A method for predicting the degree of fragmentation of a concrete structure under explosive loading

Abstract

The application discloses a kind of prediction methods of the degree of fragmentation of concrete structure under explosive load, belong to the field of explosion mechanics and impact dynamics.The application analyzes the propagation process of explosion energy by detonation theory;Based on the deformation potential theory, the deformation energy of the concrete structure under the action of explosive load is calculated;Combined with Griffith fracture theory, the energy dissipation in the fragmentation process of concrete structure is calculated;Using kinematics theory and kinetic energy theorem, the initial kinetic energy of secondary fragments of concrete structure under explosive load is determined;Then, based on the principle of energy conservation, the degree of fragmentation of concrete structure under explosive load is determined;The energy dissipation and the parameter information of secondary fragments of concrete structure at different periods in the explosion process are effectively predicted.The application is suitable for military defense and blasting fields, and the parameter information is used to optimize the concrete structure, improve the explosion defense effect or the blasting effect on the concrete structure.

Description

Technical Field

[0001] This invention relates to a method for predicting the degree of fracture of concrete structures under explosive loads, belonging to the fields of explosion mechanics and impact dynamics. Background Technology

[0002] Numerous experiments have demonstrated that concrete structures fracture and break up under explosive impact loads, with the fracturing becoming more severe as the explosive load increases or the distance from the blast source decreases. Under explosive loads, the spalling and fragmentation of concrete generates numerous high-speed secondary concrete fragments. These fragments possess high energy, exhibit strong randomness in their movement, and cover a large area, potentially causing damage and harm to personnel and equipment within the blast zone, posing a significant post-explosive threat. Furthermore, blasting technology is widely used in urban construction projects such as ore mining, railway construction, and water conservancy and hydropower projects. Factors such as the energy consumption and utilization rate of explosives during blasting, the distribution of ore fragments after blasting, and the particle size of the fragments directly affect the effectiveness and cost of blasting operations.

[0003] At present, the methods for determining the particle size and block size distribution of secondary fragments in explosion scenarios are mainly divided into two aspects: (1) Based on existing experimental laws and combined with the fitting parameters of some experiments, a prediction method for the degree of concrete structure breakage under explosion load is established through numerical simulation software. For example, Rabczuk used the Smooth Particle Hydrodynamics (SPH) method to simulate the fragment mass and particle size distribution of concrete blocks under explosion impact. However, this type of method requires a large number of experimental fitting parameters, which limits the application scope of the method; (2) Combined with experimental testing instruments, a prediction method for the degree of concrete structure breakage after being subjected to explosion load is established by observing the explosion impact experiment process. The main determination methods at present are high-speed photography, television photography and sieve analysis. Wu et al. collected secondary concrete fragments generated by explosion experiments under various particle size distributions through sieve analysis and found that the size of the recovered fragments followed both the Weibull distribution and the Rosin-Rammler-Sperling-Bennet (RRSB) distribution. However, current prediction methods are limited to calculating the general distribution trend and pattern of concrete fragments, and cannot quantitatively predict the degree of concrete structure fragmentation under unknown explosion conditions. Therefore, further in-depth research is still needed. Summary of the Invention

[0004] Given the limitations of existing methods in quantitatively predicting the degree of concrete structure fragmentation and secondary fragment parameters under explosive loads, the main objective of this invention is to provide a method for predicting the degree of concrete structure fragmentation under explosive loads. By coupling the propagation and diffusion of the explosive shock wave with the main mechanisms of energy dissipation at each stage of the explosive impact, this method overcomes the bottleneck in quantitatively calculating the fragmentation parameters of concrete structures under explosive loads. It effectively predicts the energy dissipation and secondary fragment parameters at different stages of the explosive impact, providing key technical support for the structural optimization of explosive defense and the formulation of blasting schemes.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] This invention discloses a method for predicting the degree of fracture of concrete structures under explosive loads. It analyzes the propagation process of explosive energy using detonation theory; calculates the deformation energy of the concrete structure under explosive loads based on variable kinetic energy theory; statistically analyzes the energy dissipation during the fracture process of the concrete structure using Griffith fracture theory; determines the initial kinetic energy of secondary fragments of the concrete structure under explosive loads using kinematic theory and the kinetic energy theorem; and then determines the degree of fracture of the concrete structure under explosive loads based on the principle of energy conservation. This method effectively predicts the energy dissipation and secondary fragment parameters of the concrete structure at different stages of the explosive impact, providing key technical support for the structural optimization of explosive defense and the formulation of blasting schemes.

