Experimental Study and Damage Effect Analysis of Concrete Structures under the Combined Loadings of Penetration and Explosion

+e penetration-explosion warhead is one of the most effective weapons for use against concrete structures. In order to study the phenomena and results for concrete damage caused by the combined effects of penetration and explosion, field experiments were performed on damaged concrete targets with different penetration speeds and explosive charges. +e damage to the targets was analyzed, the causes were determined, and prediction methodologies were developed. Dimensional analysis was used to fit experimental results, a formula for calculating the damage depth and volume was proposed, and the dependence of the damage depth and volume on the aspect ratio of the explosive (or charge) and the kinetic energy of bullet penetration were determined. For a given projectile size and quantity of explosives, the damage depth and volume of the concrete target increase with the increasing projectile impact coefficient, but this trend gradually decreases. +is observation can also provide a reference for the optimal design of penetration-explosion warheads, exhibiting the desired performance-price ratio.


Introduction
With the continuous development of penetration weapons for modern warfare, the antiexplosion capabilities of buildings or facilities with significant strategic value have received increasing attention. As an essential building material, concrete is widely used in the construction of various buildings or facilities [1], and the penetration-explosion warhead is one of the most effective weapons used against concrete structures. Its combined damage effects cause the blast side of the structure to be damaged and the rear side to collapse, causing severe damage to the building structure and personnel inside [2][3][4].
erefore, it is of great importance to study the combined loadings due to penetration and explosion and their effects on concrete structures [5].
Research on the dynamic response of concrete structures under the combined damage of penetration and explosion primarily involves studying the process of projectile penetration and the process of the explosion within the context of the initial penetration damage. Although there is considerable literature describing the damage effects of penetration or explosion on concrete structures, there are few studies on the combined effects of penetration and explosion.
In the study of concrete penetration damage, Frew et al. [6] found that when the ratio of the target diameter to the impact body diameter was significant, penetration depth and projectile body overload were not significantly affected, but the surface damage volume was significantly affected. Xue et al. [7] conducted an experiment comparing corundumrubble concrete (CRC) and reinforced concrete and proposed an improved Taylor model to predict the penetration depth into CRC targets. Xue et al. [8] established an engineering calculation model based on the surface splitting mechanism and rigid kinematic equations in order to study the effects of oblique angle and angle of attack on projectile penetration. Zhang et al. [9] developed a new method to predict the real-time penetration depth of ogive-nose projectiles into concrete targets based on acceleration data measured in penetration tests involving ogive-nose projectiles and semi-infinite concrete targets. Zhang et al. [10] describe an in-depth investigation designed to identify critical effective properties related to the penetration depth of small caliber nondeformable projectiles in cement-based materials across a wide range of compositions and material properties. Liu et al. [11] carried out experiments on the impact of medium carbon steel long-rod projectiles on concrete targets and studied the impact behavior of projectiles and concrete targets with different impact velocities.
In the studies of concrete explosion damage, Cofer et al. [12] created a finite element model for prestressed concrete beams and studied the effect of blast loads on the structure with two explosion tests. Fu and Zhang [13] studied the damage to the free surface of a reinforced concrete target subjected to an internal explosion load. Li and Hao [14] studied the damage mode for reinforced concrete slabs under aerial initiation conditions, and Zhang and Wang [15] studied the antiexplosion performance of concrete gravity dams under the impact of underwater explosion shocks. Rabczuk et al. [16] used field tests and numerical simulations on concrete slabs of different thicknesses and initiated explosive contact to compare the diameters and depths of craters on the front and back of concrete targets.
ere are basically two kinds of treatment methods for research on the explosion resulting after the projectile penetrates the concrete structure: (1) burst the explosive directly inside the concrete for detonation or (2) place the explosive inside a shot hole in the concrete and do not block the shot hole. Leng et al. [17] used method (1) to study the dynamic response of cavity formation and developed predictive rules for the concrete structure under the effect of internal explosion load, and Lai et al. [18] studied the failure characteristics of super-strength concrete under conditions of different burial depths and different loadings. Yang and Wang [19] used method (2) with field experiments and numerical simulations to develop a suitable algorithm for numerical simulation of explosion problems in concrete dielectric targets, and Zhang et al. [20] studied the critical collapse thickness and the corresponding critical charge for a concrete target. It is noteworthy that none of the above studies considered the penetrating effect of the projectile.
In practice, due to the randomness in penetration speed, the depth of the explosion (penetration depth) often exhibits considerable uncertainty; this makes it difficult to evaluate the situation accurately, and the ultimate damage effect cannot be accurately judged. On one hand, if the penetration speed is very slow, the explosion point will be extremely shallow, and the explosive energy of the charge will be released into the air. e damage area on the blast side is small, typically consisting of visible pits, and the effect on the rear side is not apparent. On the other hand, if the penetration speed is very high, the explosion point will be extremely deep and the projectile will explode inside the concrete medium to form a gourd pit. e area of damage on the surface layer is then relatively small; although some bulges and cracks will be formed, they often do not contribute significantly to pit opening. Only the appropriate penetration speed will allow the penetration-explosion warhead to inflict maximum damage. In addition, the charge and aspect ratio are also important factors affecting the power of the penetrationexplosion warhead, and differences in these parameters give rise to significant differences in damage effects [18][19][20][21][22]. In this paper, theoretical analysis and experiment are used to study the influence of related variables, such as penetration speed and charge, on the damage inflicted on concrete targets from the combined effects of penetration and explosion. Calculation models of the frontal damage depth and volume are established, and they provide a reference for research on damage effects and protection of concrete buildings subjected to penetration and explosion, while also providing a guide for the optimal design and the best performance-price ratio for penetration-explosion warheads.

