) 20.6 (0.8) 47.8 (0.7) 58.3 (1.3) 48.7 (1.7) 80.9 (2.0) --

Poisson’s ratio, 28 days 0.30 (0.03) 0.28 (0.01) 0.26 (0.01) 0.21 (0.02) 0.21 (0.01) 0.20 (0.01) 0.21 (0.01) 0.21 (0.01) 0.23 (0.01) 0.21 (0.02) 0.21 (0.01) 0.21 (0.01) 0.20 (0.01) 0.20 (0.00) 0.26 (0.02) 0.22 (0.01) 0.20 (0.01) 0.21 (0.03) 0.20 (0.01) 0.23 (0.00) 0.22 (0.01)

Rockwell hardness (HR15T) 28 days 34.8 (3.2) 46.4 (3.9) 71.7 (3.9) 43.7 (7.7) 65.3 (4.9) 72.4 (4.6) 44.1 (8.1) 72.3 (4.4) 78.8 (4.6) 44.4 (7.7) 51.7 (6.5) 59.9 (6.5) 66.2 (5.7) 67.3 (6.3) 45.2 (7.8) 45.2 (6.7) 76.4 (4.2) -77.8 (3.3) 79.2 (4.1) 93.7 (3.3)

Age of impact test 39.5 (3.4) 52.8 (2.9) 73.6 (3.7) 46.2 (7.9) 69.3 (5.3) 76.2 (5.9) 50.1 (8.0) 74.2 (4.2) 80.0 (4.0) 47.3 (8.0) 55.6 (7.5) 64.2 (6.1) 69.1 (5.1) 69.7 (6.3) 47.4 (6.2) 54.1 (6.6) 76.8 (3.2) 83.4 (5.7) 77.9 (4.0) 80.5 (3.3) --

Effective hardness index

Splitting tensile strength (MPa), 28 days

28 days

Age of impact test

34.8

39.5

3.82

46.4

52.8

4.6

2

71.7

73.6

8.32

43.7

46.2

65.3

69.3

72.4

76.2

44.1

50.1

72.3

74.2

78.8

80.0

66.6

68.2

70.6

72.8

75.1

77.5

78.6

80.2

79.4

80.7

45.2

47.4

45.2

54.1

76.4

76.8

--

83.4

77.8

77.9

79.2

80.5

93.7

--

Flexural toughness (J), 28 days

4.1 (0.3) 6.4 (0.8) 13.6 (0.6) 4.9 (0.1) 8.8 (0.4) 14.8 (0.3) 4.6 (0.3) 5.8 (0.2) 8.8 (0.3) 9.8 (0.4) 11.0 (0.7) 8.9 (0.4) 7.1 (0.2) 19.9 (1.3) 22.8 (1.7) 26.0 (0.8) 19.2 (2.2)

15.6 (0.6) 18.4 (2.9) 57.3 (8.4) 15.9 (0.4) 19.1 (2.1) 71.8 (11.7) 18.1 (3.5) 35.4 (4.3) 84.3 (6.2) 17.4 (1.6) 17.7 (1.0) 33.7 (1.7) 51.1 (4.8) 51.2 (5.5) 61.8 (1.9) 22.1 (2.3) 198.9 (15.3) 240.3 (16.1) 167.3 (5.8) 116.7 (21.2)

10.62

--

Table 6. Penetration depth in cement-based materials and granite targets subjected to high-velocity non-deformable projectile impact Number of Compressive target Coarse Fiber strength at Impact Mix ID w/cm Fine aggregate specimens aggregate (by volume) impact tests velocity (m/s) for impact (MPa) 1 tests FRCP-0.35 0.35 --0.5% steel 72.4 (4.6)3 3 397.0 (11.1) Cement FRCP-0.28 0.28 --0.5% steel 93.8 (5.7) 3 399.2 (13.1) pastes FRCP-0.17 0.17 --0.5% steel 136.0 (2.3) 3 409.9 (6.7) FRM-0.60 0.60 Siliceous (4.75mm) -0.5% steel 37.9 (0.2) 3 412.3 (10.5) FRM-0.28 0.28 Siliceous (4.75mm) -0.5% steel 93.4 (1.4) 3 396.8 (0.0) FRM-0.17 0.17 Siliceous (4.75mm) -0.5% steel 146.9 (1.4) 4 409.2 (11.0) Mortars FRM-0.60B 0.60 Bauxite (4.75mm) -0.5% steel 45.0 (0.3) 3 426.1 (2.1) FRM-0.28B 0.28 Bauxite (4.75mm) -0.5% steel 120.0 (2.4) 3 420.3 (9.2) FRM-0.17B 0.17 Bauxite (4.75mm) -0.5% steel 190.9 (3.4) 4 425.6 (4.7) FRC-0.60 0.60 Siliceous (4.75mm) Granite (10mm) 0.5% steel 43.8 (1.3) 5 405.7 (16.0) FRC-0.50 0.50 Siliceous (4.75mm) Granite (10mm) 0.5% steel 61.1 (0.2) 5 404.2 (12.0) Concretes FRC-0.35 0.35 Siliceous (4.75mm) Granite (10mm) 0.5% steel 93.5 (2.8) 6 396.0 (10.3) FRC-0.28 0.28 Siliceous (4.75mm) Granite (10mm) 0.5% steel 118.1 (3.4) 6 411.2 (11.8) FRC-0.28-20 0.28 Siliceous (4.75mm) Granite (20mm) 0.5% steel 114.6 (3.6) 7 417.9 (10.8) 0.5% steel + ECC-ST+PE 0.25 --78.8 (3.8) 4 410.7 (3.2) 1.5% PE ECCs ECC-PVA 0.25 Siliceous (0.25mm) -2% PVA 42.0 (1.2) 4 408.3 (8.7) UHPC 0.17 Siliceous (4.75mm) -2% steel 161.0 (7.6) 4 400.4 (14.8) Proprietary-1 -Siliceous (0.6mm) -3% steel4 202.3 (8.5) 4 408.9 (19.0) UHPCs Proprietary-2 -Siliceous (2mm) -3% steel5 175.6 (13.9) 4 407.8 (15.8) Proprietary-3 -Bauxite (4mm) -1.2-1.4% steel6 229.4 (4.1) 4 398.4 (3.1) Granites Granite ----238.5 (12.2) 1 409.87

Penetration depth (mm)

Normalized penetration depth2 (×10-3 mm/(m/s))

