A vulnerability analysis method for concrete piers subjected to shaped charge penetrators

Abstract

The present invention discloses a method for analyzing the vulnerability of concrete piers under the action of shaped charges, specifically, performing structural analysis on the target concrete pier and characterizing the projectile-target intersection conditions; using the residual height of the destroyed concrete to characterize the damage level of the destroyed concrete pier; obtaining residual height data of the shaped charge on the concrete pier under different shaped charges, different attack directions, and different action positions through simulation analysis or experiments; obtaining equal damage curves of different damage levels of the concrete pier; calculating the vulnerable area through a damage probability calculation function; and then judging and selecting appropriate attack conditions. Compared with the prior art, the present invention, based on the characteristics of the concrete pier structure, adopts a method combining experiments and numerical simulations to study the damage of the shaped charge on the concrete pier, obtain the damage criterion for the concrete pier, and construct a vulnerability characterization and evaluation method for the concrete pier under the action of the shaped charge.

Description

Technical Field

[0001] The present invention relates to the field of efficient barrier breaking technology, and in particular to a method for analyzing the vulnerability of a concrete pier under the action of a shaped charge penetrator. Background Art

[0002] Concrete piers, the typical foundations of anti-landing obstacles, are typically placed on beaches and other convenient landing areas to hinder or delay enemy landings. They are a key target during landing operations. Due to their large size and high strength, conventional explosive munitions struggle to effectively damage them. However, shaped charges (such as JET, JPC, or EFP) are an important barrier-breaking method for destroying concrete piers. In military applications, effective strikes against concrete piers can significantly shorten barrier-breaking time and improve efficiency. Therefore, studying the vulnerability of concrete piers to shaped charges is of great significance.

[0003] Since the 1990s, domestic and international researchers have conducted numerous experiments on shaped charge penetrators impacting concrete targets, with most studies focusing on the influence of shaped charge structure on penetration patterns. For example, Murphy et al. at Lawrence Livermore National Laboratory (LLNL) in the United States conducted a series of experiments on the fundamental principles of shaped charge jet penetration into concrete targets, examining the influence of factors such as detonation method, charge caliber, explosive type, liner material, and liner cone angle on concrete damage. The results showed that increasing the liner cone angle increased the penetration aperture, while increasing the liner thickness effectively increased the penetration depth, but decreased the penetration aperture. Compared with copper liners, the jet formed by an aluminum liner formed a larger penetration aperture when penetrating concrete. Wang Cheng et al. systematically conducted experiments on shaped charge structures with different liner materials, cone angles, and wall thicknesses penetrating concrete slabs at different blast heights, and determined the influence of these structural parameters on the funnel crater diameter, penetration hole diameter, funnel crater depth, and penetration depth. Hu et al. conducted experiments on EFP penetration into concrete targets, studying the effects of liner material, explosive type, concrete type, and target type (spaced and integral) on concrete target damage. The experimental results showed that EFPs formed with B explosive and copper liners had better cratering performance. Li Bihong analyzed charge design through a combination of theoretical analysis and experiments, finding that EFPs formed by shaped charge explosions could be used to crush concrete piers. The results showed that short, thick, blunt-nosed projectiles with small aspect ratios are more effective in crushing concrete piers. Duan Jian et al. conducted experiments on EFP penetration into concrete targets and found that compared to high-cone-angle liners, EFPs formed by spherical segments had greater penetration depth and a larger penetration aperture.

[0004] Because concrete is a complex multiphase material, the penetration of a shaped charge into concrete is a transient, complex, and nonlinear mechanical process. Numerical simulations can be used to investigate various aspects of material behavior, including plastic flow, hardening and softening, damage and fracture, and strain rate effects. Resnyansky et al. numerically simulated the penetration of shaped charge jets into concrete and verified their experimental results with those of Murphy et al., finding that the results were generally consistent with those of the experiments. The HJC model effectively describes the mechanical response of concrete when compression dominates the stress state. However, due to its inadequate description of tensile damage and strain softening, the HJC model struggles to simulate the pitting phenomenon in tensile-dominated concrete. Kong et al. introduced modified yield surfaces, strain rate effects, and tensile damage into the original HJC model to develop an improved HJC model. Using this model, Hu et al. simulated the penetration of EFPs into concrete piers and found that the penetration depths obtained by the two HJC models were essentially identical, agreeing well with experimental results. The pit size and collapse failure calculated using the improved HJC model were closer to experimental results.

