Behavior of High-Strength and Ultrahigh-Performance Concrete Targets Subjected to Relatively Rigid Projectile Impact

Although many studies have been performed on the local impact load resistance of concrete, limited research literature pertaining to the projectile nose shape coefficient is available (Li et al. 2005; Kennedy 1976; Haldar and Hamieh 1984; Zhang et al. 2017). Within the modified NDRC (Kennedy 1976), Hughes (1984), University of Manchester Institute of Science and Technology (UMIST) (Reid and Wen 2001), and Hwang et al. (2017) equations, the nose of the projectile is classified as either flat, blunt, hemispherical, or sharp (Table 1).

Li and Chen (Chen and Li 2002; Li and Chen 2003) proposed a nose shape factor dependent upon the geometric configuration of the nose (Fig. 1). However, Young (1997) (called the Sandia equation) advocated a nose shape factor based upon the geometric properties of the nose and soil penetration data under low-velocity impact.

The modified NDRC nose shape factors are defined as 0.72, 0.84, 1.0, and 1.14 for flat, hemispherical, blunt, and very sharp noses, respectively. These nose shape factors were adopted in the Kar, Haldar and Hamieh, United Kingdom Atomic Energy Authority (UKAEA), and Ammann and Whitney equations (Li et al. 2005)where $x_{pe}$ = penetration depth (m); $M_p$ = mass of the projectile (kg); $K$ = penetrability of concrete ($=2.17/\sqrt{f_c^{\prime }}$); $f_c^{\prime }$ = compressive strength of concrete (Pa); $N_p$ = nose shape factor; $d_p$ = diameter of the projectile (m); $V_{imp}$ = impact velocity of the projectile ($\mathrm{m}/\mathrm{s}$); and $G$ = impact function (dimensionless) of the modified NDRC equation.

Hughes (1984) proposed a penetration equation [Eqs. (4)–(6)] using the nondimensional impact factor ($I$) defined as a function of mass, velocity, and diameter of the projectile, along with the modulus of rupture of concrete ($f_r$). The dynamic increase factor ($S$) was used to calculate the penetration depth. Nose shape factors were defined as 1, 1.12, 1.26, and 1.39 for flat, blunt, spherical, and sharp noses, respectivelywhere $I$ = impact factor; $S$ = dynamic increase factor; and $f_r$ = modulus of rupture of concrete (Pa).

As part of the research conducted on behalf of the United States Department of Energy on Earth Penetrating Weapons (EPW), Young (1997), at Sandia National Laboratories (SNL), studied impact resistance of natural earth materials (soil, rocks, ice, and frozen soil) along with concrete. In 1967, Young proposed a penetration equation, which has been updated several times (Young 1997). The equation [Eqs. (7)–(11)] included nose shape factors for ogive, conical, and blunt noses depending upon the geometric properties of the projectile (Table 1). These nose shape factors were originally presented based on soil impact test data under low-velocity impact and applied later to other materialswhere $f_c^{\prime }$ = compressive strength of concrete (MPa); $T_c$ = ratio of the concrete target thickness to projectile diameter (if $T_c$ is over 6, set to be 6); $K_h$ = correction factor for lightweight projectile; $K_e$ = factor to consider the edge effect on the concrete target; $F_{\mathrm{reinf}}$ = coefficient related to reinforcement (20 for reinforced concrete or 30 for plain concrete); $W_1$ = ratio of the target width to the penetrator diameter; $P_{\mathrm{rebar}}$ = volume ratio of rebar (%); and $t_c$ = concrete curing time (if $t_c$ is over 1 year, set to be 1).

As part of the General Nuclear Safety Research Program, impact loading tests were conducted to evaluate the impact load resistance of reinforced concrete walls in 1985 (Reid and Wen 2001; Li et al. 2005). The penetration depth equation [Eqs. (12) and (13)] was proposed to evaluate kinetic energy and residual energy once the missile punctures the target. New nose shape factors were presented as 0.72, 0.84, 1.0, and 1.13 for flat, hemispherical, blunt, and sharp noses, respectivelywhere $f_c^{\prime }$ = compressive strength of concrete (MPa); and ${\sigma }_t$ = rate-dependent strength of concrete.