[0007] This invention discloses a method for predicting the degree of fracture of concrete structures under explosive loads, comprising the following steps:

[0008] Step 1: Calculate the TNT equivalent of different types of explosives to obtain the initial explosion energy of each explosive;

[0009] TNT equivalent is an important indicator reflecting the power of different explosives. The method of converting the explosive power of various explosives into TNT equivalent is widely used in the fields of explosion mechanics and engineering blasting. Combining the explosion parameters of TNT explosives, this paper uses an energy conversion formula to convert the explosives in an actual blast field into TNT equivalents and calculates the initial energy of the corresponding mass of explosive.

[0010] Step 1.1: Use the following TNT equivalent conversion formula to convert the TNT equivalent of different types of explosives. The specific form is as follows:

[0011]

[0012] In the formula, M is the TNT equivalent, Q is the explosion conversion energy per unit mass of TNT explosive, and M s Q represents the actual amount of explosive. s This refers to the energy converted from the explosion per unit mass of actual explosive.

[0013] Step 1.2: Determine the initial explosion energy of the explosive using the following explosion energy calculation method, specifically as follows:

[0014] E0=MQ=ρ0v0Q (2)

[0015] Where E0 is the initial explosion energy of the explosive, ρ0 is the density of the TNT explosive, and v0 is the volume of the explosive.

[0016] Step 2: Based on the calculation results of Step 1, taking into account the transfer of explosion energy during the propagation and diffusion process, obtain the explosion impact energy acting on the concrete structure.

[0017] When explosives detonate in an unbounded medium, the explosion products eventually occupy a certain limiting specific volume. Based on the equation of state and energy conservation equation of the explosion products, the energy deposited in the explosion products after the explosion can be obtained. Combined with the initial explosion energy obtained in step 1, the energy transferred to the blast shock wave can be determined. By using the diffusion area of ​​the blast shock wave and the area parameters of the blast-facing surface of the concrete structure, the blast impact energy acting on the concrete structure can be obtained.

[0018] Step 2.1: When explosives detonate in an unbounded medium, the explosion products disperse over a period of time and eventually occupy a certain limiting specific volume v. ∞ At this point, the residual pressure of the explosion products equals the pressure of the surrounding medium, i.e., atmospheric pressure p0. According to the equation of state and the energy conservation equation for the explosion products, we obtain:

[0019]

[0020] Where v0 is the initial specific volume of the explosion products, and k is the gas parameter. After determining the limiting specific volume, the energy E deposited in the explosion products can be approximately calculated. ∞ .

[0021]

[0022] The energy E transferred to the shock wave after the explosive detonation can be obtained from the above formula. y for:

[0023]

[0024] According to the ideal gas equation, the limiting specific volume of the explosion products can be obtained by the following formula:

[0025] v ∞ / v0=(p H / p a ) 1 / k (6)

[0026] p H=(k-1)ρ0Q=ρ0D 2 / 2(k+1) (7)

[0027] D is the detonation velocity of the explosive. Therefore, the energy transmitted to the blast shock wave can be calculated as follows:

[0028]

[0029] Step 3: Based on the principle of strain energy density calculation of concrete materials, obtain the deformation energy of the concrete structure under explosive load;

[0030] When a concrete structure is subjected to an explosive load, it stores the energy of the explosive impact as the material's potential energy through stress and strain; this energy is the deformation energy of the concrete structure. By calculating the deformation energy density of the concrete material, the deformation energy of the concrete structure under an explosive load can be obtained.

