Local damage characteristics of reinforced concrete slabs subjected to hard/deformable projectile impact

Abstract

This study aims to investigate the local failure mechanism of reinforced concrete slabs subjected to hard and deformable projectile impacts. This is done by conducting impact tests and numerical simulations. In a series of impact tests, a hard/deformable steel projectile (8.3–8.4 kg) collided with a reinforced concrete slab with a thickness of 10–30 cm at an impact velocity of 64–90 m/s, and the impact and reaction forces were measured. The numerical simulation demonstrated that the failure of the reinforced concrete slab was affected by the rigidity of the projectile in terms of the maximum impact force and impulse.

Keywords

Projectile impact reinforced concrete slabs scabbing hard/deformable projectile

Introduction

In recent years, tornado events and volcanic eruptions have increased owing to climate change and crustal movement. For instance, 24 fatalities and 387 injuries were caused by the Moore tornado in Oklahoma, United States in 2013 (National Institute of Standards and Technology, 2013). A volcanic eruption at Mt. Ontake in Japan in 2014 (Cabinet Office Japan, 2015b) left 58 people dead, while several were injured by volcanic cinders, in addition to pyroclastic and debris flows. In such incidents, structural damage caused by missiles generated by wind pressure (called tornado missiles) and volcanic cinders (i.e., volcanic missiles) have been reported. To protect humans and structures from impact loads, a reliable design of shelters for protection from the tornado and volcanic missiles should be promptly established. With regard to designing buildings that provide protection from collisions with tornado and volcanic missiles in Japan, guidelines have been introduced that have assigned a design impact velocity of 40 m/s and 150 m/s for a tornado and volcanic missile, respectively (Cabinet Office Japan, 2015a; Nuclear Regulation Authority Japan, 2013). However, details of the impact condition or failure mechanism of the structure have not been sufficiently examined.

Numerous studies on the failure behavior of reinforced concrete (RC) slabs subjected to impact loads over a wide range of impact velocities have been conducted in the past years. Miyamoto et al. (1991 and 1994) proposed a safety verification method for an RC railing of a bridge exposed to vehicle impact, based on the concepts of load-carrying and energy capacity, by conducting scaled vehicle collision tests and finite element analysis. Other studies on the impact behavior of RC slabs subjected to low-velocity impact loads involved experiments and numerical programming (Othman and Marzouk, 2016; Xiao et al., 2016; Zineddin and Krauthammer, 2007). In these studies, the overall response of RC slabs (flexure and punching shear failures) was investigated at an impact velocity of less than 10 m/s. The local damage of RC slabs subjected to a high-velocity impact of 150–1000 m/s was investigated for bullet and aircraft collisions (Beppu et al., 2008; Chang, 1981; Chen et al., 2008; Gomez and Shukla, 2001; Huang et al., 2005; Hughes, 1984; Ito et al., 1995; Kennedy, 1976; Li and Chen, 2003; Li et al., 2005, 2007; Werner et al., 2013). These studies reported that a local failure occurred in the vicinity of the collided part because of the stress wave interaction and local deformation. That is, scabbing is caused by the propagation of cracks owing to the tensile stress wave transformed from the incident compressive stress wave at the free surface. Li and chen (2003) proposed formulas for predicting the penetration depth of concrete impacted by a hard projectile based on dimension analysis using a theoretical penetration model. Some studies have investigated the impact resistant behavior of RC structures as a function of moderate velocities in the range of 10–150 m/s (Ito et al., 1995; Li et al., 2007; Yankelevsky et al., 2000). However, few formulas have been proposed based on the detailed failure mechanism of RC slabs subjected to projectile impact on the basis of measured tests and numerical analyses. Although the impact force characteristics would significantly affect the local failure, few studies collected its detailed data (Forrestal et al., 2003). In addition to the hard projectile impact, a deformable projectile impact should be incorporated in the structural design for tornado and volcanic missiles because they have vulnerable and brittle natures in the impact event. But the impact force characteristics of the deformable impact were not investigated in the literatures.