29.9 (2.1) 24.4 (2.5) 19.8 (2.5) 30.8 (1.5) 15.8 (0.7) 12.4 (1.1) 27.6 (2.1) 12.7 (0.9) 11.6 (1.6) 20.0 (2.9) 18.0 (2.8) 12.2 (1.8) 11.2 (2.9) 10.7 (1.7)

75.3 (3.5) 61.0 (5.0) 48.3 (5.6) 74.6 (1.7) 39.7 (1.8) 30.2 (1.9) 64.8 (4.8) 30.1 (1.4) 27.1 (3.4) 49.1 (5.6) 44.5 (5.5) 30.6 (3.9) 27.1 (6.1) 25.5 (3.4)

-0.00 (0.00) 0.09 (0.01) -0.44 (0.01) 0.53 (0.03) -0.68 (0.03) 0.71 (0.07) 0.43 (0.02) 0.45 (0.03) 0.46 (0.05) 0.46 (0.05) 0.48 (0.05)

28.5 (1.8)

69.4 (4.1)

--

23.8 (2.7) 13.4 (2.1) 14.6 (2.9) 11.9 (0.8) 9.6 (1.8) 9.37

58.2 (5.5) 33.3 (4.1) 35.5 (5.4) 29.1 (1.0) 24.1 (4.5) 22.77

-0.48 (0.05) 0.45 (0.03) 0.46 (0.04) 0.81 (0.07) 0.527

Note: 1 Each target specimen is impacted by only one projectile. 2 Penetration depths are normalised with respect to the corresponding impact velocities according to Zhang et al. [5]. 3 Experimental results are presented as average of at least three specimens with standard deviation in parentheses. 4 Steel fibers used in UHPC Proprietary 1 are hooked at each end with a diameter of 0.55 mm and a length of 30 mm. 5 Steel fibers used in UHPC Proprietary 2 are straight with a diameter of 0.20 mm and lengths of 5 mm (1 vol.%), 13 mm (1 vol.%), and 20 mm (1 vol.%). 6 Steel fibers used in UHPC Proprietary 3 are straight with a diameter of 0.16 mm and a length of 13 mm. 7 Experimental result of one specimen.

27

Projectile mass loss (%)

100

Normalized penetration depth (x10-3 mm/(m/s))

Normalized penetration depth (x10-3 mm/(m/s))

100 Cement pastes Mortars Concretes ECCs UHPCs Granite

80 60 40 20 0 30

(a) 60

90

120

150

180

210

240

Cement pastes Mortars Concretes ECCs UHPCs Granite

80 60 40 20 0 15

(b) 25

35

Compressive strength (MPa) Normalized penetration depth (x10-3 mm/(m/s))

Normalized penetration depth (x10-3 mm/(m/s))

60 40

(c) 40

50

60

70

80

90

100

80 60 40 20 0 1800

(d) 2000

2200

2400

2600

2800

3000

Density (kg/m ) 100

Normalized penetration depth (x10-3 mm/(m/s))

Normalized penetration depth (x10-3 mm/(m/s))

85

3

100 Cement pastes Mortars Concretes ECCs UHPCs Granite

80 60 40

0 3

75

Cement pastes Mortars Concretes ECCs UHPCs Granite

Effective hardness index

20

65

100

Cement pastes Mortars Concretes ECCs UHPCs Granite

80

0 30

55

Elastic modulus (GPa)

100

20

45

(e) 6

9

12

15

18

21

24

27

Splitting tensile strength (MPa)

Cement pastes Mortars Concretes ECCs UHPCs

80 60 40 20 0 0

(f) 30

60

90

120 150 180 210 240

Flexural toughness (J)

Fig. 9. Influence of effective properties on the normalized penetration depth in cement-based material and granite targets subjected to non-deformable projectile impact at velocities of about 400 m/s, (a) compressive strength, (b) elastic modulus, (c) effective hardness index, (d) density, (e) splitting tensile strength, and (f) flexural toughness

28

3.2.1. Influence of compressive strength As shown in Fig. 9(a), the normalized penetration depth generally reduces with an increase in the compressive strength up to a certain level. Beyond that, however, a further increase in the compressive strength does not result in a significant reduction of the normalized penetration depth. At times, the normalized penetration depth may even increase with the compressive strength. There is a large scattering within the experimental data in Fig. 9(a), hence indicating that the compressive strength is not the only dominant parameter influencing the penetration depth in cement-based materials against projectile impact. As discussed in Section 3.1.2, when subjected to non-deformable projectile impact, the penetration depth in cement-based materials is strongly dependent on their constituent components (e.g. both aggregate and matrix), which is also reported in our earlier work [18] using 28-mmdiameter, 249-g-mass projectiles striking against cement-based materials with maximum aggregate sizes of either 10 mm or 20 mm (same as those in this study) . However, the compressive strength of cement-based materials is governed by the weakest link, e.g. ITZ between coarse aggregate and mortar matrix for NSCs, or coarse aggregate for HSCs [19, 39]. By itself, the compressive strength is not able to adequately account for the contributions of both aggregate and matrix. Accordingly, this material property fails to accurately assess the penetration depth in cement-based materials across a wide range of material properties and compositions including cement pastes, mortars, concretes, ECCs, and UHPCs. 3.2.2. Influence of elastic modulus Figure 9(b) presents the influence of elastic modulus on the normalized penetration depth. An increase in the elastic modulus in general results in a reduction of the normalized penetration depth. However, above a certain level (45-50 GPa), the normalized penetration depth does not appear to significantly reduce further. Compared to the compressive strength in Fig, 9(a), the scattering of the experimental data in Fig, 9(b) is significantly decreased.

29

For NSCs, their elastic moduli fall within a narrow range. The effect of elastic modulus on the penetration depth in NSCs is thus commonly ignored [2, 10]. This is probably valid for NSCs fabricated with coarse aggregate, sand, cement, and water. With the development of concrete technology, the compositions of cement-based materials (e.g. UHPCs and ECCs) have changed considerably. This affects the elastic modulus of cement-based materials substantially. For example, the elastic moduli of ECCs are much lower than those of concretes with comparable compressive strengths, due to the elimination of coarse aggregate. As shown in Table 5, the elastic moduli of cement-based materials investigated in this study vary in a wide range (17.1 to 80.4 GPa at 28 days). These observations indicate that the influence of elastic modulus may be no longer negligible for cement-based materials across a wide range of compositions and material properties. The nonnegligible effect of elastic modulus on the penetration depth has also been reported in our earlier work [18]. For cement-based materials, the elastic modulus can be described as a function of the properties of their constituent materials. The parallel and series models have been proposed to estimate the upper and lower bound solutions for the elastic moduli of cement-based materials [19]. With the parallel model, and ⁄

, where

and

are the elastic moduli of matrix and aggregate, and

are the volume fractions of matrix and aggregate. With the series model, ⁄

⁄

. It is thus easily observed that the actual elastic modulus, bounded by the two expressions,

characterizes the (weighted) properties of the underlying aggregate and matrix constituent materials. As mentioned in Section 3.1.2, the presence of aggregate and the enhancement of matrix are both beneficial to the resistance of cement-based materials to projectile impact. Since the elastic modulus is an overall characterization of both aggregate and matrix, it may be a more appropriate parameter for the assessment of penetration depth in cement-based materials across a wide range of compositions and material properties, compared to the compressive strength which is governed by the weakest link.