[0005] Under the action of shaped charges, the damage mechanisms of concrete and metal are different. The theory of concrete penetration is still not very complete. Murphy believes that the volume (V) formed by the jet penetrating into the concrete is proportional to the energy (E) of the jet. Under the condition that the jet velocity and energy are known, the penetration velocity of the jet can be obtained according to the Bernoulli equation, and the diameter of the penetration hole can be obtained according to the principle of E / V=const. Szendrei analyzed the relationship between axial penetration and radial hole expansion when the jet penetrates the concrete target at ultra-high speed. According to the principle of E / V=const, this ratio is related to the strength of the target plate, the density of the jet and the concrete. Miller believes that the radial hole expansion of the jet consists of two parts: the aperture formed by overcoming the resistance of the target plate and the aperture formed by the inertial expansion of the material, and thus the calculation formula for the penetration aperture is obtained. However, the above research did not consider the influence of the compressibility of concrete during the jet penetration and hole expansion process. Experimental results of shaped charge jet penetration into concrete indicate that when the penetration velocity exceeds the material's sonic velocity, the penetration aperture is not proportional to the jet diameter and velocity. Therefore, when developing a calculation formula for hole expansion in shaped charge jet penetration into concrete, the impact of shock waves in the concrete needs to be considered. Xiao Qiangqiang et al. derived an expression for the relationship between the axial penetration velocity and the penetration aperture diameter of a shaped charge jet for supersonic penetration of concrete targets. Combining the AT equation and the Szendrei / Held equation for subsonic penetration, they calculated the penetration aperture shape of a shaped charge jet into concrete targets. Using an ideal fluid dynamics model, Pan Xuchao established a theoretical equation for JPC penetration into concrete and calculated and analyzed the effects of JPC head velocity, head and tail diameter, and blast height on penetration depth and aperture shape. Using the conservation of mass and momentum, and considering factors influencing the JPC head and tail shape, he revised the engineering calculation model for JPC penetration into concrete and calculated and analyzed the effect of the JPC head and tail diameter on penetration depth. Zhu et al. divided the penetration process of a shaped charge jet into a concrete target into four stages. Combining fluid dynamics theory with a penetration impedance model, they established a model for the axial penetration of a shaped charge jet into a typical high-strength concrete. Based on the four-stage axial penetration equations, they combined the Szendrei / Held theory of pore growth rate variation and the two-stage pore growth theory to establish a radial pore expansion model for a shaped charge jet into a typical high-strength concrete. The theoretical calculation results were in good agreement with the experimental results, while the predicted values ​​from the Szendrei / Held theory were significantly lower.

[0006] The research of the above scholars mainly focused on the penetration behavior of shaped charge penetrators into concrete materials, without involving the study of the vulnerability of concrete piers, nor considering the influence of factors such as charge type and intersection conditions. Summary of the Invention

[0007] This invention provides a vulnerability analysis method for rail fortification bases subjected to shaped charges. Based on the structural characteristics of concrete piers, this method combines experiments and numerical simulations to study the damage to concrete piers caused by EFP and JPC. This method derives damage criteria for concrete piers and, based on these criteria, develops a vulnerability characterization and assessment method for concrete piers subjected to EFP and JPC shaped charges. The research findings can be applied to the effectiveness evaluation, optimization, design, and battlefield deployment of obstacle-clearing munitions.