This study aims to experimentally and numerically investigate the fundamental failure characteristics of RC slabs subjected to moderate velocity impacts. To this end, impact tests were conducted using a steel projectile. The failure process of RC slabs subjected to hard/deformable projectile impacts was discussed experimentally based on the motion of the projectile during the impact response of an RC slab. Numerical simulations of impact tests were conducted to examine the reproducibility of the projectile motion and to study the failure mechanism of an RC slab.

Tests and failure characteristics of RC slab subjected to hard projectile impact

Impact test apparatus

A moderate impact velocity test machine was used to conduct the impact tests. This machine can launch a projectile weighing 8.3 kg at a velocity of 64–90 m/s by adjusting the air pressure. A schematic of the projectile launching test and the experimental setup are shown in Figures 1 and 2, respectively. A pair of laser velocity sensors was fixed at the muzzle of an acceleration tube to measure the average velocity at intervals of 50 cm. The muzzle of the acceleration tube was approximately at a distance of 0.5 m from an RC slab because of the attachment of a projectile catcher that holds the projectile after rebounding. Consequently, the velocity of the projectile increased slightly after it passed through the acceleration tube. Hence, the velocity of the projectile was obtained by differentiating the displacement time histories from captured images using a high-speed camera (Resolution: 1280 × 152, frame rate: 32,000 fps).

Figure 1.

Schematic of launching test machine.

Figure 2.

A view of experimental setup.

Steel projectile and RC slab

Figure 3 shows the steel projectile (hard projectile) used in the tests. The 8.3 kg mass steel projectile (JIS: SKS93) had a hemispherical nose with a diameter of 80 mm. The mass of 8.3 kg corresponds to the lightest tornado missile made of a steel pipe (8.4 kg) designated in “Assessment guide for tornado effect on nuclear power plants of Japan” (Nuclear Regulation Authority Japan, 2013). Targets for tracking using a high-speed camera were set on the lateral side of the projectile. Figure 4 displays the dimensions of the RC slabs and arrangement of the reinforcing bars. The RC slabs were 1225 mm in height and width, with thicknesses of 100, 200, and 300 mm. The specimens were reinforced with reinforcing bars of a reinforcing ratio of 0.00–1.43% in both directions on the top and bottom sides. The reinforce ratio was defined as a ratio of the total cross-sectional area of the steel bars excluding the safety-reinforcing bars to the effective cross-sectional area of the concrete slab (1000 mm width × thickness). To investigate the effects of the reinforcement ratio on the failure state of RC slabs, three different 200-mm-thick reinforced specimens, including a plain concrete slab, were cast. To ensure that the specimens were intact during the transportation and replacement of an RC slab, safety-reinforcing bars (broken lines in Figure 4) were set along the four sides of the specimens. The average compressive strength of the concrete was 44.1 MPa using cylindrical specimens with a diameter of 100 mm and a length of 200 mm.

Figure 3.

A steel projectile.

Figure 4.

Dimensions of Reinforced Concrete slabs and arrangement of rebar (----: Safety rebar).

Measurement items and test case

The displacement-time history of the projectile was obtained by analyzing the images captured by a high-speed camera after the collision. The velocity and acceleration of the projectile were calculated by differentiating the displacement–time history, while the impact load of the projectile was indirectly obtained by multiplying the mass of the projectile with the acceleration.

Table 1 lists the test cases and their parameters, including the impact velocity, thickness of the RC slab, and reinforcing ratio. To investigate the effect of the impact velocity on the transition of the failure state, an impact velocity in the range of 64–90 m/s was employed for five specimens with a thickness of 200 mm and reinforcing ratio of 0.51%. The effects of the slab thickness on the failure state were investigated using 100- (Case1) and 300-mm (Cases10–12)-thick specimens with a reinforcing ratio of 0.53 %–0.57%. Finally, the influence of reinforcing ratios between 0–1.43% on the failure state of the 200-mm-thick specimens was examined at an impact velocity of 65 m/s.