30

3.2.3. Influence of effective hardness index The influence of effective hardness index on the normalized penetration depth is shown in Fig. 9(c). The normalized penetration depth is observed to linearly decrease with an increase in the effective hardness index. In comparison to the compressive strength in Fig. 9(a), the scattering of the experimental data in Fig. 9(c) is substantially reduced. As mentioned in Section 2.3.1, the effective hardness index is calculated based on the hardness of coarse aggregate and mortar matrix, and their relative fractions along the projectile trajectory (Eq. (1)). It is worth noting that, similar to the elastic modulus, the effective hardness index characterizes the net effect of both coarse aggregate and mortar matrix. As discussed in Section 3.1.2, the penetration depth in a cement-based material is strongly dependent on its constituent components, mainly aggregate and matrix, when subjected to highvelocity non-deformable projectile impact. The effective hardness index is thus more suitable than the compressive strength, which is governed by the weakest link, as a critical parameter to evaluate and predict the penetration depth. As briefly shown in our earlier work [18] and corroborated further in this study, the effective hardness index is able to adequately characterize the resistance of cement-based materials against projectile impact, across a wide range of compositions and material properties. In contrast to the small projectile used in this study, the experimental investigation in our earlier work [18] was carried out using a large projectile (28 mm in diameter and 249 g in mass) striking against cement-based material targets with maximum aggregate sizes of either 10 mm or 20 mm (same as those in this study). 3.2.4. Influence of density From Fig. 9(d), it is observed that as the density increases, the normalized penetration depth in general decreases. However, further increase in the density beyond a certain level does not substantially reduce the normalized penetration depth. In addition, a relatively large spread of the experimental data is observed in Fig. 9(d). This indicates that the density is a parameter that affects the penetration depth to some extent, though not critically.

31

3.2.5. Influence of splitting tensile strength and flexural toughness As shown in Fig. 9(e), the normalized penetration depth generally reduces with increasing the splitting tensile strength. However, beyond a threshold, further increase in the splitting tensile strength does not significantly affect the normalized penetration depth. From Fig. 9(f), a general decrease in the normalized penetration depth is observed with an increase in the flexural toughness up to a certain level, beyond which the normalized penetration depth increases somewhat with the flexural toughness instead. A noticeable scattering of the experimental data is observed in both Figs. 9(e) and 9(f), indicating that the splitting tensile strength or flexural toughness alone is not sufficient for the assessment of penetration depth in cement-based materials across a wide range of compositions and material properties. 3.2.6. Further discussions on the influence of identified parameters When a projectile penetrates into a target, the target material surrounding the penetrating projectile is subjected to high-intensity triaxial stress states, together with considerable volume changes and local material failure [4]. Thus, the shear failure envelope and the relationship between hydrostatic pressure and volumetric strain (i.e. equation of state, EOS) are of vital importance for the determination of the resistance of target materials against projectile impact. For NSCs comprising of coarse aggregate, fine aggregate, cementitious materials, and water, it is noted that the shear failure envelope and EOS can be represented as a function of the unconfined compressive strength [4, 66]. The resistance of NSCs against projectile impact can thus be described adequately by the compressive strength. This is also reflected in material models used for numerical simulations, e.g. the Karagozian & Case (K&C) concrete model in LS DYNA, which is able to generate material model parameters automatically based on the compressive strength [66, 67]. However, the advancement of concrete technology has led to an increased usage of HSCs, UHPCs, and ECCs. These cement-based materials have different material properties and compositions compared to NSCs, e.g. UHPCs generally do not include coarse aggregate and have compressive strength of exceeding 150 MPa. It has been reported in Refs. [4, 68-70] that for cement-based 32

materials, the shear failure envelope and EOS are also dependent on their constituent materials. Unlike NSCs, the general relations between shear failure envelope, EOS, and compressive strength for cement-based materials across a wide range of compositions and material properties are not yet available. Accordingly, the compressive strength alone cannot adequately describe the penetration resistance of cement-based materials across a wide range of compositions and material properties, which is consistent with the finding based on the experimental results in Section 3.2.1. It is also found that empirical and semi-empirical formulae for the prediction of penetration depth, which are developed based on the experimental data of NSCs and consider mainly the compressive strength of NSCs, may not be directly applicable for cement-based materials across a wide range of material properties and compositions considered in this study (see examples in Appendix D). As mentioned in Section 3.2.2, the elastic modulus accounts for the contributions of constituent components (e.g. aggregate and matrix) to the overall behavior of cement-based materials. In addition, the elastic modulus is related to the bulk modulus and shear modulus, which are two important parameters in the description of EOS and shear failure envelope. Similarly, the effective hardness index is also an overall characterization of constituent components to cement-based materials, and it may be related to the elastic modulus (Fig. 10). Moreover, the hardness of target materials may affect the energy dissipation in the plastic zone formed around the projectile [71], which has a corresponding effect on the target resistance to projectile impact [72]. Therefore, the parameters of elastic modulus and effective hardness index are more appropriate than the compressive strength for the evaluation and predication of penetration depth in cement-based materials across a wide range of compositions and material properties.