Experimental Setup
By dividing the target destruction process into the two stages penetration and explosion, the different destructive effects can be better understood, the coupled effect of penetration and explosion can be analyzed more accurately, and the experiment and data collection can be facilitated. A 30 mm caliber smoothbore gun was used to conduct the penetration experiments at medium and low speeds; subsequently, charge explosion was carried out with a static explosion field after target penetration to simulate the process of penetration and explosion and study the damage to the concrete structure resulting from both effects.
A 30CrMnSiNi2A solid projectile was used in the penetration experiments, and its material yield strength was 1413 MPa. Because it is challenging to remove the projectile after it penetrates the target and reaches the charge position for the explosion experiment, the projectile features a twostage detachable design in which the diameter of the projectile gradually decreases (as shown in Figure 1(a)). e length of the projectile is 100 mm, the diameter of the projectile neck is 20 mm, and the diameter of the projectile tail is 14 mm. A groove is designed into the tail of the projectile to facilitate the use of a specially made flat head screwdriver to rotate the projectile after penetration. e shape of the warhead is oval, and the caliber radius head (CRH) is 2.5. e launch of the projectile utilizes the loading method of the aluminum sabot and the bottom push structure (Figure 2), which controls the initial penetration speed of the projectile at 450-700 m/s. In order to simulate the actual damage due to the penetration-explosion projectile, the warhead part was retained after penetration, and the projectile body was rotated and unloaded to carry out an explosion experiment. e actual state of the projectile before and after penetration is shown in Figure 1 A total of 12 concrete targets were used in the experiment, and the experiment was conducted at a field test range. e strength of 7 targets was C35, and the strength of 5 targets was C40. e sizes of the targets were all 2 Shock and Vibration ϕ1000 mm × 500 mm. e 8 mm steel hoop is used for circumferential reinforcement to eliminate the radial boundary effect, as shown in Figure 3. e layouts of the experiment site and test equipment are shown in Figures 4 and 5. e explosion experiment was performed in a static explosion field. e grain was pressed in advance ( Figure 6), and the size was ϕ20 mm × 20 mm. e passivated hexogen (RDX) was arranged in the penetration tunnel, and the column charging method was adopted. e arrangement is shown in Figure 7.