Based on the dynamic cavity expansion model, Luk and Forrestal (1987) proposed an equation to estimate the depth of penetration. Forrestal et al. (1994) calibrated the factors using 6 sets of impact test data for an ogive nose projectile. Li and Chen (2003) further developed the penetration depth model [Eqs. (14)–(19)] with modified $S$ factors for concrete strength and studied the impact factor $N^{*}$ (Chen and Li 2002; Li and Chen 2003). The factor $N^{*}$ is defined as a function of the nose shape and sectional pressure, which is composed of the mass, density, and diameter of the projectile. The nose shape factor ($N_p$) was calculated based on the nose geometry of the projectile (Table 1)where $f_c^{\prime }$ = compressive strength of concrete (Pa); $h$ = thickness of target (m); ${\rho }_c$ = density of concrete ($\mathrm{kg}/{\mathrm{m}}^3$); $k$ = factor related to the target thickness and the diameter of the projectile; and $I$ = impact factor.

Hwang et al. (2017) compared impact energy with resistant energy to estimate the penetration depth and residual velocity of the projectile. Using the law of conservation of energy, an equation for the penetration depth of thick and thin concrete targets was proposed and verified by test results. The impact mechanism was divided into three stages: spalling, tunneling, and scabbing. Spalling refers to the truncated dome or bowl shape failure at the face of the concrete target. Tunneling refers to the projectile penetrating into the concrete target and making a tunnel without significant failure besides passage of the projectile. Scabbing refers to concrete cone failure at the rear face of the concrete target. The nose shape factors were presented separately in accordance with spalling or tunneling (Table 1). The shape of the spalled concrete cone was considered related to the shape of the nose of the projectile, and the nose shape factor for spalling was adopted as $\tan {\theta }_s$. It is noted that Eqs. (20)–(36) present the penetration depth of the concrete target under spalling failurewhere $d_p$, $L_p$, ${\rho }_p$, $E_p$, and $V_{imp}$ = diameter, length, density, elastic modulus, and impact velocity of the projectile, respectively; $A_{sp}$ and $V_{sc}$ = projected area and volume of the idealized concrete cone, respectively; $k_s$ = size effect factor of the concrete target $[=(300/h)0.25\le 1(\mathrm{mm})]$; $k_{bs}$ = stress concentration effect factor of the concrete target $[=4/\surd (b_s/h)\le 1.25]$; $b_s$ = average perimeter of the concrete cone $[=\pi (d_p+t_s\tan \theta )]$; $A_s$ = sum of the effective reinforcing bar area in the concrete cone in horizontal and vertical directions; $f_y$ = yield strength of the reinforcing bar; $f_t$ = concrete tensile strength; $E_{cd}$ and $f_{td}$ = elastic modulus and tensile strength of concrete affected by the strain rate, respectively; $b$ = concrete target width; $I_e$ = effective moment of inertia of the concrete target; $E_c$ = elastic modulus of concrete; $E_K$ = kinetic energy of the projectile; $E_{DP}$ = deformed energy of projectile; $E_{DC}$ and $E_S$ = deformed energy and spalling-resistant energy of the concrete target, respectively; $h$ = thickness of the concrete target; $k_1$ = coefficient related to $h$; $k_2$ = coefficient related to the steel fiber volume ratio; $k_3$ = coefficient related to the concrete density; and $k_4$ = coefficient related to the maximum size of coarse aggregates.

The experiment was planned to investigate the prediction accuracy of existing impact equations for high-strength concrete and UHPC, as well as the validity of nose shape factors in existing impact equations (Kim 2018). Test parameters included concrete strength and two projectile nose shapes: hemispherical and conical. A design compressive strength of 35 MPa was set as the reference strength, and test targets with design compressive strengths of 80, 100, 120, and 150 MPa were prepared (Table 2). To simulate field conditions, high-strength concrete specimens in the range of $80–120\mathrm{MPa}$ were developed without high-temperature curing, and steel fibers were not included. The maximum coarse aggregates size was limited to 20 mm. However, UHPC test targets having a design compressive strength of 150 MPa were developed using laboratory mix proportions without coarse aggregates and were steam cured. Because it is not known whether the effect of steel fibers on concrete penetration resistance is insignificant (Kim et al. 2017, 2018), steel fiber having a volume of 1.5% was also used.