33

Effective hardness index

100 90 80 70 60

Adj. R2=0.88

Cement pastes Mortars Concretes ECCs UHPCs Granite

50 40 30 15

25

35

45

55

65

75

85

Elastic modulus (GPa)

Fig. 10. Relationship between elastic modulus and effective hardness index The effective hardness index and elastic modulus can thus be used for a quick assessment of penetration depth: (1) For the cement-based materials with available information of coarse aggregate (e.g. hardness and volume fraction of coarse aggregate), the effective hardness index can be used. (2) For the cement-based materials without information of coarse aggregate, the elastic modulus can be used. Considering that beyond a certain level, a further increase in the elastic modulus does not significantly reduce the penetration depth, the elastic moduli of 45~50 GPa are recommended for the cement-based materials with granite coarse aggregate. Due to the logistical constraints, we have considered only a small caliber projectile in this study. It is highlighted that the main findings in this study using a small caliber projectile (diameter = 8 mm and mass = 7.8 g) are consistent with those reported in our earlier work [18] using a large caliber projectile (diameter = 28 mm and mass = 249 g). Note that the projectile size in our earlier work is 2.8 times of the maximum aggregate size in concretes while the projectile size in this study is 0.8 times of the maximum aggregate size (for one concrete in this study, the projectile size is 0.4 times of the maximum aggregate size). As presented in Fig. 11, the results in this study corroborate those reported in our earlier work [18] that the effective hardness index and elastic modulus have the most influence on the penetration depth for different projectile sizes. Together with the findings in our earlier work [18] and in this study, the beneficial effect of coarse aggregate in reducing the penetration depth is observed for different projectile sizes (see Section 3.1.2).

34

270

Normalized penetration depth (x10-3 mm/(m/s))

Normalized penetration depth (x10-3 mm/(m/s))

300 FRHSC-60 FRHSC-85 FRHSC-110 FRHSM SHCC-ST+PE SHCC-PVA

(a)

240 210 180 150 30

Projectile diameter = 28 mm Projectile mass = 249 g Wang et al., 2016

40

50

60

70

80

90

100

300 FRHSC-60 FRHSC-85 FRHSC-110 SHCC-ST+PE SHCC-PVA

(b)

270 240 210 180

Projectile diameter = 28 mm Projectile mass = 249 g Wang et al., 2016

150 10

Effective hardness index

15

20

25

30

35

40

45

50

Elastic modulus (GPa)

Fig. 11. Influence of (a) effective hardness index and (b) elastic modulus on the normalized penetration depth using a 28-mm-diameter, 249-g-mass, ogival-nosed non-deformable projectile at velocities of about 400 m/s. Reproduced from Ref. [18]. However, the results in our earlier work [18] and in this study cannot be compared directly for investigating the extent of beneficial effect of coarse aggregate against different projectile sizes. This is because of the (1) different projectile kinetic energies arising from different projectile masses (249 g in our earlier work and 7.8 g in this study); (2) different projectile nose shapes (ogival nose in our earlier work and conical nose in this study). Here, we refer to the numerical results for NSCs using 3D mesoscopic concrete model in Ref. [73]. As presented in Fig. 12, for a 25.4-mm-diameter projectile with a given impact velocity, the penetration depth generally increases with an increase in the projectile size to maximum aggregate size ratio. However, at a velocity of about 400 m/s and below, the influence of projectile size to maximum aggregate size ratio on the penetration depth is marginal. It is also observed in this study that the projectile penetration depth decreases marginally by 5.9% as the projectile size to maximum aggregate size ratio reduces from 0.8 to 0.4 (refer to FRC-0.28 vs. FRC-0.28-20 with the same w/cm and similar material properties in Table 7 later). The experimental finding for FRCs in this study is thus consistent with the numerical results for NSCs in Ref. [73]. Note that these preliminary observations pertain only to a limited range of projectile size to maximum aggregate size ratios, at a velocity of about 400 m/s. A more in-depth discussion on the beneficial effect of coarse aggregate against different projectile sizes over a wide range of velocities is beyond the scope of this study and will be left as a future work.

35

Penetration depth (mm)

1000 Maximum aggregate size = 9.5 mm Maximum aggregate size = 20 mm Maximum aggregate size = 40 mm Maximum aggregate size = 50 mm

800 600 400

Projectile diameter = 25.4 mm Projectile mass = 500 g Wu et al., 2019

200 0 0

200

400

600

800

1000

1200

Impact velocity (m/s)

Fig. 12. Penetration depth of a 25.4-mm-diameter, 500-g-mass, ogival-nosed non-deformable projectile in NSCs with different maximum aggregate sizes (e.g. 9.5, 20, 40, and 50 mm) using 3D mesoscopic concrete model. Reproduced from Ref. [73] 3.3. Influence of maximum size and volume fraction of aggregate on the penetration depth The influence of maximum aggregate size can be observed by comparing the normalized penetration depths in the concretes with 10-mm coarse aggregate (FRC-0.28) and 20-mm coarse aggregate (FRC-0.28-20), as shown in Table 7. The normalized penetration depth in the FRC-0.28-20 is generally smaller than that in the FRC-0.28, which may be explained by the fact that in spite of having a comparable compressive strength of around 115 MPa, the FRC-0.28-20 has slightly higher elastic modulus/effective hardness index in comparison to the FRC-0.28. This observation indicates that the aggregate with larger size is beneficial for reducing the penetration depth, though not significantly at velocities of about 400 m/s, which was also numerically reported in Ref. [73] for NSC (see Fig. 12). Table 7. Effect of maximum aggregate size in concretes on the normalized penetration depth Fine

Coarse

aggregate

aggregate

FRC-0.28

Siliceous

FRC-0.28-20

Siliceous

Mix ID

Maximum

Compressive

aggregate

strength

size

Granite Granite

1

Elastic

Effective 1

1

Normalized

modulus

hardness

penetration depth

(MPa)

(GPa)

index

(×10-3 mm/(m/s))

10 mm

118.1 (3.4)2

46.7 (0.2)

80.2

27.1 (6.1)

20 mm

114.6 (3.6)

48.2 (0.5)

80.7

25.5 (3.4)

Note: 1 At the age of impact test. 2

Experimental results are presented as average of at least three specimens with standard deviation in parentheses.