Results
Concrete impact experiments were performed with different initial penetration speeds, and then the damage status of each target was recorded. A high-speed camera was used to record the target's attitude, and the frames/sec speed of the camera is 4000 FPs. Each bullet had a correct attitude toward the target. Figure 8 shows the attitude of the bullet and the damage inflicted on the target during the penetration experiment on target 5. After the projectile penetrates the  target, pits will be formed on the surface of the target. e initial damage state of the target can be judged based on the pit area and the number and size of cracks. e target speed and penetration depth of each projectile were recorded. e data are shown in Table 1. e penetrated target was transported to a static explosion field for the explosion experiment. After the explosion, a funnel-shaped crater appeared on the front of the target and a few cracks appeared outside the damaged area. e cracks of some targets connected to each other to cause fragmentation in some areas, and some concrete fragments were peeled off from the front of the target. After the explosion, the pits were noticeable, and it was found that the integrity of the target was poor. During the experiment, high-speed photography was used to record the concrete throwing process during the explosion, and the frames/sec speed of the camera is 3000 FPs. Figure 9 shows a concrete throwing image recorded for target 7, when it was subjected to an explosive load. After the experiment, three-dimensional scanning and recording of the target's combined penetration-explosion damage were performed. Figure 10 shows the damage on some targets' blast sides, and Figure 11 shows 3D scans of targets' damaged areas. e explosive used in the explosion experiment was passivated hexogen (RDX) with a density of 1.5 g/cm 3 , the explosion heat was 5215 J/g, the detonation velocity was 8150 m/s, and the charge diameter was 20 mm. Other relevant data such as charge, aspect ratio, and target damage status are shown in Table 2.

Discussion
Because it is difficult to establish a complete mathematical and mechanical model for combined penetration-explosion damage, dimensional analysis is used for simplification. Determining the relationship between multiple physical quantities is useful for studying the influencing factors and formulating applicable empirical rules [23][24][25]. In this paper, we adopt the L-F-T mechanics system to conduct a dimensional analysis of the combined effects of penetration and explosion. e main parameters involved in the contact explosion following low-and medium-speed penetration are shown in Table 3 [26][27][28][29][30][31][32][33][34][35]. e damage depth is a factor representing the penetration-explosion experiment on the blast site. In addition, the study of the damage shape and volume of the blast side can provide a theoretical basis for damage assessment and the rapid repair and of concrete structures, which is of great significance. erefore, key parameters are discussed below.
From a physical point of view, the damage depth depends on the parameters related to the material and the geometric characteristics of the projectile [33,34,36,37], explosive, and target, which can be summarized as Using the Buckingham theorem [23,25], equation (1) can be expressed in the following dimensionless form: e impact energy factor I refers to the definition of the impact coefficient offered by Haldar [4,38]. is factor is a dimensionless quantity: where N represents the shape factor of the warhead, m is the projectile mass, v is the initial penetration velocity, and D is the projectile diameter. In this experiment, some parameters, such as the shape of the warhead, the projectile diameter, the density of the cylindrical charge, and the detonation speed, were held constant. erefore, the only remaining projectile variables are the initial penetration velocity and projectile mass, and the only remaining explosive variables are the diameter and length of the explosive. For a specific concrete material, the elastic modulus, Poisson's ratio, and density are definite values, the target thickness is also a fixed value, and the impact energy factor already includes the material parameters of the concrete. erefore, the dimensionless expression for the damage depth after the explosion can be simplified to where the first variable of the above formula is the CAR (charge aspect ratio), an explosion parameter that also represents the size of the charge in this experiment. e second variable is the penetration parameter, which contains the material parameters of the concrete. e relationship  between the dimensionless damage depth and impact energy factor I is shown in Figure 12. Analysis of Figure 12 shows that the dimensional damage depth is low when the CAR � 4; it is high when the CAR � 6, while for CAR � 5, it is at an intermediate level. We can make corrections by reasonably assigning adjustments. In fact, as the momentum of the penetration projectile increases, the rate of the increase in penetration depth will taper off. e impact of the initial penetration damage on the explosive load will stabilize, and the increase in the damage 6 Shock and Vibration depth will also be moderated [6,[39][40][41][42]. Finally, the combined load achieves the penetration of the target or maintains a certain damage depth, depending on the relationship between the thickness of the target and the limit of the damage depth. erefore, it can be assumed that the dimensionless formula equation (4) has a power-type asymptotic representation, which is where α, β, and c are constants which are fitted through experimental data to obtain For clarity, the relationship between equation (7) and experimental results is shown in Figure 13. e fitted formula is in good agreement with the experimental results, and the scatter does not exceed the illustrated 10% limits. Of course, this formula has limitations and is only applicable to the data range for the materials used in the experiment although the concrete structures used in this experiment are commonly used in engineering.
Similarly, the damage volume can be obtained by dimensional analysis [23][24][25]. e parameters related to the damage volume are Using the Buckingham theorem [23,25], equation (8) can be converted into the following dimensionless form: e simplified dimensionless expression is   Shock and Vibration 7 e damage process resulting from the combined penetration-explosion effect is very complicated, and it also exhibits substantial randomness. After the explosive detonated, the surrounding concrete was crushed because of the explosive shock wave. As shown in Figure 14 [43], after the shock wave passed through the crushing zone, it continued to propagate through the surrounding concrete. Since most of the explosive energy is used for crushing and compressing concrete, the energy per unit volume of concrete is reduced. e shock wave is attenuated into a compressive stress wave, which causes compressive strain in the radial direction and tensile strain in the circumferential direction. Due to the high compressive strength and low tensile strength of concrete, many radial tensile cracks are formed in the crushing zone when the tensile stress on the wave front exceeds the tensile strength of the concrete [5]. As shown in Figure 14, the degree of fragmentation in the fragment formation zone, which has the largest impact on cracking, is highly random.
is results in a situation in which the damage volumes in Figure 15 are particularly dispersed and substantially irregular.
According to the principles of penetration and explosion damage, it is easy to establish that the growth trend for the damage volume on the blast side of the concrete target is like the growth trend for the damage depth. As the momentum of the penetrating bullets increases, the increasing ability of the warheads to inflict damage with similar charges will gradually decrease. erefore, although the study of the damage volume is relatively random, basic relationships can still be drawn for reference. By fitting the experiment results, we obtain  Figure 13: Relationship between equation (7) and experimental results.
Crushing zone