Table 1.

Test cases and results.

Case	Thickness (mm)	Steel ratio (%)	Velocity (m/s)	Failure mode	Penetration depth (mm)	Maximum of impact load (kN)	Maximum of reaction force (kN)
1	100	0.57	69.7 (Estimated)	Perforation	—	Nonmeasured	138
2	200	0.51	65.0	Spalling	39	779	375
3	200	0.51	74.8	Scabbing limit	43	778	Failed
4	200	0.51	74.8	Scabbing limit	41	876	368
5	200	0.51	81.2	Scabbing	53	906	257
6	200	0.51	89.7	Scabbing	52	840	167
7	200	0.00	66.0	Spalling	39	820	339
8	200	0.99	64.4	Spalling	38	702	328
9	200	1.43	64.1	Spalling	38	870	387
10	300	0.53	74.8	Spalling	49	992	394
11	300	0.53	81.9	Spalling	48	1,055	305
12	300	0.53	85.7	Spalling	48	993	281

Failure state of RC slab subjected to hard projectile impact

Definition of failure mode

Table 1 summarizes the test results and impact velocities calculated via image analysis. The impact velocity of test Case1 was measured only by the velocity sensor at the muzzle of the acceleration tube because of the protection of the high-speed camera. Because the failure mechanism of an RC slab subjected to a moderate velocity impact was not clearly categorized, for instance, into local damage and global failure, local failure mode was applied when referring to previous studies, which included spalling (fracture on the impact surface), scabbing (failure on the rear surface without a perforation hole), perforation (perforation hole with projectile passing), and scabbing limit (Kennedy, 1976).

Failure mode and penetration depth

The failure modes of RC slabs can be understood in terms of the relationship between the thickness of an RC slab and the velocity of the projectile, as shown in Figure 5. The figure also shows the CRIEPI formula (Ito and Ohnuma, 1995; Li et al., 2005), which was proposed for the assessment of the scabbing and perforation limits, as follows:

t_{s} = α_{s} \times {\frac{V_{0}}{V}}^{0.13} \frac{{(M V^{2})}^{0.4}}{d^{0.2} {f^{'}}_{c}^{0.4}}

(1)

t_{p} = α_{p} \times {\frac{V_{0}}{V}}^{0.25} {\frac{M V^{2}}{d \cdot {f^{'}}_{c}}}^{1 / 2}

(2)

where t_s is the scabbing limit, t_p is the perforation limit, V₀ is the control velocity (60.96 m/s), V is the impact velocity (m/s), M is the mass of the projectile (kg), d is the diameter of the projectile (m), f _c’ is the compressive strength of concrete (MPa), and α_s and α_p are constants that are equivalent to 6.96 × 10⁻³ and 8.96 × 10⁻⁴, respectively.

Figure 5.

Failure mode in terms of the relation between the thickness of the specimen and impact velocity of the projectile.

The figure shows that the test results of the perforation limit show a good correspondence with the CRIEPI formula, but the CRIEPI formula slightly overestimates the scabbing limit of the 200-mm-thick RC slab by approximately 15%.

Failure state

Figure 6 shows the failure states of the 100-mm- and 200-mm-thick RC slabs categorized with respect to the reinforcing ratio and slab thickness. In all test cases, the steel projectile was not deformed after the tests. In the photos, cracks were emphatically depicted by black and white lines. Figure 6 shows the failure states of a 100-mm-thick RC slab with a 0.57% reinforcing ratio, and 200-mm-thick RC slabs with a 0.51% reinforcing ratio, with an impact velocity of 65–90 m/s. The 100-mm-thick RC slab at a velocity of 69.7 m/s (Case1) shows perforation in which a perforation hole is clearly generated in the impact area. The failure mode in Case 2 (thickness of 200 mm and impact velocity of 65.0 m/s) was spalled with circular cracks on the rear surface of the specimen, but no diagonal crack was observed in the cross section. In Case 3 and 4 (thickness of 200 mm and impact velocity of 74.8 m/s), diagonal cracks were clearly generated in the cross section, but no scabbing was observed. In Case 5, at an impact velocity of 81.2 m/s, scabbing was considered as the failure mode because a part of the diagonal shear crack reached the rear surface, and scabbing was partially generated. Note that a crack in the direction parallel to the rear surface connecting the diagonal cracks is initiated (white broken line in Figure 6) in the cross section of specimens in Case 4–6. The crack appears to be a “spalling fracture” owing to the stress wave interaction and local deformation (Chang, 1981). In Case 6, scabbing was eventually observed at an impact velocity of 89.7 m/s. Comparing the initiation and development of the cracks in the cross section in the case of 200 mm-thick RC slabs revealed that a crack was formed by the stress wave at a velocity of 74.8 m/s, and then diagonal cracks widened and formed the scabbing at velocities of 74.8–89.7 m/s.