As shown in Table 8, the normalized penetration depth in the UHPC (sand volume fraction of 38%) is higher than that in the FRM-0.17 (sand volume fraction of 49%), although the UHPC shows a 36

higher compressive strength (161.0 MPa) compared to the FRM-0.17 (146.9 MPa). Apart from the difference in sand volume fraction, the steel fiber and silica fume contents were also different for the FRM-0.17 and UHPC with the UHPC containing higher amounts of steel fibers and silica fume. As reported in Refs. [5, 8, 16], the effect of fibers on the penetration depth is not significant at low contents (e.g. less than 4% by volume [7]). Thus, the effect on the penetration depth arising from the different steel fiber contents in the FRM-0.17 and UHPC is considered negligible. The matrix of cement pastes would be enhanced with increasing silica fume content from 9% (FRM-0.17) to 15% (UHPC) by mass of cementitious materials [74, 75]. As discussed in Section 3.1.2, the improvement of cement paste is beneficial for reducing the penetration depth. However, the normalized penetration depth in the UHPC is higher despite its higher silica fume content and enhanced matrix of cement paste. This is probably due to the lower sand volume fraction of 38% in the UHPC, in comparison to 49% in the FRM-0.17. This indicates the benefit of a high volume fraction of fine aggregate in reducing the penetration depth in cement-based materials when subjected to non-deformable projectile impact. Table 8. Effect of sand volume fraction in mortars on the normalized penetration depth Fine

Mix ID

aggregate

Volume fraction of sand

Compressive strength1 (MPa)

Elastic

Effective 1

1

Normalized

modulus

hardness

penetration depth

(GPa)

index

(×10-3 mm/(m/s))

FRM-0.17

Siliceous

49%

146.9 (1.4)2

49.5 (0.7)

76.2

30.2 (1.9)

UHPC

Siliceous

38%

161.0 (7.6)

47.8 (0.7)

76.8

33.3 (4.1)

Note: 1 At the age of impact test. 2

Experimental results are presented as average of at least three specimens with standard deviation in parentheses.

Based on the experimental findings of this study, the impact resistance of cement-based materials in terms of penetration depth can be enhanced by the use of stronger, harder, and higher fraction of aggregate, and the improvement of cement paste matrix, as long as the workability of cement-based materials is satisfied for structural applications. In addition, using aggregate with large size is also beneficial for reducing the penetration depth, as long as the maximum size of the aggregate satisfies the requirements of structural members.

37

4. Conclusions This study presents an experimental investigation on the influence of identified effective properties, including compressive strength, elastic modulus, effective hardness index, density, splitting tensile strength, and flexural toughness, on the penetration depth in cement pastes, mortars, concretes, ultra-high performance concretes (UHPCs), and engineered cementitious composites (ECCs) with the Ø100×200 mm3 cylinder compressive strengths from 34.2 to 220.2 MPa and elastic moduli from 17.1 to 80.4 GPa at 28 days, when subjected to 8.0-mm-diameter, 7.8-g-mass, and conical-nosed non-deformable projectile impact at velocities of about 400 m/s. The following conclusions can be drawn: (1) The compressive strength alone cannot accurately characterize the penetration depth. Within the range of effective properties investigated, the effective hardness index and elastic modulus are the most critical effective properties governing the penetration depth in cement-based materials across a wide range of compositions and material properties. This is attributed to the fact that both the effective hardness index and elastic modulus characterize the overall contributions of constituent components (e.g. aggregate and matrix) to cement-based materials. The density is a parameter that affects the penetration depth to some extent. The individual parameter of the splitting tensile strength or flexural toughness is not adequate for the assessment of penetration depth. (2) The effective hardness index can be used for quick assessment of penetration depth in cementbased materials with available information of coarse aggregate (e.g. hardness and volume fraction), while the elastic modulus can be used for cement-based materials without information of coarse aggregate. (3) The penetration depth can be reduced by the enhancement of cement paste matrix and the use of stronger, harder, and higher fraction of aggregate, as long as the workability of cement-based materials is satisfied. Furthermore, using aggregate with larger size is also beneficial for decreasing the penetration depth, as long as the maximum aggregate size satisfies requirement of structural members. 38

(4) The penetration depths in UHPCs are in general higher than those in high performance concretes (HPCs) with coarse aggregate, although the compressive strengths of UHPCs are much higher in comparison to those of HPCs. (5) The bauxite sand is more effective in reducing the penetration depth compared to siliceous sand. Due to the logistical constraints, the impact tests in this study were conducted only with a small caliber projectile (diameter = 8 mm) at a given velocity of about 400 m/s. Note that the main findings in this study are consistent with those reported in our earlier work using a large caliber projectile (diameter = 28 mm). The applicability of these identified effective properties for different projectile sizes and different impact velocities is beyond the scope of this study and will be left as a future work. Author statement Fengling Zhang: Formal analysis, Investigation, Writing – Original Draft; Leong Hien Poh: Supervision; Project administration; Writing – Review & Editing; Min-Hong Zhang: Supervision; Writing – Review & Editing. Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement The authors wish to thank the editor and anonymous reviewers for their valuable comments and suggestions that have helped to improve the quality of this paper. This research was supported by a research grant provided by the Defence Science & Technology Agency (DSTA), Singapore, under the Center for Protective Technology, National University of Singapore (NUS). The first author

39

acknowledges the Research Scholarship provided by the NUS. The authors would like to thank Shasha Wang for her careful reading and comments on the manuscript, and Hoang Thanh Nam Le for the fruitful discussions at early stage of this project. The authors are grateful to undergraduate student Zan Hong Chin, technical staff Beng Oon Ang, Yian Kheng Koh, and Chee Wah Low for their kind assistance with some of the experimental work. The authors also thank the U.S. Army Engineer Research and Development Center (ERDC) for providing some UHPC specimens for material characterization and impact tests. Any opinions, findings and conclusions expressed in this paper are those of the authors and do not necessarily reflect the view of DSTA, Singapore. References [1] S.T. Quek, V.W.J. Lin, M. Maalej, Development of functionally-graded cementitious panel against high-velocity small projectile impact, International Journal of Impact Engineering 37(8) (2010) 928941. [2] Q.M. Li, S.R. Reid, H.M. Wen, A.R. Telford, Local impact effects of hard missiles on concrete targets, International Journal of Impact Engineering 32(1) (2005) 224-284. [3] ASTM C1856, Standard Practice for Fabricating and Testing Specimens of Ultra-High Performance Concrete, ASTM International, West Conshohocken, PA, 2017. [4] D.Z. Yankelevsky, Resistance of a concrete target to penetration of a rigid projectile - revisited, International Journal of Impact Engineering 106 (2017) 30-43. [5] M.H. Zhang, V.P.W. Shim, G. Lu, C.W. Chew, Resistance of high-strength concrete to projectile impact, International Journal of Impact Engineering 31(7) (2005) 825-841. [6] A.N. Dancygier, D.Z. Yankelevsky, C. Jaegermann, Response of high performance concrete plates to impact of non-deforming projectiles, International Journal of Impact Engineering 34(11) (2007) 1768-1779. [7] H. Wu, Q. Fang, J. Gong, J.Z. Liu, J.H. Zhang, Z.M. Gong, Projectile impact resistance of corundum aggregated UHP-SFRC, International Journal of Impact Engineering 84 (2015) 38-53. [8] M.H. Zhang, M.S.H. Sharif, G. Lu, Impact resistance of high-strength fibre-reinforced concrete, Magazine of Concrete Research 59(3) (2007) 199-210. [9] M.J. Forrestal, D.Y. Tzou, A spherical cavity-expansion penetration model for concrete targets, International Journal of Solids and Structures 34(31) (1997) 4127-4146. [10] X.W. Chen, Q.M. Li, Deep penetration of a non-deformable projectile with different geometrical characteristics, International Journal of Impact Engineering 27(6) (2002) 619-637. [11] S.E. Jones, W.K. Rule, On the optimal nose geometry for a rigid penetrator, including the effects of pressure-dependent friction, International Journal of Impact Engineering 24(4) (2000) 403-415. [12] S.C. Chian, B.C.V. Tan, A. Sarma, Projectile penetration into sand: Relative density of sand and projectile nose shape and mass, International Journal of Impact Engineering 103 (2017) 29-37. [13] A.N. Dancygier, D.Z. Yankelevsky, Effects of reinforced concrete properties on resistance to hard projectile impact, ACI Structural Journal 96(2) (1999) 259-269. [14] A.N. Dancygier, D.Z. Yankelevsky, High strength concrete response to hard projectile impact, International Journal of Impact Engineering 18(6) (1996) 583-599. [15] E. O’Neil, B. Neeley, J. Cargile, Tensile properties of very-high-strength concrete for penetration-resistant structures, Shock and Vibration 6(5-6) (1999) 237-245.