[0008] The technical solution to achieve the purpose of the present invention is: a method for analyzing the vulnerability of concrete piers under the action of shaped charge penetrators, the specific steps of which are:

[0009] Step 1: Structural analysis of the target concrete pier and characterization of the missile-target intersection conditions;

[0010] Step 2: Based on the barrier capacity of the concrete pier after destruction, the residual height of the concrete after destruction is used to represent the damage level of the concrete pier after destruction;

[0011] Step 3: Through simulation analysis or experiments, study the dynamic response of the concrete pier when different shaped charges strike different positions of the concrete pier in different directions, and then obtain the residual height data of the shaped charge on the concrete pier when different shaped charges strike different directions and different positions;

[0012] Step 4: Based on the residual height data of the concrete pier, obtain the equal damage curves of the concrete pier at different damage levels;

[0013] Step 5: Based on the equal damage curve and the damage probability calculation function, the vulnerable area of ​​each level of damage is obtained when attacking from different directions and locations;

[0014] Step 6: By comparing the sizes of vulnerable areas under different working conditions, you can determine and select the appropriate striking conditions.

[0015] Furthermore, step 1 specifically includes:

[0016] Step 1.1: The concrete pier is a regular quadrangular pyramid structure and is designed with reference to GJB 6626-2008 "Rail Barrier Specifications";

[0017] Step 1.2: Characterization of the projectile-target intersection condition; The degree of damage caused by the ammunition to the concrete pier is related to the direction and impact position of the ammunition. To characterize the projectile-target intersection relationship, a coordinate system is established with the center of the pier bottom surface as the origin O, the bottom surface as the XOY plane, and the vertical bottom surface upward as the positive direction of the Z axis. The azimuth angle ξ and the elevation angle φ are used to represent the impact direction (φ, ξ) of the shaped charge penetrator. The elevation angle φ is the angle between the shaped charge axis and the XOY plane, and the azimuth angle ξ is the angle between the projection of the shaped charge axis direction in the XOY plane and the OX axis.

[0018] Furthermore, the damage level of the destroyed concrete pier is defined as follows:

[0019] Severe damage is S level, η≤β2h c Moderate damage is M level, β2h c <η≤β1h c ; Mild damage is L level, β1h c <η≤β0h c ; Among them, β0, β1, β2 are coefficients that characterize the degree of damage to the concrete pier, h c is the height of the concrete pier; η is the residual height of the concrete pier.

[0020] Furthermore, β0=0.875, β1=0.75 and β2=0.5 respectively; when h c = 0.8m, the critical maximum residual height for judging whether the concrete pier has reached severe damage is The critical maximum residual height for judging whether the concrete pier has reached moderate damage is obtained, which is recorded as If the maximum residual height of the concrete pier is greater than 0.7m, it is considered to be undamaged.

[0021] Furthermore, in step 3, the shaped charge penetrators are two types of shaped charge penetrators: JPC and EFP.

[0022] Furthermore, in step 3, for the top surface of the concrete pier, the selected striking direction is (90°, 0°); for the side surface of the concrete pier, the selected striking directions are (0°, 0°), (-45°, 0°), and (45°, 0°).

[0023] Furthermore, in step 3, 7 typical positions are selected on the top surface of the concrete pier body and 6 typical positions are selected on the side surface of the concrete.

[0024] Furthermore, step 5 specifically includes:

[0025] Step 5.1: Calculate the probability of damage:

[0026] Project the concrete pier onto a plane perpendicular to the incident direction of the penetrator, and establish a projection coordinate system O on this plane. t x t y t , coordinate origin O t The projection point of the center of the bottom surface of the pier body; the penetration body passes through O t x t y t Any position (x t ,y t ) hits the concrete pier, the residual height of the pier is recorded as η(x t ,y t ); When the residual height reaches the corresponding level of damage, the damage probability of the pier body is considered to be 1, otherwise it is 0. The damage probability of the pier body at different levels P (J) (x t ,y t )for:

[0027]

[0028] Step 5.2: Calculate the damage area:

[0029] The projection area of ​​the concrete pier is divided into grid units. The shaped charge penetrator penetrates the pier from the center of the grid (i, j). According to the grid number and projection direction, the specific surface and position of the pier hit by the shaped charge penetrator are obtained through coordinate transformation. The corresponding damage probability of the pier is recorded as P (J) (x t ,y t ), then the vulnerable area of ​​the pier along this direction is:

[0030]

[0031] Where ΔA(i,j) is the area of ​​the grid unit (i,j); m and n are the x t and y t The number of grid cells divided in the direction.