Figure 6.

Failure states of specimens (100-mm-and 200-mm-thick reinforced concrete slab).

Motion of projectile and impact response of RC slab subjected to hard projectile impact

In this section, the failure mechanism is discussed by comparing the projectile motion before and after collision with the impact response of RC slabs in Case2, Case4, and Case6.

Motion of projectile

Figure 7 shows the displacement–time histories of the projectile in Case2, Case4, and Case6, where the origin indicates the time of collision. In the figure, the displacement indicates the position of the projectile after impact. In Case2 and Case6, the time duration of measurement was 3 ms because the tracing target in the image analysis was obstructed owing to fragments caused by spalling. In Case2 and Case4 (failure modes are spalling and scabbing limit, respectively), the displacement increases after the collision, yielding a maximum displacement of 30–40 mm in 1.0 ms. However, in Case 6, the displacement continues to increase in 3 ms owing to the scabbing failure.

Figure 7.

Displacement-time histories of projectile.

Figure 8 illustrates the impact velocity-time histories. The impact velocity curve in black represents the smoothed data with the moving average method of seven words. In all the cases, the impact velocity decreases to zero or becomes negative (called rebounding velocity) between 1.0–1.5 ms. In Case6, the impact velocity reaches zero at 3 ms.

Figure 8.

Velocity-time histories of projectile.

Figure 9 displays the impact force-time histories obtained by multiplying the mass and acceleration of the projectile. As a high-frequency wave oscillates owing to time differentiation, the impact force–time history is smoothed using the moving average method (black line in the figure).

Figure 9.

Impact force-time histories of projectile.

The measured data revealed that the maximum impact force and duration in the impact condition were approximately 1000 kN and 1.0–1.5 ms, respectively, and the impulse that can be calculated by integrating the impact force-time history was identical to the momentum of the projectile of 540–745 kg·m/s.

Impact response of RC slab subjected to deformable projectile impact and numerical simulation

Experimental results

Figure 10 shows a photograph of the steel deformable projectile used in the test. In a hard projectile impact, the shape of the impact head significantly affects the local failure of an RC slab (Kennedy, 1976; Li et al., 2005). Hence, to investigate the effects of the energy absorption of a steel tube inside the deformable projectile on the local failure of the RC slab, the shape of the projectile head of the deformable projectile was set to be the same as the hard projectile and the mass of the deformable projectile was set to be identical to the hard projectile. A 500 g steel tube with a thickness of 2 mm was installed between the spherical head and rear body. The total mass of the projectile is 8.4 kg. As the CRIEPI formula well estimated the scabbing and perforation limits of an RC slab, the thickness of an RC specimen and the impact velocity were determined based on the preliminary tests considering the scabbing and perforation limits calculated by the CRIEPI formula. Two RC specimens were prepared, and both of which had a length, width, and thickness of 1100 mm, 1100 mm, and 150 mm, respectively, as shown in Figure 11. The specimens were fixed on four sides. In the test, an impact velocity of 52 m/s and 60 m/s was applied to the RC slab because the velocities could cause the perforation of a 150 mm-thick RC slab subjected to a hard projectile impact.

Figure 10.