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Appendix A. Crater diameter and volume in cement-based materials and granite targets Table A1. Equivalent crater diameter and crater volume in cement-based materials and granite targets subjected to high-velocity non-deformable projectile impact Compressive Number of Coarse Fiber strength at target Impact velocity Mix ID w/cm Fine aggregate aggregate (by volume) impact tests specimens for (m/s) 1 (MPa) impact tests FRCP-0.35 0.35 --0.5% steel 72.4 (4.6)2 3 397.0 (11.1) Cement FRCP-0.28 0.28 --0.5% steel 93.8 (5.7) 3 399.2 (13.1) pastes FRCP-0.17 0.17 --0.5% steel 136.0 (2.3) 3 409.9 (6.7) FRM-0.60 0.60 Siliceous (4.75mm) -0.5% steel 37.9 (0.2) 3 412.3 (10.5) FRM-0.28 0.28 Siliceous (4.75mm) -0.5% steel 93.4 (1.4) 3 396.8 (0.0) FRM-0.17 0.17 Siliceous (4.75mm) -0.5% steel 146.9 (1.4) 4 409.2 (11.0) Mortars FRM-0.60B 0.60 Bauxite (4.75mm) -0.5% steel 45.0 (0.3) 3 426.1 (2.1) FRM-0.28B 0.28 Bauxite (4.75mm) -0.5% steel 120.0 (2.4) 3 420.3 (9.2) FRM-0.17B 0.17 Bauxite (4.75mm) -0.5% steel 190.9 (3.4) 4 425.6 (4.7) FRC-0.60 0.60 Siliceous (4.75mm) Granite (10mm) 0.5% steel 43.8 (1.3) 5 405.7 (16.0) FRC-0.50 0.50 Siliceous (4.75mm) Granite (10mm) 0.5% steel 61.1 (0.2) 5 404.2 (12.0) Concretes FRC-0.35 0.35 Siliceous (4.75mm) Granite (10mm) 0.5% steel 93.5 (2.8) 6 396.0 (10.3) FRC-0.28 0.28 Siliceous (4.75mm) Granite (10mm) 0.5% steel 118.1 (3.4) 6 411.2 (11.8) FRC-0.28-20 0.28 Siliceous (4.75mm) Granite (20mm) 0.5% steel 114.6 (3.6) 7 417.9 (10.8) ECC-ST+PE 0.25 --0.5% steel + 1.5% PE 78.8 (3.8) 4 410.7 (3.2) ECCs ECC-PVA 0.25 Siliceous (0.25mm) -2% PVA 42.0 (1.2) 4 408.3 (8.7) UHPC 0.17 Siliceous (4.75mm) -2% steel 161.0 (7.6) 4 400.4 (14.8) 3 Proprietary-1 -Siliceous (0.6mm) -3% steel 202.3 (8.5) 4 408.9 (19.0) UHPCs Proprietary-2 -Siliceous (2mm) -3% steel4 175.6 (13.9) 4 407.8 (15.8) Proprietary-3 -Bauxite (4mm) -1.2-1.4% steel5 229.4 (4.1) 4 398.4 (3.1) Granites Granite ----238.5 (12.2) 1 409.86 Note: 1 Each target specimen is impacted by only one projectile. 2 Experimental results are presented as average of at least three specimens with standard deviation in parentheses. 3 Steel fibers used in UHPC Proprietary 1 are hooked at each end with a diameter of 0.55 mm and a length of 30 mm. 4 Steel fibers used in UHPC Proprietary 2 are straight with a diameter of 0.20 mm and lengths of 5 mm (1 vol.%), 13 mm (1 vol.%), and 20 mm (1 vol.%). 5 Steel fibers used in UHPC Proprietary 3 are straight with a diameter of 0.16 mm and a length of 13 mm. 6 Experimental result of one specimen.

Equivalent crater diameter (mm)

Crater volume (×10-1 mL)

75.9 (4.0) 72.9 (3.0) 66.2 (6.6) 66.2 (6.3) 59.3 (2.2) 55.8 (2.7) 60.7 (3.2) 53.9 (1.5) 51.8 (5.9) 60.6 (3.3) 56.8 (3.3) 53.3 (1.2) 50.4 (5.4) 53.0 (4.2) 46.3 (5.1) 43.9 (4.9) 50.2 (5.6) 54.9 (5.4) 46.7 (4.8) 49.1 (3.4) 37.46

196.3 (18.1) 178.7 (21.0) 135.0 (49.2) 122.3 (24.8) 79.0 (4.6) 68.0 (13.1) 99.0 (5.0) 64.3 (8.7) 59.8 (19.5) 106.4 (17.4) 90.6 (13.7) 63.3 (10.0) 55.3 (8.8) 51.1 (14.2) 55.0 (17.3) 49.5 (11.9) 51.8 (15.3) 67.8 (19.5) 45.0 (11.5) 40.8 (7.4) 30.06