High-strength concrete for the $80–120\mathrm{MPa}$ test targets was designed such that compressive strength would develop after 120 days without steam curing. Zirconia silica fume (ZrSF) was added to maintain concrete strength and improve fluidity (Joh et al. 2012; Koh et al. 2012). Concrete mix proportions were considered for actual construction practical application. After material testing, ready mixed concrete was used for the concrete targets. Six specimens with the dimensions of $200\times 200\times 100\mathrm{mm}$ were manufactured for each target compressive strength.

According to the Hughes (1984) study, the penetration depth is overestimated when the ratio of the concrete target thickness to projectile diameter is less than 5. Therefore, in this study, the thickness of the concrete target was designed to be 100 mm so that the thickness-to-diameter ratio satisfies the value of 5, and the scabbing failure would not occur on the rear face of the specimen. Using the Hughes equation (Hughes 1984), a minimum thickness of 82 mm would be required when a hemispherical projectile with a diameter of 20 mm (weight of about 90 g) collides with the 35 MPa concrete target at an impact velocity of $140\mathrm{m}/\mathrm{s}$. However, the modified NDRC equation (Kennedy 1976) predicted a need for a minimum thickness of 67 mm under the same collision conditions.

Two straight steel fibers having a nominal tensile strength of $\mathrm{2,000}\mathrm{MPa}$ with a diameter of 0.2 mm were used for the UHPC targets. Lengths of 16 mm (volume ratio of 0.5%) and 20 mm (volume ratio of 1.0%) were used respectively. In order to suppress the fire-balling and poor orientation when manufacturing UHPC mixed with two types of steel fibers, these steel fibers were gradually inputted into a fan-mixer machine.

The UHPC targets were made using a premixed binder with zirconium, filler, and ground granulated blast furnace slag (GGBS). To address the scabbing limit thickness and overestimation of the penetration equation when the ratio of thickness to the diameter of the projectile is over 5, the size of the UHPC targets were designed to be $200\times 200\times 50\mathrm{mm}$. Previous test results showed that the penetration depth of the UHPC target was about $3–4\mathrm{mm}$ when subject to a 20 mm sphere projectile at $200\mathrm{m}/\mathrm{s}$ (Kang et al. 2016). The modified NDRC equation (Kennedy 1976) predicted the need for a minimum thickness of 58 mm to ensure against scabbing failure.

For impact loading tests, two types of projectiles were prepared (Fig. 2): conical and hemispherical. The conical projectile had a diameter of 20 mm, length of 40 mm, and nose length of 10 mm at 45°. The hemispherical projectile had the same configuration except that the radius of the nose was 10 mm. To increase the strength of the projectiles, the projectiles were subjected to heat treatment. The steel type projectile was SCM 440, and the featuring tensile strength and hardness were rated at 100–130 ksi ($700–\mathrm{1,000}\mathrm{MPa}$) and 18–22 HRc (Rockwell hardness).

The average compressive strength for the target specimens whose design compressive strengths were 35, 80, 100, 120, and 150 MPa were measured at 41, 103, 81, 96, and 162 MPa, respectively (Table 2 and Fig. 4).

For the high-strength concrete target specimens, measured concrete strength for that having design compressive strengths of 100 and 120 MPa was 81 and 96 MPa, respectively, about 20% less. The reason for the difference in concrete strength may be attributed to unknown cause(s), such as segregation during the moving or mix process and/or the curing temperature being relatively low in developing the target strength because the 100 and 120 MPa concrete specimens were poured in October (average temperature of 13.5°C). Although the specified concrete strengths of 100 and 120 MPa were not reached, their measured strengths were sufficient to perform the impact test for the purpose of this study. Meanwhile, the design concrete of 80 MPa reached an effective strength of 103 MPa, having been poured during September (with an average temperature of 22°C and a peak temperature of 29°C, which was 6°C higher than past years). This was an unexpectedly strong concrete specimen as a result.

The measured strains at peaks of 35, 80, 100, and 120 MPa ranged from 0.025 to 0.028 and that for UHPC was 0.0038.