8.4 kg deformable projectile.

Figure 11.

Reinforced Concrete slab.

The absorbed energy of the steel tube used in the projectile was evaluated based on the relationship between the buckling force and deformation. Table 2 lists test cases and results obtained by the static and dynamic compressive loading tests, and Figure 12 displays an example of the relationship between the force and displacement obtained by the static and dynamic compressive tests. The dynamic loading tests were conducted using a servo-controlled loading system at a constant velocity of 2 m/s. A strain type load cell with a capacity of 980 kN and a laser displacement sensor with sampling rate of 3 kHz were used to measure the force and displacement. Both static and dynamic loading tests were conducted for three steel tubes. The strain rate was calculated as the gradient of the strain-time history between the strains at one third of the buckling strength and the buckling strength. The strain was measured with 5 mm long strain gauges attached at the center of the lateral side of the steel tube.

Table 2.

Test cases and results.

Case	Strain rate (1/s)	Buckling force (kN)	Average force (kN)	Deformation (mm)	Absorbed energy per unit volume (kJ/mm³)
Static-1	3.71× 10^-5	161	78.7	58.6	169
Static-2	1.45× 10^-4	156	78.5	78.9	168
Static-3	5.11× 10^-5	158	79.1	92.5	165
Dynamic-1	2.19	234	87.7	90.0	188
Dynamic-2	1.71	230	87.9	89.3	188
Dynamic-3	1.52	238	89.2	90.4	191

Figure 12.

The relationship between force and displacement.

The buckling force shown in Table 2 is defined as the maximum value in the relationship between the buckling force and displacement as shown in Figure 12, and the notation of average load in Table 2 is the averaged force up to the maximum displacement, as shown in Figure 12. It is seen from Table 2 that the average buckling force at static (strain rate of 10⁻⁵/s) and dynamic (strain rate of 10°/s) tests were 159 kN and 231 kN, respectively, thus the dynamic buckling force was 1.45 times higher than the static one. The buckling shapes of the steel tubes in this test are shown in Figure 13, and buckling deformations occurred at the end or at both ends. However, the difference in the deformation shape did not affect the buckling force or the force-displacement waveform. The absorbed energy per unit volume due to the deformation of the steel tube can be calculated by dividing the absorbed energy by the deformed volume of the steel tube. The average absorbed energies per unit volume at the static and dynamic loading tests were 167 kJ/mm³ and 189 kJ/mm³, respectively, thus the dynamic absorbed energy was 1.13 times higher than the static one.

Figure 13.

The buckling of steel tube.

Figure 14 shows the failure state of the RC slabs. In this test condition with a hard projectile, although the perforation failure was expected to occur with a hard projectile using the CRIEPI formula, the RC slab showed spall failure at an impact velocity of 52 m/s and scabbing at an impact velocity of 60 m/s. The test results revealed that the scabbing limit velocity of the test condition was between 52 m/s and 60 m/s. Compared to the hard projectile impact case, the failure of the RC slab was significantly suppressed because the deformable projectile absorbed the kinetic energy of the projectile.

Figure 14.

Projectile and failure state of reinforced concrete models.

Numerical investigation

Numerical simulations were conducted using the hydrocode ANSYS AUTODYN (ver.15.0). Figure 15 shows the numerical model. The numerical model should be one eighth the 150-mm-thick RC slab, but it cannot be so simplified in terms of thickness direction. Therefore, to reduce the cost of the simulations, a quarter model was constructed because of the structural symmetry. The RC slab and projectile were modeled using solid elements, and the initial velocity was applied to all the nodes of the projectile model. The numbers of concrete and projectile elements were 605 160, and 1 969, respectively. The element size of the concrete was determined 5 mm × 5 mm × 5 mm, referring the previous numerical simulation conducted by the authors (Kataoka et al., 2017). The reinforcing bar was modeled with beam elements embedded in a concrete model with an element size of 5 mm. The circular steel tube and steel support were modeled using shell elements. The nodes in the hatched area of the steel support in the figure were fixed. To compare the numerical results of the deformable projectile impact case with the hard projectile impact case, a hard projectile model was made by removing the steel tube model from the deformable projectile model.