[0031] The strain energy density of concrete includes the volume change energy density and the shape change energy density. The specific form of the strain energy density is as follows:

[0032] V ε =V v +V d (10)

[0033]

[0034]

[0035] In the above formula, V ε V is the strain energy density. v V represents the volume change energy density of concrete. d For the shape-change energy density of concrete, σ m Let be the peak stress, μ be Poisson's ratio, and E be the elastic modulus of concrete. The following deformation energy equation for a concrete structure subjected to explosive loading is established:

[0036]

[0037] Where E d V represents the deformation energy of a concrete structure under explosive load, and V is the volume of the concrete structure.

[0038] Step 4: Based on Griffith's fracture theory and the energy dissipation surface area theory of fracture, obtain the energy dissipation of the concrete structure during the fracture process;

[0039] Under explosive loads, concrete structures produce a large number of concrete fragments with different particle sizes. The surface energy required for the concrete material to break and the surface area increment during the breaking process are calculated to obtain the breaking energy of the concrete structure under explosive loads.

[0040] Under explosive loading, concrete structures produce a large number of concrete fragments with different particle sizes. These fragments are all cubic in shape, with a side length of 'a'. According to Griffith's fracture theory:

[0041]

[0042] Where c is the length of the fracture surface of the concrete fragment. The surface energy γ of a concrete structure when it breaks can be expressed as:

[0043]

[0044] Calculate the surface energy required for concrete to fracture and obtain the surface area increment during the fracture process to obtain the fracture energy E of the concrete structure under explosive load. f The specific form is as follows:

[0045]

[0046] In the formula A0 represents the number of concrete fragments with a specific particle size, and A0 represents the original surface area of ​​the concrete structure.

[0047] Step 5: Combining projectile kinematics theory and the kinetic energy theorem, obtain the initial kinetic energy of secondary concrete fragments with different particle sizes;

[0048] The initial kinetic energy of secondary concrete fragments mainly depends on the fragment's own mass, the vertical height of the concrete structure, and the horizontal displacement of the secondary fragments. Based on the distribution of secondary concrete fragments after the experiment, the horizontal displacement distribution of the fragments was determined, thus obtaining the initial kinetic energy of the secondary fragments in the concrete structure under explosive load.

[0049] Step 6: By statistically analyzing the distribution of concrete fragments within various particle size ranges, the energy distribution function of fragments with a specific particle size is obtained;

[0050] The distribution function of secondary concrete fragments was obtained by fitting the results of the explosion experiment. The mass distribution function of fragments with a specific particle size is obtained by combining the fragment distribution function. Calculate the energy distribution function of a fragment of a specific particle size based on the fragment distribution function and the mass distribution function of fragments of a specific particle size. The specific form is as follows:

[0051]

[0052] In the formula R i The particle size of the concrete fragments. For the mass of concrete fragments of a specific particle size, M concrete The total mass of the concrete structure. The effective crushing energy for concrete fragments of a specific particle size.

[0053] Step 7: Based on the energy distribution function of the specific particle size fragments in Step 6 and the law of conservation of energy, obtain the parameter information of the secondary concrete fragments.

[0054] The energy expression for the fracture process of a concrete structure under explosive load is:

[0055]

[0056] Step 8: Based on the energy dissipation and secondary fragment parameter information obtained in Steps 2 to 7 during the explosion impact process, optimize the concrete structure according to the parameter information to improve the explosion defense structure or the blasting effect on the concrete structure.