Appendix B. Representative photos of post-test projectiles

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

--

--

--

(q) Fig. B1. Representative photos of the post-test projectiles, (a) initial, (b) FRCP-0.28, (c) FRCP-0.17, (d) FRM-0.28, (e) FRM-0.17, (f) FRM-0.28B, (g) FRM-0.17B, (h) FRC-0.60, (i) FRC-0.50, (j) FRC0.35, (k) FRC-0.28, (l) FRC-0.28-20, (m) UHPC, (n) UHPC Proprietary-1, (o) UHPC Proprietary-2, (p) UHPC Proprietary-3, and (q) Granite specimens (Note: Post-test projectiles are not available for those striking against FRCP-0.35, FRM-0.60, FRM-0.60B, ECC-ST+PE, and ECC-PVA)

Appendix C. Front face damage of cement-based materials and granite targets

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)

(t)

(u)

Fig. C1. Extent of damage on the front faces of the cement-based material and granite targets, (a) FRCP-0.35, (b) FRCP-0.28, (c) FRCP-0.17, (d) FRM-0.60, (e) FRM-0.28, (f) FRM-0.17, (g) FRM0.60B, (h) FRM-0.28B, (i) FRM-0.17B, (j) FRC-0.60, (k) FRC-0.50, (l) FRC-0.35, (m) FRC-0.28, (n) FRC-0.28-20, (o) ECC-ST+PE, (p) ECC-PVA, (q) UHPC, (r) UHPC Proprietary-1, (s) UHPC Proprietary-2, (t) UHPC Proprietary-3, and (u) Granite specimen (Note: The crack regions are marked in red for better visualization)

Appendix D. Comparison of experimental and predicted penetration depth Numerous empirical and semi-empirical formulae have been proposed for the prediction of penetration depth in concrete impacted perpendicularly by non-deformable projectiles. Some

commonly studied formulae, including the modified National Defense Research Committee (NDRC) formula [2, 76], Whiffen formula [2, 77], Li and Chen formula [78], Peng et al. formula [79], and Forrestal and Tzou formula [9], are considered here with their application conditions summarized in Table D1. It should be pointed out that most of these formulae were developed based on the experimental data of NSCs. The applicability of these formulae for cement-based materials across a wide range in terms of compositions and material properties is not immediately clear. To evaluate the applicability of these formulae, the experimental penetration depths of this study are compared with the predictions by these formulae, and the errors of predictions using these formulae are given in Table D2. It can be observed from Table D2 that for NSCs (FRC-0.60 and FRC-0.50 in Table D2), the modified NDRC and Peng et al. formulae provide reasonable predictions, while the predictions by other formulae are unsatisfactory. It was also reported in Ref. [79] that the Forrestal et al. formula proposed in [80], which is a semi-empirical formula, may not predict the small caliber projectile penetration depth in NSCs well. In addition, predictions using these formulae for other cement-based material targets are not satisfactory. It is also noted that in spite of considering the shear failure envelope and EOS for target materials, the prediction of Forrestal and Tzou formula is unsatisfactory. Possible reasons are (1) the shear failure envelope (shear strength-pressure relation) and the EOS (pressure-volumetric strain relation) are assumed to be linear in Forrestal and Tzou formula. However, these relations are generally nonlinear for cement-based materials during impact [81]. (2) Due to the lack of triaxial material test data, the suggested values of Y for the determination of penetration depth are adopted from Ref. [82], which may not be directly applicable for cement-based materials investigated in this study. (3) Due to the lack of triaxial material test data, the suggested values of A, B, and C for the determination of penetration depth are adopted form Ref. [9], which may not be directly applicable for cement-based materials investigated in this study. These observations above indicate that these formulae may not be directly applicable beyond the range of parameter values considered during the developmental process. From the engineering

practice point of view, the use of these formulae in the design of impact-resisting structures involving certain cement-based materials, e.g. ECCs, is not safe. Therefore, there is a need to modify these formulae for the prediction of penetration depth in cement-based materials across a wide range of compositions and material properties. It should be noted that the experimental data in this study belong to small-to-medium penetrations (ratio of penetration depth to projectile diameter is less than 5.0 [78]) using short-rod (ratio of projectile length to shank diameter is less than 5.0 [83]) small caliber projectiles at a given impact velocity of about 400 m/s. The predictability of these formulae for penetration depth also depends on the targets and projectiles, e.g. impact velocity [18]. Therefore, more experimental data including deep penetration, long-rod, large caliber projectiles at various impact velocities are needed for further comparison and modification of the formulae for predicting penetration depth in cement-based materials across a wide range of compositions and material properties. Table D1. Application conditions of some typical empirical and semi-empirical formulae for the prediction of penetration depth Empirical and semiempirical formulae

Application conditions and remarks

Modified NDRC formula [2, 76]

 The US National Defense Research Committee (NDRC) formula is developed based on the US Army Corps of Engineers (ACE) formula [2, 76] and modified by Kennedy [84]. It is for concretes with compressive strengths between 27 and 44 MPa [85] and impact velocities between 152 and 500 m/s [28].  The modified NDRC formula assumes that the contact force between projectile and concrete linearly increases to a constant maximum value at a small penetration depth [2].  For concrete target, the modified NDRC formula only considers its compressive strength.  The modified NDRC formula is not dimensionally compatible as it has a non-dimensional term on the left side and a dimensional term on the right side.

Whiffen formula [2, 77]

 The Whiffen formula is developed by the British Road Research Laboratory [2, 77]. It is for concretes with compressive strengths from around 6 to 69 MPa and maximum aggregate sizes between 0.02 and 2 times the projectile diameter, and is for ogive-nosed projectiles with masses from 0.136 to 9979.2 kg, diameters from 12.7 to 965.2 mm, CRHs from 0.8 to 3.5, and velocities from 0 to 1127.8 m/s [2, 77].  For concrete target, the Whiffen formula considers its compressive strength and maximum aggregate size.  The Whiffen formula is not dimensionally compatible.

Li and Chen formula [78]

 The Li and Chen formula is a dimensionless semi-empirical formula for shallow, small-to-medium, and deep penetration using two dimensionless numbers, namely and . It is a further developed Forrestal et al. formula [80] by considering various projectile nose shapes (only ogive nose is considered in the Forrestal et al. formula). ( )⁄ ( 3 )  The Li and Chen formula is for impact function and geometry function 3 ⁄( ) , where is the projectile mass (kg), is the impact velocity (m/s), is the projectile diameter (m), is the empirical constant, is the uniaxial unconfined compressive strength of concrete (Pa), is the density of concrete (kg/m3), and is the projectile nose shape factor [78].  The Li and Chen formula is based on the spherical cavity expansion theory which assumes that the axial resistant force on the projectile nose depending on the instantaneous velocity [80] as (1) , for , and (2) (

), for

, where

,

and

is a constant, which is originated in Ref. [86] .