Figure 15.

Numerical model.

The nonlinear Drucker-Prager yield criterion and negative pressure fracture criterion, as shown in Figure 16, were applied to the concrete material. The static compressive strength of concrete was 25 MPa and, the static tensile strength of concrete was 2.2 MPa of 7% of the compressive strength of concrete. The dynamic compressive and tensile strengths were calculated by multiplying the static yield stress by the dynamic increase factor (DIF) at a strain rate of 10 (1/s), calculated by the following equations proposed (Fujikake et al., 2000; Ross et al., 1989) respectively, as shown in equations (3) and (4).

\frac{{f^{'}}_{c d}}{{f^{'}}_{c s}} = {(\frac{ε}{ε_{s}})}^{0.006 {[\log (\frac{ε}{ε_{s}})]}^{1.05}}

(3)

\frac{{f^{'}}_{t d}}{{f^{'}}_{t s}} = \exp [0.00126 {(\log \frac{ε}{ε_{s}})}^{3.373}]

(4)

where

f_{c d}^{'}

and

f_{t d}^{'}

are the dynamic compressive and tensile strengths, respectively;

f_{c s}^{'}

and

f_{t s}^{'}

are the static compressive and tensile strengths, respectively; and

\dot{ε}

and

{\dot{ε}}_{s}

are the dynamic and static strain rates, respectively.

Figure 16.

Concrete model.

To avoid disruption of calculation due to excessive distortion of the element, numerical erosion criterion was adopted using the effective strain as shown in equation (5) (Westerling, 2002), in which the threshold value of the erosion strain of 2.5 was used.

ε_{e f f} = \frac{2}{3} \sqrt{(ε_{1}^{2} + ε_{2}^{2} + ε_{3}^{2}) + 5 (ε_{1} ε_{2} + ε_{2} ε_{3} + ε_{3} ε_{1}) - 3 (ε_{12}^{2} + ε_{23}^{2} + ε_{31}^{2})}

(5)

where

ε_{e f f}

is the effective strain,

ε_{1}

ε_{2}

, and

ε_{3}

are the principal strains, and

ε_{12}

ε_{23}

and

ε_{31}

are the principal shear strains.

The projectile was modeled as elastic, and the steel material of the reinforcing bar and steel tube was modeled using the Johnson-Cook yield criterion (Johnson and Cook, 1983).

σ_{f, d} = [σ_{f, s} + B ε_{p}^{n}] (1 + C \ln \frac{\dot{ε}}{ε_{0}})

(6)

where

σ_{f, d}

and

σ_{f, s}

are the dynamic and static yield stress respectively,

ε_{p}

is the effective plastic strain,

ε_{0}

is the reference strain, and n, B, C are material constants. The material constants were determined referring the literature (Schwer, 2007).

Figure 17 illustrates the deformation of the steel tube and velocity distribution in the RC slab at an impact velocity of 52 m/s, compared with a hard projectile impact case simulated numerically. The deformation due to local buckling was greater than that of the experimental one by 9.5%, but the buckling in the upper portion was quite similar to the experimental one. Although the velocity distribution in the RC slab in the deformable projectile case was slightly concentrated in its central portion, the overall velocity was relatively low. In contrast, the RC slab in the 8.4 kg hard projectile case shows clear scabbing. The numerical simulation indicated that the buckling of the steel projectile mitigated the failure of the RC slab.

Figure 17.

Deformation of steel tube and velocity distribution in reinforced concrete slab.

Figure 18 shows the velocity-time history of the projectile and impact force-time history obtained by multiplying the acceleration that is calculated based on the image analysis with the projectile mass. In the figure, “Nose” and “Body” denote the nose and rear body, respectively, as shown in Figures 10 and 15. The velocity of the nose and body parts obtained in the simulation successfully reproduced the experimental results. The equilibrium condition between the nose part, steel tube, and rear body, as shown in Figure 19, is given as follows:

F_{c} = F_{p} - m α

(7)

where

F_{c}

is the resistance force from the RC slab,

F_{p}

is the buckling force, mα is the inertial force of the projectile nose, m is the mass of the projectile nose, and α is the acceleration of the projectile nose.