For the concrete specimens, the average measured flexural strengths were 5.5, 8.5, 7.8, and 8.4 MPa, and the splitting tensile strengths were 3.46, 7.09, 5.73, and 4.43 MPa for the 35, 80, 100, and 120 MPa, respectively. The average direct tensile strength was 14.23 MPa for the 150 MPa.

Table 3 and Fig. 5 show the relationship between the measured penetration depth ($x_{\mathrm{test}}$) and the concrete compressive strength in the target specimens. In the context of collision experiments, the results are often significantly varied, depending on the fluctuating conditions. Thus, it may become difficult to analyze the experimental results. It could be considered a good experiment when a researcher can successfully obtain consistent results under the same conditions. Hwang et al. (2017) provide a coefficient of variation (COV) of 0.293 across 13 test programs focused on various projectile sizes [see Tables 3 and 4 in the study by Hwang et al. (2017)]. Meanwhile, the COV in this experiment was 0.116., which is indicative of this program having a strong plan and obtaining consistent results. For the conical and hemispherical projectiles, their average $x_{\mathrm{test}}$ values were 13.22, 10.10, 9.63, 9.01, and 6.97 mm for the 41, 81, 96, 103, and 162 MPa concrete target specimens, respectively. The trends and observations made were that as the concrete strength increased, the penetration depth decreased. In short, the use of high-strength concrete and UHPC can significantly improve local impact load resistance when compared to normal-strength concrete. The decrease in high-strength concrete and UHPC target specimens was linear.

In Table 3, the nose shape of the projectile is used to classify the values of $x_{\mathrm{test}}$. For the conical projectile, the average penetration depths were 13.18, 10.02, 9.26, 8.61, and 7.39 mm for the 41, 81, 96, 103, and 162 MPa concrete specimens, respectively. Meanwhile, the average penetration depth for the hemispherical projectile was 13.29, 10.18, 10.0, 9.28, and 6.42 mm for the 41, 81, 96, 103, and 162 MPa concrete specimens, respectively. In the 41 to 103 MPa concrete specimens, the hemispherical projectile achieved greater penetration depth. However, greater penetration depth in the 162 MPa concrete specimens was achieved by the conical projectile.

To address the different impact velocities and masses of the projectile in each test, the penetration depth ($x_{\mathrm{test}}$) normalized by the kinetic energy ($E_K$) for the specimen is depicted in Fig. 6. The kinetic energies of the hemispherical and conical projectiles differed by 40 J and were 630 J and 590 J, respectively.

The penetration depth according to the nose shape is depicted in Table 3. The value difference results indicate that a deeper penetration depth is achieved by the conical projectile results when compared to the hemispherical projectile for normal-strength concrete. However, the value discrepancy was not significant in the high-strength concrete and UHPC target specimens.

The ratios of ($x_{\mathrm{test}}/E_K$) of a conical projectile to that of a hemispherical projectile were 1.18 ($=0.025/0.021$), 1.06 ($=0.015/0.014$), 0.95 ($=0.0154/0.016$), 1.05 ($=0.0148/0.0142$), and 1.05 ($=0.0131/0.0124$) in the 41, 81, 96, 103, and 162 MPa concrete specimens, respectively. The value for normal-strength concrete was significantly higher than that for high-strength concrete and UHPC. It can be derived that the penetration depth of normal-strength concrete targets is sensitive to the nose shape of a projectile. However, the effect of the nose shape on the penetration depth is insignificant in high-strength concrete and UHPC targets.

Table 3 compares test results of the penetration depth with predictions of existing equations. Although the nose shape of projectiles varies in reality, impact equations except for those by Li and Chen (2003) and Young (1997) are classified into four types with rather unclear criteria.

For this study, conical nose shape factors of 1.14, 1.39, 0.685, 1.13, 0.5, and 1.8 were used in the modified NDRC (1976), Hughes (1984), Young (1997), UMIST (Reid and Wen 2001), Li and Chen (2003), and Hwang et al. (2017) equations. The Hwang et al. (2017) equation recommended 0.9 for a sharp nose shape on the basis of existing test data using very sharp projectiles, in which the ratio of $l_n$ to $d_p$ is large (i.e., 1.0 to 3.2, which are the same as 63°–81°). But in this study, the conical nose shape was at 45°. Given the nose shape factor of 1.9 for hemispherical projectiles with the ratio of $R_n$ to $d_p=0.5$, a nose shape factor of 1.8 was applied to the conical nose shape with the ratio of $l_n$ to $d_p=0.5$ in the Hwang et al. (2017) equation.