[0057] Beneficial effects:

[0058] 1. This invention discloses a method for predicting the degree of fracture of concrete structures under explosive loads. This method considers the transfer of explosive energy during propagation and diffusion, and integrates detonation theory, variable energy theory, Griffith fracture theory, projectile kinematics theory, the kinetic energy theorem, and the law of conservation of energy, while fully considering the energy dissipation throughout the entire explosive impact process. It overcomes the bottleneck of quantitatively calculating the fracture parameters of concrete structures under explosive loads, achieving effective prediction of energy dissipation and secondary fragment parameters at different stages of the explosive impact process. Based on these parameters, the concrete structure can be optimized to improve explosive defense structures or the blasting effect on concrete structures. Attached Figure Description

[0059] Figure 1 This is a flowchart of a method for predicting the degree of fracture of a concrete structure under explosive load, as disclosed in this invention.

[0060] Figure 2 This is a schematic diagram of the energy diffusion of the explosive shock wave described in this invention;

[0061] Figure 3 This is a schematic diagram illustrating the division of the secondary concrete fragment displacement region according to the present invention;

[0062] Figure 4 This example compares the number of secondary fragments in different particle size groups with experimental results.

[0063] Figure 5 This is the prediction result of the degree of concrete structure fracture under unknown explosion conditions in this embodiment. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this invention. Obviously, the described embodiments are only some embodiments of this invention, not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of this invention.

[0065] When subjected to a high-yield explosive load, concrete structures rapidly develop numerous cracks. With continued loading, these cracks propagate extensively throughout the concrete structure, leading to fracture, collapse, and overall fragmentation. Secondary concrete debris generated under explosive loads can cause significant damage to structures, facilities, and personnel in the affected area. This paper uses a real explosive impact experiment as an example to verify the effectiveness of the calculation method of this invention. The explosive type is B explosive, with a mass of 30 kg. The concrete structure is frustum-shaped, with upper and lower surface dimensions of 600 × 600 mm. 2 The height is 800mm, and the bottom surface dimensions are 1000×1000mm. 2 The compressive strength of the concrete is 40 MPa. The distances between the explosive and the concrete structure are 500 mm, 750 mm, 1000 mm, and 1500 mm, respectively.

[0066] like Figure 1 As shown in this embodiment, a method for predicting the degree of fracture of a concrete structure under explosive load includes the following steps:

[0067] Step 1: Solve for the TNT equivalent of different types of explosives to obtain the initial explosion energy of each type of explosive.

[0068] TNT equivalent is an important indicator reflecting the power of different explosives. The method of converting the explosive power of various explosives into TNT equivalent is widely used in the fields of explosion mechanics and engineering blasting. This paper combines the explosion parameters of TNT explosives and uses an energy conversion formula to convert the explosives in an actual explosion field into TNT equivalents and calculates the initial energy of the corresponding mass of explosives.

[0069] Specifically, as a preferred embodiment of the present invention, step 1 includes:

[0070] Step 101: Use the following TNT equivalent conversion formula to convert the TNT equivalent of different types of explosives. The specific form is as follows:

[0071]

[0072] In the formula, M is the TNT equivalent, and Q is the explosion conversion energy per unit mass of TNT explosive. For a typical TNT explosive, Q = 4185.85 J / g. s Q represents the actual amount of explosive. s Q is the energy converted into explosive per unit mass of actual explosive. s =5180J / g.

[0073] Step 102: Determine the initial explosion energy of the explosive using the following explosion energy calculation method, specifically as follows:

[0074] E0=MQ=ρ0v0Q (2)

[0075] Where E0 is the initial explosion energy of the explosive, ρ0 is the density of TNT, ρ0 = 1.6 g / cm³ 3 v0 is the volume of the explosive.

[0076] Step 2: Based on the calculation results of Step 1, taking into account the transfer of explosion energy during the propagation and diffusion process, obtain the explosion impact energy acting on the concrete structure.

[0077] Specifically, as a preferred embodiment of the present invention, step 2 includes:

[0078] Step 21: When the explosive detonates in an unbounded medium, the explosion products disperse over a period of time and eventually occupy a certain limiting specific volume v. ∞ At this point, the residual pressure of the explosion products equals the pressure of the surrounding medium (atmospheric pressure p0). Based on the equation of state and the energy conservation equation for the explosion products, the following can be obtained:

[0079]

[0080] Where v0 is the initial specific volume of the explosion products. For TNT explosive, p H ≈10.0 GPa, p k ≈0.2GPa, p a ≈0.1MPa. The value of k is generally taken as 1.4. After determining the limiting specific volume, the energy E deposited in the explosion products can be approximately calculated. ∞ .