Figure 18.

Projectile velocity-and impact force-time history.

Figure 19.

Equilibrium condition of projectile.

In Figure 18 (b), the impact force acting on the RC slab in the deformable impact case increased to 800 kN in 0.3 ms, similar to the hard projectile case, while it dropped suddenly and oscillated owing to the buckling of the steel tube. Comparison of Figures 17 and 18 indicates the reduced maximum impact force and elongated duration due to buckling changed the failure mode of the RC slab.

Figure 20 illustrates the inertia force of the rear body of the projectile simulated numerically in the cases of spalling and scabbing, which is equivalent to the buckling force time history of the steel tube based on the equilibrium condition. As observed, the maximum force is approximately 300 kN in both cases and oscillates with peak forces of 200 kN after 0.5 ms, which corresponds to the buckling force of the steel tube. That is, the projectile penetration into concrete is completed with the resistance of concrete in 0.5 ms. After the projectile nose part rapidly decelerates, the buckling of the circular steel tube develops by the inertia force of the rear body. A schematic of the impact force-time history of the projectile is shown in Figure 21. The peak force F_max could be generated by the penetration of the projectile into the concrete, and the penetration was completed at t₁. Subsequently, the inertia force of the nose part was negligible, and the buckling force of the steel tube acted on the RC slab.

Figure 20.

The inertia force of body part of projectile(The buckling force of circular tube).

Figure 21.

The impact force of deformable projectile time history.

Figure 22(a) demonstrates the impact force-time history calculated for a hard projectile with the same mass and the deformable projectile colliding with the RC slab at a velocity of 52 m/s. The peak force in the hard projectile case is approximately 1000 kN at 0.4 ms and the duration is 1.0 ms. Meanwhile, the peak force in the deformable projectile case is approximately 800 kN at 0.3 ms, which is 20% less than that in the case of the hard projectile. After the peak force, the impact force oscillates with the peak force of 200 kN due to the buckling of the steel tube. Herein, both the impulses caused by the deformable projectile are approximately 434 N·s. Failure status and velocity distribution of the RC slab as shown in Figure 22(b) indicates that the diagonal cracks in the cross section in the hard projectile impact are widely opened compared to those in the deformable projectile impact. Velocity distribution as shown in Figure 22(b) also revealed that the peak velocity on the rear side in the deformable projectile impact is significantly less at 3.0 ms, while the failure mode in the hard projectile impact is scabbing with the peak velocity of 10 m/s on the rear side. The numerical result indicates that the decreased impulse in 1.0 ms in the deformable projectile impact mitigated the local damage.

Figure 22.

Comparison of deformable projectile to hard projectile with 8.4 kg mass and impact velocity of 52 m/s. (a) The impact force-time histories of hard and deformable projectile. (b) Failure mode and velocity distribution of RC slab. a) Failure mode. b) Velocity distribution.

Conclusion

This study aimed to experimentally and numerically investigate the failure characteristics of RC slabs subjected to hard/deformable projectile impact. The main conclusions are as follows:

Impact tests were conducted to investigate the impact response of an RC slab subjected to a moderate velocity impact. As the impact velocity increased, the failure mode of the RC slab developed from spalling to scabbing. The failure status of the RC slab was not affected by a reinforcing ratio of 0.00–1.43%.

The buckling deformation of the deformable projectile and failure mode of an RC slab were examined by conducting projectile impact tests. The scabbing damage was suppressed owing to the buckling deformation of the deformable projectile. Numerical simulations revealed that the impact force characteristics changed significantly owing to the buckling of the steel tube, which mitigated the failure mode of the RC slab.

Footnotes

Declaration of conflicting interests

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

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Koki Mori

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