For hemispherical projectiles, the nose shape factors suggested by each equation were used. In the existing equations, the actual compressive and tensile strengths of concrete were used to predict the penetration depth. For the Hwang et al. (2017) equation, concrete tensile strength was estimated from the splitting tensile strength [i.e., $0.9f_{ct,\mathrm{meas}}$ in Eurocode 2, (CEN 2004)] or direct tensile strength test. It is noted that due to low reliability pertaining to a few of the splitting test results, the larger of the test result and tensile strength in Eqs. (33) and (34) provided by the fib model code (fib 2010) were used.

In view of Fig. 7, the Hwang et al. (2017) equation predicted the test results better than the other equations posed, with the average ratio of test results to predictions being 0.95 and a coefficient of variation (COV) of 0.156. As concrete strength increased, both the modified NDRC (1976) and Hughes (1984) equations overestimated the penetration depth. In general, the prediction accuracy summarized in Table 3 using existing impact equations according to the nose shape, with the exception of the Hwang et al. (2017) equation, decreased as concrete strength increased.

The prediction accuracy of the modified NDRC (1976) equation according to the nose shape was determined to be equal to 0.82. The test-to-prediction ratio of the penetration depth due to a hemispherical nose was slightly larger than that of a conical projectile in the concrete targets for compressive strengths of 81 through 103 MPa. The Hughes (1984) equation showed a similar trend. For these two equations, the results indicate that the penetration depth associated with a conical projectile is relatively overestimated compared to that of a hemispherical projectile in high-strength concrete.

The Young (1997) equation significantly overestimated the penetration depth, showing the average ratio of 0.48, in which inaccurate results had been already recognized; the Young (1997) equation is questionable when the penetration depth is less than about $3d_p$, and the allowable weight range of the projectile is at least 4.5 kg.

However, the UMIST equation (Reid and Wen 2001) underestimated the penetration depth, showing an average ratio of 2.64. Underestimation is attributed to impact test conditions deviating significantly from the allowable application range in which the projectile’s diameter, mass, velocity, and the ratio of the penetration depth prediction to $d_p$ are $50–600\mathrm{mm}$, $35–\mathrm{2,500}\mathrm{kg}$, $3–66\mathrm{m}/\mathrm{s}$, and 0–2.5, respectively.

The Li and Chen (2003) equation overestimated the penetration depth with an average ratio of 0.33, in which overestimation is attributed to the impact factor ($I$) being less than 0.5 in Eq. (17).

The Hertzian contact theory defines the relationship between the contact force and elastic penetration depth when two elastic bodies collide (Hannor et al. 2015). According to the Hertzian contact theory, the contact force ($F_{\mathrm{hemi}}$) related to the indentation depth ($d$) (Fig. 8) due to a hemispherical indenter can be determined from Eqs. (37) and (38) (Hannor et al. 2015), and the contact force ($F_{\mathrm{cone}}$) due to a conical projectile can be calculated from Eq. (39) (Seddon 1956)where $F_{\mathrm{hemi}}$ and $F_{\mathrm{cone}}$ = applied forces to the hemispherical and conical projectiles, respectively; $E^{*}$ = effective elastic modulus of the target with respect to the elastic modulus of the indenter (projectile); $E_1$ and $E_2$ = elastic moduli of the indenter and target, respectively; $v_1$ and $v_2$ = Poisson’s ratios of the indenter and target, respectively; $R$ = radius of the hemispherical nose; $d$ = indentation depth (Fig. 8); and $\theta$ = angle between the plane and the side surface of the conical nose.

Although the Hertzian contact theory considers the elastic condition, the indentation depth ($d$) was assumed to be equal to the penetration depth for the sake of analysis in this experimental study to evaluate the tendency of the impact force (the applied force in the Hertzian contact theory). The sectional diameter, elastic modulus, density, and Poisson’s ratio of the projectile were assumed to be 20 mm, $\mathrm{200,000}\mathrm{MPa}$, $\mathrm{7,850}\mathrm{kg}/{\mathrm{m}}^3$, and 0.3, respectively. The elastic modulus of steel was also considered not affected by the strain rate (CEB 1988).