[0081]

[0082] The energy E transferred to the shock wave after the explosion can be calculated using the above formula. y for:

[0083]

[0084] Assuming the explosion products are ideal gases, the limiting specific volume of the explosion products can be calculated using the following formula:

[0085] v ∞ / v0=(p H / p a ) 1 / k (6)

[0086] p H =(k-1)ρ0Q=ρ0D 2 / 2(k+1) (7)

[0087] D is the detonation velocity of the explosive; for TNT, D = 7000 m / s. Therefore, the energy transmitted to the blast shock wave can be calculated as follows:

[0088]

[0089] Step 22: It is assumed that the blast shock wave propagates uniformly in all directions during its propagation. Therefore, the energy of the blast shock wave acting on the concrete structure can be determined by the ratio of the area of ​​the concrete structure's blast-facing surface to the hemispherical area of ​​the explosive blast shock wave diffusion. The mechanism by which the blast shock wave acts on the concrete structure after propagation and diffusion is as follows: Figure 2 As shown. The energy of the blast shock wave borne by the concrete structure at different intervals can be calculated by the following formula, the specific form of which is:

[0090]

[0091] In the formula E concrete S represents the energy of the blast shock wave borne by the concrete structure, H is the distance between the center of the explosive and the concrete structure, and S is the energy of the blast shock wave borne by the explosive. c This refers to the side surface area of ​​the blast-facing face of the concrete structure.

[0092] Step 3: Based on the principle of strain energy density calculation of concrete materials, obtain the deformation energy of the concrete structure under explosive load;

[0093] When a concrete structure is subjected to an explosive load, it stores the energy of the explosive impact as the material's potential energy through stress and strain; this energy is the deformation energy of the concrete structure. By calculating the deformation energy density of the concrete material, the deformation energy of the concrete structure under an explosive load can be obtained.

[0094] The strain energy density of concrete includes the volume change energy density and the shape change energy density. The specific form of the strain energy density is as follows:

[0095] V ε =V v +Vd (10)

[0096]

[0097]

[0098] In the above formula, V ε V is the strain energy density. v V represents the volume change energy density of concrete. d For the shape-change energy density of concrete, σ m Let be the peak stress, μ be Poisson's ratio, and E be the elastic modulus of the concrete. For concrete with a strength grade of C40, the peak stress is 40 MPa, the Poisson's ratio is 0.2, and the elastic modulus is 3.25 × 10⁻⁶. 4 MPa. The deformation energy equation for a concrete structure subjected to explosive load is established as follows:

[0099]

[0100] Where E d V represents the deformation energy of a concrete structure under explosive load, and V is the volume of the concrete structure.

[0101] Step 4: Based on Griffith's fracture theory and the energy dissipation surface area theory of fracture, obtain the energy dissipation of the concrete structure during the fracture process;

[0102] Under explosive loading, concrete structures will produce a large number of concrete fragments with different particle sizes. Assuming that the generated fragments are all cubic in shape and the side length of the cubic fragment is 'a', according to Griffith's fracture theory:

[0103]

[0104] Where c is the length of the fracture surface of the concrete fragment. The surface energy γ of a concrete structure when it breaks can be expressed as:

[0105]

[0106] Calculate the surface energy required for concrete to fracture and obtain the surface area increment during the fracture process to obtain the fracture energy E of the concrete structure under explosive load. f The specific form is as follows:

[0107]

[0108] In the formula A0 represents the number of concrete fragments with a specific particle size, and A0 represents the original surface area of ​​the concrete structure.