[0032] Compared with the prior art, the present invention has the following significant advantages:

[0033] (1) Based on the characteristics of the concrete pier structure, the present invention uses a method combining experiments and numerical simulations to study the damage of the energy-gathering body to the concrete pier and obtains the damage criterion of the concrete pier;

[0034] (2) The present invention constructs a method for characterizing and evaluating the vulnerability of concrete piers under the action of shaped charge penetrators; the research results can be applied to the effectiveness evaluation, optimization design and battlefield use of obstacle-clearing ammunition. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Schematic diagram of the concrete pier structure and intersection position;

[0036] Figure 2 Typical locations where shaped charges act on the top or side of a concrete pier, where (a) is the top view and (b) is the side view.

[0037] Figure 3 The equal damage curves when the penetrator hits the top surface of the concrete pier along the (90°, 0°) direction, where (a) is the JPC of the concentrator and (b) is the EFP of the concentrator.

[0038] Figure 4 The equal damage curves when the penetrator hits the side of the concrete pier along the (0°, 0°) direction, where (a) is the JPC of the concentrator and (b) is the EFP of the concentrator;

[0039] Figure 5 The equal damage curves when the penetrator hits the side of the concrete pier along the (-45°, 0°) direction, where (a) is the JPC of the concentrator and (b) is the EFP of the concentrator.

[0040] Figure 6 The equal damage curves when the penetrator hits the side of the concrete pier along the (45°, 0°) direction, where (a) is the JPC of the concentrator and (b) is the EFP of the concentrator;

[0041] Figure 7 Projection of the concrete pier in the direction of the penetrator's impact. DETAILED DESCRIPTION

[0042] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0043] This embodiment provides a vulnerability analysis method for a rail fortress base under the action of a shaped charge penetrator. The method includes the following steps:

[0044] Step 1: Conduct structural analysis on the target concrete pier and characterize the missile-target intersection conditions;

[0045] Step 1.1: The concrete pier is a regular quadrangular pyramid structure and is designed with reference to GJB 6626-2008 "Rail Barrier Specifications". Figure 1 In this embodiment, the side length of the upper section of the pier body is a = 0.6m, the side length of the lower section is b = 1.0m, and the height hc = 0.8m.

[0046] Step 1.2: Characterization of the projectile-target intersection condition; The degree of damage caused by the ammunition to the concrete pier is related to the direction and impact position of the ammunition. Therefore, it is necessary to characterize the intersection relationship between the projectile and the target. Specifically, the center of the bottom surface of the pier is taken as the origin O, the bottom surface is the XOY plane, and the vertical bottom surface is upward as the positive direction of the Z axis. A coordinate system is established, such as Figure 1 The attack direction (φ, ξ) of the shaped charge penetrator is represented by the azimuth angle ξ and the elevation angle φ, where the elevation angle φ is the angle between the axis of the shaped charge and the XOY plane, and the azimuth angle ξ is the angle between the projection of the axis of the shaped charge in the XOY plane and the OX axis (counterclockwise is positive).

[0047] Step 2: Based on the barrier capacity of the concrete pier after destruction, the residual height of the concrete after destruction is used to represent the damage level of the concrete pier after destruction. Specifically: severe damage (S level), η≤β2h c ; Moderate damage (M level), β2h c <η≤β1h c ; Mild damage (L level), β1h c <η≤β0h c ; Among them, β0, β1, and β2 are coefficients representing the degree of damage to the concrete pier, which are 0.875, 0.75, and 0.5 respectively; h c is the height of the concrete pier (0.8m). When β2 = 0.5, the critical maximum residual height for judging whether the concrete pier has reached severe damage is obtained, which is recorded as When β1 = 0.75, the critical maximum residual height for judging whether the concrete pier has reached moderate damage is obtained, which is recorded as If the maximum residual height of the concrete pier is greater than 0.7 m, it is considered to be undamaged (level N); η is the residual height of the concrete pier.