 For concrete target, the Li and Chen formula considers its compressive strength and density.

Peng et al. formula [79]

 The Peng et al. formula is assessed using experimental data reported in Refs. [58, 87] (concrete in Ref. [58] with a compressive strength of 38 MPa, ogive-nosed projectile with a mass of 15 g, a diameter of 6.4 mm, and a CRH of 4.8 at impact velocities between 200 and 600 m/s, and concrete in Ref. [87] with a compressive strength of 39 MPa, ogivenosed projectile with a mass of 12920 g, a diameter of 76.0 mm, and a CRH of 3.0 at impact velocities between 200

and 500 m/s).  The Peng et al. formula uses the mean resistance approach based on the assumption that the work done by the actual and mean resistant force is equal. It is a further developed Peng et al. formula for deep penetration [88] and Peng et al. formula for small and medium penetration [89]. The Peng et al. formula is for shallow, small-to-medium, and deep penetration.  For concrete, the Peng et al. formula considers its compressive strength, density, and maximum aggregate size. The maximum aggregate size is considered by the modification of empirical constant S proposed by Forrestal et al. [90], however, the modification is based on the best curve fit for concretes with compressive strengths of about 38 MPa.

Forrestal and Tzou formula [9]

 The Forrestal and Tzou formula is assessed using experimental data reported in Ref. [90] (concretes with compressive strengths of 51 MPa, ogive-nosed projectiles with masses of 1600 g, diameters of 30.5 mm, and CRH of 3.0 at impact velocities between 300 and 1100 m/s).  The Forrestal and Tzou formula is based on the spherical cavity expansion theory with target constitutive descriptions ( )⁄ is the pressure, , idealized as (1) a linear pressure-volumetric strain relation ( , where are the radial and circumferential Cauchy stress components, respectively,

is the bulk modulus, and

is the

volumetric strain), and (2) a Mohr-Coulomb yield criterion ( , where and are parameters defining [( )⁄ ] , is the uniaxial compressive strength obtained from the the pressure-dependent shear strength, pressure-dependent shear strength failure envelope [91]).  The Forrestal and Tzou formula is applicable for projectiles penetrating into concrete targets with a depth of more than 2 times the projectile diameter [9]. Note: Shallow penetration means that penetration depth is smaller than 0.5 times the projectile diameter, small-to-medium penetration means penetration depth is between 0.5 and 5 times the projectile diameter, and deep penetration (penetration depth is larger than 5 times the pr ojectile diameter [78].

Table D2. Comparison of experimental and predicted penetration depths Compressive Fine Coarse Mix ID w/cm strength1 aggregate aggregate (MPa) FRCP-0.35 0.35 --72.4 (4.6) Cement FRCP-0.28 0.28 --93.8 (5.7) pastes FRCP-0.17 0.17 --136.0 (2.3) FRM-0.60 0.60 Siliceous -37.9 (0.2) FRM-0.28 0.28 Siliceous -93.4 (1.4) FRM-0.17 0.17 Siliceous -146.9 (1.4) Mortars FRM-0.60B 0.60 Bauxite -45.0 (0.3) FRM-0.28B 0.28 Bauxite -120.0 (2.4) FRM-0.17B 0.17 Bauxite -190.9 (3.4) FRC-0.60 0.60 Siliceous Granite 43.8 (1.3) FRC-0.50 0.50 Siliceous Granite 61.1 (0.2) Concretes FRC-0.35 0.35 Siliceous Granite 93.5 (2.8) FRC-0.28 0.28 Siliceous Granite 118.1 (3.4) FRC-0.28-20 0.28 Siliceous Granite 114.6 (3.6) ECC-ST+PE 0.25 --78.8 (3.8) ECCs ECC-PVA 0.25 Siliceous -42.0 (1.2) UHPC 0.17 Siliceous -161.0 (7.6) Proprietary-1 -Siliceous -202.3 (8.5) UHPCs Proprietary-2 -Siliceous -175.6 (13.9) Proprietary-3 -Bauxite -229.4 (4.1)

Modified NDRC formula -36.1% -26.8% -16.2% -20.7% 12.5% 30.9% -13.0% 38.3% 35.8% 14.2% 13.8% 45.3% 54.1% 65.3% -32.2% -1.9% 16.1% 1.2% 30.1% 47.7%

Whiffen formula -9.7% -0.3% 7.2% 20.3% 53.3% 65.2% 29.8% 80.8% 62.5% 67.1% 60.7% 93.7% 97.8% 98.7% -5.3% 47.3% 44.1% 20.0% 58.6% 71.4%

Prediction error2 Li and Chen Peng et al. formula formula -16.7% -22.7% -6.1% -13.3% 5.6% -2.9% 7.5% 1.2% 43.9% 32.6% 50.2% 50.3% 17.1% 10.6% 76.6% 63.7% 56.2% 54.8% 52.5% 15.6% 49.6% 13.1% 63.9% 39.0% 75.3% 47.8% 87.3% 43.7% -11.0% -17.0% 33.2% 25.0% 43.2% 30.1% 23.7% 12.1% 49.7% 46.0% 70.6% 58.7%

Forrestal and Tzou formula3 -10.4% 8.5% 36.7% 15.2% --23.7% --63.5% 60.0% ----3.5% 44.5% -----

Note: 1 Compressive strengths are determined at the age of impact test. 2 Prediction errors are calculated as (predicted value – experimental value)/experimental value. 3 Projectile nose shape coefficients N1 and N2 for conical-nosed projectiles used in this study are adopted from Ref. [81], as the expressions of N 1 and N2 given in Ref. [9] are only for ogive-nosed projectiles. Dimensionless constants of A, B, and C used in the determination of penetration depth are adopted as the suggested values for compressible, elastic-cracked-plastic cavity expansion model in Ref. [9], due to the lack of triaxial material test data. Uniaxial compressive strength (Y) used in the determination of penetration depth in Ref. [9] is obtained from the pressure-dependent shear strength failure surface [91]. Due to the lack of triaxial material test data, the values of Y for cement-based materials in this study are adopted from Ref. [82] as for MPa; for MPa; for MPa, where is the unconfined compressive strength of cement-based materials (MPa). The Forrestal and Tzou formula is applicable for projectiles penetrating into targets with a depth of more than 2 times the projectile diameter ( , where is the penetration depth and is the projectile diameter). Thus, only those targets with are utilized for comparison.