[0109] Step 5: Combining projectile kinematics theory and the kinetic energy theorem, obtain the initial kinetic energy of secondary concrete fragments with different particle sizes;

[0110] The initial kinetic energy of secondary concrete fragments mainly depends on the fragment's own mass, the vertical height of the concrete structure, and the horizontal displacement of the secondary fragments. The horizontal displacement distribution of the fragments was determined based on the distribution of secondary concrete fragments after the experiment, such as... Figure 3 As shown.

[0111] Let the distances between the boundaries of the three regions and the detonation point be denoted as X0, X1, and X2, respectively. Based on experimental measurements, X0 = 20m, X1 = 80m, and X2 = 120m. Then, the specific form of the horizontal displacement of the concrete fragments scattered across the three regions is obtained as follows:

[0112]

[0113] in Let be the horizontal displacements corresponding to the concrete fragments in the three regions. The vertical height of the concrete structure is h. According to the projectile kinematics formula, the projectile velocity v of the fragments is:

[0114]

[0115] Therefore, the kinetic energy of secondary concrete fragments can be calculated using the following formula:

[0116]

[0117] In the formula, m is the mass of the fragment, and E k This refers to the kinetic energy of secondary concrete fragments.

[0118] Step 6: By statistically analyzing the distribution of concrete fragments within various particle size ranges, the energy distribution function of fragments with a specific particle size is obtained;

[0119] The distribution function of secondary concrete fragments was obtained by fitting the results of the explosion experiment. The mass distribution function of fragments with a specific particle size is obtained by combining the fragment distribution function. Calculate the energy distribution function of a fragment of a specific particle size based on the fragment distribution function and the mass distribution function of fragments of a specific particle size. The specific form is as follows:

[0120]

[0121] In the formula R i The particle size of the concrete fragments. For the mass of concrete fragments of a specific particle size, M concrete The total mass of the concrete structure. The effective crushing energy for concrete fragments of a specific particle size.

[0122] Step 7: Based on the energy distribution function of the specific particle size fragments in Step 6 and the law of conservation of energy, obtain the parameter information of the secondary concrete fragments;

[0123] The energy expression for the fracture process of a concrete structure under explosive load is:

[0124]

[0125] Table 1 shows a comparison between the calculation results of the method proposed in this invention and the actual experimental data. It can be seen that the calculation results of the method proposed in this invention agree well with the experimental data. Figure 4 By comparing the number of secondary fragments predicted by the proposed method for different particle size groups with the experimental results and analyzing the maximum error, it can be found that the calculation results of the proposed method are in good agreement with the experimental data under different interval distances. The maximum error value appears under the condition of an interval distance of 750 mm, with a maximum error value of 22.67%.

[0126] Table 1 Comparison of calculation results and actual experimental data using the method proposed in this invention.

[0127]

[0128] The effectiveness of the calculation method of this invention is verified by the above experimental data. Based on the prediction method for the degree of fracture of concrete structures under explosive load proposed in this invention, a prediction example of the degree of fracture of concrete structures under unknown explosive conditions was carried out. In the prediction example, the explosive type is B explosive, the explosive mass is 50 kg, and the concrete structure is frustum-shaped with the upper and lower surface dimensions being 1000 × 1000 mm. 2 The height is 1000mm, and the bottom surface dimensions are 1500×1500mm. 2 The compressive strength of the concrete is 40 MPa. The distances between the explosive and the concrete structure are 750 mm, 1000 mm, and 1500 mm, respectively. Figure 5This invention aims to predict the degree of concrete structure fragmentation under unknown explosion conditions using the proposed method. The method can calculate the number of concrete fragments within different particle size groups under various explosion conditions, and the number of fragments is negatively correlated with particle size, which aligns with practical realities. Prediction examples demonstrate that the proposed method for predicting the degree of concrete structure fragmentation under explosive loads can quantitatively calculate energy dissipation and secondary fragment parameters at different stages of the explosion impact, solving the current problem of quantitatively predicting the degree of concrete structure fragmentation under strong impact loads. Based on these parameters, concrete structures can be optimized, explosion defense structures improved, and protective capabilities enhanced.