The elastic modulus of the 41, 81, 96, 103, and 162 MPa concrete specimens were calculated in accordance with ACI 318-14 (ACI 2014) to be 30,095, 42,300, 46,050, 47,700, and $\mathrm{59,821}\mathrm{MPa}$, respectively. The Poisson’s ratio of all specimens was assumed to be 0.21 (Carrasquillo et al. 1981). In a high-velocity impact test, the elastic modulus of concrete is affected by the strain rate, which can be estimated from Eq. (29) (Hwang et al. 2017) and Eq. (40) (fib 2010). The angle ($\theta$) in Eq. (39) was assumed to be equal to the angle of the conical projectile (i.e., 45° in this study), and the thickness in Eq. (37) was the measured value of each test specimen

Table 4 lists impact force predictions according to the concrete compressive strength and nose shape. Impact forces (i.e., the contact force in the Hertzian contact theory) of conical and hemispherical projectiles per the equation decrease as the concrete compressive strength increases. It should be noted that the impact force of the conical projectile on the 41 MPa concrete target specimens was 59% ($=\mathrm{12,451}/\mathrm{7,846}$) greater than that of the hemispherical projectile.

In Table 1, the ratios of the nose shape factors between conical and hemispherical noses in the modified NDRC (1976), Hughes (1984), Hwang et al. (2017), UMIST (Reid and Wen 2001), and Young (1997) equations were 1.14 ($=1.14/1.0$), 1.1 ($=1.39/1.26$), 1.06 ($=1.9/1.8$; inverted value for resistant energy), 1.13 ($=1.13/1.0$), and 1.05 ($=0.685/0.65$), respectively. The ratio predicted by the Li and Chen (2003) equation was 1.00 for the conical projectile at an angle of 45°. In other words, all the equations except for the Li and Chen (2003) equation consider the differences in the impact force between the hemispherical nose and conical nose at an angle of 45°. Actual differences in the impact force between the conical and hemispherical projectiles were 1.47 ($=\mathrm{10,115}/\mathrm{6,903}$), 1.32 ($=\mathrm{9,442}/\mathrm{7,145}$), 1.29 ($=\mathrm{8,457}/\mathrm{6,564}$), and 1.77 ($=\mathrm{7,984}/\mathrm{4,506}$) for 81, 96, 103, and 162 MPa for the concrete specimens, respectively.

The ratios of the actual differences, except for that of 162 MPa, decreased as the concrete strength increased. The average impact velocity of the hemispherical projectile in tests for 162 MPa was found to be $10\mathrm{m}/\mathrm{s}$ slower than that of the conical projectile. However, the gap between the impact velocities of the two projectiles for the 41 through 103 MPa concrete test targets was less than $5\mathrm{m}/\mathrm{s}$. A small penetration depth may have caused errors in the calculation of impact forces. Thus, if the impact velocity of two projectile types in tests for 162 MPa concrete were similar, a decreasing trend would have been maintained or be similar to that found for the other high-strength concrete specimens.

In the high-strength concrete and UHPC target specimens, a decreasing trend in contact force can be deduced from the relationship between the elastic moduli of the concrete and the projectile. The elastic modulus ratio of steel to normal-strength concrete is 4.5 ($=\mathrm{200,000}/\mathrm{44,404}$), but the elastic modulus of steel to 96 or 162 MPa concrete decreases to 2.95 and 2.23, respectively. In short, when evaluating the impact resistance of concrete, the elastic modulus of a steel projectile is relatively larger than that of the concrete target using normal-strength concrete, and the steel projectile can be assumed to be nondeformable. However, the difference of the elastic moduli between the steel and high-strength concrete and UHPC is reduced, which increases the possibility for the projectile to be deformed and absorb the impact energy. As shown in Fig. 9, deformation of the nose of the relatively rigid projectile after impact with high-strength concrete and UHPC target specimens was confirmed. Furthermore, the tip of the conical projectile received more damage due to the impact energy concentration at the tip of the nose. Hence, when developing an impact equation to evaluate the impact resistance of high-strength concrete and UHPC, projectile deformation or damage should be considered.