Shock and Vibration
For clarity, the relationship between the function curve in equation (12) and the experimental results is shown in Figure 16. Due to the large randomness of the experimental results, some data points differ from predicted values by up to 20% of the predicted value. Because there are fewer experimental data (relative to, e.g., Figure 13), this equation is restricted and only provides a theoretical guideline. e randomness of the damage caused by cracks generated by the explosion stress waves is an issue requiring further attention in subsequent studies.

Conclusions
is research on the combined effects of penetration and explosion on concrete targets has very important practical significance.
rough field experiments, the blast side damage to concrete targets with different penetration speeds and explosive charge conditions is analyzed, and empirical laws and predictions of damage are obtained. is leads to the following main conclusions: (a) For a given size and quantity of explosives, the damage depth and volume experienced by the concrete target will increase with the increasing impact coefficient of the bullet, but the rate of the increase will gradually diminish. Ultimately, the target will be penetrated or damaged at a constant depth that depends on the relationship between the target thickness and the damage limit. (b) Using fits to the experimental data for concrete targets, formulas for the damage depth and volume are proposed in equations (6) and (11), and the two equations agree well with experimental data. is establishes the dependence of the damage depth and volume on the aspect ratio (or charge) of the explosive and the kinetic energy of the penetration. Similarly, these equations can provide a guide for the optimal design of penetration-explosion warheads. (c) e damage volume in concrete targets exhibits substantial randomness and is affected by many factors. e collapse of materials caused by cracks in the fragment formation zone deserves further experimental attention. e unevenness of the aggregate and the random orientation of the cracks may prevent the concrete material from meeting performance expectations. is problem is of considerable significance when considering damage assessment and the rapid repair of concrete structures.
In addition, the combined effect of penetration and explosion will cause the rear side of the concrete structure to collapse, and the internal personnel of the building will cause casualties. e value of critical collapse thickness and the law of damage to the back of the concrete structure are the key issues to be addressed in the following research.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.