[0129] Through the above embodiments, it can be seen that the prediction method for the degree of concrete structure fragmentation under explosive load described in this invention fully considers the combined effects of the propagation and diffusion of the explosive shock wave and the energy dissipation at each stage during the explosive impact process. It overcomes the shortcomings of existing methods that cannot quantitatively predict the degree of concrete structure fragmentation under explosive load, and effectively predicts the energy dissipation and secondary fragment parameters at different stages during the explosive impact process. This prediction method can effectively predict the energy dissipation and secondary fragment parameters at different stages during the explosive impact process, and can provide key technical support for the optimization of military defense structures and the formulation of civilian blasting schemes.

[0130] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting the degree of fracture of concrete structures under explosive load, characterized in that: Includes the following steps, Step 1: Calculate the TNT equivalent of different types of explosives to obtain the initial explosion energy of each explosive; Step 2: Based on the calculation results of Step 1, taking into account the transfer of explosion energy during the propagation and diffusion process, obtain the explosion impact energy acting on the concrete structure. The implementation method for step 2 is as follows: When explosives detonate in an unbounded medium, the explosion products will eventually occupy a certain limiting specific volume. Based on the state equation and energy conservation equation of the explosion products, the energy deposited in the explosion products after the explosion can be obtained. Combined with the initial energy of the explosion obtained in step 1, the energy transferred to the explosion shock wave can be determined. The explosion impact energy acting on the concrete structure can be obtained by using the diffusion area of ​​the explosion shock wave and the area parameters of the concrete structure's explosion-facing surface. Step 2.1: When explosives detonate in an unbounded medium, the explosion products disperse over a period of time and eventually occupy a certain limiting specific volume. At this point, the residual pressure of the explosion products is equal to the pressure of the surrounding medium, i.e., atmospheric pressure. Based on the equation of state and energy conservation equation of the explosion products, we obtain: (3) in Let be the initial specific volume of the explosion products, and k be a gas parameter. , , Here are the detonation product parameters at the detonation wavefront and the conjugate point, where... It is the pressure of the initial state of the detonation wave array at the instant the detonation is completed. This refers to the pressure at a specific "conjugate point" on the isentropic expansion line of the detonation products. This pressure typically corresponds to the pressure exerted by the detonation products when interacting with the surrounding medium or structure. This refers to the pressure of the surrounding medium at the end of the expansion of the explosion products; after determining the limiting specific volume, the energy deposited in the explosion products can be approximately calculated. ; (4) The energy transferred to the shock wave after the explosion can be obtained from the above formula. for: (5) According to the ideal gas equation, the limiting specific volume of the explosion products can be obtained by the following formula: (6) (7) D is the detonation velocity of the explosive; therefore, the energy transmitted to the blast shock wave can be calculated as follows: (8) Step 3: Based on the principle of strain energy density calculation of concrete materials, obtain the deformation energy of the concrete structure under explosive load; Step 4: Based on Griffith's fracture theory and the energy dissipation surface area theory of fracture, obtain the energy dissipation of the concrete structure during the fracture process; Step 5: Combining projectile kinematics theory and the kinetic energy theorem, obtain the initial kinetic energy of secondary concrete fragments with different particle sizes; Step 6: By statistically analyzing the distribution of concrete fragments within various particle size ranges, the energy distribution function of fragments with a specific particle size is obtained; Step 7: Based on the energy distribution function of the specific particle size fragments in Step 6 and the law of conservation of energy, obtain the parameter information of the secondary concrete fragments; Step 8: Based on the energy dissipation and secondary fragment parameter information obtained in Steps 2 to 7 during the explosion impact process, optimize the concrete structure according to the parameter information to improve the explosion defense structure or the blasting effect on the concrete structure.