[0048] Step 3: Use ANSYS / LSDYNA finite element software to perform numerical simulation or static explosion test to study the dynamic response of the concrete pier when the two shaped charge penetrators hit the concrete pier at different positions in different directions, and obtain the residual height data of the shaped charge penetrator on the concrete pier at different attack directions and different action positions; select 7 typical positions on the top surface of the concrete pier and 6 typical positions on the side surface of the concrete (such as Figure 2 As shown in FIG, in this embodiment, two types of shaped charges are used: JPC and EFP. In different directions, typical positions on the top surface of the concrete pier and typical positions on the side surfaces of the concrete are struck, and residual height data of the concrete pier under different striking conditions are collected.

[0049] Step 4: Solving the equal damage curve: Based on the concrete residual height data at typical locations obtained through numerical simulation and static explosion test in step 3, the Green spline interpolation algorithm in Matlab is used to interpolate the residual height when the penetrator hits the concrete pier at different locations, and the equal damage curves of different damage levels of the concrete pier are obtained, as shown in the figure. Figure 3-Figure 6 shown.

[0050] The specific meaning of the damage curve: Figure 3 is the equal damage curve when the JPC and EFP shaped charge penetrators vertically hit the top surface of the concrete pier. This figure reflects the vulnerability of the concrete pier under the action of the two shaped charge penetrators, such as Figure 3 As shown in (a), the three curves divide the top surface of the concrete pier into four areas. When the JPC hits area I of the top surface of the pier, the concrete pier will be severely damaged (S level); when it hits area II, the concrete pier will be moderately damaged (M level); when it hits area III, it will be slightly damaged (L level); when it hits area IV, the concrete pier will not be damaged (N level). Figure 3 As shown in (b), under EFP impact, only three regions of damage appear on the top surface: moderate, light, and no damage. This means that EFP top impact does not cause significant damage to the concrete pier. Both damage elements form approximately circular damage regions, but the vulnerable areas corresponding to each level vary in shape and size. When impacted from the top, JPC is more likely to damage the concrete pier.

[0051] Step 5: Based on the equal damage curve and the damage probability calculation function, the vulnerable areas of different levels of damage when striking different directions and positions are obtained.

[0052] Step 5.1: Calculate the probability of damage:

[0053] Project the concrete pier onto a plane perpendicular to the incident direction of the penetrator, and establish a projection coordinate system O on this plane. t x t y t , coordinate origin O t is the projection point of the center of the pier bottom surface, such as Figure 7 As shown. The penetrator passes through any position (x t ,y t ) hits the concrete pier, the residual height of the pier is recorded as η(x t ,y t When the residual height reaches the corresponding level of damage, the damage probability of the pier body is considered to be 1, otherwise it is 0. The damage probability of the pier body at different levels P (J) (x t ,y t )for:

[0054]

[0055] Step 5.2: Calculate the damage area:

[0056] Because P (J) (x t ,y t ) cannot be calculated by analytical methods, so a discrete method is used to solve it. Divide the grid cells in the projection area of ​​the concrete pier (such as Figure 7 As shown in the figure, the shaped charge penetrator penetrates the pier body from the center of the grid (i, j). According to the grid number and projection direction, the specific surface and position of the pier body hit by the shaped charge penetrator are obtained through coordinate transformation. The corresponding damage probability of the pier body is recorded as P (J) (x t ,y t ), then the vulnerable area of ​​the pier along this direction is:

[0057]

[0058] Where ΔA(i,j) is the area of ​​the grid unit (i,j); m and n are the number of grid units divided in the two directions of the surface, respectively.

[0059] Step 6: By comparing the sizes of vulnerable areas under different working conditions, you can determine and select the appropriate striking conditions.