2. The method for predicting the degree of fracture of a concrete structure under explosive load as described in claim 1, characterized in that: The implementation method for step 1 is as follows: Step 1.1: Use the following TNT equivalent conversion formula to convert the TNT equivalent of different types of explosives. The specific form is as follows: （1） In the formula Equivalent to TNT The energy conversion during the explosion of a unit mass of TNT explosive. This refers to the actual amount of explosive. The energy converted into explosive per unit mass of actual explosive; Step 1.2: Determine the initial explosion energy of the explosive using the following explosion energy calculation method, specifically as follows: （2） in This represents the initial explosion energy of the explosive. The density of TNT explosive, This represents the volume of the explosive.

3. The method for predicting the degree of fracture of a concrete structure under explosive load as described in claim 2, characterized in that: The implementation method for step 3 is as follows: When a concrete structure is subjected to an explosive load, it stores the energy of the explosive impact as the material potential energy of the concrete through stress and strain. This energy is the deformation energy of the concrete structure. By calculating the deformation energy density of the concrete material, the deformation energy of the concrete structure under an explosive load can be obtained. The strain energy density of concrete includes the volume change energy density and the shape change energy density. The specific form of the strain energy density is as follows: （10） （11） （12） In the above formula For strain energy density, For the volume change energy density of concrete materials, The shape change energy density of concrete materials Peak stress, Poisson's ratio, Let be the elastic modulus of concrete; establish the following deformation energy equation for a concrete structure subjected to explosive load: （13） in This refers to the deformation energy of a concrete structure under explosive loads. This refers to the volume of the concrete structure.

4. The method for predicting the degree of fracture of a concrete structure under explosive load as described in claim 3, characterized in that: The implementation method for step 4 is as follows: Under explosive loads, concrete structures will produce a large number of concrete fragments with different particle sizes. The surface energy required for the concrete material to break and the surface area increment during the concrete structure breakage process are calculated to obtain the breakage energy of the concrete structure under explosive loads. Under explosive loading, concrete structures produce a large number of concrete fragments with different particle sizes. These fragments are all cubic in shape, with a side length of 'a'. According to Griffith's fracture theory: （14） in The length of the fracture surface of the concrete fragment. The surface energy when a concrete structure breaks down. Represented as: （15） Calculate the surface energy required for concrete to fracture and obtain the surface area increment during the fracture process of the concrete structure to obtain the fracture energy of the concrete structure under explosive load. The specific form is as follows: （16） In the formula This refers to the number of concrete fragments with a specific particle size. This represents the original surface area of ​​the concrete structure.

5. The method for predicting the degree of fracture of a concrete structure under explosive load as described in claim 4, characterized in that: The implementation method for step 5 is as follows: The initial kinetic energy of secondary concrete fragments mainly depends on the mass of the fragments themselves, the vertical height of the concrete structure, and the horizontal displacement of the secondary fragments. The distribution of the horizontal displacement of the fragments was determined by combining the distribution of secondary concrete fragments after the experiment, and the initial kinetic energy of the secondary fragments after the concrete structure was subjected to explosive load was obtained.

6. The method for predicting the degree of fracture of a concrete structure under explosive load as described in claim 5, characterized in that: The implementation method for step 6 is as follows: The distribution function of secondary concrete fragments was obtained by fitting the results of the explosion experiment. The mass distribution function of fragments with a specific particle size is obtained by combining the fragment distribution function. The energy distribution function of a fragment of a specific size is calculated based on the fragment distribution function and the mass distribution function of fragments of a specific size. The specific form is as follows: （20） In the formula The particle size of the concrete fragments. For the mass of concrete fragments with a specific particle size, The total mass of the concrete structure. H represents the effective breaking energy of concrete fragments with a specific particle size, where H is the distance from the explosion source to the concrete target plate. This represents the total energy of the blast shockwave acting on the concrete.

7. The method for predicting the degree of fracture of a concrete structure under explosive load as described in claim 6, characterized in that: The implementation method for step 7 is as follows: The energy expression for the fracture process of a concrete structure under explosive load is: （21） Where h is the height of the concrete block. For the quality of concrete fragments, This represents the displacement corresponding to the concrete fragments.

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