Claims

1. A method for analyzing the vulnerability of concrete piers under the action of shaped charges, characterized in that: The specific steps are: Step 1: Structural analysis of the target concrete pier and characterization of the missile-target intersection conditions; Step 1.1: The concrete pier is a regular quadrangular pyramid structure and is designed with reference to GJB 6626-2008 "Rail Barrier Specifications"; Step 1.2: Characterization of the projectile-target intersection condition; The degree of damage to the concrete pier by the ammunition is related to the direction and position of the ammunition. In order to characterize the intersection relationship between the projectile and the target, a coordinate system is established with the center of the bottom surface of the pier as the origin O, the bottom surface as the XOY plane, and the vertical bottom surface upward as the positive direction of the Z axis. The azimuth is used to represent the projectile-target intersection condition. and elevation angles Indicates the attack direction of the shaped charge penetrator ( ), where the high and low angles is the angle between the axis of the shaped charge and the XOY plane, the azimuth is the angle between the projection of the shaped charge axis in the XOY plane and the OX axis; Step 2: Based on the barrier capacity of the concrete pier after destruction, the residual height of the concrete after destruction is used to represent the damage level of the concrete pier after destruction; Step 3: Through simulation analysis or experiments, study the dynamic response of the concrete pier when different shaped charges strike different positions of the concrete pier in different directions, and then obtain the residual height data of the shaped charge on the concrete pier when different shaped charges strike different directions and different positions; Step 4: Based on the residual height data of the concrete pier, obtain the equal damage curves of the concrete pier at different damage levels; Step 5: Based on the equal damage curve and the damage probability calculation function, the vulnerable area of ​​each level of damage is obtained when attacking from different directions and locations; Step 5 specifically includes: Step 5.1: Calculate the probability of damage: Project the concrete pier onto a plane perpendicular to the incident direction of the penetrator, and establish a projection coordinate system on the plane. , coordinate origin is the projection point of the center of the bottom surface of the pier; Any position on the projection plane ( ) hits the concrete pier, the remaining height of the pier is When the residual height reaches the corresponding level of damage, the damage probability of the pier body is considered to be 1, otherwise it is 0. The damage probability of the pier body at different levels is for: ； Step 5.2: Calculate the damage area: The projection area of ​​the concrete pier is divided into grid units. The shaped charge penetrator penetrates the pier from the center of the grid (i, j). According to the grid number and projection direction, the specific surface and position of the pier hit by the shaped charge penetrator are obtained through coordinate transformation. The corresponding damage probability of the pier is recorded as , then the vulnerable area of ​​the pier along this direction is: ； in, is the area of ​​the grid unit (i, j); m and n are the area of ​​the projection surface The number of grid cells divided in the direction; Step 6: By comparing the sizes of vulnerable areas under different working conditions, you can determine and select the appropriate striking conditions.

2. The vulnerability analysis method for concrete piers under the action of shaped charge penetrators according to claim 1 is characterized in that: In step 2, the damage level of the destroyed concrete pier is defined as follows: Severe damage is S level, η ≤ β2 h c ; Moderate damage is M level, β2 h c <η ≤β1 h c ; Mild damage is L level, β1 h c <η ≤β0 h c ; Among them, β0, β1, β2 are coefficients that characterize the degree of damage to the concrete pier, h c is the height of the concrete pier; η is the residual height of the concrete pier.

3. The method for analyzing the vulnerability of concrete piers under the action of shaped charge penetrators according to claim 2, characterized in that: They are β0=0.875, β1=0.75 and β2=0.5 respectively; when h c =0.8m, the critical maximum residual height for judging whether the concrete pier has reached severe damage is η(S) c=0.4m; The critical maximum residual height for judging whether the concrete pier has reached moderate damage is obtained, denoted as η(M) c=0.6 m; if the maximum residual height of the concrete pier is greater than 0.7 m, it is considered to be undamaged.

4. The method for analyzing the vulnerability of concrete piers under the action of shaped charge penetrators according to claim 1, characterized in that: In step 3, the shaped charge penetrators are two types of shaped charge penetrators: JPC and EFP.

5. The method for analyzing the vulnerability of concrete piers under the action of shaped charge penetrators according to claim 4, characterized in that: In step 3, for the top surface of the concrete pier, the selected striking direction is (90°, 0°); for the side surface of the concrete pier, the selected striking directions are (0°, 0°), (-45°, 0°), and (45°, 0°).

6. The method for analyzing the vulnerability of concrete piers under the action of shaped charge penetrators according to claim 5, characterized in that: In step 3, 7 typical locations are selected on the top surface of the concrete pier and 6 typical locations are selected on the side surface of the concrete.

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